⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡿⣟⣻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⢀⣤⡿⠟⣧⣾⠋⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡏⢻⡿⠋⣠⣴⣿⠃⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣺⢿⣿⣏⣴⣿⣿⣿⡏⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⢿⢿⡿⠽⣿⣿⣁⣀⣀⣿⣿⣿⣄⣀⣀⣀⠀⠀⠀⠀⣀⣠⣤⣾⠿⠟⢻⣿⡀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⠀⠀⠀⢠⢿⣿⡃⠀⢀⣤⢶⠻⠉⠀⡠⢣⠀⠸⣄⡀⠀⠉⠻⢷⣀⣠⡾⠛⠙⠉⠀⠀⣸⣾⣿⡇⠀
⠀⠀⠀⣀⣀⣀⡀⠀⢠⡾⠉⢽⡶⠀⠀⠀⠀⠛⠋⣰⣶⠟⢉⡡⠔⣒⡋⠡⠄⠉⣓⣒⠯⢗⡲⠤⠾⠙⢷⡀⠀⠀⢀⣤⣾⣿⣿⣿⡇⠀
⠀⠀⣿⡥⡀⠈⠻⣶⣾⣷⠀⢸⡷⠀⠀⠀⠀⠀⣞⡟⡡⣞⡵⠚⠉⠀⠀⣠⣤⡀⠀⠀⠉⠒⠬⡑⠤⠔⡆⠙⣆⣠⣿⣿⣿⣿⠿⣿⡀⠀
⢀⢤⣬⣿⣾⣷⣄⠈⠛⢿⠀⠀⢹⣤⠀⠀⢀⣾⣿⣮⠞⠁⠀⠀⠀⢀⣾⣿⣿⡇⠀⠀⠀⢀⣀⠈⠳⣄⢧⠀⠘⣿⣿⣿⣿⡇⠀⣿⣁⣤
⣾⠁⠀⠀⠉⠙⡟⠀⠀⡜⠀⠀⠀⢿⡄⢠⣾⣿⡵⠃⠀⠀⠀⠀⠀⠘⣿⣿⡿⠁⠀⠀⣰⣿⣿⣷⠀⠈⢦⢳⡀⠘⣿⡇⢿⣷⠀⣿⣿⣿
⠉⠓⣶⣶⣶⣾⠁⠀⠀⠃⠀⠀⠀⢸⣿⣼⣿⡟⠁⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠏⠀⠀⠀⢧⢷⣿⣿⡇⢼⣿⣶⣿⣿⠇
⠀⠀⣏⡀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣾⣿⣷⣶⣤⡀⠈⠉⠁⠀⠀⠀⠀⠸⡼⣿⣿⡃⠈⠿⠇⢹⢸⠀
⠀⠀⠈⠉⠉⢱⣶⣤⣀⠀⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⣦⡀⠀⠀⠀⠀⠀⡇⣿⣿⡃⠀⠀⠀⢸⡟⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣦⡀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣷⣿⣿⠇⠀⠀⠀⠈⠁⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣘⣳⣄⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣫⣷⡻⢿⣷⣶⣶⣶⣿⣷⣄⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⣰⣿⣽⡇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣮⢟⡯⣉⠉⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢔⡿⠋⠀⠀⠤⡙⠿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡾⠟⠁⢻⣼⣿⣿⣿⣇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⣿⣿⣆⠀⠀⢀⣀⣀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠛⠗⢿⣟⣽⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠿⣟⣚⠭⠭⣶⢸⠀⠀⠀⠀⠀⠈⠉⠙⢿⣿⣿⣿⡟⣻⢿⣿⣿⣿⡄⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣋⣬⠵⣶⡾⠛⠉⠀⠊⠁⢸⢸⠀⠀⠀⠀⠀⢀⡴⣉⢆⣿⣿⣿⣿⣧⣍⠶⢽⣻⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⢸⡟⠀⠀⠀⠀⠀⠀⢸⢸⣶⣶⣶⣶⡶⣫⣾⠋⣮⢻⣿⣿⣿⡇⠻⣷⡀⠑⠉⠺⢷⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⡿⣫⠞⡕⠁⠀⠈⢷⡻⣿⣿⡇⠀⠈⠻⢷⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠈⡘⣿⢟⠔⠁⠀⠀⠀⠀⠀⠈⢷⡽⣿⢳⠀⠀⠀⠀⠉⠛⠷⢖⣛⢒⢄⡀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⡇⡵⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡜⢸⣧⠀⠀⠀⡄⠀⠐⠤⠄⠉⣉⣷⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣦⣀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣾⠿⣧⡀⠀⠘⢦⣄⣀⣀⠀⢀⣼⠃⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠙⡒⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⡴⢋⣩⣿⠋⠀⠙⠿⢦⣄⠀⠉⢻⡏⠉⠁⠉⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠈⠑⠀⢹⣿⡍⣹⡍⠀⠀⠀⠈⣿⡟⠁⠀⠀⠀⠀⠀⠀⠙⢷⣤⡾⠇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣌⣉⠒⠚⢡⣟⠀⢿⣿⠤⠀⠠⠔⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣿⠞⠛⠻⠿⢾⣿⣯⣍⣿⣾⣿⠆⠀⣿⡄⡤⠔⢶⣿⣿⣤⣤⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣧⡀⢀⣀⣀⣀⣬⣿⣾⣿⣿⣿⠀⠀⢹⣿⣷⣴⣾⡿⠛⠉⠉⠉⠉⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣏⣻⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢿⣿⣿⣿⣶⣶⣤⣤⣤⣶⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠁⠀⠀⢺⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠋⠉⠉⠛⠻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⠟⠉⠀