Words Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⣠⡄⠀⢠⣄⠀⠀⢠⣄⠀⡀⠀⣤⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⠟⢻⣿⡿⢻⣿⣿⡟⢻⣿⣿⣿⠟⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⢿⠇⠀⠸⡿⠀⠀⠈⢿⠄⠀⠀⢿⠇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⣀⣿⣿⣀⣸⣿⣇⣸⣿⣿⣿⣀⣿⣿⣿⣂⣸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣄⠀⢠⣤⣤⣤⡄⠀⣠⣤⣤⣤⡄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠉⣿⣿⣏⣿⣿⡇⠈⢹⣿⣿⠁⣾⣿⡟⢛⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⢿⣿⣷⠀⢸⣿⣿⠀⣿⣿⡇⠻⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠿⢱⣿⣿⣿⡇⠙⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠄⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡿⣻⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⡴⠘⣦⢀⡸⡄⣀⣠⡆⠘⢶⡄⠀⣿⢤⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢋⣿⠙⡿⣇⣿⣿⡟⣹⣧⡛⢻⣿⠀⡛⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⡇⢰⡟⢸⡇⠀⢸⡏⠓⠂⣸⡇⢠⣿⢸⡁⣶⠆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣇⣸⣿⢠⡇⢸⣿⡇⢰⣮⣽⡇⣼⡟⢰⡇⣾⠉⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠈⠂⠀⠈⠃⠀⠀⠘⠂⠈⠋⠘⠃⠋⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣷⣿⣿⣷⣼⣿⣿⣧⣿⣷⣼⣧⣽⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⢠⣿⡇⣿⡿⢷⣄⢸⡿⢷⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⠀⣿⣿⡿⠠⢸⠁⢀⡉⢻⡇⢀⡈⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⢀⣿⣿⡇⣿⡇⢈⣿⢾⡇⠈⣿⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⠀⣿⡿⠁⠀⢸⠀⢸⣷⠀⡇⢸⣷⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣧⣴⣿⠀⣾⣧⣿⡇⣿⣧⣾⠋⢸⡇⢀⣿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠘⠋⡀⣿⠣⠘⢀⢸⢇⠘⠁⣴⡇⢸⡿⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠸⠏⠈⠿⠼⠏⠀⠿⠇⠿⠏⠻⠦⠸⠿⠟⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇⣸⣷⣀⣃⣰⣿⣀⣸⣀⣸⣄⣹⣇⣊⣠⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⠟⠛⠻⠟⠛⠻⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⣿⢽⡏⠉⢙
⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠛⠛⠓⠛⠛
⠀⢀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠂⢀
⠀⢸⣿⡉⠙⠏⢉⣿⡇
⠀⢸⣿⣷⠀⢰⣿⣿⡇⠀⠟⣧⠀⡿⠁⣏⡷⡿⠇
⠀⢸⣿⣿⣤⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣀⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠰⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠓⠂⠀⠀⠀⠀⠀⠀⠀⡀⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠤⠐⠁⠀⠀⠀⠀⠀⠀⣠⠍⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠀⠀⠀⠀⠠⣶⢀⡈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠚⠫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⡉⣉⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀
⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⣀⣀⡀⠀⠐⠁⠀⠀⠀⠀⠴
⠀⢀
⠀⠀⠈⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠦⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠦⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⣀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣽⣭⣭⣿⣥⣭⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣶⣶⣶⣾⣿⣽⣿⣶⣿⣷⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠕⢀⠀⠀⠄⢀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠞⠀⢀⠚⡁⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣀⡴
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢄⠀⡃⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠆⠇⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⡏
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢠⠀⠀⠀⢠⠘⠁⠀⣀⠀⠀⠀⠀⢀⡴⠋⢃⠀⢱⠀⢀⡀
⠀⠀⠀⠀⠈⠤⠂⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⡄⡘⠀⠀⠀⡆⠸⠀⣠⠋⠀⠀⠀⠔⠋⠀⠀⢸⠀⠈⡆⢾⢋⡴⠒
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⢾⠔⠁⠙⢦⠀⠀⠀⠀⠀⢰⢡⠃⠀⠀⠸⢀⠃⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢱⣬⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣾⡃⠀⠀⢀⡦⠃⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⡍⡅
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢠⠃⢀⠔⢛⢳⠀⠀⠀⣾⠁⠀⡘⣃⣼⠋⠂⢸⣻⠉⣀⠰⠅⠈⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⡆⠀⠀⠀⠇⠘⠀⢀⡼⠃⠀⠘⠋⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠣⠀⠈⠂⠀⠠⠖⠉⠀⠀⠐⠁⢠⡄⠃⠀⠀⠀⠀⣀⠤⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠒⠶⣶⣄⠀⠀⠀⠀⠀⠀⠐⠿⠂⠀⣸⠓⠒⠒⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⡀⠀⠀⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⠇⢀⡴⠆⣠⡄⢠⡄⣴⢺⡇⠀⢠⠇⠀⠀⠀⢀⣔⡿⢄
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣰⠏⠀⢼⣏⠴⡽⡧⣾⡼⠻⠛⡃⣼⣿⠀⠀⠀⠀⢦⡜⠷⠊⠄
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢤⣾⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠈⠆⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⠙⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⣴⠾⠁⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠇⠀⠀⠘⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠄⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⢈⣀⣀⡴⠤⠤⠤⣇⡀⠠⣾⣿⣀⣀
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠒⠙⠣⠔⠋⠀⠀⠀⢠⠀⠀⠀⠈⠛⠿⠟⠁
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⠀⢀⡠⢤⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⡊⠀⠀⠀⠠⠀⠘⠀⠸⣦⣤⣤⢠⣄⣀⡀
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⣼⠀⢠⠀⣀⡄⠀⠀⢳⠖⠀⠀⠀⠀⠀⢸⣆⣀⠀⠀⠀⣈⣃⣀⣀⣀⣤⣤⣤⣤⣤⣀⣀⣀⠀⠈⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢠⡴⠉⠀⠁⠀⠁⠳⠒⠄⢠⡀⠀⡤⠀⠀⠀⣀⣉⠉⠙⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠶⣄⠀⠀⢵
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀⠀⠀⠑⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠈⡆
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡖⠈⠀⠀⠀⠀⠉⠙⠒⠤⠤⢀⣀⡀⠀⢈⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⣄⠀⠀⠀⠀⣠⠞⠁⣰⠏
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⡙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢡⣶⡞⠀⢀⣤⠞⢁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣦⣤⣴⣾⣯⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠶⠶⠶⠶⠶⠶⠒⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠈⠁⠀⠀⢰⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⢀⠀⠀⡆⣔⠀⡇⠀⢳⣠⠀⠀⡀⢻⠀⠀⠀⡠⡀⡀⠀⠀⢰⣆⢠⡄⢰⠀⣶⢠⡤⢰⣦⡆⢔⡅⡼⠀⠀⢦⢴⡅⠀⠀⠀⠀⢀⠠⢀⠄⢠⠄⣶⠐⠂⢆⠀⡇
⠀⠀⢣⡶⣦⢹⠔⠸⠊⢈⠁⡄⣮⠀⠘⢇⠀⠀⢌⢒⡈⠀⠐⡏⠹⢸⠹⠆⠟⠻⠘⠁⠈⠉⠋⠙⠐⠃⠀⠀⠉⠛⠀⠀⢀⡀⢌⠎⠳⠣⣾⠘⠢⠉⡄⠃⠒⠀⠄
⠀⠀⠀⠁⣈⠀⡀⢰⠒⡾⡗⣼⠹⠊⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⢀⠤⣄⡀⢀⣀⡀⢠⡄⢰⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⢀
⠀⠀⠀⠀⢹⣀⡜⠈⠓⠁⠀⠀⠁⣀⠀⢲⠀⠀⠀⠀⣠⠂⢰⣠⡇⣼⡄⣷⣤⠞⢸⠖⠁⣷⣃⠝⡿⣼⠇⠸⠀⠀⠀⡰⠉⠉⣧⡰⢀⡄⣀⡀⠀⠀⠀⠉⠸⠐⠂
⠀⠀⠀⠀⠀⠟⠀⠀⢠⣀⠀⢦⢠⡃⣤⠈⡇⠀⠀⠀⠧⠎⠘⠀⠋⠁⠃⠇⠉⠸⠘⠂⠀⠁⠉⠀⠃⠘⠀⠒⠀⠀⠀⠿⣤⣶⢫⡇⡼⣰⠃⢀⣟⠂⣶⠀⡄⢀⡀
⠀⢨⣗⣞⠀⢀⢠⠆⢳⣯⠓⢬⡆⠢⠻⡄⠰⠀⠀⣤⠀⠀⠀⠀⠀⠀⣄⠀⠀⢰⡗⠀⢀⡾⠀⠀⠀⠀⠀⡠⠒⡠⠀⠀⠀⠈⠃⠉⠁⠛⠂⠼⠄⡼⢻⡼⢁⡞
⠀⠀⠋⠀⠀⠀⢻⡒⠠⠁⠀⠀⠉⠀⠀⠀⠀⠀⠐⣄⠲⣣⠀⠀⠀⠈⢟⠢⣠⠃⠸⡴⠋⡇⠀⠀⠀⠀⠚⣤⡻⠂⠀⠀⠀⡆⢠⠰⠂⠀⠀⠀⠀⠀⠘⠁⡘
⠀⠀⢶⠂⢤⠀⠀⠀⠀⠀⠀⢠⢤⣶⣎⠀⠀⠀⡀⠈⠲⠉⢧⠀⠀⠀⠘⡶⠶⢶⣖⣾⣿⡅⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠐⠒⠈⠐⠰⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⢠⡵⠄⢳⡀⠀⠀⠀⣠⠀⣠⠈⢅⠂⣴⢢⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⣀⢀⠄⡤⠀⠀⡄⢠⠀⣄⠀⠂⠰
⠀⠀⠀⠙⠪⣧⡀⠀⠀⢸⠟⡎⣓⠀⠔⠃⠀⢈⠀⠀⠀⢀⡄⡄⠀⠀⣀⡀⠀⡀⠀⠀⢲⡸⠆⣰⠀⣖⡁⠸⠀⠀⠠⠇⠀⠉⢈⢀⡋⠈⠁⠉⠈⠀⠀⠀⠀⠂
⠀⠀⢀⢔⠀⠈⠙⠀⠀⠘⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣜⡧⢸⡸⡤⢹⠖⢀⠈⣢⢣⡠⡗⠘⠃⡇⡧⠂⠀⠀⠀⠀⠀⠒⠉⠁⠚⠂⠉⠀⡀⢀⡀⡔⡄⣷
⠀⠀⠂⠀⠀⠀⡀⡀⠀⠀⢀⠀⠀⠀⢀⡷⣴⠂⠀⠀⢸⠁⡇⠀⠃⠃⠼⠋⠁⠘⠁⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡠⠀⣆⡇⣿⡀⡷⡜⣇⡿⠁⣿
⠀⠀⠀⣴⡸⠓⠿⢁⡠⣀⡀⠀⠀⠀⠀⢹⠛⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣠⠆⡆⣯⠇⠀⠀⠀⠀⠀⣰⡄⠀⠀⠰⣅⡄⢹⢹⠋⠁⠃⠀⠻⠘⠀⠴
⠀⠀⢀⢀⠀⠶⠶⠜⠉⠈⠀⠀⠀⠀⡀⠀⣀⡀⠀⢠⠀⢠⡿⢀⠞⠈⡆⠀⠀⠀⠀⠃⠃⢁⣠⡐⡆⠀⠀⠙⣯⣽⠛
⠀⠀⠘⠋⠁⠀⠀⢀⡴⠂⡀⣏⠖⣸⣧⠈⡇⢶⡁⢸⠀⠀⠀⠘⠚⡆⢻⣀⡀⠀⠐⣯⣞⡎⡏⠀⡃⠀⠀⠈⠁⠈⠁⠀⣄⠀⡤⠀⢠⠀⠄⠀⣰⡀⢤⠆⡆⢸
⠀⠀⠀⠀⢄⣠⠀⢾⣠⢿⠀⡟⢦⡉⢸⠀⠃⠴⠋⠀⡄⠀⠀⠀⠴⠇⢈⠉⠇⠀⠀⠉⠀⠀⠀⠀⠁⡔⢒⠢⡀⠀⠀⠀⠩⠁⠑⠀⠸⠂⠂⠀⠀⠁⠈⠀⠁⠐
⠀⠀⠀⠰⢦⠷⠄⠀⠀⠉⠀⠀⠀⠉⠈⠁⠀⠀⠀⢀⣠⠄⠀⠀⠈⠈⠀⢀⣠⣄⠰⠂⣂⠞⠁⠀⠀⠱⠤⢃⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠌⣃⠑⠀⠀⠀⠀⠀⠈⠉⠀⠋⠈⠁⠀⠀⠀⠀⠀⠀⢉⠁⠀⢠⠀⡆⡆⢠⠄⢴⠖⡠⣄⣞⣲⠞⢦⡟⠀⡇
⠀⠀⢀⣶⣼⣰⢗⡖⡆⠰⡐⢄⠆⡄⣶⠀⡇⠀⠀⠀⢰⡂⡖⢲⡀⣶⢲⣠⡼⠐⢱⣆⡖⠐⠶⡅⣊⡄⢸⠀⠀⠸⣾⠁⠗⡧⠆⢸⠸⡤⠏⡏⠳⣄⣸⠀⠀⠃
⠀⠀⠘⠃⠀⠃⠈⠁⠉⠀⠁⠀⠀⠁⠉⠀⠂⠀⠀⠀⠸⠊⠉⠚⠂⠈⠈⠘⠀⠀⠀⠈⠈⠂⠁⠁⠈⠁⠐⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣈⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢸⣤⣼⣇⡀⣼⠈⣿⠃⠀⠀⠀⠂⡠⢰⠀⠀⠀⠀⠠⡄⠀⡀⠀⠀⠀⠀⠀⠠⢁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⢀⡠⠔⠀⠀⠀⠒⠤⠤⠀⠀⠀⠀⠀⠀⡐⠈⠈⠁⠀⠋⠙⠀⠟⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⡀⢀⠉⠀⠐⠀⠺⠁⠀⠘⠃⠾⠁⣀
⠀⠈⠀⠀⡰⠀⠐⠀⢄⠀⠀⠀⡀⠀⡠⠊⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣾⠃⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⠁⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠂⠀⠀⢀⠄⠀⠠⠀⠔⠢⠃⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠄⡀⠀⢸⠀⠀⠠⠞⢹⣿⠧⢤⡆⠀⠀⢀⢤⠶⠒⠲⠀⠀⠀⡀⠀⠀⠀⠀⠈
⠀⠀⠠⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠈⠀⠀⠀⠀⠉⠻⠄⣜⣀⢀⡄⠛⠁⠀⠀⢀⡇⠀⠀⡏⠀⠀⢠⠞⡰⠀⠀⠀⠀⠁
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠸⠋⠀⠀⠀⠀⠀⡜⠃⠀⠀⠿⠚⣦⠏⣰⢷⠄⣠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⢃⠀⠀⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⣺⠃⠀⠀⠀⠀⠀⠈⠐⠁⡜⠸⡉⠛⡼⠛⡆
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣤⠎⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠁⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣀⠀⣀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠈⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⢿⡄⠻⣷⣤⣸⡟⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠙⠁⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⣿⠁
⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⠈⣿⣀⣀⣼⣿⠀⠈⠙⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⠀⠀⣴⠀⠀⠀⠀⡀⠀⢳⡾⠁
⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠘⣿⠀⢸⣿⠏⠉⢻⡇⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠽⡀⠈⣿⡀⣤⡀⣿⠀⢸⠀⣠⡇⠀⠀⣷
⠀⢀⣀⠀⠀⠙⢻⣄⠀⣿⣷⣤⣿⠀⠈⣿⡆⠀⠈⠿⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢸⣿⠏⢳⣿⠀⠸⡃⠉⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠻⣦⡟⠈⠻⠟⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠟⠞⠀⠘⡟⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠁⢀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠁⠀⠶⠀⢀
⠀⢀⣰⣶⠀⠀⠀⠂⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡤⠀⡄
⠀⠀⢹⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣀⡀⣀⣠⠀⠱⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣓⠀⠀⣀⡀⠀⠀⠀⠠⡀⠤⠂⠉⠀⠀⠈⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠠⠄⠀⠀⠄⠀⠀⡄⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⣰⠆⣴
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠐⠠⠦⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠒⠁⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣀⠀⠀⠀⡀⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢤⠀⠀⠈⠀⠀⡠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠄⠃⠀⠀⠙⠦⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠇⠀⠀⠀⠀⠠⢔
⠀⠀⠀⠀⡀⡀⠀⢀⠶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠠⠠⡀⠈⠃⠀⠀⠁⠀⠀⠀⠀⡀⡆⠐⠈⠒⣄⣄⠀⠀⠀⠀⣰⣦⠀⣤⣿⠏⠻⣆
⠀⠀⠀⢀⡌⠓⠚⠈⢄⡸⠀⠀⠀⠀⠀⠀⠀⠀⡐⡀⢠⢀⡂⠀⢀⠀⠰⠄⢀⠔⠀⠀⠀⠀⠠⠀⠀⠀⠀⢞⠀⠁⠀⠀⠀⠙⣿⣆⢸⣧⢀⡿⢻⣤⣏⣿⡄⢠⡿
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠿⠁⠎⠁⠘⠒⠇⠀⠀⠈⡀⠀⠀⠀⠀⠐⠀⠀⠀⠰⠏⠀⠀⣀⣀⠀⠀⠘⢿⡿⠙⣿⠇⠘⠂⠘⠀⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠤⠠⠤⠀⠀⠰⠄⠄⠤⠤⠀⠀⠠⠀⠠⠀⠄⠄⠄⠀⠀⠀⠀⠰⠀⠀⠀⠀⠆⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠐⠀⠲⠀⠀⢰⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣠⠈⠡⠀⡄⣤⠀⠀⠀⠋⢸⠤⠈⠀⠤⠸⠀⠀⠀⠀⠁⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⠀⡁⣿⣜⠆⣹⠃⠸⠀⠀⠀⠀⣻⠐⠐⡀⠆⠀⠠⠐⠀⠀⠀⠀⠰⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⠀⠒⠂⠔⠲⠖⠷⠐⠚⠲⠶⠶⠶⡶⠦⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⢄⣀⢀⣀⣀⣄⣠⣴⡄⡀⢀⡇⢛⡀⠡⢈⡧⡑⢀⡇⠀⠠⠀⠀⠘⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣴⣬⣿⢿⣿⢿⣿⢿⠋⢁⠃⣠⡄⢸⣷⣧⣤⣤⣴⣤⣤⣤⠀⠰⠔⣀⠠⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠛⠛⠀⢉⠉⡑⢙⠀⠘⠀⠚⠉⡘⢛⠛⡛⢛⡛⡛⣻⣿⣀⣒⣒⢈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠎⠁⠀⠀⠨⠳⠝⠮⢻⠢⠉⠺⠀⣥⢈⡄⠇⠀⠅⡇⣿⣿⣤⣤⣤⡀⢔⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⠆⣰⣺⢣⠼⠴⢶⣏⠚⠒⣾⣿⣻⣿⣿⣟⠁⠲⣆⣨⣭⡅⢀⣀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠉⠉⡍⠁⠉⠉⡄⢁⢈⢸⡧⢐⣓⣿⣿⣿⣿⣿⣿⠀⠀⠤⠴⠅⠂⢸⣷⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠒⠾⠶⢿⠖⠲⢶⣷⡭⠹⠸⡗⢀⠀⡿⠿⠭⠻⢿⠷⠄⠫⠙⠉⣥⡥⢸⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢈⠐⣻⣍⣀⣢⣗⢰⠀⠒⢐⡞⠁⠁⠀⠀⠇⡴⠀⠂⠐⠀⠀⠀⠀⢹⣿⣅⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠈⠿⠻⡿⠛⡛⠀⠒⠠⢤⠄⢔⢠⡄⠠⠀⣥⠀⠰⠴⠴⣄⠀⠄⢼⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠸⠀⠀⠨⠇⠁⠀⠽⠀⡇⢋⡀⠀⠀⡀⠀⠁⠀⠀⠐⢠⡄⠤⢐⣿⠏⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢲⠔⠂⣷⣿⣾⡶⠿⡷⠾⡶⣿⠿⢿⢧⠰⡤⠡⠤⣄⠀⠀⠤⠄⠀⠀⠸⠿⠃⣈⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢋⠀⣿⣿⣿⡇⡃⠆⠣⠧⠸⠀⠘⢠⡱⡇⢺⢸⠀⠀⣀⣐⣒⣀⡀⠀⡗⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠁⢡⣤⣧⣴⣤⣤⣷⣤⣥⣧⣼⣬⡄⠀⡉⠁⢬⣥⣀⡀⢁⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠖⠸⠀⠀⠀⠉⠠⠀⠈⠀⠸⠀⠀⠀⠈⠉⡟⠉⠏⡛⠻⠛⢿⡟⠛⠛⠃⠀⠈⡄⠘⠛⠃⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠕⠌⠘⠈⠃⠀⠘⠃⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢀⠀⠀⠀⢀⠀⡀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢀⡀⢀⡀⠀⢀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣀⠀⠀⠀⣠⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠈⠑⠦⠞⠁⠀⢸⣷⡤⠚⠉⢉⣵⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢽⡀⠀⣄⡀⢠⣶⣄⡁⣠⠂⣰⣿⠟⠁⢀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⢦⡀⣷⠀⠀⢸⡇⠀⢻⣟⠻⡟⠈⠙⡇⣼⡿⠃⢠⠞⠉⠀⠀⣀⠈⠳⣄
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢰⣿⠇⠀⠀⣾⣿⣶⣴⡾⠉⠉⠑⢦⣙⣿⡃⡰⠃⠀⠀⣠⣾⣿⠀⠀⣿⡆
⠀⠀⠀⢀⡜⠁⠀⢠⠀⠀⢀⣿⠋⠀⣠⣾⣟⠉⠀⣸⣷⣴⠂⠀⠘⠉⠀⡽⠁⠀⠀⣼⣿⠋⣏⠀⢀⣽⣿⠆⠀⡠⢦⡀
⠀⠀⠀⡼⠀⠀⢠⡿⠀⠀⠼⠁⠀⠞⠋⠉⠉⠀⠀⣾⡯⠟⠀⠀⣴⠃⢰⠇⠀⠀⠘⠛⠳⠤⠬⣿⡻⠟⠁⣠⠞⠁⣸⣿
⠀⠀⠀⡇⠀⢠⣿⡇⠀⠀⠀⣀⣤⡶⠀⠀⢠⣤⣀⣠⣴⣇⣀⣼⡿⢇⣀⠀⠀⠀⣄⠀⠻⡖⠀⠨⡷⠴⠚⠁⢀⣴⡿⠃
⠀⠀⠀⠹⣀⣿⡟⡇⠀⠀⢸⣿⣻⠁⠀⠀⢋⡽⠛⠋⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⣿⣷⣶⠀⠀⣠⣤⣤⣤⣴⣿⠟
⠀⠀⠀⠀⠙⠿⠀⢷⠀⠀⠀⢿⣧⣀⣠⣴⠏⠀⠀⣀⣠⣤⡴⣶⣾⣿⣿⢧⠀⠀⣿⠿⠃⠀⢠⣿⠏⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠈⣿⡙⠛⣯⣴⣾⣿⢟⣫⣵⣾⠿⠛⠋⠁⠈⠳⣄⡀⠀⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠃⠀⠈⠉⠈⠻⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⡿⣿⡿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣧⣿⣿⣯⣿⣹⣾⣾⣧⣯⣿⣿⣿⣿⣷⣛⣻⣟⣿⣟⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣿⡟⣿⣿⣿⣾⣿⣿⣿⣿⢭⣭⣭⣿⣿⢿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣟⣫⣿⣿⣿⣾⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣻⣿⣏⣿⣹⣽⣽⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⡿⣝⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡌⣿⣿⢸⢇⣿⣾⡆⣷⣿⣿⠶⠶⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣾⣿⣘⣿⣸⣧⣻⣿⣇⣿⣿⣿⣯⣿⣿⣿⣿⢛⣿⣷⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣟⣿⣿⢿⡿⣿⢿⢻⢿⣿⣿⢿⣿⣹⣿⣿⣟⣿⣟⣿⣿⣟⣿⣯⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣿⣿⣿⣷⣿⣾⣽⣿⣿⣿⣽⣿⣿⣿⣼⣿⣿⣿⣿⣯⣿⣽⣽⣯⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢠⡟⢡⣾⣿⣦⣹⣿⡆⣾⣿⠙⣿⣿⡆⣾⣷⣦⣿⣿⣿⢯⡄⢿⣿⣴⣾⡆⢰⣷⣼⣿⡆⣾⣿⣆⠸⣿⣿⢆⣾⣿⡆⣾⣿⣦⣧
⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⣿⣿⣿⡇⣽⡉⢾⣿⣿⡇⣽⣯⣿⣿⣿⢏⣿⣳⡘⣿⣿⣿⡇⢸⣿⣿⣿⡇⣿⣿⣿⡆⢻⣏⣾⣿⣿⡆⣼⣥⣿⣿
⠀⠀⠀⠀⠀⠈⣷⣌⣻⣿⣻⣿⣿⣃⣻⣿⣌⣻⣟⣃⣛⣛⣛⣿⣋⣺⣿⣿⣇⣘⣿⣿⣃⣘⣿⣿⣟⣃⣛⣿⣿⣿⣀⣿⣿⣿⣿⣂⣛⡛⣛⡇
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣍⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⣿⣿⣿⣿⣿⣟⡿⣿⣿⣿⣟⣛⣛⣛⣿⣿⣿⣯⣭⣛⣻⣿⣿⣿⣿⠲⠶⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣭⡭⣿⣿⣿⣮⣭⣿⢋⣽⣿⣿⣿⣭⣛⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣞⣿⣿⣿⣿⣿⣛⣏⣿⣿⢿⣷⣭⣽⣼⢟⣿⣿⣿⢦⡍⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣶⣿⣿⣾⢷⣿⣿⣿⣧⣮⣭⣽⣿⣿⣿⣿⣻⣾⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⢿⡿⣿⣿⣿⣵⢏⣴⢽⣿⣿⣿⣿⣦⣴⡿⡿⣿⣯⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠿⣿⣿⣿⣫⣻⣿⣿⣿⣿⡿⠿⢦⣭⣿⣿⣿⣟⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣶⣿⣿⡿⢿⣷⣭⣩⣼⣿⣿⣿⣷⡲⢶⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣽⣿⣿⣿⣷⣷⣲⣦⣍⣽⣿⣿⣿⣿⣿⣻⣿⠿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠷⠦⠭⠾⠿⠿⠟⠛⠋⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠀⠀⠆⠀⠀⠰⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢠⣠⡤⣤⣤⡆⠀⠀⠀⠀⠀⠀⠀⡄⢀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠇⠟⠇⠛⠑⠚⠙⠃⡇⠠⠤⠤⠀⠀⠆⠡⠶⠶⠺⠆⠀⠀⠀⡇⢥⠁⣉⣁⣀⣀
⠀⠀⠀⠀⠀⠀⠠⠤⠄⠤⠰⠴⠈⠙⠉⢉⣈⣉⡁⢡⢤⡤⠄⣤⠀⠿⠀⠀⠘⠛⠳⠛⠙⠀⠃⠿⠀⠄⡀⣀⣀⢀⣠⣀⡀
⠀⠀⠠⠤⠤⠤⠤⠐⠂⠀⠒⠀⠒⠰⣶⣶⣾⠀⢂⣀⣠⣤⡄⢠⠀⡿⠐⡖⣶⣰⡖⣶⣚⣐⣦⡶⢈⡇⣁⡁⣈⡈⠉⠉
⠀⠀⠀⠀⢀⠀⡌⠉⠈⠀⠒⠂⠒⠖⢸⣿⡇⠀⡄⠀⢠⣤⣤⡀⢠⣤⣤⢠⣤⣤⡄⣠⣤⣤⡀⡀⣄⣀⣀⣀⠀⡤⠀⡀⡀
⠀⠀⠀⠀⠹⢸⡵⡗⡯⡇⡇⡗⢰⠄⢸⣿⡇⠀⠇⢀⣿⡏⢹⣿⠈⢿⡏⠀⣿⡏⢰⣿⠁⢹⣧⢠⡀⢀⣄⣠⣰⢠⣄
⠀⠀⠀⠆⠆⠐⠐⠂⡂⠤⢠⡄⢸⠂⢸⣿⡇⢸⣿⢸⣿⡇⢸⣿⠀⢸⣿⢠⣿⠁⢸⣿⠶⠿⠿⢨⡅⠐⠆⢰⢠⣠⣄⣤⣦⡤⣤⡤
⠀⠀⠀⡄⠀⠀⠐⠒⠐⠒⠒⠂⢨⠀⣸⣿⣇⣸⣿⠈⣿⡇⢸⣿⢀⠀⣿⣿⡏⢠⠸⣿⡀⣠⡤⢸⡇⠀⠥⠘⠙⠉⠋⢟⠋⠑⠃⠃
⠀⠀⠀⣿⣹⣻⣝⡵⡟⣻⠀⡇⢀⠘⠿⡿⠿⠿⠿⠀⠙⠿⠟⠃⠸⠃⠸⠿⠁⠸⠀⠛⠿⠟⠁⢸⠃⣆⣠⣬⣩⣡⢩⠉⠉
⠀⠀⠀⠀⠀⠠⠠⠤⠄⠤⠀⠃⠘⠿⠟⠁⣈⠋⡉⣘⢙⢃⢀⡀⣐⠂⠐⠂⠒⠒⠒⠀⠀⡆⢠⡌⣀⣋⠃⢃⣓⡀⢘⣀
⠀⠀⠀⠀⠀⠀⡀⣀⡘⣛⡚⢂⢉⠛⢙⠀⣯⠷⠯⠽⠽⠼⠺⠿⠿⠀⠘⠘⡃⠁⠃⠟⠀⠇⢸⡁⣤⢄⡄⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⢸⠘⠛⠈⣃⡁⡐⢒⢒⡂⢰⠀⠀⠀⠀⠠⠐⠇⠈⣁⣈⣉⣉⠐⡇⠴⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠈⠈⢰⠐⠒⠒⠒⠒⠀⠃⠀⠉⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣇⢸⣿⣇⣴⣶⣄⣼⣿⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣹⣿⣼⡿⣿⠿⣿⣿⣏⣿⣿⡟⢻⣿⢹⣷⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡄⣶⣶⣔⢻⣿⢻⣧⢻⡿⣁⣿⣷⡿⢸⣿⠇⣿⣇⣿⢿⣿⣿⣿⢟⣾⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⣻⢿⣷⠸⣏⣿⡎⠿⢿⣛⠪⠅⣉⠀⡉⢤⡅⢩⣘⡿⣿⡿⣾⣟⣿⢏⣾⠿⣫⣬⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣦⣶⣮⣙⣯⣿⣇⠹⣟⣁⣤⠣⡖⢿⡃⢞⠃⣷⢭⣍⣿⢸⡦⣭⡜⢛⣹⢋⣾⣿⢶⣿⣯⣿⡏
⠀⠀⠀⠀⠀⠀⢀⠄⠾⠿⠿⠟⠛⡛⣟⡛⣯⣸⣭⣹⣇⣧⡗⣾⠃⣿⣿⣿⣮⡏⣿⡾⣷⡏⠷⡟⣷⣨⡩⣅⢞⣩⣍⣦⡧
⠀⠀⠀⠀⠀⠀⠘⣷⢏⣿⣹⠿⠳⢙⣭⡴⠺⢹⡾⣿⣿⣾⣥⡾⠟⣽⡁⣟⣵⡶⣿⢹⢸⡟⡃⣿⢈⡿⢙⡛⣌⡛⣏⣠⣿⣷⣦⡂
⠀⠀⠀⠀⠀⠀⠀⢽⡓⢥⢧⡶⢻⡼⢿⠷⣿⢾⣇⡛⣧⠿⠉⠿⣛⢯⠓⠏⢻⠶⣿⠸⣿⣿⣿⣻⡉⠃⠬⢹⣸⡉⣿⣯⢻⣿⣿⠥⠂
⠀⠀⠀⠀⠀⠀⠀⢠⡛⠲⡖⢂⡓⢺⠦⣦⡶⢾⣏⣧⠀⠒⠉⠀⠈⠸⠳⠐⠘⠉⠓⢆⡉⠻⢺⣟⡁⡃⢠⠉⠸⢅⣿⢨⠶⡀⠐⣀⣐
⠀⠀⠀⠀⠀⠀⢀⡜⠷⠜⢾⠸⠱⢷⣰⣴⢰⣆⣹⣡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠰⠶⢽⠄⠉⢛⠈⠂⠘⠈⠀⠀⣀⡨⢀⡍
⠀⠀⠀⠀⠀⠀⢘⡤⢵⡎⢩⢠⣖⠄⢆⢀⠈⢈⡸⢃⡴⠓⠶⠶⠆⠴⠤⠀⠴⢠⡿⠈⠛⠓⡞⣷⣶⣦⡄⢠⢠⣴⢷⢺⡇⣏⢿⡸⡇⣶
⠀⠀⠀⠀⢀⣴⠻⣷⣖⠱⢻⢸⣄⡇⢢⡴⢛⢻⡄⠀⠀⣀⣀⡤⠿⠋⠀⠀⠀⠄⢠⢤⠴⠀⡟⣧⢸⣧⣸⣽⢿⣽⣼⣼⣇⣯⣾⢿⢣⡿
⠀⠀⠀⠀⠻⣌⠳⣱⢯⡟⣸⣼⡐⡗⣿⣅⢹⢸⣇⠟⠋⠈⠁⠁⠀⠀⠀⠀⠀⢰⡄⠈⠛⠓⢧⣻⡟⣷⢫⢻⢹⣧⣹⣿⢸⡷⠿⠾⢰⡇
⠀⠀⠀⠀⠀⠈⠳⢨⡗⣸⣭⠇⡍⡍⢃⣜⣺⡧⣶⠀⠀⠀⠀⠀⠀⠀⡀⠀⣴⣆⠁⠀⠀⠀⠀⢘⠋⣼⣤⡭⣿⡬⠁⢥⣜⣷⡶⣆⣨⡅
⠀⠀⠀⠀⠀⠀⠛⡿⢙⣻⢿⣋⣹⠀⣶⣮⠽⡝⢷⡄⠀⠀⠀⠀⠀⠓⠀⠀⠘⠣⠝⡦⠀⢰⠴⢿⣯⡆⠉⣻⠾⠞⣴⣈⣫⣷⣇⣿⣭⡅
⠀⠀⠀⠀⠀⠀⠐⢯⡼⢹⣟⣭⣥⡠⣙⣛⠚⣡⣖⢳⠀⠀⠀⢀⡤⠀⢀⠀⡤⡖⢶⢸⣧⡺⠺⣧⢸⣙⡳⡶⠿⠯⣿⡷⢺⡟⡗⢻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣂⡛⣯⢹⠃⢯⣸⠌⣿⣈⠀⠀⠀⣾⠶⠑⠛⠐⠗⠇⢾⣴⡇⠀⡶⣩⣻⡝⣇⣤⢗⣠⡶⢝⡗⢂⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⠞⣥⢸⣿⢩⡿⣹⣆⣀⣀⣧⡀⠸⠆⣠⡤⣴⠚⠓⡇⣼⣰⠆⡀⣹⠞⣽⠤⡸⡝⠠⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠓⠸⣴⢣⡄⡈⠳⣍⢟⡙⠓⠚⠉⠀⠚⠮⠨⢗⡿⠿⢹⣾⠏⠛⢆⢏⡃⢿⣨⣈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡬⢷⢉⣀⡋⣏⢸⣷⣤⣶⡀⠤⢀⣶⠣⣼⠉⢉⡡⢭⣿⣸⡛⠟⠙⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣯⣿⣷⠃⣬⠙⠗⣧⢸⣍⠂⠉⡄⠐⢈⠉⡿⢛⡀⠂⡀⣋⣽⣿⡷⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣜⣷⠏⣰⣶⢿⠁⠀⠀⠀⠀⠛⢧⣆⠧⣤⠆⣼⠀⡂⡀⡇⢸⡇⢻⠣⣼⣿⡽⣶⡗⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠾⣧⣧⣌⠀⠚⠅⠀⠀⠀⠀⠀⠀⠀⠈⢠⡉⡀⡀⢠⠥⡄⢠⠠⠄⠀⣤⠤⢀⡷⢞⣫⡴⣛⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⡿⢼⠦⢌⣓⠂⠀⠀⠀⠀⠀⠀⠠⠄⠀⠁⣸⡜⠤⢰⣁⢸⡿⣶⣿⢷⣾⠋⢿⣿⣟⣻⣯⠗⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣗⠿⢘⣿⢶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡀⢿⢣⠀⣸⠻⣜⣧⣿⣷⣿⣿⢩⣿⣛⡿⢿⣻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⣅⣱⣬⡷⢧⣄⠀⠀⠀⠀⢀⡠⣶⢆⣶⣘⠖⣤⡖⢭⣿⡟⡷⢾⣇⢻⡼⡇⢹⣿⡿⠻⣑⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣗⢾⠀⠀⠀⠀⠸⣿⣹⡾⢦⡿⣇⣹⣟⢐⣅⣦⣿⢸⠟⠇⠀⠀⠸⣷⠾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠫⣶⡇⣾⣭⣇⣿⣟⣙⠠⠁⠈⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡷⣾⣘⠿⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢾⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠉⠁⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡈⠑⠂⠃⠐⠚⠂⡄⡠⣀⣀⡠⢄⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢠⣤⢤⣶⢄⢈⠀⡀⠠⠀⢀⡄⢀⠀⢀⡀⣥⠌⡀⠈⡉⡁⣂
⠀⠀⠀⠀⠀⠀⠀⢚⠁⠛⣛⢈⠑⢖⣛⣀⣀⢈⠳⠚⠂⠸⠃⡷⠂⠿⠛⠧⠛⠷⠴⢦
⠀⠀⠀⠀⠀⠀⡄⠂⠀⠀⠀⠈⠀⠉⠀⠀⠀⠈⠀⠈⠀⠀⠀⠵⠉⠀⠀⠈⠈⠁⠈⠍⠡
⠀⠀⠀⠀⠀⠞⠂⠒⠀⠐⠛⠓⠐⠿⠐⠃⠒⠒⠒⠐⠐⠁⠀⠀⠀⠀⠀⠈⠁⠈⠉
⠀⠀⠀⠀⠀⠸⠤⠰⠐⠀⠖⠰⠦⠦⠶⠀⢶⠶⡾⣿⢷⠀⠀⠀⠀⠀⠀⠀⣠⣤⠠⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠰⠆⢢⠀⠀⠀⠀⠀⠀⠶⠀⠀⠈⠂⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢚
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠠⠿⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⡌⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡸⡗⢒⡞⢹
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⠲⢽⢿⣫⣿⣇⠀⠉⠏⢉⡀⢠⡥⠃
⠀⠀⠀⠀⠀⠀⢹⣿⠟⠠⡌⠳⢿⡏⠐⡄⠀⠀⠀⢈⣶⠶⠟⡆⠴⢤⢬⠰⠂⠀⠉⠀⠂⣛⠀⡈
⠀⠀⠀⠀⠀⠀⣄⣻⣿⠾⣵⡖⠴⠊⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⠀⠀⢉⠈
⠀⠀⠀⠀⠀⠀⢘⢻⡁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⣠⣶⠄
⠀⠀⠀⠀⠀⠀⠈⠢⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠨⣥⣌⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠂⠐⠆⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⠀⠀⢀⠀⣠⢴⡀⣸⠗⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠚⠀⠁⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠞⠑⢒⠻⡀⣀⡿⡖⣆⢡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠸⠓⠚⠒⠛⠸⠆⠖⠇⠦⢬⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⡀⠀⠀⠀⠀⠀⣠⣄⠀⠁⠀⠠⠄⠁⠁⠁⠨⠀⠌⠉⢉⡅
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠀⠀⠐⠃⠀⠀⠐⠂⠐⠂⠋⡅⠀⠀⠤⠀⠤⢠⠠⠄⠀⡄⣀⢤⡄⢠⠄
⠀⠀⠀⣰⡛⠩⡛⢂⠹⠋⠁⠀⠀⠀⠀⠀⠐⠀⠒⡒⡆⢠⠤⠀⠀⠄⠠⠀⠀⠀⠀⠀⡤⡄⠀⡠
⠀⠀⡤⠤⡧⠴⠠⠄⠰⠀⡻⠚⠚⠐⠘⠶⠧⠠⠨⠀⠘⠳⠰⠾⠦⠤⠴⠵⠞⠦⠼⠠⠤⠼⠶⠦⠵⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠊⠀⠄⠀⠀⠀⠀⢰⠀⠀⡆⠀⣶⠀⢸⢣⣞⢆⢲⠀⡶⠀⠀⠀⠀⢀⢀⠀⢀⠀⢀⠀⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠖⠀⠀⠀⠀⠀⠀⢸⠖⠒⡇⢰⠧⣇⢸⠎⢸⠎⠈⡿⠁⠀⠀⠀⠠⠁⠀⠙⠁⠀⠀⠃⠁
⠀⠀⠀⠀⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⣸⠀⠸⣸⡄⢸⠀⢰⠃⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠁⠀⠀⠉⠁⠈⠀⠉⠀⠀⠀⠀⠀⠐⠈⠑⠄⢀⠔⠁⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠓⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠏⡡⢈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⡄⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⡤⠀⠀⠀⢠⠀⢠⡄⠀⠀⠀⠀⠀⠀⡿⠀⠀⠈⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠄⡇⢀⡀⠀⢸⠀⠈⡇⠀⣀⣀⠀⠀⠀⣇⠀⢀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⣸⠀⠀⡇⠸⡇⠀⢾⠀⠨⣧⠀⢧⣠⠂⠀⠀⢹⡀⢰⠆⢠⠇
⠀⠂⠀⡀⠀⠠⢀⠀⠀⠀⠀⢠⡙⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠋
⠀⠀⠀⠀⠈⠀⠀⠀⠂⠀⠰⢮⣙⠒⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠳⢤⡍⢀⠀⠃⠀⠀⠀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢀⢄⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠖⠰⢈⠀⠁⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠄⡀⠀⠀⠀⠀⠀⠈⠒⠈⠉⠀⠁⠈⠛
⠀⠀⢠⠄⠀⠒⠲⠒⠒⠒⠐⠂⠀⡸⠃⠀⠤⡈⢃⣀⢠⠤⠄⠒⠒⠒⠂⠀⠀⠒⠲⠤⢄⣠⠃⠔⠊⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠨⠀⠀⠰⠂⢠⣄⢤⠆⠀⠘⠢⣀⠀⢠⠌⠈⠍⠟⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠓⠂⠤⠀⣃⠀⠀⠀⠀⢀⠔
⠀⠀⠘⠂⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡤⡀⣤⠄⣤⡄⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⣂⠒⠀⢠⠀⠀⠀⠀⠀⠀⢸⡗⢸⢿⣹⡧⢸⡧⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠁⡀⠔⠁⠀⠀⠀⠀⠀⠀⠘⠃⠘⠈⠛⠓⠘⠗
⠀⠀⠀⠀⢠⡄⣤⠀⠀⠀⠀⠀⠀⠄⠉⠁⠀⢀⠄⠠⡀⠂⠈⠐⠄⠀⠈⠢⡀⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⢸⡟⣿⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠘⡇⣰
⠀⠀⠀⠀⢸⡇⠿⠸⠷⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠸⠠⠤⠶⠀⠀⠖⠆⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⢃⠖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠉⠀⢀⣀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣡⠞⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⣀⠄⠂⠄⠄⠁⠀⠀⡀⠐⠈⠁⠛⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⢚⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠚⣿⠀⠀⠀⠀⠀⠘⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒
⠀⣀⣀⣀⣀⣀⣀⠀⠀⣿⠀⠐⣈⡙⢳⡄⢸⡇⢠⣄⣀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠙⠃⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⢲⡈⠷⠁⣼⡇⠘⠳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠁⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⠀⠀⣀⣼⣏⠁⠀⠀⡀⡀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣶⣾⣷⣫⣿⣿⡏⢻⣿⢟⣯⠯⠝⡟⡿⠋⠙⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣋⣿⡏⢿⢷⡿⣟⡧⠛⠟⠛⠛⠙⠓⠳⡟⡽⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡪⠙⠿⡿⡿⣻⢻⣿⣼⢏⡆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠯⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠼⠿⠿⠿⡿⠿⠿⠿⠟⠺⠃⠀⠀⠀⠤⠤⣄⡀⠀⠀⠀⠀⠈⢺⣶⣣⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣲⠭⠃⢀⣀⡉⣠⣙⣷⡓⡐⣠⠒⠁⠀⠀⠐⢦⣀⣰⡷⠀⠀⠀⠀⠀⢸⣷⢶⣿⠋
⠀⠀⠀⠀⠀⠀⢀⡰⠚⣕⣿⠞⣛⣯⢩⣿⣛⣽⡁⢯⠙⠀⠀⠀⠀⠀⠉⠃⠈⠀⠀⠀⢿⠿⢷⡄⣿⣶⢯⡄
⠀⠀⠀⠀⠀⡠⣏⠀⡆⣯⢹⡟⣷⣾⠿⣽⠭⠭⠾⢉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠈⣷⣿⣏⣫⡀
⠀⠀⠀⠀⠠⣕⣭⢡⠴⢢⣾⣧⢻⡿⢿⠀⠠⡊⣓⡛⠀⠀⠀⠀⣀⡀⠀⠠⠬⣿⣷⣦⠀⠀⠈⢀⡳⣿⣽⣮⠇
⠀⠀⠀⠀⡚⣯⣥⡜⣧⢺⣟⣮⣷⣥⣾⣟⣾⣩⢯⡏⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⡉⠛⠀⠀⠀⢈⣯⣽⠛⡷⣤
⠀⠀⠀⠠⠿⢼⠿⠶⠶⠡⣟⡾⣻⣶⣾⣿⣍⡹⢾⡅⠀⠀⠀⠀⠀⠀⠀⠲⢤⠀⠘⠂⠀⢠⣠⡮⡟⠮⠬⠿⣚
⠀⠀⠀⢸⣦⡤⢟⡘⣟⠗⠸⠛⣿⣿⣿⣶⡹⡟⣽⣷⡄⠀⠀⠀⠀⠀⣽⣦⣤⣤⡦⢸⣷⣝⣿⣿⡾⡟⠿⠒⠯
⠀⠀⠀⣾⣟⣀⡋⢉⡁⢛⢁⢠⡸⣏⣭⣽⡦⢌⡦⣾⣿⣷⢢⣠⣄⣀⡈⠙⠚⠁⢠⣿⣿⣯⣳⣧⣛⣛⣛⣫⡵
⠀⠀⢀⢡⣧⠈⢰⡆⣦⣰⣶⣮⣫⣭⣹⡿⣧⢸⣷⡙⣾⢛⡟⣿⣿⣿⡷⣦⣠⣤⣿⣟⣮⣖⡇⢡⠝⣺⢯⢜⠃
⠀⠀⡈⢸⣟⣰⣸⣧⣷⣿⣿⢺⣹⠿⣏⣷⣞⡘⢯⣿⣿⣿⣹⡽⡿⣿⣿⣾⣧⠐⣿⣧⢹⣿⡎⡱⠞⢙⣿⣻
⠀⢀⣁⣺⣼⡞⢟⣟⣽⣋⡫⣉⢷⣾⣷⢿⣿⡛⣎⢫⣿⣿⣿⢿⣾⠾⣽⡿⢳⣬⣿⣟⣘⢮⡏⢻⡾⣿⣿⢹⡀
⠀⠀⠖⣬⡿⣿⢼⡿⣧⢹⣟⣯⣼⣻⠾⣯⢿⣿⡾⣅⢻⣹⣷⣿⠟⢋⣤⠶⢃⣾⡿⣻⣿⣿⣆⣟⡄⣥⢹⠿⡫⠄
⠀⠀⣭⣞⠿⢼⢽⡤⢯⣞⡏⠳⣇⠿⡿⣿⡷⢞⣿⠫⡄⢛⣬⡱⠒⠋⠁⢀⣾⣿⣮⣽⣿⣿⢾⢿⣧⢹⣿⡅⠾⠄
⠀⠀⣿⣉⣓⢃⡂⠲⢎⠛⢗⣙⣛⣣⣡⡿⢿⡿⣷⢧⢿⠿⠂⠀⠀⠀⡰⢿⠿⣿⣾⣝⡷⣿⣿⢿⣿⣟⡿⣇⠶⡂
⠀⠀⢻⡼⠷⣋⣁⠤⢄⢀⣘⠋⣟⣟⣛⡁⠀⢳⣹⣿⡟⠀⠀⠀⣀⣾⣿⡿⣱⣤⣿⣿⢗⣼⠍⠈⣽⡎⢁⠻⡆⢻⡄
⠀⠀⢨⣿⣾⣿⣟⠿⣏⡿⣿⣿⣿⣿⣿⣧⠀⠀⢻⡿⠁⠀⠀⣴⣯⣽⣿⠹⠍⣼⣟⣧⣾⡶⠀⠀⢸⡗⠈⡇⠩⣄⢻⡄
⠀⠀⠀⢿⣷⣾⢒⣎⢪⣿⣿⣿⣿⡟⣑⠀⠀⠀⠀⠁⠀⠀⣰⢟⣿⡛⠃⣿⠴⡿⣿⢛⣻⡏⠀⠀⠀⣵⠀⠹⠆⠙⡀⠠
⠀⠀⠀⠘⡴⢯⣶⣶⠟⣿⣻⣶⣯⠉⠀⠀⠀⠀⠀⠀⠀⣠⠟⣸⠛⠀⢀⣿⠘⡿⠺⢿⣿⣇⠀⠀⠀⠹⠀⠀⢹⡄⢥⠐⠆
⠀⠀⠀⠀⡇⠀⢰⠀⢆⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢀⣛⠀⠀⢨⠎⠀⠃⠀⠀⣧⠈⢣⣀⠀⠀⠀⠀⠀⠅⠈⣆
⠀⠀⠀⠀⢾⡄⠀⠃⠈⢂⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣬⠃⠀⠀⣿⠃⠀⠀⠀⠀⠹⣆⠀⠘⠷⣀⠀⠀⠀⢾⠀⣱
⠀⠀⠀⠀⢸⠁⠀⠰⡄⠀⢣⠀⠙⠠⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠉⠲⡄⠀⢸⠄
⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣒⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠌⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣿⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⣠⠰⠹⢿⣿⣿⣿⣷⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠀⢀⡴⠲⣶⣶⢶⣄⡀⢀⣿⡶⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁⣠⢤⡀⠂⠈⠹⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣰⢏⡈⡔⢡⣁⠊⠑⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⠄⣸⣥⣤⣤⣤⣭⣿⡿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠐⢶⣿⣷⣾⣿⣿⡿⢃⠀⠁⢹⠛⡁⢁⣤⡄⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⣠⡾⠁⢈⡼⢣⡈⠀⠁⠈⣌⠁⠀⠀⢿⣿⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢢⢄⡄⠀⠀⢸⠁⠉⡀⠉⠒⠤⣄⣀⡀⠀⠀⠀⠀⠀⡠⠈⠹⠧⠖⠋⠀⢀⠑⠀⠀⡔⠙⠀⠀⣤⠈⣿
⠀⠀⠀⠀⠀⠀⠐⠀⠸⣿⣿⣿⡏⢡⢇⡃⠃⠀⠀⠈⠀⠘⣧⠀⣀⣠⠤⠚⠁⠀⠀⠀⠠⣎⡀⢀⣀⠠⠤⠔⡚⢿⢃⡤⠊⠀⢀⠃⠀⠰⠀⡉
⠀⠀⠀⢄⡶⡾⣆⠀⠀⠹⣿⡟⡅⣵⡎⠙⢓⢠⠄⠀⠀⡀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡸⠀⠀⠀⠀⡇
⠀⠀⠀⠾⣿⢾⣧⠀⠀⠀⠙⢷⣴⡹⡇⠂⠈⠁⠀⠀⠀⣿⠒⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⢰⠁
⠀⠀⠀⠰⣿⣷⠁⠀⠀⠀⠀⠀⣿⣇⠈⣺⠀⠀⠀⠀⠀⠈⢳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⠁⠀⢸⡆⠇⠀⠀⠀⣀⠔⠁⠀⠀⠀⢀⡌
⠀⠀⢀⣄⠘⣻⡅⠀⠀⠀⢀⣉⠁⠹⢆⣿⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡑⢌⣣⠸⢸⠀⠀⢰⠀⠐⠃⠀⠀⢀⡠⠖⣹⣷⡄⠀⠀⠐⣉
⠀⠀⠀⠏⠳⠹⣗⠀⠀⠈⠙⠛⠋⠀⡜⠛⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠑⡄⣏⠦⡘⠀⠀⠸⣄⢸⣤⡠⠖⠁⢀⣼⣿⣿⣷⠀⠀⠀⠈⠐
⠀⢠⣶⡆⠀⠀⢋⣄⠀⠀⠀⠀⢰⣾⡀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⣠⠀⠠⢸⠄⠃⠀⠀⢠⣿⣿⣯⠀⠀⢠⣾⣿⣿⣿⣿⡄⠀⠀⢠⠂⠠
⠀⠀⠻⠇⠀⠶⡀⠉⠀⢀⡠⠴⢏⡈⠙⠳⢷⢶⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⢀⡧⠔⢻⡄⠀⠘⢃⣿⠻⠀⣰⣿⣿⣿⣿⣿⣿⣿⡀⠀⠉⠀⠉
⠀⠀⠀⠀⠀⢸⠁⠀⣿⠙⠓⣿⠌⠉⣲⣤⣀⣀⣀⣹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠾⢿⡧⠶⠀⠸⣶⣾⣿⣷⡀⠀⣸⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⡰⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⣸⡀⢼⡷⠟⠀⣈⢻⢫⣮⢿⡄⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀⢻⣿⣿⣿⣷⣠⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⢠⠟⣡⣤⠀⢰⣯⢓⠾⡀⠡⠊⢀⣀⣀⠀⠀⠀⢀⡴⠴⠦⠼⢄⣀⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⢠⡄⢀⡎⠀⠀⠀⡎⢸⠯⠜⡲⠆⠞⠁⠀⣀⠤⣊⠖⠲⣭⠻⢆⠀⠈⣞⣙⣋⠱⠂⠀⡝⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⣠⢿⠀⡜⠀⠀⠀⣸⢁⣤⣦⠞⠀⣴⣶⣶⣿⣶⣶⣶⣾⣷⣿⣶⣾⣶⣶⣿⣷⣶⣶⣶⣶⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⣰⣷⡾⣷⠁⠀⠀⠀⠧⣛⣃⣍⠀⠀⠈⠉⠹⠋⠉⠉⣉⣉⣭⣭⠭⢭⣿⡉⠉⠉⠉⠉⢩⣿⣿⠉⠉⠀⠀⢀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠉⢉⣿⣸⣄⣀⣀⣀⣀⣀⢠⡭⣍⡁⠚⠻⢞⣁⢾⡏⢩⣟⠷⠀⢠⣞⠛⣿⡀⠀⠄⠀⢸⡇⡀⠀⠀⠀⣠⠊⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠙⠋⠛⠛⠛⠛
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣢⡠⢀⢽⢏⡀⣤⠀⢀⣐⡄⠀⠀⢹⣯⠆⢤⣴⣾⣿⡇⠀⠀⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠓⢾⡎⣧⡻⠃⠀⠺⠙⠁⠀⣾⠎⢹⣯⣱⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣦⣸⡆⢹⢁⣶⡿⠂⢠⣶⡇⠀⣴⡿⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢻⣇⣀⣀⣀⣀⣀⣀⣀⣀⣰⣿⣷⣾⣿⣷⣇⡈⢉⣤⠤⠽⡿⠒⠋⠙⣇⠁⠀⠉⢻⣿⣿⣿⣿⣿⣏⠙⣷⢀⠤⠀⠰⠄⠂⢀⣩⣽⡮⠁⠈⠈⠁⠚
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢿⠉⠀⠀⡰⠉⢦⠀⠀⠹⣆⠀⠀⣾⠉⢿⣿⣿⣿⣿⣦⢹⡄⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠉⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢻⠛⠉⠀⡆⠀⢠⡅⠀⠀⠳⡀⠀⠹⣦⣀⣿⠀⠀⠙⣿⣿⣿⣿⣷⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⣇⣀⣀⡈⢻⡇⠀⠀⠀⠈⠻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢠⣁⠀⠘⣆⠀⠀⠀⠙⣿⣿⢿⣿⣿⣶⣤⣤⣀⢀⣽⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡞⠀⠀⠀⢸⣿⠻⢿⣿⣶⣄⣀⠀⠈⣧⠀⣼⠀⠉⠛⣻⣿⣿⡿⠋⠈⠋⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠓⠚⠁⠀⠀⠀⠀⠃⠀⠀⠈⠙⠛⠿⠿⠗⠛⠚⠋⠠⠶⠟⠛⠋⠁⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠖

⠀⠀⣈⣙⣒⡛⠂⠈⠉⠉⠁⠠⠴⠒⠂⠀⠀⠤⠤⡤⢀⣤⣀⡀⠀⠀⠀⠀⠐⠧⣀⠀⡑⠢⠤⠀⣈⡑⠀⣌⡢⠄⠀⢠⣄⠀⠱
⠀⠀⠠⠶⠤⡄⠒⢉⡉⠉⠁⠀⡨⠭⠥⠐⣛⣙⠓⠀⠀⠀⣄⣉⠀⠀⠀⠀⢍⠙⠂⢈⠓⠦⠄⠠⣄⠙⠄⠳⠍⠂⠀⢤⣎⣙⠂
⠀⠀⠀⠘⠒⠆⠀⡀⣈⣑⠒⠂⠐⣒⣒⡀⠔⣒⠉⠉⠠⠤⠦⠬⡀⠀⠀⢤⡀⠁⢀⠈⠑⢂⠘⠢⠍⠓⠀⢤⡀⠀⠒⠦⣄⠁
⠀⠀⠀⠒⢛⠒⠂⠀⡂⢀⣀⣀⠈⣀⣀⣀⢀⠬⢭⣁⠐⠒⠒⠒⠒⠀⠐⢦⡉⠀⠈⠙⠂⠠⣝⠆⠀⠲⢌⠒⠉⣀⠉⠓⠦
⠀⠀⠀⠀⣀⣉⣁⠀⠀⠉⠡⠤⣀⠀⣒⣂⠀⠐⠲⠦⡄⠀⠭⡉⠀⠀⠒⠤⡉⠀⢘⠲⠄⢐⢤⠉⠠⣝⠦⠁⢀⣈⡙⠓
⠀⠀⠀⠀⠀⢀⠀⠀⠑⢲⣴⡂⠀⠀⠵⠶⠅⠀⠠⢠⡀⠀⠵⠯⢭⡁⠲⡀⢄⡠⣌⡓⠀⢨⣑⠂⠈⣪⡅⠀⠴⢌⣙⡃
⠀⠀⠀⠀⠀⣀⣉⡏⠀⠥⠤⠭⣄⠀⠤⠤⠤⠀⡒⠢⠀⠂⣈⠛⠀⠀⠦⣁⠀⠙⢀⠈⡡⠂⠉⠁⠀⠈⠳⠐⠦⠄⠉
⠀⠀⠀⠀⠀⢀⠠⠤⠀⠚⠛⠒⠀⠐⠺⠗⠒⠌⠈⡉⠂⠀⠈⠉⠑⠂⠀⠈⠁⠀⢊⡞⢡⠞⠰⢡⣯⢀⢄⠞⡀⢠⠖
⠀⠀⠀⠀⠀⠀⠊⠓⠂⠈⠉⠉⣉⡀⢉⠫⣄⠈⠉⢍⣑⠂⠉⠉⣉⠈⠓⣠⠀⡶⠘⠀⠈⠀⠀⠋⠃⠃⠎⠈⢰⡇
⠀⠀⠀⠀⠀⠀⠠⠒⠒⠚⠀⠠⠤⠮⠅⢀⣉⣠⠀⢀⣂⠤⠄⠈⣉⣑⠀⡏⠰⠃⡸⢡⠏⢰⢂⢄⠄⣰⢀⢠⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣕⣀⠈⡉⣅⡀⠐⠦⢤⡀⠀⠀⠈⠁⠈⣉⡀⠀⢀⡔⠀⠀⠁⠈⠈⠈⠊⠀⠁⣋⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠤⠀⠒⢒⣀⠀⠤⠶⠤⣄⡘⠂⢉⠂⡀⠀⡀⠘⠴⠹⢡⢂⠎⠚⠜⣶⠏⡜⠡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢦⣭⠀⠒⢒⡒⠀⠀⠀⠉⢹⠃⢰⢁⡖⢰⠆⢀⡄⣰⢠⠂⡄⣀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣅⣐⠦⠤⠤⠄⠭⢭⡅⠀⡔⠀⠘⣠⢀⠈⣠⠈⠀⠘⠀⢃⠁⠘⠁⠑⠁⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠉⠑⠢⠐⠒⠶⠤⢴⠁⡸⠃⠇⠎⠀⠇⠞⣰⠋⢰⢃⡖⡔⠀⡼⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡈⠙⣂⡄⢠⠄⡜⢈⡁⡈⠀⠁⣰⠃⣰⠎⡄⢀⡄⢠⢀⠈⡉⣠⠄⣢⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢼⠜⠀⠘⠙⠀⠎⠸⠃⢰⠹⠁⠈⠸⠸⠀⠌⠐⡏⠘⢸⠰⠃⠼⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⠚⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⣤⣶⣿⣶⣯⣭⣿⣧⣿⣿⡿⣿⣿⡧⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢿⣿⣿⠟⠹⠿⠟⢻⡟⢻⣿⡶⠖⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣼⡷⡌⣿⣿⡆⠀⠀⠀⢈⠉⠉⠈⢳⡦⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣿⣿⣿⠀⠀⢺⣿⣿⣿⠀⣸⣇⡇⠀⠀⠀⠀⠀⣶⣾⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢨⣿⣿⣿⣿⡟⠀⠀⠀⠉⠉⠛⢀⣿⠿⠁⠀⠀⠀⠀⠀⠹⣿⣿⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠗⠀⢤⣾⣿⣻⢋⣿⣿⣶⣤⣀⡀⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⢰⣿⡽⣱⣿⣼⣿⡇⠙⠋⠉⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⢀⣿⣟⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠙⢶⣤⣿⣿⣷⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⣿⢁⠀⢀⣠⣤⣴⣶⠿⣿⡿⣇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡃⠀⠀⠘⡟⢜⢿⣿⣿⣷⡻⣧⠄⠀⠀⣾⣧⣭⣿⣿⣿⣿⡟⣼⣿⢟⣿⣿⣿⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠀⠀⠀⣰⡿⢸⠘⠿⣿⣿⢿⣟⠛⢦⣠⠏⠀⢺⣿⣿⣿⠟⣱⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⢀⣼⣍⠀⠀⠀⢠⣿⢣⣯⣴⡇⠨⣿⣿⡿⠃⠀⠘⠂⢀⠀⢹⡿⢻⣾⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⢀⣠⣾⣿⣿⣿⣿⣿⠀⠚⠁⠀⠀⠀⠀⠁⠘⡀⠀⠃⠈⠉
⠀⠀⠀⠀⠀⠀⠘⢿⣇⣀⣩⣿⠟⠉⢻⣿⣿⡏⢇⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⢿⣿⣇⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⢣⣿⣿⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣭⡤⠀⠀⠀⠰⠀⢀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠛⠶⠿⡥⠀⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠀⠀⠒⠤⡀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠎⠀⠲⠤⠦⡤⠤⠀⠈⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⢆⠸⠖⠲⠒⠒⠒⠀⣰⣿⣿⣿⣷⣿⣿⣻⣿⣿⣿⣿⣿⣯⢽⣆
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠑⠠⠄⠀⠀⠤⢰⣿⣿⣿⣿⣯⣷⣯⣿⣿⣿⣶⣻⣳⣿⣿⣿⡆
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣮⡯⣿⣿⣟⣿⡿⣿⣿⣿⣿⣭⣿⣷
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢙⣇⠀⠀⠀⠀⠀⠀⠀⢸⣏⢾⣿⣿⡿⣷⣿⣿⣿⣿⣷⣷⣿⣿⣿⣿⡿
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣻⢯⣯⢿⣿⡟⣿⣫⢭⣿⣿⣛⣿⠇
⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠉⠉⠉⠉⠉⠉⠒⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡰⠳⣄⠀⠀⠀⠀⠀⣠⠞⠑⣄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣠⠖⠉⠙⠦⣀⠀⠀⠀⢸⠁⠀⠈⠓⠦⣄⡀⢰⠃⠀⠀⠈⢧⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠈⠙⠲⠤⣬⡦⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡰⠓⢶⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣠⠶⠚⡇
⠀⠀⠀⠀⠀⠇⠀⠀⠘⠦⣀⡇⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠉⠁⠀⠀⠇
⠀⠀⠀⠀⠀⢢⠀⣀⠀⠀⠈⠁⠀⡜⠉⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠈⢳⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⢹⡹⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡿
⠀⣴⣤⣶⢀⠀⠈⢇⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢰⠃⠀⡀⣶⣤⣦
⣻⣽⠞⠻⢯⠇⠀⠘⢎⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢡⠃⠀⠸⡽⠟⠳⣿
⠙⢯⡀⠀⠸⢤⡀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⡴⠶⠶⠶⠶⠶⠶⢦⠀⠀⠀⠀⠀⠀⠀⢀⡜⡱⠃⠀⢀⡤⠃⠀⢀⡽
⠀⠀⠈⠳⡀⠀⠙⠦⣀⠀⠙⢿⣄⡀⠀⠀⠀⠀⠀⠹⡍⠉⠉⠉⠉⢉⠏⠀⠀⠀⠀⠀⢀⣠⣯⠞⠀⣀⠴⠋⠀⢀⠞⠁
⠀⠀⠀⠀⠙⢦⠀⠀⠈⠳⢄⡀⠙⠻⣦⣄⠀⠀⠀⠀⠈⠓⠒⠒⠚⠁⠀⠀⠀⠀⣠⣴⠿⠋⢀⡠⠞⠁⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠉⠳⢤⡀⠉⠛⠷⢦⣤⣤⣀⣀⣀⣀⣤⣤⡴⠾⠛⠋⢁⡤⠞⠉⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠉⠳⡶⣄⠀⠀⢘⡇⠀⠀⢸⡃⠀⠀⣠⢶⠞⠉⠀⠀⠀⢀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⡰⠃⠀⠙⠒⠋⠱⢤⡤⠞⠙⠒⠋⠀⠈⢆⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣴⣾⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢗⢀⠃⠁⢐⠸⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣴⡰⣲⡄⠀⣤⡟⣥⡏⠐⢀⠀⠄⠂⣺⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢹⠐⣿⠁⣼⡟⠫⣴⠀⢃⠄⠐⠈⡌⠎⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢀⡜⢳⡆⠀⡖⣿⠀⣞⣀⠢⠉⢐⠒⠠⠁⢀⡂⠠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠘⢳⡄⢰⡀⡇⢸⠀⣿⠂⡎⠃⠐⠂⠠⠀⠠⢂⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠻⡄⢳⣼⢸⡄⣸⣆⢣⠁⠀⠀⠄⠀⠄⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠹⡄⠹⣶⠇⠘⣷⡾⡊⠲⠆⢀⠰⢠⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠘⡄⢿⣷⠀⠘⡿⣵⣬⢁⣂⡲⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡿⣎⠌⢦⠀⠈⢮⠉⢉⠽⠊
⠀⠀⠀⠀⠀⠀⡇⠘⣇⠈⢳⡀⢸⠀⡌
⠀⠀⠀⠀⠀⠀⡇⠀⠻⣆⠀⠙⣯⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⢻⡀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠒⠒⠒⠒⠖⠒⠤⣄
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠷⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⡰⠋⠑⠀⠀⠀⡀⠂⠀⠀⠀⠈⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠃⠀⠀⡁⡄⣷⡀⠀⠀⠈⢦⠀⠀⠀⢀⡞⠀⠀⠀⠈⡶⠊⠀⠀⠀⠀⢀⡀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⣿⣧⠀⠀⠀⠀⢣⠀⠀⡸⠀⠀⠠⠐⠈⠀⠀⠀⠀⡠⠂⠁⠀⠀⣀⡤⠞⠓⠒⠒⠒⡆⢄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢸⢀⠀⠀⣧⣿⣿⢧⡀⠀⠀⠀⢳⡖⠉⠚⣅⠀⠀⠀⠀⠀⢀⠚⢄⠀⠀⣠⠞⠁⢣⡀⠀⠀⠀⠈⠙⠢⡈⢢⡁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⣏⠁⠘⢷⡄⠀⠀⠀⠱⡀⠀⠘⣦⠄⠀⠀⠀⠂⠀⠀⠑⠴⠁⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠈⣿⣷
⠀⠀⠀⠀⠀⠀⢸⡄⢀⡔⠛⠃⠷⣄⠀⠻⣄⠀⠀⠀⠰⡄⠀⠘⡄⠀⠀⡆⠀⠀⠀⢀⣧⡠⠔⠈⠻⣿⠿⠗⢀⠀⠀⡀⠄⠛⠿
⠀⠀⣠⠒⠉⠁⠙⣇⠬⠷⢀⠀⠀⠈⠳⠤⠈⢂⠀⠀⠀⠘⢄⡰⠃⡏⠈⠁⠂⠀⠀⠸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠊
⠀⠀⡇⠀⠀⠀⠈⢧⡀⠀⠀⠉⠒⠤⠄⠀⠀⠘⢧⡀⠀⠀⠈⢣⣀⠘⢆⠀⠀⠐⠀⠀⠷⢄⠀⢀⣀⣄⠀⠀⠀⠀⡀
⠀⠀⢣⡀⠀⠀⠀⠎⠙⡇⢄⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄⠀⠀⠀⠹⡑⡄⠉⠈⠹⠤⠤⠒⡀⠙⣿⣿⣿⣷⡄⠀⠈⠁⠀⢄⣀⡰
⠀⠀⠀⠉⠀⠀⠒⠛⢄⣘⣦⡽⠂⠀⠀⠀⠀⠀⠀⠀⣈⣦⠀⢀⠀⣧⣸⠀⠔⠃⠀⠀⠀⠑⢤⠘⠻⠿⢏⠀⠀⠀⠀⠀⣸⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠄⠊⠑⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⠈⠧⠄⠀⠀⠂⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣻⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⣼⢛⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡖⡼⢣⣟⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣀⣀⣀⣀⡀⢀⣠⣾⣼⣿⣇⣴⣾
⠀⠀⠀⠀⠀⠀⣠⢶⣶⣶⢦⡤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⢞⣿⡿⣹⣿⣿⡿⣰⣿⡿⢻⣿⡟⡟⣹⣿⠟⣿⣿⢻⡏
⠀⠀⠀⠀⠀⠀⣿⢸⣿⢃⣿⠇⣿⣿⡿⣵⡟⣿⠟⣿⣿⢸⣏⣾⣿⢡⣿⣿⣿⡇⣿⣿⢣⣿⣿⣸⢱⣿⣿⣸⣿⡇⣼⡇
⠀⠀⠀⠀⠀⠀⢻⣸⣟⢼⣿⢰⣿⣿⢧⣿⣸⡏⣸⣿⢣⣿⣿⣿⣧⣾⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣣⣿⡇
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡿⡟⣿⣸⣿⡿⢿⣿⣷⣿⣿⣿⣿⢟⡍⣾⠏⣿⣿⣿⢫⣿⢫⣿⢹⣿⣿⡟⣿⣿⡿⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡼⣸⠟⣿⣿⢣⣿⢣⣿⡏⣿⣿⣯⣼⣿⡏⣼⣿⣿⣧⣿⢇⣿⡇⣿⢃⣿⡇⣿⣿⢃⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣾⣿⣟⣾⡏⣸⣿⣵⣿⢿⣿⡟⣿⢿⣿⣿⣿⣿⣯⣾⣿⣧⣿⣘⣿⡧⣿⣿⣼⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣿⣾⣷⣿⣿⣿⡇⣼⢟⣼⠇⣾⣟⡽⢩⣿⢿⡿⣹⣿⡿⣿⣿⣷⡿⣻⣿⡟⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⣿⣴⣿⣿⣿⢸⣿⣸⢇⣿⡟⣼⢡⣿⣿⢱⣿⢇⡿⢱⣿⣿⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣇⣿⣿⣿⣼⣿⣿⡯⣼⣿⡇⣿⣿⣼⣿⣿⣿⣇⣿⣿⠟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⣻⣿⢹⣿⣷⣿⣿⣰⢟⣿⢻⠏⣽⢟⣿⣿⣿⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢓⣿⡟⣸⢏⣿⣿⢋⡏⣸⠇⣿⢸⣿⢸⣿⣿⣏⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⣿⢸⣿⣏⢼⡇⣿⣞⣿⣸⣧⢸⣿⣿⣿⣼⡿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⢿⣾⣿⣿⡏⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣼⣿⣿⣿⡿⣿⣿⣽⣿⣿⣿⡟⣼⣿⣿⣿⠇⣿⡇⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢹⣿⡏⣾⢰⣿⡏⣼⣿⣿⣿⡇⣿⣿⣿⣿⣷⣾⡇⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⢸⣿⣇⢿⡜⣿⡇⢹⣿⣿⣿⣇⣿⣿⣿⣿⣿⡿⡱⣫⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⠿⣷⣿⣧⣾⣿⣿⡿⣿⣿⡿⣿⣿⣿⢟⣽⣿⣿⣿⢸⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⣿⢸⢳⣿⢻⡟⣼⡟⣼⢡⣿⣿⢣⣿⢻⢏⣿⠏⣹⣿⡟⣼⢩⣿⣿⢣⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠿⠋⠉⣇⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡹⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣍⠀⠀⠀⣿⡈⠀⠀⡀⠀⠀⠀⠀⠀⡀⠆⠀⠔⠈⠀⡇⠀⠀⠀⠀⢀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⡏⠐⢤⣴⣿⣿⡆⠀⠀⠀⣀⠀⠀⠀⠀⠘⣦⠀⠀⢀⠃⠠⠀⢀⠔⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡟⠋⠉⠁⠀⠈⠙⢻⣿⣿⠆⠀⠰⠂⠈⠀⠄⡀⠀⠁⠐⠠⠊⠀⠔⠀⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⡀⠀⠀⠀⢹⠀⠘⣿⡷⠀⠀⠀⠀⠄⠀⠀⠁⠄⠀⠀⠀⠙⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠠⠁⠀⠀⠀⡆⠀⠀⠡⠀⠀⠀⠁⠂⠀⡔⠀⠀⠀⠀⠀⠀⠀⢡⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢜⠀⠀⠀⣰⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠏⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣤⣤⣤⣼⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢳⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠖⠀⠈⠒⠇⠀⠀⠀⢠⣤⣤⣀⣀⣀⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠿⠿⠿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⣿⣿⣿⣿⣿⠿⠛⠉⠙⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⢉⠙⠉⠀⠈⠁⠈⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢄⢀⠆⠀⠈⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠰⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣊
⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠃

⡿⢿⠿⠿⠿⡻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢋⡀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⠁⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠴⢚⡿⠀⠀⠀⢀⣶⣰⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠉⢳⡄⠀⠀⢰⡏⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⢿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠒⠺⡏⠙⠹⠓⠗⠛⠉⡷⠦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠇⠀⠀⢀⣠⡴
⠀⣀⡀⠀⠀⠀⠀⠈⢳⡝⢦⡀⠀⠀⠀⠀⠀⠀⢀⡟⢠⡄⠀⣧⠀⠀⠀⠀⠀⣸⠃⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⣾⠤⠶⣾⢕⡠⠶⠚
⢀⣬⡿⣷⣶⡖⠶⠒⠉⠀⠀⠙⡆⠀⠀⠀⠀⢀⡾⠀⡾⠀⠀⢸⡀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠠⡿⠟⡒⠒
⠀⢬⣭⣻⣯⠶⣠⡤⠦⢤⡀⠀⣷⠀⠀⠀⠀⣼⠃⢸⠇⠀⠀⠈⡷⠶⠶⢶⡞⠀⠀⠀⢹⠀⠀⢻⡄⠀⠀⠀⠀⠀⣸⠃⠀⡴⠛⠉⠉⠉⠉⠙⠛
⠀⠀⠀⠾⠖⠋⠁⠀⠀⠀⣧⠀⢸⡄⠀⠀⢰⡏⠀⢾⠀⠀⠀⠀⢷⠀⠀⣸⠁⠀⠀⠀⣿⠀⠀⠈⣷⠀⠀⠀⠀⢠⡏⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣇⠀⠀⣿⢄⡀⠘⣆⠀⠀⠀⢸⡄⣰⠃⠀⠀⠀⢀⣿⠀⠀⠀⠸⡆⠀⠀⠀⡞⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢹⠀⢰⠇⠀⠉⣱⠘⢧⣤⠤⢬⣧⣏⣀⣀⡀⢀⡾⠙⣧⣤⠴⠞⣧⠀⠀⣸⠁⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⣇⡏⠀⠀⣰⠏⠀⣎⣵⣤⡴⠷⠾⢤⣀⡿⡾⠁⠀⠘⣇⠀⠀⠸⡆⢠⠏⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⡿⠀⠀⢠⡏⠀⠀⠀⢈⣆⣀⣀⣀⠀⠈⣹⠇⠀⠀⠀⠘⣆⠀⠀⠙⠞⠀⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡾⠀⠀⣠⡴⠋⠁⠀⠉⠉⠉⠉⠛⢦⡀⠀⠀⠀⠘⣆⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⢀⡞⠁⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠈⢦⡀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⡾⠁⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠾⠃⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤
⠀⠀⠀⠀⠀⠀⡔⠶⢖⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡿⢿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠐⠈⠱⡤⢈⣏⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡆⢠⣻⣓⢲⣹⡇⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠘⠙⢻⠶⠊⡁⠀⠙⠃⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⣟⠁⠀⠀⡀⠀⠀⠀⠀⠀⣀⠀⢀
⠀⠀⠀⠀⠀⠀⣠⠄⣿⠡⣤⠀⠀⠀⠹⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⡀⠴⠆
⠀⠀⠀⠀⠀⡿⠿⣶⣷⣾⠀⠀⠀⠀⠰⣀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠿⠜⣿⣧
⠀⠀⠀⠀⠀⠌⠂⠐⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠚⠻⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠀⠀⠀⢀⠀⠺
⠀⠀⠀⠀⠀⠞⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⠀⣭⣧⣀⠀⣀
⠀⠀⠀⢰⣤⣀⡈⣯⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢰⣖⣐⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⡽⢉
⠀⠀⠀⠀⠉⠙⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣾⣇⣹⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠡⢤⣶⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠙⠋⠉⢉⣿⣷⣴⣿⣦⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢴⣾⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢻⣿⣿⠁⠉⠉⠢⠀⢀⡐⢀⠀⠀⠀⠀⠀⠀⢠⡟⠘⠛⣿
⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠋⠁⠀⠀⠀⠀⠘⠂⠠⠎⠀⠀⠀⠀⠀⠀⠀⠀⣠⣢⠆
⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠑⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠁
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢠⢤⣦⡀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⢀⣴⣥⠞⠀⠀⡠⢴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠚⠶⡀⠀⠀⠀⠀⠠⢿⣀⠸⣄⣁
⠀⠀⠀⣀⠀⡷⠟⠁⠀⠀⠀⠹⠯⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡁⠀⠁⠠⣤⡀⠀⠀⠀⢀
⠀⠀⠀⠈⠳⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⡬⠀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⠀⠈⠹⠾⠇
⠀⠀⠀⠀⠀⢻⣿⣶⣤⣀⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣭⣿⣇⡀⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣮⠁⠀⡀
⠀⠀⠀⠀⠀⠈⣿⣿⡟⠛⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣽⠟⢋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⢿⠉⠉⠁⠛
⠀⠀⠀⠀⠀⠀⠈⡹⣿⣴⠻⢿⣆⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣟⣤⣧⠀⢀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠉⢰⣥⣤⠆⠈⠙⠂⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⣿⣿⠶⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄
⠀⠀⠀⠀⠀⠀⠘⠀⠜⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⢠⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡘⢀
⠀⠀⡤⢌⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⡡⠃
⠀⠀⠑⠢⢽⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠔⠒⢻⡄
⠀⠀⠀⡠⡾⠀⠈⢉⠋⠑⠒⢒⡶⠤⡤⠤⠤⠤⠤⢤⠤⠤⠤⢤⠤⠤⠤⠤⠔⠒⠒⠞⠉⣉⠀⠀⢀⡘⡀⠀⠀⢊⠓⠄
⠀⠀⠈⠐⠁⠀⠀⡘⢐⡆⠀⠈⠂⠀⠇⠀⠀⠀⠀⢸⢀⡀⠀⠐⠃⠀⡀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠑⠁⢃
⠀⠀⠀⠀⠀⠀⠀⡆⡀⠀⢠⣢⠀⢠⠀⠀⠀⠀⠀⢸⠈⠁⠀⡠⠀⠀⡇⠀⠀⠀⠀⠀⡄⣀⠋⠃⠀⣖⠜⡀
⠀⠀⠀⠀⠀⠀⢠⠀⠚⣀⢄⠀⠶⢮⠀⠀⠀⠀⠀⠀⢰⡆⠀⠉⠠⡲⠅⠀⠀⠀⠀⠀⢚⠚⢀⠊⠐⠠⢀⣃
⠀⠀⠀⠀⠀⠀⠸⠔⠈⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠈⠢⢄⣀⠀⠀⠀⠀⠀⠘⡔⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣶⣤⣤⡄⠀⠀⠀⠛⠋⠙⠻⠿⠿⣿⣄
⠀⣄⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠿⠛⠉⠀⣰⣤⣶⣤⣴⣦⣤⣄⡀⠀⠙⠻⣶⡄
⠀⢹⡄⠀⣿⠀⢀⠀⡀⢀⠀⣀⠀⣤⠀⡀⠀⠀⠀⠀⢸⣿⡟⠁⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⡷⢶⣾⣶⣦⡀⠘⢿⡀
⠀⠀⠿⠀⣿⠀⢿⠀⠁⠸⡀⡸⠂⠹⡆⢻⠄⣠⠀⠀⣾⡿⠁⠀⢠⣿⠞⣻⢿⣿⣿⣿⣿⣿⣷⣭⣽⣿⣿⣷⡄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⢰⣿⣟⣧⣥⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠰⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣤⣀⣀⣀⣀⣀⣀⠀⢀⣤⣤⣤⣶⣿⡏⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣆⣼⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠔
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠎
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡿⠟⠛⠿⠿⣿⣿⡿⠿⠟⠧
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣄⡀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂



⢸⣷⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⡀⠐⠇⠀⣦⡀
⠸⣿⠟⠋⠉⠁⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⡀⣄⠀⠀⠈⠙⣿⠃⠀⠘⣁⡀⣠⠶⠿⢶⣄⠀⠀⠀⠀⠀⠀⠈
⠀⠈⠀⠀⠀⠀⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⠉⠙⣆⠀⠀⠀⠁⠀⠀⠀⠘⠛⠿⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠁⠀⢀⠒⠂⠀⣠⣷⣽⠆⠀⠀⠀⠀⠐⠂⠺⠂⠀⠀⠐⢂⠀⠀⠀⠀⠀⠀⠐⣂⠠⠀⠀⠀⠀⠀⠀⠤⠤
⢸⣦⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⠁⣤⣾⣿⠏⠋⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠁⠀⠀⠀⢶⡞⠀⠀⠀⠀⠀⠉⠐
⠸⢿⠇⠀⠀⠙⢿⣿⡇⠀⠀⠀⠀⠀⢻⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐
⢠⣴⣦⣄⠀⠀⠘⠿⢷⣦⣤⡆⠀⠀⠘⠟⠀⠀⠀⣀⡀⠀⠀⠀⠀⠈⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂
⢠⣌⠙⠋⠀⠀⠀⠀⠀⠀⠀⠓⠠⣤⠀⣀⣀⠀⠄⠛⢻⣷⣤⣦⠀⠀⠀⠟⠓⠀⠀⠀⠀⠀⢀⠀⢰⡋⠗⠀⢰⣦⠀⠀⠀⠀⠀⢰⣦
⠈⠛⣿⣦⣼⠄⠀⠀⠀⠀⠀⠀⠀⠛⠈⠩⠀⠀⠀⢀⣿⠉⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠐⠷⠸⡇⠀⢡⠄⠀⣘⣿⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠉⠁⡿⠧⡄⠀⣀⡀⠘⠳⣦⠀⢀⠀⣾⠛⠳⢌⣧⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⣚⠉⢁⣀⣀⣋⡉⠁⠀⠀⠀⠀⠀⢀
⠀⣀⠀⠀⠐⠲⠾⠛⠙⠛⣿⣦⣁⠀⠎⠀⠹⢶⣶⣎⠈⢁⡄⠀⠀⠀⣠⣤⣀⢶⡶⠀⠲⡄⢸⢿⣀⠈⠿⣿⡿⢷⣀⠀⠀⠀⠀⠀⠘
⢸⣿⣷⡆⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢻⠀⠘⠣⠀⠀⠀⠈⠉⢻⡆⢻⣤⡄⠀⠸⠋⢙⣦⣴⠀⠀⠈⣛
⢸⣿⣿⡇⠀⢠⡀⠀⠀⠀⣼⣿⡏⢴⣦⣤⡀⠀⢀⡈⠀⠀⠐⣧⠀⠀⢠⣤⢾⢷⣿⣿⡁⣠⣄⠀⠈⠏⢸⡗⡄⠀⣉⡀
⢸⣿⣿⡇⠀⠀⣹⣦⣤⣶⣟⠿⣿⣿⣿⣿⣿⣯⣽⠁⠐⠀⣴⣿⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣧⣼⠃⠀⠀⣸⣿⡀⢨⣷⠀⠈⠀⣠⣴
⢸⣿⣿⠇⠀⠀⠛⢿⠉⠀⠈⢡⣄⡉⠛⠁⠈⠉⠉⠀⠀⠀⣩⣿⠀⢰⣿⣿⣿⠟⠛⠛⢿⣿⣿⣿⠀⠀⠀⠈⢭⣭⠛⠀⠀⠀⢰⣿⡇
⠈⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⣿⣇⣀⡀⠀⠀⠀⠀⠀⠀⠙⠿⠀⠘⢿⠏⠁⠀⢀⡀⠀⠀⠉⢻⡆⣰⡆⠀⠀⠉⣦⠀⢠⡄⠈⣿⣷
⢸⣿⣿⣿⣷⣶⣄⠀⠻⣦⣴⣿⣿⣿⣿⣅⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢀⣤⣴⣆⠁⠀⠠⠀⠜⢠⣿⣿⣦⡀⠀⣿⡄⠘⠃⠀⠙⢿
⢸⣿⣿⣿⣿⣿⣿⣿⡄⠙⣿⣿⣿⣿⣿⣿⣿⢀⠀⣀⣀⣀⣀⣀⠀⠀⠐⠻⠲⣶⠿⣷⡀⠀⡀⢀⣾⣿⡿⢿⣿⣦⣙⡇⠀⠀⠀⠄⠈
⠘⠻⣿⣿⣿⣿⣿⣿⡷⠀⢻⣿⣿⠿⢿⢿⣿⣴⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠴⢉⣀⣤⣭⡀⠉⠋⠰⡦⢠⣿⣿⣷⣶⢢⡀⠀⣤
⠀⠀⠀⠉⠀⢹⣿⣿⠇⠀⠀⠹⠛⠿⠶⠂⣸⣿⣿⣿⣿⠏⡿⠟⠃⠙⠂⠀⠀⠀⠀⠈⠻⠃⠈⠙⠀⠀⠀⣀⣼⣿⣿⣿⣟⠀⠀⠀⣈
⠀⢠⢠⣤⡀⠈⠛⠋⠀⠀⢀⣀⠀⢀⠀⠀⣿⣿⣿⣿⠄⠀⠀⡀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⣀⣤⡉⠛⣿⣿⣿⣿⣿⡀
⢠⣷⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⣼⣷⣦⣼⠿⠛⠗⠆⠀⠀⠁⢀⣠⡀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠿⠟⢁⣾⣇⠀⣄⣀⣨⣿⣷⣶⣦
⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣨⣿⠿⢿⡷⠀⠀⠀⢰⠚⠲⣿⡞⣩⣿⠟⠛⣶⠂⠀⢀⣀⣀⠈⠀⠀⢸⡟⢿⠀⢸⣿⣿⣿⡏⠁⣀
⠀⠉⠻⣿⡆⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⢨⣧⠀⠀⠀⠿⡄⠀⠻⠈⠛⠙⠓⠀⢀⣤⣼⣿⡏⠙⡇⠀⣠⣾⣿⣿⡄⢈⣥⣶⣿⣿⣿⣿
⢈⣡⣀⣼⣷⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠈⠀⠀⣠⣤⣤⣀⠀⢀⣄⠀⣶⣶⣶⡿⢻⣿⣿⣇⣴⡧⠎⢹⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣦⣤⣶⣶⣤⣤⣤⣿⣷⣦⣴⣿⣾⣯⣄⠙⢻⣿⣿⣿⡄⣹⣿⡉⠀⢾⣿⣿⣿⣛⠃⠀⢻⡏⣉⢙⡘⢻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⢂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠁⠊⠀⣱⣶⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠛⢻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⢀⣴⠟⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⣠⡾⠃⠀⠀⣰⡾⠋⠉⠉⠉⠻⣦⡀⣸⠀⣠⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣤⣿⣾⠷⢿⣶⡄⢀⢄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⡾⠋⠀⠀⠀⢀⣿⣇⠀⠀⠀⠀⠀⣨⣿⠋⣰⡇⠀⠀⠀⠀⣿⣍⣽⡞⢀⣾⣿⠟⠁⠀⠀⣿⣿⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡇⠀⠀⠀⠀⠀⣼⠏⠛⠷⠶⠶⠾⠛⠉⢸⡀⣿⠀⠀⠀⠀⠀⠀⠀⠸⣷⣸⣿⡏⠀⢀⣠⣾⠟⠁⠈
⠀⠀⠀⠀⠀⢀⣴⠏⠁⣿⣧⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣿⡄⠀⠀⠀⠀⠀⢀⣀⣿⣿⣿⡷⠾⠛⠋⠁
⠀⠀⠀⠀⢀⡞⠁⢈⠐⢸⣿⡄⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⣼⠀⢻⣷⠀⠀⠀⠀⠀⠀⣸⡏⠹⣿⣇⠀⠀⠀⠀⠀⠴⠦
⠀⠀⠀⠀⢸⡁⠀⠄⠠⠈⢻⣿⣄⡀⠀⠀⠈⢷⡀⣠⠆⠀⠀⢀⣴⠃⠀⠘⢿⣧⡀⠀⠀⠀⢠⣿⠁⠀⠻⣿⣆⡀⠀⠀⠀⠰⣤⡃
⠀⠀⠀⠀⠀⠀⠀⠁⠄⢠⠀⠉⠿⣿⣶⣶⣴⣾⠿⢷⣶⣶⡶⠟⠁⠀⠠⠀⠈⠻⣿⣦⣤⣴⡿⠁⠀⠈⠀⠙⠻⣿⣷⣶⣶⠾⠋⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠉⠁







⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⡀⢀⡀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣀⡘⣁⡀⢀⣾⣿⡟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠖⠾⠟⠀⠀⣠⣾⣿⣿⣿⠟⣿⠿⢿⣿⣿⣧⣌⣉⣩⠿⠿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡎⠉⣩⣤⣔⠀⠈⠀⢸⣿⣿⡟⠉⠀⠀⠀⠀⠈⠿⠿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣴⣿⣿⣿⡇⣿⣿⣩⣽⣦⠑⢠⣾⣿⣿⣷⠀⠀⠀⠀⠀⠦⠀⠀⣨⣿⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣮⣿⣿⠿⠿⣲⣄⠸⣿⣿⣿⡖⣀⡀⠀⢠⣤⣾⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢲⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣶⣩⡽⠛⣋⣵⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⣿⣿⣿⢻⣿⣿⠿⣿⣿⣿⣿⠋⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣿⣿⡿⠋⣿⣿⠋⠵⠚⠉⠁⠈⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠻⠿⠧⠈⠩⠀⠀⢀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣅⠀⡰⠀⠀⢠⣠⣾⣿⣄⣴⠾⢋⠁⣁⣀⠀⠤⠛⣁⢀⢰⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣧⣸⣤⣾⣿⣿⣿⢏⣁⠴⠊⠀⢹⡄⠡⠠⢾⣟⢢⣸⣿⠀⠀⢀⣀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢘⣭⣿⣿⡟⢿⣿⣿⣿⣿⣿⣿⡿⠉⠂⢀⣐⣢⡶⣾⡇⢸⣿⣨⣿⣿⠿⠛⠛⠛⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⣿⣿⣿⣿⠏⠁⢸⡏⠙⠛⠟⠛⠋⢀⣉⣠⣽⣿⣷⣦⣍⡤⠿⢿⣿⠟⠁⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⠛⠁⠀⠀⢤⣷⣤⡀⠀⠀⠀⠈⡻⢿⣿⣿⣿⣿⣿⡇⢠⣿⣬⠀⠄⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣿⣿⣭⣶⣾⣾⡇⣤⠀⠈⠋⠁⠀⠀⠀⠀⠁⠀⣿⣿⣿⣿⣿⠀⢾⣿⠇⣀⣴⢀⡀⠀⠁⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⡛⠿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⢿⣦⣉⣀⣿⣿⣿⣷⣤⣶⣶⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⡿⠃⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠒⠠⠘⠟⠀⠀⣸⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠠⠹⠿⠿⠿⠿⠒⠾⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⡛⠻⠿⢿⡿⠿⠷⠄⠜⠛⠛⣿⣿⣶⡞⠃⠀⠘⣿⠿⣿⣋⣉⠚⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢦⣿⣿⣦⡜⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⣄⠀⡀⢭⠔⠀⠀⠉⠁⠀⢹⣿⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡄⠀⠀⠀⠀⠀⢀⠻⣿⣿⣿⣿⣿⡀⠀⢀⠴⢤⠄⢀⣴⣋⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠿⢿⣿⣶⣄⣤⠀⢀⣀⣼⣿⣿⡿⠛⠁⣠⢄⠱⣦⣄⣴⡿⢟⣛⣑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣶⣆⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣾⣿⣾⡿⢟⣿⣿⡿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡀⠀⠙⠿⣿⣧⠉⠙⠛⠋⠺⠷⠿⠛⠻⣽⣴⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⣀⡀⠤






⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣤⣴⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠿⡿⠟⠉⡹⠷⣾⣿⣿⣿⣿⣿⣿⣧
⠀⠀⢰⣿⣿⣿⣿⣿⣿⠿⠛⣿⣿⡿⢹⣿⠛⢱⣿⣿⣿⡟⠁⠀⠀⠀⠀⢀⣾⣷⣎⠁⠘⣿⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣇⣀⠀⢀⣿⠋⡁⣸⠏⢠⣿⣿⣿⣿⣿⣿⣿⣦⢠⣶⣿⣿⣿⣿⣷⣀⣹⣿⣿⣿⠆
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣤⣸⣇⣨⣇⠋⡀⣾⣿⣿⣿⠋⠙⢿⣿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣏⢻⣿⣿⣇
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⠋⠐⢹⣿⣿⣿⣿⣀⣴⣿⣿⣿⣿⡿⠇⠛⢿⠧⠘⠻⣿⣮⣿⣿⡟
⠀⠀⣼⣿⣿⣿⡼⣿⣿⣷⣾⣿⣇⣶⡀⢸⣿⢿⡋⠛⠃⢿⣿⣿⣿⣿⣿⠄⠀⠈⠀⠀⠀⠀⢿⣽⣿⣧
⠀⠀⣿⣿⣿⣿⠀⣿⣿⣿⣽⣿⣿⣿⣿⣆⠛⠀⠀⠀⠀⢸⡟⢻⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣿
⠀⠀⢹⣿⢿⠋⠀⢿⣿⠟⣿⣿⣿⣿⣿⡟⢠⡀⠀⠀⠀⠸⠇⣀⡽⢏⣇⠀⠀⠀⠀⠀⠀⠀⢰⡛⢿⡏
⠀⠀⢸⡇⠀⠀⠀⠈⠙⣷⣯⣍⣽⣦⢓⣙⠉⠰⠔⠒⠂⠲⣒⣬⡶⣿⡇⠀⠀⠀⠀⠀⠀⢀⠇⠙⣾⠁
⠀⠀⠀⠃⠀⠀⠀⠀⠘⠓⢹⡌⡟⢻⠹⣿⠛⣿⠿⡿⢶⡾⠋⠋⠀⠂⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠁⠘⠃⠀⠀⠀⠀⠀⠀⠀⠰⠢⠤⠤

⠀⠀⢀⠤⡂⠀⠉⠙⡌⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠐⠉⠙⡆
⢀⠔⠁⠀⠈⠓⣄⠀⠸⠀⠀⡜⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠁⠀⠀⠀⠈⠙⢗⠢⢌⣒⠒⠁⠀⣀⣀
⡄⠀⠀⠀⠀⠀⠈⣇⠀⡇⡼⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢠⣚⡉⣉⣥⣴⢾
⡧⢄⣀⠀⠀⠀⠀⢸⠀⣧⣃⡠⠞⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⡴⣩⠖⠊⠉
⢱⡀⠀⠈⠉⠐⠒⡞⢺⠛⡅⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡞⡴⠁
⠀⠑⢤⣀⠀⣠⠞⠀⡞⢀⡹⠖⠁⠀⠀⠀⠀⣠⠔⠐⠒⢔⠒⠦⢤⡀⠀⠘⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⠟
⠀⠀⠀⠀⠉⠉⠒⠋⠉⠉⠀⠀⠀⠀⠀⢠⠎⢀⡉⢦⡀⠈⢂⠀⢡⠈⢣⡀⠘⠢⢝⡒⠶⠤⠤⠴⣒⡪⠵⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡔⠁⢀⡠⢷⠀⢸⠀⠘⠀⢸⢳⡀⠀⠀⠈⠉⠉⠉⠉⠀⠀⢀⣀⠤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⡠⠃⠀⣀⣄⢸⠀⢠⣀⣸⠼⡇⠀⠀⠀⠀⠀⠀⠀⡠⢚⣅⡢⠾⣿⠷⢦⡑⣄
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠸⡇⠀⠁⢀⠾⢄⣀⠈⠉⠉⢀⣀⢴⠇⠀⠀⠀⠀⠀⢠⢊⣴⢷⡏⢨⠞⢄⡜⠃⢼⠸⡆
⠀⠀⠀⣠⠔⠛⢧⡔⠋⠀⠈⢟⠦⡀⠀⠱⣄⠀⢸⠤⣀⠈⠉⠉⢉⣁⣠⠞⠀⠀⠀⠀⠀⠠⢡⣳⠗⢅⡜⠑⠦⣎⠈⡰⢺⠀⡇
⠀⠀⡌⠀⠀⠀⢠⡀⠀⠀⠀⡘⠲⣝⣆⠀⠈⠑⠮⢷⣤⣬⣭⡭⠽⠛⠁⠀⠀⠀⠀⠀⢠⢣⡿⠋⡦⡂⢈⠖⢄⡠⠋⡲⡞⢰⡇
⠀⡜⣸⠦⠤⡖⠁⠙⠦⡠⠴⣄⠀⣸⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣼⢉⠶⣀⡼⠓⣤⡊⢩⠾⡕⡡⢣⠁
⠀⣏⠀⠀⠀⠱⣄⣀⡜⠀⠀⢠⠋⠈⢦⡇⠀⠀⠀⠀⠀⢀⠤⠀⠲⠤⡀⠀⠀⠀⠀⠀⡇⡧⠉⣦⡎⠑⠴⣁⡜⡳⢊⠔⡱⠃
⠀⠘⣄⢀⣀⠊⠀⠀⠑⢢⠖⠣⣀⠀⡼⠁⠀⠀⠀⠀⢠⠊⠐⠢⡀⠀⢈⣆⠀⠀⠀⢐⢠⡘⠶⣁⣨⡳⠤⢛⡩⢔⡡⠊
⠀⠀⠈⠳⢄⣇⠀⢀⠠⠯⣄⣰⠧⠋⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠆⠊⢸⠀⠀⠀⠌⣬⠶⢋⡠⠴⡒⠉⠁⠂⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣠⠔⠋⢉⡷⠃⠀⣀⡌⢈⡵⢊⠕⠊⠁⠀⡠⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠒⠒⠒⠲⢤⠤⣀⡀⠀⠀⠈⠉⠉⠁⠀⢀⠾⠉⢍⢫⠈⠀⠀⠀⠀⢸⡀⣀⣸
⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⣀⣠⢤⠴⠤⢦⠈⡍⡗⠀⠀⠀⠀⠀⡰⡉⢦⢱⢸⠎⠀⠀⠀⠀⢀⣼⣖⣗⣮⣄
⠀⠀⠀⠀⢀⠜⢄⠀⡠⠴⠎⠙⠉⠀⠀⠀⠀⠀⠇⢸⠃⠀⠀⠀⠀⡾⠤⡙⡼⡤⠃⠀⠀⠀⠀⠀⣾⢏⡏⢿⢙⢿⣄
⠀⠀⠀⠀⠊⠡⡀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠑⢄⣈⡷⠁⠀⠀⠀⠀⢀⣎⡟⣹⠓⢼⠉⣍⣷⢆
⠀⠀⠀⠀⠀⠀⢱⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢧⠾⢁⣼⠑⣾⠁⣤⢹⠛⠧⡀
⠀⠀⠀⠈⠢⢄⣼⣠⠁⠀⠀⠀⠀⠀⣀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠘⣅⠘⡹⠃⠫⣀⣨

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠛⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠻⡿⠰⢀⠐⠸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⣤⣤⣀⣾⠋⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠙⠻⢷⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣆⣀⣀⣀⣀⣀⣠⣾⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⣦⢸⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣰⣾⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣎⠻⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⢡⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⢀⣴⠶⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠀⠀⠀⠉⠳⡼⣟⢿⠈⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡚⠁⣠⣄⣀⡤⠬⡟⠳⣄⣹⡈⠩⣿⠗⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠠⠆⠀⠉⣤⡀⠘⠁⣹⠀⠱⣄⡀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢶⣶⡄⠈⠛⣇⠐⠖⠀⢀⣠⢄⠀⢰⠁⢀⡠⠚⠃⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠻⠏⡇⠀⠀⠘⣆⠀⠘⢿⣀⡼⢠⡾⠚⡏⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠶⠿⢧⠀⣀⡴⢾⢓⡶⣶⣲⢶⢋⠿⣄⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⡋⠁⣀⡤⣼⣿⠿⢳⡿⢯⡠⠜⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⢀⣀⣈⡧⣄⣀⣠⣴⠟⣠⠴⣇⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠉⠙⠛⠛⠻⡖⠚⠁⠀⢨⠿⠟⠋⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⣰⠋⠂⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣔⠦⢄⣀⠀⠀⠈⠳⢶⠇⠉⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⣼⠟⠒⣶⠦⣄⠙⠲⠤⣄⣀⣀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⣠⠞⠁⠀⠈⢢⡀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠾⠋⠀⠀⠀⠀⡴⠟⢦⡀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡎⢳⠀⠀⠈⠁⠀⠀⠀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠘⣆⣀⣤⠤⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣤⡽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢺⣷⡄⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢿⠋⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡀⡌⢀⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠄⠀⠀⡠⠄⢯⣷⠈⡴⢸⣇⢀⠀⡀⠀⣤⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢣⠈⠋⢠⡇⠸⠟⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠐⠂⠐⠂⠸⡄⡀⠂⠘⣿⡆⢠⢏⡄⠄⠂⠐⠂⠀⠀⠀⠘⠁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠠⠀⡀⠀⠀⠀⠀⠙⢞⣧⡀⣽⣿⢨⣿⠀⠀⠀⠀⠀⠀⠔⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⢷⠸⢃⡾⢣⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠒⠀⠐⠂⠚⠁⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠉⠉⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠈⠉⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠁⠀⣀⣀⣀⣀⣈⠑⢄⠀⠀⠆⠰⠀⠀⡠⠊⣁⣀⣀⣀⣀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⢻⡈⠉⠉⠉⠙⢦⠃⠀⢀⠀⠀⠜⡴⠋⠉⠉⠉⢉⡟⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠙⢦⣀⠀⠀⣀⡵⠀⠀⠀⠀⢎⣀⠀⠀⣀⡴⠋⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⡀⠒⠰⠶⠖⠒⠂⠀⠂⠀⠀⠐⠀⠐⠒⠲⠶⠆⠒⢀⡄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠒⠉


⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣻⣛⣻⣿⣛⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠰⠀⠀⠀⣠⣤⣀⠀⢀⣤⣄⡀⠀⠀⢀⣿⡟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠇⠀⣀⠀⠀⢰⠀⢀⣾⣿⠟⢹⡇⣿⠏⢠⠟⠀⠀⣼⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⢀⣿⡇⢀⣞⣠⣼⣿⠏⠀⣼⠁⠻⢦⣤⡾⠀⣴⣿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠉⠛⠷⠞⠉⠀⠈⠻⠤⠞⠁⠀⠀⠀⠻⠇⠀⠸⠏⠘⢿⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⢰⠀⠀⠀⢀⡀⠀⠀⠀⡴⠤⡀⠀⠀⢠⡦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⡸⣇⠀⠀⠀⡇⢀⡽⠀⠀⢸⡀⠀⠙⣦⠀⢠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡷⠶⠆⢸⠀⠀⢠⣧⣿⡀⠀⠀⡿⣏⠁⠀⠀⢸⡇⠀⠀⣸⠃⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⣼⠀⠘⣇⠀⠀⣧⠈⠳⡄⠀⢸⣇⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⣾⣿⠇⢠⣶⣶⡄⠀⢀⣴⣤⡀⠀⢀⣀⣠⡀⠀⢀⠠⣤⣀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⢹⣿⡿⠀⢿⣿⠐⣡⡀⣿⡿⠫⠃⣼⡿⠋⣡⡄⢠⠎⣰⡿⢡⡿⢋⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⣠⢾⣿⠃⣀⠜⠛⣾⡿⢀⣿⡋⣀⠼⣿⣃⣴⣿⣡⠏⠠⣿⠃⣾⠃⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠉⠁⠀⠀⠙⠛⠁⠀⠉⠁⠀⠈⠉⠀⠉⠁⠀⠀⠁⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢈⣛⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡇⠀⢉⠀⠸⠙⡆⠀⠀⠀⠀⠈⠀⢸⠀⠀⠀⢀⡴⢛⠋⠉⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣤⣾⡿⣅⠀⠀⠀⠀⢰⠀⢸⠀⠀⢠⣿⠁⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢸⠀⠀⡇⠈⢧⠀⠀⠀⢸⠀⢸⠀⠀⢸⡇⠀⣿⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⣇⣀⡞⠀⠀⠀⢸⡀⢸⠀⠀⠸⣿⡀⡇⠀⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠞⠛⠛⠉⠉⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠈⠙⠛⠛⠉⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⠀⣠⣤⣤⣤⡸⣷⡀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⡟⠁⠀⢹⣷⢹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣰⡏⢻⣆⠀⢀⣾⠇⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠙⠛⠛⠁⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⢁⣴⠶⢶⣦⠀⠀⠀⠀⠀⠀⢹⠉⣭⠀⠀⣶⠄⣴⠶⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡿⠁⠀⠀⣿⠆⠀⠀⠀⠀⠀⢸⡄⣿⣤⣶⣿⡀⣿⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠈⣷⣄⣀⣼⠟⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⣿⠀⣿⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠈⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⣀⣤⣴⣦⡄⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠘⣿⠀⢠⣄⠀⣼⡇⣠⡾⠛⠻⣦⠀⣟⢀⣀⣼⡟⢰⡇⠀⠀⠀⣿⠀⠀⠹⣿⡄⣾
⠀⠀⠀⠀⠀⠀⢻⣇⣿⣿⣷⣿⢡⡟⠀⠀⠀⣿⠃⣿⣿⣟⠉⠀⢸⣿⠀⠀⠀⣿⠀⠀⣠⣿⠇⣿
⠀⠀⠀⠀⠀⠀⠸⣿⡟⠘⣿⡿⠈⢿⣤⣤⣾⠏⠀⣿⠀⠻⣷⠄⢸⣿⣤⣤⡀⣿⣴⡾⠟⠃⠀⡛



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀
⠀⠀⠀⠀⣠⢲⣶⡄⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡤⣶⢦⣄⣼⠟⣴⢲⣦⡄⠀⠀⠀⠀⠀⠀⠀⣀⠀⡞⣿⡄
⠀⠀⠀⠀⢸⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⢠⣯⣴⡏⠀⠹⡆⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⣿⠃
⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⢠⣮⡆⠀⢀⡟⣾⣿⣿⡇⠀⠀⣿⠀⠈⣿⣿⣿⠀⠀⢰⣽⡆⠀⢸⡇⠀⣿⣿
⠀⠀⠀⠀⠀⠸⣿⣿⡆⠀⣼⣿⣇⠀⣸⠁⢿⣿⣿⡇⠀⠀⡿⠀⠀⢹⣿⣿⡀⠀⣾⣿⡇⠀⡾⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠹⣿⣿⡴⠉⢿⣿⣤⠏⠀⠘⢿⣿⣧⣀⡼⠃⠀⠀⠀⢻⣿⣷⡴⠘⣿⣷⣴⠃⠀⠀⣙⡉
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠉⠁⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠉⠁⠀⠀⠀⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠶⢒⡒⣛⣛⢋⠉⣉⠙⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠉⣶⣶⣴⣦⢸⣿⠃⢹⡇⠘⢾⡟⢠⡟⠉⠉⠉⢛⣲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠋⠁⢸⡄⣟⠁⠛⠹⠆⠉⠓⢀⣁⣑⣛⣁⣸⣇⣀⣀⣀⣙⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠠⡄⢀⠀⠛⣻⠂⢀⣸⣧⣤⠤⠶⠶⠚⠛⠉⠉⠉⠉⠉⠉⠉⡁⠀⠀⠀⠀⠉⠉⢁⣀⣴⠊⠀⢀⠴
⠀⠀⠀⠀⠀⠀⢰⢸⡇⢴⠀⢰⣧⠖⠋⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⢺⡇⠀⠀⠀⣿⡷⢲⣒⡶⣶⣻⠛⢆⣿⠀⣀⢸⣯
⠀⠀⠀⠀⢀⣀⣸⣸⣇⣿⠀⠈⠁⠀⠀⡶⣶⠲⡖⢲⢺⣿⣿⡇⠸⣮⢿⠀⠀⠀⠛⢀⡘⠟⠀⠈⠛⠀⠀⠁⠀⣿⢸⣿⢀⣶⣆
⠀⢀⡞⠩⠁⣀⡈⣉⣁⠉⠍⠙⢦⡀⠀⠯⡏⠐⡷⢾⠀⠿⠛⠇⠀⠁⣀⠀⣀⠀⢀⣼⡅⠀⢾⡆⠀⠰⣿⡆⠀⣿⡜⠋⠀⠈⠀⣀⡀
⠀⠀⡇⣤⣤⣴⢶⢠⡶⣄⣶⣦⢈⡇⠀⠀⠀⢀⠀⣤⠀⠀⠀⠀⢷⢴⠻⠔⣇⠀⣼⠽⡇⠀⣟⢳⡀⢀⣯⡿⣄⠙⢁⢠⣿⣆⡆⠘⠁
⠀⠀⢻⣇⠻⠿⢾⣼⠧⠿⠃⣿⣼⠃⠀⠀⢀⣸⣿⣿⣽⣃⠀⠀⠘⠄⠑⣒⠋⠘⠳⠛⠃⢸⣯⢈⣧⠸⠷⠿⠛⠀⠈⢳⣻⠯⠂
⠀⢠⠼⢯⣔⣆⣈⣩⣄⣀⣺⠴⠛⠑⣆⢏⣉⣩⣿⣧⠤⢼⡇⠈⣏⣧⣼⣹⠀⠀⢠⢒⠤⢠⡬⠉⡁⠀⣀⣀⠀⢀⡤⠠⡁⠀⢴⣤⠄
⠀⢸⠈⣀⠀⣠⡀⣰⣦⠀⣠⡀⢠⣄⢹⠈⡇⠀⣿⡇⠀⣸⠀⢺⡿⣿⣿⠿⡿⠀⠜⠬⠗⠠⠽⠖⠁⢸⡁⠈⠳⠏⠀⢀⡇⣀⠈⠁
⠀⠘⡟⢹⣾⠇⣿⣿⢸⣸⡏⢧⣾⠘⡾⠃⣇⠀⣿⣷⣀⡏⠀⠘⣷⠀⢐⢿⡇⠰⠀⠀⣠⡴⠲⣄⠀⠘⠧⣄⠀⠀⢀⡼⠁⣿⣿⠟
⠀⠀⣧⣠⢉⠠⡙⠇⡀⣙⣂⢬⡗⢔⡿⠀⢈⡅⢠⡀⢀⣀⡀⠀⠻⠼⠿⠾⠃⠀⢀⣠⡟⠀⠀⢸⣇⡤⢄⠀⠉⢷⡟⠁⠀⠈⣁⡀
⠀⠀⠛⠬⣏⣙⣙⣋⣹⡥⠽⠖⠚⠉⠀⠀⠘⢦⣾⣷⣯⡴⠃⢀⣤⢀⣀⠀⢀⣰⣋⠸⡇⠀⠀⢸⡏⠀⢸⡇⠀⠸⣅⠀⢠⠞⠁⠀⠉
⣀⠞⢦⡄⣀⠀⣀⣤⡤⡄⠀⡀⠀⢿⡷⠀⡏⠉⣿⠀⣿⠁⢹⣾⣿⣿⠟⣰⠏⠀⠉⣷⢳⣀⣠⣾⡞⠋⠉⢳⡄⠀⢸⡆⡏
⢨⡶⠼⠆⢹⡽⠛⠛⠉⠃⣸⣽⢠⣏⣷⠀⢻⠀⢿⢀⡯⠀⣼⢸⣿⢹⠇⣿⠀⠀⠀⣿⡏⠉⣷⣼⠁⠀⠀⢸⠇⢀⡾⠁⢹⣄⣀⣠⠼
⢠⣄⡄⠀⠀⠀⠴⣿⡆⠀⠧⠿⢀⠌⡄⠀⠘⠲⠺⠞⠓⠒⠋⠘⠛⠚⠀⠘⠦⣤⠞⣿⠀⠀⣿⡿⢄⣀⣠⠟⠀⠀⠀⠀⡾⠉⢠⣤⣤
⠚⢶⠛⠠⠴⣱⠴⢋⡀⣰⣆⢻⡿⠀⡗⣠⡀⠀⠀⠀⣀⢤⡎⣳⣀⠀⠀⠀⠀⢩⠀⡻⣄⣠⠏⡀⠘⢋⡴⠊⠉⠑⢦⠀⢇⠀⠮⣿⠿
⠴⠆⢀⣀⡉⠋⠀⠈⠙⠾⠋⠁⠀⢀⣔⣛⣓⣄⠀⢴⡙⠦⠟⠗⣚⣳⠀⠤⠀⠀⠄⢃⠘⠉⠠⠁⠌⢸⠀⠀⠀⠀⠈⡇⠈⡆⢀⣁
⠀⠀⣿⠁⡭⠉⠉⣉⣷⡆⠀⠀⢠⡗⠢⠗⡒⢚⡇⢸⣸⣿⢻⢫⣿⠇⠀⡿⡄⠀⠀⠱⣄⢀⢀⠊⠀⠸⣄⠀⠀⣀⡾⠁⣠⠇⠺⠿⠂
⠀⠀⣿⣀⣠⣴⠞⠛⣩⡿⡵⠀⢪⣤⣑⣭⣤⡭⣼⠀⠛⠛⠛⠛⠋⡤⠀⠛⠳⠤⡀⠀⠸⡶⠁⠀⠀⣠⠟⠛⠉⠁⣤⡀⠁⣤⣤⡄
⠀⠀⠈⠙⣯⣄⡴⢞⡥⠚⣁⢀⠈⢿⣿⣿⣶⣧⠏⢀⢀⣴⡄⠀⢺⡁⠀⠀⠀⠀⣈⠇⢰⣧⠀⠀⠀⡇⠀⣴⣶⠀⠉⢁⡄⠘⠋
⠀⠀⠀⠸⣯⠵⠚⠉⠀⠠⣻⣟⠄⠀⠀⠀⠀⠀⠀⢹⠾⡿⣿⠃⠀⠹⡟⡟⣿⣿⣿⠀⠸⠁⠀⠀⠀⢸⠀⠈⠈⢀⣽⡁⡷⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣁⣀⣀⣀⣧⣿⣟⣛⣛⣀⣀⣀⣀⣀⣴⣃⣀⣀⣀⣈⣉⣉⣃⣀⣀⣀⣀
⣿⣿⠛⡿⢛⠻⢻⡿⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡀⢀⠀⢾⡀⣿⢦⡘⡄⠚⠀⠉⠀⠀⠘⢤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠉⠠⠴⠃⣇⢼⠃⣤⢺⢀⡖⠂⢰⠃⠀⠀⡀
⣳⢰⠰⡌⠏⠓⠀⠁⠀⣀⢀⡤⢲⠏⠀⠀⠀⠀⠀⠃⢀⡀⠀⠀⠀⠀⠲⠤⠄⡀⠀⠀⠋⠀⠀⢇⠿⠀⠠⠃⠀⠀⠸⠘⡰⠀⠀⠀⢠
⠌⠃⠉⠈⠀⠀⣠⢔⡉⢛⣡⠴⠋⠀⠀⠀⠀⠀⠀⠖⡀⢀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠉⠀⠠⠀⢀⣹
⠀⠀⠀⠀⢠⠾⠋⠹⠓⠉⠀⠀⠀⠀⠀⠀⣀⢠⠀⠀⠠⠄⠃⠀⠀⠙⠋⣁⣄⡀⠀⠀⠀⢦⠀⣄⠀⠀⠀⠀⡠⠠⣄⠀⠀⠐⠼⠁⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⠀⣀⠀⣦⣰⣐⡤⠸⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⣠⠎⠀⠀⠀⠈⢟⣄⠣⡀⠀⠘⢄⡹⢪⠀⠀⠀⠀⡀
⠆⠀⠀⠰⢧⡀⣦⣸⢧⡿⡎⠟⠀⠃⠙⠉⠁⠈⠀⠀⠀⠀⠀⡠⢦⠴⠁⡴⠁⠀⠀⡀⠀⠀⠈⠀⠶⠁⠀⠀⠀⠒⠁⠀⠀⠀⢀⣹⠶
⠃⠀⠀⢾⠉⠇⠇⠙⠈⠁⠁⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⠈⣳⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⣦⠀⠀⠀⠀⠈⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠁⠀⠀⠘⡷⢶⡃⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢀⡠⣄⣀⠀⡤⣄⣦⡀⣿⠀⢿
⠀⠀⠀⣂⠄⠀⠀⠀⠀⠀⡏⢣⡴⡀⠀⠀⠀⠉⢻⠋⠉⠀⠀⢀⠀⢀⠀⢀⠀⠀⣶⢹⣤⠎⢸⣼⣁⡜⢻⠙⣾⠀⢈⡀⠀⢀⣰⢆
⠀⠀⠀⠐⠘⠀⠀⠀⠀⠀⠙⢆⡱⢵⡀⠀⠀⠀⠀⠀⢀⠀⡄⢸⡆⣼⣧⠸⡷⣼⠋⡇⢇⠀⠈⠃⠉⠁⠈⠀⠈⠀⠈⠀⠀⠙⢭⣼
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠳⠀⠀⠀⠀⢰⠋⡀⣷⠉⡇⠏⠙⡆⠇⠈⠀⠙⠈⠀⠀⠀⠀⠀⠀⠀⣼⠂⢄⣠
⡠⣄⠀⡄⠀⢧⡠⠀⠀⡀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡴⠃⠈⠀⠁⠀⠀⠀⠀⢀⣀⠄⠀⠀⠀⡄⣀⢀⠀⢀⠀⠈⠰⠇⢡⠀⠀⡀
⡇⣧⠄⠷⠊⣈⠁⡔⣯⠀⠘⢇⠀⠀⠀⠀⢀⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⡞⠂⠀⠀⠀⠷⣁⢎⢿⢾⣲⠄⠀⠀⠀⠀⠀⢣⣸
⠁⣀⡀⣰⠲⣼⡳⣥⠱⠊⠀⠙⠀⠀⠀⢀⡤⠆⢧⠀⠀⠀⠀⢀⣄⠀⠀⣿⠀⠀⠀⠀⣰⣇⡔⢀⢶⣠⠈⡋⢁⢠⢀⠀⢀⠀⠀⠀⠙
⣇⢀⡟⠘⠚⠁⠁⠈⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⠀⠀⠀⠀⠘⡾⣄⢰⠙⡆⠀⠀⠀⠋⠀⠋⠀⠉⠟⡏⢰⢻⠐⣣⠄⠞
⠸⠏⠀⠀⠀⠀⠀⠀⠀⢀⣠⣰⢺⣁⠀⠀⠀⢀⠀⠀⠩⢷⠤⢰⠇⣀⣭⣶⣧⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠈⠐
⠀⠀⢠⣀⡀⠀⠀⠀⠀⠹⠌⠙⢉⠡⠄⢴⠂⡟⠀⠀⠀⠀⠳⢴⢛⡩⠟⠋⠁⠀⠀⠀⠀⠀⠀⠠⣯⠧⠀⠀⠀⠀⠀⠀⡔⠋⡹⢆
⠀⠀⠊⡽⡄⠀⠀⣤⡺⠀⣞⠅⠈⣑⡆⠘⠀⠃⠀⠀⢠⣄⠀⠈⠁⠀⠀⠀⠀⢰⣩⠒⠄⠀⠀⠀⠀⠀⠀⡄⢀⡄⠀⠀⠣⢹⠤
⠀⠀⠀⠀⠀⠀⠀⢸⣉⡟⠱⠒⠈⠁⠀⠀⠘⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠪⠁⠂⠀⠀⠀⠀⠀⢸⡵⢋⠎⣠⠄⣀⣀⡀
⡄⡄⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡂⢠⠔⡤⢀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠊⠺⠖⢀⡞⡥⠒⡄⡶
⠁⢹⠔⠃⣴⠀⠀⠀⠀⠀⠀⠔⡕⠀⠀⠀⢤⣤⡶⠀⠀⠀⠀⠤⠤⠄⢁⡘⠂⠘⠠⠁⡞⢱⡀⠠⠄⢠⠀⠀⠀⠀⠀⠈⠈⠓⠊⡜⢿
⠰⠃⠀⡼⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢧⡿⠶⠀⠀⠀⠀⠀⠘⠋⠐⠒⠂⠀⠀⠀⠀⠁⠀⠠⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈
⠀⠀⠴⠀⠀⣏⣃⠆⠀⢠⡄⠀⠀⢀⡀⠀⠀⠀⠃⠀⠀⢀⣴⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠺⢍⡉⠓⢄⡀⠀⠀⣠
⠃⠀⠀⠀⠀⠈⠀⢀⡀⠀⢳⠀⠀⠈⠋⠀⠀⠀⠀⠀⡴⢯⠗⢸⣰⢂⢔⡥⠤⢀⡤⠀⠀⠀⠀⠀⠑⠐⠀⠀⠀⠰⠮⢥⣻⣄⡀
⣀⣀⣀⣀⣀⣄⣐⣃⣓⣓⣀⣡⣀⣀⣀⣤⣄⣀⣀⣊⣀⣜⣀⣚⣼⣃⣞⣉⣁⣹⣀⣔⣹⣆⣇⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣁⣀
⣿⣿⠋⣋⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⡄⣿⡀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣬⡻⠟⠋⠁⡱⠒⡑⠊⣁⣠⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⡠⠚⣡⣾⣿⣿⡿⢃⠀⠀⠀⠀⠀⠀⠀⢠⡤⣄⠰⢯⣟⡣⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠗⣠⡅⣰⠟⠋⠀⢀⣤⠀⠈⣹⠶⡀⠀⠀⠀⠀⢈⡎⠱⡄⠉⡿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢡⡴⠀⠀⠋⢀⠀⠀⢄⢰⠜⢆⠀⠀⠀⢀⣷⢠⡤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡘⠇⠀⠀⠀⠙⠁⠀⣤⣉⠆⠈⣇⠀⢀⣾⣷⣙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡀⠀⡄⡰⢊⡁⠀⣀⡠⠤⠀⣿⣠⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⡄⠁⠁⠸⣶⣶⣶⣾⠏⢀⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣦⡐⢄⠈⠛⠛⢉⢄⣾⣿⣿⣿⣿⠃⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣦⣥⡒⢂⣵⣿⣿⣿⣿⣿⢵⣾⢫⣯⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⣿⣿⣿⣿⡇⠈⠑⠼⡏⠙⠉⠙⢟⠛⠛⠻⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠁⢃⡀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠛⠛⠿⠿⣿⣿⣿⣶⠶⢤⣤⣀⠀⠀⠀⠒⠒⠰⠀⠓⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢁⠇⠀⠈⠸⣩⢻⢦⡀⠀⣠⡼⢤⣀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⣼⡀⢀⢃⢇⠀⠄⢋⢞⠃⢀⠀⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢻⢩⠇⡸⠌⠈⡄⣴⠟⡌⣄⣴⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⡏⠈⠊⡤⢇⣄⣠⠟⢁⣤⡾⡿⡱⡘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⢰⢰⠀⢡⣠⣟⡥⢶⣏⠁⠁⠁⠃⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣯⣤⡆⠆⢾⣠⡾⠛⠁⠀⠀⠙⣶⡰⡆⠀⡀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣶⡞⠁⠀⠀⠀⠀⠀⠀⠈⠻⣦⣴⣥⣼⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠛⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠙⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⣠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄
⠀⠀⠀⡤⡄⢰⠁⡼⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀⡜⢠⠃⢔⡉⠑⠢⢄⣀⡎⣹⠀⠀⢀⠤⡀⢸⢁⡜
⠀⠀⠀⠣⢤⡷⠊⡀⢀⠀⣤⠀⣠⡀⠀⠈⠢⢤⠗⢁⢤⠀⡄⢠⢀⠤⡌⣯⢤⠀⠀⠈⠢⢤⠷⢊⣤⣀⡀⢠⡄⢀⣄
⠀⢀⠤⠤⣸⠀⠀⣇⡰⢇⡸⠙⣏⠀⠀⡠⠤⣜⠀⢸⣸⣀⣇⣸⣸⣀⡇⡇⢜⠀⢀⠤⢄⣜⠀⢸⣈⠏⠹⣠⠏⢻⡁
⠀⢪⣀⡠⠋⠙⠢⢄⡀⠀⠰⢑⠆⠀⠘⠤⠔⠉⠑⠦⡀⠠⢢⢀⠤⠀⡇⠀⠈⠀⢇⣀⡰⠃⠙⠢⢄⡀⠀⠀⠎⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣒⣭⣷⣶⣿⣛⣟⡻⣿⣷⣾⣭⣖⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⣾⣿⣿⣿⣿⢿⣿⣿⣧⡘⢿⣿⡏⠹⣷⣾⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣇⠻⠿⠿⣿⣯⣴⣿⣿⣿⣿⣿⣶⣮⣍⣀⢛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣿⣿⣿⡿⠋⠉⠙⠻⣿⣿⣿⣿⣿⣿⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⠿⠿⠧⠀⠀⠀⠀⠤⠬⠭⡙⢿⣿⣇⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⡿⢁⣤⣤⡀⢶⡀⠀⠀⢀⣤⣀⡀⠀⢿⣿⣿⣷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢁⣹⣿⣿⡇⠘⠋⠀⠀⠀⠁⠀⠀⠉⠀⠈⠉⠀⢸⣿⣿⣄⢹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣿⣿⣿⢿⠀⠀⠀⠀⠀⢾⣇⠰⠄⢀⠀⠀⠀⠀⣾⣿⣿⣿⢾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣾⡇⠀⠀⢀⣤⠤⠀⠶⠦⣌⢳⠀⠀⢰⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠈⠻⢿⠿⣿⣿⣷⠀⠀⠘⣿⣿⣿⣿⣿⡾⠋⠀⠀⣸⣿⣿⠿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⣴⣞⠀⠀⣠⣿⣿⣿⣆⠀⠀⠈⣉⣉⡋⠍⠀⠀⠀⢠⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠉⠁⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣿⣿⣿⣿⣯⣽⣿⣿⣿⣿⣿⣿⣦⣤⣤⣴⠾⠟⠈⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣷⣤⣴⣤⣤⣤⣿⣿⣿⡟⠻⣿⠋⠉⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣏⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⣿⡿⣿⣿⣿⣿⣿⣿⣿⠃⠃⠀⠛⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⢈⢷⣹⣿⣿⡏⠘⠻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⠙⢿⣿⣿⣿⠟⠛⠁⠑⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⢀⣦⡸⡞⣇⢻⣿⣦⡀⠑⠺⢻⣆⠀⠀⠀⠀⠀⠀⣴⣿⠟⠀⠀⢸⣿⢿⠟⠀⠀⣀⡄⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣾⣿⣿⣿⣹⡜⣿⣿⣿⣷⣦⣄⡙⠳⡄⠀⠀⢀⣼⠟⠁⢀⣠⣶⣿⡿⠀⠀⠀⣼⣿⣵⠏⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣻⣿⣧⢻⡏⢻⣿⣿⢿⣿⣿⣷⣌⠢⣠⣞⣡⣶⣾⣿⠛⡉⡁⠀⠀⣇⣼⣿⣿⡏⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⠃⠈⠋⠛⠁⠂⢻⠛⣿⣷⣽⣏⠋⠉⠁⠀⠈⠀⡐⠀⣆⣿⣿⣿⡾⠀⣤⣤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠈⠀⠀⠐⠀⠈⠃⠈⠃⠘⠛⠀⠀⠀⠀⠀⠘⠁⠀⠛⠛⠛⠛⠁⠘⠙⠋⠐⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠴⠚⡝⠉⠙⠍⠓⢂⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡀⠁⠀⡘⠀⠀⠀⠈⠀⠀⠑⢄⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⢃⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠂⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⣀⣀⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠿⠛⠛⡋⢉⣉⣀⣀⣉⣉⣉⡛⠛⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣛⠭⠆⠒⠂⠉⠅⠀⠀⠀⠀⠀⡇⠀⠀⠉⡙⠒⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠠⠀⠀⠀⢠⠀⠀⠀⠀⠀⠃⠀⠀⠠⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠱⡀⠀⠀⠄⠀⠀⠀⢰⠀⠀⠠⠃⢠⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢗⢄⠑⠄⠀⠀⠀⠀⠀⠄⠀⡠⢂⠔⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠢⠢⣄⣢⡀⣀⣠⠴⠐⠁⠠⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠈⠁⠀⠀⠰⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠘⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠓⠾⠀⠀⠀⠀⠇⢀⠆
⠀⠀⠀⠀⠀⠰⠀⢄⠀⣀⢀⣀⣀⣀⣀⡀⢀⠄⠰⠘⡤⠇⠀⠀⠀⠀⠘⢾⠀⠀⠀⠒
⠀⠀⠀⠀⢀⠃⠀⡀⠀⠀⠀⠁⠀⠁⠀⠀⠐⡀⠀⠆⢠⡄⠀⡄⢠⡔⢰⡖⠀⠀⣰⣆
⠀⠀⠀⢀⠊⠀⡰⠀⠀⠄⠀⠀⠀⡄⠀⠄⠀⠡⠀⠀⢴⠃⠘⠃⠈⠃⠘⡇⠀⢔⣿⣿⡢
⠀⡠⠔⠁⢀⠔⠀⠀⠜⠀⢀⠀⠀⢀⠀⠘⡀⠀⠑⢀⠀⠑⠆⡀⠀⠀⠀⠡⢂⠊⠃⠁⠁⠐
⠛⠛⠛⠛⠟⠛⠛⠻⠛⠛⠛⠛⠛⢛⠛⠛⠻⠛⠛⠛⠟⠛⡛⠛⠀⢀⠔⢠⠂⠌⠀⠠⢠⠀⡈⠢⡀
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⡠⠀⠁⡠⠁⠀⠀⡀⠀⠀⠂⠈⢄⠈⠂⢄
⠀⠀⠀⠀⢠⠀⠀⠀⣯⠝⠛⢻⣽⠛⠋⢍⡇⠀⠀⠀⠀⢰⣥⣤⣤⣮⣤⣴⣥⣤⣤⣤⣤⣬⣦⣤⣵⣤⣤⣥⣦
⠀⠀⠈⠀⠈⠀⠀⠀⣿⠀⠀⢸⣿⡀⠀⢸⡇⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⢠⠀⢘⠀⠀⡀⠀⡆⠀⢀⠁
⠀⠀⠀⡇⠀⡆⠀⠀⣿⠀⣆⣿⣿⣇⡇⢸⡇⠀⠀⠇⠀⠃⠀⠘⠀⠆⠀⢸⡟⠋⢻⣟⠉⢻⡇⠀⠘⠀⠃
⠀⠀⠀⠀⠀⠃⠀⠀⣿⢀⣿⣿⣿⣿⣧⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠈⡇⣐⣾⣿⣄⢸⠀⠀⡆⠘
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡼⣿⣿⣿⣿⡽⡎⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣧⣿⣿⣿⣿⣼⠀⠀⠃
⣤⣤⣤⣴⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣤⣤⣤⣶⣾⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣤
⣿⣿⣥⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣳⠀⠀⠀⠀⠀⠒⠠⠀⠀⠀⠀⠀⠈⠀⠀⠁⢀⠀⠀⣰⣾⠤⠀⠀⠀⠀⡠⠄
⠀⠈⢄⠀⢀⣀⢀⠂⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⣀⠔⠉
⠀⠀⠀⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢀⢀⠀⠀⠡⣀⠀⠀⠀⠔⠀⠀⠠⢂⠴⠊⠀⠀⠀⣠⠆
⠀⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⣤⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⡠⠈⠀⢀⠀⠀⠉⠈⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⠰⠛⠂⠀⢴⣢⣄⠀⠀⠉⠁⠀⠈⠀⠀⠀⠙⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠒⠀⠁⠀⠁⠀⠀⠀⠈⢪⠘⣆⠀⠀⠀⠀⣦⠀⠀⠀⠠⠀⠀⢀⠔⠉⠀⠀⠀⠞⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⣺⠟⠓⠲⡀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢀⡀
⠀⠀⠀⠐⠤⣤⠠⠔⠀⠀⠑⠤⠀⠀⢠⠏⠓⣾⠇⠀⢇⠀⠀⢀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢀⡞⠁
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢜⠁⠀⣠⠞⠀⠀⠀⠀⠀⡰⠀⠐⠂⠀⠀⠀⠀⠀⠃⠀⢠⡞⠀⠀⠀⠀⢐
⠀⠀⠀⡯⡧⢸⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠑⠊⠀⠀⢠⣼⡦⠀⠀⢃⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠠
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠉⠃⠀⠀⠀⠀⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠠⢤⡦⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠐⠲⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁
⠀⢀⠀⠀⠀⠀⠀⠀⠀⡰⠆⠀⠀⠈⠲⢄⡀⠈⠀⠀⠀⣀
⠀⢸⡀⠀⠀⠀⠀⣠⣾⡀⣀⣀⠀⠀⠀⠀⠈⠁⠘⠉⠉⠀⠀⠀⠀⠴⠠⢰⠄⠀⠀⠀⡠⠀⢀⡴⠶⠀⠀⠒⠁⠀⢠⠀⡄
⠀⠀⠳⢤⠀⠐⠛⠛⠻⠻⣛⣙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⠀⢀⡀⠀⠀⡐⠂⠀⢀⣠⠤⢤⠀⢀⠀⠀⢸⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠣⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡈⠁⠀⢀⣿⠇⠰⣿⣿⡆⠃⠀⠈⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⣶⣤⠄⡘⠁⠀⠀⠈⡉⣄⣀⠉⠩⣠⡤⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠉⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠹⢿⣿⠂⡴⠿⠁⠀⠀⠀⡇
⠀⠀⠁⠀⣀⠀⢀⠀⠀⡀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⡀⠈⠀⠀⠁⠀⠁⠀⠀⠀⠚⠁⠀⠀⠀⠀⠠⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⣠⣤
⠀⠀⠀⠀⣀⡄⠀⢸⣿⡆⠀⢸⣿⡇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣷⠀⠀⣿⣿⣆
⠀⠀⠀⠘⣿⣿⠀⠈⠻⠃⠀⢸⣿⣧⣤⢀⣶⡿⢳⡄⠀⠀⠀⠀⠀⣿⣿⠀⠀⡏⢿⣿⣆
⠀⠀⠀⠀⣿⣿⠀⠀⣶⣶⠀⠀⣿⣿⠀⢸⣿⡇⠀⡷⠀⠀⠀⠀⠀⢿⣿⡆⢠⣷⡌⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣆
⠀⠀⠀⠀⢻⣿⡆⠀⣿⣿⡀⠀⣿⣿⠀⢸⣿⣇⣼⠃⠀⠀⠀⠀⠀⢸⣿⡇⢸⡟⠃⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⠀⠀⠀⠀⢸⣿⡇⠀⢹⣿⡇⠀⢻⣿⡇⠸⣿⣟⠁⠀⠀⠀⠀⠀⠀⠘⣿⣷⡾⠻⣶⡾⠟⠁⠀⠀⠀⠀⠀⠀⢀⣀⣿⣿
⠀⠀⠀⠀⢸⣿⣧⠀⢸⣿⡇⠀⢸⣿⡇⠀⢿⣿⣤⣤⡟⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⣠⣶⣤⠀⠀⣴⣿⠋⢻⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣀⣸⣿⣿⣶⠿⣿⣿⠀⠀⠙⠛⠋⠀⠀⠀⠀⢀⡀⠀⢀⣴⡾⢷⡄⠀⣼⣿⠁⣹⣧⣠⣿⣿⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠹⣿⡿⠃⠈⠛⢋⡞⣿⣿⠀⠀⠀⠀⠀⠀⣴⡶⢾⣿⣷⠀⣼⣿⠁⢸⣿⣴⣿⣿⠀⠙⣿⠁⣿⣿⠀⠘⣿⣿⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⣿⣿⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⣿⠀⣿⣿⠀⠈⢻⡇⣿⣿⠀⠀⢿⡇⢻⣿⡄⠀⣿⣿⣤⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⡿⠟⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⣿⡄⢸⣿⡇⠀⢸⡇⢸⣿⣧⣀⣿⠃⠘⣿⣿⣾⠛⠿⠟⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⣿⡇⢸⣿⣷⣤⣾⠇⠀⠻⣿⡿⠏⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣤⣾⣿⣷⠟⠉⠻⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⣩⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⠟

⠀⠀⠀⠀⣄⠀⢠
⠀⠀⠀⠀⠹⡗⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣤⣤⣤⣄⣤⣤⣄⣤⣤⠀⣠⣤⣤⠀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠉⠉⠉⠉⠉⠉⠈⠉⠉⠛⠀⠉⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡄⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣶⣶⡶⠂⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⢠⡆⠈⠋⠀⠀⠰⠀⠐⠀⠀⠀⠀⠀⠀⢀⠀⣤⠀⠠⠈⣀⣋⠄⠀⠀⠀⠀⠀⠁⠀⠘⠁⠀⠈⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢀⣩⣀⡠⠘⠠⠰⠦⠈⠐⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠃⠙⠂⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠢⠂⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⣠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⡀⠀⠀⠀⠀⢀⡀⠀⡀⡠⣖⡕⡟⣛⠉⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⠀⡀⠀⠀⠀⠀⣜⣯⣢⢿⣿⡿⡗⡽⠗⠚⠇⠃⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⢸⠏⢉⡎⡇⠗⠀⠁⠀⠠⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡀⠉⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣽⣟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⡀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⡀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣻⣯⣿⡽⠀⠀⠀⠀⠀⠀⠀⠁⣧⠠⠐⠲⠐⠙⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠁⢀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⡀⢄⢩⠂⡤⡤⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⣳⡍⠚⠛⠂⡉⡉⠤⠄⢤⣘⡄⠀⡀⠀⠀⠀⠀⠀⠈⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠘⠻⠛⠲⠧⢸⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠁⠄⢠⠀⠠⠄⡠
⠀⠉⠀⠔⢀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⡀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⢫⣿⠓⡖⠀⢀⠔⠂⠉⡀⠀⢠⠀⠀⢀⢀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠘⠲⠖⠀⠀⠀⢀⠇⠀⢸⠤⡰⢃⣅⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⡏⠀⠀⠀⠀⠁⠃⠌⠏⠙⠞⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢙⡀⠀⠀⠠⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢾⡔⢷⣄⣸⠇⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⢠⠀⠀⠀⠀⠀⢄⠀⣰⠂
⠀⠈⠀⠀⠀⠀⠀⠀⢾⡆⢿⣤⡼⣧⠀⠉⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢠⡀⠀⠀⡆⢀⠀⢀⠀⢲⠃
⠀⠀⠀⠐⢶⡀⢠⣤⣸⡇⠸⣏⠀⠹⡆⠀⠘⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠀⣷⡼⢦⡇⠸⠄⢿⠀⢸⡄
⠀⠁⠀⠀⠀⠳⡼⠉⠻⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠶⠀⢸⠃⠈⠃⠀⠀⠈⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢀
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠐⡀
⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⢀⠀⠄⠂⠀⠘⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⢄⠀⠀⠀⠀⠁⠀⠀⠀⢈⡀
⠀⠀⠀⢤⢠⡰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠠⠀⠀⠰⣤⠀⣀⠀⣾⡄⣶⡟⠙⡆
⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⡆⠰⠂⠴⠄⠁⠀⠁⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠙⣷⡿⣶⠃⠏⠻⠹⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡦⠀⠀⠀⢀⡴⠒⠲⡄
⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⣤⣀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⣿⠀⠀⠀⢻⠀⢠⣾⠂⠀⢠⣿⣧
⠀⠀⠀⣠⠴⠋⣉⣐⣦⣀⢦⡈⠳⣄⠀⠀⠀⠀⠀⣿⡇⠀⠀⣹⣦⣀⣀⣸⣀⣸⣿⠀⠀⢸⠘⣿⡄⠀⠀⠀⠀⢀⣤⣄⡀⠀⣰⣶⣄
⠀⠀⠀⠈⠓⠦⣄⣩⡟⠋⣽⣫⠽⠋⠉⠉⠉⠉⠉⢹⣿⡴⢺⣿⠀⠀⠀⡼⠀⠈⣿⠀⠀⡞⠀⣿⣧⠴⠋⠉⠉⠉⠛⠛⠉⠉⢹⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⡤⢺⣿⠀⠘⣿⣄⣀⡼⠁⠀⠀⠙⠓⠚⢁⠴⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣿⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢀⠞⠁⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠛⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⠆⠀⢿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⣀⠘⣿⡇⣴⣾⡇⣴⣿⠂⢀⣿⢁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⢰⣿⠁⣿⣹⡿⣿⣇⡿⣧⠄⣼⣧⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣠⠏⣿⢀⡟⣿⠁⡾⠁⣴⠋⢠⡿⢻⣇⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠏⠀⡏⡸⢸⡟⣸⠃⣼⢃⡴⣿⠃⠈⢿⣶⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠈⠛⠁⠀⠉⠉⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠒⠀⣼⢼⣨⣦⡸⡗⣞⡴⠀⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⣛⠛⢲⡄⠀⣠⣅⠀⠀⣀⡀⠀⢀⣀⡀⠀⠀⡀⠀⢀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⣿⡇⠀⣿⠀⣿⣏⠀⣼⢏⡟⣴⡟⣹⡿⢀⣼⣇⠖⣿⣣⣾⡿⢁⡄
⠀⠀⠀⠀⠀⠀⣿⡇⠀⢠⣿⠁⢰⡿⠞⣵⠏⣼⡟⠋⣸⣏⡴⣿⣣⢾⣿⠋⢸⡿⠃⣿⣡⡾⠁
⠀⠀⠀⠀⠀⠀⠙⠃⠀⣼⣏⣴⠏⠀⠸⡷⠞⠙⠓⠛⠙⠋⠀⠙⠁⠈⠁⠀⠈⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⣠⡤⢰⣴⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠟⠟⠯⠃

⠀⠀⠀⡠⠖⠋⠉⠈⠉⠒⢄⠀⠀⠀⣠⠔⠋⠉⠉⠉⠒⢤⠀⠀⠀⢀⠔⠚⠉⠁⠉⠓⢤⡀⠀⠀⢠⠖⠉⠒⠢⢄
⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢣⠀⡰⠁⠘⢡⡄⠀⠀⠀⠀⠱⡀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠱⡀⢰⠁⠀⠀⠀⠀⠀⠑⢦
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⡇⠴⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢆⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⢣⡀⢿⠧⠀⠀⠀⠀⠀⡼⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠸⡀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠑⢄⠀⠀⠂⠀⠀⣀⠇
⠀⠀⠀⠑⠤⣀⣀⣀⣀⡤⠊⠀⠀⠀⠙⠦⣀⣀⣀⣀⡠⠚⠁⠀⠀⠈⠢⣀⣀⣀⣀⡠⠞⠁⠀⠀⠀⠀⠀⠙⠢⠤⠠⠔⠁
⠀⠀⢀⡀⢄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡤⠄⣀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢤⣀
⠀⠀⡇⠀⠀⣠⠄⠉⠲⢄⠀⠀⠀⢀⣴⠁⢀⣴⣶⣄⠀⢱⣄⠀⢀⡔⠋⠀⠀⠀⠀⠀⠙⢆⠀⠀⡴⠋⠀⠀⠀⠀⡈⠙⢆
⠀⠀⢧⠀⠀⠀⠑⢕⠄⠀⠱⡀⠀⣾⠃⠀⠈⠿⠿⠏⠀⠀⠹⡄⡼⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢸⠁⠀⠄⠀⢠⠀⡀⠂⠈⡆
⠀⠀⠈⢆⠀⠀⠀⠀⠈⡦⠀⢱⠀⠇⢠⣤⣄⠀⠀⠀⣠⣤⢀⠇⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠐⠑⠁⠀⠇⠈⠌⠀⢂⡇
⠀⠀⠀⠀⠓⢄⡀⠀⠀⠀⠀⢘⠀⠈⢾⣿⣿⠆⠀⠐⢿⣿⠏⠀⠈⢧⡀⠀⠀⠀⠀⠀⢀⠞⠀⠈⠳⡀⠀⠀⠀⡐⠀⣀⠞
⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠊⠀⠀⠀⠉⠒⠢⠤⠔⠊⠁⠀⠀⠀⠀⠉⠒⠶⠤⠔⠚⠁⠀⠀⠀⠀⠉⠓⠲⠦⠖⠚⠁
⠀⠀⠀⢀⠴⠂⠉⠉⠑⠢⣄⠀⠀⠀⢀⡤⢆⣉⠉⠓⠢⣄⠀⠀⠀⢀⡴⠒⠻⠉⠓⠲⢄⠀⠀⠀⠀⠀⠀⡐⠳⢤
⠀⠀⡰⣡⡶⡻⣶⡄⠀⠀⠈⢣⠀⠰⠃⠀⠀⠀⠀⠀⠀⠈⢣⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⢰⠄⠀⠀⠙⢄⡀
⠀⠀⡃⣿⠰⢡⣾⡇⠀⠀⠀⠈⠃⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣰⣿⣦⡀⠀⠀⠀⠑⣄
⠀⠀⢣⠈⠛⠟⠋⠀⠀⠀⠀⣰⠁⢣⠀⠀⢀⠀⠁⠀⠀⠀⣰⠁⢸⡀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⢴⣿⣿⣿⣿⣦⣄⠤⠔⠊
⠀⠀⠀⠳⢄⡀⠀⠀⠀⣀⠔⠁⠀⠀⠑⢄⡁⠀⠀⣀⣀⠔⠁⠀⠀⠑⢤⣀⠀⠀⠀⣠⠔⠁⠀⢀⠀⠙⡿⠛⠉
⠀⠀⠀⠀⠀⣉⣉⣉⣉⡀⠀⠀⠀⠀⠀⠀⣈⣉⣉⣉⡀⠀⠀⠀⠀⠀⠀⣈⣉⣉⣉⡀⠀⠀⠀⠀⠁⠈⢀⣀⣀⣀⡀
⠀⠀⢀⡴⠋⠀⠀⠀⠀⠉⠢⡀⠀⠀⡴⠋⠀⠘⣄⠀⠈⠲⡄⠀⠀⡠⠊⠁⠀⠀⠀⠈⠓⡄⠀⠀⡠⠊⠁⠀⠀⠀⠈⠑⣄
⠀⠀⡞⢰⡷⠀⠀⠀⠐⣷⠆⢹⠀⡜⠀⠀⠀⠀⠈⠱⢄⡀⢘⡄⣸⠁⠀⠀⠀⠀⠀⠀⠀⠘⡄⢰⠁⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡗⠒⠠⣀⠀⠀⠀⠀⠈⠉⠇⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠘⣄⠀⠀⣠⣀⠀⠀⢀⠎⠀⠘⣄⠀⠈⠳⡄⠀⠀⢀⠜⠀⠘⢄⠀⠀⠀⠀⠀⠀⢀⡜⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠈⠑⠶⠬⠥⠤⠚⠁⠀⠀⠀⠈⠑⠢⠄⠼⠤⠒⠁⠀⠀⠀⠀⠑⠢⠤⠤⠤⠒⠉⠀⠀⠀⠀⠑⠢⠤⠀⠤⠔⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣤⠀⠀⠀⠀⠀⢸⠛⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡏⠀⠀⠀⠀⠀⡿⠀⠀⠈⣷
⠀⠀⠀⠀⠀⢀⣀⠀⢰⠛⢦⠀⠀⣀⡤⠖⠚⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠓⠶⣤⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⠇⢀⡴⠛⠁
⠀⠀⠀⠀⠀⡏⠉⠳⣾⠀⢸⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⡴⠶⠦⣄⡀⠀⠀⠸⠶⠋
⠀⠀⠀⠀⠀⢻⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⣀⣤⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢀⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣤
⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣠⠞⠈⣇
⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⡴⣄⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⡴⠋⠀⠀⢹
⢠⡏⠀⠀⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⠀⢰⣄⣀⡸⠁⠈⠒⠀⠚⠁⠈⠑⠦⠴⠈⠳⢄⣀⣀⣀⣠⡶⠋⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⢘
⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⢀⡴⠒⠒⠦⡀⠀⠀⠀⠀⠘⡆⢀⡤⠚⠛⢤⡘⡇⠀⠀⠀⠀⠸⠧⠶⠶⠒⠛⠋⠉
⡏⠀⠀⠦⠼⠂⠀⠀⠀⠢⡄⠀⠐⣦⣤⠜⠀⠀⡎⠀⣠⣤⡀⠹⠀⠀⠀⠀⠀⢹⡏⠀⣶⣶⠀⢷⡇
⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢁⠀⠀⠀⠀⢧⠀⠙⠿⠃⢠⠇⠀⠀⠀⠀⠈⣧⡀⠙⠋⢀⡿⡇
⢻⡀⠀⢀⠀⠀⢠⠞⠉⠀⠈⠦⠤⠎⠀⠀⠀⠀⠈⠳⠤⠤⠴⠋⠀⠀⠀⠀⠀⠀⣧⠉⠒⠒⠉⠀⢹⠀⠀⠀⠀⠠⣶⠒⠒⠲⠶⠤⢤
⠈⣧⠀⠀⠁⠀⡇⠀⢀⣰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⣸
⠀⠈⢧⡀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠳⡄⠀⢰⠇
⠀⠀⠀⠙⢦⣀⠀⠙⠓⢲⡆⠀⠀⠀⠀⠀⢸⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠁⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠹⣦⡏
⠀⠀⠀⠀⠀⠉⠛⢦⡄⢸⠇⠀⠀⠀⠀⠀⠸⡄⠀⠀⠈⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠶⣯⡞⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠈⠙⠒⠤⢤⣄⣀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠁⠀⠀⢀⡾⠃
⠀⠀⠀⠀⢀⣤⠤⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⢑⡞⠁⠀⠀⠀⢀⡴⠋
⠀⠀⠀⣴⠋⠀⢰⠋⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⡾⢄⠀⠀⠀⢠⠞⠁
⠀⠀⢰⡇⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⣉⣀⠜⠀⠀⢠⠏
⠀⠀⠀⢷⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠘⡇⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⢠⡞⠳⣄⡀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⢹⡀⠀⠀⠀⠑⢄⡀⠀⢀⡴⣏⠀⠀⠈⠙⠳⢤⣄⣀⣠⡴⠟
⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠙⣢⠞⠀⠘⡆
⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⣠⣾⣁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣧⢀⣠⠞⠁⠀⠈⠙⠶⣄⣸⡄

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠈⣤⡄⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡀⢀⣴⡄⠀⠀⠀⠀⠀⣀
⠖⠠⠀⠀⠀⠀⠀⠀⣿⠁⠀⡀⠄⠀⣤⢠⡀⠀⠀⠀⠉⠁⠀⢀⣤⣤⣾⠟⠃⠄⡀⠀⠀⡀⢰⠏⠛⠉⠀⠀⠀⣼⣾⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠟⠛⠇⠀⠉⠀⢠⠃⠟⠁⠀⠀⠆⠀⠀⢰⡇⠀⠀⠙⣧⠀⠀⠉⠓⠘⠏⠀⠀⠀⠀⠀⠀⢰⣏⣠⣶⣿
⢺⡏⠀⠀⠀⠀⠀⠀⣾⣷⣶⣶⣆⢸⣶⣦⡀⢀⠀⠀⠀⠀⠈⠁⠀⡀⢀⣍⠀⠀⠀⠀⡹⠀⣤⠶⠀⠀⠀⠀⣿⢻⡟
⠘⠁⠀⠀⠀⠀⣠⢾⡿⠛⠋⠁⢙⣿⣭⣥⣿⡿⠿⢷⡀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⢻⡿⠇⠀⠀⠀⠀⠀⠻⠘⠃
⠀⠀⠀⠀⢀⣀⡛⠚⠃⠀⠀⠀⠈⠉⢨⣿⠁⠀⠀⠀⢹⠀⠀⠀⠀⠸⠟⠃⠀⠀⠀⠀⠘⠟⣀⣤⣶⣶⣦⣴⣄⡀⣦
⢀⡄⠀⠀⢀⣇⣿⠛⠂⠀⠀⠀⠀⣿⣿⢻⠀⠀⠀⠀⢸⣠⣤⣼⣷⣷⣶⡄⠀⠀⠀⠀⠀⣇⠝⠛⠿⣿⣿⣿⣿⣿⣿⣦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠠⡀⠀⠀⠠⠂⠒⠀⡄⠀⠁⠀⠀⠀⠀⠁⠠⡀⠀⠀⠀⠀⢀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠁⢰⠒⠂⠒⠀⠀⢂
⠀⠀⠀⠀⠀⠀⢐⠉⠐⠀⠀⠀⠀⠠⠁⠀⡀⠀⠐⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⡠⠀⠀⠠⠄⣄⠀⠀⠀⠤⠐⠀⠠⠀⠠⠠⠬
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠄⠀⠃⠀⡐⠁⡀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠰⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⢠⡀⠀⠐⠅⣠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠄⠊⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠠⠀⠐⠒⠃
⠀⠀⠀⠀⡀⠀⣀⠁⠄⠀⠀⠉⠀⢀⠄⠀⠀⠰⠀⠀⠘⡀⠀⢀⡀⠤⠒⠇⠀⠀⡄⣀⠈⠀⠀⠀⢡⠀⠀⡰⠀⠀⠂⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠂⠀⠀⠀⠀⠑⠀⠂⠁⠀⡄⠀⠀⠀⠑⠂⠈⠀⠀⠀⠀⡀⠀⠀⠁⠀⠃⠒⠀⠃⠀⠂⠀⠀⠀⠀⠀⠀⠂
⠀⠀⡀⠀⠠⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠁⠀⠀⠀⢀⠀⡄⠒⢤⢀⠀⠀⠀⠀⠀⢐⣰
⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠃⠁⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⢈⢉⠣⡀⠇
⠀⠐⢄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠒⠐⠤⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠈⠀⠀⠀⠢⢀⠂⠀⠀⠀⠀⠐⡄⠂⡀⠀⡡⢄⠀⠀⠀⠀⠀⡠⠤⠄⡀
⠀⠀⠀⠈⠀⠐⠁⠀⠀⠰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂⠀⠀⠀⠑⠰⢉⡈⠄⠐⠀⠀⠀⠀⠂⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠄⠀⢀
⠀⠀⠀⠀⠒⣤⠒⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⡎⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠐⠀⠒⠁
⠀⠀⢄⠈⢢⠦⣔⠁⡰⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠈⠠⠄
⠀⠠⠌⣠⠝⠰⢂⣈⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠁⠐⠁⠀⠀⠀⢀⡠⠣⠀⡀
⠀⠀⠀⠠⠄⠓⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢄⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⢀⠔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⢀⢐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⡀⠀⢢⠀⠀⠀⠈⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠈⠀⠀⠀⠀⠀⢀⠤⠄⡀⠀⠀⠀⠀⠀⠉⠀⠈
⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⢀⠀⢁⠀⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠄
⠀⠀⠀⠐⢄⠀⠁⠀⠀⠀⠀⠢⠀⠀⠠⠊⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠠⠀⠀⠀⠀⡀⠆⠀⠀⠀⠄⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠡⠀⠐⠈⠀⠀⠀⠀⠀⠃⠄⠁
⠀⠀⠀⠀⠐⢠⠉⢒⢀⠆⢠⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⢀⠠⠔⠠⠰⣅⠀⠀⠀⠀⡐⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⢄⡀⠄
⠀⠀⣀⡀⠁⢠⠄⠐⠢⢀⡈⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⡡⠊⠀⠀⠀⠀⠀⠈⠁⢀⠀⠒⠀⠀⡐⠀⠀⠀⠀⠀⡠⡅⠙⢠⠁⠀⡃⠜⠠
⠀⠈⠄⠈⠖⠀⠀⠀⠀⠈⢃⡀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡅⠀⢀⠂⠉⠁⠢⠀⠀⠈⠀⠀⠀⠜⠀⠀⠀⠀⠀⡀⠴⠐⠦⡀⠆⠬⠁⣀⠈⠰
⠀⢀⠦⠠⢆⠀⠤⠀⠴⠀⡈⠀⠢⠈⠀⠀⠔⠁⠀⠂⠁⠀⢀⠃⠀⠐⢀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢈⠆⠠⠤⢄⡀⡀⢅⡀⠈⠱⠄
⠀⠈⠰⠁⢀⠱⠤⢤⡄⠊⢋⠐⡆⠀⠀⠀⠈⠢⠀⣀⡀⠀⠊⠡⡀⠀⠀⠈⠁⠀⠀⢀⠴⣀⡀⢠⠀⠀⠀⠀⠀⠀⠈⠚⢀⡠⠎⠀⣧⠀⠑⡈⠄
⠀⠀⠀⠀⠁⠼⡀⣤⠈⠦⠜⠀⠀⠀⠀⠥⠂⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠤⠤⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠐⢂⡠⠂⡐⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⡿⢿⠿⡿⡿⢟⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣻⣿⣿⣿⣻⣟⣿⣛⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣼⣿⠀⣾⡆⢠⡾⠷⣄⢸⣿⣶⡄⠀⢰⣆⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠏⢸⣿⡏⠀⢹⣇⣼⡿⢸⡿⣿⣁⡀⠈⣿⣯⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠀⠀⠀⠉⠉⠀⠀⠁⠀⠉⠉⠀⠉⠈⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢸⡆⠀⠀⣼⣆⠀⠀⠀⢰⣶⣦⣄⠀⠀⢀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⡀⢸⣟⣀⣀⣺⡇⠀⢰⣿⠹⣆⠀⠀⢸⣇⣀⣼⡷⠀⠀⠉⢹⡟⠻⣦⠀⣰⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠃⠸⣿⠛⠛⢿⡇⠀⣼⡿⠿⢿⡀⠀⢸⣿⣍⠉⠀⠀⠀⠀⠈⣇⠀⣸⡇⠹⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⢿⡇⠀⠈⣧⠀⠸⡇⠙⠳⣶⣤⡀⠀⣤⣿⣶⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠉⠁⠀⠈⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣤⡀⠀⣤⣄⡀⠀⣀⣀⡀⠀⢀⣀⠀⠀⣀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠃⠙⣦⣿⣽⡷⠀⣿⣯⡥⠀⣼⣿⡄⠀⣿⣇⣰⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣶⣾⠿⡟⠳⣦⣄⢹⣧⣶⠔⡿⠉⢷⠘⡏⠈⠛⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⣀⠀⠀⣶⣶⣦⡀⠀⠀⢠⣤⣤⣤⡄⠀⠀⣀⣤⣤⣄⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠀⠀⣿⠁⣀⣿⠀⠀⠀⠉⣿⠋⠉⠀⣾⡿⠋⠉⠉⠧⠀⠀⢾⣿⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣴⣶⡄⠀⠀⣿⠿⠿⠿⣦⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⡀⢀⡀⠀⠀⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⣿⣀⣀⣠⣼⡇⠀⣀⣿⣤⡀⠀⢻⣄⠀⣹⣿⣿⡆⠀⠈⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠀⠀⠀⠙⠛⠛⠛⠋⠁⠀⠛⠛⠛⠃⠀⠀⠙⠿⠿⠿⠉⢷⠀⢲⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠚⠛⠉⠉⠉⠉⠉⠙⠒⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⣀⣴⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⣡⠿⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠁⠀⠀⠀⠉⠙⠳⣄⠀⠀⠉⢽⣒⠦⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⣾⣣⡼⠖⠋⠉⢑⡜⠂⠀⠀⠀⠉⠉⡿⠒⠂⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢙⣲⣤⠤⠤⠤⣿⠄⠀⣀⣀⠞⠁⠀⠀⠀⢀⡀⠀⢧⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠘⠄⠀⠁⠀⠀⠘⠉⠉⠁⠉⠁⠀⠀⠀⣠⣏⠏⠁⠀⣁⡤⣤⣄⠹⡄⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣔⢛⡶⠋⠀⠀⣀⣀⣉⣁⣠⠼⠁⠀⣠⠀⠀⣦⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⠉⠒⠦⠤⠤⠤⠤⠴⠒⠋⠉⠀⠘⢉⡴⠚⠑⠺⣄⠀⠀⠈⠑⠢⠤⠴⢻⣀⣠⠿⠴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣤⣀⣀⣀⣀⣀⣀⣠⠤⠤⠒⠚⠙⠁⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⡖⠒⢜⣯⣍⣠⣟⠔⠊⣉⠆⠀⠀⠀⠀⠀⠀⠀⣠⣞
⠀⠀⠀⠀⢀⣴⣾⠏⠁⠉⠹⣿⣦⣄⠀⠀⠀⠀⠀⠀⠸⣉⣱⢇⡠⠤⣽⠏⠇⠠⢐⠄⠁⠀⠀⠀⠈⣦⡠⢾⡿⢿
⢠⠞⡑⠠⡟⠋⠑⣄⣀⣀⡠⠋⠙⠻⣆⠀⠀⣀⠤⡄⠀⢉⣒⣊⣀⣴⠃⠀⠢⢈⡁⠔⠁⠀⠀⠀⠀⣧⢠⠼⠀⠘⠓⡄
⡄⠀⠇⣶⡅⠀⢠⣿⣿⣿⣇⠀⠀⠀⣻⡀⢈⡟⢠⢞⣆⣸⡄⠀⠀⠈⠙⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⢻⠈⢆⣠⠤⠚⠁
⠃⠀⠀⢻⡟⠀⠙⢿⣿⠿⠛⠒⢤⣴⣿⠁⠈⠻⡈⢧⠚⢇⣻⣄⠀⠀⠀⠀⠀⠈⠉⠉⠓⠒⠒⠒⠚⠛⠦⡄⢡⣊⠙⢶⡄⠀⠀⢄
⠀⠀⠀⠈⢅⠀⠀⠀⡇⠀⠀⠀⢰⣿⠃⠀⠀⠸⢵⡌⠁⠛⠁⠈⠳⡀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡷⢺⠉⣇⠀⢣⠀⠈⡆⠱⠀⠀⠑
⠀⠀⠀⠀⠀⠑⠲⠾⢿⣶⡶⠖⠋⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠈⠒⠊⠁⠀⠱⣄⠀⠀⠀⠀⢀⣴⣿⣁⡼⢾⡽⣇⢈⡿⠀⠁⠀⠄⠘⠃⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣤⠤⠖⠉⠀⠀⠀⠀⠈⠫⣈⡼⠟


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⢀⢠⠀⡄⢀⠀⡄⢀⠀⡄⠀⡀⠀⡀⠀⡀⢀⠀⡀

⠀⠀⢀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠈⡃⢄⠀⠸⣧⠯⠃⠀⠀⢀⣀⣐⠀⠉⠁⠀⠀⠐⠀⠠⢀⠀⠀⠐⠻⡟⠂⠀⠀⠀⠀⠐
⠀⠐⢤⠃⠀⢀⠔⡅⠀⠀⠐⣋⠤⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⢀⣀⣂⣀⠀⣴⠆⠾⠇
⠀⠀⠀⢀⠔⢁⠢⡇⠀⠀⠀⠀⢀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⠽⠒⠅
⠀⢀⡔⠁⢌⢢⢳⡇⠀⢹⡃⠀⣸⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠈⠀⠤⠑⡄⠀⠀⠀⠀⣤⡞⠀⠹⠆⠬
⠀⠫⣉⠉⠚⢦⣻⠁⠀⡈⠳⠎⢸⣀⠄⡟⢃⡠⢧⣀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡠⠒⠀⠋⠀⠑⢲⠊
⠀⠀⠈⠉⠓⠒⠛⠀⠀⡷⠴⢶⣺⢅⡜⠀⠀⠹⢪⠋⣹⠒⠶⠤⢤⠴⠶⡊⠟⣄⠴⠄⠈⠁⠲⠉⠀⢠⠄
⠀⠀⢀⣀⣀⡀⢀⣀⠀⠫⠻⣷⣮⡟⢠⢒⡒⢄⠀⠉⠀⠃⠰⠢⠌⠦⠆⠈⠃⠈⠀⠀⠀⢀⡈⠀⠀⠈⠂
⠀⠀⠙⢄⠀⢠⡋⠶⠥⡀⠀⠀⣀⠀⢧⡇⠈⢪⡄⣰⠞⠉⢢⠀⠀⢤⠀⠀⢰⠠⠂⠀⡠⢊⢁⠝⠑⠒
⠀⠀⣀⠀⠑⢼⢢⣔⠀⠉⠳⣄⣈⣯⠚⠿⣄⠌⣷⡟⠀⣀⠎⠀⠒⠈⣁⣠⠤⠒⠂⠀⠀⠁⠃⠔
⠀⡰⢤⡂⠐⣢⠉⠈⢳⡉⣉⠽⡏⠉⡑⠲⢬⡟⢙⣶⣚⣉⠙⢧⠀⣸⠑⠀⡗⠀⢀⠀⠀⡠⠀⠀⠀⠠⡀
⠀⠰⠔⠄⢀⡽⡄⠀⠀⠻⠴⡞⠁⠀⢦⠀⢠⠀⢀⡀⢀⡰⠀⠀⠀⢇⢀⡔⠱⢄⡜⠀⢠⠁⠀⠀⠀⠀⠄
⠀⠀⢀⣀⣸⢀⠇⢀⠀⠀⠀⢹⠀⠀⡆⠀⢸⠀⠀⠀⢠⠀⠀⠀⠀⡨⠉⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢠
⠀⠀⢘⢒⠢⡿⠤⠒⡃⠀⠀⢸⠀⠀⡇⠀⢸⠀⠃⠀⡆⠀⠀⠀⠴⡇⠀⠀⠀⢠⡼⠤⢀⡆⠄⠤⠒⠁
⠀⢀⣸⠂⠈⠑⠎⢸⠀⠀⢿⡛⣏⠀⠉⠉⠉⠘⠒⠒⠃⠀⢠⡤⠐⠀⠤⠶⠂⠀⠀⠀⠙⠂
⠀⠘⠤⣑⣦⣤⣔⡃⠴⠀⡰⠉⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⡇⠃⡰⡟⣭⣕⡄⢯⡟⠀⠀⠀⢀⣸⠙⣳⠆
⠀⠀⠀⠈⣒⣒⡉⠀⠀⠀⠀⠀⠴⡀⠀⠀⠢⡁⢀⡀⢀⣀⢧⣆⠘⠷⢝⠿⠃⢀⠀⠂⠀⡠⠢⡀⢙
⠀⠀⢠⠊⡉⢳⣹⣀⠠⠰⣷⠄⠣⡁⠠⠀⢠⣌⠀⠲⠟⠉⠀⠉⠑⠒⠀⠀⠀⠀⠀⠀⢀⡫⠒⣠⠏
⠀⠀⠈⠦⣑⣊⣁⣀⠤⠒⠉⠀⠀⠈⠢⠘⠋⠈⠀⠈⠀⠈⠀⢠⡀⢢⠘⢑⡀⠀⠀⠀⢏⣋⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠁⠊⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢖⠫⠉⢍⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢞⠍⠊⠀⠀⠀⠀⠈⠒⢍⡻⢿⣿⣿⣿⡿⠟⢋⠡⠐⠀⠀⠀⠀⠉⡳⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⡫⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠋⡡⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡙⢦⡀
⠀⠀⠀⠀⠀⠀⣠⡎⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄
⠀⠀⠀⠀⠀⣴⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣦
⠀⠀⠀⠀⣼⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧
⠀⠀⠀⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡆
⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⠟⡁⠤⠈⢐⡀⠀⢀⡀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⢀⡀⠄⠀⠒⡈⠈⠀⠙⢿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⠟⡡⠊⠀⠀⠀⠀⠀⠁⠀⠒⠁⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢩⠄⠒⠀⠈⠀⠀⠀⠀⠀⠀⠙⢿⣿⡇
⠀⠀⢸⠋⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠈⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣸⠁
⠀⠀⠀⠸⡔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢜⠉⠉⠉⠉⠉⠉⠩⠉⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠇
⠀⠀⠀⠀⢳⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡡⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⡞
⠀⠀⠀⠀⠀⠳⡌⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⠞
⠀⠀⠀⠀⠀⠀⠙⢦⣤⣤⣤⣤⣤⣤⣤⠡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣤⣤⣤⣤⣶⣶⣶⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣼⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠶⠤⠬⠥⠤⠤⠤⠴⠖⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡄⠤⠤⠤⣶⣿⣿⣴⣦⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⢤⠀⠀⠀⠀⠈⠉⠀⢀⣤⣤⣤⣄⠀⠛⠺⢏⣯⢻⡷⣾⣧⡀⠀⠀⠀⢀⣴⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⣀⣀⣤⠴⣶⠟⠁⠀⠉⢻⠀⠀⠀⠀⠀⠉⠉⠘⠋⠀⠀⠀⠀⣠⣽⣿⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢡⠞⣁⠀⣏⠀⠀⠀⠀⠀⠀⠀⠠⣤⠶⢀⣤⣴⣤⡀⠀⠀⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣎⡁⣴⣾⣶⣶⣽⣿⣴⣶⣶⣄⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⣿⣿⣿⡄⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⢯⣾⣎⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠈⠻⣿⡿⠿⠛⢻⠄⠀⠀⠀⠀⠀⣠⠀⠘⣿⣿⡇⠀⢀⣵⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠉⢸⣿⣿⣷⣯⣽⣯⣿⡟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣴⣶⣿⣶⣦⠘⠻⠃⢰⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣼⣧⣰⣿⣷⣄⡀⠀⠙⠻⠿⣿⣿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠟⢁⡄⠀⠘⢿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣼⣻⠀⠀⠀⢈⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠛⠿⠿⠿⠟⠃⠀⠀⠀⠀⢰⡄⣶⠀⢠⡀⢰⡖⣤⢰⡀⠀⢰⡒⠀⣄⠀⠐⡖⠂⠀⠀⢰⢏⡏⠀⠀⠀⡼⣼⣄⡀
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠸⠇⠿⠠⠈⠷⠸⠏⠧⠀⠛⠀⠸⠉⠀⠌⠛⠀⠧⠀⠀⢠⡛⡾⠁⣠⣴⢾⣿⡗⣿⣻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⢠⣾⣿⣿⣿⣆⠀⣄⠀⠀⠀⠀⠀⠀⠀⢠⡀⢀⡀⣠⠀⢠⡀⣄⠀⠀⠀⠀⠀⠀⠀⠈⡉⠀⣼⣿⣵⡿⠻⣿⡿⣷⣝⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠹⠿⣿⣿⠿⢟⣼⣿⠆⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇⠈⠷⢸⡇⣿⢀⠀⠀⠀⠀⠀⠀⢠⠃⠀⣿⠟⠋⠀⠀⠙⠇⠀⠉⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣡⣤⡌⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⣴⣾⣿⣦⣿⣿⣢⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣿⣿⣿⣿⣾⣿⣷⡴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣤⣶⢁⣤⣀⣿⣿⣿⣿⣧⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⣾⣿⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣐⣮⣿⡿⠆⢺⣿⣿⣿⣿⢿⣿⣸⣿⣿⣿⣯⣀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⡏⣾⣿⣿⣿⣿⣿⡏⡿⣿⣿⠇⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⣾⣶⡻⡯⠊⠀⣰⠀⠻⢿⣿⡿⠘⠿⢿⢸⢫⣿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣧⣈⣿⣿⣿⣿⣟⣡⣿⡿⠁⢀⣠⣴⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⡀⠀⢀⠀⠹⡆⠀⠄⠘⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠘⠚⠋⠈⠉⣉⣴⣾⣿⣿⣿⡟⠁⠀⠀⢠⣀⠀⢲⡀⠀⠀⠀⠀⢀⣿⣿⣇⠀⣟⡇⠀⠁⠴⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠋⠀⠀⠙⠠⠀⠀⠀⠜⠳⣂⠀⠀⣠⣾⣿⣿⣿⠀⢱⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⣿⣿⠟⠁⠠⣤⡀⠀⠀⠐⠀⠄⠠⠞⠁⢠⣾⣿⣿⣿⣿⡿⠀⠈⠣⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠃⠈⠉⠁⠀⠀⠀⢀⣭⠀⢆⣀⠔⢿⠆⠀⠀⢻⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠿⠁⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢀⣠⣤⠄⠀⠘⣿⠋⢈⡻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣴⡟⠉⠀⠀⣀⠀⠘⢇⠿⠿⡜⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣶⣿⣿⣷⣀⠀⠑⠀⡀
⠀⠀⣠⣾⣟⣠⡴⢾⣿⠋⠀⠀⠈⠻⣷⣸⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡈⠂
⠀⠈⢿⣿⡿⣯⣠⣤⡿⠂⠀⠀⠀⠀⠹⡝⠹⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣤⢽⡿⠿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠟⣽⣿⣿⣿⣿⣿⠀⠀⠀⠀⣴⡟⣼⣿⣶⡄⠀⣠⣶⠀⠸⣿⡿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀⠀⠀⠀⠀⠀⠀⡏⣿⣿⣿⣿⣿⣿⠀⠀⠀⠐⣿⠁⣿⣿⣿⣧⣄⣉⠙⠛⠦⡛⢷⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⢀⣴⠖⠀⠀⠀⠀⠀⠀⠀⢁⡛⢿⣿⣿⣿⣿⠀⠀⠀⠀⡀⠸⣿⣿⣿⣿⣿⣤⡈⠰⠆⠁⢨⣿⣿⣿⡿⠃
⠀⡄⢀⣠⣠⣤⣾⠃⠄⢀⣀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠙⠿⣿⠀⠀⠀⢀⠁⣀⣿⣿⣿⡿⠋⠃⢉⣁⠀⠀⠘⠉⠉⠉
⠀⠁⠈⠉⠉⡡⠀⠀⣠⡞⠛⠃⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⡇⠀⣀⣼⢰⣿⣿⣿⣿⣿⣄⠀⠀⠉⢀⡔
⠀⠀⠀⠀⡀⣠⠖⠚⠉⠀⢀⠀⠀⣠⠀⡧⣼⠇⠀⠀⠀⠀⠀⣃⡤⣻⣯⣾⣿⣿⣿⡟⠁⠀⢀⣤⡶⣿⣳⣶
⠀⠀⠀⠘⠿⢣⣤⣠⣤⣴⣿⣶⢿⠏⢰⣇⣿⣤⣤⠴⠶⠖⠛⠿⢆⣾⡳⣭⣻⢿⣏⠀⠀⠀⣼⣿⢿⣵⣿⣿⣿⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣤⠿⠿⠏⠀⢀⣤⠟⣭⣵⣶⣶⣤⣶⣾⣤⡾⢫⣾⡇⣿⣿⣷⣯⣿⣦⠴⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠲⠤⢤⣀
⣀⣀⣀⣀⡐⠞⠿⠧⠀⢀⣀⣰⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣥⡿⠟⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠉⠛⠛⠛⠛⠉⠉⠉⣿⣿⣿⢢⣤⣨⡑
⠹⣟⠛⢻⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣽⠏⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⢇⣿⣿⣿⣿
⠀⠈⠳⠬⣉⠙⠛⣛⣛⣻⠟⣱⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠑⠊⠙⠻⣾⣿⣿⣿⣿⡻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿
⠉⠉⠉⠉⠉⠉⢉⣁⣙⣀⠠⠄⠀⣨⡛⢷⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⢠⡀⣀⠀⡀⠀⠀⠀⠉⠻
⠀⠀⠀⠀⠀⡰⢫⡴⢿⣿⡷⣶⣤⣙⣟⠊⡏⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠈⢿⣿⣴⡇⠀⠀⠘
⠀⠀⠀⠀⠸⡇⠠⣶⣿⣿⣿⣿⣿⣿⣿⣧⡁⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢿⣿⠁
⠀⠀⠀⠀⢠⣿⡗⢋⣠⣴⣿⣿⣿⣽⣿⣿⣿⣤⠤⠶⠶⠚⠓⣚⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠠⠁
⠀⠀⠀⣀⠚⣁⣴⢟⣫⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣿⣦⠃⠀⠀⠀⡠
⠀⠀⠀⢹⣿⢟⣵⠿⢋⣵⠆⢰⣞⣴⣶⣶⣶⣶⣶⣾⢇⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣿⠏⠞⠁⣠⣈⣠
⠀⠀⠀⢸⣰⣿⣥⣾⣿⡏⠀⡟⣾⣿⣿⣿⣿⣿⣿⡟⣼⣿⣿⣆⠀⠀⠀⠀⠀⠀⠈⠛⠦⠄⢀⢂⠀⠀⠀⠈⣧⠀⠀⠀⢻⣿⣶⣾⣿⣿⣿
⠀⠀⠀⢻⣿⠿⢿⣿⣿⣧⠐⠸⠟⠻⠏⠻⠏⠻⠛⠁⣿⣿⣿⣟⣵⠀⢰⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠐⣏⢻⣴⣾⡿⠿
⠀⠀⠀⠀⠈⠙⠢⣝⠷⢾⣀⣄⣀⣀⣀⣀⠀⠀⠀⠀⠻⡿⣫⣾⣿⣤⠸⠇⠈⠙⠻⢄⠱⡄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⢠⣿⢾⡿⠁⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠉⠀⠀⠀⠀⠀⠀⣽⣿⣿⣷⣶⣾⣷⣿⣿⢿⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣠⡾⠾⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠻⢿⣿⣿⣿⣿⣿⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢘⣿⣿⣯⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠈⠙⠛⠛⢡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡷⠞⠋⢉⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣴⣶⣿⠟⠋⣀⣤⣶⡿⠁⠀⢀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⣠⣴⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠟⠛⠉⢀⣠⣴⡾⢟⣿⣿⣿⡃⠀⠀⠀⢠⠀⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⣠⡀⠰⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣤⣴⣶⣾⣿⠿⣫⣾⣿⣿⣿⡿⣷⣄⠀⠀⢺⠂⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣿⣷⣄⡀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣍⣭⣭⣶⣿⣿⣿⣿⠿⢋⠜⠹⣿⣷⣤⣀⣰⣿⠋⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⠀⠛⢻⣏⣉⣀⣠⣿⣀⣀⡤⠀⠋
⠀⠀⠀⠀⢀⡴⠚⠛⠛⠒⠦⣄⠀⠀⠀⢻⣿⠀⠀⠀⠀⣸⣿⠀⢀⣿⡏⠉
⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠁⠀⠀⠀⠀⣿⣿⠀⣸⣿⠁⠀⠀⠀⠀⠀⢀⡴⢲⡆
⠀⠀⠀⠀⠘⠦⣄⣀⣀⣀⣀⣀⣀⣀⣳⡄⠀⠀⠀⠀⠀⢹⣿⠀⣿⣿⠀⣴⠀⠀⠀⠀⠸⣧⡈⣠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⢸⣿⠀⢿⣿⢠⡇⠀⠀⠀⠀⠀⣸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠈⠛⠛⠀⠀⠀⠀⠀⢰⣏⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⢀⣤⣤⡀⠀⣴⣶⡄⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⠀⠀⠀⠙⠛⠀⠀⡶⣶⣶⣶⣶
⠀⢀⣴⣿⣿⣿⡿⠿⠀⠀⢸⡏⢻⣇⣸⢿⣸⡇⢀⣾⣿⣿⡿⠿⣷⡄⠀⡤⣘⡻⠗⣤⣄⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠀⠀⢸⣿⣿⡇⢰⡇⡟⠉⠉⠉
⠀⢾⣿⣿⣯⣀⠀⠀⠀⠀⢸⣧⣷⡻⢯⣿⢻⡇⣼⣿⡟⠋⢠⠆⣿⣇⢠⢀⠻⠋⠀⢍⡻⠃⠉⠀⠩⣿⣿⠀⠀⢰⣶⠀⢰⣶⡆⠠⣿⣿⡇⢸⣇⡭⠯⠽
⠀⠈⠻⢿⣿⣿⣿⣿⣦⡀⣸⢹⣿⢷⡿⣿⢸⡇⣿⡏⠀⢠⠏⠀⢸⣿⠀⡺⡇⠀⠀⢸⡟⡄⠀⠀⠨⢿⣿⠀⠀⢸⣿⣦⣼⣿⡇⠀⣿⣿⡇⢸⣿⡇
⠀⠀⠀⠀⠀⠈⢹⣿⣿⡇⣿⢸⡟⠀⠀⢻⣿⡇⢻⣿⠄⣉⣀⣠⣿⡏⠸⣿⡦⣀⠀⣴⢈⡃⠀⠀⠈⣿⣿⠀⠀⢸⣿⠋⠙⣿⡇⠀⣿⣿⡇⢸⣿⠁
⠀⠀⣤⣤⣤⣶⣾⣿⣿⠃⣿⢸⡇⠀⠀⢸⣿⡇⠘⣿⣿⣿⣿⣿⡿⠁⠀⠉⢁⠿⣿⢆⡝⠁⠀⠀⠀⣿⣿⠀⠀⢸⣿⠀⢀⣿⡇⠀⣿⣿⡇⢸⡿⣶⣶⣶⣶
⠀⠀⠛⠛⠛⠛⠛⠉⠁⠀⠛⠛⠃⠀⠀⠈⠉⠁⠀⠈⠛⠛⠛⠉⠀⠀⠀⠀⠀⠉⠂⠈⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠉⠀⠀⠉⠁⠀⠉⠉⠁⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣾⣇⣀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⠤⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣼⣿⠁⠰⠆⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⣼⡆⢠⣷⡜⣿⡇⣠⣤⠀⠀⣴⡾⢻⠄⠀⠀⠀⠀⠻⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢠⣿⡇⣼⣿⠁⣿⣿⢫⣿⡇⣼⣿⠧⠋⠀⡴⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣼⢿⣷⢿⡏⠀⣿⡇⠘⢿⡿⢻⣿⡀⣀⡾⠁⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠀⠀⠘⠁⠀⠉⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⡿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡝⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣏⢿⡙⣿⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⣧⣻⣮⢻⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⣶⣇⢿⣿⣜⣿⣿⢷⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡟⣿⣧⢻⣿⣎⢻⣿⡿⣿⣜⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣿⣿⢷⡜⣿⣷⣻⣿⣿⣿⢿⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡜⣿⣾⣿⣾⣿⣿⣟⢿⣜⢷⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡜⢿⣿⣮⣿⣿⣿⣿⢹⣿⣮⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⢏⢿⣦⣿⣿⢿⡹⣏⢿⣷⣽⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢯⡹⣮⣿⣿⣿⡝⣌⢷⣜⣧⡹⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⢣⡹⣮⣿⣮⡻⣧⠹⣿⣸⣷⣿⣿⡝⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣝⢿⣿⣿⣿⣮⣧⡹⣿⣿⣿⣿⡝⣞⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣏⢿⣿⡟⠛⣿⣿⣿⣿⣜⢿⣿⣹⣿⣎⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠷⠟⠁⠀⡇⣿⡸⣿⣿⣿⢻⣧⣿⣿⣿⣏⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣹⣧⣻⣿⣯⣿⣿⣿⢿⣿⣴⡇⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣿⣿⡿⢿⣿⡟⣿⡇⣿⣿⣿⣿⡸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣿⡸⣿⣇⣿⣧⢹⣿⣿⣿⣧⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣹⣧⣻⣷⣿⣿⣾⣿⡾⣻⣿⣿⣿⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⢿⣿⢰⣿⣿⡇⣿⣿⣿⣿⣿⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣿⣿⣿⢸⣿⢸⣿⡿⣇⢿⡏⣿⣿⣿⡄⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣿⣿⣿⣼⣿⡈⣿⣟⣿⣼⣷⣿⡿⣿⡇⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣹⣿⣿⢻⣿⣷⣿⣞⢹⣿⣿⡟⡅⣿⣿⡜⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⢹⣿⢟⣿⣿⢸⣿⣿⣿⣿⢸⡇⣿⣧⣿⣽⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡰⢄⠈⠀⠀⢀⠀⠀⠅⠑⢶⣦⣄⣀⠀⠀⠀⠀⠀⠈⠀⠀⠰⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⣁⣀⡴⠖⢾⡟⠀⢀⠀⠀⢀⢀⡄
⠀⠀⠀⠃⠦⠈⢱⠚⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠶⠈⠡⠈⢲⣶⠄⣠⠠⣤⡀⢠⡤⣀⣀⣀⢀⠄⣀⣤⠀⠄⠰⡶⠒⠄⠉⠏⠁⢀⠀⠀⠀⠈⠀⠐⠲⠖⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠀⠛⠀⠀⠀⠈⠟⠁⠁⠀⠙⠁⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣈⠻⣤⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣀⡸⠟⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠠⠉⠀⠀⠀⠀⠀⠁⠀⠀⠊⠀⠈⠓⠖⠒⡀⠤⢤⠀⠀⢀⣀⠀⠀⢌⡀⢀⠀⠀⣠⠶⠤⡤⢀⠀⠰⠛⠀⠸⠁⠉⠉⠀⠅⠀⠀⠀⠈⠁⠀⠀⡏⡆
⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠤⠀⠠⡖⢆⠀⠰⣴⡄⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠶⠈⠀⠀⠀⠃⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⣀⠈⠀⠀⠈⠀⠀⠀⢱⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠽⠁⠀⠀⠀⠁⠀⠀⠀⠺⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠘⢶⡄⠀⠀⢀⣀⠀⢀⡈⠰⠆⠀⠀⠀⠁
⠀⠀⢤⣴⠾⠶⠶⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⠀⠀⠘⣛⢂⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢺⠂⠄⠈⠁⡀⠈⠈⠒⢀⣀⠀⠰⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⣤⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠁⠈⡀⠀⠀⠈⠁⠀⠀⠆⠁⠀⠐⠦⡈⠉⢠⠀⠀⠀⠉
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠀⠈⠁⠀⠀⠀⢀⡰⠒⠇⠀⠰⠂⠀⡀⠀⢀⠀⠈⡧⢀⠀⠀⣀⠈⠉⠁⠀⠀⠀⣃⡦⠀⢀⠇⠐⠀⠀⠀⠺⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠈⠋⠀⠀⠀⠀⣀⣷⣄⢈⡧⠀⣧⠈⡷⡀⢨⣦⣀⠀⠀⠀⣠⡝⠀⠀⠀⠀⢀⠤⠈⠀⢠⡦⠀⢀⠀⠘⠛⠅
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⢀⠊⠀⠀⠀⠀⠀⠀⠒⠈⠀⠐⠣⡾⢀⡨⠉⡍⢛⡍⣯⠉⡍⡈⢺⠀⠀⠁⠛⠀⠀⠀⠘⡐⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⢤⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⣇⡘⡄⢀⢁⠉⡍⣀⢠⢀⡁⣸⠀⠀⠀⣀⡀⠀⢀⠟⠀⠀⠀⠰⠆⠘⠇⡀⢀⠀⡀⠌
⠀⠀⠀⠀⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣘⣋⡶⣀⠏⡇⠀⢿⡜⠙⠇⠘⢿⣟⠃⢙⠛⡆⠀⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠆⣁⠘⠀⠀⡀
⠀⠀⢀⠀⠀⠀⠀⠀⠉⠀⠸⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡟⠘⠃⢀⠻⠃⢀⠓⠀⠘⠀⠐⠎⠁⠆⠉⠰⡧⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⣀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢆⠂⠀⠀⡀⠀⠘⠋⠀⢀⠘⠁⠀⠘⠁⠀⠀⠖⠀⠛⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⢢⣶⠱⠀⢿⠎⠀⣀⢠
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢘⢥⠀⡛⠩⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣣⣾⠃⠀⠀⠀⠸⢛⠄⠀⠀⠶⠃⠚⠛⢠⣤⣿⠂⠁
⠀⠀⠀⠀⡀⠀⠄⠀⢀⠀⠀⠀⡠⣤⠀⠀⠀⠀⠘⣞⠀⣟⠢⠤⡉⣀⠒⠀⠀⠀⣀⠤⠤⠤⠐⠒⠀⠀⣈⠔⠀⡀⠀⠀⠀⠀⠀⠀⠚⠠⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠁⠀⠀⠈⠇⠀⠘⠛⠁⠀⠀⠀⡀⠀⠉⠀⢨⠙⠲⢤⣄⣀⣀⡀⠀⠀⠀⢀⡀⠠⠄⠒⠋⣀⠄⠨⢁⣀⠀⠀⠀⠀⢀⣀⠂
⠀⠀⠀⢠⣊⣅⡰⢄⡀⠀⠂⠀⠀⠀⠀⠀⠀⠛⢋⠉⠉⠀⠑⠢⠤⠄⢈⣉⣉⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⢀⠀⠀⠉⠀⡀⠀⠀⠀⠄⠀⡄⠠
⠀⠀⠀⠘⠉⠞⠀⠙⢍⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠠⠄⠀⣰⣆⠀⡀⠀⠀⠀⠀⠠⠊⠀⠰⣤⠶⢎⡛⣠⣀⢠⡄⠀⠀⢈⠀⠈⠱⠀⠀⠠⡄⢸⠀⡇⢀⠆
⠀⠀⢠⡄⠀⠀⠀⠀⠀⠘⠌⡆⠀⠀⠈⠀⠀⠀⠀⢹⠀⠀⠀⠘⠳⠦⠴⠁⣁⣀⣴⣄⠀⠐⠀⠀⢬⣻⢨⣻⣯⢹⣶⢃⡢⠀⠠⠀⠁⢨⠀⠀⠀⡇⢸⠀⣇⢸
⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠾⠿⡧⣥⢿⣼⡇⠀⠐⠐⠒⠐⠀⠀⠀⠁⠈⠀⠁⠈
⠀⠀⠀⠀⠠⠤⠀⠛⠠⠤⠤⠀⠀⠈⠑⣄⡀⠐⠀⠉⠁⠀⠁⠘⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠁⢻⠶⠜⠃⠀⠰⣤⠖⡩⡀⠀⢴⣤⠀⠀⠠⠈⠓
⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢑⠑⡇⠀⠀⠁⣀⠀⢀⡤
⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠉⠀⠀⠀⠀⠾⢗⠀⠀⢤⡀⠀⠀⠀⠀⠄⡀⢸⣦⠀⠀⠈⠀⠀⡅⠀⠀⢀⠀⠑⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠙⠛⠉⠀⠒⠀⠀⠀⠄⠀⠀⠀⠀⠈⠙⠀⠀⠀⡐⠿⠁⠈⠋⠀⠀⠠⠀⠰⠀⠀⠀⠈⠀⠀⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠄⠀⠀⠠⠠⠄⠤⠀⠄⠀⠠⠀⠴⠤⠀⠐⠀⠀⠙⠿⠂⠀⠀⠀⠀⠀⠀⠀⢂⡟⠁⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⢐⡈⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠠⠇⠀⠀⠀⠀⡀⠀⢀⡄⠀⠀⠀⠀⠀⣰⣷⢀⢤⠀⠀⠀⠀⠈⠀⠐⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠠⠀⢠⣿⣄⠂⠈⣦⡰⠙⢄⣾⣝⣻⠀⢸⠀⠀⠀⠐⠀⠂⢀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡝⣿⡿⡿⣄⣰⢿⡟⣤⣿⠟⠻⣿⣦⣼⣿⡿⠒⡇⠀⢀⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣘⠉⠐⣿⣦⣿⣿⣿⣿⡿⠿⣿⣿⣷⠶⢴⣿⣿⣿⣿⣤⣶⣿⣿⡿⠠⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣭⣷⣦⣯⠷⢷⠋⠙⠋⠀⠀⠀⠙⠁⠀⠈⠉⠙⠉⠀⠙⠙⣿⡟⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢻⣛⣛⣿⠁⢀⣀⡀⠀⣠⣤⣤⣀⣴⣶⣤⣰⣶⣤⣶⣆⠀⢠⣟⣛⣟⣛⣲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠟⠀⢾⣟⣿⣿⢸⣿⡿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⡄⠀⠙⣿⣿⢿⣩⣂
⠀⠀⠀⠀⠀⠀⠐⢎⣉⣿⣿⣿⣄⠀⢸⣿⠿⣿⣿⣿⣧⣿⣿⣷⣶⣿⣿⣿⠙⠛⣿⣷⢀⣰⣿⣿⠉⣻⣿⡿⠟⠂
⠀⠀⠀⠀⠠⢶⣿⣿⣿⣋⠉⣽⣽⠃⠈⣿⠷⠿⠟⠙⠛⠛⠁⠉⠉⠉⠉⢁⣀⡀⠉⠀⠀⣿⣿⣿⣺⣍⠙⣄
⠀⠀⠀⠀⠀⠀⠈⠙⡻⢿⣟⡿⣿⠀⠀⡀⠀⢀⡀⠀⠀⢰⣀⠀⣰⢦⣤⡼⣹⣷⣶⣶⣾⣻⡿⣿⡿⣟⣯⡁
⠀⠀⠀⠀⠀⠀⡤⠊⠠⢤⣼⣿⡿⣿⣿⣿⣤⣼⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⢉⢁⣿⣿⣿⣿⡉⢻⠻⠷⡄
⠀⠀⢀⠄⠴⠀⠀⠀⣠⣿⠿⠿⠋⣽⣿⣿⣿⣿⣿⣿⠞⠉⢉⣷⣿⣿⣿⣿⣿⣾⠿⣝⡟⠳⢝⢻⣷⠒⠂
⠀⠀⠣⡀⢀⠀⠀⠄⠉⠀⠀⠓⠁⠹⠴⡟⣻⠟⢻⣝⣦⣤⣯⡟⠹⠿⢋⣿⣻⡿⠀⠉⠀⠁⠀⠙⠿⡇⠅⠀⢰
⠀⠀⢸⡀⠸⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠟⠡⢀⠊⢿⣿⣿⠟⠐⠃⠀⠀⢹⡟⠀⢳⠀⠀⠀⠀⠀⠀⡠⠀⠠⢈⠆
⠀⠀⠀⠉⠳⣀⢀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⣷⠏⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣀⠖⠉

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤⡀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠉⢹⣆⣾⣿⣥⡄⣠⣶⣆⣴⠟⣿⣿⢠⣿⠗⣼⡟⢰⡿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⣇⠀⢸⣿⢈⣿⡿⢰⣿⠗⣻⡟⢠⣿⣇⣾⡿⠰⣿⡇⣿⣃⡜
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢹⣿⡏⢀⣾⠇⠸⣿⡷⠻⠿⠖⠙⠛⠉⠉⠁⠉⠃⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠋⠛⠛⠁⠀⠀⠀⣴⡿⠀⢰⡄⠀⠀⠀⣀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢧⢀⣶⠄⣰⡿⢻⣿⠇⠀⠀⠬⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠓⣾⣿⡿⢰⣿⠁⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣯⡴⠃⠻⠟⠉⢛⣿⣿⢡⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⣀⠀⣏⣾⢃⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⡤⡄⢀⣀⣰⣿⣣⣌⠁⣼⣿⠊⣿⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣸⡿⣰⠆⢹⢡⣿⠟⡟⢹⣿⠏⣠⣿⣷⡾⠛⢡⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣿⣇⣿⢀⠎⢸⣿⡼⠃⠻⠿⠞⠹⢿⠉⠛⠚⢋⡀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⠁⢀⣄⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠈⢁⡀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⣿⡇⢀⡀⠀⣠⣤⣴⡄⢿⣿⣾⡗⣴⡟⢹⣿⠇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠞⣸⣿⣼⡟⢰⣿⠃⡜⣿⣟⣸⣿⢀⣿⣿⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⣿⡟⠀⣿⡿⢿⣧⠾⡿⠞⠀⠛⠋⠀⠛⠋⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠇⠀⠉⠁⠀⡀

⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⢠⡈⠳⣄⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠱⠂⣠⡞⠁
⠀⠀⠀⠀⠱⣄⠈⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢀⡞⠉
⠀⠀⠀⠀⠀⠈⢡⠊⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⠶⣿⠷⢦⡄⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠙⡀
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠈⢿⣦⠀⠀⠀⠀⠀⢸⠃⡀⠀⢀⡀⢿⡄⠀⠀⠀⠀⣠⡾⠋⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠹⣷⡀⠀⠀⠠⢾⠀⠁⠂⠈⠁⣸⢧⠀⠀⣴⡾⠋⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠈⠻⢦⡀⠀⢻⡄⠺⣯⡗⢀⡿⠃⢀⣾⠟⠀⠀⣠⠞⣠⣴⣴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠙⢦⡀⢻⠦⣤⡴⣿⣠⣴⡿⠋⠀⣠⣾⢫⡞⡀⠀⣀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣦⠀⠀⠈⢷⡈⢰⣦⣴⠛⠛⠁⠀⢀⣾⠛⠁⢸⠀⣉⣁⡀⠀⢙⠆⠀⢤⡀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠁⠈⠀⠉⠀⠀⠀⢀⡾⠁⠀⠀⠸⣆⠻⠾⢁⢠⡋⠀⠀⡂⢿⠋⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡀⠀⠀⠈⢓⡖⠉⠸⣀⠀⠀⢹⡄⠀⡼⠁
⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣆⣤⣶⣋⢳⣤⡾⠉⠳⣶⠟⠀⡸⠁
⠀⠘⡕⢦⣄⣏⢳⡀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣻⣿⢋⠀⠀⠀⠙⢿⣿⠀⠤⠤⠄⠒⠒⣲⡾⠁⠀⣼⠃
⠀⠀⠙⣦⡈⠁⠘⣇⡀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⣼⣿⡇⢠⡄⡄⢠⡦⠸⣿⣿⡆⢒⣛⣛⣻⠏⠀⢀⡾⠃
⠀⠀⠀⠈⠙⠶⣤⡈⠛⠷⣤⣄⡀⠀⠀⢿⣇⠀⠀⠀⣿⣿⡇⠈⠁⠀⠀⠀⠀⢻⣿⡏⣉⣁⣼⠏⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠉⠛⠷⣦⣸⣿⠲⢤⣀⣙⢿⣿⡀⢿⣥⣽⠃⣰⣿⠟⢀⣠⡿⠃⠀⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠙⠿⣧⣤⣀⣀⠀⠉⠳⣄⣉⣡⢴⡏⠀⣴⣿⡋⠙⢦⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⡀⠀⡿⠙⢻⣿⣷⣦⣼⠉⠁⢘⣧⣾⣿⣿⣿⣦⡾⠋⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⢧⣠⣿⣿⣿⣿⡏⠛⣶⠛⠀⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠉⠻⣿⣿⣿⣷⣾⣿⣷⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠈⠙⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠉⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⢿⣿⣿⣿⡿⣿⣻⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣾⣹⣷⣿⣷⣾⣿⣿⣿⣿⣿⣭⣿⣽⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣻⡟⣿⢻⣻⣿⡏⡟⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⡿⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣾⣿⣿⣿⣻⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣼⣿⣽⣿⣿⣷⣿⣽⣿⣿⣿⣿⣿⣿⢿⣿⣿⢿⡿⣿⢿⠿⡿⣿⣿⠯⢿⣿⣿⣻⣽⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣇⢻⣿⢸⡣⣿⣿⡇⣿⣿⣟⣻⣻⣿⣿⣿⢽⣿⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣶⣿⣾⣷⣿⣿⣶⣿⣿⣿⠶⣿⣿⣿⡯⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣹⣟⡏⣯⣻⣟⣻⣯⣟⣿⢏⣿⣜⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢠⣿⠿⣛⣛⠻⣿⣟⢛⣛⡿⣿⣿⡛⢛⣛⡛⣿⣿⣿⡿⠻⣿⣾⠗⣛⡚⢚⡛⢿⣟⠛⣿⣟⠛⣿⣿⣟⢛⣿⡛⢛⣛⡛⣷
⠀⠀⠀⠀⠀⢸⠃⣾⣿⣿⣷⣿⣿⠸⡿⢇⣼⣿⡇⠸⠿⣿⣿⣿⡿⣱⣇⢹⣿⣿⣿⡇⣿⣿⣿⣿⠀⣿⣿⣆⢹⣿⢏⣾⣿⡇⠸⠿⣿⣿
⠀⠀⠀⠀⠀⢸⡄⢻⣿⣿⡿⣿⣿⢰⣷⡌⢿⣿⡇⢸⣿⣿⢿⡿⢣⣶⣶⡄⢻⣿⣿⡇⣿⣿⣿⣿⠀⣿⣿⣿⡄⠛⣼⣿⣿⡇⢸⣿⣿⢿
⠀⠀⠀⠀⠀⠘⣿⣷⣾⣿⣾⣿⣷⣶⣿⣿⣦⣿⣶⣶⣶⣶⣾⣷⣾⣿⡿⠷⣶⣿⣿⣶⣾⣿⣿⣷⣶⣾⣿⣿⣿⣾⣿⣿⣿⣷⣶⣶⣶⡞
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠶⣾⣿⣿⣿⣟⣛⣻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣖⣿⣿⣿⡿⠿⣷⡾⢿⣿⣿⡇⠮⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣭⢽⣿⣟⣿⣿⡿⠯⣿⣿⣿⣟⣛⣻⢸⡿⣿⣿⣟⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣻⣿⣟⣿⣿⣟⣿⣿⣿⣽⣏⣛⡛⢻⣶⣿⣿⡿⣭⣽⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣗⣺⣿⣿⣿⣿⣿⣷⣿⣿⣿⣯⡿⣛⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣿⡷⢾⣿⣾⣿⣿⣿⣇⣙⣻⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣯⣷⣿⣿⣿⣿⣛⢛⣹⣿⣿⣷⣦⣭⣹⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣾⣿⣿⣿⣧⣮⣭⣽⣛⣻⣿⣿⣿⣿⣶⣾⣷⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣭⣋⣽⣿⣿⠿⠿⠛⠋⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢉⡉⣿⠟⢿⠻⣟⣿⢿⡿⠟⡿⢿⠿⣿⡟⣻⢿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠔⣒⠃⠈⠥⣒⣂
⠀⠀⠀⠀⠀⡀⠰⡀⠀⢀⠄⠈⠔⣚⡠⠈⣡⠤⠀⡀
⠀⠀⠀⠀⢠⡘⢆⠉⠀⠚⢉⠤⠤⠀⣀⡀⠐⣊⠭⠋
⠀⠀⠀⠈⢢⡑⠀⠀⠀⠀⠀⠒⣉⠀⣀⣅⣁⠠⢒⣩⢥⣄
⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠒⣃⠘⠋⣁⡁⠀⠩⠴⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣄
⠀⠈⠙⠓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠵⠒⠀⠐⡶⠔⡤⢖⣛⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⣀⣇⠘⠘⠘
⠀⠤⠤⡷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠴⣐⠚⠋⠀⢀⣒⣂⣀⠀⠀⠀⠀⢀⠀⢠⠸⡄⠣⠉
⠀⠚⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠭⠶⠀⣀⣉⡀⠲⠶⠂⣀⢰⠀⠀⢣⡈⠣⠉
⠀⠘⠓⠂⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢛⡓⠀⢰⡀⣶⡀⣼⠸⡀⢻⠀⠁
⠀⠀⠀⣀⠄⠠⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡄⠳⣄⠁⢸⠅⠸⠀⠑
⠀⠀⠀⠀⠫⠄⡀⠞⢁⠴⣠⢦⢤⠄⠀⢀⡀⡆⢰⠃⡇⢱⡀⠈⠃⣠⠤⠀⠠⠤⠔
⠀⠀⠀⠀⠀⠊⡰⠂⣨⢄⢁⡁⠁⠀⢀⣸⠀⡇⢸⠘⡇⠀⠓⠀⠈⣀⣙⣒⡂⠀⢉⡡
⠀⠀⠀⠀⠀⠀⠀⠘⠁⠃⠞⠀⡎⠮⠋⢿⠀⠇⠀⠃⠀⠀⠐⠚⣍⡀⠈⠥⠶⠄⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢐⣂⠐⠋⣀⣒⡊⠔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠬⠄⠈⠭⠴⠂⠀⠒⣛⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢖⣂⠈⠉⠉⣐⠉⠠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢚⣃⠉⠭⠅⠀⠀⠴⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣀⠀⠉⣀⣀⠐⠒⠦⠄⠰⠖⣋⣀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠠⠀⣴⠂⠐⣠⢀⠤⡄⣤⠀⢀⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠰⠇⠸⣇⠀⢀⠀⠀⢁⣀⡀⣿⡆⢰⠇⣿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡆⢻⡄⠸⡆⠀⣾⠁⠠⢿⡤⠋⠀⣿⠁⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠙⡂⠁⠈⠟⠀⠱⠀⠸⡆⠄⠸⠈⠂⠂⠿⠀⠑⠀⠇⡤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠾⠁⣶⠐⠀⣶⠀⠀⣶⠀⠀⣶⠓⢦⠀⣶⠒⢦⡂⠐⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣿⠀⠀⣿⠀⢠⡇⠀⠀⣿⠀⣸⠁⣿⠀⠀⣿⡀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣐⠀⠀⢿⠦⠀⣿⡀⣸⣃⣀⡌⢻⡴⠋⠀⣿⠀⠀⣾⠣
⠀⠀⠀⠀⠀⠀⠠⣄⡳⠈⠀⠂⢸⠀⠀⢸⠁⣿⢀⠀⠀⢸⡟⢦⡀⢿⣠⢴⣣⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⣠⠆⣠⡀⠀⣈⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠙⠳⠾⠛⠋⠀⢔⠓
⠀⠀⠀⠀⠀⠀⠀⢠⠎⢹⡇⠈⠈⣷⡘⣅⠀⠀⢀⣤⠀⠀⣠⠅⣶⣠⠐⢻⡄⢀⠸⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⡏⠀⠀⣿⣇⠀⢹⠆⣿⢀⠆⣾⡇⠀⡟⣻⡆⠸⣧⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⡇⠀⢴⡿⠁⠀⣿⠀⣿⣀⡀⢿⣇⡜⢣⠻⠃⠀⠁⠀⢻⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢁⣠⠟⠁⠀⠀⠈⣁⡈⠉⠀⠀⠀⠐⠈⠀⠀⠀⢁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠉⠁⠀⠀⢼⡇⡐⠀⣷⢀⣀⡀⢠⡞⠉⠂⠀⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⡅⠀⢸⠁⢸⡷⢀⡼⠃⠈⠻⠁⣿⠀⠀⡀⢸⠈⠷⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠻⠀⠀⢸⡟⠀⠈⣷⡤⣿⠀⣿⠀⣀⡀⠈⠀⠀⠘⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⢧⠔⠁⣿⠇⢿⠀⣿⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢠⣀⡴⠋⠀⠈⠋⠈⠧⠠⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⣿⣿⡿⣹⣿⢩⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣾⡟⣼⡇⣿⡇⣿⡇⣿⣿⣿⢟⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢀⣠⠤⣶⡶⣶⡖⣿⣿⡇⣿⣇⣿⣷⢿⣼⣿⣷⣿⣿⣿⣿⡿⣱⣾⢟⡀
⠀⠀⠀⠀⠀⠀⢀⣴⢲⡶⣿⡹⣿⣿⣿⣿⣿⡆⣿⡇⣿⡇⣿⣿⣷⣿⣿⣿⣿⣾⣿⣿⢿⣿⡇⡿⣻⡿⠻⣷⢟⣿⣄
⠀⠀⠀⠀⠀⣴⣷⢹⡎⣧⢻⣧⠹⣿⣿⣿⣿⡇⣿⣿⢹⣿⢸⣿⣿⡟⣿⡟⣿⣿⣿⣿⢸⣿⢸⡇⣿⡁⠀⠈⠙⠻⠛
⠀⠀⠀⠀⢠⣟⢿⡆⢿⡜⣷⣿⣧⠹⣿⣿⣿⣷⣿⣿⡏⣿⣇⣿⣿⣷⢸⡇⣿⣿⣿⣿⣸⣿⡞⣷⣿⣷⡀
⠀⠀⠀⠀⢸⢻⡎⢿⣮⢿⣾⣿⣿⣧⢻⣿⢿⣿⣿⣿⣿⣿⢿⣾⣿⣿⡇⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⣷⡀
⠀⠀⠀⠀⠸⣧⡙⣿⣿⣿⣿⣿⣿⣿⣸⡇⣿⣇⣿⡿⣿⡿⣼⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⢟⣟⢸⣿⣧
⠀⠀⠀⠀⠀⢻⣿⣼⡇⢿⣿⣿⣿⣿⣿⢿⣿⣽⣿⡇⣿⣧⣿⣿⣿⣿⣿⢻⣿⡿⢸⣿⣿⣻⡏⣾⣿⢸⣿⣿⡆
⠀⠀⠀⠀⠀⠸⣿⣿⠀⣼⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇⣿⣼⣧⢸⣿⢿⣿⣿⣿⣿⢸⡟⣿⡇
⠀⠀⠀⠀⠀⠀⠙⠃⠀⢻⡇⣿⣇⠁⣿⣿⣿⣿⣿⣿⣿⣿⢹⣿⡿⣸⣧⣿⣿⣿⣾⢇⣿⣿⣿⣿⣿⣾⢣⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⢹⣿⢸⣿⣿⣿⣿⢟⣿⡇⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡟⣹⡟⣻⣿⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⢿⣾⣿⣇⢹⣿⢸⣿⣼⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣼⣿⣷⣿⣷⣿⣟⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣿⣿⣿⣸⣿⡔⣿⡿⣿⢸⣿⢇⣿⣿⢰⣿⣿⣿⣿⡿⣻⣿⣿⣿⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⢿⣿⣷⣿⡅⣯⣿⣿⡞⣿⣿⣿⣿⣿⣿⣿⢣⣿⢿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⢸⣿⣿⢹⣷⣿⣿⣿⣿⣿⢛⣿⣿⡟⣿⣿⢸⣿⢸⣿⢟⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⣿⣿⣾⡟⣻⣯⢿⢏⣿⢸⣿⢹⣇⣿⣿⢸⣿⣿⢏⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡇⣿⡏⣾⣾⣿⣸⣿⣿⣿⡿⣻⣿⣿⡟⣾⣿⢿⡟⣴⡇⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⢻⣿⣿⣿⣿⣯⣿⣏⣿⡇⣿⣿⢹⣷⣿⣿⣾⣧⣿⡇⣿⢿⣶⢶⣶⣶⠶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⣿⣿⡿⣿⡏⣿⣿⣿⣽⣿⣿⣿⡇⣿⣿⣾⣿⣿⣿⣿⣿⣿⣇⣿⢸⣏⣾⡟⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣿⣿⣯⣧⣿⣇⣿⣿⣿⣿⣿⣿⣿⣷⣿⢏⣿⣿⣿⣿⣿⣿⣿⣾⣿⣸⣿⣿⢣⣿⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢠⠀⠀⢰⠛⠱⡀⠀⠀⠀⠀⠀⠔⠀⢢
⠀⢀⣤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡆⠀⢸⠀⠀⢱⠀⠀⠀⠀⡘⠀⠀⢸
⠀⢸⢁⠀⠠⢌⠳⡄⠀⠀⠀⠀⢀⠤⠒⠉⠉⠈⠉⠑⠠⡀⠸⡴⣚⠧⢀⠼⣴⢤⣸⡀⠀⠀⢀⠃⠀⠀⡌
⠀⠈⢮⡈⠁⠀⣹⣼⣆⠀⠀⠰⠃⠀⡀⠀⠀⠀⠈⠀⠀⠈⢆⠹⡀⢀⠀⣀⠈⠓⠺⡇⠀⠀⢸⠀⠀⢸⠁
⠀⠀⠀⠑⣤⠀⣩⡅⠈⢆⠀⡅⠀⡀⠀⣠⠔⠢⣄⠀⠈⠀⠘⡀⠈⢦⠀⠀⠀⠉⢀⡇⠀⠀⡧⠂⠀⡎
⠀⠀⠀⠀⠈⠻⡻⣠⣤⣼⡄⡇⠀⠁⣰⠃⠀⠀⠈⡆⠀⠄⠀⡇⠀⠀⢏⠀⠀⠀⠨⠇⠀⢸⣣⡠⣰⠁
⠀⠀⠀⠀⠀⠀⠙⡟⠿⠟⢃⢸⠀⠀⠜⢦⡀⠀⡰⠁⠂⠆⢠⠁⠀⠀⢸⣤⣤⣍⣸⠀⠀⣇⣈⣍⡏
⢀⡤⡀⠀⠀⠀⠀⢸⡄⢒⢻⠀⢃⠀⠠⠀⠈⠉⠀⠠⠂⢀⠎⠀⠀⠀⠤⠸⠿⠿⠇⠀⠘⠯⠿⡾⠁
⣏⠀⠈⢂⠀⠀⠀⡸⠁⠀⠉⠀⠀⠳⢄⠀⠀⠀⠀⣀⠔⠁⠀⣀⠴⠚⠫⢲⡵⠃⠀⢀⣤⢬⡉
⠱⡀⠀⠀⡱⣲⢾⡅⠀⢠⠁⠀⠀⠀⠀⠉⠉⠈⢉⠔⠒⠊⠉⠀⠀⠀⣠⠞⠀⠀⢰⠁⢿⡄⢸
⠀⠑⠤⢀⡇⢘⠂⢉⠷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⠀⠤⠔⠊⠀⠀⠀⠀⠈⠢⠿⠧⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠑⢦⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠈⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢠⠀⢀⠅⠀⢠⡣⠖⠛⢳⡤⠠⣄⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠹⡄⠀⠈⠀⠁⠀⡠⠺⡀⠀⠀⠧⠜⠀⠸⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠈⠓⠦⠐⠒⠋⠀⠀⠳⣄⠀⠀⠀⣀⠜⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣠⡉⠛⠉⠁⠀⠀⡰⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣤⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⡼⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡸⠀⢰⡆⣿⡀⠀⣿⠀⠀⣼⠂⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠴⣰⠀⠀⢈⣛⢶⡌⡇⢸⡇⠀⣿⠀⠀⠿⠔⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢈⠉⢀⠀⣞⠛⠈⣷⠟⠸⠧⠤⠏⠉⡉⠄⠂⡿⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⢀⠀⠘⠦⠔⠁⠀⡇⣆⠄⠀⡀⠀⠀⣰⠇⢤⣀⣀⣸⡇⠤⠐⠂⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡠⠂⠀⢠⠊⠑⡀⢀⠁⠠⡄⠀⢘⣶⡚⢉⡴⠒⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠊⠄⣷⠀⣸⠂⠠⠇⣿⡄⢠⡇⢀⡾⠠⠂⠘⠷⣤⡀⢰⡏⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⡟⠀⠻⠤⠚⠀⠻⠁⢸⡇⠘⢧⣀⠔⠁⠀⢈⡇⠸⡇⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣦⠀⡟⠀⣇⢠⢠⠎⠀⠱⠀⠀⠘⣧⡇⢠⣡⢰⠀⢀⡜⠀⢢⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠻⠆⣾⠀⠠⠀⠀⣤⠀⠀⠠⣜⠀⠛⠀⣸⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠂⠀⠀⠀⠀⠀⣿⠐⠓⡆⢰⡇⠀⣷⠀⣼⠀⢀⠄⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣴⡞⠁⠸⣇⠜⡿⠀⣿⠀⣿⡀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⣷⠀⠀⠀⠀⠃⠀⢿⡘⠉⠀⠘⢧⡐⠀⠀⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣤⠀⢀⡤⠶⠒⠾⠥⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠢⡔⠁⠀⡆⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⢠⠁⢠⠈⠹⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠉⡠⠃⠀⠘⣄⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠊⠀⠀⠀⠀⠈⠙⠒⠁

⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⣠⣚⢢⠀⠀⠀⠀⠀⣷⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⢧⠀⠀⠀⠀⢀⠼⣁⣪⠉⠀⠀⠀⠀⠶⠿⣿⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠻⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⡛⢄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣵⠃⠀⠀⠀⠀⠀⠀⣠⣜⠣⠙⠋⠀⠀⠠⠒⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡙⡅⠀⠀⠀⠀⠀⠀⠀⠛⠁⠙⠁⠀⠀⠀⠐⠄⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠀⠀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣱⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡧⠄⠀⠀⠀⠀⡠⠢⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠈⠈⠃⠀⠀⠀⠀⠀⠀⠈⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡂⣣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠠⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠢⣀⡀⠀⠀⠠⢄⠚⠈⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣄⠀⠈⠒⡤⠂⢄⠀⠀⠀⠀⠀⠀⣶⢑⣈⡄⠛⠁⠀⠀⠀⠀⣥⠐⠺⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠉⠢⡀⠀⢄⣀⣴⠀⠀⠀⢴⡙⣄⣨⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⢙⣄⠀⠀⠀⠑⢶⡑⣤⡥⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⢠⣾⠉⠨⠿⠁⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⣰⣿⣿⣷⣄⠀⢠⣶⡷⡉⠀⠀⠀⠀⡊⠀⢐⠀⠀⠀⠀⠤⣾⠇⠀⠙⠁
⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⣠⣾⣿⣿⣿⠿⠋⠉⠢⡀⠀⠈⢆⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⣼⡟⠀⢀⣴⣿⣿⡿⠟⠁⠀⠀⣀⣤⣾⣷⣦⣤⠇
⠀⠀⠀⠀⠀⣸⡟⠀⣴⣿⣿⠟⠋⠀⢀⣠⣴⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⢰⠟⣠⣾⡿⠛⢁⣠⣴⣾⡿⠟⠛⠉
⠀⠀⠀⢠⢏⣼⠟⣋⣤⡶⠟⠛⠉
⠀⠀⢀⣿⡿⠷⠛⠉
⠀⠀⠈⠁

⡿⢿⠿⠿⡿⠻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⢿⣿⣿⡿⣿⣿⢿

⠀⠀⠀⠀⣀⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⣄⡀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀
⠀⠀⡠⠊⢱⠤⠒⠒⠈⠙⢆⠀⠀⠀⣰⣿⡘⣯⣵⣶⣶⣶⡄⠀⠀⢀⢾⡁⠀⢀⡤⠤⣌⢢⡀⠀⢠⡸⣿⣿⠿⣛⣿⡛⢦
⠀⢠⣇⠀⠀⠣⣀⡠⠤⣄⣈⡆⠀⠐⢿⣿⣷⣝⠿⣟⣛⢛⡿⠀⠀⡎⠀⠉⠉⠁⠀⠀⠀⢣⠇⠀⣿⣿⣶⣶⣿⣿⣿⣿⡎⡇
⠀⠘⡏⠣⣄⢀⡎⠀⠀⠇⢀⠇⠀⠸⣮⡻⢿⡿⣸⣿⣿⣸⣿⠀⠀⢇⠀⣀⣀⡀⠀⠀⠀⡜⡆⠀⣿⣿⠿⠿⣿⣿⣿⣿⢇⡇
⠀⠀⠙⢄⣨⠏⠀⠀⣼⡠⠊⠀⠀⠀⠙⢿⢗⣵⣿⣿⢇⡿⠃⠀⠀⠈⠻⣀⠀⠈⠙⠒⣫⠜⠀⠀⠈⢵⣿⣿⣶⣭⣯⣥⠞
⠀⠀⠀⠀⠉⠑⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉
⠀⠀⠀⣠⡶⠓⠀⠺⣶⣤⠀⠀⠀⠀⠀⠀⣠⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢦⣀⠀⠀⠀⠀⠀⠀⣠⣴⣤⡙⠻⣦
⠀⠀⠈⠁⢀⣤⣤⡆⠀⠉⠀⠀⠀⢀⣾⣿⡟⠛⠛⣿⣿⣾⣧⠀⠀⠀⠀⠀⠀⠀⣠⡦⠙⢷⡄⠀⠀⢀⣾⣿⣿⠏⢙⣷⣌
⠀⢰⣦⠀⠸⢿⡿⠇⠀⣠⣶⡆⠀⠈⠻⣿⣅⡀⢀⣽⣿⠟⠙⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⢀⣾⣿⡿⠁⣰⣿⣿⠏
⠀⠀⠿⠀⠀⠀⠀⠀⠀⠸⠿⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠘⢦⣀⠙⠁⠀⠀⠀⠀⠀⠀⢈⠻⣿⣤⣾⣿⣿⠏
⠀⠀⠀⠀⠐⢾⣿⡶⠁⠀⠀⠀⠀⠀⠀⠙⠏⠁⠈⠹⠟⠉⠀⠀⠀⠀⠀⠉⠳⠦⠀⠀⠀⠀⠀⠀⠘⢷⣦⡉⠻⠛⠁

⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⣴⣶⣷⣶⣦⡀⠀⠀⠀⠀⢀⡤⠂⠈⠀⠒⢀⡀⠀⠀⠀⢀⢰⣶⣿⣷⣶⠄
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠠⢁⠇⠀⠀⡴⠚⠉⠑⡀⠀⣰⡇⣾⣿⡿⢫⣴⣾⣷⡀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣟⣿⣿⣿⣿⣿⣿⠀⠀⣧⡞⠀⠀⢸⠁⠀⠀⠀⡁⠀⠛⣼⣿⣿⠅⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣯⣿⣿⣿⣿⣿⠟⠀⠀⠸⡀⠀⠀⠸⡄⠀⠀⢠⠃⠀⠸⣿⣿⣿⡅⢿⣿⣿⡿⠁
⠀⠀⠀⠁⠀⠠⠀⠀⠐⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠛⠉⠀⠀⠀⠀⠈⠂⠄⠀⠉⠶⠒⠁⠀⠀⠀⠈⠻⠿⢿⡦⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆
⠀⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⣲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠄
⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠉⣀⡠⠄⢀⡀⠀⠀⠀⢀⣿⣧⢀⣀⣀⣀
⠀⠀⠈⢿⢆⠀⠀⠀⠀⡀⠀⠀⠀⠙⣤⡀⠀⠀⠀⣀⣠⣤⡀⠀⠀⠀⠈⢀⠞⠁⠦⡀⠀⠈⢢⠀⠀⣾⣟⣵⣿⣹⢿⣿⣷⣄
⠀⠀⠀⠀⢂⠁⠒⠈⠁⣔⠀⠉⢐⡄⠘⣿⣶⣶⣿⡟⠽⣷⣶⣶⠦⠀⠀⢸⠀⠘⠂⠉⠀⠀⠀⡇⠀⢿⢹⣿⣧⣿⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠢⠀⢀⣀⡁⠤⠀⠀⠀⠀⠘⠿⠿⠿⠷⠽⠟⠛⠛⠉⠀⠘⢌⣄⠀⠀⠀⠀⢀⡔⠀⠀⠘⠯⢿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠉⠀⠀⠀⠀⠀⠀⠉⠛⠛⠉⠁
⣟⣿⣻⣻⣛⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣛⣿⣿⣛⣛⣟⣿⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡐⠂⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡀⠀⠀⠀⠒⠐⠓⠂⠀⠠⠀⠀⠀⠀⠀⠠⠁⠀⠀⠉⠉⠉⠉⠑⡂
⠀⠀⠀⠀⠀⠀⠠⠤⠀⢀⠀⠀⠀⠀⠀⠠⠀⣠⠤⠀⠀⠠⠤⡄⠱⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⣧⠀⠀⠀⠁⣀⣀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⣀⣬⡅⠀⠸⠗⢀⠆⠈⠟⠀⠀⣯⢤⡀
⠀⠐⠒⠀⠀⠁⠀⠀⠉⠀⠀⢠⠀⢇⠈⢧⠀⠀⠀⣎⣀⡀⠀⠀⢀⡿⢁⠇
⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠘⠀⠈⠑⠚⣆⠀⠀⠀⢭⠤⠄⠀⡸⠓⠉
⠀⠄⡀⠀⢀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠐⠒⢒⠶⠖⠀⢒⠆⠀⠀⠀⠀⠀⠀⠈⢻⠶⠶⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⢀⣠⣤⠉⡀⠤⣄⠖⠲⢤⡀⠀⠀⠀⠀⠀⠁⣄⠒⠒⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⢀⠴⠋⠁⠀⠈⢢⡀⠉⠀⠀⠀⠉⠳⢄⠀⠀⢀⡠⠁⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠈⠙⠁⠀⢰⠀⠀⠀⢀⠀⠀⠀⠀⣤⡀⠀⠀⠱⡖⠁⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠶⠚⢻⠀⠀⠀⢸⠀⠀⠀⠀⣿⠙⠲⢤⣄⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢸⠀⠀⠠⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠘⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠒⠐⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣠⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢠⠇⢳⡀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⢀⡟⠀⠀⠻⣄⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡞⠀⠀⠀⠀⠘⢦⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⢤⠎⠀⠀⠀⠀⠀⠀⠀⠐⡉⠅⠒⠂⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⣶⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⡇⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠘⠋⢹⣿⠉⠃⣸⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢀⡜⢻⡇⠀⠉⠀⢠⣄⠀⣄⠀⠀⠀⠀⣿⡃⠀⠀⠘⣿⠀⢀⣤⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡟⠉⣷⠀⣴⠛⠦⠀⠀⠀⣸⡏⢱⣄⠎⠀⢸⡇⠀⢹⡇⠀⣿⠃⢸⡧⠀⣴⠖⣿⠃⠀⠀⠀⣿⡄⠸⣧⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⣿⠀⣿⠀⠀⠀⠀⠀⣿⡇⠈⠋⠀⠀⢸⣿⠀⣿⡇⠀⣿⠀⢸⣧⠸⣿⠀⣿⡁⠀⠀⠀⢸⡇⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠀⠀⠚⠋⠀⠛⠁⠈⠓⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⠛⠀⠀⠀⠀⠈⠉⠙⠁⠀⠀⠀⠈⠉⠞⢁⡿⠁

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠙⣀⡀⠀⢀⣀⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⠀⠀⣀⣿⡀⠀⣿⠀⠀⠀⠀⠛⠀⣀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢹⣇⠀⡘⢁⣴⣳⡄⢹⣿⠀⠿⢤⣤⠀⢀⡄⢸⣟⠀⠀⣿⡟⢻⡆⠀⣿⠂⢸⣿⠋⢻⡆⢰⡟⠛⣶
⠀⠀⠀⠀⠀⠀⠀⣿⡗⠺⠂⠀⢻⣶⠁⢸⡏⠀⠀⠸⣿⠀⠀⠀⢻⣄⣾⠀⠸⣿⢀⡀⣿⡇⢸⣿⠀⣿⡇⢸⣿⠀⢸⣇⠈⠛⢿
⠀⠀⠀⠀⠀⠀⠀⠿⠃⠒⠶⠀⠈⠉⠀⠈⠛⠖⠂⠘⠛⠀⠀⠀⠀⣻⠇⠀⠀⠻⠬⠃⠿⠃⠠⠟⠀⠉⠁⠸⠟⠀⠈⢠⡶⠃⠛⢇⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠂⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⣠⡀⠈⠉⣿⠀⠀⠀⠀⠀⢀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⢹⡇⠀⠀⣿⠘⣦⠐⠛⣦⠘⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⢿⠀⠀⣿⠀⣿⠐⠻⣿⠈⣧⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⡴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡼⠃⣤⢄⠀⣤⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⠧⠜⠠⣏⡸⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⡄⠠⣿⠀⠀⠀⠂⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠖⣶⠀⣶⠈⣷⠙⡆⢸⣇⡐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⣿⡄⣿⠀⡿⠀⣷⠀⠷⢸⡏⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣼⠃⣀⢀⠀⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⢧⠸⠐⣟⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠆⠀⠀⠀⠀⠉⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡖⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣼⠃⣠⡀⢀⡔⢦⣰⠖⣆⢰⣄⣤⡄⢢⡀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣸⠇⣿⠀⠙⣦⠀⠈⠓⠉⢘⡏⠸⠃⢸⡇⢿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀





⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡏⠁⠈⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣾⣶⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢰⡄⠀⢀⡀⢠⠀⠀⠀⠀⠀⠠⠖⡲⢦⡀⠀⠀⠀⠠⡊⢳⣿⣿⣿⡏⢑
⠀⠀⠀⠀⣤⣷⣿⠇⠀⠀⠀⠀⠀⠈⢃⠀⣾⡿⠟⠀⠀⠀⠀⣈⠂⠜⢠⠃⢽⠀⠀⠀⠀⠙⠺⣿⣿⣿⠗⠁
⠀⠀⠀⠘⣿⣿⣿⡆⠀⠀⠀⠀⠠⣶⣾⡟⢀⣤⡀⠀⠀⠀⠀⠘⢕⣒⣣⡈⠎⠀⠀⠀⠀⠀⠀⢉⣿⠁
⠀⠀⠀⠀⠘⠿⠛⠁⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛

⠀⠀⠀⠀⢀⠀⢀⣤⡄⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⢀⡀⠀⠀⠀⠀⣰⣧⡂⠀⠀⠀⠀⠀⢠⣤⡄⣀⡀
⠀⠀⠀⠀⢨⣿⣿⡿⠋⠀⠀⠘⢟⢿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⣰⣿⡣⣹⣦⡄⠀⠀⠀⢻⣿⣧⣿⡿⣦
⠀⠀⢀⣴⣿⣿⠏⠀⠀⠀⠀⠀⠀⠻⡟⠉⠉⠉⠀⠀⠀⠀⠀⠰⢟⣱⠿⢛⠁⠀⠀⠀⠀⠀⠻⣿⣿⣿⣾⡥
⠀⠀⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠞⠋⠓⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁

⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⢀
⠀⠀⢀⡈⣶⣷⠆⢳⡀⠀⠀⠀⢀⡤⡴⠗⠳⠤⢤⠄⠀⠀⠀⢠⣿⢃⡼⣭⣤⠀⠀⠀⠀⠀⣼⡙⣎⣣⠶⣀
⠀⠀⠘⢇⣈⠉⢰⣶⠀⠀⠀⠀⠀⠙⣷⠀⠀⣴⠃⠀⠀⠀⠀⠰⣟⣶⣽⣷⡝⠀⠀⠀⠀⡼⠡⠗⢉⣤⠶⣉⡄
⠀⠀⠀⠈⠛⠃⠈⠁⠀⠀⠀⠀⠀⠰⠿⠛⠛⠾⠀⠀⠀⠀⠀⠀⠈⠛⠓⠉⠀⠀⠀⠀⠘⠀⠀⠀⠀⠉⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣟⡿⣶⠄⠀⠀⠀⠀⠀⠘⣿⠇⣴⡿⠃⠀⠀⠀⢐⣴⣿⠟⢻⢹⣿
⠀⠠⠞⠋⡳⠤⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡋⠀⠀⠀⠀⣶⣿⣿⡾⠋⠀⠀⠀⠀⠀⣾⢏⠘⡐⣼⡼⡋
⠀⠀⠀⠀⠁⠢⢈⠗⢦⡄⠀⠀⠀⠀⠛⠛⠟⠃⠀⠀⠀⠀⠀⢻⣿⣿⠟⠀⠀⠀⠀⠀⠀⠿⠦⠾⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣟⣿⣿

⠀⠀⢀⡀⠀⡀⠄
⠀⠀⣀⠀⠀⠂⢠⡔⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠒⠀⡀⢤
⠀⠈⢹⠀⠸⡇⠘⠁⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢲⡘⠀⠞
⠀⠐⠀⠀⠀⠤⠄⣠⡁⠄⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢴⡄⠈⠋⠠⠖⠐⢀⠖
⠀⠀⢣⠀⠀⠀⠀⠀⠁⡰⠶⠾⠀⠀⠀⠀⠀⠰⣶⠀⣀⠀⠐⣀⠀⠶⠄⠠⢆⠀⠀⠀⠀⠈⠓⢦⠀⢥⠀⠀⠀⢀⠻⢦⡀
⠀⠀⠀⠓⣤⡀⠀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠘⠀⠀⠁⠀⠀⠞⠁⠈⣃⠀⠀⠀⠀⠀⢸⡀⠀⠙⠀⠀⡜⠁⠒⠛
⠀⠀⠀⠀⠀⠹⠂⠸⡄⠀⠀⠀⠀⠀⠀⢀⠰⠎⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣐⠆⠀⠀⠀⢱⠄⢀⡠⠴⠁
⠀⠀⠀⠀⠀⠀⣧⠀⢿⡀⠀⠀⠀⠀⠀⣘⡷⠄⠚⠓⠂⠘⠛⠒⠤⣀⠀⠀⠀⠀⢞⠁⠀⠀⠀⡰⠃⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠙⡄⠘⣧⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠳⢄⠀⠀⠈⢓⠀⢀⡞⠁⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⢃⡀⢘⣄⣠⠏⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⠀⠀⡀⠀⠈⠆⠀⠀⣸⣄⠎⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⢰⡞⠉⠉⢹⠇⠀⠀⠀⠀⠀⠊⠁⠙⠀⠀⣀⡤⠚⡁⠀⠀⠸⠀⠀⣿⠏⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⡎⠀⠀⠀⣤⣤⠤⠤⠤⠔⠒⠋⠁⣠⣼⡇⠀⠀⠐⠓⢶⣟⡀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⡇⠀⠀⠀⢻⣿⣄⣀⣤⣤⠤⠚⠛⢻⡟⠀⠀⠀⢦⡤⠎⠀⠙⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⢰⠀⠀⠀⠈⢿⣿⡿⠿⠇⠀⠀⣸⠋⠀⠀⠀⢠⠟⠀⠀⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⢳⡀⠀⠀⠀⠙⠓⠀⠴⠖⠊⠀⠀⠀⢀⣴⠋⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠙⠢⣄⣀⡀⠀⠀⠀⠀⢀⣀⣤⠶⠋⠀⠀⠀⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⡇⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠉⠉⠉⠉⠙⠛⠒⠒⠢⠤⠤⣄⣀⣀⣀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢻⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠰⡆⠀⠀⠀⠀⠰⠒⠒⠂⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠉⠉⠉⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠈⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢣⡀⠀⢀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠉⠁⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣤⣤⣤⣤⠤⠒⣇⣀⣀⠀⠀⠀⠀⠀⠀⢀⣸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⡄⠀⠀⠉⠉⢹⠉⠉⠚⠟⠓⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠇⠀⠀⠀⠀⠸⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣰⠀⠀⠀⠀⠀⠀⣧⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠉⣳⠀⠀⠀⠀⣠⠜⠁⠀⢠⡄
⠀⠀⠀⣀⠀⠀⢀⣤⠔⠊⠁⠀⠀⠀⢻⣀⠠⠔⠊⠁⠀⠀⠀⢸
⠀⠀⢘⠁⠄⢀⣈⣃⣀⣀⠀⢀⡠⠛⠊⠉⠣⠀⠀⠀⠀⡀⠁⢰
⠀⠀⠈⠁⠀⠤⠤⠤⠤⠤⠀⠿⣈⠀⠄⠀⠀⠰⠀⠤⠄⣛⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠁⠈⠁
⠀⠀⠀⠀⠀⠄⠠⠄⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠈⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠐
⠀⠀⠀⠀⠀⠠⠌⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠹⠈⠀⠀⠀⠂⠀⠀⠀⠀⠰⠁⠀⠀⠂⠀⠀⠀⠀⢀⠃⠀⠡⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠐⠀⠐⢦⠀⠃⠀⠀⠀⠀⠀⡀⠀⠀⡃⢀⡴⠀⠀⠀⢀⠄⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠠⠄⢐⢄⠀⠑⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡀⠠⠄⠀⠀⢂⠔⠁
⠀⠀⠀⠀⠀⠀⢀⡀⠢⢀⡀⠒⠠⠊⢊⠳⠦⠕⣇⠛⠰⠀⠀⠀⠀⠄⠛⢈⠠⠴⠚⡓⠑⠄⠒⢁⡀⠔⢀⡀
⠀⠀⠀⠀⠰⠏⠙⠃⠉⠄⢠⠈⠖⠀⠀⠀⠀⠠⣞⢆⠀⡄⠀⠀⠈⠀⠐⣣⠄⠀⠀⢀⠀⠰⠂⣈⠠⠙⠴⠋⠽⠆
⠀⠀⠀⠀⠀⠀⠀⢀⣤⢀⡀⠢⠑⠲⠁⠀⢀⠀⠣⡀⠂⠀⠀⠀⠀⠐⢀⠜⠠⠌⠔⠉⠖⢊⠔⣀⠠⣤⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡀⠋⠃⠈⠉⠀⠀⠐⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠐⠃⠢⠀⠀⠙⠃⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠘⠀⠆⠀⠐⠀⠁⠀⠀⠀⠀⠃⠀⠱⠀⠃⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢤⣤⡄⠀⠀⠀⠀⢠⣤⡤⠀⡀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂


⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⢀⠀⢰⠇⠀⢀⢀⢀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠘⠃⠃⠸⢸⠀⠀⠘⢸⠟⠀⢸⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⢄⠤⠌⠀⠀⠀⠸⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠃⠈⠀⠈⢯⢨⠍⢃⠉⡏⢩⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣄⠀⣠⠀⢈⡈⠀⡅⠈⣀⠁⠈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⣿⠂⢸⡇⠀⡗⠀⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠉⠀⠈⠁⠀⠉⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⢠⠂⡀⢀⠈⠇⢠⡆⡄⡀⠀⡀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠛⠀⡇⠼⠈⠃⠃⠘⠄⠀⠀⡏⠃⠐⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢀⠀⡐⢀⡀⢀⢀⢀⢀⠘⡀⠀⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢄⡆⢐⡀⢨⠲⢐⡀⠢⠀⡂⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⣤⠀⠀⢠⠆⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⣿⠀⢀⡟⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠈⠁⠀⠀⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣰⠦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠄⣀⣤⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢠⠖⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠁⣰⠷⢾⣖⣹⠂⠀⠀⠀⠀⠀⠀⢀⠞⡴⣡⣾⣿⡟⠻⠇⠀⠀⠀⠀⠀⠀⠐⢄⠀⠃⠀⢸⣦⠛⢀
⠀⠀⠀⠀⠀⣀⣴⠞⢁⣴⣾⠻⣦⡀⠹⠏⠀⠀⠀⠀⠀⠀⣠⢎⡜⣴⣿⡟⢹⣟⣸⡇⠀⠀⠀⠀⠀⠀⠀⠈⣧⡚⢳⣌⢿⣿⠟
⠀⠀⢀⡴⠞⠉⢰⡾⣿⠓⠈⠻⣉⡻⠃⡀⠀⠀⠀⠀⠀⠈⡡⢊⣼⡿⢹⣇⢸⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡈⣿⣦⡇⡐
⠀⡰⢋⣴⠚⡳⠀⠁⠈⢧⣠⠀⠋⣠⠞⠁⠀⠀⠀⠀⢠⣤⣶⣿⢻⣷⢛⣿⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠄⢻⣷⣌⡛⢱⡇
⠀⣀⣈⠙⢶⡓⠀⠀⠀⠋⣁⡤⠚⠁⠀⠀⠀⠀⠀⠀⢸⡟⣿⠹⠘⣧⢸⡟⠠⢀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣼⣄⠀⠹⣿⡿⣼⠰
⠸⣯⡙⠿⡄⠿⠃⡠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣿⠀⢰⣿⠈⡠⣡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⣴⡄⠚⣡⢧
⠀⠙⠿⠶⠃⠐⠁⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⠀⠀⠀⢸⣿⡇⠘⠁⠈⠔⠁⠀⠀⠀⠀⠀⠀⡄⢀⢤⡀⠀⠈⠿⠿⠃⠔⠱⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣚⠹⣄⢻⣏⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⣨⣿⣞⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣅⠈⠻⣿⢿⣦⡹⡷⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣳⢻⣧⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⣌⠷⣈⡧⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣌⣟⠛⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠑⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⢛⠿⠘⢠⡄

⠀⠀⠀⠀⠀⠀⠀⢠⠖⠠⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡄⠀⢰⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠀⣤⣶⣶⣦
⠀⠀⠀⠀⠀⡀⢠⣧⣾⡀⠈⢿⣿⡄⠀⠀⠀⠀⣠⠤⠒⠚⠛⠻⠿⣿⣦⣌⠛⠤⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢰⣏⣿⣿⠿⣿
⠀⠀⠀⢀⡞⢡⢸⡍⢿⣧⡀⠘⣿⠇⠀⠀⠀⢸⠁⣀⢤⣄⠀⢀⣤⣬⠟⠿⣿⣶⣿⡀⠀⠀⠀⠀⢀⡾⠁⢠⡆⢸⡟⢻⣿⠀⣿
⠀⠀⢀⡾⢀⠂⠈⡁⠈⢿⣧⣤⠏⡀⠀⠀⠀⢠⠟⠦⣤⠾⠃⠀⠻⢿⣷⣦⣼⡟⠛⠁⠀⠀⠀⢠⠏⠀⠀⢻⣿⡈⡇⢸⣯⠀⣿
⠀⣠⠟⢡⢇⣾⣆⢳⠀⠈⣿⢋⠎⠀⠀⠀⠀⠈⢆⣴⣒⡆⠲⣿⣧⣀⠈⡙⢿⠿⠘⡆⠀⠀⠀⠁⢀⣄⠀⢿⣿⣧⡇⢸⣿⣶⣿
⠀⢀⣴⠃⠀⢻⠻⣿⡆⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⣯⠉⢶⣴⣏⠙⢿⣿⣿⡀⠀⣠⡇⠀⠀⠀⠀⣿⣿⠀⠘⠀⣿⡇⢸⣿⣿⠟
⠀⠉⣀⠀⠀⠈⣄⠈⢻⡄⡸⠀⡤⠂⠀⠀⠀⠰⠾⠏⣀⡘⠛⢿⣷⣤⣍⠋⡥⠞⣹⠃⠀⠀⠀⠀⡿⣿⠀⢰⡆⢿⡇⣼⠟⠁⢀
⠀⢾⣿⣦⠀⠀⢸⡄⢀⡼⢁⡾⠁⠀⠀⠀⠀⢀⣀⣼⣿⣷⣄⡀⡍⠿⣟⣼⠁⠰⣧⡀⠀⠀⠀⢸⣇⣿⡆⢸⣧⢸⡇⠁⣠⡖⠉
⠀⢸⡟⢿⣷⣤⣈⡗⠋⢀⡾⠁⠀⠀⠀⠀⠀⠸⢿⢀⡏⠙⣿⣿⣿⠈⢧⠀⠀⠶⠻⡄⠀⠀⠀⢸⡋⣹⣷⢸⡿⠀⠁⣰⠏
⠠⢶⣷⠋⣿⠋⣼⠇⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣶⣿⠉⠛⠀⡼⠀⠀⢶⡞⠁⠀⠀⢰⣿⡿⣿⣿⠸⠃⢀⡼⠃
⠀⠐⠛⠃⠐⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠠⠴⠿⠒⠓⠲⠚⠁⠀⠀⠀⠘⠛⠋⠋⠁⠀⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠆⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠐

⠀⣀⣀⣀⣀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣀⡀⠀⠀⣀⣀
⠀⣿⣿⠛⢿⣷⡆⢸⣿⡀⠀⠀⠀⠀⠀⢠⣿⣷⡀⠀⢠⣾⡿⠻⢿⣷⠀⢸⣿⡅⠀⣼⣿⠋
⠀⣿⣿⣀⣰⣿⡇⢸⣿⡀⠀⠀⠀⠀⠀⣾⡟⢿⣇⠀⢸⣿⡅⠀⠀⠀⠀⢸⣿⣄⣾⡿⠁
⠀⣿⣿⠛⢻⣿⡄⢸⣿⡇⠀⠀⠀⠀⢰⣿⣇⣸⣿⡄⢸⣿⠃⠀⠀⠀⠀⢸⣿⣿⣿⣷⡀
⠀⣿⣿⣀⣰⣿⡏⢸⣿⣇⣀⣀⣀⠀⣿⣿⠛⠛⣿⣧⠸⣿⣦⣀⣴⣶⠄⢸⣿⡏⠀⢻⣷⡄
⠀⠛⠛⠛⠋⠉⠀⠘⠛⠛⠛⠛⠛⠀⠛⠃⠀⠀⠛⠛⠀⠉⠛⠛⠛⠁⠀⠘⠛⠃⠀⠈⠛⠛⠀⠀⠈⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀




⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿