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

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