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