⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣸⢡⣾⡏⠀⢀⡚⠉⠉⠙⠻⣿⣿⣿⣖⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⢀⠄⢠⣻⢫⢻⢻⠘⠀⣾⠂⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠀⡟⠄⢂⠫⣿⡿⡿⣿⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠋⡾⣠⠂⣼⣷⣿⣷⣼⡇⣞⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣤⣤⠃⡏⢰⣿⣎⣹⣿⡏⢧⣿⡔⠀⠀⣴⣿⣿⣿⠿⠿⣶⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⡧⡿⣼⢰⣿⣿⣿⡿⡿⣼⣾⣿⡃⠀⠀⢀⣤⣤⣤⣤⣄⠀⠹⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣠⠃⠏⣸⣿⣿⣻⣿⢡⡇⣿⣿⠃⢐⠸⠿⢿⣿⣿⣉⣿⣷⡀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⣿⢸⠀⣿⣿⣿⣻⣿⡿⣸⣿⡫⣷⠀⠀⠈⠂⠉⠓⠂⠀⠀⠀⣿⡿⠡⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⣿⢯⢰⣿⣿⢣⡟⣼⢇⣿⣿⠁⠛⠢⡘⠄⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⢾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢃⣿⠏⣿⠿⣿⢻⣿⡿⣸⣿⣿⣶⣄⡀⣤⡄⠀⠀⠀⠀⠀⠀⢠⣿⡃⠀⢸⠻⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⣟⡀⣿⣼⣯⣿⣿⢷⡿⣿⣿⣂⣉⡁⠈⠁⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⢸⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⢰⣯⣿⣿⣻⢻⣼⣶⣿⣾⣭⣷⣶⣴⣠⣀⡀⠀⠀⠀⢀⣿⠁⠀⠀⠈⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢫⣺⣇⣿⣷⣟⡟⣿⣿⣿⣯⣯⣿⣿⣉⡨⠏⠁⠀⠀⠀⣼⡟⠇⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣻⢯⣯⣿⣿⣿⣿⣿⢻⡉⠉⠛⠛⠫⠀⠀⠀⠀⣠⣾⢿⡇⠀⠀⠀⠀⢽⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢰⣹⣿⣿⣿⣿⣿⣿⣧⣏⣸⠂⢀⠀⠀⠀⠀⢀⡤⠚⡿⣿⣷⡇⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⡤⠒⠒⠒⠛⠉⠹⠀⠀⠀⠀⠀⠀⠀⢠⢻⢟⣾⣿⣿⣿⡟⢿⣿⡿⣔⣀⣀⣀⠤⠚⠁⠀⠀⣯⣿⣿⣿⡀⢸⡆⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⠀⠀⠀⠀⠀⠀⢠⣿⡯⣿⣿⣿⣿⣿⡞⠹⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠹⢹⡿⢿⣮⣷⣄⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠰⠀⢀⡎⣩⣿⠋⣿⣿⣿⣿⡏⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⢲⠀⣹⠠⡛⠘⠻⢳⣶⣦⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣦⠀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⠖⢠⣞⣼⠃⠜⣿⣿⣿⣿⣿⡀⠀⠦⠀⠀⠀⠀⠀⠀⠀⣾⠃⣾⡴⢃⣰⣿⣾⣿⣷⣯⣾⣿⣿⣿⣿⣷⣶⣶⣤⣄⡀⠀⢀⣿⡿⠀
⠀⠀⠀⠀⠀⡴⠁⢀⡴⠋⠀⠀⠀⡠⠂⣽⣯⡾⠀⣰⣿⣿⣿⣿⣿⡇⠀⠀⠂⢊⡜⠀⡀⠀⢠⣿⣦⣽⣯⣾⣿⢛⣿⡟⣿⣿⣟⠻⠛⠛⠻⠿⢿⣿⡿⠻⣾⣦⣼⣿⡇⠀
⠀⠀⠀⠀⠀⠷⠁⠉⠀⢀⡀⠔⠀⢀⢨⣾⡟⠁⢠⣿⣿⣿⣿⣿⠟⠙⠐⠤⣠⠾⠁⠉⠀⠀⠚⣻⣻⡹⡇⣶⣑⡿⡇⣸⣿⣏⠋⠀⠀⠀⠀⠀⠀⣈⣡⡐⢦⠙⣿⣿⠀⠀
⠀⠀⢀⡤⠀⢀⡠⢔⡚⠉⡠⠂⠰⣳⣿⢏⣔⣁⣾⣿⣿⣿⣿⡉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡱⣷⣟⣧⢉⢾⣻⠃⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⠙⠓⢷⣆⡄⠀⠻⣒⠀
⠀⠰⢛⠖⠋⢁⠐⠀⠀⠤⠀⢫⣶⢟⠽⢣⡾⢻⣷⣟⠇⣿⣯⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢠⣿⣿⢪⠨⣿⣹⣿⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠐⣄⠄⢻⡦
⡀⠾⣃⡡⠚⢁⡀⠀⠄⠀⠀⢈⠵⠁⡰⠋⠁⠘⡽⢸⣴⡟⠸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⢯⢸⡆⠀⣷⡿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠈⡇