⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠸⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣶⠲⣍⡟⣛⡗⡅⠖⡽⢱⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣟⣾⡄⠗⠛⠛⠊⡈⠘⢒⢇⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢻⠀⠀⠀⡿⢸⠬⠤⠙⠲⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣜⠀⠈⠳⣄⢨⠐⠁⠌⡴⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⠻⢶⣄⣹⣌⡙⠄⠀⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⣬⠛⠶⢾⡟⡜⠂⠰⡰⠍⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡝⣿⢗⠛⣬⢾⢵⠬⡊⣿⣿⡿⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠄⡾⡗⠄⠾⠋⠀⣾⣿⣿⣿⡇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢹⡵⢸⣿⣿⣿⡯⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡺⣿⡘⣿⣿⣿⡇⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣗⣿⡕⠘⣿⠩⢉⣭⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢿⣿⡷⠹⡂⠉⡉⣥⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣤⣶⣶⣶⣶⣤⡤⢄⣤⣄⣀⣀⠀⢻⡳⠾⠮⠼⠀⠀⠛⠊⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣿⣿⠟⠿⣿⣿⣿⡇⣸⡇⣸⠇⣾⣟⣟⣿⣿⣿⣿⣶⣶⣦⣄⠀⢕⣀⠀⠀⠀⠀⠀⠀⠀
⠀⣿⣿⣿⣿⣿⣦⡙⣿⠀⣿⡀⣿⠀⣿⣧⣿⣿⣿⣿⣿⣿⣿⣻⢯⡻⢦⠀⠆⠀⠀⠀⠀⠀⠀
⠀⠸⣿⣿⣿⣿⣿⣿⣷⡀⣿⠄⣿⠀⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡱⠿⠘⣀⡀⠀⠀⠀⠀
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣽⠠⡿⢰⣿⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣝⡇⠄⠌⠲⡀⠀⠀
⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣄⠉⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢕⢅⠀⠈⢦⠀
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡄⣤⢰⢶⣶⣥⣛⣿⣿⣿⣿⣿⣿⣿⣿⡿⠠⢸⡇⢹⢎⣀⢑
⠀⠀⠀⠀⠀⠀⢨⣟⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢷⡳⣤⣉⠛⠿⠿⠟⣩⣾⡄⡸⡝⢣⡜⢳⣎
⠀⠀⠀⠀⠀⣿⣿⡟⠙⣿⣿⣿⣿⣿⣸⠻⠳⡏⢱⡇⡱⢢⣜⣻⣿⣿⣿⣿⠆⠴⣗⣳⣷⢗⢪
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠈⢡⣊⣃⣎⠪⠽⠟⠑⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠙⣟⡿⢿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⡿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡸⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣏⠿⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠀⣿⣷⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⡟⠀⠈⠛⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀