⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢰⠀⠀⣶⠒⠒⠒⠒⠀⣠⠴⠦⣄⢰⡆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⠏⠳⡄⢸⠀⠠⠭⠭⠭⠭⠭⠄⠻⢤⡤⠟⢸⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⣥⠀⠀⠀⠸⠀⠀⣲⠶⠶⠶⠶⠀⠤⠤⠤⠤⢼⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠀⠀⠙⠒⠒⠒⠒⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⡄⠀⢀⡤⣄⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⠒⣦⠀⡇⠀⡏⠀⢸⡆⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡭⠭⠥⠤⡅⠀⢧⡀⣸⠃⢸⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠤⠤⠤⠇⠀⠀⠉⠁⠀⠸⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠠⠤⢄⠀⡄⠀⡀⠀⠀⠀⠀⢀⣀⠀⢠⠀⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠤⢤⠼⠤⡇⢀⣓⣒⣒⣒⡀⡇⠈⡆⢸⠀⡇⠀⠀⠀
⠀⠀⠀⠀⠤⠤⠤⠴⠥⠀⢰⣈⣀⣉⡃⠀⣖⣉⣉⡢⠀⠣⠴⠁⢸⠀⠅⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢠⣤⣤⡤⠀⣀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢬⣿⣿⣿⣾⠈⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠶⠾⠆⠸⠿⠿⠯⠈⠚⠁⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣠⣄⢀⡄⣀⢀⣠⣠⠀⣤⠀⣄⡄⠀⣄⣀⣀⡀⠀⣠⣤⣄⠀⠀⠀⠀
⠀⠀⠀⠈⠣⠜⢸⡗⣿⢾⣿⣿⣫⠿⣝⣿⡇⠀⠾⣿⣿⠷⢨⣽⣶⣯⡄⠀⠀⠀
⠀⠀⠀⠀⠧⠤⠤⠅⠙⠚⠹⠿⠉⠛⠉⠿⠇⠀⠹⠿⠿⠅⠸⠦⠤⠤⠀⠀⠀⠀
⠀⠀⠀⣀⣀⣀⣀⠀⣀⣀⢀⡀⠀⠀⠀⡀⠀⠀⠀⣀⡀⢀⡀⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢹⡏⣿⣿⢸⣿⣿⢽⡗⠀⣲⣚⣙⣲⡂⠸⣧⡿⢺⢇⣻⣶⣶⣆⠀⠀⠀
⠀⠀⠀⠾⠿⠿⣿⠀⢿⣿⣿⡂⠀⠀⠈⡇⠀⠀⠸⣷⣿⡿⣄⢷⣀⣀⣀⠀⠀⠀
⠀⢀⡀⢀⣀⠀⣀⠀⣀⡀⢀⡀⢀⡀⠀⣀⠀⣀⣀⠀⣀⡀⢀⡀⢀⡀⠀⡀⠀⠀
⠀⣸⣧⢼⣿⠈⠉⣿⣿⡷⣏⣹⢾⡇⠀⢿⣶⡿⣿⢈⡽⢯⣹⡇⡏⢹⡄⡇⢸⠀
⠐⠋⠘⢻⣿⠰⠞⠁⣿⡗⠚⠓⠺⡇⠀⠸⣷⣶⡿⠀⠛⠛⢻⡆⠳⠞⠀⡇⠨⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⠛⣿⢀⣈⣉⣉⣉⣉⣀⠸⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠤⠴⠂⣿⠀⣶⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⢲⡆⣾⢀⡴⠒⢦⡤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢸⡇⣿⠾⢧⣀⡼⠓⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡿⠼⠷⣿⠀⣶⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠙⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠤⠤⠤⠤⢤⡤⠤⠤⣤⠀⣶⠠⠤⠤⣤⠀⣶⣠⡖⠒⣶⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡖⠒⠋⠒⣿⠀⠀⢠⡟⠀⣿⣌⢀⡴⢻⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⣿⠛⠋⠉⠿⢀⣠⠞⠁⠀⣿⠀⢨⡅⢨⡅⠀⠀⠀
⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠛⠒⠒⠒⠒⠈⠁⠀⠀⠀⠛⠀⠀⠀⠀⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢷⢸⣇⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡾⢸⡇⠧⠤⠴⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⢈⠁⠀⠀⠀⠉⡁⠀⠀⠀⡀⣀⣀⣀⡀⠀⠀
⠀⠀⢸⠉⢹⢸⡌⠉⢹⢸⡷⣏⣳⢸⡇⠰⣏⣱⢸⡇⢉⣏⠉⣇⣺⣿⣿⣯⠀⠀
⠀⠀⠸⠤⠼⢸⠤⠴⠋⢸⡷⠾⠷⢾⡇⠰⠾⠷⢾⡧⠟⠘⠧⡇⣽⣿⣿⣗⠀⠀
⠀⠀⠀⠀⢀⡤⣄⢠⡄⡄⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠘⠧⢞⢸⣧⣿⣿⣿⣧⢸⡇⠀⣿⣿⣾⣛⣿⡿⣸⣧⣸⡷⠂⠀⠀⠀
⠀⠀⠀⠀⠀⠴⠞⠶⠄⠧⠤⠤⠄⠈⠛⠛⠿⠿⠉⠉⠉⠿⠋⠈⠻⠇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⣦⣶⣤⣶⣄⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣛⣋⣿⣿⣤⡿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣀⡀⡀⡀⡀⠀⠀⡀⠀⠀⠈⠉⠉⠛⠈⡉⠁⣛⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢾⣿⣿⣿⣿⣿⣶⣶⣿⣛⣿⣟⡃⢸⣇⢸⣷⣿⣹⡷⣿⣴⠻⡆⣿⡼⠻⡶⡇⣾
⠸⣿⠿⣿⣿⣿⣉⣉⣉⣉⣁⣈⣹⡿⠻⣾⡇⣼⣉⣀⣟⠻⣴⠇⣿⠳⡴⠛⡇⣻
⠀⠀⠀⠉⠁⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠉⠀⠀⠀⠁⠀⠀⠀⠁⠀
⠀⠀
