⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⣀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⢀⣤⣄⠁⣠⣾⠥⢶⣿⣆⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠃⠀⠠⣴⡷⢯⠥⡶⡿⠿⠿⣿⣿⣷⣶⡱⠦⠤⡀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢟⣤⣠⣾⢷⣿⡿⡧⠈⠀⡠⠀⠈⢿⢿⣿⡻⡆⠀⠀⠀⣬⡻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡿⡽⠛⣡⡿⢫⠡⢠⣤⣯⣷⣬⣭⣥⡣⠙⠛⠂⠀⠀⠀⢸⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⡤⣼⠿⣡⡄⣧⣿⣿⣿⣿⣿⣿⣿⣷⣄⡰⡄⡀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⡟⠁⡔⠛⠟⠛⠛⣻⢿⣿⣿⡿⠟⠛⠛⠛⠊⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠁⢈⣴⣿⣆⢮⣥⣤⣾⣿⡿⢣⣢⢤⣭⣟⣻⠷⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣧⠁⢸⣭⣉⣤⣄⢴⣶⣿⣿⣷⣿⣷⣆⣤⣄⣌⢩⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⣇⠂⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⠻⣿⢟⣵⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠔⠧⠹⡆⢹⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣇⣵⣿⣿⣿⣿⡇⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁⢺⢄⢀⢂⠨⣏⢿⣿⣿⣿⣿⣿⡿⢛⡫⢛⣿⣿⣿⣿⣿⡟⢑⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⢀⢀⠨⡎⢰⠘⣶⠰⣎⣿⣿⣿⣿⢡⣪⣽⣓⠶⠤⠭⠟⣛⢯⣢⢆⠌⢠⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢰⢰⡆⢐⢨⡀⡢⢸⢃⣿⡈⡻⣿⢋⠨⢋⣿⣿⣿⣿⣷⡿⠊⡠⠃⠀⢌⢠⡾⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⢀⣀⠟⡳⡪⢈⢰⣾⢋⡼⣥⣤⣿⡯⢨⣴⠟⢋⣩⣭⠉⣉⣠⡀⠓⣢⡄⠀⠈⢠⠰⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⠠⢊⠦⠂⢀⡱⠢⠪⡂⢀⢴⣫⣾⡹⣽⣾⣿⠦⠉⣴⣷⡏⣿⠀⣿⡿⢇⢜⢼⣝⢄⠀⢺⣐⢶⡀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠐⠀⡂⣠⠰⢀⠐⠜⢐⢄⣤⣶⣿⣿⡇⢩⡼⣿⠏⣼⠟⡌⣏⡇⣿⣶⣶⣿⢿⠘⠐⢹⣷⣄⠈⠙⠲⡠⠱⢭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⢄⢺⠚⠔⢉⠀⠔⠢⣀⣦⣜⣴⣿⣿⣿⣿⣿⣷⣜⡿⣣⣾⠏⡰⣿⡛⡇⢿⣿⣿⣿⠆⢇⣸⡌⣿⣿⣿⢆⡠⡁⢨⢪⡈⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠐⢐⣁⠄⢀⣀⣲⣤⢴⣖⡺⣫⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⡟⡁⢸⣿⡿⡗⠷⠦⣻⣿⣿⣰⣼⣜⡃⢿⣿⣿⣮⣿⣦⡐⠄⠙⠢⣰⢑⠒⠀⡀⠀⠀⠀⠀⠀⠀⠀
⣼⣭⣤⣶⣮⣵⣾⢿⣿⣷⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⡿⣿⢀⣇⠿⣻⣭⣥⣤⡆⢸⣿⢿⣿⣿⠇⣼⣕⢝⢿⣿⣎⣿⣿⣦⣄⠑⠀⠠⣈⡒⢐⠀⠀⠀⠀⠀⠀⠀
⣟⣵⡼⣿⣫⣿⣾⣿⣛⢛⢿⣭⢿⣿⣷⣿⣿⣷⡝⣿⡟⣱⡿⢈⣴⡿⣛⣩⡍⣀⣬⢪⡻⣾⣿⢣⣾⣿⣿⣿⡳⡙⢿⣭⣋⣟⠻⣷⣤⣌⠐⢴⠐
⣿⣿⣿⡿⡿⣿⣿⣿⡟⣴⣿⣿⣿⣷⣾⣿⡟⢿⣿⠌⢸⣯⣾⣿⢟⡼⢿⣛⡔⡟⣣⢏⠅⡻⢣⣿⣿⣿⣿⣿⣿⣾⢦⡻⣿⣿⣿⣶⣯⣬⣁⠀⠡⢂
⣿⣿⣋⣷⣵⣻⣿⣿⠽⢿⣿⣿⣯⣿⣾⣿⣿⣿⣿⡯⢸⣿⣿⡃⣿⣿⣿⣿⢇⣷⣪⣾⡱⣁⢿⣿⣿⣿⣿⣿⣿⣿⣿⣝⢮⡙⡿⢿⣿⡿⣟⡵⣫⣿