⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⣶⣶⡶⠶⠶⣦⣄⣀⣀⣠⣤⣤⣤⠶⢶⣶⠶⠶⣶⣾⣟⣋⣩⠭⢭⡭⠛⠭⠯⣭⣽⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣻⣿⡿⠟⠉⠙⠟⠙⢿⣾⣿⣹⣿⣿⠿⠿⠿⠟⢿⣿⠿⠿⠿⠿⢿⣄⡀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣎⢿⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣤⡾⣿⡾⠋⠀⠀⠀⠀⠀⠀⠀⢠⡤⠾⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠤⠀⠀⠀⠀⠀⠙⢷⣉⣷⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣟⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣧⡿⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣛⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣠⣶⣤⣤⣦⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢦⡤⠀⠀⠀⠀⣠⣶⡶⠿⠛⠛⠋⠀⠀⠀⠀⠙⠛⢻⣷⣶⣶⣀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣿⣽⣟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠸⣿⣿⡟⠙⣷⣀⡀⠀⠀⠀⠀⠀⢻⡿⣧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣾⠟⠁⠙⠿⠟⠁⠀⠀⠀⢀⡼⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣇⠀⠀⠀⠀⠀⠈⣷⢿⡄⠀⠀⠀
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⣠⣶⠟⠛⠻⢶⣦⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⣷⣶⡶⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡆⠀⠀⠀⠀⢹⣾⡇⠀⠀⠀
⠀⠀⠀⠀⢸⣿⣿⡇⠀⣾⠟⠁⢰⣤⢀⣤⡙⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⢸⡏⣿⡆⠀⠀
⠀⠀⠀⠀⢸⣧⣿⡇⢸⡏⠰⣶⣞⠛⣻⡏⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠸⣇⣿⡇⠀⠀
⠀⠀⠀⠀⢠⣿⣿⠇⢸⡇⠀⠀⣿⠋⠇⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⣿⢿⣧⠀⠀
⠀⠀⠀⠀⣸⣿⣿⡀⢸⡇⠀⠀⠈⠳⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡄⠀⠻⣯⣽⡆⠀
⠀⠀⠀⢀⣿⣿⠟⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠙⣦⡀⣿⣿⣿⠀
⠀⠀⠀⣾⣿⡟⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠙⣷⡿⢿⣹⡆
⠀⠀⣰⣯⡿⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠸⣷⣾⣿⣿
⠀⢸⣿⣿⣇⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⣿⣷⡿⣿
⠀⢸⣿⣿⠁⠈⠛⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣠⣼⠋⠙⣷⣿
⠀⢸⣿⣿⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⢸⣿⡿
⠀⢸⣿⢿⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣾⢻⡇
⠀⢸⣿⣼⠇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠈⢻⣼⡇
⠀⠘⢿⣿⡄⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⣠⣾⣻⡇
⠀⠀⢸⣿⣧⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⣿⣷⡟⠀
⠀⠀⠈⣿⢿⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⣼⢿⣿⠇⠀
⠀⠀⠀⣿⣼⡇⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣴⢏⣿⠏⠀⠀
⠀⠀⣠⣿⣿⣧⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣴⡿⣾⠇⠀⠀⠀
⢰⣞⣻⡿⠛⠉⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⣀⣽⣼⠏⠀⠀⠀⠀
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣿⣿⡿⠃⠀⠀⠀⠀⠀
⢹⣿⣷⢤⣤⣤⣤⣤⣴⣦⣤⣤⣤⣼⣷⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⢀⣀⣤⣿⣥⢶⣤⣿⣦⣤⣄⣀⡀⠀⠀⣀⣀⣀⣴⣿⣻⣵⠟⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠉⠛⠛⠿⠞⠛⠓⠺⠿⠉⠉⠽⠏⠛⠿⠿⣭⣭⣭⣭⣭⣭⣽⣿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠿⠾⠿⠿⠿⠿⠯⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⣤⠀⠄⢀⣀⣀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⣀⣀⣤⣠⣄⣀⣀⠀⣀⡀⡀⠀⢀⠀⠀⣀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀