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

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

Warning: This item may contain sensitive themes such as nudity.

⠀⠀⠀⠀⡀⡀⢀⠀⠀⠀⠀⠀ ⠀⠀⡂⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢨⠀⠀⠀⠠⠤⠄⠤⠤⢄⡀⠀ ⠀⠢⢄⡀⣀⣀⠤⠤⠀⠀⠘⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅ ⠀⠀⠀⠀⠀⢀⢀⠀⡀⠄⠃⠀ ⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀
(\__/) (ONO) me when i look up “funny” |>📱<| - oh no! inappropriate stuf! v——-v
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠢⡀⠤⠄⡀⠀⠀⡀⠀⢀⠀⠀⢤⠄⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢎⢀⡐⢐⢂⢄⣤⠔⢤⡀⠰⠈⢁⢄⠀⠁⢂⠐⡄⡠⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⢠⣢⡧⠙⣣⠉⢢⣠⢃⣄⠔⡊⠇⢁⡠⣄⠠⡁⠈⠟⣎⣁⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⢩⣎⡸⣯⡡⢰⢴⣞⣿⣻⣷⢤⣺⣿⣟⡟⣯⡄⠅⢨⣽⢃⢆⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⡵⢦⣡⣟⠔⢆⡻⢼⢾⣿⡿⢯⣺⢿⢿⠧⠿⡅⢎⠈⢭⢻⡎⠌⡁⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡈⠔⣊⣶⡣⣿⠋⢀⣁⠱⣼⣲⣮⣵⣿⣿⣮⣾⡲⣔⠀⠈⠁⠸⣧⠿⠩⣥⡀⠕⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡃⣏⠏⠼⡝⢃⠀⣀⢰⢭⣿⣿⣿⣿⣿⣯⣿⣿⣿⣏⣎⣀⠀⠀⠙⠗⣏⡮⡴⠨⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡼⢿⡤⠃⠀⠀⠄⣠⢜⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣼⡀⠀⠀⠀⠀⠿⣟⢧⠻⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡀⠞⡩⡟⣤⠀⢐⢈⡔⢪⡣⠣⣝⠿⣿⣿⣿⣿⣿⡿⡿⠇⠏⠹⠁⠠⠄⠀⠈⣻⠷⡃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠊⠛⡽⡷⢐⠁⢀⢈⡣⠼⢐⠑⠘⠌⡍⣿⢫⠥⡈⡧⢈⠐⡁⠈⡄⠐⡨⠀⡟⡩⠒⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢌⡐⢈⢯⠸⢠⢊⡊⠂⡿⢪⣘⡡⠱⠁⢰⠈⡀⠘⠖⣌⠄⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⡿⣿⣾⣠⣼⣧⣴⣵⣼⠷⠿⠷⣧⣶⣬⣦⣥⣤⣤⢾⡤⡑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣟⠿⣏⡷⡀⢀⡁⢀⡀⠢⢀⣐⢜⡩⢷⡽⠗⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣵⣿⣿⣻⣿⣿⣷⣾⣿⣿⣾⣿⣿⣻⣯⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⣂⣶⣿⢿⣽⣷⡟⢷⡛⡞⢫⠳⠩⠓⣊⢁⠱⠬⢀⢄⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣜⢫⠙⢎⡚⣼⢱⣩⡄⠌⡴⡅⠍⠐⡈⠍⡐⢣⠂⡥⣃⠔⢠⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡰⠡⠑⡔⣔⠏⣻⡻⣼⢩⡝⡼⢊⠇⣘⠹⡂⠡⡢⢜⡘⣍⠢⢷⣙⣄⡒⠠⠈⠠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠄⠘⠉⠁⠑⡦⡛⣩⡷⡙⡸⣸⢎⡥⢪⡚⠯⢒⡂⢰⣡⡵⢠⡢⢁⡉⠳⣤⠉⡶⣏⠁⠂⡄⠈⠠⠀⠀⠀⠀ ⠀⠀⠔⠀⡀⠆⠖⢸⢭⠞⠘⢉⠫⡒⠼⡨⡬⡧⡸⠳⠱⢒⡙⢝⣣⠑⡸⢈⢄⠔⠄⢰⠈⠘⠐⡜⠄⠠⢀⠀⠈⠀⠀⠀ ⢀⢃⠄⡮⡶⡽⡅⠌⠘⡀⠀⢐⢞⣵⣽⣳⢣⡕⢶⢋⠼⢟⣻⢻⣈⡣⢇⣌⢰⠡⠀⠈⠇⠀⠘⠼⣑⢠⡭⠾⣈⠀⠁⡀ ⠆⠥⠭⢚⡾⠓⡠⡀⣁⠆⢠⠳⢳⢣⣱⢚⣬⣛⡧⢕⣔⣴⣸⠘⣎⣴⣔⡈⠦⡨⡐⠂⠅⠀⠸⠱⡈⢱⠋⢹⣎⡘⡀⡅ ⠁⠄⠤⠑⠀⠀⠀⠀⠀⠀⠈⡲⡛⣿⢇⢿⣹⢨⡵⡾⡎⡔⡞⡃⠱⡌⢗⠉⡤⡡⢒⠀⢰⠀⠀⠀⠀⠀⠀⠀⠛⣕⠠⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣟⢮⢯⢟⡦⡞⠑⡄⢹⢤⢇⣽⢠⠑⣏⢣⠄⠣⢑⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢨⣿⢸⠘⡜⣥⡏⢳⢰⡞⢱⠀⡗⣴⠃⠘⢪⠃⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣷⣘⣎⡵⡆⣑⠸⢪⢆⡞⠤⣢⢃⡊⠔⡡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣹⢿⢽⣻⣯⣾⢡⢏⢞⢫⡸⡀⣃⣁⠇⢟⣠⢓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⡼⢸⢰⢞⠻⡝⠀⠀⠀⠀⠈⢻⣿⢻⢽⢰⢣⡂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⢼⣬⡞⣎⣑⡌⢅⠀⠀⠀⠀⠮⣢⠯⣅⣍⡭⡬⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⡄⢦⣚⣪⡙⠊⡜⠣⠀⠀⠀⠀⢸⡔⠪⢍⡣⢥⠣⡄⠈⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠄⡵⡠⣟⣱⠙⠅⠀⡐⠀⠀⠀⠘⢊⣑⢣⡉⢚⡯⠘⢢⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠦⠰⣑⢇⡋⠄⡂⠌⠀⠀⠀⠀⠀⠀⠂⢡⢚⢆⡛⣪⡃⠜⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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🧃💕💗🐾 Petition to NOT make this an app since the website will then get taken off :/ྀིྀིྀིྀིྀི °❀⋆.ೃ࿔*:・
PLEASE NO MORE NSFW CONTENT. I HATE THEM AND I ALWAYS PRESS 👎 EVERY TIME WHEN I FOUND THEM. THESE NSFW CONTENT MAKES DECRASE MY MORAL! SOME OF YOUNG CHILDRENS WANT SOME COOL AND CUTE EMOJIS BUT PEOPLES THAT POSTING NSFW CONTENTS RUINING THEM! EVERYONE IS BORING FOR NSFW CONTENT. SO PLEASE, EMOJICOMBOS.COM! DELETE EVERY NSFW CONTENTS FROM THIS WEBSITE AND EVERYONE, WHEN YOU LOOK THIS, PLEASE COPY AND SUBMIT COMBO THIS AND SPREAD THIS. NO MORE POSTING NSFW CONTENT. ALL IS FOR NOT LOOKING NSFW CONTENT. PLEASE.
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