⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣶⣶⣶⣿⣷⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⣿⣿⡟⢹⠀⢙⣿⣿⡀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⣠⡿⠿⠷⠾⠾⠿⠿⣿⣇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⠓⡖⣖⠒⠲⣒⣒⣯⠉⡀⣹⡓⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣟⠀⣰⢗⣻⡄⡷⣷⣾⣿⣿⡟⠹⣷⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣷⣻⡿⠓⢼⠈⡹⠛⠛⠹⠀⡇⡔⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⡆⣷⡈⠁⠀⠉⠑⠀⠀⠀⢀⢧⡏⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠯⣛⢄⡀⠀⠐⠒⠁⣠⡎⠈⡇⡄⠀⢸⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠈⠂⠈⠻⣿⡲⠤⠴⠊⢰⠁⠀⢱⡷⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⠀⠀⠀⠈⠻⣯⣄⣂⣚⢶⣤⡈⠁⠱⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⢋⡄⠀⠀⠀⢻⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⢀⡠⠀⠀⡴⢁⣾⣿⣦⣀⡔⠁⢣⡀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⣿⣷⣶⣤⣤⣄⣀⠀⠀⠀⡔⠳⢄⡀⠀⢠⠀⠀⡸⢁⠴⠊⠠⣿⣿⣟⣿⣿⣿⣷⣾⣷⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠉⠙⠿⣿⣿⣿⣿⣿⣶⣶⣽⣦⣀⣈⠓⢾⡀⢠⠟⠁⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣷⣧⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⣄⢉⡏⠀⠀⠀⠀⡔⠁⠈⠛⠿⠿⣿⣿⣿⡟⣸⢠⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠿⢿⣿⡇⢀⠃⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢈⣸⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣯⠁⠀⠀⠈⠹⡎⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠉⣁⣠⣧⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢜⣐⠁⠄⣀⣀⣀⡀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣶⣿⣿⣏⣰⡚⠥⠈⣀⠀⠀⠒⠢⢄⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣦⣀⢼⣿⣿⢷⣦⣍⡒⠬⣉⠀⠀⡆⣸⣿⣿⣿⣿⣿⣷⣿⣿⣿⣽⠖⣿⣿⣿⣇⣀⣀⡀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠟⠀⠀⠀⠀⠈⠙⠫⢟⡿⣮⣕⢾⣴⣿⣿⣿⣿⣇⣈⣽⠟⠙⣿⣟⡯⢽⣿⡿⣿⣻⢿⡎⡏
⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⡀⠀⠈⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡟⢸⣿⣿⣿⣿⣀⡀⠀⠀⠀⢋⠉⠁⠀⣏⣏⣹⡞⣏⡓⢸
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠀⢉⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢸⣿⣿⣿⣿⡿⠿⣿⣷⣦⡘⠦⡀⠀⠘⢿⣿⣳⠸⢦⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⣼⣿⣿⣿⣿⡇⠀⠀⠉⠻⣿⡢⡈⢢⡀⠀⠀⢨⣧⢒⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⡔⢣⣀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⢿⣾⣦⡑⢄⠰⡶⢡⣜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠓⠒⠒⠒⠤⣀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠎⠠⡵⢹⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠙⢿⣝⢦⡙⠒⠬⠥⠖
⠀⠀⠀⠀⠀⠀⠀⠀⣎⣀⣀⣀⠀⠀⠀⠉⠒⢄⡀⠀⠐⠀⠀⢠⠃⡠⠊⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⣷⣶⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⠀⠀⠈⠉⠐⠂⠤⣀⠈⠲⢄⡠⢔⡡⠊⠀⣠⠖⠁⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢤⠗⠉⡠⠔⠋⠀⠀⢠⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠉⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡏⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⡞⠻⣿⣿⣿⡿⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠑⢄⠀⣰⡴⡇⠈⠙⠻⡃⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡏⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠳⡍⠀⡇⢠⠀⣰⢡⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⢠⣿⣿⣿⠟⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣱⠘⡆⢿⡱⠀⠀⠀⠀⠀⠀⠱⡀⠀⣰⣿⣿⡿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⡆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡸⣸⡇⠀⠀⠀⠀⠀⠀⠀⠱⣾⣿⠿⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⣡⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢀⣠⠾⠋⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠙⠃⠀⠀⠀⠀