Tv man Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣴⣤⣶⣶⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠟⠛⠛⢛⣛⠛⠛⠛⠿⣿⣿⣽⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠟⠻⡷⠀⠀⢀⣿⣿⡻⠛⠻⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⡄⠀⠀⣨⣴⣀⠀⠀⢠⣿⣿⠀⣠⣤⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣅⣠⣿⣿⣨⣿⣷⣄⣸⣿⣿⠀⣨⣏⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣭⣯⣿⣯⣿⣿⣯⣽⣿⣿⠀⠻⠞⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⣻⡟⠛⠛⠛⠻⣿⡿⣟⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⠀⠂⣄⣀⡔⠋⠀⣸⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡆⠀⢹⣿⠁⠐⠀⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣼⣿⡇⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣿⣿⣷⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣽⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠋⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⡉⠀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡇⡀⠀⢻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣛⣿⣟⣛⣛⣻⣟⣟⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⢿⣦⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣿⠃⠲⠤⣄⡀⣘⠂⢠⣄⠀⠀⣿⣧⠀⢠⠎⣼⠉⠓⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⣇⠀⠀⠀⠀⣀⠉⠀⠞⠀⠀⣰⣿⡿⠂⣿⠀⣿⠀⠀⠀⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⢸⠰⣆⡠⠆⠀⠀⠉⣽⠀⣿⠀⣿⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢹⡆⠀⠀⠀⠸⣄⠉⠁⠀⠀⡰⠀⠀⠀⢸⡆⢹⡇⠀⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠸⠤⠷⠤⠐⠚⠧⣨⣖⠂⢀⡔⢦⣄⡀⠀⠸⡇⢸⡇⢰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⡇⣤⣄⡀⠀⠀⠀⠀⡠⢤⣄⣀⣸⡄⡀⢠⡀⠄⠀⢀⠀⠀⣀⣼⠉⡐⠁⡄⠀⠈⠉⠛⠦⣿⢸⡇⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣇⣇⢸⡇⠀⠀⠀⠈⣇⠀⢳⡀⠀⢀⠇⠀⡣⠀⢠⠂⢠⡼⠋⠀⢄⡀⠀⢥⣄⣀⠀⠀⠀⡸⣸⢣⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠻⢸⣷⠰⣿⡒⠲⠦⠤⠤⡥⣄⣀⣁⣈⣀⣤⢈⠐⠋⠀⠀⢠⡏⠀⠀⢠⠇⠉⢙⣒⣴⡟⠋⣸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠞⠻⠰⣞⣿⡷⠈⢳⣀⠀⠀⣄⡀⠀⠀⢀⡀⠀⠀⠀⠀⣬⠃⡀⠈⣀⣤⣤⣶⡶⠿⠟⠋⠉⠁⠀⣿⣿⣿
⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣉⣉⣁⠈⠉⣉⠒⠚⠛⠶⢤⣤⡔⣿⢰⡇⠈⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡏
⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠁⠀⠀⠀⠀⠀⢸⡇⠤⢤⣤⣄⣀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠁⠐⢀⠀⠀⡄⡀⠀⠻⡠⠤⠤⠤⠴⢶⠒⠈⠀⠀⠀⠀⠀⠀⠀⢻⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⡆⠸⠀⠀⠃⠃⢰⢠⠇⠀⠀⠀⢳⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡸⠿⠿⠦⠤⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠃⠃⠀⠀⠀⠀⢈⢸⠀⠀⠀⠀⠈⠇⠑⠐⠒⠲⠶⠤⢤⣀⣀⠸⠀⡿⢀⣀⣀⣤⠤⠶⠶⠚⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉

⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠐⠂⢀⡄⠂⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠊⠁⡀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⢄⠀⠀⠀⠀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠐⠦⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢀⠄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠈⠀⠂
⣏⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠀⠀⠀⠀⠐⠀⠐⠂
⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡄
⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⡔⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡇
⠀⠈⢧⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠂⢀⠀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠘⣇⠀⠀⠀⠂⠰⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⢀⠔⠉⠐⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⢹⡄⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠈⠅⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⣧⠀⠀⢸⠀⠀⠀⠘⢄⠀⠀⠀⢀⣼⠂⠄⠀⠀⠀⠠⠀⠐⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠸⡆⠀⣸⣄⣀⣀⣀⣀⣑⣀⣀⣙⣛⣀⣠⡀⠠⠤⠀⠀⠀⠠⠀⠄⠐⠄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⡇
⠀⠀⠀⠀⠀⣷⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠈⢢⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠀⢢⠀⠀⡹⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠃
⠀⠀⠀⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⡔
⠀⠀⠀⠀⠀⠘⡏⠁⠀⠒⠒⠀⠀⠠⠄⠤⠄⢡⡀⠀⢀⠜⠀⣀⡀⡤⠀⠀⠀⠀⠀⠠⠃⢀⠎⠀⠀⠀⠐⠒⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢀⠂⠀⠀⠀⠀⠀⠀⠆⠄⠀⠄⠀⠀⠀⠦⠤⠤⠤⠤⠤⠤⠤⠤⠇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢨⠤⠄⠰⠃⠀⠀⠀⠀⡠⠁⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⠀⢀⠂⠀⠀⠀⠀⢠⢁⡀⠁
⠀⠀⠀⠀⠀⠀⠨⡉⠑⠒⠆⡤⢀⣀⠀⠀⠀⠀⢀⡀⠼⠐⠚⢠⠀⠠⠀⣀⠁⠀⠀⠉⠈⠐⠀⠀⠀⠠⠀⠀⠀⠐⠀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠉⠀⠀⠈⡍⠁⠚⠉⡈⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⡤⠀⠐⠒⠃⠀⠐⠂⠋⡐⠀⠀⠆⠀⠀⠀⠀⠆⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠼⠉
⠀⠀⠀⠀⠀⠀⠀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠑⣄⠐⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠸⠆⠀⠠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣤⡤⠤⠅⠀⠀⠀⣀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠄⠀⠀⠀⠀⠀⠀⡐⠒⣂⠂⡢⠀⠀⠀⠀⢎⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠢⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠶⣦⠄⠉⠁⠀⠀⠀⠘⡌⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⣦⡗⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠸⠋⡄⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠂⡀⢀⠏⣿⣷⡄⠀⠀⠀⠀⠀⠀⢀⠀⢀⢀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢴⠘⠀⠀⠀⠀⠀⠐⠔⠰⠥⢽⠘⠞⣮⣩⣠⠄⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢁⠂⠈⠀⠀⠈⠀⠺⠏⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⠉⠐⡃⣀⢰⡇⢠⠀⠀⠀⠀⠇
⠐⠂⠀⠀⠈⠐⠇⠁⡀⣀⡰⢃⡎⢂⢴⣿⣰⢰⠂⠄⠄⡀⠀⠀⠀⠀⠀⠙⢿⣿⡇⢀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠑⠈⠁⠠⠈⠰⣇⠙⠻⠞⠜⠀⠀⠀⠀⠀⠀⠐⡀⠘⠀⠈⠀⠀⠀⠀⡆
⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⢉⡀⠀⠐⠖
⠀⣄⡀⠀⠀⠀⠀⡠⠄⠀⢀⠠⣂⠲⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠉⠈⠉⠀⠀⠀⠀⠈⠂⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⠀⠨⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣂⣀⣀⣀⣀⣀⣈⣁⣀⣈⣉⣑⣀⣂⡒⠀⠂⠐⠒⠒⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⣿⡿⠛⠛⠛⠛⣛⣛⡛⠛⠛⠛⢻⣿⡇⠀⠋⠉⠉⡃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠸⠛⠻⡧⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢸⣿⡇⠀⢀⣠⡀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⡇⠀⠀⠄⠀⠈⠁⠈⠐⠀⠀⢸⣿⡇⠀⠘⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣯⠥⠈⠭⠥⠭⠭⠭⠠⠩⠨⣿⣿⡇⠀⢰⣛⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⢠⡿⠀⠀⠀⠀⠀⢻⣿⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⢴⡶⣿⡇⠀⠀⣄⣀⣤⠋⠁⠀⣼⣿⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣩⠵⠖⠻⣿⡻⢮⣿⠄⠠⢛⡿⠋⠄⠀⢀⣟⢿⣿⣿⠿⢿⣷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⣳⡤⠿⠛⢋⣻⣧⡻⡇⠀⣌⠻⣧⠀⠀⣰⡻⣶⣿⣩⣛⣾⡌⢯⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣠⢋⠷⡴⠷⠻⣿⣦⡹⣾⠀⠻⣷⣤⡀⢠⡝⣷⣘⣷⣏⣹⣆⢳⣎⣧⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⡏⡜⣸⢧⡾⠚⣛⣿⣷⡹⣿⣧⡈⠻⣧⣯⢻⣼⠿⠶⣴⣿⣽⢾⢿⡼⡞⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⣼⣹⠃⣾⣻⣋⣭⠼⣿⣿⡙⣍⠻⣶⣾⣜⣷⣟⣻⣶⠟⠁⠀⡀⡞⣿⣻⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣵⢧⣏⣸⠧⣽⣷⣶⡾⣟⡟⠳⠾⣷⣼⣷⣿⣟⠻⢿⣯⣴⣖⣶⠞⠷⢼⢽⡹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣡⡧⣼⠤⣿⢑⡿⠋⠀⠀⣯⣍⣙⠓⠶⠤⣥⣉⣛⡗⠶⣤⣈⡉⠉⠋⠙⠛⠛⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⢰⡟⢘⣯⣾⡷⣶⣂⣾⢶⣯⣍⡙⠛⠲⠦⣬⣍⡛⠲⠦⣄⡉⠉⠛⠚⠛⠚⢻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⣼⡏⢹⣿⡿⣝⣳⠮⣉⡛⠲⠿⣽⣿⣶⢤⡤⣈⡙⠻⠶⣤⣍⡉⠛⠘⠛⣉⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣿⠀⠹⣿⡻⢤⡙⠳⢬⣉⡛⠂⡦⢀⡍⣙⠃⣿⡿⢿⣛⣿⠿⡟⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⣘⣧⡀⣽⠶⢦⣤⣿⣾⠒⠚⢻⠿⠛⢛⣉⣉⣄⣴⠶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣛⣛⣓⡛⠒⡶⠏⠄⠀⢸⠞⠟⠛⠉⢉⣁⣠⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣭⣉⣉⣉⡉⣙⢛⡃⠄⠀⢸⡖⠓⠘⠛⠉⠉⢈⣀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡏⠉⠉⠉⠉⠉⠉⣿⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡇⠘⠀⢆⢀⣶⠀⣿⣯⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⡇⠀⠀⠀⠉⠙⠆⣿⡧⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠿⠿⢿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣤⣶⣶⡖⢰⠆⢠⣿⣷⣶⣤⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⣿⣿⣿⡇⣾⢀⣾⣿⠝⣿⣿⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣿⣿⢰⣿⣼⣿⢜⣿⣿⣿⣿⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⣦⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠛⠳⠶⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠛⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡏⠁⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠋⠀⠀⠟
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡾⢏⣼⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡀⠘⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠎⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⢦⠀⠀⠔⠐⠤⡀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣐⣀⠄⠻⣄⠐⢄⠀⢳⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⢠⠤⠤⠤⠄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠰⠟⠂⠀⠑⠊⠀⠀⠀⠀⠐⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⢖⠛⠒⠀⠀⠀⠀⠤⢤⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠨⠁⠀⠀⠀⡌⠀⠤⣀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⢰⠓⠒⠂⠒⠰⠄⠀⠤⠀⠀⢀⣇⠀⠀⡈
⠀⡀⠀⠄⠒⠀⠀⠐⠒⠤⡀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢘⠨⣭⣭⣉⡈⠉⢒⠀⠀⠀⠀⠀⠼⣘⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠍⠂⢢⠄⣐⠢⠄⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠏⣼⡿⠈⠀⢸⠀⠀⠀⠀⠀⢠⠏⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢆⠀⠷⠿⠇⣉⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠀⢺⠀⢸⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠣⠀⠑⢄⠀⣠⠧⣺⡿⢷⡄⠀⠀⠀⠀⠀⠠⠀⠀⢀⡀⠀⣀⠀⠀⠀⠀⠀⢙⠀⢸⠀⠀⠀⠀⠀⠸
⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢁⡆⠹⠂⠉⠁⠀⠀⠀⠀⠴⡠⠤⣏⣈⣷⠜⢦⢵⣍⢪⠑⣄⠐⠀⠀⠀⠘⠀⠀⠀⠀⠀⡀⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⢰⠂⡠⢂⠖⠀⠀⢈⠖⠄⣰⠤⠄⠀⠀⠀⠍⠀⠒⠀⠈⠈⠫⠔⠢⠘⠟⠋⡞⠁⠀⣠⡆⠀⡀⠀⠀⠀⠀⠀⡏
⠀⠀⠠⠀⠀⠀⡴⢁⡔⣠⠃⠀⠀⠀⣈⠀⣀⠈⠉⢀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣠⣤⣼⡇⠀⠇⠀⠀⠀⠀⠀⡇
⡌⠉⠀⠀⠀⠀⠀⠘⠂⠉⢤⠉⣁⣀⠋⣽⠤⠡⠖⣳⣿⣼⣉⠏⠹⢠⡆⣢⠀⠀⠀⠀⠀⠀⢀⡈⠛⢿⣿⡇⠀⡆⠀⠀⠀⠀⠀⡇
⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠁⠑⠌⠉⠁⠡⠈⠁⣼⡣⠉⢛⢧⠼⠴⠃⠀⠀⠀⠀⠀⠀⠀⠈⣆⠁⠚⠀⠀⠃⠀⠀⠀⠀⠀⠆
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⡙⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⠀⠒⠆⠀⠀⢀⣒⡜
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡰⠤⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢐⠃⠠⠀⠀⢀⢓⠀⠀⠀⠈⠁
⠀⠢⠤⠀⢀⡀⠀⢀⡀⡴⠐⠓⠂⠠⡐⢪⡍⡁⠿⠃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡠
⠀⠀⠀⠀⠀⡌⠁⠉⠙⠀⠀⠀⠀⠀⠀⠑⠦⠤⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡃⠀⠀⠀⢀⣭⡄⠀⠁
⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣑⣴⢄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠉⠉⠉⠀⠈⠉⠉⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠂⣁⠢⡀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⡀⠊⠀⡀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠆⠶⠤⣴⠿⣀⠀⠀⠀⠀⠀⠁⠀⠸⡁⠀⠐⠡⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠐⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠝⠲⠤⠤⠀⠀⠗⠀⣰⠃⠀⠁⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡃⣀⣀⣀⣀⣀⣀⣀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠲⠊⠭⠤⠬⠭⠤⠤⠞⠃⠀⠀⠘⠁
⠀⠀⠀⠀⢄⠀⠀⠀⠈⠈⠉⢻⡿⠿⠿⠿⠿⣿⠿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋
⠀⠀⠀⠀⠐⠛⣇⠀⡀⠀⠀⢨⡿⠿⠶⢶⠿⠻⢿⠇⠀⢀⠀⠠⠀⢀⡀⠀⠀⠈⣳⠒⠒⠒⠒⠠⠠⠠⠠⠐⠂
⠀⠀⠀⠀⠀⠀⠘⠊⢇⣉⣀⡸⣃⠀⣀⣀⣐⡀⢚⣡⠆⠑⢄⠣⡈⡀⠀⠂⠀⠈⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠉⠉⠁⠈⠀⠉⠁⠉⠉⠁⠀⠤⠰⠵⠄⠨⠁⠄⠤⢼⣤⣠⡤⣤⠤⣤⠤⠤⢠⣤⡤⣤⣥⡤⣀

⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣠⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠓⠒⠤⠀⣀⠀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣽⣭⣽⣯⣿⣿⣿⣾⠷⢾⣶⣀⠀⠤⠖⠒⠋⠁⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠒⠢⠀⠤⢀⣀⣀⡀⠉⣿⣿⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢀⣀⣀⣀⠤⠀⠤⠒⢺⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠉⠀⠉⠈⠈⠉⠁⠘⠛⠐⣿⣿⣿⣿⣿⣿⠀⠈⢡⣇⠀⠀⢰⡆⠀⠀⠀⠀⣷⡄⠀⠀⠀⣿⡟⠛⠋⠀⠉⠉⠉⠉⠀⢹⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⣿⠀⠀⠈⠙⠄⢠⣼⣿⠀⠀⠀⠰⣿⣷⠀⠀⠀⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠐⠂⠀⠉⠉⠉⠀⢀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⠷⠰⣷⡶⣿⣷⡆⠀⢸⣿⡇⠀⠈⠉⠁⠀⠐⠂⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣀⠄⠐⠒⠉⠉⠙⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡄⣼⣿⠉⠉⠒⠂⠠⣀⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠐⠉⠁⠀⠀⠀⢀⡠⠔⠊⢹⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣬⣥⣿⣿⠢⢤⡀⠀⠀⠀⠈⠉⠃⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣠⣤⣤⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⠿⣿⣟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⡟⠛⠛⠛⠛⠻⢿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠈⣻⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠉⢛⠋⠁⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠐⠄⠀⠀⠀⣠⣿⣷⡀⠀⠀⠀⡀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠈⢢⡀⣰⣿⣿⣿⣷⡀⢠⠎⠀⢰⣿⣿⣿⣿⢿⣿⣿⣿⣿⣇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣯⣛⢿⣿⣿⣷⠀⠀⠙⠁⢻⣿⣿⠏⠘⠁⠀⢀⣿⣿⣿⡿⣋⣼⣿⣿⣿⣿⣿⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣛⢿⣇⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⣼⡿⣛⣵⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⣵⣿⣿⡀⠀⠀⣼⣿⣿⡇⠀⠀⢰⣿⣷⣬⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⢿⣿⣿⣧⠀⢠⣿⣿⣿⣷⠀⢀⣿⣿⣿⡟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⡇
⠀⠀⠀⠀⠀⣿⣀⣈⣩⣉⣉⣉⣉⣉⣉⣉⣉⣉⣍⣉⣉⣀⣉⣉⣉⣠⣈⣉⣉⣉⣉⣀⣀⣉⣉⣉⣀⣉⣉⣉⣉⣉⣉⣉⣉⣍⣉⣉⣀⣼⡇
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠔⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠅⠐⠀⠠⠄⠀⠈
⡔
⢳⠀⠀⠀⠀⠀⠀⠀⠄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠈⢇
⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢠⠀⡀
⠀⠀⠀⣇⠀⢰⠀⠀⠐⢄⠀⠀⣠⡗⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢸⡀⠘⠂⠀⠀⠀⠀⠂⠈⡡⠒⠂⡀⠀⠀⠄⠀⠠⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠰
⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⢹⠁⠀⠂⠀⠀⠀⠠⠀⡤⠀⢠⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠢⢐⡀⠀⠘⠒⠒⠒⠒⠒⠒⠁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡈⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⢉⠐⠂⠤⠀⣀⠀⠀⢀⡀⠄⠐⠠⠀⡄⠀⠁⡁⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⢀⣁⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠒⠀⠈⠁⠀⠁⠁⠁⠀⠀⠀⠀⠀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡖⠛⠛⠋⠉⢹⡆⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡇⠀⠰⠠⣇⢸⡏⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣧⣤⣤⣤⣬⣿⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢠⣤⣴⢭⡍⢹⣷⣤⣄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣾⣿⣿⣸⢠⡿⣏⣿⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⢀⣿⣿⣿⣿⣾⣿⣾⣿⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠈⠙⠓⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣇⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠃⢸⠏
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⣀⣀⣀⣀⣄⣀⣰⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠋⠉⠉⠉⣉⣭⣍⡉⠉⠉⠉⠻⣿⣿⣷⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢟⠛⢿⡇⠀⠀⠀⠀⣿⣿⣿⠻⠿⠿⠿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠨⣀⡜⠀⠀⠀⠀⠈⣿⣿⣿⠀⢀⣀⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⢸⠀⢀⣤⣶⠋⢻⣶⣦⠀⠀⠸⣿⣿⣿⠀⠻⣿⠟⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⣴⣾⣿⣿⣦⣾⣿⣿⣷⣶⣾⣿⣿⣿⠀⣴⢶⣆⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣯⣥⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿⣿⣿⡏⠀⠙⠟⠃⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿⣿⣿⣿⣿⠿⠶⠶⠶⠶⠶⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠣⢀⠀⠀⠀⠀⣺⡿⠋⠹⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⡀⠀⢹⣶⣤⣶⠁⠀⠀⢴⣿⣿⣷⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢹⣿⡁⠒⠈⠀⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣿⣿⣷⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⣿⣿⣿⡄⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣋⢿⣻⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣀⣄⣥⣽⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣏⣀⣀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣟⠋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠿⢿⠿⠿⢿⣿⠿⠿⠿⢿⡿⠿⠿⢿

⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⣀⠀⠀⣀⣀⢀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡆⠀⠀⡟⠀⢹⡧⢻⡅⠀⢿⡃⠛⡇⠀⢀⣘⣸⣣⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣘⣀⣀⣀
⠀⠀⠀⠀⣇⠀⠀⣿⠀⠈⡆⠀⠃⡀⢘⠀⠀⡇⠈⠀⠀⢸⠸⡄⠀⠀⢈⠁⠀⠀⠀⡀⣄
⠀⠀⠀⠀⣿⡄⠀⢹⠀⢀⡁⠀⣇⡿⣽⣿⠁⡇⢲⠆⠀⢸⠠⡇⠀⠀⢸⠀⢠⡀⠀⡇⠀⠀⣀
⠀⠀⠀⠀⢿⡹⠀⢸⡼⣿⡟⠀⡿⡅⣿⣿⠁⡇⢸⠀⠀⡌⠀⡇⠀⠀⢸⠀⠈⢧⠀⠁⢀⠜⠁
⠀⠀⠀⠀⠈⠁⠀⠸⠘⠉⠀⡀⠀⠈⠿⠋⠀⡇⠸⢤⠀⡇⠀⠁⠰⠀⠸⠀⠀⠈⡆⡠⠃
⠀⠀⠀⠀⠀⣄⠀⠀⠀⡠⢐⣻⠷⠀⠀⠀⠀⡇⠤⢾⠤⡧⠤⠤⢀⣀⣀⣀⣀⣤⠚⣑⣦⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⢻⠈⢑⠤⡀⠀⠀⡇⠀⣸⠀⡇⠀⠀⡏⠀⡤⠤⠤⠔⠒⠒⠒⠀⠠⣄⠀⣷
⠀⠀⠀⢠⣴⣿⣿⡋⠉⠳⡸⣇⠀⣄⣏⠀⠀⡇⠀⠀⠀⡇⠀⢸⢴⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠈⠛⢿⣿⣷⣦⣝⣏⠀⠀⣙⠄⠀⡇⠀⠀⠀⡇⠀⢸⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⢠⠈⢹⡿⣿⣿⣿⣭⣻⢦⡀⠃⠀⣀⣀⣃⣀⢸⠈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣼
⠀⠀⠀⠀⠀⢸⢸⠀⠈⠫⡈⣹⢿⣿⣿⣷⣮⣶⣄⡀⠀⠀⠀⠘⡄⠸⠀⠀⣀⣠⣴⣶⣿⣦⡀⢸⠀⡏
⠀⠀⠀⠀⠀⢸⠀⣴⠀⠀⠈⠲⣡⠙⢿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣾⣿⡿⠿⠛⠋⠙⠻⣿⣷⣬⡁⠀⢀⣴⠟
⠀⠀⠀⢀⠀⢸⠀⣯⠀⠀⠀⠀⠈⠲⣙⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⠋⠁
⠀⠀⠀⢸⠀⢸⠀⠹⠀⠀⠀⠀⠀⠀⠈⠢⡄⠈⢙⠛⠿⠿⠿⣿⠿⠛⠛⠛⠋⠛⡏⠉⠀⢀⣼⣿⠏
⠀⠀⠀⠈⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣟⠗⠚⠛⠛⠒⠛⠚⠲⣲⡒⠓⠋⠀⠀⢀⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⢠⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢹⣿⣅⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠉⠉⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠈⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢂⠐⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄⠁⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣞⡻
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⣀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠤⠠⠄⠃⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒



⣀⣀⣀⣀⣀⣐⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣂⣂⣄⣄⣠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣠⣂⣀⣐⣴⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣴⣶⣶⣶⣶⣶⣴⣦⣦⣤⣴⣤⣤⣤⣤⣦⠀⢀⣀⣀⣀⣀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣿⡟⠉⠀⠀⠀⣠⣤⣤⡈⠁⠁⠉⠙⣿⣿⠀⠨⠀⠀⠀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠋⠉⠻⠇⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠂⠂⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢀⣤⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣿⡇⠀⠀⠠⠀⠀⠉⠁⠉⠢⠀⠀⠀⣿⣿⠀⠀⠙⠿⠏⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣿⣇⣋⣀⣁⣁⣐⣃⣋⣃⣀⣁⣀⣟⣿⣿⠀⠀⣴⠻⡆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⠀⠀⠈⠛⠁⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠐⠂⠀⠀⣠⡄⠀⠀⠀⠀⠀⢤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣿⠁⠄⠀⠀⠀⠀⡰⠟⠉⠘⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⣒⣪⣽⣯⣛⢿⡄⠀⢸⣶⣶⣾⠀⠀⠀⢼⣿⣿⣿⣗⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣵⠞⠛⣉⣈⣿⣤⡹⢾⣟⠀⠂⢸⣟⡅⠒⠁⠀⢾⡌⢿⣿⣯⣍⣻⠿⣙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣾⢣⣿⡞⠛⡉⢨⣬⡿⢯⡽⠀⠀⣦⡙⠷⠀⠀⢰⣏⠻⣿⢷⣴⣩⡿⣦⠻⡼⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⣾⣹⢳⡾⢟⠛⣿⣷⣍⢿⣧⢈⠻⣿⣦⡄⢠⣧⣹⣦⡹⣿⣥⣼⣧⢹⣇⣹⡜⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⣼⢡⡏⡾⢥⡾⠛⣋⣹⣿⣧⠿⣾⣦⡈⠛⢧⣾⡘⣷⡿⠷⠶⣼⣿⣽⢷⠿⣦⢳⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢇⣞⣸⠃⣾⢻⣋⣩⡥⣿⣿⣏⢹⡙⢿⣶⣾⣏⢿⣾⠳⣿⣾⠟⠁⠀⡂⢴⢻⣞⡟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣏⣾⣱⡏⢸⣇⣹⣯⣴⣦⣿⠿⠿⢦⣿⣦⣼⣿⣿⣿⠿⢿⣿⣋⣠⠤⢤⠴⢿⣬⣏⣟⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣼⢁⣿⢉⣿⠢⣿⠟⠉⠁⢸⣙⠗⢶⢤⣥⣈⣋⠙⠿⢷⣤⣈⡉⠙⠛⠛⠷⠲⠶⠷⠿⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⡏⣹⡇⠼⣟⣼⣥⣤⡄⣀⣎⣙⠛⠻⠶⣦⣤⣍⡙⠛⠲⢤⣌⡋⠙⠷⠶⢶⠤⢤⠤⢶⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⣿⠤⣾⣿⣿⢯⣟⣳⠿⢭⣿⣛⣷⣶⣦⣤⡉⠙⠛⠶⣦⣬⣉⠛⠶⠦⣤⠤⣤⠤⢤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢹⡟⠀⢾⣽⣏⠳⢦⣍⠓⠶⢄⣍⠉⠛⠻⠿⢽⡟⢳⣶⣤⣭⣉⣻⣷⣦⣤⣤⡤⠤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣼⡏⠀⠘⢷⡍⠳⣦⡈⠙⠶⢤⣍⣸⠃⢰⣦⣴⣤⣼⣿⡭⡿⠅⠟⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣬⣷⣄⣶⡟⠛⠶⠾⡿⡏⠉⠉⢹⠋⣋⣉⣥⣤⣴⠶⠾⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣭⣍⣩⣉⣉⣋⣛⣛⠇⠄⠀⢸⡟⠛⠉⢉⣀⣠⣤⣴⠶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣭⣀⣈⣀⣉⣉⣉⣹⠠⠀⠀⠈⡗⠛⠀⠛⠉⠉⡁⢀⣀⣿

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢸⠁⡀⠀⡈⣉⡉⠉⠉⠉⠉⠉⠩⠭⠭⠭⠭⠭⠭⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢄⡀⠀⠄⠤⠀⠀⠤⠄⡉⢱
⠀⠀⠀⠀⠀⠀⣾⢸⠈⠆⢐⠶⠖⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠶⠶⠶⡒⠒⠊⡇⣿⣿⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠀⠀⠀⠀⡏⢸⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠇⡇⢸⣿⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠀⠀⠀⠀⡇⢸⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡇⢸⣿⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠀⠀⠀⠀⢡⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡇⢸⣿⣿⣿⣭⣭⣿⣟⢸
⠀⠀⠀⠀⠀⠀⢸⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⢸⣿⣿⣿⣿⣿⣿⣿⢸
⠀⠀⠀⠀⠀⠀⢸⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠘⡇⢸⠟⠻⠿⢿⣯⠭⢿⢸
⠀⠀⠀⠀⠀⠀⢸⢸⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⡈⢴⠅⣴⣿⠵⣕⢼⢸
⠀⠀⠀⠀⠀⠀⢸⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⡇⢴⠎⢳⠤⠴⢟⢚⢸
⠀⠀⠀⠀⠀⠀⢸⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠨⡇⡇⠰⠆⢀⠉⣋⢁⢸⢸
⠀⠀⠀⠀⠀⠀⢸⢸⠀⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡄⡇⡇⠲⢲⣎⣋⠟⣿⣸⢸
⠀⠀⠀⠀⠀⠀⢸⢸⠀⡅⠓⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠤⡤⠤⠤⠖⢒⣉⣠⠁⡇⢇⡺⡆⠙⠟⠛⠝⢩⢸
⠀⠀⠀⠀⠀⠀⢸⠈⠪⠤⠬⠤⠈⠉⠭⠭⠭⢭⡭⠭⠭⠭⠉⠉⠁⠁⠈⠁⠀⠀⠀⠀⠄⠀⠉⠁⠀⠀⠄⠰⠃⠸⠿⠿⠿⠿⠿⠿⠟⢸
⠀⠀⠀⠀⠀⠀⠈⠧⣄⣀⣀⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⡤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠖⠒⠖⠒⠒⢂⣀⣀⣀⣀⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⢤⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠠⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠐⢀⠀⣼⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⢠⠔⠈⠉⠁⠀⠉⣀⣀⣀⠀⢀⡀⠉⠉⠐⠢⢄⠀⠀⣾⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⠃⠀⠀⣠⣴⡟⣭⣿⡟⠉⠠⣿⣿⣶⣿⠂⠀⠀⠡⠀⣿⠐⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡞⠀⠀⠀⣻⠛⣉⣉⣿⡇⢀⣆⠀⠉⣁⠀⢄⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⡇⠀⣀⠰⠇⠐⣉⣓⠸⠇⠶⣉⠙⢣⢉⠀⠻⠇⢀⠀⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇⠈⠋⣼⠂⢂⣀⠦⠀⠀⠐⣄⠘⠃⢀⠄⡶⢹⠔⠃⡃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠈⠢⠉⠀⠈⠏⠀⠀⠄⠁⠀⣼⢀⠚⠁⠀⢀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⢅⣈⡀⠈⠙⢂⠈⢁⠘⠁⠀⠀⠀⡈⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⣉⠒⠠⠤⢀⣉⡀⠊⠀⠉⢀⡀⠀⡀⡀⠠⠊⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠸⠐⠒⡒⣈⠉⠭⠭⠥⠤⠔⠖⠒⠒⠂⠂⢀⣀⣄⢀⠀⠀⠀⠙⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠐⠰⠐⠒⠒⠒⠀⠀⠠⠠⠤⠤⢤⠤⠀⠀⠀⢀⡀⣀⢀⠀⠀⠀⠃⡇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠠⠀⠆⠀⠀⠀⢒⠀⠀⠁⠀⡀⠀⠐⠀⢈⠐⠀⠁⠃⡇⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠈⠐⠂⡀⠀⠁⠁⠀⠀⢠⠀⠀⠀⡆⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠠⡤⠄⠄⠀⢀⣀⣀⣀⡁⠀⠈⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠨⠀⡇⠀⢀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡏⢉⠉⠉⠈⠑⠛⠛⠓⠒⠚⠉⠬⠬⠶⠦⡄⠠⡜⠂⢀⣀⣤⣧⠶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠜⠉⠉⠉⠉⠉⠹⠉⠋⠉⠉⠉⠑⠢⠤⡇⠀⠗⠒⠒⠒⠒⠺⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄⠀⠀⠀⠀⠀⠀⠀⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⢃⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡇⠀⠀⠀⠀⠀⠈⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠁⠀⡴⠀⠴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡀⠙⠀⠀⠀⠐⠐⠂
⢀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠉
⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠹⡄⠀⠀⠀⠀⠀⠀⠀⠣⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡆
⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡇
⠀⠈⢧⠀⠀⠀⡄⠠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⢻⠀⠀⢸⠀⠀⠐⡄⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠈⡇⠀⣸⣀⣀⡀⠈⡀⢀⠐⠛⢂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⢹⡰⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠈⢂⠀⠀⠈⠀⠀⠈⠀⠀⠀⠰⠀⢀⠃⠀⠀⠀⠀⠀⡀⠀⠀⠁
⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠁⠀⠀⠀⠖⠀⢰⠃⠀⠀⡐⠀⠀⠀⠀⠠⠁⠠⠁⠀⠀⠀⠉⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⢨⠀⠀⡀⠀⠀⠀⠀⠠⠁⡐⠁⠀⠀⠀⠀⠀⠈⠑⠢⣅⣀⣀⣉⣉⣉⣉⣉⣉⣉⣉⣀
⠀⠀⠀⠀⠀⣺⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠀⢠⠀⠀⠀⠀⢠⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⡁⠒⠠⢤⢀⣀⠀⠀⠁⢀⡀⠤⠀⠂⡄⠀⠀⡀⠁⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠰⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠈⡉⠙⠉⡨⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠄⠀⠒⠃⠀⠐⠘⢉⠀⠀⠂⠀⠀⠀⠂⠀⠂
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣾⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡀⠀⠀⠀⡇⠀⢼⡿⢲⣶⠀⠀⣶⢶⢳⡖⡆⠀⠀⠀⡖⡖⡄⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢀⡔⠒
⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⡗⠃⢸⠀⠀⢸⠮⠭⢸⡇⠠⠤⠤⠥⢷⢾⠒⠠⠤⠤⢼⠆⠶⠶⠤⠤⠤⠾⠒⠒⠒⠒⠒⠒
⠀⠀⠀⠀⠀⣧⠀⠀⠀⡇⠀⠀⣧⠀⢸⠠⡀⢸⢀⢀⢸⡇⠀⠀⠀⠀⣿⠘⡆⠀⠀⠀⢸⠀⠀⠀⠀⢀⡤⠶
⠀⠀⠀⠀⠀⣿⡆⠀⠀⡇⠀⢀⡇⠀⢸⢀⡿⣽⣿⡇⢸⡇⠒⡆⠀⠀⡇⠀⡇⠀⠀⠀⢸⠀⢀⣄⠀⢸⡦⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣿⢱⡆⠀⡇⡴⡯⣿⠆⢸⢹⣃⢿⣿⡗⢸⡇⠠⡇⠀⠀⡇⠀⡇⠀⠀⠀⢸⠀⠀⢻⡀⠘⠃⠀⣠⠊⠁
⠀⠀⠀⠀⠀⠘⢳⠀⠀⡟⣵⠟⠃⠀⠈⠀⠳⢾⡻⠃⢸⡇⠰⡇⠀⠀⡇⠀⠧⢀⠀⠀⢸⠀⠀⠀⢷⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⢰⠀⠀⡁⠀⠀⠀⣰⣀⡄⠀⠈⠀⠀⢸⡇⠉⢉⡇⠐⠇⠀⠀⠈⠁⠀⠈⠀⠀⠀⠘⣦⠊
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⣀⣔⣪⣤⣞⠋⠀⠀⠀⠀⢸⡇⠒⢒⡗⢚⡗⠒⠒⢢⡤⠤⠤⠤⠤⠴⠯⠤⠬⠵⠤⠤⠤⠤⠤⣤
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠟⢙⡇⠈⢙⠦⣀⠀⠀⢸⡇⠀⣀⡇⠀⡇⠀⠀⡾⠀⢠⡶⠖⠒⠒⠒⠒⠒⠒⠒⠀⠦⣄⠀⢹⡀
⠀⠀⠀⠀⣀⣴⣾⣿⡿⠋⠈⢣⡀⣗⠀⢀⡀⢞⠁⠀⢸⠀⠀⠀⠁⠀⡇⠀⢠⣧⣲⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢸⡇
⠀⠀⠀⠀⠈⠙⢿⣿⣿⣶⣤⣀⠙⢼⡋⠀⠈⠙⡄⠀⢸⠀⠀⠀⠀⠀⡇⠀⢸⢃⡀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣾⣷⣤⠤⣶⣇⠀⢸⠀⠀⠀⠀⠠⡇⠀⢸⠓⠟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢠⠀⡇⠀⢸⣟⡿⣿⣿⣿⣷⣾⣟⠲⣌⠀⠀⠴⠦⠤⠤⠤⠸⡆⠀⡇⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢸⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠱⣄⢠⠝⣿⣿⣿⣿⣿⣶⣽⣦⣀⠀⠀⠀⠀⠀⢧⠀⠙⠀⢀⣀⣤⣶⣾⣿⣿⣷⣤⡀⠿⠀⡿⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⠀⢀⡆⠀⠀⠈⠳⢎⡅⠙⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⠿⠛⠉⠙⠻⢿⣿⣷⣬⡁⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⢸⠀⢸⠃⠀⠀⠀⠀⠀⠑⢤⠛⡊⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⣾⣿⣿⣿⣿⣗⡶⠟⠁
⠀⠀⠀⠀⢸⠀⢸⠀⠘⣼⠀⠀⠀⠀⠀⠀⠀⠙⣤⠁⠈⠹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⢿⠟⠛⠛⠋⠉⣽⣿⡿⠁⠛
⠀⠀⠀⠀⢸⠀⠈⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣠⣐⣀⣈⣍⣉⣙⣻⣈⣁⣀⣀⣀⣀⣨⡼⠀⠀⠀⢀⣾⣿⡟
⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡡⠋⠀⠀⠀⠀⠉⠉⠉⠉⠻⣽⡍⠉⠁⠀⠀⠀⢀⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠀⠀⠀⢠⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⢙⡿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠙⠉⠙⠛⠛⠿⠿

⠀⠀⠀⠀⠀⢀⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠶⠖⠒⠒⠒⠶⠤⠤⠤⠤⠤⠤⠴⠖⠲⠦⠤⡄
⠀⠀⠀⠀⠀⢸⠀⠲⡀⢀⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣭⣭⢭⣭⣭⣭⣭⣅⣀⣉⣉⣉⣀⣉⠱⡀⣮⣤⣤⣤⣤⣤⡆⢨
⠀⠀⠀⠀⠀⢸⢸⠀⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡀⡀⡅⣿⣿⣿⣿⣿⣿⡇⢸
⠀⠀⠀⠀⠀⢸⢸⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠄⣿⣿⣿⣿⣿⣿⡇⢸
⠀⠀⠀⠀⠀⢸⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣿⣿⣿⣟⣛⣿⡇⢸
⠀⠀⠀⠀⠀⢸⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡀⣿⣿⣿⣿⣿⣿⡇⢸
⠀⠀⠀⠀⠀⢸⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢛⠀⡿⠛⠿⢿⣿⠭⠇⢸
⠀⠀⠀⠀⠀⢸⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠄⠀⠆⣴⠿⠶⣯⣸⢸
⠀⠀⠀⠀⠀⢸⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠀⠀⠛⠙⠖⣚⠻⢁⠸
⠀⠀⠀⠀⠀⢸⢸⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⣋⡀⣦⣶⣦⣘
⠀⠀⠀⠀⠀⠈⣼⠀⠎⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠴⠁⠂⠀⠀⣍⠳⣶⡧⢿⠿⡄
⠀⠀⠀⠀⠀⠀⡇⢤⠃⠀⠉⠒⠲⠶⠶⠶⠶⠶⠶⠖⠒⠒⠒⠚⠛⠓⠒⠉⠉⠉⠑⠂⠀⠀⠈⢠⠁⣷⣿⣶⣶⣶⣶⡾⢰
⠀⠀⠀⠀⠀⠀⢇⣀⠀⢀⣀⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣀⣈⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⡜
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠠⢤⣄⣀⠀⠀⠀⠀⠀⠀⣾⣿⣶⣶⣾⣿⣿⣿⣿⣿⠿⣿⠿⡿⡿⢿⣿⢿⣿⣿⣿⣻⣟⣛⣆⡀⠀⠀⢀⣀⣠⠤⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⢀⡀⠀⠀⠀⠀⠉⠀⠐⠢⣴⣶⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠉⣹⣽⠖⠂⠈⠉⠀⠀⠀⠀⣀⣸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠀⠐⠒⠒⠤⠤⠀⣼⣿⣿⣿⣿⣿⣿⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠤⠤⠄⠒⠒⠁⠈⠉⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡧⡄⠀⣀⣀⣀⣀⡀⢀⣀⣀⣸⣿⣿⣿⣿⣿⣿⠐⢿⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣿⣷⣀⣀⡀⣀⣀⣀⣀⣀⠀⣼⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠀⠀⢴⣷⠀⠀⠀⣷⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣼⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠃⠰⡶⢿⣆⠀⠀⠀⠸⣿⡇⠀⠀⠀⣿⣿⣄⣀⣀⣀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠐⠂⠀⠀⠉⠉⠀⠀⢀⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⠻⠆⢻⡿⠿⣿⣿⡆⠀⢠⣿⣇⠀⠀⠀⠉⠀⠀⠀⠐⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣠⠄⠐⠒⠉⠁⠈⠛⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡆⣸⣿⡇⠈⠁⠒⠀⠤⣀⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠊⠉⠁⠀⠀⠀⠀⣀⠴⠒⢩⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣨⣥⣿⣿⠷⢤⡀⠀⠀⠀⠀⠈⠉⠓⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡇⣠⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⣿⣿⣿⣿⣿⡿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠙⢿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⠙⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢀⠀⠀⠀⠀⠀⣴⣷⡀⠀⠀⠀⠀⡠⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠱⡄⠀⢀⣼⣿⣿⣷⡄⠀⢀⡔⠁⢠⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡆⠀⠈⢢⠞⢿⣿⣿⣿⠛⡤⠋⠀⠀⣾⣿⣿⣿⣿⠎⣿⣿⣿⣿⣿⣇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣛⢿⣿⣿⡀⠀⠀⠀⠀⣿⣿⡃⠀⠀⠀⠀⣸⣿⣿⠟⣣⣶⣾⣿⣿⣿⣿⣿⣿⡄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢎⣹⣧⠀⠀⠀⢠⣿⣿⣇⠀⠀⠀⢠⣿⣏⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⣴⣿⣿⣿⡆⠀⠀⣼⣿⣿⣿⡀⠀⢀⣿⣿⣿⣷⡍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢿⣿⣿⣿⠀⠠⣿⣿⣿⣿⡇⠀⢼⣿⣿⣿⠋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇
⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⡇




⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠄⠒⠈⠁⠀⣀⣀⢠⠤⢤⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠊⠉⠀⢀⣀⠤⠐⠒⠈⠁⠀⠀⠀⠀⠈⠇⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠱⠀⠀⢲⠉⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠘⡀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢣⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠊⣤⣄⢠⣄⠀⢧⠸
⠀⠀⠀⠀⠀⠀⠀⠀⡎⢣⠀⠈⠆⠀⠈⠄⠀⠀⠀⠀⠀⢰⢦⣃⢋⢻⡌⠶⠊⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⣇⠀⠈⠄⠀⠘⣄⣀⠤⠄⡶⡎⡇⠛⠈⠈⢁⡞⡩⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠸⡀⠀⠈⠄⠀⢀⣀⠤⣔⢧⡘⠃⠀⣀⠠⠞⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠱⠀⢀⡠⠂⠉⢀⡼⠓⠤⢈⢶⠊⠀⠀⠀⠘⡀⠈⠉⠁⠒⠒⠒⡖⠲⢄⠀⠀⢀⠀⠀⠂⠁⠈⠑⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠓⠛⠒⣨⠝⡟⠹⡦⣄⠀⠈⣧⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⢀⣁⠠⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠎⠀⠀⠑⢄⠉⠒⠃⢃⠀⠀⠀⠀⠘⢄⠀⠀⢸⠯⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠀⠀⠀⡜⠀⠀⠀⠀⠀⠑⢤⡀⠀⢃⠀⠀⠀⠀⠀⠳⣄⠀⡖⠀⡞⠫⢄⣀⠠⢀⠀⢀⠤⠐⢨⡒⠞⠀⢀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⣠⠎⠁⠤⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠡⡀⠀⠀⠀⠀⠈⠓⡆⢰⠁⠀⠀⠀⠉⢱⢸⠀⠀⠀⠀⠈⠔⠊⠁⡌
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠳⣄⠀⠉⠁⠈⠉⠉⠉⢹⠁⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⢇⡘⠲⢤⣀⠀⠀⡜⠀⡄⠀⡠⠔⢻⡠⠖⠊
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⣚⣀⣠⠤⠖⠚⠁⠈⠢⣄⠀⠀⠀⠀⠈⠑⡦⠄⣉⠛⠁⠠⠁⢸⡁⠠⣾⡦⣀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡄⢹⠢⢄⠀⠀⠀⠘⣄⠀⢉⣒⡶⠲⣁⠁⢘⡟⠰⡈⠓⡄
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠱⡄⠀⠀⠈⡗⠉⠙⢱⣄⡜⢙⡜⡁⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢠⢘⠀⠀⠀⡇⠀⠀⠸⢄⡀⠀⠹⠀⡞⢹⢠⡇⡜⠀⠇⡇
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠇⠀⠀⠀⠀⢈⡆⠰⣰⠀⢸⡜⠋⠣⣠
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠘⠁⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠒⠊⠉⠉⠘⠛⠋⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠠⠀⠀⠀⣄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⣰⣄⠀⠀⠀⠀⠀⠘⠋⠀⢙⠄⠁⠠⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠈⠀⠠⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠐⣧⣀⢀⠀⠀⢠⡄⠀⢠⠎⠀⠂⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣣⠀⠀⠀⠈⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⠤⠀⠈⠥⠀⠀⠁⣰⡋⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠷⠶⣶⣶⣶⣶⣶⣶⣶⣾⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠰⢀
⠀⠀⠀⠀⢀⣦⢤⠀⠀⠀⠀⠀⢿⣯⣍⣉⣩⣽⣿⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣼⠋⣉⣙⣊⣋⡛⢙⣻⣛⡛⡭⣾⡿⣽
⠀⠀⠀⠀⠀⠀⠸⣄⣴⠠⠄⠀⣿⠏⠩⠉⠉⣊⠈⣱⠅⡀⢔⠀⢈⠡⠀⠂⠀⠀⢀⠔⡏⠈⠉⠁⠅⠍⠉⠉⠉⠉⠉⠉⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠶⠶⡭⠦⠀⠶⠶⠶⠆⠴⠶⠁⠀⠑⢈⡆⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠈⠉⠁⠈⠀⠀⠐⠑⠳⠒⠛⠒⠓⠒⠓⠚⠓⠐⠒⠓⠲⠶⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣕⣴⠄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠀⠀⠀⠉⠉⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⠂⣀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡀⠂⠀⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠆⠶⠤⣴⠿⣀⠀⠀⠀⠀⠀⠁⠀⠨⠁⠀⠐⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠐⠀⠀⠐⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠝⠲⠴⠤⠀⠀⠖⠀⣰⠃⠀⠁⡏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡃⣀⣀⣀⣀⣀⣀⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠲⠊⠭⠤⠬⠭⠤⠤⠞⠃⠀⠀⠸⠁
⠀⠀⠀⠀⢄⠀⠀⠀⠈⠈⠉⢻⡿⠿⠿⠿⢿⣿⠿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⣤⡤⠤⣀⢤⣠⣠⣤⣤⣤⠤⣀⣮⣴
⠀⠀⠀⠀⠐⠛⣇⠀⡀⠀⠀⢨⡿⠷⠶⠶⡻⠻⢿⠇⠀⢀⠀⠠⠀⢀⡀⠀⠀⠈⣳⠇⠶⠖⠶⠶⠦⠴⠾⠶⠦⠯⢿⣯⡇
⠀⠀⠀⠀⠀⠀⠈⠊⢇⣉⣀⡸⣃⠀⣀⣀⣐⡀⢚⣁⠆⠑⢀⠡⡈⠀⠀⠁⠀⠊⢸⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠚⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠉⠁⠈⠀⠉⠁⠉⠉⠁⠀⠤⠱⠵⠄⠠⠁⠀⠤⢼⣤⣠⡄⣤⠤⣤⠤⠤⢠⣤⡤⣤⣥⡤⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠀⠐⠀⠀⠀⠀⠠⠄⠀⠐⡄⠡
⠀⠀⠀⠀⠀⠀⠀⠀⡴⡈⠀⢀⡠⠄⠒⠈⠁⠀⠀⠀⠀⠀⠀⠘⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢘⠀⠡⠀⠘⡄⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⢃⠐
⠀⠀⠀⠀⠀⠀⠀⡜⡆⠀⢂⠀⠐⡀⠀⠀⠀⠀⢠⣄⠝⠗⣏⢢⠼⠀⡀
⠀⠀⠀⠀⠀⠀⠰⡀⠱⡀⠀⠄⠀⠰⣀⣀⠠⢤⠞⡎⠃⠁⠉⡰⣒⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠡⡀⢃⠀⠈⠂⠀⣀⡤⢄⠾⡘⠃⢀⡠⠔⢋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⢂⣀⠔⠉⣀⣤⡋⠂⠀⢳⡁⠀⠀⠀⢀⠀⠉⠉⠉⠉⡟⠙⠆⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡠⠔⡹⠁⠫⡒⢄⣀⢧⠀⠀⠀⠀⢂⠀⠀⠀⣀⠅⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⡰⠁⠀⠀⠑⢄⡀⠀⠡⠀⠀⠀⠀⠡⡀⠀⢉⠁⣠⣄⠀⠀⠀⠀⠀⠀⡀⠀⣀⠄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⠔⢉⡀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠈⠒⠤⠡⡀⠀⠀⠀⠈⠲⣼⠀⡃⠀⠉⠐⠲⡔⠆⠁⠀⠈⢊⠤⠐⠹⠁
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠈⠲⣄⠈⠒⠒⠒⠒⠒⢐⠂⠀⠀⠀⠐⡄⠀⠀⠀⠀⢸⡘⠦⣀⡀⠀⢠⠃⣄⠀⣀⠔⣆⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⢘⣀⡤⠴⠒⠋⠈⠢⣄⠀⠀⠀⠈⠐⠦⠌⡑⠊⠀⠁⢸⡁⢰⣷⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠆⠛⠢⢄⠀⠀⠘⢄⢀⣽⣜⠒⢤⡀⢸⠃⢇⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⠀⠀⢸⠁⠀⢨⠧⢎⣹⢣⠀⡜⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠀⠀⠀⢸⠀⠀⠈⠒⢄⠘⣄⠃⢈⣸⢼⠀⠁
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠎⠀⠻⠀⠸⠁⠀⠱

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠂⠠⠄⢀⡆⢠⠀⠈⣿⡀⣠⢠⠋⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⡆⡀⠉⠀⠸⠿⡁⣇⢸⡀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣹⡄⠀⠀⢧⠙⠉⠀⠠⠈⠁⢻⢸⡇⢀⣿⡦
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠓⠂⠈⠧⣷⢀⠄⠲⢤⣀⢸⡄⡇⣼⣿⡇
⠀⠀⠀⠀⠀⠀⣷⡇⡟⡆⠀⠀⠠⡎⢲⠒⠁⡄⠲⠀⠀⠂⣠⠞⠁⠀⢰⡀⠀⠈⠙⣇⣧⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠃⣷⡰⣖⠢⠥⠬⠅⢀⣁⣈⡠⠀⠚⠁⠀⡜⠀⠀⠏⢙⣒⣴⠚⣸⣿⡏
⠀⠀⠀⠀⡀⠀⠉⠉⠘⠿⠃⠘⠦⠤⠰⠤⢀⣠⣄⡀⠀⣰⢃⡄⣴⠶⠶⠛⠋⠉⠁⠀⣿⣿⠃
⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⣤⠒⠀⠉⠁⠀⡧⢀⣀⣉⡉⢹⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠁⠀⡄⠀⠠⠀⢛⠴⠀⢒⢲⠀⠁⠀⠀⠀⠀⢸⡘⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠦⠁⠀⠀⠀⢸⠀⠀⠀⠆⠇⠤⣄⣀⣀⠀⠈⡇⡇⠀⠀⣀⣀⣤⠤⠴⠚⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠐⠋⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠖⠒⠖⠒⠒⢂⣀⣀⣀⣀⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢤⢤⠄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠠⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠐⢀⠀⣼⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⢠⠔⠈⠉⠁⠀⠉⣀⣀⣀⠀⢀⡀⠉⠉⠐⠢⢄⠀⠀⣾⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⠃⠀⠀⣠⣴⡟⣭⣿⡟⠉⠠⣿⣿⣶⣿⠂⠀⠀⠡⠀⣿⠐⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡞⠀⠀⠀⣻⠛⣉⣉⣿⡇⢀⣆⠀⠉⣁⠀⢄⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⡇⠀⣀⠰⠇⠐⣉⣓⠸⠇⠶⣉⠙⢣⢉⠀⠻⠇⢀⠀⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡇⠈⠋⣼⠂⢂⣀⠦⠀⠀⠐⣄⠘⠃⢀⠄⡶⢹⠔⠃⡃⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠈⠢⠉⠀⠈⠏⠀⠀⠄⠁⠀⣼⢀⠚⠁⠀⢀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⢅⣈⡀⠈⠙⢂⠈⢁⠘⠁⠀⠀⠀⡈⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⣉⠒⠠⠤⢀⣉⡀⠊⠀⠉⢀⡀⠀⡀⡀⠠⠊⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠸⠐⠒⡒⣈⠉⠭⠭⠥⠤⠔⠖⠒⠒⠂⠂⢀⣀⣄⢀⠀⠀⠀⠙⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠐⠰⠐⠒⠒⠒⠀⠀⠠⠠⠤⠤⢤⠤⠀⠀⠀⢀⡀⣀⢀⠀⠀⠀⠃⡇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠠⠀⠆⠀⠀⠀⢒⠀⠀⠁⠀⡀⠀⠐⠀⢈⠐⠀⠁⠃⡇⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠄⠈⠐⠂⡀⠀⠁⠁⠀⠀⢠⠀⠀⠀⡆⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠠⡤⠄⠄⠀⢀⣀⣀⣀⡁⠀⠈⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠨⠀⡇⠀⢀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡏⢉⠉⠉⠈⠑⠛⠛⠓⠒⠚⠉⠬⠬⠶⠦⡄⠠⡜⠂⢀⣀⣤⣧⠶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠜⠉⠉⠉⠉⠉⠹⠉⠋⠉⠉⠉⠑⠢⠤⡇⠀⠗⠒⠒⠒⠒⠺⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄⠀⠀⠀⠀⠀⠀⠀⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⢃⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡇⠀⠀⠀⠀⠀⠈⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡟⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⢦⣈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣏⣀⣡⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⡳⠶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢦⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣜⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢏⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢟⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣵⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡌⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⣣⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠱⣄⠀⠀⠀⠀⠀⢀⣴⢫⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠗⠛⠛⠋⠉⠉⠉⠙⠛⠛⠓⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣶⣯⣤⣤⣤⣤⣤⠤⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⠶⠶⠶⠲⠶⠦⢤⣄⡀
⢰⠖⠚⣛⣛⡙⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⣩⣭⣭⣭⣍⣉⠁⢸⡆⠀⠀⠀⠉⠛⠲⠦⣄⡀
⢸⠘⠖⢒⣾⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠾⣩⠟⠛⠙⢻⣦⡈⢻⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄
⢸⠀⣴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠳⣦⡀⠀⠀⡗⡏⠁⠀⠀⠀⣿⡇⣸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⣼⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⡇⠱⣄⣀⣤⣞⣵⠇⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⢸⡇⠀⠀⠉⠉⠉⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡀
⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⣤⠞⣿⢿⣶⣄⠀⡿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠈⠳⡄
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⢰⡇⠀⠁⠀⢹⡽⣧⡇⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠈⢷⣀⠀⢀⡾⢡⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⢰⣏⣉⣉⣹⡇
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⠀⠀⠙⠛⠛⠛⠋⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⡇⠰⣧⣀
⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⢀⠤⣤⡀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣤⣤⣤
⡇⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⢧⣀⣼⡿⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢙⠛⠛
⠃⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠉⠁⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⢰⠒⠒⠒⢺⠃⢿⣿⣿
⠀⠀⠘⠳⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⣿⠀⢠⠊⠙⣷⡀⠀⢸⠃⡿⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⢻⠅⡴⠤⣴
⠻⠤⣀⠀⠀⠉⠛⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡟⠀⠈⠲⠾⠛⠁⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠉⠁⢸
⠀⠀⠀⠉⠓⠶⣤⣀⡴⣾⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⡇⠀⠀⠀⢀⡀⠀⠀⢸⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣍⡻⢿⣿⡏⠛⠶⠶⢦⣤⣤⣤⠶⠾⠋⠀⠀⣧⡀⠀⠦⠤⠟⠀⠀⣸⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠶⠶⣤⠤⠴⠞⢻⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣄⣀⠀⠀⠀⠀⠀⡷⣏⣉⠙⠛⠛⠛⡇⠸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⣤⣄⡓⠤⣄⣉⠑⠒⠾⠇⡀⢸⠀⠀⠀⠀⢀⣀⣴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠮⠍⢑⡒⠤⠇⡀⠀⣀⡤⠞⠋⠁

⠀⣠⠤⠤⠐⠒⠒⠒⠒⠒⠚⠛⠋⠉⠉⠉⢈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣩⡭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠤⠤⠤⠤⠤⠭⠭⠭⣍⣉⣉⣙⣛⣒⠦⣄⡀
⣼⢡⡞⠛⠉⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⠀⠂⠄⠰⣢⠎⢹⡌⣿⢢
⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡮⢸⡇⣿⣩
⣿⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⡇⢻⡳
⣿⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠄⡇⢸⡶
⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣿⢸⣤
⣿⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡷
⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣞
⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣏
⣿⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠏
⣿⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡞
⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⢸⡴
⣿⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢁
⣿⠀⣿⢐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢏
⣿⠀⣿⢨⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡟
⣿⠀⣿⠘⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡷
⢿⠀⢿⠈⠡⢢⠞⡄⡀⡠⡠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⡷
⢸⡀⠘⠦⠀⠀⠈⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡜⠀⣾⡾
⠀⠉⠐⠒⠀⠦⠤⠤⠤⢀⣀⣁⠉⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⣰⣋⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠃⠀⠀⠐⠒⠒⣶⠒⠒⠒⠂⠀⠀⠠⠤⠤⠤⣤⣴⠒⠒⠒⠒⠒⠒⠊⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣧⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣛⣛⢛⡛⠛⠛⠛⠓⠒⠁⠈⠉⠒⠒⠒⠒⠒⠒⠒⠶⠖⠚⠉⠉⢉⣉⣋⣛⣛⡓⣚⣛⣻⣿⣽⣷
⣶⣶⡶⠶⢶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⣀⣤⣤⣤⣄⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣄⣀⣀⣀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⡿⠿⢿⣛⣛⣛⣻⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣟⣛⣛⣻⠿⢿⣿⣿⣿⢛⣭⢫⣭⡻⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⢸⣿⠟⢛⣛⣉⣭⣭⠭⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠻⣿⡇⣿⣿⢣⣿⠏⠈⢻⣿⢸⣿⡇
⠀⠀⠀⠀⢸⣿⣿⡏⣿⡏⢰⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢹⣿⣏⠻⣷⢰⣿⢟⣼⣿⡇
⠀⠀⠀⠀⢸⣿⣿⡇⣿⡇⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢸⣿⣿⣷⣶⣷⣶⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣧⣿⡇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡞⣿⡟⣡⣶⢰⣶⣝⢿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡹⣿⡅⠀⣸⣿⢸⣿⡇
⠀⠀⠀⠀⢸⣿⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣷⣙⠿⡸⠿⣣⣾⣿⡇
⠀⠀⠀⠀⢸⣿⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⣿⠛⢿⣿⡿⠛⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣿⣿⣴⣾⣿⣷⣶⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢸⣿⢸⣿⣒⣒⣒⣒⣒⣒⣒⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⢹⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⢛⣃⣿⡟⣿⣿⣖⡖⣶⣶⢶⡶⣲⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣮⣟⣛⣛⣛⠿⠷⠶⠶⠶⠶⢶⣶⣶⣶⣶⣶⡶⠶⠶⠶⠶⠿⠿⣛⣛⣛⣿⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⢿⠿⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠒⠛⠛⠛⠛⠛⠒⠒⢲⠀⠀⠀⠀⠀⠀⠀⠀⠠⣰⣄⢄⢶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⣨⣭⣿⣾⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⢀⡠⠔⠋⠀⡇⠀⢰⠒⠒⠒⠒⢻⠆⠀⢸⡇⠀⠀⠀⠀⠀⠒⣺⠽⣿⠟⠛⠻⢿⣿⣿⣿⡀
⠀⢰⠚⢁⣀⣀⣀⣀⡇⠀⠈⠉⠉⠉⠉⠁⠀⠀⢸⢹⠀⠀⠀⠀⠀⣀⣀⡰⢁⠈⠂⠀⢸⣿⣿⡿⠁
⠀⣼⠀⠠⠤⠤⠤⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⢧⣀⡀⠸⠀⠀⠀⠸⠛⣿⠁
⠀⡏⠀⠰⠶⠤⠤⠴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠖⠟⠀⣀⢴⣤⡄⣪⡵⡧⠤⠤⠤⣀
⠀⡇⠀⠘⠛⠛⠛⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠇⠀⠀⠀⠘⡟⠺⢯⠃⡞⢱⢟⣿⡾⠁⠀⡀⠀⠀⠑⢆
⠀⣧⠀⠈⠉⠉⠉⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠀⠀⠀⠀⠀⠉⣲⡜⣆⠀⠀⠈⣾⡽⠀⠀⣧⡄⠀⠀⠈⣇
⠀⢹⠀⠀⢰⡶⢰⡦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⢠⠞⠻⠿⣿⣷⣲⣻⣿⡤⠀⣸⡿⠀⠀⠀⠀⡿
⠀⠈⠓⠦⢄⣀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⡇⠀⠀⢠⡇⠀⠀⠀⠘⢀⣴⡟⢀⣀⣠⣴⡚⢱
⠀⠀⠀⣀⣀⣤⣭⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⣀⠃⠤⢤⣾⢧⣄⣀⡤⠶⠛⠛⠛⠛⠛⠋⠉⠀⠀⡇
⠀⣰⠞⣉⣁⣀⣀⣀⣹⣤⣤⣤⣤⣤⣤⣤⣶⣶⡿⡄⠀⠀⠀⢣⠀⠠⣠⡇⠀⠀⡀⠘⠲⣤⣀⣀⡀⢀⣀⣀⣠⡼⠓
⠀⢹⡀⢯⣤⣤⠤⠤⠤⠤⣤⣤⣤⠤⠤⠤⣤⣤⠤⠇⠀⠀⠀⠈⢧⡀⠀⢳⡀⠀⠈⠙⠛⠻⡉⠉⠉⠉⠉⠀⠀⠀⣀
⠀⠈⡇⠀⢸⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⠀⠀⠀⠀⠀⢀⣠⣽⠶⣤⣽⣦⡀⠀⠀⠀⠘⢿⣟⣛⣛⣩⣭⣽⣿
⠚⠛⠁⠀⣸⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣼⡀⠀⢀⡴⠚⠻⠿⠿⢛⣡⠤⢶⣿⣷⣤⣤⣤⣤⠟⣟⢛⡇⢸⠁⢀
⠀⠀⠀⢸⣗⣲⣱⠀⠀⠀⠀⠀⠀⠀⠰⡷⣋⢇⡇⠀⠘⠿⣶⣶⠶⢯⡵⠞⠛⠛⠿⠿⠋⣈⣉⣀⠴⠋⠉⠀⠈⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣶⣿⣯⣿⣷⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣹⠟⣛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⡓⢿⡍⣭⣭⣭⡍⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣼⣿⣿⣿⣿⣿⠟⠉⠉⠉⢉⣽⣿⣿⡿⣻⣿⡆⠁⣿⣫⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣿⣿⣿⣿⠟⠁⠀⠀⢀⣴⣿⣿⡿⣫⣾⣿⣿⣧⠀⣿⣿⣿⡇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⠟⠁⠀⠀⢀⣴⣿⣿⡿⣫⣾⣿⣿⣿⣿⣿⠀⣿⣥⣾⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⡃⠀⠀⠀⣴⣿⣿⡿⣫⣾⣿⣿⣿⡿⠋⣼⣿⠀⠛⣛⡛⠃⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣿⡇⠀⣠⣾⣿⡿⣫⣾⣿⣿⣿⡿⠋⣠⣾⣿⡏⠀⣾⣿⣿⡆⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⢹⣧⣾⣿⣿⣯⣾⣿⣿⣿⣿⣉⣤⣾⣿⣿⣿⢃⡄⣿⣿⣿⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣙⣓⣀⣈⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣊⣀⣒⣛⣁⣈⣛⣋⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠿⠿⠶⠶⠿⠷⠶⠾⠿⠿⠷⠶⠾⠿⠶⠶⠿⠿⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⢠⠞⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠳
⣿
⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⣴⠖⢲⡄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⠴⠖⠚⠋⠉⠉⠀⠀⣿⠀⢸⡇⠀⢀⣤⠴⠖⠚⠋
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠁⠀⠀⢹⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⡆⠀⠀⠀⠴⠤⠤⠆⠠⠶⠄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣀⣀⣸⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⡉⠉⢿⠙⠓⠶⠤⣤⣀⣀⠀⠀⣿⠀⢸⡇⠀⠰⠤⣤⣀⣀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠘⣟⠛⢳⠀⠀⠀⠉⠉⠛⠛⠶⠼⠃⠀⠀⠀⠀⠀⠉⠙
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢹⡶⠚
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⣀⡗
⣿⠀⠀⢠⡖⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⣿⠉⠉⢹⣇⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⣿⣀⣀⣀⣉⠉⢀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠉⠉⠉⠉⠀⠈⠉⠉⠁⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠘⢦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⡄⢠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡄
⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣆⠀⠐⠀⠄⡆⠐⠂⠀⢆⢠⣂⠄⡆⠀⢐⠀⠀⢄⠀⠀⡆⢰⠀⠄⡔⠐⡄⣆⠄⢐
⣀⣀⣀⣀⣀⣀⣀⣡⣄⣠⣤⣂⣇⣀⣀⣎⣈⣸⣤⣇⣤⣄⣤⣤⣀⣤⣝⣀⣇⣸⣈⣆⣣⣤⣁⣇⣢⣨⣤⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠒⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠰⡓⡀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠈⢀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠀⢀⠌⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡁⠠⠤⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠄⠀⠘⠀⡀⠀⠀⠀⠀⠀⠘⠈
⠀⠀⠀⠀⠀⠀⠀⢀⠄⡰⠊⠉⠀⠀⠀⠀⠀⠉⠉⠑⠢⢤⣀⠀⠀⠀⠀⠀⠀⠆⢀⠀⠁⠈⠀⠐⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡔⠁⡜⠀⠀⢀⠔⠈⠉⠀⠒⠂⠤⠤⢀⣀⠈⠑⢄⠀⠀⠀⠀⠀⠢⡉⠒⠤⠀⠁⠀⠄⡇
⠀⠀⠀⠀⠀⡸⠀⢰⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢢⡈⢆⠀⠀⠀⠠⠀⠈⠢⢄⠠⠀⢀⠀⠑⠒⠒⠒⠒⠒⠂⠈
⠀⠀⠀⠀⠀⡇⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁
⠀⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣷⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠔⠀⠀⠀⡟⢸⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠋⠻⠤⠀⠢⢄
⠀⠀⠀⠀⠸⠀⠀⠇⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠉⠁⣀⣀⠠⠔⠁⢸⠀⠀⢰⠀⠀⠀⠀⠀⠀⠘⠀⠈⠀⠀⠀⠀⡀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⡇⠀⠰⠀⠀⠀⠀⠈⠑⢒⠒⡀⠉⠉⠁⠀⠀⠀⠂⣠⠋⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⡄⢀⠠⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠘⢦⡀⠱⣀⠀⠀⠈⠀⠈⢀⡀⠠⠤⠄⠒⠶⠍⢏⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⢃⣀⣑⠬⣐⠒⠈⢀⠠⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⠌⣉⠄⠉⠉⠉⠉⠀⠀⠀⠀⠆⠂⠀⠀⠀⠘⡀⠀⠀⠀⠂⠒⠂⠄⠂⠤⠖⠐⠂⠀⢀⡴⠙⠚⠡⠀⡀
⠀⠀⠀⠀⡀⠄⡌⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⣀⠀⠄⠀⠀⠂⠀⠀⠀⠁⠀⠰⠄⠉⢁⠀⠀⡸⠀⡇⠀⠀⠀⠠⠄⣀
⠀⠄⠂⠉⠀⠂⠚⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠭⠐⠀⠈⢀⠂⠠⠅⠊⢀⡚⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⡂⠔⠂⠀⠑⠤⠄⠐⠊⠀⡀⠘⠀⠁⠕⠦⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠚⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⡠⠄⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠈⠻⣷⣄⠀⠀⠀⢀⣴⡿⠋⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠈⠻⣷⣄⣴⡿⠋⢀⣴⡿⠋
⠀⠀⣠⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⡄⠈⠻⠋⠀⣴⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⡀
⢠⣾⠟⠁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠙⢿⣦
⣿⡇⠀⣾⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣿⡆⠀⣿
⣿⡇⠀⣿⡇⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⣿⡇⠀⣿
⣿⡇⠀⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡇⠀⣿
⣿⡇⠀⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡇⠀⣿
⣿⡇⠀⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡇⠀⣿
⣿⡇⠀⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢻⣿⣿⣿⠀⢀⣀⡀⠙⣿⡏⠀⢀⣀⣀⣽⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡇⠀⣿
⣿⡇⠀⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⡀⠈⣿⣿⣿⠀⢸⣿⡇⠀⣿⡇⠀⠙⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡇⠀⣿
⣿⡇⠀⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠘⠛⠀⠸⣿⣿⠀⢸⣿⡇⠀⣿⣿⣶⣶⣦⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡇⠀⣿
⣿⡇⠀⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡁⣠⣶⣶⣦⡀⣻⣿⡀⠈⠉⢀⣠⣿⣟⠉⠉⠁⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡇⠀⣿
⣿⡇⠀⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡇⠀⣿
⣿⡇⠀⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡇⠀⣿
⣿⡃⠀⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⡇⠀⣿
⣿⡇⠀⣿⡇⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⣿⡇⠀⣿
⢿⣇⠀⠻⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡿⠃⢀⣿
⠈⢿⣦⣀⡈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣀⣠⣾⠏
⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⡿⠁⢠⣿⣿⣿⣿⣿⣿⣿⣧⠀⠹⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⢹⣷
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⣀⣤⣤⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡆
⠀⠀⠈⣿⠀⢸⡇⠀⢠⡤⠖⢒⣒⣚⣛⣛⣛⣛⣛⣛⣛⣛⣒⣀⣀⣉⣉⣉⣭⣭⣤⣤⣬⣽⡛⢳⠀⠀⣀⡀⣀⠀⠀⠀⡇
⠀⠀⠀⣿⠀⢸⡇⠀⢸⢇⡼⠋⠉⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣸⡇⢸⡏⠀⠈⣷⠀⠀⡇
⠀⠀⠀⣿⠀⢸⡇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠈⠳⠤⠔⠃⠀⠀⡇
⠀⠀⠀⣿⠀⢸⡇⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣤⣤⣄⠀⠀⡇
⠀⠀⠀⣿⠀⢸⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⡟⠀⠀⣹⠃⠀⡇
⠀⠀⠀⣿⠀⢸⡇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⠒⠊⠁⠀⠀⡇
⠀⠀⠀⣿⠀⢸⣇⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣿⠀⠈⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣾⠉⠙⢣⠀⠀⣿
⠀⠀⠀⣿⠀⠀⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢹⠀⠀⠻⠤⠤⠟⠀⠀⣿
⠀⠀⠀⣿⠀⠀⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⢸⡄⢀⣤⠤⣤⣄⠀⠀⣿
⠀⠀⠀⣿⠀⠀⣿⠀⢸⡏⠳⢦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣴⢖⣋⣀⣼⠁⠸⣇⠀⣀⡟⠀⠀⣿
⠀⠀⠀⢹⠀⠀⣿⠀⠘⠓⠒⠒⠒⠒⠛⠒⠛⠛⠛⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠀⠀⣸⣿
⠀⠀⠀⠈⢻⣷⡿⣶⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⠛⠛⢳⣶⣿⣿⠟⠛⣿⣿⡿⣿⠉⠉
⠀⠀⠀⠀⢸⡟⠁⠏⠹⣿⣄⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠙⠀⠀⢿⠉⠁⡏
⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠉⠉⠁⠈⠉⠙⠛⠶⠶⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣤⣄⡀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⢀⣤⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⢀⣾⣤⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⢡⡉⢯⠀⡇⢀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠛⠃⡰⢸⠇⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠈⢷⣍⣈⡳⢿⣌⢣⡘⡔⡆⢲⠀⡇⡜⢀⡀⢐⡴⠋⠀⠀⠀⢻⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⣀
⠀⠀⠀⠀⠀⠈⠉⠀⢀⣿⡧⠙⡀⠁⢘⣨⣤⡒⠉⠛⠋⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⣴⣿⠏⠀⠀⠉⠉⠉⠁⠈⠙⢆⠀⠀⠀⠀⠀⠀⠀⢀⡠⠆⠾⠁⠀⠉⠀⠀⠀⠀⠀⠉⠛⠛⡛⣥⡀
⠀⠀⠀⠀⢀⡤⠞⣽⠃⠀⠀⠀⠀⠀⣶⠀⠀⠀⢸⡄⠀⠀⠀⠀⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠈⠻⣆
⠀⠀⠀⠀⣾⠁⠀⣿⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠈⡇⠀⠀⠀⠀⠸⣦⣀⣤⠤⠖⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⢀⡽
⠀⠀⠀⠀⠛⠦⠄⢻⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⢷⠚⠻⢶⡀⠀⡟⠀⠰⡀⠀⠓⠦⠤⣤⠤⠤⠤⠤⠤⠤⠞⢯⡉⠉
⠀⠀⠀⠀⠀⠀⡾⠛⠛⠓⠶⠖⠒⠚⠃⠹⡇⠀⠀⢹⠀⠀⣸⠃⠀⠳⣄⡣⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⢿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠿⠖⢒⢙⡶⡟⠁⠀⢀⣰⡞⠛⠛⠛⢷⣦⣄⣀⣀⣀⣀⣀⣀⣠⣴⢋⣀⣀⡀
⠀⠀⠀⠒⠀⠀⠈⠍⠛⠛⠛⠛⠿⠿⠿⠅⠻⢿⣸⠗⠛⠁⠀⠀⠀⢀⣘⡛⣒⡚⣒⣂⣉⡉⠛⠉⠉⠉⠉⠁⠀⠨⠭⠭⢥⣤⢄
⠒⠒⠀⠀⠀⠤⠤⢄⡀⠀⠀⠀⠀⠀⢀⣉⣁⡤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⢉⣁⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠡⠈⠠⠭⠭

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠁⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠀⠀⠀⢐⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠠⠈⠐⠢⠄⣀
⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠄⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠃⠀⠀⠀⡀⢀⠀⠀⠉⠐⠂⠀⣀
⠀⠀⠀⠀⠃⠁⠀⠀⠀⢐⣀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠀⢠⣄⠀⠀⡤⠀⠀⠀⠉⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠤⠄⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⣤⢬⠽⢭⠂⣠⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠄⡀
⠀⠀⠀⠀⠰⢸⠀⠀⠀⠀⠀⡠⠀⠉⠉⠑⠢⠤⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠲⠄⣠⠀⢉⠏⠀⠀⠀⢠⠐⢲⡆⠀⠀⠀⠀⠀⠈⠙⡆
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⣸⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠒⠀⡂⠐⢀⠜⠁⠀⠀⠀⠀⠀⢠⠁⡸
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⡎⠀⡀⠀⡀⠈⠀⢿⠁⠀⠀⠀⠀⠀⠀⠐⠤⣀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⡐⠀⠀⡎⢀⠃
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠘⡀⠖⠂⠐⠾⢡⡊⣀⣀⣀⣀⠀⠀⢀⡀⠀⠤⣭⡖⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⢰⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠠⠤⢒⠡⠶⠙⡿⠶⢖⢤⠞⠛⠨⠲⠤⡑⢬⡈⠀⠈⠑⠲⢤⣀⠀⠀⠀⠀⠀⠀⡇⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⡄⠁⠁⡄⠸⡍⠛⠙⠃⠛⠓⠚⠁⢨⠀⠀⠀⠀⠀⠈⡐⠤⡀⠀⠀⢘⠉⢳⣠⣄⡀⢠⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠧⡔⠒⣇⡀⠯⠂⠒⣰⣤⠖⠁⠀⠀⠑⢄⠀⠀⠀⠀⠢⠀⠀⠑⠢⢄⣀⠉⠐⣯⠛⠻⢅⡁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠀⠀⠀⠑⢀⡠⠄⢖⠈⠀⠉⠑⡄⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠠⠀⠈⠉⠉⠁⠀⠀⠤⠀⠑⠆
⠀⠀⠀⠀⠀⠀⠙⠄⠀⠘⢤⠀⠐⠂⠀⠀⠀⠸⠀⠀⡀⠤⠤⠈⢶⣄⠀⠀⠀⠀⠑⢄⠀⠁⠀⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠑⠢⠤⣀⣀⣀⡜⠚⠀⢀⠀⠀⡀⠌⠀⠑⠤⡀⠀⠀⠀⠑⢄⡀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⣀⣀⣀⣀⣀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠬⠖⠀⠀⠀⠀⠙⠦⠤⠤⠤⠴⠒⠒⠂⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠤⠶⠶⠦⠤⠤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡖⠒⠂⠐⠀⠀⠀⠀⠂⠐⠀⠀⢀⡀⠈⠉⠉⠉⠉⠉⠉⠀⠁⠀⠀⠁⠈⣍⢹⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡟⠀⠀⠀⠀⡀⠀⣀⠀⠀⠽⠠⣾⡇⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢰⢔⠀⠀⠀⠀⠀⢠⢠⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠈⢸⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⢀⠀⠀⠙⣅⠀⠀⠀⠀⡰⠟⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⠀⣎⢆⢤⣿⠟⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠐⠋⠈⠀⠀⠀⠀⠀⠀⠀⢸⢿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡏⣦⢹⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣸⣿⣧⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡸⠟⠿⣯⣋⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡼⡇
⠀⠀⠀⠀⠀⢀⡴⠋⡠⠘⠆⠈⢿⣶⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡠⣸⣾⡗
⠀⠀⠀⢀⠔⢫⢄⣬⡔⠁⠈⢡⣿⣿⠿⠿⠷⠶⠶⠶⠶⠶⠶⣶⢶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⠿⠿⠗
⠀⠀⡖⠁⡠⠣⡧⣯⢇⣠⡶⠟⠁⠀⠀⠀⣀⣀⣤⠔⠒⢊⣉⣀⣤⡟⠙⠒⠦⣤⣄⣀⡀
⠀⠀⢳⣄⠐⠀⣀⣴⣿⠋⠀⢠⣴⣶⡬⠭⠴⠞⠓⡛⢛⣉⠉⠀⠤⠄⠉⠉⠙⠒⠚⠭⣿⣿⣶⣦⣤⣄⠀⢀
⠀⠀⠀⠙⠓⠛⠛⠋⠉⠻⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⣛⣻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠐⠀⠀⠀⠀⠀⣁⡀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠀⠀⠀⢠⣿⠟⠻⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠘⣿⠶⣘⡁⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣟⣁⠁⡀⠀⣤⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⢀⡀⣠⣴⣾⡏⠟⢸⣿⠁⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⣿⣿⣿⠏⠀⣤⣼⣿⣿⣿⣆⣄⠀⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣼⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠿⡡⢾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⢿⣿⡿⢿⠿⣿⡟⠻⠉⠉⢀⣀⣨⣬⣬⣵⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣚⣚⣿⣭⣭⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⡛⠛⠛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣟⣻⣯⣩⡅⢠⡄⠹⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠹⡷⢸⠃⢀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⠶⠒⣂⣠⣤⣤⣶⣶⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣩⣽⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠟⣻⣿⠛⠿⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⢀⠀⠱⠄⠀⠀⠠⠂⡀⠀⠀⢀⠀⠀⠀⢀⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠈⠁⠴⡄⠀⠀⢀⡄⢰⠢⣤⡀⣀⣠⡖⣏⠎⢀⣀⠀⠿⠆
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠳⣼⣄⣀⣠⡀⢹⣶⣔⠃⢨⣦⣿⡵⢿⣇⣰⡏⢀⠘⡻⠛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠛⢙⣹⣯⡁⣊⣛⣽⣯⣿⣤⣽⣿⠅⠀⣽⠿⠸⣿⡟⡤⢆⢬⢀⢲⡆
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣢⣼⣭⣯⣓⣛⣙⣿⣭⣭⣭⣬⣭⣭⣽⣽⣞⢋⠒⠻⢾⣿⣿⣩⣡⠋
⠀⠀⠀⠀⠀⠀⢻⣿⡟⡹⠿⣿⡿⢛⡻⠟⢲⡷⢶⠶⠶⠴⠆⠔⠒⠂⢐⣂⠐⣂⣢⣦⣤⣤⣤⡁
⠀⠀⠀⠀⠀⠀⢸⣿⣾⠉⠛⡿⠿⠷⠶⠖⠒⠲⠤⠤⠤⠬⣭⣿⣟⠟⢺⣧⢈⣽⡯⠥⣌⠑⡏
⠀⠀⠀⠀⠀⠀⠈⣿⢹⡄⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄⣾⣿⢸⣏⣠⠞⠉⡆⡇
⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻⣿⢈⠻⣧⣤⠞⢠⡇⢀
⠀⠀⠀⠀⠀⠀⠠⣿⢸⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⢤⣡⣄⣩⣤⡯⣆
⠀⠀⠀⠀⠀⠀⠸⣿⢸⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣿⠚⠛⠛⠛⠛⠃⣿⡆
⠀⠀⠀⠀⠀⠀⢰⣿⡀⡇⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠸⢿⠀⣛⡙⠛⢃⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠈⣿⡇⢱⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢸⠀⠿⠿⠿⢿⠘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⣹⣇⡘⢦⣝⣿⢤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣾⠿⠀⠀⢸⠀⡛⠛⣻⠀⠈⣿⡔
⠀⠀⠀⠀⠀⠀⠀⡿⣯⣧⣤⣤⣤⣤⢤⣤⣤⣀⠌⣉⣩⣽⣷⣶⡤⢦⠄⢼⢈⠡⣤⡳⠂⠠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣇⡻⣯⠼⢾⣌⡾⠰⠼⠀⠒⠤⠼⠇⠺⠧⠯⢧⡀⢠⣾⠤⢬⣤⣤⣤⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⢿⡿⡟⠛⢿⣿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⢠⣤⢤⡤⡬⠭⠭⠭⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠆⢠⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠒⠒⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣖⠀⠀⠀⠁⠠⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠀⠀⠐⠖⠀⠀⠈⠢⡀⠀⠀⡀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⠃⢀⠀⢢⠀⠀⠀⠈⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠠⡀⠀⡠⠁⠀⠐⡀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠐⢊⠀⠉⡁⠀⠘⠢⢄⠀⠑⢄⠀⠀⠀⣀⡠⠔⠒⠒
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠐⠀⠑⢄⠶⡀⠀⠀⠀⠉⠦⡀⠑⡎⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠢⠀⠂⠀⠀⠀⠘⠂⠠⠄⠠⠤⠀⣀⣘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠐⠁⠁
⣿⡿⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡶⠾⠿⠿⠟⠛⠿⠿⠷⢶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣦⣄
⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⡀
⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⣀⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄
⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣂⣚⣉⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⣰⡿⠁⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠈⢿⣆
⢠⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⢇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢟⡛⣿⣿⣿⣷⡘⣿⡇⠀⠀⠀⠀⠀⠀⠈⣿
⣸⡏⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⣿⣿⡿⢟⣛⣛⡛⣛⣭⣶⣿⣿⡇⢿⣿⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹
⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⣿⡏⣾⣿⣿⣿⡇⣿⣿⣿⣿⣿⡇⣷⢹⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⣿⣷⣜⠛⣛⢛⣃⠻⢿⣿⣿⣿⡇⣥⣿⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈
⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⣿⣿⣿⡇⣿⡎⣿⣿⣶⣮⣝⡻⠃⣿⣿⣿⣿⡇⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸
⢻⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣎⢿⣿⣿⣿⣿⣬⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣱⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸
⠘⣿⡀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠷⢶⣶⣶⠶⢶⣶⣶⣶⣶⣶⡶⠶⠶⢶⡶⠶⠾⠿⣿⡇⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠹⣷⡀⠀⠀⠀⠀⠀⢸⣿⡰⠿⢎⣿⡇⠿⢇⣿⣿⣿⣿⣿⡘⠿⠿⢸⣇⠿⠿⠇⣿⡇⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠹⣷⡀⠀⠀⠀⠀⠘⠛⢛⣛⣛⣛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⣛⣛⠛⠃⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠙⣿⣄⠀⠀⠀⠀⠀⢸⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠀⠀⠀⠀⠀⣠⣿⠋
⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠷⢶⣶⣶⣦⣴⣶⣶⡶⠾⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠠⡴⠟⠛⣢⠤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣉⣰⢸⢁⢎⢜⢃⡾⠣⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠈⢸⡅⣪⣣⠾⢃⡸⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠊⡇⠸⢼⡧⠇⢀⢞⣼⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠂⣤⠀⠀⠀⠀⠀⠀⠀⠈⣀⡅⣰⣿⢏⢀⠒⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠈⠈⡉⠂⠀⠀⠀⠀⠀⠀⣶⣊⡀⣋⢪⢡⡷⢱⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⣠⣥⣌⠛⡿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠄⣰⣷⡷⠀⠀⠀⠀⠀⠀⢠⣭⣤⠆⣗⢀⡝⡱⣻⢿⣿⡅
⠀⠀⠀⠀⢀⡼⢭⣴⠟⠛⢁⢀⡀⢀⠀⠀⠀⠀⠀⠈⠀⣠⠀⢸⣽⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⡇⠴⢰⢡⠟⣽⣿
⠀⠀⠀⣰⣿⣿⣿⣛⣖⠚⣁⣀⣠⡭⡜⠀⠀⠀⢀⣤⣶⠖⠎⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣏⣿⡇⢠⣃⣋⣰⣿⣿⣀⣀
⠀⠀⠀⠙⠛⠛⠻⠿⠿⠿⠿⠿⠿⠷⠧⠤⠶⠿⠿⠋⠁⠄⠸⠤⠀⠀⠄⠀⠀⠀⠀⠀⠀⠢⠊⠓⠰⠾⠯⣝⣻⢠⣽⠟⠐⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣶⣒⣒⣶⣆⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⣯⣀⣉⣹⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠉⠉⠉⠉⠉⠉⢉⣉⣛⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠋⠉⠉⠛⠛⠛⠷⢦⡄
⠀⠀⠀⠀⠀⢀⡾⠁⢀⣤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣦⡀⠀⣿⠀⠀⣠⢞⣻⣷⣄⠀⢻⡄
⠀⠀⠀⠀⠀⢸⡇⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⣿⠀⠀⢿⡻⢤⣼⡿⠀⢸⡇
⠀⠀⠀⠀⠀⣼⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠹⠿⠍⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢹⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⣤⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣦⠀⠀⠀⠀⠀⠀⢠⡇⢸⡇⠀⠀⡴⠊⣛⢲⡄⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠘⠃⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠈⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⢸⡇⢾⣉⡷⣿⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠑⠢⢽⠞⠁⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⢀⡭⢭⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠈⣳⡞⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢸⡇⠀⠀⢠⠞⢣⠀⠀⠀⣼
⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⣀⣀⣀⣠⡴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⠈⢿⠇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⢸⡇⢰⢲⠞⣺⠛⡗⢦⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⢸⡇⡿⢺⠦⡾⢶⡷⣾⢠⡏
⠀⠀⠀⠀⠀⢸⡇⠀⠈⠛⠛⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⣼⠃⣯⣼⣤⣇⣸⣇⡟⢸⡇
⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⢰⣾⣛⣻⡛⠲⠶⡶⠶⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣶⠶⠶⢶⡤⢤⡄⠀⠀⣿⠀⣧⣼⠤⡧⢼⢶⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠈⠳⣦⣤⣼⣯⣤⣽⣍⣉⣩⣏⣉⣹⣇⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⠒⢻⠒⠒⢺⠒⠚⣿⠀⠀⣿⠀⠓⠻⠴⠷⠞⣛⣡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠶⠦⠤⠤⠤⠭⠭⠭⢭⣭⣉⣉⣉⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⣛⡛⣛⣛⣛⣛⣛⣛⣛⣛⡛⣻⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠤⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣄⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣷⣯⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠿⠤⠤⠤⠤⠿⠤⠤⠤⣤⡤⠤⠤⠤⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣦⠀⠀⣿⠀⣠⣤⣤⣄⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⣿⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⢠⣄⠀⠀⣠⣠⣄⡀⠀⠀⠀⣿⠀⠀⣿⠀⠙⣛⣛⡋⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⢠⡟⢻⡄⠀⣿⠀⠈⢿⡄⠀⠀⣿⠀⠀⣿⠀⣼⠋⠉⣷⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⢀⡿⠛⠛⢿⡄⣿⣤⣤⠿⠁⠀⠀⣿⠀⠀⣿⠀⠹⠷⠶⠟⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⢤⣤⣤⣤⣤⣤⣤⣤⣤⠀⢤⡤⠀⣿⠀⠀⣿⠀⣶⠶⠶⢶⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⣿⣤⣤⣼⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠛⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠞⠋⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠶⠶⢶⣶⣶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠤⠤⠤⠴⠶⠶⠶⠖⠒⣒⣒⣒⣒⣒⣒⣒⣛⣓⣒⣒⣛⡒⠒⠶⠶⠶⠶⠦⠤⠤⠤⢤⣄⣀⡀
⠀⠀⠀⢠⠎⣡⣤⢶⣶⣶⣾⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣶⣶⣶⣤⡉⢳⡀
⠀⠀⠀⢸⠀⣿⣷⣿⣿⠿⠿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⢿⣿⣷⢻⣿⣿⣿⡿⣿⡿⣿⣿⣿⢸⡇
⠀⠀⠀⢸⠀⣿⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⣿⣿⣿⣿⣿⣎⣿⣿⢸⡇
⠀⠀⠀⢸⠀⡿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⣿⣿⣯⡻⣿⡿⣳⣿⣿⢸⡇
⠀⠀⠀⢸⠀⣧⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢿⣟⡿⢿⣿⣿⢸⡇
⠀⠀⠀⢸⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣿⣿⣿⣯⣿⣿⢸⡇
⠀⠀⠀⢸⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣯⡻⠿⡿⣫⣿⣿⢸⡇
⠀⠀⠀⢸⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠛⠛⢿⠟⠛⢻⣿⢸⡇
⠀⠀⠀⢸⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠾⠿⠿⠿⠶⢾⣿⢸⡇
⠀⠀⠀⢸⠀⣧⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⣿⣿⠭⠭⠭⠭⠭⢽⣿⢸⡇
⠀⠀⠀⢸⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣿⣿⠭⠭⠭⠭⠭⢽⣿⢸⡇
⠀⠀⠀⢸⠀⣿⣼⣿⣷⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣿⣿⢹⣿⣿⠭⠭⠭⠭⠭⢽⣿⢸⡇
⠀⠀⠀⢸⡀⠿⣧⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢸⠇
⠀⠀⠀⠀⠙⠒⠦⣬⣭⣍⣙⣛⣛⣛⣛⣛⣛⡛⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣋⣉⣭⣭⣥⠴⠒⠋
⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⡇⢸⠀⡇⣿⢩⡏⣿⢹⡏⣿⢹⡏⣿⢹⡏⣟⢹⡏⡏⢹⠉⡏⢹⢉⡇⣿⢸⡇⣿⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⣽⠉⠉⠉⠉⠉⠉⠉⡏⠃⠆⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⢸⢿⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⣼⢸⣜⣀⣀⣒⣒⣒⣀⣒⣣⡂⣮⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡟⠀⠀⠉⠿⠉⡈⠉⡟⠁⠀⠙⣯⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⢀⡆⠐⢦⣖⠥⣶⡠⠂⢸⣆⠀⠄⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⡸⡇⠀⢺⢞⣶⡿⡆⠀⠸⠘⡆⠰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢠⠇⡇⠈⠉⠀⠆⠀⡏⠀⡇⠀⡇⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⢸⠀⡇⠈⢸⠤⠖⠰⡏⠀⢱⠀⣷⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⢒⡚⢠⠁⢀⡄⠀⣀⠀⣇⡀⠘⠀⡼⡌⠁⠀⠀⠀⠀⠀⢶⣦⣄⣀⣤⣴⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠰⣬⠃⡀⠀⠈⠅⢰⠉⡇⢹⠀⠀⠃⠠⠷⠃⠀⠀⠀⠀⠀⠀⠉⢻⡏⠈⠙⠻⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢰⠀⠀⢰⠀⡏⠀⢸⠈⡀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢐⠠⢶⣷⣶⣦⣄⡉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⢸⠀⠀⠀⡇⢁⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⣾⣿⣿⣿⣿⣿⣷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠙⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠁⠀⠈⠈⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠈⠃⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠄⠠⠒⣤⡄⣀⠀⠀⠁⠀⡁⠀⠔⡟⠧⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠊⠈⠈⠁⠀⠀⠀⠈⠀⠈⠂⠀⢰⡄
⠀⠀⠀⠄⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠮⠔⠐⠒⠀⡀⢀⠀⠀⠀⠈⢇⠉⠉⠉⠀⠈⡆
⠀⠀⠀⠈⢀⠀⠀⠀⠀⠁⠀⠠⠄⠀⠀⠀⢀⣀⡤⠆⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠠⠄⠀⢄⠀⠃
⠀⠀⠀⠀⠈⠒⠒⠒⠒⠢⣄⡰⠀⢀⡠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⡃⠀⠀⣀⣀⠀⢀⡀⠀⠀⣀⣀⣀⡀⠠
⠀⠀⠀⡄⠀⠄⠀⠀⠀⠀⢀⠂⠀⡀⢠⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⣀⠁⠨⣼⣿⡟⠛⡟⢉⡏⠉⣏⠀⢀⣀⣀⡀
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠁⠃⢀⡀⠁⠀⡀⠘⠈⠀⠉⠍⠐⠠⠀⠀⠀⠀⠀⠀⠠⠰⠀⠀⠀⠀⠀⠠⠀⠀⢀⣠⡀⠤⣷⢞⢁⣀⣭⠽⠧⠴⠒⠋⡇
⠀⠀⠤⢐⡆⠉⠋⠉⡌⠀⠀⠀⢢⠀⢀⢀⣀⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠁⠂⠀⠀⠀⠀⠀⠉⠀⠀⠐⠒⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠈⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣤⣽⣿⣷⣤⣤⣤⣤⣾⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⡇
⠀⠀⢀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⠀⠀⠹⣿⣿⣿⣇
⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⡀⠀⢀⣸⣿⣿⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣶⡀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⣦⣤⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⣿⣧⠀⠀⠀⠀⠀⣿⡏⠉⠉⠉⠉⠻⣿⣦⠀⠀⠀⠀⢸⣿⣿⣿⡟⠁⠀⠈⠻⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠘⣿⣧⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⣿⣿⣇⠀⠀⠀⣠⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣿⣿⣤⣤⣤⣽⣿⣆⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣷⣶⣾⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣾⡿⠛⠛⠛⠛⠛⠻⣿⣆⠀⠀⣿⣇⣀⣀⣀⣠⣴⣿⠟⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⠀⠀⠀⠛⠛⠀⠀⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⢸⣿⣏⣉⣉⣉⣿⣉⣉⣉⣉⣿⣿⠇
⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠿⠟⠛⣿⠟⠿⠿⠻⣿⣿
⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⣶⣶⣿⣶⣶⣶⣶⣿⣿
⠀⠀⠈⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⣀⣀⣀⣿⣀⣀⣀⣈⣿⡏
⠀⠀⠀⣿⣿⣿⣿⣿⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋
⠀⠀⠀⠀⠀⢠⣶⣶⣤⡤⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠠⣤⣴⣶⣦
⠀⠀⠀⠀⠀⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀
⠀⠀⠀⠀⠀⡤⢤⠲⠎⠅⡛⠗⠓⠋⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⣭⠤⠴⢭⢅⠉⠦
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠁⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠄⠀⠀⡡⢱⢀
⠀⠀⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠄⠀⠀⠀⢰⢡⠀⠣⡀⡄⠂⠀⠠⣀
⠀⠀⠀⠀⠀⡇⠇⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠁⠀⠀⠀⢄⣾⠘⢄⢹⠈⠢⡀⠀⠀⠑⠤⡀
⠀⠀⠀⠀⠀⡇⠀⠄⠀⠀⠀⠀⢀⠄⣹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠄⠀⠔⢡⡿⡖⠀⢻⠀⠀⠀⠑⠤⡀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⢡⢸⠀⠀⠀⠠⢒⠕⡊⠤⠠⠀⠀⣀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠉⠁⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠮⣀⣘⠀⠀⠀⠀⠀⠈⡆⠀⠀⢈
⠀⠀⠀⠀⠀⢸⢸⠨⢐⣥⡞⢥⡊⠁⠀⠀⡠⠚⢡⠀⠀⠀⠔⠀⠀⠀⠀⣤⣶⣲⣶⢰⠀⠶⡖⠀⠀⣠⠀⠠⠐⠈⢢⠣⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠸⠄⢴⡁⠀⢀⠀⡠⢃⠴⠋⠀⠀⡸⠄⢀⠎⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⠀⢱⡅⠀⢤⠀⣀⣀⣠⠴⠥⠤⠜⠀⠀⢄⠀⡇⠀⠀⠀⠃
⠀⠀⠀⢀⠠⠂⠁⠀⠀⠀⠀⣀⠔⠁⠀⠀⡠⠊⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢡⠀⠀⠀⢂⡐⢠⠒⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⢰
⠀⠀⠎⠥⠀⣀⠀⡀⢀⠄⠊⠁⠀⠀⡠⠊⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣸⠀⠀⢀⠈⠁⡇⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢸
⠀⠀⡆⠀⠀⠀⠀⠀⠁⠀⠀⠀⡠⠊⠀⠀⠀⠺⠀⠤⠀⠤⠠⠤⠤⠤⠤⠤⠤⠤⠤⢸⠂⠺⠭⠯⠭⠽⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⡆⠀⣠⠞⠀⠀⠀⠀⠀⠰⠀⡤⠤⠤⠤⠤⠤⠤⠄⠤⠤⠤⡤⠸⠃⠀⠀⠀⠀⠀⢰⠀⡄⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢸
⠀⠀⠧⠤⠤⠄⠀⣀⠁⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠑⠒⠒⠒⠂⠉⠉⠉⠉⠉⠁⠂⠉⠈


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣤⠴⠶⠦⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⣠⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠓⠒⠒⠒⠒⠒⠒⠒⠚⠓⠒⠒⠲⣄
⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣧⠀⠀⠀⠀⠀⠀⡏⠈⠉⠉⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠸⣆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⢹⡄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠛⠛⠛⢻⡀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⣇⣀⣀⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠻⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠹⢦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛

⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⣾⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣷
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠶⠿⠿⠿⠿⢿⠶⣤⡄



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡁⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡞⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣠⣼⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡹⡄⠀⠀⠀⠀⠀⠀⠀⣀⢔⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀⣀⣀⡀⠀⠀⠀⠈⣧⢹⡀⠀⠀⠀⢀⡤⣪⠵⠋
⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠟⠛⠋⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠣⠻⣟⠛⢛⡵⠚⠛⠻⠟⠛⠛⠶⠶⠶⠶⠶⣶⣦⣤⣤⡀
⠀⠀⠀⣀⣤⣾⣯⣭⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣶⠶⠟⠛⣿
⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠶⠶⠶⠶⣶⣶⣶⣤⡶⠾⠛⠋⠉⠉⠀⠀⠀⠀⠀⢰⡿
⠀⠀⢸⡇⠀⡖⠒⠒⠒⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣦⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣸⠀⠀⡇⠸⢉⢉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡆⠀⢀⠀⠀⠀⢀⢀⣀⠀⠀⢸⡇
⠀⠀⢸⡆⠀⡇⡇⠞⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⡴⠿⣶⡀⣿⠀⠀⢿⢸⢰⣾⢸⣸⣿⠀⠀⢸⡇
⠀⠀⢸⡇⠀⡇⢧⣀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠘⢧⣤⡿⠃⣿⠀⠀⣾⢸⢸⠿⠸⠛⠛⠀⠀⢸⡇
⠀⠀⢸⡇⠀⣷⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⢀⣿⠀⠀⠙⠈⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣤⣤⡀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⠇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢾⠀⢈⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⢸⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠳⠟⠃⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡶⠶⢶⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⣿⠀⠀⠘⠓⠶⠶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡇⠀⢸⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⢿⣤⣀⣀⣀⡀⠀⠀⠀⠉⠉⠉⠛⠛⠓⠒⠲⠶⠶⠶⠶⢤⣤⣤⣤⠞⠀⢧⣤⣾⢠⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣼⠇
⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠷⠶⠶⣦⣤⣤⣤⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⣠⣤⣶⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠿⠿⠿⠷⠶⣶⣶⣾⣷⠶⠿⠛⠋⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⡋⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣼⣿⠀⠉⠉⠙⠒⠒⠦⠤⢤⣤⣤⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠉⠉⠉⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠀⢀⡈⠉⠢⡀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠀⣰⠋⠀⠀⢰⢦⡀⣿⠾⢦⣱⢸⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠆⠀⣇⢸⡀⡀⡜⢊⠙⠃⠲⠀⢯⢸⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠄⢘⠶⢧⠟⠁⠈⠀⣀⡁⠀⢸⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠲⢥⣀⠘⠃⢮⠥⢇⣠⡾⠉⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⡟⠻⢧⣀⣸⣿⠾⣇⣰⣻⢉⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⡏⠉⠲⣌⡿⠁⠀⢈⣽⣿⠿⡿⠛⠛⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⣠⢻⡄⠀⠸⠀⠀⢠⠎⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠹⡦⣀⢀⣴⡡⠞⢹⣿⠀⠀⠀⢰⠒⢒⣒⣒⡆⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⢛⣉⡤⠞⢹⣿⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡍⠘⣦⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⢯⡀⠑⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠓⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⢻⣿⡤⠤⠤⠤⠖⠒⠒⠒⠛⠛⠛⠓⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⢳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣤⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⢀⣴⣿⡿⠋
⢀⣤⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠶⠶⠿⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣤
⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⣿⠀⠀⢀⣤⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣄
⣿⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣴⠟⠛⠛⢷⡄
⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣿⠀⠀⠀⢸⡇
⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⠷⣶⡶⠟⠁
⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⡾⠛⠻⣶⡀
⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠰⣿⠀⠀⠀⢸⡇
⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⢷⣤⣴⠟⠁
⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠹⣦⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡾⠃
⣿⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠙⢷⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡾
⠀⠀⠉⠉⠉⠉⠉⢹⡟⠉⠉⢹⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⠉⠉⠹⣯⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠿⢧⣤⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢷⣤⣴⠿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⣀⣀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣆
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⡈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣰⡿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠻⣦⡀⠀⡇⡠⡢⣀⡢⡀⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⡇⠰⣗⡠⡗⡀⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠑⠈⠑⠂⠀⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠔⣠⣴⡔⠄⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⡘⣗⣬⠟⡄⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠈⠉⠀⠈⠀⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⣸⣽⣿⣿⡇⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠲⠶⠶⠶⠇⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⣬⣭⣭⣭⡇⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⡇⠾⠿⠿⠿⠇⡇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠈⠻⠷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠟⠁⠀⠳⠶⠶⠶⠶⠾⠃⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⡋⠋⠛⠛⠛⠛⠛⠛⠛⠋⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠛⠛⠙⠛⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡆⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠇⠀⠀⠏⠀⢀⡴⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⡄⠀⠀⠀⡏⠉⠒⠪⠥⢒⣦⢤⣀⡀
⠀⠀⠀⣀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇⠀⢠⢖⡀⠀⠀⠉⠙⠛⠯⢦⣠⡄
⠀⠀⠀⠈⠙⠂⠀⠀⠀⡴⠒⠈⠉⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠁⠐⡿⢲⡶⠆⢴⠆⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢀⡌⠚⡟⠀⠀⣀⠔⠒⠦⡀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢙⢘⠋⠀⠙⠁⠀⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⡸⠄⢠⢨⠇⡜⠁⠀⠀⣠⢺⠀⠀⠀⠀⠑⣢⠄⣀⠠⠏⢿⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣇⡇⢰⡃⣰⠚⣋⣀⢣⡀⠰⡉⢀⣈⡄⡤⢀⠉⠀⠀⠀⣀⠭⠷⠲⣤⣄⡀⠀⠀⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⡟⠙⢼⢸⠉⣹⠀⣨⣞⣠⡖⣻⡠⠇⠀⠊⠙⡦⠤⢈⠑⠒⠤⡌⠕⠈⠙⠲⠶⠓⠠⢄
⠀⠀⢀⡤⠤⠤⢄⣀⡼⠀⢣⡠⠾⠋⡼⢁⡞⠁⠀⠀⠈⠳⣹⡦⠊⡤⠒⠃⠀⠀⠈⠐⠢⢄⣀⠀⠀⠀⠀⠀⢀⠤⠚⡇
⠀⢠⠏⠀⠀⠀⠀⠈⠑⠦⣄⠙⠤⠾⢂⡞⠀⠀⠀⠲⣤⣎⠉⣠⠞⠀⠀⢰⠀⢰⠀⠁⠀⠄⣀⠉⠒⠦⡔⠊⠀⠀⠀⡇
⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢯⣽⠀⠀⠀⠀⢀⡇⠉⠫⢁⠀⠀⠀⢸⠀⢸⠀⠀⢀⡠⠔⢻⠀⠀⡇⠀⢀⡠⠖⠃
⠀⠀⠈⡏⠀⠐⠦⣄⣀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⢸⡧⢬⡐⠠⣈⠒⠤⢀⢉⡡⠔⠊⣁⣤⠖⢹⠢⢤⡧⠖⠉
⠀⠀⠀⡇⠀⠀⠀⠀⠈⠁⢠⡀⠀⠀⠀⠀⠀⠘⣧⠼⠋⣉⡭⠧⣄⠉⠒⢤⣍⣠⠖⠋⠁⢸⣸⡸
⠀⠀⠀⣇⡀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣀⠀⢀⡀⢹⠔⠊⠁⠀⣀⡤⡇⠀⡇⠈⢸
⠀⠀⠀⠀⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⣿⢀⣠⠔⠊⠁⠀⡇⠀⠣⢤⠼
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⣿⠉⠀⠀⠀⣀⡤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣀⠀⠀⣿⢀⡠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⠀⠒⠂⠉⠉⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠓⢤⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⠀⡀⣀⡄⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡯⢹⣿⢸⠀⡇⣿⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⡇⡒⠊⠀⠳⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢉⡉⠀⠉⠈⠉⠁⠉⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣁⣹⣿⣦⣀⠀⠈⠛⢤⡄⢀⠀⠀⠀⠀⠀⠘⠯⠽⢿⣿⣛⣷⣯⣭⡅⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣯⢩⣋⣿⠋⠀⠀⠙⣜⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣍⣀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢾⣷⣧⡵⠁⠀⠀⣦⣴⠟⠁⠀⠀⠀⠀⠈⠿⡆⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠖⠀⠀⠭⠽⠇⠀⠀⠸⠿⠏⠀⠀⣀⣀⣀⡀⠀⠴⠤⠀⢀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡔⢦⠤⢤⡴⡄⠀⠰⠶⠴⠀⢀⣴⡅⠸⣿⣷⣦⣤⡄⠀⠈⠋⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡾⠞⠉⢻⠃⢸⡆⢠⣴⠆⠀⢰⡶⠃⠀⠀⢿⡆⢀⡿⠛⠻⢿⠀⠀⣻⣷⣦⣤⣤⠤⠤⠤⠤⠔⠚
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠚⠛⠻⠄⠸⠇⠼⠯⠄⠀⣤⠵⠴⠦⠤⠤⢤⣽⣟⠀⠀⠛⣻⡿⠉⠉⠁