⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢢⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀
⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀
⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢇⠀
⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⡀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀
⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢦⣿⠏⡟⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀
⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠲⠇⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠺⢧⠀⠉⢢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡨⣷⡀⠈⠇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫
⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢆⢧⢿⣧⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠘⡽⣿⠁⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠡⢊⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀
⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣄⠂⠁⠁⠐⠋⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀
⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡓⠀⠀
⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⠤⠤⠄⠐⠊⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀
⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⢡⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠓⠤⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠉⠲⠤⢀⠀⠀⠀⠀⢀⣀⡀⠤⠒⠉⠀⠀⢸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣦⣸⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠐⣆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⡄⠀⠀⠀⠀⠀⠀⣸⣿⡿⠛⠭⣿⣷⡄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⠀⠑⠢⣄⡀⠀⠀⠀⠀⠀⢀⡠⠖⢹⡄⠀⠀⠀⠀⠀⠀⠀⠈⢿⢄⠀⠀⠀⠀⠀⠀⠀⠀⡘⠄⠹⡄⠀⠀⠀⠀⣼⣋⣀⢧⣿⡿⣾⣿⣿⣦
⠀⠀⠀⠀⢀⣤⣴⢿⣶⣿⣅⠀⠀⠀⠀⠀⠉⠉⡻⠋⠉⠁⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠜⠀⠀⠈⠑⠠⢄⣀⣀⠀⠁⠀⠀⠀⠀⠘⣄⠀⠀⢸⠖⡞⣵⣚⣒⠬⣽⢿⣹⣿
⠀⠀⢠⡴⢛⣈⣝⠻⡮⡻⢶⢷⠀⠀⠀⠀⡰⠊⠀⠀⠀⠀⠀⠀⠀⠀⡝⠦⠀⠠⣶⠁⠀⠁⠉⠉⠀⠀⠀⠸⣿⣷⠀⠀⠀⠀⠀⠀⠈⢆⠀⡿⠿⣛⡧⡦⢵⡙⣒⠚⢃⢻
⠀⢰⣏⣞⢥⠒⠢⢍⣓⣿⡜⣧⣧⠀⣀⠎⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⣿⠃⠀⠀⠀⠺⠈⠀⢀⣠⣬⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠣⣇⢿⢯⣿⡷⢙⣛⢒⠀⠀⠀
⠀⢸⡧⢽⠧⠀⢭⡻⠓⠒⢣⢻⣿⡆⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⣾⣿⡇⢰⣶⠶⠀⠀⠀⡛⣉⣡⠊⣿⣿⣦⡈⠢⡀⠀⠀⠀⠀⠻⡆⢿⣿⢶⡁⠜⠣⠅⠀⠀
⠀⣼⠓⠂⡠⡟⣽⢯⠭⠴⢿⣸⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⣧⣿⣇⠰⠤⠔⠃⠀⠀⠉⠀⠀⢸⣿⣿⣿⣧⠀⠹⠀⠀⠀⠀⠀⠘⣌⣿⠩⠥⠴⠖⠤⠤⠀
⠀⣿⠿⢽⣊⡮⣽⣻⠭⠍⡎⣏⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⡆⠀⢣⠀⠀⠀⠀⠀⡇⠃⡢⠀⠀⠀⠀⠀⠀
⠀⠙⢆⠁⠈⠀⠀⠉⠉⠉⢙⢶⣄⡟⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣽⢺⣿⣿⡀⠀⢣⠀⠀⢀⢿⠫⣦⣛⣓⡣⠤⠄⠀⢀
⠀⠀⣾⡀⡀⠀⠀⠀⠀⠀⣀⡇⡟⢡⣿⠂⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢸⣼⣯⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣇⠀⣀⣧⠀⣸⡆⠉⣛⠠⠤⠈⢉⠓⠂⠐
⠀⢰⠯⠤⠍⠓⠂⠀⠀⠠⠤⣇⢻⢻⣿⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠛⣽⣿⡟⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⡻⢸⣼⡟⢿⣿⣞⠏⠀⣾⠡⠤⣬⣍⡁⠀⠀⠀⠓⠄⠀
⠀⢸⠥⠄⣀⠈⠉⠀⠀⠬⠤⣹⡈⣾⣿⣧⣄⣀⠀⠀⠀⠀⡇⠀⠀⠀⣸⠫⡿⡿⣿⣿⣿⡏⠉⣻⣧⡉⣍⣱⣳⣷⣻⣽⣿⣾⣿⣿⣀⣷⠀⠠⠦⠬⣍⣁⠀⠀⠀⠀⠀⠀