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⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⠉⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢻⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣠⣦⡀⠀⠀⠀⣿⡟⣆⢿⡄⠀⠀⠀⠀⠀⣠⣴⠟⠋⢿⠟⠋⣡⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠛⢿⡄⠀⠀⢸⣿⣟⣮⢿⣄⣀⣤⠶⠛⠉⠁⢀⣠⡴⠖⠛⠉⠀⣀⣬⣽⣷⣤⣀⣀⠀⠀⠀⠀⣀⣤⡴⠾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣿⡶⣌⣷⣄⠀⠼⣿⣿⣿⣿⣿⠋⠀⠀⢀⣴⠞⠋⠁⠀⢀⣠⣴⠾⠋⠁⠀⠀⠉⠉⠙⠛⠛⠛⠛⠋⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢺⣷⣟⡶⢿⣦⣀⣼⣿⣿⡾⣿⣦⡀⠈⠉⠀⠀⣠⡴⠾⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢿⣯⣟⡷⣽⣿⡏⠀⢿⣿⡽⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠤⠊⣩⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢾⣮⣿⡿⠿⠿⠿⣅⣀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⣀⡠⠘⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣇⠀⢰⡀⠀⠀⠀⠙⠛⠒⢿⣿⡛⣀⠀⠀⠀⠀⠀⠀⠤⣤⣀⣀⡀⢀⣀⡀⠹⠏⠁⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⡄⠀⢷⡄⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠉⠉⠋⠛⠛⠶⣤⡀⠀⠀⠀⣿⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⢷⣌⣷⣄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠛⠳⠶⣤⣄⣀⡀⢀⠀⠀⠀⠀⠈⢻⣆⠀⠀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣯⢿⣾⣿⡷⣦⣀⠀⠀⠀⠈⠳⣦⣀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠒⠒⠒⠒⠒⠛⢷⣾⣏⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠻⣶⣿⡏⠀⢀⡿⢷⣤⣀⠀⠀⠈⠙⠷⣶⣤⣤⣤⣤⣤⣤⣠⣤⣤⣤⢶⣶⣾⡿⠿⠟⢹⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣇⠀⣼⣿⢟⣫⣭⣷⣦⣤⣄⣀⠀⠙⠻⠷⣷⣾⣧⡿⢿⢿⣿⣟⠉⠀⠀⠀⠈⢿⣇⠙⠛⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⣄⣿⠃⣿⣿⣿⣨⣿⡟⠈⢹⡿⠛⠛⠂⣴⣾⣯⠀⢘⢸⡿⠛⠷⣤⣀⠀⠀⠀⠙⢶⣾⣟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠁⠀⠛⠛⠻⢷⣶⠿⠁⠀⣠⡾⠋⣠⠟⠀⣠⡿⠃⠀⠀⠉⠙⢷⣶⣶⣦⣤⣬⣉⠻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣤⣾⡍⠀⣴⠀⢰⣿⡟⠀⣼⢱⡆⠀⠀⠀⢹⣦⠀⠀⠉⠛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⣟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣡⡴⠞⠋⠉⠷⣤⣛⡶⣿⡟⠀⣤⢁⣿⠁⢳⡀⢦⠀⠛⢷⣦⣤⣀⣈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠛⢷⡆⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢀⣜⠛⣻⣟⣡⡾⣃⠚⠁⠀⠀⠱⡈⣧⠀⠀⠸⣇⠉⠻⢯⣁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⢀⠘⠀⠀⠀⡍⠲⡄⠀⠉⠳⢦⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⠀⠀⠀⠀⢀⣠⣴⠈⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⡈⠃⠀⠀⠀⣟⠀⠙⣦⡀⠀⠀⠉⠛⠶⣤⣀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣦⣤⣤⣶⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⢻⣷⣄⠀⠀⠀⠙⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⢿⡿⠁⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣏⣿⡿⣦⠀⠀⠀⠀⡆⠀⠀⠙⣿⠓⠛⠛⠋⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡾⠁⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⢷⡆⠀⠉⢹⣟⠉⠷⠶⠶⣤⣤⣤⣤⠶⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣦⣄⣤⡾⢫⣿⣿⣿⣿⡿⢿⡟⠋⠉⠀⢸⣿⣿⣷⡟⢻⠛⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⣰⡫⠛⢿⡿⠛⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣶⠄⠀⠀⠙⢫⣿⠋⠙⢢⠀ ⠀⠀⢻⣴⡄⠀⠀⢠⣴⣿⠃⠀⠀⠀⠀⠀⣀⣴⠶⠟⠛⠻⠿⢿⣿⣿⣟⠛⠻⣷⣶⣤⣀⡀⠀⠀⠀⠀⠻⣇⣄⣼⣷⣆⠀⠈⠀⠀⠀⠑ ⠀⢶⣾⡿⠁⢀⣄⢈⣿⡿⠀⠀⠀⣀⣴⡾⠫⠖⠉⠀⠀⠁⠈⠀⠄⠉⠛⢷⣄⠡⠄⢈⣙⠿⣶⣄⠀⠀⠀⠈⠙⢿⡮⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠻⢿⣻⠟⠀⠀⣤⣾⡛⣡⠞⡡⠀⠀⠀⠁⠁⠀⠁⠁⠀⠀⢀⢿⣦⠀⢷⠉⠻⣾⣝⢷⣼⡟⢶⡄⠀⠙⠲⠷⢄⠀⢀⠴⠀ ⡀⠀⠀⠀⠀⣀⢈⠟⠀⣠⣿⣿⢟⡴⠁⠀⠙⢃⣴⣻⣇⣾⠱⣤⡄⢤⣄⡬⠈⢿⣇⠚⠀⡀⠈⢻⣷⣿⣧⠀⢻⡄⠀⠀⠀⠈⠉⠉⠀⠀ ⣇⠀⠀⣸⡾⠛⠋⢀⣴⣿⡿⠁⠄⠈⠓⡀⠀⣾⢣⡿⢸⣿⠀⠀⠹⠀⠀⠀⠀⠈⢿⣆⢼⠁⠀⠀⠻⣿⡿⣧⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠋⠋⠀⠀⢀⣾⣿⠟⠀⠀⠀⠀⢰⢇⣾⣿⡿⠁⣾⣿⠀⡛⢳⣄⢰⠟⠙⢦⣸⣿⠎⠇⠀⠀⠀⠹⣿⣻⣿⡟⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣿⠏⠀⠀⣴⠆⠀⠙⣾⣿⠁⠈⣸⣿⣿⣧⠀⠀⢻⣆⠀⠀⠀⠻⣿⡀⡀⠠⣦⠀⠀⢿⡗⣿⣰⣿⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⣼⡏⠀⠄⠄⣿⡇⠈⢲⡿⠛⠻⢿⡄⠀⠘⣿⡄⠀⠀⠀⣿⡇⠂⠀⣿⡄⠀⢸⣿⢹⣿⣥⣈⣿⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⠇⠀⣰⡿⠀⠄⠀⢵⣿⠀⢦⣿⠡⣄⠀⠀⢻⣎⠂⠘⣷⡀⠀⠀⢻⣿⡄⡂⠘⣿⡀⠀⣿⣼⣿⣿⠿⠛⢶⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⠀⣇⣿⡇⡆⠀⠀⣹⡟⢀⡾⠁⠀⠈⠙⠓⠦⢽⣦⡀⠘⣿⡀⠂⢺⡿⣷⡂⠀⠙⣷⡀⣿⣿⣿⣡⣤⣤⣤⠟⠀⠀⠀ ⠀⢀⣀⠀⠀⢸⣿⡇⣹⣿⣇⠂⠀⠀⣿⣧⡟⠁⠀⠀⠀⠰⠦⣄⠀⠀⠻⢦⣬⣿⡆⢸⣷⠘⢷⣄⠀⠹⣷⣿⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡞⣉⡛⠶⣼⣿⣧⣿⡿⣿⡀⡀⠀⠹⣿⠑⢷⣶⣿⠿⠿⠿⣶⣄⠀⠀⠀⠈⠉⢷⡄⠹⣧⠀⠙⠷⢦⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⣯⡰⣯⣹⠀⣤⣿⣿⣿⣷⢿⣧⠀⢠⡄⣿⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣾⣷⡀⠀⠀⢀⣿⢁⣿⡇⠀⠀⠀⠀⠀⠀⠀ ⠘⢧⣤⣉⣼⠃⢹⣿⡿⠃⣀⣿⣧⣾⡇⣿⡇⠀⠀⠀⠀⠀⠀⢠⠔⠒⠲⠤⢤⣄⣀⠀⠀⠙⠻⠿⣿⣾⡿⣿⢰⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣽⠂⠘⢿⣤⣼⠏⠀⢹⣿⡇⢿⡇⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡾⢸⡇⠀⢸⣿⢿⡆⠘⢹⣿⠁⣿⡇⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣾⣿⡄⠀⠀⠀⠀⠀ ⠀⣼⡋⠀⣼⠃⢀⣼⠋⣸⣿⣦⡾⠁⠆⣸⣿⣤⣀⠀⠀⠀⠀⠙⠦⣄⣀⣀⣠⠔⠁⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⢻⣟⣦⠏⢠⣾⠋⢠⣿⣿⣿⡇⢀⣴⣿⣿⣿⣿⣿⣶⣦⣤⣀⣀⣀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣶⣿⣿⣿⡛⠿⣿⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢁⣴⠟⠡⢄⣿⡟⢹⣿⣷⣿⣿⣿⠿⣏⠀⠤⠌⠙⢿⣿⣿⣿⣿⣽⣿⣿⣛⣉⣹⠿⣿⢿⣿⣿⣿⣷⡀⠈⢷⡄⠀⠀⠀⠀⠀⠀ ⠀⣠⡾⠟⠁⠀⢯⣿⠏⠀⢿⣿⣿⣿⣿⣿⡗⠂⠁⠀⠴⠒⢂⡽⣿⣿⢿⣿⠿⠿⣿⣿⣯⣒⠃⢸⣿⣿⣧⠈⣷⣤⣾⡟⠀⠀⣀⠀⠀⠀ ⢸⡟⠀⠂⠀⢠⡿⣿⣄⠀⠘⢿⣿⣿⣿⣿⣿⡿⠿⣿⣶⣶⣾⣎⡠⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷⠟⢻⣿⣿⣷⣛⠛⠋⠀⠀⢠⡿⣷⠀⠀ ⢸⣧⠀⠀⢠⣿⢱⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⠀⣙⣻⣿⠋⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⣿⣿⣶⣤⣤⣼⠇⢹⡇⠀ ⠈⢿⣷⣦⣜⣿⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣠⣿⠃⠀ ⠀⠈⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⡿⣿⣟⡻⢿⢟⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠛⠁⠀⠀

⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡼⠋⠀⣀⠄⡂⠍⣀⣒⣒⠂⠀⠬⠤⠤⠬⠍⠉⠝⠲⣄⡀⠀⠀ ⠀⠀⠀⢀⡾⠁⠀⠊⢔⠕⠈⣀⣀⡀⠈⠆⠀⠀⠀⡍⠁⠀⠁⢂⠀⠈⣷⠀⠀ ⠀⠀⣠⣾⠥⠀⠀⣠⢠⣞⣿⣿⣿⣉⠳⣄⠀⠀⣀⣤⣶⣶⣶⡄⠀⠀⣘⢦⡀ ⢀⡞⡍⣠⠞⢋⡛⠶⠤⣤⠴⠚⠀⠈⠙⠁⠀⠀⢹⡏⠁⠀⣀⣠⠤⢤⡕⠱⣷ ⠘⡇⠇⣯⠤⢾⡙⠲⢤⣀⡀⠤⠀⢲⡖⣂⣀⠀⠀⢙⣶⣄⠈⠉⣸⡄⠠⣠⡿ ⠀⠹⣜⡪⠀⠈⢷⣦⣬⣏⠉⠛⠲⣮⣧⣁⣀⣀⠶⠞⢁⣀⣨⢶⢿⣧⠉⡼⠁ ⠀⠀⠈⢷⡀⠀⠀⠳⣌⡟⠻⠷⣶⣧⣀⣀⣹⣉⣉⣿⣉⣉⣇⣼⣾⣿⠀⡇⠀ ⠀⠀⠀⠈⢳⡄⠀⠀⠘⠳⣄⡀⡼⠈⠉⠛⡿⠿⠿⡿⠿⣿⢿⣿⣿⡇⠀⡇⠀ ⠀⠀⠀⠀⠀⠙⢦⣕⠠⣒⠌⡙⠓⠶⠤⣤⣧⣀⣸⣇⣴⣧⠾⠾⠋⠀⠀⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣭⣒⠩⠖⢠⣤⠄⠀⠀⠀⠀⠀⠠⠔⠁⡰⠀⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣀⣀⠉⠉⠀⠀⠀⠀⠀⠁⠀⣠⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠒⠲⠶⠤⠴⠒⠚⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⢀⣾⠿⠻⢶⣄⠀⠀⣠⣶⡿⠶⣄⣠⣾⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢻⣿⣿⡿⣿⠿⣿⡿⢼⣿⣿⡿⣿⣎⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠛⢛⣛⡉⠀⠀⠙⠛⠻⠛⠑⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⣤⣴⠿⠿⣷⣤⡤⠴⠖⠳⣄⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣀⣟⠻⢦⣀⡀⠀⠀⠀⠀⣀⡈⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠉⡇⠀⠀⠛⠛⠛⠋⠉⠉⠀⠀⠀⠹⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠑⠪⠷⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣦⣼⠛⢦⣤⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠲⠖⠛⠻⣿⡿⠛⠉⠉⠻⠷⣦⣽⠿⠿⠒⠚⠋⠉⠁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣾⠛⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀ ⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀ ⠀⠀⠀⣰⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀ ⠀⠀⠀⣿⡾⢿⣀⢀⣀⣦⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣫⣿⡿⠟⠻⠶⠀⠀⠀⠀⠀⢳⠀ ⠀⠀⢀⣿⣧⡾⣿⣿⣿⣿⣿⡷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⣧⠀⡀⠀⢀⣀⣀⢒⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⡾⠁⠙⣿⡈⠉⠙⣿⣿⣷⣬⡛⢿⣶⣶⣴⣶⣶⣶⣤⣤⠤⠾⣿⣿⣿⡿⠿⣿⠿⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣸⠃⠀⠀⢸⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⠟⡉⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⣿⠀⠀⢀⡏⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠉⠠⠿⠟⠻⠟⠋⠉⢿⣿⣦⡀⢰⡀⠀⠀⠀⠀⠀⠀⠁ ⢀⣿⡆⢀⡾⠀⠀⠀⠀⣾⠏⢿⣿⣿⣿⣯⣙⢷⡄⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣻⢿⣷⣀⣷⣄⠀⠀⠀⠀⢸⠀ ⢸⠃⠠⣼⠃⠀⠀⣠⣾⡟⠀⠈⢿⣿⡿⠿⣿⣿⡿⠿⠿⠿⠷⣄⠈⠿⠛⠻⠶⢶⣄⣀⣀⡠⠈⢛⡿⠃⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⡀ ⠟⠀⠀⢻⣶⣶⣾⣿⡟⠁⠀⠀⢸⣿⢅⠀⠈⣿⡇⠀⠀⠀⠀⠀⣷⠂⠀⠀⠀⠀⠐⠋⠉⠉⠀⢸⠁⠀⠀⠀⢻⣿⠛⠀⠀⠀⠀⢀⠇ ⠀⠀⠀⠀⠹⣿⣿⠋⠀⠀⠀⠀⢸⣧⠀⠰⡀⢸⣷⣤⣤⡄⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⢼⡇ ⠀⠀⠀⠀⠀⠙⢻⠄⠀⠀⠀⠀⣿⠉⠀⠀⠈⠓⢯⡉⠉⠉⢱⣶⠏⠙⠛⠚⠁⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠻⠄⠀⠀⠀⢀⣿⠀⢠⡄⠀⠀⠀⣁⠁⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢠⡇

⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⢻⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇ ⢸⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⢤⣶⠶⠶⢶⣶⡤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⢀⠇ ⠈⣇⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⢉⡴⠞⠋⣿⠀⠀⠀⡯⠙⠳⣦⡉⠙⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⣼⠀ ⠀⠹⣆⠀⠀⠈⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⢀⣰⠏⠀⠀⠀⢻⡄⠀⢰⠇⠀⠀⠈⢻⣄⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⣰⠃⠀ ⠀⠀⠹⣇⠀⠀⠀⠀⠉⠳⢦⣄⡀⠀⠀⠀⢀⡾⠃⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠉⠙⢷⣄⠀⠙⢧⡀⠀⠀⠀⢀⣠⡶⠛⠁⠀⠀⠀⠀⣴⠃⠀⠀ ⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢤⣿⣄⣀⣸⠋⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢹⣆⣀⣨⣷⡤⠶⠚⠋⠁⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀ ⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠈⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣼⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣧⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⡟⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⢀⡟⠀⡏⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⢿⡀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠉⢻⡶⢤⣀⡀⢀⡾⠁⣼⠃⠀⠀⠀⠀⠀⠀⣸⠹⣆⠀⠀⠀⠀⠀⠀⠹⣆⠘⢧⡀⢀⣠⡤⢶⡟⠉⢰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⣧⠀⢸⠃⠀⣨⠿⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⢸⡏⠀⣹⡆⠀⠀⠀⠀⠀⠀⠘⢦⣈⠛⢿⡅⠀⢸⡇⠀⡿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡕⣿⣧⣸⡀⠀⠛⡶⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣾⠃⠀⢸⣇⡼⡿⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠘⢯⡙⠷⣄⣸⠇⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠹⣄⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⢹⣆⣠⠞⣫⡿⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⢀⠙⢷⡘⣿⣷⡶⣄⠙⠷⣄⡀⠀⠀⠀⠘⠁⠀⠀⠀⠈⠃⠀⠀⠀⢀⣴⠞⢁⣤⢶⣾⡿⢡⡾⠋⡀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠸⣇⠈⣻⣷⣿⠳⣤⡈⠙⠓⠄⠀⠈⠳⡄⠀⣰⠛⠁⠀⠠⠞⠋⢀⣴⠟⣇⣿⡟⠀⣾⠀⠀⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠻⣾⠏⠸⣿⣦⡈⠛⠶⢤⣤⣤⣤⠴⡷⠶⣿⠦⣤⣤⣤⡤⠾⠋⢁⣼⣿⠁⠹⣶⠏⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⠀⣿⠀⠀⠘⠿⣿⣦⣤⢴⣿⡿⠃⠀⡷⠛⣦⠀⠘⢿⣷⠦⣤⣶⣿⠟⠁⠀⢀⡿⢀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠘⣷⣄⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⡇⠀⡟⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⣠⣾⠁⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣴⡏⢹⢷⣦⣄⡀⠀⣀⣤⡤⢤⡀⡧⠀⠇⢀⡤⢤⣤⡀⠀⣀⣠⣴⣿⡏⢻⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⣧⢸⡾⠁⣨⣿⡟⠙⢯⣀⠀⠀⠀⠀⠀⠀⢀⣀⡿⠉⢻⢿⡁⠘⣿⠃⡿⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡓⠶⠶⠿⡛⠥⠞⠉⢠⣿⣄⡀⠉⠉⠻⣦⣀⡴⠛⠉⠉⢀⣴⣿⡀⠙⠲⠬⣻⠷⠶⠶⢚⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⣀⣀⣠⣴⡋⢻⣿⡛⢳⠒⣤⠼⣿⠧⣤⢲⡞⢻⣿⠋⢹⡦⣄⣀⣀⣀⣤⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣆⠈⠛⣾⣿⣧⣿⠙⠛⠓⠛⠚⠛⢋⣇⡾⣿⣷⠋⠀⣼⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⣿⣿⣆⠙⠃⠀⠀⠀⠀⠀⠘⠋⣼⡿⣿⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡿⣮⡙⠛⣟⣻⣯⣯⣽⣟⣿⠛⢋⣴⣷⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⣏⠛⣋⣤⠶⠒⠶⣤⣙⠛⣹⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡉⠉⠉⠀⣠⣤⡄⠀⠉⠉⢁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠤⠞⠋⠀⠙⠶⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀ ⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀ ⠀⠀⠀⠈⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⢿⣿⣶⣦⠈⣿⡟⢻⡟⢻⣿⠁⣴⣶⣿⡿⠛⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣉⠛⠋⣠⡿⢀⣾⣷⡀⢿⣄⠙⠛⣉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣄⠀⣿⡉⢉⣉⣤⣾⣿⣿⣷⣤⣉⡉⢉⣿⠀⣠⣦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⠀⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠀⣿⡟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⡀⢹⣧⠈⠉⠛⠋⢁⡈⠙⠛⠉⠁⣼⡏⢀⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⠈⣿⣦⣀⡀⠄⢸⡇⠠⢀⣀⣴⣿⠁⣼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠀⠸⠿⣏⠀⢤⣾⣷⡤⠀⣹⠿⠇⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡤⠀⣀⣉⣉⣀⠀⢤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⠀⡀⢀⠀⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢶⣶⣶⡶⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠃⠀⠀⢀⡀⠤⠔⡢⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⠉⡀⠀⠀⡜⢀⡀⣠⠂⠁⠀⠈⡆⠠⠤⠄⠀⢠⣆⠀⠀⠀⠀⠀⠀⠀ ⠦⠔⢲⠧⠊⡕⣀⣠⡐⠀⡍⡄⠀⠀⠀⠃⠀⠀⠃⠀⣩⠋⢿⡄⠀⠀⠀⠀⠀⠀ ⡪⠷⠚⠉⠑⡿⠈⠻⣃⣃⡀⠀⡀⠰⠁⢀⠄⢄⡠⠊⠀⣰⠸⠀⡘⡄⠀⠀⠀⠀ ⠀⠊⠥⠀⡀⢱⠲⢄⠊⠀⠀⠑⡅⣥⠬⠀⠀⠀⠈⠢⡴⠁⠃⠀⢀⢄⠀⠀⢀⡠ ⠀⠐⠆⣀⠤⡫⠱⠁⠀⠀⢠⡳⣜⢦⠂⣧⡀⠀⠀⠀⠈⠪⡀⠀⠊⠤⠱⠖⠁⠠ ⠀⠉⠔⢐⡡⠋⠀⠀⠀⣠⢟⠈⠉⠋⠁⠈⣒⢄⠀⠀⠀⠀⠈⠐⠶⠍⠏⣁⡀⠀ ⠀⢴⠚⠉⠀⠀⠀⢀⣴⠚⠿⢳⠀⠀⠀⡼⠾⠚⢗⢠⢈⠂⠀⣀⠀⠠⠒⣿⣶⣟ ⠐⠒⢽⠆⣖⠄⠔⢈⢖⣒⣠⣢⠁⠀⠀⢠⣤⣒⣴⢇⡽⠙⠒⠬⢔⢦⡼⠈⠉⠙ ⠀⠀⣰⣦⣗⣸⢄⠀⡗⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢦⠃⠀⢜⡸⢊⢧⡀⠀⠀ ⠒⠈⢁⣀⣀⡠⠑⣄⠥⠀⠀⠠⡀⠀⠀⠠⠼⠀⠀⠀⣜⣠⠾⣳⢅⢪⡛⠂⠀⠀ ⠉⠙⢹⣒⣡⣤⡼⣿⣬⣶⣤⣄⡑⠀⠀⠐⣁⣠⣤⣞⡋⠄⠀⠁⠈⢞⢿⣄⠀⠀ ⣖⢺⢿⣿⡿⣙⡽⣼⣿⣿⣿⣈⢛⢻⣽⠟⣟⣷⣃⣟⣼⣶⣆⠀⠡⢻⣿⣿⠟⣱ ⠹⣯⠃⠸⡙⠛⠉⣾⣿⣻⢿⢟⢿⣷⣟⣿⣞⣫⢾⣿⡿⡿⠗⣖⡥⡒⠻⠯⡼⠃ ⣘⠆⠀⠀⣘⡀⠈⢉⢋⣻⣼⠟⠀⠙⡗⠉⠉⢿⣿⣞⡿⣶⡻⣷⡎⡇⠀⢠⡃⢀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣭⣷⣶⡦⠤⠿⠛⠒⠒⠠⠤⠸⢄⠀⢸⠦⠤⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠱⡈⢧⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠵⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⣂⠀⠀⠀⠀⠉⠒⢄⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠁⣀⡤⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠉⢳⡀⠀⠀⠀⠀⠀⠙⢦⣶⣾⣿⣿⣿⣭⣕⣦⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠻⣦⣤⣄⣀⡉⠉⠻⢷⣗ ⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡼⠁⠀⠀⠀⢠⠂⠀⢀⢞⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⡀⠀⢹⣿⠿⠟⠛⠓⠀⠀⠙ ⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⣰⠁⠀⠀⠀⢀⠇⠀⠀⣼⠆⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠐⠀⠀⣧⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠜⠀⠀⠀⢠⠃⠀⠀⠀⢀⡞⠀⠀⢰⡟⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠻⣷⣤⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⣠⣺⠁⠀⠀⢸⠛⣵⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣀⣼⣿⣿⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠠⡾⠋⠸⠁⢠⠀⢸⠀⣿⢇⠀⠀⠀⡇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡰⠁⠀⢸⠀⠀⠀⠘⡇⠸⡎⢢⠀⠀⢣⣰⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢿⣿⣿⣿⣿ ⠀⠀⠐⠁⠀⠀⠀⠘⠀⢢⣴⣁⡀⠢⢬⠀⠀⠀⠀⢱⡀⠘⣄⠑⢄⠘⡅⢸⡅⠉⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠹⣿⣿⣿ ⠀⣠⠃⠀⠀⠀⠀⠰⠶⣾⠟⢻⣿⣧⡈⣆⡀⠀⠀⠀⠳⢀⠌⠒⡴⠿⢿⣾⡇⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢱⠀⢿⣿⡇ ⠀⡼⠀⠀⠀⠀⠀⢰⡆⢻⠀⣿⣿⣿⡷⠘⡾⡀⠀⠀⣠⠾⣾⠿⣿⣶⣦⣹⣧⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢇⢸⣿⣇ ⠀⡇⠀⠀⠀⣷⠀⠸⣧⡏⠀⢡⡀⢹⠃⡸⠀⠳⡤⠚⡡⠚⠁⣼⣷⣾⣯⣿⣿⣖⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠈⢆⣇⠙ ⠀⢹⢸⠀⠀⣿⣇⠀⢿⡆⠀⠀⠀⠀⡰⢥⣴⠾⠒⠉⠀⠀⠰⣇⠸⠙⢿⣿⣿⢿⠞⠀⠀⠀⠀⡰⠂⠀⠀⠀⡇⠀⠀⠈⣎⠑⠂⠤⠽⣄ ⢇⠸⣾⡄⠀⣿⣿⣷⣌⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠉⠛⣡⠎⠀⠀⠀⢀⡜⠁⠀⠀⠀⡸⠹⣴⡀⠀⠈⢆⠀⠀⠀⠘ ⠸⡄⣿⣷⠀⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⡠⠊⠀⠀⣠⠃⢠⠃⠀⠹⡝⠢⣀⠀⠳⣄⠀⠀ ⠀⡇⣿⣿⣷⣄⢿⠉⠛⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⣀⠴⠊⠀⠀⢀⡴⠃⢠⠃⡇⠀⠀⠙⢆⡀⡏⠙⡟⠁⠀ ⠀⠃⢸⡿⠋⣸⣿⠷⣄⠀⠘⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡋⢀⣠⠔⠋⠁⠀⠀⢀⣴⠟⢁⡰⠁⢸⢡⠀⠀⠀⠀⣹⠇⠀⢻⢀⡴ ⡸⠀⢺⣇⡀⣿⡟⢧⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⣀⣠⡴⣯⣶⠟⣋⠴⠋⠀⣠⣿⠃⠀⠀⢠⣾⠃⡇⠀⣼⠟⠁ ⣓⡶⠴⠗⠭⢿⣇⠸⡆⠀⠀⠀⠀⠈⠳⣄⣀⣀⣀⣀⡄⣺⣯⠟⠉⠉⠉⠉⠠⠔⢚⡵⠋⢻⠳⣤⣞⣿⣡⣄⡼⠒⡡⠋⣺⠛⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢴⣷⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⠋⢰⡟⠁⠀⡔⠀⠀⠀⢀⣴⣿⠃⣠⣼⣦⡀⠀⠈⠁⠀⣠⠞⢁⠜⠁⠀⠠⣶⠤⠤ ⠀⠀⠀⠀⠀⠀⠀⢀⣸⠏⠀⢀⣾⣿⠤⠛⠻⢿⡟⢠⣾⠆⠀⣸⠇⠀⡠⠖⠁⢸⣧⡾⢋⣉⡙⢻⣿⣿⣿⠿⣿⣶⣷⣤⣤⣀⠀⢸⠒⠒ ⠒⠐⣚⡻⠿⠛⠉⠽⠁⣠⣴⠽⡿⠁⠀⢀⡴⠿⢧⠟⡎⠀⣶⣿⡶⠋⠀⠀⠀⣼⣿⣿⣾⣿⣿⡏⢹⣏⠁⠀⠙⢦⣴⡿⢋⡟⠀⠙⠛⠛ ⠀⢀⣠⠴⠒⠒⠋⠉⢉⡁⠤⠴⢅⣠⠎⢡⡼⠃⢸⢸⠀⠀⢻⠋⠀⡰⠠⠐⣈⣼⣋⣽⣿⡉⢥⣶⣧⡙⢧⡀⠀⢸⡇⢀⣞⣒⣲⣶⣶⣀ ⡄⡈⠁⢀⣠⠔⠒⠉⠁⠀⠀⠀⠀⠈⠀⠾⠒⠀⢸⣾⠀⠀⠘⣦⠞⠒⠈⠉⠀⢹⣿⣿⡿⠃⣸⠿⢿⡷⠌⢷⣀⣼⣧⠋⠈⠉⠉⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠘⣎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣉⠤⠒⠋⠙⣏⣿⠗⠊⠉⠉⠀⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣁⣤⣤⣤⡄⠘⠉⠀⠤⢄⣀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢊⢔⣪⣾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠑⠢⠤⠤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠄⠀⠀⠀⠀⠀⠀⢳⠤⠤⠖⢉⡰⣣⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠤⣀⡀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣎⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⣴⡟⣱⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⡀⢱⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣌⢢⡀⠀⠀⠀⠀⠀⠀⠀⣰⡽⣱⣿⡿⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⡇⣧⣿⡿⠁⠀⠀⠀⠇⠀⠀⠀⠀⡄⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠁⠲⡊⠁⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⣿⠿⠋⠀⢀⡠⠤⠲⣾⠀⠀⠀⠀⢃⠈⠉⡟⠙⢗⠒⢦⡄⠀⠀⠀⠀⠙⠦⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣶⣿⣿⡶⠋⠀⠀⠀⣴⣴⣁⣧⢠⠀⠀⠘⡄⣰⣿⣶⣬⣷⣤⡇⢠⠀⢀⡀⠀⠀⠈⠙⣲⠶⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⢯⣛⣀⣀⣀⣴⡿⢻⣿⣿⣾⣯⣧⠀⠀⠸⡟⣻⣿⣿⣿⡍⣿⡞⠀⢀⣿⡿⡆⠉⠙⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⠮⢄⣀⣤⠿⡇⠀⢿⠀⢈⣟⣻⡿⠃⡹⢷⣦⣀⡘⢧⠿⠿⠿⠃⣿⣡⠀⣼⣻⣠⠏⠒⠤⠬⠷⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣰⠳⡀⠸⣧⣀⠀⠀⠀⠾⠗⠋⠀⠀⠈⠉⠁⠠⢤⡾⠋⢁⠞⢻⠿⠛⢄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⢹⠒⠿⣯⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⣺⠁⠀⣼⠀⠀⠀⠑⢄⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⡄⠀⡇⠀⠯⢦⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣀⠴⡇⠀⠀⡟⡆⠀⠀⠀⠀⠓⠺⣹⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⠣⡀⢱⠀⠸⡀⠈⠓⠤⣀⡀⠀⠀⠀⣀⠔⠊⠁⢀⠃⠀⢸⠀⢃⠀⠀⠀⠀⢰⡞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠱⡀⠀⣴⣶⣿⣷⣶⣋⣀⣀⣀⡴⠋⠀⣠⣿⣷⣾⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡘⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣤⣾⣿⠿⠟⠻⡄⠀⠀⠀⣀⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠔⢫⡽⠯⣍⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠉⠁⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⣠⠔⣶⣤⣀⣸⣦⡀⡘⢠⠿⡝⣲⠇⠀⠀⠀⠀⠀ ⠖⣧⠘⢆⠓⣦⣿⣏⣓⠒⠦⠤⣀⣀⣀⣴⣎⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡜⠁⣼⠏⠀⣸⣿⣿⠟⠡⠃⠀⠘⢅⠀⠀⠀⠀⠀⠀ ⠳⡌⠳⣉⣻⡙⣿⡄⠈⠉⠙⠓⠲⢦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⠀⡔⠓⠀⡀⠀⠀⣀⣀⣤⣼⣄⠀⠀⠀⠀⠀ ⠳⢌⠢⢸⣿⠈⠻⠃⠀⠀⠀⠀⣠⠋⢼⡏⠉⠛⠛⠻⢿⠿⢿⣿⣿⣿⣿⣿⣿⡿⡄⠀⠹⢧⠡⣘⣒⣃⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀ ⣷⣄⠑⢄⡟⠀⠀⠀⠀⠀⢀⠜⠙⡄⢸⡇⠀⠀⠀⠀⢸⠀⠀⢱⢸⠀⢠⠃⡞⠀⠘⢄⠀⠀⠀⡰⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀ ⣿⣿⣷⣌⠷⠴⣒⠉⠉⠉⠛⡖⢤⣥⠘⡇⠀⠀⠀⠀⠀⡀⠀⠸⡈⣄⡎⡜⠀⠀⠀⠀⢹⠆⡖⠁⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀ ⣿⡿⠋⠁⠀⠀⠀⠀⠀⠑⠀⠐⢆⠉⠲⡇⠀⠀⠀⠀⠀⡇⠀⠀⣇⡟⢰⠁⠀⢰⠦⠔⢊⡀⢣⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⢦⠀⠀⠀⠀⢀⠔⠛⢢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠛⡙⣄⠀⠀⠱⣄⡠⠖⠁⠀⡴⠋⡰⠋⠉⠒⠢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢀⣀⠠⠼⠚⢢⡀⠀⠈⠀⢀⡰⠮⠤⣚⡓⠒⠤⠤⣀⡀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠼⣿⣤⠤⠔⠒⠉⠉⢦⣀⡠⠋⠀⢄⠀⠀⠈⠉⠒⢤⣠⣽⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⢠⠋⢀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⡼⠀⠀⠀⠀⣸⡄⠀⠀⠀⠲⣄⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⡰⠃⠀⠀⠀⠀⠀⠀⣼⠀⠀⡇⠀⠀⠀⠀⡁⢱⠀⠀⠀⠀⠈⠣⡀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⡰⠁⠀⠀⠀⠀⠀⢠⢾⡇⠀⢰⠁⠀⠀⠀⠀⡇⢸⣧⠀⠀⠀⠀⠀⠹⡄⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡾⠀⢰⠃⠀⠀⠀⠀⠀⣰⢃⠾⡇⠀⡜⠀⠀⠀⠀⢰⠀⣼⠀⢣⠀⠀⢀⠀⠀⠘⡄⠀⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡗⢀⡇⠀⠀⠀⡘⠀⢰⣧⠊⠀⡇⢠⡇⠀⠀⠀⠀⡇⢠⠋⢆⠀⢇⠀⣸⣦⣀⠀⢣⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡼⠁⡸⠀⠀⠀⠀⡇⢠⡿⠛⠊⠉⣏⣹⡇⠀⠀⠀⡜⢰⠟⠒⠚⢦⣼⣿⣿⣿⣿⠃⠈⡆⠈⠛⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠊⠀⠀⡇⠀⠀⠀⢰⣀⢿⣤⣶⣶⣿⣿⠛⡇⠀⢀⣼⡿⠃⣴⣶⣶⣤⣵⣼⡆⣿⡟⠀⠀⢼⠀⠀⠀⠑⠦⡀⠀⠀ ⣀⣠⠤⠊⠀⠀⠀⣸⠀⠀⠀⠀⣿⣿⣼⣿⣿⣿⣿⣿⠿⣇⡠⠞⠉⠀⠼⣿⣿⣿⣿⢿⣯⣷⣿⠀⠀⠀⠈⡇⠀⠀⠀⠀⠈⣱⠆ ⠉⠛⠤⣀⣀⣀⣾⡏⠀⠀⠀⠀⣿⡟⠉⠀⣿⣯⣽⣿⠀⠉⠀⠀⠀⠀⠈⣿⣯⣽⣿⠀⠉⣻⣿⠀⠀⠀⠀⢸⣖⣀⣠⠤⠊⠀⠀ ⠀⠀⠀⠀⣠⠞⢰⠇⠀⠀⠀⠀⢹⣿⠀⠀⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠂⢠⣿⣿⠀⠀⠀⠀⠀⡇⠙⡄⠀⠀⠀⠀ ⠀⠀⠐⠻⡷⠷⣿⠁⠀⠀⠀⠀⠸⡏⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢻⣷⠀⠀⠀⠀⢰⡇⠀⠘⡄⠀⠀⠀ ⠀⠀⠀⢸⠁⢸⡿⠀⠀⠀⠀⢀⠀⠇⠈⢆⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⢀⡞⠀⣼⢸⠀⠀⡀⠀⠀⣧⠀⠀⢸⡀⠀⠀ ⠀⠀⠀⢸⡀⡼⣷⠀⠀⠀⠀⣼⢤⢸⡀⢀⣹⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣏⠀⢀⠇⡸⠀⠀⡇⠀⠀⡼⢣⠀⣸⠃⠀⠀ ⠀⠀⠀⠈⢿⡇⡇⠀⠀⠀⠀⡇⠘⡄⢷⣿⠻⣟⠙⠻⠷⣦⣤⣤⠤⢲⡾⠟⠛⣿⣿⣷⠎⢠⠃⠀⢰⡇⠀⠀⡇⢸⣤⠋⠀⠀⠀ ⠀⠀⠀⠀⢸⡇⢳⠀⠀⠀⠀⡁⠀⢣⠘⣿⣆⢻⣇⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⢈⣿⠏⡠⠋⠀⠀⣸⡇⠀⢠⣧⠞⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⣇⠸⡀⠀⠀⠀⢷⠀⠀⣧⡈⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢷⡾⠁⠀⠀⣠⠃⡇⢠⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡄⢳⡀⠀⠀⢸⠀⠀⢻⣿⣾⣿⣿⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣥⡤⠔⠊⣽⡾⠳⡅⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⣿⣿⣆⣿⠀⠀⠘⣧⠀⠈⣿⣇⡽⠟⠁⢠⣿⣀⣀⣀⣤⣀⣀⡤⠾⠛⠉⠀⠀⠀⢡⠤⠀⠼⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠿⣿⣿⣿⣷⣶⣶⣾⣦⣀⢸⣿⠀⠀⢀⣾⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢀⣠⠼⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⠟⠁⠀⠈⠛⣿⣿⠟⢿⠄⠀⣻⠏⠀⠀⠀⠀⠀⠀⣠⠒⠤⠤⠤⠤⠔⣁⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⣿⡆⠀⠀⣀⣀⡤⢾⡏⠀⠀⠀⣰⠟⠢⠄⣀⣀⡀⠴⠊⠀⠀⣀⡠⠤⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⢸⣧⣖⣠⠞⠋⠒⠒⠒⠒⠒⠒⠒⠒⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢸⣦⡀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣏⠻⣶⣤⡶⢾⡿⠁⠀⢠⣄⡀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⣀⣼⠷⠀⠀⠁⢀⣿⠃⠀⠀⢀⣿⣿⣿⣇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠴⣾⣯⣅⣀⠀⠀⠀⠈⢻⣦⡀⠒⠻⠿⣿⡿⠿⠓⠂⠀⠀⢂⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢻⡇⣤⣾⣿⣷⣿⣿⣤⠀⠀⣿⠁⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣿⡿⠏⠀⢀⠀⠀⠿⣶⣤⣤⣤⣄⣀⣴⣿⡿⢻⣿⡆⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠟⠁⠀⢀⣼⠀⠀⠀⠹⣿⣟⠿⠿⠿⡿⠋⠀⠘⣿⣇⠀⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⣶⣶⣿⣿⣇⣀⠀⠀⠙⣿⣆⠀⠀⠀⠀⠀⠀⠛⠿⣿⣦⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⠿⠋⠁⠀⣹⣿⠳⠀⠀⠀⠀⠀⠀⢀⣠⣽⣿⡿⠟⠃ ⠀⠀⠀⠈⠀⢰⠿⠛⠻⢿⡇⠀⠀⠀⣰⣿⠏⠀⠀⢀⠀⠀⠁⣾⣿⠟⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⣰⣿⣿⣾⣿⠿⢿⣷⣀⢀⣿⡇⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠙⢿⣿⣿⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀ 𐙚 -`♡´-˙✧˖°📷 ༘ ⋆｡˚˙✧˖°📷 ༘ ⋆｡˚˚˖𓍢ִ໋🌷͙֒✧˚.🎀༘⋆˚‧｡⋆🌻⋆｡‧˚⛷🧚‍♀️🛖

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣴⣦⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡄⠀⢿⠀⠘⠃⠀⢼⡏⢸⡷⠀⠘⠃⠀⡿⠀⢠⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⢲⣆⠀⠋⠀⣠⡴⠶⠖⠛⠛⠛⠛⠛⠛⠳⠶⢦⣤⡀⠘⠁⢠⡶⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣴⣾⡿⢻⡟⢻⡟⢿⣿⣶⣤⡼⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠉⠁⢾⡃⢘⣷⠈⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠈⢻⡾⠁⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⣶⡀⠀⠀⢠⡀⠀⢀⣄⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀ ⠰⣶⣤⠶⠞⠃⠀⢀⣤⠄⢸⡟⢷⡀⠀⢸⡿⣦⡀⠉⠁⣄⡀⠀⠈⠻⠶⣤⣴⠆ ⠀⠈⠙⢻⡟⠛⠃⠈⠁⠀⣿⣀⡈⠛⢶⣤⣿⣌⣻⣦⡀⠈⠙⠛⠛⢻⡟⠋⠁⠀ ⠀⠀⠀⣸⡇⠀⠀⠀⠀⢸⣿⠋⢻⡆⠀⠀⠉⣿⠉⣿⣧⠀⠀⠀⠀⠘⣷⠀⠀⠀ ⠀⠀⠀⣿⠀⢰⡇⠀⠀⣿⠙⠳⠞⣡⣤⣤⣤⠛⠶⠋⣿⠀⠀⢸⡇⠀⢿⡄⠀⠀ ⠀⠀⠀⣿⠀⠘⣧⠀⠀⢻⣆⠀⠀⢻⣄⣠⡿⠀⠀⢠⡿⠀⠀⣸⡇⠀⣸⠇⠀⠀ ⠀⠀⠀⠹⣆⠀⠹⣦⣀⠀⠙⣷⣶⣤⣀⣀⣠⣴⣾⠛⠁⣀⣴⠟⠀⣠⡟⠀⠀⠀ ⠀⠀⠀⠀⠙⠷⣤⣀⡙⠿⣿⣭⡅⠀⠉⠋⠁⢀⣭⣿⠿⠋⣁⣠⡾⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣿⣷⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠈⠻⠿⣟⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⠭⠿⢷⣶⣷⣶⣶⣶⣯⣭⣖⣲⢤⣀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠗⠋⠉⢀⣐⡿⢾⣶⣶⣶⣮⣟⡿⣿⣿⣿⣿⣷⣿⣶⣤⡀⠀⠈⢻⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣾⡟⠀⢀⣀⣤⣤⣤⣭⣛⣿⣾⣿⣿⣿⣿⣿⣷⣝⡻⣿⣿⣿⣿⣿⣿⣗⡶⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⣼⣿⣷⣄⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣝⢿⣿⣿⣿⣿⣿⣮⡻⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣾⣟⣼⣿⣿⣿⣿⣿⣶⣬⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⣿⣿⣿⣿⣿⣿⣌⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣄⣀⠀⢀⣴⣾⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣦⡘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⣿⡿⣿⣿⣾⣿⣿⢣⣿⣿⣿⣿⣷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣆⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⠻⢿⢇⣸⣿⣿⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⣷⣝⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⣿⣭⠛⠃⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣾⣿⣦⣤⣀⡀⠀⠀⠀⠀ ⠀⠸⣿⣿⣿⣿⡿⠋⠀⠀⢀⡇⣿⣿⣿⣿⢸⣿⣿⣿⣷⡹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣏⣟⣿⣿⣿⣆⠉⠁⠀⠀⠀⠀⠀ ⠀⢀⣼⣿⣿⣷⣤⡀⠀⠀⢸⡇⢻⣿⣿⣿⡿⣿⣿⣿⣿⣷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣟⢿⣿⣜⣻⣇⠸⣿⣿⣿⣿⡹⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀ ⠀⣼⣿⣿⣿⣿⡿⠁⠀⠀⢸⢇⠀⠛⢿⣿⡿⠉⠛⢻⣿⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠈⣩⡿⠿⢿⣍⠙⠛⢿⣿⣿⣿⣿⣧⢺⣿⣿⡘⣿⠀⠀⠀⠀⠀⠀ ⠀⠹⢿⣿⣿⣿⣿⣿⡆⠀⣸⢸⠀⢀⣤⣿⠃⠀⠀⠈⢹⣴⣿⣇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣛⡿⠋⢸⡿⢠⡶⢧⣤⣆⠀⠈⣿⣿⣿⣿⣿⣾⢸⣿⡇⠸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⣿⣿⣿⣿⣷⣶⡏⢸⢸⣸⣿⣿⣦⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⢺⠿⣿⡷⡄⢳⣿⡆⠀⠘⣿⣿⣿⣿⣿⠘⡟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢰⡾⡀⣇⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⡇⠀⠀⠈⠙⢿⣿⣿⣷⣿⠟⠁⠀⠀⠀⠀⠈⠀⠙⠯⢤⣀⣩⠕⠈⠀⣿⢿⣿⣿⣿⡗⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⢸⣇⣷⠸⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣠⣴⣶⣶⣾⣯⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣿⢸⢿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⠿⡼⣦⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⠟⡟⠧⣰⠚⣯⣯⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⣼⠀⢀⡤⠴⢶⡀⠀⠀⠀⠀⠆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠹⣿⣦⢿⣿⣿⣿⣿⣷⠻⣿⣿⣿⠃⠀⠹⣿⠛⠦⠽⠿⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⣿⠞⠁⠀⠀⠸⡇⠀⠀⠀⠰⠀⠢ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢹⣿⣎⢿⣿⣿⣿⣿⣷⣜⢿⣿⣦⠀⠀⠙⠓⠤⠤⡤⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡰⠋⢹⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⢣⠀⠀⠀⡄⠀⡜ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⢻⣿⣮⢿⣿⣿⣿⣿⣿⣷⣶⣝⠻⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠗⠉⠀⠀⠈⡆⠀⠀⠀⢀⡾⢶⣴⣀⡄⠀⠀⠈⢳⣦⣰⢁⡴⠂ ⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⢻⣿⠋⠻⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣏⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⢀⣾⡁⠀⠈⠉⠀⠀⠀⠀⠀⣿⣿⠏⠀⠀ ⠘⢿⣅⠉⠳⣄⠀⠀⠀⠀⠀⠀⠙⠀⢀⡿⠻⣧⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠦⠤⠄⠀⠀⠀⠀⠀⠈⠑⠢⠤⠤⠤⠞⠁⠀⠀⢠⡞⣈⣿⠦⢤⣀⣀⣀⣀⣀⡼⢻⣿⣦⡄⠀ ⠀⠀⠙⢷⡄⠈⠓⣆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⢷⣄⠈⠻⣿⡛⠿⢿⣿⣿⣿⣿⡷⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣯⣾⣿⣿⣷⡀⠉⠓⣢⡴⠋⠀⠠⡻⣿⣿⣠ ⠀⠀⠀⠀⠙⢦⡀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠈⠻⢦⣄⠈⠉⠛⠛⠀⠈⠙⢲⣤⣤⣀⣀⣀⣀⣀⣠⣤⣤⣤⡤⠞⣳⣿⣿⣿⣿⣿⣿⣿⠛⠉⠀⠀⠀⠀⠀⠙⢿⣿ ⠀⠀⠀⠀⠀⠀⠱⣄⠀⠘⢦⡀⠀⣀⡀⠀⢀⣠⡀⠀⠀⠉⠳⠄⠀⠀⠉⠁⠀⠀⠀⢀⡴⠋⠀⠁⠀⣿⠃⠀⠈⣷⣶⣶⣶⣶⣶⣿⡿⢾⣿⣿⣟⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻ ⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⣠⡷⠞⠁⠉⢳⣏⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣼⣿⡷⠛⠉⠀⠀⠀⢈⣻⡿⢿⣿⣖⣚⣛⣋⣛⣛⣛⠒⣾⢶ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣇⣠⠔⠒⢦⡙⢦⡀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⣿⣦⡀⠀⠀⠀⠀⡼⢹⣠⣿⠁⠀⠀⠀⠀⠀⣼⣷⣻⡁⠀⠀⠀⠀⠀⣾⣿⣿⠏⢩⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣤⠔⠲⡄⠱⡄⣱⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠃⠀⢹⣿⣿⣶⠒⠒⠚⠛⠉⠁⢿⣦⣤⣤⣤⣴⣾⣿⣿⣷⣳⡀⠀⠀⣀⣼⣿⣿⠏⢰⣿⣿ ⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⡿⠿⠷⠤⢤⣽⣄⣹⣿⣿⣷⡀⠀⠀⠀⠀⢀⡴⢺⡟⣡⠔⠚⢿⣿⣿⣿⡆⠀⠀⠀⠀⣠⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣼⣿⣻⢋⡏⠀⣿⣿⣿ ⠀⢀⣀⡴⠞⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⢿⣿⡆⢀⣠⠞⠉⢀⣾⡟⠁⠀⠀⠈⣙⣿⣿⣧⡄⠀⢀⣴⣿⠋⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⠟⣿⣿⠁⣴⣿⣿⣿ ⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⣰⠏⡏⠀⠀⠀⠀⠸⣿⣿⣿⡿⠇⣰⢟⠿⠁⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣁⣤⠿⣯⣀⣿⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣃⣸⠁⠀⠀⠀⠀⠀⠈⣻⣿⣧⡼⠋⠋⢀⣀⣤⢤⣴⣻⣿⣿⣿⣿⣿⣿⠟⠛⢩⣰⠈⢆⠀⢻⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢀⣀⣀⣠⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠛⠋⠉⠉⠛⣷⡄ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⢀⣀⡤⣤⢤⡤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⣀⣤⣶⠿⠛⠋⠁⠁⠀⠀⠀⠉⠛⣯⣳⡀⠀⠀⠀⠀⠀⠀⢠⡿⠃ ⠀⣠⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡻⣿⠀⠀⠀⠀⠀⣠⡿⠃⠀ ⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⢹⡆⠀⠀⢸⣿⠀⠀⠀⠀⢠⡿⠁⠀⠀ ⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⠀⢀⣮⠏⠀⠀⠀⠀⠘⣷⡀⠀⠀ ⠀⠙⠿⣶⣤⣀⠀⠀⠀⠀⠈⠻⢦⣤⣤⣤⡶⠟⠁⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀ ⠀⠀⠀⠀⠉⠛⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⣤⣤⣄⣀⣀⣤⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠈⠉⠉⠙⠛⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀ ⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀ ⠀⡏⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢻⡇ ⠀⡧⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⢸⡇ ⠀⣿⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⣾⠁ ⠀⢿⡷⡀⠀⠹⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⢀⣤⣿⠀ ⠀⠘⣧⢳⡀⠀⠈⠻⢷⣤⡀⠀⠀⠀⠀⠀⢲⣦⣴⣞⡛⠳⠶⠞⢛⣳⣤⣤⡖⠀⠀⠀⠀⠀⢀⣠⡾⠟⠁⠀⢀⡞⣼⠇⠀ ⠀⠀⠹⣷⢿⡄⠀⠀⠀⠙⠿⣶⣤⣤⣶⣦⣾⣇⡀⠉⠙⢦⠀⠰⠋⠉⢀⡘⣿⣦⣶⣦⣤⣴⠿⠋⠁⠀⠀⢠⡾⣸⡏⠀⠀ ⠀⠀⠀⠹⣮⢿⣆⠀⠀⠀⠀⠈⢻⣿⣿⡉⠙⠷⡝⣷⣤⠀⣷⠀⢤⣾⣻⡿⠋⢉⣿⣿⡟⠁⠀⠀⠀⠀⣠⡿⣱⠟⠀⠀⠀ ⠀⠀⠀⠀⠹⣷⣻⣧⡀⢀⣀⡴⣿⠃⠈⠙⠂⠀⠙⠾⣷⣾⣿⣷⣾⣿⡏⠀⠀⠋⠁⠘⣧⠳⣄⡀⢀⣴⢟⣽⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⢷⣟⠻⠿⢋⣴⢃⣠⡄⠀⠀⠰⣧⣤⡿⣈⣿⣁⢻⣦⣸⠆⠀⠀⠀⣄⡘⢧⡙⠿⠟⣫⡾⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣿⠛⠛⢛⡟⡿⢧⣠⣾⠋⢀⣠⡽⠔⠙⣿⠋⠠⢯⣀⡀⠘⣷⢄⡼⢯⢳⡙⠟⠛⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⡾⢸⠁⡼⢽⠋⣽⡿⠛⠓⣦⠀⠛⠀⣤⠚⠛⢯⣯⠙⡏⢧⠈⡇⢻⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⣇⠘⣶⠃⢾⢸⢹⠁⡴⠛⠛⢷⢀⡴⠛⠛⢦⠈⣷⡇⣹⠘⣷⠇⢸⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢙⣦⣼⡄⠘⢿⡘⣆⣧⡄⠀⣸⣿⣇⠀⢀⣼⣡⢏⡷⠃⢠⣧⢴⡋⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⣼⣱⣿⣿⣦⣤⣷⣤⣭⣤⣾⣷⠿⣾⣷⣤⣬⣤⣾⣥⣤⣾⣿⡞⣧⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠐⣿⣿⣁⡀⢻⡘⢿⣿⣿⣿⣿⣿⠿⠻⡏⠁⠀⠈⢹⡟⠻⣿⢿⣿⣿⣿⡿⢃⡿⠀⣀⣿⣷⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⣷⠈⠹⣾⠉⠓⠺⠟⠛⣫⢵⡿⢾⡇⠀⠀⠀⢘⡷⢶⡬⣝⡛⠻⠟⠚⠋⣷⠟⠁⣾⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⠀⣤⠏⠀⠀⠀⢀⡾⠁⠘⣧⡀⠁⠀⠀⠀⠈⢀⣸⠇⢈⢻⡄⠀⠀⠀⠹⣄⠀⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⣟⠀⢼⡿⠦⣤⣄⣨⣿⡉⠛⠲⣽⣆⠀⠀⠀⣰⣿⠾⠛⠻⣿⣇⣠⣤⠴⢾⣧⠀⣻⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⣆⠈⢳⣹⡗⣿⡿⣤⢷⣦⣤⣄⣿⣿⠿⣿⣟⣡⣤⡴⣶⣤⢿⣿⣻⣟⡿⠁⣰⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⣿⣾⡟⢀⣿⡟⢰⡇⠀⡏⠙⣶⠋⢻⠁⢸⡇⢻⣿⡀⢻⣧⢿⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾⣷⠟⢀⣾⠃⣠⡟⣿⣿⡷⠶⣿⠶⢾⣿⣿⠻⣄⡙⣷⡀⠻⣏⢷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠛⠁⣠⣾⣿⣿⣿⣴⣿⣴⣿⣶⣿⣷⣾⣧⢼⣇⣿⣿⣿⣿⣄⠈⠓⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡠⠞⠁⢀⡤⡞⠁⣿⢹⣿⣫⡷⠛⠉⠉⠉⠉⠉⠉⠉⠛⠾⣽⣿⣟⣿⠀⢳⢦⡀⠈⠳⢤⡀⠀⠀⠀⠀⠀ ⢀⣀⣤⣴⣚⣁⠤⠴⠚⠁⠀⣇⠀⣿⡺⣿⣽⠀⣠⡶⡟⠛⠛⠛⢻⢶⣄⠀⣿⣿⢗⣿⠀⢸⠀⠈⠛⠢⠤⣌⣛⣢⣤⣀⡀ ⠀⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⣿⣄⡈⠻⣾⡟⢰⣏⡞⠁⠀⠀⠀⠈⢳⡽⣆⢻⣷⠟⢁⣠⣿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢻⠀⠈⣠⢟⡼⠀⠀⠀⠀⠀⠀⠀⢣⡹⣆⠁⠀⡿⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠯⠤⢾⣀⣴⣯⣞⢁⠀⠀⠀⡀⠀⠀⠀⠈⣳⡝⢧⣄⣿⠤⠽⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠁⠉⠲⢮⣭⣥⣾⣿⣿⣿⣷⣦⣭⡭⠖⠋⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡀⠀⢀⣀⢀⡀⣀⡀⡀⢀⠀⡀⠀⠀⡀⢀⠀⣀⡀⠀⠀⠀⡄⠤⢀⡀⣠⢀⢤⣠⣄⡤⠀⡄⠠⢀⠀⠀⠀⠀ ⠀⠀⠀⠀⠊⠙⠓⠙⠘⠚⠛⠓⠓⠓⠓⠛⠒⠛⠒⠓⠐⠊⠋⠈⠈⠁⠒⠒⠒⠚⠒⠒⠁⠋⠈⠁⠚⠉⠁⠀⠀⠃⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠰⣿⣭⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠛⠋⠉⠉⠉⠉⠉⠉⠛⢳⡶⣿⣾⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣼⣧⡟⣼⢋⣥⠶⠲⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⠈⠉⠻⠦⣤⣀⣀⣀⣶⣿⣷⣟⠋⠙⠳⢦⣄⡀⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣩⡿⠶⠶⠖⠲⠿⠿⠿⣿⣻⣿⣿⣦⣄⣀⠀⠈⠛⢶⣄⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠈⠉⠙⠛⠿⣿⣛⠛⠋⠻⠄⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⡀⠀⠀⠀⣀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⡶⠶⠶⠶⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⡍⠙⠛⠛⠋⠉⠁⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢷⣄⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣭⣍⣹⡏⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠂⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢙⣷⠀⠀⠀⣰⢟⣵⣿⣥⡀⠀⠀⠈⠻⣧⠀⠀⠀⠀⠀⠀⣠⠞⣿⠀⠀⠀⠀⠀⠀⢀⣧⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡟⠁⠀⢀⣼⠋⣼⣿⣿⣿⣷⠀⠀⠀⠀⠘⣇⠀⠀⠀⢠⡾⠁⣀⣽⣦⣤⣀⡀⠀⢠⣾⠿⣧⣀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀ ⠀⢰⡟⠀⠀⢠⡾⠁⠀⢿⡛⠛⠛⠁⠀⠀⠀⠀⢠⣯⠀⠀⣰⠏⣰⣟⣉⡀⠀⠀⠈⠻⣶⣿⡛⠀⠈⣿⣷⠖⠀⠙⢷⣄⠀⠀⠀⠀ ⢠⡟⠀⢀⡠⠟⠀⠀⠀⠈⠻⣤⡀⠀⠀⠀⢀⣴⠟⠹⣆⢠⡏⢠⣿⣿⣿⣿⡆⠀⠀⠀⢹⡏⠻⣷⣶⡟⠁⠀⠀⠀⠀⠈⣻⡆⠀⠀ ⣼⠃⠀⠘⣤⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⣛⠉⠀⠀⠀⠙⢿⣇⠘⣟⠛⠟⠋⠀⠀⠀⠀⢰⣧⡀⠘⣿⠀⠀⠀⠀⢠⣤⠾⠋⠀⠀⠀ ⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣦⣤⣤⣤⡄⠀⠀⢀⠙⢦⣄⡀⠀⠀⣀⣴⣟⢸⡇⠀⠀⠀⠀⢿⠀⠈⢷⣄⠀⠀⠀⠀ ⢿⡀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠛⠋⠉⠉⠛⠛⢾⡟⠁⠀⠈⠉⠛⠋⠉⠀⠙⢿⡇⠀⠀⠀⠀⢸⡇⠀⠀⠉⠳⠶⣤⡀ ⠘⢷⣀⣤⠘⢷⣄⡀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⡾⠁ ⠀⠈⠛⠿⣦⡀⠈⣿⣶⣤⣀⠀⠈⠓⠦⣀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀ ⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣟⣻⣶⣦⣤⣀⡉⠑⠒⠦⠤⠴⠟⠀⠀⠀⠀⠀⠀⠀⠀⣴⣏⠀⠀⠀⠀⠀⠀⢸⡇⣿⣄⠀⢀⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⢿⣟⡙⣛⣿⣿⣿⢟⣿⣿⠶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⣾⣿⣟⣿⢀⡾⠃⠀⠀ ⠀⠀⠀⠀⠀⢠⡾⠃⣼⠈⢿⣿⣯⣡⣾⡿⢻⡿⠀⢺⡟⠻⢿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⠛⣿⣫⣥⣤⠀⠀ ⠀⠀⢰⡟⢷⣯⣤⣴⡇⠀⠀⠈⠉⠉⠁⣴⣿⡁⢠⣾⡷⣶⣶⠻⢿⣦⣄⡉⠓⠶⠤⠴⢶⡾⠃⢀⣠⣾⣿⣷⣾⣿⣛⣉⣉⣿⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠒⠒⠒⠤⡼⣷⣿⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠤⣖⡒⠒⢒⣷⣹⠴⣖⡓⠢⢄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣈⡵⠶⠒⠛⠫⠿⣻⢿⣤⣀⣉⣲⣄⡈⠲⡀⠀⠀⠀⠀ ⠀⡀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⠥⠤⠟⠀⠀⠀⠀ ⠀⢏⠉⠉⠉⠀⢀⣠⢤⡤⠤⡆⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀ ⠀⠈⣳⠀⠀⡴⣿⣯⡉⠉⠙⢇⠀⠀⠀⡠⢺⠁⠀⠀⠀⣆⠀⠘⣆⠀⠀⠀⠀ ⠀⡴⠁⢀⠞⠸⡿⠿⠃⠀⠀⢸⠀⢀⠞⣴⡚⠋⠒⢤⣾⠉⢳⡤⠘⢦⡀⠀⠀ ⢰⠁⡄⠊⠀⠀⠙⠦⣀⣠⠔⠋⢧⡞⢸⣿⡿⠂⠀⠘⡍⢳⡟⠀⠀⣀⣨⠇⠀ ⢜⠀⢸⠀⠀⠀⠀⠀⠀⣹⣤⣤⣄⣉⣈⠢⣀⣀⣠⢼⣹⠀⠁⠰⡄⠻⣄⠀⠀ ⠸⣄⡘⢦⡀⠀⠀⠀⡞⠉⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⢟⠀⠀⠀⡇⠀⠀⢉⠇ ⠀⠈⠛⠤⣹⣶⣤⣌⡑⠢⠄⣀⣀⣰⠃⠀⠀⠀⠀⡰⠁⠀⠀⠀⡇⡀⠀⡇⠀ ⠀⠀⠀⠀⣠⠻⣛⣻⡿⣿⣶⠶⣤⣤⣄⣀⣀⣀⣼⠟⠀⠀⠀⢰⣿⣻⣠⠃⠀ ⠀⢀⠤⣜⣁⠇⠙⠛⠚⣩⡟⣨⣧⣭⠿⣟⡙⠭⠀⠤⡤⢀⣰⣿⣭⣽⣒⣷⠀

⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡏⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣸⠁⠀⡇⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⢠⡇⠀⢠⠇⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡿⡄⠀⠀⠀⡸⠀⠀⢸⣀⡼⠁⠀⠀⠀⠀⠀⠀⢀⣠⡶⠚⠋⠉⠁⠀⠀⠀⠀⠀⠉⠙⠲⢦⣀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠹⡄⠀⠀⡇⠀⠀⢻⠟⠀⣀⡠⣄⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠘⢦⡀⡇⠀⠀⠘⡦⠊⠀⢠⠏⢠⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀ ⠸⡄⠀⠀⠙⢿⣤⣀⣀⡇⠀⠀⡾⠒⠛⢳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠙⣦⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢦⡀⠀⠀⠹⠷⣈⠑⠢⠤⠧⣤⠚⠁⠀⠀⠀⣠⡴⠶⠒⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠓⠲⠦⣤⣈⣧⠀⡼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠲⢤⣤⠖⠛⠓⣒⠀⠀⠈⢣⡀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⡁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣤⡾⠁⠀⣀⣠⡇⠀⠀⠀⠀⣇⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀ ⠀⢀⡼⠋⢰⠃⡤⠊⡏⠀⣳⣄⣀⣤⠤⠾⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⠀⣾⠁⠀⠈⠟⣇⠀⢣⣀⣿⡆⠀⣼⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡷⣆⠀⠀⠀⠀⠀ ⢠⡏⠀⠀⠀⠀⠈⠓⠒⣿⣿⡀⢀⡿⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣧⠛⢳⡀⠀⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⢀⣿⡏⠛⢹⠇⠀⠀⠀⠀⠀⠀⠙⠓⠦⠤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡤⠤⠖⠛⠁⠀⠀⣿⣆⡈⢹⣤⠀⠀ ⢸⠁⠀⠀⠀⠀⠀⢀⡞⠉⠁⢾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢏⣈⢀⣇⠀ ⢸⡄⠀⠀⠀⠀⣠⡞⠃⢰⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠘⢏⡀⠈⣷ ⢸⡇⠀⠀⢀⣼⠉⠡⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠘⣏⠀⢹ ⠀⣧⠀⠀⢺⠀⢲⡞⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡏⠀⢻ ⠀⠻⣦⣴⣾⣶⠋⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡟⠁⢰⣿ ⠀⣴⣋⠁⠈⠹⡄⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠙⠰⡏⠀ ⠀⠿⢻⡀⢠⠶⠧⣤⣼⣧⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣴⠿⡇⢀⢾⡇⠀ ⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠓⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣀⢠⣀⣀⣠⣀⡤⠤⡄⡄⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⣿⣿⣿⣹⠿⣿⡏⠋⡿⠟⡿⠇⢖⣯⣿⣯⢿⣏⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⢱⡄⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠋⢉⣩⠿⠿⣶⠒⣿⣼⡤⠤⠤⠤⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣡⠴⠋⠁⠀⠀⠀⠸⣆⣿⠋⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⣠⠴⣲⣲⠶⠦⠀⠈⠀⠠⠤⠤⠤⢄⡀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣡⠔⢋⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠉⠳⠤⣀⣀⠴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⢰⣆⡀⠀⣠⡴⠚⢁⡞⣡⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡉⠉⠁⢠⣶⢏⣴⣿⣿⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠈⠉⠳⣎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣶⣳⠃⣾⣿⣿⠃⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠤⣀⣀⣸⡤⢴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⡇⣼⣿⣿⠃⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠚⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣸⢱⣿⣿⠟⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠤⡤⠔⠊⠉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣇⣿⣿⣿⠋⠀⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⠘⡄⠀⣤⣤⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠘⣶⡿⠟⠋⣀⡀⢀⡴⠖⠋⠉⣿⢧⠀⠀⠀⠀⠀⢻⠀⠀⢰⡏⠈⠳⡀⠉⠙⡶⠄⠀⠀⠀⠀⠀⠀⠙⢦⣀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠁⠀⠀⠀⠀⠸⣿⣾⣿⣿⣿⠟⠁⠀⠀⠀⢀⣼⣰⣋⡘⣆⢠⡀⠀⠀⠈⣇⠀⡿⣿⣭⣥⣬⣷⣄⣷⠀⢢⠀⢤⡀⠀⠀⠀⠀⠈⠙⢒⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣟⡿⠋⠀⠀⠀⣀⣴⣿⣿⣿⣿⣶⣽⣎⢧⠀⠀⠀⠸⣾⠿⣿⣿⣿⣿⣿⡛⢿⡆⡎⠀⠀⣽⣗⢲⠒⠒⠒⢻⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠓⢒⡶⠒⠋⢿⡟⠁⣼⣿⣿⢿⣿⡍⢯⣧⣄⠀⠀⠘⣴⢻⡿⡯⣽⣻⠁⢸⡵⠃⠀⢰⢷⢹⠋⡷⣄⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠒⠒⢺⠏⢹⡀⠀⠸⣇⠀⠠⣯⣭⡤⠔⠁⣸⢉⣿⢝⠲⢤⣜⣮⡓⠛⠛⠉⢀⣼⣥⠂⢀⣯⣨⡿⣸⠁⠈⠉⠒⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢠⡞⢳⡀⠘⣝⢦⣀⠀⠀⠀⠠⠾⠗⠋⠀⠀⠀⠀⠀⠈⠁⢀⣤⡴⡿⠋⠀⣠⠋⢻⡽⠞⠳⢤⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⣿⡦⢬⣿⣟⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠧⢶⡿⠁⠀⣿⠀⠀⠀⠀⠙⢆⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠘⡇⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠤⢴⠆⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⣿⡆⠀⠀⠀⠀⠈⠳⣄⣀⡾⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⢹⠀⠀⢻⠀⠀⣧⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⡿⠀⠀⢀⡇⢹⠀⠀⠀⠀⠀⠀⣈⠁⡲⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠎⢧⡀⠘⡆⠀⠹⡄⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⢀⣠⠖⠋⠀⠀⢠⠇⠀⠀⣼⠀⠸⡄⠀⠀⠀⠀⠀⠻⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠳⡀⠀⠀⣤⣴⣾⣿⣶⣶⡾⠋⠀⠀⠀⢀⣠⠏⠀⠀⣰⣿⣷⣠⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠙⠦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⠄⠀⣠⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⠤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣤⠼⠷⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣾⠿⠿⠿⠛⠛⠉⠀⠛⣆⠀⠀⠀⣤⠶⣜⣦⣀⢀⡀⠀⠀⠀⠀⠀⠀ ⠞⢙⣤⠚⠳⣯⢽⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢪⣷⡦⣤⣠⣼⣶⣄⢀⠇⢠⠞⢧⠉⣹⠃⠀⠀⠀⠀⠀⠀ ⡴⢏⣀⠱⣏⠛⢦⣌⣿⣍⠓⠲⠶⢦⣄⣀⡀⠀⠀⢀⣴⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢀⢯⠏⠀⠈⣿⣿⣿⣿⢏⡴⠋⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀ ⢦⠈⢱⣠⠼⢷⡮⣧⣹⡉⠙⠓⠶⠶⢦⣌⣉⠉⣷⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⠀⠀⢸⡘⠀⢀⣼⠋⠉⠛⠁⠉⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀ ⣤⠳⢄⠈⢦⣴⡷⢬⣟⣧⠀⠀⠀⠀⠀⠀⠀⡽⠛⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠘⣵⠀⡏⠸⡄⢀⡆⢀⣀⣤⣶⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀ ⡉⠳⣌⠓⢾⣿⡄⠀⠙⠋⠀⠀⠀⠀⠀⢠⣾⠁⢰⢣⠀⠀⠉⠉⠙⠛⢻⡟⠻⠿⡿⢿⠿⠿⠿⣿⢿⡿⠻⡄⠀⠀⠙⢷⠙⢦⣍⣉⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀ ⣿⣦⡈⠳⣄⢻⠁⠀⠀⠀⠀⠀⠀⠀⣠⠋⢹⡀⠸⣼⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⢿⠸⡀⠀⣠⠃⢰⠃⠀⠙⢦⡀⠀⠀⠀⢀⡼⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⠀⠀⠀ ⣿⣿⣿⣤⠈⣾⣀⣠⠤⠶⠶⠖⠲⠶⣧⣀⡀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠘⡄⣇⢠⠏⢠⠇⠀⠀⠀⠀⠙⢶⠄⣠⠞⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀ ⣿⣿⣿⣿⠟⠉⠀⠙⠦⠔⣀⣀⡀⠀⠸⡀⠛⢾⡄⢸⡄⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡇⢻⡜⢀⡏⠀⠀⠀⠀⠀⢀⡼⠀⡇⠀⠀⠀⠀⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀ ⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠘⣆⠀⠉⢻⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣹⣸⠃⡾⠀⠀⠈⢻⠛⠛⠋⣠⡄⠹⡄⠰⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧

⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⢖⡒⠒⠚⠛⠻⢦⣄⡀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡏⠙⠦⣄⡀⠀⠀⠀⢀⣀⡤⠖⣛⡉⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⠀⠈⠉⠛⠓⠚⠛⠛⠉⠉⠉⠉⠙⠓⠦⣄⠀⢀⠀⠈⠂⠀⠀⢀⣠⣤⣌⠳⡄⠀⠈⠻⢤⣀⠀⠀⠀⠀⠀ ⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠉⠉⠓⢄⣀⠔⠉⠀⠀⠀⠑⢅⢀⣀⣀⠀⠻⡇⠀⠀⠀⠀ ⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠔⠋⠀⠀⠀⠀⠀⠀⢀⠈⢁⡾⠓⣄⠀⠀⠀⠈⢧⠀⠉⠙⠲⣽⣄⠀⠀⠀ ⠀⠀⠀⠀⣨⠟⢒⣦⠴⠒⠋⠉⢁⠜⠁⠀⠀⠀⠀⠀⠀⣠⣾⡽⠷⠿⠗⠶⠿⡄⠀⠀⠀⠘⣧⠀⠀⠀⠀⠹⣆⠀⠀ ⣴⡶⠶⠶⠛⠛⠉⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⢿⢧⠀⠀⠀⠀⠹⣆⠀ ⠈⠣⡀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⣠⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⣷⠀⠀⠀⢸⠈⣧⠀⠀⠀⠀⢻⠀ ⠀⠀⠈⡷⠲⠤⣤⡠⠞⠁⠀⠀⠀⠀⠀⢠⠏⢀⡞⢀⣀⡤⠤⠤⠀⠀⠀⠀⢸⢀⡿⠀⠀⠀⣾⣄⡸⡆⠀⠀⠀⢸⡇ ⠀⠀⠀⣧⣤⠖⠋⠀⠀⣠⠆⠀⠀⠀⢀⣼⠀⡾⠀⠀⠀⠀⠀⣀⣠⠀⠀⠀⡟⢸⡇⠀⠀⢰⠃⠀⠀⢷⠀⠀⠀⢸⡇ ⠀⠀⠀⣿⠈⠙⠓⠒⢛⡏⠀⠀⠀⠀⠀⡟⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⠇⢸⠇⠀⢠⣿⣿⣿⣿⣿⠀⠀⠀⣼⠁ ⠀⢰⠻⣿⣇⠀⠀⡴⣿⡇⠀⠀⠀⠀⠀⣿⡟⡇⣿⠤⠄⣤⣦⢚⡇⠀⢀⡟⢀⣾⠀⣠⣟⠛⣯⢹⡏⣿⠄⠀⢠⡿⠀ ⠀⢸⠀⠈⠛⣶⢶⡇⢻⣇⢷⠀⠀⠀⠀⣿⠇⠀⠙⢞⢳⠎⠁⣸⠃⠀⢼⠗⢫⣧⠔⠁⢿⣲⠋⣸⠁⡼⠀⣠⠟⠀⠀ ⠀⠈⡗⠀⠀⡏⣸⠇⣸⠛⢿⣷⡀⠀⠀⠸⡄⠀⠀⠈⠛⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠼⢷⣾⠁⠀⠀⠀ ⠀⠘⣇⣠⣶⣿⢦⣘⣾⡞⠉⠉⠉⠢⣀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⠀ ⠀⠀⣘⠿⠋⠀⠀⣠⠸⡇⠀⠀⠲⠦⠈⠙⠒⣚⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡼⠁⠉⢉⣽⠃ ⢿⡋⠁⠀⠀⢀⠔⠁⠀⠹⣄⣀⠀⠀⠀⣀⡶⢤⣉⡲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠉⠐⢶⣾⣉⣀⠀ ⠀⠉⢓⣲⠞⠁⠀⠀⠀⡇⠀⠉⠉⠉⠉⠙⡆⠀⠙⢿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⡚⠛⠉⠁⢦⡀⠀⠀⠀⣠⠴⠋⠀ ⠀⠀⠘⠯⠤⣤⣤⡒⠀⣧⠀⠀⠀⠀⠀⠀⠹⣦⣄⣀⣉⣻⣿⣿⣹⣿⣿⣿⣿⣿⡿⣆⣀⠀⠀⣙⣳⠶⠋⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠲⢼⠗⠲⠴⠦⣤⣄⣀⣨⣿⣿⣾⠿⢦⣼⣿⣿⣿⣿⣩⣿⣷⣿⡍⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠋⠁⢠⠏⣰⣿⣿⣿⣸⣿⣿⣧⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠸⡄⠹⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠹⣿⣷⣤⣤⣴⡿⣶⡿⣿⡁⣿⢻⢿⣆⣼⠟⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⢺⣿⡿⢉⣻⣿⣿⣧⡈⠻⢃⣼⣆⠙⠁⢀⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣠⣶⡟⠁⠀⣾⣿⣿⣿⣿⣿⣶⣾⣿⣿⣧⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣤⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣿⣆⠀⠀⠀⢀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣀⣤⣶⣶⣌⠻⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠁⣰⣿⣿⣿⣿⣿⣦⣙⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣦⣹⣟⣫⣼⣿⣿⣶⣿⣿⣿⣿⣿⣿⣯⡉⠉⠉⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⢿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣄⣐⣀⣀⣀⣀⣀⡀ ⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠁⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

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⠀⠀⠀⠀⠀⠀⠀⢀⣼⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡤⠖⠒⢻⡟⣻⡏⠉⠑⠒⠦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠶⣖⣿⡇⢫⣛⣶⡶⠶⠖⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⠖⠋⠙⠋⠀⠀⠉⠙⠲⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡰⢫⠁⠀⠀⠀⠀⠈⣲⣲⠂⠀⠈⠢⣀⣀⠀⠀⠀ ⠀⠀⢠⠃⠇⢀⠀⡇⠀⠀⡸⡉⠙⡧⡀⢀⢀⣀⡼⠀⠀⠀ ⢰⡊⠁⠞⢠⠇⠼⢡⠀⠀⠧⠐⢄⢣⠀⠀⢂⠈⠓⡲⠀⠀ ⠀⠉⢹⠀⢸⡾⢲⣶⡛⣦⡗⢻⣿⡻⠀⠀⢸⠙⡍⠀⠀⠀ ⠀⠀⠈⠀⢸⡆⠘⠻⠃⣍⡀⠘⠛⢀⠀⠀⢸⠀⡇⠀⠀⠀ ⠀⠀⢰⣢⠀⢻⣶⣦⣼⣬⣷⣶⡞⢃⡀⠐⡮⣾⡤⡄⠀⠀ ⠀⠀⠀⢉⣱⡶⢯⣚⣟⡛⠽⠧⠀⠯⢤⡒⠳⡉⢂⡻⣹⡟ ⠀⠀⠀⢸⢸⠧⢼⠥⣀⡀⠀⠀⠀⠀⢀⠛⡷⢇⣁⠭⣁⠀ ⠀⠀⠀⠘⣍⠽⣤⠥⠬⣰⣤⣄⡀⠰⠥⣔⠣⠤⠤⠔⠊⠀ ⠀⠀⠀⠀⠀⠀⢸⡉⠉⡗⡌⠙⠙⢄⣀⠼⣄⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⢩⣡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠉⠻⣦⡀⠀⠀⠀⠀⠀⣴⠞⠛⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠈⣷⠀⠀⠀⢀⡾⠃⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⡇⠀⠹⢦⡤⢤⣄⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⣾⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡴⠞⠋⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢸⡇⠀⠀⠀⠀⠀⠀⠘⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢧⣄⡀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠇⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⣿⠀⠀⢀⣀⣀⣀⣱⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⣤⠶⠋⠀⠈⠉⠁⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠘⠳⠛⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⠃⠐⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠐⠀⠀⠂⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⢀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠊⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠋⠙⣧⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⠻⡧⠀⠀⢻⣄⡀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠁⠀⠀⠘⠛⠳⢦⣀⠀⠀⠀⢀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⣤⣤⣤⡄⠀⢹⡆⠀⠀⠀⣽⡷⣿⡋⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡁⠸⣇⡀⣀⡤⠀⢸⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠈⠛⠉⠀⣠⠞⠛⢳⡶⢤⣤⣤⣴⡶⠶⠶⠚⠛⢩⡿⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢻⡁⠀⠀⠀⠙⠳⠶⠖⠛⠀⠀⠀⠀⣴⣋⣠⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣌⠙⠳⢶⡶⠶⠶⠞⣫⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡞⢻⠄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠛⠛⠶⠶⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠉⠉⠀⠈⠳⣤⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠂⠀⠀⠀⣤⠟⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠤⠶⢤⣀⡿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀

.　 +⠀ ⠀ ⠀˚⠀ ⣴⠟⠉⠉⠛⢦⡀⢀⣴⠛⠉⠈⠙⠻⣄ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠹⣦ ⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀⠀⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆ ⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃ ⠀⠀⠀⠀⠀⠻⢦⣄⠀⠀⠀⠀⠀⣠⡴⠛ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⠶⠋ ⠀⠀⠀+. *

⣷⣶⣶⣶⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠈⠣⡀⠙⢿⣷⣻⣿⣴⣿⣿ ⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⡄⠠⣿⣿⣿⣿⣿⣿ ⠙⢿⣿⣿⡟⠁⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢣⠻⣿⣿⣿⣿ ⣤⣾⣿⡟⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⡰⢻⠁⠀⢀⠎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢇⠹⡀⠀⠀ ⣿⠋⡜⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡠⠀⣠⠞⠁⡜⠀⠀⡜⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⡀⠱⡄⠀ ⢁⣰⠁⢠⠇⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⡶⠊⡠⠚⠙⠛⠶⣧⣄⡸⠀⠀⡇⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⣠⢶⠀⢸⠀⠀⡇⠀⠈⢦ ⠉⡏⠀⡎⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⡷⡊⢠⠀⠀⠀⠀⡏⠻⣷⡄⠀⡇⠀⠀⠀⡜⠀⠀⠀⠀⣠⣶⢰⠇⢸⣤⣿⠀⠀⡇⠀⠀⠘ ⣰⠇⢰⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠈⠲⢶⣷⠿⢿⣿⣷⣶⣶⣿⣦⡉⠁⠀⢳⠀⣠⠎⠀⠀⢀⡤⣶⣻⣿⢸⠀⠘⡿⡟⠀⠀⡇⠀⠀⠀ ⠁⠀⡎⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⣏⡖⢺⡻⣿⡛⢿⡿⣄⠀⣸⠖⢁⣀⣤⠞⠁⢀⠇⠀⡝⢸⠀⠐⢇⠘⡄⠀⡇⠀⠀⠇ ⠔⠺⡇⠀⢠⠇⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠛⠉⠚⠤⠽⠁⠈⢳⠐⠚⠛⠉⢹⣰⠃⠀⠀⡿⠀⠀⡇⢸⠀⠀⠈⠀⢸⠀⡇⠀⠀⠀ ⢀⣀⡇⠀⡎⠀⠀⠀⢁⠀⠀⠀⠀⠀⢣⡀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⣦⣴⡄⡇⠀⢀⡇⡆⠀⠀⡰⠀⣿⢠⠃⣀⠀⣠ ⠉⠉⣧⣸⠀⠀⡆⠀⠘⡆⠀⠀⠀⠀⠀⡗⢄⡱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢿⣿⡇⠀⢸⣾⠀⠀⢠⠇⠀⣿⡞⡀⠘⣄⠃ ⠀⠀⢹⡟⠀⠀⡇⠀⢀⠘⡄⠀⠀⠀⢆⢡⠀⠉⠺⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⡀⢧⠀⠈⢣⠀⠘⣷⣤⣤⣸⠀⠀⡇⣷⠋⠑⠚⠳ ⠀⠀⠀⣿⠀⢠⢷⠀⢸⡄⠘⢄⡀⠀⠈⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡄⠀⢸⠀⠀⠀⢸⣿⡏⠀⠀⠁⡞⠀⠀⠀⠀ ⠀⠀⠀⣿⢀⡇⢸⢧⣸⢣⠀⢸⢿⠢⠤⠤⠬⠷⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠘⡄⠀⠀⢸⣿⡇⠀⠀⢸⣁⠀⠐⠢⣀ ⠀⠀⠰⠁⢿⠀⢸⠀⠉⢈⢧⠸⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠉⠀⠀⣾⣿⣇⠀⠀⣸⠀⠉⠉⠉⠉ ⠀⠀⠀⠀⠀⠀⡞⠀⣠⢋⣀⣟⠇⠈⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢐⣦⠀⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⢀⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣇⣼⡵⠋⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠁⠀⣇⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⢸⡇⠀⢤⡄⠀⠀ ⠀⠀⢀⠄⠀⣸⠛⠁⠀⢀⣴⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⢀⣿⣿⢿⣿⡇⡾⣇⠀⣿⣷⢠⣠ ⠀⢀⠎⠀⢀⠇⠀⠀⠠⠚⠁⣼⠤⠤⣀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⠀⢀⣾⣿⡏⠈⣿⣿⣗⢿⣵⣿⣿⣿⣿ ⡶⠃⠀⠀⡞⠀⠀⠀⠀⠀⢰⢹⠀⠐⠒⠮⣍⠒⢤⡀⠀⠈⠳⢄⡀⠀⠀⠀⢀⣀⣤⣶⠋⠁⢈⣿⣿⣿⡟⠀⠀⢸⣿⣿⢴⣿⡿⣿⣿⣿ ⠀⠀⠀⡼⠁⠀⠀⠀⠀⢀⠇⡾⠒⠓⠒⠲⠤⢽⣦⡙⢦⡀⠀⢀⡙⢳⣶⣾⣿⣿⣿⣿⡇⣸⣿⣿⠛⠋⠀⠀⠀⠀⠻⡇⠀⠈⠙⢿⣿⣿ ⠀⠀⡼⠁⠀⠀⠀⠀⢠⠎⠀⣧⣾⣶⣶⣶⣶⣶⣶⣿⣿⣿⣦⠎⠱⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⢻⡷ ⣤⠞⠀⠀⠀⠀⠀⡠⢃⠄⠀⡿⢯⢿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢴⣦⠌⢻⡟⠛⢻⣿⣿⠛⠻⣿⡟⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⣧ ⠁⠀⠀⠀⠀⠀⠀⣡⠊⣀⠔⠁⠈⢿⣿⣿⣿⣿⠛⠉⣡⣿⣦⣈⣿⢠⣿⣿⣿⣿⣿⡿⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠓⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣷⠀⠀⣿⠀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠾⠟⠋⠉⠉⠙⣿⡄⠀⣿⢠⡇⠀⠀⠉⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠛⠁⠀⠀⠀⠀⠀⢀⣀⣿⣻⡿⢿⡿⠛⢤⠤⣤⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠀⢀⣀⣠⣤⡴⠶⠿⢿⣟⣛⣛⣿⣦⣬⣷⡶⠶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠶⠿⠶⠶⠛⠀⠀⠀⢈⣉⣩⣩⣭⣭⣭⣤⣤⣥⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠾⠟⠛⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣀⣀⣀⣠⠿⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡷⣤⣀⡀⠹⣷⣤⣀⣀⣀⠀ ⠀⠀⣾⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⡟⠀⠀⠀⠈⠉⢩⡿⠀ ⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠙⢿⡇⠀⠀⠀⠀⣠⡟⠁⠀ ⠀⠀⠀⠙⢷⣦⣤⣀⡀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⢳⡀⠀⠀⣾⡉⠀⠀⠀ ⠀⠀⠀⢀⣼⠁⠀⠈⡉⠉⠉⠁⢀⡔⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⡼⠃⡇⠀⠀⠀⠀⠀⠀⡇⠻⡄⠀⠀⠀⠀⡀⠁⠀⠀⠈⠻⣦⣤⣤ ⠀⠀⠀⣾⠃⠀⢀⣾⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣾⣋⡀⢳⠀⠀⠀⠀⠀⠀⡇⠐⠛⣟⠒⠀⠀⢧⠀⠀⠀⡀⠀⠀⢀⡾ ⠀⢀⣾⠃⠀⠀⣾⠈⡀⠀⠀⣸⢻⡀⠀⠀⠀⠀⠀⡞⠁⠀⢈⡿⠋⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⡇⠀⠀⢈⡳⣄⠀⢸⠀⠀⠀⢧⣀⣴⡿⠁ ⠀⣼⠇⠀⠀⣼⠇⠀⢇⠀⢸⠇⢸⡇⠀⠀⠀⠀⠀⡇⢀⣴⣟⣠⣤⣤⣤⣤⡀⠘⣆⠀⠀⠀⠀⣇⣴⣾⣿⠿⣿⣳⢜⡄⠀⠀⢸⡏⠁⠀⠀ ⢸⡇⠀⠀⢰⡿⠀⠀⢸⣶⠛⠋⢹⡇⠀⠀⠀⠀⠀⣿⣯⣿⡿⠛⣩⣿⣯⣿⣿⡆⠘⢧⣄⠀⠀⠸⣿⣿⣿⡇⢾⡿⠀⡇⠀⠀⠘⣿⠀⠀⠀ ⠘⣇⠀⠀⣾⠃⠀⠀⢸⣿⠀⠀⢶⣇⠀⠀⠀⠀⠀⣿⠸⠏⠀⢠⣿⣿⡿⣿⡏⠁⠀⠀⠈⠙⠲⠶⣾⢹⣿⡇⠀⣇⢰⠀⠀⡀⠀⣿⠀⠀⠀ ⠀⢻⣆⢸⣿⠀⠀⠀⢸⡿⣄⠀⠀⠸⡄⠀⠀⠀⠀⢸⡄⠀⠀⠘⣿⣿⣧⣿⠃⠀⠀⠀⠀⠀⠀⠈⠻⠿⠋⠀⠀⣻⡼⠀⢰⠃⠀⣸⠀⠀⠀ ⠀⣀⣙⡿⠿⣇⠀⠀⢸⡇⠙⠛⠒⠲⣿⡀⠀⠀⠀⠈⢧⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡤⠤⢶⠄⠀⠀⠀⣠⠟⠀⡰⣻⠀⠀⣿⠀⠀⠀ ⢸⣟⠉⠛⢛⣿⣷⣤⣀⣿⣄⡀⠀⣰⣿⠳⣀⠀⠀⠀⠈⢷⣤⣛⣂⠀⠀⠀⠀⢠⠏⠀⠀⠀⢀⣼⣀⣠⣴⣾⠋⠀⠀⢠⠃⠀⢰⡿⠀⠀⠀ ⠈⢿⣇⠀⣠⣭⣿⣿⣿⣿⣿⣿⠷⠋⠈⢹⣿⢶⣄⡀⠀⠀⠙⢿⣿⣿⣿⣷⣶⣿⣶⣶⣶⡶⣿⣿⣶⡿⠛⠁⠀⢀⣴⠋⠀⢠⣿⠃⠀⠀⠀ ⠀⢀⣭⣿⠿⣿⣿⣿⣿⡟⢻⡀⠀⠀⠀⠀⣿⠀⠀⠉⠉⠉⠛⣿⣿⣍⣛⡿⢿⣿⣿⣿⣿⣿⣟⠁⠉⠉⢳⠖⢟⡿⠁⣀⣴⢿⣥⠀⠀⠀⠀ ⠀⠸⣿⣤⡒⠻⣿⣿⣿⡇⠸⣃⠴⢦⣀⠀⣿⠀⠀⢀⡜⠉⠳⢮⡿⠿⡏⠛⠛⠛⠋⢹⣿⠉⠙⠷⣤⣀⡾⠛⠛⣶⠚⠉⠀⢀⡿⠀⠀⠀⠀ ⠀⠀⠈⠛⠻⠿⠿⠿⠿⣧⠀⠁⠀⠀⠹⡄⠸⣄⣀⣼⠀⠀⣠⠴⠦⢤⣇⠀⠀⠀⢰⡟⣿⠀⠀⠀⠈⢿⣦⣄⣸⣁⡀⣀⣠⡾⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⣀⣹⣦⡀⠀⠀⠀⣷⠶⠿⣷⣤⣠⠎⠁⠀⠀⠀⠙⣷⠀⠀⣿⣿⠋⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣰⠋⠉⠛⣿⡟⢦⣤⣀⣠⢤⣀⣈⣿⣿⣦⣤⣄⣠⣤⣴⣻⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡇⠀⠀⢴⠁⠏⠳⠦⢌⡹⠿⡏⢉⡏⢸⠃⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⡁⠀⠀⣿⠀⠀⠀⠀⠀⠀⣼⠇⢸⡇⢸⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠷⣦⣤⣾⠻⠶⣤⣤⡤⠾⠋⠀⠀⢿⣬⣷⣤⣤⡴⠞⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠋⠉⠉⠉⠉⠉⠙⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⠿⠛⠛⠛⠛⠛⠛⠛⠛⠳⣦⠀⠀⠀⠀⠀⠀⠀⢸⡷⠶⣤⠀⠀⠀ ⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠆⠀⠀⠀⠀⠀⠀⢸⣇⣀⠽⢦⣤⠀ ⠐⠯⣉⠹⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣴⠟⠀⠀⠀⢀⣀⡤⣴⢾⡿⢶⣺⡏⠀⠀ ⠀⢀⡤⠛⢻⡿⣯⠭⠭⣭⣉⣉⣉⣉⡥⠤⠔⠒⠋⣩⠔⠊⠁⢸⡇⠀⠈⢣⡀⠀ ⣰⠋⠀⢀⣼⡇⠈⠓⠦⣄⣠⠞⠑⢦⡀⢀⡠⠖⠋⠁⠀⠀⠀⢸⡏⠓⢦⠤⠛⠂ ⣧⠖⠉⠁⣿⡀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀ ⠀⠀⠀⡼⣿⡭⢉⣉⣟⣻⣒⣒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠠⢼⡇⠀⢸⠀⠀⠀ ⠀⢀⡞⠀⣿⡄⠀⠀⠀⠀⠀⠀⢉⣉⣉⣉⠉⠉⠉⠉⠉⠁⠀⢻⣇⣀⣼⢣⠀⠀ ⠀⡞⠀⠀⢸⣇⠀⠀⠀⠀⠀⢀⣿⠋⠙⠻⣇⠀⠀⠀⠀⠀⠀⣿⠻⡍⠁⠈⡇⠀ ⠀⡷⢣⣠⠋⠻⣦⣀⠀⣀⣠⡾⠃⠀⠀⠀⠻⣦⣀⠀⠀⣠⡼⠋⠀⢳⡀⡦⠝⠦ ⠀⠁⠈⠁⠀⠀⠈⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠈⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣢⣶⢷⠢⣶⠁⢾⡦⠠⣠⣔⡖⡶⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠔⠲⣣⠀⠡⡠⠐⢀⢜⠕⠒⠢⠄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣧⣔⣂⠥⠕⠄⢀⠔⡁⠚⠊⢅⣐⣠⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠰⢁⠀⠈⢢⠀⠀⢈⠢⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠂⠄⠀⠀⠀⢀⠃⠈⠀⠀⠈⡆⠀⠀⠁⡀⠢⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠃⡜⠀⠀⠀⡠⣹⠀⡇⠀⠀⡀⡘⠄⠀⠀⠘⡄⢡⠀⠀⠀⠀ ⠀⠀⠀⠀⡼⠰⠀⠀⡆⣰⡕⣸⣠⠀⠀⢠⢡⠱⡈⡄⣦⣀⢰⠈⡆⠀⠀⠀ ⠀⠀⠀⡐⠁⠆⠀⢠⡠⣋⣡⣼⢾⠀⢀⡦⢋⣈⣑⣿⣻⡟⠀⡆⠈⠢⡀⠀ ⢤⡔⠀⠀⣰⠀⠀⢸⣷⢿⣿⣿⡛⠤⠋⠀⢻⣿⣿⠿⣿⠀⠀⠰⡀⠀⢀⠱ ⠀⠈⢀⠜⡍⠀⠀⠘⡇⠘⠿⠟⠁⠀⠀⠀⠘⠿⠟⢀⣿⠀⠀⠀⡇⢎⠁⠀ ⠀⠈⡹⢸⡇⠀⠀⠈⡋⡄⠀⠀⠀⠀⠤⠄⠀⠀⠀⠌⡟⠂⠀⠀⡇⠀⠆⠀ ⠀⠀⢃⡈⠆⠀⠀⠧⢃⢨⣦⣄⡀⠀⠀⠀⣀⣤⣎⢀⢃⠀⠀⠀⡘⡄⡜⠀ ⠀⠀⠈⡇⡀⠀⠀⠀⡌⣯⠹⡄⠉⠛⠚⠓⠉⠘⣿⢋⠌⠀⣿⠀⣇⠗⠀⠀ ⠀⠀⠀⢃⢃⠀⠀⡆⢸⣌⣻⣷⡀⠀⠀⠀⠀⠘⣳⠃⢀⢴⣈⠜⠀⠀⠀⠀ ⠀⠀⢠⣶⣮⣦⠀⢣⠀⢿⡹⠟⢠⣆⣀⣀⣀⠠⠟⠋⠀⢩⠀⠣⡀⠀⠀⠀ ⠀⠀⠀⠙⢛⡿⠛⠿⣶⣼⡇⠠⡞⠀⠀⠀⢀⢀⣀⣀⡠⢃⠠⠒⠁⠀⠀⠀ ⠀⠀⠀⠰⣏⣀⣀⠤⣻⠀⠀⡜⠂⠤⠠⠔⢉⡀⠤⠐⠈⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⡠⠖⢓⣫⣃⠹⡇⠀⠀⠀⠀⡰⢁⣦⣄⣀⣀⡀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀ ⡰⠋⣠⠖⠁⠀⣈⠵⠧⣄⠐⠒⠚⠓⠛⠒⠓⠿⢽⣧⣀⣠⠴⠋⣸⠀⠀⠀⠀⠀ ⢁⠞⠁⢀⡠⢴⠁⠀⠀⠀⠱⣄⣀⣀⣀⣬⣭⣶⣤⣈⡑⠒⠢⢴⣧⢤⡀⠤⢤⠀ ⢼⡒⣲⠊⠀⢸⣆⠀⠀⠀⠀⡈⠓⣾⠱⣖⡒⢺⠈⠳⣍⠑⢤⡀⠈⠙⢦⡴⠋⠀ ⠀⣹⠁⠀⠀⢸⢈⠷⣔⡒⢮⡤⠤⠬⠷⠒⠒⠉⠁⠀⠉⢣⠀⠙⠄⠀⠀⠱⡄⠀ ⠀⡇⠀⡀⢀⡏⡏⡶⡎⠉⠙⢚⠷⠒⢲⠦⢄⠀⠀⠀⠀⠈⡇⠀⠘⣆⡀⠀⢹⠀ ⢸⡀⠀⢰⡜⣇⣛⡵⠃⠀⢠⠃⠐⠚⠁⠀⠀⠱⡄⠀⠀⠀⡇⠀⠀⢸⠹⡄⡼⠀ ⡸⡇⠀⠈⢧⠀⠀⠌⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⢰⠣⡀⢠⠎⠰⠟⠳⣄ ⠃⢣⠀⠀⠈⢷⡁⠀⠀⠀⠈⢇⠀⠀⢀⡠⠒⠒⠁⠀⣠⠋⠀⠈⡏⠀⣧⡀⠀⠘ ⠀⢼⡄⠀⠀⠀⠙⠦⣀⣀⠀⠀⡑⠒⠉⠀⠀⠀⣠⣴⣷⣶⣶⠒⡗⢠⣧⢼⡆⢀ ⢀⡎⠱⡀⠀⠀⠀⠀⠐⠶⣾⠭⣤⣤⣤⣴⣶⣿⣿⣿⣿⢿⡟⠚⠋⡡⢻⠈⠉⠁ ⠾⠤⡤⠛⣄⠀⠀⢠⢤⣀⣀⡩⠝⠛⡩⠿⣿⡿⣭⢁⣴⠋⠀⠐⢯⡀⣼⠦⣄⣀ ⠀⢠⡇⢿⣿⣿⡶⠾⢦⣀⣠⠀⣴⠊⣳⠚⠁⢀⣫⠏⠁⠀⠀⠀⢠⢃⠇⠀⠀⠀ ⠀⠘⣇⣆⢼⡟⠀⠀⣠⠚⠚⠀⠈⠉⡹⢶⡚⣿⠀⠀⠀⠠⡴⢚⡡⠋⠀⠀⠀⠀ ⠀⠀⠙⠚⠓⣇⠀⠀⠣⠤⢴⡿⠀⠘⠦⢞⣨⠟⠀⢀⣀⣴⠗⠋⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⠤⣄⣀⡀⠀⠀⠼⠿⠿⠿⣷⣶⣶⣶⠂ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣾⣿⣿⣿⣿⣟⠻⢿⣿⣿⣿⣿⣿⣶⣶⣤⣀⠒⠦⡀⠀⠉⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⢦⣸⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡏⠀⠀⠀⠈⢿⣇⢻⡿⢿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢳⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⡇⠀⠀⠀⠀⠈⢻⣮⢂⠀⠁⠀⢠⠀⠀⠹⣯⣿⣿⣿⣿⣿⣿⣿⣿⡏⢰⣆⢰⠁⠀⠀ ⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡏⡇⠀⠀⠀⠀⠀⠀⠟⣏⢢⠀⠘⢄⠑⣄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣿⡟⠀⠀⠀ ⣠⣴⣾⡏⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⡏⠀⢣⠀⠀⠀⠀⠀⣠⠖⠈⠳⣷⡄⢈⣳⣌⠳⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⡇⠀⠀⠀ ⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣰⣿⣧⣿⣿⣿⣇⠀⢸⠀⠀⠀⣠⣞⡁⣠⣴⣾⠛⠻⣏⣌⣻⣷⣌⠻⡟⣿⣿⣿⣿⣿⡄⠀⠹⣿⠁⠀⠀⠀ ⣿⡿⠃⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣤⣿⣇⠀⠐⠉⠛⠿⣿⡟⠟⢣⠀⠁⢹⠈⡟⢻⠛⢶⡿⠿⠃⣿⣿⣿⣶⡀⠹⡀⠀⠀⠀ ⠁⠀⠀⠀⠀⠀⠀⣠⠞⢙⣿⠻⣿⢿⣿⣿⣿⣿⠿⢿⡄⠀⠀⠀⠀⠹⡃⠫⣿⡤⠀⢸⠀⡟⣿⠀⢸⣧⡜⣰⣿⣿⣿⣿⣷⡀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠞⠁⠀⢸⡟⣷⣼⠄⢤⣶⢾⣿⢷⡟⠻⢄⠀⠀⠀⠀⠓⠈⠁⠀⠀⢸⠀⢹⣿⠄⣸⣯⣴⣿⣟⣿⢻⣿⣿⣷⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⣇⢿⣿⣷⠺⣇⠀⢿⢲⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣠⣿⡟⢰⣿⣿⣿⣿⡿⠃⠀⣻⣿⠿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⣼⣿⣿⠘⣿⣿⣷⡀⠀⠘⠃⠀⠀⢀⣠⠒⠓⢤⡀⠀⠀⠀⣰⢷⣿⢋⣿⣿⣏⣹⡇⢽⣁⠀⠀⢸⢿⣷⣶⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠚⠻⢿⣿⣿⡇⠁⠘⢿⣷⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠱⡀⠀⠈⠀⣼⢃⣾⣿⡟⠀⡸⠛⣤⣹⠃⠀⠀⢣⠹⣿⡄⠀⠀ ⠀⠀⠀⠀⠁⠀⠀⠀⠀⣸⣿⣇⡇⠀⣼⣿⣇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇⠀⠀⢀⣧⣾⣿⢿⡇⢠⣧⣤⣤⣹⡆⠀⠀⠀⢣⡈⢇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡏⢁⢰⣼⣿⣿⣆⠀⠀⠀⠀⠀⠠⡀⠀⠀⠇⠀⠀⣼⣿⠏⠁⣸⡇⣾⣿⣿⣿⣿⣿⣦⣀⣀⣀⠑⢾⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⢿⠘⣿⣿⣿⣿⣿⡝⠢⠄⣀⠀⠀⠈⠒⠊⠀⢀⣴⣿⠏⢀⣴⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠉⠐⢇⠀ ⠀⠀⠀⠀⢀⡀⠤⢄⠀⣠⡎⠈⡆⣿⣿⣿⣿⣿⣷⡀⠀⠀⠈⠑⠂⠤⠤⢺⣿⣏⡇⣠⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆ ⠀⠀⠀⠀⠁⠀⠀⠐⠉⢸⡀⠀⡇⢹⣿⢷⣿⣿⣿⣷⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠀⡠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠁⢺⢹⣦⣝⣿⣿⣿⣇⠀⠀⠀⣿⣿⣿⡿⣿⣿⠿⠛⣛⣁⣀⣠⣤⣶⠿⠷⠶⠴⠾⠿⠦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢀⣨⠼⢯⡙⢿⣿⢿⣿⠀⠀⣸⣿⣿⠟⠉⢁⠰⣶⠖⣋⠕⠋⠉⠉⠙⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⢪⡿⠁⠀⠀⠘⡄⣧⣈⡀⠀⠰⢟⣉⡏⢀⠊⣧⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀ ⠀⠀⠀⠀⠀⠀⢀⣤⡾⠧⠟⠒⠳⠀⠀⠀⠀⡇⣿⣿⣿⣿⣿⣿⣭⣧⣦⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⢰⣿⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣽⣿⣍⠙⠉⠉⠛⠋⢉⣭⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿

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⠀⠀⠀⠀⠀⠀⣠⠄⠀⠈⠀⠀⠀⠀⠀⠐⠄⠈⠢⠳⡈⢆⠄⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⡀⠀⠑⡱⠀⢪⠁⠀⠀⠀⠀⠀⠀ ⠀⡈⠀⢲⠁⠀⠰⠀⠀⠀⠀⠀⠰⢀⣀⡼⠼⣔⣄⠀⠘⣥⠈⡄⠀⠀⠀⠀⠀⠀ ⠀⠂⢠⠏⠀⢠⠃⠀⡌⠀⠀⠠⠋⢀⢠⠁⠀⠈⠢⠈⠁⠘⡄⠇⠀⠀⠀⠀⠀⠀ ⠀⢢⡆⠀⠀⢨⠠⠺⡳⡀⡰⠃⢠⢢⢛⣿⠶⠶⢤⣤⣄⠀⢠⢰⠀⠀⠀⠀⠀⠀ ⠠⠎⢹⠀⠀⠈⢀⢃⣦⣗⡇⢠⡣⠁⠈⠀⣼⣿⣂⠈⢻⣿⣫⠈⠆⠀⠀⠀⠀⠀ ⡘⠀⢸⠀⠀⠀⡾⣿⢫⣿⠴⠋⠀⠀⠀⠀⢿⡧⣽⠂⠀⢹⡿⠓⠚⠄⠀⠀⠀⠀ ⠇⡘⢸⠇⠀⠀⣫⣻⠸⡿⠀⠀⠀⠀⠀⠀⢷⣐⠎⠀⠀⢊⠃⠀⠀⢈⠦⠀⠀⠀ ⠀⢷⠈⡘⡀⢄⠘⡅⡜⠃⠀⠀⠀⠀⠀⠀⠠⠄⠐⠂⢁⠂⢀⢀⢀⠂⠀⠑⡤⡀ ⡄⠀⡄⠀⠐⣜⡶⠟⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠑⢪⠗⠁⠁⠀⢀⣴⢃⡼ ⢡⡄⠰⠀⠐⠈⢻⡄⠀⠀⠄⢄⠀⠀⠀⠀⠀⠀⠢⢤⡒⠁⠄⢀⠠⡐⠏⢻⠇⢦ ⠀⢧⠔⠑⢄⠀⡑⠱⡆⠀⠢⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢩⠋⠀⡜⡘⡘⡞⡀⠀ ⠀⠀⠁⠀⠀⠉⠐⡟⢸⠦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠁⢀⢊⡔⠀⢰⠀⠈⠀ ⠀⠀⠀⠀⠀⠀⢰⡀⡈⠯⠈⠢⡀⢀⣀⢠⣴⡾⢋⠊⠀⠀⣡⠿⠁⢀⠋⡅⠀⠀ ⠀⠀⢀⠬⠀⠀⠔⢀⢜⢔⠀⠀⡠⡢⡀⢚⡭⢠⠁⠀⢀⡞⢁⠃⠀⡤⠔⠂⠀⠀

⠀⠀⠀⠀⠀⠀⠤⣄⡀⠀⠀⢠⠔⠁⠀⠀⠀⠀⠀⣠⡴⠛⠲⢤⡀⢀⣠⠯⠂⠀⠀⠩⠭⠶⣦⣄⡘⠽⣖⡦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠐⠁⠀⠀⠀⠀⢀⡴⠚⠁⢀⣀⣤⠶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠈⠉⠓⢿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠔⢋⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⣰⣯⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⢄⡐⢦⡀⠀⠈⠳⢿⣦⡀⠀⠀⠀⠀⠀⠀⠈⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢠⠞⢁⡤⠆⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠡⠀⠙⢦⡀⠀⠀⠀⠈⠣⣄⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⢏⡴⠋⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠑⠂⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⣿⡯⣤⠀⣠⠃⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠉⢳⡄⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⠀⣠⠖⠋⠀⢰⣿⠋⠛⠀⠀⠀⠀⢠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠞⢡⠞⠁⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⢠⠏⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠐⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⡏⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⢠⡞⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠻⢷⣄⠀⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⡀⢀⡴⠋⠀⢧⠀⠀⠀⠀⢀⡎⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠙⢦⡀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⡀⠀⢍⣓⠀⠀⠀⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣷⡞⠁⠀⠀⠈⣆⠇⠀⠀⡼⠁⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⣙⢦⡄⠀⠀⠀⣠⠜⣽⡄⠀⠀⠀⠀⠀⢣⡀⠘⣯⠳⣄⠀⠀⢀⠀ ⠀⠀⠀⠀⠀⠀⣠⠟⢻⡇⠀⠀⠀⠀⠈⢷⣀⠈⠁⠀⠀⠀⠀⣿⡇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠈⠳⢽⣷⣴⡊⠁⠀⠻⢳⠀⠀⠀⠀⠀⠘⣷⠀⠸⡆⠙⢦⡀⠈⠆ ⠀⠀⠀⠀⠀⠀⡇⠀⠘⡇⠀⠀⠀⢀⣠⣾⡏⠀⠀⠀⠀⠀⢀⡟⢹⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣏⡤⠶⠛⠉⠻⢿⡶⣄⣀⠘⡆⠀⠀⠀⠀⠀⣿⢧⠀⢿⠀⣇⠳⡄⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠹⣄⣠⠾⠏⠚⡏⠀⠀⠀⠀⠀⠀⣸⠁⡎⣧⠀⢸⠀⠀⠀⠀⠀⠀⣠⠀⠀⣹⣿⠁⣀⡤⣴⣲⣦⣾⣿⣤⣬⡿⣿⠀⠀⠀⠀⠀⢸⣾⡆⠸⡇⢿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⡟⢦⣦⡀⠀⢻⠀⠀⠀⠀⠀⢠⣧⡾⢁⣨⣧⣼⠀⠀⠀⠀⠀⢠⡟⠀⢠⣿⠇⠚⣿⣾⣿⠟⢻⣿⣿⡟⠻⣿⣿⠖⠀⡀⠀⢸⡏⣟⣇⠀⡇⣸⣧⡀⠀ ⠀⠀⠀⠀⠀⠀⠈⢷⠀⢰⢱⠀⠹⣧⠀⢹⣏⠉⠁⠒⢲⣿⡿⠛⠉⠉⢸⣿⠀⠀⠀⠀⢀⡾⠃⣠⣿⠇⠀⢸⡟⢹⣿⣶⣿⣶⣿⣿⠀⠹⣽⠀⢰⠃⠀⢸⡇⣿⣿⢴⣿⣿⣿⣧⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⣧⣸⠜⠀⠀⠹⣆⠈⣿⡄⠀⣰⣯⠿⠄⣐⣒⡂⢶⡇⠀⠀⠀⣠⠟⢁⣴⡿⠃⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⠀⣰⡏⢀⡿⠀⠀⣸⡇⣿⣿⣿⣇⡿⠈⢿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣀⣀⠀⠀⢻⡀⠸⣤⣾⣿⣿⡿⣿⠿⣿⣿⣿⣧⢀⣠⠾⣽⠶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠙⢿⣅⣀⡤⠎⠀⡻⣀⣾⡇⠀⣰⣿⡏⡜⣧⣿⡿⠁⠀⢸⠆ ⠀⠀⠀⠀⢰⡄⠀⠀⣼⠃⠀⠈⠛⠲⣼⠃⠀⢻⣿⣿⠏⠀⣿⣤⣾⣥⣽⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡿⢹⣀⣴⣿⡿⢳⢷⣼⣿⠃⠀⠀⠀⠠ ⠀⠀⠀⠀⠈⢷⠀⠀⣏⠀⠀⠀⠀⠀⠘⢧⡀⠸⠿⣯⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣿⣯⣿⢟⣵⣿⠘⣿⠻⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⣿⡄⢳⡀⠀⠀⠀⠀⠙⣆⠀⠙⢧⠀⠐⠿⡏⢀⣤⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢟⣿⠋⣿⡄⠸⣷⢲⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡿⠋⣧⠘⣷⡀⠀⠀⠀⠀⠈⠳⣄⡀⠙⢦⣀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢿⣿⢻⡿⠃⠀⢸⠀⠀⢻⣏⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠃⢸⡟⣆⠘⣿⢦⣀⢀⡀⠀⠀⠘⢯⠻⣗⣟⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⢀⣾⣿⢻⡇⠀⢀⡾⠀⠀⠀⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⠟⢳⣻⣷⣜⣿⡿⠲⣭⣛⠷⠿⣟⢿⣖⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⢀⣾⣿⣿⣾⡇⠀⡼⠃⠀⠀⠀⢹⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠋⠀⠈⠻⣿⣮⠉⠛⠂⣿⡍⠙⠂⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⢀⣾⣿⣿⡟⠁⣇⡼⠁⢀⡆⠀⠀⢸⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣷⣄⢀⠈⣿⠙⠛⠛⠛⠛⠻⣿⡷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⢀⣾⣿⣿⠏⢀⣼⠟⠁⠀⣼⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠾⣧⠀⠀⠀⠀⠀⠈⠻⣿⢯⣙⢶⡒⠛⠲⢤⣄⣀⣀⣀⣀⣀⣀⣠⡾⠁⠀⢀⣾⣿⣟⣡⠴⠟⠁⠀⢀⣼⠃⠀⢀⠀⢸⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠘⢦⣀⡀⠙⠿⣿⣿⣿⣄⠀⠀⠹⣿⡄⠀⠈⠛⣿⡟⠀⠀⢠⡞⠀⢹⣏⣀⣀⣀⣤⣶⣿⠇⠀⠀⡏⠀⠈⡆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠙⠛⠷⣶⣿⣿⣽⡿⣆⠀⠀⢻⣿⡀⢠⣤⠟⠀⠀⠀⠘⠀⠰⣼⣿⣻⡛⠛⠉⣿⡟⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⣧⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⢤⣄⡀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠘⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣷⠀⢀⡟⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀ ⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣶⣦⣤⣤⢿⡆⣄⠀⠀⠀⠀⢀⣀⣀⣤⣶⣧⠀⠀⠺⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢾⡁⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀ ⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣛⣻⡾⠿⡟⢦⠀⠀⠀⠀⠈⠙⠻⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠶⠋⠁⠀⢀⣀⣠⡴⣎⢷⣷⣤⡀⠀⠀⠀⠀⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠣⠄⠀⠀⠂⠀⠀⠀⠉⠉⠁⠀⠀⢠⣿⣰⡿⢩⡿⠀⠉⠉⠀⡠⣼⣾⠏⠋⠷⢦⣄⡀⠀⢠⠴⠆⢺⡇⢾⣧⠀⠉⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀ ⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡟⠀⢸⡇⠀⠀⠀⠀⠀⡟⣸⠃⠀⠀⠀⠀⠉⠉⠀⠀⠀⢸⡇⣾⠿⡆⠀⠀⠀⠀⠀⠐⣇⠀⠀⠀⠀⠀⠀⣿⠀⠉⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣸⠀⢻⡄⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠐⠀⡇⠀⠀ ⠆⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⢇⡤⢸⡇⠀⠀⠀⢀⣼⠃⢸⡇⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⣿⣿⠀⠘⣿⡄⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠐⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⢸⣇⣤⣤⣤⣸⣿⠀⠸⡇⠀⣤⡄⠀⠀⠀⣿⡄⠀⠀⢻⣿⣤⣤⣘⣧⡠⠀⠀⠠⠄⢿⡆⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢤⠀⡇⠀⠀ ⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⣀⡤⠶⢺⣿⡟⠛⠛⢻⡿⠀⠀⣷⠀⣿⣧⠀⠀⠀⣏⣿⡀⠀⡻⣿⡍⠉⠉⠛⣿⣶⣄⠀⠀⠘⣿⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡆⡇⠀⠀ ⣸⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠷⠒⠉⠀⠀⠀⠸⣿⢿⡄⠀⢸⡇⠀⠀⢹⡇⣿⢹⣆⠀⠀⣿⠈⣧⡀⠀⠹⣧⠀⠀⠀⠈⢿⣯⣿⣷⣦⣹⣷⠀⠀⠀⠀⠙⠁⠀⠀⠀⡎⣷⡇⠀⠀ ⡇⠀⠀⠀⠀⢀⣀⣴⠟⢹⡏⠀⠀⠀⠀⠀⠀⠀⢻⡜⣷⣄⢸⠃⠀⠀⠸⣿⣿⠀⢿⡄⠀⢹⠀⠘⢷⡀⠀⣿⠀⠀⠀⠀⠀⠹⣿⡞⢿⡿⣿⣦⠀⠁⠀⠀⠀⠀⠀⡀⣧⣿⡇⠀⢀ ⠁⠀⠰⡀⠀⢸⣿⠁⠀⣸⠁⠀⠀⢲⣤⣤⣀⣳⣌⣇⠘⣿⣿⣦⡀⠀⠀⢹⣿⡆⠈⢿⣦⣿⣇⠀⠀⠻⣦⣼⡧⠤⠤⠤⢄⣀⣀⡙⠮⢻⣎⢿⣿⣧⣄⠄⠀⠀⠀⠀⢻⣾⡧⠞⠋ ⠀⠀⠘⡃⠀⢸⣿⠀⢀⡿⠀⣲⣶⣿⠿⠛⠛⠛⠛⣻⣷⣮⣿⡇⠁⠀⠀⠀⢻⡇⠀⠈⢿⡟⣿⠀⠀⠊⠉⢛⣷⣠⣤⣤⣴⣞⣉⣉⣀⣀⠙⢿⣿⣯⠻⣷⠆⠀⠀⠀⢸⡿⡇⠀⠀ ⠀⠀⠀⣧⠀⢸⣿⣧⣼⣷⣾⡿⠋⠀⠀⠀⠀⢠⣿⡟⠻⠟⢻⣷⡄⠀⠀⠀⠀⢹⠀⠀⠀⠙⠊⠁⠀⣴⣾⣿⣿⣿⣿⣯⡉⠙⠻⣿⣿⣦⣀⠀⠈⢻⣇⢹⣷⡀⠀⠀⠀⣿⡇⠀⠀ ⠀⠀⠀⣿⠀⢸⣿⣷⢹⡇⠈⠛⠆⠀⠀⠀⢀⣿⣿⣷⣆⣀⣾⣿⡇⠀⠀⠀⠀⠀⣧⢀⠀⠀⠀⠀⠈⢡⣾⣏⠉⠉⠁⣹⣿⡆⠀⠀⠙⠻⣿⣿⠉⠁⠻⣼⡿⠿⣦⡀⡀⢿⡇⠀⢰ ⠀⠀⠀⢸⡇⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠚⠁⠀⠴⠊⠁⠀⠀⠘⠋⠀⠀⠀⠀⠀⠘⢿⣿⣶⣶⠾⢽⣿⡇⠀⠀⠀⣀⡾⠿⠷⢦⣀⣽⡇⠀⢸⣿⣿⣾⡇⢀⣿ ⠀⠀⠀⠀⣧⢼⣿⣿⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠈⠉⠀⠀⠀⠀⡀⣠⣿⠁⠀⣼⣧⡘⠻⣇⣾⣿ ⠀⠀⠀⠀⢻⣿⡏⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣒⡭⢡⣿⣧⡶⠛⠋⠉⢷⣀⣿⣿⣿ ⡆⠀⠀⠀⢸⣿⡇⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠨⠒⠉⠁⠀⣸⣿⠋⠀⣠⢴⠂⣾⣿⣿⣿⣿ ⢣⠀⠀⠀⠈⣿⡇⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⢠⠞⠷⠾⠀⣿⣿⣿⣿⣿ ⢸⠀⠀⠀⠀⢿⣷⠀⢿⣧⠀⠀⣠⣴⠄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢫⠃⢠⠋⢳⠀⠀⠀⣿⣿⣿⣿⣿ ⠘⣇⠀⠀⠀⠘⢿⢳⣄⣹⠴⠋⠁⡼⠀⠀⠀⠀⠀⠀⢰⣿⣯⣗⣶⠒⠢⠤⠤⠤⠤⠤⣔⣻⣿⣷⡄⠀⠀⠀⠀⡿⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠈⣇⡼⠀⣠⠞⣿⣿⣿⣿⣿ ⠄⢿⡆⣠⣤⡶⠞⠓⠉⠉⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⣼⡿⠋⠀⠉⠙⠒⠒⠒⢶⠚⠉⠉⠀⠳⣿⡇⠀⠀⠀⠀⡇⠘⢦⠀⠀⠀⠀⠀⠀⢠⣶⡿⠟⠒⠋⣠⠞⠁⣼⣿⣿⣿⣿⣿ ⠀⡸⠋⠉⠀⠀⠀⠀⢀⣠⢶⡏⠀⠀⠀⠀⠀⡀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀⠀⠀⣿⠀⠈⢳⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠇ ⠛⠀⠀⠀⠀⣀⣤⣖⣹⡇⢸⣿⣄⠀⠀⠀⠷⠁⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠂⠀⠀⠀⠀⠘⡆⠀⠀⠘⢳⣤⣴⣦⣀⠨⢃⣠⠴⣶⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⣴⠟⠁⠀⢸⣿⣼⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠘⢿⡿⢿⣿⣿⠃⢠⣿⡟⢸⣿⣿⣿⣿⡟⠀⠂ ⠀⠀⣠⡞⠁⠀⠀⠀⣸⠋⠉⢻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠘⢷⠤⣀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⡤⠲⠤⣄⠀⠀⣠⣤⣿⣆⠀⠀⠈⠳⡀⢠⠏⠀⢸⣿⡇⠈⣿⣿⣿⡟⠘⠀⠀ ⠀⢀⣿⠁⠀⠀⠀⢀⡇⠀⠀⢸⠀⠉⠛⣿⣿⣦⣄⠀⠀⠀⠀⠘⡆⢨⠙⢦⣄⡀⠀⢀⡠⠞⠀⡞⠀⠀⠀⠈⣱⠾⢻⠽⠛⠙⣆⠀⠀⠀⠙⢿⠲⣄⣸⣿⡇⠀⢸⣿⠏⠀⠀⢀⡀ ⠀⠜⡜⠀⠀⠀⠀⣸⠀⠀⠀⢸⡄⠀⠀⢸⣿⣷⡈⠳⣄⠀⠀⠀⢧⡄⠀⠀⠈⢏⢙⡏⠀⠀⣸⠁⠀⠀⡴⠋⠁⢼⠁⠀⠀⠀⠘⢷⠦⣀⡀⠀⠀⠈⢻⣿⡇⢀⡾⠏⠁⠀⣠⠞⣱ ⠀⡐⠀⠀⠀⢀⡞⠁⠀⠀⢀⣾⡇⠀⠀⠀⢿⣿⣧⠀⠀⠳⣤⡀⠘⣇⠀⠀⠀⠘⠚⠀⠀⣠⡿⠀⠀⢰⡇⠀⠀⢸⡀⠀⠀⠰⡄⣸⠀⠀⠀⠀⠀⠀⢸⣿⣷⡟⠁⠀⢀⡴⠗⠋⠉ ⢠⠃⠀⠀⣠⠋⠀⢀⣠⣾⣿⣿⢷⡀⠀⠀⠈⢿⣿⡄⠀⠀⠘⢿⣷⣭⡀⠀⠀⣀⣤⣴⡿⣿⠀⠀⠀⢰⡇⠀⠀⠀⡇⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⢤⡾⠀⠀⠀⠀ ⢸⡆⢀⡞⠁⢀⡔⠋⣿⣿⠛⠋⠀⠙⢦⣀⡐⡈⠻⣿⣦⣤⣄⣀⣙⣿⣿⣿⣽⣿⣿⣿⡀⢸⡀⠀⠀⢸⣿⠀⠀⠀⡝⠀⠀⠀⣏⠑⣒⡒⠒⠒⠂⠀⠀⠘⣿⣏⠀⣿⠃⠀⠀⠀⠀ ⠀⠛⠚⠒⠒⠉⠀⣸⣿⣿⣦⣴⠶⠒⠒⠿⣍⠛⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⡟⢦⠀⣼⣿⣄⠀⠀⢹⠀⠀⠀⢹⡎⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠴⠛⠉⠉⠀⠀⠀⠀⠀⠀⢳⡷⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣷⠟⠻⢿⣦⡀⠈⢧⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⡏⠙⢯⡛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠟⠀⠀⠀⠉⠳⣜⠻⣷⠢⣄⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣦⣤⣤⡀ ⠀⠀⠀⠀⠀⠀⣀⣦⡤⣶⣿⣏⣿⠇⢸⣿⠇⠀⠀⠈⠳⢤⣀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠳⡄⠀⠀⠀⠀⠈⠓⠾⣇⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷

⠣⠄⠀⠀⠂⠀⠀⠀⠉⠉⠁⠀⠀⢠⣿⣰⡿⢩⡿⠀⠉⠉⠀⡠⣼⣾⡏⠋⠷⢦⣄⡀⠀⢠⠴⠖⢺⡇⢾⣧⠀⠉⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀ ⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⡟⠀⢸⡇⠀⠀⠀⠀⠀⡟⣸⠃⠀⠀⠀⠀⠉⠉⠀⠀⠀⢸⡇⣾⠿⡆⠀⠀⠀⠀⠀⠐⣇⠀⠀⠀⠀⠀⠀⣿⠀⠉⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⠀⠀⢸⠇⠀⠀⠀⠀⢸⡇⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣸⠀⢻⡄⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠆⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⢇⡤⢸⡇⠀⠀⠀⢀⣼⠃⢸⡇⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⣿⣿⠀⠘⣿⡄⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠐⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⢸⣇⣤⣤⣤⣸⣿⠀⠸⡇⠀⣤⡄⠀⠀⠀⣿⡄⠀⠀⢻⣿⣤⣤⣘⣯⡠⠀⠀⠠⠄⢿⡆⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⢤⠀⡇⠀⠀ ⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⣀⡤⠶⢺⣿⡟⠛⠛⢻⡿⠀⠀⣷⠀⣿⣧⠀⠀⠀⣏⣿⡀⠀⡻⣿⡍⠉⠉⠛⣿⣶⣄⠀⠀⠘⣿⡀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡆⡇⠀⠀ ⣸⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠷⠒⠉⠀⠀⠀⠸⣿⢿⡄⠀⢸⡇⠀⠀⢹⡇⣿⢹⣆⠀⠀⣿⠈⣧⡀⠀⠹⣧⠀⠀⠀⠈⢿⣯⣿⣷⣦⣹⣷⠀⠀⠀⠀⠙⠃⠀⠀⠀⡎⣷⡇⠀⠀ ⡇⠀⠀⠀⠀⢀⣀⣴⠟⢹⡏⠀⠀⠀⠀⠀⠀⠀⢻⡜⣿⣄⢸⠃⠀⠀⠸⣿⣿⠀⢿⡄⠀⢹⠀⠘⢷⡀⠀⣿⠀⠀⠀⠀⠀⠹⣿⡞⢿⡿⣿⣦⠀⠁⠀⠀⠀⠀⠀⡀⣧⣿⡇⠀⢀ ⠁⠀⠰⡀⠀⢸⣿⠁⠀⣸⠁⠀⠀⢲⣤⣤⣀⣳⣌⣇⠘⣿⣿⣦⡀⠀⠀⢹⣿⡆⠈⢿⣦⣿⣇⠀⠀⠻⣦⣼⡧⠤⠤⠤⢄⣀⣀⡙⠮⢻⣎⢿⣿⣧⣀⠄⠀⠀⠀⠀⢻⣾⡧⠞⠋ ⠀⠀⠘⡃⠀⢸⣿⠀⢀⡿⠀⣲⣶⣿⠿⠛⠛⠛⠛⣻⣷⣮⣿⡇⠁⠀⠀⠀⢻⡇⠀⠈⢿⡟⣿⠀⠀⠊⠉⢛⣷⣠⣤⣤⣴⣞⣉⣉⣀⣀⠙⢿⣿⣯⠻⣷⠆⠀⠀⠀⢸⡿⡇⠀⠀ ⠀⠀⠀⣧⠀⢸⣿⣧⣼⣷⣾⡿⠋⠀⠀⠀⠀⢠⣾⡟⠻⠟⢻⣷⡄⠀⠀⠀⠀⢹⠀⠀⠀⠙⠊⠁⠀⣴⣾⣿⣿⣿⣿⣯⡉⠙⠻⣿⣿⣦⣀⠀⠈⢻⣇⢹⣷⡀⠀⠀⠀⣿⡇⠀⠀ ⠀⠀⠀⣿⡀⢸⣿⣷⢹⡇⠈⠛⠆⠀⠀⠀⢀⣿⣿⣷⣆⣀⣾⣿⡇⠀⠀⢀⠀⠀⣧⢀⠀⠀⠀⠀⠈⢡⣾⣏⠉⠉⠁⣹⣿⡆⠀⠀⠙⠻⣿⣿⠉⠁⠻⣼⡿⠿⣦⡀⡀⢿⡇⠀⢰ ⠀⠀⠀⢸⡇⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠚⠁⠀⠴⠋⠁⠀⠀⠘⠋⠀⠀⠀⠀⠀⠘⢿⣿⣶⣶⠾⢽⣿⡇⠀⠀⠀⣠⡾⠿⠷⢦⣀⣽⡇⠀⢸⣿⣿⣾⡇⢀⣿ ⠀⠀⠀⠀⣧⢼⣿⣿⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠈⠉⠀⠀⠀⠀⡀⣠⣿⠁⠀⣸⣧⡘⠻⣇⣾⣿ ⠀⠀⠐⠀⢻⣿⡏⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣒⡭⢡⣿⣧⡴⠛⠋⠉⢷⣀⣿⣿⣿ ⡆⠀⠀⠀⢸⣿⡇⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠩⠒⠉⠁⠀⣸⣿⠋⠀⣠⢴⠂⣾⣿⣿⣿⣿ ⢣⠀⠀⠀⠈⣿⡇⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⢠⠞⠷⠾⠀⣿⣿⣿⣿⣿ ⢸⠀⠀⠀⠀⢿⣷⠀⢿⣧⠀⠀⣠⣴⠄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠰⢫⠃⢠⠋⢳⠀⠀⠀⣿⣿⣿⣿⣿ ⠘⡇⠀⠀⠀⠘⢿⢳⣄⣹⠴⠋⠁⡼⠀⠀⠀⠀⠀⠀⢰⣿⣯⣗⣶⠒⠢⠤⠤⠤⠤⠤⣔⣻⣿⣷⡄⠀⠀⠀⠀⡿⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠈⣇⡼⠀⣠⠞⣿⣿⣿⣿⣿ ⠄⢿⡆⣠⣤⡶⠞⠓⠉⠁⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⣼⡿⠋⠀⠉⠙⠒⠒⠒⢶⠚⠉⠉⠀⠳⣿⡇⠀⠀⠀⠀⡇⠘⢦⠀⠀⠀⠀⠀⠀⢠⣶⡿⠟⠒⠋⣠⠞⠁⣼⣿⣿⣿⣿⣿ ⠀⡸⠋⠉⠀⠀⠀⠀⢀⣠⢶⡏⠀⠀⠀⠀⠀⡀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠀⠀⠀⠀⣿⠀⠈⢳⡀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⠇ ⠛⠀⠀⠀⠀⣀⣤⣖⣹⡇⢸⣿⣄⠀⠀⠀⠷⠁⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠂⠀⠀⠀⠀⠘⡆⠀⠀⠘⢳⣤⣴⣦⣀⠨⢃⣠⠴⣶⣿⣿⣿⣿⣿⣿⣿⡟⠀ ⠀⠀⠀⠀⣴⠟⠁⠀⢸⣿⣼⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠘⢿⡿⢿⣿⣿⠃⢠⣿⡟⢸⣿⣿⣿⣿⠟⢀⠂ ⠀⠀⣠⡞⠁⠀⠀⠀⣸⠋⠉⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠘⢷⠤⣀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⡤⠲⠤⣄⠀⠀⣠⣤⣿⣆⠀⠀⠈⢳⡀⢠⠏⠀⢸⣿⡇⠈⣿⣿⣿⡟⠘⠀⠀ ⠀⢀⣿⠁⠀⠀⠀⢀⡇⠀⠀⢸⠀⠉⠛⣿⣿⣦⣄⠀⠀⠀⠀⠘⡆⢨⠙⢦⣄⡀⠀⢀⡠⠞⠀⡞⠀⠀⠀⠈⣱⠾⢻⠽⠛⠙⣆⠀⠀⠀⠙⢿⠲⣄⣸⣿⡇⠀⢸⣿⠏⠀⠀⢀⡀ ⠀⠜⡜⠀⠀⠀⠀⣸⠀⠀⠀⢸⡄⠀⠀⢸⣿⣷⡈⠳⣄⠀⠀⠀⢧⡄⠀⠀⠈⢏⢙⡏⠀⠀⣸⠁⠀⠀⡴⠋⠁⢼⠁⠀⠀⠀⠘⢷⠦⣀⡀⠀⠀⠈⢻⣿⡇⢀⡾⠏⠁⠄⣠⠞⣱ ⠀⡐⠀⠀⠀⢀⡞⠁⠀⠀⢀⣾⡇⠀⠀⠀⢿⣿⣧⠀⠀⠳⣤⡀⠘⣇⠀⠀⠀⠘⠚⠀⠀⣠⡿⠀⠀⢰⡇⠀⠀⢸⡀⠀⠀⠰⡄⣸⠀⠀⠀⠀⠀⠀⢸⣿⣷⡟⠁⠀⢀⡴⠗⠋⠉ ⢠⠃⠀⠀⣠⠋⠀⢀⣠⣾⣿⣿⢷⡀⠀⠀⠈⢿⣿⡄⠀⠀⠘⢿⣷⣭⡀⠀⠀⣀⣤⣴⡿⣿⠀⠀⠀⢰⡇⠀⠀⠀⡇⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⢦⡾⠀⠀⠀⠀ ⢸⡆⢀⡞⠁⢀⡔⠋⣿⣿⠛⠋⠀⠙⢦⣀⡐⡈⠻⣿⣦⣤⣄⣀⣙⣿⣿⣿⣽⣿⣿⣿⡀⢸⡀⠀⠀⢸⣿⠀⠀⠀⡝⠀⠀⠀⣏⠑⣒⡒⠒⠒⠂⠀⠀⠘⣿⣯⠀⣿⠃⠀⠀⠀⠀ ⠀⠓⠚⠒⠒⠉⠀⣸⣿⣿⣦⣴⠶⠒⠒⠿⣍⠛⠲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⡟⢦⠀⣼⣿⣄⠀⠀⢹⠀⠀⠀⢹⡎⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠠⠴⠛⠉⠉⠀⠀⠀⠀⠀⠀⢳⡷⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣷⠟⠻⢿⣦⡀⠈⢧⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⡏⠙⢯⡛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⠟⠀⠀⠀⠉⠳⣜⠳⣷⠢⣄⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣦⣤⣤⡀ ⠀⠀⠀⠀⠀⠀⣀⣦⡤⣶⣿⣏⣿⠇⢸⣿⠇⠀⠀⠈⠳⢤⣀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠳⡄⠀⠀⠀⠀⠈⠓⠾⣇⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷

⠀⠀⠀⠀⠀⢀⣠⣴⣷⣀⣴⣾⣦⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⡯⠙⠛⠿⠋⢅⠛⠩⠿⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠊⠀⠀⠰⢱⠀⠀⠂⠀⢈⢂⠀⠀⠀⠀ ⠀⠀⠀⢀⢃⠁⠀⣐⡇⡀⠀⠰⣨⠄⠀⢂⢡⠀⠀⠀ ⠀⠀⠀⠜⡄⠀⡶⢓⣲⡇⢀⡶⣋⢮⢿⠊⡘⢆⡀⠀ ⠠⢔⣁⣠⠀⢸⡿⣿⣗⠧⠋⢰⣿⡿⢿⠀⢠⣀⡈⠆ ⠀⠠⡶⡌⠀⠀⣷⣿⡅⠀⡀⠀⣽⣷⣯⠀⠈⠘⠄⠀ ⠀⠀⣧⠃⠀⠀⣿⣯⣄⣀⢀⣀⣬⣿⡏⠰⠀⢣⡼⠀ ⠀⠀⠸⢀⠀⠉⣹⣿⣿⣿⣿⣿⣿⣿⠀⣼⡠⠞⠀⠀ ⠀⠀⢠⣯⣆⠐⣸⣿⣿⣿⣿⡿⠿⠛⠉⣏⣢⡀⠀⠀ ⠀⠀⠀⣩⣿⣿⣿⣿⣿⠁⠀⣀⣦⣤⠴⠛⠉⠀⠀⠀ ⠀⠀⠀⠉⠉⠁⠛⠛⠉⠙⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⡠⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠀⠀⠀⠀⢀⠠⢄⡠⠊⠉⠉⠉⠍⡉⠉⠚⠲⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀ ⠑⡀⠀⠀⠀⠀⡠⢁⡴⠫⠃⢀⠐⠆⠀⠀⠈⠒⡂⠕⢍⣳⡇⠀⠀⠀⠀⠀⠀⠀ ⢟⠛⢤⠀⠀⠀⠑⡞⡡⠁⠀⠀⠁⠢⢄⣀⡀⢀⣀⠔⠚⠡⠙⣦⠀⠀⠀⠀⢀⠁ ⠈⠫⣙⣧⡀⡀⢐⠡⢁⠀⢰⠀⠀⠀⠈⠄⠀⡺⣄⣁⠀⠀⢡⠑⡀⠀⠀⠀⠘⠀ ⠀⠀⠘⣠⣤⠀⢼⠀⢸⡀⠀⠡⡀⠀⠀⣼⣞⣤⡼⢼⠀⢸⠀⠢⠬⠂⠀⠀⢀⠀ ⠀⠀⠀⠟⠁⣰⢞⠠⠈⣴⣭⣵⣜⠢⡤⢘⣍⠛⠛⢰⢀⣿⣴⣂⠚⠀⠀⠀⠠⠀ ⠀⠀⠐⠠⠂⡜⢸⡈⣄⠹⣧⠛⠛⠀⠊⠀⠀⡀⠀⠒⠃⣩⠵⠏⠀⠀⠀⢀⠀⠀ ⠀⠀⡰⢁⡾⠁⠀⠟⠼⠢⣕⠤⠀⠀⡴⠘⠃⢉⠀⢀⣬⠂⠀⠀⠀⠀⠀⠁⠀⡀ ⠀⠐⢁⡞⠁⠀⠀⠀⠀⠀⠀⠑⢀⠀⠑⠀⠠⠊⣠⢎⣷⣄⠀⠀⢀⡀⣀⠀⠀⢰ ⢀⡦⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣷⢂⠤⠊⣠⣿⣿⣿⠖⠊⠀⠀⡠⠁⠄⢡ ⡄⠉⠂⢀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣽⡇⢠⣼⣿⣿⠟⣏⠀⡀⠠⠎⠂⢰⣾⣧ ⢣⢸⣶⣾⣶⡀⠀⠀⠀⠀⢀⢻⣿⣿⠏⠀⣸⣿⣿⣿⣿⣍⣀⡇⢀⣔⣺⣿⡏⠁ ⠀⠀⠈⠻⣿⣿⠀⠐⠁⢠⠥⠞⠛⠻⡿⠼⠿⢁⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⡻⣡ ⠐⠂⠤⠴⠽⢣⠁⠀⢠⠏⠀⢀⠴⠃⠐⠨⢠⣬⣼⣦⣼⣿⣿⣿⣿⣿⣿⣯⣶⣾

⣷⠁⡠⠀⡰⠁⠀⡰⡁⠤⠐⠊⠡⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⡇⡐⠁⠰⠁⠀⠰⠁⠀⠠⠤⡀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠒⢄⠀⠀⠀⠀⠀⠀⢸ ⡗⠀⢑⢳⣶⢯⠛⠛⡻⠷⣦⢌⠐⠄⠀⠀⠀⠀⠀⡀⠤⠄⡀⠈⠂⠀⠀⠀⡀⢸ ⡇⠀⡌⠀⠙⣶⣤⡼⠤⡬⡥⠯⠃⢘⠀⠀⠀⠠⣤⠶⠦⠶⠾⣶⣦⣄⠀⠀⠰⣸ ⡇⢀⠁⠠⡸⠈⠥⠐⠃⠉⠀⠀⠀⠊⠀⠀⠀⠀⠈⠁⠒⠤⢔⡁⠤⠙⣿⣦⣀⣸ ⡇⠘⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠛⠋⠀⢸ ⡇⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾ ⡇⠀⠀⠀⡀⠀⠀⠀⢹⣾⣥⣄⣀⣉⡀⠂⠤⡀⠀⠀⠀⠀⠀⠀⢀⡐⠀⠔⡈⢸ ⡇⠀⢸⣆⠷⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣶⣾⣶⡆⠀⠀⠀⠀⠈⢀⠞⠁⡠⢺ ⡇⠀⢸⣿⣦⠀⠀⠀⠀⡏⠀⠀⢠⠋⠉⠉⠙⢿⠟⠀⠀⠀⠀⠀⢠⠎⣠⢟⠁⢸ ⡇⢰⠸⠋⢿⣷⡄⠀⠀⠡⡀⠀⠈⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⡠⡏⠾⠁⣸⣴⢺ ⡇⠀⡆⡄⠸⣿⣿⣦⡀⠀⠐⢄⣀⠠⠐⠈⠀⠀⠀⠀⣠⡔⢉⣼⠈⣰⣾⣇⡧⢺ ⡇⠀⢡⢃⠀⢹⣿⡿⡗⣄⠀⠀⠀⠀⠀⠀⣀⣠⠴⣿⠟⡢⠋⣸⣶⣿⣿⣿⠀⢸ ⣧⡀⠀⢻⡄⠸⡟⠜⠦⡟⢷⣤⣤⣤⢶⠿⣿⣿⡿⠓⣈⡤⢞⡕⢱⣿⣿⣿⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠶⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢸⠀⠀⠀⠀⠀⠀⠀⣠⠶⠞⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢸⠀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⣸⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⡀⠀⠀⠀⠀⠀⡾⠀⠀⠀⣿⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠾⠟⠛⠛⠛⠛⠛⠛⠛⠿⠶⣤⣀⡀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⢳⠀⠀⠀⠀⢸⡇⠀⠀⢠⣿⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠈⢷⡀⠀⠀⢸⠁⠀⠀⠈⣿⠋⠀⣀⣀⠤⢤⠀⠀⢀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⠀⠀⠳⣄⠀⢸⠀⠀⠀⠀⢿⣠⠞⠁⠀⢠⡟⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡄⠀⠀⠈⠳⣼⣇⠀⠀⠀⢀⠇⠀⠀⢀⣟⣀⠼⠯⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢻⣄⠀⠀⠀⠈⠻⡷⣶⠦⢼⣀⠀⠀⢸⡏⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣶⡶⠶⠶⠶⠶⣶⣤⣤⣄⣀⣀⡀⠀⠀⠈⢿⣄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⣦⡀⠀⠀⠀⠙⠯⢦⣀⠉⠙⠒⠾⠲⣶⡋⠁⠀⠀⠀⠀⢀⣤⡶⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠓⠶⣦⣌⣻⡄⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠳⢤⣤⣤⡶⠛⠛⠛⢲⠂⠀⠀⠀⠳⣄⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢹⡄⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣶⠟⣹⠃⠀⣠⢴⠖⠺⣇⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⠟⠁⠀⡇⣠⡞⠁⣾⠀⠀⣽⡗⠦⠤⣶⠒⠚⠃⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡟⠀⠀⠀⠸⢻⡇⠀⠘⣄⢸⣿⣷⠄⠀⣾⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⣧⡀⠀⠀⠀⠀⠀⠀ ⠀⣼⠁⠀⠀⠀⠀⠀⠙⠦⠤⠼⣿⢻⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⣇⠸⠿⣇⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡞⢳⡴⢾⡏⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠋⠀⠀⣿⡆⠀⠿⣷⡀⠀⠀⠀ ⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⣠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠒⠚⠛⠉⠉⠀⠀⠀⠀⠀⣿⣷⣤⣄⢸⠟⢦⠀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠈⠀⢛⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠻⣄⣀⠀⣼⣀⠀ ⢸⡇⠀⠀⠀⠀⠀⠀⣀⣾⠻⠀⢴⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⣍⠀⠁⠸⣯ ⢸⣿⠀⠀⠀⠀⠀⣸⠻⢇⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢨⡗⠂⠘⢳ ⠀⣿⠀⠀⠀⢠⡾⠇⠀⠀⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣳⡄⢀⡼ ⠀⢹⣆⠀⠀⢸⡇⠘⢛⡟⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⡇⠀⠉⢸ ⠀⠸⣿⣄⣰⣾⠷⣾⠉⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⡏⠁⠀⢾⡿ ⠀⢀⣼⠟⠋⠙⠚⢿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣛⠳⠤⣶⠟⠉ ⠀⢸⣧⡶⠀⠀⡀⢸⡆⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⣀⢿⠂⠀ ⠁⠘⠁⢻⣄⢰⡟⠛⠛⠶⠶⠿⢷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣀⡀⣀⣀⢀⡀⡀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣶⠾⠋⢸⡄⢠⠟⡿⠀⠀ ⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄⢠⣤⡄⣧⣤⣤⣤⣶⣼⣟⣛⣽⡆⣇⣤⣄⠀⢀⣤⣤⢀⣤⡄⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⢾⡻⣿⡇⢿⣿⡐⠟⠿⢽⡇⠉⠸⠇⠟⡿⠿⠰⢛⠧⡷⡻⢴⢇⣧⡹⣝⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣷⣶⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⡆⠀⠀⠀⠡⡈⣿⣿⣾⣿ ⠻⣿⡟⠁⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠡⠘⢻⠿⠿ ⡾⠻⢀⠎⠀⠀⠀⠀⠀⠀⠃⡀⡠⠊⠇⢀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⢢⠀ ⢤⠁⠆⠀⠀⠔⠀⠀⠀⢰⡨⡊⠉⠹⢦⡄⠸⠀⠀⠠⠀⠀⠀⡀⠔⣆⡇⢸⠀⠱ ⠼⠸⠀⢀⠊⠀⠀⠀⠒⢼⠷⡷⢶⣦⣦⡙⠀⡆⡠⠁⣀⢤⠺⣷⠀⡿⡃⢸⠀⠀ ⠤⡆⢀⠂⠀⠀⠀⠀⠀⢸⠘⠞⠅⡻⠙⠏⠴⠏⣖⠏⠀⡎⠀⢉⠀⠁⢱⢸⠀⠀ ⠤⡇⡈⢀⠀⠄⠀⠀⠘⣄⢆⠀⠀⠀⠀⠀⠀⠀⠙⡳⣦⡇⢠⡌⠀⡄⢸⡈⢒⠰ ⠀⢹⡃⢸⠀⡜⡄⠀⠠⢃⠑⠢⠀⠀⠀⠀⠀⠀⠀⣃⠉⠆⠸⠥⣤⠁⢈⡟⠐⠓ ⠀⠀⡇⠎⣆⣧⠈⣦⠀⣙⡤⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠀⢀⣿⠀⠀⠃⠠⢀ ⠀⠘⠸⢀⠃⡡⢢⡎⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⠈⠀⢸⣿⠀⢸⠀⠀⠉ ⠀⠀⠀⢸⡴⠁⢩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⢃⠀⠀⠀⣿⣿⡄⡇⢠⡄⠀ ⠀⡐⠀⠃⠀⡰⢋⡄⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣂⠀⣸⡿⢹⣷⣽⣼⣷⣶ ⠊⠀⡜⠀⠀⠀⢄⡁⢁⣚⣕⡢⡀⠑⠠⣀⣠⣤⣶⡏⣠⣿⠿⠁⠀⢿⠓⠻⣷⣿ ⠀⡐⠀⠀⠀⠜⢸⣴⣶⣤⣾⣿⣾⡦⠑⢾⣿⣿⣿⣷⣿⡇⠀⠀⠀⢸⠀⠀⠈⣿ ⠋⠀⠀⠀⢈⢂⠜⠙⣿⣿⡿⠟⣻⣅⢻⣠⣧⣼⣿⠇⠹⡇⠀⠀⠀⠈⠀⠀⠀⢸

⠀⠀⢀⡴⣪⣶⢿⠟⠋⠁⣀⣀⣉⣑⣦⣀⣀⡩⠽⢷⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡰⡷⣫⠊⢠⣏⡴⠒⠫⣉⠀⠀⠀⠑⠌⣉⠙⠿⣟⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⣝⡕⣁⣀⣾⠋⠀⠀⠠⠙⢗⠠⡀⠀⠀⠀⠈⠑⠪⢷⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⡿⠋⢡⡟⡏⠀⠀⠀⡆⠀⠀⠓⢄⡉⠀⢒⠒⣖⠢⣀⠀⠀⠀⠀⠁⠂⠀⠀⠀ ⣿⠁⢀⡾⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⣆⣏⢡⣝⡗⠤⡄⠒⠀⠉⠉⠀⠀ ⢿⠀⢼⠃⢰⠀⠀⢀⠀⠀⠀⣠⠀⠀⠀⠀⠀⡅⠙⡿⣿⠁⠀⣸⠀⠀⠀⠀⠀⠀ ⠚⠦⣿⢀⢸⡄⠀⠀⢂⡆⡝⠁⡀⠀⡀⢀⡷⢀⣴⣞⢮⡾⠁⢀⡗⠂⠠⢄⠀⠀ ⠀⠀⢸⡄⢣⡇⠀⠀⠀⢿⣠⣼⣷⠶⠕⠁⠀⠻⣏⡹⢀⠁⢀⡞⣕⣬⣷⠁⠀⠀ ⠀⠀⠀⢣⡨⠳⠐⡀⠀⠈⢚⢍⣉⠇⠀⠀⠀⠀⠀⠀⣼⡴⢻⠫⣀⡔⠁⠀⠀⠀ ⠀⠀⡠⠊⣀⡀⠵⣔⣄⣀⣀⡑⠀⠀⠀⢔⣊⠇⡀⢴⠗⠁⣼⣀⠈⠢⡀⠀⠀⠀ ⠀⠈⡨⢒⣈⢩⠏⡉⡗⢉⠿⠋⠃⣖⢦⣄⣤⡞⡯⠋⠀⡰⡏⠀⠑⠠⡐⠄⠀⠀ ⠀⠪⠛⠁⣠⠾⣮⣄⠗⠁⡾⠂⠺⡓⢿⣿⣿⣿⠀⣠⡚⢀⣇⣀⣤⣾⢿⠂⠄⡀ ⠤⠧⣖⣈⠉⠉⡜⡁⠀⣸⢧⡀⠠⠣⣀⣼⢷⣬⣄⡇⠀⠈⡟⢍⠈⠁⠸⠀⠀⠈ ⠉⠒⠐⢸⠀⠘⠜⠱⡀⢻⠀⠣⣀⢀⠿⡁⠀⢈⠋⠉⢲⢟⡖⢜⠂⠀⠀⠀⠀⠀ ⠂⠀⠀⠸⠀⠀⠀⢀⣯⢳⡩⡖⣏⠀⢀⠔⠉⠉⠲⠤⢸⢸⣇⠈⠕⢄⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠰⣆⠤⠤⠤⣄⣀⠤⣖⠞⢋⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣤⡾⢗⡪⠯⣭⣹⣨⡁⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⢀⠀⠀⡴⠚⢡⡞⠁⠀⠀⡠⢖⢟⠉⠀⠀⢀⡀⠀⠀⠈⢑⣄⢀⠀⠀⠀⠀⠀ ⠐⠄⠑⡀⣳⣴⠏⠀⠀⡠⠊⠀⠂⢸⠠⡀⠢⡀⡈⠲⣄⡠⡀⠹⣟⢒⡀⠀⠀⠀ ⠉⣚⠠⣸⣽⢍⡀⢀⠔⡠⠂⡠⢣⠇⢰⡹⠀⠸⢖⠀⠈⢷⣹⡌⣺⡷⠖⠀⠀⠀ ⠤⣸⢧⡼⢛⠢⣗⠵⠊⢀⣠⣿⢿⣜⣸⢵⠷⡑⠈⢆⠀⠀⢹⣿⣾⢧⠀⠀⠀⠀ ⢰⠓⢾⣢⡰⠻⠳⡾⢻⡿⡟⢸⡊⠀⠀⢸⠀⠙⢦⣸⡀⠀⢾⡎⢻⡄⠀⠀⠀⠀ ⢬⠀⠈⣷⣿⡆⠈⣾⣎⣞⣀⣀⣇⠀⢀⣾⠒⣉⣥⢽⣷⢀⢷⣿⣧⠃⠀⠀⠀⠀ ⠋⠐⠀⣼⢿⡤⣾⡗⡿⡖⠶⠆⡼⣠⢻⠃⠈⠈⠙⢁⠟⣿⣿⣿⣑⡠⣄⣒⣠⠀ ⣀⣀⠜⢹⣾⣧⠹⣷⣧⠀⠀⣰⠟⠁⠁⠀⠀⠀⠀⠀⢠⠻⣿⣟⡗⢻⠿⡏⡙⣆ ⠊⠟⠆⡞⣾⡷⡀⡟⣿⣧⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⣿⣋⢱⣤⣧⡇⡇⠸ ⠀⠀⣸⣇⣿⡈⠀⡠⣺⡿⡑⣄⠀⠀⠀⠀⠀⠀⠀⡠⠁⣸⢹⢻⠘⣿⣿⡇⡇⠀ ⠀⣠⣱⡻⠉⠁⠀⠀⣹⣿⠳⣹⣿⡦⡀⠀⠀⡠⠊⣀⡼⠁⡞⠆⡄⣿⣿⡇⡇⠀ ⢈⣽⠟⠑⡰⣄⢀⣾⣟⡇⣇⠹⣿⣇⠈⢙⣽⠿⣾⣯⡀⣸⠀⠏⠱⣿⣿⣇⡆⠀ ⠅⠂⠉⠉⠁⠲⣿⣿⣾⡇⢹⣿⡷⠻⠴⡛⠰⢷⡷⠣⡵⡇⠀⠀⠀⣿⠿⣿⠇⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣒⠦⡼⣁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⢡⡤⠤⠙⠁⠤⢄⠀⠈⠑⠄⡀⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡄⠠⢐⢕⣵⠋⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⢈⡀⠝⠀⠀⠀⠀⠀⠀ ⢃⠀⠀⠀⠀⠀⢲⢯⣿⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠐⠀⠵⡆⠀⠀⠀⠀⠀⠀ ⠁⠁⠀⠀⠀⡀⢻⣿⠏⠀⠘⠀⠀⠰⢀⣰⣀⠀⠀⠀⠐⢖⠈⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣼⣯⠔⠐⢈⣹⢣⠀⠀⠆⣸⣬⣢⣹⢀⢀⠀⠁⠚⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡠⠚⢁⡄⢲⠛⣿⢿⠻⣄⡈⢽⣿⣿⢹⠆⢰⡟⡍⡉⢂⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢧⠣⡘⣦⡉⠁⠚⠊⠈⠉⠁⢤⢞⡡⠻⠟⠄⠀⠀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⡄⠃⢹⢅⠀⠀⠀⠆⠀⠀⢀⢼⠁⡸⠀⠀⠐⠤⡃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠑⠘⡀⠄⠈⣒⣤⣀⠄⠊⢀⠌⢀⣇⡇⠀⠀⢉⠀⠀⠀⠀⠀ ⢀⢀⣀⠀⠀⠀⠀⠀⠀⠐⢠⠰⠿⠿⠿⣿⣿⣧⠴⠿⠛⠣⠀⢀⢼⣀⡀⠀⠀⠀ ⠕⡣⡻⣽⣆⡤⠄⣀⡀⣠⣁⡀⠀⠀⠀⠀⣀⣀⠔⣹⠋⣾⣷⡮⠊⠲⠁⠀⠀⠀ ⢕⢝⣽⠱⡇⠀⠉⢁⠚⠿⠿⢿⣿⣿⣿⣿⣿⣿⠀⢣⢈⠅⢄⣤⣴⣶⣧⡀⠀⠀ ⣦⡑⢽⠀⣀⣀⡠⠙⠸⠀⠀⠀⠁⠀⣌⢀⢣⠁⠡⢀⢀⠝⢿⣿⣿⣿⣿⣧⡀⠀ ⣿⠟⠉⠁⠀⠀⠘⠌⠣⡆⠀⠀⢠⠀⢁⡎⠂⢠⠤⢜⢀⠀⠈⢹⣿⣿⣿⣿⣷⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⡈⢇⠀⠀⠀⠀⠀ ⠀⠀⠀⠊⠉⠉⠐⢄⠀⠀⡸⠁⢀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠈⠌⠆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠌⠀⡐⠁⠀⡼⢀⠀⠀⠀⠀⠀⠀⠧⠆⠀⠀⠈⣴⠀⠀⠀⠀ ⠀⠀⡀⠀⣀⡔⠁⢀⠌⠀⢀⠊⡠⡌⠀⠘⠔⠄⣀⡘⠀⠩⠀⠀⠀⠸⡆⠀⠀⠀ ⠀⠀⠠⠃⢸⠀⠐⠒⢒⠖⠁⢡⠒⢀⠀⠀⡀⠀⠠⠁⠉⠉⠑⡀⠰⠀⠃⠀⠀⠀ ⠀⢠⠁⠀⢸⠂⡠⠐⠁⠀⠠⠃⡰⢺⠀⠰⠀⡐⠓⠀⠀⠀⠀⠈⢢⣾⡄⠀⠀⠀ ⠀⣸⠀⠀⠀⣾⠶⣴⣤⣴⣧⣥⡀⡜⡐⠁⠈⠀⠸⠷⢶⠶⣷⣶⣻⢷⠇⠀⠀⠀ ⠀⡟⡁⠠⠀⢹⠀⠷⠲⢻⡿⡇⠐⡡⠂⠀⠀⠀⠀⠀⠘⣛⠻⠟⠻⠼⠀⠀⠰⠀ ⠀⠹⡰⡀⠡⡀⢃⠀⠷⠆⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠘⡠⠂⠀⠀⣠⠂ ⠣⡀⠑⢕⣄⠙⡢⠵⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢮⠄⢂⡠⡞⠁⠀ ⠈⠻⠔⠢⡛⠱⢨⢙⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⣰⣀⠀⢐⠀ ⢀⣤⣾⢷⠬⡀⣩⣦⡀⠀⠀⠀⠀⠀⠀⣀⠤⡀⠀⠀⠀⠀⠀⣠⣼⡇⡐⢀⡅⠀ ⢻⠟⢅⢈⡇⠈⡋⡟⠉⠑⠂⠄⡀⡠⢂⣁⠤⡈⡄⢀⣠⡴⠚⣹⠣⠁⢃⢾⠀⠀ ⠁⠀⠀⢨⡃⠀⡇⢇⠀⠀⠀⠀⠜⠀⠀⢄⠉⠐⠻⠟⠉⢀⡼⢻⠃⠀⡠⡏⠀⠀ ⠀⠀⢸⠸⢀⢦⣰⢹⡀⠀⢀⡾⣧⠀⠀⠀⠈⣉⢐⣤⠞⠁⠀⡆⡄⣰⠃⠁⠀⠀

⠀⠀⠀⠀⠀⠀⣾⠎⡇⠀⠀⣟⠉⠑⠂⠐⠈⣾⢆⠀⠀⢸⠀⠀⠈⡆⠀⠀⠁⠀ ⢀⠀⠀⠀⠀⣸⠋⠀⡇⠀⢠⠋⠀⠀⠀⣀⠀⣿⠘⡆⠀⠀⡆⠀⠀⠇⠀⠀⢸⠀ ⡈⠀⠀⠀⢰⣏⠠⠄⣿⡛⢻⠀⡇⣧⠀⡟⡄⢻⠛⠛⣦⣀⠸⡀⠀⢸⠀⢀⣾⠀ ⠃⠀⢠⠔⠻⠀⣀⠀⣸⢣⣜⠀⢱⡏⢆⣰⠘⣄⣇⡀⠈⠻⣻⣷⣀⠀⠀⠸⣻⡠ ⠀⢀⢸⣄⣧⡶⠛⠉⣩⠷⢿⠀⠀⢣⠈⠿⠄⣨⣽⣴⡶⢭⣄⡙⢻⢳⡀⠀⣿⠀ ⠀⢸⢸⣿⡇⠉⠀⠐⠛⠓⠞⠀⠄⠀⠀⠀⠀⠸⢧⠤⣿⠀⢈⡿⠅⢹⠙⣦⣽⢰ ⠀⠀⣾⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂⣿⠔⠳⣽⣿ ⡆⠀⢻⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⠊⢸⣿⣿ ⢠⠀⣘⡧⠕⢊⠇⠀⠀⢸⠷⠖⠂⡀⠲⠶⣦⠀⠀⠢⠀⠀⠀⢀⣤⠡⡣⢺⣿⣿ ⠔⠉⢀⡠⡔⣇⠀⠠⠀⢉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠇⠑⢄⣀⡈⢀⣠⣴⣿⣿⡏ ⠀⡠⠋⠀⠟⡿⣧⣀⠀⠈⠢⢀⠀⠀⠀⢀⢃⠄⡀⢈⣦⠀⠹⣙⠇⣾⠹⣿⠟⠀ ⠀⠃⠀⡘⠀⣄⠈⢿⡗⢄⠀⠆⠈⢒⠖⠁⠃⢠⠘⡝⠁⠱⠄⠈⠑⣿⢠⠏⢀⣦ ⠈⢀⠌⣠⣴⠿⡀⠘⢷⡀⠑⢦⣀⣠⣴⠞⠀⢸⠀⢁⠀⢗⣀⣀⠀⢻⡇⢠⠋⠀ ⠐⠓⠊⡼⠷⠐⠚⢫⣺⣿⣿⣿⣿⣿⣿⣾⢂⣾⣄⠰⠀⢰⠀⠀⠀⠀⢻⡇⠀⠀ ⠀⠀⠀⣀⣠⣔⢶⡏⠙⢝⡛⠻⠿⠿⠿⠿⠾⠀⠈⠢⢳⢢⡆⠀⠀⠀⠀⢿⣶⣦