⡇⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⣀⣀⣠⣤⣬⣭⣭⣭⣭⣉⣉⡀⠈⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠈⠀⠀⠁⠈⠈⠉⠉⠉⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠙⣟⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⠀⠀⠐⢀⠰⠤⠘⣆⠀⠈⡙⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠸⡄⠪⣻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠹⡄⠘⣎⢯⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠁⠀⠘⡎⢧⣈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⣴⢏⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠹⡜⡎⠑⢌⢷⣄⠀⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⢀⡾⢃⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⣆⠀⠀⠀⣦⠀⢳⢹⠀⠀⠙⣿⣄⠀⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⠀⢠⡾⠁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⣦⣻⡄⠀⠀⠘⡄⠘⣟⡇⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀
⡇⠀⠀⠀⠀⢠⡿⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡜⠀⢳⣻⡀⠀⠀⢹⡀⢹⣁⠀⠀⠘⣆⢿⡤⠤⠒⠒⠚
⡇⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣥⣤⣤⡥⣿⡄⠀⠀⢧⠘⡟⣆⠀⠀⠘⡜⣧⠀⠀⠀⠀
⡇⠀⠀⠀⢀⡿⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠀⠀⠈⠉⠙⠻⡄⠀⠸⡄⣧⠘⣇⢠⡀⠹⢹⡆⠀⠀⠀
⡇⠀⠀⠀⢸⠇⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⢳⢸⠀⢸⡀⢳⠀⠈⣧⠀⠀⢸
⡟⠋⠉⠉⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢠⠂⠀⢀⡼⠁⡇⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⢀⡠⠤⠤⠤⠤⢄⠹⡄⠘⡾⡆⠀⡇⠈⣇⠀⢻⠀⠀⢸
⡇⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠏⡇⠏⠀⡠⠋⠀⠀⡇⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠠⠞⣡⣴⠾⣛⣛⡛⠛⠶⢷⡀⠱⣇⠀⢹⠀⢸⡀⢸⠀⠀⡎
⣇⠀⠀⠀⣿⠀⠀⣷⠀⠀⠀⠀⡇⠀⠀⠀⣰⣛⣫⡗⢠⡞⡓⠦⠀⠀⢻⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⣺⣾⣷⣾⣿⣿⣟⡛⠷⣦⣧⠀⢿⠆⠸⡆⠀⠇⢸⡇⢰⠃
⡿⡄⠀⠀⣿⠀⠀⢹⠀⠀⠀⠀⠀⠀⢀⡴⢛⣭⣽⣇⣯⣍⣻⣧⠆⠀⢸⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⣾⣿⣿⣿⣿⣉⣿⡄⠀⠙⣆⠘⣧⣀⡇⠀⠀⢸⡇⡞⠀
⡇⠹⣆⠀⢹⠀⠀⠘⡇⠀⠀⠀⠀⠀⢈⡴⠋⣵⣿⣿⣿⡿⢿⣟⠧⠀⠘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠠⣄⢸⡆⢻⢿⡇⠀⠀⣼⣿⠁⠀
⡇⠀⠙⣇⢸⡆⠀⠀⣷⠀⠀⠄⡀⣰⠋⠀⢸⣿⣿⣿⣿⣷⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣼⢿⡼⣾⡦⡄⠀⣿⡏⠀⠀
⡇⠀⠀⠘⣾⡇⠀⠀⠸⡆⠀⢰⣇⢷⠀⡤⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠒⠛⠿⠿⢥⣤⣾⡿⠋⢷⣷⠀⢻⠀⣿⠀⠀⠀
⡇⠀⠀⠀⠘⣿⠀⠀⠀⣿⡄⢘⣯⡻⣇⡀⠀⠻⣿⣿⣿⣹⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡀⢸⣄⡏⡇⠀⠀
⡇⠀⠀⠀⠀⣿⣄⠀⠀⡼⠻⣌⣧⠙⠿⣗⣶⠶⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠹⡇⠈⣿⡇⡇⠀⠀
⡇⠀⠀⠀⠀⣷⣙⠳⣏⣠⡖⢻⡻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⣇⡿⠁⠀⠀
⡇⠀⠀⠀⠀⢸⡟⣱⠦⣉⠛⠿⡄⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⡇⠀⣼⣧⠀⠀⠀
⡇⠀⠀⠀⠀⠸⣶⠃⠀⠀⠙⣶⡃⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢠⠃⣸⣱⠃⠀⠀⠀
⡇⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⣿⡇⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⢀⡏⢠⣷⢿⡄⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢻⡝⢆⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠁⠀⠀⠀⢸⡄⣼⣿⣸⣧⡀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢸⡇⠈⢳⡀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠁⣿⢸⠹⣿⠷⠂⠀
⡇⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠘⣿⡄⠀⢳⠀⠀⠀⠀⠈⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣏⡏⠳⣜⣦⡀⠀
⡇⠀⠀⠀⠀⠀⠀⠈⣇⠀⡀⠀⢻⣹⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣤⣤⣀⣀⠀⠀⠀⠀⣀⣠⡴⠞⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣿⠞⠳⣄⠈⠉⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⢹⡀⢧⠀⢸⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣄⠈⠉⠉⠙⠛⠋⠉⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠿⡅⠀⠀⠈⢧⠀⠀⠀
⡇⠀⠀⠀⠀⠀⠀⠀⠈⣧⢸⡀⠈⢿⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⢸⠀⠀⣧⠀⠀⠀⠈⡇⠀⠀
⡇⠀⠀⠀⠀⠀⠀⣠⠞⠹⡎⣇⠀⢘⣧⠀⠙⣟⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠦⣄⣀⣀⣀⠴⣺⡇⠀⠀⠀⠀⠀⠀⢠⣟⠝⠀⢸⠀⠀⡟⠀⠀⠀⠀⢸⠀⠀
⡇⠀⠀⠀⠀⠀⡴⠁⠀⠀⠹⣼⡄⠘⡿⣷⡄⠸⡄⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⢸⡙⠒⠒⠓⠒⠉⠀⣧⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⢸⠁⢀⡇⠀⠀⠀⠀⢸⠀⠀
⡇⠀⠀⠀⠀⢰⠃⠀⠉⠢⠄⠹⣷⠀⢷⣆⠀⠀⢻⠢⡀⠀⢉⡗⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⢻⠀⡎⠀⡼⠀⠀⠀⠀⠀⠸⠀⠀