⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⣡⣾⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣡⣶⣿⣿⣿⣿⢣⠟⠡⠒⢒⠬⡙⢿⣿⣿⣿⣏⢰⡉⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣵⣿⣿⣿⣿⣿⣿⠃⠈⡌⠊⡔⡱⡁⢰⠘⣿⣿⣿⣿⡄⢊⠪⣙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⣼⣿⣿⠟⠉⠉⠁⠰⠀⠠⠰⣌⠎⠈⢊⠎⣰⣿⣿⣿⣿⣿⣆⡑⠄⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣾⣿⡟⠁⠀⠀⠀⠀⡆⠀⠀⠑⠤⠉⢉⣡⣴⣿⣿⣿⣿⠿⠿⢿⣿⣶⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠀⠀⠀⠀⠀⢀⠀⠀⣀⣠⢤⣀⢼⡛⠁⠉⠫⣟⠬⢄⠀⠀⢿⠏⢕⡀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⠀⠀⠀⠀⠀⠀⣸⡐⢝⢏⠀⠀⣙⠂⠙⢄⢀⣐⠎⠀⢑⣅⡤⣰⠁⠈⣒⢄⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡥⢀⠀⠀⠀⠀⠀⠀⠀⣎⡙⠀⢠⣧⡲⡌⢀⣤⣽⣦⣾⣷⣦⣽⣿⣶⣷⣥⣬⣿⣮⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⠱⢠⠐⣠⠀⠀⠀⠀⠀⢀⡣⠆⠤⠖⠁⠈⠤⠐⠚⠋⠉⠉⠉⠉⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢨⡇⢃⠡⡈⡕⢀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠉⠿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢋⢠⠪⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠐⣒⡈⣭⣤⣴⣶⣶⣶⣶⣶⣶⣶⣄⠬⠭⢉⣛⠛⠿⠿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠠⠐⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠤⠀⢒⣂⣈⣥⣤⣶⣶⣿⣿⠋⢉⣿⣿⣿⣿⡟⢻⣿⢻⣿⣿⣿⣆⡀⠀⠀⠈⠉⠑⠒⠀⠭⠉⣛⠂⠄⡀⠀⠀
⠀⠀⡠⠔⣊⣀⣀⠀⠀⠠⠤⠄⢒⣂⠩⠥⠐⠒⠂⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣤⠜⠝⠋⠙⠁⣧⣼⣇⣼⣿⣿⣿⣿⢯⡑⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡘⠦⠀
⠀⠑⠠⠖⣒⡒⠒⠒⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡟⣸⣿⣿⡄⠁⠀⠀⠀⠘⣿⣿⠀⣏⣿⣿⣿⣿⡆⠈⠁⠀⢀⡀⠤⠄⠒⠀⠉⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠂⠀⠠⠤⠤⠀⠀⠀⣼⢿⣿⣿⣿⣿⣿⣿⣿⣎⠣⠴⠀⠀⠀⠀⠀⠀⠅⠜⠀⣼⣿⣿⣿⣿⠅⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠘⣿⣿⣿⣿⡿⠛⣻⣿⡗⢄⠀⠀⠀⠀⠂⠀⠀⠀⢀⣿⣿⣿⣿⣻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢻⣿⣿⣿⠃⢸⠉⣿⣿⡀⠇⠀⢀⠠⠀⠀⠀⢀⣼⣿⡿⣿⣿⣧⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⢸⢠⣿⣿⣧⣀⡀⠀⠀⢀⣤⡾⠟⢹⠘⣿⡜⠿⣻⢌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠙⢿⣿⠀⠈⠸⣿⣿⣿⣦⣍⠳⣾⠟⠉⠀⡀⢸⠀⢸⠻⢦⢪⣀⡐⢗⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠐⠂⠘⠀⠀⠀⣿⣿⡎⠛⢿⣾⡟⠒⠠⢀⡇⢸⠀⣾⡇⠀⡗⣉⠛⢿⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠩⠶⠶⢶⣦⡇⠰⡌⠃⡇⢸⡙⢁⠠⠄⠂⠱⣸⠀⣿⣥⡒⠂⠸⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⣿⣧⠀⢡⡤⣿⣼⠁⠀⠀⠀⠀⠀⣹⠀⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠐⢣�