Kawaii Text Art

⢤⣦⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡀ ⠀⢿⣿⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⢿⡿⠁ ⠀⢸⠀⠁⠈⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⡿⠃⠀⢸⡀⠀ ⠀⢸⠀⠀⠀⠈⣎⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣟⡀⡇⠀⠀⠀⡇⠀ ⠀⢸⠀⠀⠀⠀⢸⣄⠹⣿⣿⣿⣦⡀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⢠⣾⣿⣿⣿⣿⣫⣾⡇⠀⠀⠀⣷⠀ ⠀⣾⠀⠀⠀⠀⠘⡜⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⢽⠁⠀⠀⠀⣿⠀ ⠀⢸⠀⠀⠀⠀⠰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠶⣄⡀⠀⠀⣿⠀ ⠀⢸⡆⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠄⠀⠀⢰⣿⠀ ⢳⡸⣿⣤⣄⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠤⢴⣿⣳⠀ ⠠⣽⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣡⠏ ⠤⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠥⠄ ⠀⠰⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⠄ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠒⠊⢻⠈⢿⣿⣿⣿⣿⣿⣿⡏⠙⢻⡇⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡏⠘⡇⠀⠀⠸⡄⠈⣿⣿⣿⣿⣿⡏⠀⠀⢸⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣶⣶⣤⣀⠡⠀⠈⢻⣿⣿⣿⠀⢀⣤⣶⣶⣦⣄⣿⣿⣿⡟⠛⢻⣿⣿⣧⠀ ⠴⠛⠁⠈⣿⡀⠉⢻⣿⣿⣿⣿⢹⣾⣿⣿⣿⡆⠀⠀⠙⢿⡄⠀⢿⣽⣿⣿⡏⣿⣿⣿⡟⠀⢀⣾⠇⠀⠉⠛ ⠀⠀⠀⠀⠈⣷⡀⠈⢿⣿⣇⠘⠘⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡽⠛⣣⣿⣿⠃⢀⣾⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠟⠙⢦⣌⡻⣿⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣥⡶⠋⠛⠧⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⠛⣿⡳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢟⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⣼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣬⣁⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⡿⢓⢤⣀⠀⠀⠀⠶⠿⠷⠀⠀⠀⣀⣤⣾⣿⢿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀ ⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⢃⡞⣰⠈⠓⢦⢄⣀⠀⣀⣠⣴⠞⠁⢸⠇⣿⡀⣿⠿⣿⣿⣿⣿⣿⣷⡄⠀ ⠀⠀⠀⣿⣿⣿⠟⠋⠉⠉⠉⠣⣼⠃⣟⠂⣄⠈⠳⡍⠉⢉⡾⠁⠀⠀⡿⣸⡟⠋⠀⠀⠈⠉⠹⣿⣿⣿⡇⠀ ⠀⠀⠀⣿⡿⠁⠀⠀⠀⠀⠀⠀⢻⣦⠙⢇⠀⠉⣶⢿⠀⡿⣆⠈⠁⣰⣇⣿⣧⡀⠀⠀⠀⠀⠀⠈⣿⣿⠇⠀ ⠀⠀⠀⣿⣧⠀⠀⠀⠀⢠⠴⠶⢾⣿⠆⡌⠆⣰⣧⡄⣤⣠⣿⡀⣰⢻⣷⣮⣉⡀⠀⠀⠒⠲⠆⣰⣿⣿⠀⠀ ⠀⠀⠀⢻⣿⡈⠙⠛⠛⠛⣀⣐⣤⣶⣿⣯⠈⠀⠘⣿⣷⣿⠏⡟⠁⣸⣿⣿⣿⡟⠻⠥⠴⠶⠾⢻⣿⣿⣆⠀ ⠀⠀⠀⣸⣿⣟⠒⠠⠄⠂⣠⣿⣿⣿⣿⣿⡄⠀⠀⢻⣷⣿⠀⠀⠀⣿⣿⣿⣿⣿⣄⠀⠀⢀⣴⣿⣿⣿⡏⠀ ⠀⠀⢠⣿⣿⢿⣷⣦⣤⣾⣿⣿⠙⢿⣿⣿⣷⡀⠀⣸⣿⡿⡄⠀⢰⣿⣿⡿⢋⣿⣿⣷⣶⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠘⣿⣿⣻⣿⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⣷⠀⣟⣽⣾⣿⢠⣿⡿⠋⣰⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⡆⠀ ⠀⠀⢠⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣝⡿⣿⣿⣿⣿⣿⡿⢋⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡏⣿⣿⠇⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀

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⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠸⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⢻⡄⠀⠀ ⢀⠀⠀⠀⠀⡞⠀⡀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠈⢧⠀⠀ ⠀⠀⠀⠀⢰⢁⠀⣇⠀⠀⠀⠀⠀⠈⠀⠐⣄⡀⠀⠀⠤⢤⠊⢮⠢⡄⠀⠘⡇⠀ ⡀⠀⠀⠀⡎⡜⣄⣌⣆⠤⡂⡄⠀⠀⠆⢄⠙⡛⠲⡔⢳⢊⠁⢛⣾⠁⠀⠀⠁⠀ ⠁⠀⠀⠀⣧⣁⣈⡳⡀⠑⠜⠾⢔⡤⣘⡀⠉⠻⢍⡉⠉⠀⠺⡑⢼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⠿⣽⣿⡀⠀⠒⠒⠂⠀⠉⠢⢴⣵⣶⣻⣷⣦⣬⢺⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣷⢃⠀⡿⡯⣻⠀⠀⠀⠀⠀⠀⠰⣿⣽⣻⣽⡍⠛⣿⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡆⠐⠪⠽⠉⠀⠀⠀⠀⠀⠀⠀⠀⣻⡥⠚⣀⡀⠁⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠉⢀⢜⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⠰⡲⣟⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⠏⠀⠀⠀⠀⠀⠀ ⢠⡀⡀⠱⣄⠹⢇⡑⠠⡀⠘⠏⠙⠽⠀⠀⠀⠀⠀⠀⡀⡴⠋⠀⠀⢀⠄⣀⠀⡆ ⠀⢳⣿⡦⣄⣁⣦⠤⡝⣫⣑⠤⣀⣀⡀⠠⠤⠐⠈⢡⡮⠀⠀⢀⣴⡫⠔⠉⠢⣱ ⠀⠀⠈⠉⠉⣁⠤⡰⠒⡩⡽⠋⢩⣿⠄⠠⠄⠄⢊⠩⠒⠒⢻⣍⣴⣤⡀⢀⣀⠀ ⠀⠀⠀⢠⠎⠀⢠⠁⡴⡱⠀⠀⠈⠅⠀⢀⠠⠂⠁⠀⠀⠀⡘⠘⠀⢀⠀⠁⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⠀⣀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡗⠋⠁⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢻⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢰⡇⠀⠀⣸⠀⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⡞⠀⢸⠀⢀⡟⡆⠀⠀⠀⢀⠀⠀⢃⠀⠀⠀⠀⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸⠃⠀⢀⡇⠘⡇⠀⠀⠀⠀⠀⢰⡟⠀⢰⠃⠀⢸⠀⡸⠀⣇⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⢀⡀⠀⢸⠀⢸⡄⠀⣸⠀⠀⡇⠀⠀⠀⠀⢠⠛⠃⢀⡟⠀⠀⢸⢠⠃⠀⢸⠀⠀⠀⡇⠀⠀⠘⡆⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⣼⢳⠀⡆⢀⣀⡇⠠⣏⣀⠀⢱⠀⠀⠀⣰⠏⢰⠀⡜⠀⠀⠀⣸⡎⣠⠔⢻⢀⣠⣼⡷⠶⢤⣤⣁⠀⠀⠀⢸⠀ ⠀⠀⠀⠀⠀⠇⢀⣷⣿⣿⣿⣿⣾⣄⠙⠣⡘⡆⠀⢰⠏⠀⣼⡜⠀⠀⠀⢀⡿⠛⢁⣠⣾⣿⠿⠛⠓⠒⠿⢧⣝⢳⣦⠀⢸⠀ ⠀⠀⠀⠀⢸⣴⣿⣿⠟⠁⠀⣈⣽⣿⣷⡄⠀⢹⣤⠃⠀⠀⠟⠀⠀⠀⠀⠘⠃⣠⡿⢛⣡⣶⣾⣿⣷⣦⣄⠀⠉⢳⣝⣿⣩⠀ ⠀⠀⠀⠀⣼⣿⣿⠃⠀⢠⣾⣿⣿⣿⣿⣿⣆⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⢰⣿⣿⣿⣷⣿⣾⡟⢿⣷⠀⠀⢻⡜⣿⠀ ⠀⠀⠀⠀⣿⣿⡏⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣟⣿⣿⣟⣷⡀⢸⡆⠀⢸⡇⣹⡷ ⠀⠀⠀⢻⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠿⣯⣿⠟⡛⠓⣾⠁⠀⣼⣷⠟⠁ ⠀⠀⠀⠀⣇⠙⠿⣦⡈⢿⡛⢷⠁⢠⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣟⣀⡀⠰⠂⠀⡠⠋⠀⠈⢁⡞⠀⠀ ⠀⠀⠀⠀⠸⡄⠀⠀⠁⠈⠛⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣀⣀⠀⠀⠀⠈⠉⠛⠒⠒⠋⠀⠀⠀⢀⡞⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⠒⠶⠾⠍⠛⠛⣛⠻⣾⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢀⣀⣠⣌⣙⣛⡏⢧⠀⠀⠀⠀⠀⢶⣖⣚⣉⣀⣠⠄⠀⠀⠀ ⠀⠀⢠⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⡴⠒⠉⠉⠀⠀⠀⠀⠀⠉⠻⡄⠀⠀⠙⠁⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⢳⣄⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀ ⠀⠙⠲⢦⣬⠵⠟⠦⣄⡀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠤⣴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⢳⣦⠀⠀⠉⠓⠲⠭⢅⣀⡀⠀⠀⠀⠀⠙⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⣿⡳⠒⠒⣀⣀⡤⠤⠀⠀⠀ ⠀⠀⠀⠀⢀⠏⢻⡀⠀⣠⠷⣦⡀⠀⠀⡿⣍⠙⠓⠒⠶⠦⠤⣤⡤⠤⠀⠀⠀⠀⠈⠁⠀⠀⠀⣿⠁⡴⢋⠀⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠈⢠⠞⣧⡴⠁⠀⠀⠙⠒⣤⡷⠌⣳⣄⢀⡴⠳⣄⣴⡷⠤⢤⣤⣤⣤⠤⠤⠤⣤⣴⣿⣾⣤⠚⡄⠀⠀⡆⠀⠀⠀ ⠀⠀⠀⠀⠠⠃⠀⠈⠀⠀⠀⠀⡰⠋⣩⡾⠛⠉⠙⠉⠀⢠⠟⠽⠳⠤⣤⣀⣀⡤⠔⠒⠉⠉⠀⠀⠁⠉⠢⡙⠆⠀⢿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⣼⠟⠀⠀⠀⠀⠀⢀⣈⣧⣀⣤⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠲⠄⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣼⡏⠀⢀⣠⣤⡶⠾⠛⠉⢹⠋⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢘⡆⠀⠀⠀⣀⣤⣤⣤⣂⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣆⠀⢀⢔⣾⣯⣶⣿⣿⣿⣿⣿⠛⠉⢉⠞⢀⣾⠀⠀⠀ ⠀⠀⠀⠉⠉⢹⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣴⣿⡟⠀⠀⠀ ⢀⣄⣀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⡀⠀ ⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄ ⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡉⠕⠀⠀ ⠘⠁⢸⣿⣿⣿⣿⣿⣿⡟⠏⠀⢰⣿⣿⣿⣿⣿⠈⢿⣿⣿⣷⡈⠂⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⡏⣀⣈⣥⣄⢻⣿⣿⣿⣿⣐⠈⣿⣿⣿⡧⠔⠀⠀ ⠀⠀⠈⠙⢿⡿⢿⣿⢧⠀⠁⢀⠠⠀⠟⠁⠈⠉⠛⠋⢿⡟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⢨⠐⡶⠝⢀⠤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠢⣸⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠓⠤⠍⠡⢄⡀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⠀⠀⡖⠒⠋⠁⠀⠀⠀⠰⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠎⠐⠠⢇⡀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠈⠑⠂⠽⠮⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣋⠹⠤⢤⣄⡀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⠗⠛⢉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡼⠀⠀⡄⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⣴⠞⣫⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠉⠀⠀⠀⠀⣀⡾⠁⠀⣸⣇⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⡤⠶⠶⠾⠿⢿⣿⣿⣷⣶⣶⣾⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⢤⣀⣤⣾⠟⠀⢀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢸⣿⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⣧⡀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⢶⣽⣿⣿⣿⣿⣿⣟⡿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠒⠀⠀ ⠈⠻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀ ⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠗ ⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⢁⡤⠀⠀⠀ ⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⠴⠞⠋⠀⠀⠀⠀ ⣴⡿⠟⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⡿⣿⠟⠀⠀⠘⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⠳⣄⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⡟⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡟⡄⠀⠈⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡿⠁⠈⣀⣤⡤⠄⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣇⣷⠀⠀⠀⣤⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠈⠉⢀⣀⣀⣤⣤⣀⡈⢿⣿⣿⢻⣿⣿⣿⣿⣿⣿⠀⠉⠓⠆⢻⣿⣿⣿⣿⣿⣿⣷⣶⣦⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠘⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠾⣿⣿⠿⠿⠟⠛⠛⠁⠈⢿⡿⣼⣿⠿⢿⣿⣿⣿⣿⣷⣦⣤⣾⣿⣿⣿⣿⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢈⣿⠟⠁⠀⠀⠀⠉⠙⠛⠛⠛⠉⣹⣿⣿⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟⠉⠻⣿⣿⠈⠛⠷⠀⠀⠀⠀⢀⡴⠚⠉⠀⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣹⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⢠⠶⠶⣤⡈⢿⡇⠀⢀⠀⢀⡤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⢹⡇⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⢸⣍⠉⠁⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⠤⠤⠤⠶⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣶⡤⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⣾⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢯⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢤⡀⠀⠀⠀⣸⡏⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠈⠓⠦⣴⣏⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠉⠓⠲⣤⣀⠀⠀⠙⢷⣄⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢦⣤⣈⠛⢦⡈⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠈⠻⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠿⠿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣀⡀⠀⢀⣠⣤⣶⣶⣶⣷⣶⣶⣿⣿⣷⣶⣶⣶⣶⣮⣝⡻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⡤⠔⠒⢤⡀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡜⠉⠀⠀⠀⠀⢳⠀⢀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⠀⠀⠀⠀⠀⠀⠈⡇⣼⢁⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⣇⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⡇⢀⣀⣀⣀⣀⣀⠀⡿⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡻⡆⠀⠀⠀⠀⠀ ⡇⠘⠙⠻⠛⠛⠛⠃⢧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡽⡄⠀⠀⠀⠠ ⡇⠀⠀⠛⠛⠙⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠠⠁ ⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢀⣠⠄⠻⣿⣿⣿⣿⣿⣿⠹⣷⠠⠤⣈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡉⠓⢤⠆⠀ ⢣⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⢀⠴⠋⠁⠀⠀⠀⠹⣿⣿⣿⣿⣿⡇⠻⡇⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢠⠞⠀⠀ ⠈⡆⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡼⣧⠀⠻⡄⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀ ⠀⢱⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⢿⠀⠀⢙⣀⠀⠀⠀⢿⣿⣿⢿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀ ⠀⠀⠙⠒⠦⠤⣼⣿⣿⣿⣿⣿⣿⣿⢻⡏⠀⢀⣤⣖⣲⣭⡶⠀⠀⠀⠀⠀⠙⢿⣞⠀⠼⠶⣾⣭⣤⣀⠈⢿⣿⡞⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡿⣻⣿⣿⣿⣿⣿⢸⠀⣠⣾⡿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠈⠉⠛⣿⣦⣿⡇⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠃⢿⣿⣿⣿⣿⣿⠸⠴⢫⣱⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣧⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⠀⢸⠙⣿⣿⣿⣿⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⡰⠊⠉⠀⠀⠈⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣂⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠀⠘⡇⣿⣿⠟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡆⠀⠘⢾⣿⣸⢻⣷⡄⠀⠀⠀⠀⣀⣀⠀⣿⠀⣀⡀⠀⠀⠀⠀⠀⡽⠀⠀⠀⠀⠀⢀⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢿⡟⢙⢿⣆⠀⠀⠀⣴⠁⡸⠀⡼⠋⣱⠃⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢠⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⢸⣷⣤⣘⡛⣦⣀⠠⠃⠀⡇⡼⠀⣼⢁⡴⠊⣹⠀⠴⠋⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠎⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⡾⠀⣿⠙⣿⣯⠈⢿⣇⠀⡿⠃⠀⠷⠟⢠⠞⢁⡠⢤⡄⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⡈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢸⢠⡿⣿⡆⠀⠛⠈⠀⠀⠀⠀⡄⠛⠚⣡⣴⣾⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢰⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⡀⠠⠊⠀⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⠋⠁⠀⡿⢿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢠⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣠⣤⣯⠽⠛⣇⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢀⡿⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣇⠈⢧⢠⠏⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠈⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⢸⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣆⣨⢋⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠘⣿⣿⡗⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢟⣵⣶⣿⣿⠉⢍⢠⡈⠻⠶⣬⡙⢷⣮⠙⠿⣿⣷⣶⣄⠀⠀⢀⣠⢖⡡⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠒⠤⠄⣈⡑⠢⠤⢀⡴⠛⣵⣿⣿⠟⠉⢹⡶⠈⣌⢻⡄⠀⠘⣿⣷⣹⣷⣄⠹⣿⠛⢻⣷⣶⡯⠶⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣹⠟⢲⡞⠁⣼⣿⣿⠏⠀⢠⢸⣇⡀⣿⡎⢿⣆⠸⡌⠻⣿⣿⣿⣧⠈⢷⡀⡿⣝⣧⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡟⢀⡞⠀⣼⣿⡿⢃⠀⣠⠏⣼⣿⡇⢿⣧⢘⣿⣿⣧⠀⠙⠿⣿⣿⣷⡈⢷⡀⠘⣞⢧⡀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⣷⡾⢡⢤⣯⣿⢣⢎⣾⡟⢠⣿⡿⣿⢸⡏⢿⣿⣿⣿⣷⡀⠘⣿⣿⣿⣷⡈⢷⡀⠘⣯⣳⣦⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣧⡟⣟⣾⣯⡟⣼⢻⢃⣿⡿⠁⠸⡌⣿⡀⠻⣟⣿⣿⣿⣄⠈⢿⣿⣿⣿⣌⢿⣄⠘⢷⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⢹⣿⣿⢿⢱⡇⢸⣿⡿⠁⠀⣀⣷⣿⣧⠀⠙⢦⡙⠻⣿⣷⣦⣻⣿⣿⣿⣎⣿⣦⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⢧⣿⣿⡿⠈⢸⢇⣿⣿⣡⠔⠊⠁⠀⢳⣿⡆⠀⠀⠙⢦⡈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣧⡀⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣼⣿⣿⣯⢇⣿⣸⣿⠁⠀⢀⠀⣀⠀⠀⠻⣿⡄⠀⠀⠀⢛⣽⢧⣤⣌⡿⣿⣿⣿⣿⣿⣿⣆⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⣿⣿⢿⣿⡇⣸⠃⢀⣾⣿⣿⣦⡀⠀⠀⠙⢿⡄⠀⠀⢼⣅⣼⣿⣿⡿⣯⣽⣿⢻⣿⣿⣿⣷⡀⠙⢦⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⢸⣿⡇⣿⢙⣿⣏⣠⣿⣿⡇⠀⠀⠀⠈⠻⣆⠀⠸⡿⢿⣿⣿⠇⢹⠿⣿⡈⣿⣿⣿⣿⣿⣷⣾⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⠸⣿⣷⣿⣿⡇⢿⠿⢿⡟⡋⠀⠀⠀⠀⠀⠈⠣⡀⠑⢤⣤⣶⠀⠀⠀⣿⡇⣿⣿⣿⣿⢹⡟⠿⣿⣿⣷⣤⡀⠀ ⠀⠀⢠⣿⣿⠏⣿⣿⣿⢀⣿⡏⣿⠉⠛⠊⠳⣤⣶⠇⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⣿⣧⣿⣿⣿⣿⣷⣷⡀⠀⠈⠉⠉⠙⠓ ⢀⣴⣿⣿⠃⠀⣿⣿⣿⢸⣿⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣿⣿⣿⡏⠿⣿⣿⣧⡀⠀⠀⠀⠀⠀ ⠋⣸⡿⠁⠀⠀⣿⣿⣿⣿⣿⡄⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢸⣿⣿⣿⣿⣦⣤⠟⠋⠉⠒⢦⡀⠀⠀ ⡴⠏⠀⠀⠀⠀⣿⡿⠋⢹⣿⣇⠘⣇⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⣿⣿⣿⣿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡴⠁⠀⠀⢸⣿⣿⡄⢹⡄⠀⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠀⠀⠀⠀⠈⣿⠻⣿⣟⣿⣄⠀⠀⠀⠉⢲⡤⢄⡀⠀⠀⠀⡠⠞⡟⠀⣠⠀⠀⣾⡿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⡄⠈⠻⣿⣿⠓⠤⠀⠀⠀⠙⠦⣈⠉⠒⠉⢀⡞⢀⠜⠁⠀⣸⠟⣠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⢂⠀⠀⠀⠘⠆⠀⠀⠉⠓⣄⠀⠀⠀⠀⠀⠀⠉⢲⣤⣞⡊⠁⠀⠀⠚⠁⢰⢻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⣇⠀⠈⢆⢀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⢠⠋⠘⡄⠈⠢⡀⠀⠀⢀⠇⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⡟⣆⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⢠⠃⠰⠲⡜⡆⠀⠈⠢⣠⠎⠀⣿⡟⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⡄⠀⠀ ⠀⠀⠀⣿⣿⠁⣿⣦⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠃⠀⠘⠂⠃⠸⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢠⠃⠀⠀⠈⣇⠀⠀ ⠀⠀⠀⣿⣿⠀⣿⣿⣷⡄⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⢠⣿⠀⠀ ⠀⠀⠀⣿⣿⠀⢻⣿⣿⣿⣦⣄⠀⡳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⢀⡜⢁⠄⠀⠀⢸⣿⠀⠀

⣿⣿⣿⣿⣿⣿⣇⠤⠂⠠⣱⣆⣁⡙⣑⡀⣠⡤⣤⣤⣤⣄⣄⡐⠇⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠿⠿⣏⣏⣀⡼⣤⣿⡿⣿⠌⠁⢀⡂⢁⣀⡰⢡⠉⠩⡒⢄⡀⠀⠀⠀ ⠿⢿⡿⣅⠀⢸⢣⠁⡙⠩⣰⣿⣾⢷⡤⠛⠛⠒⡞⠉⠉⠒⠛⢳⠹⢶⣻⣆⣀⠀ ⡿⠅⣰⠋⢹⣿⡀⢳⠃⢱⢻⠛⠚⡯⡇⠀⠲⢶⣶⠀⠀⣀⣀⢰⣧⠄⢹⠋⢽⠁ ⠣⢬⣣⢄⣾⣇⣧⡜⠀⡏⠁⠀⢠⣿⣀⣆⡀⣿⣿⠀⢀⠀⠀⢸⡇⠃⢹⠉⢻⠀ ⠀⠃⠀⢹⣿⣿⣸⣇⠀⡇⠀⠀⢸⣿⠀⣷⠈⡟⣿⠀⡌⠀⣸⣾⡇⣿⣾⠀⢸⣇ ⠂⡀⠀⣸⣿⣿⣿⡏⡇⡇⠀⢠⢨⠉⠁⠙⠚⠃⠻⠦⠿⠠⠿⠯⠷⢿⡏⠀⣾⣿ ⠀⠂⢊⣿⣿⣿⡿⡇⣿⣧⠀⢸⣾⠗⠓⠒⠯⠀⠀⠀⠀⠀⠤⠴⣶⡼⡀⠀⣿⣿ ⠀⠀⣸⣼⣿⡏⡇⣿⣿⣿⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠥⠐⠛⠛ ⠀⢠⡇⣿⣿⣇⡇⣿⣿⣿⡆⣧⣟⢧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡼⠁⠀⠀⠀⠀ ⠀⣞⢱⣿⣿⣿⡇⡇⢿⣿⣿⣧⣿⢄⠁⠀⠀⠀⠀⠀⠀⠉⢀⣵⠀⠀⠀⠀⠀⠀ ⡼⢁⣾⣿⣿⣿⡇⡇⠘⣿⣿⣿⣿⣦⣈⡂⠄⣀⢀⣠⣴⣾⣿⡏⠀⠀⢀⣀⢠⡤ ⠃⢸⣿⣿⡟⠩⠁⠉⠉⠈⣻⣿⣿⣿⣿⣿⣿⢷⠞⣉⣉⣙⣿⠁⠀⠀⣸⠀⠈⡝ ⢀⣿⣿⣿⠇⠃⠀⠀⠀⠀⠈⢦⠙⣿⠻⠦⣳⣿⡤⠙⡄⢳⡄⠀⠀⠀⣿⠀⠀⠃ ⣼⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠈⢳⣹⠀⠀⢫⡤⣜⠀⢹⡜⠀⠀⠀⠀⡿⡆⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠒⠒⠒⠒⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢠⡴⠚⠛⠛⢦⡀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⢀⣿⣤⠤⠤⣤⣼⣇⡀⢀⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠼⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⠻⢤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀ ⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀ ⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀ ⠀⠀⡇⠀⠀⠀⠀⢠⣖⠀⠀⣿⢸⠀⠀⢸⠈⡇⠀⣤⠀⠀⠀⠀⠀⠘⡇⠀ ⠀⢀⡇⠀⡶⠶⠶⣼⣹⣦⠤⠗⠸⣤⣤⣼⠀⣧⣠⡿⣧⣤⣤⡀⠀⢠⡇⠀ ⢀⡾⠁⠀⣽⠀⣼⠋⠙⢻⣷⡀⠀⠀⠀⠀⠀⢠⣾⢿⣷⣦⠸⡇⠀⠈⢧⠀ ⢸⠁⠀⣼⠁⠀⣧⠀⣀⡾⢻⡇⠀⠀⠀⠀⠀⣿⠀⠀⡿⣿⠀⠳⡄⠀⠈⣇ ⠘⣇⠀⣿⢦⡤⠼⣿⠿⠿⠋⠀⢀⠀⠀⡀⠀⠙⠿⢿⠿⣯⠤⣤⢿⡇⢠⡏ ⠀⠈⢧⢸⡆⠳⣤⣸⠂⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⢼⣁⡴⠋⡼⢰⠏⠀ ⠀⠀⠺⠞⠀⠀⠀⠙⠶⢤⣀⡀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠉⠀⠀⠹⠿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣀⡶⠄⠐⠂⢳⣤⠖⠋⠉⠙⠉⢦⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⡸⢷⠒⠤⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣾⣁⡤⠀⠀⣨⠚⢻⣖⣲⣶⣦⡄⢲⡷⠴⠒⡞⠛⣻⠛⠟⠳⡛⢿⠿⣷⣴⣀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣩⡏⠀⢀⣸⡷⢤⣼⣿⣿⢿⣿⣇⠀⠁⠀⠀⠘⡄⠀⠀⠀⠀⢱⠘⡄⠀⠈⢫⡚⢵⡤⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⠟⠋⠀⠀⢸⣏⠛⠓⠻⢿⣿⠖⠋⣿⣿⣻⣾⣿⠅⠀⣤⣶⣾⣟⣁⣠⡿⠿⠿⢿⣅⣙⣶⣶⣔⠛⣄⣈⢻⣷⡀⠀⠀⠀⠀ ⠛⠛⢿⣿⠟⢦⣀⠀⢀⣿⠸⣆⠀⢀⠏⠀⢢⣰⣿⣿⣾⡿⢿⣶⠖⠋⠁⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠈⠉⢻⡛⠛⠿⣦⣹⡳⣤⣄⠀⠀ ⣶⣶⠋⠁⢠⡿⠛⣿⣿⣿⡀⠙⣦⣾⠖⢒⣶⢿⡿⠯⢭⣍⣿⣿⣀⣒⣢⣤⣤⣼⣧⡄⠀⠀⣀⣀⣀⠀⢀⣸⣇⠀⠀⢈⣏⡷⢻⣿⡇⠀ ⡟⠉⠠⣠⡿⠁⠀⣿⣿⣹⣇⠀⢸⡇⠀⢸⣿⣸⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⢉⣿⣿⡇⠀⠀⠐⠒⠒⠒⠀⣿⣿⠫⡤⢤⣧⣀⣀⣻⠇⠀ ⠓⠤⣀⡟⠣⣄⢠⣿⣿⡇⣿⣄⡾⠀⠀⣸⠀⠀⠀⠀⠀⣼⣿⣇⣀⣇⠀⠀⣸⣿⣿⡇⠀⠀⡄⠀⠀⠀⡄⣿⣿⠀⣧⠀⣿⠁⠈⣿⡆⠀ ⠀⢀⡞⠋⠑⠺⣿⣿⣿⣷⢸⣿⡇⠀⠀⣿⠀⠀⠀⠀⠘⣿⣿⠋⠉⣯⡙⠛⣿⣿⣿⣧⠀⠀⡇⠀⠀⢠⣇⣿⣿⣤⣿⣀⣿⠀⠀⢸⣷⠀ ⠆⠀⠀⠀⠀⠀⣿⣿⣿⣿⡆⣿⣧⢀⠀⣧⠀⠀⠀⠀⠀⣿⣿⡄⠀⣿⡇⠀⣿⡇⡟⣿⠀⢸⡇⠀⠀⣾⣿⣿⣿⢰⣿⣿⣿⠀⠀⢸⣿⣴ ⡶⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡿⢸⠀⣼⠀⠀⠀⡀⢰⠛⠛⠛⠒⠓⠷⠤⣿⡇⠇⣿⡄⢸⡇⠀⢠⣿⣿⢿⣇⣾⣿⣷⡏⠀⠀⣼⣿⣿ ⠀⠠⠂⠀⣔⣼⣿⣿⣿⣿⣿⣿⡇⢸⣇⣿⠀⠀⠀⣧⢨⡇⡀⢀⠀⠀⠀⣀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡟⠁⠀⠀⣿⣿⣿ ⠀⠀⠂⠚⢀⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⡄⠀⠉⣿⣿⡿⠿⠛⠛⠻⠷⢶⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⢶⣶⣖⣾⠇⠀⠀⢰⣿⣿⣿ ⠀⠀⠀⠀⣸⠟⣿⣿⣿⡿⡇⠘⣧⣼⣿⣿⡇⠀⠀⢸⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡿⣼⠀⢀⣸⣿⣿⣿ ⠀⠀⠀⢀⡿⢾⣿⣿⣿⡇⡇⠀⣿⣿⣿⣿⣷⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠚⠉⠉⠉⠉⠉ ⠀⠀⠀⣾⠃⣾⣿⣿⣿⠉⡇⠀⣿⣿⣿⣿⣿⡀⢰⢤⣿⠿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⢀⣿⣿⣿⣿⣼⡇⠀⡇⣿⣿⣿⣿⣧⣸⡿⣿⡇⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢚⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⠀⢸⣿⣿⣿⣿⣿⡇⠀⡇⢸⣿⣿⣿⣿⣿⣇⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⠉⠀⣿⣿⣿⣿⣿⣿⡇⠀⡇⠀⢿⣿⣿⣿⣿⣿⣾⣿⡀⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠃⠀⣼⣿⣿⣿⣿⣿⣿⡇⠀⡇⠀⠈⢿⣿⣿⣿⣿⣏⣿⣷⣤⣄⣈⣑⢲⣤⣀⣀⣀⣤⢶⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢀⣀⡤⢴⣶⡿ ⡏⠀⣀⣿⣿⣿⣿⣿⠛⢻⠗⠐⠉⠉⠑⠚⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠼⠟⠋⠋⠉⠉⣿⣿⡟⠀⠀⠀⠀⠀⡟⠀⠀⠀⣏⢷ ⠁⠀⣼⣿⣿⣿⣿⡇⢀⠇⠀⠀⠀⠀⠀⠀⠈⢺⡟⢿⣿⣿⣿⣿⣿⠿⢿⠿⢛⢻⡟⠲⣶⡲⠤⣤⠞⢻⠃⠀⠀⠀⠀⢰⡇⠀⠀⠀⢻⠨ ⠀⢰⣿⣿⣿⣿⣿⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠉⢻⣿⠛⠿⢷⣦⣲⡿⠿⡧⠤⠛⣷⠀⢻⣆⡎⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠸⠀ ⢀⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠈⣿⠁⠀⠀⠈⡿⠋⠉⢻⡆⠀⠸⣧⠀⡟⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⣧ ⣾⣿⣿⣿⣿⣿⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⣸⣆⠀⠀⠀⢙⣿⠿⢿⣄⡀⠀⢻⡶⠁⠀⠀⠀⠀⠀⠀⢸⠻⣧⠀⠀⠀⢹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠛⠛⠉⠉⠉⠁⠀⠀⠈⠉⠉⠙⠛⠿⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀ ⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠹⣧⡀⠀⠀⠀⡏⠉⠙⠋⢹⡆ ⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠉⠛⠿⣦⡀⠀⠸⣷⡀⠀⠀⠹⣄⠀⠠⡹⠃ ⠀⢀⣿⠃⠀⠀⠀⠀⣠⣶⠾⠟⠛⠉⠉⠛⠿⣶⣄⠀⠀⠀⠀⣰⠃⢀⣠⣤⣄⠀⠈⢻⣦⠀⢻⣧⠀⠀⠀⠈⠓⠋⠀⠀ ⠀⢸⣿⠀⠀⠀⣠⣾⠋⠁⠀⠀⢀⣠⣤⣤⣤⣈⠙⣷⣄⠀⢠⣏⣶⣿⣿⣿⣿⣿⣦⠀⢻⣧⠘⣿⢀⢸⡛⠛⢲⠀⠀⠀ ⠀⣾⡇⠀⠀⢠⡿⠁⠀⠀⣠⣾⡿⢿⣿⣿⣿⣿⣷⣌⢿⣆⢸⣿⡋⠉⢉⣿⣿⣿⣿⣧⠈⣿⠀⣿⣿⠀⠹⠶⠋⠀⠀⠀ ⠈⡟⣿⠀⠀⢸⠇⠀⢀⣼⣄⠈⠀⣸⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣶⣿⣻⣿⣿⣿⣿⣤⣿⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⢷⢹⡆⠀⢸⡄⠀⣾⣿⣿⣿⣿⣿⣩⣿⣿⣿⣿⣿⣇⣿⢹⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⠏⣸⢧⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣇⢳⡀⠈⢧⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢠⢁⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢎⠃⠀⠈⠳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠟⠁⠀⠀⠈⠻⣿⣿⣿⣿⡿⠟⠁⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠳⣄⠀⠀⠈⠙⡻⠿⢿⣿⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠃⣀⡀⣰⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⡤⠬⣷⣄⡲⣤⣈⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⢛⡵⠚⠁⠀⢀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣇⠀⠀⠀⢻⣿⠒⠭⣟⣷⢶⣤⣤⣤⣤⣤⣤⣤⣤⣶⢾⣟⠯⠗⠊⠁⠀⠀⠀⣾⠟⠁⠀⢘⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢹⣧⠀⠀⠈⣿⡄⠀⠀⠈⠉⠛⠛⠛⠛⠛⠒⠋⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣿⠇⠀⠀⠙⠛⠛⠒⠒⠛⠛⠛⠻⠿⢷⡢⣤⣔⡶⠿⠟⠛⠛⠛⠻⠿⠽⠟⠁⠀⠀⢺⡿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⢿⣿⠒⠲⠛⠙⠲⠦⢼⣿⡿⠟⠛⠃⠀⠀⠀⠀⠀⠀⠀⢸⣇⡇⠀⠀⠀⠀⠀ ⠀⠀⠹⠿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⡻⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⢀⡾⡿⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⢀⣠⣴⢯⠞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⠶⠶⣖⡿⠚⠁⠀⠀⠀⠀⠀⠀⠀⠘⠮⣷⣶⡤⡤⠴⠾⠟⠋⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠇⡇⠀⢰⢰⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢏⠉⠁⠀⠀⠀⠀ ⠀⠀⢰⠀⡇⢀⠀⠡⣧⡀⠀⣧⠀⠀⡀⠇⠀⠀⠀⡆⠀⢀⠀⠀⠀ ⠀⠀⠘⠐⣷⢸⡀⠀⠀⡉⠀⣇⡱⠁⡀⢻⠀⠀⠀⢱⠈⠁⠀⠀⠀ ⠀⠀⡌⡰⠊⢋⣧⡀⠀⢧⠀⡇⢀⠈⠢⣸⠀⠀⠀⢸⠀⠀⣀⠄⠀ ⠀⠀⡗⣡⣶⣼⡟⠕⢄⣘⣂⡽⣿⣿⣿⣮⣤⡀⢠⢸⠀⠉⢸⠀⠀ ⠀⠸⡿⠍⠷⠿⡵⠀⠀⠀⠀⠀⢸⡙⣭⣛⠋⠀⡀⢸⢣⠀⢸⠀⠀ ⠀⠀⡏⡆⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠶⢼⠀⢠⠃⢸⡸⠀⠂⠀⠀ ⠀⠀⡇⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡜⠀⡟⠁⢠⠀⡄⠀ ⠀⠀⢃⠀⡅⠂⠄⡀⠀⠀⠀⢀⠀⠀⢐⠇⠈⠀⢀⠃⢠⠀⣴⣇⠂ ⠀⠀⢸⠀⣇⠀⠀⠀⡩⢙⡏⠀⠀⣀⣌⠀⠀⡰⣘⣰⠏⠷⠿⡁⠀ ⠘⠄⠀⢇⠏⠴⢊⢋⡔⠁⡀⠀⠀⣠⡂⠄⠊⢘⠡⢊⠂⢄⠐⠀⠑ ⠀⠈⡲⢤⠵⠥⠁⡮⠐⠠⢈⢢⡍⡲⡀⠀⡀⠀⠴⠁⠀⠀⠡⠀⠀ ⠀⠈⠀⠈⡢⠀⢠⠀⠀⠀⠀⠙⠃⠀⠈⠪⠠⠊⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣠⡶⢦⣄⠀⠀⠀⠀⠀⠀⠀⣠⡶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡟⢀⡀⠙⣷⡀⠀⠀⠀⢀⡾⢋⡤⡙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠃⠇⠙⣄⠘⠧⠤⠤⠤⣾⢡⠏⠀⢱⡈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡟⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⡏⠀⢀⡖⠲⣄⠀⠀⠀⣀⠤⠊⠁⠀⢣⡀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣠⠤⠞⠀⠀⠈⠑⠦⠊⠁⠀⠀⠀⠀⠀⠙⠒⡂⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀ ⢀⡇⢱⠀⢱⣶⡄⠀⢠⣤⣤⡄⠀⠀⣴⣶⡆⠀⠰⠥⡀⠘⣧⠀⠀⠀⢀⣀⣀⡀ ⢸⡇⡞⠀⠈⠋⠁⠀⢈⣩⣭⣁⠀⠀⠉⠉⠀⠀⠀⢠⢇⣤⡿⠀⣠⡶⠛⠉⢸⠃ ⠘⠷⠿⣤⣄⣀⡀⠀⠹⣏⣠⠟⠁⠀⠀⣀⣀⣤⡶⠟⠋⠁⢀⡾⠋⠀⠀⠀⢸⡄ ⠀⠀⠀⠀⠀⠉⠉⡟⠛⠒⠒⠒⠚⠛⠋⠉⠁⠈⠻⣦⠀⠀⢸⢇⡠⡄⠀⠀⠈⡇ ⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢸⡄⠀⠀⠀⣤⠀⠀⠀⠘⣧⠀⢸⠉⠀⠧⠴⠲⣸⡇ ⠀⠀⠀⠀⣾⠛⢷⣧⡀⢀⣸⡇⠀⣀⢤⣿⠞⠛⢻⡄⢹⣆⣿⠀⠀⠀⠀⣠⡟⠀ ⠀⠀⠀⠀⢹⡆⠀⢿⡈⠉⠸⡟⠊⠁⢸⡇⠀⠀⣸⡇⢈⡟⠁⠀⢀⣠⡾⠋⠀⠀ ⠀⠀⠀⠀⠀⠻⠶⠾⠷⠶⠶⠷⠶⠶⠾⠧⠤⠾⠿⠴⠾⠷⠶⠛⠋⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠾⢳⣦⡀⠀⢀⣠⣶⣦⡄⢠⣾⠟⢷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠙⣿⣷⡾⢿⣿⠀⣼⡟⠛⢿⣦⣿⠇⢹⣧⣼⣿⣦⣄⣿⡟⠙⣷⠀⣤⣤⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⠀⣿⣦⡀⣿⡏⠀⢸⡿⠀⢿⡇⠀⠈⣿⡿⠀⢸⣿⣿⡀⠈⣿⣿⠃⠀⢿⣿⡟⠉⠻⣷⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣀⠀⣿⡏⠀⠈⣿⣿⡿⠹⣇⣿⠁⠀⣼⡇⠀⢸⣿⠀⠀⣿⡇⠀⠀⣿⣿⡇⠀⢸⣿⠀⠀⢸⣿⠁⠀⢰⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⠉⢻⣧⠸⣇⠀⠀⠸⣿⡇⠀⢻⣿⠀⠀⣿⡇⠀⠀⣿⡄⠀⣿⡇⠀⠀⣿⡿⣷⠀⠈⣿⡆⠀⣼⡟⠀⠀⣼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠀⠀⣿⡄⢿⡀⠀⠀⣿⡇⠀⠸⣿⠀⠀⣿⣿⠀⠀⢸⡇⠀⢸⣇⠀⢀⣿⠁⣿⠀⠀⢻⣇⢠⣿⠀⠀⢠⣿⣷⣤⣄⡀⠀ ⠀⠀⢀⣀⡀⢿⣇⠀⠹⣧⢸⣇⠀⠀⣿⡇⠀⠀⣿⡀⠀⢿⣿⡆⠀⢸⣇⠀⢸⣿⠀⢸⡟⠀⣿⡆⠀⠈⣿⣼⡇⠀⠀⢸⡏⠀⠀⢻⡇⠀ ⠀⣰⡿⠛⢻⡞⣿⡀⠀⢻⣆⣿⠀⠀⣿⡇⠀⠀⢻⡇⠀⢸⣿⣇⠀⠸⣿⠀⠈⣿⡄⣿⠇⠀⢹⡇⠀⠀⣿⣿⠀⠀⠀⣿⠃⠀⠀⣿⠇⠀ ⠀⣿⡇⠀⠀⣿⣾⠿⣿⡌⢿⣿⡆⠀⢸⡇⠀⠀⢸⡇⠀⢸⣿⣿⠀⠀⣿⠀⠀⢹⣷⣿⠀⠀⣸⡇⠀⠀⣿⡏⠀⠀⢀⣿⠀⠀⢸⡟⠀⠀ ⠀⠸⣷⡀⠀⣿⡁⠀⠹⣧⠈⢿⣧⠀⢸⣇⠀⠀⢸⣇⠀⠀⣿⣿⡇⠀⣿⠀⠀⢸⣿⡇⠀⣠⣿⡇⠀⠀⣿⠁⠀⠀⢸⡏⠀⢠⣿⠃⠀⠀ ⠀⠀⠹⣧⠀⢸⣧⠀⠀⢿⡆⠘⣿⠀⠸⣿⠀⠀⠸⣿⠀⠀⢸⣿⣇⠀⣿⠀⠀⠀⣿⠁⢠⣿⢹⡟⠀⣸⡟⠀⠀⠀⣼⡇⠀⣾⡏⠀⠀⠀ ⠀⠀⠀⣿⣧⠀⢿⡄⠀⠈⣿⡀⣿⡇⠀⣿⡀⠀⠀⣿⡄⠀⠀⣿⣿⢠⣿⠀⠀⢸⡟⠀⣼⡿⢸⡇⢀⣿⠇⠀⠀⠀⣿⠀⢰⣿⠻⢷⣤⠀ ⠀⢀⣠⣿⣿⡄⠘⣷⠀⠀⠘⣷⣿⣇⠀⢹⣧⠀⠀⢸⣷⣀⣀⣸⣿⣼⣿⣆⣠⣾⣇⣠⣿⡁⣸⡇⣼⡿⠀⠀⠀⢰⣿⠀⣾⢿⣦⠀⠹⣷ ⢰⣿⠋⣠⣼⣿⡀⢹⣧⠀⠀⣹⣿⣿⣶⠿⠿⠟⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠿⢷⣿⣇⡀⠀⠀⣸⡇⢰⣿⣾⡟⠀⠀⢿ ⣿⡇⠀⣿⣿⣿⣧⠀⣿⣷⡾⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣄⣿⡇⣸⣿⡿⠁⠀⠀⣿ ⢹⣷⠀⠘⢿⣿⣿⣷⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⣿⣿⠃⠀⠀⢀⣿ ⠀⢿⣧⠀⠀⢻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏⠁⠀⠀⠀⢸⡿ ⠀⠈⢿⣧⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⣿⡇ ⠀⠀⠈⢿⣧⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢠⣿⠀ ⠀⠀⠀⠈⢻⣧⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢸⡟⠀ ⠀⠀⠀⠀⠀⢿⣆⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⡇⠀ ⠀⠀⠀⠀⠀⠘⣿⡄⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⢹⣷⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⣠⣶⣶⡶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⡿⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⢰⣿⣿⣿⡀⢀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⣀⣸⣷⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠈⢿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣤⡄⠀⠀⢴⣶⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣀⣀⣀⣀⢔⡊⠙⠟⢠⣄⠀⠀⣿⣉⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣮⣾⠿⠛⠀⣁⠠⠄⠒⠒⢒⠀⠄⣘⠿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣧⣶⠞⠁⡐⢁⠀⠀⠀⠀⡑⡀⠀⠳⢄⠀⠀⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⣿⠏⠀⡐⢀⠃⠀⠀⠀⠀⠀⢠⣰⣷⣶⢆⠀⣿⣿⣄⠀⠀⠀⠀ ⠀⣰⣿⣿⠿⠀⠀⠀⡈⢰⠀⠀⠀⡇⢀⡈⢿⣿⣿⠀⢻⣿⣿⣿⣣⡀⠀⠀ ⢰⣿⣿⠏⠀⠂⢰⠀⡇⣀⡀⠀⠠⢣⠀⡏⢂⠉⠀⠃⣼⣿⣿⣿⣷⡇⠀⠀ ⠈⢻⠣⠀⢠⠀⢸⠀⣇⠹⡇⠇⠸⠶⣦⣵⣸⠀⠀⠀⠸⣿⣿⣿⠃⠀⠀⠀ ⢀⡳⠀⡔⣼⢠⢈⡧⠿⠆⠘⠈⠀⠀⣾⡿⡙⠀⠀⡀⠀⠹⡿⠇⠀⠀⠀⢰ ⣼⡇⡞⠠⠏⡼⠜⠣⡀⠀⠀⠀⠀⠀⠀⠠⡇⠂⠀⡇⠀⣠⢧⠀⡀⠀⠀⠸ ⠘⠐⠧⣡⡎⠀⠀⠀⢰⣄⡀⠀⠀⢀⣠⠗⠃⢀⢰⡙⡄⣟⢸⡘⠀⠀⠀⠀ ⠀⠀⡜⡜⠀⠀⠀⠀⠈⢣⡾⣷⠘⠋⠀⢄⡀⡘⢆⠜⠈⣎⢤⡇⠀⠐⢄⠀ ⠀⠀⣿⣀⠀⠀⣀⠤⠀⣊⠌⠻⣒⠄⢒⡡⠔⠈⡱⢁⠜⠁⠘⡿⣄⠀⠀⠃ ⠀⢸⡸⠺⣉⠀⠀⢀⡠⠘⠀⠀⣞⡺⠀⠀⢠⢏⠔⢱⠀⠀⠀⡇⠘⠡⠀⠘ ⠀⠃⠋⠀⠀⠀⠈⡞⠀⠀⠀⠀⢸⠊⠀⠀⣜⠎⠀⠀⢂⠀⢀⠇⠀⠀⠀⠀

⠀⣾⡿⠿⣿⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⣿⠿⣿⣶ ⢸⣿⠃⠀⠀⠀⠈⠉⠙⠛⠿⢿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠟⠛⠋⠉⠁⠀⠀⠀⠸⣿ ⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣦⣴⣶⣾⠿⠿⠿⠟⠛⠛⠛⠿⠿⠿⢿⣶⣶⣤⣴⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⢻⣿⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⣿ ⠸⣿⡆⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⢸⣿ ⠀⢿⣷⡀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⢀⣿⡟ ⠀⠈⣿⣧⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣾⡿⠀ ⠀⠀⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠃⠀ ⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀ ⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀ ⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀ ⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀ ⠀⠀⢻⣿⡀⠀⠀⠀⠀⣤⣼⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠁⠀⠈⠙⣷⣤⢾⠂⠀⠀⠀⠀⣿⡟⠀ ⠀⠀⠈⣿⣧⠀⠀⠀⠸⢯⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠀⠀⠀⠀⠀⠸⠷⠞⠃⠀⠀⠀⣸⣿⠃⠀ ⠀⠀⠀⠘⢿⣧⡀⠀⠀⠀⠀⠙⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⢤⣀⣀⣦⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀ ⠀⠀⠀⠀⠈⠻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢯⣏⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣷⣶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠿⢿⣶⡀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠈⢿⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⡀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⡇⠀⢰⡆⠀⠀⠀⢰⡄⠀⠀⠀⢠⡆⠀⠀⠀⢰⡆⠀⢸⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠙⣿⡀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⢀⣿⠉⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣶⣾⣿⣾⣷⡀⠀⢀⡿⠁⠀⠀⠀⠈⢿⡀⠀⠀⣾⣷⣿⣷⣶⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠿⣿⣶⣶⣶⣶⣶⣿⣿⣶⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣶⡿⠟⠛⠛⠛⠛⠛⢿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠟⠛⠛⠛⠛⠛⠿⣷⣦⡀⠀⠀⠀ ⠀⠀⣰⣿⠟⠁⠀⠀⣀⣀⣀⣀⣀⠀⠈⠙⢿⣦⡀⠀⠀⢀⣀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣤⣤⣤⣀⣀⡀⠀⠀⣰⣾⠟⠁⠀⢀⣀⣀⣀⣀⡀⠀⠀⠙⢿⣦⡀⠀ ⠀⣼⡿⠁⠀⣠⣶⡿⠟⠋⠉⠙⠻⢿⣦⡀⣀⣿⣷⣾⠿⠟⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠿⠿⣾⣿⣅⣀⣴⣾⠿⠛⠉⠉⠛⠿⣷⣄⠀⠀⠹⣷⡀ ⢸⣿⠀⠀⢰⣿⠋⠀⠀⠀⠀⠀⢀⣠⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣧⣄⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⢻⣷ ⣿⡇⠀⠀⣿⠇⠀⠀⠀⠀⣠⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⡀⠀⠀⠀⠈⣿⡇⠀⢸⣿ ⢻⣧⠀⠀⣿⡆⠀⠀⣠⣾⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⡀⠀⠀⣿⡇⠀⢸⣿ ⠈⣿⣆⠀⠸⣷⣄⣾⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣼⡟⠀⢀⣿⠏ ⠀⠘⣿⣦⡀⣸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⣠⣿⠏⠀ ⠀⠀⠈⠻⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡟⠁⠀⠀ ⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀ ⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣀⣼⣿⣿⠀⠀⠀⠀⣀⣴⡾⠿⠛⠋⠙⠻⠿⣷⣦⡀⠀⠀⠀⢸⣿⣇⣀⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠀⠀⣠⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⢀⣼⡿⠋⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠻⣿⡄⠀⠈⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀ ⠀⠀⠀⣿⡇⠀⠀⠀⢀⣤⣴⣶⣶⣶⣶⣶⣤⣄⠀⠀⣾⡟⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠂⠀⠀⠀⠀⠸⣿⡄⠀⣠⣤⣶⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⣾⡇⠀⠀ ⠀⠀⠀⢻⣧⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢸⣿⠀⢠⣧⡀⠀⠀⠀⢘⣿⣟⠁⠀⠀⠀⣠⣶⡄⢻⣷⠀⠻⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢀⣿⠇⠀⠀ ⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⢸⣿⡀⠀⠙⠻⠿⣶⡾⠿⠋⠻⠿⣷⡶⠿⠟⠉⠀⣼⡿⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀ ⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣦⣄⣀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠷⠶⠶⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⣶⣦⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣴⣶⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠔⠁⠀⢀⠎⠀⠀⠀⢁⠀⠀⠈⠢⠀⠈⢢⡀⠀⠑⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠎⠀⠐⠀⠘⠀⠀⠀⠀⠀⢃⠀⠀⠀⠡⢀⠙⣶⠀⠀⠘⡄⠀⠀⠀ ⠀⠀⠀⠀⡌⠂⠀⡇⠀⡆⠀⠀⠘⡄⠀⢸⣄⠀⠀⠀⢃⠑⢴⡆⢀⡴⢳⠀⠀⠀ ⠀⢄⠀⠀⢻⠀⠸⣇⡀⢇⠀⠀⠀⡑⡤⠐⡙⡀⠀⠀⠸⡠⡙⡷⣏⣀⢀⠀⠀⠀ ⠉⠚⢆⠀⢸⠀⢰⢰⣈⣏⣇⠀⠈⡄⢼⠟⢍⢳⡦⠀⢀⠣⠜⠙⢌⠙⢻⠀⠀⠀ ⠀⠀⣀⠀⣾⡀⠘⡸⡏⣎⣇⠑⢄⢃⠘⣖⡺⠘⠁⠀⣿⠐⢰⡛⡘⠀⢸⠀⠀⠀ ⣠⢤⡿⠀⢹⢱⡄⠑⣧⡑⠃⠀⠀⠈⠀⠀⠀⠀⡆⡸⠃⠐⠚⡡⠁⢸⢸⠀⠀⠀ ⡠⢜⣠⠀⠀⠁⠙⠦⣷⠁⠀⠀⠀⠀⠀⠀⠀⠤⠜⠀⡐⣹⣿⡇⠀⠸⡄⠀⠀⠀ ⠀⠩⢧⣶⠆⠀⠀⠀⠀⠢⡀⠀⣀⣀⡀⠀⠀⠀⣠⠎⠀⣿⣿⣇⠀⠀⣧⠀⠀⠀ ⠀⠀⠀⠉⡀⢀⣀⣀⠠⡔⢾⢟⢭⣀⣀⣀⣤⡾⠁⠀⠀⢻⣿⣿⡆⠀⢸⠀⠀⠀ ⠀⠀⠀⣠⢋⠬⠉⢻⠇⠀⠈⣸⡘⣿⣿⡟⠋⠀⠀⢀⠔⠁⠀⠀⠙⢀⠀⠃⠀⠀ ⠀⠀⠀⡅⠁⢈⢰⠁⡠⠂⠈⢹⠋⡩⡻⠻⠀⠀⠀⠆⠀⠀⠀⢡⠀⠀⢂⠘⡀⠀ ⠀⠀⠀⠅⠀⢸⡆⠰⠢⡀⠸⠠⢋⠌⠀⠲⠠⠒⢨⠀⠀⡠⠄⠒⢄⠀⠀⡄⢡⠀ ⠀⠀⢀⣾⠀⢘⢿⠇⠀⠈⠗⢠⠂⠑⠤⠤⠐⠈⢹⠔⠡⠀⠀⠀⠀⠱⡀⠃⠀⡄ ⠀⠀⢪⣙⠐⡑⠹⠠⢀⡊⣠⡁⠀⠠⠂⠀⠀⢀⢿⢠⠁⠀⠀⠀⠀⠀⠐⡄⢰⢀ ⠀⠀⡙⣀⠠⠐⠘⢨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⢎⢷⢸⠸

⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⢀⣙⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠘⣽⡆⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢹⡟⠀⠀⠀⠀ ⢁⡀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢿⣦⠀⠀⠀ ⠈⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠖⢢⣸⣆⣀⠀⠀⠀⠈⣿⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⠁⣰⠀⢸⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⣷⣦⣀⠀⠀⠀⣞⠉⢉⣦⣤⢬⣇⣀⣭⡿⠀⠀⠀⠸⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⢀⡟⢠⠟⡆⢸⡀⢱⣄⣠⣶⠀⢣⠀⠀⠀⠀⢸⡰⣄⠀⠘⣏⠛⠻⢶⡞⠙⢲⠏⡁⠀⠐⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⢸⡇⠸⠀⠘⢿⣿⠛⠛⣄⠀⠳⣌⣧⠀⠀⠀⠀⣇⠢⠙⢶⣾⢧⡤⢾⡤⠶⠿⣤⣁⣤⠴⡎⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣷⣇⢠⣦⣬⣙⠢⡀⠈⠑⠢⠿⠛⠳⢼⡗⠤⣸⣄⠀⠀⠈⠛⢳⣄⠄⠀⠀⠀⠀⠙⢦⡈⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣻⣷⣌⠂⠀⠀⠠⠤⣤⠴⠆⠀⠈⠉⠹⡄⢀⡴⣋⣤⣶⣶⣶⣶⣶⣄⡀⠙⠲⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡟⣿⠟⠛⢻⠟⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢺⣾⣿⣿⣿⣷⣧⣽⣿⣿⣿⣷⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡟⣆⠀⢸⣿⣿⣝⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣛⣿⣤⡾⢷⣤⣸⡇⠉⠛⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣇⠈⠀⣀⡁⠾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⣽⡿⠋⠈⣿⠃⠀⠀⣸⠋⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣽⡀⠀⠉⠙⠳⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣓⣒⣋⠁⣀⣠⡎⠁⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠤⠼⠋⠉⠁⣆⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⠀⠸⡗⣶⣶⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢛⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⡀⠀⠹⣦⢨⠙⢦⡀⠀⠀⠀⢸⣿⠗⠲⣖⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀ ⠀⣶⠀⣀⠀⠀⠳⣄⠀⠙⠿⢄⣀⠉⢲⣄⠀⠀⠙⠋⠉⠙⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣾⠏⠀⠀⠀⠀⠀⢀⡖⠀⣠⡄⠀⢸⠀ ⠀⠘⣧⣹⣷⣤⣀⠀⠉⠲⢤⡀⠈⢉⣹⢿⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⡒⠋⢁⡤⣞⠁⠀⠀⠀⠀⢀⣴⡟⣁⡔⠃⠳⡄⠈⣶ ⠀⠀⠈⠿⣿⣮⣽⣿⣦⠶⠿⠛⠛⠻⠬⣮⡳⣤⣌⣙⣶⡶⣶⡖⠒⠛⠉⠁⠀⠀⠀⣀⣬⠞⠉⠀⢀⣀⣀⣴⡿⠷⠚⠉⠀⠀⠀⠈⠓⠾ ⠀⠀⠀⠀⠀⠉⠉⠉⠀⣀⣤⠶⢶⠒⠒⢲⣯⣽⠟⠉⠀⡾⣯⣧⠀⠠⢤⣀⣠⠔⠋⠁⡠⠋⠉⠉⠉⠙⣷⠶⢶⡎⠤⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⢰⠃⠀⣠⡏⡼⠁⠀⠀⠈⢿⠟⠁⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⠀⠀⠀⢠⠏⠙⠛⠉⠉⠉⠀⠴⠛⠛⠲⣄ ⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⢠⠏⠀⢰⡏⠰⠃⠀⠀⠀⠀⠈⣦⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⢀⡎⡠⠂⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀

⠀⢀⣴⣆⠀⠀⣴⣶⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣐⡀⠀⠀⠀⠈⠁⠀⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣩⠝⢸⡭ ⢀⣿⣡⣿⠀⣾⣣⣼⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢠⣆⢦ ⣾⠋⠉⠹⢿⠟⣩⡙⢷⣤⠀⠀⢸⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠟⠹⢸ ⠇⠞⢻⠛⠛⢀⡟⠀⢸⡟⠀⠀⡿⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⣸⡃⢀⣚⠁⠀⢸⣥⢞⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠀⠀⠛⠃⠈⠛⠁⢀⣟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠻⣿⣆⠙⢮⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣳⢯⡟⣿⡟⣿⡿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⢿⣧⣸⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠉⢀⣿⠁⣿⢿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⠃⠀⣸⢻⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢡⡀⣼⠃⢰⣿⣿⣿⣿⣿⣿⢸⢸⣿⣿⣿⣿⣿⡏⣼⣿⡟⢀⡼⢱⠸⣿⣿⣿⡽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣻⣿⣿⣿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⡾⣣⡟⠁⣿⣿⣿⣿⢻⣿⣿⢸⣾⣿⣿⣿⣿⣿⠇⣿⣿⢀⣮⣴⡾⡟⢻⣿⣿⢿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣿⣷⣼⣿⣿⣿⡿⢸⣿⢹⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⡟⠋⠀⠀⠀⠀⠉⠙⠋⠻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⢹⣿⣿⣿⣿⡇⢸⣟⠸⣿⣿⣿⣿⣿⣿⢧⢀⣴⣿⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⠓⢌⣿⠀⠻⠻⠿⠿⠿⠿⠈⠉⠀⣧⠀⠀⢿⣹⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠞⠛⠉⠓⢶⡆⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠳⠇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⣭⡿⠋⠁⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣷⡈⣇⠀⠀⠀⠀⠀⠘⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠖⠋⠁⠀⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢀⣠⣴⣾⣿⣏⣼⣿⣿⣿⣿⣿⣷⡼⣆⠀⠀⠀⠀⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⣰⣇⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⣼⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏ ⠀⢀⣴⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢧⡀⠀⠀⣠⡴⠋⠀⠀⠑⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⣀⣤⣾⡿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇ ⠀⢺⣿⣿⡿⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠙⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⢀⣠⣤⠶⠒⠋⢉⡿⢹⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀ ⢀⣿⣿⣿⠃⣼⡿⠿⠛⠉⠉⠉⠉⠉⠉⠻⣿⣿⣷⠀⠀⠀⠀⠀⠀⢀⠖⠒⠋⢉⣠⠴⡶⠏⠉⠀⠀⠀⠀⢠⠏⠀⢸⣿⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀ ⠚⣿⠟⣿⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄⣿⣿⣿⣇⠀⠀⠀⡀⠀⣼⣆⡠⢞⣡⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀ ⣤⠋⣴⣁⢸⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣆⠀⠀⣇⡀⢸⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⢁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀ ⢡⠎⠁⠈⠙⢿⡀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣆⠀⠈⠁⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⡴⠛⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⠉⠁⠀⠀⠀⠀⣿⣿⡿⣿⣿⣧⣀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⣀⣼⣿⣿⠟⣡⣿⡿⡿⠛⠉⠀⣰⠟⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠲⠤⣄⣀⣛⠀⠀⢸⣿⣷⠸⣿⣿⣿⣿⣶⣤⣀⡈⠉⠓⠲⠶⠶⠶⠶⠚⠉⠁⣀⡴⢋⡽⠛⠉⠀⠈⢀⠽⠊⠀⠀⢀⡾⠁⢠⡆⠀⠀⠀⢀⡄⡈⠀⠀ ⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠉⠀⠀⠀⠉⠛⠺⠿⣿⡇⠙⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⣀⣠⣴⡿⠋⠀⠀⠀⠀⣀⡤⠚⠁⠀⠀⠀⣠⠟⠀⠀⣼⠁⣀⣝⣷⣽⣿⡇⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⣈⣻⢿⣿⣿⣯⠙⣛⡛⠻⠿⠿⠯⢩⡿⡟⠁⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⣴⠋⠀⠀⢠⡇⣺⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⡏⠛⠂⠉⠈⠉⠉⠙⣋⠉⠁⠀⢀⣤⠖⠋⠀⡇⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⣸⠁⢀⡠⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠ ⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠰⣿⣧⣄⡀⣀⡀⠀⣠⠞⠁⢀⣀⣀⣾⡝⢦⠀⢰⠃⢀⡴⠊⠀⣀⠤⠴⠶⠶⠶⠖⠋⠉⢹⣙⣟⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠⣮ ⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⠋⡡⠖⢀⣀⢻⣿⣿⣿⣿⣿⣷⡄⡛⣷⣦⣴⣶⣮⣅⡸⢇⠘⠒⠛⡀⢘⣭⣶⣾⣶⣶⣶⣤⣿⣖⠀⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡤⣿ ⠉⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⠜⢉⡀⠀⠀⠀⠀⠐⢺⣿⣿⣿⡿⠋⠛⠃⢣⣿⣿⣿⣿⣿⣿⣿⣷⣤⢤⢤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣰⣿⢷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣿

⠀⠀⠀⠀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⢔⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡜⠁⠀⠀⠀⡀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡜⠁⡎⠀⠀⢸⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠈⠙⡒⠒⠢⠤⠤⢤⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡆⠀⡇⠀⠀⠀⢧⠘⡇⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠁⠀⡇⠀⠀⠀⠈⢦⣳⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⣧⠀⣆⠀⠀⠀⠙⢿⣄⡀⠀⢸⠹⡄⠀⡠⠔⠂⢸⡀⠀⠀⠀⠀⠀⣇⠀⣀⡠⠔⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⡎⠘⢦⣿⡀⣿⡄⠀⠀⠀⠀⡀⠈⠀⢸⠀⠘⠎⠀⠀⡀⠛⡇⠀⠀⠀⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡧⣀⣀⣭⣧⢸⣧⠀⠀⠀⠀⣧⠀⠀⢻⠈⠉⠒⠶⣎⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡇⣸⠋⠀⠈⢆⣿⢧⡀⠀⠀⢻⣆⠀⢸⡀⢀⡀⣀⡈⠳⣄⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣠⡔⠋⠀⠀ ⠀⠀⠀⢸⡿⠃⢀⣤⣖⣞⣿⣦⠳⡄⠀⠈⣿⡄⣈⣿⣿⣿⣿⣶⣿⣬⣳⠀⠀⠀⠀⡀⢸⠀⠀⠉⠁⠀⡇⠀⠀⠀ ⠀⠀⢀⢸⣧⣾⣿⡿⢿⣿⣷⠀⠁⠘⠒⠒⠾⡟⠿⠉⢿⣿⣿⣿⣿⣿⣿⣿⡦⠀⢀⠇⢸⣄⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⣿⣿⣇⢸⣾⢿⣿⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣋⠙⠫⣡⣏⣻⠉⠀⠀⢸⠀⢸⠉⣆⠀⠀⢰⠇⠀⠀⠀ ⠀⠀⠀⢸⢷⡀⠠⠅⠤⠴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⢘⡉⠁⣿⠀⠀⢀⡎⠀⢸⠀⢸⠄⠀⡼⠀⠀⠀⠀ ⠸⠀⠀⢸⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠂⡿⠀⠀⢺⠃⠀⣸⢄⡿⠀⠈⠁⠀⠀⠀⠀ ⠀⠀⠀⢸⡄⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⢀⡟⠀⢘⣿⡛⠀⠀⡀⠀⢀⡄⠀⠀ ⠀⠀⠀⢸⡇⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢀⡞⠀⠀⠀⡇⠀⠀⠀⢳⠀⣸⠇⠀⠀ ⠀⠀⠀⠈⡇⠀⢰⡈⠓⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡟⠀⠋⠀⠀⠀⣸⠁⠀⣰⠀⢸⣠⣿⢀⠆⠀ ⠀⠀⠀⠀⣧⠀⠀⡇⠀⠀⠀⠈⠙⠒⠦⠤⣤⡶⠒⠉⠁⠀⠀⠀⡼⠁⠀⠀⠀⢀⢀⡇⢀⣤⢿⡆⣸⣿⠿⠋⠀⠀ ⠀⠀⠀⠀⢸⡀⠀⣧⠀⠀⠀⠀⢀⣠⡴⢋⣵⠏⠀⠀⠀⠀⣠⣼⣥⠀⠀⠀⣠⢾⣼⠤⣸⡛⠂⠛⠛⠛⢀⣀⠀⠀ ⠀⢦⠀⠀⠀⣇⢸⡇⠁⣤⡴⢋⡽⢋⡔⠉⠀⠀⠀⠀⠀⠀⠀⡰⠃⢀⡠⠞⠃⠸⠃⣠⠞⢳⣄⠀⢀⡠⠄⠀⠙⢆ ⠀⠈⢢⠀⠀⠈⢦⡁⣨⠋⣠⠊⢠⠿⠒⠉⠒⠤⡀⠀⣠⣤⠾⡷⠚⠉⠀⠀⠀⡰⠊⢀⡴⠁⠈⠙⠫⡀⠀⠀⠀⠀ ⠀⠀⠀⢉⡵⠦⠤⢉⣧⣴⠁⢀⣯⠴⠒⠒⢤⣀⠈⠢⡄⠉⠻⣄⠀⠀⠀⡴⠋⠀⣰⠟⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀ ⠀⠀⢠⠊⠀⠀⢷⡄⠀⠀⠀⢸⠁⠀⠀⠀⠀⠈⠲⣾⠓⠚⠃⠈⠣⣀⠜⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠀⠀⠀⠄⡙⠊⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠓⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣾⣿⣶⣶⣦⣤⣨⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣬⣿⣼⣷⣄⠀⠀⠀⠠⠀⡠⠀ ⠀⠀⠀⠀⠀⡺⣿⣿⣿⣿⣿⣿⣿⣿⢸⢇⢹⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⡠⠊⢀⣶⢶⣷⣿⣿⣿⣿⣿⣿⣿⠟⠈⢑⢯⣛⠛⢡⠓⠛⣿⣿⣇⠀⠀⠀⠀⠀ ⣵⡷⣹⣧⢼⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⠀⠁⠀⠈⠃⢀⢿⣿⣿⡆⠀⠀⠀⣠ ⡿⡉⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⡶⣒⡌⠀⠀⠀⠌⠉⣿⣿⣿⣷⢀⣀⠈⠻ ⣷⣁⠴⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣇⠂⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡟⢸⡿⠷⣦ ⣇⠫⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠻⠁⠀⠀⠀⠠ ⣿⣷⠏⠀⠀⠀⢀⠽⢉⠀⠨⠉⡛⠳⡓⠨⠔⣲⣶⠾⣿⡍⠍⡈⠣⡀⠀⠀⠀⣀ ⣿⡿⠤⠀⠀⢀⠂⠀⠀⠆⠀⠀⠀⠉⠐⠱⣢⣤⣿⣍⣯⣿⡕⢌⡢⠘⡤⢶⣄⢀ ⡍⠁⠀⠀⠀⢸⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠙⢿⢷⡀⠈⠳⣹⣚⢿⠀ ⣇⣤⢄⣤⣠⠘⡄⠀⠈⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠎⢄⠈⠪⠫⡛⣳ ⣿⢋⠚⡿⢿⢠⠿⡀⠀⠈⢧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠄⠀⠑⠹⢿ ⢧⢇⢤⡂⢹⠑⠠⣪⡢⠄⣸⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢳⠀⠀⠀⠀⡦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⢤⣀⠀⠀⠀⠀⢠⠞⠉⢧⢀⡴⠚⠁⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠙⠦⣄⣰⠏⠀⠀⠈⠋⠀⠀⠀⠸⡇⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣀⣀⣀⣸⡄⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁⠀⢀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢳⡀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢾⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠉⢉⡿⠂⠀⠀⠀ ⠀⠀⠀⠈⠛⢶⡴⠶⢶⣶⣶⣾⣿⣾⣶⣶⣶⣶⣶⣶⣶⣴⣦⡁⠀⠐⡆⣠⣴⣿⣵⣶⣶⣶⡶ ⠀⠀⠀⠀⠀⣼⣀⠄⠇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⠟⠃⠀ ⠀⠀⠀⠀⠀⣿⡳⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⢋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣥⣤⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⢲⣩⡔⢯⡀⠀⠀⡇⠀⠀⠀⠀⢀⣠⢤⣀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⡀ ⠀⠀⠀⠀⠀⢀⡾⠃⣿⣇⡠⠃⠀⠀⡇⠀⠀⢀⢰⠉⠀⡠⠜⢧⢰⠀⠈⢿⡙⠛⠿⠿⠿⢿⣿ ⠀⠀⠀⠀⠀⣾⠁⠀⠘⠉⠀⡐⠉⠀⢱⣶⠀⡞⠯⠴⠛⡲⢀⡞⠀⢸⡶⢼⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡄⠀⠀⡰⠀⡈⠉⠁⠈⠸⡜⠀⣄⠀⠊⣠⠞⢱⣤⣀⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠶⣜⡁⠀⠈⠁⠀⠀⠀⠀⢀⡈⢻⡉⣽⢤⣀⣷⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣶⡶⢶⠋⠉⠉⠉⠉⠉⠉⢹⡆⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢼⡅⣯⢰⢀⠀⠀⠀⢀⣀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⡟⣿⣾⣾⣿⣿⣿⣿⢿⣿⣷⣄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢸⣿⣿⣿⣿⠿⣛⢿⣿⣓⣼⣻⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡶⢿⣥⣿⢇⡿⡉⠭⡑⢄⠣⣙⣦⣍⡛⠧⠹⣏⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣯⣐⣉⣿⣿⢰⡇⡱⢂⠍⢢⡑⢄⠺⣽⣳⣬⣑⣤⠷⣋⢙⣳⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠶⠏⠀⣩⣾⣿⣿⣼⣧⣦⣵⣮⣥⣼⣌⣱⣧⣯⣽⣏⡰⢡⣶⠟⠛⠖⠲⣄⠀⠀⠀ ⠀⠀⠸⡇⠀⠀⣸⠋⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢿⠛⠉⢻⠀⠀⢀⡿⠀⠀⠀ ⠀⠀⠀⠙⢲⡖⠋⠀⠀⠀⢸⡏⢹⠋⢩⣼⠉⡌⢩⠉⡍⣽⡅⢰⣾⠀⠀⠘⣧⣴⡞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡰⢉⣛⡾⢡⡉⢜⡠⢃⣾⡯⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⡱⢐⣣⠞⡡⠒⣌⢢⣴⣿⣿⣿⣿⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⢡⠌⣻⣶⣋⠔⣡⢓⣼⢿⣵⣿⡿⢿⣱⡾⢋⠽⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣦⡾⡽⢃⠝⣷⣴⠟⠁⠀⠙⣿⠵⣋⠳⣝⢮⣲⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣴⣻⣿⣿⣦⣾⣿⣧⣝⢷⣌⣒⣤⠟⠀⠀⠀⠀⠈⠳⣦⣱⣾⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀ ⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⢙⣿⣿⣿⣿⣾⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠛⢿⣿⣿⡿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠻⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⡠⠴⠒⠒⠢⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⡀⠀⠀⠀⠀⠀ ⠀⣼⡧⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠛⢦⡀⠀⠀⠀ ⡞⠉⢠⠀⠀⠀⠀⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⡀ ⣟⠒⠛⠢⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣣ ⠀⠉⣲⠤⣄⣀⣀⣀⣀⠀⠀⠀⡀⠀⠀⣦⠤⢴⣖⢊⣽⡄ ⠀⠀⠙⡾⠁⣴⡄⢀⢀⠀⠀⠀⢈⣅⠈⠁⠀⠀⣇⢹⣻⠀ ⠀⠀⠀⡇⠶⠉⠀⠈⠊⠓⠊⠀⠘⠛⢠⠤⠀⠀⡏⠀⠁⠀ ⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀ ⢦⣶⡶⠸⡈⠙⠢⠤⣀⣀⡀⠀⢀⣀⡠⡴⠊⠁⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠹⣿⣿⠆⠀⠀⠀⠀⠀⠸⣿⡏⠉⣻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠔⣒⣶⣶⣶⠖⢋⡤⠖⠉⠀⠀⠀⠀⠻⠿⠗⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣡⣾⣿⡿⠛⠋⠉⠁⢀⣀⡠⠤⠒⠚⠛⠛⠓⡒⠂⠤⢀⡀⠻⢿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⡿⢃⣀⣠⣤⠔⠊⠉⡠⠄⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠈⠑⣦⡈⠉⠉⠉⠉⢩⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠁⠀⢀⠎⠀⡰⠁⠀⠀⠀⠀⠀⠐⡈⢣⠀⠀⠀⠙⠙⢦⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟⠀⠀⢀⠎⠀⡼⠀⠀⠀⠀⠀⠀⢠⠀⢱⠀⢇⠀⣾⣷⣦⣤⣧⠀⠀⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣾⣿⣿⣿⡿⠀⠀⠀⠏⠀⢰⠁⢠⠀⠀⠀⠀⠀⡌⠀⠀⠀⢸⣿⣿⣿⣿⣿⡍⢣⠀⣿⣿⣿⣿⣷⣤⠂⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⡿⡇⠀⠀⠸⠀⠀⡆⠀⡘⠀⠀⠀⠐⠀⣧⠠⢀⣀⠈⢿⣿⣿⣿⣿⠃⠀⢻⣿⣿⣿⣿⣿⣏⢆⠀⠀⠀⠀⠀ ⠀⣰⣿⣿⣿⣿⡟⢠⠀⡄⠀⢀⠀⠐⠇⠀⡇⠀⠀⠀⠀⢀⡿⠀⠀⢹⠑⠈⠙⠛⠋⠙⡆⠀⣼⣿⣿⣿⣿⣿⣿⣼⣿⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⠏⠀⠠⠀⢃⠀⣸⠀⢰⡀⢠⡇⠀⠀⡀⠀⣸⠀⡇⠀⢸⡄⠈⡄⠀⠀⠀⡇⠀⢿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀ ⠀⠘⢿⣿⢏⠄⠀⠀⡀⠀⠀⢸⠀⢸⣇⠀⢳⣴⠀⡇⠀⣇⣷⣾⣦⣀⡁⠀⣧⠀⠀⠀⡁⠀⠸⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀ ⠀⠀⣸⢃⠈⠀⢀⢠⡇⠀⠀⢸⡇⠈⠿⡄⠈⠻⡆⢹⡄⠃⠁⢘⣻⣿⣿⢿⡎⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢀ ⠀⢠⣳⠇⠀⢠⠋⢸⡇⢰⠀⢸⣷⠼⠛⠻⠄⠀⠁⠀⠀⠀⠀⢸⣟⣿⡟⢸⠁⠀⠀⠀⡄⠀⠀⠀⠻⡷⢻⠀⠀⠀⠀⠀⠀⠀⣾ ⠀⣿⣿⠀⣶⠃⢀⣦⢿⠸⣆⣼⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢠⠀⠀⠀⣧⠀⠀⠀⢀⡇⢸⠀⠀⠀⠀⠀⠀⠀⢿ ⢸⡟⢧⢀⡿⢠⠎⠸⣸⠖⠋⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣸⠀⠀⡀⢀⣿⡀⠀⢠⣾⠇⡏⣀⣠⠔⠀⠀⠀⠀⠈ ⠀⠛⠈⢦⣷⡎⢀⣴⠁⠀⠀⠀⠀⠀⢱⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠞⠛⠀⠀⡁⢸⢻⢷⠀⣸⢟⠀⡇⠺⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠟⣽⠋⠀⠀⠀⠀⠀⠀⠘⢿⠉⣳⣦⣄⣀⣤⣶⠞⠉⡇⠀⠀⠀⢠⠁⣞⠎⡴⢣⡟⡟⢰⠃⠇⠀⠀⢀⡀⠀⠀⠀ ⠀⠀⠀⠀⡏⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣟⢻⣿⡇⠈⠃⠀⠀⠘⢀⣴⢀⡌⡜⢡⠞⠀⠀⣹⣡⠞⣤⠀⠀⠀⠀⠉⠢⡀⠀ ⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡞⣨⠿⣯⣷⣄⣀⣀⡤⠖⠁⣀⠞⡸⠙⣅⠞⠀⡨⠋⠀⠈⢾⣷⡄⠀⠀⠀⠀⠹⡀ ⠀⠀⠀⢠⢿⡓⢦⣄⣀⠤⠤⠒⠛⠉⠀⠰⣿⠁⠀⠈⠓⣦⢤⣤⡤⠖⠚⠁⠀⣀⡔⠁⡠⢺⠁⠀⠀⠀⠈⡇⠻⢢⡀⠀⠀⠀⡅ ⠀⠀⠀⣯⠈⡻⢾⡉⠀⠀⠀⠀⠀⠀⣀⠤⠊⠀⠀⠀⢰⠋⢙⡇⠀⠀⠀⠀⣼⠋⢠⠞⠁⡎⠀⠀⠀⠀⠀⡇⠀⠈⠈⠄⠀⠀⠘ ⠀⠀⣰⠛⡦⠇⠀⠉⠁⠐⠒⢲⢒⡟⠁⠀⠀⠀⠀⠀⠈⣿⢫⠆⠀⠀⠀⢰⡏⡰⠃⠀⠀⠳⡀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⢀⣏⣽⠁⠀⠀⠀⠀⢣⠀⠀⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣶⣿⣷⣶⣶⣦⣤⣀⡀⠀⢈⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣍⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡈⣿⣿⡘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡇⠸⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣇⠀⢿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣷⣖⠀⠀⠀⠀⠀⣠⢈⠀⠀⠀ ⠀⠀⢀⠀⠀⠀⠀⠀⢸⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣸⡏⢢⣸⢿⣿⣿⣿⣿⢹⡟⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠠⠁⠀⠀⠀ ⣠⠜⠁⠀⢰⣶⣶⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠛⣿⣼⣛⠛⠉⣡⡞⠋⠛⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀ ⠅⣠⣖⠴⣻⣿⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠀⣷⠈⢿⠉⠀⠀⠸⢳⡇⠀⢸⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⡷⣪⢽⣿⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢻⣿⣿⣿⣿⣇⠀⠀⠀⢀⠀⢀⣲ ⣿⡵⠋⠀⢸⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⣦⣤⣤⠶⠊⠀⠀⠀⠀⠀⠀⠐⢚⢡⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⢿⣿ ⣿⠯⡖⠀⢸⣏⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠒⠈⠺⠾⠆⠀⠀⠀⠀⠀⠈⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⢰⣶⣦⡀⠀⠋ ⣗⡯⢀⡠⢼⣿⣯⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡟⠃⣿⣻⣿⣽⣷⣦ ⣿⣿⡟⠂⠀⠉⠉⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠐⠒⠒⠒⠒⠒⠒⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠁⠀⠉⠁⠀⠀⠉⠙ ⣻⠭⠔⠂⠀⠀⢀⠀⠘⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⠽⠏⠀⠀⠀⠀⠀⠀⠀⠒ ⣿⣿⣶⣶⠇⠈⠀⠀⠀⠈⠀⠈⣿⡟⠋⠁⠀⠉⠙⠛⠿⠿⣷⠼⢦⣉⡒⠢⠤⣤⣤⣤⣾⣿⣿⣟⣙⡙⠉⠉⠣⡀⠀⠀⠀⠀⠀⠀⠀⡀ ⣿⣟⣛⡛⠋⠀⠀⠀⠀⠀⢠⠎⠀⠉⠲⣀⠔⠉⠉⠑⠢⠤⣈⠑⢤⡀⠀⠉⠒⠮⣿⣏⣙⣿⣓⣢⣄⠉⠒⢄⠀⠘⢦⠀⠀⠀⠀⠀⠐⠢ ⠞⠓⠂⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠉⠒⠜⢷⣯⣭⣭⣿⣯⣁⣹⣿⣿⣧⡙⠢⣄⠱⡄⠈⢇⣠⣰⣆⣀⡀⠈ ⠭⠭⠥⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⡿⣿⣿⣿⣧⠀⠈⠳⣜⣶⠸⡦⢰⣿⡿⠤⠨ ⣿⡭⠁⠀⠀⠀⠀⠀⠀⢏⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠿⠀⠀⠻⡟⠿⢆⠀⠀⠈⠙⢦⣿⠭⠽⢿⠭⠩ ⣿⣓⡀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠰⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠑⢤⡷⡀⠀⠈⠠⠙⢿⣻⣯⠥⠬ ⣿⣶⣭⠭⣺⣿⣷⣿⡇⠈⣿⡀⠀⠀⠀⠱⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡘⢄⠀⠀⠑⣄⠹⣄⣴⣿ ⡯⣝⡊⠉⢺⣿⠿⢾⡇⢠⣿⣧⡀⠀⠀⠀⠘⣿⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⡄⠀⠀⠈⠆⠘⣿⡿ ⣿⣗⠬⠀⢸⡇⠠⢼⣷⣇⡄⡈⠳⢄⠀⠀⠀⠘⡇⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⡆⢣⠀⠀⠀⠀⠀⣔⣊ ⠿⡛⢯⡒⢼⣇⠁⢺⡇⠈⠑⢦⡑⣦⡑⠢⠤⣘⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠏⠁⡃⢸⠀⠀⠀⠀⠀⢰⣒

⠀⠀⠀⠀⢨⢊⠠⠐⠂⠈⢀⠤⢈⠉⠙⠛⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡠⠂⠁⠀⠀⢀⠔⠈⠀⠀⠈⠀⠀⠀⠈⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡔⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠰⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⢀⠀⠀⠀⢁⢄⠀⡑⢄⠀⠈⡢⠀⠀⠀⠀⠀ ⠀⡆⣦⢄⠀⠤⠦⢅⠀⠀⠀⠀⠎⡄⠀⠀⢸⠀⢢⠑⡀⠁⠢⠌⣑⡂⠤⡤⠃ ⢪⡗⠻⢬⡦⠤⠔⢠⠂⠀⡀⡘⠀⣠⠠⠀⠀⠀⠐⢃⠐⡄⡀⢱⠇⢡⠀⠀⠀ ⢀⢘⡊⡜⡌⠀⠀⠇⠀⠰⡐⠂⠁⠘⠀⡇⢸⠀⠀⠀⡄⣯⢺⡆⠇⢸⠔⠀⠀ ⢸⣇⡰⠂⠰⡀⠀⠸⡠⠋⠀⠀⣀⠀⠜⣡⠂⡶⠶⠆⢰⣿⡌⢈⡴⠊⠀⠀⠀ ⡄⠎⢢⠀⠀⢑⠄⢄⠃⡠⠶⠛⠋⠁⠀⠁⠀⠀⠀⠀⣼⢸⢟⠜⠀⠀⠀⠀⡀ ⢀⠴⡁⠀⠀⢻⠐⣄⠑⢬⠢⠤⠖⠀⠀⠀⠀⡠⠐⠒⠛⠈⠀⠀⠀⡀⠐⠀⠄ ⠚⠀⢰⠀⠀⢠⠁⠚⣁⠀⢢⢀⡀⠀⠀⢀⠜⠀⠀⠀⠀⢀⡀⠀⠀⠈⠂⠊⠀ ⠀⠀⡈⠀⠀⠸⠀⠊⠉⠱⡈⢧⣀⠉⢧⡏⠀⠘⠁⠘⠭⠟⠁⠀⠀⠀⠀⠀⠀ ⠁⡰⠀⠀⠀⠆⡘⠠⢀⠀⠐⣸⡌⠣⡊⡇⠀⠀⠀⠀⠰⢤⡀⠰⠿⠃⠀⠀⠀ ⠠⠁⠀⢀⠌⡗⠀⠀⠀⠈⠐⣿⡁⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⡠⢂⢼⠀⠀⠀⠠⢠⡊⣁⡈⠦⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠙⢞⢎⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⡠⠂⠀⠀⠀⠀⠀⠂⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠈⢣⡣⡳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄⡀⠀⠀⠀⠀⠀⠊⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡷⡄⠀⠀⠀⠀⠹⣕⠵⠄⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠙⢌⠢⡀⠀⠀⠀⠈⢮⡀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡚⠀⠀⠀⢀⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡏⠀⠀⠑⢝⠢⡀⠀⠀⠀⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠑⠅⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡇⠑⠦⢀⣼⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⣼⣟⣾⣯⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠣⣤⣿⣝⡿⣾⣿⣿⣿⣿⠇⢸⣿⣿⣿⣿⣿⣿⣿⢿⣿⡇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣹⣿⠱⣷⣿⣿⣿⣟⠀⢸⣿⣿⣿⣿⣿⣿⣿⠸⣿⡇⠀⢀⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⡀⠀⠀⠀⠀⠀⣾⣿⣯⣏⣼⣿⣿⣿⣿⠏⢧⢸⣿⣿⣿⣿⣿⣿⣿⡆⢿⣧⣠⠞⠀⢻⣿⣷⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⢳⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡇⠀⠀⠀⠀⠀⣿⣿⡿⣰⣿⣿⣿⣿⣿⠶⢦⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⢿⣤⠶⠞⠛⠛⣿⣿⣿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡌⡆⠀⠀⠀⠀⠀⠀⠀ ⠶⠋⠀⠀⠀⠀⠀⢸⣿⣿⣧⣿⣿⣿⣿⣿⣿⠀⠀⠈⠻⣟⢿⣿⣿⣿⣿⣟⣵⠟⠁⠀⠀⠀⠀⠀⠙⣿⣯⣿⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⣿⣿⡇⢳⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⠀⢸⡟⣸⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣤⡘⠆⠀⠉⠉⠁⢸⡏⠀⣤⡀⠀⠀⠀⠀⠀⢿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀ ⠞⠛⠀⢸⠃⠀⠀⣾⠁⣿⣽⣿⣿⣿⣿⣿⣷⡁⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⠀⠀⠀⠀⠀⠀⠀ ⣀⣤⠀⣋⠀⠀⢠⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡸⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠁⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠉⠛⠀⠀⠲⠤⠀⠀⠀⠀⠀⣠⠐⠖⠒⠚⠛⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⡀⠀⠛⣷⠤⠤⠤⠤⠖⠒⠛⠛⠋⠉⣛⣦⣄⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⢹⣿⣇⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢫⠙⢶⣶⠢⢤⣤⣴⡶⠖⠛⠉⠀⠈⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠻⣿⠈⢿⣿⣿⣿⣿⣿⣿⣆⠀⠘⣄⠀⠐⠢⠖⠋⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣻⠂⠀⠀⠈⠳⠈⠻⢿⣿⣿⣿⣿⣿⣿⣶⣝⣦⣼⠁⠀⠀⠀⠀⠀⠀⣀⡴⣫⣿⣿⣿⣿⡿⣟⡿⣫⡾⣿⣿⡿⠟⠋⠁⠀⣠⠟⠓⠒⠶⠖⠒⠒⠂⠀⠢⢀⠀ ⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⡝⠻⢿⣿⣿⠿⣶⣭⣟⣓⠒⣚⣛⡯⠵⢿⣟⠛⠿⠛⠁⡼⠁⠀⣠⠞⠁⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⠉⣹⡿⠃⢀⡴⠋⠈⠳⣶⣠⠞⠁⣠⠞⠁⠀⠀⠀⠀⠀⡰⠫⠤⠤⡤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⢰⣿⠁⣠⣏⣈⣡⢶⡄⢽⢁⣤⠞⣡⣤⠀⠀⠀⠀⣠⠞⠁⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠆⠀⣿⠇⢻⣿⣶⣶⣶⣝⣿⠉⢹⣵⣡⣴⣾⣆⠀⢀⠞⠁⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣿⠀⠘⡄⢸⡏⠀⠈⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡴⠋⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠛⡄⠀⡇⢸⠁⠀⣰⣃⠀⢹⣿⣿⣿⣿⡟⢿⣿⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣼⡾⠀⣰⠟⠁⠀⠀⠛⢿⣿⠋⢠⠊⠛⢷⣭⣛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣇⡎⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⢠⠇⠀⠀⠀⠀⢹⠀⢸⣇⡴⠋⠀⠀⠀⠀⠀⠈⣇⠀⢸⡤⠂⠀⠻⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣿⠁⠈⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⢀⠞⠁⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠘⡆⢸⡿⠁⠀⠀⠀⠀⠀⠀⢰⠃⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠈⠀⠀⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⣠⠎⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⣸⣁⣼⠃⠀⠀⠀⠀⠀⠀⢀⠇⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⡇⡄⢀⠇⠀⠀⠀⠀ ⣀⠀⠀⠀⣀⣀⡀⠀⢀⡴⠁⠀⠀⡀⠀⠠⠃⠠⠀⠀⠀⠀⠀⠀⠁⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⡈⠀⠀⠀⠀⠀⠀⠀

⠄⡀⠠⢀⠀⢀⣴⣿⣾⠿⣙⠴⠌⠓⣮⡳⣍⢻⡷⣦⣀⢄⣪⠂⠁⠀⠀⠀⠀⠀ ⠀⠀⠈⡶⢲⠃⣾⡿⠁⡀⣇⢸⡼⣆⡎⢻⣿⣧⠱⡌⢟⢅⠘⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣥⢇⣘⡿⣵⡶⢱⡿⡾⡧⣽⣿⣄⠩⣿⣷⡘⡄⢫⣦⡸⡀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣮⣽⠻⡜⣧⡿⠁⢣⣧⠙⣝⢿⣦⡙⣿⣷⡝⣄⠻⣷⡇⠀⠀⠀⠀⠀ ⠀⠀⢸⡿⣽⡿⣆⢧⣿⠥⠒⠉⢻⡆⠈⠃⢉⡛⠿⣿⣿⣿⣧⡙⣧⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⣿⣷⣼⢸⠁⣤⣦⡂⠀⠻⡄⠀⢰⣛⣷⣾⣻⡿⣿⣷⣌⠣⡀⠀⠀⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⡝⣧⣿⠧⠀⠀⠘⢆⠘⡛⢛⠃⠛⣧⣿⣿⡿⣷⣿⣦⡀⠀ ⠀⣠⣿⢻⣿⡇⡿⣿⠓⠑⠮⠞⠀⠀⠀⠀⠁⠈⠉⠀⠀⣿⣿⣿⣷⣧⠈⠉⠙⠒ ⢘⡿⠁⢸⣿⣷⣇⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣼⣿⣷⣙⡿⠃⠤⡀⠀ ⠚⠀⠀⡸⠛⢹⣿⡘⡌⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⣿⣿⡏⠁⠀⠀⠀⠀⠀ ⠀⠀⢰⠀⠀⠈⡟⢷⣻⣄⠀⠁⢢⠄⣀⢀⠠⡚⢀⠀⣸⢿⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⢀⠀⠘⠄⠙⠳⡅⠀⠀⠁⠂⢄⣴⠐⠁⠀⢃⢻⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⢆⠈⢐⡀⠀⠀⠀⠈⠢⡀⠀⠠⢁⢃⠑⢄⢀⠌⣾⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⢸⣦⠀⠳⡀⠀⠀⠀⠀⠈⠐⠁⠀⠂⠆⠀⠀⢰⡿⠀⠀⠀⠰⠁⠀⡇⠀ ⠀⠸⣿⠸⣿⣷⣄⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⢊⠀⠀⣿⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⠉⠉⠀⠀⠀⠈⠉⠛⢲⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠶⠶⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⠀⠈⠉⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣀⡴⠶⢻⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣷⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠋⠁⠀⣠⡟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣄⡀⠀⠀⠀⠀⠀⣿⠛⠁⠀⠀⠀⠀⣴⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣷⣄⠀⠀⠀⠻⣇⠀⠀⠀⢀⣾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠹⡷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠻⣷⡀⠀⠀⠙⢷⣄⣰⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⡀⠀⠀⠀⠀⢿⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢿⣆⠀⠀⠀⠉⢋⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠘⢷⣄⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣿⠇⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠈⠙⢷⣤⣀⠀⠀⢿⡄⠀⠀⠀⠀⠀⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⢠⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⢸⡄⠉⠙⠛⠛⠛⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣿⢻⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡀⠀⢸⣿⢧⡀⠀⣿⡀⠀⠀⠀⠀⠀⠀⣆⠀⠀⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠃⠀⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠹⣧⡀⠀⢻⣆⠙⠶⣬⣷⡀⠀⠀⣀⣀⠾⠿⣦⣤⡌⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢹⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⠷⣦⣀⠹⣦⡀⠠⠞⣷⠀⠀⠉⠝⡷⣤⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠈⠙⠛⠿⣿⣦⠀⣹⣧⠀⠀⠸⠟⠁⠙⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠙⠻⣦⢻⡄⠀⠀⠀⠀⠀⠘⠳⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⡙⠃⠀⠀⠀⠀⠀⠀⠀⠈⠻⡷⠀⠀⠀⠀⠀⠀⠀⠙⢿⡛⠷⢦⣤⣄⣀⠀⠀⠀⢀⣀⣤⡾⠟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⣟⣻⠿⠆⡀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⢀⣀⠀⠀⠀⠈⢿⣆⠀⠈⠉⠉⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⣶⡾⠫⢄⣴⡞⠛⠒⢾⣃⣠⣤⢆⣠⠶⣶⣤⣀⠀⣠⢿⡏⠀⠀⠀⠀⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡶⠟⠉⠀⠀⣼⠏⠉⠁⠈⠉⠉⢧⠀⠀⣹⠃⠙⠉⠁⠀⠘⣦⠉⠙⠡⢾⣇⣀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠈⢧⣠⡏⠀⠀⠀⠀⣠⡴⠛⢠⡀⠀⣀⣀⣽⡿⠆⠀⢀⣠⣼⣗⣚⠛⠛⠛⠶⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠙⠉⠉⠉⣧⢸⠁⠀⠀⢠⡴⠞⠛⠉⠉⠉⠛⢷⣦⡀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⣀⣠⣴⣦⠀⠀⠀⠀⠀⠙⣿⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⣿⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣦⣤⣤⣤⣤⣤⣤⡶⠶⠶⠿⠛⠋⠉⠈⢿⣆⡀⠀⠀⠀⣀⣿⡉⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣼⡟⢠⣿⠀⠀⠀⣠⣤⣴⣶⡾⠛⠁⢀⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡛⠚⠛⠁⣿⡷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣄⣄⣀⣠⣴⠟⠀⠀⣠⣾⠟⠀⣾⣧⡀⠀⠀⢸⣇⠀⠀⠠⣾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⡶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠛⠻⠿⠤⠶⠾⠟⠋⠁⠀⠀⢿⣦⣉⠛⠛⢋⣿⠦⠤⢴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠿⠶⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄ ⠀⢻⠻⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡞⠋⡟⠁ ⠀⠘⠀⠀⠀⡿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡟⢹⠀⠀⢱⠀ ⠀⡀⠀⠀⠀⢳⣌⣿⣿⣷⣄⢀⣀⣠⣤⣤⣤⣀⣀⡀⣠⣾⣿⣿⣿⣵⡇⠀⠀⢸⠀ ⠀⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⢸⠀ ⠀⢸⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠍⠀⠀⣼⠀ ⠰⣼⣧⣄⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠦⣴⣿⡄ ⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠈⠩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣋⣹⡟⢿⣿⣿⣿⣿⣿⡯⣿⡏⢻⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⣼⣿⣿⣿⣿⣿⡏⢿⠀⠀⢧⠘⣿⣿⣿⣿⡟⠀⢸⠁⠈⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⣰⡿⣿⣿⣿⣿⣿⣇⣤⣤⣤⣈⠀⠘⢿⣿⡿⢀⣤⣴⣦⣤⣽⣿⣿⠛⢻⡿⣷⡀ ⠘⠉⠀⠹⡄⠈⣿⣿⡿⠏⣿⣿⣿⠃⠀⠀⠙⠃⠘⣿⣿⣿⣽⣿⣿⠇⢀⡾⠁⠀⠈ ⠀⠀⠀⢠⡿⢦⡘⢿⣧⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⣿⣋⡴⠿⣇⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⣽⠟⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣠⣤⣿⣧⣀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀⣼⣿⣶⣤⣄⠀⠀⠀⠀ ⠀⠀⠀⣴⣿⣿⣿⣿⣿⡟⡈⡗⠢⣄⡀⠉⠉⢀⣠⠔⢺⡟⡏⢿⣿⣿⣿⣿⣦⡄⠀ ⠀⠀⢸⣿⣿⠟⠉⠉⠙⢥⡇⣗⠀⡈⢫⡁⠈⡽⠁⠀⣼⣹⠟⠉⠀⠉⠙⣿⣿⣿⠀ ⠀⠀⢸⣿⠁⠀⠀⠀⠀⢘⣧⠙⢆⠀⡾⠃⠸⣇⠁⢠⣧⠿⠦⠀⠀⡀⠀⢈⣿⡟⠀ ⠀⠀⢸⣿⠀⠤⠤⠴⠈⣙⣻⣥⡎⠚⢻⣾⣷⡿⡶⠁⣿⣿⣶⢤⣀⣀⣠⢾⣿⣧⠀ ⠀⠀⢀⣿⣗⠀⠀⠀⣹⣿⣿⣿⣧⠀⠈⣿⣿⡁⠀⢸⣿⣿⣿⣄⠀⠀⣠⣾⣿⣿⠀ ⠀⠀⣼⣿⣿⣷⣶⣾⣿⣏⠻⣿⣿⣆⢀⣿⢿⣇⢀⣿⣿⢟⣽⣿⣷⣾⣿⣿⣿⡇⠀ ⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣬⡻⣿⣼⣿⣿⣿⣾⢟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀

⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠤⠒⠒⣲⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠁⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⣠⣶⣿⠿⠛⠉⠁⠀⠀⠻⠿⠿⠋⠉⠁⠀⠀⠀⠀⠈⠙⠿⢿⣿⣿⡿⢿⣦⣄⡀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡴⠋⠀⠀⠀⢀⣴⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⢰⡄⠀⢳⡌⠉⠃⠀⠈⠛⠿⣷⣤⡀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡴⠋⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠀⢿⠀⠀⠈⠳⣄⣸⠃⠀⠀⢹⡄⠀⠀⠀⠀⠀⠈⠙⢿⣦⡃⠀⠀⠀⠀⠀⢠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣥⡀⠀⠀⣠⠟⠁⠀⠀⢠⠖⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠈⠹⣄⠀⠀⢸⣇⠀⠀⠀⠀⠀⢠⡀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢶⣴⠃⠀⠀⠀⠀⡞⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⢷⣀⠀⠀⠀⠈⢧⠀⢸⡿⣆⠀⠀⠀⠀⠀⠻⡄⠀⠈⢮⢧⡀⠀⠀⠀⠀⠰⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⢳⣄⣀⠀⢘⡶⠋⢳⢻⡄⠀⠀⠀⠀⠀⠹⣄⠀⠈⢧⡻⡄⠀⠀⠀⠀⠱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠘⣦⠈⠙⠻⣅⠀⢸⡆⢳⠀⠀⠀⠀⠀⠀⠹⡄⠀⠈⢧⠻⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠇⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠤⠶⠒⠉⠉⠉⠙⠒⡏⠀⠀⠀⠈⠳⣤⣀⠙⣶⠿⢤⣸⣧⡀⠀⠀⠀⠀⠀⢻⡄⠀⠈⣷⢻⡄⠀⠀⠀ ⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⣿⠈⠙⢿⡄⠈⡇⢻⡝⠲⣦⢠⠀⠀⠈⢷⠀⠀⠈⡎⢷⠀⠀⠀ ⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⠀⠀⠀⠀⠀⠀⣶⠄⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠙⢧⣀⠀⢹⣼⠃⠈⢧⠀⠈⠙⡆⠀⠀⢸⡄⡆⠀⢹⠘⡇⠀⠀ ⠀⠈⢳⣀⠀⠀⠀⠀⠀⠰⡾⠷⣿⠀⠀⠀⠀⠀⠀⡏⠀⠀⡞⠀⢀⡄⠀⠀⠀⢸⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠿⢿⠳⡄⢸⡄⠀⠀⢧⠀⠀⠀⡇⢹⠀⠸⡆⢻⣀⠀ ⣀⠠⣴⠟⠳⠦⣤⣀⣀⣀⣀⣠⣽⠀⠀⠀⠀⠀⢀⡇⠀⣠⡇⠀⢸⡆⠀⠀⠀⣸⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠀⢻⡀⣧⠀⠀⢸⡄⠀⠀⢳⢸⠀⠀⣧⢸⡇⢧ ⠀⠀⣿⠀⠀⠀⠀⠀⠉⠉⠉⠀⢸⡇⠀⣴⠀⠀⣸⠀⢠⣿⠀⠀⣼⠃⠀⠀⣰⡏⠀⠀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⣀⣴⠞⠃⢿⢀⠀⠸⡇⠀⠀⢸⣼⠀⠀⠛⠘⡇⢸ ⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢀⡇⠀⢠⣟⣠⢯⠏⠀⣰⣿⣀⣀⣴⣿⠒⢒⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⢸⣸⠀⢸⣧⠀⠀⢸⣿⠀⠀⠀⠀⠁⣿ ⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⠀⠀⠈⠉⠁⢸⣷⣾⣿⡿⢿⣿⣿⣿⣿⣿⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣓⣒⣲⠶⠦⢸⣿⡇⠀⣿⠀⠀⢸⣿⠀⠀⠀⠀⢀⣿ ⣶⡴⠟⠋⠀⠀⠀⠀⠀⢀⠀⢀⣴⠟⢿⠀⠀⠀⠀⠀⠀⠸⡇⢻⣷⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⢿⣿⣿⣿⣿⣿⣿⣧⣸⣿⠀⠀⢸⣿⠀⡀⡄⠀⢸⣿ ⣧⡀⠀⠀⠀⠀⠀⢠⣴⠟⠛⡿⢵⡶⣾⠀⠀⠀⠀⠀⠀⠰⡇⠈⣿⡟⠻⢿⣿⠟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿⢿⣿⣟⢳⣦⡞⣽⣀⣿⠁⠀⠀⠙ ⠙⣻⣦⣤⣤⣤⣤⣤⡤⠴⠺⡇⠀⣷⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⢿⡀⠀⢠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⣿⣿⡇⢸⠃⠀⣾⡟⣧⠈⠉⠉⠀⠀⢸⣶ ⠀⠉⢻⣾⡟⠁⠀⠀⠀⠀⠀⢧⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠻⠿⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⠀⠀⣶⣿⠟⠀⠀⠀⣸⠃⢻⣿⠀⠀⠀⠀⠀⢸⣿ ⠀⢠⣿⡟⠀⠀⢀⡄⠀⠀⠀⡘⢧⡀⢹⠆⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠯⠍⠀⠀⠀⠀⢰⡏⠀⢸⣾⠀⠀⠀⠀⠀⢸⣿ ⢶⣿⡟⠀⠀⠀⡿⠁⠀⠀⢸⡇⠀⠙⣾⠆⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⣿⠀⠀⠀⠀⠀⢸⣿ ⣾⣿⠁⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿ ⣿⢿⣇⠀⠀⠀⣧⠀⠀⠀⢸⡇⠀⠀⣾⣰⠀⠀⠀⠀⠐⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⣸⣿ ⠀⠀⠹⣄⠀⠀⠘⣇⠀⠀⢸⣧⠀⠀⣿⡇⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠏⠀⠀⡇⠀⠀⠀⠀⢠⣿⣿ ⠀⠀⠀⠙⢦⡀⠀⠘⣦⡀⠘⣿⡆⢠⡟⢀⡾⠀⠀⢈⣾⠋⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠏⠀⠀⣼⠀⢸⡇⠀⠀⢸⠀⡾⢸⣿ ⠀⠀⠀⠀⠈⠳⣄⠀⠈⠻⣄⡸⣿⡾⠁⣼⠁⠀⠀⣸⡟⠀⠀⠀⠙⠓⠦⣄⣀⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠛⣡⡿⠀⠀⣰⡇⠀⣼⠀⠀⢀⡟⣰⠃⢸⣿ ⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⡀⢙⡿⠃⣸⡇⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⢲⣶⢤⣤⣤⣤⣤⠤⠤⠴⠖⠒⢻⣿⠏⢰⣏⣼⡟⠀⠀⣰⠟⢀⣼⡏⠀⠀⣾⣷⠟⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡟⢱⣾⡟⠀⠀⣤⡿⠟⢧⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢀⣿⣿⠏⠀⢀⡾⢁⡴⢛⡟⠀⢀⣼⣿⡏⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⣾⣿⣾⣿⢋⣴⣿⡟⠀⢠⣾⡟⠁⠀⠈⢷⠈⠧⣄⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣠⠶⢛⣷⣼⠟⠁⠠⢴⣫⠶⠛⠲⣾⠡⢄⣼⣿⣏⣀⣀⡀⢸⣿ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣿⣿⢏⣀⣠⣿⠟⠀⠀⠀⠀⠈⠳⠤⣄⠙⠛⠓⠲⠤⠤⠤⠤⠧⠤⢀⣀⡤⠴⠛⠛⠁⣠⡏⠙⢿⣦⣤⣴⣿⣆⠀⢀⣼⢃⣠⡾⠟⠁⠀⠀⠀⠀⠈⢻ ⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⠟⠛⠛⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢳⢤⡴⠶⠤⠤⠶⠤⢶⣄⣤⠤⠴⠛⠋⡉⠀⠀⠀⠹⣿⣿⣿⣿⣖⠛⠛⠛⠉⠀⠀⠀⡀⣀⣀⢀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⡴⠂⠀⠀⠀⠀⢦⠀⠀⠀⠀⠙⠢⡀⠀⢀⠈⠱⡀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⡸⠁⠀⠀⢀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠘⢆⠀⠉⠂⡘⣦⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⢠⠄⠀⢠⠇⠀⠀⠀⢸⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⢣⠀⠀⢙⣿⣇⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⡏⠀⠀⢸⠀⠀⠀⠀⠘⡄⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⢣⠀⢄⠈⢿⡇⠀⠀⠀⠀⣸⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡞⡘⠀⠀⢰⠃⠀⠀⡞⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠈⡆⠀⠑⣾⣿⠀⠀⢀⣼⠟⣧⠀⠀⠀⠀⠀ ⠼⠀⠀⠀⠀⠀⢰⠃⡇⠀⠀⡾⡄⠀⠀⣷⠀⠀⠀⠀⠀⢸⢧⠀⠀⠀⣹⢿⠀⠀⠀⠀⠀⠀⢹⠈⠢⣼⣾⣇⣴⠛⠁⠀⢹⠀⠀⠀⠀⠀ ⠀⠀⢢⠀⠀⠀⢸⢸⠁⠀⠀⠃⡧⢄⣰⡿⡄⠀⠀⠀⠀⢨⣀⠷⣖⠉⢹⠀⣧⠀⠀⠀⠀⠀⠸⡆⠢⣀⣿⡟⢿⣤⣀⣀⣸⡆⠀⠀⠀⠀ ⠉⠒⢤⣧⠀⠀⢺⢸⠀⠀⢈⡆⢳⠀⢘⡟⢻⡂⠀⠀⠀⢹⠀⢀⣼⡷⣟⡛⠻⣶⣤⡀⠀⠀⠀⡿⣀⣸⠟⠷⡀⠙⠻⠿⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠉⠓⠀⢸⢸⡄⠀⠘⡇⢸⣷⣾⢟⣲⠷⣤⡀⠀⢸⡆⠉⢸⠃⠀⢻⡄⢯⡿⠀⠀⢠⣴⠃⢹⠁⢠⡄⠘⣆⠀⠀⢿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡀⢸⣿⡇⠀⠀⢱⠈⣿⣁⡏⣈⣧⠈⠙⢤⡐⢇⠀⠸⣎⠛⣹⡇⢺⠁⠀⠀⣼⣿⢠⠃⢠⠟⡋⢠⠟⡅⠀⣼⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⠁⠀⣿⣿⣄⠀⠀⢧⢹⡈⢧⣉⡿⠀⠀⠀⠉⠺⠄⠀⠈⠛⠉⠀⠈⡇⠀⢀⣿⠏⢀⣀⣸⡞⢀⠇⠀⢡⠀⡇⠀⠀⠀⠀⠀ ⣤⠶⢻⡿⠿⠆⠀⠸⡇⢻⣧⠀⠈⣷⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡾⠇⠀⠉⠀⢀⣠⠜⠀⠀⠸⡄⡇⠀⠀⠀⠀⠀ ⠀⢀⣸⠃⠀⠀⠀⠀⠘⠀⠻⣧⡀⢹⡇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢹⠏⠀⠀⣨⢛⣿⣿⣿⠀⠀⠀⠸⣇⡀⠀⠀⠀⠀⠀ ⠾⢋⣥⣶⠟⠀⠀⠀⠀⠀⠀⠈⠋⠛⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⢀⡴⠁⢸⣿⣿⣿⡄⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀ ⠀⠉⠡⡿⣶⣶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢸⣿⣿⢹⣇⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣱⣦⣶⠿⠛⠋⠉⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀⢸⣿⣿⣿⣿⡄⠀⠀⠘⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡤⠤⢤⣀⣔⣶⠤⠔⣚⠭⢻⠘⡏⢱⣦⣄⣀⣀⣠⣴⣾⣿⠏⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⢻⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠗⢀⣉⣉⠹⠿⣾⡍⠀⠀⠈⡖⣷⠈⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠉⠙⢦⡀⠀⠈⢇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⢋⡠⠋⡁⠀⠀⡠⠟⠁⠀⠀⢀⣱⣿⣧⣸⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⢠⠀⠀⠀⠱⡄⠀⠸⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⡇⠀⠀⠈⢀⠔⡏⠀⠀⡤⠊⠉⠀⠀⢸⠋⠉⢉⠹⡿⠋⢇⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠹⡀⠀⢣⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⠀⠀⠀⢸⢰⠃⠀⡜⠀⠀⠀⢠⠀⠙⣤⠞⢡⠞⠀⢀⡼⠀⠀⣀⡠⢾⠀⠀⠀⠀⠀⠀⠀⡉⠀⠀⠀⠀⢣⠀⠘⡆⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿⠀⢸⠁⠑⢄⠀⢸⢀⠔⠁⣰⠁⠀⠀⠘⠃⠜⠁⠀⢀⡆⠀⠀⢀⡠⠒⠉⠁⠉⠑⢄⠀⠀⠈⡆⠀⢹⠀⠀ ⠀⠀⠀⠀⠀⣠⡆⠀⠀⠼⣿⣧⡇⠀⠀⠀⠑⡷⠋⢀⡜⠉⠦⣀⡀⠀⣀⡠⠔⠊⠉⡇⡠⠖⠁⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⢱⠀⠀⣇⠀ ⠀⠀⠀⠀⣼⣷⡇⠀⢀⠜⣡⣿⠃⠀⠀⢀⡜⠁⢠⠎⠀⠀⠀⠈⢉⡉⠁⠀⠀⠀⢸⡇⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⢸⠀⢇⠸⡀ ⠀⠀⠀⠘⣧⡉⠓⠒⢁⠜⠩⣇⢀⠀⣠⠎⠀⣠⠃⠀⠀⠰⢀⠔⠁⠀⠀⠀⠀⠀⡟⡇⢀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠀⢸⠀⡇ ⠀⠀⠀⡴⣇⠈⠁⠀⠉⢀⠀⡼⠠⡶⠉⠉⠈⠉⠉⠑⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠁⡇⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⡄⠀⡇⢸ ⠀⠀⠀⢦⡈⣉⡡⠖⠊⠁⠀⣑⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢠⢛⣷⠀⡇⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢠⡖⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⡀⠈⠹⣄⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠛⣄⠀⠈⠓⣄⠈⢷⢀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⡀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠳⣄⢧⢣⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⡼⠃⠀⠀⢸⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠐⠬⢿⡎⣇⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢀⠀⠀⠀⢰⠇⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠈⢧⠐⠢⣄⠀⢻⢹⡀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⡟⠀⠀⠀⣼⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠈⠳⣼⡏⣇⠀⠀⠀⢀⣼⡿⢿⡀⠀⠀⠀⠀⠀⠀ ⠤⡄⠀⠀⠀⠀⠀⠀⢀⡟⣸⠀⠀⠀⢸⢁⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⣏⢳⣤⠄⠀⠀⠀⠀⠀⠀⢹⠐⠦⡀⠹⣇⢹⡀⢀⣴⡿⠋⠀⢹⡇⠀⠀⠀⠀⠀⠀ ⡊⠁⠀⠀⠀⠀⠀⠀⢸⠁⣿⠀⠀⠀⡎⢸⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⢸⡇⢳⡄⠀⣀⣠⣾⠋⢇⠀⠀⠀⠀⠀⠀⠀⠸⡆⢀⠈⠳⢿⢸⡇⣾⠉⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀ ⡀⠀⠈⣦⠀⠀⠀⠀⣿⠀⡏⠀⠀⠀⡇⢸⡷⢤⣀⣿⢸⡄⠀⠀⠀⠀⠀⠈⣇⣀⠹⣎⠉⠀⢸⠄⢸⡆⠀⠀⠀⠀⠀⠀⠀⣿⡈⠳⣄⢸⣼⡇⢻⣷⣤⣄⣀⣀⣿⠀⠀⠀⠀⠀⠀ ⠙⠓⢦⡈⣧⠀⠀⢀⢾⠀⡇⠀⠀⠀⡇⠈⣧⠀⠈⢿⠛⢷⡒⠂⠀⠀⠈⠙⡏⠀⠀⢈⣷⣶⠟⠛⠿⣷⣦⣄⠀⠀⠀⠀⠀⣇⣇⠀⠈⣻⡿⣧⡀⠙⠻⣿⣛⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠻⢧⡀⠀⢸⢀⡇⠀⠀⢰⣇⠀⢹⣆⣤⣿⣤⣌⣳⡄⠀⠀⠀⢀⢳⠠⠾⠋⣵⠂⠛⢷⡄⠸⡏⣿⠏⠀⠀⠀⣀⣿⠉⣿⠚⠁⢀⡀⠙⣆⠀⠀⠈⢹⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⢾⠰⣿⠀⠀⠈⢼⡀⢸⣿⡿⢅⡶⠸⣍⠙⢷⣄⠀⠨⢿⡄⠀⠀⣇⣠⣤⣨⣿⠀⣷⠟⠀⠀⠀⢸⡏⡇⠀⡿⠀⢠⢞⣇⠀⢹⡄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⣤⠀⠸⡄⣿⡀⠀⠀⠘⣇⠸⣿⣇⢸⠁⣤⣽⡆⠀⠉⠳⣄⠋⡇⠀⠀⢿⣄⢉⣸⡿⠀⢹⠀⠀⠀⠀⣺⢿⢃⡼⠁⢠⡟⢫⡅⢠⠞⠁⡆⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡇⠀⠀⣧⣇⣷⣀⠀⠀⠸⣆⠹⡈⠸⣦⠉⣼⠇⠀⠀⠀⠈⠛⢺⠆⠀⠀⠙⠛⠋⠀⠀⠘⡇⠀⠀⢰⣿⡟⠀⠀⠀⣈⣷⡟⢀⡞⠀⠀⣷⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⣤⣶⣿⣿⣇⠀⠀⠹⣿⠘⣾⣆⠀⠀⠙⣦⣻⡀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢠⣿⡇⠁⠐⠋⠉⠉⠁⢀⡸⠁⠀⠀⢿⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠟⠋⠀⣿⡏⠉⠁⠀⠀⠀⠹⡄⠙⣞⢆⠀⠠⣿⣟⠿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⡞⠘⠀⠀⣦⣀⣠⣤⣶⣏⠉⠀⠀⠀⢸⡇⠘⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣤⠿⠀⢀⡀⠀⠀⠀⠀⠛⠀⠘⢿⡷⣄⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣠⠋⠀⠀⠀⣰⠃⣸⣿⣿⣿⢸⠀⠀⠀⠀⠈⣱⠀⠀⠀⠀⠀⠀⠀⠀ ⡾⠋⣡⣴⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠙⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠋⠀⠀⢀⡼⠁⠀⣿⣿⣿⣿⢸⠀⠀⠀⠀⠀⣿⣜⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠋⢀⣿⣥⣤⡤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠟⠀⠀⠀⣿⣿⣿⣇⢸⢀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠸⡿⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⠑⢦⣀⠀⣀⣤⣶⣤⠴⠶⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠁⠀⠀⠀⠀⣿⣿⣿⣷⢸⣼⡄⠀⠀⠀⢸⣾⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠻⠃⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⡤⢜⡛⣽⠯⣏⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠟⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢸⡏⢇⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⠒⠤⣤⣜⣁⡧⠔⠛⣉⡥⠖⠛⡇⠘⡄⠈⣿⣦⣤⣀⣀⣤⣴⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣼⣷⣸⡀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡵⠋⠉⠉⠉⣉⣩⠷⢶⡏⠀⠀⠀⠀⢹⢰⣷⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⠈⠉⠓⢷⡀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⢶⡟⠁⣰⠞⠋⢉⣁⠤⠔⣻⠟⠀⠀⠀⠀⠸⡄⣧⣇⠘⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠠⡄⠀⠀⠀⠙⢦⠀⠀⠀⢳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢨⠏⠠⠞⠁⡠⠒⠉⣀⠔⠊⠁⠀⢀⣠⡤⠴⠒⠛⢻⣿⣦⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠈⢧⠀⠀⠘⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢰⠋⣹⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⣻⠀⠀⢀⡠⠞⡱⠋⠀⣇⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠈⢇⠀⠀⢻⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡇⢠⡇⠀⠀⡾⠀⠀⠀⠀⠀⡄⠀⠛⣆⡴⠋⢠⠞⠀⢀⣀⡼⠀⠀⠀⠀⣀⢴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠸⡆⠀⠈⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢹⣼⡁⠀⣸⠁⠳⢄⠀⠀⢠⡇⠀⣠⠏⠀⡰⠃⠀⠀⠀⢿⡁⢠⠖⠊⠉⠁⢸⠀⠀⠀⠀⠀⢀⣠⠶⠒⠊⠓⠦⣄⠀⠀⠀⠀⢳⡀⠀⠹⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⣸⡟⣇⢠⡏⠀⠀⠈⠳⣄⢸⢧⠞⠁⢀⡼⢧⠀⠀⠀⠀⠀⠀⠉⠀⢀⣠⠤⣿⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠸⡇⠀⠀⢷⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠾⡇⠀⠀⠰⢋⡿⢿⣾⠁⠀⠀⠀⠀⠈⣿⠋⠀⢠⠎⠀⠈⠳⣤⣄⣀⣀⣤⠔⠚⠉⠀⠀⣿⢠⠔⠋⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⣇⠀⡀⠘⡆⠀ ⠀⠀⠀⠀⠀⣼⣷⣷⡇⠀⠀⣀⠞⣡⣾⡇⡇⠀⠀⠀⢀⡞⠁⠀⣰⠋⠀⠀⠀⠀⠀⠉⣉⠁⠀⠀⠀⠀⠀⢰⣿⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⢸⠀⢹⠀⢳⠀ ⠀⠀⠀⠀⠀⣏⠙⠻⢧⣠⠞⢁⡼⢃⣿⠁⣇⠀⠀⣠⠏⠀⠀⡴⠃⠀⠀⠀⡀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⣿⣿⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⢸⠀⠈⡆⢸⡇ ⠀⠀⠀⠀⢀⣯⠙⠦⡄⠀⠠⠚⠀⠀⠙⡆⢻⢀⡾⠡⠐⠒⠺⠧⢤⣤⣄⣀⣃⣋⣀⣀⣀⣤⣤⣤⣤⣤⣤⠃⣿⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣸⣼⠀⠀⣷⠀⡇ ⠀⠀⠀⢠⠛⠻⣄⣀⡀⠀⠀⣀⡤⠀⢸⠁⠘⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡜⢱⣿⢀⠀⣿⠀⢰ ⠀⠀⠀⠀⣷⣀⣀⣀⡴⠒⢋⠁⠀⠀⢈⡇⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⡞⢸⢸⠀⣿⢠⠈

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀ ⠀⠀⣰⠃⠀⢀⣀⡀⠀⠀⠀⠀⢀⣀⡀⠀⠈⣧⠀⠀⠀ ⣠⢪⠏⠀⠀⢸⣿⡆⢀⡀⠀⡄⢿⣷⠇⠀⠀⠘⣿⣆⠀ ⣿⡻⣄⠀⠀⠀⠀⠀⠈⠛⠚⠁⠀⠀⠀⠀⠀⣀⣿⣼⠀ ⡇⠙⠻⠿⣷⣶⣤⠤⢤⠤⠤⢤⣤⢤⣶⣶⠿⠟⠋⢸⠂ ⢷⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣸⠀ ⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀ ⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀ ⠀⠀⠀⠀⠙⢲⣤⣄⣀⣀⣀⣀⣀⣤⡖⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⢣⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠦⣄⣀⠀⠀⠀⠀⣀⣠⠴⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⡿⠉⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⡿⠁⣀⡀⠀⠙⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⢠⣤⡄⠙⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠃⢰⠏⠻⣄⠀⠈⢿⣷⠀⠀⠀⠀⠀⠀⣼⡿⠁⣴⠏⠀⢻⣆⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⡟⠀⡟⠀⠀⠹⣦⠀⠘⠿⠿⠿⠿⠟⠻⠿⠿⠅⢸⠃⠀⠀⠀⢹⡄⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡇⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⡟⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠈⢻⣄⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⣿⠁⠀⠀⢀⣾⠁⠈⠻⣦⡀⠀⠀⠀⠀⢀⣤⠶⠋⠁⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠇⠀⠀⢀⡾⠁⠀⠀⠀⠈⠙⢷⣄⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠤⢤⣄⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⢰⡟⠉⠉⡁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡏⠈⣷⠀⠀⣿⣿⣷⡄⠀⠀⠀⢠⣤⣤⣤⣤⠀⠀⠀⠀⢠⣾⣿⣿⠀⠀⠀⠰⢿⣤⣄⡀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀ ⣿⡇⠀⣸⡆⠀⠹⣿⣿⠇⠀⠀⠀⠸⠿⠿⠿⠿⠀⠀⠀⠀⠸⠿⠿⠋⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⣿⡆⠀⠀⠀⣠⣴⣾⠿⠛⢻⣿⠃ ⣿⠁⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣠⣴⣿⠿⠃⠀⣴⣾⡿⠋⠁⠀⠀⢸⡇⠀ ⣿⣷⣬⣿⣄⣀⠀⠀⠀⠀⠀⠀⠘⢿⣏⠙⢀⣽⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠛⠉⠀⠀⣠⣾⡟⠋⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠈⠉⠛⠛⠻⠿⢷⣶⣦⣤⣀⣀⣘⠛⠿⠟⠋⠀⢀⣀⣀⣀⣤⣴⣶⣶⠿⢿⣿⣅⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⡟⠛⠛⠿⠿⠿⠿⠿⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠙⣿⣧⡀⠀⠀⠀⢸⡿⠀⣠⣤⡆⠀⠀⠀⠀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⢸⣷⠞⠋⢰⡇⠀⢀⣀⡀⠀⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⢸⡇⠀⠀⠀⠷⠴⠟⠁⢷⣼⣿⠀ ⠀⠀⠀⠀⠀⠀⣾⡿⠿⣿⣾⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢠⣿⣥⣶⡿⠿⢿⣦⠀⠈⣿⡇⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⢿⣿⡶⣄⣀⡴⠿⣿⣄⠀⣠⠶⠛⢹⣿⠟⠁⠀⠀⠈⣿⡇⠀⢹⣷⣾⡿⠁⠀⠀⠀⠀⠀⣠⣾⡿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣷⡀⠀⠈⢿⣇⠈⠉⠀⠀⣿⠛⠛⠁⠀⠀⢸⡇⠀⠀⠀⠀⢀⣿⠇⠀⢸⣿⠉⠀⠀⠀⠀⢀⣠⣾⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⡀⣸⣿⡀⠀⠀⢀⣿⡄⠀⠀⠀⠀⣸⡇⠀⠀⢀⣠⣾⡟⠀⢀⣾⣟⠀⣀⣠⣴⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⣶⣾⣾⣷⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⡋⠉⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣖⠷⠖⠒⠲⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣮⡳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡀⢻⣿⣿⠙⣿⣿⣌⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠄⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⣿⣷⡘⣿⣿⣷⡜⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠘⡀⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⡇⠈⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠠⠜⠃⢡⠂⠀⠀⠀ ⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡇⠀⢹⣿⣿⣿⣿⣿⣿⣿⢹⡿⣿⣿⣿⣿⣿⣿⣭⠀⠀⠀⠀⠀⠀⢠⢄⢠⠀⠀⠀⠀ ⡠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣼⢇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠇⠈⣿⠘⢦⠈⣿⣿⣿⣿⣿⣿⣿⠀⡷⢻⡟⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠄⠄⠉⠀⠀⠀⠀ ⠀⢀⡴⠉⠀⠀⣤⣤⣤⣤⣴⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⡿⠖⠛⠛⠳⢾⣷⣇⣹⡿⠿⠟⠛⢃⣼⠷⠶⢿⣼⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡴⠋⠀⠀⠀⣠⣿⣿⠿⢫⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡏⠀⠀⠀⠀⠀⣄⠹⣿⢷⣦⠀⠀⠀⢻⣏⡄⠀⠀⢸⢿⣿⣿⣯⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢ ⠞⣠⢞⣵⠞⣡⣿⡟⡀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠘⣿⠀⠸⠇⠀⠀⠀⠀⠘⢽⡇⠀⠀⢸⢸⣿⣿⣿⡞⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡷⣋⡴⢟⡵⣿⡷⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢸⣿⣿⣿⣿⢿⣿⡄⠀⠀⠀⠀⢀⠀⠀⣀⠷ ⣿⢟⣥⠞⠃⠀⣿⣃⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢳⡀⠀⢀⣀⣠⡴⠟⠀⠀⠀⠀⠀⠀⠀⠠⣤⡾⠃⣾⣿⣿⣿⣿⢸⣿⣇⠀⠀⠀⠀⠈⠑⢦⣿⡻ ⢿⣫⠄⣀⠄⠒⣿⢿⡷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣻⠋⢍⣏⣁⡄⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠰⠘⣿⣿⣿⣿⣿⣸⣿⣿⡄⢀⣀⠀⠀⣀⠀⢫⡿ ⣫⠔⣊⡥⠂⠀⣿⣼⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠉⠁⠈⠋⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⢿⡇⢸⣟⠿⣶⣆⡀⠈⠁ ⢶⣫⠵⢂⣠⠴⣿⡟⣭⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⡇⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠸⠁⢸⣯⣻⣿⣬⣿⢷⣦ ⣯⠵⣛⣭⠤⠂⠛⠉⠛⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⠀⠀⠸⠛⠋⠉⠉⠉⠛⠷ ⣚⣯⠥⢂⡀⠀⠀⠀⠀⠀⠸⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠹⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐ ⠷⣒⣋⠉⠁⠀⠀⣀⣤⠄⠀⠘⣧⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠙⢿⡦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣽⡆⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉ ⡭⠿⣶⣶⣿⣯⠥⠤⠀⠀⠀⠀⠈⠂⠀⢘⣫⠟⠋⠀⠀⠀⠀⠉⠙⠻⠿⠯⣿⠷⠤⢷⣄⡉⠉⠒⠶⣤⣤⣤⣤⣶⣿⣿⢿⡿⣋⣉⠑⠃⠀⠉⠳⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲ ⣉⣭⠽⠿⠷⠖⠂⠀⠀⠀⠀⠀⠀⠀⣴⠏⠉⠑⠲⡀⠀⣠⠞⠙⠒⠦⢄⣀⠈⠙⠦⣄⠀⠈⠉⠑⠲⢬⣛⠮⣽⠛⠿⣾⠿⠭⣁⠈⠙⠳⣄⡀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠂⠤⢤⣉ ⣒⣛⣛⡻⠋⠠⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⢹⡈⠁⠀⠀⠀⠀⠀⠀⠉⠓⠦⢄⡙⢦⣤⠤⠤⠤⠬⣿⣻⠷⠞⢿⣿⢶⣭⡟⢦⣄⠀⠙⢦⠀⠀⢳⡄⠀⢀⣀⠀⠀⠒⠂⠠ ⣒⣒⣒⡒⠒⠒⠒⠒⠒⠒⠒⠀⢠⠇⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣸⣿⣿⣿⣶⣯⣓⣦⣼⣿⣿⣿⣷⡄⠉⠓⢦⡈⢳⡀⠀⢳⠸⢵⢬⣭⣦⣤⢀⣀ ⠭⠭⠭⠥⢤⠤⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢻⡄⠀⠀⠙⢦⣹⣣⠈⣷⢄⠲⣶⡾⠶⠀⠠ ⢿⣍⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣾⣿⡿⠀⠀⠹⡟⠿⣿⣧⠀⠀⠀⠐⠋⠻⣄⢻⣟⣛⣛⣛⣋⣉⣉ ⣿⣓⡒⠢⠄⠀⠉⠉⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠰⡀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠉⠀⠀⠀⠀⠈⠳⣄⡈⠳⡄⠀⠀⠀⠦⡈⠻⣧⣬⣬⡤⠦⠤⠶ ⣿⡶⠬⣭⣀⡀⣀⣀⣀⢀⣀⠀⢻⣤⠀⠀⠀⠀⠀⢳⡀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡈⢦⡀⠀⠀⠘⢄⠈⢳⣶⠖⠒⣚⣉ ⡿⢭⣓⡲⠬⣭⣿⣟⠿⢿⣿⡄⠀⣏⣆⠀⠀⠀⠀⠀⢳⡀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⢳⡀⠀⠀⠀⠳⡀⠙⣦⣬⣽⣽ ⣭⣒⠮⢍⠓⠲⣿⣟⢿⣶⣿⠇⢀⡟⣟⡄⠀⠀⠀⠀⠀⠹⣼⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⢳⠀⠀⠀⠀⠹⡄⠈⣿⡻⣛ ⣷⢯⣝⠲⠄⠀⣿⢏⡀⡴⣿⣆⡟⠉⠙⠾⣄⠀⠀⠀⠀⠀⠹⣷⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢺⡇⠈⡆⠀⠀⠀⠀⠀⠀⢈⣉⠽ ⢯⡓⢦⣙⡀⠀⣿⠄⢳⠛⣿⠻⢾⣛⠲⢄⡈⠳⢄⠀⠀⠀⠀⡿⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡜⡾⢰⠀⡇⠀⠀⠀⠀⠀⠀⢸⡦⠒ ⠳⣌⠻⢬⡙⠲⣿⣄⠀⠙⣿⠆⠀⠈⠳⣄⣙⡦⣄⠙⠒⠤⣄⣷⣤⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡸⢱⠁⠁⢸⠆⡇⠀⠀⠀⠀⠀⠀⠀⣗⣉

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⠀⠀⠀⠀⢀⣴⣧⣽⣶⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⡐⣿⣽⣿⣥⣟⣿⢹⣿⣿⣿⡟⢿⣿⣿⣿⣟⣧⣿⣿⣆⠀⠀⠀⠀ ⠀⠀⢰⣸⣿⣿⣶⣿⠞⣸⣺⣿⣻⣿⣇⠀⢻⣿⣼⡿⣿⣿⣿⣿⡄⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣏⠠⣿⣿⣿⡟⢿⣿⠒⠠⢹⣿⣷⣾⣄⣿⠹⣧⡀⠀⠀ ⠀⠀⡟⣿⣿⣿⡟⣁⣴⣏⡅⣿⡇⠸⣯⣦⣤⣦⣿⣿⣿⣿⣿⣧⣰⡉⠁⠀ ⠀⠐⣇⣾⣿⣿⣜⣻⣟⡛⡵⠃⠷⠃⠁⠻⠽⠃⢻⣿⡟⣹⣿⣿⣿⡻⣢⡄ ⠠⠴⢿⣿⣿⣯⢚⠏⠀⠊⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⢷⠘⣿⣿⣯⠉⠉⠀ ⠀⢀⣽⣿⣿⣿⣜⠨⠙⡀⠀⢀⡀⠀⡀⠀⣠⣵⣿⡶⠙⡀⣿⣿⣹⡇⠀⠀ ⠀⣾⣿⣿⣞⢿⣏⠛⠻⢷⣤⡀⠀⠀⠀⢰⡟⡿⡏⢀⠌⡠⡟⣿⣿⡇⠀⠀ ⠀⣟⣿⣿⢿⣷⣟⠦⠀⠀⢙⣷⣄⠠⣴⣿⠄⡇⡷⡀⢊⣔⡿⢉⣿⣿⡄⠀ ⢰⡇⢾⣿⣧⢝⣻⣿⢑⣶⣿⣿⡇⣸⠃⡿⣲⣸⣷⣎⢻⣿⣿⣿⢿⠃⢸⠀ ⠈⡷⡈⣏⣽⣼⣿⣿⣾⣿⣿⣿⡇⣿⣀⠤⢹⣿⣿⣿⡟⠛⢿⣽⡟⣣⡞⠀ ⠀⠫⣻⣶⣶⡿⠋⢡⣿⣿⣿⡏⣀⢻⣷⡄⠀⠻⣿⣿⣿⣦⠯⢵⣢⢿⡄⠀ ⢀⡼⣽⣷⠺⡗⠛⣿⣿⠛⣿⣷⣕⠋⠻⣿⣦⡀⠸⢿⣿⣿⣧⠀⡓⢃⣿⡄ ⣼⢱⡊⢰⠠⠌⢹⣿⣿⠀⢿⣿⣻⡧⡤⠬⣯⠛⢆⡀⢻⣿⣿⡇⣧⣼⡟⢻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡿⠿⠛⠉⠉⠉⠛⠻⠿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⠁⠀⠀⠀⠀⠀⣠⣴⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣄⠀⠀⠀⠀⠀⠈⣿⣧⡀⠀⠀⠀⠀ ⠀⠀⢀⣴⠿⣻⡟⠀⠀⠀⠀⠀⢸⣿⣿⣦⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣿⡇⠀⠀⠀⠀⠀⠹⣿⣿⣶⣄⠀⠀ ⠀⢰⣿⢃⣴⡟⠁⠀⠀⠀⠀⠀⠸⣿⣿⣿⡿⠃⠀⢠⣦⠀⠀⠀⢰⣆⠀⢻⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠹⣿⣎⢿⣆⠀ ⠀⣿⡇⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣤⣤⣿⠇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠈⣿⡆ ⢰⣿⣷⡜⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⣼⣿⡇ ⢸⣿⠙⢿⣶⣝⡻⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡿⢛⣩⡿⠋⢹⡇ ⢸⣿⠀⠀⠉⠻⢿⣶⣾⣭⣛⡿⠿⣶⣶⣶⣦⣤⣤⣤⣄⣀⣤⣄⣤⣤⣤⣤⣤⣤⣶⣶⡾⠿⢿⣋⣭⣷⠿⠟⠉⠀⠀⢸⡿ ⢸⣿⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⠿⢶⣦⣤⣤⣭⣭⣭⣍⣉⣉⣩⣭⣭⣭⣭⣤⠶⠶⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇ ⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀ ⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀ ⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣷⣶⣤⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣴⣶⣟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠛⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠋⠉⠁⠈⠙⠻⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢷⣶⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣶⡶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠄⠒⣒⣲⣿⣿⣿⣿⣿⣶⣶⣤⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⣀⡤⠒⠉⠁⣠⣴⡾⠿⠛⠛⢿⣿⡿⠿⠛⠋⠉⠙⠻⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⡤⠚⠁⠀⢀⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢄⠀⢯⠙⠛⠉⠛⠷⣦⣄⠀⣸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡴⠊⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⢀⡖⠀⠀⠀⠀⢸⠀⠀⠙⢦⡎⠀⠀⢳⠀⠀⠀⠀⠈⠙⢷⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠳⠦⣀⡰⠋⠀⠀⢠⠃⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠙⣄⠀⢸⡄⠀⠀⠀⠐⣄⠀⠙⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⡎⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡏⠙⢢⣀⠀⢘⡦⠻⣿⡀⠀⠀⠀⠘⢆⠀⠙⡿⣄⠀⠀⠀⢳ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢠⡇⠀⠀⠀⠏⠀⠀⠀⢀⣀⣀⠀⡇⠀⠈⢆⠉⠻⣅⠀⡇⢳⠀⠀⠀⠀⠈⢇⠀⠘⡜⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠀⠉⠇⠀⠀⠈⢱⠦⢬⡟⠓⡾⣷⢄⡀⠀⠀⠘⡆⠀⠸⡜⡄⠀⠀ ⢣⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⢆⡀⠙⣤⠇⠸⡀⠙⢳⠀⠀⢹⢀⠀⢳⢹⠀⠀ ⠀⠑⣄⡀⠀⠀⠀⠴⠾⢾⠀⠀⠀⠀⠘⠁⠀⡎⠀⡄⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠉⡿⢻⠳⡄⢧⠀⠈⡇⠀⠘⡞⡆⠘⡄⡇⠀ ⠐⢲⡏⠉⠓⠲⠤⠤⠴⢾⡀⠀⡀⠀⠸⠀⣸⠁⢠⡇⠀⠀⣰⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⣧⡈⢀⣥⢸⠀⠀⢃⠀⠀⡇⡇⠀⠇⡇⢰ ⠀⠸⡇⠀⠀⠀⠀⠀⠀⠈⡇⢸⠁⢀⣇⣴⡏⠀⣼⡃⢀⣴⡧⢤⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠋⠁⠈⣧⠀⢸⠀⠀⢹⡇⠀⠀⠀⢸ ⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣷⡇⠀⠈⠉⢸⣷⣾⣿⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣐⣒⣒⣤⢄⣿⡇⢸⡄⠀⢸⡇⠀⠀⢀⣾ ⡶⠛⠁⠀⠀⠀⢀⣤⢀⡜⣉⡇⠀⠀⠀⠀⢸⡇⢿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣅⡀⣾⡇⣠⠄⠘⢿ ⠳⣤⣀⣀⣀⣀⣋⣠⣾⠘⣯⡇⠀⠀⠀⠀⢸⡇⠘⣷⠈⠙⣭⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⢹⠛⢸⣿⡟⠓⠛⠀⠀⣤ ⠈⢙⣿⡟⠉⠁⠀⠀⠸⡀⢹⡇⠀⠀⠀⠀⢸⡇⠀⠈⠻⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣍⣉⣼⠿⠁⠀⢀⡏⢻⡇⠀⠀⠀⠀⣿ ⠀⣼⡟⠀⢀⡄⠀⠀⢠⠱⣄⡗⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⡞⠀⢸⡇⠀⠀⠀⠀⣿ ⣽⡟⠀⠀⢸⠁⠀⠀⣿⠀⠈⡏⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠀⠀⣿ ⠿⢷⠀⠀⠸⡄⠀⠀⣿⠀⠀⣧⡀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡀⢸⡇⠀⠀⠀⢰⣿ ⠀⠈⢧⡀⠀⠻⡀⠀⣿⡄⢀⡟⢀⠀⠀⢠⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢘⡁⢸⠇⠀⢀⠀⣼⣿ ⠀⠀⠀⠱⣄⠀⠙⣄⠘⣷⡼⢁⡞⠀⠀⣾⠃⠉⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⣺⠃⠀⣸⠁⢸⠀⠀⣼⢰⠁⣿ ⠀⠀⠀⠀⠈⠑⢦⣈⠙⣿⠃⡾⠀⠀⣰⣿⠀⠀⠀⠀⠈⠉⠓⠲⢤⣤⣤⣄⣀⠤⠤⠤⠴⢶⡾⢉⣏⣼⠏⠀⣴⠇⣠⡇⠀⣰⣿⠏⠀⣿ ⠀⠀⠀⠀⠀⣴⣿⣿⡟⢱⣿⠃⢀⣴⠟⠻⡔⢄⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⠀⣠⡇⣼⡿⠁⣀⢞⡡⠊⣿⠀⢰⣿⠏⠀⠀⣿ ⠀⠀⠀⠀⣸⣿⣿⣯⣴⡿⠃⢠⣿⠃⠀⠀⠸⣄⡑⠢⡤⣀⣀⣀⡀⣼⠀⠀⠀⣀⡤⠔⠋⡼⢿⣏⠀⣈⣷⠉⠉⣽⠁⣴⡿⠛⠒⠀⠐⢿ ⠀⠀⠀⠀⣿⣿⣿⣿⠟⠳⠿⠟⠁⠀⠀⠀⠀⠀⠈⠒⠒⣦⡠⠤⠤⠤⠤⢤⣉⡤⠤⠒⠊⠁⠀⠙⣿⣿⣿⡶⠾⠓⠋⠁⠀⠀⢀⡀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡠⠖⠁⡴⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠊⠀⠀⠜⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣄⠀⠀⠀ ⠀⠀⠀⢠⢃⠁⢀⡞⠀⢰⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠘⣆⠀⠀ ⠀⠀⢠⡇⠁⠀⣾⠁⠀⣦⠀⠀⠀⠀⠀⠀⠀⡄⢀⠪⠵⠑⡄⠀⠀⠀⠀⢹⡄⠀ ⠀⠀⢆⠁⡄⢸⠹⡀⢀⠀⠀⢀⠀⠀⠀⠀⡀⢁⠈⢆⣀⣀⠕⠆⠀⠀⢃⠈⡇⠀ ⠀⢸⢸⠀⠀⡏⢩⢇⢈⢰⠀⠸⡰⠀⠀⢃⡇⠈⡆⠈⠀⠀⡆⠘⠄⠀⠈⠀⢇⠀ ⠀⠘⡔⡀⡀⣁⣴⣿⣼⠪⢦⣂⡱⣅⣢⣼⣶⣤⣴⡄⢸⠀⡧⣀⠂⡐⢄⣷⡼⠀ ⣠⢾⢿⣳⣷⣿⡟⠉⠛⡄⠀⠀⠀⠀⠘⠟⠉⢛⣿⣧⣸⠀⡏⠢⠝⢨⣿⣿⣷⠒ ⡅⢦⡌⣏⠉⣏⢀⣈⣡⠇⠀⠀⠀⠀⠀⣄⠈⢀⡸⣿⠙⠀⡿⠍⡄⢸⣧⠿⠘⢀ ⠫⠭⠊⣿⡄⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣿⡄⣸⠩⢉⠟⡙⢏⠀⠓⣤ ⠀⠐⠖⠋⡼⡞⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⣠⠇⢈⠠⠊⠀⠘⠧⠤⠄ ⠀⠀⠀⠀⠀⠹⡀⠑⠠⣀⠀⠀⠀⠀⠀⣀⠠⡰⣹⢃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠂⢄⠀⠀⠙⠓⠂⣀⠉⠤⠼⠯⠇⢑⣚⠚⠋⢑⠒⠈⠉⠁⠀⠈⠐⢄⠀⠀ ⠀⠀⠀⠀⠈⢢⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠃⠤⠀⠀⢀⠀⠉⠉⠁⢂⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣻⠀⠀⠐⣢⡤⠄⠒⠂⢹⡄⣠⡴⠛⠉⠉⢫⠉⢳⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢷⡶⠦⣄⠀⠢⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠛⢻⣠⡴⠛⠁⠀⠀⠀⠒⣠⣿⣧⣀⣀⣤⣄⡈⡄⣀⣳⡄⠤⣔⣒⣲⣾⣍⣵⣯⣵⣖⣒⣒⢦⡴⣆⡀⡰⠁⠜⠀⠀⠀⠑⠀⠆⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⢶⣶⠟⠀⠀⢠⡞⠁⠀⣿⣿⣤⣟⣮⣻⢯⠐⢾⠏⠙⠁⠘⡄⠀⠼⠀⠈⠃⠈⢦⠈⣏⠉⠶⠻⣷⢖⡄⣀⠀⠀⡀⠈⠀⡀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⠿⠿⢵⣿⢃⣾⠇⢀⣀⣠⡿⠽⠳⢤⣿⣿⣿⠟⣿⣿⣼⠀⠉⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠈⣇⠸⡄⠀⠀⠈⢧⢍⠳⠿⡂⢀⠀⠀⠀⠄⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⢸⣏⠙⠿⠞⣻⡿⢟⣻⠴⠛⢻⣿⣿⡻⣦⣿⢞⣁⠀⢠⣤⣶⣾⣏⠛⢀⣀⣻⣿⣿⣿⣿⣜⣀⠹⣤⣤⣤⠬⠯⢦⡀⠘⢿⣷⡒⠂⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⢠⣾⠹⣆⠀⠀⠀⣴⠉⠙⡄⢀⣾⣿⣽⢩⣿⣿⣯⣢⣤⡴⠟⠛⠉⠉⠙⢉⣿⠋⠀⠀⠀⠀⠉⠙⠛⠛⠛⠻⣿⠶⣾⣿⣷⡀⢻⡽⣆⠀⠀⠀⠀⠀ ⣀⠀⣀⣿⠿⠑⢨⣿⣶⣤⣄⣼⣧⠀⠻⣆⠀⢰⠇⣀⣀⠙⢺⣾⣏⡿⠿⣯⣄⣽⣿⡇⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠉⠻⣶⣿⡸⣻⣿⣂⡀⠀ ⣿⣿⡏⠀⠀⢀⣿⡟⠈⢻⣿⣾⣿⡀⠀⠹⣷⡿⠞⠉⢨⣿⠇⡿⠚⠓⢶⠦⢴⣧⣽⣅⣉⣉⣛⣒⣲⣶⣾⡇⣷⠀⠀⠀⢠⣀⣀⣀⡀⣀⣠⡜⣿⣀⣀⣀⣀⣷⠨⠏⢳⡝⣷⠀⠀ ⣿⠁⠙⢤⣀⣿⠏⠀⠀⢸⣿⣿⢻⣇⠀⠀⢸⡇⠀⠀⣼⣿⢸⠃⠀⠀⠀⠀⣼⡇⣿⠀⠀⠀⠀⠀⠈⣉⣿⡟⣿⠀⠀⠀⠐⠒⠒⠒⠲⡤⢸⡇⣿⠭⢥⣤⣀⣸⣄⣀⣀⣻⡽⠀⠀ ⣧⣀⠀⠀⣻⣯⡀⠀⠀⣾⣿⣿⠘⣿⣆⠀⣿⠁⠀⠀⡟⠙⠉⠀⠀⠀⠀⢠⣿⣷⡇⠀⢰⡀⠀⠀⠀⣿⣿⡄⡏⡄⠀⠀⠀⠀⠀⠀⠀⢀⢸⡇⣿⠀⠘⡇⠀⢻⣿⠉⠙⣿⣧⠀⠀ ⠀⠉⠛⣶⣧⣌⡙⠶⣴⣿⣿⣿⡇⢹⣿⣾⡏⠀⠀⢠⡇⠀⠀⠀⠀⠀⢀⣼⣿⣿⡷⠶⣾⣧⣤⣤⣰⣏⣇⣿⣧⡁⠀⠀⣿⠀⠀⠀⠀⢸⢸⡇⣿⠀⠀⡇⠀⢸⣿⠀⠀⢸⣿⡀⠀ ⠀⠀⣼⠋⠁⠀⠉⠙⣿⣿⣿⣿⣿⠈⣿⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡀⢿⣿⣿⠁⠀⢸⣤⡄⠈⢹⣿⡷⣿⢸⡇⠀⠀⣿⠀⠀⠀⢀⣿⣼⣷⣿⠶⢶⡷⣤⣸⡟⠀⠀⠀⣿⡇⠀ ⡇⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇⢙⣿⣆⢀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣾⡟⣿⡄⠀⣾⢧⡇⠀⢸⣿⡇⣿⢸⣇⠀⠀⣯⠀⠀⠀⣼⣿⡟⡿⣿⠀⣼⣿⡧⣿⡇⠀⠀⠀⣿⣷⣼ ⣦⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣼⣿⣿⢸⡀⠈⡇⠀⠀⠀⠀⠈⢀⡾⠷⢸⠿⠤⣼⣼⣧⣀⣾⣿⡇⣿⢸⣧⠀⢠⣿⠀⠀⢀⣿⣿⣻⣧⣟⢰⣿⣼⣆⣿⠃⠀⠀⣄⣿⣿⣿ ⠏⠀⠀⠂⢀⠀⡀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⡇⢸⡇⠀⠀⠀⢀⡆⠈⡇⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠃⠛⠸⠹⢧⣬⣿⣤⣤⣼⢻⣯⣿⣸⠥⠿⠿⢿⣿⡟⠀⠀⠀⣿⣿⣾⣿ ⠀⠀⠫⠃⢈⡖⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷⡎⣷⠀⠀⠀⠀⣷⢀⣷⢤⣀⣠⣀⡀⠀⠠⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣸⡏⠐⠀⠀⠀⣿⣿⣷⣿ ⠀⠀⠐⠊⠚⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣇⣿⠀⠀⠉⠉⣿⣿⣿⡿⠿⠛⠓⠻⠿⠿⣶⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣲⣷⣖⣢⣿⠃⠀⠀⠀⢸⣿⣿⣿⣼ ⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⡟⠈⢿⡇⣸⣿⣿⣽⡆⠀⠀⠀⣿⡏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠙⢋⣿⡏⣰⠇⠀⠀⢸⣟⣿⣿⣿ ⠀⠀⠀⠀⠀⣼⣏⣸⣿⣿⣿⣿⠁⣿⠀⢸⣿⣿⣿⣿⣿⣇⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣱⡟⣠⣤⠴⠿⠿⠯⠿⠿ ⠀⠀⠀⠀⢠⣿⠋⣽⣿⣿⣿⣿⢠⣿⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡿⠛⠉⠁⠀⠠⠀⠐⠂⠀ ⠀⠀⠀⠀⣾⠏⣨⣿⣿⣿⣿⣿⠀⣿⠀⢸⣿⣿⣿⣿⣿⣿⡆⠀⣿⢴⣿⡟⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⠁⢹⣿⣿⣿⣿⡟⣸⣿⠀⢸⡇⣿⣿⣿⣿⣿⣷⠀⣿⠾⣿⣧⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢾⡿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⠋⠀⣿⣿⣿⣿⣿⡟⣿⣿⠀⢸⠂⢻⣿⣿⣿⣿⣿⣧⣿⡀⣿⣿⡄⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠁⠰⢋⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠀⣼⢋⡄⢠⣿⣿⣿⣿⣿⣧⣿⣿⠀⢸⠀⠸⣿⣿⣿⣿⣿⣿⣿⣧⢸⣿⡟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⡟⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⢸⣿⣇⠀⠉⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⡟⠁⢠⢰⣿⣿⣿⣿⣿⣿⣿⣽⣿⠀⢸⡀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡏⢿⣿⣦⣄⡀⠀⠉⠳⢦⣄⡀⠀⠀⠀⢀⣠⣴⢾⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣿ ⡿⠁⠀⠘⣾⣿⣿⣿⣿⣿⣿⣯⣭⣿⣀⡨⠧⠤⣄⣈⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣾⠋⠓⣾⣿⣯⡾⠿⠿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢰⡟⠋⠁⠀⣿⢿⣄ ⡇⠀⢠⢢⣿⣿⣿⣿⣿⣿⠁⠀⡼⠃⠀⠀⠀⠀⠀⠀⠁⢽⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣿⣿⣿⣾⣛⡒⠂⠀⠀⠀⠒⠐⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡆⢻ ⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣿⡙⢿⣿⣿⣿⡿⣿⣽⡛⠛⣿⠿⠟⣋⢿⡍⠉⢿⣷⡒⠒⡒⣖⠛⠛⡏⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⡇⠤ ⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣵⡀⠙⢿⣿⣷⠿⣿⣿⣶⣌⠲⣶⣿⣾⣇⣠⡤⢿⣷⠀⠘⣞⡆⣸⠁⠀⠀⠀⠀⠀⠀⢠⣿⡆⠀⠀⠀⠀⢷⠀ ⠀⣸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⣿⣿⠆⠈⠀⠉⠻⣿⣷⠶⠦⣽⡆⠀⠀⢷⢧⠀⠸⣾⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠸⡄ ⢠⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣂⠘⡿⡀⠀⠀⠀⠀⣿⣁⠀⠀⣠⡇⠀⠀⠈⡟⡆⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⡀⠀⠀⠀⠀⡟ ⣾⣿⣿⣿⣿⣿⣿⣿⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣦⣱⣷⠀⠀⠀⠀⠈⣻⣿⠛⢿⡢⣀⡀⠀⢸⣾⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⢿⣇⠀⠀⠀⠀⢻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠀⠀⠀⠀⠀⣼⣿⡤⠤⢤⣤⣤⣤⣶⣾⣿⣿⣿⣷⣾⣿⣴⣂⠀⡖⠀⠠⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⣠⠴⣿⣿⣯⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⢉⡿⠀⢰⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⢀⠤⠴⠒⠚⠛⣿⡿⣶⣶⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣶⠋⢀⣴⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀ ⠀⣄⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀ ⠰⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠂⠀ ⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤ ⠀⠀⢀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣉⠉⠁ ⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⡧⣤⠔⠊⠁⠀⠀ ⠼⠛⠉⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠇⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⣧⠈⠳⡄⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠈⣀⡀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⣿⣿⣿⣿⣿⣿⡇⠀⠈⡀⠀⠀ ⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠈⢉⣀⣠⣤⣄⡘⣿⣿⣿⣿⣿⣿⣿⣏⠉⠒⠘⣿⣿⣿⣿⣿⣷⣦⡴⠃⠀⠀ ⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠛⠟⠛⠛⠉⠉⠀⠘⢿⣿⠟⠛⠻⠿⣿⣿⣷⢶⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢿⣿⠿⢿⣿⡟⠻⣆⠀⠀⠀⠀⡠⠔⠀⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠰⢻⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡟⢡⠶⣤⣈⡿⠀⠀⢀⡀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⢸⡇⠓⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠧⣅⣀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⠄⠀⠀⠀⢀⣀⣠⣤⠴⠖⠛⠉⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠙⠢⣄⣀⡞⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠉⠓⠢⢤⣀⠀⠙⢷⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⠬⣷⡎⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠶⠶⠶⠶⠶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⣠⣤⡶⠶⠶⣶⣤⡀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⢠⡾⠋⠁⠀⠀⠀⠀⠙⣿⡆⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⣿⣇⣠⣤⣤⣶⣤⣤⣀⣼⡏⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣷⣴⡶⠟⠛⠉⠉⠀⠀⠀⠈⠉⠉⠙⠛⠿⣶⣶⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀ ⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡁⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀ ⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⣸⡏⣿⡇⠀⠀⠀⢠⡟⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀ ⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡄⠀⠀⠀⣿⠇⣿⡇⠀⠀⠀⢸⡇⢸⡇⠀⠀⣸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀ ⠀⠀⢸⣇⠀⠀⣠⣤⣤⣤⣤⣤⣿⠻⣷⣤⣄⣠⣿⠆⢸⣇⣀⣀⣀⣸⡇⢸⣇⡀⢀⣿⣿⣇⣀⣀⣀⣀⡀⠀⠀⠀⢸⣿⠀⠀ ⠀⠀⣼⠏⠀⠀⢹⣇⠀⠀⢀⣼⣿⣾⣷⣾⣬⡉⠁⠀⠀⠉⠙⠛⠛⠋⠁⠈⠉⠉⣹⣟⣬⣟⡋⠉⠉⢻⡟⠀⠀⠀⢸⣧⠀⠀ ⠀⣼⠏⠀⠀⠀⢰⡿⠀⢀⣾⠋⠁⠀⠈⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠿⣿⣿⣿⣷⡀⢸⣇⠀⠀⠀⠀⢻⣧⠀ ⢰⡟⠀⠀⠀⣰⡿⠁⠀⢸⡏⠀⠀⠀⢀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⣿⣿⣿⡇⠀⢿⣄⠀⠀⠀⠀⢻⡆ ⠘⣧⠀⠀⢼⣿⣄⠀⠀⠘⣿⣦⣤⣴⣾⣏⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⣀⣠⣿⣉⣿⠇⠀⠀⠻⣦⣄⠀⠀⢘⣿ ⠀⢿⣄⠀⠸⣿⣿⣦⣤⡶⢾⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣯⣤⣶⣤⣾⢟⣿⠀⠀⣼⡟ ⠀⠈⠻⣦⠀⠹⣧⠙⢿⣄⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠸⢷⣶⣶⡾⠗⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⣠⡿⠃⣼⠇⢀⣾⠟⠀ ⠀⠀⠀⢹⡇⢠⣿⠀⠀⠙⢿⣶⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣤⡾⠋⠀⠀⣿⢀⣾⠏⠀⠀ ⠀⠀⠀⢸⣧⡾⠃⠀⠀⠀⠀⠉⠻⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠉⠀⠀⠀⠀⢻⣼⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠶⠶⣦⣤⣤⣤⣤⣤⣴⡶⠶⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀

⠀⣰⢦⠀⣠⢶⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠸⠭⠳⠭ ⣼⠷⢺⣴⡿⠾⣇⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⢾⢐ ⠧⠴⡶⠚⢸⠇⢸⡏⠀⡸⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⡇⠀⣿⠀⣘⡀⢀⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢿⣧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⢻⣧⣹⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⢰⠏⣸⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⢿⣿⡏⠀⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣽⣿⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⢣⣧⣾⢠⣿⣿⣿⣿⣿⣾⣽⣿⣿⣿⡏⣾⣿⢀⣎⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⣾⣿⣿⡟⣿⢻⣿⣿⣿⣿⣿⡇⢹⣷⠟⠋⠉⠀⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠁⣿⠸⣿⣿⣿⣿⡟⣄⢼⡏⠀⣠⡀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣟⣹⡿⣄⣉⠛⠛⠙⠃⠀⠸⠇⠀⠸⣿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠋⠁⠀⠀⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⡼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇ ⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣧⢹⡀⠀⠀⠀⠐⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠴⠒⠉⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣷⣧⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⡀⠀⠀⢀⡤⠀⠀⠄⠀⠀⠀⢀⠔⠉⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟ ⠀⣿⣿⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⠒⠐⠁⠀⠀⠀⠀⢀⡠⠐⠁⣀⣠⠤⠖⠊⣹⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⣰⣿⣿⢁⡾⠛⠉⠁⠀⠀⠀⡉⢻⣿⣇⠀⠀⠀⠀⢠⠊⠉⡠⠔⣺⠉⠀⠀⠀⠀⠐⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀ ⣸⢏⡝⢸⡀⠀⠀⠀⠀⠀⠀⠃⢸⣿⣿⣆⠀⢠⠀⢸⠳⠾⠒⠉⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀ ⠡⠊⠉⠛⢏⠀⠀⠀⢀⡀⠀⠀⠀⣿⣿⣿⣆⠀⠁⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁⣾⣿⣿⣿⣿⣿⣿⡿⢟⡿⠋⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠑⢄⡀⠈⠀⠀⡀⠀⢿⣿⣿⣿⣧⣄⡀⠈⠣⢄⣀⠀⠀⠀⢀⣀⠤⠛⢁⣠⣾⡿⠟⠽⣿⡿⠋⠁⣠⠊⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠂⠤⣼⣿⡇⢻⣿⣿⣿⣷⣶⣤⣄⡉⠉⠉⠁⣀⣤⡶⠁⠊⠁⢀⡠⠒⠁⠀⢀⡜⠁⢠⠃⢠⣤⣴⣶⠀⠀ ⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⣙⣿⣿⣿⡝⠻⠿⠿⠿⠖⣻⢿⠋⠀⠀⢀⠔⠉⠀⠀⠀⢠⠎⠀⠀⣾⣰⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞⡏⠉⠁⠀⠀⠈⣩⠅⠀⠀⣴⡚⠁⢸⠀⠀⡰⠃⠀⠀⠀⠀⢀⣏⣤⣴⣾⣿⣿⣿⣿⣿⣿⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣉⠀⢸⣿⣶⣴⣶⣤⠚⣥⣠⣶⣾⡿⢱⡄⢇⡴⠊⢠⣴⣪⣉⣉⣉⣅⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣄⢱ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠁⠀⠀⠀⠑⣿⣿⣿⠟⠛⠃⣿⣿⣿⣿⣿⣿⣧⡄⢄⣴⣿⣿⣿⣿⣿⣿⣿⢇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿

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⠀⠀⠀⡆⠀⠳⣦⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣦⣤⣀⠀⠀⠠⡡⠂⠀⠀ ⠀⠀⠀⠳⣄⠀⠙⠅⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⡀⠀ ⠀⠀⠀⠀⠈⠣⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀ ⠀⠀⠀⠇⠂⣾⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠂⠀ ⠀⠀⠀⠈⣾⡟⣿⣿⠇⣿⣿⣿⡿⡇⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀ ⢒⠀⠀⢰⣿⣷⣿⣿⢕⣿⣿⣿⣇⣷⡠⠼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀ ⣁⢀⠀⢸⣻⣿⣿⣿⠀⢈⠍⠛⠻⠋⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠸⠀ ⠠⠘⠀⡏⣿⣿⣿⣿⡦⡀⠀⠀⠀⠀⢁⣀⡀⢾⣿⣿⣿⣿⣿⣿⣿⣿⠘⠀ ⠀⠀⠀⡇⢿⣿⣿⣿⣷⠀⡶⣀⣒⣂⣁⠴⢄⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀ ⠀⠀⠀⢇⠈⠣⠻⣿⣿⣦⣰⣀⠒⠁⠀⢀⢼⣿⣿⣿⣿⣿⡿⠟⡹⠀⠀⠀ ⠀⠀⢠⠃⠀⠀⠀⠈⠙⠙⠛⡻⠛⢡⠟⡩⠫⣍⠜⡠⠊⠀⢀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⡏⣾⣴⣷⣳⣎⣴⡀⠔⠁⡠⠁⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠘⡀⣼⢀⡎⢹⣿⡟⣿⣿⡇⠀⠀⠀⠀⠀⢸⠄ ⠀⠀⠀⠀⠀⢀⠊⠀⡐⠀⠀⢃⢩⠊⠀⠀⠸⢘⠂⠙⠁⠀⠀⠀⠀⡆⠺⠐ ⠀⠀⠀⠀⡡⠁⠀⠐⠀⠀⠀⢢⠆⠀⠀⠀⢂⠃⠀⠀⠀⠀⠀⠀⠀⠰⡀⠘

⠀⠀⠀⠐⡀⠀⠀⠀⣀⠠⠐⣒⣤⢼⣿⣿⣿⠶⢶⣶⣦⡀⠀⠀⠀⠀⡔⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠔⠈⢀⠴⠋⠁⠀⠀⠉⠁⠀⢀⠠⠈⠝⠋⠓⠦⣄⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢅⣀⠔⠁⠠⠀⠀⡌⠀⠀⠀⢆⠀⠙⠄⢸⡀⠀⠀⡈⠳⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡌⠀⠀⠇⠀⢰⠀⠀⠀⠀⠀⠑⡤⢨⠊⣧⠀⠀⠘⡄⠩⢆⠀⠘ ⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠐⠂⠉⠁⡇⠀⠑⡤⢷⢳⢧⢄⠀⠰⡀⢩⡆⠀ ⠑⣄⠀⠀⢠⢼⠀⠀⠀⠂⡄⠀⠀⢰⠀⢠⠀⠀⠀⠑⢠⠮⡘⡀⢠⠀⠇⡀⡼⠀ ⠀⡇⠉⠐⠒⠚⡀⠄⠸⢠⠁⡖⠀⡜⢀⠆⠀⠀⠀⠀⢸⡄⠔⢇⠈⠀⢸⡇⠁⢰ ⢀⡇⠀⠀⠀⠀⣷⠀⠁⠹⣾⣷⣾⣷⣿⠄⠀⠀⠀⠀⣐⣒⣤⣸⡀⡇⢸⠇⠀⣸ ⢏⡀⠀⠠⣒⡎⣺⠀⠀⠀⡇⢿⠛⢻⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⡻⢳⡾⠴⠃⢈ ⠈⡿⠁⠀⠀⣃⢻⠀⠀⠀⡇⠀⠛⠉⠀⠀⠀⠀⠀⠀⠘⠤⠞⠃⢀⠋⣿⠀⠀⢸ ⣼⠁⢰⠁⠀⡇⢹⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⢸ ⠉⢆⠈⢆⠀⡇⢸⢂⠀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⡂⡏⠀⡀⣿ ⠀⠀⠣⢈⠢⢹⢆⠎⢀⡏⠈⠒⠠⠀⣀⠀⠀⠀⢀⣀⣀⢤⢲⠇⢠⢁⠇⢰⡙⢸ ⠀⠀⠀⣴⣷⢪⡞⢠⠞⠣⢄⠀⠀⠀⠈⡏⠉⠁⠀⢀⣝⡾⢋⢔⢕⡟⢠⡿⠁⢸ ⠀⠀⢸⣿⣿⠿⠴⠋⠀⠀⠑⠪⢤⣒⠒⠓⢂⣒⠩⠔⠉⢲⣶⣧⠼⠔⠋⠀⡀⢹

⣤⠀⣰⣿⠋⠀⡇⠀⠀⠀⠀⢸⠁⠀⠀⠈⠛⣗⠢⠤⠊⠉⠣⡀⡈⡇⠀⠀⠉⠣ ⢰⣾⣿⠟⠀⠀⠇⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢅⠘⢄⠀⢀⡀ ⠀⠉⡍⡇⠀⠀⣴⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⢸⡀⢄⣒⡠⠤⠤⠀⣣⡀⡩⢝⢕ ⠀⠀⣿⠁⠀⠀⢿⡀⠀⠀⠀⡇⠀⢀⡠⢄⣒⠌⠟⠉⠀⠉⠉⠉⢹⣿⣵⣾⢿⣥ ⠀⠀⢸⡶⢄⣸⡽⠁⠀⠀⠀⡧⣲⢵⣮⠗⠁⠀⠀⠀⠀⠀⠀⠀⢸⢁⣢⣜⡼⠟ ⠀⠀⠈⡿⠵⠶⢭⣄⣒⣒⣚⣿⣿⣿⠁⡞⠁⠀⢀⠎⡅⠀⠀⢠⠋⠉⠀⠀⠀⠀ ⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⡧⠃⠈⠀⠊⠀⠧⣀⠀⡌⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⠀⠀⡤⡀⠀⢠⢤⠀⠀⢇⠀⠙⠁⠄⠘⠓⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠇⠄⠃⣇⠀⢸⠉⠤⢜⢸⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠀⢠⠆⠀⠠⠶⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠌⡨⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡇⡆⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⡇⠇⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡆⣧⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠐⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡆ ⠀⡆⠀⢙⢦⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞⡍⠀⡆ ⠀⡇⠀⢸⣾⣿⣷⣶⣶⣶⣶⣶⣴⣿⣿⣿⠃⠀⡇ ⢀⢧⡀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣊⣠⡇ ⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡟ ⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠀⣿⣿⣿⡿⡏⢹⢹⣿⣿⡿⢻⠉⣿⣿⣿⣿⠀ ⠀⡼⢿⢿⣿⣧⣥⣤⡄⠻⣿⢁⣬⣤⣼⡿⠛⡿⢆ ⠀⠀⢨⢆⡻⡏⠘⠿⠁⠀⠈⠈⠿⠛⣿⣃⢾⠀⠀ ⠀⠀⠀⠀⠛⣿⠀⠀⠀⠀⠀⠀⠀⢀⣟⡇⠀⠀⠀ ⠀⠀⣴⣾⣿⣿⢫⡂⢄⣈⣁⡠⢲⢻⡻⢿⣷⣦⡀ ⠀⠀⡿⠉⠀⠈⣧⢣⠂⠇⢸⠀⣘⣯⠀⠀⠈⣿⠇ ⠀⠀⣿⡐⠒⢥⣽⣿⠈⢿⡿⠖⣼⣷⡒⠤⢐⣿⡆ ⠀⢠⣿⣷⣴⣿⡛⢿⣆⣸⣿⢠⡿⣻⣿⣶⣿⣿⡁ ⠀⢰⣿⣿⣿⣿⣿⣷⣽⣿⣿⣫⣾⣿⣿⣿⣿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣏⢉⣿⣄⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡔⣹⣿⣤⣿⣿⣧⣤⡿⣹⣿⡇⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣯⢹⣷⣼⣿⣶⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡸⢠⣿⣿⣿⣿⢙⣿⣿⣧⡟⣿⣇⣿⣿⣿⣿⣿⡟⣿⠀⠈⣻⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⡿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣧⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⣿⣏⣻⣿⣿⣭⣿⣿⣿⡀⠀⠀⢻⣿⣿⣾⣿⡟⢿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠤⢀⡀⠹⣿⣿⣿⣤⣾⣿⠁⢸⣿⠛⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠖⠊⢹⣿⣿⠿⣿⣿⡇⠈⢿⣿⡇⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣷⣿⣿⡆⠁⣿⢧⣄⣀⠀⠀⠀ ⠀⠀⠀⠀⣿⠻⣿⣿⣿⣿⣿⡟⠀⣀⠤⢾⡇⣧⠀⣿⣿⡁⠀⣼⣿⣡⣶⣾⣭⣅⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢉⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡏⠀⣿⣿⣿⣿⡿⢡⣼⣿⣿⣿⣷⡿⢠⣿⠁⡇⣰⠃⠟⣹⣿⣿⣿⡿⠋⣿⣿⣿⣿⡿⣯⣿⣿⣿⣿⡿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠸⣧⣸⣿⣿⣿⣿⣿⢯⣩⣿⣟⣭⠟⣷⠞⠁⠠⠟⠁⠀⠀⠀⠉⠓⠋⠁⠀⣸⣿⣿⣿⢙⣼⣿⣿⣿⣿⣿⣮⣳⠯⢶⡤⠀ ⠀⠀⣀⣠⢿⣿⣿⣿⣿⣿⢩⠞⢯⠏⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣇⡾⠘⣿⣿⣿⣿⣏⠛⠛⠓⠉⠀⠀ ⠀⠀⠉⠉⣉⣽⣿⣿⣿⣿⡇⢰⠉⣀⡠⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣿⡈⠛⢯⣿⠀⢻⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣧⡘⠁⡠⠜⠁⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣶⠈⢿⠀⢹⣿⣿⣿⢹⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣿⣿⣿⡟⢿⣿⣿⡿⣶⣷⣤⣾⣄⡀⠀⠈⠉⠁⠀⠀⠁⠀⠀⣼⣿⣿⣿⡟⠋⠁⢀⡼⠃⣸⣿⣿⣿⠈⣿⡆⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣿⣿⣌⠻⣿⣧⠀⠀⠉⠛⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣸⣿⠃⣿⢻⡇⠀⡠⠋⢀⡜⢹⠃⣿⣿⣀⣿⡇⠀⠀⠀⠀ ⠀⠀⢸⡟⢿⣿⣿⢿⣿⣷⣝⢿⣷⡀⠀⠀⠀⠈⢻⣿⣆⠀⠀⢀⣀⣴⣿⡇⠀⣿⢸⣧⠀⠀⠰⠋⣠⢼⣿⠟⢻⣿⣿⣷⡀⠀⠀⠀ ⠀⠀⣿⡇⣸⣿⣿⣮⠻⣿⣿⣷⣮⣍⡉⠀⠀⣠⣴⣿⣿⡟⠋⢉⣿⠛⣿⠉⡆⢸⣸⣯⠣⣤⣴⣾⣿⣿⣃⣤⣾⣿⣿⠇⢹⡀⠀⠀ ⠀⠀⣿⠀⢷⣿⣿⣿⣧⣬⠛⢉⣿⣿⠉⢲⣾⣿⣿⣿⣿⡇⠀⣾⠃⠀⡿⡆⣧⢀⣿⣿⣿⠁⠹⣿⣿⣿⣿⣿⣿⢿⡟⠀⠀⡇⠀⠀ ⠀⠀⣿⡇⠈⢿⠛⢿⣟⠉⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⣿⡇⢸⣿⠀⠀⣇⢹⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⠿⣵⣿⣷⠀⢠⡇⠀⠀ ⠀⠀⣿⡻⣄⠸⢧⢴⣿⣷⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡀⠴⠾⠀⢻⣿⣿⣿⣿⣿⣯⡉⠉⠻⣿⣾⣿⡟⢨⣷⡿⠁⠀⠀ ⠀⠀⠹⡝⢿⣿⣦⣤⣶⣿⣿⠟⠙⢡⣿⣿⣿⣿⣿⣿⠋⠀⠸⣿⣷⡄⠀⠀⠀⠻⣿⣿⣿⣿⣿⣷⣆⣸⡛⣛⣦⣀⣸⣿⡅⠀⠀⠀ ⠀⠀⠀⢙⣾⣿⡿⠿⣿⣿⢡⣐⣀⣾⣿⣿⣿⣿⣿⣿⠐⡶⣤⣿⣿⣿⣿⡂⠀⠀⠙⣿⣿⣿⣿⣿⣿⣯⠉⠹⢧⡞⢣⢻⣷⡀⠀⠀ ⠀⠀⣰⡿⢡⣿⠿⣟⣻⡟⠚⠛⣿⣿⣿⣿⠛⣿⣿⣿⣷⣖⠚⠃⠛⣿⣿⣿⣦⡀⠀⠪⢿⣿⣿⣿⣿⣿⣧⠀⠈⡗⠻⡄⣿⣧⡀⠀ ⠀⣰⡟⢀⣏⠟⢫⡁⠀⢙⠶⠦⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣦⡀⠀⠈⠛⣿⢿⣿⣆⠀⠀⠹⣿⣿⣿⣿⣿⡴⢀⡇⠀⢹⣿⡏⣷⠀ ⢀⣿⡇⣸⡁⠀⣾⡄⠼⡏⠀⢸⣿⣿⣿⢿⠀⠸⣿⣿⣿⠽⣿⡻⣖⠚⠓⢙⣏⠙⠙⢷⣀⠀⠘⣿⣿⣿⣿⡏⢹⣿⣿⣿⣟⠁⢻⡇

⢠⣣⣰⣣⠀⠘⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣶⣤⣤⣀⠀⠀⠀⠀⠀⠀⣟⡗ ⠧⡞⢳⠊⡇⠰⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠉⠁ ⠀⠁⠘⠐⠂⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣟⢷⡀⠀⠀⠀ ⠀⠀⠀⠀⢸⡿⢻⢿⣿⣿⢹⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣿⣿⣿⣎⢧⣿⡄⠀⠀ ⠀⠀⠀⠀⢸⣥⡇⣾⣿⣿⣮⣿⣿⡇⡿⣰⣡⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⡏⡇⣿⣿⣿⣇⡿⢁⡀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⠝⠓⢬⠉⠉⠀⠃⠀⠾⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆ ⠀⠀⣀⣤⣼⣿⣟⡅⠀⠀⢦⠀⠀⠀⠀⠀⠀⠤⠐⠊⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⣸⣿⣿⣿⣿⣿⣷⠄⠀⢀⠀⠀⠀⠀⠀⠔⠂⠉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢸⣿⢳⡿⠿⠿⠿⣿⣎⠁⠁⠀⠀⠤⣊⠤⠐⠂⠩⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⡹⣅⣇⠀⠀⠀⠘⢸⣿⡄⢠⠐⠂⠓⠈⠀⠀⠀⢀⣾⢏⣿⣿⣿⣿⣿⣿⠟⠁⠀ ⠊⠀⠑⢄⠀⠂⢀⠀⣿⢿⣄⡀⠣⣀⠀⠀⠀⡀⠞⣁⣾⢟⣿⠟⢋⠕⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠁⠒⠻⡏⢿⣿⡷⣶⣤⣍⢠⡴⠊⠈⡠⠀⠁⢠⠊⡸⣠⣶⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⢔⡟⠋⠉⢙⠄⠀⣔⠋⠇⡠⠊⣀⣀⡠⠥⢴⣿⣿⣿⣿⢠ ⠀⠀⠀⠀⠀⠀⠊⠂⠀⣿⣿⠿⢾⣾⣿⣧⣇⠈⣠⣷⣶⣶⣶⢸⣿⣿⣿⣿⣿⣺

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ଘ(੭*ˊᵕˋ)੭* ੈ♡‧₊˚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠻⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⢸⡿⣿⠇⠰⠟⠀⠀ ⠀⠀⠀⠀⣀⡤⣤⠶⠛⠉⠉⠀⠀⠉⠉⠛⠲⣤⣤⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⡼⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⢧⠀⠀⠀⠀ ⠀⠀⡼⢁⡆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢰⡈⢧⠀⠀⠀ ⢀⡞⠁⣸⠁⠀⢠⠬⠓⠀⣀⠀⠀⢀⠀⠛⠥⣄⠀⠀⡇⠈⢳⡀⠀ ⡞⠀⠀⠹⣆⠀⠀⠆⠀⠀⠓⠊⠙⠚⠁⠀⠀⠀⠀⣰⠇⠀⠀⢻⠀ ⣇⠀⠀⠀⠈⣹⠶⠦⠤⠤⣤⣤⣤⡤⠤⠤⠴⠶⣏⠁⠀⠀⠀⣸⠁ ⠈⠓⠲⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠶⠚⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠤⠤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣻⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣢⡀⠀⠀⠀⠀⠀ ⣐⡽⠋⠀⢀⣀⠀⠀⠀⠐⢤⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣄⣀⣀⠀⠀ ⣾⣧⡀⠀⣸⣏⠀⠀⠀⠀⣴⠀⠀⠙⠛⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣽⠏⠀ ⢹⢿⣉⠉⠁⠈⠓⠶⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣿⡆ ⠀⠀⠉⢓⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⣄⠀⣀⣀⣤⡶⠶⠚⣛⣭⡁⠁ ⠀⠀⠀⠀⣸⡇⢈⣽⠛⠛⠓⠲⠶⠶⠶⠶⠶⠶⠶⠶⠾⢷⣄⣀⣀⣤⠟⠉⠉⠈⢻⡷⠦⣾⣽⠟⠃⠀ ⠀⠀⠀⠀⠈⠙⣿⠃⠀⣴⣶⡄⠀⢰⠀⢀⠀⢀⡀⠀⠀⢀⣨⡉⠉⠀⠀⠀⠀⠀⠈⡇⠀⢧⠹⡆⠀⠀ ⠀⠀⠀⠀⠀⢰⡇⢀⢀⠻⠟⠁⠀⢻⣤⠿⣤⣬⠇⠀⠀⢿⣿⣿⠂⠀⡀⠀⠀⠀⠀⡿⠀⠈⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⢸⣷⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠛⠀⠀⠀⢠⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀ ⠀⡀⢀⠀⠈⡆⢸⡯⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠋⠀⠀⠀⠀⠀⠀⠀ ⠘⣻⣿⣿⡟⡗⠘⣧⡀⠀⠉⠙⠳⠦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⡤⣶⣟⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⢰⡟⠛⠳⠶⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠚⠛⣷ ⣾⠀⠀⠀⠀⠀⠀⠉⠛⣶⣤⠶⠶⠚⠛⠛⠛⠶⠶⢦⣴⡞⠋⠁⠀⠀⠀⠀⠀⢸ ⣿⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢦⡀⠀⠀⠀⠀⢸ ⢻⡄⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⣼ ⠘⣧⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢠⡟ ⠀⢹⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠁ ⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⢻⡆⠀⠀⢀⣴⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠓⢦⣠⡄⠀⠀⣼⠇ ⠀⠈⢷⡀⠀⠛⠻⣿⣿⠟⠀⠀⠀⠀⠀⡀⠀⠀⠀⠘⠂⠀⠀⠈⠛⠁⠀⢠⡟⠀ ⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀ ⠀⠀⠀⠀⠉⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡶⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⡷⠲⠦⠤⠤⠤⠤⠤⠴⠖⣾⠛⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡶⢶⣄⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣧⠀⠻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢷⣤⡇⢀⠀⠀⢀⠀⠀⢀⠀⠀⢀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣾⡛⣧⣸⠀⠀⢸⠀⠀⢸⡀⠀⢸⢀⡟⢻⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠷⠤⣯⣤⣤⣤⣷⣤⡿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢻⠊⠁⢾⠀⠀⠀⠀⠀⠀⠗⡆⢠⡄⠀⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡜⠸⠀⡘⢸⠀⠀⠀⢠⠆⠸⠀⡇⡌⠃⠀⠀⠂⢸⠀⠀⢰⠀ ⠀⠀⠀⣠⠀⠃⢰⢀⠇⠸⠀⠀⢠⢻⢠⠃⠀⣧⢁⣰⠀⣸⣀⡀⠄⠀⠘⠀ ⠀⠀⠀⢃⣷⡾⠿⣾⣝⠂⠆⢠⠃⣨⠂⠀⢀⠗⣡⡼⢿⣛⠒⠯⣕⣆⣀⠀ ⠀⠀⢠⣿⠏⢀⣴⣿⣿⣦⠘⠃⠀⠁⠀⠀⠈⠼⣩⣾⣿⣯⡿⣦⠀⢫⢷⠀ ⠀⠀⣼⣿⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣿⣿⡹⣿⢷⣸⠀⢸⣸⠇ ⠀⠀⢹⠛⢦⠹⡻⢋⣭⠿⠃⠀⠀⠀⠀⠀⠀⠀⠻⢿⣈⠕⢀⠜⠀⢩⠃⠀ ⠀⠀⠀⡆⠀⠀⠈⠀⠀⠀⠀⡠⠤⠤⠢⢴⠶⣦⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠠⡇⢀⠠⠤⠐⠩⠭⣇⠀⠠⠔⠢⠭⡄⠂⠀⠀ ⢀⡈⢆⣇⠀⠀⠀⠀⠀⠀⠀⢋⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀⠤⠊⠀⠀⠀⠀ ⠀⠈⠑⢭⡉⠒⠤⢂⣀⠀⠀⠈⠂⡀⠀⠀⠀⠀⠀⢀⡙⣧⠤⠄⣀⡀⠀⠀ ⠀⠀⠠⢉⠆⡰⠑⠤⣀⣟⣍⠁⣒⡒⣒⡂⠀⠀⠉⢀⣀⢇⢌⡅⠀⡀⠀⠀ ⠀⠀⠠⠁⠈⠀⠀⡐⣪⠗⠊⠋⠁⡟⠗⠤⣍⠭⠔⠊⠉⠉⠑⢜⣄⡛⠀⠀ ⠀⠀⠀⠀⠀⠀⡌⣰⠃⢀⣀⡤⠖⠳⠺⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠛⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠙⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠋⠀⠀⠻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⢀⣀⡀⠀⠀⠙⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠟⠀⣠⡶⣶⡀⠙⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⣼⠋⢻⣦⠀⠀⠈⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠏⢀⣼⠟⠀⠘⣷⡄⠈⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⣿⠁⢸⡏⠀⠀⠻⣧⡀⠀⠀⣿⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⠃⢀⣾⠋⠀⠀⠀⠘⣷⠀⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⡇⠀⣸⠃⠀⠀⠀⠹⠷⠀⠀⠈⠉⠉⠉⠉⠉⠁⠈⠉⠉⠉⠁⠸⠏⠀⠀⠀⠀⠀⠸⣧⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⠃⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⢶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⣠⣶⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠁⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⣿⠃⠀⠀⠀⠀⣰⡟⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠋⠀⠀⠀⠀⠀⠀⠹⢷⡀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⡏⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠙⠿⣦⣀⠀⠀⣠⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⣀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠁⣤⣤⣤⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢙⡗⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⠸⣿⠀⠀⠀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡏⠀⣿⡆⠀⠀⢸⣿⣿⣿⣆⠀⠀⠀⠀⠀⣤⣶⣶⣶⣶⣤⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⡇⠀⠀⠀⠀⣾⣏⣀⣀⡀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀ ⢸⣿⠁⠀⠘⣧⠀⠀⠸⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠈⠙⣷⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⡿⠿⣿⣿ ⢸⣿⠀⣤⡾⠛⠀⠀⠀⠘⠛⠛⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⣀⣤⣿⣿⠀⠀⠀⣀⣴⣿⣿⠟⠋⠁⠀⠈⣿⡏ ⢸⣿⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⠿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⣴⣾⣿⡿⠛⠁⠀⢠⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⣿⡇ ⣿⣿⣶⣤⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣯⡀⠛⠂⣠⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠿⠟⠋⠀⠀⠀⠀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇ ⠀⠉⠙⠛⠿⠿⢿⣿⣿⣶⣶⣤⣀⣀⠀⠀⠀⠈⠿⣿⣶⣾⠿⠟⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⣼⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣴⣶⣾⣿⣿⠿⠿⠟⠛⠋⠉⠁⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢻⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡄⠀⠀⠀⠀⢸⣿⠃⢀⣤⠾⢻⡇⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⢠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⢸⣿⡶⠟⠉⠀⢸⠀⠀⠀⣠⣤⡀⠀⣾⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣶⡖⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡀⠀⠀⢸⣿⠀⠀⠀⠀⠸⣧⣠⡾⠋⠉⣧⢀⣿⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣶⣤⣄⣿⣇⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⣀⣤⣤⣤⣤⣄⠀⠀⠙⣿⣷⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠛⢿⣿⣿⣷⠀⠀⠀⠀⠀⣀⣿⡇⠀⠀⠀⠀⢀⣀⣀⣿⣿⣿⣿⠿⠛⠙⠻⣿⣷⠀⠀⢻⣿⡆⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠛⣿⣿⠳⣦⣄⣠⡾⠛⣿⣿⣀⠀⣠⣴⠟⠉⢩⣿⡿⠛⠁⠀⠀⠀⠀⢹⣿⡆⠀⠘⣿⣧⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⢹⣿⡇⠀⠉⠉⠀⠀⣿⣿⠛⠿⠋⠁⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⣿⡟⠛⠁⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣄⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣴⣿⡟⠀⠀⢰⣿⡇⠀⠀⠀⠀⢀⣠⣶⣿⣿⠿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣤⣤⣿⣿⣧⣤⣤⣤⣤⣼⣿⣤⣤⣤⣤⣤⣤⣼⣿⣀⣀⣀⣠⣴⣾⣿⣿⣀⣠⣤⣿⣿⣥⣤⣤⣶⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡛⠛⠛⠛⠛⠋⠉⠉⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠉⠉⠉⠶⠤⠄⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠑⢦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢧⠀⠀⠀⠈⡢⢀⣀⠀⠀⠀⠀⢀⡠⠗⠂⡝ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠳⡀⠀⠀⠀⠀⠀⠙⠢⣀⠀⢇⠀⢠⠎⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⡀⠀⢩⡀⠀⠀⠀⣀⣰⠀⠈⢦⠀⠑⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⡦⠤⠥⠀⠀⢸⣿⡏⠀⠀⠀⢣⢰⡅⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡴⡄⠹⡢⢰⡀⠀⣀⢆⡘⠟⠁⠀⠀⠀⠘⠇⢱⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⡄⠈⠒⠵⣄⢱⡀⠹⠚⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣂⡀⠀⠀⠑⠇⠀⠀⠈⢳⠠⢄⣀⣀⣀⠤⠋⠀⠀ ⠀⠀⠀⣀⠤⢤⠔⠩⢟⠳⡤⡤⠴⡤⠠⡶⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡜⠁⠀⡟⠀⠀⠀⢢⠃⠀⠠⠦⡄⠌⠑⣠⠤⠷⣖⠒⠢⡄⠀⠀⠀ ⠀⠀⣇⠀⠀⢧⠀⠀⠀⠀⢱⡀⠀⠀⠸⠀⠈⣀⡀⠀⠈⢧⠀⡷⠀⠀⠀ ⠀⠀⢸⠄⠀⡼⡧⠀⣀⣠⠴⢓⡶⠒⠒⠊⠉⠁⠘⣦⠤⢺⠽⠃⠀⠀⠀ ⠐⠶⠯⠴⠊⠀⢗⣂⣸⢤⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⠴⠤⠶⠶⠶⠶⠶⣶⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠰⡹⣏⠀⠀⠽⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠻⠿⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠷⣦⣀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⡻⣷⣶⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣶⠶⣋⡁⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⠷⢶⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠿⢋⣵⠿⠋⠁⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣠⣾⠛⠁⠀⠀⠀⠀⠀⠀⣤⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢂⣾⠟⠄⠀⠀⠀⠀⠀⠀⠀⠐⣺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠋⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⣀⠞⠀⣿⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣴⡾⠋⠀⠀⣼⠟⠁⠀⠀⢀⠀⠀⠀⠰⠟⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣼⡿⠏⠀⠀⠀⣼⠏⠁⠀⠀⣠⣿⠀⠀⠀⠀⠀⠰⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⠟⠋⠀⠀⠀⠀⣰⠋⠀⠀⢀⣾⠋⣿⠐⠀⠀⠀⠀⠐⠀⡀⣿⡆⠀⠀⠐⠒⠒⠂⠀⠀⠀⠀⢸⡿⣿⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⣿⡀⠀⠀⠀⠀⠀⢠⡀⠀⠀ ⣾⠟⠁⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⣾⠃⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⣿⠐⠀⠀⢴⣤⣤⣀⠀⠀⠀⠀⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠈⣿⣦⠖⠋⠀⣀⣤⠀⢻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠸⡇⠀⢲⣄⣀⣈⠛⠿⣦⣄⠀⢸⡆⢸⡿⡇⠀⠀⠀⠀⠀⠀⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⣠⠾⠛⣿⣤⣴⠟⠛⢻⣇⡀⠋⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠳⠀⣌⣛⣿⣽⣿⣷⣮⣙⢷⣾⠁⣼⡧⡇⠀⠀⠀⠀⠀⠀⢻⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠁⣠⣾⣿⠿⣿⠀⠀⠚⠛⢻⣧⡄⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡏⢩⠭⠍⣿⣿⣿⣿⣷⣜⠃⡟⢡⡇⠀⠀⠀⠀⠀⠀⠘⣷⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⣾⣿⠟⠁⢸⡿⠀⠀⠀⠀⢸⣽⣿⠀⠀⠈⠙⠒⠒⠀⠀⠀⠀⠀⠀⣾⣿⡁⠀⠀⠀⢙⡿⣷⡝⢿⣿⣿⡁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠹⣆ ⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⣿⠃⠀⢠⣿⡿⠋⠀⠀⠛⢻⣷⠀⠐⠀⠀⠉⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⢹⡟⠀⠀⠀⠀⠁⢻⣷⠀⠹⣾⣿⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻ ⠀⠀⠀⠀⠀⠀⣼⠁⠀⢠⡟⠀⠀⢸⣿⠁⠀⠀⠀⣠⡾⠋⠀⠀⠀⣰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣟⠁⠆⠀⠀⠀⠀⢸⣿⠀⠀⠙⣇⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⢺⣿⠀⠀⠀⠀⠸⣷⡄⠶⣿⣄⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⠀⠶⣶⢖⣿⠏⠀⠀⠀⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡟⠀⠀⢸⡇⠀⠀⠺⣿⡤⠀⠀⠀⠀⠘⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣧⣤⣿⠿⠋⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡇⠀⢀⣿⠁⠀⠀⠀⠈⢀⣀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⠃⠀⢰⣿⡄⠀⢸⣧⠀⠀⠀⠀⠈⠹⣶⣖⣻⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣍⣉⣙⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⣰⣿⠃⠁⡄⠹⣿⠀⠀⠀⠀⠀⠀⠩⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰ ⠀⣴⡿⢿⡇⠀⠆⠀⠇⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣚⡛⠛⠛⢷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⢸⡿⠁⣾⠃⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏ ⣿⠃⢰⡿⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁ ⡟⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠂⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀ ⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀ ⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣻⠷⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⠀

⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠑⠲⠂⠄⣀⠀⣀⣀⢀⡠⠊⠀⠀⠀⠣⠀⠀⠀⠀ ⠀⠀⣀⠄⠂⢡⠀⠀⠀⠀⢀⣴⡗⣷⡀⠀⢉⠇⠀⠉⠢⡄⠀⠀⠀⠀⣆⠀⠀⠀ ⠖⠁⠀⠈⠢⡀⢢⠀⢀⡔⢫⠎⡇⡇⠱⡀⡀⠘⡤⠒⢢⠱⡀⠀⠀⠆⠁⠂⠀⠀ ⠄⠀⠀⢀⡴⠗⠤⡵⠋⡠⡏⢀⢸⢸⠀⠱⢶⡒⠁⡆⠀⢳⠈⠑⢔⡠⠋⢱⠀⠀ ⠈⢂⠀⠋⠁⠀⡰⢁⠜⢡⠁⡇⠀⢇⢇⠀⣼⡇⠀⢣⠀⢸⡌⠒⠂⠀⣈⠽⡂⠀ ⣀⠀⠉⣿⠁⢨⡣⠓⠒⢸⢸⠀⠀⡌⢾⣦⠇⢠⠠⠌⡄⠈⡉⠋⠏⠙⢢⡠⠼⣔ ⡀⠑⠄⢿⡀⣼⠃⣀⣀⣘⣼⠀⠀⣧⠁⠙⢦⠈⢇⠀⢻⣄⢣⡆⢰⠙⣥⣄⠀⠈ ⠀⠀⢀⣾⣧⣿⣴⠋⡜⣷⣻⣇⠀⣿⡄⣇⣤⣀⣈⢆⢸⢸⢪⣇⠘⠀⡏⣿⠑⢄ ⢀⡠⢚⢃⡿⣽⣿⡀⣿⣿⠇⠉⠢⠾⠟⢩⣦⣿⣿⣿⡫⣾⣄⡙⢰⠀⣿⠸⡧⡀ ⠀⠀⢸⣼⣵⠩⡏⠉⠉⠁⠀⠀⠀⠀⠀⠸⣏⣿⠟⣸⡇⡏⠈⡠⣺⠀⡍⢣⠱⠈ ⠀⠤⠞⢿⡇⢰⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡼⣧⠃⠈⡵⠧⢵⣇⠀⠣⡣ ⠀⠀⠀⣸⣼⡘⣷⡈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠏⠁⢠⣎⣶⣶⡤⠒⠓⠒⠌ ⠀⠀⠼⣟⠈⢻⢸⢘⡄⢹⣑⠆⢠⣤⡀⠀⠐⢈⠏⡠⢶⠋⢡⡑⡏⠀⠀⠀⠀⠐ ⠀⠀⠀⢻⣆⣿⢀⠏⢈⣉⣀⠑⣏⢰⣷⠀⣠⢾⠊⣰⣅⠄⠖⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⣋⡣⠁⠀⠀⠤⢄⡁⠊⢿⣿⠔⢁⣮⠎⠘⡇⡈⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⡴⠋⠑⢯⠆⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⡔⡱⠋⠀⠇⢣⠀⠀⠀ ⠀⠀⠀⠀⣧⠀⠀⢸⠀⠀⠀⡀⠀⠈⢆⠀⠀⠀⠄⢀⢼⠋⠉⢦⣶⣸⢸⡇⠀⠀ ⠤⣀⠀⢰⠋⢫⠐⠊⠢⣠⠞⠓⠤⠤⠜⠚⠻⡁⠀⠀⡘⠀⠀⠈⡄⠈⢵⣼⠀⠀ ⠉⠉⠀⠀⠀⠀⡀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠈⡂⠤⠅⡀⠀⠀⠃⠀⠠⠏⡇⠀ ⠀⠀⠀⠾⡄⠀⠗⢉⠂⠀⣠⠄⠀⠀⠀⠀⠀⠀⢡⠀⠀⠘⡤⠤⢦⡀⠠⠀⠁⠀ ⠀⠀⠀⠀⢸⣼⢃⠂⠀⣰⠙⡄⠀⠀⠀⢧⠀⢠⢻⡄⠀⣀⠱⣀⡀⠼⢶⠄⠀⠀ ⠀⠀⠀⢐⣿⢇⡌⠀⢠⡇⠈⠀⠀⠀⠀⠸⠀⠀⠘⠇⠠⠙⠸⡄⢱⠀⠸⡎⠀⡆ ⠀⠀⠀⢈⡿⣾⠀⢀⡆⣳⠀⠀⢀⠀⢸⢸⠀⠀⠀⠂⠀⠀⠀⢁⣦⡤⣴⣿⠶⡼ ⠀⠀⢀⡾⣇⣿⠀⢈⠣⣿⠀⢀⣸⣀⣼⣿⣠⢄⢒⡆⠀⠀⠀⢸⡇⡇⣻⣿⡯⡚ ⠀⣠⡟⠁⠹⢯⠈⣉⣀⣀⡁⠀⠀⠀⠀⣀⣀⣀⣈⡇⠀⠀⠀⢸⢶⢻⢑⡾⢗⡬ ⣰⢻⠃⠀⠀⢸⠛⠛⠋⠉⠀⠀⠀⠀⠀⠙⠛⠛⢻⡿⠀⠀⡀⢠⡄⣶⠵⢿⠛⠁ ⠇⡜⠀⢰⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⢀⠃⠘⣷⠙⠀⠸⡇⠀ ⠁⠻⣧⢘⡀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⠻⠀⣸⡇⠆⠀⠀⠀⠀ ⠀⠀⠘⢮⢷⣿⣿⡦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠰⢃⠃⡠⢱⡇⠀⠀⠀⠀⠀ ⠀⠀⢀⠊⠒⢺⢻⠁⠀⢁⠂⠤⣀⣀⣠⡄⡶⣻⣔⣲⡮⣬⣵⠗⢿⢤⠀⠀⠀⠀ ⠀⠀⡸⠀⠀⣼⣮⣀⣀⡞⠄⢀⣜⡯⠌⠋⣀⠏⠉⠚⢽⢋⢸⠀⠀⠀⡆⠀⠀⠀ ⠀⠰⣁⣐⣲⡟⡇⠘⠁⠀⠀⣤⣿⣕⣶⠿⡞⠀⠀⢠⠓⢌⡆⠆⠀⠀⢰⠀⠀⠀ ⠀⠀⣀⢬⠛⡆⠃⡏⠀⠀⠘⠚⠛⠁⢠⡼⣓⡲⢤⠃⠀⠀⠉⢺⠒⠖⡦⣇⠀⠀ ⠀⠀⠀⢎⠔⡄⠀⠁⠙⠓⢄⢀⡀⢀⣼⠉⠓⠓⡿⠀⠀⠀⣀⣰⣀⠴⠃⠘⠀⠀ ⠀⠀⢐⠌⠀⢳⢸⢰⠀⠠⠄⠒⢃⡟⠴⠓⠂⢸⡉⠭⠭⠕⠂⣉⣀⡀⠠⠃⠀⠀

⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⡿⠛⢿⣿⡆⠀⠀⢰⣿⡿⠛⢿⣷⡄⠀⠀⠀ ⠀⠀⠀⢸⣿⡇⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⢸⣿⡇⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⢸⣿⡇⠀⠀⠀ ⠀⠀⠀⠈⣿⣿⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⣿⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣀⣤⣿⣷⣶⣶⣾⣿⣤⣀⣿⡿⠀⠀⠀⠀ ⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀ ⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀ ⢠⣿⣿⣿⣿⣿⠟⠛⠻⣿⣿⣿⣿⠟⠛⠻⣿⣿⣿⣿⣿⡄ ⢸⣿⣿⣿⣿⣿⣤⣤⣤⣿⣿⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⡇ ⠘⣿⣿⣿⣿⣿⣿⣿⣿⡋⠉⠉⢙⣿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠙⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⠋⠀ ⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠿⠿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠢⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣶⣶⣏⡁⣄⣀⣀⠀⣀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣀⠤⠴⠻⢗⠋⠁⠀⠀⠈⠉⠛⠦⢿⣾⡳⠾⣤⣄⡀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⡠⠤⠤⠬⣿⡶⢤⣠⠖⠉⠀⢀⠀⠀⠀⢁⣀⡠⠤⠄⠀⠀⠀⠤⠬⣻⠿⢦⣙⡋⢼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠶⠋⠀⠀⠀⠀⠀⢸⡅⠀⣧⠀⠀⢀⡤⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠉⠒⠮⣷⣶⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠏⠀⠀⠀⠀⠀⠀⢠⡄⠇⢠⠟⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡏⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⢹⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢳⡄⠀⠀⠀⠀⠀⣰⣿⠇⣠⢿⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⣿⣤⣀⢀⣤⣼⣏⡟⠀⣇⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠛⣿⣶⠿⣿⣿⣿⣄⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⢙⡿⣄⣀⣰⠇⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⣼⢧⡀⢠⠃⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⡀⠀⠀⠰⡄⠀⠀⠀⠀⣰⠀⢇⠀⣴⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀ ⠀⠀⠀⠘⠀⣸⡏⠀⢃⡸⠀⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣸⠤⠄⠱⣄⠀⠀⢳⡄⠀⢀⡼⠃⠀⣸⣴⣿⡆⠀⠀⠀⠀⣇⠀⠀⠀⠀ ⠀⠀⠀⢸⢀⣿⠀⠀⠘⡇⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⡿⠛⣛⡓⠊⠙⠒⠚⠉⠓⠋⠀⣠⡾⠿⠿⣿⠃⢀⡄⠀⡀⠸⡄⠀⠀⠀ ⠀⠀⠀⢸⣾⠃⠀⠀⠀⣿⣿⢰⠃⢀⡆⠀⠀⠀⠀⣀⣴⣿⠏⡐⠉⣠⣹⡆⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⢀⣿⣖⢩⠇⠀⢹⣆⢣⠀⠀⠀ ⠀⠀⠀⢸⡟⠀⠀⠀⠀⢸⡏⢿⠀⣼⠁⠀⠀⠀⠀⠉⢹⣯⠀⣏⣿⣿⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣟⣭⣿⣿⣤⣄⡄⠘⣾⠀⠀⠀ ⠀⠀⠀⣼⠇⠀⠀⠀⢀⣿⣷⣎⡜⢹⠀⠀⠀⠀⠀⢀⠀⠹⣇⠙⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⡉⠀⠀⠀⠀⠀⠀⠉⠳⣿⣀⠀⢀ ⠀⠀⠀⢹⠀⠀⠀⠀⡼⡽⠋⣿⠀⠘⡀⠀⠀⠀⠀⠈⢿⣶⡼⠗⠀⠀⠀⠀⠀⠀⠐⠒⣡⢴⡟⠋⣉⣽⡆⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠈ ⠀⠀⠀⡏⠀⠀⠀⡼⢡⢧⢰⠋⢧⡀⡇⠀⠀⠀⠀⠀⠀⠻⣽⡯⠶⠶⠦⢤⡤⢤⣶⠛⠀⠼⠤⠯⠿⠛⠁⠀⣠⡤⢤⡀⠀⠀⠀⠻⠇⡀ ⠀⠀⢸⠁⠀⠀⡜⢠⠇⡸⠈⡇⠀⠉⠱⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢤⡄⠙⢯⣿⣏⡀⠀⠀⠀⢀⡿⠃⠀⢠⡿⠀⠀⠙⢧⠀⠀⠀⠀⠉ ⠀⠀⡌⠀⢠⠎⣠⠃⢠⠇⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠒⠚⢽⣆⣰⠟⠉⠉⠻⣦⠀⠀⠿⠇⠀⠀⢸⡆⠀⠀⠀⣸⡇⠀⠀⠐⣶ ⠀⡰⢁⠔⢁⡴⠁⠀⡜⠀⠀⠀⠀⠈⠙⡄⠀⠀⠀⠀⠀⠀⠀⠑⢢⡄⠙⣷⡄⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠻⢦⡤⠴⠟⠁⠀⠀⠀⠉ ⡴⡥⠦⠔⠁⠀⠀⣰⠁⠀⠀⠀⢀⣠⣤⠬⢷⣄⡀⠀⠀⠙⠻⣍⠁⠀⠀⠈⠷⣶⣄⣀⣽⢷⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⣠⢟⣿⣋⣡⣿⣻⠛⠓⢾⣏⠉⠁⠀⠀⠀⠀⠀⠙⢿⠛⠛⣛⣷⣬⡝⣲⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣀ ⠀⠀⠀⠀⣀⡞⠀⡔⡶⠛⠉⠉⠉⣹⣧⣼⣿⠛⠀⣤⡴⢿⠷⣤⣀⠀⠀⠀⠀⠀⠀⢱⡾⠏⠁⠉⠉⠋⠉⠉⠉⠛⠻⣷⣶⣞⠁⠙⠢⢄

◝(ᵔᵕᵔ)◜

°ʚ(*´꒳`*)ɞ°

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠘⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⢀⡾⠁⢠⠖⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣁⠀⣾⠃⠀⠨⠄⠘⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠉⠁⠀⠉⠳⡀⠀⢀⣀⣀⣀⣀⣀⡀ ⠀⠀⠀⠀⠀⢠⠮⣉⡿⠀⠀⠀⠀⠀⠀⣽⠟⣋⠥⠒⠛⢶⣤⡽ ⠀⠀⠀⠀⠀⠸⡂⢰⣰⡂⠀⠀⠀⠀⠀⠀⢙⣧⣦⣔⡾⠟⠋⠀ ⠀⣀⡐⢢⠀⠀⠘⡬⠒⠂⡄⢿⡿⠀⠀⢀⡽⠃⠀⠀⠀⠀⠀⠀ ⠘⢦⣁⢸⠀⠀⢠⠞⠀⣄⣙⣒⣀⣤⡴⣿⡁⠀⠀⢀⡀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠘⣻⣧⠀⢰⠃⠼⢄⠀⠀ ⠀⠀⠀⠀⠀⢀⡷⠠⠞⠃⠀⠀⠀⠐⠒⠦⢿⡀⠑⠒⠂⠋⠀⠀ ⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢹⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⢾⠟⠉⢷⡀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⢸⡵⢀⣟⣸⣇⡼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠓⠒⠒⠒⠚⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀

⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠈⠈⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡾⠿⠛⠋⠉⠁⠈⠀⠀⠀⠀⢑⣴⡾⠿⠿⠿⣿⣿⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠟⠛⠛⠛⠻⠶⣤⡀⠀⠀⠘⣠⡾⠋⠁⠀⠀⠀⠀⠀⠙⠳⣌⢹⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣄⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠈⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⡿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡘⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⣼⡟⢱⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠉⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⢁⣾⡟⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆⢸⡄⢰⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣡⠀⠘⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⠁⣾⣿⠁⠀⠜⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠃⢸⢳⡀⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡈⠀⠈⠈⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⠁⣸⣿⡇⠀⠀⣷⣼⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠈⢻⣇⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠇⢀⣿⣿⣧⠀⠀⣿⡟⠀⠙⢦⣀⡀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠈⠙⠒⠦⠤⠤⠖⠛⠉⠀⠀⠀⠈⢿⡄⢠⠀⠘⢻⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⣸⣿⣿⣿⠀⠀⣿⠁⠀⠀⠀⠀⠉⠙⠒⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠤⣄⠀⢸⣧⢠⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⣿⣿⣿⣿⡆⠠⡏⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡆⢈⣿⡷⠀⠀⠂⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⣿⣿⣿⣿⣧⡔⣿⠀⠀⠀⠀⠀⠈⠷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⣸⣿⠻⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⣿⣿⣿⣿⣿⣧⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣄⣀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠊⠉⣰⡿⠟⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⣿⣿⣿⣿⢿⠿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠅⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⢿⣿⡿⢗⢈⠀⠹⠟⠻⣷⣄⠀⠀⣀⣀⣀⡀⠀⠀⣠⡤⠶⠒⠒⣒⣒⣚⣛⣛⣒⣒⡶⠛⠉⠉⠙⠛⢶⣤⣤⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠚⣇⠀⢸⣿⠀⣴⡸⠀⠀⠀⣶⣿⡿⠟⠋⠉⠁⠈⠉⣻⣿⡿⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⣩⡿⠆⠀⠀⠀⠀⠀⠙⣷⣾⠀⠀⠃⣾⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⡀⠈⣿⣇⠈⠁⠀⠀⠀⣿⡟⠁⠀⠀⠀⠀⠀⠀⠻⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣇⠀⢿⡍⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠀⠀⠀⠀⠀⠀⢠⣿⢿⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⡄⠸⣷⣄⡁⠀⠀⠀⠛⢿⣤⡀⠀⠀⠀⠀⠀⣻⣿⡟⣛⣷⣤⣤⣤⣤⣤⣤⣤⣤⣼⡷⣤⣀⣀⣀⣤⣾⣿⣥⣤⣤⣿⣏⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣌⣿⠤⠿⠗⠛⠛⠛⠛⠛⠉⠉⠙⠓⠦⠤⠴⠞⠋⠁⠀⠉⠉⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉ ⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠶⠚⠛⢋⣩⣭⠿⠿⣿⣿⣿⣿⣏⣩⣭⣿⣿⡿⠶⠶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠻⢶⣦⣤⣿⣽⣶⣛⠛⠉⠉⠉⠉⠁⠉⢿⣍⣀⣀⣠⣴⡾⠿⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⡻⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⠟⠋⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⡀⠀⣠⠴⠃⣠⣴⣾⣷⣄⠀⠂⣤⣶⣶⣤⡀⠀⢀⣤⣶ ⠀⠀⠀⠀⠈⠙⡇⠈⢦⡀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⡇⠀⢰⣿⣿⣻⣿⣿⣷⣼⣿⣿⣿⣿⣷⠀⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠘⢿⣀⠝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠈⠿⣿⣿⣿⠟⠈⢻⣿⣿⣿⣿⠏⠀⠻⣿⣿ ⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠱⡄⢰⠈⡟⣇⠀⠀⠀⠳⡈⠁⠀⠀⠀⠀⠀⠉ ⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⢱⡿⠀⢣⠸⡄⢀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⣀⠀⠀⡜⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢧⠀⡜⢠⢧⠈⣧⠀⠀⠘⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣸⣉⠳⣼⣱⡥⢧⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⡄⡇⡜⢸⡀⢹⢧⠀⠀⠸⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡴⢻⠋⠙⢄⠘⡆⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣧⢣⠇⠈⡇⠈⡆⠳⡀⠀⢹⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⡇⠀⠀⠈⢧⢹⡄⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⣯⠤⠒⠒⠒⠽⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⢳⠎⠀⠀⡇⠀⢹⠀⠙⢆⠀⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣸⠀⠀⠀⣀⢀⣑⠷⡀⠀⠀⠀⠹⡷⢄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠒⠉⠀⠀⢸⠀⠀⠀⡇⠀⠀⢧⠀⠀⠑⠾⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⣇⡇⠀⢀⠞⡡⠔⠚⠋⠹⣆⠀⠀⠀⠱⡄⠙⠦⣄⠀⠀⠙⣟⡶⠤⣄⣠⡤⠤⠤⣈⠙⠫⣅⢳⠀⠀⠀⠀⠀⢸⠀⠀⢸⠃⡄⠀⠈⢇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⠈⣇⠀⠀⢻⠀⠀⡾⠋⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠙⣄⠀⠀⠙⠢⢴⣉⡷⣟⣽⣿⣿⡯⣭⡉⠛⢯⡁⠸⡆⠀⠀⠀⠀⠘⣆⣀⡎⠀⢷⡀⠀⠘⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢧⠀⠸⡄⠀⢸⡀⠀⠀⠀⠀⠀⠀⠠⠴⣶⡄⠈⠢⡀⠀⠈⢦⠀⠀⠀⠠⢿⣿⠏⠘⠉⠈⢷⣞⢹⣿⣦⡙⣖⡇⠀⠀⠀⠀⠀⣇⡙⡇⠀⢸⠙⣄⠀⠘⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡆⠀⠹⡄⠀⡇⠀⠀⣠⡴⠒⠚⠓⠲⣯⣄⣀⠀⠈⠲⣄⠀⢳⡀⠀⠀⠀⢻⢠⡄⠀⣠⣠⣿⢿⢿⡏⢷⣽⡇⠀⠀⠀⠀⠀⣇⡱⢹⠀⣼⠀⠈⠳⢄⡘⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢱⡀⠀⡟⢦⢳⢤⡼⢏⣾⠟⠛⣿⣶⢿⣿⡀⠀⠀⠀⠀⠙⠲⠽⠀⠀⠀⠘⠈⣿⡽⢻⣿⣾⣿⠈⡇⠘⢉⡇⠀⠀⠀⠀⠀⡇⠀⢸⠀⡇⠀⠀⠀⠀⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠣⠀⡇⠈⠙⢸⣣⡟⡁⠀⠀⣸⣿⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠉⠛⠁⣰⠃⠀⢸⠁⠀⠀⣠⠀⠀⡇⢀⡏⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠚⢻⣼⡅⢰⣤⣾⣿⣳⣿⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢒⣲⡎⠁⠊⠀⡼⠀⠀⡰⡏⠀⠀⣧⡎⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡘⡄⠈⠻⠇⠈⣿⡘⠿⠵⠟⠐⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⡼⢹⠃⠀⠀⡇⢣⡜⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠱⡄⠀⢲⡀⠀⠀⠳⡜⣆⠀⠀⠀⠈⠳⢤⣀⣤⡜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡠⢺⢠⠏⠀⠀⠀⡇⠘⣇⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢆⡀⢷⣄⠀⠀⠘⢮⣆⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⡎⠀⠀⠀⢀⡇⠀⠘⣇⢀⣀⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠺⠈⢳⠢⢄⣀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⢸⡇⢀⠴⠚⠉⠀⠀⠈⢳⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠙⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⡇⠀⠀⠀⠀⢸⠞⠁⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠹⣶⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣇⠀⠀⣴⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡞⠁⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠈⢹⣠⡀⠘⡄⠀⠈⢷⡶⠤⢤⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠔⠚⠉⠀⡼⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⣇⠱⣄⠹⡄⠀⠀⠳⡀⠀⣾⠀⠀⠈⠉⠉⢿⣍⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡀⠈⠲⣹⡄⠀⠀⢳⢰⢻⠀⣀⡀⠀⠀⠀⠉⠳⠤⣀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⠀⠑⠦⡀ ⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⡇⠀⠀⠈⢱⡀⠀⠈⣿⣌⡿⠁⢹⠀⠀⠀⠀⠀⡼⠛⠋⠱⡄⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⢁⡜⠁⠀⠀⠀⠙ ⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⢀⣠⢿⣰⠃⠀⢠⠀⠀⠀⠀⣸⡁⠀⠀⠀⣼⣆⣠⠤⠖⠒⣚⢺⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡤⠚⠉⠉⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠈⣇⠀⠀⢀⡽⠋⠀⠀⠈⢧⠀⢸⠓⠉⠉⣉⡙⠛⠲⠉⢙⠋⠁⡀⠤⠖⠋⠁⣸⠇⠀⠀⠀⠀⠀⠀⠀⢠⠞⡡⠞⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡰⠋⢦⣀⠀⣀⠀⢹⠀⡰⠋⠀⣀⡤⠤⡄⠘⡇⣸⡀⠀⠀⠀⣉⣩⢷⠤⡞⠓⣖⠒⠒⠒⠒⢤⢿⠀⠀⠀⠀⠀⠀⣲⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀ ⣶⣶⣶⣶⣶⣶⣾⣶⣶⣶⣌⡉⠻⡙⠦⣷⠁⠐⠋⠀⠀⠀⠹⡄⢣⢹⠙⠒⠚⢉⡏⠀⡟⠀⢸⡀⠘⢆⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⠳⠧⢤⠃⠀⡠⠖⠋⠉⢳⡀⢰⡜⠘⡄⠀⠀⡜⠀⢀⡇⠀⠈⢇⠀⠈⢧⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀

٩(ˊᗜˋ*)و

⠀⠀⠀⠀⠀⣀⣠⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀ ⠀⠀⢀⣴⠟⠋⠉⠉⠉⠉⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠉⠉⠉⠉⠙⠻⢷⣄⠀⠀ ⠀⣴⡟⠁⢀⣤⡶⠞⠛⠷⢶⣄⠀⣻⣧⣴⠶⠞⠛⠛⠋⠉⠉⠉⠉⠉⠛⠛⠛⠷⢶⣴⣿⡁⣠⣴⠾⠛⠛⠶⣦⣄⠀⠹⣧⠀ ⢰⡟⠀⢠⡿⠁⠀⠀⠀⢀⣠⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣦⣄⠀⠀⠀⠈⢻⣆⠀⢹⣇ ⢸⡇⠀⢸⡇⠀⠀⣠⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⡀⠀⠀⣿⠀⢸⣿ ⠘⣿⡀⠘⣧⣀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣸⡏⠀⣼⡇ ⠀⠘⢷⣄⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣀⣼⠏⠀ ⠀⠀⠀⢹⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⠀⠀ ⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠠⣿⣇⣨⣿⣷⠀⠀⢀⣠⡶⠟⠛⠛⠛⠷⣦⣄⠀⠀⢰⣿⣅⣸⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⡿⠏⠀⣴⡟⠋⠀⠀⠀⠀⠀⠀⠈⠹⣷⡀⠈⠻⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⢀⣀⣤⣤⣤⣄⡀⠀⠀⣾⠋⠀⠀⠀⢰⣶⣶⣶⠀⠀⠀⠈⢿⡄⠀⢀⣠⣤⣤⣤⣀⡀⠀⠀⠀⢀⣿⠀⠀ ⠀⠀⠘⣿⠀⠀⠀⠿⣿⣿⣿⣿⣿⠿⠀⣸⡇⢠⣦⣀⠀⠀⣹⣿⡃⠀⠀⣀⣤⠘⣿⠀⠿⣿⣿⣿⣿⣿⠿⠀⠀⠀⢸⡟⠀⠀ ⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠉⠛⠛⠛⠋⠉⠛⠻⠛⠋⠁⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀ ⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠶⠶⠶⠶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠾⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠷⢶⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⡶⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⢀⡤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢄⠙⣠⠇⠀⠀⣠⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠳⠁⠀⠀⢰⠁⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⣆⢀⣀⠤⠖⠒⢢⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡮⠁⠉⠁⠒⠤⢀⡼⠖⠀⠐⣗⠢⡀⢸⣏⡁⠀⠀⢀⡠⠥⠒⠲⠤⢄ ⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⣀⣈⣍⣈⡿⡘⠁⣹⡚⠁⠀⠀⠀⠀⠀⣼ ⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⣇⣠⡶⣍⣀⣠⠴⠛⠻⢇⣜⡁⠺⠽⠀⠀⠀⢠⡞⠁ ⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢷⡀⠀⠀⢀⡏⠀⠀ ⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡉⢳⡄⣸⠁⠀⠀ ⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠿⢻⡖⠒⠂ ⠈⠉⠸⡍⠈⠀⠀⠘⣶⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣶⡄⠀⠀⠠⢸⠅⣀⠀ ⠀⠀⠔⢷⠈⠀⠀⠀⠘⠛⠁⠀⠀⠀⣤⢤⠀⠀⠀⠀⠸⠿⠁⠀⢀⣠⠟⠀⠀⠀ ⠀⠀⠀⣀⠷⢎⠁⠀⢀⡀⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠈⠒⠀⠀ ⠀⠀⠀⠁⠀⠀⠉⡖⠀⠈⠑⡦⠤⠄⠄⠀⠤⠤⠤⡖⠉⠉⠹⡁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠒⠛⠊⠁⠀⠀⠀⠀⠀⠀⠀⠙⠒⠲⠞⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣄⠀⠀⢀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⡀⢀⣠⣾⡿⠃⠀⢀⠀⣀⠀⡀⠀⠀ ⠀⣠⣐⢣⢎⡕⡣⢖⣠⠈⠛⠿⣿⣿⡿⠟⠋⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠙⠻⠿⠿⠟⠋⢀⠰⡸⣌⠳⣌⠳⣔⢢⡀ ⡴⢱⡘⠮⡜⣌⣓⢣⡌⣏⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⣠⣄⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⡱⢓⡬⠳⣌⠳⡜⢦⡱ ⡇⣇⢹⢱⠾⣀⢇⠷⣸⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣾⡿⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢇⠹⡎⣰⠏⣈⢷⡸⢇⣱ ⢗⠬⣓⠎⣎⠵⣊⠳⢥⣓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣎⠳⣩⠖⡹⣌⠶⣉⠶⡑ ⠈⠳⢬⡙⢦⢛⢬⣹⠦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⢡⢞⡱⢎⡲⣭⠚⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠒⠚⠋⠉⠁⠀⠀⠀⠀⠈⠉⠙⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠒⢛⣻⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠁⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠉⠑⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⡀⠀⠀⢠⠞⠁⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠉⠑⠶⣋⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠳⡀⠀⠀⣀⣀⣀⣀ ⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⣹⠖⠋⠁⠀⠀⠀ ⣶⡶⣦⣄⣀⠀⠈⡆⠀⠀⡜⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠘⣇⣀⡤⠤⠾⠷⠤⠤⢄⣀⠀⠀ ⢿⣏⣿⣯⠉⣦⣀⡇⠀⠀⡇⠀⠀⠀⠀⠸⠋⠉⠁⠀⠈⠉⠽⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠛⠛⠛⠻⠿⠷⠀⢀⣤⠖⣿⣿⣿⣶⣤⣛⣉⣻⣀⣤⣌⠳⡄ ⠀⠙⠿⠤⣾⣿⣽⣷⣄⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⠒⠒⠒⠒⠒⠒⠒⢲⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠞⠉⣿⡇⠿⠛⠿⠏⠁⠉⠁⠀⢿⣿⣾⠇⠸ ⢤⣀⣀⣠⠽⠿⣿⣥⣹⡳⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢲⡄ ⠀⠀⠀⠀⠀⠀⠈⠙⢿⣧⣼⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠄⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢀⣰⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣤⠞⣱ ⠀⠀⠀⠀⠀⠀⠀⢀⠄⢚⡿⣧⡈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢣⡿⠋⠀⠈⢧⠀⠀⠀⠀⠀⠀⣠⣾⣿⣻⡆⢁⡼⠛ ⠀⠀⠀⠀⠀⠐⣁⡤⠞⠋⠀⠁⠛⢿⣾⣿⡭⠟⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠾⢿⣏⣳⢀⡤⠋⠀⠀⠀⠀⠀⠀⠙⠿⠿⣿⣷⠟⠁⠀ ⠒⠒⠒⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⢹⡙⠗⠀⠀⠀⠉⠷⢤⣓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠻⣦⣿⣥⣤⣤⣤⣀⠀⠀⠀⢀⣀⣤⣾⠛⠃⠀⠀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⡄⠀⠉⠉⠉⠛⠒⠒⠒⠒⠂⠠⠤⠤⠤⠀⠒⠚⠁⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠁⠉⠉⠉⠉⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣔⠢⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠞⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡤⠴⠒⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡇⠀⢀⣀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀ ⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠉⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⣡⣾⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣷⣌⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀ ⠀⠘⣿⣿⣿⣿⣿⣿⡿⠁⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⡄⠀⠙⢿⣿⣿⣿⣿⣿⣿⠃⠀ ⠀⠀⠸⣿⣿⣿⣿⠟⠀⠀⠀⣿⣿⠀⠀⠀⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣦⠀⠀⠀⢻⣷⠀⠀⠸⠿⣿⣿⣿⣿⠏⠀⠀ ⠀⠀⠀⢘⣿⡿⠋⠀⠀⠀⠀⢿⣿⠀⠀⠀⢿⣿⣿⡇⠀⢠⣤⣀⣀⣤⣄⠀⠸⣿⣿⣿⠂⠀⠀⣾⡟⠀⠀⠀⠀⠹⣿⣿⣃⠀⠀⠀ ⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⣸⣿⣧⣀⣶⣿⣿⡏⠀⠀⠘⠻⠛⠛⠟⠋⠀⠀⠉⣿⣿⣿⣄⣼⣿⣇⠀⠀⠀⠀⠀⠈⠙⢿⣷⣄⠀ ⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣯⣛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠿⣿⡆ ⢸⣿⡀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣿⡇ ⠈⢿⣷⣄⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣠⣾⡿⠁ ⠀⠀⠈⠙⠛⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠛⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣼⠟⠉⠙⠻⠶⣤⣤⣤⣤⡤⠤⢤⣄⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠁⠀⠉⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡾⠉⠙⣧⣀⠀⠀⠀⠀⠀⢀⡴⠁⢀⢤⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⠃⠀⠀⢸⠛⠛⠛⠛⠛⠛⣿⡁⠐⢸⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⢀⡿⠧⢤⣄⣀⠀⠀⡘⣷⣤⡉⠀⠀⠛⠢⠴⠀⠀⢰⡳⠀⠀⠀⠀⠈⠙⠷⢤⣄⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⡏⠀⠀⣼⠃⣆⠀⠈⠉⠻⡟⠉⠉⢻⣿⡷⠦⣄⣀⠀⠀⠀⣔⠒⠢⢰⡆⠀⠀⠀⠀⠀⠀⠉⠙⢷⡆⠀ ⠀⠀⢀⣴⡧⢄⣰⠇⠀⢻⠀⠀⠀⠀⠙⢦⡀⢈⡏⠀⡠⠂⠈⠉⢳⡶⠖⠴⣶⡟⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀ ⠀⢠⣿⠁⠀⣧⢹⠀⠀⣾⠀⠀⠀⠀⠀⠀⠙⠾⣧⣘⠧⠖⠂⠀⠘⡁⠠⢤⠈⡟⠀⠈⠛⠷⣦⣤⣀⣀⣀⣴⠿⢷ ⣴⠟⠹⣄⣰⣋⡞⢳⡀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠤⠴⡽⠶⠯⣴⣿⣀⠀⠀⠀⠀⣈⣽⠟⠋⠀⠀⣾ ⣯⠀⣠⣾⠙⡇⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣴⡾⠋⠀⠀⠀⠀⢰⡏ ⠙⠉⠉⢹⣆⢻⡀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠸⡉⣍⠙⠓⠒⠲⠤⢤⣄⣀⡀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⣼⠀ ⠀⠀⠀⠀⠙⠿⣧⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢷⡸⡆⠀⠀⠀⠀⠀⠀⠈⠹⡄⠀⠀⠀⠀⢰⡟⠛⠓⠲⠶⣴⡇⠀ ⠀⠀⠀⠀⠀⠀⠘⢷⣄⣠⡿⠙⠛⠛⠒⠶⠶⠾⣷⡹⡄⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠙⢦⡀⠀⠀⠘⢷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡹⣄⠀⠀⠀⠀⠀⠀⠀⠘⣿⠛⠛⠻⠶⠾⠻⣦⣄⠀⠘⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣜⢦⡀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠉⠻⠶⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣙⠦⣄⣀⠀⠀⠀⠀⠘⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⣮⣭⣍⣛⣒⣒⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⢀⣀⣠⣀⠀⠀⠀⠀ ⠀⠀⠀⣴⠟⠛⠛⠶⣤⣤⡴⠶⢶⣿⣟⣿⣻⣿⡋⠉⠁⠹⣇⠀⠀⠀ ⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣾⣿⣿⡿⣿⣷⣶⣶⣿⡄⠀⠀ ⠀⠀⠀⣿⡖⠀⠀⠀⠀⠀⠀⠀⠘⠿⠷⠿⢿⣽⣷⣿⣿⣯⢿⡟⠀⠀ ⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣿⣽⣾⢿⡅⠀⠀ ⠀⠀⣾⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣨⣧⣀⡀ ⠘⠛⢻⡛⠃⣰⡏⠙⠉⠛⣦⠀⠀⠀⠀⢠⡞⠋⠙⠉⣷⢈⣡⣇⡀⠀ ⠀⠰⠾⣿⣳⡋⠀⠀⠀⠀⡿⠀⣞⣿⠆⢸⡄⠀⠀⠀⠈⢷⣽⠋⠉⠀ ⠀⠀⢠⡼⣷⣿⣷⠂⣠⡾⠁⠠⡀⣀⣀⡠⠿⣤⣴⣿⠟⢘⡏⠳⠀⠀ ⠀⠀⠀⠀⠙⠻⠷⠛⠛⠶⠶⠶⣤⣤⣤⠶⠶⠾⠛⠲⠖⠋⠀⠀⠀⠀

⣿⣻⣟⣿⣻⣟⣿⣻⢟⣿⣻⣟⣿⣻⣟⣿⢻⣟⡿⣽⣻⣟⡿⠛⠉⡀⡤⢴⡰⣒⢖⡲⣚⠴⡳⣜⢲⡒⢦⠤⣤⣀⠄⠉⢉⠛⠿⢿⣻⡿⣿⢿⡀⠈⢧⢫⡜⣣⠝⣮⢱⢫⡜⣣⠝⣮⢱⢫⡜⣣⠝⣮⢱⢫⡜⣣⠝⣮⢱⢫⡜⡥⠀⢹⣿⢿⣻⡿⣟⣿⢿⣻⡿⣟⣿⢿⣻⡿⣟⣿ ⣷⣻⣞⣷⣻⣞⡷⣯⣟⣾⣳⣟⣾⣳⣟⣾⣻⢾⡽⣷⣻⠞⠁⣠⠖⡽⣘⢧⠳⣍⢮⡱⣍⢞⡱⢎⢧⡙⣎⠳⢦⡙⣎⡛⢦⢤⣂⡀⠉⡙⠿⣻⣧⠐⠨⡳⡜⣥⢛⡴⣋⠶⣙⢦⡛⡴⣋⠶⣙⢦⡛⡴⣋⠶⣙⢦⡛⡴⣋⠶⣙⠶⠈⢘⣿⣟⣯⣿⣻⣽⣟⣯⣿⣻⣽⣟⣯⣿⣻⣽ ⣿⣳⣟⣾⣳⢯⣟⣷⣻⣞⣷⣻⣞⣷⣻⢾⣽⣟⣿⣳⠏⠀⡴⢣⡛⡴⣋⢎⡳⡜⢦⠳⡜⢮⡱⣋⠶⡹⣌⡛⢦⡛⡴⢭⡓⣎⠶⣩⠳⣤⡀⠄⠙⢣⠀⠱⣙⢦⣋⠶⣩⢞⡱⢎⡵⢣⡝⢮⡱⢎⡵⢣⡝⢮⡱⢎⡵⢣⡝⢮⡑⢎⡐⠀⣿⣾⢯⣷⢿⣽⠠⢸⣷⢿⣽⡾⣯⣷⢿⣽ ⣷⣻⣞⣧⠟⠛⠾⢳⣟⣾⣳⣟⣾⣳⢯⣿⣳⣯⣿⡍⠠⢸⡱⢣⡝⡲⣍⢮⡱⣙⢎⡳⣙⢦⠳⣍⢞⡱⢎⡝⣲⠹⣜⢣⡝⣬⠳⣥⢛⡴⣩⢓⡦⣀⠌⠀⠌⠶⣩⢞⡱⢎⡵⢫⡜⣣⠞⣥⢛⡼⣘⢧⡚⣥⢛⡼⣘⢧⡚⢥⠚⡬⠐⠈⣿⣽⠏⠛⢋⠗⡠⢹⣾⢿⣳⠿⣯⣟⣯⣿ ⣯⢷⡛⠀⣀⢦⣄⠠⠘⣷⣻⣞⡷⣯⣟⣷⢿⣳⣯⠇⠀⡧⣝⢣⢞⡱⢎⠶⡹⡜⢮⡱⣍⢎⡳⡜⢮⡱⢫⡜⣥⢛⡬⢳⡜⢦⡛⡴⣋⠶⣡⢏⠶⣩⠖⣥⠂⡀⠳⢎⡵⢫⡜⣣⠞⣥⢛⡴⣋⠶⣩⢖⡹⢆⡏⠶⣉⠦⣙⢢⡙⠴⠁⡘⣿⣽⣶⣿⣤⠆⢡⣂⠌⡙⢃⣐⣾⢿⣽⣾ ⣯⣟⡁⠄⢏⠶⣌⠃⠠⠈⢁⠉⠉⠁⡉⠘⠛⠋⠿⠇⢀⠳⣎⠳⣎⠵⣋⢞⡱⣙⢦⠳⣬⢣⢳⡙⡦⣝⢣⠞⡴⢫⡜⣣⠞⣥⢛⡴⣍⢞⡱⢎⡳⢥⡛⡴⣋⢦⡀⠌⠚⡵⢪⡕⣫⠖⣭⠲⡍⠞⡱⠎⠑⠣⠘⠱⢈⠒⠡⠢⠙⠌⡐⠸⢿⣽⣾⣳⣿⣈⣴⡿⡿⠐⣂⠌⡙⠿⢓⠻ ⣷⣫⢷⣤⣀⣂⡀⠌⠠⢁⠂⠌⠠⠁⠄⡁⠂⠌⠠⠐⠠⠘⣬⠳⣬⠳⣍⢮⡱⣍⢎⡳⢬⢣⢧⡙⢶⡩⢎⡽⣘⢧⡚⣥⢛⡴⣋⠶⣩⢎⡵⢫⡜⣣⢝⡲⡍⢦⡉⢦⠐⠈⠳⠘⠁⡉⢀⡐⣀⣂⠤⡤⢥⠦⡥⢦⠤⢦⠥⣆⢥⡰⣀⣂⠄⡀⠉⡙⠾⣟⣯⡿⣷⣳⣾⠿⡐⠌⡂⢾ ⡷⢯⣻⢞⡽⡽⣇⠈⡐⠠⠈⠄⣁⠊⡐⠠⠁⡌⠄⡁⢂⠁⡀⠻⣔⢫⡜⢦⠳⣬⢣⡝⣎⠳⣎⡝⢦⡝⣎⠶⣩⢖⡹⢆⡏⢶⡩⢞⡱⢎⣜⢣⢞⡱⢎⡱⡘⠆⠉⠄⡁⣌⠴⣘⠶⣩⢧⡹⡜⣬⢳⡙⣎⢳⡙⢮⡙⣎⠳⡜⢦⢳⡱⢎⡽⣱⠲⣤⣀⠀⡉⠻⢿⣽⡾⣷⣴⣷⣌⣼ ⣟⣯⡽⣏⡿⣝⡧⠀⠄⠡⠘⠠⢀⠂⠄⡁⠆⡐⢀⠒⡀⠂⠄⡁⠘⢧⡚⣥⢛⡴⢣⠞⣬⠳⡜⣜⢣⠞⣬⢳⡱⢎⡵⢫⡜⣣⠝⣮⢱⢫⡜⡣⢎⠑⠊⡀⣐⣠⢓⠮⡕⣎⠳⣍⢞⡱⢎⡵⣙⢦⢣⡝⣬⢣⡝⣲⠹⣌⠻⣜⢣⢧⡙⣎⠶⣡⡛⡴⣩⢓⠦⣄⠂⠙⢿⣯⣷⢿⣽⣻ ⡿⣼⣳⢯⡽⡾⣽⠀⠌⠠⠑⠠⠁⠌⡐⢀⢂⠐⠄⠂⠄⡑⠠⡀⠡⠀⠙⠦⣫⢜⣣⢛⡴⢫⡜⣎⢧⡛⡴⢣⡝⢮⡜⣣⠚⠁⡈⢀⠉⠢⠑⢁⠠⣈⡴⢪⡕⢮⡙⢮⡱⢎⡽⣘⢮⡱⣋⠶⣩⢎⡳⡜⢦⠳⡜⣥⢛⡬⣓⢎⡳⢎⡵⣊⠷⣡⢛⡴⢣⢏⡞⣬⠳⣄⠂⠙⢾⣟⣯⣿ ⣿⣱⣟⡾⣽⢽⣳⠄⡈⠄⡑⠈⠤⢁⠐⠂⠄⡨⢀⠉⡐⠠⠁⠄⡡⢈⠐⠠⢀⠙⠦⢫⡜⣣⠞⡜⢦⡹⣜⢣⢞⡱⢎⠁⢠⢒⠩⡌⢆⡁⠌⢰⣋⠶⣩⠳⣜⢣⡝⣲⡙⣎⠶⣩⢖⡱⣍⢞⡱⢎⡵⣙⢎⣳⣽⣦⣿⣶⣿⣾⣿⣿⣿⣿⣿⣿⣷⣾⣷⣮⣜⢦⡛⣬⠳⣄⠂⠹⣿⢾ ⣷⣻⢾⡽⣏⡾⣽⠆⢀⠂⠄⡁⠢⢀⠊⡐⢈⠐⠠⠈⠄⠡⡈⢐⠀⡂⠌⡐⢀⠂⠄⠂⢉⠐⠛⠜⢣⠳⠬⣓⢮⠱⡃⠈⠴⡉⢂⠁⣊⠰⢀⠂⡝⢮⡱⢫⡜⣣⠞⣥⢛⡬⢳⡱⢎⡵⣊⣮⣵⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢀⢈⣿⣿⣷⣯⣖⡹⣌⢧⡀⠘⣿ ⡿⣽⢯⣿⣹⡽⣞⣇⠠⠐⠈⠄⡁⢂⡐⠄⡈⠤⢁⠡⠈⠔⠠⢁⠂⡐⠐⡀⠆⡈⠄⡁⠂⠌⠠⠈⢄⡐⣠⢀⠈⠡⢀⠁⢂⠐⡠⠒⡠⢘⠠⢀⢸⢣⡝⣣⠞⣥⢛⡴⢫⡜⣣⣽⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠠⣈⣴⣿⣿⣿⣿⣿⣿⣷⡜⣦⢳⠀⡘ ⣿⣹⢻⡶⣻⣼⢳⣏⠀⠄⡁⠂⠐⠠⠐⣀⠂⠔⡀⢂⠡⢈⡐⠀⠆⡈⡐⠀⠆⡐⠐⡈⠐⡈⠄⣩⠒⢬⡐⢎⠀⠡⠌⡘⠠⠐⡀⠑⡀⠃⡀⢢⢏⠶⣙⢦⡛⡴⢫⣜⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣬⣶⣿⣿⣿⣿⣿⡿⢟⡛⡛⢿⣶⡍⢧⠀ ⡷⣭⢷⡻⣵⣫⢟⣮⢇⠀⡐⠈⠠⠁⢂⠀⠌⠐⡀⢂⠐⠠⢀⠁⢂⠐⠠⠁⠂⠄⢁⠠⠁⠠⠀⢥⠚⡰⢈⠠⢈⡐⠈⠄⣁⢢⡑⠦⣤⠱⣜⢣⢎⡳⣍⠶⣹⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠄⠛⠋⠛⠙⠋⠛⠙⢋⢖⣷⣾⣿⢆⢺⣿⡸⠀ ⢿⡜⣧⢟⣧⢟⣯⢞⣯⢆⠀⠌⠐⡀⠂⢈⠀⠂⠄⠠⠈⠄⠂⢈⠠⠀⠡⢀⠁⠂⠄⠂⠌⠠⠁⠂⡝⠰⡁⢢⠡⠄⠃⡐⡌⢦⣙⠳⣌⠗⣎⢧⣋⠶⣩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣥⣬⣴⣤⣥⣦⣴⣤⣥⣮⣘⠫⣍⣱⣮⣿⣿⣇⠃ ⣟⡼⣫⣞⢮⡟⣮⠿⣼⢯⡷⣬⣀⠄⠁⢂⠈⡐⠈⡀⠂⠄⡁⠂⠠⢁⠂⠄⡈⠔⡈⢐⠈⠄⡁⢂⠈⢡⠐⡁⠆⣉⠐⢠⡙⢦⣍⠳⣎⠽⣘⢦⣹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⣉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠺⣵⢳⡝⣮⣽⣳⢿⡽⣯⣟⢷⣫⢟⡷⣶⣲⣤⡥⠄⡁⢂⣠⡅⢉⠻⣦⡔⢀⠂⡐⠂⠌⡐⢀⠂⠌⡀⠌⢀⠃⠠⢐⢢⡙⠶⣌⠗⣎⠳⣍⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠒⢋⣁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁ ⠀⠌⢻⡼⣳⢯⣟⣯⣟⡷⣯⣻⢼⣛⡾⣵⠳⠉⢀⣰⡴⣯⢷⡀⢂⢐⣯⣞⡆⠐⠠⢁⠂⡐⢈⠐⣴⣴⣬⣀⡂⠁⣎⠶⣩⡓⢮⡹⣌⢻⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⡁⢈⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠀ ⠐⡀⠂⠹⢧⡻⣜⣳⢯⡟⣧⢯⣛⡮⠗⠁⢠⡼⣞⣧⢟⣞⡧⣟⣞⡻⡶⡽⣆⠡⠈⠄⢂⠁⢂⣼⣿⣿⣿⣿⡇⠀⣏⠞⣥⢛⢦⡓⣎⣿⣿⠿⠛⠋⠉⢁⠀⠠⢀⡐⠈⡐⣸⣿⣿⣿⣿⣿⣿⡿⠟⠉⢀⠄⡊⠔⣁⢊⠘⠠⠁⢉⠈⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡧⠀ ⠐⠠⢁⠂⠩⣗⢯⡞⣧⠿⣭⢷⠋⠁⠄⢼⡏⢁⠡⠀⠌⡾⣝⡾⣭⢷⡻⣕⠫⠿⢀⠘⠠⠈⣴⣿⣿⣿⣿⣿⡇⠀⣏⠞⡴⣋⠶⡹⣼⣿⡀⢠⣐⣨⣴⣶⣾⣿⠟⠀⣐⣴⣿⣿⣿⣿⣿⣿⡟⠁⢠⠊⠔⣨⢐⡡⢂⠂⠌⣴⣿⣿⣿⣿⣿⣦⣄⠈⠻⣿⣿⣿⣿⣿⣿⣿⣟⣾⠁⡀ ⠐⠠⢈⠐⡀⠹⣎⢷⡹⢶⡹⠎⠐⠠⠐⡈⢷⣬⣀⣢⢴⡳⣏⡷⡽⢮⢗⣻⠦⠀⠌⡐⢀⠂⣿⣿⣿⣿⣿⣿⡇⠠⣙⠶⣡⠻⣔⡣⣿⣿⣷⣾⣿⣿⣿⣿⡿⠋⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⡈⠐⠠⠉⢈⠃⠎⠠⣰⣿⣿⣿⣿⣿⣿⣿⣿⣆⠠⠹⣿⣿⣿⣿⣿⢿⣽⠏⠀⣡ ⢈⠐⠠⠂⠄⡁⢹⣎⡟⡧⠁⡐⠈⠄⠡⠐⠠⠙⠽⢣⡿⡹⠝⠚⠽⣳⠆⡈⠐⡈⠐⡀⠆⣼⣿⣿⣿⣿⣿⣿⡇⢀⠹⣎⠵⣋⠶⡱⣿⣿⣿⣿⡿⠿⢿⠟⠀⢄⣵⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠠⣤⣷⣿⣷⣦⡌⠠⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠘⢿⣿⣿⢯⣿⠏⠀⣰⣿ ⠠⠈⢄⠁⡂⠐⡈⢾⠉⢀⠐⠠⢁⠊⠄⡑⢂⠁⠂⠄⡐⠠⢈⠐⠄⣀⠂⠄⢡⠀⢃⠐⣠⣿⣿⣿⣿⣿⣿⣿⠁⡀⠂⡝⢮⡱⢫⡕⣿⣿⡟⣡⣼⣷⣌⠦⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢠⣿⣿⣿⣿⣿⣿⣿⣆⠐⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⢿⣯⡿⠁⢠⣼⡿⣽ ⠠⢁⠂⡐⢈⠐⠠⢈⠐⠠⠈⠔⠠⢈⠐⡀⠂⠌⡁⠂⠄⡁⠂⠌⡐⢠⣈⣴⣤⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣰⡁⠈⢧⡙⢧⡚⡼⣿⡇⠼⣿⡿⢟⡰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠘⠉⡀⠤⣿⣯⢿⣻ ⠐⡀⢂⠁⠂⠌⡐⠠⠈⠄⠃⠌⡐⠠⠁⠤⠑⡀⢂⣉⣰⣤⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣷⡈⠀⢏⢧⡙⣖⢻⣿⣧⣶⣼⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠈⠰⢤⡐⠈⠙⢿⣿ ⠐⡀⢂⠡⠌⡐⢀⠂⠡⠈⠔⠂⠄⠡⣈⣤⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⣿⣿⣿⣿⣿⣿⣄⠈⠒⡹⢌⠧⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡘⢦⡘⡱⣈⠀⡙ ⠐⡀⠢⠐⠠⠐⠠⢈⠐⠡⢈⠐⣬⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⡴⠊⣠⣿⣿⣿⣿⣿⣿⣿⣷⣀⠄⠉⢎⡱⡘⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣄⠠⠀⠧⡱⢌⡳⡄ ⠐⠠⠁⠌⠠⢁⠂⡐⢈⡐⢀⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣢⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⡀⠄⠙⠢⢍⠳⢿⡾⣽⣯⢿⣽⣻⣽⢿⣽⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢈⠄⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣄⠠⠑⣏⠶⣙ ⠀⠂⡁⠄⠡⢀⠂⡐⠠⠐⡀⣿⣿⣿⠿⠿⠛⠛⠉⠉⡀⠄⢀⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣿⣿⣿⣿⣿⣷⡦⢁⠠⠉⠐⡈⠙⠚⠿⠯⠿⠽⠻⠞⠃⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⢀⢸⣧⠀⠹⣿⣿⣿⣿⣿⣿⣿⣷⡿⣽⣻⣧⡀⠌⢳⡍ ⠀⡁⠠⠐⡀⢂⠐⠠⢁⠒⢰⣿⣋⢀⣄⣢⡔⠈⠠⠁⠄⡈⠄⠠⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢐⣾⣿⣿⣿⠿⠋⢁⢀⣂⠴⣈⠖⡤⢡⠆⡤⣀⢄⡐⣠⢠⡁⠄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⢻⡿⣷⡄⠘⠻⣿⣿⣿⣿⣿⣿⣽⡿⣽⣻⣷⠀⠂⢹ ⠀⠄⡁⠐⠠⠀⠌⡐⠠⢈⢸⣿⣿⣿⣿⣧⣠⣬⠀⡁⠂⠄⡈⠄⠡⠐⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⢁⣰⣾⣿⠟⠋⠀⢄⡰⢦⢫⡜⣳⣬⡾⣴⣧⡞⡰⢡⠎⡴⢡⠆⡥⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣀⠐⢨⣿⢯⣿⣦⣥⣿⢿⣿⣿⣿⣿⣿⣽⣟⣷⢿⡇⠈⡀ ⢶⡲⣖⣻⠀⢁⠂⠤⢁⠂⠸⣿⣿⣿⣿⣿⣿⣿⣷⣤⠁⠂⠄⡈⠐⡈⠐⣸⣿⣿⣿⣿⣇⣀⠉⠉⠉⣀⣀⣤⣶⣿⣿⠟⠁⢠⡌⡞⣥⢛⡬⢳⡜⣭⢣⣓⡶⣴⣢⣑⢣⠚⡔⢣⠚⡴⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⠀⢢⣿⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣟⣇⠠⢀ ⡷⣹⢎⡷⡌⠀⠌⡐⠠⢈⠐⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣔⣀⡡⣀⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠌⡳⣜⡱⢎⡳⣜⣧⡾⡞⢿⡹⡹⢥⣋⠗⣮⠱⣌⢣⡙⠄⡐⠸⣯⣿⣿⣿⣿⣿⣿⣿⣻⡾⡿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠰ ⡽⣣⢟⣼⢣⠈⠐⠠⢁⠂⠌⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠠⠑⢮⡱⣋⠖⣏⢧⠳⠙⢂⠁⠡⠁⡈⠙⢦⢛⡬⢣⠍⢀⣔⢀⣿⣿⣿⣿⣿⣿⣿⣟⣷⢿⣇⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠑ ⣽⢣⡟⣼⢫⡆⠁⢂⡐⢈⠐⠠⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠫⢭⡉⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠠⠑⠭⠚⡈⠄⣐⣬⣶⣾⣿⣿⣿⣦⠀⠙⡜⠁⣠⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢢ ⡞⣧⢻⡵⣫⢞⡄⠂⡐⠠⢈⠄⠡⠙⣿⣿⣿⣿⣿⣿⠟⡡⢎⡙⢦⡙⢆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⠷⠆⢀⣡⣴⣿⣿⣿⣿⣿⣿⣿⣿⣯⡇⠐⢀⣶⡉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⠈⣼ ⡽⣎⡷⣹⡷⣯⢞⣄⠠⠁⠂⠌⠠⠁⠌⢻⣿⣿⣿⡏⡜⡱⢊⡜⢢⣙⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣽⣻⠿⠍⢁⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡇⠀⣿⣿⠨⣽⡣⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⣿ ⣿⣽⣻⣽⣻⢧⡻⣜⣣⡄⠡⠈⠄⠡⠈⠄⡘⠻⣿⣿⣶⣥⣯⣼⡿⠿⠛⠛⠋⠉⠉⢁⠠⢀⠠⠀⠄⠉⢈⠉⠙⠛⠺⠋⢁⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡳⢀⣸⣿⡟⣡⣿⢡⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣼⣻ ⣞⡳⢟⡾⣽⢣⡟⣼⣓⡞⣦⣁⠐⠠⢁⠠⢀⠐⠀⠙⠻⠛⠉⢁⠠⠐⡈⠐⡈⠄⡁⢂⠐⡀⢂⠡⢈⠐⠠⢈⠐⠠⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⡾⠁⣰⣿⡿⠱⣼⡏⢦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣰⣯⣟ ⢮⠽⣹⠼⣥⢻⣜⡳⣼⢹⡲⢭⣛⠶⣤⣀⡂⠈⠄⠡⠐⠠⢁⠂⠄⠡⠠⢁⠰⠐⡈⠄⢂⠰⢀⠂⠂⠌⢁⠠⠈⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⡟⠋⢀⣴⡿⢏⣒⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⣺⡽⣾⣹ ⣏⠆⠀⠄⡀⠄⠀⡁⠁⢃⠛⠵⣋⠾⡥⠃⠁⠌⠠⠁⠌⡐⠠⠈⠄⢃⠐⠂⠄⠡⠐⡈⠄⠂⠤⠈⡁⢈⠠⢀⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠞⠋⢁⢠⣴⣾⢿⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣼⡳⣟⡵⣯

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⠀⠀⠀⠀⠀⠀⢠⣴⡟⠁⡀⠆⡐⢈⠌⡐⠠⢈⠂⣁⠂⡐⡇⠀⣿⣿⡇⠀⠀⠀⠘⠻⠶⠿⠋⠀⠀⢐⣿⣿⠃⡐⠀⢂⠡⢈⠐⠈⠶⣯⣴⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⡐⢈⠀⠌⠐⡀⠄⠡⠌⣿⣧⠀⠀⢰⠰⠀⠀⠙⣿⣿⣿⡟⠁⠀⠀⠀⠀⠉⠿⣦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡿⠋⢀⠂⡐⠠⢁⠢⠐⠠⢁⠂⡡⢀⠒⡀⠅⢂⢸⡿⣿⣄⠀⢀⣠⡄⠀⠀⠀⠀⠀⣸⡿⢆⠡⠠⢁⢂⡐⠠⣸⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠙⢿⣶⡌⢀⠂⠄⡐⢀⠂⢼⣿⠄⠀⠸⠀⠀⠀⣼⣿⣿⠟⣦⡀⠀⠀⠀⠀⠀⠀⠈⠛⠷⢦⣀⡀⠀⠀ ⠀⠀⠀⢀⣴⠟⠀⡀⢂⠐⠠⢁⠂⡰⢉⠐⠂⠌⡐⠠⢂⠐⡈⠄⡀⠡⢈⣿⣿⣿⣿⣄⡀⠀⣀⣠⣾⡿⢃⠌⡀⠂⠄⣀⣤⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠉⢿⣦⠈⠠⠐⠠⠀⠌⣿⡇⠀⢀⠀⣄⣼⣿⣿⠏⠀⠈⠙⢷⣤⣤⡀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦ ⠀⠀⣠⣿⠋⠀⢂⠁⢂⠌⡐⠠⠘⡀⠆⡘⠠⠁⡄⠃⢄⢂⠐⠠⠐⢠⣶⣿⣿⣿⣿⢿⣿⣿⠿⠛⡍⢀⠃⡐⠢⢁⣼⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠻⣧⡑⠈⠤⢁⠀⣿⡇⠀⠚⢀⣿⣿⣿⠋⠀⠀⠀⠀⠀⠈⠉⠙⠣⠄⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⠃⢀⠐⠠⠌⢂⠐⠠⡁⢁⠢⠐⠠⢁⠂⠄⡁⠢⠀⠌⢠⣸⣾⢿⣿⡿⢹⣇⠢⡌⠐⡀⢃⠰⢀⠐⡀⢂⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⢹⣧⠁⡀⠂⠀⣿⡇⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀ ⢠⡟⠁⡀⠂⠌⠒⡈⠄⡘⠠⠠⢁⠂⠡⢁⠂⠌⡐⠠⠑⠨⣰⡷⠿⣧⣿⠏⠀⣿⠇⠰⠤⢁⠠⢀⠆⠈⠐⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⡆⠄⠁⠠⣿⡇⢠⣿⣳⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⣀⠀⠀ ⡿⠁⠠⠁⡌⠠⠁⠄⢂⠐⠠⢁⠂⠌⡐⠠⢈⠐⠠⠁⣌⣳⣷⣾⣿⣿⢋⣀⠀⣿⠀⢂⠐⠠⠀⠌⢂⠁⢲⡿⠁⠀⠀⣴⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠹⣱⣿⣧⣿⣳⡟⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀ ⡗⠀⡀⢣⠠⢁⠘⡀⠂⠌⢀⠂⠌⡐⠠⢁⠂⡉⢄⣣⣶⣿⣯⣾⠟⠁⠀⠀⠀⣿⠌⠠⠌⠠⢁⠂⡄⣸⣿⠁⠀⢀⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣿⣿⣿⣽⠏⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠰⠁⡀⠄⠂⠄⡈⠄⡁⠂⠄⡈⠐⡄⢁⠂⢄⢳⣼⣿⣿⣿⠟⠁⠀⠀⢀⠀⣀⣿⡇⠐⡈⠐⢢⠀⠼⣿⠇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⢀⣼⣿⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⢁⠐⠌⡐⠠⢈⡐⠠⢁⠂⠄⢁⠐⢤⣸⣾⣿⣻⣿⠟⢁⡀⠀⠀⠀⠀⠀⠀⣿⣷⠀⢀⠁⠂⠌⣸⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢞⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣁⣼⣿⢫⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⡄⢈⡐⠠⠁⠆⠠⠁⠀⡈⢔⣢⣾⣮⣻⣷⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠌⡐⠃⣽⡇⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠽⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣿⣿⣣⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⣷⣦⡐⠠⠁⠌⡐⢌⣂⣱⣿⣿⡿⠟⠉⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡈⠐⠠⠀⣿⡇⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣿⣟⣩⣿⣻⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠛⠿⠿⠿⠿⠿⠟⠛⠋⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠁⢢⠁⢻⡇⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠁⠀⠀⠈⠙⠻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠠⠹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢄⠡⠀⠀⠀⠀⠻⣷⣀⠁⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣦⣤⡀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄ ⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠿⡿⡟⠛⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠏⠉⠳⣌⠙⠲⢄⡀⠀⠀⠀⠀⢀⣀⡤⠞⢡⠷⠊⢹⡀⠀⠀⠀⠀⣠⠴⠚⢉⡴⠋⠉⡇⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠈⠳⣄⠀⢉⣶⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠑⠲⢴⡋⠁⢀⡴⠋⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⣸⠗⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡄⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⣇⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢳⡀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⡄⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠇⠀⠀⢠⣤⣴⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣶⣤⡄⠀⢘⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⠏⠀⠀⠀⠀⠁⠀⠀⠀⠈⠙⠃⠀⠀⢤⣤⠄⠀⠀⠋⠉⠀⠀⠀⠀⠁⠀⢸⠀⠘⢦⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⣠⣧⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣷⠖⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣸⠀⠁⢻⣀⣀⣀⣀⣀⡀⠀⠀⠐⠃⠀⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⠶⣄⠰⣾⣍⣉⣓⣲⡤⢭⣿⣿⣦⣤⣾⣦⡀⢀⣀⣈⣉⣩⣿⠖⢀⡴⠋⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⢺⣷⣄⠀⠈⠉⠉⠉⢹⠏⣉⢻⠉⠉⠉⠉⠀⣀⣴⣿⠚⠉⠀⠀⢠⡟⠉⠈⠉⠲⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⠉⠀⠛⢳⡀⠀⠀⢀⣸⠀⣿⢹⣀⣀⡀⠀⡼⠛⠂⠈⢳⡀⠀⠀⠀⠳⣄⠀⠈⠢⡈⢣⡀⠀ ⠀⠀⠀⠀⠀⠀⣇⠀⠀⠠⢼⣧⠀⠀⣽⣙⣀⣙⣋⣀⣀⣉⣽⡷⠤⠀⠀⢨⠇⠀⠀⠀⠀⠈⢣⡀⠀⠱⡄⢣⠀ ⠀⠀⠀⠀⠀⠀⠘⢶⣤⣤⡟⠙⠀⠀⡇⠀⠀⠉⠀⠀⠀⠀⠀⠙⡦⣤⣴⠋⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠁⠘⡄ ⠀⠀⠀⠀⠀⠀⠀⡟⠀⡇⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⣠⣶⣿⣷⣤⣇⢱⠸⠀⠀⢸⠈⠻⠿⠃⠀⣾⡄⠀⢸⢸⣣⣾⣷⡶⣄⠀⠀⠀⠀⠀⡸⠀⠀⠀⣸⠀ ⠀⠀⠀⢰⣿⣾⣿⣿⡟⢿⢼⠀⡇⠀⢸⣠⢿⠏⠁⠐⢙⡻⠃⡟⣸⠋⣿⣿⣿⣿⡇⠀⢀⣠⠞⠁⠀⠀⣰⠃⠀ ⠀⠀⠀⠘⣟⠛⢻⠁⢹⣿⡘⡄⣇⠀⢸⣿⣧⣤⣿⣦⢾⣿⡆⡏⡿⣏⠉⢳⠻⢻⠟⠈⠉⠀⠀⢀⡠⠟⠁⠀⠀ ⠀⠀⠀⠀⠘⢦⠈⠛⠉⠈⡇⡇⣿⠿⣧⣼⣿⡟⢻⣿⣶⠀⢠⠃⡇⠈⠛⠋⣠⣏⣀⣠⠤⠴⠚⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⣇⠙⢮⣑⠛⠛⠿⠃⠘⠿⢏⡠⠞⢸⠃⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⠼⠓⠦⠤⢭⣉⣉⣉⣉⣩⠥⠴⠒⠻⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣁⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠝⠉⠉⠛⠷⣦⣤⣶⣶⣶⣶⡾⠃⠀⠈⢻⡾⠛⠉⠉⢻⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣼⠁⠀⣾⢻⡶⠛⠲⣄⣤⠼⢧⣄⠀⠀⠀ ⠀⠀⠀⠀⣿⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⢙⣿⡀⠀⠀⣹⢶⡄⠀⣹⡀⠀⠀ ⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠒⢺⡛⠛⠁⣰⠏⠀⠀⠀ ⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⢹⡇⠀⠀⠀ ⢠⡶⢼⣷⢤⠄⠀⠀⢀⣀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣀⠀⠀⠀⠤⠾⣿⠖⠶⠆ ⠀⠀⢈⣿⣀⡀⠀⠀⢿⡿⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠸⣿⠇⠀⠀⠠⣴⣿⣄⣀⠀ ⠀⠘⠋⠹⣷⣀⣀⠀⠀⠀⠀⠀⠀⠀⠯⣦⠽⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⠃⠀⠀⠀ ⠀⠀⣠⡴⠟⠻⣧⡶⠳⣦⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡟⠋⠛⠶⠄⠀ ⠀⠀⠁⠀⢀⡾⠛⠂⣀⡈⠀⢹⣧⣤⣄⣀⣀⣠⣤⣤⣴⣶⣾⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣷⣤⠄⠛⠃⠈⢿⢹⣄⠀⠀⠀⢠⡿⠀⠈⢷⡉⣻⣦⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⠏⢿⣤⣴⡷⣶⡟⠀⠙⠳⠶⠶⠛⠁⠀⠀⠈⣿⡋⠀⠈⣿⠆⠀⠀⠀ ⠀⠀⠀⠀⢻⣆⠀⠀⢸⣿⣜⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⣽⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⣶⠞⠃⠙⠶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡶⠾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡿⠶⢶⣤⣤⣤⣤⣤⣿⣤⣤⣤⣤⣤⣤⡶⢾⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⣀⣀⣀⣀⣠⣿⣀⣀⣀⣀⣀⣠⣴⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀ ⠀⡠⢔⡶⠂⠉⠀⠀⠀⠀⠉⠛⢍⢢⠀ ⢰⢡⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡇ ⠈⠇⠀⠀⢠⣦⠀⠤⠀⢰⡆⡀⠀⠀⢡ ⣸⡀⣏⣹⠨⡄⠀⠀⠀⠀⠁⠁⠀⠀⢘ ⠘⡵⣈⡯⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠑⡴⠛⠤⡀⠀⠀⠀⠀⠀⠀⠀⢠⠇ ⠀⠀⣅⠀⠀⠓⠀⠀⠀⠀⠒⠚⠀⠑⡀ ⠀⠀⠈⢰⠲⠀⠀⠀⠀⠀⠀⠀⢱⠀⡁ ⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⡸⠖⠁ ⠀⠀⠀⠀⠀⡇⠀⢠⠤⢄⢀⢀⡇⠀⠀ ⠀⠀⠀⠀⠀⠈⠒⠉⠀⠈⠁⠈⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠚⠓⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣤⣀⣀⣀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠛⠷⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣦⣄⣀⣀⣠⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣀⣀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣟⠧⠀⠀⠉⠙⢿⣝⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⡟⠳⠮⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠘⣧⡀⠀⣶⠆⠀⢠⣤⠰⣶⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣿⣧⡴⣦⣈⣹⣷⣄⣀⣀⣈⣉⣤⣾⣯⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣀⣠⣇⣀⠀⠀⢀⣀⣀⣠⡶⠛⠉⠉⠀⠉⠁⠀⠀⠈⠁⠀⠈⠉⠉⠉⠉⠁⠈⠛⠈⠉⠛⠶⣤⡀⠀⠀⠀⠀⣀⣀⣤⠤⠤⣤⣀⠀⠀ ⢀⡶⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠛⠋⠉⠁⠀⠀⠀⠀⠙⢷⡀ ⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇ ⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠀⠀⢸⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⡇⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇ ⠀⠻⣦⣄⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞⠛⢹⡇⠀⠀⠈⠛⠃⠀⠀⠀⢦⣤⠤⣤⠄⠀⠀⠙⠛⠃⠀⠀⣸⠟⠶⣤⣄⣀⡀⠀⠀⠀⢀⣠⣤⠞⠃⠀ ⠀⠀⠀⠈⠙⠛⠓⠚⠛⠛⠉⠁⣠⡴⠶⠶⣿⠶⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⣰⠟⠀⠀⠀⠀⠉⠉⠙⠛⠋⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⡀⠀⢻⡄⠀⠙⠷⠶⢶⡞⢻⣶⣦⣴⠶⣦⣶⠋⠉⢻⡖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠻⢶⡾⠛⠂⠀⠀⠀⠈⠷⠾⠛⠛⠻⠶⠿⢻⣆⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣤⡿⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠶⣶⠆⣲⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⡤⢶⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⠞⠋⠀⣸⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡴⠋⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣴⣏⣀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠁⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣶⣶⡄⣠⣴⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠹⡿⠿⠟⠁⡏⠛⠻⠀⠀⠁⠿⠛⠿⠇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⣇⠀⠀⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣧⠀⠀⠀⢻⣀⣠⣇⠀⠠⣄⣀⣠⡾⠃⠀⠀⢀⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⢸⣷⣶⣾⣦⣄⣈⣩⡝⠈⠉⠉⠉⠀⠀⠀⠀⠈⠉⠐⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠲⠆⣄⡀⡀⠀ ⠀⠀⠀⠈⠁⠀⠘⠛⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠼⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⢀⢀⣀⡠⠤⠒⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠯⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣿⠿⠿⠿⠿⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⠶⠶⠶⠶⠦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠾⠟⣿⣿⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣤⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠉⠀⠀⠸⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣀⠈⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⢠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⢀⡿⠁⠀⠀⣰⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠐⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡇⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠉⠁⠉⠈⠉⠀⠀⠀⠀⠀⠀⣠⢤⣀⠀⠀⠀⠀⠀⠉⠿⠿⠁⡀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⠀⠀⠀ ⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠤⠠⠐⢀⡀⠀⠀⠀⠀⠀⠋⠁⠉⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⢁⠀⠀⣼⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀ ⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠻⢶⣤⣴⡾⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣤⠀⠜⣀⣴⠟⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠀ ⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⣿⠃⠀⠀⢸⡟⠳⠶⠶⠶⢦⣶⣴⣶⣴⣶⣶⣿⠉⠀⠹⣷⣿⣿⣥⣄⡀⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢿⣆⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠀⢀⣿⠟⠉⠉⠉⠛⣷⡄⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇ ⠘⢷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠃⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠿⣷⡀⠀⠀⣀⠀⠈⣿⡄⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⣀⣼⠏⠀ ⠀⠀⠉⠛⠷⠶⠶⠶⠶⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣤⣴⠏⠀⠀⣽⡇⠀⠀⠀⠈⠛⠿⠶⠶⠶⠶⠿⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡾⠋⠀⠁⠀⠀⠀⠀⠀⢀⣾⠛⠉⠙⠓⠀⠀⢀⣴⠟⠛⠿⠾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠐⢶⣶⣶⣶⣶⣾⣿⡀⠀⠀⢶⡶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⣠⡿⠁⠀⠀⠀⠀⢹⣇⡀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣀⣄⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣦⣶⠟⠛⠉⠙⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡿⠛⠙⠛⠛⠿⣷⣶⣶⣶⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⠀⣀⣸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣽⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣽⣿⣿⣿⣯⣿⣻⢿⣿⣿⣿⣯⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠛⠛⠛⠿⢿⡿⣿⣿⣿⣿⣯⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⢿⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣤⣰⣄ ⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡆⠀⠀⠀⠾⠟⣿⣟⠛⠋⠉ ⢀⣤⣶⣶⣿⡷⠷⡶⠀⠀⠀⣾⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⠧⠀⠀⠀⣤⣿⣿⣶⣴⡄ ⠈⠉⠁⠀⠈⣿⣆⣀⠀⠀⠀⠻⡿⠛⠀⠀⠀⠀⢀⢼⡶⣷⡄⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⣸⣿⠃⠉⠀⠀ ⠀⠀⠀⣶⡿⠿⣿⡍⠀⡀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠛⠛⠛⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⣻⣿⢿⣷⣦⣤⠀ ⠀⠀⠀⠁⠀⠀⣈⣿⣿⣟⢠⣴⣿⣿⢿⡿⣶⣄⠀⠀⠀⣠⣾⡿⣟⢿⡿⣶⡄⣀⣴⣿⠟⠁⠀⠈⠉⠀⠀ ⠀⠀⠀⠀⢤⣾⡟⠃⠈⣙⣿⡿⠿⢾⣧⣛⢷⣻⡷⣠⣾⡿⣣⢟⡼⣳⣿⠟⠛⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠁⠀⠀⣰⡿⠋⠀⠀⠀⣹⣯⡞⣵⠫⡟⣧⢹⢥⡻⡼⣿⣇⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣴⣿⢣⡟⣼⢃⡟⣼⡹⣎⢷⡹⣝⣿⣇⠀⠀⢀⣿⡃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣦⣤⣼⡟⣮⢳⡝⣮⢣⡝⡶⣹⢎⡷⣹⢺⠼⣿⣷⣶⣿⢿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠉⠛⣿⣽⢎⡷⣹⢎⡷⢺⡵⢫⡞⣵⢋⣷⣿⡿⠛⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠽⣿⠀⠀⠀⠀⠈⠛⣿⣞⣵⣫⠎⢧⣛⢧⡻⢼⣯⣿⠏⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠈⠻⣷⣿⣎⠷⣭⢳⣽⣿⡟⠁⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⡠⡿⠛⢿⣿⣼⡿⠛⢿⣧⡀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠦⢤⠴⠞⠋⠀⠀⠀⠙⠏⠀⠀⠀⠙⠻⠦⠤⠴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠒⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢠⣢⠐⡄⠀⠉⠑⠒⠒⠒⣄ ⠀⠀⠀⣀⠴⠋⠀⠀⠀⡎⢀⣘⠿⠀⠀⢠⣀⢄⡦⠀⣛⣐⢸⠀⠀⠀⠀⠀⠀⢘ ⡠⠒⠉⠀⠀⠀⠀⠀⡰⢅⠣⠤⠘⠀⠀⠀⠀⠀⠀⢀⣀⣤⡋⠙⠢⢄⣀⣀⡠⠊ ⢇⠀⠀⠀⠀⠀⢀⠜⠁⠀⠉⡕⠒⠒⠒⠒⠒⠛⠉⠹⡄⣀⠘⡄⠀⠀⠀⠀⠀⠀ ⠀⠑⠂⠤⠔⠒⠁⠀⠀⡎⠱⡃⠀⠀⡄⠀⠄⠀⠀⠠⠟⠉⡷⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠤⠴⣄⡸⠤⣄⠴⠤⠴⠄⠼⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⠟⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣯⣷⣿⣻⣾⣟⣾⡿⣟⣷⣿⡾⣷⡿⣷⣿⢯⣿⣽⣿⣽⣷⣿⣯⣷⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⡙⢿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣯⣿⣷⣿⣿⣳⣿⣿⣽⣿⣿⣾⣿⢿⣽⣿⣻⣿⢯⣿⣾⣿⣭⡛⢷⣿⠃⠀⠀⠀⣀⡀⠀⠀⢀⠀⠈⠈⣻⣿⢛⣩⣿⣿⣿⣿⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣳⣿⣾⣟⣿⣽⣾⢿⣳⣿⢷⣿⣿⣻⣽⣿⣯⣿⢿⣿⣿⣿⣿⣶⣿⣦⣤⣄⣀⣀⡉⠙⣉⣀⣠⣴⣾⡟⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣽⣷⣿⣻⣽⡿⣾⣿⣟⣯⣿⣿⢾⣿⣯⣷⣿⣻⣿⡷⣿⣷⣿⠛⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣿⡷⠇⠀⢻⣿⣿⣟⣿⣯⣿⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣽⣾⣟⣿⣽⡿⣟⣾⣿⣻⣷⡿⣿⣯⣿⣯⣿⡽⠿⠟⣿⣿⣯⣄⡙⠛⠻⣿⡿⠟⠋⠙⠻⠿⣿⠋⠀⠀⠀⢸⡌⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣯⣿⣾⢿⣽⣷⣿⢿⣯⣷⣿⣯⣿⢿⣳⡿⠋⠁⠀⠀⢰⣿⣿⣿⣿⣿⣶⡶⢾⣍⡀⠀⠀⠀⣀⡟⠻⢿⣿⡇⠀⣇⠀⠀⠀⠀⠀⠂⢉⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣟⣷⡿⣿⣻⣾⢿⣻⣯⣿⣞⣯⣿⡿⠋⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⢻⣦⡀⢻⣿⣿⣿⡿⠏⣀⡤⠖⠻⡆⢹⡟⠀⠀⢤⡀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣟⣿⡿⣿⣻⣿⣟⣧⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⡼⢻⣿⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⡟⠛⠃⠀⠀⢀⣿⣿⡇⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠘⠛⢿⣿⣿⣿⣻⣿⣿⣿⣿ ⣿⡷⣿⣻⣟⣿⣻⣽⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡿⠏⠀⠀⠀⠀⢀⣾⣿⣿⠁⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿ ⣿⣿⣟⣿⣽⣟⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣻⣿⣤⣀⣠⣤⣤⣴⣿⣿⡿⠁⠀⠀⠀⠀⠀⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿ ⣿⣷⢿⣻⣾⠟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠚⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿ ⣿⣯⣟⡿⠋⠀⣿⡶⣤⡤⡤⢤⣀⣀⣄⣼⡟⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿ ⣿⣷⠏⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣞⣶⠮⠁⠀⠀⠀⠀⠈ ⣿⠃⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⢡⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣏⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⣾⣿⣿⣿⣄⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣷⡿⠉⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⢠⣷⣶⣾⣷⣿⣾⣿⣿⣿⣿⣿⣿⣻⡙⠚⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⡿⣷⣦⣤⣤⣤⣀⠀⠀ ⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡉⢢⣀⡀⠀⠀⠀⠀⠀⣀⣼⠇⠀⠀⠘⣿⣶⣦⡀⢀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣤⣾⣿⣿⣿⣿⣾⣿⣻⣿⣿⣿⡿⠋⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⠟⠃⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡟⠀⢀⣼⣿⣿⣿⣟⣿⣿⣿⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣽⢳⣿⣿⣿⣿⣽⣿⣽⡿⣯⣿⡯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣿⣿⣿⣖⣾⣿⣿⣿⣿⣿⣽⢿⣿⣿⣿⡣⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⣻⣿⡿⢾⡼⣳⣿⣿⣿⣿⢿⣾⣿⡿⣟⣯⣷⡞⡜⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠟⠈⠿⢿⠿⠛⠉⠀⢻⣿⣞⣯⣿⣿⣿⡷⡁⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣛⡷⢯⣟⣿⣿⣿⣿⣿⣿⡾⡝⣿⣿⣟⣿⣿⣧⡿⣬⢣⡖⠥⠎⠒⠓⠬⢤⣤⣀⡀⢄⠢⡄⢐⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣞⡿⣞⡿⣿⡿⣅⠂⠀ ⡄⠀⠀⠀⠀⣾⣿⢳⣯⣽⣯⣿⣿⣿⣿⣿⣽⣷⢣⡍⠐⢫⡟⣿⣿⢻⡟⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠘⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡞⣿⣽⠛⣿⣿⢳⠘⠀ ⡀⠀⣀⣤⠾⠿⣯⣷⣛⠾⣼⣿⣿⣿⣿⡿⣿⣽⢮⡔⢠⡀⡐⠡⢌⠦⡴⢤⠀⠀⢀⢠⣴⣶⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣽⣳⢯⣟⣿⠿⠿⠶⡄ ⡇⠀⠈⠀⠀⠀⠈⢻⣮⢟⡵⣻⣿⣿⣿⣿⣿⣽⣷⣯⢷⡼⣥⣋⢤⡙⣦⣏⣾⣿⣿⣻⢿⣻⣯⣷⡶⢶⣀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣞⡽⣳⡾⡁⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⣴⣆⠀⠻⣮⢳⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣽⣶⣟⣾⣽⣷⣿⠻⠍⠆⠁⠈⠑⠾⠵⠙⠯⢿⣷⣿⣷⣮⢤⣡⢤⣰⣤⣤⣤⣴⣶⣿⣿⣿⣿⡞⣽⠟⠰⣷⠀⠀⠀⠀ ⣷⢀⠀⠀⠀⢿⣿⣧⡀⠘⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⣷⣶⣶⣦⣤⣤⣤⣖⣶⣾⣷⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⠋⢠⣼⣿⡆⠀⠀⢀ ⣿⣿⣆⡀⠀⠰⣿⣿⣿⣀⣀⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣰⣿⣿⣿⣄⣰⣮⣿ ⣿⣿⣿⣿⣿⣧⠈⠻⣿⣟⢯⣛⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢷⣏⠿⣽⣿⣿⣿⣿⣿⣿ ⣟⣿⣿⣿⣿⣿⣷⣶⡼⣟⠾⣜⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡾⣭⠿⣽⣿⣿⣿⣿⣿⣿ ⡷⢾⣭⣯⣽⣫⣟⣵⢯⣝⣻⣜⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡷⢯⣟⣧⣟⡾⣽⣛⣾⣳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠋⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠓⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠀⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀ ⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀ ⠀⣸⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀ ⢠⡇⢀⣤⣶⠿⠾⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⠀ ⢸⢣⣿⠟⠁⠀⠀⠈⢿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠾⠋⠁⠻⣿⣶⣶⣄⠀⠀⢸⡅ ⢸⣿⣿⡀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡄⠈⡇ ⠀⢿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣼⣿⣿⡆⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⡇⢠⠇ ⠀⠘⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿⣿⣷⣤⣤⣶⣿⣿⣿⣿⣿⣿⢃⡞⠀ ⠀⠀⠘⢦⠙⢿⣿⣿⣿⣿⡿⠛⢻⣿⣿⡏⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣫⠞⠀⠀ ⠀⠀⠀⠀⠙⢦⣈⠙⠿⢿⣷⣦⣾⡿⠟⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡁⢀⣹⣿⣿⠝⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⢴⣀⡀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⡿⢿⣟⡯⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠉⠲⡤⠤⠔⠲⠤⠤⣤⠤⠤⠤⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠀⣬⠣⢄⡀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠟⠀⢰⣃⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠄⠢⣆⠀⠀⠀⣀⢀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡄⠀⠀⠀⠠⡍⠂⠀⠀⠀⠐⠂⠠⠉⠉⠈⠅⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣥⡗⢻⣥⠀⠀⣀⠀⠀⠀⠠⠘⠂⠀⠀⠀⠀⠸⠀ ⠀⠀⠀⠀⠀⣴⣦⡄⠶⠁⠀⠀⠉⠆⣀⠀⠀⠈⢤⠀⠀⢠⣿⣶⠀⠀⢁⣠⠖⠀ ⠀⢀⠀⠀⠀⠻⣿⣶⣄⣀⠀⠀⠀⠀⠈⣷⠀⠀⠀⣰⣦⣾⣿⠋⢤⠀⡈⠀⠀⠀ ⠀⢸⠀⢀⠀⠀⢿⣿⣿⣿⣿⣶⡀⠀⢠⡟⣠⣶⣿⣿⣿⣿⠟⠁⠀⠐⠃⢀⠀⠀ ⢀⢻⢘⠡⣮⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣁⠂⢄⠠ ⠐⠾⠌⠹⠆⠂⠀⠙⣿⣿⣿⣿⡿⣉⠉⡉⣿⣿⣿⣿⣿⢫⡅⠀⠄⠃⡰⢈⢆⠂ ⠀⠈⠂⠩⢵⣤⣬⣴⣿⣿⠟⠋⠛⠶⠶⠶⠛⠙⠻⣿⣿⣿⣅⡢⠄⢡⣆⣧⠋⠀ ⠄⠲⡡⡐⢚⠻⡤⣿⣿⠃⠠⠤⠀⠀⠀⠀⠀⠠⠆⠸⣿⡟⣠⣤⣶⣶⣶⣾⣶⠆ ⠠⢶⣷⠯⠐⢛⠴⠋⡙⣦⣀⠀⠀⠀⣹⠀⠀⠀⣀⣼⣋⢀⣸⠿⠿⣿⣿⣿⡟⠀ ⣀⣶⣿⣴⣴⡏⣰⣿⣿⣿⠏⠙⣾⠟⠁⠻⣿⠉⢫⣿⣿⣿⣿⣧⢽⣤⣤⣶⣦⣤ ⠛⠿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋ ⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠢⣴⣿⣿⣷⠤⠄⠀⠀⠤⠤⠠⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢀⠀⠀⢀⡿⠛⠋⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡀⢀⣴⣿⣿⡦⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣤⡟⣇⠔⠉⠓⠂⣤⣴⢯⡿⠤⣴⣧⣀⣀⠀⠀⠀⡀⣸⣿⣿⠋⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡝⢠⣧⠐⢂⣿⣿⣿⣎⣼⡏⣿⣿⣳⣷⣹⡏⣥⠉⢱⣿⣿⠇⡆⣠⣄⠀⠀⣌⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢁⢿⣟⣆⢼⢸⡿⠁⢴⡏⡅⣿⣏⡮⠘⣸⣿⢼⣿⣶⣿⣿⣦⡷⡟⠙⣶⡇⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⣾⢿⣼⡌⣿⡷⠛⢶⡇⠣⡟⢻⡶⠻⠻⣆⣾⡇⣿⣿⣿⣿⡇⠀⠀⠏⢳⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣜⣿⣷⢸⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠟⣯⣧⣿⣿⡟⣿⡇⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠘⢧⣻⣿⣿⠀⠀⠀⠠⠄⢄⠠⠀⠀⠀⣼⣿⣿⣿⡿⠃⣿⢹⠀⠀⠀⡟⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⣿⠃⠀⣹⠈⠀⠀⢰⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⡇⠀⣿⢿⣿⣿⣿⣿⣿⡖⠒⢚⡭⣾⣿⣿⣿⡀⠀⠀⠀⢸⢀⠀⠀⣞⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣷⠀⢻⣿⣿⡿⠋⢙⢿⠳⣀⣠⣴⣿⣿⡟⠚⠓⠢⡀⠀⢸⢹⢀⡀⣿⣿⣿⣿⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢠⡘⣿⣿⠀⠀⢸⢸⢠⠛⢿⣿⢻⣿⠀⠀⠀⠀⢻⡄⢸⣸⢸⠇⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢞⣿⡿⣿⠘⣇⢻⣿⡄⠀⣹⠈⢿⣤⡟⠻⠟⢸⠀⠀⠀⠀⢸⠃⢸⣼⢻⢰⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣷⠿⠋⢡⣿⠀⣿⠈⣿⣇⠀⢸⠀⠀⠛⡇⠀⠀⠸⢦⠀⠸⠶⣿⠀⢸⣼⡇⡿⣾⣿⣿⣿⠈⠻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣾⡿⠛⠉⠁⠀⠀⣼⠋⠀⢣⢧⠈⣿⣠⡇⠀⢘⠀⡗⣮⣽⣇⣿⣤⣤⣤⣿⠀⣿⣿⢸⡇⣿⣿⣿⣿⡆⠀⠙⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⡏⠀⠀⠀⠀⠀⢠⣧⡇⠀⠸⣾⡄⢻⣿⣿⣿⣿⡀⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣿⢿⣼⣶⣿⣿⣿⣿⣧⠀⠀⠈⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⢀⠞⣿⠁⠀⣷⣷⣧⠸⣿⣿⣿⣿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣇⠀⡟⡌⠉⠏⣿⣿⣿⣿⣾⢇⠀⠀⠈⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⡀⠀⢀⢎⡼⣿⡄⠀⢹⣧⢿⠀⣿⣿⣿⣧⣹⠀⣿⣿⣿⣿⣿⣿⣿⣿⣄⣧⠁⡇⣰⣿⣿⣿⣿⣿⣿⡄⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺⣦⢞⡾⢁⣿⠁⠀⢸⣻⣟⡇⢹⣿⣿⣿⣿⡆⡏⣿⡌⣿⣿⣿⣿⡇⢻⡼⢰⣷⣟⣿⣿⡟⠻⣿⣿⣿⣄⡀⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣫⡾⠀⡼⡏⠀⠀⠀⠙⣿⡇⢸⣿⣿⣿⣿⣷⣧⠸⣿⣿⣿⣿⣿⣷⣾⡇⢸⣿⣄⡿⣿⣿⣦⠈⢿⣿⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢮⣿⠃⡰⣻⡇⠀⠀⠀⠀⣿⣿⠘⣿⣿⣿⣿⣿⡿⠃⢻⣿⣿⣿⣿⣿⢙⠁⠈⣿⣿⢹⠹⣿⣿⣷⠛⢿⣿⡿⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢻⣿⡰⣱⣿⠃⠀⠀⢠⠸⣿⡇⢠⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣴⡀⠀⢱⡻⡜⣧⣿⣿⣿⣦⢼⣽⠿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡸⠋⢠⣿⡟⠀⣼⠀⡼⡇⣿⡇⣸⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣿⣿⣿⣧⡇⠀⠀⠹⣿⣽⣿⣿⣾⣿⣟⡇⠀⢸⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠋⠀⣰⣿⡿⠁⢼⠍⣼⣻⢱⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠙⢿⣿⣿⣿⡇⢀⠇⠀⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠤⣤⣶⡿⢛⣵⡶⢋⣴⣿⠟⣠⡾⢃⣼⠟⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣧⠙⢦⣄⠘⣿⣿⣟⡀⣜⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⢀⢔⣭⣶⣿⣿⢥⣾⠟⠋⣰⣿⣿⣿⠞⣫⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠻⣷⣮⣿⣦⡹⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀ ⠀⢠⣻⣿⣿⣿⣿⢞⣋⣤⣴⢿⡻⣯⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠙⠻⠿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⢸⣿⣿⣿⣟⠿⣹⣶⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⢄⣀⡈⠉⠀⠂⠀⠉⠉⠛⠛⢿⣤⣤⣤⣄⣀⡀⠀ ⠀⠀⠈⠛⢿⣿⣿⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣾⣎⠻⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣞⣭⠍⠓⠒⣒⣒⣲⣶⣶⣿⠟⠛⠛⣉⣿⣿⠆ ⢠⣶⣾⣿⣿⣛⡛⠛⢛⣻⣿⣿⣿⣿⣟⣿⣯⡉⠁⠀⠀⠀⠀⠙⠿⠽⣾⢽⡿⠝⠺⢝⡇⠀⢜⡩⠖⠋⡿⣿⣿⢿⡿⣚⠷⠚⠈⠙⢿⣷⡀⠉⠙⠛⠒⠒⠛⠛⠛⠋⠁⠀⠀⠸⠟⠉⠁⠀ ⢀⣙⣛⣛⣯⣿⡿⢶⢽⡟⠛⠛⠉⠉⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠁⠀⠊⠃⠀⠉⠀⢠⣤⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠉⠉⠉⠁⠀⠀⠉⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⢀⠄⢮⢑⠌⠢⢀⡀⠀⠀⠏⢠⢇⡀⢀⠀⠄⠀⣄⡇⢸⣇⢄⡿⢠⡯⡱⣗⡿⡜⢢⣹⣫⢃⣞⡼⡻⠿⣶⠿⡄⣇⠀⠀⣀⣀⠼⣿⡗⡘⢿⣯⠹⣄⣤⣌⠑⠫⠓⠱⠽⠮⠽⠶⢀⡤⣄⡈⢮⣷⣯⣴⣿⠄⡟⣾⣿⡃⢿⡟⠀⠀⡧⢹⠀⠍⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⠀⠄⠐⠂⢄⣀⠈⠐⠈⠅⢸⠀⢸⠘⠀⠈⠉⢹⣷⢨⣿⣾⣛⠟⣴⡽⠜⠓⠉⠀⠀⠀⠀⢀⣾⣿⣶⣄⠀⣇⣿⢢⠀⠀⠘⣰⡿⣄⢱⠛⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢩⠀⢯⡘⡏⢻⣿⣏⢸⣾⡆⠀⢣⡏⢠⢁⠟⠈⠂⠀⠑⠀⢄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠣⠭⠋⠢⠁⣅⠟⠀⣼⠸⣀⠀⠀⠀⣿⢸⡟⢁⣼⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢰⢟⣿⣿⡿⢿⣇⡏⣆⠡⡀⠀⢻⢻⡜⡼⢀⣿⠃⢸⠛⢉⢼⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢨⠐⡄⡒⡇⣇⢈⣷⡇⢸⣿⠁⠀⣾⠁⡮⠂⠀⡠⠒⠀⠢⡀⠘⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠔⠁⢢⠀⠻⢦⣄⠀⠀⠀⠂⢀⢆⠔⠘⣈⣿⢑⣄⠀⡿⢸⣁⣾⠟⡿⠿⠛⠻⡄⠀⠀⠀⠀⠀⢨⠠⠀⢠⠂⠀⡾⡷⣯⢢⢱⣀⠙⣾⣧⡇⢸⢎⣣⠀⢢⣫⠝⠀⠀⠀⠀⠀⠐⠛⠛⠻⢷⣦⠀⡆⡸⠀⣽⣳⣇⠌⣿⡆⢘⣵⡃⢰⢃⣾⡕⠀⠠⠁⠰⣁⢀⠇⠀⢈⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠣⠀⡊⠀⠀⠀⠉⠁⠀⡐⡨⡕⠀⡀⢈⡧⡟⣆⣾⣍⠇⡞⠻⠛⠀⠱⡀⠤⠢⠁⠀⠀⠀⠀⠀⠀⠱⠶⠁⠀⣼⣾⠏⡟⡖⢩⡛⣄⠈⣿⢷⣸⣀⡿⢇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣹⠃⢸⡏⢿⠁⠀⡾⣇⡏⠛⠁⡆⣯⠁⠀⡂⠀⠑⠤⠤⠀⠀⢠⠌⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠅⠲⡀⠀⢀⢔⡌⢰⠇⡀⢀⠀⢟⡯⢴⢷⣸⢰⣇⣁⣗⡄⠀⠈⠘⠉⠀⠀⠀⣀⡀⣄⠀⠀⠀⠀⢠⡿⡟⢰⢷⢁⣿⡟⡘⠀⢻⡜⡷⣷⣮⢻⡦⡀⠀⠈⡏⠁⢻⠀⠀⠀⠀⠀⢤⣊⣴⡧⣀⢮⢼⣄⠹⡶⢹⠃⠁⠀⠀⣇⡿⡀⠀⠈⠑⠄⠤⠀⠀⠂⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠄⠈⢨⠃⣎⠁⡾⢀⢁⠤⠈⣸⠷⣹⣮⣇⠘⣿⠙⣿⣟⠦⡀⠀⠀⠀⠀⢻⠐⠃⡏⠀⠀⢀⡴⢻⣷⡇⠸⠇⢸⡟⢠⡅⡀⢼⡿⡌⢻⢯⣥⠃⠈⠂⢄⠘⠠⠜⠀⠀⠀⠀⠀⠔⠨⡬⣕⣄⠘⢮⣙⣦⠈⢦⠄⢄⡀⠀⠈⠷⡑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⣀⠸⢰⠃⠸⠘⡔⠁⡘⣧⣃⠷⣌⠢⣿⣧⠘⣿⣧⣘⡦⢤⣀⣀⠀⠃⠐⠁⡠⣖⢕⢽⢧⣿⠁⢀⠀⠈⠀⠇⢋⡔⠁⠱⣱⠀⡯⢁⢀⠀⠀⠀⠈⡒⠢⡲⡲⠉⡀⠤⣐⠬⠑⡂⠈⠑⠄⡁⠢⠅⠠⡀⡏⠠⡆⠀⠀⠈⠢⡉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠒⡎⠀⠀⠀⠳⣄⡎⢀⠇⢸⠬⢴⣀⡧⠧⣍⠻⢷⡌⠻⡇⠸⡟⠁⠚⠩⢜⡨⢚⠍⡉⢹⢊⢵⠏⣁⠚⠋⠄⡀⠊⡄⠀⢠⡋⢷⡀⠀⢻⡦⠁⡇⠀⡕⢄⠠⢲⠃⠀⢰⠙⠕⠊⠁⠀⠀⠀⠣⠄⡀⢸⡈⠂⠀⠇⢰⠓⠁⠠⠀⡠⠀⠀⠈⠆⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⣸⠀⢸⠀⠘⣄⠀⣯⠴⡯⠔⣳⣄⠙⠀⠀⠀⠙⣆⡠⠂⠔⠈⠑⢭⡦⡩⣳⠁⢀⠂⡗⣄⠀⠀⠀⠀⢠⢳⡩⢘⣷⡀⡨⠚⠺⠁⠐⠀⢀⠊⣼⠟⠂⠨⢮⣄⠀⠀⡄⢀⡌⠖⠈⠀⠀⠈⠁⠻⡀⠈⠑⠀⠀⢫⠀⠃⢀⠀⠘⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⡏⡆⠀⢉⡫⢽⠣⣍⠖⣤⢈⠁⢘⣭⡀⠤⠊⠀⠚⠂⢤⠀⣀⠈⣻⣿⢔⠁⠀⢣⢷⣷⣎⠂⢒⡮⡯⠻⢣⡛⣇⡱⣔⠉⠐⠁⠑⡘⠶⢧⣞⡦⣔⡄⡻⠃⠀⡍⠁⠀⡠⠊⠀⠀⠀⠀⠠⡀⠑⣄⠀⠄⠃⠩⣰⢇⠀⡠⢠⠏⡆⢀⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⡓⣤⡤⡀⠀⠀⠀⢸⠀⡇⢧⠀⠀⡇⣺⢱⣚⠍⠀⠀⠢⡀⠀⠀⠀⢀⡆⠀⠀⢀⢈⡠⢘⣃⣙⣁⣤⣼⡏⣿⣣⡀⡀⠀⠈⢷⣀⢻⣗⠇⡇⣯⠀⣌⠐⠀⠁⡠⡪⠃⡖⠜⠂⠉⠉⠉⠀⢠⠊⠀⡀⠀⠀⠀⢠⢁⢠⡞⠉⠡⠄⠂⢀⡟⢛⠯⣱⠥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣟⢺⠧⣤⡀⠀⠀⢆⢯⢎⡧⠈⢦⡝⢪⡼⠀⡀⠄⠀⣿⡖⣪⣍⡯⠣⡀⠐⡁⠀⡼⠝⠉⠿⠛⠁⠈⡿⠈⡿⠷⠽⠤⠤⢚⡣⣿⠎⢰⣫⠙⣴⠁⢀⡔⡩⠊⠀⡸⠸⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⡦⠁⠀⡜⠀⠀⠀⢱⡒⠉⠀⡠⠑⠄⠀⠀⢀⠔⠉⠉⠑⠦⠤⢄⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣎⣃⡲⠃⠀⠀⠀⠸⢳⣾⠀⢻⡞⢸⣇⠀⠀⠀⡞⢰⡇⠀⠀⠸⢣⢲⠀⠀⢋⢣⢆⠀⠀⠀⠀⢰⡜⠀⠷⡈⠏⢳⠉⠀⠀⠈⢷⠳⠁⢠⠃⠈⢲⠰⢁⣒⣀⠃⣦⢶⢦⠀⠀⠀⠀⠀⠀⠀⠈⠁⢨⠃⢀⠤⠣⠀⠀⠀⢸⠛⡐⠈⠀⠀⠈⠂⠀⠸⠀⠀⠀⠀⠀⠀⠀⢣⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⡠⠔⡄⠀⢀⠆⣰⠟⢇⡘⠆⠠⢤⠀⠻⣹⡷⠀⠀⠀⣎⠇⠀⠀⠘⢤⠈⠛⢶⣄⣡⡗⠀⡌⠀⢡⠸⣌⢆⠀⠀⠀⠀⠳⠀⠇⠀⠀⠆⡇⠀⠀⠸⢰⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢀⡰⠐⡠⠖⠠⠀⠸⢠⡛⡄⠀⠀⠀⠀⠑⡄⢣⠀⠀⠀⠀⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠒⠒⠈⠀⠈⠉⠈⠀⠀⠀⠉⠉⠺⣄⣧⡶⠿⣓⠒⡒⢲⣃⠁⠀⠀⠀⠀⠉⠂⠨⠈⣿⠥⠊⠀⣀⡬⢃⡟⠎⠦⠄⡀⠀⠀⠑⡀⢀⣤⢰⣀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⡕⠑⠒⠁⠀⠀⠠⠃⢇⠃⠙⠄⠀⠀⠀⠀⠈⡄⠑⠤⠄⠒⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⡄⠀⠀⠈⠀⠁⢡⠀⠀⠀⠠⠀⠀⠀⢀⣤⣼⣧⣶⡆⠈⢈⣁⠖⠈⡦⣀⠁⠀⠀⠀⢰⠈⢻⡸⠤⠌⠩⢕⢸⢟⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠘⠈⢹⠐⠢⡈⢄⠀⠀⠀⠀⢠⠠⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠒⠐⠊⠀⠀⠀⢣⠀⠀⠀⠀⢀⠀⡀⠀⢠⣄⣀⣀⠀⢡⠀⠂⠀⠀⠀⠈⡀⠀⠄⠀⠐⠠⠀⠐⠿⠛⢿⠉⠀⠀⠎⠁⢀⣤⠃⢀⢲⠀⠀⠀⢰⠀⠘⢇⡴⡢⠀⢸⢸⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⡎⠠⣀⣠⣤⣤⡄⡤⣀⡀⠸⠀⠆⠈⠢⢡⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠌⠀⠀⠀⡀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠸⠀⠐⠙⠁⠈⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⢌⠕⠁⠀⠀⢹⢃⡼⡂⢠⠗⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢀⠳⡆⠀⠀⠀⢈⠄⠀⠘⢆⠀⠀⠇⢐⠑⠁⠀⠀⢀⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢀⠀⠀⠀⠀⠀⠀⡠⡲⠒⡂⠄⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⡠⠄⡐⠃⠉⡗⠁⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠁⠠⠀⡀⢠⡔⠂⠉⠀⠀⢆⢍⠂⠌⣠⠏⠁⠀⠀⠀⠀⢧⠞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡡⠀⠱⠀⠀⢀⢮⠊⠀⠀⠀⠑⠔⣄⠀⡀⡀⠀⢀⣀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢡⠀⠀⠈⠈⠑⠀⠀⣇⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠸⡀⠀⣀⠴⠋⠀⠀⠀⠀⠀⡀⠌⠡⠃⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠨⢀⡸⡇⠀⠀⠀⢠⡴⡾⠋⣨⠀⠄⠊⠀⠀⠈⠢⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣊⡀⠀⠀⠑⠈⠀⠀⠀⠀⠀⠀⠀⠠⠁⠂⠀⠀⠀⠀⠀⢀⠤⣂⡁⠀⠀⠢⡑⡀⠀⠀ ⠀⠀⠀⠀⠀⡏⠇⠀⠀⠀⠀⢀⢲⠀⠀⠀⣰⠏⠜⠀⡠⠚⠈⠈⠉⠁⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⡆⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠐⠌⢂⠀⠀⠨⡢⡀⠀⠐⡠⠀⠀ ⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⡀⡵⠃⢀⡠⢼⠏⡸⢀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠢⢀⡧⢤⡄⠀⠀⠀⠀⠀⠀⠀⠈⠣⠈⠣⠈⠠⢤⠈⣴⠂⢄⡀⠐⠔⡄⠀⠡⢃⠀ ⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⡼⠁⢸⡁⠀⠀⣸⡦⢀⠋⠱⠢⢀⠀⠰⠂⣀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⢄⣁⣂⠄⠀⡀⠀⠁⠀⠶⡀⠀⠀⠀⠀⠀⠀⢀⡀⣇⠠⠃⠤⡃⡇⢉⣷⡟⠁⠀⠈⢪⠄⠀⠡⢂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠂⢳⡆⠘⡀⡘⢸⠀⠀⢁⣀⢃⠂⠁⠈⠀⠀⠀⠀⠀⢁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⢱⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠐⠂⠀⢁⠀⠈⣱⠀⠀⠀⠀⠀⢀⠁⠀⠀⠊⠀⠀⢻⣇⣎⣇⡗⠀⠀⠀⠀⠛⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⠠⠐⠀⠷⡔⡍⠁⢨⢄⠀⠀⠛⢉⡖⠀⠀⠀⠀⠀⠀⠀⠈⡆⠠⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⠀⠪⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⡀⢔⠒⠲⠶⣧⠀⠣⣆⡀⠤⠐⠂⠙⡄⠀⠀⠀⠀⠀⡜⠻⣿⠀⡇⡇⠠⡀⠀⢸⠂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣦⡼⠞⠁⠈⠁⠁⢈⠆⠠⠐⠊⡌⡀⠀⠀⠀⠀⠀⠀⠀⡟⡀⠁⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠙⣄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠠⠡⠀⠀⠀⠀⠀⠀⠰⠸⠀⠀⢀⡰⠋⡤⠓⠀⠀⠀⠀⠀⠀⠈⠢⠄⣀⢀⠜⠀⠀⢨⡇⡇⡇⠀⠀⢴⠊⠀⠀⠀ ⠀⢀⠀⠠⢄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⡠⠤⢄⠀⠘⢔⠀⠀⠀⠀⠀⠀⠁⡞⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠢⡀⠀⠘⠄⣀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠛⠉⢀⠎⠀⠀⠀⡠⠂⠁⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣧⠁⠢⠀⠀⠑⠄⡀⠄ ⠀⠈⠉⢀⢦⡑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠎⢀⠤⠀⡆⠀⠰⡀⠠⣄⠀⠀⠀⠀⢃⠱⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠃⠀⠈⠂⢤⠶⣜⠂⠊⡦⡀⠀⠀⠀⢀⡀⠤⠂⣀⣀⣀⠠⠐⠁⠀⠀⠀⠐⠀⠀⠀⠀⠉⠀⢈⣄⢁⠐⡄⠀⠀⠀⢸⡋⠀⠐⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠐⢁⡷⢳⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⡆⠀⠣⡀⠉⡁⠄⠀⡔⠉⠲⢴⢀⠀⡠⠜⡓⣊⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⡅⠀⠀⠀⠃⢀⠉⠨⢀⠀⠁⠣⣢⠍⡀⠀⡐⢁⠂⠀⠀⠆⠀⠀⠀⣀⡔⠥⠀⡴⢂⠆⠀⡤⠠⠠⠦⠄⠲⠀⠀⠀⢰⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠀⡸⠘⠀⠀⠑⠠⠀⠀⠀⠈⠢⡀⠈⠥⢀⠀⠁⣀⡰⠊⢄⠀⠀⠀⠪⣿⢾⣁⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠒⣠⠃⠀⠀⠀⡰⠁⠀⠀⢀⠃⠀⠀⠀⠰⡉⢶⠄⡀⡀⢹⡄⠡⡀⠑⠂⠀⠈⡄⠀⠀⠀⠀⠀⠐⠚⠑⠀⠒⠒⠑⠘⠛⠀⠀⠀⠀⠀⠸⠰⢁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⠌⢄⠀⠄⠂⠒⠢⣀⣀⠀⠈⠢⡀⠀⠈⠀⠀⠀⠀⠀⣡⡀⠀⠀⠰⠘⠀⠈⢔⢢⠄⣀⠀⠀⠐⢀⣀⠰⠞⠁⠀⠀⣀⣀⠀⠀⠀⡠⠚⠠⠀⠳⢤⡀⠈⠀⢀⠀⠐⢊⠇⠀⠀⠉⠀⠀⠀⠘⣄⠀⠀⠀⢀⠀⠀⣀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠇⣇⢸⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⢄⠀⠀⠀⠀⠀⠀⢟⠮⠦⠀⠠⡻⠀⠀⡐⡄⠀⠀⠀⠉⠀⠀⠀⠀⠀⡀⠄⠃⠠⡰⠗⠂⡀⠡⡀⠀⠁⠀⠀⠉⠢⠀⠀⡠⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠊⠀⢠⢊⠜⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠀⠀⠁⠀⠢⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⠀⠀⢀⠞⡀⠀⠀⢡⡀⠀⠀⠀⠀⠀⠈⡧⡔⠈⠀⠀⡀⠲⢀⠃⠀⠀⠀⠀⡠⡂⡀⠁⣀⡤⡖⠀⠀⠀⠀⠇⠀⠀⠁⠂⠤⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⢀⡎⠀⡠⣤⣄⠀⠀⠀⠀⠀⠀⠀⡎⠀⡠⠊⡠⡈⠰⠀⠘⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⣀⣀⠠⠒⠁⠀⠑⡀⠹⠤⠒⡀⠀⣔⠒⣒⠖⠁⠐⡀⠀⠀⢡⠁⡘⡼⢀⠀⠀⠀⢣⠔⠑⠁⠘⠒⠁⠀⠀⠀⠀⠇⠀⠀⠀⡠⢄⠑⠀⢰⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⡀⠈⢶⣼⡰⢤⣿⣀⠀⠀⠀⠀⠀⠐⡁⠀⢇⠀⠄⣂⠔⠀⢀⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠧⢐⡃⠄⠙⠂⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠈⠂⠀⠀⠣⠖⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⡀⠀⠀⡇⠀⠀⠈⠫⣅⣽⢜⠇⠀⠀⠀⠀⠀⠘⢇⡀⠁⠒⠂⠀⠀⠜⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢹⠉⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⣀⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠘⡆⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠉⠋⠭⠀⠀⠀⠀⠀⠀⠀⠑⠒⠂⠀⠂⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣼⣿⢟⣹⣷⠶⠶⠶⠶⠶⠶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣴⠾⠛⠋⢉⣿⡟⢷⣾⡇⠿⣦⡀⠀⢀⠠⠐⢠⢀⡉⠛⠻⣶⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢻⣿⢛⣿⢻⡶⣤⣸⣾⣯⣽⣾⣨⣿⠀⣿⣷⡄⠠⠀⠀⠂⡐⠌⡑⢢⢀⠉⠻⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⣿⣴⣉⣧⣛⣼⣿⢿⣯⡋⢻⣱⣞⣦⢝⣿⡇⣤⣿⡄⠀⠈⠀⡀⠠⠈⠐⡈⠆⡁⠘⣿⡄ ⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⢹⣿⣏⡉⢧⣎⣻⡖⣿⡿⠟⠳⣭⣿⡼⠟⠛⣻⣾⠛⢷⣤⣂⠀⢀⠁⠈⠀⠐⠐⠱⣸⡇ ⠀⠀⠀⢀⡼⠏⡀⠐⠈⠀⠀⣾⡧⢉⣿⠋⣿⠖⡿⠀⢀⠠⢀⣈⣉⣍⣯⣏⣆⣀⠀⡈⢙⣿⠶⠶⣤⣥⣦⡾⠾⠋⠀ ⠀⠀⢠⡟⡁⠒⡄⠁⠂⢈⠀⢼⣿⡁⣾⡟⣡⠞⢁⣴⠶⠛⠋⠉⠉⠀⠀⠀⠈⠉⠛⣶⡸⣻⠷⠲⠀⠀⠈⣧⠀⠀⠀ ⠀⢠⡟⣨⠔⠃⠄⡁⠀⠐⢨⣿⠈⠛⠿⢿⣳⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⢷⣦⡶⠂⢸⣇⣿⣠⣄⠀⠀⠀⣹⠀⠀⠀ ⠀⣿⠁⡜⢨⠁⠂⠀⡀⢦⣾⠃⠀⠀⢤⡿⠋⠀⢀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢀⣾⡿⠋⠁⠀⠀⠀⠘⢿⡄⠀⠀ ⢸⡏⠀⡎⡀⠆⠀⡀⣰⣿⡇⠀⠀⢁⣾⠁⠀⢀⣾⡆⠀⠀⠀⢾⣉⡿⠀⠀⢀⣶⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀ ⠸⣷⠀⠕⢄⠠⠐⣰⡿⠋⢿⣤⠀⠈⣿⡀⠐⠛⠋⠀⠀⠀⠀⣈⣽⣧⣖⠛⠛⢯⣽⣛⡶⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀ ⢸⡿⢷⣬⣤⣶⠿⠋⠀⠙⠉⠙⢻⣶⣬⣷⣦⣤⣤⣤⣤⢶⣾⠏⠈⠁⣹⣆⣠⡀⠀⢹⡆⠀⠀⠀⠀⠀⠰⠀⣼⠀⠀ ⢸⡇⠀⠀⠀⠀⠠⠀⠀⠀⠀⠺⠋⠉⠀⢀⣠⠞⠋⢁⣰⠏⠀⠀⣴⠞⢏⣭⣯⣓⡶⠾⢥⣄⠀⠀⠀⠀⠀⣴⠇⠀⠀ ⠈⢷⡀⢀⡄⠀⠀⠈⠑⢦⡀⠀⡀⠔⠉⠈⠹⠶⠦⠷⠿⣤⣤⠾⠧⢷⡿⠉⠀⠈⣷⠀⠀⠹⡆⠀⠀⢰⠟⠁⠀⠀⠀ ⠀⠈⠛⢾⡇⠀⢠⢀⢄⠊⠙⠢⣄⡀⠀⠀⠀⠀⠚⠶⣤⣿⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣿⠀⢠⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢷⡋⠉⠳⣀⢀⠀⠀⠀⠉⠂⠀⠀⠀⢠⣤⣏⣿⡀⠀⠀⠀⠀⠀⠀⣸⢷⡀⠀⢀⣟⡴⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⣄⠀⠈⡉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠤⠽⢦⣀⣴⠏⠀⢉⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠙⠲⠮⣥⣤⣼⣦⡀⠀⠀⠀⠀⠀⠀⣀⣶⣀⣀⣀⣀⣀⣤⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠒⠛⠉⠁⠀⠀⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠶⣄⢀⣠⣤⠴⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⢠⡿⠉⠉⡉⠛⠶⠶⠖⠒⠒⣾⠋⠀⢀⣀⣙⣯⡁⠀⠀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢯⣼⠋⠉⠙⢶⠞⠛⠻⣆⠀⠀⠀ ⠀⠀⠀⢸⣧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣤⡤⢿⡀⠀⢀⣼⣷⠀⠀⣽⠀⠀⠀ ⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢏⡉⠁⣠⡾⣇⠀⠀⠀ ⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⡀⢻⡀⠀⠀ ⣀⣠⣼⣧⣤⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠐⠖⢻⡟⠓⠒ ⠀⠀⠊⣷⣀⡀⠀⠘⠿⠇⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠿⠟⠀⠀⠀⠲⣾⠦⢤⠀ ⠀⠀⠋⠙⣧⣀⡀⠀⠀⠀⠀⠀⠀⠘⠦⠼⠃⠀⠀⠀⠀⠀⠀⠀⢤⣼⣏⠀⠀⠀ ⠀⠀⢀⠴⠚⠻⢧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠉⠉⠓⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⠶⠶⠶⠶⠶⠶⠶⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣾⣶⣶⣶⣶⣦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣿⣿⡿⠟⢛⠛⡛⢛⠻⠟⠿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣿⣿⡟⢋⠠⠐⡈⠄⢂⡐⢀⠂⠌⠠⠀⠄⡉⠙⠻⢿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⠧⠅⠂⠄⠡⠐⡈⠄⡐⠂⢌⠠⢡⠈⡐⠠⢉⠐⠠⢈⠛⠿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣿⡇⠨⠄⠡⠈⠔⠡⠐⠠⠄⠃⠄⠊⢄⠘⠠⢁⠂⡌⠐⠠⢈⠰⠨⠙⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⠠⠁⠌⡀⠃⠌⠠⢁⠂⠌⡈⢌⠈⠄⠨⠐⡈⠐⠠⡁⠅⠂⠄⡁⠂⠄⠛⢻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⡅⠌⡐⠠⠁⠌⡁⠆⠌⠄⣁⠢⠌⡈⠁⠆⠄⡉⠄⠡⠈⠅⠒⢠⠁⠌⡐⠈⠌⠻⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⣿⣧⠐⡄⠡⢈⠐⡠⠌⠄⡡⢀⠢⠠⠡⠉⠤⠁⠌⠌⠡⠁⠌⡁⠆⡘⢠⢀⠡⢈⡐⠈⠻⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⣿⡆⠰⢁⠂⡐⠠⡈⢂⡐⠄⠢⠡⠘⡐⢠⠉⠄⡡⠌⠌⡐⢀⢂⠡⢂⠰⢀⠂⠄⡁⠆⠌⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣿⣿⣄⠂⡐⠠⢁⠂⠄⡐⣈⠐⣁⠒⡐⢠⠘⢠⠐⣈⠐⡀⠆⣀⠒⣀⠒⢠⠘⢠⠐⡈⠄⠡⠘⠿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⣿⣦⠐⡁⢂⠌⡐⠠⢀⠒⡀⠒⡐⢠⠈⠄⡒⢀⠒⡀⠒⣀⠒⠠⡈⠄⡘⢀⠒⠠⠈⠄⠡⢈⠙⢿⣿⣷⣄⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣷⣄⠃⡐⠠⢁⠢⠐⡈⠰⢀⠢⢈⡐⡀⠆⠂⠔⠡⢀⠘⢠⠐⠠⠄⠃⠌⡑⠈⠄⡁⠂⠌⡀⠻⣿⣿⣧⣠⣴⣾⣿⡿⢟⠛⡁⠂⠄⡀⢂⠐⡀⢂⠐⡀⢂⠉⡙⠻⢿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠛⢿⣿⣷⣤⣁⠂⡐⠡⢈⠐⡀⠢⠄⡐⠤⢈⠡⠌⠄⠡⠘⠠⠈⠔⡈⠐⠡⢀⠡⠒⠠⢁⠂⢄⠡⣿⣿⣿⣿⡿⠟⡉⠄⠂⡄⠡⠌⡐⠈⠄⠢⠐⡀⢊⠐⠠⢈⠐⡀⢊⠹⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣶⣄⠁⢂⠰⠀⠅⢂⠐⡠⢁⠂⠌⡈⠅⠌⢂⠩⠐⠠⢉⠐⡀⢂⠡⠂⡄⢈⣰⣾⣿⣿⠿⠉⠒⡀⠒⡈⢐⠠⢁⠒⠠⠁⠌⡠⠁⠆⡁⢊⠁⠆⡐⢀⠂⡐⢀⠻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣦⣆⠡⢈⠄⢂⠐⡠⢈⠐⣀⠊⢌⠰⢀⠑⡈⠄⢂⠰⢀⠂⠅⢰⣰⣿⣿⣿⡉⢂⠁⠒⠠⢁⠐⡀⠢⠐⡈⠄⠡⠒⠠⢁⠂⡐⠠⢈⠐⡈⠄⠒⡈⠄⠂⠜⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣷⣮⣐⠈⡐⣀⠂⢂⠄⠌⣀⠂⠔⡀⠂⠌⣀⠂⠄⢊⠰⣽⣿⣿⠟⠢⢀⠂⠌⢠⠁⠂⡄⢁⠂⡡⠐⡈⢄⠁⡃⠌⡐⠠⢁⠂⠔⠠⢈⡐⠡⠘⡈⠄⡘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠟⢿⣿⣿⣦⣄⠂⠄⢊⠰⠀⠌⡐⠠⢁⠂⠄⣈⠐⢂⣾⣿⡿⠧⠬⢁⠂⠌⠠⠁⠌⡐⢀⠂⢒⠠⠑⡐⠠⢈⠐⠠⣀⠁⠂⠌⢂⡁⠂⡄⢁⠂⡐⠄⠠⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣮⣄⠂⣁⠢⠄⡁⠂⠌⡐⠠⡈⣼⣿⣿⠋⠄⠂⢄⠈⠤⢁⠡⢂⠐⡈⡐⢂⠂⡡⢂⠁⠂⠌⡐⠠⢈⠌⡐⣼⣷⠨⡔⢂⠐⠠⠌⠂⠄⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠉⠻⢿⣿⣿⣦⣴⣂⣐⣁⣒⣰⣠⣼⣿⣿⡯⠜⡈⠐⡠⢈⠐⠄⠂⢄⠂⠅⡐⠄⢊⠐⠠⢈⠁⠂⠄⢡⠈⣰⣾⣿⡏⢸⠇⠠⠌⡐⢨⠐⡈⠼⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⡿⠿⢿⢿⣷⣦⣄⡉⢿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⠃⡒⠠⢁⠐⡀⠊⠄⠩⠠⠌⠠⠁⠌⠠⢈⠐⡠⢈⠡⡈⠄⣼⣾⣿⣟⠠⠉⠄⡁⢂⠐⢠⠂⠔⡈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⣃⠁⠀⠀⠀⠀⠈⢙⢿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠈⢹⣿⣿⣇⢻⠀⢂⡐⠠⢁⠊⡁⠂⠌⢠⠡⠘⠠⢁⠒⢀⠢⠘⣀⣽⣿⣿⠟⢀⠂⡁⢂⠰⢀⠊⠤⢈⡐⠀⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⢐⣛⡃⠄⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⡄⠈⡄⠠⢁⠂⡐⠠⠡⢈⠄⢂⠁⠂⡄⠊⡀⣆⣵⣿⣿⣿⠓⠈⠄⠂⠌⠄⠂⡄⠌⣰⠁⠄⡁⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠘⣿⣧⠀⠀⠀⠀⠀⠀⣴⢾⣏⠉⠙⢳⣄⠠⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣆⠠⢁⠂⠄⠡⢢⠁⠂⠌⠠⢈⠑⣀⣶⣿⣿⣿⡿⠏⡁⠄⠃⠌⡈⠌⡈⢐⠀⠒⡨⠐⠂⠄⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⢀⠀⠀⢸⡏⠖⣘⡗⠆⠀⣿⠆⠀⠀⠀⢠⣾⣿⡟⣇⢹⣿⣿⣷⣦⣌⣄⣁⠢⠠⣁⣌⣴⣶⣿⣿⣿⣿⠿⠋⠄⢂⠐⡈⠐⠂⠌⡐⠐⠂⠌⢂⡑⠨⠀⠅⣻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⢿⠀⠀⢘⣿⣂⠫⡭⠅⣠⡿⡹⠀⠀⠀⠀⠙⠻⣿⣷⣦⢉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠛⠋⠄⢂⠡⠈⠄⠂⠌⡐⢉⠐⠠⢁⡘⠠⠂⠄⢃⠡⠘⡘⢿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠁⠀⠀⠀⠀⠈⢛⢻⢶⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⢈⠔⠠⢀⢉⠉⠋⢋⠉⣁⠂⡐⠄⠡⢈⠐⡀⢂⠡⠈⠌⡐⢀⠢⠈⠔⠡⢀⠡⠌⡐⠂⠄⠡⠐⡈⠻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣨⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⣸⣿⣧⡐⢈⡐⢀⠂⠌⡐⠂⠌⡀⠒⢠⠈⡁⢂⠐⠠⠂⠄⢃⠐⠄⢂⠡⠉⠤⢁⠂⡐⠄⢂⡉⠌⠄⠡⠐⠠⠈⢻⣿⣿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣷⣦⣄⡀⠀⠀⠀⣀⣴⣿⠟⡀⠃⠄⡐⢈⠐⠂⡄⡁⠆⡀⠃⢄⠒⡀⠂⠌⢠⠁⠌⡠⠈⠔⠂⡌⠰⠈⢄⠂⡐⠈⡄⠂⡌⠌⢂⠑⢂⠡⢀⠹⣿⣿⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠿⣿⣿⣶⣤⣤⣴⣶⣾⣿⠿⢋⠁⠡⠙⠻⠿⣿⣿⣿⣿⡿⠟⡁⠆⡐⢁⠂⡐⠠⢁⠂⡐⡀⠆⡈⠔⡀⢂⡐⠡⢘⠠⢈⡐⠄⠃⡌⠂⡄⣁⠊⢄⠒⢠⠁⡄⢃⠐⡈⠂⡜⠀⠆⡀⢂⠘⣿⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⣧⡓⡀⠩⢹⠛⢟⠛⠛⡍⠠⢁⠂⡘⠄⠃⠌⡐⢀⠂⠡⢀⠒⠠⠐⠠⠐⡀⢂⠄⡁⢂⠰⢀⠒⠠⠐⡐⠐⠂⢄⠑⠠⠒⠠⡐⡈⠂⡄⠡⡐⠠⠘⢠⠈⠄⠒⣀⠂⠒⠠⠁⠄⢃⢂⠐⠠⣈⠘⣿⣿⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢃⣻⠁⠤⠁⠌⡈⠄⡈⠡⢀⠁⢂⡄⢁⠈⡐⡐⠈⠄⢨⠐⡀⢂⠡⢈⢂⠡⡈⠄⢢⠐⠄⠢⠄⠌⠄⢡⢀⠉⢌⠠⢈⠂⠡⠒⠠⢀⠃⠄⠡⠄⡑⢈⠤⠈⠌⠰⠀⡌⢂⠡⠌⠒⠠⢂⠌⡁⢀⠂⡜⣿⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⣐⠠⠈⠄⡁⢂⠐⡐⠠⢁⠂⠌⢠⡐⣠⣥⣵⣤⣧⣾⣴⣶⣶⣶⣦⣥⣦⣥⣄⣧⣀⣌⢠⠁⢌⠐⡈⢂⠐⠨⢀⠒⠠⢈⠡⢈⠁⠆⠡⠈⠅⠂⠔⠠⢂⠉⠌⠠⢃⠐⠄⠂⠌⡐⢁⠢⠐⣨⠀⠒⡀⢻⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⣿⠀⡁⢂⠐⡈⠐⠠⣁⣬⣴⣿⣿⣿⡿⠿⠛⠛⠛⠛⠛⠋⠉⠙⠛⠛⠛⠛⠿⠿⠿⣿⣿⣿⣶⣶⣥⣦⣈⡁⠂⠌⡐⠀⠆⠂⠌⡠⢁⠡⢈⠡⠌⠰⠈⠌⡈⠔⡈⠌⡈⠅⠂⠌⠠⠌⠡⠐⠌⡐⢠⠈⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠄⡧⠐⡀⠂⠌⠤⣧⣷⣿⡿⠟⠋⢉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢿⣿⣷⣶⣥⣁⡸⠈⡐⢀⠂⡐⢂⠐⣈⠡⠘⢠⠐⡐⠠⠁⡔⢈⠡⢈⠡⢘⠠⢉⠐⠄⠂⠌⢿⣿⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠂⡑⠠⡁⠍⣼⣾⣿⡟⡏⢀⠀⢀⣲⣼⣷⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣷⣤⣆⠰⠄⢂⠐⡀⢂⢁⠂⡐⡀⢃⠡⠐⢂⠂⡂⡐⣁⠂⠄⠊⠄⠡⠈⢼⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠐⠡⢐⣾⣿⡿⠕⠁⠀⠀⢢⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣮⣄⠢⡐⢀⠂⡐⠐⡀⠆⢂⡑⢂⠂⠔⡐⠠⠘⠠⠉⠄⠡⢈⢸⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⢈⠡⣼⣿⡟⠈⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⠻⣿⣿⣦⡑⣠⠀⠡⠐⡈⠄⡐⠂⠌⡐⠠⠃⡌⠠⠁⠌⠠⢁⢸⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠂⣿⣿⠁⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡈⠛⢿⣿⣶⣘⢠⠡⢀⠡⠄⡑⢂⠡⠡⠌⠠⠁⠌⠠⢱⠀⣾⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⢻⣿⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣶⣄⠀⣀⠛⣿⣿⣄⣢⠀⠐⠠⠐⢂⠁⢂⠌⠠⠑⡈⢁⠂⢴⣿⣿⡇⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣆⠐⠀⠈⢻⣿⣧⡀⡡⠌⡐⠡⠈⠄⡈⠄⡑⠠⠚⢁⣾⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢻⣯⡍⠛⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⢻⣿⣧⠐⠠⢀⠡⠌⡐⠠⠁⡄⠑⡈⣶⣿⣿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣝⣑⣡⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⣷⡈⣅⠂⡐⠠⠄⣁⠢⠄⠡⣲⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡀⠈⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⢻⣿⡇⡅⠂⠄⠡⠂⡄⠂⢌⣾⣿⣿⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣶⣶⣶⣶⣦⣄⣀⠀⠀⠀⠀⢠⠈⠻⢿⣦⣤⣂⣤⣤⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⣦⠁⠌⡀⠃⢄⣩⣿⣿⡿⠁⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀ ⠀⡴⠈⠉⠦⡀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠑⣄⠀⠀ ⠣⠀⠀⠀⠀⠀⢣⣠⠤⠤⠤⡈⠀⠀⠀⠀⠀⢸⠀⠀ ⠀⡂⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀ ⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⢀⡀ ⠀⠀⠀⠀⠈⠀⠀⠀⣄⣠⠆⠀⠀⠀⠀⠀⡞⢠⠃⠀ ⠀⡏⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠀⠀ ⠀⠀⠐⡄⠀⠀⠀⠆⠀⠀⠀⠀⠘⠄⠀⠀⢘⠀⠀⠀ ⠀⠀⠀⠉⢄⡠⠎⠀⠀⠀⠀⠀⠀⠘⠢⠜⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠛⠳⢦⣄⡀⢀⣀⣀⣀⣠⣤⣤⣄⣀⣀⡀⠀⢀⣤⣶⣦⣤⣶⠛⠛⢷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢀⣤⣤⡈⠛⢯⣍⠁⠀⠀⠀⠀⠀⠀⠉⠉⣻⣿⡿⣯⣟⡿⣿⣦⠀⠂⠹⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣀⡔⣱⣿⣿⣿⣆⠀⠻⢧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⡿⣧⣟⣿⣻⣿⣤⣤⡄⢻⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⢾⡇⢠⠏⣴⢿⣿⣿⣿⣟⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⢿⣽⣿⣿⣿⣟⡿⣿⢿⣿⣿⣷⡀⠀⠀ ⠀⠀⠀⠀⠀⣠⡞⠁⢸⠃⢧⣹⣿⡿⣽⣿⣿⣿⣮⠳⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣽⢯⣿⣿⣿⢿⣿⢿⣽⣻⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⣰⠏⠀⠀⣿⠀⣧⣿⠿⢛⡿⡯⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣟⣾⣻⣿⣿⣿⣯⣷⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⢰⡏⠀⠀⠀⣿⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠉⠉⠛⢿⣿⣽⣷⡿⠁⠀⠀ ⠀⠀⠀⡿⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠛⠉⠛⢦⡀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣀⣀⣀⠀⠀⠀⠙⠛⣿⡀⠀⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠴⠓⢝⠚⠉⠙⠂⠂⢟⣦⡀⠀⠀⢸⡇⠀⠀⠀ ⠘⠒⢿⠷⠶⠤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⢻⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢙⣤⡤⢾⡗⠒⠒⠂ ⠀⠀⢸⡆⠀⠀⠀⠈⠩⣏⡛⠲⠆⠀⠀⠀⠀⠀⠀⢀⣦⣄⠀⠈⣷⣿⡄⠀⠀⠀⠀⠀⠀⣿⠀⢀⣠⡶⠀⠁⠀⣼⠇⠀⠀⠀ ⠀⠀⠈⣧⠀⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡆⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠃⠀⠚⢛⡟⠛⠒⠀⠀ ⠀⠀⠀⢹⣆⣀⣤⡤⠶⠞⠛⠻⣷⣄⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣟⡠⢀⣀⣼⡁⠀⠀⠀⠀ ⠀⢠⡴⠞⠻⣍⠀⠀⠀⠀⠀⠀⣹⣿⣧⡀⠀⢀⠀⢿⣿⡿⠃⠀⠀⠀⠀⠀⢠⣴⡶⣤⠀⠀⣠⡾⣻⡮⢤⣾⠿⢿⣷⣦⡀⠀ ⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⣀⡾⠁⠈⢿⣿⣆⠈⠹⠏⠿⠷⠶⠂⠀⠀⠀⠀⠸⣿⡿⠿⠀⠸⠋⠳⢏⣰⡿⠀⠀⣼⠇⠈⢿⠀ ⠀⠀⠀⠀⠀⠀⠘⢳⣤⡾⠋⠀⠀⠀⠈⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣾⣿⣿⠇⠀⢰⡏⠀⢀⣾⡇ ⠀⠀⠀⠀⠀⠀⢀⡾⠋⠛⠶⣄⡀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡟⠇⢀⡞⢁⡇ ⠀⠀⠀⠀⠀⠰⠟⠁⠀⠀⠀⠈⠉⣳⡶⢦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣏⣾⣿⣿⣿⣿⣿⢻⣿⣿⣿⡟⠁⠀⠀⠀⠀⠋⠀⣸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⢣⡟⣼⣛⣿⡀⠀⠀⠀⠀⠀⠀⣰⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⢸⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⡼⣓⢾⡱⢮⡽⣷⣄⣀⡀⣀⣤⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣤⣄⣀⣀⠀⢸⣟⡞⡼⣭⣛⠿⣹⢻⠽⣭⢳⡹⢶⣙⢮⡳⣝⣣⢞⣽⠏⠉⠉⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠉⠉⠛⠻⣿⣜⡳⢧⣝⣫⢗⣫⡝⣮⢳⡝⣣⢏⡾⣱⢧⣋⢾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣝⡳⣎⡳⣎⢧⡻⡜⣧⡛⣵⢫⢞⡵⢮⣝⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢀⣤⣶⠿⣎⡵⣫⢵⢫⣞⣱⢻⡴⣛⡼⣹⢞⡼⣳⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⡀⠀⣀⣤⡿⣏⣗⢻⣬⢳⡝⣮⢳⢎⣧⢳⡝⡮⣵⢣⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠹⣿⡵⢫⣜⡳⣎⠷⣹⠖⣯⢺⣬⢳⣾⣵⣿⣿⣿⠟⠋⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢣⡏⣷⡎⡟⣥⢻⡜⣷⣿⣿⣿⢹⡏⠁⠀⣴⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣮⣝⣶⣭⢳⡝⣎⣷⣧⣷⢾⡏⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣍⠉⠙⠛⠙⠉⠉⠁⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠶⠖⠖⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⣴⡏⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡸⠟⢹⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠘⣇⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⠀⠀⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⣷⣠⣿⣤⣤⣦⠀⠀⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣶⠆⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠘⣷⣄⠀⠀⠀ ⠀⢸⠟⢁⣴⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⡈⠙⠀⠀⠀ ⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⣿⣿⡇⢸⣿⣿⣿⣿⣿⣯⠉⣹⣿⡟⢉⣿⣿⣿⣿⣿⣿⣿⠀⠀⣸⣿⢿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣼⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣷⡈⢿⣿⣿⣿⣿⣿⣦⡈⠉⢀⣾⣿⣿⣿⣿⣿⣿⠏⠀⢠⣿⡿⠀⣿⡇⠀⠀⠀⣿⣿⣿⡂⠋⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢠⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⣤⣄⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⣿⣧⠈⢿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⡟⠀⢠⣿⡿⠁⠀⢹⣿⡀⠀⠀⢻⣿⣿⣿⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⣠⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣼⡿⣿⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⣧⡈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀⣴⣿⡿⠁⠀⠀⠀⢻⣿⣄⡀⠀⠻⣿⣿⣿⣏⣻⣿⣿⣿⣿⣿⣿⡿⠏⠀⢠⣾⣿⣿⡿⠃⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⣿⣿⠘⣿⡟⣱⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣿⣿⣮⣿⣯⠛⠻⠿⢿⠿⠿⠟⠋⠁⢀⣴⣾⡿⠋⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣤⣈⡙⠿⠿⠿⡿⠿⠿⠟⠉⠀⠀⢀⣴⣿⣿⣿⢿⣵⣶⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠘⣷⣿⣏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣆⣤⣄⣤⣤⣴⣶⣿⣿⠿⠉⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣷⣶⣶⣴⣤⣔⣦⣴⣶⣿⣿⣿⣿⣿⣿⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣶⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣤⣶⣦⠀⠈⢹⣿⣿⣿⣿⣟⠛⢙⠙⠉⠀⢠⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣄⢩⣽⣿⣿⣿⣿⣿⣿⣿⣟⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠛⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⣿⠛⣿⣧⠀⣼⣿⠈⢙⣿⣿⣿⣿⣿⣴⣶⣿⠟⠉⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⠿⠛⠉⠀⠉⠙⠛⢿⣿⣶⣶⣴⡄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣠⣤⣤⣿⣿⡇⠀⢻⣿⡆⢹⣿⣷⣿⠟⠋⠀⠉⠛⠻⠿⣿⣶⣤⣤⣤⣀⡀⡀⡀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣿⣯⣻⡿⠃⠀⢸⣿⡇⠀⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠻⣿⣿⣿⠷⣿⡿⠿⠿⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢴⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠻⠿⠿⣿⣿⣶⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣠⣤⣤⣤⣀⠈⠻⡷⢽⣛⠣⠤⣤⣴⣶⣶⡶⣿⣻⣟⣿⣻⣟⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠿⠿⣟⣷⣶⣤⡀⠀⠈ ⠀⢠⣤⣶⡶⣾⣟⡿⣟⣿⣧⠀⢀⣠⠶⠿⡿⣽⣻⡿⠛⠛⠂⣼⡿⣿⠆⠻⠟⠚⠓⠛⣻⣷⣻⢾⣽⣿⠉⠠⠐⣠⠖⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⢹⣿⣷⡀⠀ ⠀⠸⠿⠚⠛⢋⣉⣉⣉⣀⣤⣴⡟⢁⣶⣿⡶⣤⣈⣷⠦⣕⢦⣿⣻⡟⠀⠀⠀⠀⢀⣼⣿⣳⡏⣿⣞⣿⢂⡵⠋⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⡁⠊⠄⠂⢻⣿⣧⠀ ⢠⣶⡾⣿⣻⣟⣿⣯⣿⢿⣽⣻⡇⠘⠛⠺⡿⢽⠟⣸⡀⣠⣿⢯⣿⠣⡀⠈⢠⣴⣿⣻⡾⠃⠘⣿⣟⣾⣯⠴⢋⠡⢄⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠡⠈⡔⠈⣿⣿⣧ ⠠⢛⢛⣉⠟⡉⢄⡀⢠⣾⡷⣿⠁⠀⠀⢸⠅⠀⢀⣯⣾⢿⣯⢿⣄⣣⠘⡞⠻⣿⡾⠋⠘⢷⣿⣻⣽⣾⠏⢄⠣⡈⡔⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠄⠁⠘⣽⣿ ⡤⣘⢤⡸⣸⢣⣤⣼⣿⣟⣿⠃⢀⠇⠀⣼⣤⣼⣿⢿⣻⡿⠃⠀⠀⠻⣇⢻⡠⢇⠼⢇⠀⠘⠧⡟⢻⠀⠸⢄⠠⠃⢄⠣⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢿ ⢧⢘⣦⢷⣿⣻⣟⣯⣷⠟⠁⠀⣸⠀⠀⣽⠿⡿⡾⠋⣥⡇⠀⠀⠀⠀⠈⢏⣧⠄⠠⠈⢳⡀⠀⠹⡌⣷⡀⢣⠜⡁⠊⠔⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻ ⣻⡐⡾⣿⣷⡿⣾⣏⡆⠀⡀⠀⡿⠀⢀⣿⢀⡼⠁⠀⣿⡇⠀⠀⢀⣀⠤⠈⢏⣷⡀⠁⠈⢿⡄⠀⢻⣿⣇⠌⣚⠀⡉⠈⠁⢊⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡽⣗⡽⣲⢧⡳⣾⢿⠀⠀⡇⠀⡷⡇⢸⢇⣾⠁⢀⡀⣿⡗⠛⠉⣁⣄⣀⡀⠘⡽⢿⣦⣍⣢⣿⡴⡀⠻⣸⡐⢌⣃⠈⠀⠉⠐⡸⣀⠐⡈⠄⠂⢄⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣟⡧⠙⠩⠇⠉⣿⣿⠀⠀⡇⠀⣿⡄⣿⣼⠿⠀⣸⡽⡟⠀⠠⣿⣾⣿⣟⡿⣷⣿⡎⢳⣿⡵⠐⠾⡵⣄⠙⣧⡢⣜⡐⣂⢂⠒⡀⢧⠈⡐⠈⡌⠄⢒⡀⠂⠌⠠⢀⠀⠀⠀⠒⣘⠠ ⣯⣿⡔⠒⠜⣰⡟⢿⠀⠀⣇⠀⣿⣿⣋⣼⣀⡴⠟⠝⠀⠀⠀⠿⣷⣿⣿⡅⢸⠟⡇⠀⠁⡇⠀⠘⣇⠸⣷⣌⠳⣄⡁⠈⠈⠑⠈⠊⠓⠈⠓⠔⠪⡔⣤⢡⣌⢡⢂⠌⢂⠁⠂⢭⠒ ⣿⡆⣧⠛⡜⣸⡇⠸⡄⡄⢹⡀⢸⣿⣿⡷⣶⡄⠀⠀⠀⠀⠀⠀⠻⣭⡶⠇⠀⠀⣷⠀⢈⡧⠀⢠⣿⡀⢻⡹⣕⠦⣙⡲⢤⡀⠀⠁⠉⠀⠄⠢⢁⡀⡀⠄⠈⠄⠋⠚⠡⠋⠜⢦⡝ ⣯⡗⢸⡅⢳⠈⣇⠄⢧⣇⠘⣇⠾⣿⠘⣿⣿⢵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣼⡅⣴⣿⣯⡇⠈⣿⡈⣕⠢⣉⠁⠀⠈⠀⠈⠈⠀⠀⠀⠀⠀⠉⠉⡘⠒⠒⠢⠱⠄⠦⣀ ⣿⣻⢘⡧⢍⠲⢹⡀⠘⣿⡀⢻⡆⣟⡦⣈⡱⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⣿⣿⣿⢿⣿⡇⠀⢻⣿⡼⣆⠀⠨⠐⠦⣄⡀⠐⡐⠨⢐⠠⠁⡂⠅⡒⠐⡀⠣⡐⢈⡐⠀ ⣿⡇⠚⡇⠊⠑⠈⠳⡀⣿⣇⠈⣿⣿⣷⢦⠄⠀⠀⠀⠀⢀⣀⡤⠴⢆⠀⠀⠀⢰⢃⠞⢻⡙⣻⣿⣿⣧⠀⢸⣿⣷⣌⣙⠦⣤⠤⠦⣍⣓⠦⣄⠀⠢⠑⡠⠒⣈⠱⡀⡃⣌⣤⡴⣤ ⣿⡇⠰⡇⠀⠀⠀⠀⢰⣿⠿⡆⢹⣿⣏⣇⠀⠀⠀⠀⠹⣿⠇⠀⠀⣸⡇⠀⠀⣾⠏⠀⢸⣿⣇⠀⠹⣿⠀⢸⡿⡿⡏⢁⠀⠉⠉⠹⣶⡹⣏⠾⡿⣶⡰⠀⢁⡀⢁⠷⡸⣾⡸⣿⣹ ⣿⠁⠠⠁⡀⠀⠀⠀⣾⠏⠀⠙⣌⢿⣯⣻⣧⣀⠀⠀⠀⠈⠛⠶⠴⠞⠀⢀⡴⠁⠀⢤⣿⣿⣹⠀⠀⣿⠀⢸⣷⠛⢁⠀⡀⢀⡐⠠⣰⡟⠺⣧⡈⠓⣽⣿⢗⣦⣄⡈⠁⢳⡝⣳⢿ ⡟⠀⠀⠀⠀⢀⣠⣞⣁⠀⠀⠀⢸⡾⡏⠙⣿⣻⣷⣶⣤⣤⣀⣀⣀⣠⣔⣃⣀⣤⣶⡿⠋⣘⠴⡇⠀⡏⠀⡟⠙⠦⣄⠂⠐⠠⠐⣰⣿⠇⠀⠈⢷⣰⡿⢛⠛⣯⣀⡍⣙⠒⠯⣁⠠ ⡇⠀⠀⠀⠴⣌⣁⠈⠉⠉⠒⢤⣊⠃⣷⣀⠘⣿⣿⢖⣿⢻⣿⠏⠉⠁⢸⡟⠛⠋⠉⠀⡞⡁⠀⠃⢰⠃⡸⠀⠀⠀⢈⣻⡤⡁⢰⣿⠏⠠⠑⢬⣺⣿⠳⡁⠲⢤⠰⠰⣌⡜⠰⣜⠢ ⡇⠀⠀⠀⠀⠀⠉⠉⠒⠢⣄⡀⠈⣳⠏⠀⠀⣀⣉⡛⢿⣿⡃⠀⠀⠀⢸⠙⣆⠀⠀⣸⢧⠁⠀⢠⡎⣰⡷⣶⡟⢫⡉⢅⡐⡍⣾⢃⡞⢠⢩⣶⣿⠃⠦⢉⡑⡊⢥⢓⣦⣙⡼⢡⡐ ⣉⣱⠀⠀⠀⠀⠀⠀⠀⣰⢏⣽⡶⠁⢀⡠⠚⠉⣀⣵⢸⡇⢃⣠⡆⠀⠘⡀⠈⢣⣠⢻⠀⠀⢀⡞⣰⢻⠇⢸⠏⢦⢱⡂⡔⣸⡏⢸⠄⢂⣿⣿⣧⡍⠢⢵⠋⠓⣎⡞⠈⢻⡜⣢⢝ ⣖⢳⡂⠀⠀⠀⠀⠀⢠⣏⡾⣽⢣⡜⠉⠀⣠⠎⠀⣈⠹⣿⣻⡟⣇⠀⠀⡇⠀⢰⡛⣽⠀⢀⠞⣰⢃⣼⠀⣼⡉⢆⠣⠿⣿⢸⡇⡿⢀⣿⣿⣏⠁⠙⢧⣋⠗⡺⣙⡇⠀⢸⣞⡱⢮ ⣤⣲⣤⡴⣤⣲⢤⣤⡟⣼⠟⣡⠃⣧⡀⠔⠁⠀⣴⠃⠈⢸⣧⣿⡯⢱⣦⡸⠀⠀⠈⠀⢣⠏⣰⣧⠋⢸⠀⣿⢈⢎⡱⣍⠹⣾⣿⠣⢼⣿⢣⢊⠷⣄⠀⠙⣮⢱⢸⡇⠀⢸⣾⡹⣯ ⠒⢿⣶⣿⣷⡿⣞⣾⡹⠋⣰⠷⣽⣳⣽⣄⠀⠈⠁⠀⠀⠀⣿⢻⣯⠸⣿⣷⣄⠀⠀⠀⡎⠀⡩⡇⠀⣼⠀⣿⠈⠆⡑⠠⢁⣻⣿⣀⣻⣏⠥⢋⠀⠙⢦⠀⠘⣧⡿⠀⣠⣾⣳⢿⣵ ⣴⣟⡿⣷⢿⣻⣼⡟⠁⡼⣯⡿⣱⢇⣿⢿⣿⡦⣄⡀⠀⠀⣾⣷⢻⠀⣏⢿⣯⢆⠀⠸⣷⠀⠉⢧⢀⡏⢠⢿⠀⢃⢠⣾⣿⣿⣿⣿⣿⣷⣦⣄⠂⠀⠈⠳⠈⠘⠃⠔⣾⣿⣽⣻⣞ ⣷⣾⢹⡏⣯⢳⡏⠀⢰⣿⠋⣾⢣⣾⣿⡇⢹⣷⣦⣭⣵⡟⣽⡟⣼⡄⢹⠈⢻⣯⣦⠀⠘⣧⣤⡌⡟⣧⣼⡏⠈⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢠⠀⠀⠀⠀⣶⣿⣿⡞⣷⢻ ⡷⣎⠿⡼⡭⣿⠀⢂⢘⣡⣾⢏⣶⠻⢻⡏⠢⣈⠛⠛⣋⣴⠟⣱⠻⠇⠸⣇⠈⢻⣮⢆⠀⣿⣏⡼⣛⢓⣮⡙⠲⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢀⣴⣾⢿⣿⣿⡿⣽⣻ ⢤⣉⠜⡠⠡⣭⠗⣢⣼⡿⠒⠚⠳⢴⡠⠹⣦⣈⣙⣋⡵⢁⡾⠁⢴⡛⢩⡛⢛⣿⣿⣷⣷⣿⣳⣿⡄⣮⢱⢻⡄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣭⡚⡿⣿⣿⡿⣷⣻ ⠀⠈⠡⡰⢛⡕⠊⠁⠀⠳⣄⡀⠀⠀⢱⣧⠘⠷⣿⡏⠀⣻⠁⠈⠸⣔⣣⢡⣾⣿⣏⣿⠿⣿⣿⡯⣽⢲⠏⣼⡇⣳⠏⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⢷⣽⣿⢿⣳⢿ ⠀⠀⠀⢠⠚⠀⠀⠀⠀⠀⠩⠻⠷⡏⠈⢸⣍⡲⢼⣶⡀⢿⠀⠑⠒⠹⣇⣾⢯⢏⣼⣿⠀⠸⣿⣷⢿⣿⣼⡿⣿⡁⠐⢌⠒⡈⢉⠛⡿⣿⣟⣿⣿⣿⣿⣿⣿⣿⢿⣶⣿⣻⣿⣯⢿ ⣧⡀⣀⣂⠀⢀⠀⡰⠄⡄⢀⡑⣔⣋⠒⣿⣿⡟⣵⣿⢙⢺⡟⢦⣬⣟⣟⣿⣿⣾⡿⡇⠀⠁⣿⣩⡿⣽⡟⣵⢯⣹⣑⠎⣴⣡⣎⡽⣞⣽⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿

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⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣾⡿⠿⠿⠿⢿⣷⣤⡀⣠⣾⡿⠟⠛⠛⠛⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠟⠁⠀⠀⠀⠀⠀⠉⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⢀⣀⣀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣄⣿⣇⠀⠀⣾⣿⣿⣷⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣆⠀⠀⠀⠈⠿⠿⢿⣿⡿⣿⣆⡀⠘⠻⠿⠋⢀⣴⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⡿⠻⢷⣦⣤⣤⣴⣾⠿⠋⠀⠈⠙⠿⠷⠶⠶⠿⠟⠋⠉⢿⣷⠀⠀⠀⠀⣠⣶⣿⡇⠀⠀⠀ ⠀⢸⣿⡇⠀⠀⠀⠈⣁⠀⢀⣤⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠐⣾⣿⡇⠀⣠⣾⣿⡿⢿⣿⠀⠀⠀ ⠀⢸⣿⡇⠀⠀⠀⠀⠈⢀⣿⡟⠁⠀⠀⠀⠈⠻⣿⡄⠀⠀⠀⣼⢿⣿⣧⣾⣿⡿⠋⠀⢸⣿⡀⠀⠀ ⠀⠀⢿⣿⡀⠀⠀⠀⠀⠸⣿⣄⠀⠀⠀⠀⢀⣴⣿⠇⠀⣠⡾⢃⣾⣿⣿⠟⠁⠀⠀⢀⣿⡿⠀⠀⠀ ⠀⠀⠀⠻⣿⣦⣤⣀⣀⠀⠙⠻⠿⢷⣶⣿⣿⣛⣡⣤⣿⣵⣾⣿⣿⠟⠁⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⡟⠉⠙⢿⣿⣀⡀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀ ⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⣿⣿⣿⣧⣀⣠⣾⣿⣿⣿⣷⡄⠀⢸⣿⣷⣾⣿⣶⡀ ⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⡟⠿⠿⠿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠋⠈⠉⢀⣿⣿⣿⣿⣿⣷⣄⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠙⠻⠿⠿⠿⠋⠀ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢿⣿⣿⣿⣿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠁⠀⠀⠻⢿⣿⡿⠿⠿⠿⠿⠿⠟⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⣴⡾⠋⠉⢀⣀⡈⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⢉⣶⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⠀⣾⡏⠀⢀⣮⣁⣀⣈⣣⠀⠘⠛⠛⠛⠋⠛⠛⠓⠶⠟⠃⣰⣋⣀⣠⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣧⡀⠀⢈⠀⢹⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠉⢠⡀⠀⠀⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⢳⣇⠀⠈⠓⠤⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠤⠐⠁⠈⢦⠀⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠳⡄⣿⣿⣿⣿⣿ ⠀⠀⠀⢠⠃⠀⢀⣀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣶⣦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣳⡘⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢀⣿⣿⣧⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⣀⣴⣪⠿⠛⠉⣩⡟⢻⣭⠙⠻⣝⢦⡀⠀⠀⠀⠀⠀⠀⢱⣷⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣀⠀⠀⢸⡏⠀⠀⠀⠀⠀⢀⡴⣵⠋⠁⠀⠀⢠⡟⠀⠀⢻⡀⠀⠈⢳⡱⡄⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷⣦⡞⡇⠀⠀⠀⠀⢀⣾⡾⣱⠀⠀⠀⠀⡼⠀⠀⠀⠈⣗⠰⠆⠀⢻⡽⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠋⢸⡇⠃⠀⠀⠀⠀⣸⣹⢡⡇⠀⢀⣁⣾⠇⠀⠀⠀⠀⠿⣤⣀⢀⠀⣷⣇⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢿⣿⣿⣿⠋⠀⠀⠀⣇⠀⠀⠀⠀⠀⢹⣿⢸⡷⣾⣿⣿⣿⠂⠀⠠⠄⠀⢸⣿⣿⣿⡆⢸⡟⡆⠀⠀⠀⢰⡟⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠈⢿⣿⡿⠀⠀⠀⠀⢹⣴⠀⠀⠀⠀⢸⣿⣾⡏⠁⠙⠛⠋⠀⠐⢤⡴⠃⠈⠙⠛⠁⠁⢾⣿⠇⠀⠀⢠⡿⠁⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢀⣾⠃⢻⡀⠀⠀⠀⠀⢳⣇⠀⠀⠀⠀⠹⣯⠀⠀⠀⠀⠀⠀⢠⡼⠻⠦⠀⠀⠀⠀⠀⣠⡟⠀⠀⣰⡿⠁⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣾⠇⠀⠈⢧⡀⠀⠀⠀⠈⢧⠳⣄⠀⠀⠀⠈⠛⢶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠀⣠⣾⠟⠀⠀⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢠⣯⠳⣄⠀⠀⢹⡄⠀⠀⠀⠀⠑⢬⡓⠤⣀⠀⠀⠀⠈⠉⠛⠛⠛⠛⢶⡄⠊⠘⠉⢁⣀⣴⡾⠋⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⣇⠈⣧⠀⠀⣇⠀⠀⠀⠀⠀⠀⠈⠓⠈⠙⡦⣄⣀⡀⠀⠀⠀⣀⡬⠧⠴⠶⣾⠛⢻⡅⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⣷⣿⣿⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠈⠉⠁⠀⠀⠀⣠⠞⠃⠀⠘⣧⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⢻⣿⠟⠁⠀⠀⠀⠈⠑⠒⠤⠔⠒⠙⠒⠊⠁⢀⡀⠀⠀⠀⠀⠀⠀⢰⣯⠁⠀⠀⠀⠀⢻⣆⠀⠠⡀⠀⡔⠁⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⢀⣤⣄⣀⣀⣀⣀⣀⣠⣤⡄⢷⡀⠀⠀⠀⠀⠀⢸⣿⣷⡀⠀⠀⠀⠠⣿⠀⠀⡠⠊⠀⠀⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⢀⣴⠟⠉⠈⠉⠉⠉⠉⠉⠉⠁⠁⠈⢷⣄⠀⠀⠀⠀⠈⣿⠈⠛⠷⠶⣼⠾⠋⡠⠊⠁⠀⠀⠀⣿⣿⣿⣿⣿ ⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣷⣤⣤⣤⣽⣿⣤⣤⣤⣤⣤⣴⣯⣤⣤⣤⣤⣤⣤⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣀⠀⠀ ⠀⣤⡶⠶⠶⠶⠶⢦⣤⣄⣀⣠⣤⡶⠶⠿⠿⠛⠛⠛⠛⠻⠿⠶⠶⣦⣤⣀⣀⣴⠾⠟⠋⠉⢀⣀⣀⠀⢻⡆⠀ ⠀⣿⠀⡆⠀⠀⣒⣢⡄⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠠⢔⣒⠉⠉⠀⢈⠀⢸⠇⠀ ⠀⣿⠀⡇⢀⣬⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠥⡄⢸⠀⣿⠀⠀ ⠀⣿⠀⣇⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡌⠀⣿⠀⠀ ⠀⢿⣄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣸⡇⠀⠀ ⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀ ⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⣷⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠸⣧⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡇ ⠀⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⠀⢀⣀⣤⣴⣤⣤⣄⣀⠀⡸⠀⢸⡇ ⢠⡟⠀⠀⠀⠀⣀⣘⣿⣿⡿⠃⠀⠀⠀⢀⣆⠀⠀⠀⠀⠈⠻⠿⠟⣁⢀⣴⡟⡫⢟⣒⣒⡢⢍⠛⢷⣅⠀⣾⠁ ⠘⣧⠀⠀⠀⠎⠀⠀⢹⠀⠀⠀⠀⠀⠀⠛⠉⠓⠀⠀⠀⠀⠀⠀⣎⢠⡿⡳⢫⢞⣡⣤⣤⣌⢣⣱⡈⣿⣶⡟⠀ ⠀⢿⡀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⢳⢣⡿⣳⢺⣿⣿⡇⡇⡇⢹⣿⠀⠀ ⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣸⣸⣣⣧⣘⢛⣻⣇⣷⠇⣼⣿⠀⠀ ⠀⠀⠀⠈⠛⠷⢦⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣧⡧⣑⢷⣫⣭⣽⠿⢋⣼⣾⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⡟⠁⠀⠀⣀⢀⣀⣀⣀⠀⣀⣄⣀⣠⡾⣿⣿⡿⢿⣮⣁⣛⣛⣋⣩⣿⠿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠉⠛⠉⠉⠙⣿⡋⠉⠉⠙⠛⠛⠃⠈⠒⢬⠉⠛⣿⡉⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠰⠶⠾⠛⠋⣿⣿⠟⠉⠛⠻⠶⠶⠶⠀⠀⠀⠘⡄⠀⢹⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⢿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠘⠃⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠞⠁⠀⠈⠑⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠁⠀⠈⠳⣄⠀⠀⠀⠀ ⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠤⠤⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⢠⠄⢄⠀⠀⠀⠈⠳⡀⠀⠀ ⠀⣠⠋⠐⠒⢂⠀⠀⠀⠀⠢⠔⠁⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠘⠤⠜⠀⠀⠀⠀⡠⠽⣆⠀ ⢸⠧⡀⠈⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢖⠤⣙⢆⠀⠀⠀⠀⠀⠀⡠⠊⣀⠤⣰⡖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠪⢤⡿⡇ ⠈⠳⣈⠳⣄⠀⠀⠀⠀⢀⣀⠀⠀⠀⡔⠀⢻⠪⣑⢷⡖⠦⠶⣒⡾⢓⡩⠔⠉⡃⢈⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢁⡼⠁ ⠀⠀⠈⠳⢌⡳⢤⡀⠀⢇⢀⠇⠒⠤⣬⡦⠥⠄⠀⢹⡸⠀⣀⢀⡏⠡⣤⡀⠶⠚⠉⠀⠀⠀⢸⠩⢱⡠⢞⡡⠖⠉⠀⠀ ⠀⠀⠀⠀⠀⠉⢑⣻⠷⠲⣤⣤⣄⣀⣀⣠⣬⣭⢽⡻⣆⣀⣇⣠⣛⢦⣤⣤⣄⣀⣀⣀⠤⠤⠔⠿⢿⡊⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡤⠾⡍⠀⠀⠀⣀⡠⡔⠒⡄⣠⣖⣵⠿⡲⡿⠀⠀⢿⢦⠑⢵⣄⠉⠛⢳⣦⣖⡀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀ ⠀⣠⣶⠋⠑⠄⠃⠄⠒⠋⠁⠀⠑⢒⣿⣻⡟⣍⠞⢡⠃⠀⠀⠘⡎⠳⡄⠙⢧⣴⠋⢣⠈⠉⠒⠄⠀⡉⢈⠆⠉⠳⣄⠀ ⣜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠐⢈⣴⣃⡁⡞⠀⠀⠀⠀⢱⠀⠈⢦⡀⠙⢖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳ ⠘⢦⣎⠀⡁⠀⠀⠀⢀⠀⡀⠈⠀⢀⡴⠋⠀⠀⢰⠁⠀⠀⠀⠀⠈⣇⠬⢄⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡹⠃ ⠀⠀⠻⣍⠀⠀⠀⠀⠣⣈⠞⢀⡴⠋⠀⢀⠀⣀⡏⠀⠀⠀⠀⠀⠀⢸⡤⠜⠀⠀⠙⠦⡀⠀⡔⠐⡄⠀⠀⠀⣠⠞⠁⠀ ⠀⠀⠀⠈⠑⢤⡀⠀⢀⡡⢶⠃⠀⠀⠀⠸⠄⢼⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⣷⢥⡂⠁⢀⡠⠞⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠉⢠⠇⡄⠢⡀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠂⠐⡸⡄⠈⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠃⠔⠁⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣠⡕⠟⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠠⣰⢏⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⡺⡁⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣠⡆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⣆⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡴⠁⢇⢰⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⠄⣸⠈⢦⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⡜⠁⠀⠸⡌⠁⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⢡⠇⠀⠀⢫⡈⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⡟⠀⠀⠀⠀⠹⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠎⠀⠀⠀⠀⢻⣸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠹⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠎⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠞⠉⠉⠀⠀⠀⠀⠀⠀⠈⠓⠒⢄⠀⠀⠀⠀ ⠀⠀⠀⢀⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⠀⠀ ⢀⡄⠠⠼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀ ⠈⠢⠤⡖⠛⢀⡤⠴⠺⢤⣀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢱⡀ ⠀⠀⠀⢳⠀⣿⢠⣀⡀⠀⠀⠀⠀⠉⠀⢖⠀⠀⢀⠐⢆⡾⠁ ⠀⠀⠀⠈⢇⢸⡀⠉⠐⡷⠀⠀⠠⣤⡀⠸⡍⠀⠘⢆⡀⢉⡆ ⠀⠀⠀⠀⢎⡝⠑⣤⣀⢯⠃⠀⠀⠀⠀⢠⠃⠀⣀⠜⠉⠉⠀ ⠀⠀⠀⠀⠀⢳⣀⡔⠈⠑⠒⠒⠒⠒⠛⠉⠉⠉⠓⡤⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠗⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⢸⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢳⠦⣟⣲⣄⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠚⠃⠻⣭⡽⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣾⡿⠿⠿⠿⢿⣷⣤⡀⣠⣾⡿⠟⠛⠛⠛⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⠟⠁⠀⠀⠀⠀⠀⠉⢿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⢀⣀⣀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣄⣿⣇⠀⠀⣾⣿⣿⣷⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣆⠀⠀⠀⠈⠿⠿⢿⣿⡿⣿⣆⡀⠘⠻⠿⠋⢀⣴⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⡿⠻⢷⣦⣤⣤⣴⣾⠿⠋⠀⠈⠙⠿⠷⠶⠶⠿⠟⠋⠉⢿⣷⠀⠀⠀⠀⣠⣶⣿⡇⠀⠀⠀ ⠀⢸⣿⡇⠀⠀⠀⠈⣁⠀⢀⣤⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀⠐⣾⣿⡇⠀⣠⣾⣿⡿⢿⣿⠀⠀⠀ ⠀⢸⣿⡇⠀⠀⠀⠀⠈⢀⣿⡟⠁⠀⠀⠀⠈⠻⣿⡄⠀⠀⠀⣼⢿⣿⣧⣾⣿⡿⠋⠀⢸⣿⡀⠀⠀ ⠀⠀⢿⣿⡀⠀⠀⠀⠀⠸⣿⣄⠀⠀⠀⠀⢀⣴⣿⠇⠀⣠⡾⢃⣾⣿⣿⠟⠁⠀⠀⢀⣿⡿⠀⠀⠀ ⠀⠀⠀⠻⣿⣦⣤⣀⣀⠀⠙⠻⠿⢷⣶⣿⣿⣛⣡⣤⣿⣵⣾⣿⣿⠟⠁⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⡟⠉⠙⢿⣿⣀⡀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀ ⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⣿⣿⣿⣧⣀⣠⣾⣿⣿⣿⣷⡄⠀⢸⣿⣷⣾⣿⣶⡀ ⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇ lovely♥ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠋⠈⠉⢀⣿⣿⣿⣿⣿⣷⣄⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠙⠻⠿⠿⠿⠋⠀ ⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢿⣿⣿⣿⣿⠿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠁⠀⠀⠻⢿⣿⡿⠿⠿⠿⠿⠿⠟⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢉⣤⣤⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣴⣿⣿⣿⣷⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⡿⠟⣋⣡⣤⣶⣶⣶⣶⣶⣶⣤⣭⣁⡛⠿⣿⠿⠟⠛⠻⢿⣿⣿⣿ ⣿⣿⣿⠟⢉⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡒⢿⣿⣷⠈⣿⣿⣿ ⣿⣿⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⡿⢠⣿⣿⣿ ⣿⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⢺⣿⣿⣿ ⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠻⠿⣿ ⠁⣿⣿⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣇⢸⣶⠈ ⠀⣿⢏⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡹⣿⣿⣿⣿⣿⣿⠘⢋⣴ ⠀⣇⠿⠷⢄⣴⣿⣿⣷⣬⣉⣉⣩⣤⣿⣿⣿⣦⡠⠾⠿⣸⣿⣿⣿⣿⡏⢰⣿⣿ ⡇⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⠻⣿⣿ ⣿⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣾⡇⢸⣿ ⣿⣿⣦⡙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢋⣠⣭⣥⣴⣿⣿ ⣿⣿⣿⣿⣷⣤⣉⡛⠛⠿⠿⢿⣿⣿⣿⣿⠿⠿⠿⢛⠋⣥⣶⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⠏⣸⣿⣖⠶⣶⣶⣶⠖⣲⣾⣿⡈⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⢠⣯⣙⣛⣃⣽⣿⣇⣚⣛⣫⣽⣧⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⠇⠘⢠⣌⣭⢻⣿⣿⣿⢫⣍⣥⠘⠿⠀⣀⣈⠉⢹⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣄⠻⡿⣿⣿⢨⣿⣿⣿⢸⣻⡟⣿⠃⣠⣿⡿⠗⣸⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣦⡉⣓⣋⡘⠛⠛⠛⠂⠓⢚⣡⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠚⠉⣸⣿⣅⣀⠀⠀ ⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣾⠿⠿⠿⠿⠛⠉⠀⠀ ⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡎⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠛⠛⠛⠛⢛⠛⠛⠻⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰ ⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉⠉⢀⣤⠞⠋⠀⠀⠀⠀⢀⡤⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⣠⠴⠂⠀⠈⠉⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⢀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿ ⣿⣿⣿⣿⠏⣠⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿ ⣿⣿⣿⢏⡴⠃⠀⠀⢠⡞⠁⠀⣠⠔⠀⣠⢞⣡⠞⠁⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⡠⢻⠁⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⢀⣴⣿⣿⠉⠉ ⣿⣿⡷⠋⠀⠀⠀⣰⠋⣀⠴⠋⠀⣠⠞⢡⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⣀⡴⠊⢁⡴⠊⢁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣦⡀⣠⣾⣿⡟⠉⠀⢀ ⡿⠏⡀⠀⢀⣠⣾⠷⠋⠁⠀⣠⠞⠁⢠⠏⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⣀⡴⠚⠁⣠⠔⠋⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣸⠁⠙⢿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠃ ⣁⣠⠵⠞⠛⠉⠀⠀⠀⣠⡾⣡⠄⢠⡟⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⢀⣠⠴⠚⢁⣤⣶⣋⡁⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢠⡇⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣦⡤⠂ ⠁⠀⠀⠀⠀⢀⣠⢴⡾⣫⣾⠃⢠⣿⠁⠀⠀⠀⠀⠀⡀⢠⣏⡠⠴⢚⣉⠤⠖⠛⠁⠀⠀⠀⠈⠙⠳⠦⣼⠁⠀⠀⠀⠀⠀⠀⠀⡜⠁⢠⢿⡇⠀⡜⢠⠀⠀⠙⢿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⢠⠞⢁⣞⡽⢡⡏⠀⡞⡞⠀⠀⠀⠀⠀⠀⢷⣿⠵⠒⣯⡉⠀⢠⡄⠤⠤⠤⣀⣀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢸⠁⠀⠀⡟⢠⢀⠀⡀⠻⣿⣿⣿⣷⣾ ⠀⠀⠀⠀⠀⢀⣾⡿⠁⣼⠀⢸⢡⡇⠀⠀⠀⠀⠀⠀⡞⣿⣿⡿⠿⠿⠿⠿⠿⣿⣿⣶⣤⣄⠉⠳⣄⡀⡇⠀⠀⠀⠀⠀⠀⠀⡼⣲⠋⡇⢸⠀⠀⢰⠃⡆⢸⢠⢹⠀⠙⣿⣿⣿⡏ ⠀⠀⢀⣠⠴⠛⡿⣧⣴⡏⠀⡏⢸⠇⠀⠀⠀⠀⠀⢸⠁⢹⡇⠀⠀⣠⠖⢻⣟⠲⢮⡙⢿⣿⡗⢆⠘⡅⡇⠀⠀⠀⠀⠀⢀⡞⣰⠇⠀⣷⢸⠀⠀⣾⠀⢧⠈⣿⢸⢠⠀⠸⣿⣿⣿ ⣶⣚⣉⠤⠤⠾⣧⠘⣇⣷⠀⠃⢸⡀⠀⠀⠀⠀⠀⣿⠀⠘⡇⠀⡾⠥⠞⠉⠁⠹⣾⣷⠀⠘⢿⡌⠀⢹⡇⠀⠀⠀⠀⠀⡼⢠⠏⠉⠛⢿⣼⠀⢰⣇⠀⠘⠦⣿⠀⢿⠀⠀⢿⣿⣿ ⠀⠀⠀⠀⠀⢀⢿⣦⡈⠻⣇⠀⠸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⣼⠀⠀⠈⠧⠀⠀⡇⠀⠀⠀⠀⢸⢣⡏⠀⠀⠀⢸⣿⠀⢸⢻⠀⠀⢸⣿⡀⠈⠐⡆⢸⣿⣿ ⠀⠀⠀⠀⠀⠁⢈⣯⢳⣄⠘⡄⠀⢷⠀⠀⠀⢸⡀⢹⡀⠀⠀⠀⠹⠤⣀⡀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⣷⠀⠀⢰⠂⡏⡾⠀⠀⣀⠀⠀⣿⡇⡾⣾⡄⠀⢸⠃⠃⠀⠀⣧⢸⣿⣿ ⠀⠀⠀⠀⠀⣠⠞⢈⣿⡉⠛⣿⣆⠘⣆⠀⠀⠀⢳⡀⢷⡀⠀⠀⠀⠀⠀⠉⠓⠚⠉⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢸⣶⣿⠇⣀⡬⢭⣉⠲⣼⣇⡇⠘⡇⢐⡿⠀⠀⠀⢰⡟⢸⣿⣿ ⢦⣀⠀⣠⣾⠏⢀⣾⣿⡇⠀⣿⢯⣧⣘⢦⡀⠀⠀⢻⣦⣳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢸⢻⣿⣴⣾⣿⡿⢿⣷⣌⢿⡇⠀⣧⣼⠁⠀⠀⠀⣼⡇⣸⣿⣿ ⡄⠈⠛⠳⠧⣤⣾⠿⠋⠀⠀⡿⠈⢣⡘⣿⠿⠦⣤⣬⡄⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢿⠈⣿⡯⠿⠳⣝⣦⠙⣿⡾⠃⠀⣿⠃⠀⠀⠀⢠⡿⢡⣿⣿⣿ ⠛⠷⣤⡀⠀⠀⠀⠀⠀⠀⣰⠇⡇⠀⢳⡘⢦⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣸⡾⠁⠱⠄⠀⢻⣿⠀⠸⣿⣖⡾⠃⠀⠀⠀⠀⡼⢣⣾⣿⣿⣿ ⠀⠀⠈⠛⢶⣤⣤⣤⠤⢾⣿⡄⢡⠀⠀⠙⣎⢳⡀⠀⢸⡄⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⢀⡐⢻⡟⠀⢠⣿⡿⠷⠄⠀⢀⣠⢞⣵⠿⣿⣟⢻⣿ ⣦⡀⠀⠀⠀⢻⣿⣦⣴⠋⡏⣇⠘⢧⡀⠀⣏⣷⣽⣦⣄⠹⣄⠀⠀⢀⡟⠃⠈⠉⠹⠗⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⢤⠤⠊⢀⣴⡿⠋⢀⡼⠒⠚⠿⠚⢋⡇⠘⣿⠻⣿⣿ ⢹⣿⣦⡀⠀⠀⠹⣿⣿⠀⠹⣼⡄⠈⠛⡄⢹⣼⡈⢿⠈⠙⠛⠓⠒⠘⡇⠀⠀⠀⠀⠀⠈⠲⡍⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣤⣖⣋⣤⢶⡿⠁⠀⠀⢀⡾⣸⠀⠀⣏⠀⠙⣟ ⠀⠈⢿⡷⣄⠀⠀⢿⣿⣧⠀⠹⣧⠀⠀⠃⠆⢿⣧⠈⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣟⡵⠋⠀⠀⠀⢀⣾⠁⡟⠀⠀⣿⡀⠀⢈ ⠀⢀⣽⣧⠈⢷⡀⠸⡎⢻⣷⡀⠘⢧⡀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⢠⣀⠀⢀⣾⣿⠿⠋⠀⠀⠀⠀⣠⣟⣽⣸⠁⠀⠀⣿⡇⠀⠀ ⡁⠊⢿⣿⠀⠀⠙⡄⢷⠀⠙⣿⣦⡈⠛⣦⡀⠀⠹⣿⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⣠⠤⠚⠉⠀⠀⠀⠀⠀⠀⠙⣿⣭⡉⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⡏⠀⠀⢸⣿⡇⠀⠐ ⣶⣿⣿⣿⡆⠀⠀⡀⢸⡆⠀⠈⢻⣿⣦⡀⠙⢦⣀⢻⡀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢾⠁⢸⢹⠙⠛⢉⠹⣿⣿⣿⣿⣿⣿⣆⠀⠀⣾⡇⢹⠀⠀ ⣿⣿⣿⣿⡇⠀⠀⣷⠀⡇⠀⢀⡀⢿⣿⣿⣦⡀⠙⠻⣿⣆⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠴⠚⠋⠀⢸⠀⣿⠘⡆⠀⢠⢸⣿⢿⣿⣿⣿⠿⣿⣆⣾⡟⠀⢸⠀⡇ ⣿⣿⣿⣿⡇⠀⠀⡟⠀⣷⠀⡾⠀⠘⣿⣿⣿⣷⡄⠀⠈⠻⣧⡀⣹⡷⢤⣀⣤⡤⠶⠶⠞⠛⠋⠉⠉⠁⢀⠀⠀⠀⠀⢸⠀⣿⠀⢱⡀⣘⢸⢘⣿⣿⣿⡋⠄⠿⢿⣯⠀⠀⣼⡐⢳ ⣿⣿⣿⣿⡇⠀⢀⡇⠀⢺⠀⡇⠀⠀⢻⣿⣿⣿⣿⡀⠀⠀⠈⠻⣿⣷⣾⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢸⠀⡇⠀⠀⢳⡈⢹⡉⠸⡽⣜⣧⠀⠀⠀⠙⢷⡀⠻⠒⠋ ⣿⣿⣿⣿⣧⠀⣸⠁⠀⢸⢸⠃⠀⠀⢸⣿⣿⣿⣿⣷⠀⠀⠀⢀⡘⣿⣿⡿⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⡇⣧⠀⠀⠀⠹⣌⢧⠀⢳⠙⣎⢷⡀⠀⠀⠈⠻⣄⠀⠀ ⣿⣿⣿⣿⡿⢀⡏⠀⠀⣼⣾⠀⠀⠀⠈⣿⣿⣿⣿⣿⣇⠀⠀⠀⠙⠞⢞⢿⣖⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢻⡀⠀⠀⠀⠈⠻⣷⣤⣧⠘⢯⣳⣄⠀⠀⠀⠙⢧⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⠿⣷⣶⣄⠀⠀⠀⢀⢀⡀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠙⣿⣧⣠⣾⡿⠿⠿⢿⣿⡿⠿⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣿⠿⠿⠿⢿⣿⣶⣦⣄⣀⣀⣄⣤⣤⣤⣤⣤⣬⣿⣇⠀⠀⠀⠀⠘⢿⠟⠁⠀⠀⠀⠀⢿⣷⠀⠸⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠉⠛⠻⣿⠿⠿⠛⠛⠛⠛⣛⣿⣿⣿⣆⠀⠀⣠⣤⣄⡀⠀⠀⠀⢀⣠⣿⠇⠀⠀⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠛⠉⠉⠉⠀⣿⡟⠉⠻⣷⠀⠀⠠⠿⣿⣯⡀⠀⠀⢸⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠙⢷⣶⣾⠏⠀⠀⠀⠀⠈⠛⣿⣦⠀⢸⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⣷⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣤⣀⣀⣀⣤⡄⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⣹⣿⠀⢸⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣹⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⣿⡇⠀⠀⠀⠀⣸⣿⢿⣶⣶⣶⣾⠿⠃⠀⣸⣿⡁⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡄⠀⢀⣰⣿⠇⠀⠀⠉⠁⠀⠀⠀⠀⠈⢿⣿⡀⠀⠀⠀ ⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀ ⣀⣀⣀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⣀⣀ ⠛⠻⠛⣿⣿⠿⠿⡶⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠠⡾⠿⢿⣿⡟⠻⠛ ⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣍⣁⣙⣟⣛⣄⣩⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣍⣀⣘⣟⣟⣉⣹⣿⡅⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀ ⣤⣴⣶⣾⣿⣶⠶⠀⠀⠀⠀⠀⠧⣌⠙⢻⣿⣿⡿⠛⡫⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡻⢿⣿⣿⡟⡫⠋⠀⠀⠀⠀⠰⠶⣾⣿⣷⣶⣤ ⠉⠉⠀⠈⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠊⢡⢤⢤⡤⢤⡤⢤⠤⣤⢤⣤⢤⡤⠄⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠈⠉ ⠀⠀⠀⣀⣹⣿⣷⣶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠞⠓⠛⠚⠻⠟⠛⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⣿⣿⣁⠀⠀⠀ ⠀⣴⣾⠿⠟⠛⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠛⠿⢿⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣛⣿⣿⣿⣶⣶⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣴⣶⣾⣿⣿⣟⡋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣴⣶⣦⣾⣿⡿⠟⠛⣿⣿⠏⠛⠛⢿⣿⠛⠿⠿⠿⠿⠿⠿⠿⢻⣿⡟⠛⠛⢿⣿⡟⠛⠻⣿⣿⣶⣶⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⣿⡟⠉⠙⠉⢿⣿⡄⣴⣿⡟⠀⠀⠀⠹⣿⣇⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⠘⣿⣷⡀⣰⣿⠏⠙⠉⠙⢻⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⠙⢿⣶⣄⣀⣀⣠⣴⣿⠟⠁⠀⠀⠀⠀⠘⣿⣿⣿⠏⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀ ⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠈⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢹⣿⣏⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠻⣿⣦⣀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⢀⣠⣾⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⢿⣿⠿⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀

⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀⣤⠖⢀⢀⢀⢀⢀⢀⣀⡀⢀⢀⢀⢀⢀⢀⣀⣀⣀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣶⣄ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀⡠⠾⠋⢀⢀⢀⢀⢀⢀⢀⢀⠈⣿⣦⣄⣠⣴⡞⠛⠛⣿⣿⣿⣿⣿⣿⣿⣟⠛⠛⠛⣿⣿⣿⣷⡄ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣤⠤⠌⠉⠉⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢸⣿⣿⣿⣿⠇⢀⢀⢿⣿⡇⠘⢿⣿⣿⣿⣷⣄⣀⠈⢹⣿⣿⣿⣆ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣾⡇⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣿⣿⣿⢀⣸⣿⡇⢀⢹⡇⢀⢀⠻⣿⣿⣿⣿⣶⣍⠘⣿⣿⣿⣿⡆ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣾⣿⠁⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠘⢿⣿⢀⣿⣿⣿⢀⢿⡇⢀⢀⢀⠈⠛⢿⣿⣿⣿⣷⣬⣿⣿⣿⣿⡀ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀⣼⣿⣿⡄⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢻⠿⢀⢹⣿⡏⢀⣿⢀⢀⢀⢀⢀⢀⢀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡇ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀⣀⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⡄⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠸⣶⢀⢀⣩⣤⣤⡟⢀⢀⢀⢀⢀⢀⢀⢀⢀⢻⣿⣿⣿⣿⣿⣿⣷ ⢀⢀⢀⢀⢀⢀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣤⣀⣀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣠⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢸⡟⢀⢀⣿⠛⠁⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣸⣿⣿⣿⣿⣿⣿⣿ ⢀⢀⢀⢀⢀⣾⣿⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠿⢟⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠉⠉⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠈⢀⢀⠘⠉⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢠⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⢀⢀⢠⣿⣿⣿⣿⠃⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠉⠙⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠉⠁⢀⢀⢀⢀⢀⢀⢀⢰⣿⣿⣿⣿⠋⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⢀⢀⣾⣿⣿⣿⠁⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠉⠙⠛⠛⠉⠁⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢸⣿⣿⣿⡇⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⢀⢸⣿⣿⣿⠇⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠈⣿⣿⣿⡇⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠈⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿ ⢀⢀⣸⣿⣿⣿⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢸⣿⣿⣷⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠻⣿⣿⣿⣿⣿⣿ ⢀⢀⣿⣿⣿⣿⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣿⣿⣿⡇⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢹⣿⣿⣿⣿⣿⣦ ⢀⢀⢿⣿⣿⣿⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣿⣿⣿⡇⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣼⣿⣿⣿⣿⣿⣿⣧ ⢀⢀⢸⣿⣿⣿⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣿⣿⣿⡇⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣠⣿⣿⣿⡿⠋⢿⣿⣿⣧⡀ ⢀⢀⠘⣿⣿⣿⣧⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢿⣿⣿⣷⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣾⣿⣿⣿⠟⠁⢀⢀⠻⣿⣿⣷⡀ ⢀⢀⢀⢻⣿⣿⣿⣦⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢿⣿⣿⣷⣦⣤⣀⣀⣀⣀⣤⣤⣶⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣿⣿⣿⠟⢀⢀⢀⢀⢀⢀⠹⣿⣿⣧ ⢀⢀⢀⠈⣿⣿⣿⣿⣷⣿⣿⣦⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣾⣿⣿⡟⢀⢀⢀⢀⢀⢀⢀⢀⠙⣿⣿⣇ ⢀⢀⢀⢀⢻⣿⣿⣿⣿⣿⣿⣿⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠙⠛⠻⠿⢿⣿⣿⣿⡇⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢠⣤⣀⢀⢀⢀⢀⢀⢀⢀⣼⣿⣿⣿⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠸⣿⣿⣇ ⢀⢀⢀⢀⢀⢻⣿⣿⣿⣿⣿⠃⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠸⣿⣿⣿⡇⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣼⣿⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⡿⠃⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠻⣿⣿⣆ ⢀⢀⢀⢀⢀⢸⣿⣿⣿⣿⠇⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢿⣿⣿⣿⣆⡀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢠⣿⣿⣿⡿⣿⣿⣿⣿⣿⠿⠟⠋⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢿⣿⣿⡆ ⢀⢀⢀⢀⢀⣼⣿⣿⣿⡏⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠈⢿⣿⣿⣿⣿⣶⣤⣤⣤⣤⣤⣤⣄⣀⡀⢀⢀⢀⢀⣴⣿⣿⣿⡟⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢸⣿⣿⣿⡀ ⢀⢀⢀⢀⢠⣿⣿⣿⡟⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢰⣿⣿⣿⣧ ⢀⢀⢀⢀⣸⣿⣿⣿⠁⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠿⢿⣿⠿⠿⠛⠉⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣷⠖⠂ ⢀⢀⢀⢀⣿⣿⣿⡟⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟ ⢀⢀⢀⢀⣿⣿⣿⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠘⠿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣏ ⢀⢀⢀⢸⣿⣿⣿⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠉⣿⣿⣿⡟ ⢀⢀⢀⣸⣿⣿⡟⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣠⣴⣶⣶⣶⣤⡀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣿⣿⣿⣧ ⢀⢀⢀⣸⣿⣿⡇⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣼⣿⣿⣿⣿⣿⣿⣿⡄⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀⣠⣿⣿⣿⣧ ⢀⢀⢀⣿⣿⣿⡇⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣦⣤⠄ ⢀⢀⢀⣿⣿⣿⣿⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠙⠿⣿⣿⣿⣿⣿⠏ ⢀⢀⢀⣿⣿⣿⣿⣿⣄⣀⣀⣀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣤⣶⣿⣿⣶⣦⡀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢻⣿⣿⣿⣿⣿⣿⣿⠇⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣿⣿⣿⣿ ⢀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡄⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠉⠻⠿⣿⠿⠟⠃⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢠⣿⣿⣿⠇ ⠴⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀⣀⣀⣀⣀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣠⣿⣿⣿⣿ ⢀⢀⢀⠈⢿⣿⣿⣿⣿⣿⠇⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣤⣶⣾⣿⣿⣿⣿⣿⡏ ⢀⢀⢀⢀⠈⣿⣿⣿⣿⣿⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠹⣿⣿⣿⣿⣿⣿⣿⠃⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄ ⢀⢀⢀⢀⢀⠘⣿⣿⣿⣿⣆⡀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠈⠛⠛⠿⠟⠋⠁⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣈⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠒⠂ ⢀⢀⢀⢀⢀⢀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣠⣴⣿⣿⣿⣿⣿⣿⡟ ⢀⢀⢀⢀⢀⢀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠙⠛⠿⠿⣿⣿⡿⠿⠿⠛⠁⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⡀ ⢀⢀⢀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣏⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄ ⢀⢀⢀⠉⢀⢀⢀⢀⠈⠙⢿⣿⣿⣿⣿⣦⡀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀⣿⣿⣿⣿⣿⡿⠃⢀⠁⠉⠙⠛⠛⠛⠛⠛⠿⣿⣿⣿⣦⡀ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠙⢿⣿⣿⣿⣿⣷⣤⣴⣾⣿⣿⣿⡆⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣠⣴⣿⣿⣿⣿⣿⣿⡇⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠈⠿⣿⣿⣄ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⡿⠟⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢹⣿⣿⣆ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣿⣿⣿ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣴⠿⠛⠋⠉⠛⠻⣿⣿⣿⣿⣿⣿⣶⣤⣤⣀⣀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣿⣿⣿ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠉⢀⢀⢀⢀⢀⢀⢀⢀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣀⣀⣀⣀⣀⡀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣿⣿⣿ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢸⣿⣿⡏ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠋⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣴⣿⣿⡿⠁ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀⣤⣶⣿⣿⣿⣿⣿⠿⠛⠛⠉⠉⠉⠉⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠛⠛⠛⠉⠉⠁⢀⢀⢀⢀⢀⠈⡉⢛⣿⣿⣿⣿⣿⡀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣠⣾⣿⣿⡿⠁ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣠⣴⣾⣿⣿⣿⠿⠋⠉⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠛⠉⠁⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣠⣶⣶⣿⣿⣿⣿⣿⣿⣷⣤⣄⡀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣴⣾⣿⣿⣿⠟ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀⣴⣿⣿⣿⠿⠟⠃⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣀⡀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣠⣶⣿⣿⣿⣿⠟⠁ ⢀⢀⢀⢀⢀⢀⢀⢀⣠⣾⣿⣿⠿⠛⠁⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⢀⢀⢀⢀⢀⢀⢀⢀⢀⣴⣿⣿⣿⣿⠿⠛⠉⠛⠋⠉⠁⢀⠉⠉⠛⢿⣿⣿⣿⣷⡄⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣤⣶⣿⣿⣿⣿⠿⠋⠁ ⢀⢀⢀⢀⢀⢀⣠⣾⣿⣿⠟⠉⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠉⠉⠉⠙⠛⠿⠿⠿⢿⣿⣿⣿⣿⣶⣄⡀⢀⢀⢀⣴⣿⣿⣿⣿⠋⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠙⣿⣿⣿⣿⣆⢀⢀⢀⣀⣀⣤⣶⣿⣿⣿⣿⣿⡿⠟⠁ ⢀⢀⢀⢀⢀⣴⣿⣿⠋⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣴⣿⣿⣿⣿⣿⣿⡿⠋⠁⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠘⣿⣿⣿⣿⣿⣿⣦⣠⣿⣿⣿⣿⡿⠃⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠙⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉ ⢀⢀⢀⢀⣾⣿⡿⠁⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣼⣿⣿⣿⣿⣿⣿⡟⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⡀ ⢀⢀⢀⣾⣿⡿⠁⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡅⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⢨⡟ ⢀⢀⢸⣿⣿⠇⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣤⣄⣠⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⡿⠿⢛⣿⣿⣿⣿⣿⣿⠟⠋⠉⢀⢀⢀⠸⠋ ⢀⢀⣿⣿⣿⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣤⣤⣀⣀⣀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠉⢀⢀⢰⡊⣿⣿⣿⣿⡿⠟ ⢀⢀⣿⣿⣿⡆⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢀⢀⢀⢀⢀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣤⣾⣿⣿⣿⣿⣅ ⢀⢀⠸⣿⣿⣷⡀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⢀⢀⢀⢀⢀⢀⢀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣄ ⢀⢀⢀⠹⣿⣿⣿⣦⡀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀⣀⣠⣤⣶⣶⣿⣿⣿⠏⠁⢀⢀⢀⢻⣿⣿⣿ ⢀⢀⢀⢀⠙⢿⣿⣿⣿⣶⣶⣤⣤⣤⣴⣶⣿⣿⣶⣄⢀⢀⢀⢀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⡀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀⣀⣠⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⢀⢀⢀⢀⢀⢹⣿⣿⣶⣿⠁ ⢀⢀⢀⢀⢀⢀⠈⠻⢿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣶⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣄⢀⢀⢀⢀⢀⣾⣿⣿⣿⡇ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠈⠛⢿⣿⣿⣿⣿⣿⠿⠛⠉⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⠛⠛⠁⢀⢀⢀⢀⢀⠈⣹⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⠟⠛⠻⡇ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢸⣿⣿⣿⡿⠿⠿⠛⠛⠉⠉⠈⠉⠉⠉⠉⠉⠉⠋⠙⠛⠛⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠉⠉⠁⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢀⢀⢀⠈⠂ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣼⣿⣿⠋⠁⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣿⣿⡟⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣧ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢰⣿⣿⠃⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠃⠈⠙⣿⣿⣿⣿⣧⡀ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢸⣿⣿⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀⣀⣀⣤⣴⣾⣿⣿⣿⠟⠋⠉⣻⣿⣿⣿⣿⣿⣿⠟⠁⢀⢀⢀⢀⣿⣿⣿⣿⣿⣿⣦⣀⢀⢀⢠⡄ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣾⣿⡿⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀⣀⣤⣴⣿⣿⣿⣿⡿⠿⠛⠛⠻⣿⣿⣤⣤⣾⣿⣿⣿⣿⠿⠋⢀⢀⢀⢀⢀⢀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢀⠉⢤⡀ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣿⣿⡇⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⡿⠛⠉⢀⢀⢀⢀⢀⢀⢨⣿⣿⣿⣿⣿⡿⠛⠁⢀⢀⢀⢀⢀⢀⢀⢀⢸⣿⣿⣿⣿⡏⠈⠙⠛⠿⠿⣿⣾⠿⠃ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢠⣿⣿⠁⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀⣀⣠⣤⣤⣶⣶⣾⣿⣿⠿⠿⠛⠛⠋⠉⠛⠉⢀⢀⢀⢀⢀⢀⢀⢀⣤⣾⣿⣿⣿⣿⡿⠏⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣾⣿⣿⣿⣿ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢸⣿⣿⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠉⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣤⣾⣿⣿⣿⣿⣿⡿⠟⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣿⣿⣿⣿⡇ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢸⣿⣿⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠉⠙⠛⠛⠛⠛⠛⠉⠉⠁⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢸⣿⣿⣿⣿ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣸⣿⡏⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣿⣿⣿⣿⠇ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣿⣿⠇⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀⢀⢀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠁⠘⠛⣿⣿⣿⣿⣿⣷⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣸⣿⣿⣿⡟ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣿⣿⡟⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀⣀⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢀⢀⢀⢀⢀⢀⢀⢀⠛⣿⣿⣿⣿⣿⡄⢀⢀⢀⢀⢀⢀⢀⢀⢀⣴⣿⣿⣿⡿ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣸⣿⣿⣇⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢹⣿⣿⣿⣿⣿⡄⢀⢀⢀⢀⢀⢀⢠⣶⣿⣿⣿⡿⠁ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠉⠉⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣿⣿⣿⣿⣿⣿⡄⢀⢀⣀⣀⣴⣿⣿⣿⣿⡟⠁ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠈⠛⠿⠿⠿⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠁⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠙⢿⣿⣿⣿⣿⣏⠈⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠈⠻⣿⣿⣿⣿⣶⡄⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣰⣿⣿⣿⣿⡿⠟⠛⠛⠉⠁ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠈⠛⢿⣿⣿⣿⣷⣦⡀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣠⣶⣿⣿⣿⣿⡿⠁ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠈⠛⠿⢿⣿⣿⣶⣦⣤⣀⣀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⣀⣤⣴⣾⣿⣿⣿⣿⣿⡟⠁ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠈⠉⠙⠿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉ ⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⢀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⣿⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣸⠿⠿⠿⢿⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡜⠛⠀⡇⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⠛⠛⠛⠀⠀⠀⠀⠛⠛⢣⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠏⢇⣀⣀⡏⢾⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⠛⡌⢱⡈⠔⡰⢈⠞⣛⠻⢷⣦⣶⠀⣰⣶⣴⣦⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⣿⢍⠡⢎⠰⡥⢜⠬⡐⡡⢊⢄⠃⡎⠍⠭⣷⡯⠽⠉⣿⣇⣀⣀⣀⣀⣀⣀⣀⣸⣿⠉⠀⠀⠀⠀⢀⢀⣀⣿⣿⣷⣀⠀⠀⠀⠉⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⣿⠚⢲⢸⣵⣧⡜⠤⡑⡰⢉⠢⡑⢌⢊⡱⢄⠂⠀⠀⣿⡟⣛⢛⠻⣛⠛⡟⣛⢻⣿⡄⠤⠠⢤⣤⣼⣾⢟⡳⣜⠺⣟⣤⡄⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢈⣿⠀⠸⠸⢩⡿⡟⠰⣁⠖⡡⠣⢘⠢⣁⠲⣈⠓⣒⣼⡿⠷⡐⢊⠔⢢⠉⠴⣀⢋⡹⣿⢿⡿⣿⠯⠹⡍⢮⠱⢎⠳⣎⡿⣇⣀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⠃⠒⡌⢱⠠⠎⣴⣤⣮⡇⠴⡁⠦⡑⢼⣿⡇⢆⡑⢊⠜⡠⢍⠒⡌⠢⡔⢩⠒⡹⠘⣄⠣⡘⢄⠣⢌⠓⣌⠳⣍⢶⣤⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⣷⡆⠀⠀⢸⣿⣿⠴⡥⢮⢹⣿⡏⢆⠱⢂⣿⣿⢫⡕⢢⠘⡌⢢⠑⡌⠒⡌⠱⡈⢆⡑⢢⢉⡄⢣⠘⡄⠣⢌⠒⡌⢩⢜⡺⡝⣷⣶⣾⢿⠿⣖⢀⡀⡀⠀⠀ ⠀⠀⠀⠀⠀⣠⣤⠟⡿⣧⣤⣤⡜⡞⠛⠀⠀⠘⠒⠒⠚⠒⠓⣮⣿⢻⠙⢢⢁⠎⡰⢁⠎⡰⢉⠔⢣⠑⢢⠘⠤⠒⡌⢢⠑⡌⠱⣈⠒⡌⢅⠪⢱⠭⣿⡇⠀⠀⠀⠘⠛⠛⣣⡄⠀ ⣀⣰⣶⣶⣶⣏⣍⣒⣧⣿⣿⣛⣿⣷⣶⣶⣆⣀⣀⣀⣀⣰⣶⢯⢣⡓⠬⣁⡎⡔⡡⢎⡰⢡⠎⡘⢤⢉⡆⢍⠒⡡⠜⡠⢃⠬⡑⢄⠣⡘⠤⢩⠸⣍⣿⣿⣶⣶⣀⣀⣀⠀⠈⢹⣾ ⣿⣧⣼⣶⣶⣼⣾⠿⠿⠟⠼⡿⢿⡟⣼⠃⠟⠻⠛⠟⠻⠛⠘⡧⢃⡜⣰⠇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⠷⢈⡒⢡⠊⡔⢡⠊⡔⢡⠊⢵⡸⡜⣿⡇⠈⠀⠛⠛⠻⣤⣥⣼⣿ ⣿⡏⠉⠉⠭⢭⣙⣤⣃⣎⣱⣩⣷⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣾⡅⢎⠰⡁⢎⠰⣁⠚⣬⢳⣍⣿⣷⢲⠀⠀⠀⠀⠉⠉⢹⣿ ⠛⢧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡜⠛⠛⣧⣤⣤⣤⣤⣤⣤⠛⠛⢻⣤⠀⢸⢣⠵⣌⢦⢣⣍⠻⣔⣻⣿⣯⣶⣭⣿⣤⡄⠀⠀⡀⢸⣿ ⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣷⣶⣶⣶⣶⣶⣶⣶⡏⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⣶⣾⣿⣚⣜⣎⣳⣼⣿⣾⡿⠉⠉⠉⠉⠉⠉⢹⣶⣶⣶⡞⠙

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣟⡾⠐⣸⠶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣟⣾⣽⣞⡷⢯⡷⣏⣿⣞⣧⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡝⠡⠐⠠⢿⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⢾⣽⣻⣯⣿⣿⣿⡿⣽⣾⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣏⠁⢂⠁⢒⠸⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢆⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⣟⡿⣽⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠨⠐⠠⠈⠄⢂⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠉⠉⠛⠛⠓⠂⠤⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⡿⣏⢷⣫⢯⣽⣳⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢀⠁⢂⠡⢈⢺⣿⣿⣿⣿⠿⠿⠛⠛⣛⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⢿⣙⣮⡽⢞⢫⢓⢮⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⠁⡈⠄⣢⠥⠖⠛⠉⠀⠀⠀⠀⢠⠾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡽⠖⢋⠰⡐⢊⠆⡍⣲⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣼⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⢀⢴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠈⡍⠛⢿⣿⣿⣿⣿⣿⣿⡽⠋⠀⠌⠠⠒⡈⠆⡘⠄⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢪⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡇⠀⠀⢩⡻⣿⣿⣿⣛⠄⡠⠁⠌⡁⠒⠠⡘⠠⢘⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢆⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡇⠀⠀⠀⠈⠪⡙⢿⣯⠑⢀⠁⠂⠄⡁⠆⠠⠁⣼⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡄⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢀⠇⠀⠀⠀⠀⠀⠈⠢⡙⣧⡆⠈⠄⠡⠐⡈⠄⢹⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢂⠁⠀⢴⠿⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠻⣇⠘⠠⠁⠄⢨⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢫⠃⠈⠠⠈⡜⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡘⢷⡁⢌⠠⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠒⢄⡀⠀⡠⠃⠀⠀⠀⡰⠀⠁⡠⠊⠀⠀⠀⠀⠀⠀⠆⠀⢀⡄⠀⠀⢀⠌⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⣷⢀⣾⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⢈⠝⠀⣄⣠⣴⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⣠⠛⠀⠀⠠⠁⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡈⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣧⣤⣄⣀⣀⠀⠀⠀⠳⠁⠀⠁⠈⠉⠈⠀⡜⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢠⠃⠒⠂⠊⠀⠒⡰⠓⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡈⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⠿⡿⢿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⡴⠁⠀⠀⠀⠀⣠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⠞⠀⠀⠀⠀⠀⠀⠀⢠⣀⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⣤⣿⣿⡿⠛⠛⢻⣿⣿⣿⣿⣿⣿⠖⠁⠀⠀⠀⢀⡠⠀⠀⠀⡠⠊⢀⣤⠞⡡⠐⢀⡠⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⡄⣿⡟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⣶⣶⣶⣒⡈⢁⣀⣠⣴⠬⠔⢲⣿⣥⣷⣶⣾⣷⣶⣦⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠃⣿⡇⠉⠂⠠⢿⣼⣿⣿⣿⣿⣿⣿⣿⠟⠛⠻⠻⠿⢿⣿⣿⣷⣿⡟⠛⠉⢉⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣼⣷⠀⠀⠀⠀⠀⢻⣇⠀⠀⡆⠘⡇⠀⠀⠀⠈⣿⠁⠈⠉⠙⢁⣿⠃⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠀⠀⠀⡫⠁⠀⢸⣿⣿⣿⣾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⡼⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠁⠀⠀⠀⠀⠀⠈⢿⣆⢘⠇⢀⡸⢄⠀⠀⠀⠘⢆⡀⠀⣀⣾⠃⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠉⠂⠄⣺⣭⣿⢿⣿⣿⣿⣿⣿⡟⠀⠈⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⢠⠇⡌⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⠳⢦⣤⣤⣽⣒⣠⣤⣀⣀⣤⡿⠁⠀⡀⠄⡒⠉⠀⡀⠄⠊⢀⠤⢻⣇⠀⠀⠆⠀⠀⠘⣟⠀⠌⢉⠛⠉⢻⡷⠥⠤⢀⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⡎⡰⠁⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⣾⣿⡿⠿⢿⡟⡀⠀⠀⠀⠀⠉⠉⠀⠈⠋⡇⠀⢰⣿⣿⣿⣿⣿⡿⠋⠉⠉⠉⠙⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠭⠛⠁⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⡸⢁⣀⡀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣼⣿⣿⣿⣿⠋⠀⠀⢀⡀⠤⠰⠠⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠢⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠄⠀⠀⢀⣠⠚⠉⠀⠈⠛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢠⣿⣿⣿⣿⣧⡀⢀⠞⠁⠀⠀⠀⢀⣬⣷⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠿⠃⠀⠀⠀⠀⠀⠀⣀⠠⠒⠁⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢼⣿⣿⣿⣿⣿⣷⣾⡁⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⣀⣀⠠⠤⠤⠤⠀⠀⠀⠒⠚⠛⣺⣍⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠒⠉⡍⡖⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢠⡦⠾⣏⠒⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣀⣤⣶⢿⠙⢍⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡘⡄⠡⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⣱⣤⣴⡟⠁⠀⠙⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⡿⡟⠛⠛⠛⠻⠿⠷⡶⡾⣻⡟⡜⠄⢸⠀⢃⠠⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⡆⢸⣿⣿⣿⣿⣿⣿⠿⣫⢤⢴⡺⣿⣿⣿⡇⠀⠀⠀⡜⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣽⣣⡿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠁⠀⠀⢀⠔⡡⡪⠞⣹⣴⢱⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠰⢁⣼⣿⣿⣿⡿⠛⢁⡤⡻⣍⢾⣱⠏⠁⠈⢣⠀⠀⠀⡇⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣻⢷⣻⣽⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢷⠀⠀⠄⡡⡨⠊⢀⣴⣿⡸⡜⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢁⣸⣿⣿⡿⢋⡼⢏⢧⣹⡵⠞⠋⠀⠀⠀⠀⠘⡆⠀⠀⠞⠲⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢇⡠⠊⠊⠀⣴⣿⣿⣿⡄⠰⢄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡠⠪⣀⣼⣿⡿⠋⣰⣏⢶⣩⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⡇⠒⣼⡀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣐⢄⡠⣾⣿⣿⣿⣿⣿⣦⣴⠈⠂⠤⠀⠄⠀⠀⠀⢀⠐⣁⣀⣴⣿⠿⢇⣴⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⡏⠑⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡆⠀⠙⠿⣿⣿⣿⣿⢿⣿⣦⣀⣀⣧⣤⣶⣶⣶⢾⣟⡿⢯⣷⠖⠋⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣤⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠐⣄⠀⠈⠙⢻⢯⣿⣾⡽⣯⣟⣯⣟⣷⣻⠞⣫⠟⠋⠉⠛⢒⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⢑⠒⠺⡄⠈⣀⣈⣉⣉⣹⡭⠭⠚⠒⠋⠁⠀⠀⠀⠀⣼⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢕⡲⣉⡒⠤⣀⡉⠉⢹⡇⠀⠀⠀⠈⡘⠄⠀⠀⠀⣇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣋⡷⠙⠛⠽⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⢾⡃⡌⠙⡶⢻⡦⣀⠀⠀⠀⠀⠀⠀⢸⡏⠣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠈⠉⠓⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠚⡧⡀⠉⠐⠒⠠⠶⠖⣻⠢⡀⠀⠑⠢⠄⣀⣀⢀⡀⣀⣀⣠⠔⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠁⠀⠀⠀⠤⢠⠇⠀⠀⠐⠠⣀⠀⠀⠀⠀⠀⢀⡠⠜⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢣⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠚⠁⠈⡹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣎⠳⠄⠀⡠⢚⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣴⠀⠑⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢔⡲⡔⢦⠤⡤⢤⠤⡤⢤⠤⡤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠒⠒⠂⠉⠉⡉⡉⢬⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⣌⢣⠜⡜⢪⡱⡙⢎⡱⡙⢎⡱⡱⢊⠖⡬⡙⢒⡒⡲⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠀⠤⢄⠀⠀⠀⠈⡀⠐⢀⢸⣇⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⡰⢌⠲⡩⢜⡡⢖⡹⢌⡱⢩⠎⣔⠣⣍⠚⡤⡙⢢⡽⠁⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢀⠀⠀⠀⠈⠀⠀⢈⠀⠀⠧⡑⠀⠀⠀⠀⢀⢄⡴⢃⢎⡱⢊⠵⡑⢎⡔⢣⠜⣢⠱⣃⠞⡤⢓⡌⡓⢦⣹⣼⠤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠉⠙⠲⠯⠭⠷⠾⠤⠖⢉⣉⣉⣉⡉⣉⠈⠉⠐⠊⠓⠚⠐⠓⠚⠚⠒⠃⠈⠅⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣴⣶⣶⣤⣼⡟⠋⠉⣿⡶⣿⣿⣄⣤⣶⠿⢶⣦⡀⠀ ⢠⣿⠁⠀⠀⠉⣿⠀⠀⠀⠀⠀⠀⠈⢻⡏⠀⠀⠀⠘⣿⡄ ⢸⣧⠀⠀⠀⠀⠙⠷⠶⠶⠶⠶⠶⠶⠿⠃⠀⠀⠀⢠⣿⠁ ⠀⠻⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⠃⠀ ⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀ ⠀⠀⣿⠀⠀⠀⠀⠸⠗⠀⠀⡀⠀⠸⠇⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀ ⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠀⠀ ⠀⠀⠀⠀⠙⠻⠿⣶⣶⣤⣤⣤⣴⣶⡶⠾⠿⠛⠁⠀⠀⠀

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⠀⣠⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⡇⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣯⣿⡇⣿⣿⠀⠀⠀⠀⠀⢀⣀⡤⠔⠂⠀⠀⠀⠐⠒⠲⠤⣄⡀⠀⠀⢀⣀⣤⣶⣿⡿⣿⣿⣿⣿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢿⣿⣿⣿⣹⣿⡆⠀⠀⣠⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣟⣿⣯⣷⣿⣿⣿⣿⡿⠋⢀⠠⠤⠤⢤⣀⠀⠀⠀ ⠀⠘⢿⣿⣿⣿⣿⣷⡀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡿⠟⠋⢠⠔⠀⠀⠀⠀⠀⠈⢳⡀⠀ ⠀⠀⠈⢻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠏⠉⠉⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀ ⠀⠀⠀⠀⠙⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⢸⡶⠖⠒⠉⠙⠲⢤⣀⣸⣟⡀ ⠀⠀⠀⠀⠀⠈⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⢸⡽⠃ ⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠘⡧⠐⣦⡀⠀⠀⠀⠀⢀⡞⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢳⡀⠀⠀⢸⢧⠀⠀⠉⠉⠁⡀⣠⠞⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣀⠀⠀⠈⢃⡠⠤⣾⠈⠂⠀⠀⣀⣰⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⣀⣀⠀⠀⠀⠹⠿⠁⠀⠀⠀⢀⠀⢠⠇⠀⣀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠸⣿⡿⠿⠀⠀⠀⠀⠀⠀⠀⢀⠸⠓⢼⡖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠈⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡶⠖⠚⠁⠂⠚⠀⠐⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠴⠒⠒⢛⡿⢤⣤⢤⣤⣤⡤⠶⠖⠒⢯⡉⠉⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠜⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠒⠋⠉⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢰⠀⠀⣤⡿⢿⡅⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠉⠀⠀⠀⢸⠀⠸⠻⠋⡟⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⣀⣀⣠⠴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣔⣀⣀⣈⣫⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠷⠤⣄⣀⣀⣀⣀⣀⣀⣠⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠉⠉⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⣀⣀⣀⣀⣀⡠⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

♡꒰ᵕ༚ᵕ⑅꒱

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⢃⣿⢸⣿⣿⣿⣿⣿⡿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢣⣿⡏⢸⡇⢸⣿⣿⣿⣿⢻⡇⣿⠘⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣼⣿⢀⡾⠀⣾⣿⣿⣿⣿⣸⠁⣿⠀⢿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠟⠉⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⡿⣾⢀⣿⠇⢸⠇⢀⣿⣿⣿⣿⡇⣿⢸⣿⠂⣸⣿⣿⣿⡿⣇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⣰⣿⠋⠁⠀⠈⠁⠀⠀⠀⠀⠀⢹⣿⣿⢿⣿⣿⣿⢧⡇⢸⡿⢀⡟⠀⢸⣿⣿⣿⡿⢀⡟⣀⣿⠀⠘⣿⣿⣿⡇⢿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀ ⠀⢀⡴⠟⠁⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢿⣿⢼⣿⣿⣟⢹⡋⢹⠏⠽⠉⠉⣿⣿⣿⡿⠃⠈⠋⢿⡿⠉⠙⣿⣿⣿⡟⠚⠗⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀ ⠠⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⡸⣿⣬⠭⣛⣿⣿⣿⣿⣯⣵⣒⡂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢖⣛⣯⣭⣽⣷⣶⡢⢍⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀ ⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢯⢻⣿⠋⣽⠋⣙⣿⣿⣿⣿⡟⡖⠀⠀⠀⠀⠀⠀⠀⢠⢾⠟⠛⢿⣿⣿⣿⣿⡻⣷⡭⣖⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⡘⣇⠀⠀⠀⠀⢻⡄⠀⠀⠀⢸⡤⠷⠒⠋⠉⠁⠀⠈⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⣦⣤⣼⣿⡿⠿⣿⡇⠸⠛⢃⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠘⡄⠀⠀⠀⠸⣆⣀⣠⠬⠿⢷⠀⣀⠀⠊⡇⠀⠀⠰⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣽⣿⣿⣷⡀⠈⠁⠀⣀⡾⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢹⡀⡴⠒⠋⠉⠀⢀⠀⣀⣸⣦⢀⠱⠄⢷⣄⡀⠀⠀⢆⡀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠙⠛⠁⠀⠀⡞⣤⣂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠁⠀⠀⠀⢿⡇⣐⡆⠀⠀⠸⣿⣿⠿⢷⢰⠾⠶⣼⠛⠛⠷⣄⠈⡇⠀⠀⢸⡄⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⢧⡀⣀⠐⢿⠙⣷⠀⠀⠀⢻⠀⠀⠺⣼⠀⠀⢸⡦⠂⠀⠈⠃⢿⡄⠀⠠⢧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠻⣵⠖⠸⡇⢹⡄⠀⠀⠘⡇⠀⣾⣿⣤⣀⣼⣁⡀⠀⠀⢠⣾⣿⣄⠀⢸⡅⠀⠀⠰⠲⠶⠄⣰⠋⠀⠈⠉⠒⠒⠤⢄⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠹⣏⡀⢹⠈⣷⡀⠀⠀⢻⡀⣿⢛⣿⢿⣿⣿⣿⣷⡀⠀⢹⣿⣿⠀⠀⢳⠀⠀⠀⠀⠀⢺⡇⢠⣦⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠦⣄⣈⣻⣾⡇⠙⠓⠂⠀⠘⣇⠹⣿⣽⣿⣿⣿⣿⣿⣿⣄⣿⣿⣿⣷⣤⠘⡆⠀⠀⠀⠀⡼⢀⡚⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿ ⣤⡀⠀⠀⠉⠉⠋⢻⡀⠀⠀⠀⠀⡽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⢱⣀⠀⠀⣰⡇⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣦⡀⠀⠀⠀⠀⣇⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠂⠘⣯⣽⣲⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣦⣄⠀⣀⣼⡀⠀⠀⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⡀⡀⢹⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠉⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠹⣇⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣯⣿⣿ ⣿⣽⡿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢿⡆⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠐⣿⡀⣇⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢹⠇⠸⡄⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣭⣷⣿⢿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠛⢿⠟⢻⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠁⢀⡇⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿ ⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠸⡇⠘⠻⠿⣿⡀⠀⠀⠀⢀⣀⣠⣤⠖⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣞⢿⢼⣿⣿⣽⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠛⠆⣀⣠⠤⠴⡖⣺⠯⣻⠟⠛⢇⠀⠀⣀⡗⠙⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏ ⣿⣝⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣤⣴⣶⣿⣿⡿⠁⠀⠀⠠⣿⣴⡇⢀⢀⢸⡆⠀⣿⡇⠀⡁⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋ ⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠁⣴⡟⢱⡏⠉⠓⠚⠋⣇⠶⡇⠻⠾⠛⠉⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⣿⣿⣽⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠐⣰⠋⠄⡾⠀⠀⠀⠀⢸⡇⠁⣷⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⠊⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢺⠉⠉ ⡞⣗⡒⣲⣒⡲⣶⢶⣶⢶⣆⣲⣶⣰⣒⣒⢂⡠⣖⡒⠒⢶⣖⣲⡾⠛⠃⠙⠋⠳⣄⣀⡀⠀⢀⣀⣀⡀⠀⣶⣿⠏⠀⡼⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆ ⢨⣷⣿⢯⣧⣧⡿⣼⣿⣾⡟⢫⣿⣸⣿⣿⣽⣿⣹⣿⣿⣿⣷⣿⡏⠉⠀⠀⠀⠀⠀⠈⠙⠲⣋⡤⠤⢍⠻⣿⠏⠀⠀⣿⠀⢠⣴⣦⠀⠀⠀⣀⣀⡀⠀⠀⠀⣤⣤⡄⠀⢸⢫ ⠈⠏⠁⢀⣇⡉⠉⡇⠀⠀⠀⠀⠀⡇⣼⠏⡩⠉⡜⠉⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣖⠒⠢⢕⣜⣆⠀⣺⣿⠀⢸⣿⡿⣠⠖⠉⠰⡶⠀⠑⠶⡀⣿⣿⠇⠀⡾⠀ ⠀⠠⢲⣛⠛⡛⡇⠃⠀⠀⠀⠀⢀⡿⢁⠞⠀⠐⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⣠⠈⢪⡛⢳⣿⠋⢷⣄⠈⠀⢯⠀⠀⠾⠻⠄⠀⢀⡗⠈⠁⣠⡾⠁⠀ ⠀⠀⠘⣾⠫⣵⠃⠀⠀⠀⠀⡴⠋⠀⠁⠀⠀⢶⠀⠀⣶⣦⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢇⢣⠀⠙⠢⣈⠙⣄⠘⡿⠶⠶⡿⠶⠶⠶⣶⢾⣿⣷⠖⠋⢁⡆⠀⠀ ⠀⠀⠀⠈⠛⠁⠀⠆⠀⠀⢸⠁⠀⠀⠀⢀⣞⠿⡀⠸⣧⡿⠀⡤⠊⢱⣦⠉⠲⡄⢠⠶⢶⠆⠀⢠⠏⠹⣌⢆⡀⠀⢨⠂⡿⡞⠹⡆⠀⠀⠀⠀⢠⠟⠉⣠⣿⣆⠀⠀⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣄⠀⠀⣠⡾⢋⠀⢳⡄⣀⡀⠘⣇⠀⠶⠳⠄⠀⣸⠀⠀⠀⠀⣠⠟⠀⠀⢋⠷⠤⠤⠤⠛⢱⠑⢾⡃⠀⢸⠀⠀⠙⣶⣿⡿⠛⣛⢗⣢⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠉⠀⠸⠀⡇⠀⠀⢹⠉⠉⠻⣅⣠⠶⠚⠓⣄⣤⠴⠚⠁⠀⠀⠀⢸⢠⣤⣦⣤⠀⢸⠀⠈⢹⠉⡟⠉⠉⠑⢻⣓⣼⢾⣟⢻⡄⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣈⣓⡆⣠⠞⢆⡀⣀⠠⠓⠪⠽⣧⡀⠀⠀⠀⡏⢹⢡⡍⣉⣝⡆⠀⠀⣼⠛⠁⣰⣿⠛⣧⠀⠻⣷⣻⡾⠇⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣼⠉⠹⣦⣀⣩⢿⣴⣦⣄⠀⠈⣻⠀⠀⠀⠁⠈⣟⡌⢙⡎⢗⠀⠀⠙⠶⠿⠟⠁⠀⢧⡤⠴⠛⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠈⠓⢼⣿⡿⠿⠿⢿⠋⠏⠉⠁⠀⠀⠀⠀⠀⠀⠹⠏⠀⠈⠀⠀⢸⠀⠀⠘⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀ ⠀⠀ ⠀⠀⣠⠾⠛⠶⣄⢀⣠⣤⠴⢦⡀⠀ ⠀⠀⠀⢠⡿⠉⠉⠉⠛⠶⠶⠖⠒⠒⣾⠋⠀⢀⣀⣙⣯⡁⠀⠀⠀⣿⠀ ⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢯⣼⠋⠉⠙⢶⠞⠛⠻⣆ ⠀⠀⢸⣧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣤⡤⢿⡀⠀⢀⣼⣷⠀ ⣽ ⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢏⡉⠁⣠⡾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣷⣄⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠛⠛⠻⠿⣿⣿⣷⣦⣤⣀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⢯⣷⣻⢾⣽⣻⣿⣷⣿⡿⠿⠛⠉⠁⠀⠀⠈⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣟⣾⣻⢾⣽⣻⣞⣷⣻⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡼⣧⣟⣿⣼⣿⣿⣼⣧⣿⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⣻⢷⣯⣿⣿⢿⣻⣿⣿⣿⢿⡿⣿⣿⣷⣤⣤⣶⣶⣶⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢾⣽⣻⣞⣿⣿⣿⣿⣿⣟⡾⣯⣟⣷⣻⢿⣿⣿⣟⣿⣻⣽⣻⢿⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣻⣞⡷⣯⣟⡿⣿⣿⣿⢾⣽⣳⣟⡾⣽⣻⣿⣿⣿⣾⡷⣯⣟⣻⣾⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣾⣿⣷⣯⣿⣿⢿⣿⣟⣾⣳⢯⣟⣷⣿⣿⣟⣿⣿⣿⣳⢯⣷⣿⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⢯⣿⣾⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣞⣷⣻⢾⣽⣻⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡿⠟⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⣀⣀⣀⣀⠀⠀ ⢀⣀⣤⣤⣤⣤⣿⣿⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠿⠿⣿⣿⠟⠛⠛⠛⠛⠛⠂ ⠘⠛⠋⠉⠉⠉⢻⣿⡏⠉⠉⠉⠀⠀⠀⠀⠀⠀⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⣤⣿⣿⣷⣶⠶⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠾⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⡟⠛⠿⠿⠿⠆⠀⠀ ⠀⠀⠀⠘⠟⠛⠋⠉⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣄⣀⣠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⣤⣶⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣾⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠙⢻⣿⣷⣦⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⠟⠋⠁⠀⠙⠿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠟⠋⠀⠀⠀⠈⠙⠛⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣾⣿⣿⡿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡾⠲⠶⣤⣄⣤⣤⣤⣤⡿⠛⠿⡴⠾⠟⢻⡆⠀⠄⠄ ⠀⠀⠀⣼⠁⠀⠀⠀⠉⠁⠀⢀⣿⠑⡿⣿⠿⣷⣥⣥⣷⡀⠀⠀ ⠀⠀⠀⢹⡶⠀⠀⠀⠁⠀⠀⠈⢯⣡⣿⣿⣀⣰⣿⣦⢂⡏⠀⠀ ⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⣍⣭⣾⠁⠀⠀ ⠀⣀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣧⣤⡀ ⠈⠉⠹⣏⡁⠀⢸⣿⠀⠀⠀⢀⡀⠀⠀⠀⣿⠆⠀⢀⣸⣇⣀⠀ ⠀⠐⠋⢻⣅⡄⢀⣀⣀⡀⠀⠯⠽⠂⢀⣀⣀⡀⠀⣤⣿⠀⠉⠀ ⠀⠀⠴⠛⠙⣳⠋⠉⠉⠙⣆⠀⠀⢰⡟⠉⠈⠙⢷⠟⠈⠙⠂⠀ ⠀⠀⠀⠀⠀⢻⣄⣠⣤⣴⠟⠛⠛⠛⢧⣤⣤⣀⡾⠀⠀⠀⠀⠀

⡖⣢⠖⣂⠒⡄⢢⠑⡒⢆⡒⠰⢂⠔⡀⠆⡐⠄⢢⠐⢠⠂⠔⡠⠂⠔⡀⠆⠰⡈⡐⣈⠰⠐⢂⡐⠂⡔⠂⡔⢂⡐⠢⡐⢢⠐⠢⡐⢂⠰⠐⡠⠒⡀⠆⡐⠄⡂⠔⠠⢂⠔⠠⢂⠰⠠⠘⡀⠎⡑⠌⢃⡂⢃⡄⠃⡄⢃⡐⠢⡐⢂⡰⢀⠢⢐⠠⢂⠰⢀⠢⢐⠠⠂⠔⢠⢂⠰⢀⠢⢐⠠⢂⠰⢀⠢⢐⠠⢂⠰⢀⠢⢐⠠⢂⠰⢀ ⡘⢄⠊⠄⢣⠘⡠⢡⠘⠤⣈⠱⡈⠔⡨⢐⠡⢊⠤⡉⢆⡉⢆⠱⡈⢆⠱⣈⠱⢠⠑⡠⢂⠍⠢⠌⡱⣀⠣⡐⠡⡌⠱⢈⠂⡉⠤⢁⠌⠄⢃⠤⢁⠒⣈⠰⣠⣁⣌⡁⢆⡈⢆⣁⢢⣁⣅⡒⡐⢈⠄⠃⠤⠁⡄⢃⠐⠂⠌⢡⠘⠤⢂⠥⣊⠄⠣⢌⠢⡁⠎⢄⠃⡍⡘⠤⢈⠔⡌⠰⢡⠘⡄⠣⢌⠢⡁⠎⡄⠣⢌⠢⡁⠎⠥⠒⡠ ⢇⠎⡘⢌⠢⡑⢄⠢⣉⠖⡠⠑⡌⢢⠑⡈⢆⠑⢢⠑⢢⠘⢠⠃⠜⡠⢃⠄⡃⢆⠱⣀⠣⢌⠱⡈⠔⡠⢃⠌⡑⢈⠔⠡⡈⣔⣰⣬⣴⣾⣶⣾⠿⠿⠻⠟⠻⠟⠻⠟⠻⠟⠿⠻⠛⠟⠻⠟⠿⢿⣾⣷⣦⣵⣴⣬⣬⣥⣎⣄⡌⠐⡂⠰⢀⠊⡑⡈⢒⠡⢚⠠⢊⠔⡈⢆⠡⠌⡰⠁⢆⠱⢈⠒⠤⠑⠌⠒⢌⠡⢂⡑⠌⡌⠧⡑⠠ ⢎⡘⠰⠈⠆⡑⢂⠰⢀⠎⡐⢡⠘⡀⠆⠱⣈⠘⡄⢊⠄⢃⠆⡉⢆⠱⡈⢆⠱⣈⠒⡄⢊⠄⢣⠘⠄⡑⠠⠒⣈⣤⣾⣾⠿⠟⠛⡋⢉⠔⠠⠠⠌⠤⠡⠌⢡⠈⡔⢈⠡⠌⡠⠑⢨⠘⢠⠘⡄⣢⠔⣠⠉⡉⢉⠉⡉⡉⢹⠻⠿⢿⣶⣧⣬⣤⣁⠔⠡⠘⡠⠃⢎⠰⡑⢌⠒⡌⠰⡉⠰⢈⠆⢩⠐⡉⢌⠱⣈⠰⠡⣀⠣⠐⢣⠐⠡ ⢦⠣⣅⠣⢜⡰⡈⠴⣈⠦⣑⠂⣆⠱⡈⠥⡐⢌⠰⡈⠜⢠⠊⠔⡈⠆⠱⡈⠒⡄⠣⠘⠤⠉⡄⠌⣒⣬⣷⡿⠿⠛⡍⠄⠋⡔⠡⠜⡠⠌⢂⢥⣈⣔⣡⣪⣴⣦⣬⣦⣼⣴⣤⣭⣤⣭⣤⣧⣼⣁⣊⠄⡑⡈⠤⢁⢂⠁⠆⠰⡐⢂⡌⡉⣉⠛⠿⣿⣶⣥⣄⡑⠈⠤⠑⡈⢒⠨⡑⠨⢑⠨⠘⣀⠣⠘⡠⠃⢄⠢⡑⢄⠢⡙⢦⢉⡐ ⢎⠱⣀⠣⢌⠰⠁⢆⠡⠚⡄⠣⢄⠣⡘⠤⡑⢌⠒⢌⡘⢄⠊⡔⢡⠊⢅⠢⡑⠌⢂⠱⢀⣣⣴⡿⢟⠫⠙⣀⠣⠱⠠⢉⢰⣠⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣤⣧⣔⡡⠠⢁⠤⢈⡒⢠⢉⡙⠻⢿⣷⣆⡡⠘⣈⠰⢁⠣⢌⠢⡑⢄⠢⡑⢄⠣⠌⢒⠰⡈⢆⠡⢇⢂⡐ ⠎⠒⡄⠒⡈⠆⡉⢄⢊⡑⡈⢅⠢⠑⠌⢢⠑⡨⠘⠤⡘⢄⠊⡔⢂⠩⢄⠣⠐⢌⣢⣾⡿⠟⡉⠔⡁⢮⠱⢀⢢⣡⣷⣾⣿⣿⣿⣿⢿⣿⣻⢿⡽⣏⣯⡽⣞⣧⠷⣞⡵⣾⣱⣞⣶⣳⡞⣶⣛⡾⣭⣻⢽⣻⣻⣟⡿⣿⢿⣿⣿⣿⣷⣮⣤⣃⢉⠂⠇⠤⣁⢂⣉⠻⢿⣷⣄⡢⠌⠒⡈⠆⡱⢈⠔⡨⠐⡌⡘⠄⡃⠔⡈⠆⣉⠂⠄ ⡌⡱⢀⠣⡘⠰⡐⡈⢆⠰⡁⢆⠱⡈⠜⡠⢊⠔⣉⠒⠨⢄⠣⡘⠄⢃⠄⣢⣽⡾⠟⡉⢢⠐⡌⠱⣀⣦⣶⣿⣿⣿⣿⡿⣟⣯⢷⣯⣞⡷⣯⢾⣽⣛⡾⣽⡻⣼⣻⡭⢷⣿⣳⢾⣷⢯⣟⣳⡽⣽⣳⢯⡟⣶⣻⡼⣏⡷⢯⣳⡟⣿⢿⣿⣿⣿⣷⣮⣜⠰⠁⢆⡐⠢⡐⣈⠛⣿⣦⡑⢠⠊⠰⢁⠊⡔⢡⠒⣈⠒⠌⡂⢅⠒⡄⠡⢊ ⣎⠱⡈⢆⠡⢃⠔⡈⢆⠱⢈⠆⡡⠘⠤⡑⢌⠢⡐⢌⠱⢨⠐⠤⠉⣤⣾⡿⢋⠰⢁⠶⣄⢣⣴⣿⣿⣿⣿⣿⣻⡽⢾⣽⣛⣾⣛⡾⣽⢾⡽⣻⢶⣯⢟⣶⣻⡳⢯⣽⣻⣿⡽⣿⡟⣿⣿⢧⣟⣞⡷⣫⢟⣳⣏⣷⡻⣽⢯⣷⣻⠽⣾⣹⢯⡿⣿⣿⣿⣿⣮⣄⢉⠒⠍⡄⢒⠠⠙⢿⣧⣜⠠⡁⠎⡰⢁⠒⡄⢣⠘⡰⢈⠒⠤⠑⡠ ⢆⢣⠐⢢⠑⡌⢂⠱⡈⢆⠡⢂⠥⣉⠒⡰⢈⠒⢌⠢⡘⠄⢊⢤⣿⠿⢃⠐⢢⡱⠌⣰⣶⣿⣿⣿⠿⣏⡷⢾⣱⣿⢯⣳⣟⡾⣽⡛⢷⢯⡷⣯⢷⣾⡻⣞⡷⣻⢟⡾⣿⣯⢿⣿⡔⣿⡿⣏⡾⣞⠿⢯⣿⡳⣞⣧⡟⣷⣻⠶⣯⣟⡷⢯⣞⠷⣯⢟⡿⣿⣿⣿⣷⣌⡒⠌⠎⢄⡉⠤⠘⢿⣷⡄⢂⠡⢊⠔⡨⠔⢂⡑⠢⡑⢂⠥⠐ ⡎⡄⢃⠆⡱⢀⠃⢆⡑⠢⠑⡌⠢⢄⠱⣀⠣⡘⠤⠒⡀⢎⣿⠟⡁⢢⠘⡬⢐⣴⣾⣿⣿⣿⣻⣭⢿⣹⣽⣿⡿⣏⣯⢷⡾⣽⠶⣹⠳⣎⣿⣽⣿⣞⣷⣛⡾⡽⣯⢿⣿⣏⣿⣿⡱⣿⣿⡝⣷⡍⢾⣩⣿⢷⣛⣶⢻⣧⢿⣟⡷⣾⣹⣟⣾⣻⡽⣾⣹⠷⣯⣿⣿⣿⣿⣶⡈⠆⡜⠠⣁⠂⡙⢿⣦⡡⠌⠂⠥⡘⠄⢆⠱⢄⠃⡄⢃ ⡒⢌⠢⢘⡐⠢⢉⠆⡰⢁⠣⡐⢡⠊⡔⢠⠃⠔⢂⢡⣼⡿⢃⠰⢘⠢⣐⣴⣿⣿⣿⢿⣛⠶⣻⣞⣯⣿⣿⢯⣻⢽⣞⣯⣽⡳⣏⡵⣻⣼⣿⣿⡿⣞⠾⣵⡻⣗⣯⣿⡿⢾⣼⣿⢸⣿⣷⣻⢷⣻⢶⡧⣿⢿⣿⣜⠿⣜⡿⢾⣿⣷⣹⣞⣾⢳⣟⡷⣍⠻⣜⣧⢟⡿⣿⣿⣿⣶⡈⢅⠢⠌⡐⠌⠻⣷⣌⠘⡠⠑⡌⢆⠡⢆⡘⠄⡂ ⠰⡈⢆⠡⢂⠅⡊⠔⣁⠢⠑⡌⢢⠑⡌⠢⠘⢠⣮⡿⢋⠐⠤⡒⣈⣴⣿⣿⣿⣟⡯⣟⣮⢷⣳⣽⣿⡿⣝⡾⣽⣻⢮⣷⣳⠿⣽⣻⣟⣿⣿⢯⡷⢯⣻⢳⢯⡷⣽⣿⣻⣟⣾⣿⢸⣿⡷⢯⣟⣞⡿⣼⢫⣿⣿⣞⣻⠽⣞⣯⢻⣿⣷⢮⣻⢟⡾⣽⣏⡷⣽⢮⣟⠾⣽⣻⢿⣿⣿⣧⡂⠥⠘⣀⠃⠹⣿⣆⠡⠘⠤⣈⠒⡄⢢⠑⡠ ⠡⠐⢢⠑⡌⢠⠑⡌⠰⣀⠣⢘⡀⢣⠐⠡⣑⣾⡟⢁⢂⠡⢂⣵⣿⣿⣿⣟⣧⣟⡾⣽⣞⢯⣿⣿⣯⡽⣏⣿⣳⢯⣷⡳⣯⣟⣷⣻⣾⣿⣿⣫⡽⣏⡷⢯⣻⡗⣿⣿⡳⣾⣿⣯⢘⣿⣿⣛⡾⢾⣽⡳⣟⡼⣿⣯⢷⡻⣽⡺⣝⣻⣿⣿⡽⡾⣽⣳⢾⣽⢻⣾⣹⡟⣧⡟⡾⣿⣿⣿⣿⣦⠁⡄⢊⠡⠘⣿⣧⡁⢒⠠⢃⠌⡄⢃⡐ ⠠⢉⠢⡘⠰⢀⠣⢌⠡⠄⡃⢆⡘⠄⡘⣴⣿⠏⡐⢠⠊⢴⣿⣿⣿⡟⣧⣟⣮⢷⣻⢳⣾⣿⣿⣳⢷⣻⡽⣶⢯⣟⣶⡻⢷⣻⢾⣽⣿⣻⡽⢧⣟⡽⣞⢯⡷⣻⣿⣷⡻⣽⣿⡷⣈⢿⣿⣭⣟⡿⣶⢻⣭⢟⣽⣿⡾⣝⣳⣽⢫⣗⢿⣿⣿⣟⣳⢯⣟⡾⣻⢶⢯⠿⣵⡻⣝⡞⣿⣿⣿⣿⣷⡐⢂⠡⠑⡈⢿⣷⣀⠊⠔⡌⠰⡁⠄ ⠀⠇⡰⢁⠇⢆⠱⡈⠆⣁⠸⢀⠰⢈⣸⣿⠇⢰⠈⡇⢸⣿⣿⣿⣇⡿⣷⣏⡾⣹⣏⡿⣾⣿⢷⣏⡾⣷⣏⡿⣾⣹⣶⢿⣏⣹⣾⣿⣏⣷⢿⠿⣎⣷⣏⠿⣾⣹⣿⣷⢿⣹⣿⣷⡈⢾⣿⣎⣹⣾⣹⡏⣾⡏⣾⣿⣿⣉⣷⡾⣿⣸⢏⣿⣿⣿⣏⣷⢏⣷⣏⡿⣾⢿⢷⡿⣉⡿⡾⣿⣿⣿⣿⣿⡀⠸⢀⠁⠎⣿⣷⠈⡰⠈⡁⢰⠈ ⠈⡔⢁⠎⡐⠂⠥⡘⠰⡀⠎⢠⠁⣾⣿⠃⠌⠄⠛⣴⣿⣿⣿⣳⢾⣽⡳⡾⣽⣿⣟⣿⣿⣻⡟⣾⣽⣳⢾⣽⡳⣧⣟⣯⢾⣯⣿⣿⣻⣞⢯⢿⣹⢶⣏⡿⣳⣿⣿⣯⢷⣻⣿⣷⠌⡭⣿⣯⠷⣯⢷⣛⡷⣽⣫⣿⣷⢯⢾⣵⣻⢮⡟⣾⣿⣿⣿⣾⣛⣮⣽⣳⢯⣟⢾⣹⣽⡞⣽⡽⣿⣿⣿⣿⣷⡁⠌⡰⢈⡘⢿⣷⡀⡑⢠⠁⡌ ⠐⡠⢊⠰⢁⡉⢆⡁⢣⠐⠌⢄⣾⣿⠁⡌⡘⢌⣼⣿⣿⣟⣳⢯⣟⣮⢷⣻⣿⡟⣾⣿⢯⣳⣿⣳⢧⣟⣳⢾⣝⡷⣾⣭⣿⣾⣿⣳⣟⡾⣏⣿⣿⣟⣮⣽⣳⣿⣿⣯⢯⣟⣾⣿⡜⡰⢻⣿⣻⣽⣻⢞⡽⣧⣻⢿⣿⣯⣟⢶⣯⢷⡻⣵⣻⣿⣿⣿⣟⣞⡶⣯⣟⡾⣫⣗⣿⣷⠸⣿⣞⣿⣿⣿⣿⣷⡈⡐⠄⡒⢈⢿⣷⠈⠄⠒⠠ ⠠⢁⠌⢢⠁⠆⢢⠘⡄⠌⠒⣼⡿⠁⠜⠠⣑⣾⣿⣿⣻⡼⣯⣻⡼⣞⣳⣿⣯⢟⣿⣟⡯⣿⣏⣷⣛⡾⣭⣟⣮⣽⣳⡽⣾⣿⣿⣱⢟⡾⣹⣾⣿⣻⢼⢶⣻⣿⣿⣿⢧⣻⢞⣿⡧⢱⠹⣿⣟⡶⣯⢿⣽⢳⣯⢿⣿⣷⣞⣯⢞⣷⣻⡵⣫⣿⣿⣿⣿⣯⣞⡷⡾⣽⣳⡞⣽⣿⡇⢻⣿⡽⣿⣿⣿⣿⣷⡀⠎⡐⣈⠘⣿⣧⢈⠡⡁ ⢀⠃⡘⢄⠃⡜⢠⢁⠒⣨⣽⡿⢁⡘⢈⠦⣽⣿⣿⢳⣳⣿⡵⣳⢯⣽⣿⡿⣭⣿⣿⢯⣽⣿⣻⢖⣯⣟⣳⢾⡵⣾⡽⣟⣿⣿⢧⣟⡾⣹⣿⣿⢳⣭⣟⣾⣿⣿⣿⣿⢯⡽⣏⣿⣿⡅⢎⢿⣿⣽⢫⣟⡾⣽⣺⢿⣿⣿⣿⢮⣟⣮⢷⣻⡵⣻⣿⣿⣿⣿⣞⡷⣻⢷⡽⣞⣳⣿⣯⢉⣿⣿⢽⣿⣿⣿⣿⣷⡀⠆⢠⠡⠘⣿⣇⠰⢀ ⢀⠊⡁⢆⠡⡐⠡⠌⣠⣿⡟⢀⠒⣈⢢⣿⣿⡿⣽⢫⣿⣷⢻⣝⣾⣿⡿⣝⣾⣿⡟⣞⣾⣿⡽⣞⢧⡿⣭⢯⡽⣶⣻⣿⣿⣿⢫⡾⣽⣿⣟⣞⢯⡶⣿⣿⣿⣿⣿⣿⣯⣽⢣⣿⣿⡏⣌⠚⣿⣷⣏⣯⣟⡶⢯⣿⣿⣿⣿⣿⣮⢗⣯⢷⣽⣣⢿⣿⣿⣿⣿⣳⢯⣏⡿⣝⣮⢿⣿⡲⣸⣿⣏⣿⣿⣿⣿⣿⣧⠘⢠⢁⠊⠹⣿⡐⠠ ⠠⡁⠱⡈⠤⢁⠜⠰⣼⣿⠁⠌⡒⢤⣿⣿⡿⣽⢣⣿⡿⣞⡽⢮⣿⣿⣽⢣⣿⣿⡝⡾⣽⣿⣳⢯⣯⢿⣱⢯⣟⣼⣿⣿⣿⣏⣟⣾⣿⡟⣞⣞⢯⣾⣿⣿⣿⣿⣿⢻⣿⣼⡳⣽⣿⣿⢠⢋⢽⣿⣞⣼⣻⣼⡻⢾⣿⢿⣿⣿⣿⣯⢞⡿⣶⢏⣟⣿⣿⣿⣿⣟⣮⢯⣽⣻⠼⣯⣿⡷⢡⢿⣿⣚⣿⣿⣿⣿⣿⣇⠂⡄⢃⢁⢻⣯⠗ ⠐⣈⠑⡌⢒⠈⠤⣿⡿⢁⠊⠤⢑⣾⣿⣿⡽⣳⣿⣿⡽⣞⡽⣿⣿⣟⣮⢿⣿⣷⢻⡽⣿⣯⡗⣿⡼⣯⢏⣟⡾⣽⣿⣿⣿⢺⣾⣿⣳⢻⣝⣮⣿⣿⣿⣿⣿⡿⣽⢻⣿⣶⢻⡽⣾⣿⣇⠎⡆⢿⣿⡖⣿⢾⣽⢻⣿⣯⢿⣿⣿⣿⣾⣝⡾⣏⡾⣽⣿⣿⣿⣿⣮⢟⡾⣽⣏⡷⣿⣟⢢⠹⣿⣟⡾⣿⣿⣿⣿⣿⡔⡀⠎⠄⡂⢿⡧ ⠂⡄⢣⠘⡄⠡⢪⣿⠇⠌⠢⢁⣾⣿⣿⣳⣽⣿⣿⣷⢫⡽⣾⣿⣿⡿⣼⣻⣿⣳⠿⣽⣿⣷⣛⣧⠿⣭⣟⡾⣽⢷⣿⣿⣿⣿⣿⡳⣽⢫⣞⣾⣿⣿⣿⣿⣿⣹⡭⢷⣿⣯⢯⣟⠷⣿⣿⡜⣨⠹⣿⣿⣭⣟⡾⢯⣿⣇⠻⣽⣿⣿⣿⣿⣞⣭⢷⣫⣿⣿⣿⣿⣿⣯⢻⡷⢯⣞⣿⣿⡃⢇⣻⣿⣽⣻⣿⣿⣿⣿⣷⡐⢈⠒⠠⡙⡷ ⠂⠔⢃⠡⠂⢥⣿⡟⡈⠰⡁⣾⣿⣿⢯⣳⣿⣿⣿⡞⣯⢳⣿⣿⣿⣟⡷⣿⣿⡳⣟⡷⣿⡷⣏⣾⣛⡷⣯⣻⣽⣻⣿⣿⣿⣟⣧⢟⣧⣿⣿⣿⣿⣿⣿⡟⣧⣳⢏⢻⣾⣿⡷⣞⣻⣽⣿⣷⡄⢣⢹⣿⡶⣏⢿⣹⢿⣿⢠⠙⣾⢿⣿⣿⣿⣾⡳⣧⠿⣿⣿⣿⣿⣯⠿⣽⣻⢮⣿⣿⡍⠲⣌⣿⣷⢯⣿⣿⣿⣿⣿⣇⠌⡐⠡⡐⠟ ⢈⠢⠌⢂⣩⣼⣿⠁⡰⠁⢴⣿⣿⡿⣏⣿⣿⣿⡿⣼⢏⣿⣿⣿⣿⣿⣿⣿⣿⢽⢾⡽⣿⡿⣝⡾⣭⣟⣷⢻⣾⣽⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⣄⣋⣞⣿⣿⡵⣏⣾⣿⣿⣿⡄⢣⢻⣿⡽⣎⣟⢯⣿⡇⢱⡈⢯⣿⣿⣿⣿⣿⣯⣟⣿⣿⣿⣿⣿⣻⠷⣯⢷⣻⣿⢇⠳⣄⢻⣿⣯⢿⣿⣿⣿⣿⣿⠠⠘⢠⠐⡉ ⢀⠒⡈⢼⡟⠛⢃⠆⡡⠘⣾⣿⣿⢻⣽⣿⣿⣿⡟⣧⣻⣿⣿⣿⣿⡷⣟⣿⣿⣫⢾⣽⣿⡿⣭⢿⡵⣾⢽⣻⣾⣿⣿⣿⡿⡽⣽⣿⣿⣿⣿⣿⣿⣿⣿⠏⣉⠛⡛⠿⢿⣾⣿⣿⡵⣫⢿⣿⣿⣿⡄⢣⢻⣿⣗⡯⣯⢿⣷⣵⣾⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣹⢯⣿⣿⡃⠧⣌⢫⣿⣿⣿⣿⣿⣿⣿⣿⡇⡉⠄⣂⠡ ⠀⠎⡀⢿⡃⢡⢊⡔⠡⢳⣿⣿⡿⣹⣿⣿⣿⣿⡟⣧⢿⣿⣿⣿⣿⣽⣻⣿⣿⣭⢟⣾⣿⣿⡝⣾⣝⣯⢯⡷⣿⣿⣿⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⠟⡡⢊⡔⢣⡑⢎⡰⢻⣿⣿⣿⣭⢻⣿⣿⣿⣿⣅⢎⡹⣿⣽⢧⣻⣿⡡⢀⠞⣰⢡⠚⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢻⣧⢿⣿⣃⠳⣘⠧⣹⣿⣿⣿⣿⣿⣿⣿⣿⠠⠘⣀⠂ ⠈⠤⢁⢾⡁⠂⡜⠠⡁⢿⣿⣿⣟⣿⣿⡿⣿⣿⡿⣱⣿⣿⣿⣿⣳⢯⢷⣻⣿⣞⣻⣞⣿⣿⣽⢳⡾⣽⣳⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢏⢡⢊⡔⢣⠜⣡⠚⡤⢃⡌⢻⣿⣿⣾⢧⢿⣿⣿⣿⣿⣦⠱⡹⢿⣿⣜⣿⣷⡁⡚⡔⣃⠧⣈⠳⣛⣿⣿⣿⣿⣿⣿⣿⣯⣟⡼⣿⣿⢂⠧⣙⠖⡡⢿⣿⣿⣿⣿⣿⣿⣿⡆⠡⠄⠌ ⠈⡔⠂⠾⣧⡅⠰⠁⢌⣻⣿⣿⣽⣿⣿⢛⣿⣿⣟⡷⣿⣿⣿⢿⡽⣏⣯⢿⣿⣟⡶⢯⣿⣿⣞⣯⣽⣳⣏⢿⣻⣿⣿⣿⣿⣿⣿⡿⢛⠤⡒⣌⢆⠣⡜⢡⠚⢤⡙⢰⢃⠜⡄⠻⢿⣿⣿⡞⣿⣿⣿⣿⣿⣷⣥⠋⣿⣿⣾⣿⡔⢡⠚⡤⢓⢆⠣⠜⡘⢽⣿⣿⣿⣿⣿⣿⣾⣹⣿⣯⠘⢦⡙⣎⠱⣹⣿⣿⣿⣿⣿⣿⣿⣇⠡⠌⢂ ⠐⡠⠑⠬⡟⠠⠑⡨⢀⢾⣿⣿⣿⣿⣿⢸⣿⣿⡿⣼⣿⣿⢯⣟⡾⣽⢮⣟⣿⣿⡽⢯⣿⣿⣟⡾⣼⣳⢯⣻⢿⣿⣿⣿⣿⡿⢛⡰⣉⢲⠱⢌⣂⠳⡘⢦⠙⢦⡘⢥⢊⡜⢢⠑⡊⢽⣿⣿⣽⣿⣿⣿⣿⣟⣿⣷⡤⣛⣿⣿⣿⡠⣙⠰⣉⠎⡱⠣⢜⠠⣌⠛⣿⣿⣿⣿⡷⣯⣿⡧⣙⠢⣝⢢⠓⡜⣿⣿⣿⣿⣿⣿⣿⣿⠠⠘⠠ ⠠⢁⠜⢸⠀⡅⢃⠰⢀⠺⣿⣿⣿⣿⡏⠰⣿⣿⣟⣾⡿⣽⣺⣭⢿⡽⣛⡾⣽⣿⣿⣳⣻⣿⣿⣽⢳⣯⣟⣭⢿⣿⣿⡿⢋⠴⣃⠖⡡⢎⠒⣌⠢⡑⠡⢆⠩⢒⡘⠤⢃⡜⡡⢋⡜⢠⠜⣻⣿⣾⣿⣿⣿⣿⣼⢻⣿⣶⣼⣻⣿⣥⢂⠓⡌⢎⡱⣉⢎⡱⢄⠃⢾⣿⣿⣿⣟⣿⣿⠇⢦⡙⡔⣋⠞⡰⢼⣿⣿⣿⣿⣿⣿⣿⢀⠃⡡ ⢀⠃⠌⢢⠱⣤⡂⠆⣁⠂⢿⣿⣿⣿⡇⢡⣿⣿⣿⡿⣽⣳⣟⣾⢫⡽⣏⢷⣫⣿⣿⣷⣹⣿⣿⣯⢷⣻⠾⣽⢻⣿⡿⡐⡉⠦⡑⢊⠱⡈⢜⠠⢓⡙⠿⠻⢟⡶⢶⡷⢦⡰⣅⠣⡜⢢⠚⡄⠚⢿⣿⣿⣿⣿⣷⣻⢞⣽⣻⣿⣿⣿⣿⣦⡘⢢⠑⣌⠲⡘⣌⠣⠌⣿⣿⣿⣿⣿⣿⡋⢦⡙⢴⣉⠞⣡⢺⣿⣿⣿⣿⣿⣿⣿⠠⠘⡀ ⠀⠎⡐⢁⠢⢹⣷⣆⠤⠘⡈⢿⣿⣿⣷⣿⣿⣿⣟⣳⣽⣳⢟⡮⣟⣽⣾⣿⣿⣿⣿⣿⣷⢿⣿⣿⣟⡞⡿⣭⣏⣿⣿⣠⣑⣦⣵⣬⣶⣷⣾⣶⣷⣶⣷⣮⣴⣬⣒⣐⠢⡁⢆⡙⢌⢣⡙⠴⣉⠆⣍⠻⣿⣿⣿⣷⣻⢎⡷⣹⣿⣿⣿⣿⣿⣦⡑⢢⠑⡍⢲⡉⢲⢹⣿⣿⣿⣿⣿⡑⢦⡙⢲⣘⠺⣄⢻⣿⣿⣿⣿⣿⣿⣿⠠⠑⡠ ⠈⡔⣈⣦⣶⡿⠟⠋⢄⠡⢂⠹⣿⣿⣿⣿⣿⢳⣞⣳⢾⣹⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣮⣜⠢⡙⢲⢡⠚⣄⠣⢌⡙⢿⣿⣿⡽⣞⣳⣏⣿⣧⣉⠙⠻⢿⣷⡇⢌⠳⢌⠣⣘⣯⣿⣿⣿⡿⡑⢦⡹⢡⢎⡱⢬⣿⣿⣿⣿⣿⣿⣿⣿⠠⠑⠠ ⣶⣼⡿⠏⡁⠆⡘⢈⠄⣲⣴⣿⣿⣿⡿⣻⣜⣯⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣎⣷⢻⣻⣿⣿⡿⢉⠉⢻⣿⣿⣿⣿⠻⣿⣿⣛⣿⣿⣹⢻⣿⠿⣿⣿⣯⡐⡡⢃⢎⡱⢌⡚⠴⣈⠦⠙⣿⣿⣯⡷⣏⡿⣿⣧⠌⣑⠢⡐⢌⠢⡙⠤⢓⠌⣿⣿⣿⣿⡧⡑⢦⡙⣎⠦⡑⢮⣿⣿⣿⣿⣿⣿⣿⡿⢀⡉⠔ ⣿⡏⡐⠤⢁⢒⣬⣴⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡼⣳⣞⣻⣿⣿⣿⣿⣞⣯⢽⣿⡿⣷⣦⡉⣤⣏⣿⣿⣿⣧⣝⣻⣿⣿⣿⠈⡡⢈⠡⢃⡌⢣⠑⢦⡉⠖⡌⢦⢉⠖⡡⢎⡱⢠⠙⡿⣿⣯⣷⣻⣿⣎⣤⣣⣵⣌⠧⣉⠓⠬⣘⣿⣿⣿⣿⠰⣉⠶⣉⠖⣣⠙⣼⣿⣿⣿⣿⣿⣿⣿⡗⠠⡐⢈ ⣿⡡⠐⢂⢬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⣿⣿⣿⣿⣿⣿⣿⡿⣹⢧⣟⣳⡽⢶⣹⠿⣿⣿⣿⣾⢧⣿⣿⠘⣿⣿⡽⡛⢛⣍⡛⢿⡿⣶⣹⣿⠇⢂⠡⢊⠔⡣⢌⢣⠚⡴⣈⠳⡘⠆⡍⢎⡱⢌⠲⡡⢎⠰⡍⣿⢿⣿⣿⣿⣏⠩⡐⠤⠒⠤⣉⣶⣽⣿⣿⣿⢃⠳⣘⠲⣍⠺⡥⣩⣿⣿⣿⣿⣿⣿⣿⣿⢁⠒⡈⠄ ⣿⣇⠌⠄⡂⢩⠉⡍⠩⢉⡉⢉⡉⢉⠔⡠⠄⡤⢑⡠⢉⣿⣿⣿⣿⣿⣿⣿⠰⣈⠻⣾⡵⣛⣯⢳⢯⣽⠻⢿⣿⣿⡾⣿⣇⠘⢿⣷⣥⣎⣤⣝⣤⣶⣿⡿⠋⡄⢣⢌⠣⢎⡱⠌⢦⠙⡴⢨⠱⡌⢳⠘⣆⠱⣊⠱⡑⢎⠲⢌⠻⢿⣿⣿⣿⣿⣷⣾⣶⣿⣿⣿⢟⣿⣿⣿⣿⡉⠖⣍⠺⡔⢫⢴⣻⣿⣿⣿⣿⣿⣿⣿⡏⠄⣂⠡⠌ ⠟⣿⣮⣒⡈⠄⠒⣬⣅⡢⠄⢃⡐⢌⠠⣵⣍⠌⠡⡐⠨⣿⣿⣿⣿⣿⢻⣿⣧⡄⠣⢌⠛⠿⣾⣽⣞⣼⢧⡈⡝⠿⣿⣿⣿⡜⢢⠙⡛⢛⠛⣛⠛⡋⢅⢢⠱⣌⠣⣌⠳⣈⠦⡙⢆⡩⢆⠥⢓⡘⢆⠳⡄⠳⣌⠱⣉⢆⠳⣌⠒⡢⢌⡙⢛⠻⠿⢿⡿⠿⢛⠡⣺⣿⣿⣿⣿⡘⡱⢎⡱⢎⡱⢢⣿⣿⣯⣿⣿⣿⣿⡿⠐⡈⠄⠢⣌ ⠐⡠⢙⠻⠿⠿⣾⣽⠿⠿⠿⠿⠿⠿⠿⠿⣿⡎⡐⠤⢁⢻⣿⣿⣿⣿⣳⡞⣿⣿⣥⡌⢊⠴⢠⡉⢍⡉⣯⣶⣥⡃⢍⠻⢿⣿⣄⠣⡘⣤⠩⣄⠣⡍⡆⢎⡱⢠⠣⠤⢓⡰⢢⢍⠲⡐⠎⢆⠣⠜⢢⠣⠜⡑⢆⠳⠌⣌⠣⢆⡝⡰⢡⠎⡴⣈⠖⡤⣒⠤⢃⡒⣿⣿⣿⣿⣟⠰⣩⠎⡵⢋⡴⣿⣿⣿⣿⣿⣿⣿⡿⢁⠢⡁⠌⣡⡇ ⠐⡐⠄⠒⡠⠡⢀⠂⡌⠰⠐⡂⠔⡂⠌⢾⣿⣿⡔⠐⡈⠌⣿⣿⣿⣿⣷⡻⣵⣿⣿⣿⣷⣬⣂⠜⡂⢿⣿⣿⣿⠁⢎⡉⢆⠹⢿⢆⠱⣄⠳⢌⠣⡜⡰⢃⠲⠡⢎⠱⡒⢬⠣⢌⠲⠩⡜⢨⠓⣌⠣⠜⢬⡑⢎⡡⠓⡤⢋⠴⡰⣁⠇⡚⠴⣡⠚⡴⢡⢎⠡⢜⣿⣿⣿⣿⣏⠲⣡⠛⡴⣉⣿⣿⣿⣿⣿⣿⣿⡟⡁⢂⠆⠅⡒⡼⡅ ⠐⡈⢜⠡⢂⠱⡈⠖⢨⠑⢌⠢⡑⠌⡌⠠⠙⣿⣧⠘⠠⠌⡉⠟⡿⢿⣿⣿⡶⣿⣿⣿⣿⣿⣿⣿⣶⣮⣽⣍⣣⣉⠆⡩⠌⢆⡡⢊⡕⡨⠎⢬⠱⡘⠴⣉⠲⡉⠦⠱⣌⠢⣑⠪⣑⠣⡜⣡⠚⢤⠓⡜⢢⠜⢢⠱⣉⠖⡩⢆⡱⢂⠝⡌⡱⢂⠭⣐⠣⢎⡘⠬⣿⣿⣿⣿⢇⠳⣘⡳⢰⣽⣿⣿⣿⣿⣿⣿⣿⡷⢀⠡⡈⠒⣨⠅⡔ ⠠⠡⢌⠢⡁⠆⠱⡈⠆⠌⣂⠱⢈⠒⡌⣁⠊⣹⣿⣯⡐⢡⠐⠌⡠⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣍⠢⡘⡡⢎⠱⣉⢆⡓⢜⠲⢠⢃⠜⣰⣃⢾⣷⣆⡑⢢⠱⡘⢄⡋⠦⡙⠰⢃⠎⡥⠓⡬⠘⡥⠢⡕⢊⡜⢰⢡⠋⡴⢡⡙⠆⡌⢒⣿⣿⣿⡿⢌⡓⢬⢱⣿⣿⡿⢉⠉⡙⠛⢛⠛⢡⠊⡐⠄⣣⡟⢀⠂ ⢀⠃⢆⠱⢈⢂⠱⢌⡘⠰⣀⠣⢌⠒⡰⢄⠒⡠⢈⠙⠿⣷⣾⡔⢠⠡⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣕⡌⠣⠜⢢⠍⢮⡑⢊⡔⣺⣿⢿⣷⡈⠿⣿⣶⣧⣼⣐⣌⣢⣡⡙⢄⠚⡄⢓⣄⣫⠔⡱⢌⠣⡜⡡⢎⡱⡘⠦⠘⡌⣰⣿⣿⣿⣿⠏⡆⡍⣶⣿⣿⠟⣁⠢⡘⠠⠑⠂⡌⢂⡔⢐⣼⡿⠇⢨⠐ ⠀⠎⡰⢈⠆⢂⡑⠢⢌⠡⢄⠃⢆⡘⢄⠊⠴⣁⠂⡉⢄⣻⣿⠟⡀⠢⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣍⡂⠞⡰⢁⢣⠐⣿⡧⢸⣿⡜⠰⡠⢌⣉⢛⠛⡛⢛⠛⠿⠿⠿⠿⠿⢛⠛⡘⢤⢃⢇⠲⣡⠒⠤⣑⣢⣵⣾⣿⣿⣿⣿⡏⣜⣰⣿⣿⡿⠃⢌⠰⢡⢸⣷⡈⢡⢐⣾⣾⡿⠛⠡⡈⠤⢈ ⡁⠶⡀⢇⠈⡀⢆⢱⠈⡆⡈⠸⡀⠶⢈⠸⢰⢀⠸⢀⣿⡿⠁⠆⡈⢁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣁⡉⢆⠉⣿⡇⠆⣿⣇⠇⢱⠏⣸⡈⡇⢷⡈⢱⠎⣰⢁⡎⢰⠁⡎⠸⣀⠎⡀⢇⣀⣹⣶⣿⣿⣿⣿⣿⣿⣿⡿⢰⣾⣿⣿⣏⠀⢉⠀⢇⢸⣿⣿⣷⣶⣿⣿⠏⡀⢁⢁⠰⠆⢁ ⡱⢂⠱⡈⢆⠁⢆⠢⡑⢠⢁⠣⡘⠄⢣⠘⡄⢂⠒⣸⣿⡇⠑⡈⠤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣧⠈⢿⣿⡌⢢⢉⠤⠱⣈⠣⡘⢣⠘⡡⢂⠜⣠⢃⣬⣱⣤⣾⣶⣾⣿⣿⣿⡿⠛⠛⢿⣿⣿⣿⣵⣿⣿⣿⣿⣿⣿⡄⠊⠄⠿⣿⣿⠟⢋⠉⡄⢂⠜⡠⢉⠢⠘⠠ ⡣⢍⠂⡅⢊⠌⡐⢢⠑⡂⢌⠢⡑⢌⠢⡑⡈⠆⠒⣸⣿⡃⠡⠌⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢋⠡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⡘⣿⣿⣿⣶⣾⣷⣶⣷⣾⣶⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁⢱⣼⣿⣿⣿⣿⣿⠿⠛⠿⠿⠿⠛⠠⡑⣈⢾⣿⠛⡐⡈⠔⡘⢄⠊⡔⢡⠊⢡⠁ ⡑⢎⠰⡈⢆⡘⠤⢁⠆⡱⢈⠆⠱⡈⠔⡡⠘⡄⠃⠌⣿⣷⣁⠒⠠⠙⢋⠩⢁⠻⢿⠿⡿⠿⠿⠛⢋⠉⡄⠒⡌⠆⢂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣾⣿⣿⣿⣿⡅⠰⢹⣿⣿⡿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⠿⠛⠡⢠⠁⢆⠘⡠⢁⢃⠰⣶⣾⡿⢁⡐⠌⢢⠑⡌⢒⡈⢄⠃⠆⡈ ⡙⡌⢂⡑⠢⢌⠰⢈⠒⡄⠣⢌⠱⡈⢆⠡⢃⠤⢉⡐⠸⢿⣦⡌⣱⡈⡐⢂⠑⡊⠄⠒⢠⠑⡠⠣⠌⣶⡌⢙⠰⠉⡄⢿⣿⣿⣿⣿⣿⣿⠟⣛⢻⣿⡿⢿⣿⣿⣿⣿⡐⣤⣏⠛⣿⣶⣈⡙⢻⣿⣿⣿⣿⡿⠿⠻⣛⢛⡛⢟⣻⣿⣿⡛⠛⠟⡛⠟⠛⠋⢄⠂⠥⠃⢄⣫⣤⣦⣅⣦⣯⣼⡿⢉⢁⠂⠤⣉⠢⡑⠄⡃⢌⠢⡉⠤⢁ ⡓⡌⡁⢆⠱⡈⠆⢌⠒⡌⢡⠊⡔⢡⠈⢆⠩⡘⠠⡄⠃⢌⠙⠿⣿⣿⡶⠬⣸⣶⡈⡵⢊⣵⣥⣵⣷⣾⣿⣦⠌⠡⡀⠿⠿⠿⢻⣿⣿⠇⣚⣤⡙⣿⣧⠂⡌⠹⢿⣿⣿⠟⡃⣰⣤⠻⣿⣿⣿⣿⣿⣿⣿⣶⣷⣷⣬⣦⣭⣦⣼⣿⣿⣷⡌⠰⠰⠌⢧⢉⠢⠌⠰⣭⣾⣿⠯⠟⡉⠛⡋⠍⣁⠢⡈⠜⢂⠄⢣⠐⡡⢘⡀⢃⠤⢁⠂ ⡱⡘⠰⡈⢆⠱⢈⢂⠱⡈⢆⠱⡈⢆⢉⢂⠱⡈⠱⡠⢉⠄⢊⡐⢸⣿⣥⣢⣹⣿⣿⢿⡛⢋⠍⠩⢉⠛⡻⣷⣮⣴⠡⠘⣀⠓⣾⣿⣿⠀⣿⣝⣿⣈⢿⣿⣶⣥⣾⠟⡡⢬⣼⠟⢋⠰⣬⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣷⡁⠌⠩⠌⢂⢼⣿⣠⣿⣿⠁⢂⢣⠘⡰⠰⡈⠔⣂⠩⡘⠠⢊⠄⢃⠔⡡⠘⡄⠢⢁⠌ ⢣⡑⢡⠒⡈⢆⠡⣈⠒⢌⠢⡑⢌⠢⢌⢂⠱⣈⠱⢠⠉⡜⠠⣀⠃⠍⠛⣉⠛⡉⣁⠢⠐⣌⠂⢇⡂⠢⢁⠿⣿⣿⡷⠐⡠⠌⣿⣿⣿⣰⡟⣾⢾⡽⣛⡾⣿⣿⠃⣌⣴⡿⢉⠰⣼⡿⠋⠄⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢛⠹⡙⠿⣿⣿⣿⣮⡁⠌⢂⠌⢿⣿⡟⠡⠘⣈⠆⡘⠄⢃⠜⠰⣀⠣⢐⠡⠊⢌⠂⡜⢀⠣⡐⠡⠊⠄ ⠣⡜⣀⠃⡜⢠⠡⢄⡉⢆⠱⡈⢆⡑⢢⢈⠒⡄⢊⠄⠣⢌⠱⠠⢌⡘⢠⠐⡰⢐⠠⢃⠱⢠⠉⠆⡌⣑⠂⡰⢉⣿⣷⠠⢁⠌⣹⣿⣿⣷⣻⡽⣛⡾⣽⣿⡟⢿⣷⣾⡋⡐⣬⣾⠟⠠⣱⣾⠰⣿⡛⠻⢿⣿⣿⣿⣥⣐⣑⠊⡔⢢⡑⣂⢿⣿⣿⣷⡌⠠⠊⠌⢻⣿⡇⠡⡈⢆⠱⡈⠆⡘⠰⣀⠣⠌⢂⡉⠢⡑⡈⠆⡑⢨⠡⠑⡈ ⡓⠴⣀⠃⡜⢠⠂⢆⡘⢄⠣⡘⢄⠢⣁⠢⠑⡌⢂⠎⠱⣈⠢⡑⢢⠘⡠⢃⠔⡡⢊⠄⡃⢆⡉⢒⠰⣀⠣⡐⠂⢿⣿⡦⠌⡐⢈⣿⣿⣿⣷⣻⡽⣿⡟⢋⣼⣿⣿⣿⣷⣴⣿⠡⢨⣿⣿⣇⣸⣿⠇⣑⠦⡠⢍⡙⠻⠿⢿⣿⣾⣦⣵⣤⣿⡞⣿⣿⣿⠠⠑⡨⠘⣿⣇⠡⠐⠎⠤⡑⢨⠐⡡⢂⠒⠌⡂⠔⢡⢂⠱⡈⠔⡁⢆⡑⠠ ⡙⠆⡄⢃⠜⡠⠊⠤⡘⢄⠣⡘⢄⠣⠐⡌⠱⢈⠢⢌⠱⢀⠆⡱⢀⠣⡐⢡⢂⠱⡀⢎⡐⢢⠘⡄⠣⢄⠣⡘⢐⡈⢿⣿⡐⠌⡠⠘⣿⣿⣿⣷⣿⣿⠃⣾⣿⣿⣿⢿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣏⡾⡙⢆⡓⠮⣔⢣⡜⣦⠰⣈⠙⡛⠿⢿⣿⣿⣿⣿⠠⠑⡠⢁⣿⣯⠄⢃⡘⠤⡑⢂⠱⣀⠣⢘⠠⠑⡈⠆⡌⠒⡈⠆⡑⠢⠄⢃ ⡙⠬⡐⠡⢊⠔⡁⢆⠱⡈⢆⠱⡈⢆⠱⠈⢆⠡⢊⠄⠣⢌⠢⠑⢌⠢⢑⠢⠌⢢⠑⢢⠘⡄⠣⡐⢡⠊⡔⢡⠂⠰⢈⢻⣿⡄⡐⠡⢈⠿⣿⣿⣿⡷⣼⣿⣿⣿⣾⣿⣿⣽⣿⣿⣿⠿⢟⣻⣿⣿⣿⣷⣬⣌⡱⢈⠖⡘⢆⡛⢤⠓⣌⠒⡤⢌⠻⣿⣿⡇⠡⠄⢃⢾⣿⠃⠤⠘⠤⡑⠌⡒⠠⡑⠌⠢⢑⡈⢒⡈⡑⠌⢢⢁⠓⡌⠠ ⡙⢆⠡⢃⠌⡒⡈⢄⠣⡘⢄⠣⡘⠄⣃⠩⠄⠣⠌⢌⠑⡄⢊⠱⢈⠔⠡⢊⠰⠡⡘⠄⢃⠌⡡⠘⡄⢣⠘⠤⡉⢆⠁⣂⠹⣿⣤⠃⢂⠰⣽⣿⣿⣑⣾⣿⣿⣷⡿⣿⣾⣿⣿⡟⡡⢎⠦⡠⢍⠛⠿⣯⢿⣿⣿⣾⣤⣍⡢⠘⠤⡙⢄⠣⠒⡌⢂⣿⣿⡏⡐⠌⡐⢪⣿⡁⠆⢩⠐⡡⢊⠔⢡⠘⣈⠑⠂⢌⠂⡔⢡⠊⠔⣈⠲⡀⠅ ⡍⠦⡑⠌⢢⠑⡄⢊⠔⡡⢊⠤⡑⢌⡐⠌⡌⠱⡈⢆⠘⢄⠃⡜⢠⠊⠱⡈⠆⡱⠠⡉⠆⡘⠄⢣⠐⡡⠊⡔⢡⠊⡔⢠⠘⢻⣿⡤⣁⠂⠜⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡐⡱⢎⠲⡑⠪⡜⢱⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣶⣯⣷⣼⣿⣿⣿⠃⠰⢈⡐⣿⡟⢠⠘⠠⠓⡄⢃⠌⢂⠱⠠⡉⠜⣀⠣⠌⣂⠱⡈⢄⠣⡐⠌ ⢞⡰⡁⠎⣄⠣⡐⢌⢢⠱⣈⠔⡈⠆⡌⢒⡈⢅⠒⡌⡘⢄⠊⡔⢂⡉⢆⠱⡈⠔⡡⠘⢄⠣⠘⡂⢅⠢⠑⡌⠢⡑⠌⢂⠌⠌⣻⣷⣒⣋⡄⠃⢄⠂⡐⢠⠐⠠⠄⢂⠄⠄⠒⢠⠁⢂⠡⠌⢡⠐⠄⣂⠐⡠⠐⣀⠂⠔⣀⠂⢄⠂⢄⠂⡐⠄⢂⡐⠠⠌⣁⢢⣰⣿⡏⠄⠌⠱⢘⠰⢈⠜⣀⠣⢑⠠⠃⢄⠊⡔⢠⠃⠜⡠⢣⠐⡈ ⠋⠒⡙⠑⢊⠓⡙⢊⠒⡙⠄⢋⡐⠡⠘⡠⠐⠌⡰⢀⡑⠈⡔⠈⡔⠈⡄⠃⠌⢂⠡⠌⢂⠰⢁⡐⠂⢌⠂⢌⡐⠌⠰⠁⡌⢰⣽⡿⢿⣷⣾⣬⣴⣬⣴⣥⣼⣴⣌⣦⣌⡜⠨⡄⢊⠄⡣⠌⠤⣈⠂⠤⣆⣵⣦⣴⡌⣂⠤⣘⡄⣌⣂⣌⡰⣈⣆⣤⣧⣶⣴⣿⣟⣫⠇⠌⡘⠐⢂⠡⢂⠂⡄⠢⢁⢂⡉⠄⠃⢌⠂⡘⠄⡡⢂⠡⢂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣿⠉⢹⣿⠏⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⢿⡽⢿⡓⠦⠤⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢰⠇⠀⣼⡟⢠⣿⡇⣿⡮⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⠷⣼⣷⣤⡀⢀⠀⠀⠀⠀⣶⡯⠏⠀⣀⣴⣿⣿⣿⣿⣿⣷⣿⣿⢽⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡿⠈⢰⣿⠇⣸⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣼⣯⣭⡽⠻⠯⣅⣀⣀⣀⠀⠁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⢸⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⠇⢠⣿⡟⢀⡿⠒⣿⣿⣿⣶⣻⣿⣿⣿⣿⣿⣿⣿⣿⣟⡚⠉⠀⠀⠀⠀⠀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⢸⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢠⣮⢿⠁⡼⢭⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⠌⢿⣿⣿⣿⣷⣦⣤⡶⣿⣿⣿⠿⠿⠿⣿⣿⣯⣿⣿⣿⣿⢻⣿⣿⢸⣼⣿⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⡎⡟⡏⣸⣇⣿⣹⣿⣿⣿⣿⣿⣯⣘⢿⣿⣿⡵⣄⠈⢿⣿⣏⣿⣿⣿⡿⣿⣿⡿⠀⠀⣀⣠⡺⡿⣿⣿⣿⣿⣇⣿⣿⣿⣿⣿⡏⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⡹⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠩⢿⣿⣿⣮⣻⣌⢿⣿⡍⠻⠛⠛⠉⠁⠀⠀⢀⡼⠁⠀⢳⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣧⣷⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣇⣯⡈⠻⣿⣷⣿⣧⡙⢷⣀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠑⠺⣿⣿⣿⣿⣿⣿⣿⣟⡇⠈⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⢛⣺⣛⣟⣿⣿⣿⣿⡿⠹⢿⣿⣿⣿⣜⣻⣿⣿⣿⣶⣿⣿⣶⣤⣤⡿⠇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⢸⡇⠀⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⢿⣿⣿⡧⠤⣿⡧⢿⣿⣿⣿⣿⠃⠀⠀⠙⢽⣿⣿⣷⣾⡿⢿⣿⣿⣿⢿⣖⠉⠀⠀⠀⠀⠀⠀⠀⢠⢼⢻⣿⣿⣿⣷⢯⣿⡞⠀⠀⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣾⣿⡿⣿⣿⣾⢧⣿⣛⣿⣿⣏⣭⣟⣿⣿⡏⠁⠀⢀⡔⠛⠛⣿⣿⡿⣿⣿⣿⣿⣿⣆⢿⣷⡀⠀⠀⠀⠀⠀⠀⣯⡞⡉⣿⣿⣿⣿⣿⣏⠀⠀⠀⣿⡇⠀⠀⠀ ⠀⠀⠙⠒⠒⠛⣻⣿⣿⠇⣿⣷⣿⣾⡟⢐⣾⣿⢷⠶⣷⣿⣿⡀⠀⢰⠏⠀⠀⠀⠸⣿⢻⠻⢿⣿⣿⣿⣿⡜⣿⡽⡄⠀⠀⠀⠀⣠⡟⢀⡇⣿⣿⣿⡈⣿⣿⢷⠀⢀⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⣽⣿⣿⣾⢇⣿⣿⣿⣿⣯⣿⣿⣇⢧⢀⠎⠀⠀⠀⠀⠀⣿⡟⡆⠀⢻⣿⣿⣿⣿⣿⣷⣹⡀⠀⣠⣼⣯⠞⣿⡇⣿⣿⣿⣇⢹⣿⣏⣆⣼⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⣺⣿⣿⡇⢰⢫⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⡞⠀⠀⠀⠀⠀⠀⢸⣇⡇⠀⢸⣟⣿⣿⣿⢸⣿⣹⠋⠉⠉⠀⠀⡼⢹⡧⣿⣿⣿⣿⡜⣿⢹⣼⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⡏⢿⣿⣷⣯⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣸⠟⠀⠀⠸⣽⣸⣿⣿⣿⣿⡇⠀⠀⠀⢀⡴⠁⣸⡏⣿⣿⣿⣿⣿⡇⢠⣷⣿⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣇⣸⡿⣽⣟⣽⣿⢩⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣝⠿⣿⣷⣄⠀⠀⢐⣟⣴⣒⠒⢸⠍⣿⡭⢿⠃⡏⣿⠢⣀⣴⠟⠁⠀⡇⠁⣿⣿⣿⣿⣿⣿⣷⣾⣿⣏⡤⠂⠀⠀ ⠀⠀⠀⠀⣠⣿⡿⠻⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⡷⡌⠙⠛⠷⣶⠞⢻⣿⡿⠀⢸⢄⡟⢠⢾⣾⣿⣿⠀⠈⠀⠀⠀⣀⣷⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⢀⡼⡿⠋⢦⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⣸⡇⠀⠀⠠⠬⠥⠤⠭⠤⠤⣸⡾⢥⣾⣾⣫⡿⠃⠀⠠⠀⣴⣾⣿⡧⣼⣿⣿⣿⣿⣿⣿⣿⢧⣿⡇⠀⠀⠀⠀ ⠀⣴⣿⡟⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢮⣷⣿⠀⠀⠀⠀⠀⠀⠘⢶⣿⢋⣱⣿⣿⣿⡇⣠⣶⣿⣿⣿⣿⣿⣿⣯⡟⣿⣿⣿⣿⣿⣿⣿⡏⣿⡇⠀⠀⠀⠀ ⣲⣿⣿⠃⠀⡼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡏⣿⣿⠀⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⢽⣿⣼⣿⣿⣿⣿⣿⣿⣿⡿⠼⡇⣿⣿⣿⣿⣿⣿⡟⣿⣿⠃⠀⠀⠀⠀ ⢯⣿⡿⠀⣸⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢠⣿⣿⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⣿⣿⡿⠩⢹⢻⣿⣿⣿⣿⣿⣿⣿⣿⠿⡄⠀⠀⠀⠀ ⣾⡿⡇⢠⣧⣿⣿⣵⣾⣿⣿⣿⣿⣿⣿⣿⣯⣿⡯⡇⣾⣿⣿⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠙⢿⣿⣿⣿⣿⠃⠀⣼⡟⣿⣿⣿⣿⣿⣿⣿⣿⡄⡇⠀⠀⠀⠀ ⣿⣿⡇⣼⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⡇⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⢹⢯⠀⣨⠿⣿⣿⠧⠥⣠⣿⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀ ⠩⣿⣿⣿⣿⠏⣿⣿⣿⣿⣿⣿⣿⣿⠏⠙⣿⡯⡿⢩⣿⣽⡇⠈⠆⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⢸⠸⡜⣃⡼⣿⠏⠉⣑⢻⡏⢀⣿⣿⣿⣿⣿⣿⣿⡯⢿⣿⣆⠀⠀⠀ ⣨⣿⣿⣿⡟⢾⣿⣿⣿⡇⣿⣿⠟⠁⠀⠀⢸⡜⠡⣾⡿⠿⣇⣀⣀⣀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⣷⠞⣼⣟⣀⠖⣠⣿⣿⢻⣿⣿⣿⣿⣿⣿⣹⣿⠀⣷⢻⣧⠀⠀ ⡿⣿⣿⣿⣧⢽⣿⣿⢽⢣⡟⠁⠀⠀⠀⢀⠞⢁⣽⡿⢫⡿⠒⢛⡛⠉⣬⣿⢳⠀⠀⠠⡄⠀⠀⠀⠀⢸⣤⣴⡾⡯⣽⠏⠈⠉⠉⠉⢹⣿⣼⡿⠭⡭⢽⣿⣇⡾⣟⠁⢹⢧⢯⣇⠀ ⡓⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⣴⣋⣠⣾⡿⢁⣾⠁⠀⠀⠉⠢⣌⡛⣟⣷⣦⣄⣷⣀⣀⣀⣤⠞⢉⣿⣡⣳⡏⠀⠀⠀⠀⠀⣸⣿⣿⡇⣀⢀⣸⣹⣾⣧⠃⢀⣘⡏⢿⡞⡄ ⠀⢸⣿⢿⡿⣿⣿⣷⣻⠁⢀⣠⠴⣯⣥⠾⣻⡿⢡⡾⠁⠀⠈⠙⠳⢤⡈⠓⢬⣿⠬⡇⠈⠀⠉⠉⠉⠁⠀⣿⣿⡿⠀⠀⠀⠀⠀⠀⣿⠏⣿⠃⠀⠠⡿⠉⡟⡽⠷⣼⣯⣇⠘⡇⢣ ⠀⢆⠹⣸⣿⣿⣿⣿⡟⠻⠿⢾⡿⢛⣡⣾⡿⠶⠋⣀⣀⡠⠴⠶⠭⠭⠭⣽⣶⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⢀⡟⠚⠯⢄⣀⣰⠃⠀⡟⣡⠖⢉⣿⠋⠀⡇⢸ ⡀⠈⠳⣌⣻⡏⢿⡿⣷⡀⠀⢠⣍⠉⠉⣁⡴⠚⠉⠁⠀⠀⠀⣠⡴⠶⠞⠛⠓⠛⠻⠿⢧⣄⠀⠀⠀⠀⠀⢸⢿⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠙⠒⠶⣟⡁⠀⣼⠏⠀⣸⠇⠈ ⣷⣄⠀⠈⠻⢿⣌⢿⣿⣷⣞⣋⣤⢧⠞⠁⠀⠀⠀⢀⣤⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠶⣤⡀⠀⢸⢸⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣤⣶⠿⠔⠁ ⠙⠿⣮⣤⣉⠉⢿⣌⢯⣛⣹⠿⣿⣭⢄⠀⠀⣠⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠲⢼⣹⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠢⣄⠀ ⠀⠘⠈⠳⣿⠛⠛⠛⠳⣕⣤⡄⠈⠉⢉⣤⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⢄⡀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢰⣤⣤⣤⣤⣤⣤⣤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠿⠿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠉⠀⠀⠀⠨⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠸⠿⠏⠉⠀⠀⠀⠈⠹⢿⣿⣿⣷⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡯⠁⢤⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠛⣿⣽⣿⣧⠄⠀⠀ ⠀⣰⡞⠒⠒⠲⠏⠀⠀⠉⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⢲⣿⣿⡷⠆⣿⣿⣻⣿⡀⠀⠀ ⢸⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⣿⣽⣞⣿⣯⠀⠀ ⠈⠻⢧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠻⣞⣧⣿⣟⠀⠀ ⠀⠀⠀⠈⠛⠛⠛⢶⡶⠶⠶⠶⠶⢶⠶⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠻⢯⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣬⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣿⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠤⠀⢀⣀⠀⠈⢿⢷⡀ ⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠐⠀⠀⣒⣯⠀⠀⠀⣺⡇ ⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣤⣠⣾⠟⠀⠀⣠⡼⠷ ⠀⠀⠀⠀⠀⠀⠀⠹⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢀⣠⣄⣿⠋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠷⣤⣤⡄⠀⠀⢀⠀⠀⣀⢀⡀⢤⣤⣤⣼⠿⠏⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠛⠛⠛⣻⣟⠛⠛⢻⣟⠛⠁⠈⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⣤⣤⡿⠏⠀⠀⠸⢧⣄⣤⣤⠿⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⠷⠿⢞⡛⢻⢛⡛⢻⠛⡟⢻⠻⠷⡶⣯⣴⣶⣠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣰⡴⢶⢛⣋⣍⡲⢠⠍⡜⢢⠉⢆⠲⣈⠥⢚⡨⢡⠣⡑⠦⢡⠆⠭⡙⡛⠷⣮⣔⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠗⠯⡱⡸⠊⠁⠀⠀⡼⠡⠎⡔⢣⢉⠬⡑⠢⢎⡡⢎⠢⠣⢜⢨⢡⢊⠥⠱⣉⠲⠤⣉⠛⠷⣧⣂⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢕⣩⠌⡙⠴⡑⢀⡀⡤⢖⠹⠰⣉⠖⡡⢎⢂⠣⡅⡋⠦⡘⠢⡍⢣⠎⢢⠅⣊⠬⡑⠤⢃⡱⢌⠩⠜⣠⠛⠷⣗⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡚⢆⡶⠋⠀⠀⣜⢡⢮⢡⠜⡰⢌⣃⣳⣌⣒⣡⠎⡌⡒⠬⢡⠣⢍⠣⠜⡡⢊⣥⣾⡶⡿⢿⡿⡿⢷⡾⣥⣋⠤⣉⢲⢌⡻⣮⡢⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⡸⠃⠀⠀⠀⢠⡛⢤⠸⢃⣜⣿⡿⣿⢟⡿⣻⢿⣿⣄⢣⠛⡄⢣⠜⣃⢇⢣⣿⢿⣇⢿⡻⣿⢻⣛⣧⢻⡻⢿⣧⣜⠠⠘⢤⡘⢿⣜⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢔⡵⢃⠞⠁⠀⠀⠀⣰⠫⠜⡄⢣⣿⡟⣧⢻⣎⢿⣜⢧⣏⣷⣻⣷⣽⣶⠷⠾⠶⢾⣿⣏⡿⣜⢧⡻⡽⣧⣛⣾⢣⡟⣧⢏⡿⣮⡑⢄⢱⢣⡙⣯⣢⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣢⠟⡨⢍⠀⠀⢀⡠⢞⡡⠣⠍⡔⣿⢿⣹⣎⣷⡮⣟⢮⣷⡾⠟⠋⠉⠀⠀⠀⠀⠀⢸⣷⢞⡿⣜⢧⡻⢵⣫⡝⣮⢳⡝⣮⣛⡼⣿⡎⣅⠋⡤⢃⠬⢳⡥⡀⠀⠀⠀ ⠀⠀⠀⡠⣵⠣⣉⠴⢡⢋⠹⢌⡑⠦⢡⢃⠧⢼⣿⣏⢷⡹⢶⣹⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠸⣿⣎⢷⣏⢾⡹⢧⡳⣝⣮⣷⡿⣶⠿⣷⣿⣇⠆⡍⡆⠋⢆⡍⢻⡴⡀⠀⠀ ⠀⠀⡠⣽⢃⠱⠄⡎⠆⡥⢃⠖⡌⠎⣅⠪⣔⣩⣿⡽⢮⡽⣷⡟⠁⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠙⢿⣾⡜⣷⣛⢧⣿⢿⡻⣼⡱⢯⣝⡳⣏⢿⣿⣔⡱⡀⠀⠪⢥⢻⡴⡀⠀ ⠀⢠⣽⠣⢌⠎⡱⡈⠖⡡⢎⡸⢌⠱⣈⣷⣟⣯⣽⣿⣭⣻⡟⠀⠀⠀⠠⠀⠠⠀⠈⠀⠀⠠⠐⠈⠀⠀⠀⠙⠛⠷⢿⣿⡽⣳⡝⡶⣝⡳⣎⢷⣹⣞⣼⣻⣧⢥⠀⠀⢳⢌⢿⣱⠀ ⢀⢶⡇⢎⠆⢭⡐⡅⡋⡔⢢⡑⡊⢆⣿⡟⣵⣚⡶⣹⠿⣿⠀⠀⠠⠈⠀⠀⠀⠀⠀⠈⠀⠀⠄⠐⠀⠁⠀⠀⠀⠀⣾⡷⣏⢧⡻⣝⢮⡳⣝⡾⢧⣛⢶⡹⣿⣆⠃⠀⠀⢏⠼⣏⠇ ⣞⡟⣈⠲⣘⠂⡖⣈⠦⢡⢃⠬⡱⠌⣿⣽⢳⣭⣛⣧⣟⡿⠀⠀⣀⢀⠀⠈⠀⠀⠈⠀⠀⠄⠀⠄⠀⠄⠀⠁⠀⠀⢹⣿⡹⣎⢷⣫⢞⡵⣻⡝⣧⣛⢮⡳⣽⡇⠎⠀⠀⠘⡎⢿⣰ ⣿⠇⢢⡑⢢⢙⡐⢢⠊⡅⢎⢒⡡⢎⢻⣞⡳⢮⡷⣻⢼⡏⣴⣿⣿⣿⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⣀⣤⣤⣤⣀⠈⢿⣷⣹⢎⣷⢫⡞⣵⢻⠶⣭⡳⣽⣹⣇⠳⠀⠀⠀⡟⣸⡇ ⣸⢌⡱⡜⠉⢱⢌⠣⠜⣈⢆⢃⠖⣈⢒⡻⣿⣧⡻⣵⣻⣿⣿⣿⣿⣿⠀⠀⠀⡀⠤⠀⠐⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⡀⠙⢿⣾⡜⡷⣽⢎⡯⣝⢶⡹⣖⣿⢡⢃⢃⠀⠀⢰⢩⡗ ⣿⠠⠾⠀⠀⢸⢠⠣⢍⡂⠎⢆⡓⢌⠆⣒⣾⣻⢟⣿⠏⣿⣿⣿⣿⠃⠀⠀⠉⠉⠉⠉⠂⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠙⢿⣷⣹⣞⡽⣎⢷⣹⣾⠏⡒⡌⢎⠀⢀⠧⣊⡟ ⣿⠐⡆⠀⠀⠘⣌⠢⢌⡃⠖⡬⠱⡘⠴⣉⣿⡯⣞⣿⠀⢿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣠⣼⡿⣟⢿⣳⢿⣼⣿⠏⡔⢣⠱⠌⣆⠼⢠⢋⡷ ⣻⠌⡇⠀⠀⠈⡦⢑⠢⡌⣃⠆⡣⢍⠲⢄⠻⣿⣾⡽⣏⠳⠂⠀⠀⣀⣀⡀⠁⠀⠈⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⣾⣿⢯⡷⣽⢎⡷⣻⢞⣷⡘⠬⡡⢎⠱⡄⢎⢡⢺⡇ ⣸⡎⠇⠀⠀⠀⠓⣌⠱⢄⡃⢎⡑⢎⡑⠎⡔⠢⣍⠹⡩⠷⣤⡾⠛⠋⠙⠛⢷⣄⣠⣤⣤⣤⡂⠹⢿⣿⣿⣿⣿⡿⠟⠁⣾⣿⣹⣎⠷⣭⢿⡜⣧⡟⣾⡏⣅⠣⣌⢣⠘⠦⢡⢾⢡ ⡟⣧⢹⠀⠀⠀⠘⣄⠓⡢⣉⠆⡍⢆⠥⢋⡔⠣⡄⢳⠠⣿⡏⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠉⢻⣧⠀⠉⠉⠉⠁⢰⠲⠄⢻⣯⣽⢎⡿⣜⢯⡞⣵⢯⣿⠑⣂⠧⡐⠦⡙⡘⢤⡟⡄ ⢿⢿⣈⡆⠀⠀⠀⢨⢒⡱⠐⢎⠔⡉⢆⢣⣬⣵⣼⣤⣃⣻⣇⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⣀⣀⣠⣤⣶⡿⠿⣯⣟⣼⣫⢷⣹⡿⢟⡡⢋⠔⢢⡑⡱⢌⠱⣾⢱⠃ ⠀⢟⣧⠼⡄⠀⠀⠈⢦⠰⣉⠦⡙⡌⢆⣿⠂⠀⠀⠈⣹⠏⠹⢷⣤⣴⣤⡼⣇⠀⠀⠀⢀⠀⡀⠈⣿⡛⠛⠛⢻⡟⠭⡑⣌⠒⡤⢋⢍⠫⢍⡹⢐⡡⢒⡡⢎⡱⠰⣡⠊⣵⢇⠗⠀ ⠀⠈⠾⣧⢙⡄⠀⠀⠘⡵⡐⢢⠱⣘⠢⣿⠀⠀⢀⠀⣿⠀⠀⠀⠈⠉⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠈⠛⠂⠀⣿⡏⢆⡱⢠⢓⡰⡉⢆⠓⡌⣔⣡⠶⠥⠶⢆⡅⡓⣄⣳⢏⠃⠀⠀ ⠀⠀⠈⡽⣶⠘⢦⠀⠀⢸⢅⣃⠓⡤⢓⣸⡇⠀⠀⠀⣿⡀⠀⢀⠀⡀⢀⠀⠀⠈⠛⢦⣤⣴⣠⠤⡆⠀⠀⠀⣿⣏⠒⣌⠲⣈⠦⡙⠤⢋⠖⠉⠀⠀⠀⠀⠀⡧⣑⣲⢯⠊⠀⠀⠀ ⠀⠀⠀⠈⢞⣯⡢⣉⠦⡙⣤⡢⡙⡔⢣⠰⢻⡄⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⢀⣿⢣⢉⠦⡑⢌⡲⡑⢪⠃⠀⠀⠀⠀⠀⠀⣰⢓⡼⡧⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠺⣳⣤⢃⢼⠀⠈⢲⠡⣃⠥⢋⢻⣄⠀⠀⠈⠻⣦⡀⠐⠀⠀⠀⠀⠀⠂⢰⣿⠁⣿⣿⠟⢀⣾⡟⢢⠉⢦⠉⢞⠲⣍⢹⠀⠀⠀⠀⠀⢀⡼⣥⢟⠝⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⣿⣧⡎⢳⡄⢸⢰⢡⠊⣥⠒⢹⣷⡄⠀⠀⠈⠛⣶⣤⡄⠀⠀⠂⠀⠀⠉⣤⡌⠀⢠⣿⢫⠘⣤⠋⣤⠋⡌⢲⢠⠋⣦⣤⣤⡖⠊⣧⣿⣵⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠪⣷⣎⡩⣑⠢⡑⢎⠰⣘⢢⠘⡻⢶⣄⡀⠀⠀⠉⠉⠉⠉⠐⠀⠀⠀⠉⣡⣴⣟⢋⡔⢣⡐⢎⡰⡜⠉⠀⠚⠒⢤⡓⠰⣄⣿⣻⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⢦⣇⣑⢊⡑⢆⢢⡙⠤⢃⡍⣛⠷⢶⣦⣤⣤⣤⣤⣤⣶⠾⡟⢫⡑⠤⡒⢌⠒⣌⢒⠰⣣⣀⡀⣀⠤⣎⣵⢟⡿⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠫⢻⢦⣕⡪⢔⡈⠞⡰⡘⡰⣊⣲⣄⣣⣜⣌⣢⠱⣈⠖⣡⢃⡜⢢⡑⢪⠑⣂⠎⡱⢠⢎⣴⣽⢾⡯⠅⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠘⠹⢳⠾⣥⣒⣡⡙⠿⣳⣽⣻⢾⡽⣟⡿⣷⣾⠐⡆⡜⠡⡜⠢⣍⣰⣮⡵⢾⣛⠭⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠋⣩⢟⣛⣶⠶⢯⣭⣿⣽⣿⣬⣥⣽⡶⠾⢷⣿⣿⣿⡝⠓⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣴⣶⡶⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⠃⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠙⠲⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠙⠷⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻ ⠀⠀⣀⣴⣶⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⢈⣿⣯⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣀⣀⣠⡤⠶⠖⠛⠉⠀⠀⠙⢯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠀⣀⣠⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿ ⠛⠋⠉⠉⠉⣽⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠛⠛⠛⠃⠀⠀⠱⣄⠀⠀⢀⣀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⡟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠿⠿⠟⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠉⠉⠙⠳⣄⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣶⣿⣄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟ ⣄⠀⠀⠀⠀⢹⣠⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣠⣶⣿⡆⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁ ⣿⣷⣦⣀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀ ⣿⣿⣿⣿⣷⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣿⣿⣿⣄⣀⣀⣀⡤⡴⢸⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣧⠇⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣀⣀⡀⠀⡀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀ ⠈⣻⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⡟⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣥⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡻⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⣻⣟⡓⠖⠛⠉⠉⠉⠉⠉⠛⠒⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⠤⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢤⢷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡲⣭⢳⡅⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡾⠈⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠈⣷⡽⠋⠁⠀⠀⠀ ⠀⠤⠐⡀⠀⠀⠀⣠⡇⠁⠰⠜⠈⠿⠏⠀⣶⣦⡄⠠⣻⡿⢃⠀⡀⠀⠀⠀⣹⢈⠀⠀⠀⠀⠀ ⢀⠆⠠⠁⠀⠀⠀⣿⣁⠀⠀⠀⠀⠀⠀⠀⢳⠇⠂⠀⠀⠀⠈⠛⠀⠀⠀⠀⣾⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⡱⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣥⠇⠃⠀⠀⡀⠤⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⡦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣠⠴⠛⠀⠀⠀⣤⠀⠤⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡋⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠙⠓⠒⢺⡅⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠃⠂⠀⠀⠀⢛⢺⢿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠘⣗⠾⠓⠚⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⢸⡎⠀⠀⢠⣴⠶⠆⠀⠀⠀⢠⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢿⡀⠀⢠⠀⠀⣠⣬⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠘⢿⣴⠾⠚⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣔⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠄⡄⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⡿⢻⠀⢀⠀⠠⡽⡕⣄⠀⣀⡤⠿⣟⠉⠉⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢹⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⡏⡅⠀⢱⢸⡀⠘⣦⡀⠘⣝⠼⢿⠛⠡⡀⢈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠀⠈⠁⠀⠀⠀⠀⠀⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡯⠚⠉⠀⣇⠸⡄⢸⢺⣱⡤⣿⡿⣯⡥⢶⡿⢠⢃⠞⣆⣹⣿⡏⠉⠓⢶⠦⠤⣄⣀⣀⠀⢀⠀⠀⠀⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣴⠾⠛⢩⣿⢸⠀⢀⠀⡟⣆⢻⡜⠘⠀⢸⣿⣛⡛⢷⣶⢁⣾⢸⢰⠛⠁⠘⣿⣦⠀⠘⠀⠀⠀⣠⡿⠋⠁⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣤⣶⣿⣋⣟⢷⣦⡼⠁⡄⢧⠸⣤⣷⣛⣛⣿⢄⡆⠘⡿⣿⣿⢠⢏⣾⡿⣾⣿⣴⡀⠢⠸⡿⡧⣄⢀⣤⠖⠋⠀⠀⠀⠀⢘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀ ⣠⣴⣿⡯⠟⠛⠙⢷⣌⠉⠙⠛⠦⢧⢀⣶⣻⡿⢫⣽⣿⡍⣷⣧⠴⠦⠶⠯⡋⢹⡝⢹⡇⣿⣷⡀⣠⣽⣼⡚⠉⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣀⡀⠄⠀⠀⠀⠀⠀⠀⠀ ⠉⠉⠁⢀⠔⠀⠀⠀⠉⠳⣄⠀⡠⠞⣭⡟⠙⢷⡘⠿⠏⣼⡏⠁⠀⠀⠀⠀⢙⡾⢻⠀⣇⢸⣿⣿⡋⠉⣹⣿⣞⢦⠀⠀⠀⣠⠞⠁⠀⠀⢀⣴⣮⣁⣠⠞⠁⠀⠀⠀⠀⠀⢠ ⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠜⠉⢆⠈⢉⣏⣙⣛⣻⣳⢿⣁⠀⠀⣔⡫⢝⣧⣾⣅⢸⣧⢸⣿⡏⣷⢨⠾⠉⡆⢻⡆⠀⣠⡾⠣⠋⠀⠠⠆⢁⣠⡤⢿⣤⡅⠀⠀⠀⣀⢀⣠⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠁⠐⠒⣛⣿⡟⣿⢷⣗⠒⢒⣫⣶⣿⣷⠛⡿⡟⣿⡄⢿⢠⢸⡏⠀⠸⡜⠜⢷⣴⣯⡱⣄⣠⡤⠖⠚⠉⠁⠀⠘⣿⣇⠀⠀⠀⠉⠩⠜⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡤⢴⠒⠊⡏⣿⢸⡇⢹⢦⣽⣿⣿⣿⠁⠀⠙⢷⣄⡧⠟⢳⢸⠈⢷⣇⠈⠀⠀⠠⢻⣿⢿⣷⡙⢇⠀⠀⠀⠀⠀⠀⠀⢿⣸⡀⠀⠀⠀⢀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⣄⠀⠇⡟⣼⣳⡼⠗⠋⢀⣿⠺⣦⡀⠀⠀⠻⠂⣀⡈⣿⡇⠈⣿⡆⠀⠀⣧⠀⣿⡎⢷⣷⣌⠂⠀⠀⠀⠀⠀⠀⢸⡇⡇⠠⠴⠞⠋⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠹⣶⠞⡟⣿⠑⡄⠀⠀⠁⢻⡂⢹⣿⡄⡀⠀⠀⠀⠀⠸⣷⠀⠘⣷⠖⠲⣾⡀⠸⣿⡈⢿⣿⣦⠀⠀⠀⠀⠀⠀⠘⣧⢱⠀⠀⠀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢻⢀⡟⡋⠀⢙⣀⠤⢖⣊⣻⣍⣙⣷⡀⠀⠀⠀⠀⠀⠫⣠⡞⢳⣍⣛⢿⣟⠀⣿⡇⢸⡿⣿⣿⢄⠀⠀⠀⠀⠀⢹⠸⠀⠀⠀⠈⢡⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⣀⣀⣼⣯⣤⣖⣊⣹⡵⠊⠁⠀⠀⠀⠀⠀⠉⠑⠲⢤⣤⣶⣾⣿⣇⣛⣒⣺⡿⠿⣦⢸⣿⠀⣇⢹⣿⡆⠑⠀⠀⠀⠀⠸⡇⡄⠀⠈⠀⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠿⢠⡾⡋⠁⠀⡼⠁⠀⠀⠀⠀⠀⢷⡀⠒⠤⢄⡀⠈⠙⠲⣬⣉⠙⠛⢾⡦⢷⣼⠀⢿⣇⢹⠈⢿⣷⡠⣔⣪⡥⢶⣾⡷⠇⠀⠀⠀⠈⠀ ⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⣯⠀⠁⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠛⢦⡀⠀⠈⠓⠦⠄⠘⡯⠙⠦⣄⣙⢮⡻⠃⣸⡷⢿⣥⡘⣿⣿⣭⣴⠋⡏⠁⠀⣀⠀⢀⡀⠀⠀ ⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⢠⠎⠀⠀⢻⡄⠀⠀⠀⠙⣯⡁⠀⠀⠀⠀⢀⡀⠀⠉⠳⢄⡀⠀⠀⣰⡃⠀⠀⠀⠙⠷⣦⣴⠿⠱⣄⠹⢭⠚⢧⡀⠸⡄⢠⠀⠀⠈⠓⠗⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠲⣄⠀⢀⠔⠁⠀⠀⣼⠀⠀⠀⠀⠀⠈⢿⠶⣀⠀⠀⠀⠙⠢⡀⠀⠀⠙⢷⣼⠏⠈⠐⠒⠤⠄⣀⣤⣽⢿⣶⣿⣧⣄⠑⢼⡇⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠠⡟⠃⠀⠀⠀⠀⠀⠀⡷⣌⢧⡀⠀⠀⠀⠈⠀⠀⠀⠀⢳⣄⣤⣤⡴⢖⣛⠿⠭⠚⢩⡶⢮⡛⢿⣧⣸⡇⠀⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣧⣈⣷⣝⢄⠀⠀⠀⠀⠀⠀⠀⠐⠻⣿⠒⠉⠁⠀⠀⠀⠀⢸⡇⠀⠟⠢⡙⢷⣇⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣀⠤⠝⢣⡳⣄⠀⠀⠀⠀⡀⢤⡀⠘⢷⡄⠀⠀⠀⠀⠀⠀⡇⠀⢰⠀⠈⠢⡙⢷⣼⠀⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣧⣴⠶⠛⠉⠈⠻⣢⡀⠀⠀⠘⢦⡘⢌⢢⡻⣦⠀⠀⠀⠀⠀⠃⠀⠸⡄⠀⠀⠈⠪⡛⢳⣿⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠑⣄⠑⡵⠈⢷⣄⠀⠀⠀⢀⠀⠀⣇⠀⠀⠀⠀⠈⠳⣝⢷⣄⠀⢀⡄⠀⠀ ⠀⠿⣦⣍⠢⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡤⠤⠌⠣⠤⠲⠶⠿⠷⠤⠤⣼⣀⡀⢹⡀⠀⠀⠀⠀⠀⠈⣁⣽⣷⠠⠾⠀⠀ ⠀⠀⠈⠛⡷⣌⡷⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣮⡇⠀⠀⠀⠀⠀⠀⢻⠀⢹⠀⠀⠀⠀ ⠀⠀⢸⣀⡤⠞⠃⠀⠀⠀⠀⣀⡾⠟⠚⠛⠲⠤⣄⡀⣸⠁⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠠⠀⠀⣀⣠⠤⠴⠒⠚⠷⣄⠀⠀⠸⣿⠀⠀⠀⠀⡀⠠⢼⠀⢸⡀⠲⠕⢄ ⠀⠀⢸⠁⠀⠀⠀⠀⠀⢀⡞⠉⠀⠀⠀⠀⠀⠀⠀⠉⡿⣶⡀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠇⣠⣴⡞⠋⠉⠀⠀⠀⢀⡠⠀⠀⠀⠙⠢⠀⢸⣏⠁⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⢸ ⠀⠀⠈⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⡿⠁⠀⠀⠈⠉⢷⣄⠠⣤⡀⠀⠀⠘⢿⡄⢀⡤⠖⠋⢉⣀⣀⣀⣠⣴⣶⣶⠇⠉⢳⠀⠀⠀⠀⠀⡇⠀⢳⠀⡰⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⢠⠃⠀⣀⣀⣀⠀⠀⠀⡀⢿⡁⠀⠀⠀⠀⠀⠈⠈⢷⠀⢡⡤⠶⠿⢾⣧⡞⢁⡖⠚⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠸⡇⠀⠀⠀⠀⣿⠀⢸⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣆⣤⠾⠽⠤⢬⣱⣄⣀⡀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠟⠀⠈⠀⠀⠀⢘⡿⡁⣼⠠⢤⣤⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⢿⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠯⠞⠁⠀⠀⠀⠀⢄⠀⠙⠻⠄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⣿⠷⠛⠋⠉⠙⠛⠒⠒⠮⠭⢍⣓⣲⢤⣀⡐⢷⣄⠀⢸⡇⠀⢣⠀⠀ ⠀⠀⠀⠀⠀⠀⡔⣫⡴⢿⣟⢻⣶⣶⣦⣈⡇⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠴⢀⣠⡴⠶⠒⢒⣶⣶⡶⣶⡦⣀⡀⠀⠈⠉⠚⠮⣷⢸⡇⠀⠸⠀⠀ ⡶⠞⠛⠷⣤⡼⠾⠿⢤⣄⡸⠿⡏⡇⢿⡿⢧⣄⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⠸⠗⠺⢿⣓⠒⣠⣴⡿⠋⠁⢻⣿⣿⣦⣉⡑⢲⠤⢄⡀⠘⢷⣡⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⡀⠆⠠⠀⠄⡐⠠⠀⠌⡀⢡⣀⡀⠄⠂⠄⠡⢀⠢⠄⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣾⣿⣿⠂⡑⠈⠄⠁⠂⠄⠂⠡⠐⢰⣿⢩⢛⡳⣥⢈⠐⠠⡑⡎⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣼⣿⡿⠣⠠⠁⠌⠀⠂⠌⠀⠌⠠⠁⡌⢳⡇⡞⣰⠹⣆⠌⡐⠄⠧⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣼⣿⡿⠁⠀⠀⠀⠀⠈⠀⠂⠈⠀⢁⠂⠄⡁⢻⣷⣥⠫⣽⡄⠌⡘⢄⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠁⢻⣿⣕⠦⣇⠈⠐⠬⠸⣿⣿⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣣⣿⣿⠟⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣿⣿⡎⢿⠀⠀⠀⠀⢹⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢎⣴⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⢀⢃⣿⣿⣿⣹⠰⠀⠀⠀⠀⢻⣿⣧⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣵⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠸⣸⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠻⣿⣷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢐⣡⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⡗⠀⠀⠇⣿⣿⠇⣿⣿⡆⡇⠀⠀⠀⠀⠀⠘⢿⣿⣦⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⣵⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣹⠁⠀⠘⣸⣿⡿⣼⢻⣿⣷⠁⠀⠀⠀⠀⠀⢀⠄⣹⣿⣿⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠟⠁⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⡏⠀⠀⣆⣿⣿⢣⢇⠏⣿⣿⡀⠀⠀⠀⠀⠀⠎⣼⣿⡟⠁⠉ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⠟⠋⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣳⡟⠁⠤⠞⣸⣿⡏⢿⣈⠖⣹⣿⣧⠀⠀⠀⠀⠈⢸⣿⣿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⣫⢜⡳⢯⢻⣿⣿⣿⣿⣶⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣶⣾⣿⣿⡿⠟⠉⠀⢀⠖⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣱⣿⠡⣾⣿⣿⣿⣿⣶⣄⣝⠮⡐⣿⣿⡄⡄⠀⠀⡆⣼⣿⡇⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⡿⢫⡕⢣⢎⣱⣾⣿⣿⢟⡍⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠉⠀⠀⠀⣰⠖⠋⠀⠀⡠⣠⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣱⣿⡇⡔⢠⢠⣿⡿⠋⠛⠿⣿⣿⣷⣽⣿⣇⢇⠀⠀⡇⢾⣿⡇⠀⠀⠀ ⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣴⣾⣿⣿⡟⣏⢞⣱⠞⣱⣾⣿⡿⠟⡵⢫⠚⡥⢛⣴⢲⣿⡯⢽⣿⣿⣿⣿⣯⣝⣉⢉⡉⡐⢂⠁⠠⠀⠠⢀⣠⢾⠃⠀⠀⠀⢊⣴⣿⡿⢃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣵⣿⡟⡸⢀⢧⣿⣿⠁⠀⠀⠁⠂⢹⠻⣿⣿⣿⣌⠦⡀⠁⢸⣿⣧⠀⠀⠀ ⣿⠿⣿⣿⣿⣶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⣤⣴⣶⣿⣿⣿⡿⣫⢕⡺⡼⢞⣵⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣶⣿⣿⣷⣧⣆⡳⢮⣍⡛⠿⣿⣷⣦⣕⠂⡌⠠⢀⡤⢋⡴⠃⠀⢠⢖⣰⣿⣿⡿⠡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢰⣿⣿⣿⠁⢁⢎⣾⣿⠃⠀⠀⠀⠀⠀⠘⡇⢈⣿⣿⣿⣷⣜⠆⠸⣿⣿⠀⠀⠀ ⡟⡰⠛⠭⢛⡻⠿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⡿⢟⣿⣿⡿⣼⠧⣛⣭⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣍⡓⢦⣉⠛⣿⣿⣦⣡⠏⣜⡼⠁⣄⢞⣵⣾⣿⣿⡿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢱⣿⣿⣿⠇⢎⢄⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠸⡆⢻⣿⡏⢿⣿⣦⠀⢿⣿⣇⠀⠀ ⠃⠤⢉⠒⠠⢉⡙⠒⠦⣽⢫⢟⡟⠙⣛⢛⡛⢛⡙⣋⠭⡩⢔⡲⢼⣹⣿⣿⣷⣷⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⢛⠻⢿⣿⣿⣿⣿⣿⣷⣮⣓⠦⡙⢿⣿⡷⢨⣰⢕⣣⣿⣿⣿⣿⡟⠰⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡬⣠⣿⣿⣿⡏⡘⢠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢹⣿⣷⠠⠻⠿⢃⢸⣿⣿⣆⠀ ⠈⠔⠀⡀⠁⠀⠠⢁⢸⢇⠫⣼⠃⢂⠐⠠⠘⠠⡑⢠⠃⡱⢌⢲⢯⣿⣿⣴⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣦⣍⡲⢡⣴⣿⣿⢿⣿⣿⢏⠴⢁⠂⠠⠁⠀⠄⢀⠀⢀⠀⣤⢋⣴⣿⣿⣿⡟⠰⣡⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⣿⣿⡆⡌⢍⠲⡸⡽⣿⣿⣿ ⢈⠐⢀⠀⠀⠈⡀⠄⣼⢊⠥⡏⢀⠀⠀⠁⢈⠐⡀⠃⡜⣠⢋⡞⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣷⣤⣤⣀⠀⠀⠀⠀⠜⢿⣿⣿⠌⠙⠛⠿⣿⣿⣿⡿⠟⢡⣾⡿⠋⢎⠰⢀⠈⡀⠄⠁⡈⠀⠌⡠⠚⣡⣿⣿⢟⣿⣿⢣⣷⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢿⣿⡇⡜⣌⢒⡱⢣⢷⣹⣿ ⠠⢈⠀⠄⠀⢁⠠⢀⡿⣬⣾⢁⠀⠂⠈⠀⠄⠲⣿⣿⣶⣷⣮⣼⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⣊⣴⣿⣿⣿⢋⠅⢠⡙⣿⣯⣿⢿⣿⣿⣿⣷⣄⠀⠀⠈⠀⠹⣿⡆⠀⠀⠀⠀⠉⠉⠀⠸⣿⣿⣧⣜⣠⠃⢂⡂⡐⠠⠂⠔⢡⡘⢠⣿⣿⡿⢋⣾⣿⣷⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⡜⢤⠣⣜⡹⠶⣽⣿ ⠐⡀⠈⠀⠠⢀⠐⡈⣿⣿⡏⠀⡐⠀⠀⠠⠐⠀⠌⢉⢉⡛⢻⣿⣿⣿⠟⡀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⣿⣬⣛⣡⣼⣿⣳⡿⣟⡿⣞⡿⣿⣿⣧⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣷⣦⣌⡡⠘⡠⢋⣼⣿⡿⢏⢡⣿⣿⣿⣿⣟⣁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡙⢆⠳⣌⣳⢻⣿⣿ ⠠⠐⠈⠀⠠⢀⠌⢰⣿⣿⠀⠂⠄⠐⠀⠀⠀⢀⠈⠄⠂⠇⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⣿⣻⣽⢯⡿⣽⣻⣽⣳⣯⢿⣽⡿⠛⠋⠉⠙⠻⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣶⣿⠿⠯⠔⢈⣿⣿⣿⡿⠻⠟⠳⠾⠯⠭⢟⣒⣶⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⡚⣌⠳⣜⢲⣿⣿⣯ ⢀⠂⢈⠀⠄⠂⠌⣸⣿⡟⠠⢁⠂⠀⠀⠀⠀⠀⢀⠈⠼⣱⣿⡟⣿⣿⠀⠀⠀⠀⠀⠀⣰⣿⣿⣻⢽⡳⣯⢻⣯⢿⣽⣳⢯⡷⣏⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⣾⣿⣟⣉⣀⣀⣀⣂⣀⣀⢀⠀⠀⠈⡙⠚⠃⠀⠀⠀⠀⠀⠀⠀⢸⣿⡧⢜⡌⡷⣩⣾⣿⣿⢲ ⠀⡐⠀⡀⠠⠑⡐⣼⣿⡗⢀⠂⠀⠀⠀⠀⠀⠀⠂⠌⢃⣿⣿⠁⣿⣿⠀⠀⠀⠀⠀⢀⣿⣿⢣⢧⢫⡕⣫⢗⡮⢷⣫⡽⢯⡷⣭⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣻⣟⣿⣻⣿⣿⣿⣿⣿⣷⣶⣤⣀⠢⢀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢯⣸⢷⣿⣿⣿⢧⢏ ⠐⢀⠠⠀⢀⠡⠄⣿⣿⠇⠠⢈⠀⠀⠀⠀⠀⠐⢈⠐⣼⣿⡏⠀⢻⡿⠀⠀⠀⠀⠀⢸⣿⡿⢣⢎⢣⠜⣡⠞⣭⣳⣿⣿⣿⣷⣣⢞⣆⠀⢀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠛⠉⠉⠉⠉⠉⠉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣷⣦⡐⠀⠀⠀⠀⠀⢸⣿⡏⣧⢟⣾⣿⣿⣿⣚⠮ ⠐⡀⠀⡀⠄⢂⠌⣿⣿⢀⡁⠂⠀⠀⠀⠀⠀⠐⠠⢡⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠗⡣⢎⠦⡙⢆⠻⣴⣿⣿⣿⣿⣿⣏⡧⢎⠳⢦⣤⣤⠤⣶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡙⠻⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⣾⣿⠳⣭⣿⣿⣿⣿⡟⣬⠳ ⠠⠀⠀⠀⡐⢈⠰⣿⣿⠠⠐⡀⠀⠀⠀⠀⠀⠌⡐⢸⣿⡿⠐⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣜⠰⡈⠆⣍⠪⣕⢺⣿⣿⣿⣿⡿⣹⠱⣊⠕⡢⢔⣘⢣⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣾⣿⣿⣿⣶⣄⣀⡀⠀⠀⠑⠌⠻⢿⣿⣿⣿⣷⡄⠀⠀⣿⣿⣽⣿⣿⢋⣿⣿⣛⢦⡛ ⠀⠄⠈⢀⠠⠌⠰⣿⣿⠠⢁⠀⠀⠀⠀⠀⠐⠠⠁⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠌⠒⡄⢣⠘⠦⣙⢛⡻⣙⠲⣡⠓⢬⡘⡱⢪⢜⣱⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⢛⢉⠻⣿⢿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣄⢸⣿⣿⡿⢟⡴⢺⣿⡿⡜⢦⡙ ⣠⠈⡐⢀⠠⠌⢡⣿⣿⠀⠆⠈⠀⠀⠀⠀⡁⠂⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏⢠⣣⠼⠂⠙⠒⠪⢦⡑⠤⠓⠤⣉⠆⡴⢡⡓⣬⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡘⠤⠔⣰⣿⢯⣷⡿⣯⡟⣿⣿⢿⣆⠀⠀⠀⠁⠘⢿⣿⣿⣿⡌⠛⠉⢰⠩⢖⣿⣿⡳⢍⠦⡑ ⣿⠃⡐⡀⢂⠘⠠⣿⣿⠈⡄⠁⠀⠀⠀⡐⠀⡁⢾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡆⡵⠁⠀⠀⠀⠀⠀⠀⠉⢶⡉⠒⣄⠚⡔⢣⣵⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢿⣻⣞⡿⣿⢿⣻⡽⣯⣷⣻⣳⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡄⠈⢸⣃⣾⣿⣟⡱⡎⠀⠀ ⣿⡄⡱⢀⠂⡉⠔⣿⣿⠐⡠⠈⠀⠀⠀⡀⠂⢄⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠣⡔⡩⣜⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⣏⡟⣧⢟⡽⢯⣟⣷⣻⣟⣾⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⣿⣿⣿⢣⡾⠁⠀⣴ ⣿⡇⠔⡂⠤⠡⠌⣿⣿⡇⠠⢀⠀⠀⠀⠄⠡⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⣸⢣⣬⣷⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠹⣜⡹⣜⡹⣞⡻⣞⣷⣻⢾⣱⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⣿⣿⡇⢀⣿⣿⡯⠖⠁⠀⣸⣿ ⣿⣿⠐⣁⢂⠡⠌⣻⣿⡇⠡⠀⡀⠀⠀⠌⠠⣹⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣶⣶⣶⣶⣶⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢣⠏⢦⡱⢌⡳⣜⣱⣿⣾⣿⣯⢷⣫⢷⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠾⢛⡡⠀⣠⣴⣾⣿⡟ ⣿⣿⡇⢂⠌⡄⢃⢼⣿⣟⠠⢁⠀⠀⠐⡈⠄⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⢢⡙⢢⡑⢮⡱⢺⣿⣿⣿⣿⣿⣏⡗⡎⡜⠻⡗⢶⣶⣾⠃⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⡐⣡⣶⣿⠿⠛⣹⣿⡇ ⣿⣿⣷⠈⢆⠰⢈⠸⣿⣿⢀⠂⠄⠀⠂⡐⡀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠉⠓⢤⠃⡜⡰⢩⢻⣿⣿⣿⣿⡿⣍⢖⡩⢎⡵⣩⢾⣿⡿⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠸⢰⣿⡿⠁⠂⠀⣿⢽⡂ ⣿⣿⣿⣇⠊⡔⠡⠇⣿⣿⡇⠈⠄⠐⠠⢐⠰⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⢹⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠤⡑⢩⡚⠿⡿⢿⣋⠶⡡⢎⠲⡑⢶⣡⣿⣿⠇⠀⠀⠀⠀⢀⢄⣾⣿⣾⠇⡄⢸⣿⡇⡃⠀⠀⣿⢺⠁ ⢿⣿⣿⣿⡌⡔⠡⢊⢸⣿⣧⠡⢈⡐⠀⢎⢸⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⢸⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⣤⠚⣡⠞⠁⠀⠀⠈⠙⢮⡑⢌⠒⡱⢌⢣⡙⢦⣿⣿⠏⠀⠀⠀⠀⠀⢠⣾⣿⠟⡡⢊⣴⣿⣿⡇⠀⠀⠀⢻⡽⡆ ⠀⠙⣿⣿⣷⢨⠑⢢⠘⣿⣿⡆⠡⡀⢁⢺⢸⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⡉⢩⠙⡛⠿⠿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡜⠁⠀⠀⠀⠀⠀⠀⠀⠹⣄⠩⡔⣊⢦⣹⣿⣿⠏⠀⠀⠀⠀⠀⣴⣿⣿⠏⡔⣰⣿⡿⠛⣷⣧⠀⠀⠀⠀⢿⣳ ⠀⠀⠘⣿⣿⣇⢯⡐⢬⢹⣿⣧⠡⠐⡈⢼⢸⣿⣿⢼⢿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⡠⢅⠣⡘⠄⣃⠒⠤⡈⢍⡙⠻⠿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢢⠱⣌⣶⣿⡿⠋⠀⠀⠀⠀⠀⠀⠛⠋⣡⠸⢠⣿⣿⠁⠀⢿⣽⡆⠀⠀⠀⠈⢿ ⠀⠀⠀⠹⣿⣿⡎⢧⠘⡌⣿⣿⡇⠆⠱⢸⢸⣿⣿⣾⣭⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠡⡑⢂⠔⡀⢃⠰⠈⠆⡑⠂⡌⡑⠒⠤⣉⠙⡻⠿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⡀⠀⠀⠀⠀⠀⢀⣮⣶⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⢠⢸⣿⡇⠀⠘⠘⣯⣿⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⢻⣿⣿⡎⡔⠰⡘⣿⣿⡈⣅⢻⢸⣿⣿⢛⣛⣛⡻⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⡒⢡⠊⡐⠐⢂⠄⢃⠰⠠⠡⠐⡈⠅⡒⠤⢉⠔⡡⢂⠩⣙⠻⠿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣛⣖⣶⣲⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣇⢃⢸⣿⣇⠀⠀⠀⢹⣾⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣿⣿⡜⣥⠒⡘⣿⣿⡘⣾⢸⣿⣿⠘⢇⠤⠙⠒⢮⠻⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⢠⠑⡂⠡⠄⡉⠤⠈⡔⠠⠑⢂⠡⡐⢂⡐⠄⣁⠢⠐⡡⠒⡄⠣⠌⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡯⣹⡈⡌⣿⣿⡆⢂⠀⠀⠹⣿⣷⣄⠀⢠ ⠀⠀⠀⠀⠀⠀⢿⣿⣿⡜⣦⢁⣿⣿⣿⣌⠒⣿⣿⠀⡌⢦⠈⠁⢂⠳⡌⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢽⡇⢃⠜⠠⡁⠜⡀⠆⢡⠠⢁⠊⢄⠂⠔⡠⢐⡈⠄⣂⠡⠄⡑⢨⠑⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⠡⣧⢡⠸⣿⣿⣌⠂⢂⣾⣿⠿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡌⢧⣿⣿⣿⣿⡆⣿⣿⡇⡌⠀⠙⢄⠀⢂⠱⢼⣿⣿⢙⠿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⣿⣻⠄⢣⠘⡐⠨⡐⢈⠔⡀⠆⠡⢈⠄⡘⠠⡐⠄⢂⠡⡐⢂⡘⢠⠃⢎⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣹⢋⡴⢠⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠢⠹⣿⣿⣾⣿⡯⡘⣿⣿⣿⣿⡇⠀⠀⠀⠈⠑⢄⡈⢉⣿⣿⡆⡇⢈⠙⠿⣿⣿⣷⣦⣄⡀⠀⢀⡷⣟⠈⢆⢂⠡⢁⠂⠅⢢⠘⠠⠃⢌⠰⢀⠃⠔⡈⠆⡁⠆⢡⠐⡡⢎⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣹⠆⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡿⢡⠎⣴⣿⣿⠏⠀⠉⠁⠀⠀⠀⠀⠀⢀ ⢀⣴⣾⣶⣶⣦⣄⡀⠁⢹⣿⣿⣿⡇⠐⡌⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠑⠤⣿⣿⡇⠀⠂⠠⠀⠀⠉⠻⢿⣿⣿⣷⣤⣿⣋⠜⢤⠊⡄⢃⠌⡘⠠⠌⡑⠌⡐⠢⠌⡘⢄⡘⠤⠁⠎⡄⠣⠜⣼⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠡⢃⣼⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼ ⣿⡟⠉⠉⠉⡛⠿⣿⣶⣾⣿⠛⠟⠁⠀⠈⠈⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⣥⠐⠀⠀⠁⠈⢀⠠⠈⠙⠻⢿⣿⣿⣿⣦⣕⡌⠦⡘⡄⢃⠒⢌⠰⠁⢆⡑⢄⠢⢐⢂⠩⡐⣌⢑⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⡰⢁⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿ ⠏⠀⠀⠀⠀⠀⠁⠢⢙⣿⣿⡆⠀⠀⠀⠀⠀⠀⠙⠻⣧⠀⠀⠀⠀⠀⠀⠀⢺⣿⡇⠈⠣⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠙⠻⣿⣿⣿⣷⡷⣼⣦⣍⣢⠌⣑⠢⢌⡐⢢⢁⠆⡱⢐⣠⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⢡⢁⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠂⢈⣄⠻⣿⣿⣏⠛⠷⢯⣞⣿⣻⣷⣾⣶⣬⣥⣊⢎⣱⣶⣿⡿⢃⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣿⣿⡟⢡⢁⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡞⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠹⣿⣆⢈⠻⣿⣿⣶⣶⣾⣿⣻⣽⠿⢿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣤⣤⣤⣄⣤⣀⣀⣠⣀⣀⣄⣠⣤⣠⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠿⣹⢁⠃⣼⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠁⠀ ⣄⣀⣀⣀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠻⣿⣦⠁⠀⡍⣉⢉⡉⠩⣁⣀⡀⢂⠀⠉⡉⢉⠛⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⢿⡟⣿⣛⢯⢯⣝⣾⣿⣟⣹⠃⡄⣸⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⠔⠀⢠⣿⣿⡏⠀⠀ ⣾⣶⣽⣮⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⣙⢿⣧⣬⣐⣠⣴⣶⣿⠿⠛⠁⠀⠈⠀⠀⠀⢂⠘⠠⣢⣶⣿⢟⡡⢄⠢⡐⠰⢂⠆⣡⠒⣭⢿⣿⣿⣲⠷⢮⣳⣛⣧⣿⣵⣿⣿⣷⣾⣿⠿⢤⡟⠸⢱⣿⣿⠏⠀⠀⠀⠀⢀⡠⠂⠁⢀⠂⣾⣷⡟⠀⠀⠀ ⠿⠿⠿⣿⣿⣿⡇⢀⢌⠻⣿⣷⣿⣿⣿⣷⣦⣄⠀⠀⢀⣤⣤⣤⣤⣄⣠⣾⣿⠟⠛⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⢈⣴⣿⡿⡑⢊⠐⡈⠄⠡⠑⡈⠐⠠⠑⡌⢧⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⢉⣿⣿⢿⣙⣺⢁⢃⣾⣿⡟⠀⠀⠀⡠⠒⠁⠀⠀⠀⡎⢸⣿⣿⠁⠀⠀⠀ ⠀⠀⠀⠀⢈⣿⣿⣦⣡⣅⡈⠩⡁⠀⠀⠈⠻⢿⣷⣶⣿⠿⠛⠛⠛⢿⣿⠟⢁⣊⣡⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣰⣿⡿⣿⣧⠈⠑⠒⠤⠄⢀⡀⠀⠀⠀⠀⠀⣰⣿⣿⠟⠄⡑⠈⠐⠀⠈⠀⠁⠀⠁⠀⠁⢌⡸⢾⣿⠏⠉⠉⠀⠀⠀⠀⡔⣡⣿⣿⡟⣎⣶⠃⡆⣼⣿⣿⠃⠀⠐⠉⠀⠀⠀⠀⠀⡸⠀⣿⣿⡏⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⡟⠉⢿⣿⣿⣿⣷⣼⡀⠀⠀⠈⢂⢹⠿⠋⡀⡄⠀⡆⠎⣠⣶⣿⣿⣿⣿⠃⢂⣤⣶⣶⣶⣦⣄⡀⠀⢀⠄⣠⣾⣿⠟⡁⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠥⠒⠤⠖⠒⠖⠲⠒⠒⠒⠒⠓⠚⠉⠉⠁⣺⣿⠃⠀⠀⠀⠀⠀⠈⣴⣿⣿⣷⣿⣿⡿⢠⢰⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣸⣿⣿⠃⠀⠀⠀⠀ ⠀⣠⣿⣿⣟⣳⡔⡘⣶⢯⣟⣿⣿⣿⣷⣶⣤⣤⣼⣤⣭⣵⣬⣥⣴⣿⣿⣿⠿⣏⢿⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⡿⢟⠡⡊⠔⡸⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⠌⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠋⠁⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⣿⣿⣿⠀⠀⠀⠀⠀ ⢰⣿⣿⡟⣼⢣⣇⠱⢸⣛⣮⠷⣯⣳⡉⡙⢿⣿⢿⣿⣿⣿⣿⣿⠛⣉⠹⣞⡽⣭⠯⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣮⢣⡑⢌⡜⡐⢻⣿⣇⠀⠀⢰⣿⣿⣷⣦⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠰⢁⣿⣿⣿⡇⠀⠀⠀⠀⠀ ⣿⡿⢱⣛⢧⡻⢼⡆⢄⢻⣜⡻⢶⣹⢳⡈⡆⢻⡝⣞⣳⢯⢾⡹⢷⡀⢧⠹⣜⢮⣳⢭⣿⣿⣿⣿⣿⣟⣷⣿⣿⣿⣿⣿⣿⣧⡹⢆⣲⢍⣣⣿⣿⣶⣾⣿⣿⢰⢉⠻⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⣿⡇⠀⣛⢮⣝⣣⢿⡘⠌⣷⡹⢧⢯⡹⢧⠘⡈⢿⡜⣧⢟⣧⢻⣍⠷⡌⠄⠹⣞⡵⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣛⣵⣿⣿⠿⣛⢩⠉⣿⣿⡸⢌⠘⢿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⣀⣴⣾⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠷⣿⣿⡏⠀⠀⠀⠀⠀⠀

⠀⠀⢀⡶⠶⢦⣄⠀⠀⠀⠀⠀⣴⠟⠛⢧⣠⣶⣿⠻⣆⠀⠀⠀ ⠀⠀⢸⠁⡟⠦⠌⠛⠉⠉⠉⢹⠇⢨⣶⣼⣷⣞⢙⣧⣿⡀⠀⠀ ⠀⠀⢸⣤⠃⠀⠀⠀⠀⠀⠀⣿⠀⠈⢻⡃⠀⢸⡿⡄⠈⣿⠀⠀ ⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠘⠷⠖⠛⠛⠛⢿⡗⢋⣴⠏⠈⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢻⡀⢀⣀ ⡶⠾⣷⠆⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡀⠀⠐⢺⡟⠉⠉ ⢀⣤⢿⡦⠀⠀⠛⠃⠀⠀⢠⢶⣄⠀⠀⠈⠛⠀⠀⠀⣺⠓⠟⡀ ⠀⠀⣠⡿⣖⡀⣀⣀⡀⠀⠈⠉⠉⠀⠀⣀⣀⣀⢀⣲⣯⣄⠀⠀ ⠀⠀⠁⣴⠟⠉⠁⠀⠉⠛⢦⡀⢀⡵⠛⠉⠁⠈⠙⠻⣄⠀⠁⠀ ⠀⢠⣼⠃⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀ ⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀ ⠀⢠⠿⣆⠀⠀⠀⠀⠛⣿⠛⣿⠀⠀⣿⣤⣿⠀⠀⠀⣰⠷⠀⠀ ⠀⠀⠘⢻⣦⡀⠀⠀⣤⣿⣤⣿⣤⣤⠀⣿⠀⠀⢀⡼⠃⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⡀⢀⣢⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⡁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠉⠉⠻⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢤⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠠⠈⠑⠄⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠉⠉⠉⠙⠿⣿⡆⠀ ⠀⠀⠀⠀⣰⣾⣿⡟⠻⣿⣷⣤⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣷⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡀⢀⠀⠀⠀⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⡀⠀⣀⠀⠀⠀⢹⣿⠀ ⠀⠀⠀⣴⣿⡟⠁⠀⡀⠀⠈⢻⣧⣤⣀⣀⣀⣀⣼⣿⡿⠉⠉⠉⠙⠻⣿⣷⡀⠀⠀⠀⠀⠀⠈⣿⣷⣌⣆⠀⠀⣹⣿⠋⢻⣦⣤⣤⣶⣶⣦⣤⣾⡟⢀⡏⢶⣦⣍⠓⢤⣠⣾⠀ ⠀⠀⠀⠋⣇⡀⡎⠁⠉⢹⣆⢸⣿⠛⠛⣿⡟⠛⣿⠇⠀⡔⠊⠉⠲⡀⢻⣿⠇⠀⠀⠀⠀⠀⠀⠁⢽⣿⠛⠻⣶⣿⣇⡀⢸⣧⡟⠛⠉⠉⠉⠻⣿⣧⠃⣴⣾⣟⣙⠓⠒⠛⠣⠀ ⠀⠀⠀⣈⣽⣿⣽⣦⣀⡼⠛⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣇⡀⠀⠀⣠⣼⣗⠀⠀⠀⠀⠀⠀⠀⢤⣼⣆⠀⠀⣿⠉⠙⠻⣿⡏⠁⠀⠀⠀⠀⠀⠀⠈⠳⠭⠉⠙⢻⣧⠉⠁⠀⠀ ⠀⠀⢸⣿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠿⠿⢿⣿⣿⣦⡀⠀⠀⠀⠀⣯⡏⠻⢧⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣷⣤⡀⠀ ⠀⢠⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣿⣿⠃⠀⠀⠀⢰⣿⠇⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⢻⠀ ⢠⣾⣿⣟⠁⠀⠀⠀⠀⢀⣀⡄⠚⠋⠉⠉⠉⠛⠶⠄⣀⣀⠀⠀⠀⠀⠀⠛⠻⣿⣆⡀⢠⢸⡟⠋⠀⠀⢀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⣀⠀⢀⢀⣼⣻⡟⠀ ⠘⢻⣿⡟⠀⠀⠀⢀⣰⣿⣿⣿⠀⠀⣶⣶⡆⠀⠀⢾⣿⣿⡇⢀⡀⠀⠀⠀⣀⣿⢏⡇⢸⣻⣷⡀⠀⡠⢉⠇⠀⣸⣿⣿⡷⠋⢱⣶⣶⠉⠓⣿⣿⣷⡂⠀⠫⣩⡆⠀⠉⡟⡿⡄ ⠀⠈⣿⣿⠿⠆⠀⠛⠚⠛⠛⠁⠀⢰⣾⠿⣷⡶⠀⠈⠛⠛⠀⠷⠛⠀⠀⠘⢻⣿⡿⠁⠀⠛⢿⣿⠀⢧⠀⠀⠀⠹⢿⠿⠃⠀⠾⠿⠿⠆⠀⠻⠿⠟⠀⠀⠀⢠⠇⠀⢀⣷⢷⡇ ⠀⠀⢿⣿⣆⠀⠀⠀⠀⠀⠀⠒⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇⠀⠀⠀⣸⣿⡀⠀⠙⣒⠲⠔⠁⣰⡾⠭⣷⡄⢰⡾⠛⠻⣶⡀⠐⠒⠒⠁⠀⢸⣟⣿⠋⠀ ⠀⠀⠘⡿⣿⣷⣶⣶⣶⣄⡀⠀⠀⠀⣤⣤⣄⠐⣤⣴⣶⣶⣶⣶⣾⣯⠿⠿⠿⠟⠀⠀⠀⠀⠸⣟⠻⢿⡇⠀⠀⠀⣬⡇⠀⠀⢸⡏⣭⡇⠀⠀⢸⡇⠀⠀⠀⣶⣶⣿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢀⠄⣿⣌⣽⣿⣿⠙⣿⡄⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣯⡻⠿⢖⣒⣿⠉⠁⠠⠿⠃⠈⠹⠿⠇⠈⢟⣶⣶⣿⠿⠏⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣿⣷⣶⣶⡇⠀⠀⠀⠉⠿⠏⠉⡿⠿⢿⣷⣶⣶⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠤⣼⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠽⣿⡇⠀⢷⡀⠀⠀⠀⣠⠇⠀⢸⣿⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⢹⣿⣶⣦⡦⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣄⡀⠀⣤⣤⣤⡀⠀⠀⣴⣿⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣾⣿⠙⢻⣧⣶⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⣶⣽⡏⢻⣧⣤⡞⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠿⢷⣤⡴⠿⠋⢻⡆⠀⠀⠀⠀ ⠀⠀⠀⣾⠛⠙⠻⠷⢶⠶⠿⠟⢻⣿⢉⣿⣶⣿⣶⣤⣀⣤⣿⣄⠀⠀⠀ ⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣍⣿⣿⣧⣤⣩⣿⣷⣤⣿⠀⠀⠀ ⠀⠀⠈⢿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠻⠿⢿⣟⣿⣹⡟⠀⠀⠀ ⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⡛⠋⢿⣄⣀⣀ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠈⠛⢻⡏⠀⠀ ⠴⠶⠾⣟⠛⠀⠀⢸⣷⠄⠀⠀⠀⣀⣀⠀⠀⠀⠻⠟⠁⠀⠘⣿⠿⠿⠃ ⠀⢀⣤⢿⣞⠂⡄⠈⠁⠀⠀⠀⠘⠿⢿⣠⡀⠀⠀⠀⠀⠀⣿⠿⠶⣦⠀ ⠀⠀⠀⣠⣿⢿⣯⣠⣄⣀⣶⣟⠻⢿⢿⣼⣿⣀⣀⣤⣴⠟⠉⠀⠀⠀⠀ ⠀⠀⠀⠛⠀⢀⡾⠉⠉⢻⡟⢿⣧⣷⣶⡀⢈⣹⡏⠃⠙⣷⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣇⠀⠀⢺⣿⣦⢾⣏⣸⣳⣾⣟⠁⠀⠀⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠟⠻⠶⣤⣾⠿⠿⣟⣻⣯⡿⣿⣿⡶⠤⠾⠛⢷⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⢹⣧⣻⣻⣿⣽⣿⡿⠿⠁⠀⠀⠀⢸⡆⠀⠀⠀ ⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⢀⣾⠑⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⢷⣄⣀⣴⠟⠋⠉⠉⠉⠙⠻⣦⣀⣠⣴⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠉⠉⠉⠉⠛⢷⣤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣤⡶⠾⠻⠶⣶⣄⡀⠀⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀ ⠀⠀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠙⢿⣦⣿⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀ ⠀⣼⡟⠀⠀⠀⠀⠀⠀⢀⣠⣄⡈⢿⣿⠀⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀ ⢠⣿⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠈⣿⡀⠻⠿⠿⠃⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀ ⠘⣿⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃⢠⣿⢷⣄⡀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣦⡀⠀⠀⠀ ⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠙⠻⠷⠶⠶⠶⠶⠟⠋⠁⠀⠙⣷⠀⠀⠀ ⠀⠀⠙⣷⣤⣀⡀⠀⠀⣀⣠⣴⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⢸⡇⠀⢹⡇⠀⠀ ⠀⠀⢸⡏⠉⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠈⠁⠀⣸⡇⠀⠀ ⠀⠀⢸⡇⠀⣰⡆⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠆⠀⠀⠀⠀⣰⣿⣁⠀⠀ ⠀⠀⠈⣿⡀⠙⠃⠙⠁⠀⠀⣤⣄⣀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⣠⣾⠟⠉⢻⣧⣀ ⠀⠀⠀⠘⣿⣄⡀⠀⠀⠀⠀⠈⠉⠙⠛⠷⢶⣴⡟⣁⣠⣤⡶⠾⢿⣯⠀⠀⠀⢀⣽⠟ ⠀⠀⠀⠀⣾⠟⠻⠷⣦⣤⣤⣤⣤⣴⡶⠶⠶⠛⠛⠉⠉⠀⠀⠀⣀⣹⣷⣀⣠⡿⠋⠀ ⠀⠀⠀⣰⡿⠀⠀⠀⠀⣹⡏⠀⠀⠀⠀⢀⣀⣠⡤⠤⠶⠒⣿⣿⣿⣿⣿⣿⣏⠀⠀⠀ ⠀⠀⠀⠻⣷⣤⣀⠀⢠⣿⡤⠴⠖⠚⠋⠉⢁⣀⣤⠤⠴⢾⡿⠙⠛⠋⠙⠿⠟⣿⡆⠀ ⠀⠀⠀⠀⠀⠉⠛⠻⣿⣯⣠⠤⠶⠒⠛⠉⠉⠁⠀⣀⣀⣼⡇⠀⠀⠀⠀⠀⢀⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢀⣀⣀⣠⣤⣴⡶⠾⢿⡿⠋⠙⣷⣄⠀⠀⢀⣠⣾⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣽⡟⠛⢛⣉⠉⠁⣠⣄⣠⡿⠁⠀⠀⠈⠙⠛⠛⠛⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣴⠟⠻⠷⠿⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣀⣀⠀⠜⣁⣤⣀⠋⠉⢣⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡇⠀⠀⠀⠀⠀⠀⠀⢀⣤⠮⠙⠂⠀⢨⠋⠉⡩⠋⠁⠘⠣⠿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠤⡠⡮⠋⠁⠀⠀⠀⢀⠇⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠓⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⡰⠁⠀⠈⢵⡀⠀⠀⠀⠀⢸⢀⡎⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠉⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⢠⠁⠀⠀⠀⠈⠾⠀⠙⠒⠦⣇⡜⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀ ⠀⠀⠸⡎⡀⠀⠀⠀⠀⢀⠄⢀⠀⡾⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⡋⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⢷⡀⠀⠀⠀⠀ ⠀⠀⠀⢇⡇⠀⠀⠀⠀⠸⠀⠸⢼⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⣃⠴⠊⠀⠀ ⠀⠀⠀⢸⢠⠀⠀⠔⠁⠀⣎⡙⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⣠⠴⠋⡉⠀⠀⠀⠈⢳⡀⠀⠀⠸⠀⠀⠀⠀ ⠀⠀⠀⠈⡜⠀⠀⠂⢀⠂⠉⢁⡇⠀⠀⢾⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢶⣄⠀⠀⠀⠛⡟⠳⣦⠃⠀⠀⠀⠀⠀⡇⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠇⡇⠀⠀⠘⢄⠠⣸⡇⠀⠀⠈⡿⡀⠀⠀⠀⠀⢀⡴⠋⣁⠠⡄⣻⠀⠀⠀⠀⡵⢶⣮⠻⣭⡄⠀⠀⠀⡇⠀⠀⠻⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⢠⠀⠀⠀⠀⠀⣿⢹⡀⠀⠀⢱⠀⢀⠐⠒⣶⣿⣶⡾⠛⢛⣿⣾⢤⣤⣤⣤⣤⣾⡷⠒⠒⠒⠲⢦⣴⣅⠀⣘⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢛⡀⠀⠀⠀⠀⢳⣆⢃⠀⠀⠀⢧⠬⠽⠟⠻⡟⡆⣄⣠⡾⣿⡿⠀⣻⡟⢻⡿⠟⡀⠀⠀⠀⠀⡴⣿⠃⡴⠏⠀⠀⠀⠀⠀ ⠀⠀⡀⠀⠀⠀⠃⠀⠀⠀⠀⠸⡘⡌⢆⠀⠀⠘⣆⠀⠰⣻⢿⡵⡹⣿⣿⠟⠁⢠⡟⠀⠀⠳⣱⡀⠀⠀⢀⡼⢁⡏⡜⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢦⣀⠀⠒⠁⢀⡀⠀⠀⢇⠱⡈⢆⠀⠀⠈⢧⠑⢥⣈⠣⠤⣄⣠⡤⠶⠋⢰⡄⠈⢀⣠⠯⢤⣤⣾⠤⢞⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡶⠎⠓⠀⠀⠀⠀⠘⠡⢢⢜⠀⢡⠈⢆⠀⠀⠀⠳⡀⠈⠙⠲⢀⣤⠀⠀⢀⢾⠙⠓⣞⠁⠀⣰⠋⠀⡠⠓⠤⢄⣀⠀⠀⠀⠀⠀⠀ ⠀⢠⠒⠛⠽⣛⠢⠶⣤⣀⠀⠀⠘⡇⠀⢣⠀⢣⠀⠀⠀⠙⣄⠀⠀⡄⠈⠉⠛⠃⠀⠱⣄⠈⢳⡴⠃⠀⡰⠁⠀⠀⠀⠀⠈⠁⠐⠂⠀⠀ ⠀⢠⠉⠒⠤⡀⢉⠐⢠⠖⠀⠀⠀⢻⡀⠀⢣⠀⠱⡀⠀⠀⠈⣆⢠⠃⠀⠀⠀⠀⠀⠀⠈⢣⡀⠙⣆⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣵⡄⡀⢨⡟⠁⠀⠀⠀⠀⠀⠈⣗⠀⠀⢃⠀⠘⡄⠀⠀⠘⡞⠂⠀⠤⠀⣀⠀⠀⠀⣸⠙⢆⠈⢳⡷⠆⠒⠊⠉⠉⠉⠒⠒⠀⠤⠄ ⠀⠀⠈⠷⣌⠊⡗⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠈⡄⠀⠘⡄⠀⠀⢹⡒⠠⢄⡀⠀⣩⠖⠉⠁⠀⠉⠱⣖⢳⠠⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠳⢾⡢⢀⠀⠀⠀⠠⣴⡋⢻⡄⠀⢸⡀⠀⢱⠀⠀⠸⡇⠀⠀⠈⠑⢷⣄⠀⠀⠀⠀⠀⠀⠙⠞⢃⡤⣢⡍⠁⠒⢂⣤⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠈⢻⡆⣧⠀⠀⡇⠀⠀⡇⠀⢰⡇⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⣴⢋⡴⢣⠴⡣⢚⡽⠟⣀⣴ ⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣬⠷⣾⠀⠀⠀⠀⠀⠇⠀⣼⡁⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠉⠐⠋⣞⡴⢉⣴⣿⠟⠁ ⣀⠈⡉⠁⠐⠛⠡⠖⣤⢀⡀⣼⡵⣜⡵⢀⠿⠀⠀⡀⠀⠀⡇⣐⠞⠶⠯⣤⣤⣔⣸⠯⢙⣛⠰⠖⣀⡤⠄⣀⡀⢀⢼⠿⣰⣽⡿⠋⠀⠀ ⠈⠻⣦⡀⠀⠀⠀⠀⠒⠛⠉⠻⠙⢗⣀⠖⠁⠀⢀⠇⠀⢠⠻⠚⠂⠀⠀⠀⠈⠉⠛⠿⠷⣶⣬⣅⣒⠤⢉⡐⠀⠅⢕⣾⡿⠛⠒⠒⠀⠀ ⠀⠀⠈⠫⣢⡀⠀⠀⠀⠀⠀⢀⢣⠀⠀⠀⠀⢠⢎⣠⢢⢁⡀⠂⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠈⠉⠛⠻⠷⣶⣦⣴⣿⠋⠁⠀⠐⡊⠅⠀

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⣿⡿⠻⣿⣿⡿⢯⣭⣦⠀⠀⠀⠠⢤⠀⢹⠻⠽⢲⠉⠉⠹⠛⢿⣟⣿⠛⠟⢛⡏⢭⡀⠀⢠⠉⣽⠋⠟⢻⡍⢩⡽⠳⠞⠋⢩⠻⠍⢣⠀⠀⠀⠀⢀⡠⠤⣳⠾⣺⣿⣿⣿⣿⣿⣿ ⣿⣿⣷⣿⣓⣠⢤⣀⣻⡀⠀⠀⠀⠀⠧⠤⠭⠭⢥⡄⠀⠀⠉⠁⠈⠙⠛⠺⣍⠀⠀⣻⠟⠃⢠⣧⠟⠚⢹⡥⠚⠉⠀⠀⠀⠀⠉⠉⠁⠀⠀⣀⣩⠋⠀⠴⢐⢽⣽⣿⣿⣿⣿⣿⣿ ⣿⣗⣀⣽⡙⠧⠦⠿⣻⣅⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠤⢔⡲⠶⠂⠀⠀⠀⠀⡇⠰⠁⠀⠀⠟⠁⠀⢠⠇⠀⠀⠀⣀⣀⣀⡀⠀⠀⠘⡄⠀⠀⠀⠳⠧⠿⢚⠟⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⠙⠋⠻⠷⣶⠾⡅⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⣀⠤⠒⠂⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠐⠙⠦⠤⣄⠈⠑⠤⣀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⡯⢀⣿⣿⣿⣿⣿⣿⣿ ⣿⡿⢦⠀⠀⠰⠁⠀⠀⠀⠈⣄⠀⠀⠀⠀⣠⠔⠉⢀⡔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⢀⠎⠈⣷⣾⣿⣿⣿⣿⣿⣿ ⣿⡯⠬⠒⠁⠀⠀⠀⠀⠀⣄⠈⢦⣀⠔⠊⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠈⠑⢄⡀⠀⣠⠊⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿ ⡟⢁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣀⢀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⠉⠐⠁⣠⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿ ⠀⠠⢤⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⣠⡏⠀⠀⠀⠀⠀⢀⣿⣿⣆⠀⠉⠙⠛⢿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⡿⢽⣿⣿⣿⣿⣿⣿ ⠀⢰⢉⡕⠀⠀⣀⣀⣴⣿⡙⣿⣿⠀⠰⣶⣶⣶⣬⣭⣛⣿⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣿⣿⣿⣿⣿⣿⡿⠛⠋⣙⣀⠁⠀⣿⣿⣿⣿⣿⠈⢷⢸⣿⣿⣿⣿⣿⣿ ⢠⡿⠻⣷⣶⣾⣿⣾⠏⣿⣿⣾⣿⡔⠋⠉⠁⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠄⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠃⢹⣿⣿⣿⣿⡀⡾⢸⣿⣿⣿⣿⣿⣿ ⣼⣯⣤⣾⣿⣿⣿⣻⣿⠟⠿⣿⣿⣇⠀⠀⠀⠀⠀⠙⠛⠿⠿⠛⠛⠉⠛⠀⠀⠀⠀⠊⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣽⣿⠿⠛⠀⢸⣿⣿⣿⣏⣀⢀⣸⣿⣿⣿⣿⣿⣿ ⣿⣿⢉⣽⣿⣿⣿⣏⣁⣀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠀⠰⢶⠶⠶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⣿⣿⡛⠛⠿⣿⣿⣿⣿⠟⠉⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿ ⣿⣟⠻⠇⠀⠙⠉⢲⡿⠶⠇⣀⢘⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⢀⣀⠈⠉⠫⠻⠿⣿⣿⣷⣾⠿⠂⠀⠀⠰⠿⠿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣧⣴⣷⠀⢀⡤⢘⣍⠃⠀⠈⠈⠉⠛⠒⠲⠶⢿⣶⣶⣶⣤⣤⣤⣤⣤⣴⣄⠀⠀⠀⣠⢋⣾⣿⣿⡀⠀⣤⣤⣤⣤⣤⣤⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡟⢿⣯⣹⣿⣿⣿⣿⣿⣿ ⣿⣯⣂⣿⡷⠈⠀⡇⠈⢓⢦⣄⣀⢳⣶⣶⣤⣄⣀⣀⡀⠉⠩⢭⠙⡛⠛⣿⣿⣷⢶⡾⠷⣿⣿⡿⠷⣷⣖⣛⣻⣛⣏⣉⣉⠉⠉⠉⠁⠀⠀⠀⣽⣿⣿⠃⠀⠈⢿⣿⣿⣿⣿⣿⣿ ⠘⣟⠛⣟⠁⠀⡰⠑⣨⣍⠀⣬⠛⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠖⠀⠙⠛⠋⢡⠎⠀⠀⠀⠉⠛⠗⠶⢿⣿⣿⣿⣿⣿⣻⣽⡇⠀⠀⠀⣀⣾⣿⡿⢁⣀⣀⠀⣼⣿⣿⣿⣿⣿⣿ ⣶⣾⣾⣿⣶⣶⣷⣶⣿⣿⣷⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣶⣾⣷⣾⣶⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡀⡄⠤⠤⣄⠀⡀⠄⠒⠉⣉⣱⡀⠀⠀⠀⠀⠀⡀⠂⠁⠀⠀⣠⠡⡨⢂⠖⢃⠀⠀⠀⠀⠀ ⠀⠀⡐⠁⠋⠉⢢⠏⠊⠂⠢⠀⠀⣐⡖⠋⠁⠉⢑⢤⣸⠆⠑⠲⠴⠪⣠⢸⡎⠢⡀⠀⠀⢀⠂⠀⠀⠀⢠⣹⠑⠈⠁⠀⠀⠅⠀⠀⠀⠀ ⠀⠂⠀⠀⠀⠀⡚⠇⠀⠀⠀⡃⡘⠈⠀⠀⢀⠄⠁⠉⢣⡀⡠⠊⢀⡄⠈⠑⣷⡀⢣⠀⠀⠐⡀⠀⠀⠐⡠⠫⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀ ⠀⠅⠀⠀⠀⢈⠨⠃⠀⠀⠀⣂⠅⠀⠀⢀⠂⠀⠀⣜⣽⣷⣡⣶⣻⣧⠀⠀⠘⣇⠈⡆⠀⠀⠈⠁⠁⠁⠀⡫⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀ ⠀⠇⣀⡀⡀⠖⠃⠕⢄⣀⠔⢺⡆⠀⠀⡐⠠⣪⣿⡿⠟⠋⠉⠉⠋⠟⢇⡀⠀⡋⣆⠏⠄⠀⠀⢀⠁⠀⠀⡁⠁⡥⢅⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠁⠀⠈⡀⠀⠀⠸⡑⡄⠀⣇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⣍⠜⡇⠡⠀⠀⠄⠀⠀⠂⠀⡚⠀⠀⠑⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⡊⢏⡧⣄⠫⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣵⣁⡟⣌⠀⢐⠀⠀⠐⠀⠀⠅⠀⠀⢀⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⡃⣘⠀⢈⡯⠊⠁⠋⠉⠋⠦⡀⡄⠒⠆⠋⠃⡍⢗⢢⠟⣧⠀⡆⠀⡈⠀⠀⠀⠅⠀⠀⡸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⢧⡃⡃⣜⣃⣀⣀⣀⣀⣀⠀⡏⡀⣊⣀⣀⣠⠂⣩⢏⡋⢘⠑⡌⠉⠀⠀⠀⠀⠡⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠆⠙⠛⣾⡢⡶⠖⣲⣶⠂⡐⡓⠂⠚⣿⡟⢻⢦⡿⢁⠁⢈⠀⠰⠀⠀⣄⡀⠈⠘⠀⠠⡧⠤⣄⠀⠀⠀⠀ ⠀⠀⠀⠄⠀⠀⠀⠀⠁⠀⢐⠁⠀⠀⡊⢿⣋⣦⢿⡯⠔⡏⠈⡄⠐⠛⠓⢿⣰⢇⠆⣀⣲⠀⢘⢀⣞⠁⢀⠀⠀⡇⠀⡇⡄⠈⡇⠀⠀⠀ ⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⡘⠀⠀⠠⢇⠀⡑⢆⠀⠠⠼⠝⠶⠬⠒⠠⢆⣜⢻⠡⠕⠄⠸⠅⠆⡞⢐⢀⡞⠀⠨⠀⠀⡇⡇⠀⡇⠀⠀⠀ ⠀⠀⠀⠄⠀⠀⠀⠁⠀⠀⢣⠀⠀⡇⡨⣿⢒⢊⡇⠑⠴⡉⠁⣀⠄⡮⢍⠘⡜⡆⠦⠀⠸⠞⠀⡇⡸⡞⠀⡠⠃⠀⠀⡯⢱⣠⡇⣄⡀⣀ ⠀⠀⠀⢂⣀⡠⠁⠀⠀⠀⠀⠑⢴⡑⡸⣺⠧⠂⡇⠀⠀⠈⠁⠁⢸⠁⠄⠢⡈⣧⡄⠀⠬⡃⠁⠉⠀⢗⠊⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠲⢇⡼⠧⠖⠃⠀⠀⠀⠀⠀⠸⢄⡁⠢⠜⠃⠄⠀⡋⡃⠂⠀⠀⠀⠑⠤⣀⣀⣀⣀⡤⠶⠅⠄⠄⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⡥⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣶⡂⠀⢇⢛⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⡣⠃⡃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠒⣒⢍⣇⠉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⠔⡡⠊⠀⠀⣇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢹⠀⠈⠈⢣⠛⡟⣷⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡊⣠⢎⠀⠰⠒⢒⡟⠒⠢⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢸⢀⠀⠀⠀⢳⠑⢻⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣎⠎⠁⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠤⠤⠤⠤⠒⠁⠀⢸⡂⠀⠀⠀⠀⢇⢸⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⢹⢠⠒⠐⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⠊⡺⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡈⡇⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠐⣛⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⠀⡇⠀⠀⠀⠀⠀⠀⠨⣀⠀⠀⠀⠀⠀⢠⠊⠣⠄⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⠐⣽⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⠀⣇⠀⠀⠀⠀⠀⠀⠀⡃⠉⠒⠢⠠⣀⡀⣀⢀⡀⡠⠄⠤⠄⠒⠒⠉⠂⠀⠀⠀⠀⠀⠐⢨⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

☪︎ ִ ࣪𖤐 𐦍 ☾𖤓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⢠⠋⠉⠉⠒⠲⢤⣀⣠⡀⠀ ⠀⠀⠀⠀⠀⠀⣀⣀⣀⢀⡠⠖⠋⠉⠀⠀⠀⠀⠉⠉⠢⣄⠀⠀⠀⢀⠼⠤⠇⠀ ⠀⠀⠀⣀⠔⠊⠁⠀⢨⠏⠀⠀⠀⣠⣶⣶⣦⠀⠀⠀⠀⠀⠱⣄⡴⠃⠀⠀⠀⠀ ⢸⣉⠿⣁⠀⠀⠀⢀⡇⠀⠀⠀⠀⢿⣽⣿⣼⡠⠤⢄⣀⠀⠀⢱⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠑⢦⡀⢸⠀⠀⠀⡠⠒⠒⠚⠛⠉⠀⢠⣀⡌⠳⡀⡌⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⣆⠀⢰⠁⣀⣀⠀⠀⣀⠀⠈⡽⣧⢀⡷⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡤⢄⠀⠈⠢⣸⣄⢽⣞⡂⠀⠈⠁⣀⡜⠁⣩⡷⠿⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢯⣁⡸⠀⠀⠀⡬⣽⣿⡀⠙⣆⡸⠛⠠⢧⠀⡿⠯⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡀⠀⠀⡤⠤⣵⠁⢸⣻⡤⠏⠀⠀⠀⠀⢹⠀⠀⠀⡊⠱⣀⠀⠀⠀ ⠀⠀⢀⠜⠀⢘⠀⠀⠱⠲⢜⣢⣤⣧⠀⠀⠀⠀⠀⢴⠇⠀⠀⠀⠧⠠⠜⠀⠀⠀ ⠀⠀⠘⠤⠤⠚⠀⠀⠀⠀⠀⠀⢸⠁⠁⠀⣀⠎⠀⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⣀⡴⠤⠄⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⢄⠀⠀⢼⣿⢿⡿⣿⣿⡆⠀⠀⢀⡠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢜⠿⣿⣽⣷⠟⠁⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡀⠀⠀⠀⠀ ⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠌⣉⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀ ⠀⠠⠃⠀⠀⠀⠀⠀⠀⡀⡀⢠⡀⠀⡆⠀⡇⠀⢰⠀⢨⠆⢀⣠⣴⡶⣦⡀⠈⢛⣡⠁⠀⠀⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀ ⢠⠁⠀⠀⠀⠀⠀⠀⡎⠀⣇⠀⣇⠀⣇⠀⣧⠀⣟⠀⣿⠞⠋⠉⠀⠀⠈⢿⡄⠀⠉⠀⢀⣾⠛⠉⠉⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀ ⠀⠀⠀⣀⣀⡀⠀⠀⢿⠀⢻⡀⢿⡀⢿⡀⢻⡀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠻⣧⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠇ ⠀⢀⣾⠟⠋⠙⠛⠛⠺⢷⡈⠳⠈⠗⠈⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢠⡟⢀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⢲⣶⠟⢋⠍⡙⢻⣤⣤⣤⣤⣄⡀⠀⢸ ⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣇⠀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢁⠎⢰⣈⣐⠉⣷⠀⠀⠀⠉⣿⡀⠀ ⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡁⠎⠰⣿⣋⣽⡷⣿⣄⠀⠀⠀⣾⠁⠀ ⠀⠀⢻⣾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣤⣧⣼⡿⢁⠒⡠⠘⣷⢤⣤⣟⡀⠀ ⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣼⣃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣬⠂⣁⣳⣿⡆⠤⡉⣿⠀ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⠀⠀⣿⠈⠉⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠛⠿⠾⠋⡔⣠⡿⠀ ⠀⠁⣿⠀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠐⠒⢿⡗⠒⠀⠈⠁⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠘⣷⣌⣂⣵⣾⠟⠁⠀ ⣀⣠⣽⡶⠶⠂⠀⠀⠀⢿⣿⠇⠀⠀⠀⠀⢠⡚⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⣘⣧⡤⠆⠀⠀⠀⠀⠀⠀⠀⣎⠙⣦⠀⠀⠀⠀⠀⢰⣿⡗⠀⠀⠀⠀⣉⣉⣁⡿⠀⠀⠀ ⠁⠀⠈⢿⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠋⣩⡿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⣹⠏⠛⠂⠀ ⠀⠀⠴⠚⠻⣆⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠉⠀⠀⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠙⣳⢯⣄⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⢻⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⢶⡿⠛⠿⢦⣀⠀⠀⠀⠀⠀⠈⣙⣳⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣶⡾⠋⠀⠈⠀⠀⠀ ⠀⠀⠀⠀⠋⠀⠀⠢⣀⠉⡉⣙⣿⢻⡟⢻⣉⣿⣽⡋⣰⠏⢻⡄⠀⠀⣠⠿⢦⡀⠀⣠⡴⠞⣿⢡⡿⢀⢿⡉⠙⠓⣶⠶⢶⣦⠶⣶⣶⠶⠾⠛⡫⠁⠙⠧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠙⠉⠘⣿⠀⠀⠋⠁⠀⠙⠃⠀⠈⠷⣴⠞⠋⠀⠀⠙⣿⠋⠀⠀⠘⣿⠃⡌⢌⡙⢛⡋⢅⠒⣿⣀⠒⠤⣹⣷⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⢀⣿⣄⣀⡀⢰⡟⢌⡐⢢⠘⠤⢘⠠⢊⠼⣧⣼⠶⠋⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡤⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟⠛⠛⠋⠁⠈⠉⢛⣿⠑⠢⢌⢂⠩⡐⢡⠊⠔⣂⠉⢿⡆⠀⠀⠀⢀⡷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣤⣤⣤⣤⣦⣶⣶⣶⣿⣿⡇⠀⠀⠀⠀⠀⢰⢻⣧⡌⠑⢢⡌⢢⠑⠂⠉⠒⢠⠉⡄⢻⣶⢳⡞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣽⢻⡟⣿⢻⣏⣿⡹⣏⢿⣿⠇⠀⠀⠀⠀⠀⠈⠻⣟⣷⣥⣂⡘⠄⢢⠉⠜⣠⢃⣘⣴⣾⣻⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⡞⣽⢿⣿⣳⢞⡶⣻⣝⡾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢾⣭⢿⣛⣿⣻⣟⣻⠯⠟⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡿⠾⠿⢿⠻⠾⠿⠷⠾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⡀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠚⠛⠓⠒⠚⠋⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠈⠛⠶⠶⠶⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⢀⠄⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠋⠉⠉⠉⠛⠿⢷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣴⡿⠁⢰⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠶⠆⠀⣰⡆⠀⠀⠀⠀⠀⢸⣿⣿⣦⣀⠀⠀⠀⠀⠀ ⠀⢀⣴⣶⠿⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣷⣶⣤⣀⠀ ⢰⣿⣿⠌⠁⠈⠽⣷⣶⣶⣤⣄⡀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢰⣿⠙⢿⣿⣿⣿⣿⣿⣿⡇ ⢿⣏⡉⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⠿⣟⢛⡻⣷⣤⠀⠀⠀⣸⡟⠀⠀⠙⢿⣿⣿⣿⣿⠇ ⠈⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⠵⢈⣿⡆⠀⣠⣿⠃⠀⠀⠀⠈⠙⠛⠛⠁⠀ ⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣰⣿⣶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⣀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣽⣿⣿⣶⣶⣴⣤⣤⣶⡿⠟⠛⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣿⣿⣿⡿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣶⣿⣿⣿⣿⣿⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣾⣿⣿⣿⣷⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡿⢿⡟⣟⢻⡛⡿⢿⡿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡿⡿⡟⣟⢻⣛⢿⡻⢿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⡟⣏⢳⣙⠦⣝⡬⢧⡹⣜⢣⢞⡱⢏⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡟⡹⣜⡱⡹⣌⠷⡸⢦⣙⢧⡚⣭⢻⣿⣿⣿⣦⡀⠀⠀⠀⠀ ⠀⠀⢀⣼⣿⣿⣟⢣⡝⣬⢓⣮⣽⠶⠟⠛⠛⠛⠾⣮⣵⣋⠶⣹⣿⣿⣧⠀⠀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⡀⠀⢠⣿⣿⡿⢲⣍⢳⣬⡷⠿⠚⠛⠻⠷⣾⣦⡝⢦⠳⡜⡽⢿⣿⣿⣄⠀⠀⠀ ⠀⠀⣾⣿⣿⠳⣎⠳⡼⣼⠟⠋⠀⢀⠠⠀⠄⠂⢀⠀⠙⢿⣚⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣳⡼⠋⠁⠀⢀⠀⠂⡀⠀⠀⠈⠛⣯⣳⡹⣜⢫⣿⣿⣿⡆⠀⠀ ⠀⣸⣿⣿⣏⢳⢎⣝⡿⠋⠀⢀⠐⠀⡀⠄⠀⢂⢠⣬⣶⣿⣿⣿⣿⠿⣿⢛⠯⣝⡹⣜⡱⢎⠶⣩⠖⣭⢲⡱⢎⠶⣩⡍⢯⡹⣛⠿⡿⣿⣿⣿⣿⣷⣦⣅⠀⠠⠁⢀⠈⠀⢁⠀⠈⢻⡷⣌⡳⣜⢿⣿⣿⠀⠀ ⠀⣿⣿⣿⢬⡓⣮⣾⠇⠀⠐⠀⡀⠂⢀⢠⣵⣿⣿⣿⣿⢟⡻⡹⣌⠷⣌⢏⡞⡲⢵⢪⡕⣫⠞⣥⢛⢦⢳⡙⣮⣙⠦⣝⢣⠳⣍⡞⣱⢎⡼⣙⢟⡿⣿⣿⣿⣶⣄⠀⠠⠁⢀⠠⠁⠀⣿⡮⡕⣎⣻⣿⣿⡇⠀ ⠀⣿⣿⣿⢎⡵⢺⣿⠀⠀⡁⠠⠀⢄⣶⣿⣿⣿⠿⡹⡜⢮⡱⢳⡍⡞⣜⠮⣜⡝⣎⠳⡼⣡⠟⣬⢋⣎⠧⡝⢦⣙⠞⣬⢋⡗⢮⡜⣣⢞⡲⣍⠞⡼⣱⢛⣿⣿⣿⣷⣄⠐⠀⡀⠐⠀⣼⣷⡙⢦⣽⣿⣿⠇⡁ ⠠⢹⣿⣿⣞⡜⣣⢿⣇⠀⠀⠂⣸⣿⣿⣿⢻⢬⢳⡹⣜⢣⡝⣣⢞⡹⣌⠗⡮⢼⡸⣙⠶⣱⢋⣖⢫⡜⣣⢏⡳⢎⣝⡲⢭⡚⡵⢪⢵⢪⡕⢮⡹⢖⡣⢏⠶⡹⢿⣿⣿⣧⡄⠀⠐⢠⣿⢧⡛⣜⣾⣿⣿⠀⠀ ⠀⠀⢻⣿⣿⣞⡱⢎⡿⣦⡀⣹⣿⣿⡿⣍⠞⣬⢇⡳⣜⢣⢞⡱⣎⠵⣎⡝⣎⢧⠳⣍⡞⡥⢏⣜⡣⢞⡱⢮⣱⢋⠶⣙⠶⣩⢳⡙⣎⡳⣜⢣⡝⢮⣱⢋⣞⡱⣋⢿⣿⣿⣷⡈⣰⡾⣏⢶⣹⣾⣿⣿⠃⠀⠀ ⠀⠀⠉⠹⣿⣿⣿⣧⡞⣭⢻⣿⣿⡿⡱⢎⡽⢢⢏⠶⣩⠞⣮⠱⣎⢳⠼⣸⠜⣎⡳⢎⡼⣱⢋⠶⣩⢇⣛⢦⢣⢏⡝⣎⢳⡱⢣⣛⠴⡳⢬⡓⢮⠳⣌⡏⢶⡱⢭⣚⢻⣿⣿⣿⡝⣲⣭⣶⣿⣿⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⢿⣿⣿⣷⣿⣿⣿⠳⣍⡳⢎⡝⢮⣙⠶⣙⢦⣛⠬⣇⣛⢦⡛⢦⡝⢮⡱⢣⢏⡝⢦⣫⠜⣎⡳⣚⢼⡘⣧⣙⠳⣬⠳⣍⢧⡹⢣⣛⡴⣹⢲⡙⡶⣩⠞⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣿⢧⣛⢬⠳⣍⠾⡱⢎⡝⣎⠶⣩⠞⡼⣘⠦⣏⠳⣜⡣⣝⢣⡞⣹⠲⣥⢛⡬⢳⡍⡶⣙⠦⣭⠳⣥⢛⣜⡲⣍⠷⣘⠶⣡⢗⡹⢲⢥⡛⠶⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢓⡎⢧⣛⢬⠳⣍⠯⡼⣘⢧⢣⢏⡵⣋⢞⡼⣙⠦⣝⡬⢳⡜⣥⡛⡴⢫⡜⢧⡚⡵⣩⢞⡲⣙⠦⣏⠶⡱⢎⡝⣎⢳⡍⡮⢵⣋⠶⣍⡳⢽⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⢿⡸⢇⡎⣇⠿⣈⢷⢱⣉⡎⢷⠾⣸⢱⢾⡰⢏⡾⣆⠹⣇⣾⣶⣿⣷⣿⣸⣇⡹⢶⢇⡾⢱⣉⡾⣈⢷⡉⣏⡸⡎⢷⣸⢱⢇⡎⡷⣎⢱⠏⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢎⢾⡱⢫⡜⣎⢳⡍⢮⠳⡜⣜⣣⣛⠴⣋⠶⣙⣎⣶⡽⠟⠋⠉⠉⠀⠀⠉⠉⠉⠛⠿⣮⣜⢧⠳⣜⡱⣎⠵⣎⠵⣹⢒⢧⣋⠞⡼⡱⢎⣝⠺⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢺⡌⢷⡩⢞⡬⣓⠮⣍⣷⣿⣿⣷⣾⡽⣸⡙⣶⡟⠁⢀⠀⠄⠀⣰⣀⣁⣀⡀⢂⠀⡀⠀⠛⣯⡳⢎⡵⣺⣿⣿⣿⣷⣏⠶⣩⢞⡱⣭⢓⢮⣙⢾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢣⠞⣥⢛⡜⢶⡩⢞⣹⣿⣿⣿⣿⣿⣿⣥⣻⠏⠀⠀⠂⠠⠀⣱⣿⣿⣿⣿⣿⡀⠀⠠⠐⠀⠈⣿⡳⣼⣿⣿⣿⣿⣿⣿⢣⣓⠮⣕⢮⡙⣦⢋⣾⣿⣿⡇⡰⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢭⣚⠥⣏⠞⣥⢛⡬⢏⣿⣿⣿⣿⣿⡟⣶⡏⠀⡀⠁⠐⢠⡐⠌⢻⣿⣿⣿⠋⣀⠆⠁⠀⠂⠁⢘⣿⡜⣿⣿⣿⣿⣿⡟⢧⢎⡳⢎⠶⣙⠦⣏⣼⣿⣿⠃⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡷⣌⠻⣌⡻⣔⢫⡜⡳⣜⡹⢫⢻⡱⣙⣾⡇⠀⠀⠄⠡⣿⣿⣷⣾⣿⣿⣿⣶⣿⣿⡿⠀⠐⠈⠀⣿⢮⡱⢏⡻⢏⡳⣙⣎⠮⣕⡫⡝⣎⢳⡬⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡼⣙⠶⡱⢎⡳⣜⠳⣬⢓⡏⢧⡓⢧⢾⡇⠀⠁⠠⠀⠙⠛⠿⠟⠛⠛⠻⠿⢿⠛⠁⠀⠂⠀⢡⣿⢧⣙⢮⡱⢫⡕⣣⢎⡳⢎⡵⡹⣌⣳⣼⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⡭⢞⡭⢳⡱⢎⡝⢦⣫⢜⣣⠝⣎⠞⣿⣆⠈⠀⡐⠀⠁⡀⠠⠀⠐⠀⡀⠀⡀⠠⠁⠀⢡⣾⡟⢦⣋⠶⣍⠷⣸⡱⢎⡳⢭⠲⣝⡲⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⡜⣣⠝⣮⡙⡶⣱⢚⡬⣛⢬⡛⡴⣛⢿⣤⣤⣐⡀⠀⠄⠀⡁⠠⠀⡐⣀⣠⣴⡾⣟⠳⣜⡣⢞⡱⣎⢳⢥⡛⡼⣱⢋⠷⣎⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣿⣿⣿⣧⣻⠴⣙⠶⣡⢟⡲⢭⡲⣍⢳⡍⡞⡜⢮⡝⣻⢟⡿⢟⢿⠻⣟⢟⡻⡝⢮⡱⢎⡝⡦⣝⢣⢳⢎⡳⢎⡵⢣⢧⣫⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣧⣟⡴⢫⡜⣣⠳⣜⢣⡝⡺⣍⢳⡚⡵⢪⡼⣍⢮⣓⢮⡚⡵⣩⠳⣍⠯⡜⡵⢪⡝⣎⢮⡱⣫⣼⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣷⣧⣿⣬⣳⣜⡵⣊⠧⣝⡼⢳⡜⣜⢦⡝⡦⣝⡲⣍⣗⣎⣳⣹⣼⣷⣼⣾⣿⣿⣿⣿⠿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢧⡳⢭⡿⣧⣴⡾⢿⡻⣿⡟⠛⢿⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⠟⠉⠉⠙⠻⠿⣶⣤⣶⣶⡶⢶⢶⣾⣿⣧⣛⢧⣞⡿⣯⢝⡶⣹⣾⡟⠀⠘⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢟⡿⢻⣜⣿⠛⣻⣷⢫⠼⣿⣿⡁⠀⠀⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡳⡺⣜⡳⣎⢿⢿⡿⢯⢭⡳⣇⠯⣿⡆⠀⣻⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣷⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⡾⢷⣟⢮⢣⣝⣻⣶⣷⣩⣞⣽⠏⠀⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣎⡳⣮⡿⠈⠉⠉⠉⠁⠀⠀⢻⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀ ⢠⣤⣤⣤⣾⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣤⣤⣤⡄ ⠀⠀⠀⠀⣿⡇⠉⠁⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠈⠉⢸⣿⠀⠀⠀⠀ ⠀⢠⣤⣶⢿⣷⠖⠀⠀⠀⠀⠸⣿⡿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠲⣾⣿⢶⣤⣄⠀ ⠀⠀⠀⠀⠘⣿⣄⣀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣾⡛⢹⣷⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⣠⣿⠃⠀⠀⠀⠀ ⠀⠀⢀⣤⡶⠿⢿⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡿⠿⢶⣤⡄⠀⠀ ⠀⠀⠈⠀⠀⠀⠀⠙⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠿⠋⠀⠀⠀⠀⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣭⣿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣾⣿⣿⣿⣭⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⡟⠛⠛⢻⣯⣓⣾⡿⠀⠀⠸⣿⡝⡯⣝⠯⣝⢯⣿⡏⠀⠀⢻⣷⡭⣿⡟⠻⠛⢻⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⢻⣿⡿⠁⠀⠀⠀⠙⣿⣧⣝⣺⣭⣾⠏⠀⠀⠀⠈⢿⣿⡟⠀⠀⠀⠐⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⢶⣤⣤⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣤⣤⣶⠿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠿⠿⠿⠶⠶⡶⣶⣶⣶⡶⡶⠶⠶⠿⠿⠿⠛⠛⢻⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣀⠀⠀⠀⠀⠀⠀⠀⣸⣧⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⢶⣶⣶⡶⠾⠿⠻⠷⣶⣶⣶⠶⠶⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢣⢻⣿⣿⣦⡀⠀⣀⠀⣶⣆⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠉⠛⢛⠋⠉⠀⠀⠈⠉⠉⠳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣧⠗⢲⠏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣖⣤⣤⣤⣤⡀ ⠀⠀⢠⡾⠋⢀⠟⠀⠊⠀⢠⡄⠀⠀⠀⠀⠀⠀⢰⠛⠻⠿⠿⠿⠟ ⠀⢰⣿⠀⠰⠣⡀⠆⠣⡀⠈⠁⠀⠖⠀⠸⠇⢠⠊⠉⢆⠀⠀⠀⠀ ⠀⣿⢷⡀⠀⠀⠨⠶⠠⣝⠒⠢⠤⢀⣀⣀⣀⠄⠀⠀⠼⣦⠀⠀⠀ ⠐⣿⣇⠑⡄⠐⣄⠀⠁⠀⠢⠤⡀⠀⠀⣠⣃⢀⣠⠊⠤⢿⡀⠀⠀ ⠐⣿⡟⣆⡈⠲⢄⡁⠘⠤⣀⠡⣀⠀⠊⠀⠀⠑⠃⠘⠀⣼⠃⠀⠀ ⠀⠹⣇⣿⣧⠀⠀⠈⠒⠤⣀⣉⠛⠐⠂⠀⠚⠓⢃⣠⣾⡟⠀⠀⠀ ⠀⠀⠹⣿⣷⡆⡇⡀⠀⠀⠀⠀⠉⠁⠀⠈⣻⣿⣿⣴⠟⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣿⣾⣷⡄⠀⠀⠀⢀⠀⣠⣾⣯⣿⠿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠻⠷⣶⣦⣤⣠⣨⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢠⢠⠞⠀⢀⣾⣿⣿⣿⣿⣷⣟⣽⡄⠀⠀⠀⠀⣀⣤⣶⣾⣿⠿⠗⠚⠛⠉⠉⠉⠉⠉⠉⠉⠉⢙⡛⠛⠿⢿⣿⣿⣿⣽⡉⠉⠉⠹⠻⣆⠀⠀⠀⠀⠀⠀⠀⠂ ⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣯⣅⠀⣤⣶⣿⡿⠟⠋⠁⠀⠀⢀⡤⠖⠋⠉⠀⢀⡤⠖⠊⠉⠁⠀⠀⠉⠳⣄⠩⣟⠿⣿⣷⣄⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡤⠀⣼⡿⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡈⢣⡈⠙⢿⣷⣄⠀⠀⠹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡿⣶⣟⣵⣾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠙⣆⠀⠙⢿⣷⡄⠀⠹⡄⠀⠀⠀⠀ ⠀⣄⠈⢿⣇⡟⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣭⠟⠁⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠈⠂⠀⠐⣟⢧⡀⠀⢳⡀⠀⠀⠀ ⠀⠘⣆⠈⢿⣇⠈⢻⣿⣿⣿⣿⣿⣿⠿⠋⠀⡴⠃⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠘⡏⢳⡄⠈⣇⠀⠀⠀ ⠀⠀⠈⠆⠈⣿⣦⠤⣿⣿⡟⢋⡟⠀⢀⣤⡞⠁⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢹⡄⢻⡀⢹⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣇⠀⢺⡷⢀⡞⠀⢠⣿⠏⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠈⣇⠀⢳⠘⡆⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠘⠀⢠⢏⡟⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠘⣇⢣⡀⠀ ⠀⠈⢂⠀⠀⢸⣿⠀⢸⣏⡀⠀⡟⡼⠀⣰⠁⠀⢠⠇⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⡄⠀⢿⡄⠓⠀ ⠀⠀⠈⢀⠀⢸⣿⠀⢸⣿⣿⣾⣼⠇⢀⡇⠀⢀⡞⠀⠀⠀⠀⢀⡎⠀⠀⣰⠁⠀⢀⣤⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣼⠀⠀⠀⠀⢀⠀⡇⠀⢸⣷⡀⠀ ⠀⠀⠀⠈⣷⡾⣿⣏⣽⠿⢿⣿⣿⠀⣾⠀⠀⣸⡇⠀⠀⠀⢀⡟⠀⠀⡼⠁⠀⠀⣾⢯⠃⡾⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣿⢰⡆⠀⠀⢸⠀⠃⠀⢸⣿⣿⠀ ⠀⠀⢀⣾⣿⣷⠿⡏⠀⠀⠀⢻⠇⢠⠇⠀⢀⡾⠀⠀⠀⠀⡞⢀⣀⡾⠤⠤⢖⡾⠿⠛⡿⠗⢿⢦⠄⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡏⡌⡇⠀⠀⢸⠀⠀⠀⣼⣿⠃⠀ ⠀⠀⡾⠛⣟⣿⠀⠹⡀⠀⠀⢸⠀⢸⠀⠀⠀⡇⠀⠀⠀⣼⠛⢩⠏⠀⢀⣤⠟⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⣼⣁⣆⣿⢀⢿⡇⠀⠀⠘⠀⠀⠀⣿⠃⠀⠀ ⠀⠀⠻⡄⠘⠹⡇⠀⡇⠀⠀⢸⠀⡜⠀⠀⣼⢁⠀⠀⢰⡟⢠⠏⠀⣠⡟⠃⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⢠⣏⣼⡿⡟⡾⢸⡇⠀⠀⡆⠀⠀⠀⠃⠀⠀⠀ ⠀⠀⠀⢷⠀⠀⡇⠀⢹⠀⠀⢸⢀⡇⠀⢰⡿⠸⠀⠀⣾⢡⢆⣠⣾⣋⣤⣴⣤⣤⣔⠒⠀⢠⢿⡀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⣠⣾⣾⠟⢠⣽⠁⣾⠳⡀⢠⡇⢸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡄⠀⢐⠀⢸⠀⠀⣼⢸⠃⠀⢘⡇⡇⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡆⢠⠏⢠⢧⡆⢠⣿⠁⡄⠀⠀⠀⢀⣴⣟⣵⠋⢀⠟⡼⣼⡏⠀⠇⢸⠇⡸⠀⠀⠀⠀⠀⠀ ⠘⠀⠀⢸⡄⠀⢸⣄⣾⠀⠀⡇⢸⠃⠀⢸⣅⡧⠞⣋⣿⣿⣿⣿⢿⣿⣿⣿⣿⡇⠈⠃⠀⠀⣾⡜⢀⣾⡏⣰⠁⠀⣠⣴⣿⣩⣤⣤⣤⣬⣴⡷⣿⡇⠀⢰⡿⢀⡇⡼⠃⠀⠀⠀⠀ ⠀⠀⢠⠾⠃⠀⠈⠛⡞⠀⠀⡇⢸⠀⠀⠈⡇⡇⠀⢽⣿⣿⢻⣿⠛⠛⢻⡟⠛⠃⠀⠀⠀⠀⣿⣷⠏⡿⣱⠃⢀⡾⠻⣽⣿⣿⣿⣿⣿⢻⡟⠀⣿⠀⢠⢿⠃⢸⡇⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠳⣦⣂⣤⡴⢇⠀⢰⡇⢸⠀⠀⠀⡇⣇⠀⡼⠹⣿⡞⣿⣶⣶⣿⣷⡦⠀⠀⠀⠀⡸⢻⠃⢰⡿⠃⣤⣾⠁⣼⣿⣿⣿⣿⣿⡏⢸⡇⢸⠏⣰⠏⠈⠀⣸⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣷⡀⠀⠀⠈⠀⢣⢸⠀⠀⢠⡆⣿⡄⢸⠀⠈⠙⢾⣭⣭⣥⠞⠁⠀⠀⠀⠀⠁⢀⣴⡟⣱⣾⠅⡏⢰⣿⣿⣿⣟⠉⠉⢁⣿⢡⣏⣴⠏⢀⠁⠀⢺⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⠹⠦⣄⣀⣀⣾⢾⡆⠀⠸⣿⡇⢻⡜⣇⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠠⠀⢀⣾⠟⢁⠏⠀⠇⢿⣿⣿⣿⢟⡷⢀⣾⢿⢟⣾⣿⠀⢸⠀⠘⣞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⡏⢿⠙⡏⢸⡇⠀⡀⢻⠇⢸⡍⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠤⠋⠁⠀⠀⠀⠀⠀⠈⠻⠾⠾⠟⠁⠋⠀⢠⣾⣿⡇⠀⡜⠀⣆⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⡇⢸⠀⡇⢸⣷⠀⡇⠈⣸⡀⣿⣄⠈⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠀⢀⡇⠀⣻⣄⡁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⣿⢸⠛⡄⡇⠀⠛⣇⢸⡈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⡟⡟⣸⠀⢸⡇⢠⣟⠀⠹⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣧⣧⡴⠻⡸⠀⢷⢸⡀⠀⢸⡌⠇⠀⠙⢦⡀⠀⠀⠀⠀⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢳⡸⡇⣷⣹⠀⢸⡇⢸⣷⠀⠀⠉⢧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣆⡾⠋⠀⠀⢷⣇⠘⡎⣷⠀⠀⣷⡜⡀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠉⠁⠒⠒⠈⠁⠀⠀⠀⠀⠀⣀⣴⠞⠁⠀⠀⠙⢿⡀⡏⠀⢸⡇⢸⣿⠀⠀⠀⠀⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⣎⡜⣦⢧⠘⣇⠀⠸⡷⡁⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠞⠋⠁⢿⣇⠀⠀⠀⠀⠀⠹⡇⡀⣾⡇⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣞⣮⠻⣆⢻⣆⠀⢹⡀⢆⠀⠀⠀⠀⠀⠈⠑⢤⣀⣀⡤⠤⠒⠛⢉⣿⢻⣤⡄⠃⠈⢿⣆⠀⠀⠀⠀⢠⢧⢇⣯⣧⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡌⠞⢿⡆⠀⢧⡘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢹⠆⠹⣦⠀⠀⠈⢿⡢⢤⣄⡤⢋⣼⣾⠎⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡄⠇⠹⡆⠈⣷⣌⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⣾⢄⢀⣟⣧⡀⠀⠀⠳⠦⣤⣴⠿⠞⠘⣆⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢸⠀⠸⡄⢧⠈⠻⣧⣀⡤⢤⣀⣀⡀⠀⠀⠀⠀⠠⢠⡏⡈⠁⠈⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠇⠀⠷⢸⡆⠀⣤⠚⠛⠲⣤⣀⠉⠓⠦⠤⠂⣠⠟⢀⣠⠆⠀⠀⠻⠻⣴⠄⠀⠀⠀⠀⠀⠀⠀⠘⡟⣆⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⣴⣿⠫⡙⢧⡹⣌⢇⡣⡓⡜⣶⢛⡱⢊⣆⠳⣌⠲⣡⠚⡤⢓⣌⠲⣑⢎⡲⡙⢿⣌⡳⣍⡷⣩⢽⢛⣿⣿⣰⠢⣱⠀⠀⠠⢊⢕⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⢬⡁⠀⠀⠀⠀⢀⡜⣡⣳⢣⣕⠨⢙⠢⠯⣔⣣⡿⢡⠞⡰⢣⢌⠣⣌⠓⡤⢋⡔⢣⢌⠳⡌⢦⠱⣙⢬⡹⣷⠦⠗⢋⣰⢬⣿⢿⣯⣫⠥⣗⣒⣩⢜⣽⣿⣿⣿⣿⣿⠏ ⠀⠀⠀⠐⣎⠀⠀⠀⠀⢀⠏⡰⣵⢯⡟⡞⡽⣣⠮⡴⣨⣏⡘⠓⠪⠕⡇⢎⡱⠌⡓⢌⠣⠜⡡⠎⠱⠚⣈⢃⣁⣂⠴⡸⣷⣚⢏⢧⢏⡾⣟⣿⣇⠀⢀⣔⡵⠛⣾⣿⣿⣿⣿⢃⠀ ⠀⠀⠀⠸⡄⠀⠀⠀⢀⡞⢠⣿⡟⣾⢽⣙⠶⣥⢛⣴⣿⢌⡳⢍⡯⣹⣗⢢⢒⠲⣰⠢⢖⠲⡰⢍⣣⡟⣭⡳⡸⣌⢳⡱⢻⣯⣎⢯⡞⡵⣿⡿⣿⣶⡿⠋⠀⢠⣿⣿⣿⣿⡏⠄⠀ ⠀⠀⢀⠳⠀⠀⠀⠀⠘⠀⣼⣿⣻⣽⢧⣏⢿⣰⢫⣾⡗⣎⠵⣪⠷⣽⣿⢢⣋⠵⣢⠝⡬⢣⡝⣢⣽⢻⡔⣷⡱⢎⡧⣝⣣⣿⣞⢧⡻⣵⣻⣟⣿⣇⠀⠁⠀⠚⠿⣿⠏⠁⠀⡈⠀ ⠀⠀⣈⠇⠀⠀⠀⠀⠐⠁⣿⠿⣽⣾⣻⣮⢳⢧⣻⣿⠼⣌⡳⡏⡟⣿⢹⢞⡮⡱⢎⡞⡱⢭⢲⡥⡇⢻⡜⡿⣝⢧⡞⣭⣷⢻⣿⣏⢷⣳⣻⣿⣿⣿⠀⠀⠀⠀⠀⠂⠀⣀⡔⡠⠀ ⠀⠀⣞⠀⠀⠀⠁⠀⠀⠀⣿⠣⣿⣿⣳⢯⣻⢮⣽⣯⢷⣙⢾⠅⢟⣇⢀⣯⣷⡿⣳⠼⣙⢾⡭⢿⣧⣈⣟⣇⢹⣧⣛⡶⣽⣿⣿⣯⣟⣷⣻⣿⣿⡏⠀⠀⠀⠀⠦⠄⠒⠁⠀⠁⠀ ⠀⡘⠆⠀⠀⠀⠀⠀⠀⠀⣿⢰⣿⣿⣽⣯⣿⣳⢿⣟⣮⣿⡟⠚⢻⡿⠉⢹⣟⣷⢣⡟⣽⢺⣯⢿⠇⠉⢙⣿⡛⠳⣿⣾⣷⣿⣿⣷⣻⡾⣿⣿⣿⠁⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀ ⢀⠻⠄⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⣿⣧⣿⣿⣻⢿⣿⢿⣼⣀⠀⠀⢿⠀⠀⠘⡼⣿⡿⡼⣿⡿⣿⠀⠀⠀⠘⡄⠀⢸⣧⣟⣿⣿⣧⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠨⡝⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢿⣿⣿⡿⣿⣽⣻⣿⣿⣿⢿⣿⣿⣿⣾⣆⡄⠀⠈⢿⣿⣽⣧⠻⣢⣴⣾⣿⣿⣿⡿⣿⣿⣾⣿⣽⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀ ⠐⠁⠀⠀⠀⠀⠀⡀⠀⠀⠘⡀⢸⣟⢳⣿⣯⢿⣽⢿⣿⡇⠘⠉⣿⡟⣿⢿⠁⠀⠀⠀⠀⠙⣿⡀⠘⠋⢻⣯⢻⡏⡇⢸⡿⣸⣿⣿⣿⣿⡿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀ ⠀⡹⠀⠀⠀⠀⣾⠁⢠⡎⠀⠀⠀⣿⠻⣿⣿⣌⢿⣯⣷⡙⠄⢂⡑⠭⢊⡜⠀⠀⠀⠀⠀⠀⠀⠋⠀⠣⡘⠢⠋⡠⠁⠊⣰⣿⣿⢟⣿⣿⣥⠃⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡱⠀⠀⠀⡀⣿⢧⣸⣧⡀⠀⠀⠹⣿⣽⣾⢿⣷⣭⣻⢷⣄⠐⠈⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠁⢊⢀⣼⣿⣛⣵⣿⡿⣣⠿⠀⠀⠀⣸⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⢡⠃⠀⠀⢿⣾⠿⣯⢝⣫⣗⣶⣾⡿⢷⡙⣿⢿⣿⣿⣷⡈⠙⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⢉⣴⣿⣿⡟⢷⣽⣽⣋⣀⣀⣴⣿⠁⢀⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⡡⠒⠀⠀⠀⢈⣟⣾⣿⣿⣿⡿⠋⠀⠈⠻⠝⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣿⣿⣜⡯⢿⣿⣽⢫⣟⡿⡥⢴⣫⢞⠆⠀⠀⠀⠀⠀⠀ ⠀⢲⡈⡄⠀⠀⣟⡟⢹⣿⡿⢻⠃⠀⠰⠆⠀⠀⠀⠉⢻⡙⢿⣿⢿⡀⠢⣀⠀⠀⠊⠤⠀⠀⠨⠝⠀⢀⣠⠔⣾⣿⣿⡽⠋⡀⠊⠀⠈⢿⣿⡽⣾⣳⡽⡛⠧⠋⠀⠀⠀⠀⠀⠀⠀ ⠆⠀⠻⣜⠄⠀⢻⠀⠘⢿⠁⠨⠀⠊⠀⠀⠀⠀⠀⠀⠄⠱⠈⢻⡏⠎⠀⢹⢎⡷⡀⠠⣀⣀⠠⢀⡞⢧⣺⠀⣇⣿⠏⢀⠑⠀⡀⠀⠀⢈⠿⣟⣿⠻⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⡀⠱⣘⢂⠀⠈⠀⠀⠈⠢⠀⠄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⡨⡇⠀⠀⢸⠮⡜⣭⡷⣆⣠⡾⣥⢛⢦⡇⠀⠿⠃⠀⠜⠄⠀⠀⠐⠀⠈⢠⠟⠸⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠅⠀⠌⡍⡄⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠁⠀⠀⠈⡄⠀⢋⠀⡀⡇⠋⠉⠋⢘⢿⠀⢣⠨⢿⠵⣍⠾⠤⠤⠤⠃⡀⠀⠠⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠀⠈⢖⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⢁⢠⠀⠄⠀⠁⠂⡀⡠⠂⡆⠀⢠⠃⠈⠓⠀⠐⠀⠀⠀⢀⠈⢄⠠⠃⠀⠀⢀⠄⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠀⠀⢚⡜⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⢣⡌⠐⡡⢊⣡⠞⠁⠜⠀⠀⠘⠀⢰⠀⠘⡋⠖⡠⠀⠆⡐⣸⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡁⠀⠡⠀⠐⢢⢣⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠑⠀⠀⠈⡟⢀⠐⠈⠌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠉⠀⠁⠀⢀⠣⠀⠀⠀⡎⠀⠀⠀⠀⠘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠡⠀⢀⠀⠀⢹⠘⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠳⡄⠀⡡⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠠⢂⠃⡏⠀⠀⠀⢜⠀⠀⠀⠀⠀⢸⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠂⠀⠀⠀⢈⠇⡄⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠠⠠⠧⣈⣑⠒⠫⢃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡳⠤⠄⡀⠔⠡⠀⠀⢜⠂⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠀⠀⠀⠀⡞⢠⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠙⡍⠉⣭⠑⢪⣯⡄⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⢨⠈⠀⠀⠈⡆⠀⢠⠂⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⢒⡘⡄⠀⠀⠀⠀⠇⠀⠠⡀⠀⠀⠀⠀⠀⢫⠇⢄⣰⠎⢻⠣⢀⠀⠀⠀⠀⢀⠔⠁⠀⠀⡡⠂⠀⠀⠀⡜⠀⠀⠈⠀⠁⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀ ⠀⠀⠀⠀⠀⠀⠐⡆⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡷⠎⢸⡀⠀⠉⠐⢄⣀⣀⢠⣷⠀⠀⣀⠔⠀⠀⠀⠀⡐⠀⠀⡌⠊⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⢼⢰⠀⠀⠀⠀⠀⠄⠀⠀⡈⢀⠀⠀⢀⠐⠁⠀⠈⠙⣷⣄⡀⠴⢖⣎⣳⢞⠄⠘⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡆⣆⠀⠀⠀⠀⠘⡀⠀⠀⠀⠠⢀⢸⠀⠀⠀⠀⠀⠀⠙⠛⠹⣞⡩⢧⠃⡈⠀⠀⠀⠀⠀⠀⠌⠈⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣇⢹⡆⠀⠀⠀⠀⠃⠐⠀⢀⠬⠂⠁⡄⠀⠀⠀⠀⠀⣠⢖⡻⡔⠛⠛⠈⢀⡠⠀⠁⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⢰⠗⠀⠂⠀⠀ ⠀⠀⠀⢀⠀⠀⡀⠀⢼⠀⠘⡄⠀⠀⡘⠈⢀⠊⠁⠀⠀⠀⠘⡀⠀⢀⣠⠞⣥⢋⠶⡵⡄⠀⡠⠊⠀⡠⠃⢀⠐⢍⢰⡡⠥⠦⣄⠀⡀⠐⠠⠀⠀⠀⠀⠀⠀⠀⢠⡗⠦⠋⠙⠘⠉ ⠀⠀⠀⠀⠆⠀⠄⠀⢨⡇⠆⠸⠄⠀⠇⢀⢀⠄⠀⠀⠀⠀⠑⠑⠲⣆⢖⡲⢤⣛⡼⣑⡷⡀⠱⠀⡈⠀⠀⠈⠀⠈⡏⠨⠉⠀⠀⢂⠀⢼⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢣⠀⢈⠀⢠⢻⢸⠀⢡⠀⠸⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢁⠌⠁⠀⠀⠀⠈⢑⠐⢑⢄⠀⠰⠅⢸⠆⠥⠀⠀⠈⠄⠘⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠛⠛⠓⠲⢤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠉⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⠀⠀ ⠀⠀⠀⠀⢀⣠⠖⠋⠉⠉⠛⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣥⣶⠦⣄⡀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀ ⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⢀⣤⠞⣵⣛⡫⣹⠷⢦⡉⣷⣤⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀ ⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣠⠟⠀⠀⠀⠉⠛⠋⠀⠈⣿⣍⢻⣿⣶⠀⠳⣄⣠⣴⣶⣶⣶⣤⣄⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀ ⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡽⢻⣿⠇⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡇⠀⠀⣴⢤⣦⣴⡆⢴⣶⣴⣤⣶⡆⠀⠘⡇ ⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⣣⣤⡀⠀⢀⡴⢋⣥⣖⢻⡾⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣽⣿⢠⣿⣧⣼⣿⡿⣿⣯⣷⠀⢀⡇ ⠀⡇⠀⠀⠀⣶⣶⣶⣶⢲⣲⣶⣶⡆⠀⠀⠀⢸⠞⣩⠟⢃⡤⡸⡷⣫⣤⡭⢶⣇⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠋⠛⠙⠉⠋⠙⠙⠋⠙⠈⠃⠀⢸⠃ ⠀⡇⠀⠀⣶⣿⣿⣿⣿⣾⡿⢩⣿⣷⡖⠀⠀⢼⣷⣿⡻⡿⣼⣷⣽⣿⣿⣖⠀⢻⡇⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⡇⠀⠀⣿⣿⣿⣽⣿⡿⣿⣾⣿⣟⠀⠀⠀⣿⠻⣿⣿⣷⡛⠉⠀⢈⣽⣿⣴⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⢿⡿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀ ⠀⡇⠀⠀⠉⠈⠉⠉⠁⠉⠉⠉⠉⠉⠁⠀⠀⡏⠀⠈⠙⠻⠿⣶⣠⠎⢁⣿⣿⣿⣿⣿⡿⣏⠚⠛⠓⠒⠄⠈⠉⢻⠉⢸⡿⠋⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀ ⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢁⣹⠁⠀⠘⣿⣿⣿⣿⡏⢿⣿⡄⠀⠀⠀⠶⠆⠀⢨⣧⣞⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀ ⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⢀⣸⡖⠀⠀⠀⣿⣿⣿⣿⣧⠀⢿⣿⣶⣤⣀⣀⣀⣠⡾⢻⣿⣦⡀⠀⠀⠈⠙⣲⣦⣄⡀⣀⣠⠖⠋⠁⠀⠀⠀ ⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⣀⢸⣷⡆⠁⢐⣣⢶⣾⣆⣿⣿⣿⣿⣿⣧⢸⣿⣿⣷⣿⢻⣿⣏⢀⣿⣿⣛⣹⣷⡄⠀⠀⠋⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀ ⢰⣶⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣋⣸⣿⠸⣿⣇⡵⠋⠀⠈⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡾⣿⠛⣾⣿⣿⣿⡿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⢉⣽⣿⠉⣓⣲⢤⣤⣤⣶⣾⣿⣿⠿⢿⣿⣦⣿⡏⢧⠀⡐⡀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢠⣿⢀⣿⣿⡿⠕⠀⢻⣿⢠⣤⣤⣴⣶⣶⣶⣶⣶⣶⠆⠀⠀⠀ ⢸⣿⣿⡿⣿⣿⡿⠟⠻⣿⣯⡉⠈⠉⠻⣷⣜⣿⡟⢻⣿⠀⢳⡀⣳⡀⠀⣽⣹⢿⡿⣟⣿⣿⣿⣿⣿⣿⣬⣿⣿⢿⡟⠀⠀⠀⣸⣿⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡏⠀⠈⠙⠿⣷⡀⠀⠹⣿⡄⣤⣤⣾⡿⢻⣷⠸⣿⡀⠀⠻⣿⣽⣆⣿⣿⣿⣗⣀⠉⢻⣿⣎⡻⣦⣍⣂⡙⢷⣝⣿⣷⣀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⡇⠀⢿⣶⣶⡿⠟⠿⣿⢿⠇⠉⠉⠉⠀⠀⠉⠀⠈⠀⠀⠀⠹⣯⡙⣶⣤⣾⡿⠋⠙⣿⣿⣿⣿⣮⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠶⢦⣄⠀⠀⠀⠀⠀⣴⠟⠛⢧⣠⣶⣿⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡟⠦⠌⠛⠉⠉⠉⢹⠇⢠⣶⣼⣷⣞⢙⣧⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⠃⠀⠀⠀⠀⠀⠀⣿⠀⠈⢻⡃⠀⢸⡿⡄⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠘⠷⠖⠛⠛⠛⢿⡗⢋⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢻⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠾⣷⠆⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠐⢺⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢿⡦⠀⠀⠛⠃⠀⠀⢠⢶⣄⠀⠀⠈⠛⠀⠀⠀⣺⠓⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣖⡀⣀⣀⡀⠀⠈⠉⠉⠀⠀⣀⣀⣀⠀⣲⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⡆ ⢻⡈⠻⣦⣀⣀⣀⣀⣀⠀⠀⠀⠁⣴⠟⠉⠁⠀⠉⠛⢦⡀⢀⡴⠛⠉⠁⠈⠙⠻⣄⠀⠁⣀⣠⣤⣤⣤⣤⡤⠖⠋⣸⠇ ⡿⠳⣤⣀⡀⠀⠀⠉⠉⠉⠳⢦⣼⠃⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⠀⠀⠀⠀⠀⠹⣦⡞⠉⠀⠀⠀⠀⠀⢀⣠⠶⢻⡆ ⠻⣦⣀⠀⠀⠀⡴⠶⢦⡀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡴⠚⠳⡄⠈⢉⣀⣠⡾⠁ ⠀⠸⣍⣉⣁⡀⣇⠀⠀⠑⠀⢠⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢷⡀⠀⠓⠀⢀⡇⢤⣈⣭⠿⠁⠀ ⠀⠀⠀⠙⠷⠤⠿⠶⠦⠶⠞⠋⠘⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠈⠻⠦⠴⠖⠻⠶⠶⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⡀⢀⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⣀⣤⠶⠶⠶⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⠋⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⣴⣤⣄⡀⠀⠀⠀⠀ ⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⡄⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀ ⠀⠀⠈⠻⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢻⡆⠀ ⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⢀⡤⠶⠿⣿⣦⠗⠛⠒⣦⣀⠀⠀⠀⠀⠀⠐⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⡇⠀⢠⡇⠀ ⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠘⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣇⠄⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⠀⠐⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠹⣤⡀⢰⠞⠉⢳⡄⠠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠛⢶⣤⣀⣀⣀⣤⡴⠟⠃⠂⠅⠀⠀⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠠⡏⠀⠈⠓⡶⠊⠀⠀⠘⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠨⠨⠀⠰⣸⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣧⣀⣀⣠⡾⢦⣤⣤⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠐⠀⠠⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⢠⡿⠀⠈⠉⠁⠀⠀⠀⣀⣀⡀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢀⠁⠀⠀⠈⢿⡄⠀ ⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⡴⠒⠒⣞⣁⡠⠽⠭⢄⣈⣳⣊⡉⠲⣄⠤⣀⠀⠀⠀⠀⠀⢐⠠⠀⠀⠀⠀⠈⣷⠀ ⠀⠀⠀⠀⢸⡇⠀⡴⠋⢙⡵⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠳⢤⣀⣳⠤⢤⡀⠀⠨⡂⠀⠀⠀⠀⠐⢺⡇ ⠀⠀⠀⠀⢸⡇⡮⢇⡾⠁⢠⣶⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⢹⣄⡀⡂⠀⠀⠀⠀⠀⠈⡇ ⠀⠀⠀⠀⠸⣿⡁⣼⠀⠀⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠈⠳⣤⢹⢾⠀⠀⠀⠀⠀⠀⣟ ⠀⠀⠀⠀⠀⠻⡟⢿⠀⠀⠈⠛⠉⠀⠀⠀⠀⣤⠤⣄⠀⠀⠀⠀⠀⣸⣿⣿⣧⠀⠀⠝⣎⠻⡆⠀⠀⠀⢸⢰⡏ ⠀⠀⠀⠀⠀⠀⠱⣜⣆⡤⠦⠤⣄⠀⠀⠀⠀⠛⠒⠋⠀⠀⠀⠀⠀⢻⣿⣿⡏⠀⠠⠀⢸⣤⠇⠂⠀⢠⢄⡾⠁ ⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠐⣾⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡆⠀⢸⠃⡃⠁⠠⣠⡾⠁⠀ ⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⣼⣦⣤⣠⠦⢄⠙⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⡞⣡⣤⠾⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠸⣿⠉⠀⣹⣀⣙⣿⠏⠁⡽⠶⠤⣤⣤⣤⣤⣤⣴⡾⠅⠚⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⠀⠈⠛⣿⠿⣌⡝⠝⡍⣘⣧⣀⣀⣀⣀⣤⣴⣶⣾⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣳⡶⢻⠷⣮⣤⣤⣽⣥⣬⣭⣿⣿⢿⡖⠋⠉⠉⢳⡝⢧⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣠⢺⣥⣧⣽⢂⡄⠀⠓⠀⠈⢻⡄⠀⠀⠀⠀⣿⣭⣧⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣋⠴⢺⠥⠚⠁⠀⠘⠦⣽⡒⢤⣄⣀⣼⢳⣤⡀⠀⠼⠃⣠⣷⡗⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠯⠜⠉⡏⠀⠀⠀⠀⠀⡄⣧⠉⠙⠲⣾⣯⣯⣏⣳⣶⣴⣾⣻⣉⣽⣵⡦⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠸⠄⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣿⢄⠀⠀⠀⠀⠀⠀⠀⠉⢉⣽⡶⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠟⢦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⡀⠙⠒⠢⢴⣉⡦⠔⠚⠋⢸⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠦⠽⣉⣙⣟⠛⣛⠻⢿⠞⠿⡟⠿⣻⠛⣧⠀⠀⠀⠀⠁⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣉⣉⣻⣿⣃⠙⢍⣫⣁⠉⠉⠉⣉⣩⣿⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⣉⣉⣿⡀⠉⠛⠛⠧⠜⠛⠛⠛⠉⢡⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠾⠶⠶⠶⠶⠞⠳⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡶⠶⠶⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣐⣦⠽⢶⣚⡟⣖⣒⠶⢯⣴⣠⣤⠶⠶⢆⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⣰⠿⣫⡵⣞⡿⣯⢷⣻⡽⣯⣟⡿⣶⣏⠀⠀⠀⠀⢏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⣤⣤⣖⣀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⣴⠋⠉⠉⠛⢲⣴⡤⠾⣥⣻⣳⢿⣽⣻⡽⣯⣷⣿⣷⣯⣟⡳⣻⣀⡀⠀⣀⡼⠀ ⠀⠀⠀⠀⠀⠀⢀⡾⠛⠉⠀⠀⠀⠀⠉⠻⣶⡀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠧⠀⡰⠃⠀⠀⠀⠀⣯⠀⠀⠀⠈⠀⠈⠛⠙⣳⡿⣭⡶⣶⢮⣿⣎⡽⡏⣋⡘⠋⠉⠀⠀ ⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⢀⡟⠀⠀⠀⠀⠀⠘⠀⣤⡄⠀⢀⡀⠀⢀⣿⡼⣟⣿⣻⢿⡼⣿⠟⠛⠛⠛⢠⡀⠀⠀ ⠀⠀⠀⠀⢰⡟⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠬⣇⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠢⣾⣽⣻⡽⣾⣿⢿⢷⣽⣤⣀⠀⠀⠀⣷⠀⠀ ⠀⠀⠀⠀⣿⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⢌⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢞⣷⣻⡽⣿⢧⣾⣳⢷⡝⣆⢶⡶⢿⣄⠀ ⠀⠀⠀⢀⡇⠀⠀⠀⢠⡖⠛⢻⣄⡀⠀⠀⢀⣠⡾⠁⠀⠀⠀⠀⡴⠋⠉⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠾⠷⠟⢻⡽⣾⡽⣯⢧⣿⣯⣟⡷⣞⡆ ⠀⠀⣀⣺⣧⡀⣴⣾⣏⡴⠋⡼⠋⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠈⠳⣇⡀⢀⡀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠳⣷⢿⣿⣿⢿⡾⣽⣺⠇ ⢠⣼⠋⢀⣄⣉⣯⣷⣿⣶⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣔⠉⠩⣿⠒⠦⠄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⡻⢞⢯⣻⡽⠋⠀ ⡠⢨⠷⠶⢤⠾⣻⣭⠷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⣿⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢿⠀⠀⠀ ⢡⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⢹⡋⠹⡍⠉⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⣀⣀⣸⣃⣀⠀ ⣸⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠲⣤⡀⠀⠀⠠⣇⢘⣳⡤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⠉⢳⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⠈⠁⠀⣼⠒⠀⠊ ⢽⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠉⢷⡀⠀⢠⣟⠊⠭⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠚⠀⠀⠀⠀⠀⠀⠙⠟⠃⠀⠀⠀⢀⣀⣀⡏⠀⠀⠀ ⡸⣆⠀⠀⠀⡼⠃⢀⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⢿⠀⣸⠃⠀⠀⠀⢈⢿⠦⠖⠢⢄⡤⠒⠋⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣠⠟⠛⠛⠦⠀ ⠐⠿⣄⠀⢸⡇⠀⠈⢿⡿⠀⠀⠀⠀⠀⢴⠒⡄⠀⠀⠀⠀⠙⠉⠀⠀⣼⡔⠃⠀⠀⠀⠀⠰⡈⠀⢀⠠⡀⠄⠠⠄⠰⢈⣧⣄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣩⡾⢏⡀⠀⠀⠀⠀ ⠀⠈⠛⠧⣌⢧⡀⠀⠀⠀⠀⠀⠀⠀⠰⣌⣉⡠⠀⠀⠀⠀⠀⢀⡠⡞⠛⠁⠀⠀⠀⠀⠠⣡⠷⠲⣦⠑⡠⢉⠂⣼⡶⠛⠁⢸⠋⠈⢷⡶⣦⡴⠶⠒⠊⠙⠃⠁⠀⠀⠙⢶⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠛⠷⢤⣤⣤⣀⣠⣀⡤⠔⠢⣄⠴⠊⠙⠲⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣏⠀⠀⠈⠳⣆⠀⢀⣼⡄⠀⠀⢾⠁⠀⣿⡽⣷⢻⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢼⣃⡀⣠⢦⠶⠞⢤⡜⣱⢊⢧⡙⢧⡶⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠘⠙⣦⣀⣀⣠⣟⢿⣻⣟⡿⣶⣤⣳⠀⠀⣿⣹⣽⡾⢷⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⢸⣟⣿⣫⡃⠀⠀⠈⣿⠰⣋⢦⡙⢺⡄⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠈⠒⠋⢐⡿⢨⣟⡷⣯⣟⡷⣯⣟⡿⣿⣻⣟⣯⢿⣖⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡿⣞⣧⣳⣤⣤⣴⣷⣦⣌⣐⣴⣾⣟⣶⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⣹⢾⣽⣳⢯⣟⡷⣯⣟⣷⣻⣾⡽⠷⠾⠗⠛⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡔⡞⢸⡟⣯⣿⣽⣯⡟⣾⣽⢻⣽⢻⡞⣧⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠛⠛⢳⠛⢻⡟⠛⢻⠋⠉⠙⠉⠀⠀⠀⠀⠀⠀⣤⡞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⠋⠙⠛⠛⠛⠾⠵⢯⠽⢷⠭⢿⡽⠟⠽⠶⠚⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀⢀⡤⡤⢴⠛⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠲⣄⣴⣄⣠⣀⣀⢀⡀⣀⡀⣀⣀⣠⣀⣀⣀⡰⠞⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠉⠲⣲⡗⠒⠚⠓⠒⣞⠙⠋⠉⠀⠀⠀⣧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡇⠀⠁⠀⠉⠀⠹⣄⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣇⠀⠀⠀⢰⡏⠀⠀⠀⠀⢀⡴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠤⠤⠀⢀⣼⣤⡴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠳⣶⡶⠾⡷⣤⡤⡶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡿⠟⢿⣶⣤⣴⡾⠟⠛⠉⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣿⠋⠀⣀⣀⡙⣿⣇⣀⠀⠀⠀⢀⣹⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⠏⠉⠉⠙⠛⠿⣷⡾⠿⠛⠛⠋⠉⣹⡏⠀⢰⣾⢻⣿⡿⠟⠛⢿⣶⡿⠟⠛⣿⣷⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠈⠿⣿⡟⠀⠀⠀⠈⣿⣿⣦⠀⢠⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⣶⡿⣿⣄⣀⣀⣶⣿⣿⡿⠀⣼⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⣿⣍⣀⣠⣾⡿⢻⣧⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠀⠀⢻⣧⢀⣀⣀⣀ ⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠾⣿⡛⠉⠉⠉ ⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣠⠀⠀⢀⣀⣿⣧⣀⣀⡀ ⠀⠀⠀⣸⣿⣀⣄⣀⡀⠀⠳⣤⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⠙⠿⠃⣠⣤⣤⣿⣿⡉⠉⠉⠁ ⠶⠿⠛⠋⢿⡏⠉⠉⠀⠀⠀⠘⢿⣿⠇⠀⠀⠀⠀⢠⡶⠶⢶⡄⠀⠀⠀⠁⠀⠀⠀⢰⢿⣿⡿⣿⣿⣷⣀⠀⠀ ⠀⠀⠀⠀⣸⣿⣶⠶⠛⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠳⠶⠟⠁⠀⠀⠀⠀⠀⠀⢠⣿⡿⢸⣷⡦⣰⡏⠛⠛⠀ ⠀⠀⠰⠟⠋⠉⠻⣦⣄⣤⡆⠀⠀⠀⣴⡟⠻⠿⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣾⠁⢀⣻⣥⣿⣦⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⠟⠿⣶⣤⣤⣴⡿⠃⠀⠀⠀⢹⣇⣀⣀⣠⣤⣤⣤⣶⡾⣿⣻⢃⣴⠟⠉⠉⢸⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⢈⣿⠏⠀⠀⠀⠀⢀⣾⠟⠉⠉⣹⡿⠉⠉⢿⡼⣿⡏⢸⡇⠀⠀⠀⣼⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣀⣀⣠⣴⡿⠛⠛⠻⠛⠋⠀⠀⠀⠈⣿⡌⠉⠛⠻⣦⣤⡾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡿⠻⠿⣿⣧⣤⣀⣀⣀⣀⣀⣀⣀⣤⣶⠾⣿⣟⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⢠⠞⠉⠀⠉⠉⠉⠉⠉⠉⠉⠛⢦⡀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⣀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⡷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡿⠿⠶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣶⣶⣶⠶⠿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦⣤⣤⣤⣤⣬⣭⣿⣯⣥⣤⣤⣤⣤⣤⢶⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠄⣿⠂⠀⠀⠀⠀⢀⣠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣶⣦⣷⡾⠿⣿⣶⣶⣵⣾⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣶⣄⠀⢀⣀⣤⣤⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⣿⡿⠿⣿⣷⣶⣤⣀⣀⣤⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠙⣿⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠉⠙⠻⠿⠿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡿⠟⠹⣿⣇⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣀⣀⣀⡀ ⣠⣤⣤⣾⣿⣷⣦⣤⠀⠀⠀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠿⠿⣿⣿⡟⠛⠛⠛ ⠉⠉⠉⠉⣿⣿⠉⠉⠀⠀⠀⢾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⢠⣤⣿⣿⣅⣀⠀⠀ ⠀⠀⣀⣤⣿⣿⣷⡶⠆⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⢠⣶⡿⢷⣦⡀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠈⣻⣿⡟⠻⠿⠟⠀ ⠀⠀⠙⠉⠉⢻⣿⣦⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠾⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣿⣿⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣴⣿⣿⣿⣯⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⠛⠿⣿⡆⠀⠀ ⠀⠀⠀⠸⠿⠋⠁⠀⠈⠻⢿⣿⣷⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⣾⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀ ⠀⢀⣴⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠟⠛⠛⠛⠛⠛⠛⠛⠿⣿⣿⣷⣦⠀⠀⠀ ⣠⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣄⣤⣴⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶⣶⣤⣤⣄⣰⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⡀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⣀⣠⣤⣾⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣽⣿⣿⣷⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣴⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣶⣄⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟ ⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀ ⠀⠙⢿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠃⠀ ⠀⠀⠀⠉⠟⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡟⠏⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⣀⣤⠴⠖⠛⠛⠛⠲⢦⣄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⣠⡴⠛⠉⠀⢀⣶⣶⣦⡄⠀⠀⠈⠻⣦⡀⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⣴⠋⠀⠀⠀⠀⢈⣿⣿⣿⣟⠀⠀⠀⠀⠀⠙⣮⠙⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣤⣾⣿⡿⣿⣿⣷⣦⣄⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠻⠿⠿⠋⠀⠀⠉⠻⠿⠟⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣴⣶⣿⣿⣿⣿⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠉⠻⣦⣠⣶⣿⠿⠟⠻⣷⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⡟⠁⠀⠈⠉⠛⠿⣿⣾⣿⠿⠿⠿⠿⢿⣿⠃⠀⠀⠀⠀⠙⣿⠉⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⣠⣾⠟⣿⣶⠿⠿⣶⣄⣠⣤⣼⣿⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⢿⣾⡿⠁⠀⠀⠀⢻⣏⡁⠀⠈⠹⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣄⣀⣠⣼⣷⡀⠀⠀⣰⣾⠟⣿⡄⠀⢸⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠙⠻⠶⠶⣿⠛⠛⠛⠀⢠⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣤⣴⢿⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢸⣿⡀⠀⠀⠀ ⠀⣀⣠⣤⣼⣿⣤⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⠶⠾⣿⡿⠿⠿⠷ ⠈⠉⠉⠉⢹⣿⠉⠉⠀⠀⠀⢰⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀ ⠀⠀⠀⣀⣬⣿⣷⡶⠄⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⢀⡴⠶⣦⡀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠙⣿⡿⠿⠷⠶⠀ ⠀⠀⠈⠉⠉⠉⢿⣆⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⣤⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣼⠿⣿⣏⣤⡶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣽⡿⠛⠿⣶⡄⠀⠀ ⠀⠀⠀⠀⠿⠋⠁⠀⣈⣿⡏⠀⠀⣿⠟⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⠿⠋⠀⠀⠀⠀⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⡏⠁⠁⢠⠤⣄⠀⢀⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⡾⠿⣿⣿⣿⣍⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⠄⠘⠷⠋⠈⠙⣷⢻⣇⠀⠀⠀⠀⠀⢰⣿⠀⠀⠘⣿⡌⢻⣿⣦⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣾⠟⣿⡀⠀⣰⣦⣀⣴⡿⠂⠻⣷⣤⣤⣤⣶⡿⠃⠀⠀⠀⠸⣿⡿⠋⠉⠉⢻⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠛⠛⢿⣿⠹⣿⡀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⢸⣏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⢸⣿⣷⡘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⣼⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣶⠿⠋⠘⠿⣾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣶⡿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣀⣀⣀⣀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠛⠛⠛⠛⠿⠿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣀⡀⠀⠀⠀⠀⣠⣿⣄⠀⠀⠀⠀⠀⣀⣤⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠿⠟⠛⠛⠛⠛⠛⠻⠿⠿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠿⠛⠛⠛⠻⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀ ⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀ ⠀⡠⠊⠀⠀⠀⢀⡀⠸⣷⠀⠹⣷⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠙⢦⡀ ⠀⠀⠀⠀⠀⠀⠘⣷⡀⠙⣃⡀⠸⡿⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⣿⣧⣶⠿⠛⠛⠛⠛⠻⢷⣦⣄⠀⠀⠀⠀⠀⠙ ⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⠻⠃⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢀⣾⠏⠁⠹⣿⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣀⣴⡿⢿⣆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣰⣿⠇⠀⣠⣶⣶⣤⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣀⣴⢿⣿⠀⠈⠛⠁⢨⣿⠇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⣀⣀⠙⠻⠷⣶⣦⣤⣴⣶⠿⠛⠁⠸⣿⡄⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠰⠋⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⢃⠀⠀⠀⠀⠸⠀⠀⠀⠀⢀⣴⣶⣤⠀⠀⠀⠙⢿⣦⣄⣀⡀⠀⠀⣀⣤⣾⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡛⠻⣿⣆⠀⠀⠑⠀⠀⠒⠁⠀⠀⠀⣰⡿⠋⠀⣿⡇⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⢠⣿⠁⠀⠀⠀⡤⠂⠀⠢⡀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠙⣿⣦⣄⡀⠀⠀⠀⠀⣿⡇⠀⢠⣿⠃⠀⠀⠀⢸⠀⠀⠀⠀⢘⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⣀⣴⡿⠛⠉⠹⠻⢿⣶⣤⣀⡙⠿⠾⠟⠁⠀⠀⠀⠀⠈⠢⢀⣀⠠⠊⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡿⠋⠀⠀⢠⠃⠀⣠⣶⣏⠛⠻⢷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢡⠁⠀⠀⢀⠃⠀⢰⣿⣿⣿⣷⣤⣶⣾⣯⡙⠛⠿⠿⣶⣶⣤⣤⣤⣶⠾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣶⣤⣀⡌⠀⠀⠈⢻⠛⠛⠻⣿⣿⣿⡿⠁⡜⠀⠀⠙⣿⡄⠀⠀⠀⠀⣽⡿⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠈⠉⠛⠿⣷⣦⣤⣃⠀⠀⠀⢨⠛⠛⠁⡰⠀⠀⠀⠀⣿⡇⠀⠀⢀⣠⣿⡿⠀⠀⠘⠛⠛⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⣤⣀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠈⢹⣿⠿⣶⣦⣦⣀⠀⢠⠃⠀⠀⠀⡘⢸⡷⠾⠟⠛⠋⠁⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀ ⢄⠀⠀⠀⠉⠉⠀⠀⠀⠀⢻⣷⣤⣦⡄⢀⡀⠀⣿⡇⠀⣿⡏⠉⠛⠻⠷⣦⣤⣀⣰⣡⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠏⠀⠀⠀⠀⠀ ⠀⠑⢄⠀⠀⢠⣴⡟⠀⠀⠀⠙⠉⠹⠿⠿⣿⣦⣿⠃⠀⣿⣇⠀⠀⠀⠀⠀⠉⠙⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀ ⠀⠀⠀⠑⢄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠘⣿⣶⢿⣦⣠⣤⡀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠹⢿⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠄⠦⠠⠤⠄⠤⠠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⠀⠀⠀⠀⣀⣴⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⡗⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣷⣦⡀ ⠀⠀⠀⠀⠀⢀⢎⠎⠀⠀⠀⣠⣿⠛⢿⣿⣿⠿⠛⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣶⣤⣀⣠⠈⠙ ⠀⠀⠀⠀⠀⠈⠆⠀⠀⢀⣼⣿⣿⣷⠔⠋⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢈⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⣠⣴⣿⣄⠙⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡚⠛⢦ ⠀⠀⠀⠀⠀⢀⣠⣾⡿⠿⣻⣴⣾⣿⡿⣿⣿⣷⣾⣿⣿⡿⠋⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣤⣤⠀⠀⢠⣿⣿⣦⣄ ⠀⠀⠀⠀⠒⡩⠁⠀⠀⠀⣿⣿⣿⣿⠁⣿⣿⣿⣿⠟⠋⣀⡤⠔⠂⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⡟⠁⠀⢠⣿⣿⡆⠀⠉ ⠀⠀⠀⠀⣴⢇⠀⠀⠀⠀⣿⣿⣿⠳⢄⣿⣿⠟⠁⠀⠾⠋⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣐⡟⠀⠀⢀⣿⣿⣿⣷⠀⠋ ⠀⠀⠀⠀⡇⠈⣦⠀⠀⠀⣿⣿⣿⣀⣀⢸⡟⠀⠀⠘⢦⣱⣖⣶⣤⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠻⠃⠀⠀⣼⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠸⢥⡰⠁⠀⠀⢀⣿⣿⣿⡟⣙⠶⠇⠀⠀⠀⠰⢋⣤⡈⠙⢷⣄⠀⠀⠹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⠀⠃⠀⢀⣴⣿⣿⣿⣿⣷⢸⣷⠀⡀⠀⠀⠀⠘⣿⣷⠀⠀⠉⠀⠀⠀⠘⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⣼⣿⣿⡿⠹⣿⡆⠀ ⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣻⣿⣿⣷⠿⠖⡹⠀⠀⠀⠐⠺⠿⠔⠚⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠀⣀⣴⣾⣿⣿⣿⣿⣿⠇⢀⢹⣇⠀ ⠀⠀⢀⠴⠾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠏⠸⡀⣧⢹⡄ ⣤⡞⠁⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⡄⠈⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣧⠀⠀⠁⢹⡜⡄ ⣿⣿⣷⣶⣤⡀⢀⠾⠛⣿⣿⢿⡿⣿⢻⣿⣄⠀⢠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠙⣿⣿⣿⠉⠻⠷⣤⡀⠈⣷⠈ ⣿⣿⣿⣿⣿⣿⣷⣤⣀⡟⠁⢸⡇⣿⣾⣿⣿⡦⣀⠙⣿⣉⣳⠀⠀⠀⠀⠀⠀⠀⣠⡞⣿⣿⣿⡟⠀⠀⠀⠈⣿⣿⣄⠀⠀⠀⠙⠳⣝⡆ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⡇⣿⣿⣿⠏⠀⢨⣷⣭⡛⠃⠀⠀⠀⠀⡠⢴⣿⠟⢱⣿⣿⣿⠁⡀⠀⣀⡾⣿⠋⠙⠷⢄⠀⠀⠀⠀⠙ ⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⢀⣿⡿⠃⠀⠀⣾⣿⣿⣿⣦⣤⡤⠒⠉⠀⠀⠸⣦⣾⣿⣿⣇⣠⣷⣞⣿⠵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢸⡟⠀⡆⠀⠰⡏⠏⣿⣿⣿⣿⣷⡀⠀⠰⣄⠀⣽⠻⢿⣿⠿⠳⠿⡓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⠁⢀⠁⠀⠀⢿⣜⣿⡛⣿⣿⣿⣧⠀⠀⠈⠲⣁⠀⢸⣿⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⠄⠘⡜⡄⠀⠈⠻⣿⣿⣾⣿⣿⣿⣷⣄⠀⠀⠈⠳⡀⢿⠀⠀⢊⣀⡀⠤⠤⠤⠀⠒⠀⢀⣴⡆⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⢜⢆⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠈⠸⡀⠀⠛⠉⠀⠀⠀⠀⠀⣀⣴⣿⣿⠀⡀⠀ ⡿⠛⠉⢿⣿⠟⠁⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠈⠹⣿⡿⣿⣿⣽⣿⡿⠁⠀⠀⠁⠐⣶⣶⢶⢶⠶⠲⠈⡟⡿⡿⡷⣾⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠈⠀⣀⣁⡂⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠄⣠⠀⠉⢻⣶⣄⠑⢀⠀⠀⠀⠀⢀⠀⠀⣀⡀⠀⠀⠀⠀⠄⢠⣾⣄⠀⢼⣿⣿⣆⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⣸⣿⣶⣶⣼⣛⢿⡇⠈⠈⠭⣈⠀⠐⠢⠀⠀⠀⠀⠀⠈⠉⠀⢸⣿⡟⣿⣿⡟⡹⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠰⠹⣿⢳⠛⠛⡙⢮⠇⠀⠀⠀⠀⠀⢀⠠⠐⠀⠠⢀⠀⠀⠀⠀⠀⠻⢟⡴⣋⢀⡰⠃⠜⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡉⠳⠥⢢⡝⠁⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⠀⠀⠷⢂⠁⣰⡊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣵⡶⠶⠯⠂⠁⠀⠀⡠⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡈⢂⠀⠀⠀⡀⠀⠀⠀ ⠀⠀⡂⠢⠀⠀⠊⠇⠆⠁⠀⠀⠀⠀⡐⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠈⢂⠀⠀⠀⠀⠀⠈⠄⠀⠀⠈⠠⠂⠀⠀ ⠀⠀⠀⠀⠀⡀⢸⢈⣌⠁⠀⠀⢀⣠⣷⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣷⣼⣀⠀⠀⠀⠀⠀⠀⠁⡂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢁⠣⡜⢬⡂⢀⣴⣿⣿⡟⡀⣾⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣇⠘⣿⣿⣿⣷⣆⡀⠀⣠⠐⠀⠈⠄⠀⠀⠀⠀ ⠀⠀⠀⢀⡰⣡⢳⡜⢊⣴⣿⣿⣿⣿⠧⠀⣿⣿⡟⠋⣽⠤⣹⢠⠈⠛⣿⡧⠤⢘⣿⣿⣿⣿⣿⣦⡹⡇⣏⢧⡈⡄⠀⠉⠀ ⠀⠀⠀⡈⠀⠈⠁⣠⣿⣿⣿⣿⣿⣿⡉⠅⢿⠁⣇⠠⢰⡄⡀⢴⠔⡃⡇⠇⠑⢸⣿⣿⣿⣿⣿⣿⣗⣎⣫⡶⣽⣱⡀⠀⠀ ⠀⠀⡜⠀⠀⢀⣾⣿⣿⣿⣿⣿⣟⣿⣇⣲⣾⣇⠻⡴⡀⢷⡏⡆⠘⡰⣝⣢⣤⣠⣿⣺⣿⣿⠙⣼⣿⣿⣿⣽⣞⡷⢧⠀⠀ ⠀⢀⠀⠀⣰⣿⣿⣿⣿⣿⠏⣿⣿⡿⣿⣿⣛⣿⡇⠉⠚⠚⠯⠗⠚⠛⣿⣿⣿⣿⡿⣿⣼⡿⢿⣿⣿⣿⣿⣿⣿⠿⢸⣆⠀ ⠀⡆⠀⣼⣿⣿⣿⣿⣿⣿⠇⡿⣿⡘⢏⠛⠾⠉⡇⠀⠀⠀⠀⠀⠀⠰⡏⠑⠞⢩⡇⣼⡏⡱⣹⢻⣿⣿⣿⣿⣿⣷⡘⣿⠀ ⢰⢁⡞⡟⣿⣿⡿⣾⣿⢣⡆⡔⣧⠁⠙⠢⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡠⠘⠀⣰⢡⣓⣿⢣⣿⣿⣿⣿⣿⣿⣷⡇⡆ ⠈⣌⠳⣜⣿⣻⠇⠿⣿⢸⣿⣜⣿⣗⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡴⣝⣱⣾⣿⣿⣿⡿⠾⣟⣿⡿⠿⡻⡱⠁ ⠀⠈⢆⠀⢻⣿⣦⣓⣾⣸⣿⡿⠾⣿⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣼⣿⣿⠏⣽⣿⣯⣶⡳⣳⡛⢀⢴⠓⠁⠀ ⠀⠀⠀⢁⠄⡓⢿⣵⣿⣿⣿⡇⢀⢻⣿⣿⣶⣤⣄⣀⣀⠒⡀⡀⣀⣤⣴⣶⣿⣿⣿⢫⣼⣻⣿⣿⣿⡽⠏⠠⢋⠓⠁⠀⠀ ⠀⠀⠈⠐⢑⠐⠌⡒⡽⢿⢉⣷⣯⢞⣿⣿⣿⣿⡿⡟⢁⡜⠷⡍⠻⣹⣿⣿⣮⣿⢯⣦⣷⠟⡙⣻⢣⠖⢡⡁⠀⠀⠀⠀⠀ ⠀⠀⡀⠄⠂⠀⠀⠀⢹⡻⡾⣿⣿⣾⡝⣷⣹⣿⡿⢑⢠⠐⠀⠘⣿⣿⠏⠉⡻⣿⣿⣿⣿⢿⣿⣳⣋⠞⠁⠀⠀⠀⠀⠀⡄ ⠸⠀⠀⠀⠀⠀⠀⠠⢾⡹⣏⡿⣿⡿⡟⣷⣿⡍⠀⠀⠀⠑⠩⣠⢷⣻⣇⠀⣤⣬⠯⠉⠉⢿⣷⣿⣷⠄⠀⠀⠀⠀⠀⠀⠁ ⠀⢀⠄⠐⠀⠄⠴⠃⠔⡝⠉⠑⢻⣄⢎⡬⠚⠓⠀⠀⠀⠄⡀⢘⣾⣿⣿⣿⡿⣿⣦⣈⣵⡿⠿⢣⠉⡈⠂⠀⠀⠀⠀⠀⠀ ⠀⡁⠀⠀⣀⣰⠀⠸⣄⢧⠀⠀⢀⣭⡏⢌⠆⠀⠀⢀⠐⠶⣾⣿⣿⣽⣟⡜⢘⣏⠛⢛⣻⠧⡙⠂⠐⣔⡄⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠃⢄⡓⠾⣾⣷⣾⠟⢁⠈⠀⠀⠄⠂⠀⠈⠀⠙⣿⣿⣽⡏⣿⣿⣿⣌⠀⡏⠀⠀⢀⣆⠧⣜⡲⠄⠀⠀⠀⠀ ⠀⠀⠀⠐⠍⠀⠀⠈⠲⣽⠟⠁⠀⠀⠊⠀⠀⠀⠀⠀⠄⠌⠱⣸⢧⠌⠿⣜⣿⣾⣍⣗⣦⣤⣶⠿⠃⡘⡬⠳⠌⢆⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⡀⠀⠀⠀⣀⣠⣿⡟⣿⣷⡟⠋⠉⢿⣄⣠⣦⠀⠀⠀⠀⠀ ⠀⠀⢠⡾⠛⠷⠶⣶⠶⠟⣿⣯⢷⣿⣿⣷⣶⣶⣾⣿⡿⣿⣦⣀⠀⠀⠀ ⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣾⣽⣿⣾⣽⡟⡸⡹⢿⣿⠃⠀ ⠀⠀⠘⣿⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠙⠻⠿⠿⠻⣷⣀⣍⢯⣿⠀⠀ ⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⣦⣀⠚⣿⡏⠙⢬⣻⣦⡀ ⠀⣀⣸⣧⡤⢀⣴⡋⢣⠀⣠⠶⣚⣩⠦⠘⠦⠞⠿⢈⣿⠛⠛⢦⣿⠟⠁ ⠀⠉⢉⣿⡶⠈⠿⠓⠋⠀⠈⠙⠿⠛⢀⣀⠀⠀⣠⣿⠟⠻⣋⡞⣿⡀⠀ ⣠⡴⣬⣼⣿⣿⣧⣀⣀⣀⣀⣠⡶⢿⡋⠉⢻⣿⠛⣄⢦⢳⣧⠿⠟⠃⠀ ⢿⣤⣼⠟⠷⣾⡿⣿⠛⢻⣿⣿⣄⣨⣷⢶⡿⣿⡿⢾⣯⣿⠃⠀⠀⠀⠀ ⠈⠙⠉⠀⠀⣿⣁⠹⣦⣾⡍⠉⣿⡿⣭⣾⣷⠹⣧⠈⠉⠛⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠷⠋⠹⠃⠀⠛⠋⠉⠁⠁⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠉⠋⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⣿⡀⠀⠸⢿⣿⣿⢿⣿⡆⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠟⣛⠻⣛⢿⡻⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⢸⣿⣿⣿⣿⣅⠂⠈⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⠛⢉⠌⡐⠣⡘⢆⡋⠷⡹⢭⢻⡽⣻⣟⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠀⠀⠀⠀⢘⣿⢿⣿⣿⡗⠂⠄⢸⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣏⠳⠄⡍⠢⠐⢀⠁⡐⠂⢌⠡⠓⣌⠳⡸⡱⢎⡽⢭⣛⢾⡳⣟⡾⣽⣳⣯⢿⡽⣞⡷⣯⢟⡾⣝⢯⣻⡽⢯⣟⡿⣿⢿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⢿⡿⣿⢿⡿⣿⢿⡿⣿⠿⡿⢟⠿⡻⠿⠿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣟⡄⠂⢸⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⢾⣧⣶⣶⣿⣿⣿⣿⣿⣿⣶⡃⠆⡐⠀⢀⠂⢈⠀⠁⠂⡀⠁⢂⠱⠡⢑⠪⠜⡱⢊⠶⡙⠮⣝⢳⠻⣼⢫⡟⣽⡽⣞⢯⢾⡹⣏⢷⡹⣏⢾⡱⢯⣏⢿⡳⢧⠿⡼⣽⢺⡵⣫⣞⡵⣫⢞⡵⣫⢶⣩⡛⢶⡙⢧⢫⡜⣥⢫⡜⢬⡓⡜⢆⡛⠴⡉⢎⠱⣉⠒⠈⠹⢿⣿⣿⣿⡁⠀⠀⠀⠀⠀⣺⣥⣿⣯⡽⢃⠀⠸⡗⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⣿⡷⣿⣻⣟⡾⣿⣿⣿⣿⣷⡆⠠⠁⠠⠀⠂⠀⠁⠀⠀⠁⠂⠠⠑⢈⠐⡁⠣⢉⠒⣉⠓⡌⢎⠳⡡⢏⡜⢣⠝⣎⡛⣎⢷⣹⣎⣷⣹⢧⢻⡱⢎⡳⣝⢫⣛⡵⣋⠷⣙⡳⢎⡳⡝⣎⡳⡝⢦⢣⡝⡲⡍⢧⢳⡘⢦⢃⠮⡱⡘⠜⡢⣙⠢⠍⡂⢑⠠⠀⠂⠀⠈⣿⣿⣿⣷⢶⣤⣀⠀⠀⣿⣟⡛⠟⢻⡆⠄⠀⣽⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠽⣿⣳⢯⣟⡿⣿⣿⣿⣿⣇⡁⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠌⠐⡈⠡⠘⡐⢨⢑⠪⡐⢍⠜⠩⠙⢩⣤⣉⡃⠧⣙⢣⠳⣌⠳⡜⢲⡉⢞⡡⢃⡏⢴⡙⢆⠧⣙⢎⢣⡜⡱⢸⢡⠖⡩⢆⡍⢖⣡⡙⢬⡑⢄⠣⡘⠠⢈⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⢪⢿⡶⡄⢻⣿⡷⠏⠷⢆⢀⣸⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⣿⣝⣯⢾⣽⡿⣿⢿⣿⣿⡇⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠤⢂⣀⣤⣶⣾⣿⣿⣿⣿⣿⣶⣄⡂⠣⢌⠓⣌⠣⠜⢢⢍⠣⡜⢢⡙⠬⢎⡱⢊⠖⡬⢱⡉⢦⢋⡕⢪⠜⢢⠒⢌⠢⠘⠄⡒⠠⠁⠠⠀⠀⠀⠀⢸⣿⣿⣿⡽⣯⣏⣿⡄⣷⠀⠉⣿⠃⠀⠄⠀⢹⡃⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣫⢿⣿⡾⣟⡾⣽⣟⣿⣿⣿⣷⢼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣌⠁⠂⡁⣉⠢⠌⡑⡈⠡⢈⠑⡈⡐⠡⠘⡀⠡⠘⡀⠃⠌⠂⠌⠡⠈⠂⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣽⣛⣾⣽⡇⢿⡇⠀⠉⡇⠀⠧⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⣿⡟⣿⣿⣹⣟⣷⣻⣾⣿⣿⣿⣛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠂⠐⠠⠀⠅⡀⠂⠐⠀⠁⠀⢠⣄⠂⠀⡈⠐⠠⠈⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣞⣿⣮⢿⣙⢾⡇⠀⠀⢆⣰⣃⣀⡞⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡷⣿⣿⣷⣻⣞⣷⣻⢷⣿⣿⣿⣿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣠⣀⠀⠄⠀⠀⠀⠀⠘⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣻⣯⣞⣿⢧⢺⡅⠀⠀⢾⠀⠉⠙⠛⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⣟⣧⢻⣿⣷⣻⢾⣽⣻⢾⣿⣿⣿⣚⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀⠀⠀⣿⣿⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣳⢯⣿⣻⣾⣋⣿⡇⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⣜⣻⣿⡷⣯⣟⡾⣽⣻⣽⣿⣿⣏⡧⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠤⣈⠟⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⣽⢯⣾⢿⣽⢳⣿⡃⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⢮⣳⢿⣿⡷⣯⣽⣳⢿⣞⣿⣿⣿⡧⡅⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠌⠳⢌⠺⣤⢻⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣻⣽⣻⣯⣿⣯⢳⣿⠀⠀⢘⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢂⠀⠄⢸⣿⣟⣧⡟⣿⣻⢷⠾⣽⣻⢾⣻⣿⣿⡷⡍⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡋⠔⣈⠩⠳⡝⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠠⠘⡀⢣⠁⡙⠣⢿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⣿⣿⣿⣿⣳⢯⣟⣿⣷⡿⣿⣷⠀⡐⠨⢼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠄⣈⠈⣿⣯⢶⡻⣽⡿⣯⣟⡷⢯⣟⡷⣿⣿⣗⡧⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⠁⠚⠠⠐⡁⠙⣦⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⠀⡡⠐⡁⢂⠡⠑⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⢸⣿⣿⣿⣯⣟⡿⣾⣽⣿⣽⣿⡇⡐⢠⠃⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡡⢂⠄⢣⠹⣿⢯⣟⣽⣿⣷⣛⣾⣻⣽⣻⡽⣿⣯⡗⡡⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⡿⠸⠌⡇⠧⠀⠧⢠⡁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠼⡀⢑⡐⠠⢈⠄⡱⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢸⣿⣿⣿⢾⣽⣻⢿⣿⣿⣾⡷⢧⡘⢠⠓⡌⣡⡈⢄⠡⡐⣀⢁⡀⠀⠀⠀ ⢡⠂⡜⢠⢋⣿⣟⡾⣯⣿⣷⣻⢾⡵⣯⢷⣻⣿⣯⣿⠰⡡⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⡇⢳⠈⡄⠃⠄⣿⠀⡈⠅⡘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⠀⢂⠄⡃⢌⠢⡑⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⢿⣯⢿⣽⣻⣿⣷⢿⡟⣸⢁⠣⠜⡠⠅⣷⢒⠲⢡⠐⣆⣦⡇⠀⠀ ⠢⢡⠘⡄⠎⣿⣾⣽⡳⣿⣯⣟⡿⢾⣽⣫⢷⡿⣿⣯⢇⡱⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⡇⢻⡀⠒⢨⠀⠛⣁⠐⡀⠂⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢼⠐⡈⠰⠈⠆⡡⢒⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢾⣯⣿⣿⣯⣿⣿⢫⠔⣊⠱⡌⠥⣃⣭⣈⡇⢣⣍⠷⣿⡇⠀⠀ ⢃⠆⡱⢈⡒⢭⣿⡾⣽⣻⣿⡾⣽⣻⢾⡽⣯⣟⣿⣯⢆⡇⢌⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣧⡉⣧⠙⡐⢨⠍⢡⠂⡡⠌⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⠐⠌⡱⠈⢆⠱⠌⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣽⣿⣿⣽⣿⢂⠧⣠⢻⣍⣛⣯⡀⠙⢿⣦⣎⡽⣿⠀⠀⠀ ⢌⠢⡑⢢⠘⡆⣿⡿⣽⡷⣿⣿⡷⣯⢿⣽⣳⢯⣿⣿⡇⡞⢠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⠈⢇⠢⡁⢆⠡⢒⠈⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⢈⠒⡰⢁⠊⠤⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣻⢿⣿⣿⣾⣿⢧⡉⠖⣽⣻⣎⡿⣿⣷⣤⣶⡿⣦⣿⡟⠀⠀⠀ ⢌⠢⡑⠢⡑⡌⢻⣿⣽⣻⡽⣿⣿⣽⣻⢾⣽⣻⣿⣿⣯⠗⠦⡈⠀⠄⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠻⡛⠰⡀⠥⡈⢆⠡⡊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢥⠒⡁⢪⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣯⣿⣿⠦⣍⢿⣟⢷⡻⡼⢿⣿⢿⣿⣗⣿⡿⠃⠀⠀⠀ ⢌⠢⡑⠤⡑⢌⢺⣯⢷⡯⣟⣿⣿⢾⣽⣻⣞⣿⣿⣿⣿⣿⣶⣅⡁⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠱⣁⢒⠠⢡⠈⡶⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡒⢱⣢⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣾⣿⣿⣿⣻⡟⣿⡘⡖⢮⣿⢎⢷⡹⣳⣎⢻⢿⣿⣼⠁⠀⠀⠀⠀ ⢌⠢⡑⢠⠑⡊⡔⣿⣯⢿⡽⣾⣿⣻⣞⡷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡖⡈⠦⣑⢢⡏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣽⣿⣿⣜⠧⣘⣿⣏⣞⣣⡝⢶⣋⣿⣾⣿⢯⡇⠀⠀⠀⠀ ⡈⢆⠱⢀⡘⢄⡳⢰⣿⣟⣞⣿⣽⡷⣯⢿⡽⣿⣿⣿⣻⣿⣿⣝⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣥⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢻⡿⣜⢧⠻⣜⡻⣟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⡿⣹⢏⡾⣽⣿⢿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡷⣽⢋⣖⣯⣝⣞⣲⢣⢞⣣⡿⢯⣽⣟⣽⠀⠀⠀⠀⠀ ⠈⠂⠅⠂⡜⣢⣿⠐⣿⣯⢾⡽⣿⣿⣯⣟⣿⣻⣽⣿⣷⢸⡇⠣⡙⣌⠲⣉⢏⠻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⠻⣭⣷⣉⠧⡼⡭⢞⡵⣻⣿⣷⣌⡳⢎⡳⢮⡝⣾⡱⢏⡼⢎⡼⣍⠳⣏⣾⠟⣡⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡵⣯⣿⣉⣉⡙⣿⣿⣿⠞⠻⠷⣿⢏⣿⡟⠀⠀⠀⠀⠀ ⠁⠀⠀⠹⠧⣾⣻⣗⢻⣿⣾⣽⣿⣿⣷⣻⣞⣿⣿⠏⠁⢸⡇⡰⢡⠌⡱⣈⢎⡱⣱⢃⠞⣛⢟⡻⣟⠿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣟⢻⣙⡋⣖⢩⡓⡼⣿⣿⣼⣙⣣⣏⣶⣿⡿⣭⠲⣭⠳⣭⢳⡝⡶⡭⢯⡜⣋⠶⣉⣿⣾⣭⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣳⣾⣿⣿⡇⡟⣻⣿⣿⡁⠀⠀⣶⠟⣾⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢹⣇⣟⣿⣯⣿⣽⣿⠟⠛⠛⠁⠀⠀⢀⣼⢃⠡⣃⠮⠱⣌⠆⢧⣡⠏⡼⣈⠦⡱⢌⡓⢦⠓⡜⢦⠳⡜⢦⠳⡜⢢⢇⡚⣌⢇⠶⣉⢦⠓⡼⡰⣍⢻⠿⡿⠿⠿⣻⢭⠞⣴⢛⡖⡻⣔⣏⢾⡱⣍⠣⣜⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⣿⢿⣟⣿⡽⡍⢏⣵⣿⣿⣿⡇⠀⣠⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⣾⣯⣤⡷⣁⣋⠵⣿⣾⣿⣿⣯⣴⣭⣞⣱⢎⣜⣃⣛⡜⢦⡛⣜⢣⡓⣭⠓⢮⡑⣎⡚⣬⢃⢮⡙⡴⢳⡜⣫⢞⡱⢯⡹⡵⣪⢽⣘⠧⡞⡵⣍⡚⢦⣱⣮⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢷⣻⢾⡝⣧⠻⣌⠧⣿⠟⠷⡮⠾⠟⢠⣿⣿⡤⣿⣯⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣴⣧⣹⣜⣚⣖⢦⡣⡝⣻⢿⣿⣿⣿⣾⣾⣶⣧⢞⡧⢳⣎⠶⣩⢖⡹⢢⢝⢢⠝⢦⢋⡖⢭⡒⢧⢚⡵⢪⡝⢧⡛⡵⣩⠞⣜⣛⣼⣱⣾⣷⣿⣿⣿⡿⣟⣾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣾⣧⣿⣨⠘⠃⠀⠀⣿⣿⣋⣽⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢺⣿⣯⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣵⣮⣽⣭⣮⣧⣟⣬⢷⡼⣧⣽⣮⣷⣾⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣳⣟⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣡⣴⣟⣿⣾⡿⡿⠟⢦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⣻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡿⣿⣿⢿⣿⣟⣿⣟⡿⣿⣿⢿⣯⣿⣽⣿⣿⡿⣽⣻⢷⣯⣟⡷⣯⣟⣷⣿⣿⣿⣿⣿⣿⣿⡿⣽⡿⣿⣿⣿⣿⣿⣿⣿⠟⠃⣔⣪⣽⣿⣿⣿⡏⠀⠈⠀⠀⠉⠛⠿⣿⣶⣤⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⣷⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣞⣷⡿⣾⣽⣻⣾⢷⣿⣟⣾⣟⣷⣻⣟⣾⣟⣯⡿⣟⣿⣽⡿⣽⣻⣿⣿⡽⣯⢿⣽⣻⣷⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⢷⣻⢿⣿⣿⠽⠛⠉⢄⣲⣽⣾⡿⠋⠡⣿⡿⢽⣧⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⠄⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⡿⣞⡷⣯⣿⢾⡽⣾⣽⢾⣿⣽⣻⣞⡿⣽⣿⡽⣾⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠽⠿⠿⠿⢚⠃⣀⣠⣴⣿⠿⠋⠀⠀⠀⢸⣿⡇⠀⠀⠙⠢⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠛ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠿⣏⡞⣧⢫⣟⡿⣟⣶⡡⢒⡖⣩⢿⡍⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣿⣟⣾⣽⣷⡿⣿⣻⢾⣟⡷⣿⣿⣿⣟⣞⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⣤⡒⣪⣥⣶⣾⡿⠟⠉⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠉⠒⠲⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⢥⡛⢦⣙⢶⢫⣜⡳⣭⢻⣷⣡⠊⠴⣊⡝⣪⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣟⣾⣿⣿⣿⣿⡿⠿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣀⣶⣶⣶⣿⡿⠿⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⢩⡝⣹⢫⣵⡛⣚⡳⣌⣎⠧⣌⠷⣯⣟⠽⣿⣿⣿⣿⣽⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠈⠀⠈⠉⠀⣁⣌⣉⠉⠽⢏⣻⡿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠟⡰⡘⡖⡸⢄⡳⣯⡗⢃⠤⡄⢛⡮⣍⢟⣲⢻⠭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀⠀⠀⠀⢀⣠⡖⢚⡛⡛⢛⡝⣋⣤⣽⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰ ⠀⠀⠀⠀⠀⠀⢀⡾⢏⠱⣈⢅⡓⣌⠱⢎⡵⢮⡗⠢⡐⢐⠂⢷⡬⢣⡬⣏⢞⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠠⠀⠤⠴⠾⢻⣉⣛⡿⠗⢋⣄⣮⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿ ⠀⠀⠀⠀⠀⢠⣾⠋⡜⠒⠐⠊⡴⡙⢎⡜⣬⢣⢳⣄⠑⣊⣈⡜⡴⢣⢳⢎⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣍⣌⣱⣈⣇⣨⣉⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿ ⠀⠀⠀⠀⠀⠘⢻⡀⠽⠟⠨⡐⣄⠣⡜⡸⢶⡉⣦⠿⡷⣤⣭⢲⣽⣉⣾⣮⣋⣶⡟⠛⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠈⡙⠦⠬⣥⠼⡤⢯⠼⡭⢭⠭⠽⠻⠝⠋⠉⠉⠉⠈⠉⠉⡁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣤⣄⣀⣀⣤⣤⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣼⣓⠏⠋⠀⠉⣇⠈⠂⣨⣙⠉⠞⣴⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡦⣞⠹⢻⠯⠃⠀⢀⠀⠀⡇⠀⠀⠈⠽⠄⠀⠈⢫⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠛⠁⠀⠀⣩⠞⠀⠀⣴⡇⢠⣶⡀⠀⠀⠀⠫⡀⠀⠀⣞⠙⠿⣂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⠁⠀⠀⠀⡖⣥⡇⠀⠀⣁⠀⣼⡞⣧⠀⠀⠀⠰⡁⠀⠀⢈⠆⠈⠵⣂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢷⡆⠠⢄⠀⠀⣾⡽⠀⠀⢠⣟⢼⣭⡦⢤⡀⠀⠀⠀⣿⠀⠀⢸⢀⠀⠈⣳⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢺⣎⡅⡴⠚⠀⢰⡿⢷⠀⠀⢸⣟⢮⡋⠷⢬⣅⠀⠀⠀⣿⠀⠀⢸⢚⠀⠀⠹⣆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣍⠻⠀⣤⡇⠀⣨⣽⢷⠀⠀⣾⡯⠟⠠⣬⢽⣲⣂⠀⠀⡿⠀⠀⠸⢸⠀⠀⢸⡗⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⢻⡾⠀⠿⣇⡤⡮⣉⣃⣄⠀⢳⢻⠀⠈⠡⢶⣊⣾⣇⠘⠅⠀⠀⣼⡛⠀⠀⣸⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣦⡲⣆⡦⣵⣼⣣⣽⣽⣔⡦⡬⠽⣂⠀⢛⠾⢽⢽⣩⣣⠀⠀⠠⠮⠁⠀⠀⠏⣿⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡧⡫⣿⣯⡶⣷⢳⣷⣽⠛⠊⣾⠴⢴⡀⠀⣱⢻⢟⠋⠀⢰⠈⠁⠀⠀⢠⣦⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⡭⠏⠼⣿⢮⡥⠰⣿⣻⠇⠀⠀⠀⠀⠀⠀⠈⢽⣞⢂⣈⣩⠀⠀⢀⠀⢬⡪⢏⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⢀⣶⢏⡾⣗⡀⠉⠈⠀⠰⡆⠀⠀⠀⠀⠀⡲⠿⠹⣿⢄⠀⢀⡒⢮⢻⠅⣭⠧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣻⣏⣾⣞⠫⣿⢒⡇⣖⡀⠀⠀⠀⢀⠀⢀⠀⠀⠬⡁⡆⢠⣶⣿⡄⣨⠎⠋⡮⢧⢨⢟⡧ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠘⢻⡻⣼⡁⠀⣃⣶⣟⣿⡤⣄⡀⠈⠃⠘⠁⡘⢟⣻⣂⢰⢞⣯⡽⠅⡰⠋⠈⠀⠈⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠯⣄⢁⡿⠞⠁⠽⠷⠃⠉⠲⢴⢀⡦⣖⡟⠊⠀⠹⢵⣯⠎⠃⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⠋⠁⠀⠀⠀⣈⣵⠄⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡤⡴⡦⡶⣶⣏⠀⠀⢀⢀⣼⡓⠉⣝⡏⣯⣥⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣔⠋⣣⢷⣃⡷⣫⡏⠀⣀⠜⣜⡽⡷⣦⡹⢷⣏⢝⣪⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠼⣚⢿⡯⠲⢑⠿⠞⠉⢀⡰⡨⣗⣤⠻⠙⠉⠈⠙⠧⣘⢿⣋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠾⠳⠿⡿⡳⠐⠋⠉⠀⣠⣺⡾⡼⠗⠁⠀⠀⠀⠀⠀⠈⣵⣷⣣⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡎⡡⣵⠿⠁⠁⠀⠀⠀⠀⣮⡛⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⡏⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣖⡼⠁⢭⡀⢀⢀⠀⠀⣀⣶⣕⡴⠏⠀⠀⠀⠀⠀⠀⠀⢠⡝⢻⣜⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⣏⣀⠀⠈⠱⠹⠴⠺⠙⠀⣼⡻⠌⠀⠀⠀⠀⠀⠀⠀⣀⠛⢀⣶⠟⠀⠀⠀⠀

⢂⠁⠂⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠁⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣤⣤⣤⠄⠀⠰⣦⣤⣤⣤⣤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⢻⠍⠙⣋⣿⣿⣿⣿⢟⣻⡛⣟⣻⣿⣀⠀⣀⣀⣀⣀⣀⠀⣿⣿⣿⣿⣷⣿⣠⠀⠀⠀⠀⠀⠀ ⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣬⣦⣦⡦⣶⣼⣿⣯⣟⢶⡹⣮⡝⣞⣿⡿⠿⠿⠿⠿⠿⠿⠿⡄⠀⠄⢢⠀⣿⡧⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⡿⣻⢟⣿⣶⡿⣟⢿⣻⣿⣾⣷⡿⡼⡽⣿⣧⢋⠈⠀⠉⠉⡇⠌⠡⣐⠀⠈⠉⠛⣷⣶⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⡝⣧⣾⣼⣿⣟⢯⢶⣹⣿⣿⣿⣼⣷⣽⢿⠇⠞⠀⠀⠀⠀⠀⠘⠆⠀⠀⢀⡀⣭⣿⠿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣝⣳⣟⣿⣟⣿⣾⣷⣿⡟⠛⠛⠛⠛⢻⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣿⡇⡀⠀⠀⠀⠀ ⠈⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣉⣹⢿⣷⣮⣽⢿⡏⠭⠩⠹⠍⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⣿⠂⠀⠀⠀ ⡀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣿⣧⠜⠟⡛⢿⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⣾⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⡿⣿⡿⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⣿⣿⠿⣧⣤⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠂⣿⣇⡂⡄⡄⠀⢀⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣷⡂⡀⢀⢠⢦⣿⣿⠂⠛⠋⠁ ⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⢿⣿⠿⠗⢠⣤⣹⣌⠉⠀⠀⠀⠀⠀⠨⠡⠿⠁⠀⠀⠀⠀⠀⠙⣨⣄⣤⡀⡹⠿⣿⡿⢿⣴⣄⠀⠀ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠚⢛⣾⡧⢈⠓⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢚⡛⠫⢼⣷⠛⠃⠘⠛⠓⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠋⢿⠿⡿⣇⣠⣰⣠⣄⣆⣆⣆⣴⣰⣰⣠⣆⣆⣆⣆⣴⣠⣐⣸⡿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀ ⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠄⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⡴⣫⠉⠀⠈⢻⡗⣶⣶⣶⣦⣄⠀⢈⣷⣼⠋⠀⠉⠛⠶⢶⣤⣴⣿⣀⠀⠀⠀⠛ ⠗⠁⠀⠀⢠⣿⡞⠁⠀⠀⠙⢾⣷⣾⠋⠩⣿⠀⣤⠀⠀⠀⢿⣿⣿⣧⣹⢀⡀⣤ ⡶⢤⣀⠀⣼⣿⣠⣤⣴⣶⣤⣴⣿⠁⠀⣈⣥⣶⣶⣶⣤⣄⠰⠉⢻⣿⣿⠇⠉⠀ ⠀⠉⠹⣿⣿⣿⣿⣿⡿⣟⣿⣿⠿⣿⣾⠛⣿⣷⢻⣿⣽⣻⣷⣄⠿⠉⢹⠆⠀⠀ ⡀⠀⣼⣿⣿⡿⣼⣿⣿⣿⣥⣤⣾⣿⣿⣧⠈⢿⣿⣷⣿⠿⠟⢿⡆⠀⣿⠀⠀⢀ ⡇⢰⣿⣧⣤⣴⡿⠛⠉⠁⠀⠉⠙⢿⣿⣿⣷⣿⣿⣧⡀⠀⢀⣾⠁⣰⠏⠀⠀⢨ ⡇⠈⣿⣿⣿⠋⠀⢀⠀⠀⠀⠀⠉⢨⣿⣿⡿⣷⣿⣿⣿⣿⣿⣥⠾⠋⠀⠀⠀⢸ ⡇⠀⠘⢿⣿⣥⢤⠉⠀⠀⢀⣠⣴⣾⣿⡟⢻⣉⣿⡿⡽⣿⡿⢔⡠⡀⠀⠀⠀⠸ ⠂⠀⢀⡠⡛⠛⢛⣿⣾⡿⢻⣿⣿⡿⠿⣷⣾⠿⣯⣳⠿⣽⡇⠀⠀⠙⠲⢤⣠⢀ ⣀⠖⡌⠀⠀⠀⣸⣿⣿⣧⣫⣼⣧⠀⠀⣿⣯⣿⣷⣯⣿⣽⡇⠀⠀⠀⠀⠀⢀⣍ ⢮⣀⠀⠀⠀⠀⢻⣿⣷⣿⣿⣿⡿⡱⣾⣏⠀⣿⠉⠉⢉⣽⠁⠀⠀⠀⣠⢞⡝⠊ (your beatful just the way u are)

⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⡀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⠷⠿⠟⠛⢻⡿⠿⠍⣉⣉⣿⣿⣿⣿⣆⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣽⣿⡇⠀⢰⣾⣿⣿⣿⣷⣶⣄⠈⠛⠻⢿⣦⡈⠛⢿⣿⣶⣀⡀⠀⠀⠀⠀⠀⢿⡙⢤⣶⡄⠀⠀⠀⠀⠀⠀⠀ ⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⡟⢿⠁⡄⠀⠙⠁⠉⠙⢿⡝⢿⣗⠀⠀⠀⠙⢿⣶⣄⠙⢿⣿⣿⣶⣀⠀⠀⣖⡽⣒⣾⠿⣿⠄⠀⠀⠀⠀⠀⠀ ⣧⠘⢷⣆⡀⠀⠀⠀⠀⠀⢀⣀⢸⣿⣿⣿⡸⣹⠟⣧⠴⡞⠀⣷⠀⠀⠀⠀⠀⠀⠁⠈⢻⣆⠠⡀⠀⠈⠻⣿⣷⣼⣿⣿⣿⣿⣷⡀⠐⣧⡳⠃⣶⣤⡗⠀⠀⠀⠀⠀⠀ ⠹⣦⠀⠙⣿⡷⣶⠤⠶⠶⢿⢿⡿⣡⣾⠿⠉⠁⠀⠁⣴⡄⠀⣸⣆⠀⠀⠀⠀⠀⡀⡄⠸⢿⣆⡷⣶⡄⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠙⠲⢾⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢷⣶⣚⣛⣛⣠⠴⠞⣡⡟⣼⣿⣿⠀⠀⠀⣀⠀⣿⣟⣿⣿⣟⣦⡸⣬⣷⣦⣿⣧⣤⣸⣿⡀⠉⠉⠛⡄⢹⣿⡺⢿⣿⣿⣿⡿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠉⠀⢠⣾⣿⣼⣿⣿⣿⡄⢶⣷⣽⡶⣿⣿⣿⣿⣿⡜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⡂⠀⠀⠀⣿⡇⠠⢈⢿⣿⣿⣌⢿⡧⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⠈⢻⣿⣿⣿⢷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠛⢿⣿⣿⣿⣿⣿⣿⣿⡘⣿⡄⠀⡀⣿⣿⣼⣿⣌⢿⣿⣿⣾⣷⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡟⢸⡇⠒⣿⣿⣿⡇⣸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⢦⢒⣛⣿⣿⣿⣿⣿⣿⣇⣿⣀⠀⢹⣿⡿⣿⣿⣷⡼⣿⣿⣿⣿⡎⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⣾⠇⠀⣿⣿⣿⣿⡶⠻⣿⣿⣿⡿⠛⣩⠽⡏⠙⣿⣻⠉⢩⡍⠩⠝⢿⢻⢻⣿⣿⣾⣦⣾⣿⣧⢿⣿⣿⣏⢻⣿⢿⣿⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣧⣿⣆⣿⣿⡟⢿⣯⣀⠀⠈⠛⣓⠴⠊⠀⠀⢳⠀⡿⠠⠀⠀⠆⠀⠶⢿⡘⣸⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣟⣺⣿⣸⣿⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⣿⣾⣿⣿⣿⣟⣿⡄⠀⠀⠀⠀⢸⠀⢗⣠⣄⣤⣿⣴⣿⠽⣀⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢻⣿⡙⠳⣦⡀⠀⢠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⠹⣿⣿⣿⡿⣿⠻⣷⡀⠀⠀⣀⡼⣤⣸⣭⣽⣿⠶⠿⠿⠿⠟⠛⡿⣷⣾⣿⣿⣿⣿⣿⡿⣿⣇⣠⢾⣾⣯⣽⣿⣷⡒⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣆⠈⡿⣿⣷⢻⣿⣿⣇⣤⣪⠗⠋⠉⠉⠀⠀⠀⠀⠀⠀⣀⠤⠔⠓⠚⠻⣯⣿⣿⣿⡾⠃⣿⣿⣿⡿⠹⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣦⣷⠋⢻⡏⣷⣿⡿⠛⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠓⢂⣶⣶⣶⣿⣿⣿⣿⠟⠁⢸⣿⣿⠟⠀⠀⣿⣿⣿⣿⣿⣿⣟⢿⣿⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⣿⠟⠓⠚⢓⣴⠟⠁⠀⠀⣿⠁⠀⠙⢦⠀⠒⠢⠴⠲⠾⠿⣿⣿⣿⡿⠟⠋⠁⠀⢠⣿⡿⠋⢀⣠⠜⣸⣿⣿⣿⣿⣿⣿⡆⠛⣿⠀ ⠀⠀⠀⠀⠀⠀⠈⠳⣤⣴⣿⣿⢿⣿⣿⣿⢿⣿⣏⠀⠀⠀⠀⠹⣄⢰⣲⠀⡇⠀⠀⠀⠀⣠⣾⣿⠋⠈⠻⣄⡀⠀⠺⠛⠀⠀⠘⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢀⡝⣿⣿⡋⠙⢯⡳⢤⣀⣀⠀⠈⠙⠒⠊⠀⢀⣠⡴⠟⢻⣿⡿⣄⣤⣀⠀⠀⠀⠀⠀⠀⢀⣀⣂⣾⣿⣿⡿⠟⣋⣿⡿⠛⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣼⣿⣷⡓⠆⠀⠀⢈⡯⠛⠻⠷⠶⣶⣏⠉⠁⢀⣠⣿⡛⣷⡿⠛⠛⠛⠶⣤⡀⠀⠰⣿⡿⠿⠛⠛⠥⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡸⣿⡻⣿⣿⣿⣿⣷⣿⣷⡿⠇⠀⠀⠀⠀⣸⡿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡞⠛⠣⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣶⣾⡿⠛⠛⠉⠋⠀⠀⠀⠀⣴⣿⡟⠰⠁⠈⠉⠁⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⠚⣿⢳⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⡇⡏⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⢾⣇⣽⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⣧⣃⠀⠀⠀⠉⠓⠇⠀⠀⠀⠀⠀⠀⠀⠀⣰⢷⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢟⣷⡄⢀⠓⢲⡄⠀⠀⠀⠀⠀⠀⠀⢸⣧⠘⢿⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡎⠻⢚⣷⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠈⢻⣄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡾⢡⡿⣀⣞⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⠀⠧⣋⣹⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠘⣿⣽⣶⣶⡇⠀⠀⠀⠀⠀⠀⢰⣷⣿⢿⡿⠯⡼⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⠞⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠈⣧⠐⠈⡇⠀⠀⠀⠀⠀⠀⣾⠳⢻⢆⠘⡄⢱⡱⣻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠘⣦⣸⡇⠀⠀⠀⠀⠀⢰⣇⠀⢻⢯⣆⠘⡄⢳⡙⣟⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⢹⣻⠇⠀⠀⠀⠀⠀⢘⡏⢣⠈⠊⢿⣆⠰⡀⢳⣘⢮⢳⣄⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⢉⠤⠐⠋⠈⠡⡈⠉⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡀⢠⣤⠔⠁⢀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠈⠱⡤⣤⠄⣀⠀⠀⠀⠀⠀ ⠀⠀⠰⠁⠀⣰⣿⠃⠀⢠⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢞⣦⡀⠈⡇⠀⠀⠀ ⠀⠀⠀⢇⣠⡿⠁⠀⢀⡃⠀⣈⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⢢⠰⠀⠀⢺⣧⢰⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⠁⡘⠀⡌⡇⠀⡿⠸⠀⠀⠀⠈⡕⡄⠀⠐⡀⠈⠀⢃⠀⠀⠾⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠇⡇⠃⢠⠀⠶⡀⡇⢃⠡⡀⠀⠀⠡⠈⢂⡀⢁⠀⡁⠸⠀⡆⠘⡀⠀⠀⠀⠀ ⠀⠀⠀⠸⠀⢸⠀⠘⡜⠀⣑⢴⣀⠑⠯⡂⠄⣀⣣⢀⣈⢺⡜⢣⠀⡆⡇⠀⢣⠀⠀⠀⠀ ⠀⠀⠀⠇⠀⢸⠀⡗⣰⡿⡻⠿⡳⡅⠀⠀⠀⠀⠈⡵⠿⠿⡻⣷⡡⡇⡇⠀⢸⣇⠀⠀⠀ ⠀⠀⢰⠀⠀⡆⡄⣧⡏⠸⢠⢲⢸⠁⠀⠀⠀⠀⠐⢙⢰⠂⢡⠘⣇⡇⠃⠀⠀⢹⡄⠀⠀ ⠀⠀⠟⠀⠀⢰⢁⡇⠇⠰⣀⢁⡜⠀⡄⠀⠀⠀⠀⠘⣀⣁⠌⠀⠃⠰⠀⠀⠀⠈⠰⠀⠀ ⠀⡘⠀⠀⠀⠀⢊⣤⠀⠀⠤⠄⠀⠀⠸⠀⠀⠀⠀⠀⠀⠤⠄⠀⢸⠃⠀⠀⠀⠀⠀⠃⠀ ⢠⠁⢀⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠸⠀ ⠘⠸⠘⡀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⢁⣀⠃⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⢠⠀⠀⡇ ⠀⠇⢆⢃⠀⠀⠀⠀⠀⡏⢲⢤⢀⡀⠀⠀⠀⠀⠀⢀⣠⠄⡚⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀ ⢰⠈⢌⢎⢆⠀⠀⠀⠀⠁⣌⠆⡰⡁⠉⠉⠀⠉⠁⡱⡘⡼⠇⠀⠀⠀⠀⢀⢬⠃⢠⠀⡆ ⠀⢢⠀⠑⢵⣧⡀⠀⠀⡿⠳⠂⠉⠀⠀⠀⠀⠀⠀⠀⠁⢺⡀⠀⠀⢀⢠⣮⠃⢀⠆⡰⠀ ⠀⠀⠑⠄⣀⠙⡭⠢⢀⡀⠀⠁⠄⣀⣀⠀⢀⣀⣀⣀⡠⠂⢃⡀⠔⠱⡞⢁⠄⣁⠔⠁⠀ ⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠶⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⢶⣦⣄⠀⢀⣀⣤⣤⣤⣤⣼⠟⠁⢀⠀⠀⠈⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⡀⠀⠙⠿⠛⠉⠉⠀⠀⠀⠈⠀⠀⣿⣿⣦⡄⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⣠⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⡈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⢰⣦⠀⠀⠀⣠⡀⠀⠀⠻⠋⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠈⠉⠀⠀⠘⣻⣏⣀⡀⣀⣤⣤⣄⣼⡟⠀⠀⠀⠀⢀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣤⡀⠀⠀⠀⠀⠛⠉⠉⣩⣿⡿⣟⢿⣻⣿⣷⣄⣤⣶⡿⠿⠛⠋⠉⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⣤⣄⣀⡀⣀⣽⡿⠿⠻⢷⣦⣤⣤⣼⣿⢯⡳⣝⢮⡵⣚⢿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣿⠟⠉⠉⠉⠉⠛⠛⣿⡟⠉⠀⠀⠀⠀⣿⡟⢻⣿⣏⢷⡹⣎⣷⣿⣿⣾⣿⣿⣶⣦⣄⣀⣠⣤⣤⣴⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⣀⣤⡾⠏⠀⣾⣿⢎⡷⣹⢾⣿⣧⣿⣿⢻⡭⢯⡝⣿⣿⣿⢻⣝⣻⢻⢿⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠛⠛⠉⠀⠀⠀⢹⣿⡞⣵⢫⡞⡽⣻⣿⣏⢷⣚⢧⣛⠶⣿⣿⣷⣮⢧⣛⢞⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢿⣷⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣿⣾⡿⠿⠻⣿⣮⣓⣯⣼⣿⣿⣯⣿⡟⣮⣝⣾⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⣿⣯⡽⣭⢳⡝⣶⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣿⡿⠟⠋⠀⢹⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⣄⣠⣤⣤⣀ ⠀⠀⠀⠀⢸⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠛⢿⣿⠋⠉⠉⠉⠁ ⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀ ⣠⣤⣤⣶⣾⣿⣿⠶⠶⠆⠀⠀⠀⠀⣴⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠹⢶⣤⣴⠟⠁⠀⠀⠀⠀⠘⠻⣿⡿⠿⠟⠿⠖⠀ ⠙⠉⠁⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠻⣿⡿⠁⠀⠀⠀⠀⠀⠀⢀⣴⠶⢶⣤⡀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣼⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⣤⣿⣿⡶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣤⣦⡿⠃⠀⡂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⢿⣶⣦⣄⡀⠀⠀ ⠀⠀⠀⠛⠋⠉⠉⠻⣿⣄⣀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣦⣤⣀⣴⣾⠟⠁⠀⠀⠈⠙⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⠟⠉⠉⠙⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠛⠉⠀⠈⠙⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⡾⠟⠉⠀⣿⡇⠀⠀⠀⠀⠀⠈⠙⠿⢷⣦⣀⣀⣀⣀⣀⣀⣀⣄⣤⣾⠟⠛⠉⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣟⡛⠛⠛⢛⣛⣛⣿⣿⣄⠀⠀⠀⠀⠀⠀⣀⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢻⣿⣶⣤⣤⣤⣤⣶⣿⣿⣉⠩⡙⢛⠛⢫⠩⣉⣽⣿⣿⣷⣶⣶⣶⣶⣾⠿⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⢆⠢⢍⡹⡉⢏⣽⣿⢋⡙⠻⠿⡶⣷⢾⡷⠿⢛⠋⡍⢿⣿⣤⡩⢘⡐⢢⢡⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⣥⣮⣴⣷⣿⠿⠷⣦⣥⣭⣦⣵⣤⣦⣦⣥⣭⣼⣴⠾⠟⠻⢿⣷⣾⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⢀⣠⣴⣾⢿⡿⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⣿⢻⡝⣬⣓⢮⣕⢫⡽⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣟⠻⣏⢟⡻⣟⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣮⣷⡞⢱⡎⢳⡜⢣⣷⣭⣿⣷⣾⣿⣿⡟⣿⡟⣿⣿⣿⣷⣶⣦⣤⣼⣿⢱⡎⢻⣬⡏⣶⢣⣮⣽⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡟⠋⠛⠻⢷⣽⣣⣽⣿⢿⢻⢏⣏⡳⢳⡬⣓⠧⣝⠶⣱⢎⡳⣭⣛⠿⡿⣷⣿⣎⡗⣮⢜⡞⣼⣶⣷⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣇⠀⠀⠀⣠⣿⢿⣛⡬⢏⣮⢓⡮⣝⡣⢷⣩⣛⣬⠻⣬⠳⣝⢦⡝⣞⡱⣭⢛⡿⣿⣞⣼⡿⠋⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢿⣄⢀⣼⡿⣝⡺⢴⣋⠷⣬⣯⣶⡷⠿⠿⠿⠿⠿⠿⠷⠿⣾⣶⣽⣘⡳⣜⡳⢎⡽⣻⣿⡁⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢻⣿⡟⡵⢎⡵⣫⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢷⣯⣜⡏⢶⢣⠿⣿⣄⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⡟⡽⣜⣫⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣣⠻⡼⣹⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⡝⡞⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⢫⢵⡓⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡿⣜⡹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣟⢦⡛⢧⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⡈⣷⣿⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡎⣹⢇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣷⡝⣾⣟⠀⠀⢀⣿⣿⣿⣷⠀⠀⠀⣀⠀⠀⢀⡀⠀⠀⢠⣿⣿⣿⡆⠀⠀⠀⠈⣿⣞⡱⣎⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢿⣟⣼⣿⠀⠀⠀⠻⠿⡿⠏⠀⠔⠁⢠⣶⣶⠀⠀⠑⠀⠘⢿⣿⣿⠇⠀⠀⠀⠀⣿⢧⢳⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣞⣿⡀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣨⣿⣿⣄⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢫⢮⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢿⣿⣧⠀⠀⢀⣴⣿⢿⣷⣄⠛⢛⣿⣿⠛⠟⣴⡾⡿⣷⣦⠀⠀⠀⠀⣠⣿⢏⣳⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣷⣄⢸⣧⠈⣹⣾⠿⣟⡟⢯⡻⣟⢿⣿⣷⠛⠉⣹⡇⠀⣠⣾⣿⣭⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⠟⣿⡿⢎⡽⢲⢭⣓⠧⣝⣎⠞⣿⣷⣶⣿⣷⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⢠⣿⣽⣩⣾⣝⡶⡽⣞⣱⣾⡻⢴⣻⣏⠁⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠻⠛⠿⣿⡿⡟⢸⣧⡘⣿⣿⣿⣧⣿⣿⣤⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⢸⣟⡵⣻⢬⢷⣻⡟⠁⠀⠉⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠷⣶⣿⡿⣷⣷⣿⣾⢿⣿⣤⣄⣀⣀⣤⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠸⣿⣷⣿⡜⠁⠀⠈⢷⢮⣿⣽⡿⠉⠁⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠻⠛⠂⠛

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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣟⣿⡹⡝⣎⠱⠌⠂⠉⢉⣠⣴⡿⠛⠁⠀⠀⢀⣴⣿⣷⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡌⠻⣷ ⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⡽⡻⡝⢦⠓⠑⠈⢀⣠⣴⡾⠟⠋⠁⠀⠀⠀⠀⣰⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣁⠐ ⣿⣿⣿⣿⢿⣯⢟⡞⣏⠧⠓⠑⠉⠀⣠⣴⡾⠟⠋⠁⠀⠀⠀⠀⠀⠀⢀⣼⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂ ⠛⠋⠛⠙⠛⠈⠋⠘⠀⠀⣀⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣀⠤⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠒⠐⠉⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠐⠦⣤⢦⡄⣴⣾⣿⣶⣄⢀⣀⣀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡴⢤⣀⠀⠈⠳⣯⡔⢪⢍⡛⣿⣿⣿⡿⣷⣶⣦⣤⣀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣿⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⠀⠀⠀⠀ ⣿⢧⡸⢤⡀⠀⢻⣿⡄⡜⣠⢃⠤⣠⢇⡇⣟⠻⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⡀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢠⣤⣿⡧⠃⠘⠛⠘⡃⠀⠀⠀⠀ ⣿⣷⣻⢖⡅⠀⠈⠻⢿⣷⣄⠊⡔⠡⠎⡼⢌⢏⣿⣿⠁⡆⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⢰⣷⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣿⠋⠸⣿⡄⠀⢸⣆⢸⡄⠀⠀⠀ ⣿⣿⣽⣯⡞⣤⢠⣀⡀⠙⢿⣷⡌⠰⡈⠔⡩⢾⣿⠇⣼⠃⠀⠀⠀⠀⡀⠀⠀⠀⣿⠀⠀⠀⠀⣿⣷⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢀⡏⠀⠀⠀⢻⠀⠸⣿⡞⣷⠀⠀⠀ ⣿⣿⣿⣷⡿⣧⢳⣄⠻⡆⠀⠻⣿⣷⣤⡜⣰⣿⡟⢰⡗⠀⠀⠀⠀⢸⡇⠀⠀⠠⡇⠀⠀⠀⢀⣿⣿⣆⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⣠⣶⣾⣿⣶⣿⣧⣿⡇⠀⠀ ⣿⣿⣿⣿⣿⡿⣷⣎⢷⣀⠀⠀⠀⠈⠙⢻⣿⣿⠁⢸⠃⠀⠀⠀⠀⢸⡇⠀⠀⠰⣧⠀⡆⠀⢹⣿⠈⢿⣇⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀ ⣿⣿⣿⣿⣿⣿⣿⣞⡷⣎⢆⡀⠀⠀⠀⠀⣽⡟⠀⢸⠁⠀⠀⠀⠀⣿⠁⠀⠀⠀⣿⠁⡄⠀⢸⣿⠀⠈⢿⡶⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠻⣿⡟⣿⣿⣿⣿⣾⣿⣿⣦ ⣿⣿⣿⣿⣿⣿⣿⣽⣻⡜⢦⠐⣠⡎⠀⣼⣿⡇⠀⣸⠀⠀⣼⠀⢰⣿⣦⠀⠀⠀⣿⣧⣧⣀⣸⣿⣶⣶⣶⣤⣔⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⠛⢻ ⡿⠻⣿⣿⣿⣿⣿⢯⡷⣋⠖⣼⡟⢠⣾⣿⣿⠀⠀⣿⠀⠀⣯⠀⢸⣿⣿⣷⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡟⠀⠞ ⣧⣴⣿⣿⣿⣿⢯⣟⡼⢱⣾⡟⣠⣿⣿⣿⡟⠀⠠⣟⠀⠀⣏⠀⢸⣿⣿⣿⡆⠀⠸⣿⢻⣿⣿⣿⣿⣿⣧⣹⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠉⠀⡠⠀ ⣿⣿⣿⣿⣿⣯⡟⣞⣰⣿⡟⣰⣿⣿⣿⢿⡏⠀⠰⣿⠄⢠⣏⠀⠘⣿⣿⣽⣿⡄⠀⢿⣎⠻⣿⠿⠿⠈⠻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀ ⣿⣿⣿⣿⣟⡾⣙⣶⣿⠋⣴⣿⣯⣿⡏⣼⡇⠀⠰⣿⣇⢸⡷⠀⠈⣿⣿⣷⢹⣿⡄⠀⢻⣦⡙⣷⡀⠀⠀⠘⠻⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀ ⣿⣿⣿⣯⡟⡼⡱⠟⢁⣾⣿⢿⣿⡏⠀⣿⡇⠀⠐⣿⣿⡄⣿⡀⠀⣻⣿⣿⣦⠙⣿⣄⠀⠙⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⢯⠳⡙⠎⠱⠁⢀⣾⣿⢏⣿⡿⣿⡄⣿⣧⠀⠀⢸⣿⣧⣻⣇⠀⢸⣿⣿⣷⡌⢚⣿⣷⣀⣼⠿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⠀⠀⣴ ⠛⠌⠣⠑⠈⠀⠀⣾⡿⢣⣿⣿⢳⣿⠇⣿⣷⠀⠀⠸⣿⣿⣿⣿⣄⠀⣿⣿⣻⣷⠈⣿⣿⡿⠏⠀⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⡼⠏ ⠀⠀⠀⠀⠀⠀⡜⠋⢀⣿⡿⣳⣿⣯⠀⣿⣿⠀⠀⠀⣿⣇⠛⣿⣿⣤⣼⣿⣿⣿⣾⠿⠛⠀⠀⣸⡿⠙⠛⠻⢿⣶⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠀⠀⢠⡄⢲⠁⠠ ⠠⢄⠠⠀⠀⠀⠀⠀⣾⡟⢱⣿⡿⡧⣘⣿⣿⣧⠀⠂⠼⣿⣄⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⣠⣿⣿⣷⣄⡀⠈⠘⠿⠟⠿⠿⣿⣶⣶⣤⣄⣀⣠⣴⠾⠉⠀⠀⠀⠀⠀⡘⢂⡜⠁ ⠘⠀⠂⠀⠀⠀⠀⠘⣿⠀⣾⣿⠁⣿⣽⣿⣿⣿⡇⠈⡄⢻⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⢹⣿⣷⠀⠀⠀⠀⠀⠛⠉⣿⣷⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠒⠙⠀⠀ ⠈⠄⠀⠀⠀⠀⠀⠈⠁⢀⣾⠇⠀⣿⣷⣿⣿⣿⣿⡔⡀⠂⣿⣿⣍⠉⠛⠉⣉⣁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣭⣍⣀⡀⠀⠀⠀⠀⠀⠿⣿⡄⠀⠀⠀⠀⠀⠀⢀⠠⠂⠁⠀⠀⠀⢀ ⠨⠀⠀⠒⠀⠂⠰⠀⠀⢸⣿⠀⠀⣿⣯⣿⣿⢻⡝⢿⣦⠁⠘⣿⣿⣷⣾⣟⣛⣛⣛⣩⣭⣽⣿⣿⣿⣭⢯⣛⠟⡿⢿⣶⣤⣀⠀⠀⠀⠈⠻⢦⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⣸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⣿⣧⣿⣿⡟⣿⡈⢿⣧⡒⣼⣿⣿⣿⢿⣿⣿⣿⣿⡿⢿⣿⡟⢧⡻⡹⣌⠾⡰⣯⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟ ⠄⠀⠆⣀⠀⣤⠁⠀⠀⠀⠀⠀⠀⢿⣷⣿⢻⣇⠹⣇⠀⠻⣿⣜⢿⣿⣿⡞⣼⢶⡹⢶⣙⣯⢟⡜⣧⢳⡱⣎⣷⣿⣿⣿⣿⣿⣿⣷⣀⣠⣴⣾⣷⣶⣦⣀⠀⠀⠀⠀⠀⠀⣴⣿⣷ ⠆⠀⣣⠽⠋⠶⠀⠀⠀⠇⠀⠀⠀⠸⣿⣟⠀⢻⠆⢻⣦⠀⠈⠻⣮⡻⣿⣿⢮⡷⣛⣧⢿⣟⣮⣝⢶⣫⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠀⠀⣠⣾⣿⡿⢁ ⠇⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⢻⣇⠀⠀⢻⣿⣦⣛⢿⣟⣧⡟⣿⣿⣷⢯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣽⡿⠋⠀⢠⣾⣿⣿⠏⣰⣾ ⡇⠀⡐⢧⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠹⣧⡀⠀⢿⣿⣿⣿⣞⣷⡿⣽⣿⣿⣟⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⣿⢿⣯⣾⠿⠋⣀⣴⣾⣿⣿⡟⣡⣾⣿⣿ ⡽⠀⢱⢊⣟⣧⠄⠀⠀⢀⠀⠀⠀⣠⣿⡀⠀⠀⠀⠀⠀⠀⠙⢿⡀⣿⣿⣿⣿⣿⣟⣿⣟⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⣿⣾⣶⣶⣿⣿⣿⣿⢟⣳⣾⣿⣿⣿⢿

objection the meaning of nsfw goes from nudity to gore and here on this website yes there is nsfw. but you spreading awareness more than people sharing these so called nsfw thing is ruining the website more than so called "thorny" people, and to me in my eyes this is an over exaggeration. as i said at the top of this, a woman in a bikini will not damage a nine year old as it is not entirely nsfw or doesn't have any nudity. yes sure it is meant for sexual purposes but you really can't do anything about it put it in a 3 word sentence. if a bikini counts as nsfw then so does swearing. -Kage ✮˚. ᵎᵎ 𖦹彡⋆｡˚ 𝐄𝐍𝐃

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⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⠂⠂⠠⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⢀⡀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠁⠂⠄⠊⣑⡯⠎⠈⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠀⠄⠀⠈⠀⠀⠁⠀⠈⠀⠠⠈⠆⢠⠒⠤⠁⠒⠀⡤⠄⠠⡀⡄⠄⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣊⠢⡄⠀⠀⠠⣋⠈⠄⠀⢀⠁⠄⠀⠁⠠⢁⠀⠀⠀⠀⠀⡀ ⠀⠀⠐⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⣉⡥⠀⠁⠀⠀⠠⠀⠀⠀⠀⠀⠠⠁⠀⠀⠈⠄⠀⠀⠀⡀⠀ ⠀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠌⠆⢷⡓⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠅⠀⠀⡀⠀⠀ ⠀⡀⠀⠀⠀⠀⢁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠖⠀⠀⠉⡀⡀⢁⠐⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠄⠂⠐⠀⠀⠀ ⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⢀⠈⢀⠀⠀⠀ ⠀⠀⠂⠀⠀⠀⠀⠀⠀⠄⠅⠀⠀⠀⠀⡀⠀⡁⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⢀⡀⠈⠀⠀⠀⡀⠀⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠲⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠁⢀⠀⢀⢀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠀⠀ ⠀⢀⢔⠦⡂⢄⠀⠀⠀⠀⠀⠁⠂⠄⠈⠀⠀⢆⠄⠀⠀⠂⠈⠠⠐⠀⡀⡂⡦⢆⠂⠠⢄⡂⠄⠤⠀⢄⢀⠀⠀⠀ ⢀⠁⠀⠀⠅⠨⠀⠀⠀⠀⠀⠁⣀⠄⡐⠁⠀⡀⠀⠀⠃⢀⠀⠀⠁⢀⠁⠀⠀⠀⠡⠰⠀⠄⠀⠀⠀⠀⠀⠠⢁⠀ ⠑⠀⠀⡅⡂⠠⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠀⠀⠄⠐⠈⠄⠀⠄⠀⠂⠂⠁⡄⢀⠈⠀⠀⣘⠀ ⠈⠄⠀⠚⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠒⠀⠀⠀⠬⠀⠀⠘⠀⠀⠀⠈⠀⠁⠁⡀⠀ ⠀⠀⠁⠁⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠀⠉⠄⠀⠀⠠⠠⣔⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠁⠀⠄⠀⠀⠀⠈⠀⠁⠊⡘⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠈⠀⠄⠀⠄⠐⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⢀⠀⢀⠀⠀⡀⠂⠀⠠⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⡿⣟⣿⣻⣟⣿⣻⣟⢿⣽⣻⢽⢯⡟⡿⣽⢯⣟⠿⣽⣻⡽⢯⣟⣯⣟⢯⣟⡿⣽⣻⣽⢻⣯⡟⡿⣽⢯⣻⡝⣯⢽⣩⢏⢮⡱⢎⢲⡑⠆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣽⣫⢿⣹⣝⡺⡔⢢⠀⡀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⡾⣟⣯⢿⣻⣞⣷⣻⣞⡷⢯⣻⠶⣏⢿⡺⣽⣹⡞⣽⣚⡟⣧⢷⣛⡿⡼⢶⣫⣟⡾⣽⣳⢯⣞⡿⣶⣻⣽⣳⢯⣷⣹⢧⡻⣜⣚⢦⡙⢮⡱⢬⡙⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣻⡜⣧⡙⢆⡡⢀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⡿⣯⣟⣿⣽⣻⢷⣻⣞⡷⣯⣻⢏⣷⢿⣿⣾⣷⣿⢯⣽⣝⡛⠾⣧⣟⡼⢳⡝⣯⢳⡞⣽⠾⣵⣻⢾⣽⣳⡟⣾⡽⣳⢧⡟⣧⢻⡼⣩⠶⣙⢦⠳⡌⢞⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⢻⡴⣩⠦⡑⠂⡌⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣿⣟⣿⣽⣟⣾⣳⢿⣯⢷⣯⣟⣷⣯⢿⣭⡟⢯⣽⢃⢆⢺⣴⣊⠙⢦⡀⠈⠙⠧⣞⢌⡳⣹⢧⣛⠷⣯⣻⢶⣯⢟⣷⣻⡽⢯⡽⣝⣧⢻⣥⢻⡜⣎⢧⡙⣎⢆⣿⣿⣿⣾⣿⣟⣿⣿⣿⣿⣿⣿⢿⣻⣾⢯⣿⡱⣏⠼⣁⠒⡈⢄⠂⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣾⣟⣷⣟⡿⣾⣽⣷⣻⣟⣾⣻⣾⣿⢿⣸⣿⢫⢼⣷⡏⣷⡾⠟⠏⠃⠀⠀⠑⢆⠀⠀⠈⠳⣔⠱⢮⡝⣯⢳⣏⡿⣞⡿⣞⣷⣻⢯⣟⢷⣭⣳⢎⡷⣚⡼⢢⡝⡜⢮⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣟⣮⠷⣭⢻⡔⣫⠔⣊⠔⡁ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⣟⣷⣿⣻⣾⣟⣿⢾⣳⡿⣞⣷⣿⣿⣟⢣⣾⡏⢆⣿⢼⡇⠋⡁⠀⢸⠠⠰⡀⡀⠀⢢⠀⠀⢂⠈⠳⣜⠺⣵⡛⣞⡽⣯⢿⡽⣾⣽⣻⣞⡿⢶⣫⢟⡼⣣⡝⣧⡝⡞⣥⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣳⣛⡾⣵⢫⡖⣍⠲ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣿⡾⣟⣾⣟⡷⣿⢯⣿⣻⣽⣿⣿⣿⣿⢏⣾⣿⢘⡞⡽⢸⢣⠀⠇⠀⠀⡆⡇⣷⡈⠀⠀⢣⠀⠀⢠⠘⢿⣧⠳⣝⣎⡳⣏⡿⣽⣳⢯⡷⣯⣟⣯⢯⣟⢾⣱⣛⢶⡹⣝⢮⡳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣯⢷⣻⡜⣯ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⡿⣯⣷⢿⣟⣿⢾⣿⣻⡿⣽⣿⣿⣿⣿⣿⡿⢎⣿⡟⢸⢡⣷⠈⣇⠣⣀⡃⠀⣧⢧⡛⠻⣦⡀⠄⢇⠀⠀⢆⠈⢿⣧⢻⣎⣷⢺⣽⣳⣟⣯⣟⣷⣻⣞⡿⣞⣯⣳⢏⡷⣝⢮⡳⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⣽⣏⣯⣗⣿⣳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣳⣯⣷⢿⣻⣽⡿⣯⢿⣻⣽⣷⣿⣿⣿⣿⣿⣿⣿⡿⡞⣿⡇⡘⣾⢱⠀⣿⣤⠞⠑⢲⣿⣿⣇⠀⠈⠳⣜⣿⡀⠀⠈⡆⠈⢾⡧⢿⡜⣟⣾⣳⣟⡾⣽⣞⡷⣯⢿⡽⣞⡷⣯⡟⣾⣭⢷⣛⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣽⣾⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⢿⣽⡾⣟⣿⣳⣿⣻⡿⣯⣿⣾⣿⣿⣿⣿⣿⣿⣿⣳⡛⡿⡇⢹⠇⢈⣾⠻⣿⡄⢠⢾⣿⡾⡏⠈⠉⠉⠙⢿⡇⠀⢠⠸⠰⡀⢻⡞⣽⢯⣞⡷⣯⣟⣯⢿⣽⢯⣿⡽⣯⣟⣷⣻⠷⣞⣯⣳⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣟⣿⣳⡿⣿⣽⢯⣷⡿⣽⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣥⢃⣧⣧⡞⠊⠁⠻⣧⠿⣘⣏⣾⠿⠽⣷⣿⠿⢿⡻⣾⣷⡇⢸⡌⡇⢱⡄⣙⢧⣿⣾⣟⣷⣻⢾⣻⣽⢿⣾⣻⣷⣻⢾⣽⣻⡽⣶⢯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⡿⣷⣟⣷⣯⡷⣿⣽⣟⣾⢿⣯⢿⣟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⣼⢁⣤⣶⡿⠟⠒⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢰⣿⠆⢨⣿⢹⡀⣷⣌⢻⡝⣻⢼⣳⢯⡿⣽⡾⣟⣷⣿⣳⡿⣟⣾⢷⣻⣽⣻⢾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣻⣟⣾⣟⣾⣽⣟⣾⣯⢿⣻⣽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡿⣧⠘⢿⠯⠤⠉⠀⠀⠀⠀⠀⣲⠀⠀⠀⠀⠀⠀⠀⠎⣿⡂⠐⣿⠀⣧⢸⡞⣆⢻⡜⣧⣻⢯⣟⡷⣿⣻⣽⣾⢿⣽⡿⣯⣿⢯⣷⢿⣯⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢷⣿⢯⣷⢿⣽⡾⣯⣷⢿⣻⣿⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣽⣿⢯⣷⡀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢠⣣⠀⢀⣿⢠⡏⣿⡗⣽⢸⣟⡶⣯⣟⣾⣽⣟⣯⣿⣯⣿⣟⣿⣿⣽⡿⣯⣿⢾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣻⣿⢯⣿⢯⣿⣞⣿⣳⡿⣟⣿⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡟⠛⡆⠈⠻⣷⡭⡂⠀⠀⠀⠀⣤⣶⠶⠿⢿⡆⠀⢸⢀⣾⡇⠀⣸⠀⣸⣷⠸⣿⣾⣿⣯⣷⣿⢾⣽⣾⣟⣿⣷⣿⣻⣿⣿⣾⣟⣿⡿⣯⣿⡿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⢿⣽⡿⣯⣿⢷⣯⣿⡽⣟⣿⣯⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣻⠇⣸⡁⠀⣹⡄⠠⡙⢷⡌⠑⠀⠀⠀⠛⠁⠒⠂⠉⠁⠀⠐⣡⡿⠀⢀⡇⢀⡏⣼⢸⣿⣿⣿⣯⣿⣿⣞⣿⣷⡿⣿⣾⣿⣿⣿⣾⣿⣿⡿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣻⣽⡿⣽⣯⣷⣟⣿⣟⣿⡾⣟⣾⣿⣿⣯⣿⣾⣿⣿⣿⣽⢠⡟⣇⢳⡘⣿⡄⠑⠌⢻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣧⠀⣼⣿⢸⣧⢇⣿⣼⣻⣧⢻⡿⣿⣿⣿⡿⣽⣿⣷⣿⣿⣽⣿⣷⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣽⣿⢯⣿⣟⣷⡿⣾⣻⣾⢯⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⡼⣏⣷⣹⣆⢻⣽⣿⢦⠀⠂⢹⣿⣿⣿⠒⡤⣄⣀⡤⠊⣡⢿⣿⡇⢀⣧⣿⣎⣿⣸⡿⣼⣿⣧⡟⣯⢻⣱⣿⣻⣟⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ 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⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣠⣤⡜⠀⢈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠏⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠰⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⡆⢤⡄⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠘⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⢁⣀⠀⠀⠀⠀⡀⢈⠻⣿⣿⣿⢿⡿⣿⢿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢳⣦⣤⣠⠜⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠙⠒⢤⣤⣄⣀⣀⣀⣀⣤⡶⠇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠉⠀⢀⣈⡉⠰⠄⣈⣀⣠⡈⠻⣞⣯⢿⣽⣻ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣉⠉⣡⡾⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠋⠉⠀⠀⠀⣀⣀⠀⠔⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⡾⢯⡷⣳⢯ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣥⢶⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠋⠀⣼⠀⠀⠀⠼⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠚⠝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⢾⠱⡏ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠶⢦⣤⣤⣶⠞⢤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣺⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡘⢧⡸ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠣⢞⣿⠤⢹⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡍⢲⠱ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡑⠌⠾⣧⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡅⢂ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⠓⡌⠱⡹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⢝⠒⢂⣀⣠⣤⣤⣶⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠄⡡ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡄⢃⠌⡑⢄⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠻⢿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⢈⡐⠄ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠇⡌⠌⣳⠈⡜⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠴⣤⢳ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠣⠌⢂⢍⠒⢬⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠑⡌⠢⢌⡘⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣛⠿⣟⢻⡿⣿⣿⠰⣈⠑⢢⡐⣿⡇⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣯⣟⡾⣽⣳⢯⣟⣿⣿⠿⠿⠷⠳⢦⣈⡛⠬⠆⡙⢌⢻⠰⢠⠉⢆⣸⣿⠁⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⣿ ⣿⣿⣿⣿⣿⣿⡿⣿⡽⡾⣝⠾⣜⡳⢭⡳⢫⠞⡽⣛⡿⣳⢶⣤⣀⠈⢁⠢⠑⡌⠢⢽⡎⠤⡉⢆⣾⡿⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⡳⢟⡽ ⣿⣿⣿⣿⣟⣯⡟⣷⣹⢳⣭⢻⣬⢳⢫⢵⢫⡽⣱⢫⣜⡷⠿⠻⠿⠿⠦⢁⠃⡄⠣⡘⠷⢂⡱⣪⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⡰⢉⡒⠄ ⣿⣿⣟⣷⢻⡼⣽⢲⣏⠷⣎⠷⣜⣣⠟⣎⢷⡺⣵⣫⣟⡿⣶⣶⣤⣤⣤⣀⣦⣰⣵⣼⣷⣷⣶⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⢢⠁⢆⠡ ⣿⡳⣞⡾⣹⢞⡵⣫⢞⡽⢎⡟⣬⡓⣿⡸⢧⣛⣶⣻⣼⢿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢈⠆⡑⠈⠄ ⣷⢻⡵⣫⢗⡯⣞⡵⣫⢞⡽⢺⣱⢛⣶⣹⣧⣟⡶⠯⠿⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠐⠚⠒⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠡⡈⠔⡈⠡⠀ ⡽⣣⢟⡵⣫⢞⣬⡷⠽⠚⠛⠋⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢀⠌⠐⡀⠡⠀ ⡻⣵⢫⣞⠵⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⢤⣀⠀⠀⠀⠀⢰⣠⠀⠀⠀⠀⢸⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢂⠈⠄⠠⠐⠀ ⣟⠼⡳⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠀⠀⠀⢿⡆⢠⠀⠀⢸⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⡀⠈⠀⡀⠂⠀ ⢮⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠸⡿⢆⠀⠀⠘⣀⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢀⠈⠀⠀⠀⠀ ⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡙⣄⠀⠀⣿⣮⣆⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⡀⢻⣿⣿⣄⣰⣿⡆⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣟⣿⣿⠍⠰⡀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡞⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⣽⠙⣿⡄⡀⡱⡄⢠⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠳⡍⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢯⡒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄⠀⠀⢀⠄⠀⠀⠈⠀⠀⢀⠿⡇⢹⣧⡀⠌⠈⠙⢢⣡⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢱⢊⠴⡙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⡜⠀⠃⢸⣿⣷⣧⣆⣀⣀⡈⠓⣤⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⡍⠰⢈⠂⡙⢮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠿⣦⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢂⠀⠀⠀⠀⠀⢀⡰⠯⠇⢀⣾⠻⠛⠛⠉⠉⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢂⠄⡁⢂⠐⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⢀⣀⡤⠔⠋⢀⡠⠶⠋⠀⠀⠀⠀⠀⣀⠤⠴⠋⠌⠙⠩⢛⠿⣻⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠀⠂⠈⠀⠂⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣶⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣴⣾⣭⣤⢤⣴⣶⠉⠒⠈⢉⡠⠞⠉⠉⠉⠀⠀⠀⠀⠀⠀⠁⠀⠂⠙⣻⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⡀⠈⡀⠄⡁⠄⣁⠢⣔⡹⣆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠉⠈⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠐⣀⠒⣤⢫⣞⣷⣯⣷⣿⣷⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢋⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⡧⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠄⡒⢬⣻⣞⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡻⠍⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢀⠂⠀⢀⠀⠄⠀⠀⠀⢀⠀⠀ ⠀⢂⢹⣚⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠿⣝⠣⠐⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⡿⠃⠞⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠈⠀⠀⠀⠀ ⠀⢊⢶⣹⡾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣏⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠄⠂⠠⠀

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⠀⠀⠀⣀⣤⣶⡿⠿⢿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀ ⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠈⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⠛⠋⠉⠙⠻⢷⣦⡀⠀⠀ ⠀⣾⣏⣀⣀⣀⣀⠀⠀⠀⠀⠀⠘⢿⣄⣀⣠⣤⡴⠶⠶⠶⠾⠿⠷⠶⠶⢶⣤⣤⣀⣀⡀⠀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀ ⢸⣿⠋⠉⠉⠙⠻⣷⣄⠀⢀⣠⣶⡿⠿⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀ ⠸⣿⡀⠀⠀⠀⠀⠘⣿⣼⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣄⠀⢀⣤⣶⡶⠿⠶⢾⣿⡇ ⠐⠹⣧⡀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣿⠏⠁⠀⠀⠀⢰⣿⠇ ⠀⠀⠘⠻⣦⣤⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⠀⠀⠀⣴⡿⠋⠀ ⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⠶⠞⠋⠁⠀⠀ ⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀ ⠀⠀⢀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀ ⠀⠀⠈⢸⡇⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⡿⣿⣿⣿⣿⡷⠀⢀⣠⡴⠿⣿⡟⠶⣶⣄⡀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠐⠛⠿⠿⠟⠀⢀⡾⠁⠀⢰⣿⣿⠀⠀⠈⢻⣄⠀⠻⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡃⢀⣰⣶⡿⢿⣦⣀⠀⠀⣿⡆⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣜⡛⠉⠈⠀⠙⠛⠁⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠓⠒⠲⠖⠒⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡶⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠛⠛⠛⠿⠿⠷⣶⣶⣾⣿⣿⣿⣿⣿⣷⠶⠶⠾⠛⠛⠛⠋⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⢀⣤⣴⠶⠾⠓⠒⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⠀⠀⠀⠀⢸⡆⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢸⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⠀⠀⠀⣾⠇⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣷⣄⠀⠀⣸⣿⠆⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⣸⣿⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠙⢿⣿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀⠀⣠⣾⡿⠃⠀⢀⣿⠇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⡿⠋⠀⠀⢀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⢿⣧⠀⠀⠀⠀⠀⠀⠈⠻⠶⠤⠤⣄⣀⡤⠤⠶⠛⠉⠀⠀⢀⣲⣾⠟⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠀⠀⠀⠀⢀⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⣷⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠒⠒⠚⠛⠛⢿⣧⣄⠀⠀⠈⠀⠀⠀⠀⢀⣴⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠳⠶⠶⠖⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣴⣀⣤⡶⠶⠿⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡾⠶⠾⢷⣶⣤⣠⣤⣤⡶⣿⣿⢿⣽⣻⣿⡅⠀⠀⠀⢹⡇⠀⠀⠀⠀ ⠀⠀⠀⣿⠃⠀⠀⠀⠀⠈⠁⠀⠀⠰⣿⣯⢿⣿⣿⣿⢿⣿⣶⣿⣿⣿⡦⠀⠀⠀ ⠀⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣯⣿⡿⢿⣯⡿⣾⣿⣿⣾⣽⣿⠀⠀⠀ ⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⣻⣾⠿⣦⠀⠀⠀ ⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⣿⣆⣀⣀ ⠀⠀⢨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠈⠋⣿⠍⠀⠀ ⠐⠒⠻⣿⠛⠁⠀⠀⢸⣿⠄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠹⠟⠀⠀⠀⢘⣿⠷⠲⠄ ⠀⠀⣤⣽⣷⠒⠀⠀⠀⠁⠀⠀⠀⠀⠻⠭⠏⠀⠀⠀⠀⠀⠀⢀⣰⣾⢯⣄⣀⠀ ⠀⠀⠀⢀⣸⣷⣾⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡏⠉⠛⠛⢾⣍⠀ ⠀⠀⠀⠿⠉⢀⣨⣿⣿⣷⣶⣶⣤⣤⣤⣤⣤⣴⣶⡶⣿⣿⡿⣿⣄⠀⠀⢀⣿⠀ ⠀⠀⠀⢀⣴⣿⣿⣻⣿⢿⡱⢎⡿⣿⣟⣿⣻⣿⢏⡳⡹⢿⣿⡽⣿⣦⣤⠞⠃⠀ ⠀⠀⢠⣿⠁⠀⠙⢿⡟⡦⡝⢮⡜⣱⢫⢏⡽⣘⢮⡱⣍⡛⣿⣿⠿⠋⠋⠀⠀⠀ ⠀⠀⠨⣿⡀⠀⠀⣾⠻⣔⢫⢖⡹⢆⡏⡞⡴⣍⠶⡱⢎⡵⢻⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠛⢻⣿⡹⣌⡳⢎⡵⢫⡜⣱⠳⣌⡳⣍⡳⡜⡭⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡿⠷⠻⠷⠿⠾⠷⠿⣿⠿⠾⠷⠿⠞⠟⠳⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠷⢶⠦⠶⢴⢦⡞⠻⢶⠦⠶⠴⢦⠶⠟⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⣶⣶⡶⠶⠶⠶⠤⠶⣶⣤⣄⠀⠀⠀ ⠀⠀⠀⡤⠶⡝⠿⣻⣻⣷⣦⡀⠀⠀⠀⡠⢀⣲⣮⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⣿⣿⣶⣿⣿⣿⣿⠾⠻⣿⣿⡄⠀⠀ ⠀⠀⠀⢀⠀⠀⠀⠀⠙⠛⠿⢿⢦⣔⣷⣿⡿⠟⠋⠀⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢾⣏⡿⣻⣽⣴⣦⣶⡿⢻⣿⡄⣭⢾⣿⣧⢿⢸⣷⠀⠀ ⠐⢢⣴⣤⡴⠿⠿⠷⠶⠾⠾⣿⣾⣿⡟⠛⠛⠛⠛⠻⠿⠿⠶⠶⣦⣤⣍⣓⢤⣘⣦⡀⠀⠀⠀⢸⣿⣋⢐⣀⡙⢿⣻⢿⣿⠷⠛⠟⠞⣿⣿⣿⣟⣾⡇⢻⣇⠀ ⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣼⢫⡟⠽⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠉⠓⠾⣿⣦⣀⠀⠈⠷⣿⣫⢿⣺⣏⣇⢳⣬⠮⣐⢸⠄⣿⣷⠞⢩⣿⡧⢼⠗⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣴⠸⢐⡑⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣄⣉⠛⣷⣾⣭⣛⣷⣦⣭⣥⣗⣲⣿⠂⠀⠈⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢸⣷⠀⠘⢿⣬⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⢿⡿⢿⣿⣌⡙⠛⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⡅⡈⣭⡄⠀⠈⣻⡧⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣿⣿⣾⣶⣬⣿⣿⡻⣦⢶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣹⣿⣿⣀⣀⣿⣿⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣞⣿⣿⣿⠁⣸⣬⣿⣆⢀⡠⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣿⣾⣿⣷⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣾⣿⣿⣿⣿⣿⣿⣿⢀⣼⡿⠁⣹⣿⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⡴⡷⣿⣿⣿⣿⢋⣴⣛⣿⠿⢏⣠⣴⣿⡿⠿⠻⣿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⣚⠉⣾⠣⠰⣗⠋⡧⣿⣿⣿⡿⠿⣿⣿⣿⠿⠛⠋⠉⠁⠀⠀⠀⠈⠛⢿⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⢫⢿⣄⣼⣻⣽⣻⣿⣿⣿⣿⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣯⣹⣿⡿⠟⠻⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡇⠀⠀⠀⠀⠈⠫⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠈⠛⢿⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀nah i'm leaving this site⠀⠀⠀ ⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ain't no way yall beefin⠀⠀⠀ ⠀⠘⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀over pixels💀💀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣽⠆⠀⠀⠀⠀⠀⠀⠀⠀⢰⢭⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⢴⣞⣟⣻⣦⣤⣤⣖⣒⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣫⣿⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠶⢦⣄⠀⠀⠀⠀⠀⣴⠟⠛⢧⣠⣶⣿⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⠀⠀ ⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⠁⡟⠦⠌⠛⠉⠉⠉⢹⠇⢠⣶⣼⣷⣞⢙⣧⣿⡀⠀⠀⢠⠤⣄⠀⡏⠀⡏⠀⠀⠀ ⠀⠀⡖⢲⡎⠘⡆⠀⠀⠀⠀⠀⢸⣤⠃⠀⠀⠀⠀⠀⠀⣿⠀⠈⢻⡃⠀⢸⡿⡄⠈⣿⠀⠀⠀⡇⠀⠈⠿⠀⠀⡇⠀⠀ ⠀⠸⡄⠈⠀⠀⡏⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠘⠷⠖⠛⠛⠛⢿⡗⢋⣴⠏⠀⠀⠀⠹⡄⠀⠀⠀⠀⠇⠀⠀ ⠀⠀⠉⠣⢄⡼⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢻⡀⢀⣀⠀⠀⠀⠑⠦⡄⠀⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠾⣷⠆⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠐⢺⡟⠉⠉⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢿⡦⠀⠀⠛⠃⠀⠀⢠⢶⣄⠀⠀⠈⠛⠀⠀⠀⣺⠓⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣖⡀⣀⣀⡀⠀⠈⠉⠉⠀⠀⣀⣀⣀⠀⣲⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⡆ ⢻⡈⠻⣦⣀⣀⣀⣀⣀⠀⠀⠀⠁⣴⠟⠉⠁⠀⠉⠛⢦⡀⢀⡴⠛⠉⠁⠈⠙⠻⣄⠀⠁⣀⣠⣤⣤⣤⣤⡤⠖⠋⣸⠇ ⡿⠳⣤⣀⡀⠀⠀⠉⠉⠉⠳⢦⣼⠃⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⠀⠀⠀⠀⠀⠹⣦⡞⠉⠀⠀⠀⠀⠀⢀⣠⠶⢻⡆ ⠻⣦⣀⠀⠀⠀⡴⠶⢦⡀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡴⠚⠳⡄⠈⢉⣀⣠⡾⠁ ⠀⠸⣍⣉⣁⡀⣇⠀⠀⠑⠀⢠⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣰⢷⡀⠀⠓⠀⢀⡇⢤⣈⣭⠿⠁⠀ ⠀⠀⠀⠙⠷⠤⠿⠶⠦⠶⠞⠋⠘⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡼⠃⠈⠻⠦⠴⠖⠻⠶⠶⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⡀⢀⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠙⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⠃⢠⡴⠇ ⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠋⠁⠀⠀⢸⠀⠀ ⠠⡏⠀⠈⣧⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⣾⠀⠀ ⠀⠙⠒⣦⠀⠀⠉⠉⠛⠒⠲⠦⠤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡆⠀⠀⠀⣀⣠⡤⠶⠖⠒⠒⠒⠒⠒⠶⠦⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⠶⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀ ⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⡤⠖⠲⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀ ⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠚⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢰⣿⡆⠀⠀⣾⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠶⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣛⡀⣤⣀⢩⡽⠏⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢀⣠⡴⢤⣀⠀⠈⠓⠛⠛⠚⠀⣀⡤⠞⠉⠙⠓⢦⣄⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠈⠛⠦⣄⣀⣀⡤⠞⠉⠀⠀⠀⠀⢀⣠⣞⣷⣄⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣼⠃⢀⣀⣀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⠘⡆⠀⠀⢸⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⡇⠀⠀⠉⣉⣽⠷⢦⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢿⣿⡿⣿⠀⠀⣿⠀⢠⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⢷⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠯⡿⠟⠀⢠⡀⠀⠀⠀⠉⡟⠹⣆⣠⠇⣠⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠳⢦⠤⣤⠶⣯⠀⠀⠀⢀⡞⠁⠀⠀⠙⣾⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣈⡳⢤⣀⡀⠀⠀⠀⠀⢸⠀⢿⠀⣸⠀⣀⣀⣸⣇⠀⠀⠀⢀⣟⣾⡻⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠺⠿⣭⡟⠛⠛⠛⠳⠤⣴⡋⠉⠉⠁⠀⡾⡟⠂⠀⠸⡿⠉⠛⠁⢀⣠⢶⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢾⢳⣾⣥⢴⣾⣄⣀⡤⠞⠋⠉⠛⠲⠦⣟⣽⡟⠀⠀⢀⡇⠀⠰⣞⡉⠀⠘⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⣼⠃⠘⠿⢾⡏⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠦⠤⡾⠁⠀⠀⣸⠃⢀⡶⠿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠚⠷⠀⠀⢀⡼⣇⠀⠀⠀⣴⠞⠉⠉⠙⠓⠀⠀⠀⢹⣤⣤⠞⠃⣠⡞⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢰⣯⡞⠛⠦⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⠦⠤⠴⠚⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣄⣀⣠⡴⠟⣞⡄⠀⠀⢀⣧⠤⠀⠀⠀⠀⠀⢠⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⣤⣤⡤⠿⠶⠦⠤⠴⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠕⠒⠉⡀⠄⠠⠐⠠⠀⡄⣄⡰⠔⠊⠉⠁⡀⠄⠠⠀⠄⡐⠀⢀⣀⠤⡔⢢⡝⣌⠣⣝⣢⠝⢊⡉⠱⠀⢆⡰⠐⢂⡈⠄⠐⠈⢀⡠⠔⠒⣉⠐⠂⠁⠀⠀⠀⠀⠀⠉⠐⠲⣍⠓⢦⡈⢣⡘⡄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠛⠉⠉⠀⠀⠀⠀⠀⠐⠂⠐⠙⠓⠶⢤⣄⡀⢠⠏⠀⣴⠟⡤⢃⠎⡔⢣⠜⣢⠑⡎⠴⡡⢎⠴⡡⢎⠴⢱⡈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠠⠁⢀⠂⣡⣤⠵⠞⠉⠀⠀⠀⠀⠌⠐⠀⠄⢁⣈⡤⢔⢪⠱⡌⠳⣌⠧⠜⢊⠉⠤⠠⢘⠠⠄⢃⡉⠤⠂⠈⣀⣠⠔⢊⡉⠴⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⢱⣧⠀⢧⢹⡀⠀⠀⠀⠀⢀⡶⠋⠀⢀⣤⠶⢟⡛⣛⢛⡛⢟⢻⣛⠶⣶⣤⣄⣀⠈⠁⠟⠀⣰⡟⡸⢰⡉⢞⡨⡑⢎⠴⡩⢜⡡⠱⡌⢦⠱⡌⡜⢢⡑ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⢀⣠⡥⠶⠞⠋⠁⠀⠀⠀⠀⠀⠠⠀⢂⣠⡤⠶⡚⢭⠡⢜⣨⡦⠳⠚⠉⡄⠘⢈⠤⠈⢒⠉⠠⠐⠈⣀⡤⠤⢒⠩⠡⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⣄⡀⠀⠀⠀⠸⡆⢹⣆⠘⣆⢳⠀⠀⠀⣰⠏⠀⢠⡼⢋⠦⡙⢦⠱⡌⢦⡙⣌⠲⣌⢣⢓⠺⠾⣭⣟⡶⣤⣰⡟⡰⢡⠣⡜⢢⡑⠭⣘⢢⡑⢎⡔⢣⠜⢢⡑⢒⡌⠥⡘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠒⠋⠁⠀⠀⠀⠀⢀⣠⣤⣤⣤⣦⣴⣦⣉⠦⢘⣡⡼⠶⠛⠋⠁⡀⢂⡡⠁⠐⡈⠅⠐⠈⣁⡤⠴⠒⢋⠡⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠉⠁⠀⠀⠀⠀⠉⠓⠦⡄⠀⢻⡈⣼⡆⠸⡌⣇⠀⢰⡏⠀⣰⢏⠲⣉⠖⡩⢆⠳⡘⢦⠱⡌⡓⡌⢦⡉⢎⡱⢢⢍⡛⡛⣍⠲⣡⢃⠳⣌⠣⡜⡱⢌⠆⣍⠲⡨⢅⠎⡅⢎⠥⡘⢆⡱ ⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⣀⣠⡴⠾⠛⠉⠉⠈⠀⠀⠉⠉⠉⠛⠻⢿⣿⣤⡀⢀⣠⠴⠒⣀⠥⠀⠈⢁⣠⠴⠒⠋⠡⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⢷⢈⢳⡀⢱⡘⡆⢸⡇⠐⣏⢎⡱⢌⢎⡱⢊⠵⣉⢆⠳⣌⠱⡘⢦⠙⢦⡑⢣⠎⡴⠱⣌⠱⢢⢍⠲⣄⠳⡘⠴⣉⠎⡔⢣⡑⠎⡜⢌⠲⢌⡱⠌⡔ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⢀⣴⣼⠟⠋⠁⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠈⠻⣿⣆⠐⠈⠁⡀⠤⠒⡉⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠘⣇⠈⣷⠀⢧⢹⡸⣇⠈⣷⣈⠖⡩⢆⡱⣉⠖⡡⢎⡱⢌⢣⡙⠦⣙⢢⡙⢢⡙⡔⢣⢌⢣⢃⢎⡱⢂⠧⡙⢦⠑⡎⡜⡡⢜⡘⢬⢘⡂⠧⢰⠩⡐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢁⣴⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠀⠀⠘⣿⣆⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠘⣇⢛⣇⠈⣆⢳⣻⡀⠹⣦⠙⡔⢣⠒⡥⢊⡕⢪⠔⡩⢆⡱⢣⠜⣢⠙⣆⠱⣌⠣⢎⠦⣉⠲⣬⣕⡬⡑⣊⠱⡘⠤⠓⡬⢘⠢⣅⠚⡌⢥⢊⡱ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠁⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢹⡄⠞⡆⠸⡄⢏⢷⠀⠹⣎⠜⣡⢋⠴⢣⠜⡡⢎⡱⢊⡔⢣⠚⡤⢋⡔⢣⢌⠳⣌⠲⣡⡿⠁⠈⠙⣷⣌⡷⠛⣷⡉⠴⡉⠖⡤⢋⠜⡰⢢⠡ ⠻⣦⣄⡀⢀⣠⡴⠛⠉⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⢀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠤⠴⠶⠶⠦⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⢳⡈⢻⡀⢱⡘⡎⢧⡀⠙⣞⠤⣋⠜⣢⠙⡔⢣⠜⡡⢎⠥⣋⠔⡣⢜⡡⢎⡱⣤⣷⣬⣹⣆⠀⠂⢸⣿⠀⣼⡟⣐⢣⡉⢞⢠⢋⠬⡑⢆⠣ ⠐⠠⡈⠙⠛⠷⠦⡴⣤⣤⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡆⢰⣶⣤⣰⡿⠋⠀⠀⠀⠀⠀⠀⠤⣄⠈⠉⠙⠿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠘⣇⠐⣳⠀⢧⢸⡄⠳⣄⠈⠳⣌⠞⡤⢋⡜⡡⢎⡱⢊⠖⡡⢎⡱⢊⡔⢣⢒⡙⢦⣄⣉⠛⣷⣤⣽⠧⠞⡭⢰⠡⢆⡙⢢⢃⢎⠲⣉⢎⡱ ⢿⣤⣡⡈⠄⠠⢀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⣠⣾⡟⠉⠀⠀⠀⢠⠙⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⢻⣦⣶⡶⢶⡆⠤⣄⡀⠀⠀⢧⠀⠘⣦⠹⣧⠈⣆⢧⠀⠘⢦⡀⠈⠻⣔⠣⡜⡱⢊⠴⣉⢎⡱⢊⡔⢣⠜⣡⠎⡜⡡⢎⡍⣛⠹⣂⠦⡙⡜⡰⢃⡍⠦⡙⠦⣉⢎⡱⢌⠲⡐ ⠀⠉⠙⠛⢶⣥⣤⣄⣠⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡼⠁⠀⠀⠀⠀⢠⣼⡿⠁⠀⠀⠀⠀⠀⢸⡇⢸⠂⠀⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠲⣄⠉⠛⠲⢮⣇⡀⠱⡜⣞⡆⠸⡌⢧⠀⠀⠙⠢⣄⠈⠛⢦⣱⢉⠖⣡⠎⡔⢣⠜⣡⠚⡤⢋⠴⡑⢎⠴⡡⢓⡌⢲⠱⡌⡱⢃⡜⣡⢃⠳⢌⡒⠬⠌⡥⣹ ⠠⠀⠂⠉⠀⠀⢀⣠⠽⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠁⡃⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠐⣧⢸⡂⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⣿⠂⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⠙⢷⣷⡈⠽⡄⢱⡸⡆⠀⠀⠀⠈⠳⢤⡀⠉⠻⢼⣄⠫⡜⡡⢎⠥⣋⠴⣉⠖⡩⢎⡒⢥⠣⡜⣡⠚⡴⢡⠣⡜⢤⡉⢞⡰⢌⢃⢣⢲⡝ ⣧⡀⠀⠠⠒⠊⠉⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠐⡀⠀⣠⣶⠿⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⢸⡡⠀⠀⠀⠀⠀⠀⠀⣴⡇⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢙⡦⠀⠀⠈⠹⣿⡆⢹⡀⢣⠹⡄⠀⠀⠀⠀⠀⠉⠳⢦⣀⠈⠳⠮⣕⣊⠖⣡⠚⡤⢋⡔⢣⠜⣢⠓⡜⢤⢋⡔⢣⢓⡘⠦⣉⠖⡰⢊⢌⠲⡝⠀ ⢹⣷⡀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣀⣱⡿⠉⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⠀⠀⣿⠈⣷⡀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠞⡽⢐⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⠎⠀⠀⠀⠀⠀⠙⣿⡀⢷⠈⣇⢳⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⣄⣈⠉⠛⠦⣽⣐⠣⡜⣡⠚⣄⢋⡜⢂⢣⡘⣡⣦⡟⣶⡡⢊⡱⢌⢪⡽⠁⠀ ⠌⣻⣿⡄⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⠀⠀⠀⠀⠀⣎⢹⣆⠀⢀⣠⣤⣴⣶⠿⠶⠾⠷⠲⠶⠾⠿⠷⠦⠤⣤⣄⣀⣾⠁⣾⡏⠇⠀⠀⠀⠀⠀⡠⢠⠏⠀⠀⠀⠀⠀⠀⠀⣿⡇⠎⣇⠘⡎⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⢻⡙⣶⢤⣀⠉⠛⠶⣥⣍⡲⢌⠢⣍⢢⠒⣉⢧⢻⡜⢷⣥⣒⢬⡿⠁⠀⡸ ⠒⡄⢿⣷⡄⢀⣀⡤⠖⠊⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⡀⠀⠀⠀⢹⣠⣼⣷⣿⡿⠷⠶⠚⠚⠛⠛⠛⠛⠙⠓⠒⠒⠦⠤⢤⣀⣈⠙⠛⠿⢾⣄⡀⠀⠀⠀⣸⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⠐⠸⡆⠹⡘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⢧⠘⣦⠉⠳⣆⠀⣀⠈⠉⠳⠷⣴⣌⡘⣤⠟⣠⡟⠶⣤⣭⠟⠀⠀⡔⠀ ⢱⠈⡆⣿⣿⠉⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⢀⣰⣿⡿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠷⣆⡀⠈⠹⠷⣆⣶⠇⣾⠀⠀⠀⠀⠀⠀⢀⣰⠰⢿⣿⣶⣁⢹⠀⢷⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡎⡇⢿⡆⠀⢹⡆⠈⠹⣷⣶⣀⠀⠈⠹⢉⣰⣏⣰⣱⣾⠏⠀⣀⡿⠀⠀ ⣇⠎⡰⢘⣿⣆⠀⠀⠀⠀⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢤⡈⠙⠲⣇⡀⠀⠀⠀⠤⠖⠋⠠⢀⡴⠈⠉⠻⢿⣇⠘⣆⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣹⡈⡞⣆⠀⢳⡄⠀⠽⣄⠉⠙⠒⠶⢤⣅⣀⠀⠁⠀⣠⡴⠋⠀⡀⠠ ⣎⡳⡈⠥⡘⣿⡄⠀⠀⠀⠀⠀⠀⠹⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣌⡙⢦⣤⡴⠞⠋⠠⣱⠟⠀⠘⣄⡀⠈⣿⡇⠘⡜⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢳⠱⡸⡄⠀⢳⡀⠀⠈⠙⠺⣥⡢⠀⠀⠉⠉⠛⣉⡭⠖⠋⢁⣠⣶ ⢿⡵⢣⢑⢢⣹⣷⡆⢀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡙⣶⣄⢡⣶⠏⠀⠀⠀⠀⠉⠃⠈⢿⡄⢳⡸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠎⣇⢡⠸⡆⠈⢳⡀⠀⠀⠀⠀⠉⠓⠦⠴⠚⠉⢀⣠⢄⣶⡿⠟⠁ 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⠜⠠⠁⣌⠰⠘⠊⠁⠀⠀⠠⠄⠄⠒⠀⠉⣀⠤⠂⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢴⠞⠁⠀⠄⡁⠂⠐⠀⢀⡆⠳⢡⢆⡛⣤⢋⣊⣁⠂⣉⠻⢾⠿⠳⡜⢦⡹⣙⢿⡋⣡⣾⣿⡿⣞⣿⣽⣇⠉⢀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⢉⣴⣾⠿⣭⢯⣵⡋⣰⣦⠿⣙⠲⢦⣨⣷⠿⣾⣿⣷⣧⠾⣥⣪⢟⣯ ⡌⢂⠩⠀⠐⠀⠂⠁⠀⠄⡀⢀⣄⡴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⣁⡰⠏⡀⠄⡈⡐⠠⠄⠂⡐⢈⠀⢂⣵⠲⡽⣭⣳⡜⡴⢪⢥⠛⣦⠛⠛⠺⢧⣳⢍⡞⣻⡿⣝⣶⣽⢿⣯⣿⡿⢟⡿⠀⠀⠀⠀⠀⢀⣰⢏⣳⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋⠀⣰⠏⣼⢯⡟⣳⡏⣶⠟⣩⡵⢯⣬⣙⣇⠻⢧⣟⣿⣹⣏⢛⣿⢞⣹⣯⠧ ⠠⠀⠀⠈⢀⠠⠐⢈⣠⠴⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠐⢬⣘⡡⢉⠡⠐⠠⢁⠠⠁⢀⠂⠌⡀⠿⣶⣛⡶⣹⠖⣭⢓⢮⡹⣔⠲⣍⢳⢦⡹⣎⣾⡋⠻⠿⡼⢾⣿⡿⠋⠘⠁⠀⠀⠀⠀⢀⣤⢟⣡⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠋⢀⠂⢀⣼⣃⡼⠟⠻⡿⢿⣞⣡⣞⣧⡽⣞⣭⣵⡾⢟⡹⣿⣉⣿⡿⣯⣵⣯⣟⣛⣛ ⢦⡀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠖⣴⠋⡄⠀⠄⡀⠄⠡⡔⢀⠂⡁⢂⣤⣦⠙⢦⡈⠐⠄⠂⠌⡉⠛⠳⣏⠶⣩⢖⡱⢎⡳⣌⠳⣮⡵⢋⠡⡙⠳⠖⣋⡾⢋⠁⠀⠀⠀⠀⠀⣠⡴⡛⣥⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⡡⠁⢌⠠⠀⣽⢻⡶⣶⢖⣻⢟⡿⡷⡼⣻⠵⠚⣉⣡⠤⢖⡿⣞⢵⣫⣵⡾⢿⣭⣚⣬⣧⣭ ⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠒⠒⠚⠉⣉⣡⡤⢾⡿⠁⡼⢀⣬⣔⣼⣦⡄⠙⠃⢄⠁⢾⣿⣽⣷⠈⣉⠡⢈⠌⡲⠜⢁⠂⢌⡻⢔⡫⣜⢣⣕⣮⠟⢁⣠⡤⢶⣶⠞⠛⠉⠈⢀⡀⣀⣤⣄⣴⣞⣋⣴⣉⣥⣄⣠⣄⣤⣀⣀⣀⣀⣀⣀⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢁⡐⠠⢁⠂⠄⣡⠻⣶⣟⣖⡺⣇⡞⢾⣿⣜⣧⣞⣋⣷⡿⢿⣛⣿⣻⣽⣿⠽⠾⠛⠛⠉⠁⠀⠀ ⠀⠀⠀⠹⣆⣠⠤⠤⠒⠂⠉⠈⡀⠀⠀⠀⣀⣤⠴⠋⢡⠞⣷⣿⡿⣀⠄⣿⣛⠾⣧⣿⡇⡜⡰⠬⠃⠌⡙⠛⡉⣰⣉⠦⡆⢯⡱⣚⢬⡚⣬⢣⢏⣲⡽⠫⢉⡤⢦⣬⣥⣶⣿⣯⠶⠾⠿⠛⠛⠛⠋⠉⠉⠉⠉⠉⠈⠉⠀⠈⠁⠈⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠻⠶⠶⠦⣼⣥⣤⣂⣄⡁⠂⠬⠞⠁⠀⠈⠻⢵⡶⣽⣻⣶⣬⣿⣷⣯⢿⠶⠿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢻⡄⠀⠀⠀⠄⠈⠀⠀⠁⠄⢒⡩⠴⢒⡛⠛⠛⡞⢟⣣⠓⠠⠙⣯⡟⣶⡟⠠⡘⢣⣙⠚⣤⣰⢡⡔⣡⢎⢳⡙⢦⡓⡷⣮⣕⡾⠶⠟⣻⣤⣴⢯⡷⢾⠛⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡙⠛⠲⠶⠦⢤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠔⠲⣉⣍

⠰⣂⠳⢌⠦⠱⡌⠦⠱⡌⠦⠱⡌⢦⠱⣌⠲⡱⡘⠆⠃⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡘⢦⡑⢎⡔⠣⡜⢢⠱⡌ ⢓⡌⠳⡌⢎⡱⢌⢣⠓⣌⢣⠓⡜⢢⠓⡌⠑⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⢢⡙⢦⡘⡱⢌⢣⠓⡜ ⢬⡘⣱⠸⣌⠲⣉⠆⡏⡔⢣⡙⡌⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠧⡘⢦⠱⡑⡎⢥⢋⡜ ⢢⢱⢂⠗⣌⠳⣌⢚⠴⣉⠦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖⡩⢆⡳⡑⢎⡱⢊⡴ ⢎⠦⣋⡜⢆⡳⢌⡚⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡴⣲⢦⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢲⣉⠶⣉⠶⣡⠝⡬⣑⢣⢒ ⡸⢸⢁⡾⡈⡶⢉⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣱⢏⡾⣱⡎⣷⠹⣏⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⢷⣈⢱⠾⣀⠿⣰⢉⢶⢉ ⡱⣩⠎⡴⡹⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣹⢞⣜⣣⢯⣕⡻⣜⡳⠉⠚⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣎⠳⣎⡱⢣⢇⣏⠺⣌ ⠑⠂⠝⠲⢱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡱⣏⠾⣜⢮⢳⢎⡷⢣⠇⢸⡱⣖⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡳⢬⡱⣋⠮⣜⠳⣜ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣹⢎⠛⠂⠋⢟⢮⡝⡯⣝⢶⣹⠚⠀⠀⠀⢠⣶⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠘⡥⢳⡍⡞⣥⠛⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣝⠀⡲⣝⢧⣚⢮⡳⣝⡚⠶⣁⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠘⢧⡚⡵⡂⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠝⠮⠳⢹⢎⡇⠍⠞⠈⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⢣⣛⡴⢳⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠐⣣⠞⣭⢋⡦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣦⣤⣤⣤⣤⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠙⠚⠿⢏⣿⣿⡀⢼⡹⣬⢛⡴ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢀⣤⣶⣶⣶⣤⣠⣾⣿⣿⡇⢸⡱⢮⡹⣜ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣴⣿⣿⣿⣿⣿⢯⣿⣿⣿⣿⡗⣭⠳⣍⡳⢎ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⣿⡇⣜⡳⣭⢓⢯ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⣎⢷⣉⡾⢇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣁⣒⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢼⡹⢦⡳⣜⢫ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⣀⣀⣉⡉⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣱⢫⢗⣫⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡯⠁⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠉⠉⠉⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣡⠞⣝⢮⡱⠀⠐⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣬⣁⠀⣴⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣜⣜⢫⡞⣥⣛⠀⠐⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⣿⢧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⠿⢡⣶⣲⢦⡶⣴⢢⣦⣀⣈⣀ ⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⠟⣉⣠⣞⡷⣭⣟⠾⣭⢷⣣⢟⡼⣳ ⢿⣚⣷⣻⢾⡵⣯⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⣶⣾⣿⣿⣿⣿⠟⣫⣵⣌⢟⣳⡟⣾⣳⣞⡿⣎⡷⣝⣮⢳⢧ ⣯⣻⡼⣏⣯⢿⣽⣻⣞⡷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣛⣛⡿⢿⣿⣿⣿⢟⣻⣭⣭⣟⣋⠁⠀⠀⠀⠉⠀⠁⠀⠀⡷⣎⢷⡹⡞⡵⣎⠿⣸ ⢿⣵⣻⢿⡽⣟⣾⣳⣯⣟⣯⡿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⢟⣵⣾⣿⣿⣿⣿⣿⣧⡍⠟⣱⣿⣿⣿⣿⣿⣿⣷⣆⢿⣿⣿⣿⣇⢦⣼⠱⢯⣏⢷⣫⠷⣭⡛⡵ ⣟⢾⡽⢯⡿⣽⢳⢯⡷⢯⡏⠙⠳⢯⢟⡀⠀⣠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⢘⣠⣝⡳⢎⡷⣩⢗⣣⢛⡵ ⢿⡾⣹⡏⣷⡏⣿⢏⡾⣏⠀⠀⠀⠀⠈⠸⢹⣇⢷⡾⡹⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢶⢇⣎⡹⢇⢷⢱⡾⣈⠷⡾ ⣻⢼⡳⣝⣧⢻⣎⠿⣜⡇⠀⠀⠀⠀⠀⠀⣠⠜⠃⠁⠁⠀⣠⣤⣶⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⡾⢭⢎⣳⡙⣎⠳⡜⣥⢛⡴ ⡽⣎⢷⡹⣎⢷⣚⢯⣳⠀⠀⠀⠀⠀⠀⢟⣴⡿⢦⡌⣰⠃⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠣⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡱⢎⡗⢯⢎⡲⡝⣎⡳⣙⢦⣋⠖ ⣻⠼⣧⢻⡜⣯⢞⡵⡃⣀⡄⣤⡄⠀⠀⠈⠍⢳⠟⡰⢍⡇⣿⣷⡙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢁⣺⠱⣬⢜⡻⠿⠿⠿⠿⣟⡋⢁⠮⡝⣝⢮⣋⠮⡵⣙⠦⡝⡜⢦⡙⡞ ⢯⣛⣮⢯⣝⣮⢻⡼⣏⢷⡳⢆⠳⡀⠀⠀⠀⠉⠘⠛⠈⠀⣿⣿⣿⣷⣬⣛⡿⠿⠿⠿⠿⠿⢟⣛⣥⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠜⣢⡍⣾⢰⣫⢳⡱⣍⢞⡱⣙⢮⡱⡹ ⡯⢝⣮⢗⡯⣞⡽⣺⠽⣮⣝⢯⡡⠁⣄⣀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡵⢺⠴⣋⠶⣣⠳⡜⢮⡱⢭⢲⡱⡹

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠋⢻⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠛⠉⠉⠉⠉⠉⠙⠓⠲⢤⣀⡀⠀⣼⢧⠀⢠⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⠤⠤⠬⠽⣶⣿⠦⣡⣞⣠⠴⠖⠶⣄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣇⠀⠀⠀⢀⣠⠶⠚⠋⠁⠀⠀⠀⠀⣀⣠⠤⠴⠒⢚⡿⣿⡋⣀⢦⣄⣠⣾ ⢀⣴⡾⠛⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣶⣾⠋⠁⠀⠀⠀⠀⢀⣤⠶⠛⠉⠀⠀⢀⡴⠋⠀⡏⣷⣾⠟⠉⠁⠀ ⣾⠏⠀⠀⠀⠀⠈⠙⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣷⡀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⢀⣴⠟⠀⠀⣸⠃⢸⠙⣆⠀⠀⠀ ⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⣻⡿⠟⠛⠛⠛⠛⠛⠛⠛⠳⠶⢦⣤⣀⠀⠀⢈⢻⣶⣶⡟⠁⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⣰⠏⠀⢸⡄⠸⡄⠀⠀ ⢽⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣶⠟⠛⠛⢻⣇⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⣰⠏⠀⠀⣼⠀⠀⣷⠀⠀ ⠀⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠙⢳⣶⣶⡟⠁⠀⠀⠀⢀⣼⠃⠀⠀⢀⡟⠀⠀⢹⠀⠀ ⠀⠀⠈⠙⠿⢶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⡟⠁⠀⢀⡤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢛⡴⠻⣇⠀⠀⠀⢠⡾⠁⠀⠀⠀⣼⠁⠀⠀⣾⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⣼⣿⠁⢀⡀⠸⣄⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢷⡴⢋⣵⠋⠀⠀⠙⠳⢶⣶⡟⠀⠀⠀⠀⣼⠃⠀⠀⢀⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⢿⣆⠀⠀⠉⢳⠀⠀⠀⠀⠘⢷⠤⢤⣴⠆⠀⠀⠀⢾⣀⡗⢀⡴⢋⣴⠛⠛⠛⠛⠻⠶⠶⠶⠿⣧⡀⠀⢀⣼⠋⠀⠀⠀⣸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢠⡶⠿⠿⢦⣄⣊⠀⠀⠀⠀⠀⠸⣦⡞⠁⠀⠀⠀⠀⢈⣭⡴⢋⡴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣿⠃⠀⠀⠀⣰⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣌⢿⣄⡀⠀⠈⠙⠛⠷⠦⣤⣄⣀⣀⠀⣠⡴⣦⠀⣠⣿⣯⣴⣯⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢷⣄⣠⣼⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⡏⣾⣛⡿⣏⡀⠀⣻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣬⣩⠶⠋⣥⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣤⣤⣤⣤⡄⠀⠘⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⡟⠉⠙⠻⣷⣤⣶⡶⣶⣶⣦⣶⠟⠻⣿⠋⠉⢻⣥⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⢀⠠⣄⣀⣀⠀⠘⠣⢄⣴⠿⣷⣤⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⠠⠀⠀⢒⠃⡃⠀⠀⠀⡀⠀⠀⢠⠙⠛⠟⠩⠹⣿⠀⠀⠀⡀⠎⠣⢀⠀ ⠀⠀⠀⠀⠀⢀⣀⣷⣈⡉⠉⠀⠑⠬⠤⠔⠊⠙⠴⠦⠔⠉⠉⢶⣶⣶⣇⣀⠀⠀⠑⢀⣀⡏⠀ ⠀⢀⠀⠀⠀⣙⣛⣿⣛⡛⠀⠀⠀⣤⡄⠀⠀⠀⠀⣤⣄⠀⠀⠀⣛⣻⣿⣛⡃⠀⠀⠀⠀⠀⠀ ⢰⡝⢤⠀⠀⢉⣭⣿⣯⡥⠉⠉⢪⠻⠃⠀⡔⠀⠀⠛⠛⡊⠉⠉⣭⣽⣯⣭⡁⠀⠀⠀⠀⠀⠀ ⠈⠁⠁⠀⠀⢈⣽⡿⠿⢷⣤⣊⡁⠀⠀⠀⠀⠀⠀⠀⠀⠉⣒⣦⣿⡿⠿⣿⣅⠀⠀⠀⡀⣀⠀ ⠀⠀⠀⠀⠀⢸⣇⠀⠀⣾⡍⣿⡿⠿⠿⣿⣿⣿⡿⠿⠟⠛⠛⢹⡇⠀⠀⠀⣿⠂⠀⠰⠇⢷⠁ ⠀⡤⠀⠠⡀⠈⢿⣄⠀⠘⣿⡟⢀⡀⢀⡀⢻⣏⠛⠿⣶⣶⣶⡿⠁⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀ ⢸⠇⠀⠀⡁⠀⠈⣻⣦⣤⣿⡇⠘⢃⡺⠁⠸⠿⣶⣶⣶⣶⣶⡶⡷⣿⣯⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠁⠀⠈⠀⠀⢰⣿⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠄⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠿⣾⣤⣤⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣧⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡉⠉⠉⠛⢻⡿⢻⣟⠛⠛⠋⠉⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢶⣶⡶⠟⠁⠀⠻⢷⣶⣶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⠐⠺⠂⠁⠉⡀⠀⠀⠪⠉⠉⠻⠳⢦⣄⣈⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣶⠿⠀⢜⠆⠀⢀⠀⠀⠈⠠⠀⠀⠈⠐⠀⡒⠁⢄⠹⢿⡉⠹⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡾⠋⠀⠈⠀⠀⠀⢀⢅⠁⠁⡀⢈⠀⠨⠀⠂⠁⠠⢧⠰⠈⠁⠀⠈⢻⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣞⠁⢀⠀⠀⠀⡅⠂⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠄⠊⠌⠀⠀⠀⢀⠀⢻⡄⠀⠀⠀⠀ ⠀⠀⠀⢀⡾⠃⢰⡟⠀⠁⠐⠀⠈⠀⡀⠉⡀⠀⠀⠀⠀⠀⢀⠀⠎⠘⠄⠀⠀⠀⠹⣧⠈⢿⣄⠀⠀⠀ ⠀⠀⣠⡟⠁⠀⣾⠁⠐⡐⢿⢓⠛⣯⠓⠀⠀⠀⠀⠀⡀⢂⠊⠑⢥⠸⢃⡏⠇⠀⠀⣿⡄⠀⠻⣦⡀⠀ ⠀⣸⠏⠀⠀⠀⢷⡀⠂⠀⣿⠐⠁⢲⢧⠂⣿⣨⠑⠠⣤⣓⠦⢬⠇⠀⣸⠃⠀⠀⠀⣿⠀⠀⠀⠘⣷⠀ ⢀⣿⠀⠀⠀⠀⠈⢿⣤⡀⣾⠀⠀⣿⠀⠀⠂⠀⠀⠂⠀⠡⠀⢨⠁⠀⢸⠄⠀⣠⡼⠃⠀⠀⠄⠀⢹⡇ ⠈⣿⠀⠀⠀⠀⠀⠀⠈⢿⣷⣷⣆⣹⣄⣀⣀⣀⣀⣀⣀⣒⣅⣀⣸⣇⣾⣿⡿⠉⠀⠀⠄⠀⠀⠀⢸⡇ ⠀⠹⣦⡀⠀⠀⠀⢀⣠⡾⠃⠀⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠉⠀⠈⠻⣦⣀⠀⠀⠀⢀⣠⡟⠀ ⠀⠀⠈⠙⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠀⠀

………… im so talented right?

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠈⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠄⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⡤⠄⠀⠀⠀⠀⠀⠀⠀⢀⣀⠼⠀⡣⡀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠠⠊⠀⠉⠰⠀⠀⠀⢸⠇⠀⢠⠘⠁⠘⢢⡀⠀⠀⠀⠀⠀⠐⠒⢄⠀⣠⠼⠃⠀⡰⠊⠉⠀⢉⡉⠳⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡆⠀⠀⠀⠀⠃⠀⠀⣼⠀⠀⠈⠙⠆⡰⠉⠁⢀⣤⢤⡄⠀⠀⠀⠈⠤⠁⠀⠀⣜⡁⡐⠁⠀⠀⠈⢂⠘⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⡇⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢀⣠⠬⠵⠒⠒⣾⠖⣶⡧⣄⣀⠀⠀⠀⠀⠀⠀⣼⠀⠱⠀⠀⠀⠀⢀⠀⢻⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣴⡯⣖⠺⣍⢻⡙⢯⡹⢜⣓⡒⠮⣍⡳⢤⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠠⠀⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣮⣳⢌⡇⡞⢥⡚⡼⢤⢋⡳⢦⣙⠳⣿⡀⣰⠇⠀⠀⠀⠀⠀⡠⠁⢠⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⠉⡄⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠳⠾⠷⢼⣵⠮⠧⣷⣦⣭⠿⠛⠙⠁⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠰⣊⠁⠀⠋⣒⡄⠀⠀⠘⠲⣄⣰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⢤⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢱⢀⠏⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡠⢎⠰⢆⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠊⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠠⡤⠤⢤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠁⠀⠸⢅⡈⢀⣈⡵⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠶⠶⢤⡀⢠⠏⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⣶⡄⠀⠀⠀⠀⢠⣤⣀⡀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⢱⡰⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢐⠁⠂⠀⠀⠙⠏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣴⡾⣧⣀⣸⡆⠀⠀⠀⠀⠉⠙⠃⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢠⢄⠀⠀ ⠀⠀⠀⠀⠘⣆⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣠⠖⠛⠓⣆⢠⠔⠃⠈⠢⠄ ⠀⠀⢀⡀⠀⠙⣦⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⣾⠀⠉⢊⢰⠋⠁ ⠀⣠⠆⠸⣄⠀⠈⠳⡼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠊⣴⠋⠀⠀⠀⠁⠀⠀ ⠘⠃⠄⢰⠄⠃⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠊⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⢸⡁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢸⠅⣀⠼⠁⠳⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⣾⠀⠐⠲⠀⡴⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢇⡀⣀⢀⡀⣀⢀⡀⣀⢀⡀⣀⢀⡀⣀⠀⣀⢀⡀⢀⡀⣀⠀⣀⢀⡀⢀⡀⣀⠀⣀⢈⠀⡀⢀⡀⡇⠀⠀⠀⠑⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡀⣀⡤⢤⡄⡀⠀⠀ ⠀⠀⠀⠈⢠⠞⠉⠓⡶⠄⠀⠀⠀⢠⠏⠀⢀⢹⠅⠀⠀⢷⠀⠄⠀ ⠀⠀⢀⠀⢼⠀⢀⠁⠀⡀⠀⡀⠀⢸⠀⠐⢵⠉⠉⢳⡚⠛⢳⠀⠀ ⠀⠀⠀⠀⠘⡁⠀⢀⠁⠂⡀⠀⠂⠉⠛⢛⠛⠦⣤⠾⠜⢀⡾⡀⠃ ⠀⠀⠐⢠⠃⠡⠀⠀⠀⠀⠀⠀⠀⠠⠀⡘⠀⠀⠀⠛⠒⠋⣀⢄⠃ ⠀⠀⠠⢬⣧⠤⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⠍⠉ ⠀⠀⠀⢀⣿⡴⠒⠘⠛⠀⠀⠀⠐⠒⡄⠀⠀⠉⠈⠯⢀⣜⡏⠉⠀ ⠀⠀⠀⠀⣀⡵⢾⣀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣀⡴⠋⠙⠂⠀ ⠀⠀⠀⡾⢭⣱⢀⡭⠟⡶⢶⠶⠤⠤⠤⠴⠶⣾⠻⢭⡀⠀⠀⠀⠀ ⢀⣠⠎⢀⠐⠞⣝⣩⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠉⠒⢦⠀⠀ ⠸⣌⣧⣛⣙⡼⢡⠏⡀⠀⢀⠀⡀⠀⢀⠀⡀⡀⢀⠙⡀⠀⣩⠀⠀ ⠀⠀⠀⣎⣘⣦⡼⠒⠈⠀⠁⠈⠈⠀⠁⠁⠈⠀⠁⡒⢣⠒⠁⠀⠀ ⠀⠀⠀⠀⠀⠸⣇⢄⠄⣀⢀⡀⠀⠀⢀⢀⢀⢠⠨⡰⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠃⠁⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠦⠄⣀⣄⣀⠥⣀⣀⣀⠠⠴⠊⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⢿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣤⣀⡠⠤⡶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣙⠿⢿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣦⣾⣿⣭⣯⣭⣭⣭⣭⣭⣯⣷⣤⣤⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣷⣶⣤⣬⣉⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⡛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣄⠙⢿⣿⣿⣿⠁⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⡛⠃⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣷⣄⠹⣿⡏⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠟⣩⣴⣶⣿⣷⣶⣬⡙⢿⣿⠿⣯⣍⠛⢁⣴⣷⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣧⣸⡇⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠏⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⠹⠷⠈⠁⣠⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠜⠻⣿⣿⣿⣿⣿⣿⣿⣇⠀⣀⣤⣤⡘⢿⢸⣿⣿⣿⠸⣿⣿⣿⣿⠟⣿⣿⣿⡿⠿⠆⠀⣠⣦⠹⣿⣿⠟⣡⣶⣦⡌⢿⣿⣿⣿⣿⣿⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⠇⡾⠉⠋⠉⢿⣦⠸⣿⣿⣿⣧⣬⣙⢉⣵⣦⣬⡟⢡⣶⠿⠿⢦⡙⣿⣿⣿⢃⣾⣿⣿⣿⣿⠘⠻⣿⣿⣿⡇⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡙⠿⣿⣿⠘⣧⣌⣶⣆⣴⣿⡆⢿⣿⣿⣿⣿⣿⢸⣿⣿⣿⢠⣿⡁⢀⡂⠈⣧⢹⣿⡇⣼⣿⣿⣿⣿⠏⣼⣷⣤⣹⡟⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿⣇⠻⢏⣾⣿⣿⡘⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⣿⡿⣽⡏⠼⣋⣴⣿⣿⣿⡟⣡⣾⣿⣿⣿⣿⠁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⠟⢻⣷⡘⣿⣿⣿⡏⣸⣿⣿⣿⣿⣿⣷⡮⣶⠟⣰⣿⣿⡿⠿⠟⠡⠾⠿⠿⠿⠿⠿⠏⠴⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣯⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡶⠿⠿⠿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠂⠀⠒⠲⡴⢉⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠑⣦⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡾⠀⠀⠀⡐⢲⠀⠀⠀⢠⣿⣡⣶⣷⣦⣄⠀⠀⠀⢀⣾⠟⠀⠀⠀⠀⠀⣨⣶⡿⠿⠛⠛⠋⠉⠉⠛⠛⠿⣿⣦⠀ ⠀⠀⠀⠀⠀⠀⢀⡶⠋⠁⠀⠀⠀⠀⠀⡠⣣⢆⠳⢄⡀⢸⣿⣿⣿⣿⣿⣿⣦⣀⠀⣿⣯⣶⣶⣶⣶⣶⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇ ⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠘⠤⡙⢦⣧⠞⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀ ⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⡆⠲⡄⠀⠀⠀⠹⣤⠇⠀⢠⣾⢻⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠃⠀ ⠀⠀⠀⢀⡠⠾⠀⠀⠀⠘⢄⡰⠁⠀⠀⠀⠀⠀⠀⢠⣿⠃⠈⠋⠉⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠛⠀⠀⠀ ⠀⠀⡴⠋⠀⠀⠀⣀⣤⣴⣤⣀⣴⣶⣦⣦⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠉⠳⡄⠀⠀⠀ ⠀⢰⠁⠀⢀⣤⣾⣿⣿⣿⣿⣃⣭⣍⠉⠉⠃⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⠿⠛⠛⠻⣿⣄⣀⢸⡀⠀⠀ ⠀⢸⣀⣴⣿⣿⣿⣿⣿⣿⡿⠋⢙⣿⣤⣄⣀⡀⣸⣿⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣠⣴⣶⠿⠿⠛⠻⠿⣿⣶⡀ ⠀⣼⣿⣿⣿⣿⣿⡿⣿⣗⣯⣴⣿⣿⡿⠛⠛⣛⢿⣿⣦⢴⣷⣦⡀⠀⠀⠀⠀⠀⢀⠀⠀⢄⡀⠀⠀⠀⠀⢀⣾⣷⣿⠛⠁⠀⠀⠀⠀⠀⠀⣼⣿⠇ ⠀⣹⣿⣿⣿⠿⣫⣾⣿⣿⢟⣿⠟⠁⠀⢠⠦⡀⢑⢯⣿⣧⡉⠁⠀⣀⠀⠀⠀⠿⢿⣿⣦⠀⠈⢦⠀⠀⣠⣿⠟⢿⣷⣤⣶⣶⡄⠀⠀⠀⣰⣿⠃⠀ ⢀⠇⢠⣿⣃⣀⣿⣿⣿⡿⢻⠋⡢⢀⣀⢸⠀⠈⢦⠀⠙⣝⢿⣶⣤⣽⣃⡀⠀⠀⠈⢻⠁⢈⣀⣬⣴⡿⠛⠁⠀⠀⣿⡿⣶⠿⠃⠀⠀⣰⣿⢯⠀⠀ ⢸⡅⠘⠻⢿⣿⣿⣿⣯⠀⣀⣩⣁⣘⣿⣿⢀⣜⣿⣷⣄⠈⢿⣿⣿⡙⠛⠻⠿⠿⠿⠿⠿⠿⣛⣯⣷⠶⢿⣿⠇⢸⣿⡄⠀⠀⣀⣠⣶⡿⠃⢸⠀⠀ ⠈⣇⠀⢠⣿⣿⣿⣿⣿⢏⣇⣿⣿⣿⣧⡀⠙⢿⣇⠀⠙⣧⡀⠹⣿⣿⣦⠀⠀⠀⠀⠀⠀⠾⠿⠿⠀⠀⠈⠁⣠⣿⠻⣿⡿⠿⢿⡿⠿⢶⣦⡎⠀⠀ ⠀⠈⢦⡀⣿⣿⣿⣯⣿⣾⣿⣿⣧⠀⠙⢿⣦⢀⣿⡄⢠⣿⠱⣄⠘⢿⣽⣷⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⣶⠾⠟⠁⠀⠸⣷⠀⠀⠀⠀⢀⣿⡇⠀⠀ ⠀⠀⠀⣿⡟⣿⣿⡟⣿⣻⡋⣠⡿⣷⣦⣄⡽⠋⠉⣉⡙⢿⣆⠈⢢⡈⠻⣾⠋⠉⠉⠛⠛⠛⠉⠉⠁⢨⡷⠀⠀⠀⠀⠀⢻⡇⠀⢠⣶⡿⠛⠀⠀⠀ ⠀⠀⣼⡟⣿⠋⣿⣿⣿⣿⣽⣿⣷⠏⢹⣇⣤⡤⠀⠻⠟⢸⣿⠀⣴⣷⡘⣿⡄⢠⡀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⣼⠷⣶⠾⠃⡇⠀⠀⠀⠀ ⠀⣸⣏⣻⡇⠀⣿⣿⣷⡜⢿⣿⣿⡀⠸⣯⣨⣷⣤⣾⣿⣿⠋⣶⣿⠇⣽⣿⣿⣛⢯⣲⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⣰⠇⠀⠀⠀⠀ ⠀⢻⣿⣿⠳⣄⣿⣸⡟⢿⣦⠻⣿⣽⣄⠈⠻⣿⣿⠟⣻⣿⡄⣀⣿⣶⣿⡟⠻⠿⢷⣷⣤⣶⠞⠋⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀ ⠀⠘⠛⠁⠀⢸⣏⣿⣷⠀⠻⣷⡘⢿⣿⣶⡷⣸⣄⠚⡟⡾⢷⣿⣻⡿⠀⠀⠀⣠⡿⣻⣿⡏⠀⠀⠀⠀⠀⠀⣠⡾⠋⢰⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣹⡟⠸⣆⠀⠘⢿⣦⡹⣿⣿⣿⣇⣴⣷⡾⠿⠇⠈⠉⢀⣴⡾⣫⡾⠋⠘⢿⣽⣦⣤⣤⡶⠟⠋⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠀⠀⠙⢶⡀⠀⠻⣿⣿⣿⣶⣿⡿⢿⠇⠀⠀⢀⣴⢟⣡⡾⠋⠱⣕⢲⡀⠈⠉⠉⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⠚⢿⣿⣀⣉⣀⣀⣤⡴⢞⣿⣷⠟⠉⠀⠐⠂⠘⠓⠋⠀⣸⠢⠄⠀⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣷⣶⡾⠟⢋⣤⢦⣄⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠈⠉⠁⠀⠀⠉⠁⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⢰⡏⠀⡄⢠⣾⣿⣷⡄⢠⡎⢰⡇⢠⣾⠋⠀⢠⠀⢰⡞⠁⠀⠀⠐⠀⠀⠀⠀⠂⡄⠁⢠⠁⠀⠂⠀⠁⠈⣼⠃⠀⠂⡔⠀⠀⠈⡄⠐⠀⠀⠀⣧⠀⠀⠐⡄⠐⠀⡄⠐⢠⠀⠙⣿⡆⠀⠉⣿⣤⠀⠀⠀⠀⠀⠀⢠⡖⠊⢡⣾⣿⠉⡄⢠⠀⣿⣷⠀⢨⣷⠛⡆⠀⠀ ⠀⠀⣴⠃⠠⢀⣴⠿⣹⢃⣿⣿⠟⠀⣼⢠⠞⠁⡀⠂⢠⣼⠟⢀⠐⠠⢀⠂⡀⠐⠀⣤⠞⠁⡐⢀⠀⠀⠀⢀⠀⣸⠏⠠⢈⠐⡀⢂⠘⠆⠀⠀⣤⠀⠂⠈⠳⠀⠄⡀⠁⡐⠠⢁⠀⠂⠄⠹⢿⡂⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠁⣴⣾⣿⠁⠄⠠⠀⠂⠸⣯⢧⠀⣯⣛⢿⡄⠀ ⠀⡼⠁⠈⣠⡿⣎⣿⡵⣟⣾⠏⠀⣰⡿⠋⢀⠂⠐⢠⣾⠋⠀⠄⡈⠄⠂⠠⢀⣡⠞⠁⠄⠡⠀⠄⡈⠄⠡⢀⣼⠏⠐⡀⠂⠄⠠⠀⠄⠠⠀⢀⣿⡆⢀⠀⠘⣆⠐⠠⠐⠀⠄⠠⠈⠄⠂⠀⠹⣯⡄⠀⠀⠛⣆⠀⠀⠀⢃⣦⣾⣿⣿⡄⠐⠀⠠⠁⠌⠀⣿⣛⡇⣿⣜⢫⣷⠀ ⢰⠃⢀⣼⣟⡱⣝⣎⣷⣿⡏⠠⣰⡟⠁⠐⢀⠠⢠⣿⠋⠀⢂⠐⠀⡀⠂⣤⡾⠁⠌⠐⢈⠀⡁⠂⠠⠐⣠⡿⠃⡀⠡⠐⠠⠈⠐⠈⣤⠂⢠⣼⣿⣿⡀⠀⠀⢹⣧⠐⠠⠈⠐⡀⢁⠒⠀⡁⠀⠹⣷⡀⠀⡀⠙⣦⣥⡴⢾⣿⣿⣿⣿⣇⠀⡈⠐⠈⡐⠀⢺⣧⢻⡗⣮⢳⣻⡄ ⡿⢀⣾⢳⣎⡷⢭⣾⣟⡿⠀⣰⠏⠀⠄⡁⠠⠀⣼⡏⠀⠄⠂⠀⠂⣐⣾⠋⠀⠄⡈⠄⠂⢀⠠⠀⢡⣼⠛⠠⠐⢀⠁⠌⢀⠁⠌⡼⢁⣴⣿⣿⢡⢿⣇⠐⠀⠸⣟⣧⠐⠀⢁⠀⢂⠈⠄⠠⠀⠄⢻⡅⢂⠀⠄⠀⢳⣾⢻⣽⣿⣿⡿⣿⡀⠄⡁⠐⡀⠀⣹⢮⣛⡼⢣⢷⣹⡇ ⣿⣼⢏⡗⣾⣝⣿⣟⣾⠇⢰⡏⠁⠀⢂⠐⠀⢰⣿⠀⠈⡀⠄⢁⣼⠟⠁⢀⠐⠠⠀⠂⠀⢂⣠⡾⠏⠀⢂⠐⡀⠂⠌⢀⠂⢀⣼⣧⠿⣽⣿⣧⡟⣞⣿⠀⠀⠀⣿⢞⣆⠡⠀⢈⠠⠐⢈⠐⠠⠀⠘⣧⠲⡄⠀⠂⣹⢧⣏⣿⣾⡷⣿⣿⡇⠀⠄⡁⢀⠀⣼⣳⣿⡜⡯⢮⣽⠀ ⢹⣯⢞⣹⣿⣿⣻⣾⢿⢂⡏⠀⠀⠀⠂⠈⠀⣾⡇⠐⠀⠀⣰⡟⠃⠀⠂⢀⠈⠀⢀⢠⣰⣟⣻⡇⠐⠀⢂⠠⠀⠌⠀⠄⢠⣾⢻⡜⣿⣿⣿⠋⠀⢸⣿⡅⠀⠀⣿⣏⢿⡀⢂⠀⡐⠈⠠⢈⠠⠐⠀⣿⠀⢷⡀⠁⣼⡳⣾⣿⡿⣱⣿⣿⠇⠂⡐⠠⠀⣰⣯⣽⠀⢻⣭⢳⠏⠀ ⠈⢻⣮⣽⣿⣳⣿⠧⣿⠈⢀⣾⡀⠡⠐⠀⠁⣿⠀⢂⢁⣾⠏⢀⠠⠁⠀⢂⣠⣶⡾⠋⣹⣿⡿⣇⠈⠀⠄⠀⡀⢂⠁⣠⡿⣎⢷⣿⣿⠟⠁⢀⡀⠼⣿⠇⠀⠀⣿⣿⡽⡇⠀⠄⠠⢁⠂⠄⠐⠠⠀⣻⡀⠸⣷⠀⣿⣽⣿⣿⢳⢧⣿⣿⡀⠁⠄⠂⣰⣟⣾⠃⠀⢸⡾⠋⠀⠀ ⠀⠀⠙⣿⢷⣿⠻⣽⣿⠀⣼⣻⠅⠀⠄⠠⠀⣿⠀⢈⡿⠧⣄⣀⣀⣄⡷⣾⣽⣿⣧⢀⣿⣿⣿⣿⡄⠁⠀⠀⢤⣤⣴⣿⣳⣽⣿⣷⠿⠚⠋⠁⠀⠘⣿⡃⠀⢸⡿⣸⣷⢿⠀⠂⢁⠂⠄⢈⠐⡀⠀⣿⠀⠀⣿⣯⣷⣿⣿⣏⠷⣺⣿⠇⠁⠈⢀⣴⣿⡾⠁⠀⠀⠋⠀⠀⠀⠀ ⠀⠀⢸⣯⢿⠃⠀⢸⡿⣰⠿⢿⠀⠀⠂⠐⠀⢹⣠⣟⣁⣤⠼⠛⠛⠿⣶⣽⣿⣿⣿⣿⣯⡟⠸⣟⣿⣄⠀⢁⣠⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⣿⢣⣝⣿⣻⠀⡐⠠⢈⠐⢀⠂⠠⢀⣿⠀⠀⢼⣿⣿⡿⣗⢮⣻⣽⠏⠀⣀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣟⣯⡿⠀⢀⣿⣧⡿⣦⣼⣦⢤⡤⠶⠶⠚⠛⠉⠁⠠⠀⢂⣀⣤⡤⠿⣿⣽⣎⣻⣽⣷⣦⣽⣿⣿⣷⣾⣿⡿⠟⢹⠉⠉⠙⡲⠒⠒⠠⠤⢄⣀⣿⠀⣸⣯⡟⢸⣿⣿⠀⡀⠡⠀⠄⠂⠄⠁⣰⡇⢀⣼⣿⣿⣟⡳⣝⣮⣟⣣⣤⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣷⣿⣇⠀⣼⣿⣿⠃⠀⢹⡷⣶⣤⣤⣀⣄⡀⢬⠴⠒⠋⠉⠄⠠⠀⠄⠹⣿⣿⣿⣿⡿⣿⣿⠿⠟⠛⠉⠁⠀⣰⠏⣀⡴⠋⠀⠀⠀⠀⠀⠀⢠⠏⣱⣿⠏⠀⠘⣿⡟⠀⠀⠁⢂⠈⡐⢀⣰⣿⣶⣿⣿⡿⣏⢾⡱⣏⡼⣹⣿⢿⡷⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠋⠛⣾⣿⡏⢹⡀⠠⢤⣿⣴⣭⣾⣿⣏⣻⣤⣤⣤⣴⣶⣶⣶⣾⣿⣿⣽⣿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⣉⣿⣉⣉⣉⣉⣉⣁⣤⣤⣤⣏⣴⣿⣧⣤⣶⠛⣻⠄⠀⢁⠈⠀⠠⠀⢀⡽⣿⣿⡿⠋⠀⣟⢮⡵⢎⡷⣽⣟⣿⣏⢧⡻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣿⡟⠀⠀⠃⠀⢰⣿⣯⢻⣝⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣷⣾⣦⢤⣀⡀⠂⠁⢐⡼⠃⣯⠁⠀⠄⠁⣿⣳⠺⣝⣼⡿⣯⣿⡹⢮⡵⣻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣼⣿⠟⠀⠀⠀⠀⠀⣿⠞⣷⡈⠙⠷⠿⣿⡿⣿⣿⠉⠉⠉⠋⣿⣿⠛⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠓⢸⣿⣿⢸⣿⣿⣿⣿⣿⠀⠀⠐⠂⠈⣿⣿⣿⠿⠛⠛⠋⠀⣠⡟⠁⢠⡇⢈⠐⠠⠀⣿⢎⡟⣼⣿⣻⣿⢧⠻⣵⣚⠽⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣼⠃⠀⢹⣷⡄⠀⠀⢹⣷⠘⣿⡆⠀⠀⠐⣿⣿⣷⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢸⣿⣿⣿⡟⣽⡯⢿⡇⠀⠀⠀⠀⢠⣿⣿⠋⠀⢀⣼⢃⡴⠋⢀⠀⢸⡇⠀⡄⠁⠂⣿⢫⣾⣿⣷⣿⢣⣏⢟⡦⢏⡯⣽⡎⢆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠸⡟⢿⣅⡀⠀⢿⣇⠻⣷⡀⠀⠀⢿⣿⣽⣿⣹⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢿⣿⠟⠻⢾⣹⡟⠀⠀⠀⢀⣠⣿⣿⠇⢀⣤⣿⠇⡠⠀⢂⠀⠀⣿⠀⠡⠀⠌⡀⡿⣍⠿⣹⢿⡱⢯⡜⣮⠽⣙⢶⡹⣷⠈⢆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⡇⣸⣿⣷⡄⠈⢿⣯⠹⢿⣄⠀⠈⢻⣯⠀⣹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣦⣤⣾⣏⣠⡤⠴⠖⠛⠋⣱⠏⣠⣾⣿⠏⣰⡇⠀⠂⠀⢰⡟⠀⡀⠅⢂⠀⣿⢎⡟⣥⠯⣝⢾⣿⡜⣻⡝⣮⢓⣿⠀⠘⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⡇⣽⢶⡹⣿⣧⡘⣿⣦⠀⠈⠙⠒⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣼⡵⠚⣹⡿⠃⢠⣿⠇⠀⠁⠀⣸⡇⠠⡄⠈⠠⢈⣟⢮⡝⣮⡝⢮⣿⢸⡽⣹⡟⣼⣙⢾⡇⠀⠸⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢰⡇⢾⣣⢟⣿⣿⣿⣶⣽⣧⡀⠀⠀⠀⠀⠀⠀⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠚⠋⠁⣠⡾⠋⢀⣠⣿⡿⠀⠀⠁⢠⣿⠃⢸⡇⠀⠁⢸⡯⣞⣱⢳⣚⢷⡇⢸⢷⣹⣟⢶⡹⢾⡇⠀⠀⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⠃⡇⠀⠀⠀⢸⢃⣻⠵⣮⣿⣿⣿⣿⠀⠉⠛⠦⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⣉⣠⣴⣏⣻⣷⠃⠠⠁⢠⣿⣟⠀⣾⠀⠀⠀⣼⡳⡽⣸⢇⡯⣾⠀⢸⡧⡿⣟⢮⡝⣻⡇⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡅⢻⡄⠀⠀⢸⠀⣹⢟⡲⣿⣯⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠛⠛⠓⠛⢋⣭⠶⠋⣱⣿⠏⠠⠁⠐⣾⣿⡇⣸⡏⠀⠀⣀⣾⡷⣹⠵⣎⣷⠇⠀⣻⣼⠇⣟⢮⡹⣽⠇⠀⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠙⠦⣄⡾⠀⢸⣏⠷⣿⣏⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⠉⠀⠀⣼⡿⠋⠀⡐⠀⣿⣿⡯⢇⣿⠁⠀⢀⡼⠁⣷⡹⢞⣱⡏⠀⢀⣿⡏⠀⣟⣎⢷⣻⠀⠀⠀⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢗⡄⠀⠀⠀⡀⠸⣏⡟⣿⣎⠷⣻⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢾⡟⠁⠀⠆⢠⣽⣿⣿⣝⣻⠃⠀⢀⣼⠃⠀⣷⣹⢫⡟⠀⠀⣾⠟⠀⢸⡗⣮⢻⡏⠀⠀⡼⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⣄⣁⠐⠀⣿⢺⡝⣮⣛⡭⣿⣿⣿⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣱⡟⢀⠁⢀⣰⣿⣿⢿⡟⣼⠃⠠⢈⡾⠁⠀⢰⡗⣧⠟⠀⢀⣺⠋⠀⠀⣼⡝⣶⡟⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠄⢺⡧⣟⠶⡭⢞⡹⣿⣿⡗⣮⠽⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⢫⡽⠃⢀⠀⣠⣾⣿⡟⢁⣾⠟⠁⣀⣤⠟⠀⠀⢀⣾⡽⠋⠀⣨⠞⠁⠀⠀⣰⠿⣼⠟⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡎⠀⠘⣿⡟⡿⣽⢭⡳⣭⢻⣿⡮⣝⢮⡝⡿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢞⡹⢌⣶⠟⠁⢀⣦⠾⢻⡏⢩⡷⠏⠁⣠⣴⠋⠀⠀⠀⢠⡾⢋⣀⡴⠛⠁⠀⠀⠀⣰⣯⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⢻⡇⠘⢬⡙⠷⣧⡻⡼⢿⠮⣗⣾⡱⢧⣫⡷⠦⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⢖⠻⣉⠧⡘⢦⣱⡞⣁⣤⢞⠫⣅⢋⣶⣿⡿⠵⢶⣿⡿⣿⢷⣄⡀⠞⠛⠚⠉⠀⠀⠀⠀⢀⣤⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⣿⡀⠀⠑⢦⣄⠉⠙⠉⠳⢤⣉⣹⠛⠉⠀⠀⠈⠑⠒⠒⠒⠚⡿⠻⡟⠷⣜⣌⠳⣌⠲⣩⣾⠷⡛⣍⠲⢌⡓⣌⣲⡞⠁⠄⠀⠸⣿⡽⣯⣟⣿⣿⢷⣦⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢌⣿⣄⡀⠀⠈⠉⠛⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡟⠀⢰⣿⡄⠀⠉⠙⠲⠿⣭⣆⣣⡱⢌⡚⢤⢳⡼⠋⠀⡀⠂⠁⠀⣿⣿⣷⣻⣞⣿⣯⣟⡿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢨⢌⢣⢣⠹⣯⣿⡧⣼⣿⠟⣱⢊⢥⣿⣾⢿⣿⠋⢀⠞⠀⠾⠤⣄⡙⠢⣈⢻⣿⣳⡿⣟⣷⣿⠟⣣⠙⡤⢃⡍⣒⢩⠒⡌⠎⡥⠛⢿⣔⠩⣆⠹⣰⣾⡿⣯⣟⣯⠿⡝⡛⠞⣽⣯⢿⣽⣻⣽⣻⣞⡷⣯⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠰⣊⢆⢣⠓⡜⢿⣿⢋⡕⢪⠡⣾⣿⣻⣾⣿⣿⣇⠁⠀⠐⠠⡀⠄⢉⣁⠈⠛⣿⣿⣿⣿⢋⡜⡸⢄⠫⢔⠣⡘⢤⠣⡙⣌⠳⣈⠳⡌⢻⡖⢬⣿⡿⢻⡙⢭⡑⢆⠳⣌⠱⣹⣿⣞⡿⣞⡷⣯⢷⣯⢿⣽⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠰⡡⢎⠦⡙⡜⣸⣟⠣⡜⣡⢃⠻⣿⢛⣱⣿⣿⣿⡄⠀⠰⠀⠀⠁⢀⣠⣴⣿⣟⣿⣿⣥⢊⠴⡑⢎⡱⢊⡒⡍⢆⢣⡑⢆⡓⠬⡱⢌⣹⣿⢏⠲⣌⠱⡘⢆⡜⡌⢣⢌⠣⣽⡷⣯⢿⣽⣻⣽⣻⣞⡿⣾⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡕⣊⠖⡱⡘⣼⣷⠱⡘⢤⢋⠖⡤⢣⢼⣿⣿⡝⣷⣤⣤⣤⡴⣾⣟⢯⡳⣾⣿⠻⣯⣿⠎⡆⢍⠲⣐⠣⡜⡘⡌⢦⢙⠢⣍⠲⣱⣾⣿⢋⡌⡓⢬⠡⣍⠲⢌⡜⡡⢎⣱⣿⣻⣽⣻⣞⡷⣯⢷⣯⢿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⢜⡡⢎⡱⢑⣾⡻⣧⡙⠦⡩⢜⡰⢃⢞⣿⣿⣽⢖⣳⢾⡷⣝⠶⣟⣧⣿⡿⢡⢣⠙⡤⢓⡘⣌⠣⣌⠓⡬⢱⡘⠦⣉⠖⣬⣾⡿⣿⠡⢎⠴⣉⠆⡳⢄⡋⠖⡬⡑⢎⣾⣯⢷⣯⢷⣯⢿⣽⣻⣞⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢤⠓⣌⠲⡡⣾⡑⢻⣇⠣⡕⢪⠔⡩⢌⣿⣷⣻⣿⣮⣷⣽⣾⣿⢿⣿⠟⡰⢃⢎⡱⢌⡱⠌⢆⠳⣄⠫⡔⢣⠜⡱⣨⣾⣿⢯⣿⢣⡙⣌⠲⠌⡜⡰⠣⢜⡱⢢⡙⢼⣟⣾⣻⣞⡿⣞⡿⣞⣷⣻⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⢤⢋⡔⢣⡑⣿⢌⢣⠻⣷⡘⢥⢊⡕⣊⢿⣿⣽⢲⡝⣮⣳⣟⢿⡿⢃⢎⡱⣉⠦⣑⠪⡔⡩⢎⡱⢌⡱⢌⣃⣮⣷⣿⠿⣽⣿⡏⢦⠱⣈⠖⣉⠖⣡⢋⠦⣑⠣⠜⣿⡽⣞⡷⣯⢿⣽⣻⡽⣾⣽⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⢃⠎⣌⠣⡜⣿⠌⣆⢣⠹⣷⣌⠚⣤⢃⢻⣿⣿⣷⣿⣛⢷⣽⠟⣡⢋⠦⡱⢌⠲⣁⠳⣌⠱⢢⡑⢎⣴⣷⣾⠿⣋⠕⣾⣟⣿⠏⡔⢣⠜⡘⢤⢋⡔⣊⠖⣡⢋⢼⣿⡽⣯⢿⣽⣻⣞⣷⣻⢷⣻⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣎⠜⡤⢓⣸⣿⡘⢤⢃⠧⣘⠻⣷⡠⢫⠜⣿⣷⡯⣝⣻⣿⠏⡜⢤⢃⢎⡱⢊⠵⣈⠇⠦⡙⣦⣽⠾⡛⢭⢂⠳⢬⣾⡿⣽⣿⠱⢌⠣⢎⡑⢎⠢⡜⢤⢋⠴⣉⣾⣯⢿⣽⣻⣞⣷⣻⢾⡽⣯⣿⢿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡜⡰⢣⢼⣿⡍⢦⡉⢖⡡⢓⡌⢻⣦⡩⠜⣿⣿⣿⡟⢣⠜⡘⢦⡉⢦⠱⣉⣦⡵⢾⠳⡛⡍⢆⢣⡙⢦⡉⢮⣿⢯⣟⣷⡟⡸⢌⡓⢬⡘⢬⠱⡘⢦⡉⢖⣸⡿⣞⡿⣞⣷⣻⢾⡽⣯⢿⣽⣿⣻⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣞⣿⡔⠣⣿⣿⣏⠴⣉⠦⣑⠣⡜⡡⢎⡹⢷⣸⣿⢋⡌⢣⣎⣵⣶⠿⢛⡛⡍⢦⡑⢎⠥⡓⡜⡌⢦⡉⢦⢱⣿⢯⣟⡾⣽⢣⡑⠎⡜⡰⠘⣆⢣⡙⢤⡙⠆⣾⢿⣽⣻⡽⣾⡽⣯⢿⣽⣻⣿⣳⢯⣟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣻⣞⣯⡑⣿⣻⣿⠰⣡⠚⢤⠓⡬⡑⢎⠴⣉⢿⡝⣷⣾⣿⠿⢋⠦⡙⠦⡱⡘⢆⡩⢎⢒⡱⡘⢜⠢⢍⣲⣿⢯⣟⡾⣽⣿⢢⡙⡜⡰⢡⢋⡔⢢⠍⢦⡙⣌⣿⣟⣾⣳⣟⣷⣻⣽⣻⣞⣿⡷⣯⢿⣯⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⣯⣟⣿⣿⣳⢿⣷⠡⢏⢢⡙⡰⣉⢎⠲⣁⠎⣿⡘⢷⢠⢋⡜⡰⣉⠖⣡⠑⡎⢔⡊⢖⡰⣉⢎⡱⣺⣿⣽⣻⢾⣽⣻⡗⢢⠱⣌⠱⡡⠎⡔⢣⠚⡴⡘⢼⣷⣻⣞⣷⣻⣞⡷⣯⢷⣻⣿⡽⣯⣟⡧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⡷⣯⣟⡷⣯⣟⣿⣷⢈⠦⣑⠱⣂⢎⡱⠌⡎⣽⡘⢆⡃⢎⡔⠱⡐⢎⡔⢩⠒⡥⠚⡤⠓⣌⢲⣴⣿⣳⢯⣟⡿⢾⣽⡏⢆⠳⣈⠕⣢⠙⣌⠣⡙⢤⢃⡿⣞⣷⣻⣞⡷⣯⢿⡽⣯⣿⣷⣻⢷⣻⡇⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣦⣄⠀⠀⢀⣠⣤⣶⣶⢿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠛⡁⢄⠈⡛⢿⣷⣾⣿⠟⠉⠁⠀⠀⠀⠙⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣶⣾⢿⣿⣶⣦⣤⣀⠀⣀⣀⣠⣤⣶⣶⣶⣾⡟⠡⢁⠔⠂⠡⠐⡈⢿⣿⡅⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠈⠙⠛⣿⣿⡟⠛⠉⠁⠀⢠⣿⡇⠁⢢⠈⣼⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣴⣶⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢀⠉⡄⠂⣿⣏⢄⣿⠟⡉⠄⡉⠻⣿⣿⠋⠍⠩⢉⠛⣿⣆⠀⠀⠀⠀⠀ ⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠌⠠⡁⠌⠻⣿⣟⠠⠐⡈⠤⠁⣼⣿⣾⣄⠁⠆⢂⢼⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣮⣴⣤⣼⣶⠿⣿⣤⡡⠐⢂⣱⣾⣏⣸⡿⢈⡐⠂⣼⡿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠈⠛⠿⠿⢿⣿⠋⠛⡉⠐⡠⢀⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣴⣤⣧⣾⠿⠋⠙⣿⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⣿⡿⠿⠿⠗ ⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠙⣿⠁⠀⠀⠀ ⠀⠀⠀⢘⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠒⢶⠄⠀⠀⠀⠀⠀⣠⣤⣿⣀⣀⡀⠀ ⠲⠿⠿⠟⣿⣿⠛⠉⠀⠀⠀⠀⢀⡴⠖⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⡿⠛⠛⠛⠁ ⠀⠀⠀⠀⠘⣿⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⡃⠀⠀⠀⠀ ⠀⠀⠀⣤⣶⡿⣿⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⠿⢿⣿⣦⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⢻⣷⣤⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣾⣿⠿⠿⠶⠶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡿⠿⠛⠿⠷⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⠟⠀⠀⠀⠀⠀⠀⢻⣿⣧⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠻⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⣛⠛⠛⠻⠛⠛⢛⣛⣽⣿⣿⡿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⠀ ⠀⠀⠀⠀⠀⠻⣧⡀⠀⢀⣤⣤⣤⣤⣾⣿⣿⣻⢾⣿⡈⡙⠛⠻⠿⠿⠿⠟⠛⢋⢱⣿⣿⣽⣻⢿⣿⣦⣤⣤⣤⣤⣀⣀⣠⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⣶⣧⣷⣦⣷⣶⣼⣶⣶⠿⠿⠿⠿⠟⠛⠋⠉⠀⠀⠀⠈⠉⠛⠋⠀⠀⠀⠀⠀

⠁⠀⢰⡿⣇⠉⠉⠉⢹⡇⠀⣿⣼⡿⠋⠉⠁⠀⠉⠉⢀⣤⠾⠋⠁⠀⠀⠀⠀⢀⣤⣾⣿⣿⣷⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡟⠀⣿⠶⢦⣤⣼⣧⠾⢿⠁⡇⠀⠀⠀⠀⣀⡴⠟⠁⠀⠀⠀⠀⠀⣠⣶⡿⢿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⠁⣼⣿⢠⠐⠠⠘⣿⠀⢻⠀⡧⢀⣀⣴⡞⠋⠀⠀⠀⠀⠀⢀⣴⠿⠿⣫⣴⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡾⠁⣼⢇⢻⠈⢠⡀⡄⣿⠀⢸⢀⣷⡾⠛⠁⠀⠀⠀⠀⠀⣠⡾⠫⢹⣴⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⣰⠏⠀⣿⠷⢶⣅⣁⣿⣤⡾⠟⠉⠀⠀⠀⠀⠀⣀⡴⠿⠁⣠⣴⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣰⣏⡴⢟⣿⠇⠀⠈⠙⠻⠋⠀⠀⠀⠀⠀⢀⣠⠾⠋⢀⣴⣾⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠶⠒⠛⠛⠛⠛⠛⠛⠛⠛⠓⠲⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠏⣿⣴⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⣠⣶⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⢀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣡⡾⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⣀⣴⣾⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠀⠀⠀⠀⠀⣰⣿⠋⢹⣧⠀⠀⠀⠀⣰⣿⠿⣷⠀⠀⠀⠀⠀⠀⠉⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀ ⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢁⣠⣶⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⣰⣿⠁⣀⣾⠛⠀⠀⠀⣸⡟⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣧⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⢀⣴⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣶⣿⣟⠃⠀⠀⢠⣿⣇⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀ ⠀⠀⠀⢀⣠⠶⠋⠁⣠⣾⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠁⠀⠀⠀⣾⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀ ⠀⣀⣴⡟⠁⢀⣴⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀ ⠞⠉⢀⣠⣾⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⣶⣶⣦⡄⠀⠻⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀ ⣀⣴⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀ ⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⣠⣴⣦⣤⣤⣤⣤⣀⣀⣀⣀⠀⠀⢻⣅⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠤⠤⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠙⣿⠿⣯⡙⢿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣼⣿⢸⣿⣿⡇⣿⣿⢫⣶⣌⢿⣿⡿⣋⣭⠟⠋⠉⠉⠉⠉⠙⠳⣦⡄⠀⠀⠀⠀⠀⠀⠀⢠⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢈⣛⣛⡃⣿⡇⣿⣿⣿⢸⣿⢱⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⣻⣿⢸⣿⣿⡇⣿⡘⣿⣿⣿⢸⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⢤⣀⠀⠀⣤⣿⣷⣭⣵⣿⣿⣼⣿⣿⣇⣿⣧⡙⠛⢣⣿⣿⡼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠟⢀⡾⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣶⣤⣤⠾⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠻⠿⠿⠿⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢶⣤⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀

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⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⢷⠨⡷⡄⠀⠸⣷⡀⠀⠀⢠⠈⣿⢻⣿⡿⣇⠸⠾⣿⣴⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⡠⠔⠁⠀⠀⢀ ⢸⡄⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⣹⣇⡇⠙⣄⠀⣿⣧⠀⢀⢸⡄⣿⠀⠛⠥⠟⠀⠀⠙⣿⣧⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢱⡀⠴⠊⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠸⡀⢢⠀⠀⠀⣏⠸⣼⠀⣼⣧⣾⣿⣦⠞⣸⣧⡟⠀⠀⠀⠀⠱⡄⠼⠟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀ ⠘⡆⠀⠀⠀⠀⠀⢲⡹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡸⡄⠀⢰⡇⠀⢿⡀⢿⣿⣿⠁⢹⣶⡏⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠘⣤⠀⠀⠀⠀⠀⠀ ⠀⡇⠀⡆⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⢸⠃⠀⢸⡇⣾⣿⣿⣄⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⡸ ⠀⢻⡀⢻⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⢻⣇⡿⠀⠀⡸⢰⣿⣿⣿⡿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠀ ⠀⠘⡆⠘⣆⠀⠀⠀⠀⠀⠀⠙⡇⠀⢀⠀⠀⠈⢆⠀⢢⠀⠀⠀⢻⠇⠀⢠⠃⣼⣿⣿⢿⡯⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠂⠀⠀⠀⢀⡠⠚⠉⠀⠀⠀⠀ ⠀⠀⠹⡄⠈⢧⡀⠀⠀⠀⠀⠀⡃⢠⠀⢣⠀⠀⠀⠑⢄⠑⠲⣄⠀⠑⢆⡀⠀⣿⠿⢿⡙⢁⣸⡡⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣸⣟⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠿⠿⠟⠛⠛⠿⠿⠿⠿⢿⣿⣿⣿⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⣀⡴⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢳⡀⠀⠳⣄⠀⠀⠀⠀⠀⠠⢧⡀⢣⡀⠰⡀⠀⠑⠤⠈⠙⠲⣦⣍⣾⢿⣷⡖⠛⠛⠉⣀⠖⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠋⠉⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢳⡀⠀⠈⠳⣄⠤⣄⣀⡟⠦⣳⡄⣻⣄⡿⣦⡀⠐⠀⠀⠀⠀⠛⠿⣍⣉⣙⣻⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⣞⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⢀⣀⣀⡠⢄⡠⠀⠀⢤⢀⣀⣀⣀⣀⣀⠀⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⡄⠀⠀⠈⠣⣱⠿⣄⡐⠠⠙⢿⣿⣽⣯⡙⣿⣖⠲⠶⠶⠦⠶⠚⢿⡉⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣵⣀⣦⣤⣤⣤⣤⣤⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠓⢼⣮⡳⣍⠂⠉⠛⣳⢿⣼⣿⡄⠙⣯⣭⠽⠿⣄⣃⡲⣅⣉⡢⣙⢓⣦⣴⣶⣶⣿⠏⠻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⢿⣀⠀⠠⠤⣌⡹⢄⣀⣀⣠⠤⢿⣿⣋⡿⠻⠿⠻⠟⢉⣉⡤⠟⠀⠀⠀⠈⢿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣿⡟⣿⣦⠢⢄⠀⠭⣓⠲⢦⡄⠌⢒⣻⡀⠉⠉⠉⠉⠛⠉⠁⠀⠀⠀⠀⣀⣠⣴⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⡇⠘⠻⣿⣿⣿⣿⣽⡿⣯⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⡾⠿⢁⣿⣿⣷⣦⡀⠀⣿⣷⣦⣽⣯⡄⣹⣦⣄⣀⣀⣀⣀⣀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠹⡄⠀⠈⠙⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⠿⠛⠋⠐⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠛⠋⢯⡹⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠱⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡇⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣳⣦⣾⡋⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠛⠿⣻⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡽⠷⠚⠋⡍⠉⠩⠂⠀⣀⠁⣀⠠⢀⡉⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡟⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣻⢬⠁⠀⠀⠠⢿⣿⣿⣿⣿⣿⢟⠟⠉⠁⣀⢤⣲⣷⣿⣟⣿⣾⣼⡶⣿⣿⣮⣒⢡⣣⡂⢄⢄⠀⠉⠛⠿⣟⡿⣿⣿⢿⣿⣿⢿⣿⢿⣻⡽⠃⠀⠀⢈⡿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⢿⣳⣆⣀⣤⣴⣿⣿⣿⣝⠝⠈⠁⢀⢴⠕⣣⣿⡟⡻⣼⡿⣏⠷⡹⢞⡵⣻⢝⣿⢶⡢⡕⢠⠑⢕⢄⠀⠀⠈⠫⡳⣻⢿⣻⣾⣽⢿⣻⡿⣽⣆⣀⣠⣜⡿⣽ ⣿⣿⣿⣻⣟⣯⣿⣾⣿⢿⣿⢿⣷⣿⣻⣗⡿⠃⠀⠀⢔⠍⣠⢾⡻⠋⣜⠽⡲⡝⣌⠳⡉⠇⠞⣱⡉⢧⠛⡽⣜⠡⠓⡦⠑⡀⠀⠀⠀⠈⢧⡿⣽⣳⢯⣟⣯⣟⡷⣯⣟⣧⢿⡽⣳ ⣿⣻⡞⣯⢿⣽⣳⢯⣟⡿⣾⣟⡿⣞⢯⡟⠁⢀⢠⡶⢁⡜⢱⠞⠁⢂⡞⢱⠓⠰⠠⠡⠈⠌⠐⠡⣯⠀⠹⡘⡜⣎⠅⠨⠍⢜⠠⡀⢄⠀⠂⢪⢗⣯⢟⣾⡳⣯⢟⡵⣾⣹⠾⣝⣯ ⣯⢷⡻⣝⢻⣞⡽⣻⠾⣽⣳⢯⡻⢽⠏⠄⢀⠢⡿⣀⢮⣸⠏⢀⠀⡜⠀⡎⠁⠀⠀⠀⠀⡀⠀⠀⣾⡆⠀⠁⣩⡘⡎⠄⠈⡌⢆⠱⡈⠄⠀⠀⢳⠽⡞⣵⢻⡵⣫⢟⡵⣫⢟⡳⣞ ⠈⠃⠹⢭⡳⣞⡽⣝⣯⢳⡝⢮⣱⡵⠁⠀⡶⢍⡷⣏⢧⣟⡌⢆⡼⣁⢾⠁⠀⠀⠀⠀⠀⡇⠀⢀⡏⡗⢀⠀⠀⢲⢹⡐⡀⡘⠘⣇⠤⠉⡄⠀⠈⢏⠽⣎⢳⡹⢧⡻⣜⢧⣏⠷⣭ ⠀⠀⠀⢰⣟⣾⣳⣟⡾⣧⣿⣾⣳⡇⠀⣸⣳⣾⣿⣼⣿⢾⣼⣻⣶⣿⡾⡴⢠⡀⢀⠀⢠⠃⡄⠇⣧⣿⠸⡄⣀⠘⣾⣧⢳⢀⢧⣿⣼⣇⢰⢇⠀⠘⣞⡇⣧⡻⣶⣻⡼⣾⡼⣧⣧ ⠀⠀⠠⣌⠻⣌⠿⣙⠧⢩⠼⡛⡙⠀⢀⢇⣻⣯⢻⣻⡟⣿⣹⢿⣻⢯⣻⡙⢧⠹⢌⢣⡏⢧⣘⣻⢹⡍⡧⢿⣹⡣⡹⣿⡸⢈⠇⣿⣏⡙⣏⢸⢠⠀⢩⠟⣈⠻⣌⢣⢛⡬⢃⣏⠻ ⢨⠑⡣⢌⠓⠈⠂⠱⠈⡎⠍⢨⠁⢀⢸⣬⣿⣽⢫⣿⣽⣻⣽⣯⣿⡿⣵⣩⢷⣫⡾⣯⠞⣴⣣⣏⡿⠁⠛⢯⣷⣿⣱⣿⡇⢢⠘⣼⣷⠨⣷⡆⢸⠀⠀⠾⢀⠣⢆⠣⢎⠴⣉⢆⠣ ⢂⠱⢈⠆⠀⠀⠀⠀⢰⡌⠀⡋⠀⣼⢸⣿⡷⣯⢿⣽⣾⣿⣿⣿⡿⢝⣷⡿⣯⢷⣟⣷⣻⢽⡿⢋⣥⣤⣤⣉⣙⠿⣿⣿⣇⢂⡯⣿⣿⡱⣿⣇⢸⡀⠀⠸⡆⠱⡈⠜⡨⢆⢡⢊⠱ ⠂⠅⢊⠔⢂⡀⠀⡀⢸⢃⡐⠁⡲⣘⢶⣿⣿⣽⣿⣿⣿⣿⣽⣶⣿⣿⠿⡏⠈⢉⡩⠝⡠⠎⠀⠛⠛⡛⠛⠛⠙⠛⠪⢻⣧⢳⣽⣿⣿⣳⣿⣹⡇⣄⢀⠀⠡⠡⠈⠆⠡⢌⠂⡌⢂ ⠈⠄⠡⡘⠄⡌⠂⢅⠢⠋⢀⠔⢕⢎⡯⣿⣿⣿⣿⣿⠟⠉⣀⣴⡶⣬⣚⠀⠀⠁⠀⠀⠀⠀⠀⠀⣳⣽⣿⣿⣶⣶⣦⣄⢻⣭⡟⣿⣿⣿⣿⣻⣼⡿⠀⠂⠀⠑⢅⠈⡁⢂⠱⢀⠃ ⠐⠈⡐⣠⢥⠐⠋⢁⢠⠔⢋⠢⡡⢦⣿⣿⣿⣿⣿⡟⣬⣿⣿⣿⡿⡿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣯⣽⣽⣿⣿⣿⣻⡮⡑⣿⡿⢋⣉⠻⣿⣧⢃⠈⢄⠈⠢⡡⡢⡀⠐⡈⢀ ⠀⡠⣚⠔⢁⣤⡾⠊⠡⢂⠕⣨⣾⣿⠿⣹⣾⣿⣿⡯⡝⣿⡏⢿⡻⠿⢿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠑⠎⣣⣍⣡⣫⡿⠃⢸⡕⢐⣿⡿⠟⠩⢇⣿⣿⡏⡄⠀⠢⠀⠀⠀⠨⡢⡐⣼ ⣿⣼⠃⣠⣟⠉⡀⡀⢁⣵⡺⢯⣿⢣⣿⣿⣿⣿⣿⣷⡱⠉⠿⠶⠯⠖⠋⠁⠀⠀⢀⡠⠤⣀⠀⠀⠀⠀⠀⠉⠉⠉⠁⢀⢞⡴⣫⣿⣿⡇⡆⣸⣿⣿⡗⠠⠀⢰⠀⠠⡀⠑⠔⠘⣷ ⣿⡋⢀⢯⠂⠈⡠⣪⢟⡮⣽⣿⢧⣟⡯⣿⣿⣿⣿⣿⡵⠡⠀⠀⠀⠀⠀⠀⠀⢠⢛⣮⠭⢌⣣⠀⠀⠀⠀⢀⣀⣀⠤⢳⣡⣿⣿⡿⠛⡫⢔⣿⣿⣿⠷⠀⠀⠀⣡⠀⠀⠀⠈⠀⢸ ⣿⣻⡈⠀⢀⢄⠺⠥⣟⣽⣿⣿⢈⣿⠔⣿⣿⣿⣻⢿⣷⠁⠀⠀⠀⠀⠀⠀⠀⠘⠯⠿⠾⠛⠋⠀⠀⠀⠀⠐⠚⢒⢪⡷⣿⢿⠏⠈⢀⣴⣿⣿⣿⡫⠁⠀⡀⢰⢃⠇⠀⠀⠀⠀⢸ ⣿⣽⣿⡆⢦⢁⡯⢹⡿⣽⢾⣿⡠⠹⣊⠜⢿⣿⣿⣎⣿⡌⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⡄⡀⠀⠀⠀⠀⠀⠀⠀⢁⣼⢫⣿⣿⣿⣿⣿⡿⠟⠋⡠⣀⣲⢍⡞⡸⡀⠀⠀⠀⠀⢸ ⣿⣷⣿⠁⠦⢬⢣⣹⡽⣞⡽⣿⣞⣅⠊⠮⢌⠻⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠐⢾⡛⠛⢛⡿⠓⠀⠀⠀⠀⠀⢞⣽⣾⣿⣿⠿⢟⠫⣑⣌⡲⢭⣔⣞⡷⢫⡜⣡⠃⠀⠀⠀⠀⢸ ⣿⣿⣻⡄⢅⠞⡗⢦⣛⣯⣝⢯⡿⣷⣜⢄⢀⠑⠀⠙⣿⣿⣿⣷⣄⡠⠀⠀⠀⠀⠀⠙⠿⠖⠀⠀⠀⠀⠀⣀⣶⣿⣿⠛⣡⠖⠉⣠⢟⡱⣞⣯⢟⡾⣙⡎⢗⠱⠀⠄⠀⠀⠀⢀⣯ ⣿⣟⣿⣿⣄⠑⠼⢓⡼⣒⢯⣷⣯⡽⣻⢷⣆⢌⢢⠀⠌⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⡿⣡⡞⡉⢠⡞⡑⣾⢟⡹⢜⠮⠓⡉⠰⠈⠂⠈⠀⠀⢀⣠⡞⣾ ⣿⢿⣻⡽⣻⢟⣶⣶⡠⠍⡐⠪⡖⡻⡿⣿⣿⣬⠘⡟⣨⣽⣿⣿⣿⣿⣿⣿⣿⡿⣷⣦⣤⣶⢶⡿⣿⡻⣟⢽⡿⡇⣿⠁⠆⣟⡰⣿⢇⠊⡴⠉⠀⠕⠈⠀⠀⠀⠀⠔⣲⣛⢶⣛⡷ ⣯⣟⣧⠃⠑⢪⣟⣾⣿⣶⡔⡀⢪⣧⣾⣿⠙⡅⣝⣵⢡⣿⣟⣿⣿⣻⣻⣿⡇⣟⣷⣯⡟⣞⣯⣻⣅⠛⡜⢋⣾⣿⡙⡜⡔⣙⣼⡀⢸⣸⢀⠀⠀⠀⡄⠀⢀⣠⣰⣼⣧⣟⣾⣽⣻ ⠙⢹⣿⡆⠀⡄⢿⡿⠛⠉⠀⠙⠆⣥⠛⠛⠰⠟⠋⣴⡿⠟⠉⠘⠈⠛⠛⠋⣧⢻⡿⣯⠿⣽⠏⠷⡜⠸⡅⢻⠹⣽⣿⡶⣤⠻⠿⠿⠿⠙⠈⡴⣿⣷⣶⣾⣿⣿⡿⣿⣿⣿⣿⢿⣿ ⣀⢸⡜⣮⠱⡘⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠁⡀⠠⠀⣀⠀⠀⣀⠔⡼⢣⠞⡌⠓⡌⢌⢂⠡⠃⡴⠋⠀⠻⣻⣝⢯⡽⡄⠀⠀⠀⣁⡼⣽⣚⡞⣞⢾⡳⣏⢷⡹⢮⣝⡳⢞ ⣟⣮⣽⡒⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⢔⠊⠁⡀⢀⠀⢱⠸⣡⣰⢚⡍⢣⠎⡌⠱⡐⠨⠄⢃⠐⠀⠀⠀⠀⠀⢱⢹⡄⠉⢉⣉⠘⢓⡽⠶⢭⣚⡥⣳⠹⠌⠆⠙⢲⡘⠀⠉ ⣿⣳⢯⢿⣥⢣⠀⠀⠀⠀⠀⡠⠀⢁⠄⠂⢈⡹⣇⣷⡽⣛⣿⣼⣧⢊⠳⢯⣼⣡⣚⣔⡡⢌⡁⢎⡐⢢⠄⣀⣀⣀⣴⡟⣡⣷⣧⣥⣤⣾⣼⠁⠐⠆⡀⠑⢥⢋⠀⠀⠀⢠⠃⠀⡀ ⣷⢯⣟⣯⢾⣭⣛⡴⣂⠦⡔⢀⡄⠃⠐⠜⡉⠄⣿⣿⣷⣛⣾⣽⣿⢠⠑⠤⡑⢤⡁⠢⢉⠶⣌⠲⡜⢩⠙⣄⣣⠞⡡⢈⢴⣿⡿⣯⢿⣿⣿⠀⢄⠈⠎⢂⠈⢆⠀⠀⠀⠠⠈⠀⠀ ⣿⣿⣾⣽⣳⣞⣧⢷⡹⡾⢠⠛⡔⠨⡐⢡⠂⡌⢹⣿⣷⣻⣞⣿⣿⡝⢪⡒⣌⠒⠬⡙⢒⡚⣚⢓⡚⢆⠹⢠⠒⡌⢔⡩⣾⣿⣿⣟⣿⣿⡏⠰⡈⢢⢀⠎⠂⠘⠀⠀⢀⡀⢆⣀⠤ ⣿⣿⣿⢿⣻⢿⠾⣯⠟⢡⠃⡭⣱⠱⡈⢥⠚⡄⢻⣿⣿⣷⣿⣿⣿⢎⠰⣈⠳⡮⣵⣘⣢⣐⣄⡒⠌⡤⣓⣢⣭⠖⡍⢂⣿⣿⣿⣿⣿⣿⠇⡱⢀⢣⡟⠀⠀⠀⡏⡔⢢⣜⢯⣞⣿ ⣿⢿⣽⣻⣭⢋⣩⠂⡠⣣⢋⠴⣡⢣⡑⢎⡱⣌⣻⣿⣿⣿⣾⣿⣿⠎⡰⢀⠣⡘⣥⢫⡳⣙⠮⣍⠛⡽⣫⠷⢡⠃⡜⠠⣿⣿⣿⣿⣿⣿⠰⣡⢣⢏⠡⠀⡀⠀⢱⢭⣳⣞⣿⣿⣿ ⣿⣻⣞⡷⣏⣷⠃⢌⡞⢥⣋⠶⡑⠦⡍⢦⣙⢶⣹⣿⣿⣿⣿⣿⣿⠘⡄⠃⢆⠱⢰⢫⡜⡱⢎⡡⢏⠔⡡⠚⡄⢣⠐⡡⣿⣿⣿⣿⣿⣿⢒⡥⢏⡎⠐⠀⠅⠑⠈⠪⣷⢯⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠛⠛⠛⠛⠿⠿⣿⣶⣦⣤⣦⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣾⣾⣿⣿⡿⠿⢿⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢀⣠⣴⣿⣿⠿⠛⠛⠉⠉⠉⠉⣹⣿⡿⠻⣿⣿⣿⣿⣤⡀⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢠⣰⣿⡟⠏⠉⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣠⣤⣼⣿⣿⣿⣿⣿⣷⣶⣦⡀⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣿⣧⣾⡯⡍⣿⡷⣶⣵⢸⣿⣇⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡿⠿⠟⠿⣿⣿⣷⣾⠟⣼⣿⣿⣿⠇⠀⠀⠀⠀⣠⠤⢤⣀⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿⡟⠀⠀⠀⠀⢀⣤⣤⣶⣷⣿⣿⣿⣿⣷⣦⣤⣄⡀⠀⠀⠸⣿⣦⣀⣸⣿⣿⣿⡿⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣱ ⠀⠀⠀⠀⠀⣠⢾⡵⣲⣿⡏⠀⠀⠀⢀⣼⣾⡿⠛⡩⡣⠛⠀⠀⠀⠉⠙⠻⢿⣿⣶⡀⠀⠈⠻⠿⠿⠃⠸⣿⣯⢝⡳⡄⠀⠀⠘⢆⠀⣀⠴⠃ ⠀⠀⠀⢀⡼⡱⠋⢀⣿⣿⠁⠀⠀⢀⣾⡿⠃⣠⠜⢡⠃⡴⢲⡀⠀⠀⠀⠀⠀⠙⣿⣿⡄⠀⠀⠀⠀⠀⠀⢿⣿⡅⠱⡜⣆⠀⠀⠈⠉⠀⠀⠀ ⠀⠀⠀⡼⢰⢓⣶⣿⣿⡏⠀⠀⠀⣾⣿⣣⠋⡴⢻⢘⣲⢡⣳⡙⠢⣄⣡⠙⠦⣀⠘⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣟⡳⣼⡘⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡧⠘⣻⠟⢹⣿⡿⢷⣶⣦⣿⡿⢡⢾⠒⣦⠳⡉⢸⠀⠈⠓⠤⣉⣀⣀⡘⡇⢻⣿⠁⠀⠀⠀⠀⠀⢸⣿⡇⠙⣌⠃⢇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢇⣰⢣⣤⣼⣿⣷⠶⠿⠈⣸⣿⠋⠸⠷⠏⠀⠙⠛⠀⠀⠀⠀⣟⣿⠀⡇⣸⣿⣿⠀⠀⠀⣤⣤⣶⣾⣿⡿⠶⠾⣄⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠈⠉⠈⢿⣿⣀⣤⣤⣿⣿⠀⠀⠀⠀⠀⡤⠒⠢⢤⠀⠀⠀⠀⣼⠁⣙⣿⡏⢀⡀⠀⢠⣤⣤⣾⣿⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⡀⢠⡶⠿⣿⣿⣏⠁⢻⣿⣦⡀⠀⠀⠀⢱⠀⠀⡼⠀⠀⠀⠀⠉⣹⣿⡿⠁⡇⠈⠉⡟⣭⣹⣿⣏⡏⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀ ⢠⠞⠁⠁⠀⡣⠀⠀⠀⢰⢻⢿⣶⣬⡙⠻⢿⣷⣶⣶⣌⣑⠊⠀⠀⡀⣀⣠⣼⣿⡟⠁⠀⠈⠒⠊⣀⣽⣿⣿⣿⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠣⢄⡀⡰⠃⠀⠀⠀⡜⡜⠀⠛⢻⣿⣿⣶⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣥⣤⣤⣶⣤⣴⣾⣿⠿⠋⢈⣉⡿⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⢀⢃⡇⠀⠀⢀⡐⠰⡈⠉⢹⣿⣀⡉⠉⠛⠛⠉⡋⡽⣏⡽⢯⠉⠋⡹⣽⣿⡆⠀⠀⠘⢸⢱⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠘⡄⢰⠃⠀⢸⣿⡇⠀⠀⠀⠀⢩⠞⣹⣿⠞⣏⣇⣴⣿⠉⣿⣷⡀⠀⠈⠉⠈⣇⢷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠀⡤⡀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠈⠉⠁⠀⠀⠷⠔⠋⠁⠀⢘⣿⣧⠀⠀⠀⠀⠸⡌⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠘⠀⢇⡀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣤⣶⣶⣄⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⠇⢏⠦⢍⡓⠠⣸⠙⢾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠁⢹⣿⣰⣱⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠼⠀⠀⠈⠳⡄⢠⢬⣿⣇⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣤⣾⠟⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠈⣿⣇⣼⣿⣧⣄⣑⣀⣀⣀⣠⣠⣴⣾⡿⠀⠀⣁⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠛⠙⠛⠻⠿⠿⠿⠿⠟⢻⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠈⠑⠢⢄⠑⣄⢀⠔⢊⠤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⢿⣿⡀⠀⢀⣼⣿⣿⠿⣭⣿⣿⣿⣿⣿⣿⣻⣿⣻⡽⣯⣿⣽⠃⢽⢨⡅⣏⣸⣿⣿⣟⣿⢿ ⠀⠀⠀⠀⠀⠀⠀⠈⠁⠮⡀⠠⢸⠀⠀⠀⠀⠀⠀⠀⢀⢦⡀⠀⠀⠸⣹⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣾⣽⣿⣿⣿⣻⣯⣷⣾⣻⣽⢧⡿⣽⣏⠌⣚⣘⣢⡙⢻⣟⡿⣾⣿ ⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠰⡄⢢⠀⠀⠀⠀⠀⠀⣀⡎⠀⠙⢄⣀⣼⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣷⣾⣻⣭⣟⣷⣭⣿⣴⠀⠔⢦⡙⡖⣚⡒⣧⣻ ⠒⢄⣈⠓⡄⠀⠀⠀⠀⠀⠀⢡⠀⣁⠀⢰⠢⣀⠀⣸⠀⠀⠀⠀⠙⠸⡇⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣾⣿⣿⣿⣿⣻⣟⡿⠧⣈⣖⣈⣖⣙⣂⣡⣭ ⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡆⠀⠛⠀⠀⢇⠀⠁⠃⠀⠀⠀⠀⠀⠐⣇⠈⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠋⠉⠉⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠟⠛⣷⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⠀⢌⠃⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⣻⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⢀⣼⣿⣻⣿⣽⠆⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⢀⣀⠔⠊⢀⡴⠃⠀⠀⠀⠀⠈⢷⡂⠀⠀⠀⠀⠀⠀⡬⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠒⠒⠺⠿⣿⣷⣿⣷⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⣸⠉⠄⡀⠄⢈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠄⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⣾⡄⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣧⡀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⡄⠐⠠⠀⠌⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⠎⠀⠀⠀⠀⠀⣠⠏⠀⢀⣴⢿⠇⠀⢰⠏⢻⣄⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⠀⡀⠀⠀⠀⠀⠀⠀⠠⢶⣾⣿⣿⣿⣷⡀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⡇⠠⠁⡐⠈⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢀⡔⠀⠀⢀⣴⠏⠀⢠⠞⠁⣼⠀⠀⡎⠀⠀⠻⣆⠀⠀⠀⢻⣦⡀⠀⠀⠰⡄⠓⢢⣄⠀⠀⠀⠘⣷⣤⣤⣬⣆⣁⣈⣀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠃⠄⢁⠀⢂⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢠⡟⠀⠀⢠⢞⡟⠀⢠⠏⠀⠀⣿⠀⢸⠅⠀⠀⠀⠘⢷⡀⠀⠀⢿⡳⣄⠅⠀⠙⣆⠀⠘⢧⡀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⢸⠀⠌⢀⠐⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢠⡿⠀⠀⢠⡏⣸⣁⢤⠯⠤⢀⣀⣯⠀⡟⠀⠀⠀⠀⠀⠀⠻⣆⡀⠬⣧⠽⣿⣌⠰⢿⡄⠀⠈⢷⡄⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⣎⣀⢆⡄⡈⠀⠬⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⣸⠃⠀⢀⡾⠔⣟⢀⡟⠀⠀⠀⡄⢻⢰⠇⠀⠀⠀⠀⠀⠰⠋⠙⢧⡄⠘⣇⠈⢻⡗⢮⣻⣄⠀⠘⣧⠀⠀⠀⢹⣿⣿⣿⡇⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠈⠀⠀⠀⠀⠉⠦⡀⠑⡄⠀⠀⠀⠀⣀⡀⢤⡗⢂⡿⠀⠀⡞⠁⢰⡇⡼⠀⠀⠀⠀⠀⠸⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣙⢧⠀⠹⡆⠙⢿⢦⠀⠼⡄⠀⠀⠘⣿⣿⣿⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢸⠉⠁⠀⠀⠀⠀⢸⠆⣸⡇⠀⣸⠃⠀⢠⣿⠗⠈⠉⠉⠑⠲⡄⢻⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠬⣙⢧⠀⠹⡄⢸⠈⣇⠈⣷⠀⠀⠀⣿⣿⣿⠂⢀⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣯⣿⣿⣿⣿ ⠐⠚⠒⢂⠀⠀⠀⠀⠀⡌⢀⠸⠀⠀⠀⠀⠀⠀⢸⡂⣿⡇⣠⡇⠀⢠⠞⠃⠀⣠⢶⠟⠒⣄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⣠⣤⣤⣀⠀⠈⠙⣆⠀⠙⣶⠄⠈⡄⢹⡆⠀⠀⣿⣿⣿⠀⢸⣿⣿⣿⢟⣽⣛⠽⢭⣿⣿⣿⣷⣿⣿⣿ ⠐⠒⠊⠁⠀⠀⠀⣰⢊⠀⢤⠧⠀⠀⠐⠂⠀⠉⢹⣾⢻⡇⣿⠂⢀⡟⠀⠀⣼⠋⢣⣀⣠⠞⡆⠀⠀⠀⠀⠀⠀⠀⠀⣾⢹⠁⠀⣙⣧⠀⠀⠈⣧⠀⠀⠀⣠⠺⣻⠓⢤⣸⣿⣿⣿⡗⠸⠿⠿⣟⡚⣤⢯⣸⢿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢠⠑⠄⠀⠀⠀⠀⠀⠘⢿⠈⡇⠏⠀⢸⡇⠀⠀⣿⠄⠰⠈⠃⠸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⢓⠶⠋⣸⡆⠀⠀⢹⡇⠀⠀⠀⢀⠜⠂⠀⢿⣿⣿⣿⣿⡄⢀⠀⣿⡵⢢⡳⢼⣿⣿⣿⣿⣿⣿⣿⣿ ⡖⠒⠂⡉⢐⡄⠀⠀⠀⠀⠈⡄⠘⠀⠀⠀⠀⠀⠀⢸⠀⢱⡇⠀⠸⣧⠀⠀⠘⣦⣀⢁⣀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠊⠁⢠⡿⠁⠀⠀⢸⡇⠀⠀⠀⡞⣧⠀⠀⢸⣿⣿⣿⣿⣿⡀⢠⡿⣛⢸⡑⡜⣾⣿⣿⣻⣿⣿⣿⣿ ⠐⠒⠒⠁⠋⠀⠀⠀⠀⠀⢀⡋⢀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠆⠀⠀⠙⠂⠀⠀⠈⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠶⠾⠛⠁⠀⠀⠀⠟⠀⠀⠀⢸⠀⡇⠀⠀⡿⣿⣿⣿⣿⣿⠇⢰⡟⡸⢣⡝⡸⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠜⠀⠀⡼⠿⣿⣿⣿⣿⣿⡄⢸⡏⡜⣅⢃⣳⡿⣿⣿⣿⠿⣿⣿⣿ ⠀⠀⣀⢠⡤⠀⠴⠒⠉⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣠⠞⠀⠀⠀⠉⠛⠿⣿⣿⣿⡙⣬⣧⣹⣸⣿⣿⣿⣏⣾⣿⣏⢾ ⠀⠀⠃⠄⠠⠐⡔⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⣿⣿⣿⣿⣿⣿⣟⣿⣾⣿⢫⣾ ⠀⠀⣠⠈⠐⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣧⡀⠀⠀⠀⠀⠀⠀⠀⠺⣴⣶⣶⣶⣿⣿⣯⣿⣿⡿⣽⡿⣹⣿⣿⣟⣷⣿ ⠀⠀⠷⣀⠁⠨⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⠁⠀⠀⠀⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠉⠁⠈⠉⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣶⠬⠠⠀⠀⠀⠀⠀⠘⣿⣿⣿⣇⣻⢿⣿⣿⢵⡿⣽⢿⣟⣿⣓⣿⣿ ⠀⠀⠀⠃⠉⠐⠂⣈⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⣠⡆⠀⠀⣀⠈⠙⣦⣀⠀⠀⠀⠀⠀⠻⣀⠀⠀⠀⠀⠀⣀⠇⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⢰⣤⣤⣄⣘⣿⣿⣿⣞⣫⠿⣿⣿⢿⣿⣿⣿⢏⣻⣿⣽ ⠀⠀⢰⠄⠀⠀⠀⠀⠁⠢⢄⠑⠠⡀⠀⠀⠀⠀⠀⣇⡶⠋⣧⠀⢰⢻⣄⢢⣿⣿⣿⣶⣤⣄⡀⠀⠀⠉⠉⠈⠉⠉⠀⠀⢀⣠⣤⠖⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠹⣿⣿⣿⣿⣿⣿⣿⡻⣫⣿⡿⢿⣾⣿⢭⠟⣼⣿⣿⣾ ⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⢈⡂⢄⠀⠀⠀⠏⠀⠀⠸⣤⠃⢸⣿⣾⣿⢟⣡⣿⠀⠉⠉⠙⠛⠒⠒⠒⠒⠒⠂⠉⠉⠘⣧⠘⡀⢈⠐⢡⠈⠍⠛⠿⢿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣴⣶⣿⣿⣿⣮⡻⣿⣿⢷⣿ ⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠩⠃⠀⠀⠀⠀⠀⠀⠀⠉⠀⢸⣿⣿⡃⡬⣧⣝⣻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇⡚⠀⢜⠊⠤⠌⠭⠄⠀⢂⠈⡙⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢹⢯⢿⡷⣿⣿⣯⣿ ⢠⢀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠠⠊⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⡠⢡⢇⡿⢺⡗⣬⣝⠲⣤⣄⣀⠀⠀⠀⢀⣀⣤⠋⠁⣼⡇⠰⠙⡠⠈⠡⡀⡙⡈⡔⢧⡀⢌⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡓⣏⣺⢧⣷⣿⣟⣿⣿ ⠀⠈⠘⠒⠀⠀⠀⠀⠀⠀⡠⢁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠣⠄⠡⠆⠬⠑⢨⠙⠾⣋⣓⠎⣍⡩⣉⢛⡯⠍⡀⠠⣠⠵⠃⠙⢶⡡⢔⣊⠃⠰⠀⣄⠠⠤⠨⠆⠀⣀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣗⡰⢡⣣⡍⢿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢁⠆⡩⠁⠌⢉⠠⠁⡘⠂⠇⠉⠁⠓⠂⠁⠈⠒⠑⠋⠉⠀⠀⠀⠀⠀⠙⢦⡍⢢⠒⠑⢠⠘⣈⡑⡒⠅⣁⠊⣡⠈⣿⣿⣿⣿⣿⣿⣿⣿⡥⣓⢳⡚⣝⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⡐⢁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⣃⢘⠠⠡⠌⠥⣂⢁⡁⡺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡟⣜⣶⢚⠐⣀⢀⠜⢀⣀⢌⡌⢰⠿⣿⣿⣿⣿⣿⣿⣿⣷⣈⡓⣛⢼⣸⣿⣟ ⠀⠀⠀⠀⠀⢀⠌⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⢄⡡⢒⢈⡔⠠⢀⢲⣶⢊⢁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡖⣻⣬⡉⠄⢲⢡⢟⣫⣧⠏⠀⠀⠙⢿⣿⣿⣿⣿⣷⡒⢽⢲⠺⡜⣿⣷ ⠈⠐⠀⠠⡠⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⡂⢆⠳⢀⡉⢘⡌⡠⣿⣾⡞⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣟⢏⢶⡍⢢⡼⢷⡿⡱⠃⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣏⢲⣙⢣⢇⣻⣿ ⠀⠔⠀⠔⡠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠏⡌⣬⠉⡄⢠⠬⣁⢚⡑⣿⣿⠆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣞⢳⠘⢠⣟⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡐⢎⠧⣫⢼⣿ ⠁⢀⢊⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣛⠠⢰⢃⠽⣀⠅⠂⢐⡓⠬⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⢋⡗⣤⣻⣼⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠞⡶⣱⢪⣿ ⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠤⣩⢰⢊⠥⣉⠒⡘⠬⢎⡅⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣯⡱⢠⡙⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠈⢿⣯⠿⣽⢣⠎⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢘⡰⠰⢈⣁⡮⢱⠝⠤⣓⠴⡔⣻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢻⣯⢛⡬⢃⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡼⠛⠐⠚⠲⢤⣂⢦⡋⠽⣠⠉⠌⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠙⣯⡱⢛⡼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃⠀⠀⠀⠀⠀⣿⡻⣧⡧⠔⣂⠁⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠈⢿⣬⠳

⠿⣏⣿⡹⣝⠾⣝⣯⢳⡝⣮⢳⢿⡹⣏⠿⡹⣞⣭⢻⡟⡿⣏⣯⣝⡻⣿⡹⣏⢿⡹⣭⢯⡽⣻⡝⣯⢻⡽⣏⠿⣭⢻⡝⣯⢏⣿⣻⡽⣭⢿⡽⣯⢿⡽⣯⢟⣟⣯⣿⣽⣶⣿⣿⠿⢿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣀⢶⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣟⣳⣎⠷⣭⣛⢾⡱⣏⠾⣧⣛⠾⣝⢮⡳⢳⡜⣢⢏⡞⡵⣫⠶⣍⢷⡳⣽⡹⣞⡽⣣⢿⡼⣳⢯⣽⣳⢻⣼⣛⣧⢿⣹⢞⡯⢶⢯⡽⢯⡿⣽⢯⡿⣽⣻⡾⣽⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢷⣶⣦⣤⣳⣾⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠦⡈⢦⣹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣟⡶⣏⠿⣴⢫⢖⡱⢯⡝⢦⣍⠻⣌⠷⣩⣓⠾⣱⡞⣼⣳⢭⣳⣚⢦⣛⢶⡻⣵⢻⡽⣳⣏⠿⣽⢾⡹⣏⣶⣛⡾⣽⢺⡽⣞⣯⢾⣝⣯⢿⡽⣯⣟⣷⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣿⣿⠀⠀⠀⠀⠀⣴⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠰⢡⢊⣱⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣯⢻⣝⡻⢧⡛⣮⡝⣧⢞⣳⢮⢷⣹⡞⣵⢫⣟⣥⢻⡵⣫⣛⠷⣯⢿⡹⣞⡽⣳⣏⡾⣱⣞⡻⣽⢫⣟⡵⣣⠿⣜⡷⣯⢷⡹⣎⡿⣾⡽⣿⣽⣳⢿⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⠄⠀⠀⠀⢰⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⢈⢖⡱⢮⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢯⡻⣼⢹⢧⡝⣦⡝⣮⢻⡜⣯⢞⣧⢻⣭⢻⣜⢮⢧⡝⣧⢏⡿⣜⣧⢟⡼⣳⣻⢼⣛⠷⣯⢷⣫⢟⣮⢷⢯⡟⣧⢿⣼⣷⣹⣳⢟⣷⣻⢷⣯⣟⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣧⠀⠀⠀⣸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠰⣡⢊⣵⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡷⣻⡜⣯⠞⡼⡱⣞⡥⢏⡾⣱⢯⡞⣵⣊⠷⣎⢯⡞⣽⣎⠿⣼⡽⣞⣯⢷⣯⢷⣏⡟⣿⡽⣾⠽⣾⣭⢿⣻⠾⣭⡟⣮⢷⢯⣟⡿⣾⣽⣻⣞⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⣽⣿⣿⣿⣿⡶⢀⢀⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⢀⠠⠘⣤⠓⡆⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣟⣵⣻⢞⣯⢳⡽⢶⡹⣯⢖⣯⡻⣽⢶⣫⢟⡼⣧⣟⡷⣯⣟⣯⣟⡽⣺⢯⣛⡟⣾⡹⣷⣻⢿⣻⢷⣻⢯⣟⣿⣣⠿⣭⢟⡾⣽⣻⢷⣯⢷⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢸⡿⣿⣿⣿⣿⣿⣿⡇⢭⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠄⡘⡰⢩⡗⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣞⢧⡏⣞⡼⣣⠻⣍⠷⣙⢮⢶⣹⢣⠟⡽⣎⢷⡳⣞⡽⢶⣫⢞⣳⢿⣱⠿⣼⡽⣖⡻⣵⢫⡟⣼⢫⣟⣯⢟⡾⣽⣻⢧⣻⣞⣷⢯⣟⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣆⢼⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⣅⠳⣡⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣎⠳⣝⠮⡵⣋⡗⢮⡝⣎⢞⡮⡵⢫⡟⡽⣞⣧⡟⣼⣹⢳⣏⠾⣭⡻⣭⢟⣧⢻⡜⣷⢽⣫⣽⣞⡿⣞⣮⢿⣹⣗⡯⣟⣶⣛⢾⣻⢾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡝⣿⣿⣿⣿⣿⣿⡿⢿⣻⣿⣞⣿⣿⡀⠀⠀⠀⢈⠐⡈⠰⡀⠧⣈⠇⣷⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣮⡝⣮⢳⡳⣝⣮⢳⡞⣭⢞⡼⣝⢧⢺⡵⢫⣞⡽⣖⢯⢷⡺⣟⢧⣻⣜⣯⣞⣧⢻⡜⣧⣻⢳⡝⡾⣽⣫⣟⣳⢯⣽⣳⢯⡟⣯⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢋⡝⠃⡌⢳⠹⣿⣿⢿⣿⣷⣤⠀⠄⡀⠠⠀⡑⢌⡱⢎⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⢧⣛⣜⡣⣝⡾⣱⢧⣛⣬⢻⡜⡯⢎⡳⣜⢧⢯⡜⣮⣛⢮⢷⡹⣞⡵⣞⣳⣛⢮⣗⣻⡼⢧⡻⣝⣳⣭⡳⢯⡟⣿⣺⢽⣫⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠿⠛⠀⠗⢀⠣⣝⣿⣿⣯⣿⣿⣿⣿⣖⠠⡀⢐⡀⠦⣘⠼⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠂⢈⠀⠄⠂⠁⡀ ⡷⣭⢾⡵⣫⢜⣣⠞⡵⣎⢷⣹⢾⣭⢳⣛⣾⣳⣟⡶⣭⣻⢮⢷⣹⢞⣵⡳⣎⢷⣮⢷⡻⢯⡽⣭⢷⣳⣛⣯⣟⠷⣯⢯⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣒⣤⣿⣿⣿⢋⠐⠀⠀⠠⠀⢎⢣⢞⣿⣿⣷⢯⣿⣿⣿⣖⡱⢢⠜⡰⢡⣻⣿⡇⠀⠀⡀⢆⠤⡀⢄⠰⡀⢆⠠⡁⢂⠥⡉⠄⢃⠢⢀⠂⠄⢂⡐ ⣱⣏⡟⣷⠛⣎⣇⢻⡘⣎⢳⡏⣿⡘⢳⣿⣸⢳⡟⣿⢻⡙⣏⣾⣹⢻⣎⣷⢹⢳⡞⣏⡙⢳⢻⣸⢳⣇⢻⣶⣹⢻⣉⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠈⣀⠓⣾⣿⣿⣿⣿⣾⣹⣿⣿⣇⠓⣎⠑⢃⣿⣿⠁⢀⢃⡙⡎⣶⠉⣆⠑⡈⢂⢁⠐⠁⠂⢁⠈⡀⠑⢀⠈⠐⢂⠘ ⡿⣬⢳⣭⢻⣙⢮⡳⣝⡞⣧⣛⠶⣏⣷⡹⣞⡻⣽⢺⢧⢿⡼⢶⣭⣛⡾⣞⣿⣫⢽⢾⣹⣯⣟⣞⣧⣟⣾⣱⢯⣟⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢠⠀⠘⠰⡛⠿⣟⣿⣿⣿⣷⣿⣾⣿⣿⣗⣬⢳⢎⣿⣯⠀⢎⡾⣷⣻⣾⣿⣦⠓⡥⢊⠄⠢⣉⠒⡀⠢⢐⠡⢂⠌⡱⢌⡖ ⣳⢏⡳⣎⠷⣍⢶⣹⢮⣝⠶⣯⢻⡝⣶⡹⣎⣷⣣⢟⣞⡻⣞⡿⣶⢯⣝⣻⢶⣯⢟⣮⢷⣻⢾⡽⣞⣾⣳⢯⡿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⢀⠐⢠⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⢃⡱⣹⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⡹⣎⣿⡗⢈⠾⣵⣯⣳⢿⣿⣿⣭⢒⠡⡈⠐⡠⢁⠂⡅⢌⠢⡉⢬⡑⢮⡜ ⢧⣏⠷⣭⣟⣮⠻⣜⢯⣿⡹⢮⣗⡞⣶⡝⡿⣶⣹⣞⣮⢽⣳⡿⣽⣻⢿⣽⣳⢯⣿⣞⣯⢿⣭⣟⣿⢾⡽⣾⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣤⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⡄⠠⢀⢂⠱⡩⢟⡿⣿⣿⣿⢏⠣⠀⠹⣿⣿⣷⡍⡞⠀⢌⣻⡷⣯⢷⣻⣿⣿⣿⡄⢃⠠⠑⡠⠃⡜⠰⣈⠖⡩⢦⡹⢦⡝ ⢞⡼⢫⢷⡹⣎⢷⡹⣎⠶⣏⡻⣼⡹⢷⣻⣳⣭⢷⣟⡾⣯⢷⣻⢧⣟⣯⣾⣽⣻⢿⡾⣽⣻⣾⣽⡾⣯⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⢿⣿⣿⣏⠀⠀⠀⠀⠀⠀⢉⢀⢣⡝⡺⣜⡟⣿⣿⡊⠐⠀⠀⣿⣿⣿⣷⡄⠀⢪⣿⡷⢯⣟⣷⣻⣿⣿⡆⠄⠂⣅⢣⠱⣌⠳⡌⢎⡵⢣⣝⡲⣹ ⡿⣼⣛⢮⢳⡙⣞⡳⣭⢞⣭⡳⣽⣹⢯⣷⢧⣟⡿⣞⣿⡽⣯⣻⢯⣟⣾⣳⣟⣯⡿⣽⣷⣻⣞⣷⣻⣽⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⡯⢀⠀⠀⠀⠀⠀⡄⢪⠑⢮⢵⢣⢻⡜⣿⡅⠂⠀⠀⣿⣿⣿⣿⣿⣦⣍⢿⡿⣯⣟⡾⣷⣿⣿⡇⢈⠒⡌⢆⡳⢄⠳⣘⠮⣜⡳⢎⡵⢣ ⣳⢧⡟⡾⣧⠿⣜⡱⣟⢯⣞⡷⣽⢻⣟⣯⡟⣿⢿⣻⣯⣿⢿⣟⡿⣿⣾⢷⣯⡿⣽⣟⡷⣿⢾⣽⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢀⣰⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⡗⠀⢢⡀⡀⣀⠡⡘⢠⡙⡌⢎⢣⠓⡜⡻⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⢫⡞⡿⣿⣿⠇⢠⢋⡜⢦⡙⢮⡱⣍⠾⣱⢫⡝⣎⡳ ⣟⡾⣹⢳⢯⣟⣷⣻⣽⡷⡾⣽⣳⣟⡾⣧⢿⣯⣟⣳⣟⣾⣟⣾⣻⢷⣯⣟⣷⣟⣿⣞⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠃⣾⣿⣿⣿⣿⣳⣿⢿⣾⡿⣽⣿⣿⠂⠀⠀⠑⠰⣁⠣⡘⠄⢆⡍⠲⣀⠃⠔⡙⠆⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⠀⢣⡝⣜⢣⡝⣲⡱⢮⣙⢧⡻⣜⡱⢳ ⣻⣜⣯⢿⣻⣞⣧⣟⡾⣽⣻⢷⣛⡾⣽⣽⣻⣶⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣰⣿⠟⢰⣿⣿⣿⣟⣿⣿⣻⣿⢿⣽⣿⣿⣿⡀⠀⠀⠀⠀⠠⠑⡠⢍⠢⠌⠱⠀⠂⠀⠘⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠧⡜⣬⠳⡼⣱⡝⣣⢟⡼⣱⢮⣙⢧ ⣟⠾⣭⣛⡷⣿⣽⡾⣟⣷⡻⣯⢿⣻⣽⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠋⠉⠙⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⣾⡿⠁⠠⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠤⡑⢎⡔⡈⠄⠡⠀⠂⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢀⡻⣜⡱⣏⢷⡱⣏⢷⢫⡞⣵⢫⢞⣣ ⣯⣟⡿⣟⣿⣻⢷⣻⣽⣞⣿⣽⣿⣿⡟⠋⠀⠀⠀⠀⣤⣶⣶⣶⣶⣤⣤⣤⡄⢠⣄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⡿⠋⠀⠀⣸⣿⣿⣿⣿⣽⡿⣟⣿⣾⣿⣿⢷⣿⣿⡇⠀⠀⠀⠀⠘⢢⢉⠖⡄⢃⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢠⢳⣎⢷⡹⣎⢷⣹⢮⢷⡹⣎⡟⣮⠵ ⣷⣻⢾⡽⣮⡽⣿⣽⣻⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⣭⣭⣭⣉⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⢠⡉⠒⠨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢨⡗⣮⢏⣷⣛⢮⣛⡾⣭⢷⡹⢾⣱⢯ ⣯⣟⣾⣽⣟⣿⣳⡿⣯⢿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⣿⠄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠂⠌⠡⢓⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠲⣝⢮⡟⣶⢫⡟⣼⢳⣻⡞⣽⣏⡟⣞ ⣿⡾⣽⣻⢾⣻⣽⣻⣽⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⠿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⡿⣿⣾⣟⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠂⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠸⣝⣮⢻⣭⡟⣽⡞⣽⣣⢟⣳⢮⡝⡮ ⣿⡽⣟⣯⢿⡷⣯⢷⣻⣽⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣄⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⢘⡷⣚⣯⢞⡽⣮⢽⡖⣯⢞⡵⣫⠞⡡ ⣯⢿⡽⣞⣿⡽⣿⢯⣟⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢷⣶⣿⣿⣿⣿⣿⡿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⢿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠘⣼⡝⣞⣯⣳⠽⣮⡝⡞⣜⡲⢥⠋⠀ ⣿⢯⡿⡽⣯⣿⣟⣿⣽⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⡾⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⡵⣻⠼⣖⣯⣛⢶⣹⡙⢦⡑⠎⠀⠀ ⣿⢯⡿⣽⣳⣟⣯⢿⣾⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⣤⣤⣤⠀⠈⠻⣿⣷⣷⣶⣦⣤⣤⣤⡀⠀⠀⠀⠉⠁⠀⠀⠀⠛⠿⢿⣿⣿⣿⣿⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⢿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⢷⡻⣵⣛⣮⢗⡣⢝⠂⡘⠀⠀⠀ ⣿⢿⣽⣿⡷⣿⣾⡿⣷⣻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⠠⡄⡈⢆⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⣿⣿⣿⣿⣶⣶⣷⣾⣶⣷⣦⣶⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢪⢷⣹⡽⣎⢧⡙⠄⠂⠀⠀⠀⠀ ⣯⣿⣽⣻⡿⣟⣷⣻⡿⣿⣿⠇⠀⠀⠀⠀⠈⠖⡐⢂⠌⡥⢒⠡⢓⠤⡈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⣿⣿⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⡀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⢳⢧⡻⡜⠦⢌⠐⠀⠀⠀⠀⠀ ⣿⣽⣻⢿⣽⡿⣯⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⢒⠠⢈⠘⡔⡉⠦⡉⢆⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣶⣿⣦⣀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣷⣎⢲⡱⣍⠣⠀⠂⠀⠀⢀⠀⠄ ⣿⣾⣳⣿⣾⣿⡿⣽⣯⢿⣿⡇⠀⠀⠀⠀⠀⠂⠀⠀⠢⣄⠱⢂⡑⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠄⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠿⠿⠟⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⣿⣿⢻⣶⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⣿⣿⣷⣷⣬⠂⠀⠄⡁⢂⠤⢈⠐ ⣿⣳⢿⣷⣿⣾⢿⣟⣾⣿⣿⡇⠀⠀⠀⠀⠀⠆⡀⠀⠡⡀⢃⠣⠘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡈⠠⠄⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣶⣄⡀⠀⠀⢀⡀⠀⠀⠀⠰⣇⣿⣿⣿⣞⣿⣟⣿⣿⣷⣏⣛⡛⢣⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣇⠄⡂⠜⣠⠊⡔⡈ ⣿⣟⣮⣽⣾⢿⣟⣾⣿⣾⣿⠆⠀⠀⠀⠀⠀⠐⠀⠀⠄⠳⢌⠢⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠠⠑⠌⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠀⠈⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣭⣙⠉⠚⠃⠀⢾⣦⣀⣀⡀⠀⣸⣿⣷⢨⡓⢤⣋⠴⣁ ⣿⢾⣿⣿⣾⣿⣞⡿⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⡩⠀⠃⡁⠂⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⢩⠐⡠⢡⠐⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⠿⠿⠿⠻⣿⣧⣛⡶⣩⢖⡡ ⣿⣯⣷⣿⡽⣟⣾⣿⣽⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠁⠀⠀⠀⠀⠀⠉⣶⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢣⠐⢢⢡⡐⢌⠡⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠻⢿⣿⣿⣿⠿⣿⣿⣿⡿⠛⠛⠉⠉⠁⠀⠀⠀⠀⠈⠻⣿⣿⡵⢮⡑ ⡿⣿⢿⣿⣷⣻⣽⣿⡿⣽⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠙⢲⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠊⠔⠨⠌⡱⠈⠄⡈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠌⡐⢠⠊⡔⢡⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⠀⠉⠛⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣷⣮⣗ ⣿⣿⣟⣾⣳⣿⣾⣳⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⢻⣿⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠃⡄⠣⡜⣄⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣯ ⣿⣳⣻⣞⣿⡾⣿⣿⣽⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢀⣾⡇⠀⠀⢻⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⣓⠰⡌⣒⠰⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⣻⣽⣷⡿⣟⣿⣟⣿⣞⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⢹⣿⣿⣇⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢄⠓⡸⢄⠓⡌⡐⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿ ⣯⡽⢻⢿⣟⣷⣻⣽⣾⣿⡏⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠲⡌⠂⠀⢠⣾⡿⠁⣶⠀⠀⠀⠀⢻⣿⣿⠀⠀⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠢⡈⢜⢡⢊⠖⡰⢁⠂⠀⠁⠀⠈⠐⠠⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿ ⣿⢿⡿⣿⣾⢳⣷⢾⣷⣿⡇⠀⠀⠀⠀⣸⢇⠀⡀⠀⠌⠰⣠⣅⠸⣾⣿⠃⢠⣜⠀⠀⠀⠀⠀⢿⣿⠀⠀⣼⣿⡟⣡⠀⡀⠄⡀⠀⡀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠑⡊⡔⢊⠴⠁⢆⠈⡀⠀⠀⠀⠀⠐⠀⠀⠀⢠⡙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿ ⣿⣯⣟⠿⣟⠿⣯⣟⣯⣿⣧⠀⠀⠀⢠⣿⠌⠀⠀⠀⠌⠐⣽⣿⣿⡿⣏⣄⡸⣿⣄⠀⠀⠀⠀⠘⣿⣧⡀⠘⢿⣿⣿⣧⡐⣌⠰⢱⣀⠣⡰⣁⠎⡠⢑⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠌⠐⡡⠜⡈⢆⠉⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿ ⣿⣜⣿⣿⣾⣿⢿⣽⣿⣿⡧⠀⠀⠀⢰⣿⠂⠀⠄⠀⠰⣼⣿⡿⠋⠀⠈⠛⣿⣿⣿⣿⣶⣤⠀⠀⠘⠿⣷⠀⠀⠛⣿⣿⣷⡌⡚⡔⢢⠕⡱⣂⢧⡱⢣⢎⠆⡀⠀⠀⠀⠀⠀⣠⣾⡿⠋⢻⣿⠆⠀⠀⠀⠀⠀⠀⠐⢨⠐⡀⢎⠱⡈⠜⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿ ⣳⣿⡽⣾⡿⣽⣿⣾⢿⣿⡇⠀⠀⠀⢸⡿⠁⠀⠀⠀⣿⣿⢿⣿⡀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣶⣤⣄⡈⡄⠀⠀⠀⠙⢿⣿⣶⣽⣿⣯⣵⡘⢦⡙⣣⢏⡒⢀⠀⢀⠀⣀⣼⡟⠋⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⢀⠒⡰⢈⠂⠥⠘⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿ ⣟⣾⣽⡳⣟⡿⣾⣻⣿⣿⡇⠀⠀⠀⢺⣇⠂⠀⠀⠀⣿⣇⠘⣿⣇⣀⡀⠀⠀⡀⣀⣀⣀⣀⣈⠉⠛⣿⣷⡘⣧⣄⠀⠀⢈⣿⣿⡟⠻⢿⣿⣿⣦⣧⣕⣮⣼⣦⡾⠂⣽⠿⣏⣥⣠⡀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⢣⠑⡌⠡⠌⡐⠌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿ ⣿⣳⢿⡿⣭⡷⣏⡷⣿⣿⡀⠀⠀⠀⣹⠆⡩⠀⠐⠀⠘⠏⢠⣿⡿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣧⢸⣿⣆⣤⣎⠹⠁⠀⠀⠈⣿⠛⠛⠻⠟⠿⠋⠉⠀⠀⠁⣼⣿⣿⣿⣷⡆⠀⠀⠻⡧⠀⠀⠀⠀⠀⠀⠐⢂⠑⠀⠁⠂⠌⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿ ⡷⢯⡿⣽⣟⡿⣽⣻⣿⣿⠀⠀⠀⠀⡼⣁⠦⡁⠦⡀⠀⠀⠀⠠⠐⠘⠿⣿⣶⣤⣤⣨⣤⣀⣤⣀⣈⢿⣿⣿⣾⣿⣿⡿⢉⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⣾⠡⠠⢌⢋⡑⠈⠉⡄⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⡌⢀⠠⢁⢀⠂⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣳⡽⣾⡟⢷⣭⣿⣿⠀⠀⠀⠀⡑⢀⠒⢄⢂⠀⡄⢀⠰⠈⡅⠀⠀⣀⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣦⣦⣑⢆⠦⡈⢄⠡⢀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡠⠀⠀⠀⠂⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⣽⣳⣿⣻⣽⡻⣞⣿⣿⡀⠀⠀⠀⠆⠰⣈⠢⣉⠒⡌⢠⢐⡰⡀⢀⡐⢤⣸⣿⣾⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣼⣿⣿⣿⠀⠀⠀⢀⡀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠠⠁⠌⠀⠁⠀⢀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣳⣟⣾⢳⢯⣿⡽⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠄⠩⠐⠃⠆⡑⠠⢱⣾⣷⣿⣿⣿⠏⣽⣻⣿⣟⣯⢛⡯⣿⣿⡇⢀⣿⣿⣿⣿⣶⣿⣿⠿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⠿⣹⠛⣿⣿⣿⡏⣦⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⡀⠀⠐⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣯⣳⣟⣾⣯⣟⣯⢿⣵⣿⣧⠀⠀⢚⡁⠀⠀⠀⠀⠠⠁⢈⠂⠍⠀⠃⢿⣿⣿⣿⣿⡎⠴⣹⣿⣾⣿⣏⢖⡹⢿⣿⣾⣿⣿⣿⣿⡟⣻⣿⣷⣦⣀⠔⡘⡛⢿⣿⣿⣿⣿⣿⣷⣿⣿⣥⣿⣼⡿⣿⠃⣿⡇⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢄⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣯⢿⣮⢷⣻⢽⣾⣹⢮⡽⣿⣷⣦⣴⣆⡀⠀⠀⠀⠀⠀⠀⡌⢄⠢⢌⠀⠻⢿⣿⣿⣇⠒⣙⠃⢿⣿⣿⣂⠱⢂⠌⡍⢻⣿⣿⣿⣿⣧⠈⠉⠻⢿⣿⣦⣼⣄⣈⣉⡉⠍⠩⠙⠛⠛⢋⡙⠀⠀⡁⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣯⣛⡼⣯⢿⣟⡾⡽⣯⣟⡷⣻⣯⣿⣿⣿⣿⣷⣤⣄⣂⠠⢀⠂⠡⠈⠒⠀⠀⠙⣿⣿⣤⠁⠎⣰⣿⣿⣧⠃⡉⠐⢌⠣⣿⣿⣿⡝⢿⣷⣤⠀⠀⠈⠉⠛⠻⠿⢿⣿⣿⣷⣦⣤⣤⣀⡀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢯⡟⣽⣻⢾⣳⣝⣶⣯⣼⣻⡽⣿⡾⣿⢿⣿⣿⣿⣿⣿⣶⣬⣐⠤⣉⠆⠀⠀⠀⠻⣿⣷⣄⢻⣿⣿⣿⡇⠀⡁⠂⢒⢸⡇⣿⣧⡀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡟⠿⢿⣿⣾⣦⣤⠄⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣹⣻⣾⡿⣧⣟⣯⣟⣎⢷⣻⢷⡿⣿⢽⡿⣿⣾⢿⡽⣿⢿⣿⣿⣿⣷⣾⣬⠀⠀⠀⠀⠈⢿⣿⣦⣿⣿⣿⠗⠀⠀⢁⠂⢺⡇⢼⣿⣷⡀⠀⠙⣿⣷⡄⠀⠀⠀⠀⠉⢿⡆⠙⢿⣧⠀⠀⠉⢻⡿⠀⡼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣳⢻⣶⣽⣻⢦⣛⣾⣿⣻⡾⣽⣻⣾⣽⣳⣯⢿⣽⣭⡿⣞⡷⣯⣿⣿⣿⣿⣶⣤⡀⠈⢧⡜⡛⠿⣿⣿⡆⠀⡀⢠⠐⣸⡆⠼⣿⣿⣿⣆⠐⣈⠻⣿⣦⣄⡀⠀⠀⠈⠻⢶⣄⠉⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡷⢻⡿⣞⣳⣌⠻⣞⣧⣯⣳⡿⣕⢯⣳⣾⢽⣻⡟⣿⣞⡿⣿⡿⣵⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⡉⢄⡡⠄⡄⢊⠴⣉⢞⣿⣿⡿⣿⣿⣶⣥⣤⡙⠿⣿⣿⠄⠀⠀⠈⢿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣧⣟⣷⠯⣟⣧⢻⡽⢞⣷⢻⣯⣿⣷⣯⣛⣯⣿⢷⡻⣟⣷⣻⣭⣿⣾⣷⡾⣷⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡘⡌⡞⡥⢎⣿⣿⣷⡜⣹⣛⢟⡻⣱⢣⢖⣹⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣓⡹⢯⣻⢯⠻⣍⡿⣾⣽⣞⣿⡾⣷⣻⡾⡽⣎⣿⣿⣿⣮⣽⣻⣷⣛⣾⡷⣽⣳⣿⣵⣿⢿⣿⣛⣿⡿⣿⢿⣿⣿⣿⣷⣝⣜⠣⡞⣿⣿⣿⣷⣿⣾⣷⣿⡿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣯⠷⣯⣟⡟⣶⢾⣹⣿⣟⣯⣏⡿⣷⣿⣿⣱⣮⢾⡝⣳⣧⢟⣧⣏⣿⣾⡽⣏⡗⣾⣯⣟⢿⣧⣻⢾⣿⣽⣻⣾⣽⣻⢿⣿⣿⣿⣾⣭⣿⢿⡈⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣏⣿⣤⣿⣹⢸⣧⢏⡿⣼⣇⡿⣏⣡⢿⡼⢧⣏⡿⢸⢿⣌⡿⣼⣿⢧⡿⢿⡿⣼⣹⢧⣏⢿⣿⡿⣏⣿⡿⣧⡿⣼⣇⣿⣼⣹⣿⣿⣿⣿⣧⣇⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡺⡝⣷⢯⣗⣮⡟⣞⢻⣽⣿⠽⣻⡟⡿⢿⣻⢳⣞⡞⢻⣿⣻⣯⢷⣬⣳⣻⠷⣯⣟⡾⣻⣾⣽⡿⣾⣽⣳⢿⣽⣯⣷⢯⡳⣯⣿⣿⡿⣿⣿⣿⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣟⡳⣽⣞⠻⣾⡷⢿⣾⢣⡿⣭⢷⡿⣾⣤⢞⣧⢿⣮⢿⣯⡟⣥⢏⡷⣯⢷⣭⣿⢿⣻⣟⣿⢳⣯⡿⢷⣯⣟⡿⣯⡿⣽⣿⣷⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣯⣷⣿⣿⣿ ⢯⣳⣿⣎⡿⣝⢻⠺⣿⣤⣟⣮⣻⣽⡷⣯⢿⡜⣿⣞⡿⣼⢿⣻⣏⡿⣟⢮⣷⣯⢟⡷⣾⣽⣣⢿⣽⣣⣿⢾⡿⣽⣷⣻⣦⡽⣿⣽⢯⣟⡻⣿⣿⢿⣿⢯⢿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿ ⡿⣧⣟⣯⢷⣼⣿⡷⣏⢿⣶⣟⡷⣻⢟⣧⢿⡾⣽⢯⡹⣽⢫⡷⢧⣽⡞⣿⡽⣞⣮⢾⣽⣻⣽⢯⣟⡳⣯⣷⡽⣾⣧⣷⣫⣟⣾⣽⣻⢾⣿⣹⣿⣿⣮⣿⢮⣽⡻⣿⢿⣿⣿⣿⣶⣦⣤⡀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣾⣿ ⣱⣜⡿⣿⠻⣞⣵⣻⣽⡚⢷⣯⣻⣽⢻⣮⢷⣻⠽⣯⣳⢏⣯⡿⣟⢧⣿⣧⣹⡿⣼⣟⣮⡳⢿⣻⢯⣷⣻⣽⡿⣍⢛⣷⢻⣽⢾⡟⣯⣿⣞⠿⣽⣞⡽⢯⣿⣳⢿⣞⣯⠷⠻⡽⣿⣿⣿⣿⣿⣷⣶⣤⣐⠠⡉⢷⣶⣄⡀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣷⣿⣿ ⣟⣯⢟⣶⠿⣟⣾⣷⡻⢿⣟⡶⣏⡿⣏⣿⣸⢷⣺⣷⣿⢻⣧⢟⡾⣻⣷⣟⣷⣻⣖⣻⢾⣽⣻⢷⣯⢾⠿⣽⢻⡞⢻⢿⣯⣟⢯⣞⣵⣿⢾⣻⢏⢿⡧⣏⣷⣯⣿⡿⣟⡿⣿⡿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⣶⣯⣛⠿⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿ ⡿⣾⢽⣾⣻⣼⣟⡾⣿⣟⣣⣴⣿⡹⣟⣧⣟⣯⣳⠿⣞⣳⣾⢿⣄⡻⢧⣻⢾⣷⢿⡿⣯⢿⣿⡻⣼⢯⣳⣞⣿⡽⢾⣟⣶⣻⣾⡽⣞⣽⣻⢮⣟⣯⣚⣽⡷⣽⣾⣟⡷⣯⢿⣽⣿⡾⢿⣿⡿⣿⡿⣽⣿⣿⡝⡿⣿⣿⣿⣷⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣯⣿⡿⣿⣿ ⣿⡿⣯⡿⣝⣾⣭⢻⡷⢫⡽⣻⡜⣿⡽⢮⣿⡶⣹⢧⣼⢳⣿⢻⡿⣿⣿⢳⣻⢯⡟⣼⢯⣛⣷⣻⣟⢯⢓⡟⣾⡹⣿⣯⢷⡻⣷⣻⡽⣎⣿⢿⣿⡳⢯⣯⣿⢧⣟⣾⣻⢷⣛⡸⣯⡟⣿⣹⢿⡿⣿⣷⢾⣗⣻⡗⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣀⡀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣟⣿⣿⣿ ⣿⡽⣷⣿⢻⣾⣹⣼⠿⣖⣿⣳⣟⠷⣻⢦⣟⣿⣿⣞⣷⣛⠞⣯⢿⣷⡽⣿⣷⡿⣽⣞⢯⣟⣶⡻⢾⣥⣾⣿⢲⣟⡽⣾⣻⣗⡯⣷⣻⣽⣏⣟⢶⣻⣥⣞⣯⡛⢾⣳⢟⡿⣷⢿⡷⣭⣾⣽⣫⣼⣿⣯⢻⣽⡳⢿⣽⣮⣿⣿⣽⣯⡿⢿⣿⣿⣿⣿⣿⣷⣾⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿ ⣵⣻⣵⣫⢿⣷⢿⣽⡻⣵⢾⣱⡿⣞⣿⣿⢿⡼⣯⢿⡽⣿⣌⣼⢷⡻⣽⣻⣼⣿⣞⡿⣫⢿⣿⣟⡾⣿⢿⣌⡷⣾⢿⣷⣯⣟⣿⣷⣟⣧⣟⣯⢿⡽⣿⣾⢯⡷⣶⣍⢾⣙⣭⣿⡼⣧⣛⠷⣟⣶⣻⢿⣻⣿⣿⣽⡿⣿⣿⣽⣞⡿⣿⣵⣿⣿⡿⣿⢻⣿⣿⣿⣿⣿⣿⢿⣿⣻⢿⣿⡽⣧⣯⣽⣿⣭⡷⣟⣷⢿⡿⣿⣟⣿⣿⣿⣿⣿⣿⣿ ⣿⡽⣸⣟⡾⣼⣻⢼⣷⣷⣼⣳⣽⣿⢷⡾⣭⣟⡿⣯⡳⣵⣞⣿⣾⣿⣽⣿⡿⣷⣭⣷⣯⣷⣻⢾⣽⣟⣮⣝⣻⡭⣞⣷⣻⡿⣞⣳⢿⣮⣿⣞⡿⣽⣳⢯⣿⡽⢾⡽⣯⢿⣶⢯⣿⣵⢯⡿⣜⡷⣯⢿⣹⣿⣿⣿⢻⣥⣿⣳⢯⣟⣼⣩⠟⣼⣽⢻⣿⢻⣿⣿⣿⣿⣾⣟⣿⣽⣻⣾⣿⣟⣿⢷⣺⣭⣿⢿⣻⡾⣽⣿⣿⣿⣿⣿⣿⡿⣿⣿ ⣾⣿⣱⣿⣽⣳⢯⣛⣿⢯⣿⣽⣯⡻⢼⣿⣽⢿⡽⣿⣿⣷⢿⣞⠿⣽⣻⣮⣽⣷⡻⣟⣾⣳⣯⡟⢳⣾⣽⣾⣿⣻⢽⡶⣯⢷⣾⡷⣟⡾⣽⣾⡽⣯⣿⣯⢗⣻⣯⠻⣽⣿⣽⣻⡞⣭⢷⡻⣽⢻⣽⡟⣶⠻⣟⣯⣷⣾⣿⣽⣛⣾⣟⣯⣧⣿⣯⣿⣿⣷⣷⡿⣿⣾⣽⣷⣿⣻⣿⢿⣟⣾⣽⢾⣿⣽⢾⣟⡷⣻⣿⣿⡿⣿⣿⣿⢿⣽⣿⣿

⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⣿⡛⠉⠀⠐⠀⠡⠁⠈⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⡀⠀⢸⣿⠀⠀⠀⠀⠠⠀⠈⠙⠙⠻⣷⣦⣀⠀⠀⠀⠀⠀⠉⠙⢿⡿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣧⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢿⡤⠀⠀⠀⠀⠀⣤⣾⡿⠋⠀⠀⠈⠉⠁⠂⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠎⡀⠀⠅⠀⢸⣿⠀⠀⠀⠀⡁⠀⠘⠿⣶⡄⠀⠙⢿⣷⣄⠀⠘⣷⡄⠀⠀⢿⣦⣍⡛⠻⢿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣿⣏⣿⡇⠀⠀⠀⠀⠀⠸⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⠐⠀⠈⣿⠀⠀⠀⢠⣾⣿⠏⠀⠀⠐⢠⣴⡆⡀⠀⠀⠀⠀⠀⠀⠐⠀⡐⠠⠀⢰⣿⡿⠀⠄⠐⠀⠂⣸⣿⣦⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠙⢿⣦⡀⠘⣿⡀⠀⠈⠉⠛⠻⢿⣶⣤⣍⣙⡻⠿⢿⣶⣶⣤⣄⡀⠀⠀⠀⠀⢹⣿⣾⣿⣠⣶⣿⣿⣶⣶⣿⣿⣿⣧⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⡀⠂⣴⣿⣿⡿⠀⠀⠀⢀⣾⡿⠁⠀⠀⡀⠠⠀⠄⠀⠀⠄⠀⢠⢤⣿⣿⡧⠀⠀⠐⠀⢰⣿⣿⣿⣶⣄⠀⠀⠀⣀⠀⠀⠀⢻⣷⡀⠀⠀⠻⣷⡄⢻⣧⠀⠀⠀⠠⣆⠀⠀⠉⠙⠛⠛⠿⠷⠾⣾⣽⡿⠿⠻⠷⠾⠶⠾⣿⣿⣿⣿⣿⣿⣿⣿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣶⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠄⠀⠀⣸⣧⣾⣿⣿⠏⠀⣠⣾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠄⣠⣴⣤⣾⣿⣿⣿⠁⠀⠀⠀⢈⣾⡿⣾⣿⣏⡻⣷⣦⣐⠻⣷⣄⠀⠀⢹⣷⡀⠀⠀⠙⣿⣎⣿⡆⠀⠀⠀⢻⣷⣄⠀⠀⠀⠀⠀⠀⠉⢤⣐⠂⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣽⢯⡿⣽⣻⣟⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠏⢀⣾⠟⣱⡿⣿⡟⠀⠀⡀⠀⠀⠀⠀⢀⣴⣿⠛⣡⣿⣿⣿⡇⠀⠀⠀⢀⣾⡿⣽⣿⣿⣽⣿⡽⣩⣿⢿⣾⣿⣦⡁⠀⠻⣿⡀⠀⠀⠉⢿⣿⣷⠀⠀⠀⠈⢻⣿⣆⠀⠀⠀⠀⠀⠀⠘⢿⣶⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣟⣿⣿⣿⣿⣿⣿⣿⢯⣟⣿⣽⣷⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆⠀⠀ ⠀⠀⠀⠀⠠⠄⠀⣿⣯⣿⠏⢠⣿⠏⣼⡿⢱⣿⠇⠀⠀⢁⠀⠀⠀⣠⣿⡟⠁⣴⣿⣿⣿⣿⠀⠀⠀⢠⣼⡿⣱⣿⡿⠁⢿⣼⣗⠀⠙⠿⣶⣮⣽⣿⣄⠀⢹⣷⡀⠀⠀⠘⣿⣿⡄⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⣼⡿⢻⣿⣿⣾⣿⣿⣾⣿⣿⣿⣯⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⣿⣽⡏⢠⣿⠃⣰⣿⠁⢸⣿⠂⠀⠀⠀⢀⠀⣰⣿⠃⢠⣾⠟⣱⣿⣿⠇⠀⡀⢠⣾⢏⣽⡿⠋⠀⠀⠈⣿⣿⡆⠀⠀⠀⠀⠉⠙⢻⣷⡄⢹⣷⡀⠀⠀⢩⣿⣧⠀⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⠂⠀⠀⢸⣿⡆⠀⠀⢀⣾⡟⠀⠀⡹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢦⣿⡟⣿⣳⣿⠏⣰⣿⠃⠀⣾⣿⠀⠀⠀⠀⢀⣾⡿⠁⣴⡿⠃⣨⣿⣿⡏⠀⢀⣼⡿⠛⡿⠟⠁⠀⠀⠂⠐⢸⣿⣷⠀⠀⠄⠀⠀⠸⣿⣾⣿⣦⡻⣧⠀⠀⠘⠹⣿⣶⢶⣤⣤⣀⣬⣿⣷⠀⠀⠀⠀⠁⠀⠀⣿⣧⠀⣠⣿⠏⢀⠀⢀⣱⣿⣿⠻⠿⠟⠛⢩⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡐⣾⡿⠁⣿⣿⣯⣾⣿⠏⠀⠀⣿⣿⡃⠀⠀⣠⣾⠏⢰⣾⠿⠁⣰⣿⣿⠏⠴⢰⡿⠋⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣽⡷⠀⠀⠀⣿⣿⣶⣭⣉⣉⠙⢛⣿⣇⠀⠀⠀⠀⠀⠀⢻⣿⣾⠟⠁⠀⠀⢀⣾⣿⣿⠏⠐⠁⠰⠀⣹⡄⠀⠀⠀⠀⠀⣿⢏⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣹⣿⡇⠄⣿⡿⣿⣿⡿⠀⠀⢀⣿⣿⣧⠀⠴⡿⠛⠺⠿⠉⠀⠚⠙⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣀⡄⠘⠻⣿⣄⠀⠀⢹⣿⣄⠉⠛⠛⠻⠿⠿⣿⡀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⣰⣿⣯⣿⠃⠀⠀⠀⣹⠀⢼⣧⠀⠀⠀⠀⡀⢿⡇⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣿⡿⠁⣸⣿⣿⣿⣿⠇⠀⠀⠘⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣤⣝⣷⣆⠀⠠⢛⣿⣦⣤⣄⣀⣀⣤⣿⣇⠀⠂⠁⠀⠀⠈⣿⡧⢀⣼⡿⣿⣿⣿⠏⠀⠀⠀⢠⣿⠀⣾⣿⠀⠀⠀⠀⢰⡻⣟⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣽⣿⠇⢠⣿⣿⣿⣿⡿⠀⠀⠀⠀⣾⣿⣿⣧⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣧⡀⠌⢻⣧⠈⠉⠉⣩⡿⠿⣿⡄⠀⠀⠀⠄⠀⣻⣿⠈⣤⣸⣿⣿⡟⠀⠀⠀⠀⣸⣿⡘⣿⣿⠀⠀⠀⠀⣴⡇⢿⠀⣹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢾⣿⠀⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⢻⣿⠞⠛⠉⠀⢀⣹⣿⠀⠀⠀⠀⠀⢹⣿⠀⢸⣿⣿⣟⠁⠀⠀⠀⠀⣿⡇⣿⣿⣿⡆⠀⠀⠀⣻⡇⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⣿ ⠀⠀⠀⣿⣿⣸⢉⣿⣿⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⠀⢻⣧⠀⠀⠀⢠⣿⣿⣆⠀⠀⠀⠀⢈⣿⠂⠈⢿⣟⣿⡄⠀⠀⠀⢸⣿⢹⣿⣿⢼⡇⠀⠀⠀⣿⠇⠀⠀⠠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃ ⠀⠀⠀⣿⣿⠀⣾⡟⢹⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⣤⣶⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠘⢿⣆⠘⣿⣧⢀⣴⡿⣿⢹⣿⡀⠀⠈⠀⠀⣿⡂⠀⠘⢿⣿⣿⡄⠀⢠⣿⣯⣿⣿⣿⢸⡗⠀⠀⠀⣿⡃⠀⠀⠠⣿⣿⡆⠀⠀⠀⠀⠀⠀⣰⡟⢀⠀ ⠀⠀⠀⣿⣿⢐⡿⠁⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⣠⣾⡿⠛⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⢻⣧⡼⣿⣿⣿⣿⠋⢀⣿⣇⠀⠀⠀⠈⣿⡃⠀⠀⠈⢿⣿⣷⣤⣿⠿⠟⠋⣿⣯⢸⡗⠀⠀⢀⣿⠁⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀ ⠀⠀⠀⣿⣏⠈⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣽⣿⡟⣁⣀⣦⣿⣿⠀⠀⠀⢸⣿⣷⡄⠀⠀⠈⠻⣿⣿⡃⠀⠀⠀⣿⣿⣸⡟⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⠠⠐⢠⣟⠀⠀⠀⢠ ⠀⠀⠀⣿⡇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠄⠀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⠾⠟⠋⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡟⠛⠛⣿⣇⠀⠀⢼⣿⣿⣿⣶⣍⠀⠁⡘⣿⣧⡄⠀⠀⣿⣿⢸⣏⠀⠀⢸⣟⠀⠀⠐⠀⠀⢻⣿⠀⠀⡀⢀⣼⠃⠀⠀⢠⣿ ⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠙⠓⠋⠓⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⣿⣿⡿⣿⣿⣶⣿⣿⠀⠀⣼⣿⣿⣿⣿⣿⣷⣦⣤⣽⣿⣷⡄⠀⢿⣯⢸⣇⠀⠀⣾⡇⠀⠀⠈⠀⠀⢸⣿⡇⠀⠁⢸⡃⠀⠀⠈⣾⠁ ⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⡈⡛⢿⣿⣿⡇⢤⣼⣿⣭⡿⣿⣿⣿⠛⠋⠉⠩⠻⣿⣦⣹⣿⣼⡇⠀⠀⣿⠄⠀⠀⠈⠀⠀⠈⣿⡇⠀⠀⢸⡅⠀⠀⠘⣷⡀ ⠀⣰⡿⠀⠀⠀⠐⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠄⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣠⣄⣤⣤⣤⣀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠉⣿⡇⢈⣿⣿⣿⣿⡿⠉⠄⢁⣀⣁⢀⠀⠈⠻⣿⣿⣿⡇⠀⢀⣿⠀⠀⠀⡀⠀⠀⠀⣿⡇⠀⠄⠘⢷⡀⠀⠀⠈⠛ ⣾⠟⡯⠀⠀⠀⢀⡐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣴⣾⠿⡿⠟⢻⣟⣯⣭⣭⣭⣥⣤⣤⣄⣀⣀⣀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠈⢿⣇⠀⠀⢻⣧⠀⢸⣿⣿⠁⠀⠀⣰⣿⣿⣿⣿⣶⣄⠐⠙⣿⣿⡧⠀⢸⡏⠀⠀⠀⠀⡀⠀⠀⣿⣇⠀⠀⠀⠀⠻⢶⣄⡀⠀ ⠃⢸⠇⠀⠀⠀⠀⠉⠉⠛⠚⠖⠶⠶⠶⠶⠞⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⠟⠉⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⢸⣿⠀⢨⣿⣿⠀⢀⣾⡟⠁⠉⠉⠁⠙⣿⣦⠀⠈⣿⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠈⠻⣶ ⠀⢸⡃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡁⢀⣴⣿⣿⡿⠟⠋⠉⠉⠀⠀⠀⠉⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⢀⠙⣿⡆⠘⣿⡀⢨⣿⣿⣾⣿⣿⣤⣄⣀⠀⠀⠀⠈⢿⣧⠀⠙⣿⣆⣾⠇⠀⠀⠀⠀⠀⠂⠀⣿⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀ ⠀⢸⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠉⢀⠠⣿⣿⡿⠋⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⢿⣿⣷⣦⡀⠀⠀⠸⡇⠀⣿⡇⢘⣿⣿⡋⠀⠈⠉⠙⠻⢿⣦⣀⠀⠈⢻⣧⠀⢹⣿⣿⠀⠀⠀⠀⠀⠁⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠏⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣶⣦⣤⣤⣀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⣏⠀⣿⣧⠀⢻⣿⣅⠀⠀⠀⠀⠀⠀⠉⠻⣷⡄⠸⣿⠀⣾⣿⣿⠀⠀⠀⠀⠀⠄⠈⠀⢾⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡈⠀⠈⠙⣿⣿⣷⣿⣿⣿⣧⡀⢼⡀⢽⣿⠀⢘⣿⣿⡀⠀⠀⠁⠀⠀⠀⠀⠈⠉⢸⣿⠀⢾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣺⡗⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⠀⢸⠄⠀⠀⠀⠀⠀⠀⠄⢀⣤⣾⣿⣯⣭⣿⣤⣦⣄⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠈⢿⣿⣿⣿⣿⣿⣷⣼⣥⣸⣿⠀⢸⠀⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡧⣼⣿⡿⠀⠀⠀⠀⠀⠀⡁⠀⣽⡇⠀⠀⠀⠀⠀⠀⠀⠂⠀ ⠀⢸⡂⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣧⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡆⠀⠀⠀⡹⣿⣿⣿⣿⣿⢿⡿⢿⣿⠀⢸⠀⠀⠻⣿⡄⠀⠈⠀⠂⠀⠀⢀⣾⡿⢁⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣶ ⠀⣹⠄⠀⠀⠈⣰⣾⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⢻⢿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠘⠿⠇⠀⠀⢸⣟⢨⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣠⣴⡿⠛⣀⣾⡟⣿⡇⠀⠀⠀⠀⠀⠀⠠⠀⢻⡄⠀⠀⠀⠀⠀⠀⢠⣾⠏ ⠄⢸⠂⠀⠀⣴⣿⣿⡿⠋⠀⠀⠀⢀⣠⣴⣶⣶⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠛⠍⠙⠋⠿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢰⣿⠀⠀⠀⠀⣰⣿⣷⣶⣶⡿⠿⠛⠉⠀⣴⣿⣿⣁⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢽⡀⠀⠀⠀⠀⠀⣠⡿⠁⠄ ⣇⢸⠀⠀⣴⣿⣿⣿⠃⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠹⣿⡄⠀⢀⠀⠀⠀⠈⠉⠀⠀⣀⡁⢸⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢨⣿⠀⠀⢀⣾⡿⠋⠁⠀⠀⠀⡀⠐⣬⣿⣿⡿⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⣾⠃⠐⡀ ⢹⡄⠀⠀⣿⣿⣿⣿⠁⠀⠀⣾⣿⣿⣿⣿⣿⡿⠿⣿⡿⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⠈⠀⢀⢀⣠⣬⣤⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⢸⣿⠀⠀⢼⠟⠁⠀⠀⠀⠀⢀⣨⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠂⠀⠀⠀⠀⠀⣿⠁⠀⠀ ⠈⢧⡈⢸⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣦⣴⣿⣷⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣷⣿⡿⠿⠿⠟⠿⢛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⢸⣿⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⡿⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡆⠀⠀⠀⠀⠀⣿⠀⠀⡁ ⣦⠈⠥⢸⣿⣿⣿⣿⡀⠀⠀⣿⣿⣿⣿⣌⣻⣿⣿⣿⣿⣿⡿⣿⣟⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⡀⠀⠠⠀⠀⠀⢰⠀⣣⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠅⣸⣿⠀⠀⣠⣶⣿⡿⣿⣿⣿⣤⠸⣿⣿⣿⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⢼⡇⠀⠀⠀⠀⠀⣯⡀⠀⠀ ⠿⣷⡀⠸⣿⣿⣿⣿⡆⠀⠀⣿⣿⣿⣿⠟⠻⠻⣿⣿⣿⣯⣶⠿⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠰⠄⣰⠄⠀⣳⠄⠀⠀⢠⠀⠀⢧⢀⠞⣰⠇⠀⠀⠀⡀⠀⠀⠀⠀⢸⣿⠀⣿⡗⠀⣸⣿⣿⣿⣏⣿⣿⠃⣿⠀⣿⣿⣿⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠺⣧⣀⠀ ⠁⠹⣿⣄⣿⣿⣿⣿⣿⡀⠀⠸⣿⣿⣿⠇⢀⠀⠀⠙⠛⢉⣀⣶⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠼⢀⡇⠀⠐⡣⣜⠞⠀⠀⣿⣰⡧⠈⡔⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡄⣿⡇⠀⢿⣿⡇⣿⣿⣿⡟⠀⣿⣧⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⠀⠀⠀⠀⠀⠀⡈⠛⣦ ⠀⠀⠘⣿⣿⣿⣿⡿⠻⠗⠀⠀⠘⣿⣷⣤⣰⣶⣶⣴⣾⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠃⠸⠀⠀⠠⣔⠫⠀⠀⢸⡿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢲⣿⠇⠀⣸⣿⠥⣿⣿⣿⠁⠀⣿⣿⠾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢨⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⢀⣿⣿⣧⣐⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⢃⠂⠀⠀⠸⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⢸⣿⠀⠀⣿⣿⠇⢸⣿⡏⠀⠀⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⡀⠀⠄⠀ ⠀⠀⠀⠀⣿⣏⠙⢿⣦⡄⠀⠀⠀⣀⠏⣹⡟⠀⠀⢠⡀⠄⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣼⣿⣏⢸⣿⠀⠄⣿⣿⠃⢸⣿⡇⠀⠀⣿⣯⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⡀⠀⠄⠁⠠⠀ ⠀⠀⠀⠀⣿⣿⠀⠎⠙⣿⣦⡀⠀⠾⠀⡾⠁⠀⠀⠀⠁⠈⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⠈⠀⠀⢀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢺⣿⣿⠇⣸⡿⠀⢋⣿⣿⠀⢸⣿⡇⠀⠀⢻⣿⡘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⢐⠀⠌⡐⠈⠄⡁ ⠀⠀⣀⠀⢸⣿⣿⣷⣴⣤⢻⣷⣶⠇⠈⡗⢀⠦⠀⡞⢰⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢬⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣱⣿⣿⣯⠀⣿⡇⠀⢸⣿⡇⠀⠈⢿⣷⠀⠀⢸⣿⡅⠹⣿⣷⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠘⣿⣧⠀⠆⡨⠀⠌⡀⠆ ⣄⡀⢻⡆⠀⢻⣟⡿⣿⣿⣿⣿⡟⠀⢰⠋⡜⠀⢰⡍⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⣰⣾⣿⣿⣿⡷⠠⣿⠃⠀⠐⣿⡇⠀⠀⢸⣿⡄⠀⢸⣿⡇⠀⢻⣿⡆⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠁⠌⢀⡁⠐ ⡿⢋⢸⣿⠀⠘⣿⣷⢏⣿⣿⢻⣿⣠⣿⠜⠁⠀⡞⠠⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⡏⣾⡿⠀⣿⠀⠀⢈⣿⡇⠀⠀⠀⢹⣷⡀⠨⣿⣷⠀⠀⢿⣿⡄⠀⠀⠀⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠹⣿⣷⡅⢈⠀⡄⠡ ⠀⢸⡿⣿⡆⠀⢹⣿⣸⢿⣷⠘⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⣴⡿⢻⣿⣿⣿⣷⣿⡗⢈⡇⠀⠀⢨⣿⠄⠀⠀⠀⠀⢻⣧⠀⢿⣿⡆⠀⠀⠻⣿⡀⠁⠀⠀⠀⠀⡄⠀⠀⢀⣀⣀⣴⣦⣖⣿⣿⣿⣄⠰⡐⡈ ⠀⠘⡤⢿⣷⠀⠀⢻⣿⣾⣿⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡰⠛⠉⠐⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠋⠁⠈⣿⣿⣿⡿⣿⡁⠠⠆⠀⠀⢸⣿⠄⠀⠀⠁⠀⠀⠻⣧⣸⣿⣿⣦⠀⠀⠹⡿⠃⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⣿⣿⣿⣽⣿⣿⡿⢿⣦⣑ ⠀⢈⡷⠈⣿⡇⠀⠘⣿⣿⣿⠀⠀⠹⢿⣦⡠⠄⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢽⣆⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⡿⠋⠀⠂⠀⠀⠈⢿⣿⣗⣿⡴⠀⠀⠀⠀⢠⣿⣦⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠁⠂⢠⣿⢿⣿⣻⣿⣶⠙⣿⣿⣧⣄⢿⣷⣶⠏⣿ ⠀⡆⣿⠀⠹⣿⡀⠀⢸⣿⣿⡇⠀⠀⠘⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⡿⠃⠀⠀⢀⠂⠀⠀⠀⠀⠹⣿⣿⠇⠀⠀⠀⠀⢸⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠁⠀⠀⠀⢀⣴⣿⣻⣴⣿⣿⣻⣿⣆⣘⣯⣿⠟⠻⣿⣿⣿⣿ ⠀⣇⣿⠂⠀⢿⣷⠀⠀⢿⣿⡇⠀⠈⢳⣾⣿⣿⣿⡙⠻⣿⣿⣶⣶⣦⣤⣄⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠈⣿⡆⠀⠀⠀⠀⢈⢿⣿⣿⣿⣦⠀⠀⠐⠁⠀⠀⠀⢀⠀⠀⠀⣤⣶⣾⣿⣿⣛⣯⣡⣼⣿⣯⣵⣾⣿⣿⣦⣜⡀⣿⣿⣿⣏ ⠀⢹⣿⡁⠀⠀⢻⣧⠀⠘⣿⣷⠀⠀⠁⢻⣿⣿⣿⣧⠀⢹⣿⣇⠈⢻⣿⣿⣿⡿⠿⣿⣶⣶⣶⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣿⣇⠀⠀⠀⠀⠈⢼⣷⣿⣯⢻⣧⣄⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠻⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿ ⠀⠘⣿⡇⠀⠀⠈⢿⣧⠀⢹⣿⡀⠀⠀⠀⠻⣿⣿⣿⣧⠀⣿⣿⣷⠀⠙⢿⣿⣿⣦⡀⢠⣬⣉⣹⣿⠟⠻⢿⣿⣿⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⠀⠈⠸⣿⣿⣿⣧⡉⠿⣧⣄⠀⣀⣴⣾⣿⣿⠟⠁⠀⠸⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣯⣿⣷⣶⣿⣿⣿⣿⣿ ⠀⠈⢿⣧⠀⠀⠀⠈⢿⣇⠈⣿⣇⠀⠀⡀⠀⠘⠿⣿⣿⣧⣸⢿⣿⣇⠀⠀⣙⣿⣿⣿⣶⣿⣿⡿⠃⠀⠐⢸⣿⣿⣿⣻⣟⣿⣻⢿⣿⣿⠛⠹⣿⣿⠛⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⢡⣿⣿⣿⣿⣿⣦⣉⣻⣿⣿⣿⣿⣿⠻⠿⠿⢶⣶⣿⣿⣿⣿⣿⠟⣻⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿ ⠐⡄⢸⣿⡄⠀⠀⠐⠘⢿⣧⢹⣿⠀⠀⠄⠀⠀⠀⠙⢿⣿⣿⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⣦⣿⣿⣿⣳⢿⣞⣷⢿⣿⡿⠃⠀⠀⠘⢿⣶⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢈⣿⣿⡆⠀⠀⠀⠈⢹⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡟⠉⢻⡿⣿ ⠀⠸⡄⢿⣷⠀⠀⠀⠀⢸⣿⣦⢿⣧⠀⠀⠂⠀⢀⠀⠈⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⢀⣿⣿⣿⣳⡿⣯⢿⡾⣿⣿⠃⠀⠀⠀⠄⠈⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⢸⣿⣿⣿⣟⣾⡽⣯⢿⣿⣿⣿⠀⠀⠀⣠⣿⣿⣿⣿⣿⣟⣾⣿⣿⣿⡿⣿⢿⡏⠁⡞⠀⠀⣼⠇⣿ ⠀⠀⣿⣞⣿⡆⢀⠀⠀⠉⣿⡏⢿⣿⣆⡀⠀⠄⠀⠀⠀⡀⠀⠈⠙⠻⢿⣿⣟⡉⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⡿⣽⣻⣽⣿⣽⣿⡏⠀⠀⠀⠈⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠀⢸⣿⢹⣿⡄⠀⠀⠘⣿⣿⣿⣻⣞⣿⣻⣿⣿⠟⣿⡀⠀⣀⣿⣿⣿⣾⣿⣿⣟⣾⣿⣷⣿⣿⣿⣿⡏⢰⡋⠀⠀⣾⠁⣿ ⠀⠀⠘⣿⣿⣷⠀⠀⠀⣠⣼⣿⣸⡏⢿⣷⣄⠀⠐⠂⠁⠀⠂⠀⠀⠀⠀⠀⠈⠐⠋⠀⠉⠉⠀⣠⣼⣿⣿⣯⣟⡿⣽⣳⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣴⡿⠋⠀⠀⠀⣿⡆⠹⣷⡀⠀⠀⣿⣿⣿⡿⣽⣾⣻⣿⠇⠘⣥⢧⣀⣼⡏⣿⡧⣿⣿⣿⣿⡽⣿⣿⣿⣿⣿⣿⡇⢺⡁⠀⠀⡿⠀⣿ ⠀⠀⠀⠹⣿⣽⣷⣴⣿⣿⡿⣿⣷⣯⠀⢿⣻⣿⣦⣀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣿⣿⣿⣿⣟⣾⣽⣻⢯⣷⣿⣿⣿⠀⠀⠀⠀⠈⠀⢀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡟⠋⠀⠀⠀⠀⠀⣸⣷⠀⠹⣷⡀⠀⣸⣿⣿⣿⣻⣞⣿⡟⠀⠀⣹⣾⣿⣿⢱⣿⣸⣿⢿⣿⣿⣻⣿⣿⣿⣿⣿⣿⡇⡿⠀⠀⢐⡯⢀⣿ ⠀⠀⠀⠀⠙⣿⣿⣿⡟⠃⠀⢹⣷⣿⠀⠀⠻⣿⣟⠿⣿⣿⣿⣿⣿⢿⣿⠿⠿⡿⣟⣻⣭⣿⣿⣿⢿⣳⡿⣞⣷⢿⣻⣯⣿⣿⡯⠙⠻⣷⣦⣄⣣⣾⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⠀⠀⣀⣶⣿⡿⠀⠀⠹⣷⡀⠘⣿⣿⣿⡷⣿⣿⠁⠀⣠⣿⣿⣿⠇⢾⣿⢹⣿⢸⣿⣿⡿⢿⣿⣿⣿⣿⣿⣧⣿⠀⠀⢸⡇⠀⢿ ⠀⠀⠀⠀⠀⢘⣿⡽⣄⠀⠀⢸⣿⣿⠀⠀⠀⢈⣿⣷⣤⣍⣝⣛⠿⠿⠾⠿⠿⣛⣻⣿⣿⣿⡿⣽⣻⢯⣟⣯⣟⣯⣟⣷⣿⣿⡇⠀⠀⠀⢉⣻⣿⡏⣀⡤⠀⠀⠀⠀⠀⠀⠀⠄⢂⡐⠀⠀⠀⠀⠀⣀⣶⣾⣿⣿⣿⣿⡇⣀⠀⠀⠸⣷⣤⣿⣿⣿⣿⣿⡇⠀⢰⣿⢋⣾⡏⠀⣿⡏⣿⡟⣸⣿⣿⡇⠀⠈⢿⡻⣿⣿⣿⣘⠁⠀⠰⡇⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⡀⠀⠀⠀⣸⣿⣿⣿⣦⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠻⠿⣿⣷⣄⣀⣀⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠿⠿⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠋⠉⠉⠙⠿⠿⣷⣶⣶⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣶⣶⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⠿⣿⣶⣦⣀⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣿⣿⠟⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⣷⣶ ⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣤⣾⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣶⣿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣶⣿⣶⣶⣾⣿⣿⣿⣿⣷⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⠿⣿⣿⡿⠋⠙⠟⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣤⢻⣿⠇⠀⢰⣶⣭⣿⣿⣿⣿⣿⣿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⡜⢛⡁⣿⡿⠛⢿⡿⠛⠛⠻⠟⢿⣿⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣴⣿⣿⠀⠉⠉⠻⠿⠋⠿⠋⠙⣿⣿⣟⣁⣸⡿⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣿⡿⠃⠀⠀⠀⠀⠿⢷⣶⣄⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣷⣄⣀⠀⠀⠀⠀⠀⠉⠙⠃⠀⣶⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠛⢿⣿⣄⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣼⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠿⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣤⡄⠀⣤⣼⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠙⢿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡉⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠈⠛⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠟⠛⠁⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣀⣀⣤⣤⣀⣠⣾⣷⣄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠿⠿⠿⠿⠿⣿⣶⣶⣦⣀⣠⣶⡾⠏⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠿⠿⢿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢶⣶⣶⣶⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠒⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠄⠀⠠⠠⢄⢀⢀⡐⢀⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠉⠀⠀⠀⠀⠀⠈⠀⠀⠄⡆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠂⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀ ⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢄⠄⠀⠀⠁⠀⠀⠁⠄⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀ ⠀⠀⢀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠈⠀⠀⠁⠀⠄⢀⠆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀ ⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⡀⠀⡀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡁⠀⠂⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡐⠄⠀⠀⠉⠐⠀⠂⠂⠉⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠈⠄⠄⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⢘⠀⠁⠂⠀⠂⠄⠀⠂⠈⠀⠀⠀⠁⡣⠁⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠀⠃⠐⡘⠀⢐⠀⠂⠀⠈⠀⠂⠂⠒⠀⠀⠀⠀⢁⠃⠁⠈⠀⠌⠀⠁⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⡀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠊⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⡴⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣼⣷⣶⣷⣤⣤⡶⠖⡆⠀⠀ ⠀⠀⠀⠀⢀⣿⣿⣿⣿⡿⣿⣧⣄⡰⠀⠀⠀ ⠀⠀⠀⣴⣿⣿⣿⣿⠯⢿⣗⢿⠏⡆⠀⠀⠀ ⠀⠀⢀⣿⠻⣿⣿⣿⡴⠛⠳⣕⣿⡃⠀⢀⡀ ⢀⣴⣾⣿⣶⣿⡿⢿⣶⠆⠀⢋⠉⠈⢉⠤⠂ ⢺⣿⣿⣿⣿⣿⣿⣃⡏⡁⠀⢸⣿⠀⢐⠈⠀ ⠀⣿⣿⣿⣿⣿⡿⢫⣾⡎⠁⠀⢹⠀⠀⠀⠀ ⠀⢹⣧⡍⡉⣉⣢⣿⣯⠀⠀⢠⡿⠀⠀⠀⠀ ⠀⠀⠛⠷⠖⠛⠻⠿⠿⠿⠖⠊⠀⠀⠀⠀⠀

⣿⢿⣻⣟⡿⣟⣿⣻⢿⣻⣟⡿⣟⣿⣻⢿⣻⣟⡿⣟⣿⣻⢿⣻⣟⡿⣟⣿⣻⢿⣻⣟⡿⣟⣿⣻⢿⣻⣟⡿⣟⣿⣻⢿⣻⣟⡿⣟⣿⣻⢿⣻⣟⡿⣟⣿⣻⢿⣻⣟⡿⣟⣿⣻⢿⣻⣟⡿⣟⣿⣻⢿⣻⣟⡿⣟⣿⣻⢿⣻⣟⡿⣟⣿⣻⢿⣻⣟⡿⣟⣿⣻⢿⣻⣟⡿⣟⣿⣻⢿⣻⣟⡿⣿ ⣿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣿⣽ ⣿⣽⢾⣻⣽⣟⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣳⣿ ⣿⢾⣻⣯⢷⣻⣟⣯⢿⣞⣿⣽⢾⣻⣽⢷⣯⣿⣻⢾⣽⣟⡷⣯⣿⣻⢾⣽⣟⡷⣯⣿⣻⢾⣽⣟⡷⣯⣿⣻⢾⣽⣟⡷⣯⣿⣻⢾⣽⣟⡷⣯⣿⣻⢾⣽⣟⡷⣯⣿⣻⢾⣽⣟⡷⣯⣿⣻⢾⣽⣟⡷⣯⣿⣻⢾⣽⣟⡷⣯⣿⣻⢾⣽⣟⡷⣯⣿⣻⢾⣽⣟⡷⣯⣿⣻⢾⣽⣟⡷⣯⣿⣻⢾ ⣿⣻⣽⡾⣟⡿⣞⣯⣿⣻⢾⣽⣻⢯⣟⡿⣞⣷⢿⣯⣷⣻⢿⣽⣞⡿⣯⣷⣻⢿⣽⣞⡿⣯⣷⣻⢿⣽⣞⡿⣯⣷⣻⢿⣽⣞⡿⣯⣷⣻⢿⣽⣞⡿⣯⣷⣻⢿⣽⣞⡿⣯⣷⣻⢿⣽⣞⡿⣯⣷⣻⢿⣽⣞⡿⣯⣷⣻⢿⣽⣞⡿⣯⣷⣻⢿⣽⣞⡿⣯⣷⣻⢿⣽⣞⡿⣯⣷⣻⢿⣽⣞⣿⣻ ⣿⣽⢾⣻⣽⣟⡿⣽⣞⣯⡿⣯⣟⡿⣽⣻⣯⣟⡿⣞⣷⢿⣯⡷⣟⣿⣳⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⢾⣻ ⣿⢾⣻⣯⢷⣻⣽⣟⣾⢯⣟⣷⣟⡿⣽⣷⣻⢾⣟⣯⢿⣻⣾⡽⣟⣷⣟⣷⣻⣽⡷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣿⣻ ⣿⣻⣽⡾⣟⣯⡷⣿⣽⣻⣟⣾⣽⣻⣟⣾⡽⣿⣞⣿⣻⣽⣞⣿⣻⡾⣽⡾⣯⣷⣟⣯⡿⣽⡷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣞⣷⢿ ⣿⣽⢾⣻⣽⢯⣟⣷⣯⡷⣿⡽⣞⣿⢾⣽⣻⢷⣻⡾⣯⣷⣻⢷⣻⣽⢿⡽⣷⣻⣾⣽⣻⣽⣻⣽⡾⣟⣷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢯⣟⣿ ⣿⢾⣻⣯⣟⣯⡿⣞⣷⢿⣽⣻⢯⣟⣯⣷⢿⣻⢯⣟⣷⣯⣟⡿⣯⣟⣯⡿⣯⣷⣟⣾⡽⣷⣻⢷⣟⣯⣷⣟⣾⣟⣷⢯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣽⣾ ⣿⣻⣽⡾⣽⣳⣿⣻⣽⣯⡷⣿⣻⢯⣟⣾⣟⣯⣿⣻⣞⣷⣻⣽⣷⣻⣽⣻⢷⣻⣾⣽⣻⣽⢯⣿⢾⣻⡾⣽⡾⣽⡾⣟⣯⡿⣷⢯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⣟⣾ ⣿⣽⢾⣻⣽⣟⣾⣽⢾⣳⡿⣯⣟⡿⣽⣳⣯⣟⣾⢷⣻⣽⣻⣞⡷⣟⣷⢿⣻⣽⣾⣳⡿⣽⣻⡽⣟⣷⢿⣯⣟⣯⢿⣻⢷⣟⣯⡿⣯⢿⣳⣯⣟⡿⣾⣽⣻⣷⣯⣿⣿⣾⣿⣽⣷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⡷⣿⣽ ⣿⢾⣻⣯⢷⣯⣟⣾⣟⣯⢿⣳⣟⣿⡽⣯⣷⢿⣽⣻⢯⣷⢿⣽⣻⣟⣾⣟⣯⣷⢯⣷⢿⣻⡽⣟⣯⣿⣻⢾⣽⢯⣿⢯⣿⢾⣯⢿⣽⣟⣯⡷⣟⣿⣳⣿⡿⣛⣭⣵⣯⣶⣭⣍⡛⢿⣿⣽⡷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⢷⣻ ⣿⣻⣽⡾⣟⣷⣯⡷⣿⣽⣻⢯⣟⣾⢿⣽⡾⣯⣷⢿⣻⡽⣟⣾⣟⣾⣽⣾⣻⣾⢿⣽⣻⢯⣟⣿⡽⣞⣯⡿⣯⣿⢾⣻⣽⣟⣾⣟⡷⣯⡿⣽⣻⣷⣿⣻⣿⣿⣿⢿⣻⣟⡿⣿⣿⣧⡽⣿⣿⣯⢿⣽⣷⣯⣿⣿⣾⣽⣿⣷⢯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣿⣻ ⣿⣽⢾⣻⣽⣾⣳⣿⣳⣯⢿⣻⣽⢯⣿⢾⣽⣷⣻⣯⢿⣽⣟⣷⣿⣿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣾⣟⣿⣽⣻⢷⣯⣿⣻⢾⣽⡾⣯⢿⣽⣻⣽⡷⣿⣿⣿⣟⡷⣯⣿⣻⣞⣿⣽⣻⢿⣿⣼⣿⣿⠿⠿⠟⠛⠛⠛⠛⠛⢿⣿⣿⣯⢿⡷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣞⣷⢿ ⣿⢾⣻⣯⢷⣯⡷⣟⣷⣻⢿⡽⣯⣿⢾⣻⡷⣯⣷⣟⣯⣷⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣾⣟⣿⣞⡷⣿⢯⣷⣟⣿⣯⣿⣽⣾⣿⣿⣯⢷⣻⢿⣽⡾⣷⣻⢷⣯⣟⣯⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⣽⣟⣾⣟⣷⢯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣾⣽⣻⢯⣟⣿ ⣿⣻⣽⡾⣟⣷⢿⣯⢿⣽⣻⣟⣷⣯⢿⡷⣟⡿⣾⣽⣳⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣾⣿⢿⠿⠿⢿⠿⠿⠿⠿⣹⣿⣿⢾⣟⣯⡿⣷⣿⣿⠿⣿⣾⣯⣟⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣟⣾⢷⣻⡾⣟⣯⡿⣷⢯⣟⡿⣾⣽⣻⢷⣯⣟⡿⣽⣾ ⣿⣽⢾⣻⣽⡾⣟⣾⢿⣽⣳⡿⣾⡽⣯⣿⣻⣽⡷⣯⣟⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢯⣿⣞⣯⣿⡿⣽⣿⣿⣿⣾⣿⣿⣯⣭⣽⣿⣷⣤⣀⠀⢀⠀⣀⣀⣀⣀⣼⣿⣿⣿⣾⣻⢯⣟⣿⣳⢿⣯⢿⣯⢿⣳⣯⣟⡿⣾⣽⣻⣟⣾ ⣿⢾⣻⣯⢷⣿⣻⡽⣟⣾⢯⣟⣷⢿⣻⡾⣽⣳⡿⣯⣟⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⣯⣷⣻⡽⣿⣷⡹⣿⣿⣿⣿⣿⣿⣿⢿⣟⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣾⣝⡻⣷⣿⣟⡿⣞⣿⣻⢾⣟⣾⣟⣯⡷⣟⣿⣳⣯⣷⢿⣽ ⣿⣻⣽⡾⣟⣷⣻⣽⢿⣽⣻⣟⣾⢿⣽⣻⣽⢯⣟⣷⣟⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣳⣯⢿⣽⣟⣿⣷⣯⣟⣹⣿⣿⣻⢾⣯⢿⣽⣷⣻⢿⣷⣹⣿⣷⣟⡾⣷⣻⣟⣿⣷⡙⣿⣯⣿⣻⢷⣻⣯⢿⡾⣽⣳⣿⣻⢷⣻⢷⣯⡿⣾ ⣿⣽⢾⣻⣽⢯⣟⣾⢿⣽⣳⣯⣟⡿⣞⣯⣟⣯⡿⣾⣽⣻⣿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣯⣟⣿⢾⡽⣯⢿⣿⣿⣿⣿⡷⣟⣿⢾⣻⡷⣯⣟⣿⣿⡟⣿⣿⣿⣿⣽⢷⣯⣟⣿⣿⡼⣿⣷⣟⡿⣽⡾⣿⡽⣿⣽⣞⣯⡿⣯⣿⢾⣽⢿ ⣿⢾⣻⣯⣟⣯⡿⣽⣻⡾⣯⡷⣟⡿⣯⣟⣾⢯⣟⣷⣯⢿⣿⡀⣠⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣯⣿⣻⣟⣾⣿⣷⣿⣿⡿⣽⣻⡷⣟⣿⣞⣿⣿⣿⣿⣷⣎⢿⣿⡿⣾⡽⣯⣿⣿⣿⣿⣞⡿⣯⣟⣷⢿⣳⡿⣞⣯⡿⣷⢯⡿⣯⣿ ⣿⣻⣽⡾⣽⣳⣿⣻⢷⡿⣽⣻⢯⣿⣽⣻⢾⣟⡿⣾⡽⣯⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠉⠙⢿⣿⣯⣷⢿⣻⣷⡿⣟⣿⢿⣿⣿⠏⣼⣿⣿⣳⡿⣯⣿⣿⣿⢿⣽⣻⣽⡾⣯⡿⣯⣟⣿⣳⢿⣯⢿⣻⢷⣻ ⣿⣽⢾⣻⣽⣟⣾⡽⣿⣽⣻⣽⣟⡷⣯⣟⡿⣾⣻⢷⡿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢿⣿⣾⣿⣿⣷⣾⣶⣿⣿⣿⣳⡿⣽⣿⣿⣿⣯⢿⣞⣯⣷⢿⣽⣻⢷⣻⣷⣻⣟⣾⣟⣯⣿⣻ ⣿⢾⣻⣯⢷⣯⣷⢿⣻⡾⣽⣳⣯⢿⣯⢿⣽⡷⣿⢯⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣳⣯⣟⡿⣟⣿⡽⣞⣯⣿⣿⣿⣿⣟⣾⢿⣽⣳⣯⣿⣳⣿⣻⣽⢾⣻⣾⣽⢾⣻⣾⣽ ⣿⣻⣽⡾⣟⣷⢯⣿⣳⣿⣻⣽⢯⣿⢾⣻⣷⣻⢯⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣾⣟⣯⣷⣿⣿⣿⠟⢸⣿⣿⣞⣯⣿⣞⣯⣷⢯⣷⢯⣟⣾⣟⡿⣾⣽⣻⢷⣻⣾ ⣿⣽⢾⣻⣽⡾⣟⣷⣟⡷⣯⣟⡿⣾⣻⣟⣾⡽⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⡿⣿⠿⠿⠋⠁⠀⠸⣿⣿⣽⣳⡿⣞⡿⣞⣿⣽⣻⢯⣷⣻⣽⡷⣯⣟⣿⣽⢾ ⣿⢾⣻⣯⢷⡿⣯⣷⣻⣽⢿⣽⣻⢷⡿⣽⣾⣻⣷⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣷⣯⣿⣻⣽⣻⡾⣽⣟⣾⣻⢾⣿ ⣿⣻⣽⡾⣿⡽⣷⣻⣽⡾⣟⣷⣿⣯⣿⣷⣯⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⢈⣁⡀⠀⠀⠆⠀⠀⠀⠀⠀⢴⠶⠶⠟⠛⢿⣿⣶⣶⣶⣶⣶⣿⣿⣿⡷⣟⣷⢿⣽⣟⣾⢯⣟⡿⣾ ⣿⣽⢾⣻⢷⣟⣯⡿⣾⣽⢿⣾⣿⣿⣯⣽⣯⣽⣿⣿⣿⠛⠛⠛⠛⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡶⢿⡟⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⡿⣽⣻⣽⢷⣯⢿⣽⣟⣾⣯⣷⣻⡽⣿⣽⣻⣽ ⣿⢾⣻⣯⢿⡾⣯⣟⣷⣯⢿⣻⢿⣟⡿⣿⢿⡿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡰⣿⣮⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣻⣿⢿⣽⣻⢾⣯⣟⡿⣾⣽⢾⣳⣯⢿⣽⡷⣯⡿⣽ ⣿⣻⣽⡾⣿⡽⣷⣻⢷⣯⣿⣻⣟⣾⢿⣽⣯⢿⣽⣿⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣻⣿⣶⣤⣤⣶⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣴⢩⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⢦⣿⣿⠿⡿⣿⣿⣿⣾⣽⣻⢷⣯⡿⣯⣟⡿⣾⣽⢷⣿⣻ ⣿⣽⢾⣻⢷⣟⣯⣿⣻⣞⣷⣟⣾⢯⣿⢾⣽⣯⣷⣿⣿⣷⣤⣤⠶⠷⠀⠀⠀⠀⠀⠀⠉⠙⠿⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡿⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣶⣶⣿⣽⣿⣯⣟⡿⣾⣽⢷⣻⣟⣷⣯⢿⣾⣽ ⣿⢾⣻⣯⢿⣾⣻⣞⣷⢿⣳⣯⣟⡿⣾⣿⣿⣯⣷⣾⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣃⡐⢂⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⢯⣟⣿⣻⣟⣯⡷⣟⣿⣳⣯⣿⣻⢾⣳⣿⣻⢾⣽ ⣿⣻⣽⡾⣟⣷⣯⢿⣾⣻⣽⡾⣯⢿⣳⣟⣯⣿⣻⣽⣻⢿⣷⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠦⣤⣀⣾⣿⣿⣯⣿⣻⣞⣷⣯⢿⣽⣟⣷⣻⢷⣯⣟⡿⣽⣞⣯⣿⣻ ⣿⣽⢾⣻⣽⡾⣽⣟⣾⡽⣷⣻⣟⡿⣽⣻⢾⣳⣟⡷⣿⢯⣿⣿⣦⣠⣴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣯⣝⠻⣷⣿⣟⣾⡽⣿⢾⣽⣾⣻⣟⣾⣽⣻⢯⣟⣷⢯⣿ ⣿⢾⣻⣯⢷⣿⣻⢾⣯⢿⣽⢷⣻⢿⣽⣻⢿⡽⣯⣟⣿⡿⢟⣻⣼⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⣿⢿⣿⣶⣯⣿⣿⡿⣽⣟⡾⣷⣻⣾⣻⣞⡿⣯⢿⣾⣻⣽ ⣿⣻⣽⡾⣟⣷⣻⣟⣾⢿⣽⣻⢯⣿⣳⡿⣯⢿⣿⣿⣽⣾⣿⣿⢿⣻⡿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣻⣽⢯⣟⣯⣿⣻⢿⡿⣽⣟⣾⢿⡽⣷⢯⣷⣟⡿⣽⡿⣾⣽⣻ ⣿⣽⢾⣻⣽⢯⣷⢿⣽⣻⣾⣻⢯⣷⢿⣽⣻⣟⣿⡿⣿⣻⣽⡾⣟⣯⢿⣳⣿⣻⣿⣿⣿⣿⣶⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣿⣿⣿⢿⣻⣽⣞⣯⣟⣯⣿⣳⣯⣟⣯⣿⣻⢾⣯⣟⣿⡽⣟⣷⢯⣿⢯⣟⣷⣯⢿ ⣿⢾⣻⣯⣟⣯⣟⡿⣞⣿⢾⡽⣿⣽⣻⡾⣟⣾⢷⣻⣯⣟⣾⣽⢿⣽⣻⣟⡾⣷⣻⣞⣿⣻⢿⡿⣿⣷⣿⣯⣿⣿⣷⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⢿⣟⡿⣽⡾⣟⣯⡷⣿⡽⣾⣻⢾⣽⡾⣯⣷⣻⣽⣟⣾⣽⢾⣻⣟⣾⢿⡽⣯⡿⣾⣽⣻ ⣿⣻⣽⡾⣽⣻⢾⣟⣯⣟⣯⡿⣷⢯⣷⢿⣻⣽⣻⣟⣾⣽⣳⣯⣿⣞⡿⣞⣿⡽⣷⣻⢷⣻⣯⢿⣽⢯⡿⣽⣟⣿⣻⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣟⡿⣯⣟⣾⢯⣿⡽⣿⣽⣻⢷⣟⣯⢿⣷⣻⣯⡷⣿⣳⣯⢿⡾⣽⡾⣯⣟⡿⣞⣯⣿⣻⣽⣟⡷⣯⣿ ⣿⣽⢾⣻⣽⣟⡿⣾⣻⢾⣯⢿⣽⣻⣽⣟⣯⡷⣿⡽⣾⡽⣷⣻⡾⣽⣻⣯⡷⣿⢯⣟⣿⣽⢾⡿⣽⣻⣽⣟⡾⣷⣻⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⡿⣞⣷⣯⢿⣻⢷⣯⣿⣽⢾⣯⢿⣳⣿⣳⣯⣟⡿⣾⣻⣟⡾⣷⢯⡿⣷⣻⣽⣯⢿⣯⣟⣷⣟⡿⣯⣟⣾⣽⣳⣯⢿⣻⣾ ⣿⢾⣻⣯⢷⣻⣽⡷⣿⣻⢾⡿⣽⣻⡾⣽⣾⣻⢷⣟⣯⣿⡽⣷⣟⣿⣳⣯⢿⣽⣻⣟⣾⡽⣯⣟⡿⣽⣳⣟⡿⣽⣷⣻⣟⣾⣻⢿⡿⣿⢿⣟⡿⣯⣟⣿⣻⣟⣯⢿⣻⢷⣯⡿⣯⣿⣞⣷⢯⣿⢾⣟⡿⣾⣽⣳⣟⣿⣳⣯⢿⣽⣻⣯⢿⣽⣻⡾⣽⣟⣾⣽⢾⣯⣟⣷⢿⣽⢾⣯⣟⣿⣳⣿ ⣿⣻⣽⡾⣟⣯⣷⢿⣳⡿⣯⣟⣯⣷⢿⣻⣾⡽⣿⣞⡿⣾⣽⢷⣻⣾⡽⣯⡿⣽⣳⣯⢿⣽⢯⣿⡽⣿⣽⢾⣟⡿⣞⣷⣻⢷⣻⣯⢿⣽⣟⣾⢿⣽⡾⣷⢯⣿⢾⣟⣯⣿⢾⣽⣷⣻⢾⣯⡿⣽⣻⡾⣟⣷⣯⣟⣾⡽⣷⣻⣯⣟⣷⣻⣯⣟⡷⣿⣻⢾⣻⡾⣟⣾⣽⡾⣿⣽⣻⣾⣽⢾⣻⣾ ⣿⣽⢾⣻⣽⣟⡾⣟⣯⣿⡽⣯⣷⣟⣯⣷⢯⣿⣳⡿⣽⡷⣯⣿⣻⢾⣽⡷⣿⣻⣽⢯⣿⢾⣟⡷⣿⣳⣯⣿⢾⣻⣯⢿⣽⣻⣟⣾⣟⡷⣯⣟⡿⣾⣽⣻⣟⣾⢯⣿⢾⡽⣟⣾⢷⣻⣟⣾⣽⣟⡷⣿⢯⣷⣟⣾⢯⣿⡽⣷⣻⡾⣯⣷⣟⣾⣟⡷⣿⣻⢷⣟⡿⣽⡾⣽⡷⣯⣷⣟⡾⣿⣽⢾ ⣿⢾⣻⣯⢷⣻⣟⣯⣷⢯⣿⣳⢿⣞⡿⣾⣻⢷⣻⣽⣯⢿⣳⣯⣟⣯⣷⢿⣯⢷⣟⣯⣟⡿⣾⣻⣽⢷⣻⡾⣿⣽⢾⡿⣽⣳⣯⡷⣿⣽⣻⣽⣻⢷⣯⡷⣿⡽⣿⢾⣻⣟⣯⢿⣻⣽⣾⣻⢾⣽⣻⣽⣟⡷⣯⣟⡿⣞⣿⡽⣷⢿⣽⡾⣽⡾⣽⣻⡷⣟⣯⡿⣽⢿⣽⢯⣟⣷⣟⡾⣟⣷⣯⣿ ⣿⣻⣽⡾⣟⡿⣞⣿⢾⣻⢷⣻⣯⢿⣽⡷⣿⣻⢯⣷⣻⢿⣽⣳⡿⣽⡾⣟⣾⢿⣽⣻⢾⣟⣷⢿⣽⣻⢯⣟⣷⣯⢿⣻⣽⢯⣷⣟⡿⣾⣽⣳⡿⣯⣷⢿⣯⢿⣽⣻⣟⣾⢯⣿⢯⣷⢯⣟⣯⡿⣽⣞⣯⣿⣽⢾⣟⣿⣳⢿⣯⢿⣞⣿⣽⣻⣽⢷⣟⡿⣽⣻⢯⣿⢾⣟⡿⣾⣽⣻⢯⣷⣟⣾ ⣿⣽⢾⣻⣽⣟⣯⣟⣯⣿⣻⣽⡾⣟⣷⢿⣳⣿⣻⣽⢯⣿⣳⡿⣽⣯⣟⡿⣽⣻⣾⣻⣟⣾⢯⣿⣞⡿⣯⢿⡾⣽⣻⢯⣟⡿⣾⣽⣻⢷⣯⢿⣽⡷⣯⣿⢾⣻⣽⢷⣯⣟⡿⣾⣻⡽⣟⣯⡿⣽⣟⡾⣟⣾⡽⣿⢾⣳⣿⣻⢾⡿⣽⣾⣳⡿⣽⣻⡾⣟⣯⣿⣻⡽⣟⣾⣟⣷⢯⣟⣿⣳⣯⢿ ⣿⢾⣻⣯⢷⣻⣽⣾⣻⢾⣽⣳⣿⣻⢾⣟⡿⣾⣽⢾⣟⡷⣿⡽⣟⣾⣽⣻⢯⣷⣟⡷⣯⣟⡿⣾⣽⣻⣽⢿⣽⢿⣽⣻⢯⣿⣳⣯⣟⡿⣾⣻⢷⣻⣽⡾⣟⣯⣟⡿⣾⣽⣻⢷⣟⡿⣯⣷⢿⣻⡾⣟⣯⣷⢿⣯⣟⡿⣾⡽⣿⡽⣟⣾⣽⣻⣽⢷⣟⡿⣽⡾⣽⣻⣯⡷⣿⢾⣻⣟⣾⡽⣯⣿ ⣿⣻⣽⡾⣟⣯⣷⢯⣟⣯⣟⣷⢯⣟⣿⢾⣻⡷⣯⣿⢾⣟⡷⣿⣻⣽⢾⣻⣯⡷⣿⣽⣻⣽⣻⢷⣯⣟⣾⢿⣽⣻⣾⣻⢯⣷⣟⣷⣻⣽⡷⣿⣻⢯⣷⢿⣻⣽⡾⣟⣷⣯⣟⡿⣾⣻⢷⣯⡿⣷⣟⡿⣽⡾⣟⣾⣽⣻⢷⣟⣯⢿⣻⣽⢾⣯⣟⡿⣾⣻⢯⣟⣿⣳⣯⢿⣽⣻⣟⣾⣽⣻⢷⣻ ⣿⣽⢾⣻⣽⣟⡾⣟⣯⢿⣞⣯⣿⣻⢾⡿⣽⣻⢷⣯⡿⣾⢿⡽⣷⣻⣟⣷⢯⣿⣳⣯⢿⣞⣿⣻⡾⣽⣯⢿⣞⡿⣾⡽⣟⣷⣻⡾⣯⣷⢿⣳⣿⣻⡽⣿⣽⢾⣻⣽⢷⣻⡾⣟⣷⢿⣯⡷⣿⣳⡿⣽⢿⣽⣻⣽⢾⣻⣯⢿⣽⣻⢯⣟⡿⣾⣽⣻⢷⣟⣿⣻⢾⣽⢯⣿⣽⣳⣯⣟⣾⣻⣟⣿ ⣿⢾⣻⣯⢷⣻⣟⣯⡿⣯⣟⣷⢯⣟⣯⣿⣻⡽⣿⢾⣽⣟⣯⡿⣯⣷⢿⣾⣻⢷⣻⣽⣯⢿⣞⣷⢿⣻⡾⣿⣽⣻⢷⣿⣻⡽⣷⢿⣽⡾⣟⡿⣾⣽⣻⢷⣯⡿⣯⣟⡿⣽⣻⣽⢯⣿⢾⣽⡷⣿⡽⣟⣿⣞⣯⣟⣿⣳⢿⣯⢿⣽⣻⢯⣿⣳⣯⣟⡿⣾⢯⣟⣯⣿⣻⢾⣳⣟⣷⣻⡽⣷⣻⣾

⡖⠊⠱⢳⠬⡬⡱⢄⡀⠀⢂⢖⣃⣂⣿⢜⡂⣾⠷⠃⡿⢁⢢⢈⢻⢂ ⠁⢀⡀⠤⢼⣈⡡⡫⠜⢥⡩⠏⢱⡁⠀⠀⠀⠋⠳⣄⠪⢜⡘⠦⠸⠃ ⣐⡵⠶⠿⣼⣥⠘⢳⡤⠆⣙⣒⢫⣤⠀⠀⠀⠀⢐⣵⠻⠧⡜⢅⣿⢦ ⠁⠶⣠⠀⢸⡾⢡⢣⡼⢂⡥⢪⢅⣌⢃⡰⣴⠶⠤⡡⢌⡒⣘⢤⡁⢘ ⡈⠧⣂⣤⠟⠃⠁⢤⠤⣡⠈⠙⠛⢊⢢⠏⠳⡠⢲⠥⠧⠹⣽⢡⢷⢢ ⠞⡚⡰⠲⡄⠀⠀⣈⢡⠚⢦⣈⠔⢎⡢⢟⠁⢬⣙⠀⠀⠀⠀⢈⠁⡗ ⢆⣜⡱⣍⢁⢺⣑⣤⣭⡏⠶⡔⠺⣾⢱⢛⠒⠲⢊⣆⡌⢀⢁⡠⣜⡭ ⣊⢜⡳⣜⠲⢪⡝⢡⠠⣡⠗⢋⠻⡷⡄⢣⠾⣇⣈⡠⠚⣌⡳⡘⠴⢅ ⡞⠆⢓⢊⣏⠁⠙⣄⣋⢦⡙⠎⣠⠟⠁⠁⠑⠊⠁⠸⣤⡱⢎⡲⣦⠟ ⠘⢉⢠⡉⡆⡄⢄⠸⠆⡒⢤⢋⣑⣊⡱⡀⢠⣔⡭⣭⣬⢇⡘⡔⠁⠈ ⡪⠵⠶⣲⣬⡘⢡⢆⠰⣩⡞⠋⡉⡁⠻⢢⢍⡠⠄⣨⡶⠛⡂⠔⢪⠆ ⢦⢩⠂⠈⣷⡃⡐⠎⠐⠹⣄⠗⡚⡣⡜⢢⢺⠔⣊⢣⡌⠑⠽⣱⠝⠒ ⠊⢑⣡⡞⠺⢄⡾⣤⡀⢠⢦⣝⠬⠒⠉⠠⢤⠾⢳⣤⢇⠀⠀⣀⠷⢨ ⡍⠀⠉⢰⣤⠄⡇⢢⡙⡡⡄⣼⢂⣰⡐⠶⠧⡲⢥⠳⢴⢫⡅⢊⡇⠙ ⠄⢹⠂⠛⣅⠴⡨⠃⠑⠳⣫⠴⡡⠀⡿⢡⡔⠹⠌⡅⢤⠫⠔⣫⠀⢈ ⠊⢢⡔⡶⢩⣘⡁⠀⠀⠈⠱⢯⠱⡚⣥⠐⡆⢃⣀⢌⡵⡟⠫⠷⣌⠚ ⡏⠁⠁⠛⢒⢔⢫⢂⡬⠀⣠⠛⡵⡤⢛⠍⢆⢿⡏⠉⣸⢈⠶⣠⢸⡅ ⠀⡠⢐⣸⠺⡤⢅⡓⠜⠓⢌⢃⣴⠀⠀⠀⠀⠀⠙⡢⣅⣪⠳⡐⡸⠀ ⠭⠚⡋⠛⢟⣷⡈⣙⠲⠃⡼⢍⡮⢵⡀⠀⢀⠀⠈⡞⠙⠓⣍⠶⡿⢻ ⠰⣘⠥⠀⣸⣗⠰⠈⠏⠡⣗⢲⠐⠤⠁⡼⠯⠋⠑⢐⡙⢦⣜⡬⣒⡠ ⢸⣡⠤⠞⠉⠈⠀⠀⡆⠀⠶⠀⠀⠀⣀⠀⡀⡀⢀⢀⠈⠙⠺⢰⡵⡱ ⠋⠱⡌⣝⢃⣀⠀⠄⠥⠠⠬⠤⠀⠀⠀⠀⠐⠂⠀⠀⢀⠀⡀⠠⠀⣏ ⠹⣭⡞⣌⡲⠹⣤⠾⠿⠆⢝⣊⣹⡙⢢⠍⣉⡝⠩⢷⠢⠤⡤⢔⡸⢈

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢿⣻⣿⣦⠖⠋⠉⠳⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡞⠉⠉⠑⠒⠒⣿⡟⣯⣷⣿⣿⣿⣷⣶⣾⣿⣶⠀⠀⠀⠀ ⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⢻⣿⡽⣿⣿⣳⣟⡾⣿⣿⣽⣻⡇⠀⠀⠀ ⠀⠀⠀⠀⣷⠁⠀⠀⠀⠀⠀⠙⠛⠓⠋⠛⠾⠻⣿⣻⣽⡟⠀⠀⠀⠀ ⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡡⢼⠶⠂⠀⠀ ⠀⠀⡤⠼⡧⠤⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠴⠦⠀⠰⢼⠶⠄⠀⠀ ⠀⠀⠀⠤⢷⡒⠀⠀⠙⠁⠀⠀⠪⠯⠃⠀⠀⠀⠀⠀⣲⠷⠤⠀⠀⠀ ⠀⠀⠀⠀⣈⠷⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀ ⢠⡶⣶⡾⠷⣶⢾⡿⢶⣶⠊⠉⠙⡖⠉⠉⢹⡿⣶⢶⡶⠶⣶⡶⢶⡆ ⢸⡧⣿⣿⢄⡟⠀⠀⠀⢀⣵⠲⣶⢿⣲⢶⡉⠀⠀⠀⢧⣹⣿⡷⢨⡇ ⢸⡗⡞⠓⠋⠀⠀⠀⢠⢿⠀⠉⢧⣿⣉⣾⣷⠀⠀⠀⠀⠑⠛⠛⣏⡇ ⢸⣏⡇⡀⠀⠀⠀⠀⠸⣯⠠⡄⢀⡀⢤⠙⣿⠀⠀⠀⠀⠀⣀⡀⣧⡇ ⢸⡇⣿⣟⠻⣄⠀⠀⠀⠿⣄⣀⣘⣀⣀⣼⠇⠀⠀⠀⣠⠟⣿⡼⢛⡇ ⢸⡇⣿⡿⢰⣸⣀⣀⣀⣀⣈⣑⣛⣚⣉⣀⣀⣀⣀⣀⣇⠺⣿⡟⢸⡇ ⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢱⡄⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡅⠀⠀⢳⡀⠀⠀⠀⠀⢀⣠⡞⢫⣿⢟⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⠀⢳⠀⠀⠀⣰⠞⡡⢜⡿⢃⢼⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⡍⣙⣯⣙⣛⡓⠶⣤⣈⡇⠀⣧⠀⠀⠀⠘⡇⢠⡞⡱⢊⣱⡾⢃⣍⡾⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣍⢍⠛⡻⠷⡦⢙⢻⡄⢹⡆⠀⠀⢀⣷⠏⠴⣁⣷⠟⡡⢎⣞⣁⣀⣀⣀⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⡿⣿⢿⡿⣿⢿⣿⣾⣶⣿⣦⣿⣀⠀⣸⠏⡜⢶⣛⣥⠾⠛⠋⠉⠀⠀⢀⣠⠩⣹⠇ ⠀⠀⠀⠀⢀⣴⣿⣿⠽⡫⣍⠹⣌⢣⠜⣬⣧⣍⡙⡛⢯⣿⣽⣻⢿⣿⣾⣴⡛⠉⠀⣠⣤⡤⠶⠖⠛⠉⣁⡴⠋⠀ ⠀⠀⠀⣰⣿⢿⣾⠟⣹⡗⣌⠳⡌⢶⡿⢋⣼⢇⡚⣱⢊⠼⣷⣟⡿⣾⣽⣻⢿⣿⣿⣛⠛⡛⠶⠶⣾⣍⡁⠀⠀⠀ ⠀⠀⣰⣿⢯⢿⣇⡼⣏⠲⣌⠳⣘⠻⡷⣞⢋⠦⡱⢢⣭⣾⠟⢹⣿⢷⣯⣟⣿⣽⣻⢿⣷⣝⠻⠷⣶⢮⡝⢳⣦⡄ ⠀⢀⣿⣽⡏⢎⡜⡱⢌⠳⣌⠳⣌⠳⣰⣡⣮⣵⡿⣿⣻⣧⣴⣿⢯⣟⡾⣽⢾⣿⢯⣿⣽⣻⣷⣵⣤⠶⠞⠋⠁⠀ ⠀⣸⣿⡾⡘⢆⢎⡱⢊⡵⣈⢳⣬⣷⣟⣯⣿⣳⣟⡷⣯⣟⣯⣟⣯⢿⡽⣯⣟⡿⢋⣿⣾⢯⣟⣿⡄⠀⠀⠀⠀⠀ ⠀⣿⣷⠣⣝⣾⢾⡥⢋⡴⣽⣿⣻⣾⠋⣰⣿⣻⢾⡽⣷⣻⢾⡽⣾⢯⣟⣷⣿⣀⣾⡿⣽⣯⢿⣞⣿⡆⠀⠀⠀⠀ ⢠⣿⣯⢱⡿⢷⡿⣑⢣⣾⣟⣾⣳⣿⣾⢿⣳⣯⢿⣽⣳⣟⣯⡿⣽⣟⣾⣳⣟⣿⡿⣽⣷⣻⣯⢿⣽⣿⠀⠀⠀⠀ ⢸⣯⡗⢎⠿⢫⠱⣌⣻⣟⣾⣳⣟⡾⣽⢯⣷⣻⣟⡾⣽⣾⠏⣰⣿⣟⣾⣳⣯⣿⢿⣽⡾⠟⣿⣟⡾⣿⡇⠀⠀⠀ ⢸⡿⣿⣈⠞⣡⠳⣰⣿⣻⣞⡷⣯⢿⣽⣻⠾⣷⣯⢿⡽⣿⣶⢿⣳⣟⣾⣳⣿⢯⣿⣿⣁⣼⣿⣽⣻⢿⠇⠀⠀⠀ ⢸⡿⣽⡷⣎⣥⣳⡿⢻⣷⢯⡿⣽⣻⣾⠋⣰⣿⢯⡿⣽⣳⣯⢿⡽⣞⣷⣻⣯⢿⣳⡿⣟⣯⣷⢯⣿⡿⠀⠀⠀⠀ ⠀⣿⣯⣟⡿⣿⣋⣠⣿⣯⢿⡽⣷⢯⡿⣿⢿⡽⣯⢿⣽⣳⣯⣿⠟⢻⣯⣷⣟⡿⣽⣻⣽⣻⢾⡿⣽⠃⠀⠀⠀⠀ ⠀⢿⣳⣯⢿⡽⣟⡿⣽⣞⣯⢿⡽⣯⢿⡽⣯⢿⣽⣻⣞⡷⣿⣇⣠⣿⣿⣳⣯⢿⣻⡽⣷⣻⣯⣿⠃⠀⠀⠀⠀⠀ ⠀⠸⣿⣞⣯⢿⣽⣻⢷⣯⣟⣯⡿⣽⢯⣿⠟⢩⣿⢷⣯⢿⣽⣻⣿⣟⡾⣷⣻⢿⣽⣻⣽⢷⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣽⡾⣯⢷⣻⣿⠋⣸⣿⡽⣯⢿⣯⣤⣿⢯⣟⡾⣿⣾⣟⡷⣯⣿⡽⣯⣿⣳⣿⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢿⣽⢯⣟⣯⣷⣴⣿⢯⡿⣽⢯⡿⣽⢯⣿⣽⣿⡿⢾⣯⣿⣽⣞⣿⣳⣯⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣯⣟⣾⣽⣻⣞⣯⢿⡽⣯⣿⢿⣟⡿⣾⡏⢀⣾⣟⣷⣻⣾⠽⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⣞⣷⣻⡾⣽⣿⣻⢿⣽⣻⡾⣿⡽⣿⣿⠿⠽⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠿⠿⠾⠽⠿⠷⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⢀⢠⣄⡤⣴⣚⢿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣷⠀⣿⣋⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⣶⣤⣄⣀⣀⢹⡋⠛⠛⠛⠋⡖⣩⢎⡵⣩⠞⡥⢿⡇⠀⠀⠀⠐⣷⠀⠀⠀⠀⠀ ⣮⣷⡾⣿⢷⣫⣟⣾⣽⠿⠿⢿⠛⣩⢡⢿⣞⢛⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⣿⢿⣿⣿⣿⣷⣿⣷⣮⣖⣧⢫⢕⣻⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠄ ⣿⣛⠟⠉⠋⠱⣯⣾⣿⡄⠀⠈⣷⣩⠛⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣽⢻⣿⣿⣿⣿⣿⣿⣿⣿⣶⢮⣷⠀⠀⠀⠀⢹⠄⠀⠀⢀⢂ ⠀⢀⠌⢂⠒⣘⣉⣡⣤⣤⣶⣦⣨⣿⣾⣾⣿⣿⡿⠛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢲⡂⣝⢫⢆⡹⡐⢀⠀⢸⡍⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣖⡻⢿⣿⣿⣿⣿⣿⣿⣫⢿⡀⠀⠀⠀⠸⡆⠀⡀⢠⠂ ⣬⡳⣾⣿⢿⣟⣿⡿⣯⣿⣿⢿⣿⣿⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⢣⡝⡰⢃⢞⡰⣉⠆⡐⠈⣷⢻⠀⠀⡉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣯⡝⣿⣿⣿⣿⣿⣷⣻⡆⠠⠀⠀⠐⣧⠐⡌⢆⠡ ⡿⣽⣮⠹⣯⣿⡿⣽⣷⣻⣽⣿⢯⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣟⡣⢜⣵⣯⣶⣶⣧⣶⡤⢀⢻⡜⡇⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣶⣽⡿⣿⣿⣿⠿⣧⣤⡄⢄⢺⣿⡧⢘⠄⡡ ⣿⣳⡟⣿⣬⠻⣿⣟⢶⣿⣻⣾⢏⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⣿⡿⣏⢳⡱⢎⡼⢩⡛⠿⢿⣧⣟⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⢻⣿⣿⣴⡍⠱⣚⣿⡟⢠⠎⠄ ⠷⣯⢟⡧⣟⣿⣜⢯⢾⣍⣽⣇⣼⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⡗⢮⣣⡝⣮⣔⠣⡝⣝⠲⣌⢻⣆⠀⠂⠀⢀⣠⡴⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣞⣯⢻⣿⣯⣷⠀⢄⢻⡜⢠⠊⡐ ⣟⠾⣯⢟⣽⣻⡾⣏⣾⡿⣫⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢳⡼⡹⢧⣳⣞⡹⢿⣷⡩⢞⡽⣌⢧⣻⣦⡱⣶⠋⠁⠀⠀⠀⠀⡀⢀⢠⡿⣿⣿⣿⣿⣞⣯⣿⣿⣿⡶⢊⠜⣇⠢⡑⠀ ⣮⣟⡾⣯⣿⣳⢿⣼⢟⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣹⢳⡞⣵⣋⡜⣫⢟⡣⢿⣿⣣⢿⣼⣷⢿⡻⢷⣮⣤⣀⡀⠂⠤⢁⠄⣃⠣⣞⣿⣿⣿⣿⣿⣷⣿⣿⣿⣧⡀⠘⠦⡁⢀⣁ ⣷⣾⣿⣿⣿⣿⡿⢣⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⡧⣯⢳⡽⣿⡴⢻⣶⣯⣞⣧⣿⣿⢿⣙⣎⠶⣹⢣⡻⣜⡟⣿⣶⣄⠊⡜⡰⢋⡶⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢲⣮⣗⣻⣹⣌ ⣿⣿⣿⣿⣿⠏⢠⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⣯⣳⡽⣹⢿⣧⡦⣍⠭⣹⣻⣯⠷⣭⢎⡳⢥⢳⡱⣍⠾⣱⡞⣿⣧⣶⣷⣿⣾⢷⣿⣭⣿⣿⣿⣿⢻⣿⣿⡏⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⡟⣰⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣳⡽⣞⣯⡟⣼⢳⣎⡳⢥⢻⣯⣟⡼⣎⡳⣭⢲⡱⢎⡳⢥⡛⢷⣿⣯⢗⡳⢎⡳⣬⢣⢛⣿⢿⣿⣽⣿⣿⣗⢯⣿⣿⣿⣿ ⣿⡿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣽⣻⢾⡽⣭⢷⡺⣝⢮⣹⣿⣞⡷⣽⡳⢧⡳⣝⢮⣱⢣⡝⣮⣿⣛⢮⣝⡣⣝⢦⣋⠶⣈⠯⢿⣧⣿⣿⣿⣳⣿⣿⣿⣿ ⣵⣾⣿⣿⢳⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡡⢘⢿⣿⡽⣯⣟⣿⢮⡷⣯⣞⣦⣿⣿⣿⣷⣟⣯⢿⣼⢳⣎⣳⣾⣟⣧⣛⡞⣶⢹⡜⣦⢋⠶⣩⠖⣩⣿⢿⣿⣿⣿⠸⣿⣿⣿ ⢻⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡐⠰⡈⠬⡹⢿⣿⣽⣾⣿⣽⣿⣿⣿⡿⣿⣟⣿⣿⢿⡿⢿⠿⣟⣻⣿⣿⣿⣧⠿⣜⡧⡞⣥⢫⡳⣱⣎⣵⣿⣿⣿⣧⣿⠆⣿⣿⣿ ⠀⢹⣿⡷⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠠⢁⠢⡑⢌⠲⣉⢏⡻⡝⢯⠯⡝⢧⠻⡔⣿⣿⢽⡲⣝⣎⠳⡽⣧⣝⠮⡹⣿⣿⣽⢳⡝⣎⢧⡳⣽⣿⣿⣿⣿⣿⣿⣾⣇⢻⣿⣿ ⠀⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢃⠎⡰⠙⡌⠷⡝⣮⡳⣟⢯⠿⣝⢯⡿⡝⣿⣿⣾⢷⡿⣿⣿⣷⣿⣿⣷⣷⣝⣿⣿⣿⣿⣟⣯⢷⣿⣿⣿⣿⣿⣿⣿⣟⣿⣼⣿⡿ ⡜⠰⡌⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠁⠃⢡⠛⢆⠳⡝⠎⡎⢳⡉⢇⡷⢹⡿⣿⣿⣿⣿⣿⣯⣿⣿⣾⣻⣿⣿⣼⢿⣿⣿⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡀⠰⠘⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠘⠀⠇⠘⢃⠹⡈⠞⡎⠻⢿⣿⢿⣿⣻⣟⣿⣻⣿⣟⣿⣻⢿⣟⡹⢿⡿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡖⡀⠀⠸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⢁⠈⡀⣁⠢⢀⠅⢊⠰⣉⠞⣻⣿⣷⣟⣯⣷⣿⣽⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿ ⣿⡜⡤⠁⠙⠻⢿⣿⣿⣿⡀⠀⠀⠀⠻⣿⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢈⠠⠐⡀⠄⡰⢈⠰⠈⡔⢢⠙⡴⢫⣟⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿ ⣿⣿⡤⣁⠤⢣⢉⢿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠂⠁⠐⢀⠐⠀⡀⠀⡀⠀⠠⠀⠀⢂⠡⠐⡁⠐⣀⣂⢁⠒⠤⣉⢒⡱⣚⢼⡹⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⡿⠛⠛ ⣿⣿⣿⣄⢏⠦⣉⠌⣿⣿⣿⡆⢀⠈⠀⠀⠀⠀⡀⠄⠠⠀⠁⢂⠀⣐⣤⣤⣀⡀⠂⠠⠀⠀⠄⠠⠀⠅⠂⠌⡐⢤⣿⣿⣿⣿⣾⠐⠄⡢⠔⡭⢎⡳⣝⢾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢛⣉⣡⣤⣤⣶ ⣿⣿⣿⣿⣌⠶⡡⢞⡨⣿⣿⣿⣆⢈⠀⠄⠠⠀⠄⢂⠐⡠⢁⠢⠘⣿⣿⣝⡿⣿⣦⠀⡑⣈⠰⢀⡡⢘⡐⢈⠐⣾⣿⣿⣿⣿⣿⡏⠄⡱⢈⠖⣩⠞⣬⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢫⣸⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣎⢵⣪⣷⣿⣿⣿⣟⣳⣊⠌⠠⢁⠆⠢⢈⠔⡡⢆⠡⠙⠿⣾⣷⡿⢿⣡⣐⣀⠱⠈⡔⢡⠘⠤⢈⠹⣿⣿⣿⣿⡿⠡⣆⠱⣊⠜⣤⢋⡖⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢁⢊⡱⣈⢆⡱⣈⢒⡡⢂⠤⢀⣶⣿⣿⣿⣿⣿⣶⣶⣤⣉⡰⡡⢈⡉⡛⢛⢩⠰⡱⢌⡳⢨⣙⢦⢫⡜⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣟⡽ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠱⡰⢌⠲⢌⠲⣄⠃⢦⢁⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣆⠱⣘⢣⢣⡛⡴⢣⢣⢣⡜⣮⢳⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡼⣿⢾⣹ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⢠⣿⠃⠳⢌⡓⢎⡱⢢⡙⢂⢣⠒⡤⢉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣧⣝⡼⣡⢏⠲⣹⣎⢷⡽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⢯⣷⡟ ⣿⣽⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢸⣿⠀⠐⠀⠘⡌⠴⠡⣌⠃⣎⠱⣌⠣⡝⢎⡲⢤⣩⢩⢍⣋⠟⡿⢿⣿⣿⣿⣿⣿⣿⣾⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣷⠟⠀ ⣿⣾⣻⣿⣽⣻⣿⡿⢯⣟⡿⠃⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠠⠁⢆⠳⢄⡳⣌⢣⡝⢪⡱⢆⣣⢎⡚⡜⢪⠳⣍⠶⣙⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀ ⣿⣽⡿⣟⣾⣿⣿⡿⣿⣿⠀⠀⢀⠀⡄⢀⣧⠘⣿⣆⠀⠀⠀⠀⠀⢁⠠⠌⠐⠠⡈⣁⠊⡕⣩⠹⣌⠯⣝⢻⣏⢿⡞⡿⢶⡻⣽⣶⣿⣿⢿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤ ⣿⣻⡿⣿⣻⣿⣿⡿⣿⣿⣿⣮⣇⣞⣴⣳⣿⣆⠸⣿⣦⡀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠄⠃⡐⠢⡙⢢⠛⡬⠳⣌⠳⣭⠹⣎⣵⣿⣿⠿⣩⢏⡳⡹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⡿⣽⣽⣿⣿⣳⣿⣿⢿⣿⣿⣿⣿⣿⣿⠏⠹⣆⠘⠻⣿⣶⣶⣶⣶⣶⡆⢨⢀⡈⠀⠁⠌⡡⢌⠡⣉⠖⡩⢌⠳⣄⣻⣾⣿⠟⣡⢚⡱⢊⡵⢩⠶⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣽⣟⣾⡿⢿⣿⣽⣿⣿⣿⣿⠿⠿⠿⠏⠴⣄⡌⠳⢦⣤⣉⣉⣉⡉⠉⢀⡴⢿⣿⣷⣮⣄⣡⣀⣒⣀⣆⣥⣾⣾⣿⠿⢋⣡⡼⠃⡄⢃⠎⡐⢃⠞⡌⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣧⢊⠔⣩⡿⠉⠀⠀⣼⠃⢲⣌⡙⠻⠿⠿⡿⢿⠿⠿⠟⠛⣉⣡⣶⡿⢿⣿⣵⡈⠄⡘⠠⠁⠈⠀⠀⠳⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡙⣾⠁⠀⠰⣰⠇⠀⠀⢻⣝⠻⡶⢶⣤⣤⣴⣤⠾⡿⢻⡍⢧⣛⢧⣛⢿⣾⡐⡀⠀⠀⠀⠀⠈⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡜⣿⣠⣤⣴⣯⡀⠀⠀⣼⢯⠱⣋⠖⢢⠒⡴⢈⠧⡑⢇⠞⡥⣋⢞⡭⣞⣽⣿⣴⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⢧⣹⢳⣏⠶⣭⢻⣦⣾⣟⣢⢳⡾⠾⠛⠋⠉⠁⠚⠳⠎⣜⠰⣍⢮⢳⡞⣼⣿⣿⣷⣴⣤⣀⣀⣀⠀⣚⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⠶⠶⣦⣄⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀⣤⡶⠶⠶⣶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢁⣠⣴⠾⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⣸⡟⠁⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣼⡿⠟⠀⠈⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⢛⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⠿⠀⠀⢀⣼⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠟⠛⣿⡀⠀⠀⠀ ⠀⠀⠀⣴⣿⣿⠁⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀ ⠀⠀⠸⣿⣿⣿⡄⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⢸⣿⣿⣿⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⡿⠋⠀⠸⣿⡀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡾⠟⠛⠉⠛⠛⠿⣶⣤⣤⣄⡀⢸⣿⣿⡇⠀⠀⠀⠀⠀⣠⣴⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠿⠿⠃⠀⠀⠀⣼⠏⠉⠙⣷⠈⠻⠿⠃⢀⣠⣴⣶⡿⣿⡷⠿⣿⣦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣀⣀⠀⠀⢀⣴⠿⠀⠀⢀⣿⣶⣶⣿⠟⠛⠉⣹⡇⢹⠏⠀⠀⢸⣿⣷⠿⣷⡄ ⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⠿⠿⣿⣿⣿⠿⣿⣶⣤⣤⣾⣧⡾⠋⠀⠀⠀⢰⡿⢀⣿⠇⠀⠀⢸⡿⣿⠀⣿⡇ ⠀⠀⠀⠀⣠⡶⢟⡍⢁⣴⣿⣿⣿⡿⣿⣟⠻⣷⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢠⣿⡿⠛⠁⠀⠀⢀⣾⢃⣿⡿⠋⠀ ⠀⠀⢀⣼⣿⣷⢟⣵⠟⠹⣿⣿⣿⣄⣿⡿⣷⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⢠⣿⠋⠀⢀⣀⣤⡶⠿⢃⣾⠏⠀⠀⠀ ⠀⠀⣾⡿⢋⣴⠟⠁⣀⡄⠉⠻⠋⠉⠈⠛⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢀⣿⢃⣴⣾⠛⠉⠀⠀⢀⣼⡿⠿⢿⣶⡀ ⠀⠰⣿⣴⠟⠁⠀⠘⠿⡿⢀⣀⡀⠀⠀⣰⣿⣿⣿⡟⠀⠀⠀⠀⠀⢀⣾⢃⣾⣿⡏⠀⠀⠀⠀⠾⠋⠀⠀⠀⢹⡇ ⠀⣠⣿⠁⠾⣿⠀⠀⠀⠀⣿⣿⢿⣦⣴⣿⣿⣿⣿⡅⠀⠀⠀⠀⣠⣿⣿⠟⠁⢿⣇⡀⠀⠀⠀⠀⢀⣀⣠⣴⡾⠃ ⢸⡟⠛⣷⣤⣉⠀⠀⢀⣀⣸⣿⡿⠿⠿⠿⢿⢿⣿⣿⣶⣦⣤⣾⠟⠉⠀⠀⠀⠈⠙⠻⠿⠿⠿⠛⠛⠛⠉⠁⠀⠀ ⠘⠿⣶⣾⠿⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠘⠛⠛⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣤⣴⠶⠶⣤⡤⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⡀⣼⠿⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⢻⠶⠴⡟⡛⠟⢷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠙⠉⠛⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠷⠀⣠⣾⡶⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⡄⢸⣟⡈⠁⣹⣷⣤⣀⠀ ⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡐⣿⠁⠀⢸⡇⠀⠀⠉⠙⠉⣻⣆ ⠀⠀⠀⠀⠀⠀⠈⠙⢻⣶⣄⣀⣤⡶⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⡀⣴⢿⠉⠉⠉⠉⠛⢿⣆⠀⠈⣿⣤⣈⣡⣤⡶⠟⠀ ⠀⠀⠀⠀⠀⣀⣀⣀⠠⠍⢹⡿⠅⠀⠀⠀⠀⠀⢿⠛⠀⠀⢠⣿⣷⡄⠀⠛⢛⣫⣿⡿⠇⠀⠀⠀⠀⠀⠀⣿⠅⠀⠀⠀⠈⠁⠁⠀⠀⠀ ⠀⠀⠀⠀⣸⡟⠏⠻⣷⡄⢸⡷⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⢠⡾⣿⠻⠷⠀⠀⣻⣧⠈⠻⣶⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣧⡀⠀⠀⠀⢀⣿⠉⠀⠀⠈⢛⣷⣦⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠛⠛⠛⠛⠛⠃⠀⠀⠀⢀⣼⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠂⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣤⠀⠀⠀⢀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡶⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⡠⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣦⣀⣀⢀⡀⣀⣀⣴⡿⠟⠛⢷⣦⣄⣀⣤⣠⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠘⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣍⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣻⣿⠶⣿⣿⣿⣿⣿⠿⡛⢏⡍⠳⣌⠲⡐⠦⡑⢎⡙⢻⢿⣿⣶⣻⣷⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⡉⠛⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⢿⣿⣿⡟⣍⠳⣈⢇⡙⢢⡜⡱⢄⢣⡙⠴⣉⠦⡙⢦⡉⣿⣿⣿⣹⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⣰⠎⠀⠂⢁⠠⠐⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⣿⣿⣧⢂⠳⡌⢦⡙⢆⡜⡰⣉⠖⠬⡑⢆⢣⡙⢤⣽⣿⢏⣿⣼⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠀⠀⠀⠈⡀⠄⠁⠠⠀⢢⡿⠛⠀⠀⠀⠀⠀⠀⣠⣴⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⢸⣿⣿⡌⡱⡘⠴⣘⠢⡜⣡⠒⣌⠣⢍⠎⣆⣙⣾⣿⢋⣾⣿⣿⠏ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣦⣄⡀⠐⠀⡈⠠⠁⠈⠁⠀⠀⠀⠀⣀⣤⣶⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⢸⣿⣿⡖⣡⠙⢦⢡⢓⡸⢄⢫⠰⣉⠦⣉⣶⣿⡟⣥⣾⡿⣿⠟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣧⣄⣤⣤⣤⣶⣶⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠦⣙⠢⣑⠪⡔⢪⢅⠳⣈⢶⣽⡿⢣⣾⣿⢟⣾⠋⠀⠀ ⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣻⡟⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⣸⣿⣿⢃⠳⡄⢳⢨⠱⡌⢣⢌⢳⣼⣿⢯⣱⣿⡟⣳⡟⠁⠀⠀⠀ ⠀⠀⠀⢠⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⣿⠃⠀⠀⠀⠀⠀⠙⠹⠙⠫⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣶⣦⣶⣿⣿⡟⡌⢣⠜⡡⢎⡱⢌⢣⣮⣿⠿⣱⣾⣿⣫⡾⠋⠀⠀⠀⠀⠀ ⠀⢀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡏⠀⠂⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⢋⡝⡛⠿⠿⠿⡟⢫⠔⡩⢆⡹⣐⢣⢲⣼⣿⠿⣙⣾⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡟⣼⡷⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠿⣿⣧⠀⠀⠀⠀⣀⣠⣤⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⡿⢋⡔⢣⠜⣌⢣⡙⠦⡙⠦⣙⠰⣃⠴⣨⣶⣿⡟⣽⣾⡿⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⠻⣿⣿⣶⣿⣿⡿⠿⠛⠉⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⢟⠣⡜⡡⢎⡑⠎⡔⢢⡑⢎⡡⢓⠬⡑⢦⣷⣿⠟⣧⣽⣿⣏⠀⢠⣟⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡟⠀⠀⠀⠀⠀⠀⣠⣴⡶⢶⡤⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⡿⢛⠬⡌⢳⠰⡑⢎⡜⡱⡘⢥⠚⡤⠣⢍⣲⣽⣿⢟⣱⣾⣿⣿⠿⣿⣿⣫⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⠀⠀⢠⣿⠋⠁⠈⠁⠀⠀⠹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⢯⡽⣫⠾⡽⢮⢧⡻⣎⢷⣣⢻⢮⡻⣵⣻⣾⣿⢿⣯⣾⣿⣿⣿⣿⡿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠈⣿⣆⡀⠀⠀⢀⣠⣾⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⣿⣿⣿⡿⢿⡻⣧⢫⡷⡽⣭⢟⡵⢯⣎⣳⢞⡷⢯⡟⣮⣿⣿⣿⢟⣯⣿⣿⣿⣿⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ 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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⡙⢆⡍⠲⢌⠣⡜⡰⡉⢖⠱⣂⠭⡘⣅⠣⠎⡜⡡⢎⡌⡓⡌⢎⡱⡘⢤⡙⠜⡢⢅⠫⠜⣢⠑⡎⡔⣢⣵⣶⣿⡿⠟⡭⣮⣽⣾⢿⣯⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣻⣿⣷⣌⠜⡱⢊⠵⣨⠑⡍⢎⠲⡡⢎⡱⢢⡙⡜⡰⡑⢎⠴⢱⡘⠦⣡⠙⡆⡜⣡⠓⣌⢣⡙⣤⣫⣴⣿⣿⠿⣛⣥⣽⣾⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣧⣛⣿⣿⣯⣖⡩⢒⡡⢍⡜⠬⣑⠱⣊⠔⡣⢜⡰⠱⣉⠎⡜⡡⢜⠢⣅⠳⣘⢰⣡⣯⣴⣷⣿⣿⠿⣟⣹⣦⣿⣿⠿⠋⠁⢸⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⣬⢛⣿⣿⣿⣷⣮⣶⣘⣦⢡⠓⡬⡘⢥⢢⡑⢣⠜⡘⠴⣑⣮⣵⣦⣷⣾⣿⣿⡿⢟⡻⣍⣶⣷⣿⣿⣿⣏⠀⠀⠀⠀⣼⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣦⣍⣛⠻⠿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⠿⢿⠛⣏⣹⣔⣮⣷⣿⣿⣿⣿⣧⣳⣞⣿⣷⣦⣶⡾⣫⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣷⣭⣖⣦⣩⡍⢯⣙⣛⡛⣛⠻⡹⣍⣫⣕⣲⣬⣽⣶⣿⣿⣿⣿⣿⣿⠿⠛⠛⠿⣯⣽⣽⣭⣽⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣉⣭⡿⢻⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠿⣿⣿⣿⡿⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⣀⣀⣀⠀⠀⠀⠀ ⠀⠀⠀⣴⠟⠛⠓⠶⣤⠴⠶⢶⡿⠁⣶⣽⣯⠉⠁⠹⡆⠀⠀⠀ ⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⡁⢼⣿⡏⠙⠻⣾⡛⢿⣆⠀⠀ ⠀⠀⠀⣻⠋⠀⠀⠀⠀⠀⠀⠈⠓⠶⠞⠷⣤⣼⣯⠟⣸⡟⠀⠀ ⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠞⢙⣆⣀⠀ ⢠⡶⢾⡶⠤⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠚⢩⡏⠉⠁ ⠀⢀⣼⣷⠒⠀⠈⠋⠀⠀⠀⢶⡲⠀⠀⠀⠛⠁⠀⡈⣹⠛⠛⠀ ⠀⠀⢠⡼⠷⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠛⠷⠆⠀ ⠀⠀⠈⠀⠀⠀⠉⠙⠓⠒⠶⠶⠶⠶⠒⠚⠛⠉⠁⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⢀⣀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠟⠛⠛⠛⠿⣿⣶⣾⡿⠛⠛⠛⠛⠛⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣶⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠟⠉⠁⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠙⠛⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣰⣾⡿⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠛⠿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠛⠛⠛⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⠛⠻⣷⡄⠀⠀⠀⠀⠀⠙⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣴⣶⠿⠿⣿⠏⢿⣆⣀⣀⣀⠀⠀⠀⢀⣿⠿⣿⡿⢷⣦⣼⣿⡆⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⢿⣦⣾⡟⢀⣿⡿⠿⠿⠝⣷⠀⠀⠸⣿⡀⢻⣧⣴⡿⠏⣸⡇⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣾⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⣻⡿⣷⣤⣉⣹⣿⠿⠙⠷⠶⠶⠾⠋⠀⠀⠀⠹⢷⣮⣿⣷⣤⣶⣿⣷⣦⡀⠀⢀⣀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⡟⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣦⡄⠀⠰⣟⠞⣁⣴⠟⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣷⣍⠻⡾⣿⠀⠘⢿⣷⣿⣧⣤⣤⣄⣀⠀⠀⠀ ⢸⣿⠀⠀⠀⠀⠀⠀⢀⣿⠋⢀⣤⣿⣧⠈⢿⡆⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⣠⡀⠀⠀⠉⠉⠛⠛⠛⠻⣿⣦⡀ ⢸⣿⠀⠀⠀⠀⠀⠀⢸⣯⣰⣿⣁⣠⣿⣠⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣤⡀⠀⠀⠀⠀⠀⠀⠈⢿⣧ ⠘⣿⣧⡀⠀⠀⠀⠀⠀⠻⣿⣏⠙⠛⢛⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣾⡿⢿⣶⣶⣶⡿⢿⣧⣀⠀⠀⣀⡀⠀⠀⠀⠀⠈⠻⢿⣷⣤⣀⣀⣀⣀⣤⣿⡏ ⠀⠈⣻⣿⠆⠀⠀⠀⠀⢀⡿⣿⢷⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠿⠶⠿⠿⠋⠀⠀⠀⠀⠀⠀⠈⢙⣻⠿⠿⢿⣧⠀⠀⠀⠀⠀⠀⠀⢹⣿⠟⠿⠿⠿⠛⠉⠀ ⠀⣸⣿⠃⠀⠀⠀⠀⠀⣿⢱⠏⣸⡇⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣆⠈⠻⣷⣶⣶⡄⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⡇⠀⠀⠀⠀⠀⠀⠙⢿⡾⠛⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⣾⣿⠿⠿⣷⣦⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣿⡀⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⣸⣿⡁⠀⠀⠈⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⣷⣤⣰⣿⠁⠀⠸⣿⡀⠀⠀⠀⠀⠀⢾⣿⠟⠋⢰⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣾⠟⠛⣿⡆⠀⠀⠀⠀⠀⠀⢀⣼⡿⠟⠻⣷⣤⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢉⣿⣿⠏⠀⣀⣤⣿⣧⣄⣀⠀⠀⠀⠘⣿⡇⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠻⠶⠶⠟⣀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠘⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⣾⠟⠁⠀⣾⡟⠉⠉⠉⢙⣿⣷⣶⣤⣴⣿⣧⣄⠈⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣴⡿⠀⠀⣀⣴⣾⠟⠁⠀⠀⠀⠀⠀⣠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠃⠀⠀⠀⢿⣧⡀⠀⠀⣿⡟⠉⠉⠙⠋⠉⠉⢻⣷⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣁⣤⣶⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⣄⠀⠀⢀⣼⣿⠿⣷⣾⡿⠃⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠻⣷⣶⣤⣤⣤⣶⣶⣾⡿⠿⠛⠋⠁⠀⠀⠀⣶⣦⡄⠀⠀⠀⣀⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠻⠿⠿⠿⠛⠁⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⢸⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣶⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢿⣷⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⡿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

. _____________       | |                  /  / |       | |              /  /     |       | |          ︵__︵   |           • • •       | |        (灬'•㉨•  ).| `-- ! ! /  /  i!         i! )| --` | \      ﹂----------       \ ︵__︵ |   \ _______________ (              ) |     |                            (i        0  ) . ---• ----------------------    U---U

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(ෆ̥● ꄃ ●ෆ̥) '` (ू ͒•‧̫•ू⑅ ͒) (͒˶˙•●̫•˙˵)͒ ٩̋(ˊ ᵒ̵̶̷̤᷄ꇴᵒ̴̵̶̷̤᷅ ˋ)۶ ♡(ؔᵒ̶̷ᵕؔᵒ̷̶) ˘̴͈́ᵜ˘̴͈̀ ต( ິᵒ̴̶̷̤ ﻌ ᵒ̴̶̷̤ )ິ ૮꒰˶ᵒ̴̶̷᷄౪ᵒ̴̶̷᷅˵꒱ა ⁌꒰๑⃙⃘ˆˑˆ๑⃙⃘꒱⁍ ⋆͛*͛ ͙͛(๑•﹏•) ₍˄·͈༝·͈˄₎◞ ̑̑ෆ⃛ ꒰•·̫•꒱ྉ ˚‧(๑σ̴̶̷̥́ ₃σ̴̶̷̀ू)·˚ ꒰ •ॢ •ॢ⑅꒱ ꒰⁎ॣ●̷॔ ̴̧̇●̷꒱५₃ ( ᵒ̴̶̷̤ꈊᵒ̴̶̷̤ )✧ ·◌̊ˈ*(⁰̶̶̷ ˙̮ ⁰̴̷̷๑ॢ) Ϛ⃘๑ɞ̴̶̷ .̫ɞ̴̶̷ू꒜ ৎ •ु·̫•ूॽ♡ ꒰* ुര  ̫ രू꒱ ต( ິᵒ̴̶̷̤́ᆺ⃘ᵒ̴̶̷̤̀ )ິต દ⑅•ﻌ•૩ (  ु́•̶̤ ‧̫ ⁃ ૂ̀ )

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⡒⣦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣎⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢋⡵⠛⠁⢸⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠈⠳⣄⠀⠈⠛⢦⣀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⡤⠞⣕⡶⠋⠀⠀⠀⠘⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠈⠙⢦⣀⠀⠈⠓⠋⠁⠀⠀⠀⠀⠀⠉⠛⠲⠛⠁⣴⣋⣠⠀⠀⠀⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢠⢾⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⠀⠀⠀⠀⠀⡧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⢸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡇⠀⠀⣸⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢀⣤⣾⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⡄⢰⣾⣿⣷⣄⠀⠀⠀⢠⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⠤⣾⠤⡀⢸⣿⣿⣿⡿⠃⠀⠀⠀⣿⣿⠠⠈⠃⠚⣿⣿⣿⣿⠇⠀⢀⣨⡧⠤⢴⠖ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣴⣿⠤⠄⠀⠉⠉⠉⠁⠀⠀⠀. ..⠁⠀⠈⠀. ⠉⠙⠋⠀⠀⠨⢤⣷⣤⣤⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠉⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⠀⠀⠉⢧⠀⠀⠀⠀⠀⣰⠂⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡤⠴⠚⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠠⠔⣞⠋⠁⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⠚⠉⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠐⠦⢤⣬⣷⣄⠀⠀⠀⠀⠸⣆⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⠏⠀⠀⢀⣠⡶⠖⠒⠒⠚⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⢦⣀⠀⠀⠀⠘⢧⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⡏⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⠶⠦⠤⠤⠤⠴⠟⠁⠀⠈⠛⠲⠶⠤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢧⠀⠀⠀⠀⠈⠉⠛⠒⠒⠚⠉⠉⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠳⠦⢤⣀⣀⣀⡀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣉⡉⠛⠋⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢸⠁⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⡞⠇⡼⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢠⠇⢰⠁⠸⠀⡈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⢸⠀⠘⠀⡆⡜⢀⡈⢿⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣀⡤⠤⠧⠤⠤⢼⣐⣁⡎⡠⠜⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠛⠿⣿⣿⣶⣤⣀⠀⠀⣿⡟⠙⠳⢄⠸⡄⠀⠀⠀⠀⠀⠀ ⣶⠶⢶⣶⣦⡤⠤⠤⠤⠄⢤⣄⣀⣴⡏⠉⡟⠒⠤⠬⣻⣇⠀⠉⢛⠶⠋⠉⠉⠐⠶⣿⢿⡀⠀⠀⠀⠀⠀ ⣿⡀⠀⠉⠉⠛⠻⠒⠦⣄⡀⡰⣿⣿⣧⢠⠁⠀⠀⠀⠀⠉⠒⢴⠃⠀⠀⠀⣀⣀⡀⠘⡆⠙⢆⠀⠀⠀⠀ ⠘⣷⠀⢉⣉⣀⠒⠤⠄⠀⡝⠁⣿⡟⠻⡏⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⣾⣿⣿⣿⣷⣸⠀⣬⣆⠀⠀⠀ ⠀⠘⣷⡀⠠⠤⠬⢉⡀⣾⣄⡀⢹⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠸⣿⣿⣿⣿⣿⠋⣴⣯⡽⡄⠀⠀ ⠀⠀⠘⢷⣄⠒⠒⠒⢰⠋⠉⢉⡽⠊⠉⠉⠉⠒⢄⠀⠀⠀⠀⠀⠣⡀⠀⠉⠛⢻⡿⢷⣞⣛⣉⡤⡇⠀⡀ ⠀⠀⠀⠈⠻⣦⡉⠤⢽⠀⢠⠋⠀⠀⠀⣠⣴⣶⣤⣑⡄⠀⠀⢀⡀⠈⠉⠀⠉⠁⠀⠀⠀⣀⠤⢲⠋⣉⣠ ⠀⠀⠀⠀⠀⠈⠙⢦⣼⠀⢸⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⠀⠈⢛⣤⠤⠤⣤⠤⣤⠤⢒⡩⠤⠐⡞⣉⣁⣠ ⠀⠀⠀⠀⠀⠀⠀⠈⢻⢠⣿⡄⠀⠀⠘⢿⣿⣿⣿⣿⠃⠀⣠⠞⠁⢀⡠⠔⠚⡇⠈⠁⠒⢈⡝⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠘⠢⣄⡀⠀⣉⡩⠗⠁⠐⢏⡀⣀⠔⠉⠀⠀⢸⠀⠀⠀⡠⣾⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣠⣤⣤⣼⢟⡟⠀⢀⡠⢴⡆⠙⠧⡀⠀⠀⠀⡌⠀⣠⠞⠁⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣏⡤⣊⠤⢒⡩⢒⡡⠚⠁⠀⠈⠑⣤⡰⠇⠊⠁⠀⠀⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢋⡷⣶⣥⠴⠏⠀⠤⠤⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠔⠁⣠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣽⣦⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡇⢻⣯⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⢻⠀⠀⠀⠀⠀⠀⢀⠆⠀⠈⡆⠀⠀⠀⠀⠀⢀⠃⣸⣿⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣟⠿⠷⡈⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⣿⣿⡇⠀ ⠀⠀⠀⠀⠀⣠⡴⠚⢿⣿⣿⡌⣿⣿⣻⣿⡇⢣⠀⠀⠀⠀⠀⠈⠀⠀⠀⠃⠀⠀⠀⠀⠀⡖⠀⣿⣿⠁⠀ ⠀⠀⢀⣴⣾⣿⣿⡆⣠⠿⠛⠒⠛⠛⢿⣿⡧⢼⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠗⠒⠻⡁⠀⠀ ⠀⢀⣾⡅⠀⡹⠛⠉⠀⠀⠀⠀⠀⠀⠸⡁⠀⡀⡇⠀⠀⠀⠀⢸⠀⠀⢰⠁⠀⠀⠀⠀⣸⠀⠆⢰⣾⠀⠀ ⢀⣾⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⣸⣀⠆⠀⠀⠀⠀⢸⠂⠉⠸⡆⠀⠀⢀⠀⢈⣲⠗⠚⠁⠀⠀ ⢸⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡆⠀⡄⠀⣦⠞⠀⠀⠀⠑⠧⢀⣸⡀⠼⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⣴⠿⣶⣦⡀⠀⠀⣀⣠⣤⣄⠀⠀⠀⣀⣀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠁⠠⠀⠄⠠⠀⠄⠠⠀⠄⠠⠉⠈⢁⠉⠉⠒⠦⣴⡿⠛⠛⠻⢿⣾⣥⣩⣭⣷⣦⣴⣿⣛⡾⣝⣻⣿⣿⠟⠋⠉⠈⢹⣷⠒⠉⡀⠠⠀⠄⡈⠐⡀⠂⡁⠐⡀⢂⠐⡀⢂⠐⠠⠈⠄ ⠀⡁⢂⠈⠄⢁⠈⠄⢁⠈⠄⠂⢁⠂⠈⠄⡁⢰⣿⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⢸⣿⣸⢯⣽⣿⣷⣾⣿⣶⣤⣤⣤⣤⣿⡇⠐⠀⠡⠐⠠⢀⠁⠄⢂⠠⠁⠠⢀⠂⠠⠀⠌⠐⡀⠂ ⡠⠀⠀⠄⠘⠀⠄⠘⠀⠄⠤⠧⣤⢤⢧⣤⡤⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⡇⠘⣿⣿⢇⣿⣀⣿⣃⡿⢿⣿⣇⠀⠃⠄⡘⠀⡀⠘⢀⠀⠠⠘⡀⠄⢀⠃⠘⡀⠄⠠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠻⣯⣙⣞⣷⣿⣿⣻⠗⢻⣟⡀⠡⢀⠐⠠⢀⠁⠂⡈⠐⡀⠄⠂⠠⠈⠄⡀⠂⠄⡁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣀⣤⣀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣻⣿⣯⣿⣵⣶⣿⣯⣉⠙⠓⠒⠒⠂⠈⠀⠀⠁⠀⠐⠈⠀⠁⠀⠐⠈⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⢻⣽⣯⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣯⣟⣽⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣷⣯⣿⣽⣯⣷⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣾⡿⠶⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣿⣿⣿⣿⣿⣿⡿⠋⡔⢁⣾⣿⣿⠃⠈⣿⣿⣿⣿⣿⣿⡿⠋⡰⢃⣼⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡶⢿⣯⣿⣿⣿⣏⣠⣊⣴⣿⣿⣿⣿⣟⢻⣿⣿⣿⣿⣿⣟⣡⣎⣰⣿⣿⣿⡟⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣨⣽⣿⣃⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⠉⠈⠙⠿⣿⣟⣋⠉⠁⣰⡟⠋⠁⠈⢹⣧⠀⠈⠉⠉⣋⣻⣿⠟⠋⠀⠈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⣿⣿⡷⠀⠀⠀⠀⣿⢷⣾⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣹⡇⠀⠀⠀⣸⣿⣶⣿⣄⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⢻⣤⣤⣴⣟⠉⣷⢟⣿⠏⠉⠛⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⣿⠋⢳⢻⡟⢻⠋⢻⡝⣿⠃⣽⠋⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠋⠉⠸⣿⡶⣞⣯⣞⣯⢷⠾⣽⡇⣸⡏⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠷⣶⣦⣿⣿⣷⣥⣨⣷⣯⣿⣽⣤⣿⣤⣤⣤⣤⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠛⣻⣿⡿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⢠⣿⡗⣿⣜⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠈⣿⣿⣶⣽⣾⣿⣧⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⣴⣶⠿⠟⠛⠉⠉⠁⠀⠀⠉⠉⠛⠻⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣦⣤⣄⣀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣿⣟⡡⡜⢆⣿⠈⢉⡟⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⣿⣏⠦⣕⢎⢣⡜⡓⣎⢜⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⠿⢻⡱⢺⣀⣈⢏⡲⢸⡍⠈⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⠏⠳⢣⠱⠃⠮⡜⡜⠒⠣⠞⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠛⠛⠿⢷⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⡜⢣⢮⠓⠺⡴⣱⠉⠉⢧⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⢈⣿⡿⠟⠿⣷⣦⣤⣀⣀⣀⡀⠀⠀⠀ ⢸⣿⠙⢳⡚⠦⣔⢣⣿⡷⣲⣿⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⡀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⢸⣿⠉⠙⣿⣿⣿⣿⣆⠀ ⠈⣿⣆⠞⡱⣍⠞⢲⣿⣿⣿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⣼⣿⣶⣶⣿⡟⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣤⣶⡿⠋⠀⠀⠈⠛⠛⣻⣿⠃ ⠀⢻⣿⣾⣷⣿⣷⣿⣿⣿⢛⡦⢣⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠈⠙⢿⣿⣿⣇⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⣼⣿⠿⠿⠛⠁⠀ ⢀⣾⡟⠁⠀⠀⠀⠈⠙⣿⡯⡜⣯⢞⣿⣧⠀⠀⠀⠀⠀⣴⣿⡆⠀⠀⠀⠘⣿⡜⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀ ⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣦⣿⣿⢿⣷⣄⠀⠀⠈⠿⠟⠀⠀⠀⠀⣀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀ ⠈⣿⡀⠀⠀⠀⠀⠀⢀⣿⠏⠉⠉⠁⠀⠀⠙⠿⣷⣦⣄⠀⠀⠀⠀⣰⣾⠟⠋⠁⠀⢀⣼⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠿⣶⣤⣄⣤⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣶⣶⣿⣧⣀⠀⢀⣴⡾⠟⠈⠙⠛⠿⢷⣶⣦⣄⠀⠀⠀⠀⠀⢸⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢷⣶⣦⣤⣄⣻⣿⣿⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠉⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠻⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣠⣴⣿⣠⡶⠀⢀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⢀⡈⢻⣦⣄⣀⣀⣀⣀⣀⣠⣤⣶⣶⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣻⣿⠿⠟⠛⣻⣿⣎⣻⣷⠶⠟⠻⠶⢦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⣀⣈⣻⡿⢹⣿⣏⡉⠛⠛⠛⠿⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⡋⠀⠀⠀⠘⠋⢩⡿⣿⡿⢷⣄⡀⠀⠀⠀⣉⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠟⠉⢉⣿⣿⣿⣏⠙⠓⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⢀⣴⣿⠁⠸⣷⠀⠙⠻⣦⣄⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠁⠀⠀⣠⡾⠋⣿⠃⠹⣷⣦⣀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⡿⢹⣿⠀⠀⠹⣧⠀⠀⠈⠻⢿⠿⣿⣶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⣿⣆⠀⢀⣾⠟⠁⢠⣿⠀⠀⢹⡏⠛⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⣀⠀⠀ ⠀⠀⠀⣠⣴⣿⠟⠁⠀⠻⣷⡿⠃⠀⠀⢸⡟⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣴⣶⡿⠆⠘⢷⣆⠀⠀⠀⠀⠈⠻⢿⣷⣦ ⢀⣤⣾⡿⠟⠁⠀⠀⠀⠀⠈⢀⣼⠀⠀⣿⣃⣀⣀⣤⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⣤⣤⡀⠀⠀⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠉⠛ ⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣄⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⠿⠃⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣴⡶⠶⢾⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡄⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⢰⣿⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣦⡀⠀⠀⠀⠀⢀⣠⣤⠤⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⣿⠏⠀⠀⠀⣴⣿⠿⠿⢿⣶⣄⡀⣀⣠⣤⣾⡿⠟⠉⠻⣿⣷⣄⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠻⣿⣶⣄⣀⣴⠛⣩⣴⣶⡶⣶⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣁⣀⣀⣀⣼⣿⠁⠀⠀⠀⠙⣿⣿⠟⠛⠋⠁⠀⠀⠀⠀⠈⠛⠿⣿⣶⣄⡀ ⠀⠀⠀⠀⣠⣾⣿⠿⢋⣀⠀⠀⠀⠉⢛⡟⠁⣾⡿⠋⠀⠀⠀⠸⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⢿⣧⣄⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿ ⠀⣀⣴⣿⡿⠟⠁⢠⣿⠛⠻⢷⣶⣤⣾⠀⣸⣿⡁⠀⠀⠀⠀⢠⣿⢿⡏⠀⠀⠀⠀⠀⣠⡾⢋⣙⣷⣦⣀⠀⠀⠀⠀⠙⢻⣿⣷⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⠟⠋⠀⠀⢀⣾⠇⠀⠀⠀⠀⣹⠃⢰⡿⣿⣷⣤⣀⣀⣠⣿⠟⢸⣅⣀⣤⣤⣶⢿⡏⠀⢸⣿⠃⠉⣿⠛⠻⣿⠟⠛⠛⠁⢻⣷⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠉⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⢰⡏⢀⡾⠀⠀⠈⠙⠛⠻⢿⠏⠀⣾⡉⠉⢹⡏⠀⢸⡇⠀⢸⣿⡇⠀⢸⠀⠀⣿⡄⠀⠀⠀⠈⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⢀⡿⠀⣼⠃⠀⠀⠀⠀⠀⢀⡿⠀⣼⠛⠛⠿⢾⣷⣄⠘⣇⠀⢠⣴⣦⠀⢸⡇⠀⢸⣇⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⣼⠃⣰⡷⢤⣄⡀⠀⠀⠀⣾⠁⣰⠏⠀⠀⠀⠀⣼⣿⣤⣿⣤⣤⣽⣯⣤⣴⡷⠶⠿⠋⠀⠀⠀⠀⠀⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣯⣀⡀⠀⠀⣸⠏⢀⡿⠀⠀⠈⠉⠛⠲⣼⠃⢀⡟⠀⠀⠀⠀⢰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⡟⠀⠈⠙⠳⠶⣯⣀⣾⠁⠀⠀⠀⠀⠀⢠⡏⠀⣾⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠈⠉⠛⠲⢦⣤⣀⢀⡾⠀⣼⠃⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⢸⣿⣶⣶⡶⠿⠋⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠻⢶⣦⣤⣀⠀⣄⠀⠀⠀⠀⠀⠉⠙⠓⠶⣧⣄⡀⠀⠀⢰⣿⠀⠀⠀⢀⣴⣶⣔⡀⠀⣠⣴⡿⠿⣶⣶⣾⠟⠃⠀⠀⠀⠀⢀⣤⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢉⣙⠛⠷⢶⣤⣤⣀⠀⢀⣀⠀⠀⠀⠈⠉⠛⠲⣿⠛⠻⠿⠿⡛⠋⠉⣛⠛⠛⠛⠉⡀⠀⠀⢀⠀⠀⠀⣠⣾⡿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⡠⠖⠦⣄⠀⢀⠶⣦⡄⠀⠀⣰⠳⠷⡀⢀⡴⠒⣦⡀⠀⠀ ⠀⠀⡞⡏⡥⣄⠈⢳⡎⠀⠈⣷⢶⡔⣷⠀⠀⣷⠟⣁⡀⠹⣧⠀⠀ ⠀⢀⡏⡟⠁⠈⢧⡀⡇⠀⢠⣷⢦⡼⢸⠠⠈⣿⠋⣁⠉⡇⢻⠀⠀ ⠀⣸⣳⡇⠀⡴⠁⠀⠉⠢⠔⠋⠛⠉⠳⠤⠖⠛⣦⣛⠀⡇⢸⡄⠀ ⠀⢿⡝⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠃⢸⡇⠀ ⠐⣿⣿⣴⠂⢠⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣆⠀⡀⣸⡇⠀ ⣸⣗⠉⠀⠀⢸⣿⣿⡇⠀⣠⠴⠖⠒⣄⠀⠀⣿⣿⣿⠀⠙⢿⣦⡀ ⣿⡋⠁⠀⠀⠈⠿⠿⠁⣼⠃⠀⠶⠀⠀⢹⣄⠙⠛⠋⠀⠀⢀⣻⣳ ⠹⢿⣖⣆⠀⠀⠀⠀⢹⡏⠀⠛⠶⠛⠀⣈⡟⠀⠀⠀⠀⠀⢈⡗⠀ ⠀⠀⠛⢿⣗⣤⡀⠀⠀⠉⠛⠛⠛⠛⠛⠋⠁⠀⠀⣴⣶⡋⠉⠀⠀ ⠀⠀⠀⠀⠁⠋⠲⣷⡷⣶⣒⣖⣴⢖⡒⣒⣷⠗⠏⠿⠋⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣸⠇⠀⢸⡗⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⠤⠤⠤⢤⣄⠀⠀⣠⣾⣿⣷⣦⡱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢀⠡⢺⠇⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠒⣋⣭⠿⠻⢉⠉⡥⢂⠒⡌⢄⠀⠀⢙⣾⣿⣿⣿⣛⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⣈⢒⣿⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡃⠀⠈⠁⢀⣿⠛⢡⢂⠆⣅⠪⠰⢌⠒⣌⠢⢭⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠳⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⡬⣹⠃⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⢀⣠⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⣄⠀⠀⠀ ⠀⠀⠀⠀⢀⣇⡤⠀⣠⡿⣁⠎⡔⠨⡐⠤⠁⠧⢈⡒⠤⣹⣼⣿⣿⣯⣼⣿⣿⣿⣿⣿⣯⣿⣆⣀⠉⠓⠦⣄⠀⠀⠀⠀⠀⢀⣀⣀⣀⡄⠀⠀⢸⡱⣾⠏⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⢠⡴⠋⣁⡾⠁⠀⠀⠀⠀⠀⠀⣠⡴⠏⠠⡐⠨⢄⠀⠀ ⣿⡶⠀⠀⣼⡞⠀⣴⡟⡡⠆⡘⠠⢁⡐⠠⢃⠒⡀⢈⢲⣵⡿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢷⣤⣄⣨⣽⣦⣴⣚⣋⣩⣤⣤⣤⣧⠀⠀⣿⣷⠃⠀⠀⢠⠯⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⣠⠞⠋⢀⣴⠋⠀⠀⠀⠀⠀⢀⣴⠞⣉⠰⣈⠇⣁⠃⠚⢄⠀ ⠁⠀⠀⢀⣿⠀⣼⣿⢃⠁⡒⠠⠡⠂⠄⠃⠄⠣⡜⢄⣷⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⡾⠛⠁⢀⢀⣀⣀⡀⠀⠉⠙⠲⢾⣿⣟⣶⢿⣥⣀⡀⠀⢿⣀⣀⠀⠁⠒⠤⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⣠⠞⣅⢊⣴⠟⠁⠀⠀⠀⢀⣤⠖⠋⠀⠀⢀⠈⠐⢌⡀⠎⠡⠘⣆ ⠀⠀⠀⢸⣇⠂⣿⣏⠤⡘⠀⠀⠀⢀⠠⠀⡈⠔⡌⣾⣽⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⠟⡱⢌⢣⠩⢍⡋⠭⡉⢝⠫⡙⢍⡐⢦⡈⡍⢛⠷⣼⡭⡛⠷⣶⡤⣍⡛⠷⣦⣄⡀⠀⠲⢄⡼⠁⠀⠀⢠⡼⢃⢍⣴⠞⠁⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⠈⠄⠠⠁⠄⡀⠓⠌⡐⠈ ⠀⠀⠀⢸⣀⠹⣸⣿⠰⢀⠁⡀⠀⠆⠀⠰⢀⠇⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣿⢁⡎⢱⠎⡆⠹⢰⠈⣁⠱⡈⠶⠉⡆⠹⣀⠾⠸⢆⢁⡈⠹⣿⣱⢉⡹⣶⠉⠷⣈⠹⢿⡷⢆⣸⠁⠀⠀⣰⣏⠸⣱⡾⠁⠀⠀⠀⣰⠿⠁⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠈⢀⠰⠀⢁⠁ ⠀⠀⠀⢸⠰⣏⠜⣿⣧⡂⠔⣈⠐⡀⢂⡑⠌⢂⣹⣿⠿⠿⣟⣻⣿⣿⣿⣿⣿⢟⣱⡾⢃⠆⡘⢄⠊⡔⣁⠢⠌⣀⠂⠥⢈⠒⡈⠑⡄⢊⠔⣈⠆⣌⠱⡀⢿⣷⣬⠩⢷⣦⡈⠓⢦⡙⠻⠏⠀⠀⣴⢫⣴⡟⠋⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡐⠀⠂⠀⠆⠄ ⠋⠉⠀⠸⣇⣿⡘⡌⠿⣷⣌⠄⡘⢠⠃⡰⢈⠰⣸⣯⡀⠀⠛⠛⢿⣿⣿⡿⢍⢮⡟⠡⢌⠢⠑⡈⠰⠐⡠⠂⠑⡀⢈⠠⠀⠂⠄⠡⠐⡈⠄⢂⠒⠤⠑⡌⢄⠹⢾⣻⣄⠻⣯⢦⡀⠉⠳⣄⢀⣾⣣⡟⠃⠀⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠄ ⣠⣤⠤⠀⢿⣹⡸⢌⢧⡘⢟⡿⣦⣥⣚⣰⣬⣾⣏⠀⢀⠂⠡⢌⣾⣿⡟⡑⣪⣿⠍⢢⡁⠆⠑⡈⠁⠆⢁⠀⠈⡔⠀⠂⠠⠁⢀⠁⠂⡄⠈⠄⠂⠄⣁⠘⢤⡃⠌⡹⣞⢣⡙⢷⡙⢦⡀⠈⠻⣟⠁⠀⢀⣴⠋⠣⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊ ⠀⠀⠀⠀⡟⢿⡻⣜⢦⡙⢦⠱⣹⣶⣿⣿⢿⣿⣿⣾⣄⢊⣽⣿⣿⡛⠴⢡⣿⡯⠘⠄⡒⠈⠠⠀⢁⠂⢀⠒⠀⢠⠁⠀⠄⠀⠠⠀⠀⠀⠁⠂⠌⡐⠀⠂⠀⠹⣔⠠⠘⢷⡕⡊⠽⡶⣝⣄⠀⠘⢷⣟⠻⡝⣳⣄⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁ ⠶⠶⠆⢸⠁⠀⠙⢯⣷⣭⣷⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣾⣿⣿⠧⣉⠒⣥⣷⡧⠉⢆⢁⠂⠀⠈⠀⠀⠀⢀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠠⢷⡀⠀⠈⠀⠈⠷⣅⠂⠹⣾⡀⠍⣭⠿⣦⠀⠈⢻⣧⡙⣎⠻⢦⡀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀ ⣀⠀⠀⠋⠀⠀⣠⣴⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣿⣛⣿⣿⣿⠏⡑⠤⣩⡧⣿⡇⠘⢄⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄⠀⠀⠠⠀⠙⢷⣄⠘⢻⣄⠀⠓⠮⢷⣄⠂⠽⣿⣞⣆⠈⢳⡄⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀ ⠀⠈⠉⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⠒⠨⠴⣽⡇⢿⡧⠁⠈⢆⠡⠀⠀⠀⠀⠁⠀⠻⣆⠀⠈⣽⣆⠠⠐⠈⢤⠀⠄⠡⢀⠂⢻⣄⠀⠱⣄⡀⠠⠙⣮⠄⢻⣆⠉⠜⣂⠻⣦⠘⡌⢿⣮⢧⠀⠹⣆⠀⠀⠉⠳⠦⣀⣀⡀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀ ⠀⣠⣾⣽⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣭⣿⣿⣿⢷⡏⢆⣩⣪⢿⣿⡇⢺⣧⠀⠀⡈⢆⡀⠐⠀⡀⢀⠠⠐⡿⣆⠀⢲⡽⣦⠈⠐⡀⢣⡀⠐⠀⠂⡀⢻⣄⠂⠈⢷⡄⠡⠘⣻⡤⠹⣆⠘⢠⠋⡼⢷⡘⠌⢿⣿⢧⠀⠙⣧⡱⡀⠀⠀⠀⠉⠉⠉⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀ ⣾⣻⣼⣿⣿⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠞⢫⠡⣿⠩⣧⠘⣿⣦⠰⢀⠊⣤⠀⠡⢀⠂⠀⠀⠹⣿⣆⠀⢻⣝⣷⡀⠀⠀⢹⣤⠶⠟⠛⠛⣿⣶⠷⠦⣽⣧⡐⢀⠻⣧⠹⣧⢀⠓⣄⠋⣿⡨⠌⢿⢿⣧⠀⠻⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠈⢻⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⡟⡷⢀⢊⢇⢺⡇⠜⣻⡆⢿⣿⣷⡀⠌⢼⡆⠁⢂⡈⠄⠐⠀⠙⣿⣆⠈⢿⣿⣟⣦⡀⠋⠘⢧⡀⠠⠀⢸⣿⣷⡀⠀⠌⢻⣧⠐⡩⢷⣹⣆⠉⠤⣃⠹⣗⠨⠜⣿⢿⣆⠀⢻⡹⣧⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⢻⣿⣿⢳⣟⠀⣸⡎⣿⠐⠨⠐⢿⡌⢿⣿⣻⣄⢂⢻⡌⠀⢀⠈⠆⠀⡀⠘⢿⣆⢂⢻⣎⠻⣿⣦⡀⠈⠻⣆⠀⠀⢹⣽⡟⣧⡠⠁⠻⣧⡐⢩⢻⣿⣌⠰⢠⠃⠽⣇⢎⠸⣾⣿⡆⠀⢷⢻⣧⠀⠀⠀⠀⠀⠠⣽⠀⠀⠀⠀⠀⠀⠠ ⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠎⣼⣿⠀⣾⣹⣏⠠⠑⡈⠀⢻⣼⣿⠿⣿⣯⡍⢿⣍⠁⠄⠈⠡⡀⠀⠈⢿⣧⡂⢿⣆⠀⠙⠻⣦⣄⠘⢳⣄⠀⢻⣿⡌⠹⢦⡁⠜⣷⡢⠩⢽⣿⣀⠂⢿⡐⢻⡞⣥⠘⣿⣿⡄⠘⣏⣏⢣⡀⠀⠀⠀⠐⡻⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢿⣿⣟⣿⡿⣇⣼⣿⣿⣯⣟⠜⣸⣿⠐⡿⣹⣃⠀⠐⢀⣠⠞⠛⢾⣷⡀⠛⢿⣷⣟⢷⣀⠈⠐⠀⢅⠀⠀⠻⣿⣮⣙⣦⡀⠀⠀⠉⠛⠶⣭⣳⣄⣻⣷⣄⠀⠙⢳⣌⡻⣕⡊⣿⣷⠈⠼⣇⠘⣿⢹⡄⢳⣿⢷⠀⢻⢸⡈⢷⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣯⣿⣿⣿⣿⣟⢲⣏⠎⣿⣇⢺⡗⣽⠃⢀⡴⠟⠁⠀⠀⠈⠙⠷⣄⠀⠈⠛⢷⣽⣧⣄⠈⠀⠳⣄⠀⠘⢿⣛⢾⣳⣄⠀⠀⠀⠀⠀⠈⠉⠛⠻⣽⢦⠀⠀⠈⠛⢿⣷⡸⣿⣆⠂⣿⠠⢹⡎⣷⡀⢻⡟⡇⢸⡎⢧⠘⣷⠀⠀⢰⠃⢁⠊⡀⠀⠖⢲⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣿⣿⠆⣿⣞⣹⣿⣗⢺⡿⣿⠀⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠈⢳⡍⠻⢷⣤⣀⠈⠳⣤⡀⠙⢦⠈⠛⠷⢦⡤⠤⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠉⢷⣟⣿⠀⢼⡇⠌⣷⢸⣧⠈⣷⢹⡈⣇⢸⡆⣋⡇⠀⢸⡀⠀⠀⠀⠀⠭⠝⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⡈⣿⠾⣸⣿⣏⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠁⠈⢉⠛⠷⣬⣝⣶⣬⣳⣄⡀⠀⠉⠃⠀⢀⣰⣯⣿⣿⣷⣶⣤⣄⡀⠀⠀⠀⠹⣿⡧⢈⣿⠄⣸⡆⣿⡆⠘⣧⠐⣹⠀⢳⣹⡟⠀⣿⡇⠀⠀⠀⠀⠀⢀⣠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⡇⣿⢇⠰⣿⢱⠏⣿⡇⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡀⠀⠀⠀⠀⠀⠉⠉⠿⠿⠿⠶⡶⠀⣶⣿⡿⡏⣱⣾⣶⣷⡎⠹⢿⣶⣶⠆⠀⢹⣿⠈⣿⡇⢀⣷⢹⢿⡀⢿⣁⢸⡇⠸⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⢸⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠋⢰⣿⣿⢈⡐⣿⢌⣹⣷⣯⢼⡇⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠋⣸⣿⣿⣿⣿⣿⣧⣤⣴⡙⣧⡀⠀⠰⢿⡇⢼⣇⠈⠼⣻⠘⣧⠈⣧⠸⢻⡀⣧⡇⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸⢿⣷⠐⡀⣿⢌⣺⣿⣸⣿⡇⠘⢷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠉⣿⣤⡀⢸⣷⡹⡇⠌⣃⢿⡇⢻⡄⢻⡗⠈⢿⡼⡄⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡟⢠⠁⢻⠆⣹⣿⡇⣿⣷⠀⠈⢷⡀⠀⠀⠀⠀⣠⣶⣿⠿⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠀⣾⠁⠀⣿⣿⣵⡯⠐⣸⢸⡇⢸⡇⠘⣇⠈⢼⡇⣧⠀⠀⠚⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⢸⣿⡟⡀⢃⢹⡎⠔⣿⣿⡼⣿⡄⠀⠀⠹⡆⠀⣠⣾⣟⣿⣾⣿⣿⣿⠉⢙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣻⣿⡿⠟⠩⣘⣿⣾⠁⢀⡾⠁⣼⣟⣿⠀⣹⢸⡇⢸⣿⠀⣿⠀⣸⣯⢻⡀⠀⠀⢹⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⣿⡇⡆⡡⠸⣧⠉⠞⣿⣷⣻⣧⠀⠀⠀⠙⢳⡿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠶⠶⠶⠚⠛⠉⢉⠀⢀⣼⠃⠀⣿⣷⣿⠀⢼⡞⣧⣸⢿⠀⡿⠀⣽⣿⣾⠁⠀⠀⠀⢳⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⡇⣇⠐⢠⢿⡉⠆⠹⣿⣷⣿⣆⠀⠀⠀⣾⠁⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠂⡀⢈⡿⠀⢀⣿⣿⣏⠐⣸⣏⣧⡟⢸⣷⡇⢠⣿⣿⠃⢸⠀⠀⠀⠈⠳⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣏⡇⢷⡠⠸⣾⣧⠡⠀⢹⣿⣿⡽⣦⠀⠀⣿⠀⢹⣿⡿⠟⢛⠻⣿⠟⠋⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠠⠀⣸⡗⠀⠘⣿⣿⣿⠀⢼⣿⣿⠃⣼⣿⢀⣾⣿⡇⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⣇⢸⡇⢀⢻⣹⣦⡀⠀⠹⣟⠀⢸⡄⠈⠛⢧⡈⢻⣄⡘⣆⣂⣢⣽⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣰⡿⠁⠀⢰⡇⢹⣿⡄⢺⣿⡏⡐⣾⣿⢹⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢹⣸⣘⡇⡀⠎⢷⣻⣧⠀⠀⢹⣆⠸⣿⡄⠀⠀⠙⢶⠾⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⡟⠀⢸⣿⡧⢸⡿⢁⣸⣿⡟⣽⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠘⡿⣿⡔⠠⢹⡘⣷⢻⣧⠀⠀⢿⣆⢿⣷⡀⠐⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠟⠁⠀⠀⠀⠘⠇⠀⠀⢿⢓⢼⡗⣠⣟⣾⣹⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⢹⣿⣧⢃⠌⣧⠹⣧⡻⣧⠀⠈⣿⣆⠙⣧⡀⠂⠈⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡚⣸⣿⣿⢏⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢿⣿⡾⣔⠸⣆⢻⣿⣾⣷⠀⡹⣿⡆⠈⠛⣦⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢹⣿⣟⡾⠃⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣻⣿⡐⢻⡌⣿⣷⠙⢷⡀⢿⣿⡄⠀⠀⠙⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀⣀⠄⠤⣶⡾⠟⠉⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⣎⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠻⣿⣿⠘⣿⡜⡿⣇⠈⢻⡈⣿⣧⠀⠀⠀⠀⠀⠉⠙⠲⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⣰⣿⢯⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣇⣿⣿⣞⡿⣦⠀⢿⣱⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢠⢤⣄⣀⠀⠀⢀⣀⣀⠀⠀⠀⢐⣃⡼⢹⡟⠀⠙⠓⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣼⣆⠈⣿⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠤⠞⠛⠺⣿⡍⡿⣳⣦⣶⣛⢧⡀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠉⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⢀⡆⠀⠀⠀⠀⢿⣸⢱⡉⢿⣿⣿⠁⢿⡀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⢻⣧⡙⠻⣿⠊⠀⠀⢠⣶⣶⡶⣦⡾⠊⠉⠀⠀⠐⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣾⠀⡀⠀⠀⠀⠀⠹⣷⠟⠋⣩⣿⡿⢶⣿⡞⠂⠀⠀⣀⣠⠤⠶⠶⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠹⡏⠳⡿⣤⣀⡀⢸⣧⣿⣿⢿⣿⠀⠀⠀⠀⠀⣿⢿⣿⣶⣶⣦⣤⣤⣤⣠⣄⣠⣠⣤⣴⢾⣛⡳⣜⡟⢦⡄⠀⣠⡾⢿⣀⣼⣷⠶⠋⠉⠙⡻⣾⣃⣤⡴⠾⠵⠶⠖⠶⠶⢤⣀⠈⠑⠦⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠹⡾⠁⢠⠿⢭⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣿⣿⣏⣽⣦⡉⢟⡜⣣⢟⡽⢏⡿⣘⢮⢧⣳⡹⢎⣴⡽⣷⠀⠘⣿⡍⠍⡌⠀⠀⠂⠁⠀⠈⠈⡝⢧⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄⠈⠳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠐⣇⠀⣿⣷⡾⠟⠛⠋⣟⡁⠀⠀⠀⢀⡄⢠⣿⣿⣿⡏⣙⣇⣎⣱⣙⢮⣼⣯⣶⣹⣾⣛⣛⠿⠟⡟⠀⢸⣶⢾⡇⡘⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⢀⣀⣈⣳⡄⠘⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠍⠀⢹⡙⢢⣀⣠⡾⣿⣟⣠⣦⣶⣾⠃⢸⣿⢻⣿⠿⡍⢉⡀⠸⠿⢫⡀⠠⡷⠿⠟⡇⠙⠦⣤⡅⣀⣴⡿⣾⠿⣎⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣠⣤⣶⣾⣯⠉⠙⠻⠽⢦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣷⣾⡿⣑⢂⠙⡛⠻⡙⢾⣏⣴⡀⢿⣼⡿⠤⠼⠶⢿⣶⡷⢦⣽⣿⣷⣤⣤⣯⣤⣶⣿⣟⣫⡁⠐⠚⢙⣟⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡿⢋⣘⡦⠀⠀⠀⠀⠄⡉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣮⡟⡐⢄⢊⠰⡀⠥⡐⢡⠛⣿⣽⣿⡾⣧⠀⣀⣀⡴⠂⠈⣁⣭⣿⣿⣿⣿⣿⣿⡿⠿⣿⣽⡻⣟⡶⣿⣏⡻⢷⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣅⢰⣊⠉⠡⠀⠀⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣉⣹⡟⡘⠀⠆⡐⠀⡐⠤⠑⢢⢉⣿⣴⣾⠡⢹⣀⣶⣯⣀⣠⣾⣟⣯⣿⠋⣾⣿⢹⣿⣿⣆⣙⣎⣿⢷⣽⣖⣿⠿⣩⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡁⠘⠀⠐⢀⠀⢂

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⢄⡀⡀⡀⡀⡀⣀⠀⠔⠀⠄⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡈⠄⠁⡉⡁⢽⣧⢫⠋⠀⡉⠊⠸⡆⢭⣐⢒⠠⢀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠆⢁⠈⡧⠙⡗⠁⢎⠀⠀⠉⠀⠀⠀⠀⡀⠳⠎⡁⠈⠈⠵ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡀⡅⠁⠀⠈⡊⠀⡅⠀⠀⠀⠀⠀⠀⠀⡀⡉⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡙⡆⠅⠀⠀⠀⡁⣀⢇⡀⠀⠀⠀⠀⠀⡄⡬⢘⠀⠀⠀⠀⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠮⡏⣨⣀⣁⣈⣠⣉⣣⣫⢭⠄⢄⡇⢢⠡⠔⠀⠂⢊⠈⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠁⠋⠓⠙⠣⠥⡁⡅⠄⠒⠁⠁⠁⠈⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⠁⡂⠅⡂⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡔⢁⠂⠀⠀⠂⡉⢥⠅⣠⠀⠀⠀

⢰⣖⠾⠀⠀⠼⠳⢿⣷⡀⠀⢸⣏⣉⣸⡇⣽⣿⣿⣟⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢠⣞⡶⠞⠆⠀⠙⢿⣿⡄⠀⠀⠀⣀⣀⠀⠀⢀⣤⣾⢄⣠⣀⡈⢹⣿⣋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⢾⠀⣰⢧⣼⣿⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠛⢦⣀⠀⠀⠀⣿⣿⣿⡿⢸⠉⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⣤⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣄⠀⠀⣤⣤⣼⣿⡇⠀⠘⠻⠟⠛⠃⠛⠛⠛⠋⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠸⣿⣤⣤⣤⡤⢀⣴⠿⢟⡠⠴⠒⠈⢷⣄⣤⣿⣿⣿⣿⣭⣍⣿⣾⣿⣁⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠄⣀⣀⡠⣊⠀⠀⢀⣠⢷⣾⡊⢁⡠⢿⢇⡀⠀⢀⠀⣀⠶⠓⣠⡴⠖⢣⡌⢉⡟⠀⠀⢙⣿⣿⡁⠘⠓⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣄⠀⣀⠀⠰⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢿⣿⣷⣤⣼⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠛⠋⢁⣠⡟⠋⠀⠀⢱⡀⠒⢤⡀⠹⢿⣿⣿⣾⣿⣿⣿⣿⣿⣽⠟⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠋⠀⠀⠀⠀⡿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢩⣭⢿⣿⣧⠞⢀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠀⢁⡀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠛⠛⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⡶⣻⣷⣴⣾⡿⢱⣇⠀⠀⡀⣀⣏⣤⡀⠙⣦⡜⢿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠺⠋⠀⠀⠀⠀⠀⠀⣷⣿⣿⣾⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣮⣽⣾⢿⣟⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣼⣷⣿⣿⣿⣿⡟⢠⢿⡈⢆⠀⢻⡘⣿⡉⢿⣆⢯⢧⣦⠙⢿⣿⣿⡻⣟⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢾⠶⢤⣶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⠢⣄⢀⡤⠋⠀⠀⠀⢠⡤⠤⠤⠤⠤⠤⠤⠤⠦⠴⠾⠤⠿⣽⣿⣿⣿⣿⢧⢸⢻⣷⡈⢳⡆⢻⡽⣿⣧⣽⣾⣧⣹⣧⠀⣿⣿⣷⡍⣿⣹⡤⠤⠤⢤⠤⠤⠤⠀⠤⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⣠⣄⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣨⣷⣭⡿⣋⣀⣤⡤⠤⠄⠠⠀⠀⠀⠀⠤⠄⠄⠠⠀⠄⠀⠀⠤⠤⠤⠤⠤⠤⠦⠠⣴⣶⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣩⠟⣯⡝⢻⣷⠤⠤⠤⣉⣽⠝⠠⠐⢦⠀ 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⠀⠀⠀⠀⠀⣾⡿⣿⣿⣿⡄⠐⠈⠞⠟⢣⡌⢹⣾⣍⢯⣛⣷⣇⣾⣵⣭⡟⢁⣸⡏⡄⣃⠆⣣⡱⢬⡙⡿⣷⣶⣤⣀⡉⠉⠉⠈⢉⣀⣤⣤⠞⠀⠀⠀⠀⠀⠀⢀⣴⣷⣶⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣧⠐⣄⡄⣿⣇⡤⢀⣠⠴⠣⣄⣠⠠⡶⠞⢧⡀⠀⠀⠀⠀⣄⡴⣿⣿⣶⣶⣶⣶⠴⣆⣤⣦⣰⠆⠀⠀⠀⠀⠄⠐⠀⠄⢠⠀⠔⠐⣒⣀⣿⡷⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠠⣿⣷⣿⣿⡿⣿⡄⠀⠀⣾⢯⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠷⠋⢀⣀⣀⣀⠀⠀⢠⣾⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣼⣤⣿⣶⣿⡟⠉⠋⠉⠋⠙⠃⠙⠉⠙⠉⠋⠙⠀⠀⢀⣛⢉⣻⣟⡞⠙⢃⣋⣙⡛⣛⢋⣙⡋⢋⣓⣛⡋⠑⠈⠋⠋⠚⠉⠛⠙⠋⠉⠙⠈⠛⠙⣾⡇⠀⠀ ⠀⠀⠀⠀⠀⠟⣿⣿⣿⣽⣹⣷⠀⠡⢸⣌⢿⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⢒⢛⣻⣿⠀⠀⣿⣿⣿⣿⣿⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡿⠛⣹⠟⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣿⣉⣟⣟⣻⣄⣼⣋⣿⣻⣻⣻⣛⣏⣽⣟⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⡟⠓⠚⠶⠙⢻⣧⠀⢊⢹⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠉⠉⠉⠀⢠⣿⣿⣿⡿⠉⠉⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠩⠉⠈⢹⠀⡸⠉⠉⣟⣹⡏⠈⢙⠀⠀⠉⠈⣿⣹⡏⠉⢩⠀⠀⠀⣿⢁⡄⠅⠀⣿⡇⠀⠀⠀⢰⡛⢶⣦⡀⠀⠀⠀⠀⠀⢰⡟⢶⣢⡀⠀⠀⠀⠀⠀⢰⠟⠓⠰⢦⠀⠀⠀⠀⠀⢴⠋⠑⠒⢶⠀⠀⠀⠀⠀⠀⠀⣹⣾⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⢰⡒⢒⡆⢸⣿⡆⠀⢆⢺⣷⣿⠋⠟⠻⠿⠿⠿⠛⠛⠉⠙⠛⠛⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢀⣾⣿⣿⡿⠁⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠂⠐⠚⠀⠐⠒⠒⠒⠒⠒⠒⠚⠀⠀⠒⠒⠛⠓⠒⠒⠚⠀⠀⢀⣷⣯⣰⣾⣶⣿⡇⠀⠀⠀⠈⠧⣀⢸⣧⠀⠀⠀⠀⠀⠘⠧⣄⣸⣧⠀⠀⠀⠀⠀⢸⠆⠀⠀⢸⠀⠀⠀⠀⠀⢺⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠐⢄⣑⣋⢀⣾⣧⣿⡄⠐⢮⣷⣿⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣴⣿⣿⣿⣿⠋⠰⠂⢀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡤⠤⠤⠤⣤⣤⣤⣤⡤⠤⠤⣤⣤⢤⣤⠤⠤⠤⣤⣤⣤⡤⢤⡤⠤⠤⠤⠤⠤⣤⣾⣿⢻⣿⣿⣿⣿⡇⠀⠀⠀⣤⣤⣤⠟⢡⡄⠀⠀⠀⠀⣤⣠⣤⠝⢡⡆⠀⠀⠀⠀⣼⣿⣯⠏⠙⠀⠀⠀⠀⠀⣬⣽⣿⠟⢫⡄⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠿⣿⣿⣿⣷⠈⢩⡿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠉⢻⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣰⣿⣋⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢤⣾⡛⣜⡿⠋⠀⠀⣰⠟⠀⠄⠁⠀⠀⠰⢯⡿⠋⠀⠌⠀⠀⠀⠀⢀⡴⠟⣡⠆⠀⠀⠀⠁⣿⡇⠀⠀⠀⠈⢉⡁⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⡀⣀⣀⣀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⣁⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠼⣣⣿⣿⣿⡅⠰⢻⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⠀⡀⣿⣿⣿⣿⣿⣿⣿⠁⠀⠈⠁⠀⠁⣠⣷⡶⢴⠶⣶⡶⡶⠶⢦⠦⠴⡲⠷⡞⠷⣿⠿⢶⢶⣶⡾⢿⠶⠿⣷⡷⣶⣷⣶⣿⣷⡄⠀⠀⠀⠀⣠⣴⣿⢷⡾⣿⣶⣴⣶⣾⣿⣿⡇⠀⠀⠀⢸⣯⣽⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣤⣌⣯⣍⢻⣏⡿⣷⠀⢣⣟⢿⡇⣰⡒⢒⣶⠀⠀⠀⠀⢀⣼⢀⣰⠀⠀⢹⣶⢀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⣿⡽⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣻⡧⠝⠮⠽⠧⠿⠼⠯⠧⠽⠾⠵⠯⠾⠷⠮⡿⢮⠿⠾⠿⡿⠿⢿⠷⡷⡷⠾⢿⣿⢿⡇⠀⠀⢀⣴⣿⠿⠟⢸⢿⡿⠛⢿⣿⢿⡍⢹⡇⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⠸⣿⡇⢿⣿⣆⢚⡿⣿⣤⣝⣿⣃⡀⠀⠀⠶⡿⢫⣶⡇⠀⣰⣼⣿⣾⠅⡈⠄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠤⠚⠋⠉⠙⠋⠋⠉⠈⠛⠙⠉⠉⠘⠛⢻⡷⣶⢾⡾⠿⠼⠏⠰⢵⡶⠦⠀⠀⠀⠀⠀⠀⢴⣿⡿⠴⠇⣾⢧⡶⣶⡆⠀⠀⠀⠀⠀⠀⠶⡿⠿⠵⢸⡷⣾⠇⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⣿⣫⣿⣻⣿⠺⣿⡌⣿⡜⣧⢜⡻⢿⣻⢧⠽⣻⠏⡉⡀⠛⠻⠿⣧⡀⠈⠻⣿⡟⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⣀⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢨⣇⣀⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣀⣤⣠⣿⡇⠀⠀⠀⠀⣀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡤⠀⠀⠀⠀⠀⠀⠀⣹⢿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⣽⣿⡟⢣⣿⢿⡸⣷⠹⣮⡱⣏⣯⢧⣻⡿⠀⠄⠃⠀⠀⢀⣨⣿⣷⣤⣼⠻⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡅⠀⢠⡟⢁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣤⣀⣠⣤⣠⣤⣀⣤⣄⣠⣤⣶⣡⣤⡀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣫⣽⣿⠀⠀⠀⠀⠀⠀⢿⠿⣿⣦⠀⠀⠀⠀⠀⠀⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⠀⠀ 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