⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠉⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣀⣤⣤⡤⢤⢤⣤⣤⡾⠛⠛⠛⠛⠁⠀⣠⣤⠤⢤⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠄⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢠⣾⠟⠁⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠛⣀⣀⣠⣾⣿⣇⣰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣴⡿⠀⢠⣾⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢿⣧⡀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⢶⡶⣶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣶⠾⠛⠉⠋⠉⠉⠋⢻⣿⠃⠀⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠙⠿⠿⠾⠾⠷⠾⢿⣿⣧⣤⡀⠀⣿⠋⠉⠙⢿⣿⢿⣿⣿⣿⣿⣹⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠋⠀⠀⠀⠀⢀⣠⣴⡀⠀⠀⠀⠀⠀⠈⠻⣷⣄⣤⣠⣄⣤⣤⣄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠉⠻⣿⡍⠀⠀⢀⠀⢹⣿⣎⠿⣿⣿⣷⣿⣥⣤⣤⣤⣄⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⠀⠀⠀⣠⣾⠿⠋⠻⣿⠓⣾⣀⣤⣤⣤⣀⠈⠉⠉⠉⠉⠉⠉⠙⢷⣦⠀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⠀⠘⣿⣀⣴⠿⣷⣄⠙⢿⣿⣭⢻⣿⠉⣧⣴⣌⠉⠹⢿⣤⣼⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⠏⠁⠀⠀⠀⣿⡌⢿⣿⡉⠉⠙⠿⢷⣄⣀⠀⠀⠀⠀⠀⠈⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⢀⡀⠀⠻⣿⡀⠐⣿⡾⠳⣄⣹⣯⢿⠃⣼⣿⣿⣿⣿⣄⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠻⣿⡟⠉⢻⣶⣦⣀⣀⣿⡟⢷⣶⣶⡶⢶⡾⠛⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⣼⣧⡀⠀⠈⢻⣶⣾⣃⣠⡿⠛⢿⡇⢠⣿⣄⠀⠙⢿⣿⣦⢹⣟⠀⢿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⢿⣇⣀⣀⠀⢙⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣏⡻⣄⠀⠈⢹⣾⣿⡁⠀⢀⣾⡇⢨⣿⠛⢷⣄⣀⣸⣿⠀⣹⡇⠀⣿⡿⢿⣿⣿⣿⣿⠶⢶⣦⡀⠀⠀⠀⠀⠉⠉⠻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣟⠀⠀⠀⣹⠟⠿⣶⣿⡿⢿⣾⡋⠀⠀⠉⠉⢻⣿⠀⠹⠇⠀⢿⣆⡀⠈⠙⠉⠉⠀⠀⠘⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⣟⠀⠀⣸⣏⣰⡾⠋⠻⣦⡀⠀⠀⢸⣿⠀⠀⠀⠀⣴⠿⠁⠀⠀⡀⠀⠀⠀⠀⠀⠈⢿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢩⣿⠀⠀⣼⡟⠻⢷⡄⠀⠙⠻⣦⣤⣼⣿⠀⠀⠀⢸⣿⠁⢀⣤⣶⠟⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⣻⣇⠀⠀⢙⣦⣄⡀⣀⡼⠋⠀⣰⡆⠀⣸⣿⠟⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣰⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⣿⣿⡶⠶⠾⠿⠿⠷⢿⣧⣤⣶⡿⠃⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⣶⠾⢻⣿⣿⣿⣿⣿⣿⣿⣿⣟⣙⣩⣴⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣭⣤⣤⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⢀⣤⣴⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣶⣴⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣶⣶⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣶⣶⣶⣶⣶⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⢿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠀⠀⠀⠀⣀⣼⣧⡀⠀⠀⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠘⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠈⣿⣧⡀⠀⠀⠀⣿⠁⠀⢛⣿⡏⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠀⠉⠻⠿⣧⡀⢀⣿⠅⠀⢺⣿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠘⠻⣶⣦⣀⡀⠈⠛⠛⠿⣶⣄⣿⠿⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡶⠶⠶⡴⢦⠶⣶⢿⡿⠇⠀⣀⣀⣤⣾⢻⣧⣀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⡿⠋⢹⣿⣿⣷⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⠀⠀⠀⠀⠀⣠⣤⣾⡟⠉⠁⠀⢀⣼⡿⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣴⣤⣶⣾⠿⠏⠁⢻⣇⣀⣤⣶⡿⠃⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣿⣿⡿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠙⠟⠋⠹⣧⣤⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠋⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀