⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⣛⣉⣉⠉⢻⣿⡽⠖⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠻⠿⠛⠉⠉⠷⠚⠉⠒⣛⣛⣃⣍⣉⣉⡋⠙⠳⣤⡀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠖⠛⠉⠉⠳⣤⠀⠀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⢦⡀⠀⠀⣀⡤⠛⢋⣹⣿⣤⣾⣿⣿⣿⣬⣹⣶⣬⣻⡶⡃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀
⠀⠀⠀⠀⢀⣼⣽⡟⣹⡷⡄⠉⢶⣿⣿⣿⣿⣿⣾⣿⣽⢿⣯⢿⡟⣿⣿⣿⣿⣿⣄⣣⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⢀⣾⢫⣿⣾⣏⣷⣄⣀⣴⣿⠿⠋⡩⠈⠵⠋⢀⠟⠁⡞⠀⠹⠙⣿⣿⣿⣯⡻⣿⣿⣿⣶⣶⣤⣄⣀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣼⣯⣿⣿⣿⣿⣿⣿⣯⠟⠁⢠⡞⠁⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⢻⡼⢯⠃⢳⠘⣿⣿⣿⣿⣿⡿⠋⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣀⣼⣿⣿⣿⣿⣿⣿⣿⡿⠡⢀⡞⠏⠀⠀⠀⡴⠋⢠⢰⡇⠀⠀⠀⢠⣪⣿⣸⡄⠀⠙⡜⣿⠿⠟⠋⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠈⠙⢻⡿⣿⣿⣿⣿⣿⡟⡡⢀⣿⠏⢀⡄⠀⡼⠀⣤⡟⡎⢀⡀⠀⠀⠀⢹⡏⢣⠐⡆⠀⢻⢿⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⣿⡇⡿⢹⠏⣿⡏⢠⡇⡼⡿⠀⡞⠀⣸⠇⢠⣿⣽⡇⣜⡆⡀⡴⠀⣾⡇⢸⠀⢣⣦⠈⣿⡇⠀⠀⠀⠇⠀⠀⠀⠀⠀ MOO!! ⠀⠀⠀⠀⠀⡇
⠀⠀⢿⣿⡇⢸⠀⣿⡇⢸⢾⢡⠃⣸⡇⢠⡿⣰⡿⣿⣿⣷⣿⡽⢳⣧⣾⣿⣇⣼⡆⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⣺⡇⢘⢂⣿⡇⣿⣏⣸⠀⣿⠀⣼⢿⣿⠗⣻⡟⢹⡟⢁⡞⢡⡿⠉⣯⣿⣧⣿⣿⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀
⠀⠀⣾⠘⡇⠘⣾⣿⢀⡿⠋⣿⠀⡏⢠⣿⡾⣻⢸⢻⡷⡼⢀⣾⢡⡿⠋⢡⣿⣿⣿⢿⡏⣿⣿⡇⠀⠀⣼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀
⠀⠀⣿⠀⡇⠀⢻⣿⠈⡇⠀⣿⠀⣧⢸⠏⢀⣿⣃⣾⢾⣷⢾⣷⡟⣱⣷⠾⢿⣿⡟⣿⣷⣿⠹⣿⠀⣾⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀
⠀⢰⣿⡄⣿⡆⢸⣿⠀⡇⡆⣿⡀⢻⣸⡾⠛⠋⠉⠙⠋⠁⠋⠀⢠⡉⠀⣺⣿⣿⣿⣿⣨⠃⠀⢹⡀⠛⠛⠦⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀
⠀⢸⡿⣧⣿⣧⣼⢿⡆⢹⡿⣿⣧⣼⢿⡈⠁⠀⠀⠀⠀⠀⠀⠀⠘⠻⠾⣽⣿⣿⢿⣿⢧⣀⠀⠀⠁⠠⠄⠠⠤⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀
⠀⣿⠃⣿⣿⣿⠙⢾⣧⣸⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⣿⣿⡇⢈⣿⠀⠉⠱⣦⠀⠀⠤⢤⣀⡀⠙⢆⡀⠀⠀⠀⠀⠀⠀⠀⡤⠞⠀⠀⠀
⠀⢿⡄⣸⡟⣿⠀⢸⡹⣿⣿⡿⣿⣿⢿⠻⣷⣦⣀⠀⠉⠉⠉⣁⡴⢚⢿⡏⣿⠇⣼⡇⠀⠀⠀⠈⢣⠀⠀⠈⠙⠯⣶⡌⢷⣄⣀⡤⠶⠚⠉⠀⠀⠀⠀⠀
⠀⢸⣧⣿⣷⣿⢀⠘⣧⠙⣷⣇⠹⣿⣸⡀⠀⠙⠛⣿⣷⣴⡾⣷⡝⣿⣼⣷⡿⢰⢿⡟⣄⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠹⣿⡟⣿⣟⡄⢿⡇⡞⣿⠂⡏⣿⣿⡛⣶⣿⣿⣿⣭⣿⠛⢁⡟⣹⣿⣷⣏⠘⠙⠿⣄⡀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢿⣿⡿⣷⠸⣷⡸⢸⣴⣇⣿⡏⠓⠿⠿⢿⡋⢻⣮⠙⠺⣱⣿⠹⠋⠙⢷⣄⡀⣈⣻⣦⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣰⠟⢿⣿⢧⣹⣧⣈⣿⡋⠀⢻⡄⢀⣀⣘⣷⡀⠻⣠⣴⣿⣦⠀⠀⢀⡄⠈⠻⣦⣈⠉⠉⠒⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣼⠃⠀⠀⠙⣿⣿⣿⣿⣀⣯⠛⠉⣿⡶⠦⠬⢿⣧⣠⢾⣿⣾⠟⠀⢀⡎⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠉⠛⠳⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⡇⠀⠀⠀⠀⣼⣿⣿⣏⣵⣯⡀⠀⠸⣷⠀⠀⠀⠿⠷⠶⠋⠁⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠙⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⡇⠀⠀⠀⠀⣿⣿⣹⣿⣿⣾⣷⡀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣤⣀⡀⠀⠀⠈⠙⢧⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⡇⠀⠀⠀⠀⢿⡿⣿⣷⣏⢿⢹⣵⡀⠀⢻⡄⠀⠀⠀⠀⠈⠉⠑⠲⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⡁⠉⢱⣦⣄⠀⠈⢻⣆⠀⠀⠀⠀⠀
⠀⠀⠀⣿⡀⠀⠀⠀⢸⣧⣿⢹⣿⠈⡿⣿⡇⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠻⣿⣷⣦⠀⠹⡆⠀⠀⠀⠀
⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿⣿⡷⡹⣧⠳⢹⡇⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⣀⡘⢻⣿⣷⡄⢻⠀⠀⠀⠀
⠀⠀⠀⠀⢳⣀⠀⠀⠀⠙⢷⡷⡱⣽⣧⣸⡇⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢿⣿⡄⠛⠋⢱⣼⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠻⣽⣿⡻⣿⡇⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⢹⡞⠉⠀⠀⠀⢸⡿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠙⢿⣆⢹⣧⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣄⠀⠀⠀⠀⠀⠀⠈⣷⡀⣀⠀⠀⣸⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣤⣤⣤⠿⡆⣿⡄⠀⠀⠀⠀⢹⣿⣶⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠳⠀⠀⠀⠀⠀⠀⣿⣿⡿⠆⢸⣿⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣇⣷⣼⡇⠀⠀⠀⠀⠸⣿⠛⠒⠚⠻⠶⢤⣀⠀⠀⠀⠀⠀⠀⠈⠀⢤⠀⠀⠀⠀⢀⣿⣿⡷⣀⡼⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠉⠛⠛⠿⢻⣷⠀⠀⠀⠀⠀⢿⣦⡀⠀⠀⠀⠀⠈⠑⣦⣄⠀⠀⠀⠀⠀⠈⣇⠀⠀⢀⣼⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⡗⢄⡒⢺⣿⣆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣦⡄⠀⠘⣿⣿⣿⣦⣄⠀⠀⠀⣿⣲⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣝⡿⢭⣴⣿⣿⣄⠀⠀⠀⠀⢻⣿⣿⣿⠛⠁⠀⠀⣹⣿⣿⣿⣿⢷⣄⣴⣿⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⡟⠉⠉⠉⠙⣿⣦⡀⠀⠀⠘⢿⣿⡿⠂⠀⠀⠰⠃⢈⣻⡿⠃⢀⣿⢃⣿⣟⣻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⣷⠀⠀⠀⠙⢼⣿⣝⠆⠀⠀⠈⢯⠀⡀⠀⠀⠀⠀⢿⣿⡇⢀⣼⡇⣿⡿⠋⠈⣏⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠘⢷⣄⠀⢀⠀⠉⠻⣷⣄⡀⠀⠀⠙⢿⣦⣴⣦⣀⣀⣭⡥⠚⣯⣾⠟⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⢙⣿⣾⣷⡄⠀⠸⢿⣛⠛⠿⠿⠛⠚⠛⢿⡿⠻⢷⣦⣸⣏⢧⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡏⠙⠷⣦⣀⠉⠲⣄⠀⠀⠀⠀⠈⣇⠀⠀⢹⡽⣾⠈⣆⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢰⡏⣿⣽⣿⣿⠀⠀⠀⠙⢳⣦⣌⣳⡆⠀⠀⠀⢸⡄⣶⡄⡧⢿⣷⣼⡆⠀⠀⢸⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢺⣇⣿⣿⣿⢻⡇⠀⠀⠀⠀⠉⠛⠻⣿⣗⠒⠚⢻⡧⡿⣧⣸⣼⣿⡇⡇⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣇⡼⣷⠇⣿⣼⣿⣯⠳⠇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠋⣰⠃⠀⠻⠟⠛⠱⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢸⡇⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠋⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠈⠀⠘⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠠⠞⠁