⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠂⠤⣀⣀⡀⠄⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢀⣨⢁⣤⠄⠠⢀⣤⡀⡁⠀⠀⠉⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⡩⢸⠈⢀⠰⢈⡁⠂⠄⡈⠉⠓⠦⣙⠀⢅⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢠⠇⠀⡀⠘⠠⠡⠄⢃⠐⠀⠐⠀⠀⠈⡆⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⡁⠏⢦⣀⢁⠀⢃⠱⡈⢄⠈⠄⠀⠀⠀⢠⠃⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⠐⠄⠀⠀⠀⠀⠀⢸⠀⢸⣿⣿⡗⠚⠶⢲⣖⣮⠤⠤⢶⣶⣿⡖⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠈⢀⠀⠀⠀⠀⠈⠀⣾⡾⠘⠪⠝⠛⠌⢻⡖⠹⡻⠯⢻⣿⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⠠⠀⠀⠀⡄⠀⣿⣿⡀⠀⠀⠀⠀⢀⠙⠄⠀⠀⢰⣿⡏⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠑⡀⠀⢇⠀⢻⣿⣗⠀⠀⠀⠀⠊⠀⠈⠂⢠⣿⣿⡳⠄⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠌⢧⠀⠐⠐⠸⡀⠀⠹⡟⣳⣄⡀⠉⠘⠃⡀⠴⣿⡛⢯⢃⣀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⢳⡀⠈⢄⠑⢦⡄⠀⠀⠈⠉⠒⠲⠮⠅⠋⠓⠉⠁⠉⠓⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡰⠔⠉⣡⣾⣿⣿⣿⣯⣄⠀⠢⣄⡈⠳⠂⠤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⣠⣾⣿⣿⣿⣿⡟⠁⡈⢦⠀⠹⠻⣷⠢⡁⠢⢀⠉⠐⠀⠀⠀⠀⠀⢰⣥⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠋⠀⠈⠀⠘⢟⣠⠽⡛⡱⠌⢦⠀⠈⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡇⠀⢀⠀⠀⠀⢈⠳⠰⠚⠀⠀⠈⠒⢄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠊⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣧⠀⠸⠀⠀⠀⢸⡐⡏⠀⡀⠈⠀⣀⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠄⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢦⣄⣠⣤⡮⠶⣎⢀⠀⠊⢁⠤⠠⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠂⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠈⠻⣧⢳⢭⢃⠈⢢⠄⠊⠐⢶⠦⢆⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠁⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⠁⠀⠀⠀⠀⠀⢠⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠈⠃⣧⢸⣷⣬⣍⡉⢉⢶⢅⡿⢍⡆⠀⠀⠀⠁⠢⢀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠄⠀⠀⠀⠀⠀⠀⣬⡧⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠈⠏⢿⣿⣧⣡⣏⡖⡎⢕⠍⠀⠀⠀⠀⠀⠀⠀⠁⠂⢀⠀⠀⢂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀
⢠⠀⠀⠀⠀⠀⠀⢠⡷⣧⢏⣾⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠈⢆⠹⣿⣿⣖⠃⠌⠭⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⢢⡀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⣼⢓⡌⡝⠂⠰⡢⢉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⢂⠐⡂⠹⣿⣿⣦⠈⠄⢓⡓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠘⠀⠀⠀⠀⠀⠀⡽⢨⠔⠀⠴⠋⠀⠂⠌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠁⠄⣿⣿⣿⠀⠀⠠⠰⠤⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⡠⠐⠀⠀⠀⠀⠀⠀
⠀⠆⠀⠀⠀⠀⠀⣇⠂⡠⠊⠀⠀⠀⠀⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡐⠀⣿⣿⣿⠀⠀⠀⠀⠘⣐⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠉⠉⠉⠀⠒⠀
⠀⠐⠀⠀⠀⠀⠐⢆⠀⠀⠀⠀⠀⠀⠀⣸⢽⣻⢻⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣿⣿⠀⠀⠀⠀⠀⠀⠤⠄⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀
⠀⠀⠘⠀⠀⠀⢈⠃⠀⠀⠀⠀⠀⠀⢠⣿⢯⡹⣽⣿⣿⣿⣿⣿⣽⣿⣿⣻⣿⡿⠿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠃⢂⠀⠀⠀⠑⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀
⠀⠀⠀⢃⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣞⢾⡲⢽⣙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠑⠠⢀⢀⣀⣀⣀⣀⣀⠀⠄⠀⠀⠀
⠀⠀⠀⠈⡄⠀⠐⡆⠀⠀⠀⠀⢀⣾⢞⣻⠵⢹⡼⢺⡼⣶⠩⣙⠻⢟⢛⣿⠿⠿⠆⠀⠀⠀⠀⠀⣀⠀⠠⠀⠀⠐⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡀⠀⠀⢠⡍⢄⠀⢠⠀⠀⠀⢀⢮⣷⢮⢇⡻⢼⡣⣟⣿⣷⣥⣴⣌⡀⣤⡁⢄⣁⠜⠄⠐⢀⠈⠠⠤⠀⠀⠐⠂⠀⠀⠀⠌⠅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⢸⠈⠁⠀
⢀⠁⠢⢔⡀⠀⠁⠢⠂⠀⣠⢿⢸⡟⠸⣌⢼⢨⢳⣼⣿⣿⣿⣿⡿⠿⢛⣉⣥⠔⠀⠉⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⡈⠀⠀⠀
⠀⠈⠐⣤⠌⡁⠂⠄⢀⣔⢻⣚⠬⣇⠓⡌⠦⣉⣿⣿⠿⣟⣫⣥⣶⣾⣿⣿⣯⣄⠀⠁⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀