⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⢀⣀⡤⠤⠤⠤⠤⠤⠤⢄⡀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣬⣵⣶⣿⣿⣿⣿⣷⣶⣤⣄⣀⣿⣿⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⣾⣿⣿⠟⠛⠉⠉⠉⠉⠉⢙⠛⠿⢿⣿⣿⣿⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢇⣸⣤⠉⡭⠶⠤⠀⠀⠀⠀⠀⠠⠖⢖⠦⠀⠈⠻⢿⣇⣀⣱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢀⢀⠔⠒⢦⡀⠀⠀⡠⠐⣡⠔⢈⠲⣾⢆⠄⢀⣠⠔⠁⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣴⣵⣏⣰⣪⣷⣽⠒⠁⠀⢰⠁⣼⣵⣝⡄⠋⡏⣿⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⣿⠀⡇⣿⣿⣇⠇⠀⠀⡇⠀⢹⣿⡿⡇⡄⢣⡿⣛⢲⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡗⠺⡄⠳⣛⡳⡹⠀⠀⠀⢣⠀⢯⣛⡝⡰⠁⠀⡌⡀⠁⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⢇⣠⠛⠦⠤⠖⠡⠒⠀⠀⠀⠑⠤⠤⠞⠁⠀⠀⠁⠈⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣼⠀⠀⠀⠠⠄⣀⣀⠤⠔⠀⠀⠀⠀⠀⠀⡞⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠈⠙⠲⠦⠤⠤⠤⡤⠤⢴⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠔⢇⣀⠜⠢⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠘⠒⠊⠲⠖⢊⡟⠉⠛⠦⣄⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⡞⠀⡔⠀⢢⢀⣼⡀⠀⠀⠀⠈⡷⡄⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⢸⣽⢤⣀⡇⡴⠈⠀⢸⡞⠀⡿⢦⣀⢀⡎⡱⠑⢄⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⢀⠎⠈⠛⡤⣇⠈⠒⣢⠟⠁⡸⠁⠀⠉⠓⠚⢇⡀⠀⢳⡀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡞⡀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⣠⠞⡱⠋⠓⣲⠻⠒⠒⣇⠀⠀⠀⠀⣠⠎⠀⢀⡼⠁⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⢺⠁⠀⠀⠀⠀⠀⣠⠋⠀⢀⠞⢁⡜⠁⢀⡞⠁⠀⠀⠀⠘⣆⠀⠀⡰⠁⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠃⡎⠀⠀⠀⠀⠀⡰⠃⠀⡰⠋⢀⡞⠀⣠⠟⠀⠀⣠⡶⠾⠗⠾⣦⠞⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⡴⠁⢠⠞⢀⠖⣾⣄⡼⠁⠀⠀⠀⢻⣟⣋⡥⣄⣁⣤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⣠⣜⣒⡒⠒⠀⠜⢁⡔⠁⡶⡯⡄⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀
⠀⠀⠀⠀⣤⢯⣓⠤⣄⠀⡠⠊⠀⠀⡌⣀⠀⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠉⢿⠰⠭⠔⠉⠀⠀⠀⠀⠙⣹⠲⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢔⣡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣤⣍⠒⠤⠤⣤⣤⣤⠤⠤⠒⣫⣡⠖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⡄⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⡞⠲⠶⣷⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⢯⠢⡀⠀⠀⠀⠀⠀⠀⢸⠘⡉⢉⣿⠃⠀⠀⣿⠙⠃⣛⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣴⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣄⡀⢸⣿⠿⠿⣿⠀⣴⠀⠀⣿⢿⢿⢻⣧⠀⠀⠀⢀⡴⠊⡮⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣴⣤⣿⣰⢸⢠⢱⣸⣯⣤⣾⣿⠴⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡄⠀⠉⠀⢨⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠈⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢣⣤⣶⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣻⣿⣿⣶⣤⣄⡀⡰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣾⣿⣿⣿⡿⢿⢿⢛⠫⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡻⡿⢿⣿⣿⣿⣿⣁⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣕⣞⣑⣮⠬⠾⠤⠟⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠷⣅⣣⣋⣯⠛⣹⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⢀⣀⡤⠤⠤⠤⠤⠤⠤⢄⡀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣬⣵⣶⣿⣿⣿⣿⣷⣶⣤⣄⣀⣿⣿⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⣾⣿⣿⠟⠛⠉⠉⠉⠉⠉⢙⠛⠿⢿⣿⣿⣿⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢇⣸⣤⠉⡭⠶⠤⠀⠀⠀⠀⠀⠠⠖⢖⠦⠀⠈⠻⢿⣇⣀⣱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢀⢀⠔⠒⢦⡀⠀⠀⡠⠐⣡⠔⢈⠲⣾⢆⠄⢀⣠⠔⠁⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣴⣵⣏⣰⣪⣷⣽⠒⠁⠀⢰⠁⣼⣵⣝⡄⠋⡏⣿⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢸⣿⠀⡇⣿⣿⣇⠇⠀⠀⡇⠀⢹⣿⡿⡇⡄⢣⡿⣛⢲⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡗⠺⡄⠳⣛⡳⡹⠀⠀⠀⢣⠀⢯⣛⡝⡰⠁⠀⡌⡀⠁⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⢇⣠⠛⠦⠤⠖⠡⠒⠀⠀⠀⠑⠤⠤⠞⠁⠀⠀⠁⠈⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣼⠀⠀⠀⠠⠄⣀⣀⠤⠔⠀⠀⠀⠀⠀⠀⡞⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠈⠙⠲⠦⠤⠤⠤⡤⠤⢴⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠔⢇⣀⠜⠢⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠘⠒⠊⠲⠖⢊⡟⠉⠛⠦⣄⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⡞⠀⡔⠀⢢⢀⣼⡀⠀⠀⠀⠈⡷⡄⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⢸⣽⢤⣀⡇⡴⠈⠀⢸⡞⠀⡿⢦⣀⢀⡎⡱⠑⢄⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⢀⠎⠈⠛⡤⣇⠈⠒⣢⠟⠁⡸⠁⠀⠉⠓⠚⢇⡀⠀⢳⡀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡞⡀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⣠⠞⡱⠋⠓⣲⠻⠒⠒⣇⠀⠀⠀⠀⣠⠎⠀⢀⡼⠁⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⢺⠁⠀⠀⠀⠀⠀⣠⠋⠀⢀⠞⢁⡜⠁⢀⡞⠁⠀⠀⠀⠘⣆⠀⠀⡰⠁⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠃⡎⠀⠀⠀⠀⠀⡰⠃⠀⡰⠋⢀⡞⠀⣠⠟⠀⠀⣠⡶⠾⠗⠾⣦⠞⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⡴⠁⢠⠞⢀⠖⣾⣄⡼⠁⠀⠀⠀⢻⣟⣋⡥⣄⣁⣤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⣠⣜⣒⡒⠒⠀⠜⢁⡔⠁⡶⡯⡄⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀
⠀⠀⠀⠀⣤⢯⣓⠤⣄⠀⡠⠊⠀⠀⡌⣀⠀⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠉⢿⠰⠭⠔⠉⠀⠀⠀⠀⠙⣹⠲⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢔⣡⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣤⣍⠒⠤⠤⣤⣤⣤⠤⠤⠒⣫⣡⠖⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⡄⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⡞⠲⠶⣷⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⢯⠢⡀⠀⠀⠀⠀⠀⠀⢸⠘⡉⢉⣿⠃⠀⠀⣿⠙⠃⣛⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⣴⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣄⡀⢸⣿⠿⠿⣿⠀⣴⠀⠀⣿⢿⢿⢻⣧⠀⠀⠀⢀⡴⠊⡮⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣴⣤⣿⣰⢸⢠⢱⣸⣯⣤⣾⣿⠴⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡄⠀⠉⠀⢨⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⠀⠈⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢣⣤⣶⣶⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣻⣿⣿⣶⣤⣄⡀⡰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣾⣿⣿⣿⡿⢿⢿⢛⠫⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⡻⡿⢿⣿⣿⣿⣿⣁⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣕⣞⣑⣮⠬⠾⠤⠟⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠷⣅⣣⣋⣯⠛⣹⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
