⠀⠀⠀⠀⠀⢀⡠⢄⠲⢀⠙⠂⠠⠔⡒⠠⢁⡩⠈⠲⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⠼⢀⠘⠠⡘⠣⣀⠛⠄⠀⡀⠣⠄⡘⢄⠘⠻⡸⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡨⢦⠂⢅⣢⢈⣐⣄⣡⠒⠤⠨⠀⠒⠌⠔⠃⠆⠽⢇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡐⢁⣀⣈⡑⢤⠀⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀
⠀⢰⢉⣀⣀⡀⡀⠁⢂⠈⡆⠀⣀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀
⠀⢈⠏⠎⣷⣖⡫⠶⠂⠀⢹⠝⣁⠀⢌⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀
⠀⡌⠘⠀⠁⠀⠀⠀⠀⣀⢼⡕⢜⠀⣜⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀
⢈⠀⠀⠰⢀⠀⠀⠀⡸⢇⠷⠆⢏⣀⡎⠀⠀⠀⠀⠀⣀⣀⠎⠀⠀⠀⠀⠀⠀⠀
⠀⡹⣍⢗⡅⢸⣛⡴⢡⠠⠰⠣⡘⣓⠈⠉⠉⠉⠈⠁⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⢩⣵⢿⠵⠷⠏⡅⡑⠱⡑⠡⢄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠠⠞⠇⢮⠨⣎⠗⡅⡱⠃⠑⠈⡺⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠰⣱⣼⠾⠠⡸⠄⠷⠴⣡⠬⠂⠁⠀⠀⠀⠀⣀⣤⣶⣾⣶⣶⡄⡀⠀⠀⠀⠀
⠀⠰⣄⡌⠸⠃⣁⣍⡖⢻⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀
⠀⠀⠈⠀⠃⠃⠈⢠⣾⢠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠉⠉
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⡿⠿⠿⠿⠿⠿⠿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⣞⣉⡑⠒⠲⠤⣍⣓⠒⠤⣍⣑⠮⣝⡻⢵⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⡋⠛⠒⢦⡉⠳⢬⡉⠓⠶⣤⣄⡈⠙⠲⣄⣉⠳⢤⡙⠓⢾⣮⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠤⣉⠓⢤⡀⠉⠲⢄⡉⠓⢤⣀⡀⠉⠳⠤⣄⣩⢓⠮⣕⣲⢄⠻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠙⠿⣦⣝⢦⠬⠷⣦⣶⠿⠶⠿⠒⠛⠓⠛⠙⠛⠛⠋⠉⠛⠈⠉⠋⠙⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⢀⠀⠈⠓⣷⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣰⠃⠉⠉⠉⠉⠉⠉⠉⢠⠀⠸⡄⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣸⣶⣶⠿⠿⢶⣤⡀⢸⠂⠀⢻⢀⡴⡞⣉⠉⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢰⠃⡤⠩⣿⣿⣙⡦⠭⠧⠀⠀⢸⡶⣷⣌⣩⣙⡎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⠃⣰⠃⠀⠉⠉⠁⠀⠀⠀⠀⠀⣸⣟⣮⣹⡆⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⡟⣷⡛⢧⠽⡇⢈⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⢤⣄⣤⣤⣌⡵⢰⡤⡤⡀⣼⡏⠳⡉⣉⠈⡳⣷⡋⢦⣤⣤⣤⠤⠤⠤⠶⠒⡲⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢰⣿⣦⡻⣝⣒⠼⣟⢷⢿⠃⢧⠳⠙⠺⢳⡙⣬⣧⠀⠀⠀⠀⠀⠀⠀⠀⢐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⢻⣛⣼⣭⣽⣿⢬⡋⣞⢊⠣⢳⡸⡦⣽⣃⣾⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣫⢿⢹⡝⣆⢧⢧⡻⡸⡖⣆⠹⣝⠲⣌⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣼⣟⠛⣸⢸⢫⢺⣮⠃⢳⠠⢹⡀⠠⡬⠶⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣟⣹⣷⣳⢻⡘⡇⢿⡄⢮⢧⣪⠡⢤⡽⠚⠉⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣾⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣯⠛⡍⣧⢻⣅⢹⡘⣟⢦⣰⢿⠋⠉⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⣷⡳⣀⠘⣛⢐⡤⠷⢻⠀⡼⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠀⣰⣾⣧⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀