⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂⢄⠀⠀⠀⣀⠤⠤⢄⡀⠀⠀⠀⠀⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⠤⠒⠒⠢⡄⡰⡇⠀⠀⢘⠄⠒⠼⠁⠀⠀⠀⠘⠀⢀⠔⠒⠠⡀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠘⠁⠁⠀⠀⡌⠀⠈⠑⠀⠀⠀⠀⠘⠈⠘⢆⠀⠀⠸⡀⠀⢈⡢⢀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠺⡀⠀⠀⢀⢀⠔⠐⢢⠀⠀⠀⠀⠘⠁⠈⠞⠃⢣⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⢸⠀⢀⣰⡄⠀⡌⠀⠸⠁⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠘⡔⠒⢢⡸⡀⠀⠀⠀⠰⠔⠀⠀⠀⠀⡄⢠⠣⣑⡖⠀⠀⠀⠀⠀⠀⡀⣤⡂⠜⠁⠀⠈⠲⠀⢰⠀⠀⠀⠀⠀⠇⢀⣀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠃⠀⠀⣧⠑⠄⠀⠀⠀⠀⠀⠀⠀⢸⠈⠡⢄⣸⠀⠀⠀⠀⡆⠀⠀⢸⠀⠈⠀⠀⠀⠀⠚⢇⠀⠀⣶⡀⠀⠜⢎⠁⢠⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡔⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢸⠀⠀⠀⠠⢧⣀⣀⠌⠀⢀⣴⣛⣖⠂⠒⠉⠙⠒⠲⡁⠀⠀⠀⠀⠂⠀⠀⡆⠁⠀⠀⠀⠀⠀⢸⢀⠎⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⠟⠀⠳⠶⡞⠃⠀⠀⠀⠀⢀⣾⣷⣾⣿⣆⠀⠀⠀⠀⠀⠘⡷⠃⠀⠀⡀⠀⠀⢷⢀⣀⢰⠀⢀⣠⣾⡞⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢋⠉⠣⢄⣀⠀⠀⠀⠀⡀⠤⠃⠀⢀⡧⠄⢼⠁⠀⠀⠀⠀⠀⡜⠉⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠙⠤⢠⠜⠣⣀⡠⠃⢸⠉⠘⢣⢼⡁⠀⢣⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡕⠤⣀⠓⢤⠤⠔⠊⠀⠘⢲⠒⢹⠀⠀⡇⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠸⡀⠀⢰⠀⠀⠀⠀⢸⠀⠀⠀⠹⡄⠈⡆⠀⠈⡆⠑⠃⠈⣇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠸⡠⠊⠀⠀⠀⠀⠀⡎⠀⡜⠀⢀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢡⠀⢸⠀⠀⠀⠀⢸⠀⠒⠂⠀⠘⡄⡇⠀⠀⡇⠀⠀⢢⠘⢆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⡇⠀⢸⡇⠀⠀⠀⠘⢰⠃⠀⠒⠂⠀⠀⠀⠀⠈⡆⢘⠀⠀⠆⠀⢸⠀⠀⠀⠀⠀⠘⡁⠀⠀⡇⠂⠀⠈⣆⠈⢆⠀⠀
⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⡀⢃⠀⢸⡇⠀⠀⠀⡆⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠀⢀⠀⠀⡘⠠⢀⣀⣤⣤⣤⣵⠀⢀⠃⠀⠀⠀⢿⢢⠈⣆⠀
⠀⠀⠀⠀⢠⠃⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⡇⢰⠁⢸⠀⢸⢹⠀⠀⡀⣸⢸⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡼⠀⡸⠀⢀⢧⣾⣿⡿⣏⠉⢹⡇⠀⢸⠀⠀⠀⠀⢸⠀⢣⠘⡄
⠀⠀⠀⠀⡌⠀⠀⣾⠀⠀⠀⠀⡀⠀⢰⣸⠀⣼⠀⠈⡇⢸⢸⢆⠁⠀⢛⣬⣶⣶⣿⣿⣿⣿⠟⠛⠂⠀⡇⢠⠁⠀⡼⠘⠀⠛⠀⠸⠀⣼⡇⠀⠇⠀⠀⠀⠀⡟⠀⠈⣧⢣
⠀⠀⠀⠀⡇⠀⡸⢸⠀⠀⠀⢸⠀⠀⠘⢼⠀⣿⠀⠀⠸⣸⠈⡎⢆⢸⣿⡟⢿⡟⠛⡿⠉⠙⡆⠀⠀⡘⣠⢻⠀⡰⠃⢰⡀⠀⢀⠆⠀⢰⠁⡜⠀⠀⡀⠀⢀⠇⠀⠀⢸⣼
⠀⠀⠀⠀⡅⢠⠃⠸⡆⠀⠀⣷⠀⠀⠀⡾⣀⢿⢆⢸⡀⠱⣇⠸⡈⢣⣏⠧⡈⢆⠀⠀⠄⢄⡇⠀⠀⠋⠁⣘⠔⠁⠀⠀⠓⠀⠊⠀⠀⣎⠌⠀⡆⡸⡇⠀⡸⠀⠀⠀⠀⡿
⠀⠀⠀⠀⡇⢸⠀⠀⢧⠀⠀⡏⢧⠀⠀⡇⠿⠸⡘⢄⡞⢆⠹⣕⠵⡀⢣⠀⠀⠂⠀⠔⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢹⡀⢰⢃⠟⠀⢠⠃⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠘⢼⠀⠀⠘⣆⠀⢸⠈⠣⣀⠇⠈⢇⢳⣌⠺⡄⢙⡘⠂⢹⠪⣢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢣⢃⡎⠀⡠⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠑⠀⠀⠈⢦⡀⢇⠀⡸⠀⣠⢯⣢⡈⠓⠦⣤⣵⠀⠸⠳⢮⣓⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⣠⡞⠷⡗⣟⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡲⢁⠔⠁⠉⠒⠛⠿⣋⠁⠹⣣⡀⢇⢀⡏⠀⠁⠂⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡎⠁⠳⣐⠫⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠔⡁⠀⠀⠀⠀⠀⠀⠈⠙⡖⠚⠳⣜⡼⢄⡀⠀⠀⠀⢝⢷⣦⣤⣀⣀⠀⠀⢠⠔⠒⠋⢴⠁⠀⠀⠀⠉⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠡⣆⠀⠀⠀⠀⣀⠤⠊⠀⠀⠀⡜⠘⠦⡈⠉⠒⠢⠤⣌⡻⠉⠑⠼⠭⢉⣇⡄⠃⣉⠩⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣿⣽⣭⣅⣤⣤⢐⣊⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⠀⠀⠀⠀⠐⣝⣿⣷⣾⣣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣿⡿⠿⡿⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠛⠶⣤⠀⠀⢠⣬⣽⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡇⠀⠤⠄⢀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠛⢿⠿⣿⠗⢪⡼⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠈⠉⠁⠒⠤⣀⠀⠀⣀⠄⠒⠒⠈⠉⢘⣼⣿⣧⠃⣠⡠⠄⠘⡩⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣴⣿⣿⣿⠟⠉⢀⡠⠔⠌⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣦⠒⠁⢀⠊⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣐⡲⠁⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣠⣾⡻⣟⣛⣿⣿⣟⣿⣿⣿⣿⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠘⠀⣱⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢠⣻⡤⣫⣟⣿⣿⡿⣿⣏⣿⣜⣿⣾⣝⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⡀⢦⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀