Leaving Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠐⠀⠀⠀⠀⡀⢠⠂⠀⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⢀⣤⠖
⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠼⠀⠄⠀⠀⠠⡀⢸⡅⠷⠒⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⣠⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠁⢀⡸⠀⠀⠀⠀⣠⠐⡇⡸⠤⠤⠀⡠⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠻⠃⠈⢛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠃⠀⠀⠀⠀⢸⣄⠸⣅⡠⠤⠀⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⢠⡤⠀⠀⠀⠀⠙⠉⠉⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠦⠀⠀⠀⠀⠀⠂
⠐⠒⠦⢀⡀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⠀⠀⠀⠀⢣⠀⡀⡠⠊⠀⠀⠀⠀⠰⣷⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⣼⡇⠀⢀⠀⠀⠀⣄⢌⢇⠝⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠹⠆⠀⡆⠶⠁⠀⠀⠀⠀⢀⣴⣿⡁⠐⠀⠀⠀⠀⠘⣦⡌⣀⡤⠀⠀⠀⠐⠀⢤
⠀⠀⠀⠀⢀⡀⠛⢚⠁⠀⠀⢂⡆⠹⠃⠀⠀⠀⠀⠐⢿⡿⠟⠁⠀⠀⠀⠀⠰⡌⣸⠛⠁⠀⠀⠀⠀⠀⠀⠸⣇⠀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠈⠈⠑⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠖⠒⠁⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⢾⡄⢠⡀⠐⠊⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠉⠇⢻⡇⢸⠆⠀⡌⠀⣀⡀⠀⢀⣠⠄⢀⠂⠀⠠⢾⠟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢺⣟⠴⠾⠿⠇⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢡⣦⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣉⣀⡄⠀⠂⠀⢀⡴⠊
⠐⣄⣄⣀⡀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠉⠲⢠⣆⢋⠀⠄
⠀⠀⠺⠿⠅⣁⠐⢤⡀⠀⠀⠘⠀⣠⡶⣤⠀⠀⠀⠀⠀⢻⣶⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠪⠀⠐⠈⠀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠈⠲⢝⣆⠀⢦⠀⠸⢷⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢂⠾⠶⠒⠶⠲⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠸⠀⠄⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠋⠛⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠙⠁
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠠⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣧⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⢡⠸⣆⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢟⣯⡙⠛⠓⠲⠷⣿⣆⢿⡇⠀⠀⢀⡤⠔⠚⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠛⠛⠛⠛⠋⠛⠿⣧⠀⠰⠁⡀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡈⠳⣅⣠⢀⣤⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣷⣦⣪⣭⣿⣷⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠁⠀⠙⡄⠀⠀⢀⣤⠴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⡀⠀⠀⢡⠀⣼⣟⡵⣺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣝⢦⣀⠈⣷⣿⣿⠷⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠯⣇⣹⣿⣿⠏⠁⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⣠⣴⣾⠟⣻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⠞⡕⡽⠃⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠞⣉⣠⢶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠊⠁⢠⡾⣋⠔⣭⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣄⠀⠀⠀⢀⡘⢀⣿⣰⣡⡾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣇⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⣄⠀⠀⠀⠀⠀⠘⣿⢮⢳⡄⠀⡸⠷⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠛⣆⠀⠀⠀⠀⣿⡆⠀⠀⠀⣿⣶⣄⠀⠀⠀⠀⡿⠘⣾⠃⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⢀⠀⠀⡆⢯⢻⠀⠀⢠⡟⠃⠉⠳⣄⠀⠀⣦⣾⣿⢊⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠃⠀⠀⠀⢸⡆⠀⢧⠀⠈⢇⠀⠘⣵⣀⠡⠂⣿⠀⠀⣽⡿⣿⣿⠚⠋⠁⠈⠉⢛⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⢦⡿⠀⠀⠀⠳⠀⣎⠀⠀⠀⠉⢻⣿⣭⠶⠋⠁⠀⠀⠈⠉⠂⠒⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠹⣶⡿⠁⠀⠀⠀⠀⠐⣿⠀⢀⣀⠤⠾⠯⣤⣶⣶⣶⣤⣄⣀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠒⠲⢿⡷⠶⠶⠶⠶⠶⠶⣿⠞⠉⠀⠀⠀⠀⠀⠙⠻⠿⢽⣿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠻⣦⠀⠀⠀⠀⣸⢯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢄⡻⣇⠀⠀⣀⣿⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⣇⡟⠀⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡏⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣆⡀⠀⠀⠱⣦⣴⣿⣿⣿⣤⣤⠆⠀⠀⣀⣤⣾⡿⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣄⣼⡀⢹⣿⣿⣿⣿⣿⠃⣰⣀⣼⣿⣿⣟⠁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣻⣿⣿⣿⣷⣼⣿⣿⣿⣿⣯⣰⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣾⣡⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡿⣼⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣼⣿⣿⣷⣴⣿⣿⣿⣯⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡿⢿⡿⠛⠉⠈⠙⠻⡿⢿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠈⠉⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣼⣿⣿⣿⣿⣧⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣏⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⣿⣿⣿⣿⣿⣿⢙⣿⣿⣿⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⣻⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣝⢸⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⣿⡇⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣾⠣⢟⣽⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⢸⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⢰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠉⠉⠁

⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀
⠀⠠⠷⢨⣉⡦⡄⠀⠀⠀⠀⠀⠀⡠⠴⠒⠢⢄⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⣿⣮⣝⣧⡄⠀⠀⠀⠀⠀⠀⣠⡴⠶⠦⢄⣠⠂
⠀⠀⠙⠸⠾⠿⠧⠄⠀⠀⠀⠀⠺⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠧⠄⠀⠀⠀⠀⣾⠏⢠⣤⠄⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡝⠒⢒⡲⠊⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣓⣒⡶⠛⣹⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢉⠏⢁⢀⣠⣧⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⣻⡟⢩⣂⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠿⠿⠿⠿⠿⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠿⠿⠿⠿⠿⠟⠛⠁

⠀⠀⠀⠀⠀⣄⢈⡉⠙⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣋⣉⠛⢶⣄⡀
⠀⠀⠀⠀⠂⠈⠢⠀⠉⠉⠉⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠘⣿⣍⠉⠙⠋⣻⣦
⠀⠀⠀⠈⢆⠀⡆⠀⠰⢄⡀⠁⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣠⣿⠈⠳⣬⣉⢙⣽⣷⣄
⠀⠀⠀⠀⠀⠙⠿⠢⣤⡄⢹⣶⣲⣶⣿⣷⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢶⣿⣦⣽⣿⣿⣿⣿⣷⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠙⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢧⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⡇⠀⢀⡤⠒⢫⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⡇⢰⠃⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⢣⠀⠀⠀⢀⣀⠙⣟⠢⣑⣴⢁⠾⠤⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠈⡆⡴⠋⠉⢸⠀⠀⠉⢉⣿⣡⠔⠊⠉⠉⠒⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡉⠐⢾⠀⡁⠀⢀⡜⠀⢀⠔⠁⠈⠑⠦⣀⠀⢀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⠉⠉⠉⠑⡄⢳⡧⠔⠋⢠⣖⣁⣠⡴⠒⠉⠉⠢⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠀⠤⠛⢮⡇⢀⠔⢛⠛⠒⢦⡙⠢⠤⠤⠤⠬⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⠞⢣⠀⠀⡷⠃⠀⠸⡄⠀⠀⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠙⢦⠀⠀⠀⠈⢆⢈⢀⣾⠔⠒⠒⡶⠈⠒⠶⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⡇⢀⡴⢣⠀⢻⡿⢇⣀⡠⠞⢁⡤⠤⠤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠤⣉⠲⡇⡏⠀⢸⠀⡎⠀⢀⠷⣄⠰⠁⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠦⣄⣀⣈⡷⠼⣷⡀⢸⢰⠁⢠⢦⠳⣿⡷⠤⣴⣊⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣍⠳⣿⡷⠃⢸⠀⡇⠈⢣⢸⣠⡞⠁⠀⠀⢑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠉⠛⠿⣿⣤⣸⠀⢇⠀⢸⣼⠁⠉⣒⣒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢀⣠⠎⠀⠘⡄⠈⢦⣾⢇⡔⠉⠀⠈⠙⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣩⠄⠂⠤⣀⢳⠀⣸⣿⣋⠀⠀⢀⣀⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡁⡀⣀⣀⠜⡋⠻⡁⠀⠈⠉⢩⣍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⡜⠹⡄⠙⢄⠀⢠⠃⠈⡆⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢄⡀⢇⠀⢱⠀⡠⢵⣌⡣⣀⣷⠋⡨⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣎⠁⠀⠀⠈⣳⣕⣿⣸⡷⠮⠥⠽⠾⢏⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣉⣉⣀⠴⣏⠀⠀⠀⡠⠶⠒⠤⢬⠟⠓⠲⠦⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⢈⡍⠀⡼⠉⠱⡄⢸⡇⠀⢀⡠⠊⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⡴⠋⠀⠀⠣⡀⠀⡇⠘⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠙⢶⠇

⡿⠿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣿⣿⣟⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⡴⠀⣤⠔⠒⢒⡤⢤⡜⠁⢱⣶⡄⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢉⣼⡷⢺⣿⣠⣾⢋⡀⠀⢧⠀⠈⠙⠁⠀⠀⠀⡇⠀⣴⣿⠤⠀⠶⢤
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠃⢺⣿⣿⣿⣾⣴⢁⡼⠦⣄⠀⠀⠀⢠⣶⣿⣿⣿⣧⣤⠄⠂⠀⠲⣄
⠀⠀⠀⠀⠀⠀⠀⣤⡉⢀⣀⠈⣿⡿⠿⠿⢣⠎⢠⣀⠈⣱⣦⡀⣻⣿⣿⣿⣿⣿⣿⣦⡐⠒⠀⠾⡄
⠀⠀⠀⠀⠀⠀⠀⠘⢿⡼⢛⡟⠟⡞⡙⢍⡙⡆⠺⣿⣷⣿⡃⢱⣾⣿⢿⣿⣿⣿⣿⣿⣿⣤⠴⠤⢿⡆
⠀⠀⠀⠀⠀⠀⠰⠿⠏⢸⣿⣧⣾⠀⣷⠘⠷⣷⣿⣿⣿⣿⠿⠃⠈⢻⡾⣯⣿⠿⣿⣿⣿⣿⣧⡐⠂⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠁⠀⠈⣠⡴⢳⡄⣼⡟⠀⠀⠀⠀⣸⠃⠀⠈⠛⠿⠿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⢰⣿⣧⣾⣷⣈⣎⢯⠂⠀⠀⡿⠀⠀⠀⠀⠀⠀⠘⠯⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⣘⠉⠿⠛⣿⡇⠋⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣦⣀⠹⡿⠆⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡙⠿⠿⠿⢾⢗⣡⠤⠶⠶⠦⢴⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣶⣤⣴⠊⠙⣿⣿⣯⡉⠂⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠻⠇⠂⣿⣿⣿⣿⣆⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡿⠯⠈⠈⠃⢀⡙⢿⣿⣿⣿⣍⠀⠀⠀⠈⠻⢷⣄⣠⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⠁⠠⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣷⣄⡀⠀⠀⠀⠙⢍⣾
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡟⠡⠀⠐⠀⠀⠀⣀⣔⠹⠚⢩⡁⠈⠻⠇⠹⡓⢦⣀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣏⠀⠀⠀⠀⡀⠀⢰⣸⣿⢠⣾⢿⣿⡀⢀⡠⠞⠡⠀⠈⠙⠶⡎⢇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠠⠀⣠⠔⠊⢀⣤⣯⠉⣵⣿⣿⡿⣿⣿⣿⠀⣠⣮⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣯⡼⠕⠊⠀⠀⠀⢸⣼⠿⠀⠰⠿⠋⠀⠙⠛⠁⠀⣏⣿⠇⠀⠀⠀⠀⠐⣷⡀
⠀⠀⠀⠀⠀⠀⣼⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠳⢄⠀⡄⠀⢀⠀⢋⡴⢻⡄⡵⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠾⢷⣰⠀⢰⠿⠙⣷⣆⠀⠖⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠂⠀⡖⣡⡼⣧⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡇⠈⠀⣼⠁⢀⣤⣶⡟⠻⠶⡶⠀⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣖⡖⢛⡛⠛⢲⣄⠀⠀⠀⠸⠃⢀⣤⡿⢠⣋⣋⣭⡥⠶⠶⠶⠶⠆⣨⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠎⣁⡳⣤⡌⢳⣾⣦⣴⠀⠈⢻⣷⣷⡻⢯⣙⠀⠀⠀⣀⠠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠛⠉⠙⢻⢧⠀⣿⠀⠀⢠⡽⠟⠧⢀⠈⠉⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢘⡁⢛⡀⠀⠁⠈⣤⡇⠀⣰⠋⠀⠀⢠⣦⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠌⢡⠌⠃⠀⠀⠀⢹⠀⡴⠁⣹⠀⢴⠀⠈⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⡀⠀⠀⢰⡴⠰⣶⡇⠀⠀⠀⠀⣾⢇⠀⣤⢳⠀⡀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣟⡒⢄⠀⠁⠀⠉⠀⠀⠀⠀⢰⡏⠀⠓⠻⢾⡿⡟⠓⠁⠀⢀⡤⠶⣄⠀⠀⠀⠀⢰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢻⡇⠀⠐⠄⠀⠀⠀⠀⠀⠀⣾⠀⢸⠟⠒⡏⢻⠠⢄⠀⢀⣖⡈⠁⡼⠀⣸⠛⢲⣁⡹⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⢻⣤⠀⢠⡅⡀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠰⠂⠀⠈⠀⠀⣉⠀⠚⢃⠙⡜⢷⡿⠿⣿⣝⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣦⣻⣂⡜⠀⢻⠀⠀⠀⠈⣇⣠⣀⡀⠀⣰⠀⢀⣠⡴⣿⣤⡀⢰⣯⠘⠧⠼⢳⣦⣈⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢿⣧⠀⠈⠀⠀⡄⠘⠏⣠⡞⠙⣂⣿⣴⣯⡀⠀⠡⣄⣷⣤⠆⡀⠀⠀⠛⠈⠙⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠲⠠⠀⠹⣧⠈⠀⣦⢻⡇⢰⠃⠂⢀⡿⠋⠀⠀⠿⠃⠀⠿⣍⢩⠶⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣰⣤⠼⣿⣆⡀⣻⠸⠇⠘⠃⣰⣏⠀⠀⠀⠀⣀⣸⡷⠤⠙⠰⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢬⣿⣡⠀⣴⠀⣠⠞⠁⠈⡇⠀⠀⡼⡟⠹⠛⠰⢺⠆
⠀⠀⠀⣴⠛⢿⣿⡦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠋⢀⠀⣐⠅⠀⠀⣴⢻⡄⠀⠁⣴⣾⣤⡆⠈
⠀⠀⠀⠛⢶⡤⠛⠀⢀⠙⣿⠟⠛⣦⡀⠀⠀⠀⠀⠀⠀⡏⢀⡎⣶⠁⠀⠀⡼⠁⡸⣇⠀⠀⠀⣿⢸⠃
⠀⠀⠀⠀⠀⠀⢠⠶⢻⣶⠶⠞⢿⡉⢻⠀⠀⠀⠀⠀⠀⣧⢸⣷⠁⠀⣰⠋⠃⢰⠁⡌⠀⠀⠀⠸⡾⠀⠀⠰⢶⣛⢶⣖⣶⣶⡶⠆
⠀⠀⠀⠀⠀⠰⣏⣹⡍⠁⣦⣀⡤⠀⣾⠀⢀⣀⡀⠀⠀⠹⡿⡇⠀⠀⣿⡰⠀⠘⠟⠁⠀⠈⡠⠀⢃⢀⣀⠤⠿⠓⠋⢉⣡⡴⠃
⠀⠀⠀⠀⠀⠀⠙⢻⣄⡞⠈⠋⠀⠀⠰⣀⢻⢌⡛⠱⠀⠀⣿⠉⠀⠀⠉⡠⢀⠀⢤⡰⠀⢈⣠⡤⠚⠉⠀⡀⠀⢠⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⣠⣄⣠⡀⠀⡃⢈⡈⢦⣀⠀⢰⡗⠆⠀⠀⠞⠀⡤⠀⢺⠅⣠⠾⠅⠀⠀⠀⠈⠙⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢛⡁⠾⣄⠙⣆⠁⠈⠻⠊⠉⠀⢸⡇⠀⠀⢸⠇⠀⣇⠔⣱⣿⠁⠀⠀⢈⡡⢄⣸⣷⠋
⠀⠀⠀⠀⠀⠀⠀⢸⣇⢠⠑⣥⠀⠀⠈⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣷⣼⣫⡎⠁⠙⠓⠒⠼⢛⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠈⠋⠀⠀⢧⠀⠀⠀⠀⠀⢸⡇⡀⠀⢀⢏⣼⣋⣙⡓⠦⣾⣴⡶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠸⣇⡅⢀⣦⠎⠁⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢆⠀⠀⠀⠀⣿⣃⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠆⠀⠀⠀⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣼⡀⠀⠀⠘⣧⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹

⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣶⣷⣾⣶⣾⣶⣶⣶⣶⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣾⣶⣿⣿⣿⣿⣾⣶⣾⣷⣶⣶⣶⣾

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠑⣲⠄⢀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠙⠛⠒⠙⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠄⠀⠀⠀⠀⠁⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣋⢠⠀⢠⠂⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠂⠀⠈⠀⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢛⡿⠛⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣐⣶⠮⡵⠋⠀⠀⠈⢗⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣔⡦⠔⠟⠋⢩⠥⡖⠊⠠⠾⠒⡀⢀⡴⠃⠀⣔⠙⠎⠉⠈⠳⠀⢀⣀⠀⡇
⠀⠀⠀⠀⡞⠃⠀⡄⠀⠀⡌⠀⠹⡆⠀⢀⣀⠇⡞⠠⠀⡔⠈⠒⡾⠒⠒⠲⣞⠣⢌⣲⡇⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⢸⠀⣈⣠⡄⠀⠀⡇⠀⠀⢧⠀⠀⠀⣠⢉⣦⡸⡄⠀⠛⠒⠋⠂⣰⣌⡀⠁⠨⠱⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢠⠶⣶⣧⠀⠀⣀⡒⣗⣦⠀⠼⠷⣦⠀⠈⠀⢹⣯⢣⡸⡀⣰⡈⠀⠀⢉⣿⠄⡆⠀⣠⢴⣦⠀⠀⠀⠀⡀
⠀⠀⢸⣤⣌⣿⡂⠀⣿⠛⠟⣿⡆⠀⠀⢹⡇⠈⠳⠾⠏⠄⠙⠻⣦⠀⠀⠐⠚⢿⣆⠃⠀⠁⡀⠀⡁⠀⠀⠈
⠀⠀⠀⠙⠿⠛⠁⠀⠘⣤⣀⡿⠃⠘⠷⠛⠃⠀⠀⠀⠀⠐⡀⠀⢱⠅⠀⠀⠀⢰⣽⠀⠀⠀⠉⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠁⠀⠀⠚⢛⣰⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⢀⡤⢀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠖⡿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⠀⣠⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⣾⣷⢰⡦⠁⠀⠀⠀⠀⠰⡏⠁⠀⠀⠉⠀⠐⢳
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣠⡖⠀⠀⠸⣯⣤⣉⣉⣀⣀⣠⡿⠀⠀⠀⢘⢯⣀⠀⠀⠀⢀⡀⠄⡄
⠀⠀⠀⠀⠀⠈⢷⣤⢳⠀⠀⠀⣴⣾⡿⠁⠀⠀⠀⠻⣿⣿⣿⣿⣿⡿⠃⠀⠀⢀⣈⣧⣌⡀⠀⣀⣠⣶⣞⡁
⠀⠀⠀⠀⠀⢀⣀⡙⡧⠀⣠⣿⣿⠟⠁⠀⠀⠀⠀⠀⠈⠉⠙⠿⠉⠀⠀⠀⢠⠿⠏⠀⠀⠉⠉⢉⠛⠛⠋⠙⠲
⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⢠⣶⣿⠟⠛⢡⠀⢀⣤⣤⣄⣤⢀⣀⣀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠐⠶⠾⠛⠉⠀⠀⠀⠀⢃⣠⣿⣿⣿⣿⣿⣿⠿⠃⠀⢠⡵⢁⡀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢟⣽⠛⠁⠀⠀⠀⠀⠀⠀⠨⣧⠈⢲⣾⡷⣠⣄⣀
⠀⠀⠀⠀⣤⣀⠀⠀⠀⠀⣄⠀⠙⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠞⠛⢿⡿⠏⠁
⠀⠀⠀⠀⠘⠿⣿⣿⣶⣶⣿⣿⣦⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⡀⠀⠀⢠⡴⣶⣦
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠀⢇⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⢰⡢⠀⠰⣿⣶⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⡏⠢⣼⠀⣠⠔⠀⠀⠀⠀⠀⠀⠁⠘⢄⠀⢀⣿⢷⣿⡿⠛⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠎⠁⡈⠉⠳⣆⠻⠹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣼⡅⠀⠀⠀⠀⠰⣄⠀⣶⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣄⠀⠀⠀⢻⡀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠁⠘⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣿⣿⣤⣤⣶⣾⡇⠀⠀⠀⢸⣿⣿⡇⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⢀⣼⣿⡿⠿⠿⠛⠛⠉⠁⠀⢻⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⣾⠿⠋⠀⠀⠀⢠⣄⠀⠀⠀⠈⣇⠀⠀⠀⢻⣿⣷⣌⡙⠛⠿⠿⠿⠿⢿⠿⣦⡀
⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⠘⣦⡄⠀⠀⠙⠿⠿⠿⣦⡄⠀⠀⠀⠀⠀⠀⠙⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⡄⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣄⣀⣘⣿⣿⣿⠀⠀⠀⠹⡆⠀⠀⠀⢀⣤⣎
⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⡹⣄⠀⢠⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢻⣿⣿⠀⠀⠀⠀⠁⠙⣆⣼⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠂⣀⣀⣀⣀⠀⠘⣿⣿⣿⣴⣶⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠉⠙⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉⠉⠉⠙⣧⠙⠻⠿⠿⢿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠈⠛⠿⠿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡠⡔⣲⣮⣝⣀⠤⠒⢉⡔⠁⠀⠀⠀⠀⠀⢀⣤⣴⣾⠿⣿⣿⣿⣿⣿⣿⡷⠄⡀
⠀⠀⠀⠀⣠⣖⣹⣼⢡⢇⢋⠅⢴⡃⣠⠋⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣭⣽⣿⣿⣿⣿⡟⠋⠀⢠⣾⣦⡀
⠀⠀⢀⡴⠱⣟⣫⢨⡂⠟⡼⠀⣛⠼⠁⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⣾⠿⠟⠋⢻⣿⠀⠀⢠⣿⣿⣿⣿⣆⢀⣀⠀⠀⠀⠤⠤
⢤⣤⣮⡴⣰⢁⠎⠞⣂⣤⣶⣿⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠻⣷⣼⣷⣿⣿⣿⣿⣿⡞⠉⠀⢀⣠⣞⣁
⣿⡇⣸⢃⣫⣵⣾⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣈⣉⣉⡉
⠟⢓⣛⣛⣛⣋⡉⠉⠉⠉⣉⣀⣀⡀⠀⠀⠀⠀⣸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣟⣿⣿⣿⣿⣿⣄⣀⣉⣉⣭⣭
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠙⠛⠛⠶⣶⣿⣿⣿⠴⠶⢶⣤⡀⠀⢀⣶⣛⣉⠉⠓⢄⠘⣿⡞⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿
⣶⣿⣿⣿⠟⠛⡻⠻⣿⣿⣿⣤⣤⣶⣶⣶⣾⣿⣿⣿⣷⣾⣻⣿⣿⣿⠀⡿⣿⢹⣿⡿⠗⠀⠀⢹⣷⢿⣿⣿⣿⡗⢸⣿⣿⣿⣿
⣤⣿⣿⣏⢰⠀⢃⡀⣸⣿⣿⣿⣿⣵⡆⢨⣿⣿⣿⣿⡟⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⣿⣿⡇⢸⣿⣿⣿⣿
⣿⣿⣿⣿⣿⢀⣸⣿⣿⣿⣿⣿⣿⣭⣷⢾⣿⣿⣿⣿⣇⠀⢀⡤⢶⣀⣀⣈⣳⠶⣤⣀⣀⣀⠀⢸⣿⢸⣿⣿⣿⠃⠸⣿⣿⣿⣿
⣿⣇⠆⣜⣘⣈⣃⣺⣸⣃⣸⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⣤⣤⣍⣋⣀⣀⣤⢤⣽⡿⠙⠁⣸⣿⣾⣿⣿⣿⠈⠁
⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣛⣿⠛⠿⠇⠿⠋⠉⣿⣿⣿⣄⠈⠣⣤⣀⣠⣤⠶⠊⠀⠀⠀⣰⣿⣿⣿⣿⣿⡏
⣶⡏⢹⣿⣿⣿⡟⠁⠀⠉⢹⢏⣴⣿⣿⣿⡷⠀⠠⢿⣿⣿⣿⣷⡄⠈⠉⠭⠁⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⡿⠇
⣿⡇⠘⣿⣿⡟⠀⠀⠀⢀⠇⣾⣿⣿⣿⠟⠁⠀⣴⠀⢻⣿⣿⣿⣿⣦⣀⣀⣤⣾⣿⢻⡿⣿⣿⣿⣿⣿⣿⠃
⣿⢃⣀⠛⠛⣀⡀⠀⠀⠛⠃⢻⠿⠛⣁⣀⣤⣾⢏⡄⠈⣿⢿⣿⣿⣿⡿⠛⠋⠿⣇⡟⣿⣿⣿⣿⣿⣿⡟
⣿⠈⠛⠀⢀⣽⢁⠀⠀⠐⠀⠀⠙⠿⠿⠿⣟⠋⠀⠀⠀⠸⡜⣿⣿⣿⠀⠀⢰⢇⣼⣾⣿⣿⠟⠉⠈⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠀⡀⠋⣉⡉⢁⡀⠀⡀⠀⠀⢀⠀⠀⢉⠀⠀⠀⠀⠀⢹⣿⣿⣿⠀⠀⣧⣸⣿⣿⡿⠃⠀⠀⠀⢿⢸⣿⣿⣿⣏⣸⣿⣿⣿
⠛⣷⣶⣶⣶⣼⠤⣴⣶⣶⡆⠘⢊⠙⠉⠂⠀⠉⠀⠀⠀⠀⠀⢻⣿⣿⡆⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⢸⣿⣿⣿⣛⣛⣿⣿⣿
⣀⣤⠀⢀⣴⣤⣦⣴⣔⣀⢠⣷⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⢇⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡀⠁⠺⣿⢿⣿⣷⣧⣿⡛⠻⣿⣿⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢉⡻⢾⡟⣷⡟⢿⠙⣼⠀⢀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉
⠛⠈⠀⠐⢿⣼⣭⢭⠥⠭⠂⠀⠘⢿⣿⡽⢦⡀⠀⢀⣀⣀⡄⣲⣶⡁⢘⣿⣿⣿⣿⣧⠸⡧⠼⠓⣺⣃⣈⠀⡀
⠀⠀⠀⠀⠀⣀⡀⠴⢖⣶⠶⠆⠁⠚⢿⣿⣯⡻⣾⣟⣷⠾⠟⡻⣮⣵⣤⣭⣭⣥⣤⣤⣤⣴⣖⠨⠩⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠉⠛⠛⠋⠀⠀⠀⠀⠀⠀⠙⠻⠿⢿⣿⣿⣿⡿⠿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠙⠢⣤⣿⣿⣿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠻⣧⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⢠⠿⣇⠀⡟⢳⣾⠟⢻
⠀⠀⠀⠀⠀⠀⣠⠀⠀⣿⢀⣇⣸⣿⠀⠘
⠀⠀⠀⠀⠀⠀⣿⠀⠸⠿⠿⠿⠿⠿⢿⡇⠀⢠⣶⣷
⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠘⣧⣀⣿⠹⡇⠀⠀⠀⠀⢀⣴⣿⣿⡿⠻⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠙⠛⢛⣦⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣀⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠁⠀⠀⢀⣾⣿⣿⣿⣿⣿⡟⠉⠉⠉⠙⠻⢿⣿⣿⣿⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⠋⠀⠀⣀⣀⠀⠀⠈⢻⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠋⠀⠀⠀⠙⠛⠉⠀⠀⠀⠘⢿⡟⣿⡏
⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡃⠀⠀⠀⢠⣶⣿⣿⣆⠀⠀⣠⣄⠉⢻⡇
⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⣀⠶⠛⠻⠿⢿⣿⣿⠇⠀⠀⠀⠈⠛⣉⣴⠟⠀⢸⣿⡟⢡⣿⡇
⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⣿⣤⣴⣶⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⣀⠉⣥⣾⣿⡇
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⣿⣧⣄⣸⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡆
⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣸⣧⠀⠀⠀⠀⠀⠉⠉⠛⠛⣋⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠻⣶⣤⣤⣾⠟⠁
⠀⣠⠾⢿⣇⠀⠀⠀⠀⢠⣿⢻⣧⡀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀⠀⠶⣿⣁⠀⠀⠀⠀⠀⠀⣹⠇
⣴⠋⣠⣾⣿⣦⣄⣀⣴⡿⢿⡄⠹⣿⣆⠀⠀⠀⣠⣄⠀⢸⣿⣿⣆⠀⠀⠀⠀⠈⠙⠿⠷⠶⠶⢀⣼⡏
⣿⡐⠻⠿⣿⣿⣿⠋⠉⢿⡌⢻⣆⠈⢿⣷⣀⣾⠉⠉⢻⣿⣇⠘⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟
⠹⣿⡀⠀⠈⢻⣟⣧⠀⠀⠹⣦⡘⢧⡀⠻⢿⣧⣴⣶⣛⣻⣿⣷⣤⡉⢿⣿⣦⣄⣀⣀⣠⣾⠟⠁
⠀⠘⢿⣦⡀⠀⠻⣯⣷⣄⠀⠈⠻⣮⡷⣄⣸⣿⣥⡶⠛⠋⠀⠈⢻⣿⣾⣿⠛⠛⠿⢿⣿⠃
⠀⠀⠀⠙⢿⣦⣄⠉⢿⣿⣷⣄⠀⠉⠳⠉⠹⣿⡃⠀⣠⣤⣶⣿⣿⡿⢿⣿⣦⣀⠀⠈⣧⣀
⠀⠀⠀⠀⠀⠉⠻⣷⣄⠙⠛⡹⣷⣤⣤⠀⠀⢻⣿⣾⡿⠛⢻⡟⠛⠀⠀⢹⣿⠛⢿⣶⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣿⡏⢻⣿⠁⠀⠀⣾⢻⣿⠀⠀⢸⡟⠀⠀⠀⢸⣿⠀⠀⠈⢻⠁⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⣷⣾⣟⠀⠀⠀⣿⠘⡇⠀⠀⠸⣿⠀⠀⠀⣸⣿⡀⠀⠀⣾⠀⣿⠹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠇⠈⢻⣿⣄⡀⠀⣿⡄⠀⠀⢠⡀⠙⠀⠀⠀⡿⣿⡇⠀⠀⣿⠀⣿⢠⡿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠘⢷⣾⡏⠙⠻⣿⣿⡟⠀⠀⢸⡇⠀⠀⠀⠀⣧⢸⡇⠀⠀⢿⠀⠃⢸⣷⣈⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⢨⣿⠇⠀⠀⣿⣿⠃⠀⠀⠘⣷⠀⠀⠀⠀⢿⡼⠇⠀⠀⠈⣦⠀⣸⣿⠟⠛⢿⣧
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢸⡟⠀⠀⣠⠻⣷⠀⠀⢠⡄⢸⠀⠀⠀⡆⢸⡇⠀⠀⢸⠀⣿⠀⣿⣇⢀⣀⡾⠿
⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⢠⣿⠇⠀⠀⣿⡆⠁⠀⠀⠘⠃⠘⠀⠀⠀⡟⠀⠇⠀⠀⠸⢀⠈⠀⣿⣿⠉⣿⡇
⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⣼⣿⠀⠀⢰⡀⠻⠀⠀⢠⡆⢰⡄⠀⠀⣤⠀⡄⠀⠀⢸⡀⣼⠀⠀⣿⣿⠀⢹⡇
⠀⠀⠀⠀⠀⣰⣿⠃⠀⢠⣿⠇⠀⢀⠘⣷⠀⠀⠀⡘⢃⡘⠁⠀⠀⢋⡀⠃⠀⢀⡘⣧⠈⠀⢠⣿⣿⡆⢸⡇
⠀⠀⠀⠀⠀⣿⣟⠀⢀⣿⡏⠀⠀⠈⣷⡏⠀⠀⢸⡧⠸⡇⠀⠀⢾⠀⠟⠀⠀⠸⠇⠹⠁⠀⢸⣿⡿⠃⢸⣷
⠀⠀⠀⠀⠀⠻⣿⣦⣾⣿⠀⠀⠸⣆⡛⠀⠀⢀⣾⣠⣤⣀⠀⣠⡀⣤⠀⠀⢰⡆⢸⠆⠀⠀⣿⡟⠀⢠⡾⠇
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣤⣴⣷⣿⣧⣤⠴⣾⢻⣿⠉⠀⢀⣹⣷⠁⠀⢀⡜⢳⡄⠀⢀⣼⣿⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣷⣿⣿⡏⠀⢤⣼⣿⡎⠁⣠⡿⠟⠃⢠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠈⠛⠻⣿⣿⣿⠋⠛⠛⠛⠿⠿⢿⣿⣀⣘⣿⣿⣿⣾⣿⡇⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⡟⠉⠀⠀⢹⣧⣾⠏
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠈⣿⠋
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡇⠀⠀⠀⣰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣸⡇⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣴⡿⠁⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣷⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⣿⡿⠁⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⢸⣧⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠸⣇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣾⠟⣿
⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⢹⡄⠘⢃⠀⠀⠀⠀⠀⠀⢰⡟⠀⠘⣧
⠀⠀⠀⢠⡜⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⣿⡄⠀⠀⠀⠀⠀⡿⠃⠀⠀⢿
⠀⠀⢰⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⣄⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⣷
⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⢿⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⢻⣆
⠀⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀
⠐⣿⣯⡙⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠨⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⢸⣿⣿⣦⣌⡙⠿⣶⣄⣀⠀⠀⠀⢠⠉⣿⡄⢹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⡿⠀⠈⠙⠻⠿⣶⣮⣭⣿⡷⠶⣶⡆⠀⠘⣷⠀⢻⣦⣀⣀⣀⡠⠶⠶⠶⠆⠻⣷⡀
⣶⡀⠀⠀⠀⠀⠀⠈⣿⣭⣽⣿⠿⠟⠛⠛⠾⣿⣧⠈⢻⣏⠉⠁⠀⠀⠀⠀⢀⣤⣿⠿⠂⣀⣠⣤⣤⣤⣤⣤⡀
⠿⣿⣦⣤⣤⣤⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣀⡉⠀⣀⣀⣀⣤⣶⡟⠋⠀⠀⣠⣾⠟⠋⠉⠉⠉⠉⢿
⠀⠈⠉⠠⢿⣿⣷⡶⠄⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⡘⠻⣿⠛⠛⠛⠛⠁⠈⠻⠶⣶⡾⠋⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠉⠛⠷⠶⠿⣟⣿⣿⣿⣿⣿⡶⠶⠟⠁⠀⢹⣦⣀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣠⣤⡀⠀⠀⣠⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠿⠿⠿⠟⠋⣉⣥⣤⡴⠿⠋⠁

⠛⣁⣀⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠠⢬⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠉⡋⠀⠈⠑⠓⠄⠀⠀⠀⠀⠰
⠈⠋⠉⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⡔⠀⡄⠀⠀⠀⠣⠄⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠳⠀⠀⠐⡄⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠠⠀⠀⠐⣆⠀⠀⠀⠀⢀⡀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡁⠠⠤⠄⠐⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⢄⡀⠀⠀⠀⠂⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣵⣤⢄⠐⠂
⠀⠀⠁⠀⠀⢐⣀⣠⡀⠐⠲⠶⣶⡶⠀⠈⠙⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠒⠠⢄⠀⠀⠀⠀⠀⠀⠀⠋⠁⢠⠆⠀⠀⠀⢘⠀⠀⠀⢠⣤⣴
⠀⠐⠁⠀⠀⠀⠉⠁⣀⠀⠀⡄⠁⢐⡆⠀⠀⠀⠀⠀⠐⠈⠆⠶⣄⣀⡀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠇⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠈⠉⠑⠦⠀⢀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⠀⠀⠀⠀⠀⠈⡀⠐⠀⠀⠀⠀⠀⠀⣴⢀⠀⢰⠁
⠀⠀⢀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠧⠠⠀⠃⠀⠀⠠⢄⡂⠐⢦⠘⠱⡀⢧⠇⢀⡠⠤
⠀⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢀⡓⠦⢙⣦⣁⣆⢀⡡⠀⡨
⠀⠀⠈⢀⠀⠠⡄⠁⠈⠀⠀⠀⠀⠀⡘⠖⠉⣠⡼⢡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠚⠛⠙⠻⢿⣿⣿⡶⠒⠛⠁
⠀⠀⠀⠈⠷⠢⣤⠀⡀⠀⠀⠀⢀⠐⢁⣦⠟⡉⠈⠁⠁⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⢰⣥⠴⡺⠋⢁⠞⡿⢹⢟⢣⣀⠀⠁⠁⠀⠐
⠀⠀⠀⠀⠤⠒⠄⠁⠀⠀⠀⠀⠀⣴⠏⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠄⠤⠂⠁⠐⠀⣰⠈⣥⠜⢆⠉⠁
⢄⠀⡄⠂⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⡀⠀⠀⠀⢠⡄
⠀⠈⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠐⢆⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢎⠎⡇⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⢐⡀⠀⠀⠀⠴⠀⠀⠀⢀⡠⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠄⠀⠃⠀⠈⠸⠀⣴⡃⡀⠄⡠⠀⠀⠀⠀⠐⣡⠾⠀⠀⠀⠀⠐⠀⠂⡨⠿⢧⡀
⠠⠄⠀⠀⡀⠀⡐⠀⠀⠃⠀⠈⠁⠀⠊⠀⠀⠀⠀⢸⣿⣁⡀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⡇⢸⠀⠀⠁⠈⠁⠀⠀⡠⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⡀⠀⠀⠀⠀⠀⢀
⠅⠊⡀⠌⠀⠀⠠⠄⢀⠠⣈⣉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⡠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠈⠁⣀⣒⠒⠂⠢⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⣈⠄⡤⠈⠓⠒⠂⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡤⠊⠉⠄⠘⠉⠉⠐⡄⠀⠀⠀⠤⢀⡐⠠⠀⠠⣄⠉⣠
⠀⠀⠒⠀⠂⠉⠀⠀⠀⣀⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠰⢄⡙⣳⣄⡀⠁⠘⠛⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠱⣤⠉⠛⠶⣶⣸⠀⠋⠃⡀
⣉⣯⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡠⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠐⢒⡀⠙⢛⢃⣀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢖⣻⣭⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣡⠞⠉⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⣤⣶⣿⣿⡭⠭⢭⣝⣓⠶⢤⡀⠀⠀⠀⠀⠀⠁⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠻⣿⣿⣆
⠀⠀⠀⠀⠀⠀⡠⢊⣴⣿⣿⡿⠛⠋⠁⠀⠀⠀⠀⠈⠉⠲⢌⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡻⣿⣷⡀
⠀⠀⠀⠀⠀⡰⣡⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡽⣿⣿⡄
⠀⠀⠀⠀⠰⣱⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡄
⠀⠀⠀⢀⢧⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⣀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢹⣿⣿⣷
⠀⠀⠀⢸⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⢸⡄⣿⡟⠁⠀⢹⡀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⣿⡇⡆
⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⣠⣠⣦⠀⣶⡟⠉⣆⠀⠀⣷⠀⢸⡇⢻⡄⣀⠀⢸⡇⠀⠀⠈⣧⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⢠⣴⡾⠃⠀⣸⣷⠀⢸⡇⢸⠈⣿⠀⠀⢹⡄⢰⣿⣇⢸⡇⢸⡿⠋⠀⠈⣷⠀⠀⠀⣿⠀⢀⣀⠀⢠⣿⣿⡇⡇
⠀⠀⠀⢸⣿⣿⢸⠀⠀⠀⢸⡏⠀⠀⠀⣿⢿⣆⢸⣇⣾⠀⣿⡾⠃⠀⢷⢸⣿⢿⣾⣷⠈⣷⠀⢀⡀⣿⢀⣴⣷⢸⣦⣿⠟⢀⣾⣿⡿
⠀⠀⠀⠀⣿⣿⡎⠆⠀⠀⠈⣷⡿⠀⠀⣿⣼⣿⡺⣿⣇⠀⢹⡇⠀⢀⠈⣧⣿⠈⣿⣿⠀⢹⣾⡿⠃⢸⣿⠟⠁⠘⠟⢁⣴⣿⢟⡾⠁
⠀⠀⠀⠀⢻⣿⣻⡘⠀⠀⠀⣻⠁⠀⠀⣿⠋⢹⣇⢿⠹⣧⠀⣷⣾⡿⠀⠘⠟⠀⠈⠃⠀⠘⠋⠀⠀⠈⠁⠀⠀⢀⣤⣾⢟⡵⠋
⠀⠀⠀⠀⠈⢿⣷⡻⣄⠀⠀⢸⡇⠀⠀⣿⠀⠈⣿⠸⠀⠙⠀⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⡿⢋⡵⢋⠄
⠀⠀⠀⠀⠀⠈⠻⣿⣜⢦⣀⠠⡃⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢖⡫⠚⠁⠀⠠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣬⡳⢬⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⡫⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⡦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠮⣵⣒⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⣌⡐⠢⢀⠀⠀⠀⢠⠏⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠁⠢⡀⡞⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠙⢇⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⠀⠢⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠞⠛⠛⠛⠛⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⢀⡾⠁⠀⢠⣂⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⣸⠇⠀⢈⠏⢹⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⡇⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣄⣀⡀
⠀⠀⠀⠀⣿⠀⠀⠺⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⣾⠀⠀⠀⠀⣴⠞⠋⠉⠁⠀⠀⠈⠉⠉⠛⠶⣤⣀
⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢸⣧⡴⠇⠀⣀⣀⢰⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡉⠳⢼⡇⠀⠀⠺⠤⠜⠘⣇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠹⣆
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠳⣼⠁⢀⣤⣤⣄⣀⣀⣹⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣦⢄⢻⡄
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢰⠋⣿⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠢⠸⡇
⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⢸⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⢀⡏⠓⢾⠃⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⢸⠷⢤⡾⠀⠀⢀⡔⣶⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⡾⠀⠀⢀⠀⠀⣸⣵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠖⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠇⠀⠐⠭⠇⠀⣿⠃⠀⠀⠀⠀⣀⣠⣤⣤⠶⠶⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢠⣯⠤⠶⠶⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣌⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉



⣶⣶⢶⠶⠶⡶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⣶⡶⣶⣶⣶⡶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⢀⣤⡀
⠀⠀⢠⡆⠀⢠⡶⠀⠀⠀⣦⡄⠀⢀⣀⠀⠀⠸⡄⡏⡄⠀⠀⠀⠿⣿⣤⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠘⢷⡀⣼⠟
⠀⢀⠘⡇⡴⢋⡀⠀⣀⡀⠹⠿⣾⡿⠟⠀⢀⠳⣜⢊⡴⢀⠀⢀⣠⡛⠁⠀⠀⠀⣴⣿⣷⣦⡄⠀⠀⠀⠀⠈⠳⢁⣴
⠀⠘⣧⡈⢠⠾⠁⡄⠻⣷⣄⠀⣠⣴⡦⠀⣬⢷⡈⡡⠴⢋⡄⠘⠿⣿⣿⠀⢠⣷⣹⣯⣿⣾⣽⣷⡄⠀⠀⣈⢣⡿⠋
⠀⠀⢨⠛⠆⣠⡾⠃⠀⣨⡍⡀⠛⢋⠀⢀⡙⢇⢹⣠⠶⢟⠀⠀⢀⠀⡀⠀⣼⡛⣿⣿⣿⣿⣿⣻⣥⠀⠈⣿⢿⠁
⠀⠀⠸⣦⡀⠋⠀⠀⠀⠘⠿⣧⣾⡿⠃⠀⡳⡌⣯⣶⠞⠁⠀⢾⡿⣿⣿⠀⣻⠿⣯⣿⣿⣿⣿⢿⣿⢃⣀⠈⢿⢋⣤⡄
⠀⠀⠀⠈⠳⣠⡄⠀⠀⢿⣦⣏⣴⣶⠀⠀⠳⣘⣡⠆⠀⠀⠀⢀⣀⠀⣀⠀⢿⣋⣿⡟⢻⣏⣹⣿⣦⠈⠿⡀⡸⠚⡋
⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠙⠟⠛⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸⢿⠿⠿⠂⠀⠉⠉⠀⠀⠻⠿⠿⠃⠀⠀⠰⢡⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢏
⠀⠀⠀⣶⣄⠀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣿⣆⢀⣤⣤⠀⠀⠀⠀⠀⠀⣿⢀⡄⠀⢸⣧⠀⠀⡀
⠀⠀⠀⢻⣿⠆⠃⣀⡀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠈⢁⣈⠛⠋⠀⠀⠀⠺⣦⡀⢹⡿⠃⠀⠀⠙⠀⣾⠇
⠀⠀⠀⠀⠉⣥⣾⣿⠇⠀⠀⠀⠘⢿⡇⣠⣴⣶⠀⣤⡄⠸⡟⢷⡶⠀⢀⣤⣤⡬⢥⡄⣀⣀⣄⠻⣶⡤⡄⠀⣰⣿⠂
⠀⠀⣀⣤⣀⠘⠋⠀⣀⣀⠀⢀⣄⠀⡀⣿⡿⠃⠀⢙⣥⡄⠀⢰⣶⡆⠈⠛⣡⡀⠀⠱⠀⢉⡋⠀⠀⠀⠬⣀⠛⢁
⠀⠀⠻⣿⡿⠿⡇⣾⣿⡿⠂⠸⣿⣷⠸⡇⢀⣴⡆⠈⠻⠓⢤⠘⠛⡁⠀⠘⢿⣧⠀⢆⣾⡿⠃⠀⢀⣤⣀⢸⠐⠁
⠀⠀⠀⠀⠀⣀⣸⠈⠉⠀⠀⠀⠉⠻⡄⣶⣿⣿⠟⠀⠀⠐⣄⢀⠞⠀⠀⠀⠀⠉⢠⠋⠁⠀⠀⠀⠀⠙⢻⠘
⠀⠀⠀⠰⣾⣿⡿⣠⣴⣆⢸⣿⣷⡄⢸⠛⠋⠁⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⡄⡞
⠀⠀⠀⠀⠈⠁⠀⠟⠛⠁⠀⠙⠛⠓⠷⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠐⢀⠏⠀⠀⠀⠀⠀⢠⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠋

⢠⡖⡄⠀⠀⡠⠒⠈⠁⠀⠂
⠀⠉⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⣠⠈⢂
⠀⠀⠀⠰⠀⠀⠀⢀⠀⠀⢀⡠⠼⠁⡶⠃
⠀⠀⠀⠀⠀⠀⠀⢁⡀⠁⠀⠐⣹⣇⡄
⠀⠀⠀⠀⠀⠀⠀⢫⠸⠀⠀⠀⠉⢈⢣
⠀⠀⠀⢈⡄⣀⠴⠁⢄⡀⠀⠘⣧⠎
⠀⠀⠀⢼⣵⠏⠀⢀⡐⠁⠁⠀⠁
⠀⢰⠁⠃⠃⠀⠀⠈⡇
⠀⠈⠀⠀⢀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⢤⠀⠠⢀
⠀⢀⠀⡠⢾⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠀⡐⠀⡈⢢⠀⠁⠄
⠀⡼⡏⠀⠀⠆⠀⠀⣆⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣼⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣵⣖⡆⠀⡟⢠⠀⠀⠀⡆
⠀⢠⠃⠀⠀⠰⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⠊⠁⠢⠅⢀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢂⡉⠀⡠⠄⠀⠀⠀⠀⡁
⠀⠈⠀⠀⠀⠀⠁⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠲⢀⡀⠀⠁⠀⠀⠀⠠⡎⢹⡘⡟⠁⠀⡇⠀⠀⠀⠀⢀⠃
⠀⠀⠀⢃⠀⠀⢸⣇⠀⠀⠱⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⣀⠀⠀⠀⠈⡏⣶⡄⠐⠋⣶⣖⠐⠂⠁
⠀⠀⠀⠈⠂⠀⠘⠘⢀⣀⡤⠦⡴⠆⠲⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠒⠠⣀⡇⡆⠈⠂⠒⢛⣏⢀⡇
⠁⠆⢤⠀⣀⣀⡗⠀⠈⣧⣀⣴⢦⠖⠺⣍⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣿⠜⠁⠀⠀⠀⠸⡟⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⢿⡟⠀⠐⣽⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡇⠀⠀⠀⠀⠀⠀⠃⠀⢁
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⣌⡁⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⠀⠀⠀⠀⠀⣄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠉⠑⠒⡎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢀⠀⠀⠀⠡⡀⠀⠀⠀⢫
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⡀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠀⠀⠀⠀⠈⠐⠀⠀⠀⠣
⠀⠉⠒⠤⢤⠒⠒⠲⠄⠒⢻⠀⠑⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠘⠀⠀⢸⠀⠀⠈⠀⠀⠈⠢⣤⠚⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢻⠹⡄⠀⠂⢲⠀⠐⠋
⠀⠀⠀⢀⠘⠀⠀⢸⠀⠀⢦⠀⠀⠀⠀⢡⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠀⠰⠀⠂⠈⡇
⠀⠀⠀⠨⢀⠀⠀⢸⠀⠀⠘⡀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⠀⠀⡰⡇⠀⠀⠁
⠀⠀⠀⡙⠶⢌⠀⠸⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠈⠲⠊⠀⠀⠀⠀⠐
⠀⠀⠀⠉⠣⠔⢍⠂⠴⢄⠀⢠⠀⠀⠀⡘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⠀⠀⡅⠀⠀⠀⠠⡄⠠⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠁⠸⡀⠀⠀⠙⠂⢬⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠺⢦⣀⠈⣂⠀⠀⠀⢡⠀⠈⠂⠀⠤
⠤⠤⠤⠤⡄⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠃⠀⠀⠀⠈⣦⡀⢀⣤⢚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠙⠠⠀⣀⣀⣀⣀⡀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡴⠂⡶⠀⠀⠀⣼⠀⡖⢰⣀⠀⣀⠀⣶⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣠⡖⣠⡶⢀⣤⠆⣠⠖⡾⠁⢀⠇⡠⠀⠀⠀⠀⠀⠀⠉⢂⠏⠉⠉⠉⠛⠀⠁⠜⠋⡾⠉⡀⠈⣉⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢊⡼⠁⢏⠛⡙⠝⠊⠻⠸⣁⣀⣈⣈⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠖⠛⣶⣿⠀⠀⣀⣀⣴⠀⠀⣼⢋
⠀⠀⠀⠀⠀⠀⠀⠢⡀⠑⠋⣴⠋⣵⣤⢊⣀⣈⡄⢈⣿⣭⣭⣬⣿⠀⠀⠀⠀⠀⠀⠂⢸⡇⠀⢈⢼⡿⢠⣤⣉⣬⣄⣤⠤⣿⠆⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠙⠀⢄⠥⠞⢹⠟⠛⡠⠀⡶⠀⠖⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠛⣲⠇⣾⡗⠛⢻⡍⠓⠋⠻⠔⢿⡸⢱⣏⠀⢤
⠀⠀⠀⠀⠀⠀⠀⢸⡁⢴⡏⣴⢂⣤⢆⡥⣶⠃⠁⡼⢱⢷⣳⠋⡼⠟⠀⠀⠀⠀⠀⠀⣀⡄⠣⡴⠟⣠⠀⢸⡇⠀⢰⡆⣤⢠⠆⣸⣇⡷⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠋⠊⠉⠈⠉⠉⠃⠃⠀⠈⠛⠒⠶⠤⠤⠄⠒⠀⠀⠀⠀⠀⠀⠉⠀⠠⢴⠆⠃⠐⠾⠃⠠⠜⠋⠻⠞⠒⠙⠁⠑⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢄⠀⣤⠀⠀⠀⣠⠂⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⣄⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠰⢠⡏⣀⣘⣠⢀⡄⣠⢰⠃⠐⢲⢐⡆⣀⠃⠀⠀⢀⡀⠀⠀⠀⠀⠰⠄⢰⡏⠈⠀⡈⠀⢀⡀⠘⢃⣰⡇⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠘⠘⢇⣠⡇⠛⠙⠃⠉⠸⠄⣀⡟⠙⣦⣇⣾⡞⠋⠀⠁⠀⠀⠀⠀⢠⣀⡸⣇⠼⠘⠇⠃⠚⠇⠃⠚⢺⡇⠄⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠠⠀⢸⠀⠀⠀⠀⠀⠙⠁⠐⠃⣸⠃⢃⠀⠐⠀⠀⠀⠀⠀⢸⠾⣥⢀⡀⣤⢀⡤⠈⠀⠠⠀⠀⡁⠀⠸⣷⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠂⡴⠊⣶⠈⠀⠄⠀⢀⡞⠁⣀⠀⢀⣁⠀⠈⣡⠀⠀⠀⠀⠀⠀⢾⢀⠜⠘⢛⡿⠘⠃⠀⠀⠀⠘⠉⠃⠀⠀⠈⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠤⢸⡇⠶⡦⣾⣰⡇⣾⣹⠀⢸⠛⠀⡀⣁⣠⣰⡇⠀⠀⠀⠀⠀⠀⡴⠂⠀⠀⠠⠇⠀⢰⡆⠀⡇⠀⠃⠀⢀⠀⡆⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠸⠧⠤⠄⣀⡀⠘⠂⣼⢀⡰⠷⠿⠀⠛⠇⠀⠀⠀⠀⠀⠀⣇⠤⠺⠄⠸⠱⠰⢿⠀⠀⡇⠸⠼⡇⢏⠰⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⡏⣢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠰⡈⢇⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⣄⠀⠀⠀⠀⠀⠘
⠀⠁⣌⠡⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠈⢀⠀⠀⠀⠀⠘⠀⣸⠁
⠀⠀⠙⡣⠱⣄⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⠈⠙⢈⣳⣄⡜⣻⣧⡀
⠀⠀⠀⠐⡀⠈⠻⡆⠀⡉⠓⠦⣤⣤⣀⣀⠀⠀⠈⠠⣯⣼⣿⡙⢷⡀
⠀⠀⠀⠀⠐⠈⠑⠀⠀⠙⠀⠀⣬⠙⠻⣟⣽⠿⠢⢤⣤⡈⢉⠙⠓⠻⣦⣤
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠲⣤⡀⠀⠄⠉⠀⠁⠀⠀⠘⣧⡏⠑⠲⠠⢌⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠐⠆⠀⠈⢷⣄⡀⠀⠘⣦⠀⢁⠀⠙⠃⡀⠀⠀⠀⢠⠱⠶⢄⡀
⠀⠀⠀⠀⠀⠀⠸⠀⢠⡀⠈⢧⡀⠙⣷⡆⠀⠁⠀⠀⡀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡉⣦⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢉⠀⠀⠁⠀⠘⢮⡁⡀⠀⠁⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⡌⠷⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⡀⠀⠀⢁⡀⠀⠙⢄⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⠸⣷
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠋⠀⠂⠀⣡⠀⠀⢬⠳⣠⣷⡀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢉⡭⠀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠐⠋⠀⠀⢠⣤⡥⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠿⢠⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⠀⠀⠀⡰⠂⠈⢫⢳⣤⡄⠐⠀⠀⠀⠀⠀⠁⠀⠀⡀⠑⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⣠⠜⠃⢀⡀⠀⠀⠈⢙⣧⠀⠀⠀⠀⠀⠀⠀⢾⢀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠁⠀⡀⠀⠤⠴⠶⠶⠼⠾⣧⡀⡌⠀⠀⠀⠀⡘⠉⠹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⢿⡀⠀⠀⢰⠁⠠⠁⠀⠀⠀⠀⠀⡀⠀⠤⠤⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⠀⢀⠀⠀⠀⠀⠠⡴⠀⠀⠀⠀⠀⠐⠜⣷⡄⡀⢀⣀⠀⠀⠀⢀⡠⠀⠀⠀⢀⡀⣀⠀⢁⣀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢈⠀⠀⠘⠒⠀⠁⠀⠀⠀⠀⠀⠀⠈⠛⠿⣦⣀⠃⠀⠀⣠⣊⠅⠐⢺⣦⠥⠾⠵⠷⠿⠉⠉⠓⢉⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠠⠀⣂⣀⠀⠀⠀⠀⠄⠒⠒⠒⠛⠏⢋⡀⠀⠀⠩⠷⠒⠉⠉⠔⠀⠀⢘⠀⠰⠋⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⡀⠀⢠⣄⡀⢛⠐⠓⠀⠲⠀⠀⠤⠠⠃⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣺⠟⢉⠀⠈⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡠⠜⠁⠰⠞⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⣀⠀⠁⠈⠀⠀⡉⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣤⡼⠏⠰⠛⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⡋⠁⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠠⡀⠀⠀⠀⠀⡰⠁⠈⠉⠀⠀⠐⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠑⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⢀⠀⠀⠀⢸⠁⠀⠀⢀⣀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⡤⣄⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠈⠂⠀⠙⠀⠀⠀⠨⢤⠑⠀⠀⠀⠀⡆⠀⠀⠀⠀⠘⢢⠊⡃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⡗⢄⠀⠀⠀⠰⡄⠀⠀⠀⠈⠠⠌⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⣠⢴⠁⢐⠀⠀⠀⠀⠈⡑⠀⠀⠀⠀⠀⣧⢰⡀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⢠⠀⠀⠀⢠⡎⢨⡴⠚⠁⠈⢦⠰⠀⠀⠀⠀⠉⠀⠀⠀⠀⠙⢆⠘⠤⣀⠀⠀⢀⣠⣾⠃⠄⠰⠤⢤⡤⠄⠤⠤⢤⡴⠞
⠞⠀⠀⠀⠉⠰⡁⠀⠀⠀⠀⠀⢳⡐⢄⡀⠀⠀⠀⠀⢀⡴⠀⠈⠑⠤⢄⣌⣭⠅⠖⠁⢀⠛⢒⠒⠒⡒⠒⠒⠚⠉⠀⠀⠀⠀⠀⡀
⠆⢄⠀⠀⠈⠳⢌⣺⣿⠀⠀⠀⠈⡳⣄⡈⠁⠒⠒⣈⡥⠃⠀⠀⠀⢀⠠⡀⠀⢰⠊⠁⠀⠀⠀⠠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⠠
⠠⡀⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠉⠉⠀⠉⠁⠀⢀⢦⡀⠀⠀⠀⠈⠲⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢠⠤⠤⢄⡠⣤⡄⠀⠀⠆⢀
⠀⠘⢦⡀⠑⠂⠤⠤⠤⠰⠒⣉⠜⢀⠠⠂⠀⠀⠀⠀⠢⡓⢄⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⡘⠀⡀⠀⠀⠀⠀⠀⠸⠦⠤⠤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠑⠲⠤⠤⠤⠖⠊⠁⡄⠁⠀⠀⢀⣤⣄⠀⠀⠈⠀⠑⢄⡈⠒⢄⠀⠀⠀⠀⠠⠁⠀⡇⠠⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢠⠆⢠⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠊⠀⠀⡤⢀⠀⠀⠙⠢⣐⠹⠀⠀⠀⠀⠆⠀⡇⠰⠀⠀⠀⠀⠴⠶⢶⠶⠾⠁⠀⣼⢀⡏⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠈⠄⠃⠀⠀⠀⠀⠀⡇⠸⠀⠀⠀⠀⠒⠒⠒⠒⠲⠀⢀⡗⠚⠛⠲⠦⣄⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⣴⠒⡀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠰⠀⠁⢸⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠝⠋⠉⠚⢎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠁⠀⠀⠀⠙⠋⠀⠀⠀⢀⡆⠀⠀⠐⠀⡣⡴⠒⡟⠀⣤⠁⠁⠉⠉⠉⠃⠒⠒⠲⠁⢠⢊⠄⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⡟⠀⠀⠀⠀⠶⠖⠚⠚⠀⠀⠈⠉⠉⠓⠓⠓⠒⠆⠊⠀⠀⢸⠀⢧⡀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠶⠒⢩⣡⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⢀⡍⠿⠋

⠀⠀⠀⠀⠀⡐⠀⠀⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢲⠠⠒⠒⠆
⠀⠀⠀⠀⠀⡇⠀⡀⡀⢀⠀⠀⡠⠄⢤⠀⡤⠤⣄⠠⠀⠀⡀⠤⡄⢀⠠⡄⠔⠒⠂⠐⠀⢐⠂⠀⠀⡀⠀⡆⠀⡈⠐⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⣂⠀⢀⠀⢘⠀⡀⠀⢀⠀⠃⠊⡠⠀⠈⡄⠀⣠⠀⠀⡜⠀⢀⢂⠌⣠⡀⠈⡆⠀⠀⠃⠀⠀⢠
⠀⠀⠀⠀⠸⠀⢀⣀⣸⢀⠄⠂⢭⠀⠘⠀⠃⢠⠁⢀⠁⠀⡁⠄⠐⠀⠀⠃⢠⠀⠁⢀⠂⡆⠀⢉⠠⠔⢀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⢸⣀⣠⠀⢀⠃⠀⢃⣁⠀⣠⠀⡀⢈⡀⠘⣄⠀⢁⠖⠀⠐⠀⢀⠈⠀⠀⠂⠀⠣⡀⠈⠒⡤⢀⠀⠀⡀⣄⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠈⠁⠈⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠐⠟⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⠧⠄⠀⠀⠀⠀⠀⠷⡆⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠄⠀⠀⠀⢀⡀⠀⠀⣀⣤⡀⠀⠀⢚⠛⡯
⠀⡠⡼⣦⠀⠀⠀⠀⠀⠀⠀⢾⠀⠂⡀⡐⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠜⢉⠃⠀⠀⠀⠈⡿⢻⣷⣿⣿⣿⣿⡗⠀⢸⡞
⠀⠚⢢⢐⠀⠀⠀⠀⠀⢀⣀⢸⡄⠀⠁⠀⢄⡀⠀⠀⠀⡈⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣵⣰⣿⡟⠆⠈⠋⠀⢠⢃⠁
⠀⠀⠈⠀⠄⠀⠀⠀⡴⠟⠹⡄⠫⡀⠀⠀⢤⡈⠃⠀⠀⣠⣾⣿⣿⠿⣿⣿⣆⠀⠀⠁⠀⠀⠀⣃⣿⣿⣿⣿⠁⠀⡰⢼⡄⢁⠂
⠀⠀⠀⠆⠐⡄⠀⠚⠀⠀⠀⠈⠀⢀⠀⠀⠀⠱⢀⡔⣱⣿⣿⣛⠁⠀⣾⣿⣿⠃⠀⠠⢀⡄⠚⠓⠜⡿⡏⡇⠀⠀⠀⠙⢵⠃
⠀⠀⠀⠀⠆⠐⠀⠤⠀⠀⡀⠂⡄⠘⡀⠀⡄⠀⠀⠀⣿⣿⣿⢸⡿⠀⡤⣾⠟⠌⠀⠰⠀⠀⠂⡀⢸⡄⣆⣤⡀⠉⢁⡴⠁
⠀⠀⠀⠀⠈⠀⢸⣧⣀⠀⠈⠉⠅⠀⢐⠄⠠⠄⡀⢀⣿⣿⣿⡟⠀⡯⣤⣿⠆⠀⠀⠙⣂⠖⡀⣩⡤⠜⢇⠁⠚⢋⠕
⠀⠀⠀⠀⠀⠈⡀⠉⢃⡀⠀⠀⢰⠀⠜⠳⣐⡗⠛⠀⠈⣭⣍⣀⠀⠸⢿⡏⠀⠀⠁⢸⢭⣶⣤⠄⢤⡔⠋⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠈⡀⠈⠙⢀⠓⡜⢳⠀⠀⠀⣴⠠⠆⠠⣿⡾⢣⣷⢖⣼⠟⠀⠀⠀⠀⠀⠈⠋⠑⠂⠚⠳⡤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⣇⠀⠀⠀⠀⣿⡄⠸⠀⠘⢡⡿⠩⣺⠿⢠⠀⠀⠀⠀⠀⢀⡇⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠘⠀⠀⠀⣿⡇⠀⠀⠒⠉⠙⠋⠁⠀⠸⠀⠀⠀⢠⣦⣼⣿⣽⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢠⠀⠐⠀⠈⠛⠁⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣾⣿⣿⣿⣿⣿⡇⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⢨⣂⣤⣔⣞⡏⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣁⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣶⣤⣶⣶⣿⣻⣾⡟⠉⡍⣿⠃⠀⠓⡶⡖⠲⢶⠋⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣻⡟⢻⠈⡟⠀⠀⠑⣻⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⢿⡿⠿⠟⠋⣼
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡛⠁⠸⢰⣷⠀⣠⣾⣿⠃⠀⠒⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠁⠠⢟⡂⢕⠩⠆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢀⣄⣼⣏⠘⠉⣿⣽⣀⣀⠣⠄⣬⠂⣦⠀⠀⠀⠀⠠⣮⢀⣸⣄⠶⢶⠆⠉
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⢷⣾⣏⠹⢿⣿⣯⣤⡍⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⡍⠛⠛⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣠⢆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀
⠀⠀⠀⠰⠶⠖⠒⠀⣺⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⠀⣷⡇⢀⠀⣀⣠
⠀⠀⠀⠀⣀⣠⣀⡷⡿⠧⠀⣒⠒⢲⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣄⠀⠀⠀⠀⠀⠈⠁⣼⡿⠋⠁
⠀⠀⠀⠀⠉⠉⠉⠙⣿⠃⠰⣽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠀⠋⠤⠀⠀⠀⠀⠀⣇⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠶⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠹⣿⣤⡄⠀⠀⠀⠀⠀⢀⣀⠴⠴⢯⡿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠸⡟⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣧⠀⡄⠀⠀⠀⠁⢦⠤⠀⠀⠀⠀⠸⠀⠺⠤⠂⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣴⠂⡀⠀⠀⠀⠀⢠⣀⣠⡉⠙⠛⠿⢿⣿⣶⡇⠀⠀⠀⢷⣇⣠⣿⣿⣿⣷⣶⣶⡶⠖⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⡛⠓⠤⠀⠀⠀⢀⣹⣯⠴⠒⠀⢠⣤⡿⠿⢄⠀⠀⢀⠞⠛⠛⠻⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⣄⠀⣠⣀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠟⢻⡏⠈⠡⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⠉⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠸⡿⣶⡷⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⢀⣾⣿⣿⣿⣤⣶⣷⣾⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠈⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⢀⣤⡄⢀⠀⠀⠀⠀⠀⠀⡰⠁⠀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣦⣀⠀⠀⠀⠀⠸⠿⠏⠸⠇⠀⠀⠐⣀⣾⡡⠖⠋⠉⠀⠀⠀⠙⢿⣿⣿⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⣿⣿⣿⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣽⣿⣿⣦⣿⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣌⣿⣿⣿⣤⣿⣿⣦⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣺⡍⣀⣤⣿⣿⣷⣿⣟⣛⣿⣿⣷⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⢿⣿⣿⣿⣽⣿⣷⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢻⣿⡿⠿⢿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣀⡀⠀⣼⢀⣀⣠⡴⠞⠛⠉⠉⠉⠉⠉⠉⠚⠁⠀⠈⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⡏⢰⢛⣟⣻⣿⣿⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣠⣤⣍⣉⣻⣧⠾⠛⠛⣿⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣯⣿⣾⠟⠋⠱⣄⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣄⣀⣸⣿⣟⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠞⠛⢉⣏⠁⠀⠀⠀⠀⣹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⣴⣏⠫⣡⠀⣷⣄⣿⡍⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠷⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠚⠁⠸⣦⣷⠀⠀⢿⣬⡷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠊⠉⠀⠀⠐⠀⠀⣄⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣤⣼⡿⠀⠠⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢳⣄⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠆⠐⠂⠘⠀⠆⠐⠐⠀⠤⠢⠖⠴⠀⠂⠀⠀⠀⠐⠀⠠⠖⠐⠀⠇⠀⠰⠀⠴⠠⠒⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡆⠀⠀⠀⠀⣀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠃⠀⢀⣾⣿⣿⠟⠁⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⢿⣏⣠⡤⠶⢿⣿⣟⣒⠒⠶⣶⣿⣿⣿⣿⡿⠷⠂⠀⠀⠀⠀⠀⠀⠄⠈⠙⠺⠧⠀⠀⠈
⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⡼⣿⣥⣤⡀⠈⠻⣿⣿⣷⡀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⢐⠀⠀⠀⢹⡀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠘⢿⣆⢀⡎⠀⠈⠻⣿⣿⡄⠀⠀⠉⠉⠋⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠵⢀⠀⠀⠀⠀⠂
⠀⠀⠀⢶⣤⣄⠀⠙⡿⠀⠀⣀⣤⣤⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠬⠥⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢻⣿⣇⠀⢡⢠⡼⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠐⢛⡁⠀⠀⠀⠀⢁⠄
⠀⠀⠀⠀⠀⠉⠉⠙⠻⡏⠀⠀⠀⢀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠥⠀⠀⠀⠘⠡⠂
⠀⠀⠀⠀⠀⠀⣀⣀⣀⡘⢄⠀⢀⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣆
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣾⣷⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠆⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠙⠂⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠰⡀⢢⠸⡅⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠉⣻⠀⠀⠀⠀⠀⠀⠐⠪⠅⠳⡗⡨⠊⡁⠀⠀⠀⠀⠀⠹⣦⡄⠸⡇⠀⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⣦⠀⠀⡼⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢅⠀⠶⡗⢐⠄⠄⠀⠀⠀⠀⠀⠀⠘⢿⡄⣇⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈⡆⢀⣇⡤⠞⠁⠀⠀⠀⠀⠀⠀⢀⠁⠀⠑⢤⡷⠥⡐⢥⠀⠀⠀⠀⠀⢀⠀⠀⠻⣿⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢀⡇⡼⠋⢀⣀⣀⣀⡀⠀⠀⠀⠀⢈⢢⡀⢐⣠⡧⠊⠀⢐⡀⠀⠀⠀⠀⠘⣿⡆⠀⢹⡇⠀⣠⣴
⠀⠀⠀⠀⠀⠀⡾⢆⠀⠀⠹⣾⣞⡥⠚⠉⠀⣠⠜⠁⠀⠀⠀⠀⠈⠂⠀⠠⣄⣧⣐⠈⠄⠊⠀⠀⠀⠀⠀⠈⠻⣄⢸⡇⢠⡿⠃
⠀⠀⠀⠀⠀⠀⡇⠀⠳⡄⢠⠟⠛⠓⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⣬⣧⠐⠀⠈⠩⠀⠀⠀⠀⠀⡀⠀⠘⢾⣇⡞⠁
⠀⠀⠀⠀⠀⠀⢧⡀⠀⣷⠏⣀⡠⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠆⠉⠐⠠⣀⡇⠄⠀⠀⠰⠀⠀⠀⠀⠀⣿⣦⠀⢸⡟⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠹⣤⣿⣚⣁⣀⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢀⠊⠉⠠⣁⠈⡅⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠙⣦⢸⠃⠀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡐⠙⡟⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⣾⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠙⡟⠃⠠⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⣀⣀⣀⠀⣀⡀⢀⣀⣀⣀⠀⣀⠀⠀⡀⠀⣀⣀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⠟⢸⣿⣛⣿⡇⣙⡁⣿⣿⠛⠛⢹⣿⣷⣸⣿⢸⣿⠿⣿⣆⣾⣿⠻⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠗⠀⣿⣿⣿⣏⠠⣿⡇⣿⣿⣛⣛⢹⣿⠿⣿⣿⢸⣿⣀⣿⡟⠈⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠻⠏⠈⠻⠇⠿⠇⠿⠿⠿⠿⠋⠿⠃⠻⠟⠸⠿⠿⠛⠀⠻⠿⠟⠋

⠀⠀⠀⠀⠀⢰⣿⣦⢸⣷⢰⣿⡿⠿⠇⣾⡇⠀⣾⡆⣾⣿⠿⠿⢀⣾⡿⢿⣷⠀⠀⠀⠀⣶⣿⠿⠆⢠⣾⣷⣴⣷⠀⣼⡷
⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⢸⣿⡷⠶⠆⢻⣿⢰⣿⡇⣿⡿⠶⠶⢸⣿⣿⣿⠋⠀⠀⠀⠀⠙⢿⣶⡄⣼⣧⣼⣷⢹⣷⡟⠁
⠀⠀⠀⠀⠀⠸⣿⠀⢿⡿⠸⣿⣿⣿⡷⠈⠻⣿⠟⠀⣿⣿⣿⣿⠾⡿⠉⠻⡧⠀⠀⠀⠀⢶⣾⡿⠏⢿⠏⠙⣿⠆⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⢀⣤⣶⣦⡀⢀⣴⣶⣤⠀⣶⣶⣦⣄⢠⣶⡶⣶⣄⣴⡆⢀⣴⣄⣶⣶⣶⣶⠀⣶⡆
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⢀⣀⢼⣿⠉⣿⣧⣾⣟⢹⣿⡇⣿⡏⢹⣿⢸⣿⣷⣿⡋⠘⣿⣼⡟⢸⣿⣿⣤⣤⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣾⡿⠸⣿⣶⣿⠇⠹⣿⣾⡿⠃⣿⣷⣿⠟⢸⣿⣭⣿⡿⠀⢸⣿⠀⠘⣿⣷⣶⣶⠀⣩⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠉⠀⠀⠀⠈⠉⠀⠀⠉⠉⠀⠀⠀⠈⠉⠉⠀⠀⠀⠉⠀⠀⠉⠉⠉⠁⠀⠉⠁

⠀⠀⢠⣆⠀⠰⢆⠀⠀⠀⢀⡏⠐⠒⠐⠒⠮⠁⠀⣔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠐⠢⠅⢻⡄⢄⠈⠳⢤⣀⣸⠁⠀⠀⠀⢠⠁⣰⡟⠁⠀⠀⠀⠀⠀⠀⣶⠀⠄⢀⠀⠀⠀⠀⠈⠗⠶⠊⠉⠉⠉⠁⢀⠀⢀⣦⡀⠀⠀⠀⢠⠇
⠀⠜⠀⠀⢙⠄⠁⠀⠀⢹⡇⠀⠀⠀⢀⠀⣼⠏⠁⠀⠀⠀⠀⠀⠀⡀⠘⡇⠀⠀⠘⠂⡀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠳⣄⡀⠀⡝
⠀⡅⠀⠀⠀⣧⠀⠀⣀⣾⠁⣀⡀⠴⠂⠨⡂⠀⠀⠀⠀⠀⠘⢳⡗⠀⠀⠙⣄⠀⠀⠀⠀⠑⠄⠀⠙⢆⠀⠀⣀⣀⡀⢱⠀⠀⠀⠀⠙⣾⠁
⠼⠁⠀⠀⠀⢹⡆⠀⢩⠉⢤⣄⠒⠒⠢⡷⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠁⠂⠈⠻⡉⠉⠀⠀⠸⡇⠀⡀⠀⢠⡿⠁
⠀⠁⠀⠀⠀⠘⣇⠀⠈⠆⠁⠘⢳⣄⡰⠃⠀⠀⠐⠆⠀⠀⠀⡄⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⢀⠀⡈⠒⠄⠀⠀⡅⠀⡈⢻⡙⢟⠈⠉⠁
⠐⠀⠀⠀⠀⠀⠿⠀⠀⢠⢰⠀⠀⠹⣅⣄⠀⠀⠀⠀⠀⠠⠔⠁⠀⠀⠀⠀⢂⠀⠈⢫⠆⠀⠀⠀⣠⠎⠀⠈⠂⠀⠀⠀⢻⡀⣀⠘⠇
⠀⠀⡀⠀⠀⠀⢥⡂⠀⠀⡀⠄⠀⠀⠈⠓⣆⠀⠀⠀⠀⠀⣇⠁⠀⠀⠀⠀⠈⢄⠀⠀⠐⢱⡀⣼⠁⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⢸⡀
⢰⠀⠉⠙⠉⠓⠾⣇⠀⠀⢂⠀⠂⠀⠀⠀⠘⢷⡀⠀⠀⢠⠇⠀⠀⠠⢀⠀⠀⠀⠁⡀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⣼⠐⠒⠚⠡
⠈⠀⠀⠀⠀⠀⠀⢽⠀⠀⠈⡀⠀⠠⡀⠀⠀⠈⠿⣆⢀⡟⠀⠀⠀⠀⠈⡀⠀⠀⠀⠐⢄⠀⠀⠙⢧⡀⠀⠀⠀⠀⡆⠀⠀⠀⢀⡏
⠀⠁⠀⠀⠀⠀⠀⢸⡄⠀⠀⠁⠀⠀⠑⠀⠀⠀⠀⠻⣯⠀⠀⠀⠀⠀⠀⠈⡀⡀⠠⣀⠈⢆⠀⠀⠈⠳⣄⠀⠀⡰⠃⠀⠀⠀⢰⠄
⠀⠐⢄⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠦⠒⢒⣶⠆⠙⢷⡀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠈⠲⡂⡀⠀⠀⠙⢷⣞⣅⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠃
⠀⠀⠁⢱⠤⠤⠄⠸⣇⠀⠀⠀⢀⡄⠀⠀⠠⠊⠁⠂⠀⠈⢻⡄⠀⠀⠀⠀⠀⣣⠄⢤⠄⠀⠙⢌⠂⠀⠀⠀⡿⠀⠈⠳⠄⢰⠃
⠀⠀⣠⠋⣤⡀⠀⠀⣷⢀⠔⠁⠈⠓⢄⡰⠋⠈⠑⠇⠀⠀⣈⢽⣆⠀⠀⠀⠀⠁⠏⠁⠀⠀⠀⠈⠱⣄⠀⠐⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠰⠰
⠂⣼⠁⠀⠀⠠⠈⠓⡻⠁⠀⠀⠀⠀⡼⠃⠀⠀⠀⠌⢇⠋⠀⠀⠹⣆⠀⠀⣠⣴⣆⠀⠀⠀⠀⠀⠀⠘⢆⡀⠀⠀⠀⠀⣜⠁⠀⠀⠀⣀⡌
⣾⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣽⠶⠛⠁⠀⠈⠂⡀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⣴⠏⠙⠛⠛⠉⠙
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠂⠀⠀⠀⢀⣴⠛⠁⠀⠀⠀⠀⠀⠂⠘⣆⠀⠀⠀⠀⠀⠀⢹⡅⣼⡏⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⡆⠀⠀⢠⡴⠋⠀⠉⠉⠉⠀⠀⠛⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⢻⠆⠈⠁⠀⠈⠁⠀⠀⠀⠀⡼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠖⠛⠛⠛⠛⠛⠛⠓⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠁⠀⠀⠀⢀⣀⠀⣀⡀⠀⠀⠀⠀⠀⠉⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠟⠁⠀⠀⣀⡤⠖⠛⠉⠉⠉⠉⠉⠙⠓⢦⡀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⢤⡼⠀⠀⢀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⢳⣴⣾⣯⠶⠶⠶⠶⠶⠶⠦⣤⣄⡀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⢀⡾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢶⣄⠀⠀⠀⠀⢻⠀⠀⠀⠀⡀⠀⣸⠻⣆
⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⢀⣿⡀⢀⣆⠠⣿⣶⢿⣆⠙⣧
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠃⠀⣠⡾⢹⣧⡾⠻⣶⡏⠀⠀⠹⣆⠸⣇
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠰⠛⠋⠀⠀⠉⠀⠀⠀⠀⢻⡄⢿⡀
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠀⠀⠀⠀⠀⠀⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣆⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⣤⣶⣶⠶⠾⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠶⠶⠶⣶⣄⠀⠀⠀⠀⠀⣿⠘⣧
⠀⠀⠀⠀⠀⠀⠈⣷⢀⡴⠋⠁⠀⠀⠀⠀⣠⠶⠚⠉⠉⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠒⠓⠒⠶⣄⠉⠀⠀⠀⠀⠀⣿⣠⡟
⠀⠀⠀⠀⠀⣴⠟⣿⠋⠀⠀⠀⠀⠀⠀⡾⠁⠀⣴⣾⣿⡇⠀⠀⢳⡀⠀⠀⠀⠀⢠⠞⢁⣤⣴⡆⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⢸⡿⣦
⠀⠀⠀⠀⢨⣧⡀⣿⣀⡀⠀⠀⠀⠀⢸⡇⠀⢸⣿⣿⣿⣿⣶⡇⠀⡇⠀⠀⠀⠀⣾⠀⣿⣿⣿⣷⣴⡆⠀⠀⣧⠀⠀⠀⠀⠀⢸⡇⢸
⢀⣤⠤⡼⠋⠉⠻⡟⠋⠙⣷⠀⠀⠀⠘⠇⠀⠈⠻⢿⣿⣿⠿⠁⢠⡇⠀⠀⠀⠀⠸⠀⠻⣿⣿⣿⡿⠁⠀⠀⠃⠀⠀⠀⠀⠀⢸⣇⣼
⣿⠁⠀⣿⠀⠀⢰⡇⠀⠀⣿⠀⠀⠀⠀⠀⠉⠒⠶⠦⢤⣤⣤⣴⠏⠀⠀⠀⠀⠀⠀⠰⣦⣤⣭⠥⠶⠖⠒⠁⠀⠀⠀⠀⠀⠀⣾⠛⠁
⣿⠀⠀⣿⠀⠀⠸⡇⠀⠀⣿⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏
⣿⠀⠀⢿⡇⠀⠀⣷⠀⠀⢸⡇⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟
⣿⠀⠀⠸⠇⠀⠀⠋⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏
⣿⠀⢠⣤⣤⡶⠶⢶⣤⡶⠘⠇⠈⣷⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⢺⡀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⢹⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋
⢸⡇⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⣿⠀⠈⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠋⠁
⠸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⢨⡟⣷⠶⢦⣤⣤⣀⣀⣀⣀⣤⣤⣤⠶⢶⡟⣿⠁
⠀⠻⠶⠶⣶⠶⠶⠛⠛⢻⣟⠛⠋⠀⠀⠀⠀⣠⠟⠀⣿⠀⠀⠀⠙⠿⣭⣭⣥⠼⠋⠀⠀⢸⡇⠸⡇
⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠙⢦⣄⣀⣤⠶⠟⠁⠀⢸⡟⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⣷⠀⢿⡀
⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣠⣼⡇⠀⠀⠀⢠⣾⣿⣿⣿⣿⣧⠀⠀⠀⣿⡀⠘⣧
⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⣀⠀⠀⣀⢀⣀⠴⠞⠉⢸⠃⠀⠀⠀⠘⡏⠙⠛⠛⡿⠋⠀⠀⠀⢸⡇⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠁⠀⠀⠀⠀⣼⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⣧⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠤⠶⠶⠶⠶⠶⠶⠖⠚⠛⠛⠛⠛⠛⠋⢻⡄⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⡶⣤⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣀⣀⣀⣀⣸⣇⣹⣀⢀⠀⠀⠀⣠⣿⣿⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠉⠉⠉⠁⠀⣹⠈⠁⠀⠀⠈⠈⠉⣻⣷⣴⣯⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢀⢀⣀⣀⣀⣀⣿⣤⣤⣄⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢻⣉⣹⡏⠀⠀⢸⡇⢈⣟⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠉⠙⢿⣄⠀⣼⠟⠋⠉⠛⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⣀⢀⣀⣀⣀⣀⣿⣀⣀⣀⣀⣀⣿⣠⣏⣀⣀⣀⣀⣸⣇⣀⣀⡀⠀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠠⣿⠏⠘⣂⣣⡀⢄⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠆⠀⠁⢉⡘⢉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⢀⡃⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡟⣹⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠄⠀⣹⠀⠜⠁⠀⠀⠀⠀⠀⠀⣔⡽⣿⢸⣷⣟⣩⣤⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣀⣤⠀⠙⠂⡄⠀⣄⢀⠀⠀⠠⡕⢿⠀⢻⣾⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⣠⣠⠃⠀⠉⠁⣀⡐⢇⠉⠄⠙⠁⠀⢀⡸⣇⠘⣧⣿⣿⡿⠞⠛⡁
⠀⠀⠀⠀⠀⠀⡜⣠⣿⣷⡀⢘⠦⠈⠁⠘⡦⠀⢰⠀⣠⣾⡄⢻⣦⣿⣿⣿⡶⠛⢛⡿
⠀⠀⠀⠀⠀⢠⣆⣿⣿⣿⣷⢽⠛⠀⠈⠉⡃⠀⠐⠇⣥⡟⣷⣼⣿⣿⣯⣵⣶⣶⡿⠁
⠀⠀⡄⠀⠀⢸⣧⣹⣿⣿⣿⣿⣷⣄⠀⠀⠳⣄⡀⣸⣟⣧⣽⣿⣿⠿⠿⣿⣿⠟
⠱⡰⡆⡀⠀⢸⣿⣯⣹⣿⣿⣿⣿⣿⣧⢀⣀⡰⠀⠀⢀⣿⣿⡿⣿⣿⣷⡖⠧
⠀⠘⡄⢠⠀⠀⠻⣿⢟⡉⠵⠲⢀⣤⣴⡿⠋⠉⡄⠀⣸⠿⠛⠚⠙⢿⣿⣿⣶⣶⣄⠀⠀⠀⠀⢠⠀⣤⠰
⠀⠀⢧⠀⢆⣠⣼⣾⠿⠓⢲⣶⣿⠛⡏⣠⠀⠀⣧⡴⠁⠀⠀⠀⠀⠀⢳⢻⣿⣷⣠⡀⠀⠀⠀⢸⠀⢠⠤⠊
⠀⠀⠈⡆⢾⣿⡿⠛⢒⣿⡿⢟⡇⢀⣧⠈⠓⠦⣧⢀⣠⠄⠀⠀⠀⠀⠀⠠⣿⣿⣇⠛⠳⠀⠀⠈⡇⠁
⠀⠀⢠⠁⠾⠗⣲⣾⣿⠿⠃⣰⣇⣼⠃⠀⢀⡸⡿⢻⣿⣟⠢⡀⠀⠀⠀⠀⠉⣿⣿⣷⣦⢀⠀⠀⡀
⠀⠀⡅⠠⠚⢛⣿⣿⠃⢸⣴⠿⠛⠁⠀⠀⢸⢻⣧⡟⠹⣿⣻⣦⡀⡀⠀⠀⠀⠈⠙⢿⣶⣄⠀⠀⠇⠀⣴⠂
⠀⠰⠁⠠⢶⣿⠛⣿⣰⡟⠀⠀⠀⠀⠀⠀⣸⣿⣿⡇⣼⢻⡿⣿⣿⡇⠀⠀⠀⠀⠀⠺⣝⢋⠀⠀⠂⣸⠃⠤⠎
⠀⢠⠁⣰⡿⣿⢰⣿⡟⣤⡀⠀⠀⠀⠀⡼⡿⠙⢯⣻⡇⢸⣿⣟⣿⠅⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠋⠘⢦⡀
⠀⡸⠠⢟⣨⣿⠿⠋⠀⠈⠀⠀⠀⠢⢜⡜⠀⠀⠈⢿⣰⠛⣇⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⢀⠁⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠘⢄⠀⠀⠀⠘⣟⠸⣿⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⡒⠀⡠⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠸⡆⠻⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡘⣏⣀⠠⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠠⠀⠀⠀⠸⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠋⠀⠀⠤⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣦⣤⡀⠀⢠⣴⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⠛⠉⠛⠻⢿⣿⡿⠛⠉⠙⠛⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⠁⢠⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⢀⣿⣿⢁⡀⠀⠀⠀⠀⠙⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⣤⡄⢀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠼⠿⣿⡿⠁⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⣠⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣟⣀⣉⢩⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠰⠿⠶⡾⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣧⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⡼⠁⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⢀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⠀⠀⢠⣿⡇⠀⠀⠀⠀⠰⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢹⣧⡀
⠀⠀⠀⠀⠒⢤⡀⢀⡀⠀⠈⠑⢶⣄⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀⢸⣿⣷⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠈⠳⣝⡛⢶⣤⡀⠈⠁⠀⠀⠁⠀⠀⠀⣰⠆⠀⢛⣿⣟⠀⠀⢀⣤⣶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠍⠻⣦⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⢻⡿⠀⠀⣼⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣤⣀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠂⠀⠀⠀⠀⠀⠘⠙⣷⡄⠀⠀⠀⠀⠀⣧⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠐⠄⠀⡟⠀⠀⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠾⢿⠿⠿⠋⠁⠀⠀⣠⡔⠀⠁⠀⠀⠀⠀⡀⠀⠀⢹⣿⣎⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠙⢿⡇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⢰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⠀⣀⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⡀⠀⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠙⠒⠠⢄⣈⡀⠀⠀⠤⠀⠀⠀⠠⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠖⠀⠀⠀⠈⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⢀⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉

⣶⣶⡶⠶⢶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⣀⠀⠀⠀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠀⠰⠀⠀⠀⠀⠀⠀⠀⢰⠦⠀⡤⠈⢀⡈⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠈⠀⠀⠀⠐⠆⡀⠀⠁⣤⡐⠁⠀⢠⣤⠀⡀
⠀⠀⠀⠀⠐⠂⠄⠀⠀⠀⢀⡀⠐⠀⠀⣀⠜⠀⠀⠀⠀⠀⠛⠉⠁⠈⢄⠰⠆⠆⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⢀⠀⠀⠀⠠⢄
⠀⢀⠀⠂⠀⠀⢘⠀⠀⠀⠀⠀⠀⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢤⣤⠖⠒⢂⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⢠⠀⠈⠁⢠⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠉⢄⠀⠞⠀⠀⠀⠠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⠁⠀⢀⢨⠀⠀⠀⠐⠀⠀⠔⠁⠀⠀⢈⡲⠆⠠⢹⡀⠀⠀⠀⠀⠀⠁
⠀⠒⠤⠴⠄⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠨⠕⠂⠀⠈⠒⡄⠈⠀⠐⠀⠲⠤⠀⠀⠀⠀⠀⠀⠀⠘⠉⠃⠚⠁⠀⠈⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⡁⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠃⢄⠀⠀⠀⠀⠀⠐⠀⣤⠀⠤⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠉⠘⡀⠀⠀⠤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠁⠀⠤⠴⠒⠂⠈⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠄⢐⠶⠈⠀⢀⠂⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⠀⢀⠓⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠌⠉⠙⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠁⠈
⠀⠀⠀⠀⠀⠀⢀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡈⠀⠀⠀⠀⠀⢀⠀⠠⠀⢀⠀⠀⣀⠠⠒⠁
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⠀⠄⡀⡠⠀⠁⠀⠀⠀⠀⠰⠄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠂
⠀⠉⠓⠢⢀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠈⠊⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⡄⠐
⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠐⢀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣀⠀⠀⠀⠀⠀⠀⠉⠆
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐
⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠌⠀⠀⠀⠀⠀⠠⠄⠒⠀⠀⠒⠠⠄⣀
⠀⠀⠀⠐⢀⠀⠀⠀⠈⠀⠠⢀⠀⠂⠀⠐⠠⠄⡀⢠⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠀⠀⠁⠢⠀⢀
⠀⠀⡠⠖⠈⠈⠀⠸⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢀⠘⡀⣀⡀⠀⠒⠀⠀⠲⠒⠒⠢⠤⠄⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠄⠀⠀⠐
⢀⠘⠀⠀⠂⠈⠀⠀⠐⠈⠈⠀⠀⠀⠀⠠⠤⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⢠⠁⠀⠀⠀⠀⠀⠃
⠀⠁⠐⠒⠂⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠂⠀⠀⠀⠀⠀⢢⡤
⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢳⡀⠀⠀⠀⠀⠀⠈⠵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣐⣛⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣓⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣾⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠐⣂⠘⢦⡈⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢰⠀⠀⡇⣀⢰⡄⠘
⠀⠀⠀⠈⠀⠈⡅⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢠⠅⠌⠋⠀⠀⠁⠀⠀⠁
⠀⠔⢠⠈⠂⠐⠃⠃⠃⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠀⠀⠀⠀⠐⢶⡎⠀⠀⠀⣀⠀⠀⠀⢠⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⢸⠁⢠⢀⡆⠀⠀⠸⡖⠇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⢦⠁⠀⠀⢀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠜⠀⢀⠀⢀⠀⠀⠄⠀⢦⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠋⢲⠜⢠⠏⢰⢸⠾⡄⠘⡆⠀⠘⡄⠀⠀⠀⠀⠀⠁⡤⠀⠀⠀⠀⠀⠀⢠
⢀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠘⠀⠂⠘⠀⠑⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢰⠀⠘⢸⠊⠃
⠈⠂⠀⡄⢱⠦⠘⠏⠀⠀⠀⢠⠀⠀⠀⠦⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⡐⢆⠀⡀⢸⢀⣀
⠀⠀⠀⠀⢪⡄⠈⣀⡀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡸⠰⠸⠀⠂⠃⡇
⠀⠀⠀⠀⠀⠸⠁⠈⠃⠀⠀⠀⠰⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠖⠁⡎⠓⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠞⠚⠀⠀⢸⠁⠋⠯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⠞⢦⡜⠉⠉⠀⠛⠀⢣⣯⠄⠀⢰⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⣄⡼⠉⠳⠏⣀⠀⠀⢀⠀⠀⢸⣀⡞⢀⡀⠀⠈⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡀⠉⠀⠀⠀⠀⢉⠀⠀⠸⡄⠀⢠⠿⠚⠉⠀⡀⠀⠳⠦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠛⠃⠀⠰⡆⠀⠀⢸⠀⠀⠀⠳⣤⣏⣀⣠⠴⠚⠁⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡾⢄⡇⠀⡀⠀⠀⣇⠀⠀⠈⣇⠀⢀⡴⠋⠉⠁⠀⢀⠋⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠉⠀⠀⢹⡄⠀⠀⠘⣷⣞⣁⣠⡤⠴⠚⠁⢀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠸⣗⠾⠀⠀⠀⢰⡄⠀⠀⢳⡀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⣙⡶
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢳⡀⠀⢀⣿⠿⠤⠤⠤⠶⠒⠚⠉⠀⠀⠘⢧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢄⣒⡦⠀⣻⣶⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⡿⢿⡉⠙⠓⠶⠤⠄⠀⠶⠒⠀⠀⠀⣙⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠉⠀⠀⠳⣜⠢⠄⠀⠀⣤⣤⣐⡟⠋⠉⠁
⠀⠀⠀⠀⠀⠀⣴⡾⠟⠋⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⣱⣤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⠀⣴⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣯⡄⣰⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣬⣹⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⠉⠉⢩⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣶⠄⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣿⣿⣏⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⣼⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣏⣀⣀⣀⠀⢠⣾⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣣⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠉⠉⠉⣿⠋⠉⠉⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠈⣹⠋⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣄⠀⠐⢛⠇⠀⣠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣄⠀⣠⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠈⠐⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⡂⠀⠀⠀⠀⠀⠀⠰⢐⠁⠀⠀⠀⠀⢀⠀⠑⠠⡈⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⡄⢠⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠆⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⢀⡀
⠀⠀⠀⠀⠀⡀⢀⠀⠣⢈⣁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⢀
⠀⠀⠀⠀⠀⠘⡋⠇⠀⠀⠀⠀⢀⡲⠋⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⢹⣀⣠⣴⣀⡀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠘⠃⠙⡀⠈⠀⠀⠈⠠⠀⠀⠀⠀⠀⠀⠘⠀⢠⣤⣴⠏⠙⢣⣩⡙⠛⢶⣤
⠀⠀⠀⠀⠠⠴⣞⠁⢼⣳⡦⠈⠂⠀⠀⠀⠀⠀⠀⠘⠀⠀⠉⠙⠋⠀⠀⠀⠙⠓⠄⠀⠈⢙⠷⣦
⠀⠀⠀⠀⠀⠆⠈⠉⣦⠙⠄⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠠⡄⠀⠀⠀⡀⠀⠐⢁⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠓⢤⡀⢠⠹⣿⢀⡀⢀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⡄⡄⡄⢠⣾⣳⡎⣴⡅⠀⠀⠤
⠀⠀⠀⠀⠀⢠⠙⣼⠃⡙⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠸⣧⣾⣿⣿⣷⠙⠛⠥⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢀⢈⠳⣽⡌⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢿⣟⢿⣷⣬⡙⠂⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢁⣶⡬⠻⢼⣧⡀⡀⣄⠀⠀⠀⠈⢃⠀⠀⠀⠀⢀⣡⢀⣀⠁⠀⢀⠔⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣤⠄⠉⠛⠻⢿⡀⣠⣤⠤⠀⠀⠀⠀⠀⠒⣻⡿⡺⠀⡰⠋⠐⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣷⣶⣀⠠⠖⠙⠻⡀⠀⠀⢠⠀⠀⠂⡼⣰⣾⠇⠈⠀⠀⠀⠐⢤
⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⠀⠉⠁⠀⠀⠀⠀⠀⢡⠀⠀⢐⢆⠂⣼⠟⣭⡿⢁⠉⢶⣇⠀⠲⣄⡈
⠀⠀⠀⠀⠀⠀⠀⢀⡄⡀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠄⠐⡌⠀⢳⡯⠵⠚⠀⡀⠀⣐⣏⠣⡀
⠀⠀⠀⠀⠀⢀⣴⣼⣻⢘⣨⣜⠤⠀⠀⠀⠀⠀⠀⠊⠀⠓⠀⠸⠉⠂⠀⠀⡀⢠⠈⠳⠄
⠀⠀⠀⠀⠀⠀⠁⠈⠙⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡰⠁⠀⠀⠀⠀⢷⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠈⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣠⣤⡤⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣻⣿⣿⠋⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⠛⠃⠀⠀⠀⠀⠀⠀⢰⣶⣶⡆⢠⣿⣿⣿⣿⣿⣿⣶⣤⣤⡄⢀⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣧⣿⣿⣿⣿⣿⣟⠛⠋⠉⠹⠿⠁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣦⠶⠶⠞⠛⣿⣿⣿⣿⣿⣿⣿⣽⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣥⠀⠀⠀⣴⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣿⣿⣿⣶⡾⠛⠄⡈⢻⣿⠛⠛⠿⣿⣿⣧⣀⠀⠀⠀⠀⠀⠀⠙⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢻⣿⣿⣿⣿⣶⣄⠙⢺⣿⣀⣀⣀⣠⣿⣿⣿⣦⡀⠀⠀⠀⠀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢿⣿⣿⣿⣿⣷⣻⣟⡛⣿⣿⣿⣿⠋⢹⣿⣿⣦⡀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣷⡜⣿⣿⣅⡢⠀⢿⣿⣿⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣷⣤⣹⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠏⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⡀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢀⡤⠤⣀⢀⡀⠀⢀⣀⡀⢸⢉⠇
⠀⠀⠀⠀⠀⢀⠎⠀⢀⣷⠋⠈⠹⠉⠙⠇⣀⠘⠖⡖⢲⠊⠀⠒⢼⠃⡈⠉⠍⠰⠏⠻⣸⠉⠒⣄⢀⣀
⠀⠀⣀⡴⠋⠉⢄⠘⠉⠉⡆⠁⠠⢈⡁⠦⠀⠔⠀⠀⠀⠀⠀⢁⡠⠀⣃⡀⢀⠈⡠⠠⠆⠀⠀⠈⠁⠀⠉⠒⣄
⢠⠊⠀⠀⠀⠀⠀⠸⡠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠈⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠊
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠑⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⠀⠀⠀⠀⢀⡠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠓⠒⠶⠖⠒⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⠶⠶⢤⣄⡀⠀⠀⠀⠀⢀⣀⣀⣀⠀⣠⣤⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠈⠻⣦⡶⠛⠛⡿⠁⠀⠉⠿⠃⢈⠉⢀⣀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⢠⡄⠀⠀⣾⢳⡀⠀⠋⠀⠀⡄⠀⢠⡟⡇⢠⠀⣾⠃⣾⠏⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⣸⡇⠀⠀⣿⢸⡇⢀⡀⠀⢠⡇⠀⠸⣇⡇⡤⢸⡟⢸⡟⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⡇⠀⣦⠸⣾⣧⣿⠇⠀⢸⡇⣴⡆⡽⢻⠇⣼⢀⣼⡇⣰⡇⠀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⢸⡇⣸⢿⡀⡾⢹⡇⡴⠀⠸⠟⠘⠿⠃⠘⠋⠙⠋⠘⠷⠋⠀⣞⣥⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠃⠘⠿⠃⠈⠋⢁⡀⠀⣤⡄⠀⠀⣴⢿⡆⠀⠀⠀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⢀⣀⠀⢈⠁⠀⢿⡇⠀⠀⣻⣟⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⢻⣧⡞⡿⠀⣾⠀⢀⡞⢷⡴⠊⠁⣹⣦⣤⣤⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠏⢸⡟⠀⣧⠞⠻⠴⠋⠀⣿⡇⠀⣾⢁⣿⠀⠀⠀⠀⠀⠀⢾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠶⠀⠛⠀⠀⠀⠀⣠⣄⠀⣴⠒⢦⠉⢀⡀⠉⣋⠁⠀⠀⠀⢀⣿⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢚⡅⠀⢸⡀⠀⢀⡴⠋⣿⠀⣷⣿⣸⣤⣿⠁⣰⣿⠀⠀⠀⢀⣼⠃⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⣇⡴⠋⠀⠀⢻⡾⢹⣏⡟⠀⢿⡴⠋⢿⣄⣀⣴⠟⠁⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡀⠉⡀⠀⠀⢠⢿⡇⠀⠉⠀⠀⣠⡀⢀⡀⠉⠉⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⠁⠀⢠⠏⣸⠇⢠⡷⠦⠞⠋⠛⠙⠷⣤⡤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢸⣤⡿⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⣀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢴⠶⠶⢛⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠂⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⡴⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢰⠁⠀⠀⢯⠀⠀⣠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⢰⠃⠀⠀⡼⠀⠀⠀⢸⢖⡭⠟⠁
⠀⠀⢠⣶⣚⣋⣭⣭⠇⠀⠀⠀⠉⠉⠓⠲⢼⠀⠀⠀⢠⠀⣀⢔⡵⡏⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠙⢿⣟⠛⠛⠿⠦⢤⣀⣀⠀⠀⠀⠀⠳⠀⠀⢸⢊⡝⣿⣆⢸⠤⠒⠉⠉⠀⠀⠀⠀⠈⠉⡲⣄
⠀⠀⠀⠀⠈⠣⣍⠀⠀⠀⠀⠀⠈⠙⠲⣄⣠⣀⣠⣰⢣⠏⠀⣿⣸⠀⠀⠀⣀⡠⠄⠒⠒⠒⠒⠠⢭⣢⣟⣦
⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡟⠰⢸⣿⣿⠰⠿⠉⠋⠀⠀⠀⠀⠀⠀⠀⣀⣊⣭⡿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢒⠶⠒⠂⠙⢿⣿⣟⣻⠶⣿⣿⡻⠗⠠⠤⣄⣀⣀⣠⡤⠶⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⡀⠞⠛⠻⠟⠋⠙⠻⠿⠦⡀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠈⢢⡀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⣠⠎⠳⡀⠀⠀⠀⠀⠙⢄⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢀⡜⠀⠀⠀⠀⢀⣤⠖⢻⣿⠀⠀⠈⠢⣀⠀⠀⠀⠀⢣⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⡞⠀⣀⣠⡤⠴⠋⠀⠀⠘⣿⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢳⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣵⠟⠋⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠈⠙⠲⣄⢉⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢠⡤⡄⠀⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⠀⡀⢀⢠⠁⠀⡀⠀⡀⠀⠠⠥⠄⣤⢠⠄⢀⣄⣴⠀⢀⠀⠀⢀
⠀⠀⠤
⠨⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠈⠀⠂⠘⠐⠈⠀⠃⠛⠀⠀⠀⢀
⠀⠀⣾⡀⠀⠀⠀⢈⢢⡨⡾⡖⡏⣾⢹⣨⣷⡇⣽⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⣐⠀⠀⠀⠀⠀⢈⠁⠈⠰⠁⠈⢠⡤⢬⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣶⠠⡆
⠀⠀⠱⠿⠅⠇⠸⠟⠀⠩⠖⠧⠁⣿⠀⠘⠃⣠⡴⣤⡀⣠⠦⣤⠀⣤⠤⣿⢰⣧⠴⣄⢠⡄⢠⠄⣤⠦⣄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠂⠐⡂⠂⠐⠂⠀⠀⠀⠀⠀⣿⠀⢲⡆⣿⠀⢸⡇⣿⠀⢸⡇⡟⠀⣿⢸⡇⠀⣿⠘⣇⣾⢰⡧⠤⠿⠈⠠⠸⠅⢀⠀⠞⠄⡀⠠
⠀⢸⣇⡖⣧⡴⢢⢖⠀⠀⠀⠀⠀⢻⣄⣼⡇⢿⣄⣼⠃⢿⣄⣼⠃⣷⣠⣿⠸⣧⣠⡟⠀⢻⡇⠈⣧⣀⡶⢠⠒⢆⠠⣀⢄⡰
⠀⠈⠉⠑⠉⠙⠋⠚⠀⠀⠀⡀⢀⠠⠀⠀⠀⠀⠀⢀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠀⠀⠀⠀⠀⠘⠤⠺⠮⠟⠼
⠀⠠⠀⠀⠄⠠⠤⠄⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⣚⡀⡀⠐⠤⢤⡠⢢⣴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠁⠁⠀⠈⠀⠀⠈⠀⠀⠈⠈⠀⠀⠈⠀⠀⢀⣀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢨⠀⠁⠈⠈⠈⠁⢀⠀⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⠔⠠⠀⠠⠆⠀⠈⠀⠀⠀⠀⠈⠀⠀⡉⡀⠘⠓⠀⠈⠈⠃⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢲⣤⣤⣤⣤⠠⠄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢠⣀⣄⡀⠀⠀⠐⡶⣶⣶⡶⠶⣶⣶⣤
⠀⢹⣧⡉⠙⠷⣷⣷⡘⡦⣇⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣈⠩⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠿⡟⠛⡄⠀⠀⢘⣶⢮⡱⣞⢀⠓⠀⠁⢂
⠀⠀⠍⠿⢗⣀⠀⠈⠉⠃⠁⣿⣦⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢲⡆⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠴⢒⠓⠲⠸⠄⠀⠀⢿⣿⢿⣦⣈⢣⠀⠀⣼
⠀⠀⠘⢿⣭⡽⠞⣣⡄⡀⠀⠙⠃⠀⠀⢀⣔⠀⢸⡁⣤⠀⢠⡀⠀⠀⠀⠀⠀⠀⣠⠀⢀⠀⠀⠀⢀⠀⠀⠂⡄⠀⠀⠨⠿⣷⣎⡈⠁
⠀⠀⠀⠀⠑⠂⠁⠀⠈⠺⠷⠦⣀⠠⠀⠀⠙⠛⠎⠓⠚⠓⠲⠇⠀⠀⠀⠀⠀⠉⠀⣤⣀⢻⣄⣄⣬⡿⣿⣷⠿⠆⠀⠀⠀⠻⠯⠴⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣅⢹⣶⣽⣟⣿⠿⠛⠀⢀⢀⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠔⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡶⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠰⠀⠀⠀⡄⡏⠉⠠⠀⠢⡀
⠀⡀⠀⠖⠀⠀⠀⠀⠀⠨⢻⣤⠀⠀⠀⠀⠀⡐⢿⠇⢰⢃⠀⠀⢀⢠⢤⡄⢀⢀⠀⣤⡤⢀⡀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⢩⠀⠸⠀⠀⠰⠆
⢸⣷⠋⢰⠆⠀⠰⡄⠀⠀⠂⢽⡇⠀⠀⠀⠀⡝⣿⠀⢨⡟⠀⣰⢻⠿⣼⢣⡤⠾⠋⣁⢴⠖⠀⠀⠀⠀⠀⠀⠈⣑⠦⠀⠠⡀⠀⠀⠀⠀⠀⠀⣆
⣸⣿⡿⠁⠀⠀⣤⠘⣆⠈⣻⣲⡇⠀⠈⡐⢀⣤⡌⠀⣼⡧⣠⣿⠂⠴⠋⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠄⣀⠐⠀⠀⠀⠀⠀⠀⠀⣸
⢹⣛⡄⠂⠄⠀⠀⢀⠀⢠⣜⡟⠀⠀⠀⠁⠀⠙⠁⠀⠻⠁⠛⠁⠀⠠⠤⣼⣶⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡤⡄
⠀⢿⠡⢎⡄⠀⠀⣄⢁⡰⡎⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⡐⠷⠶⢶⣔⡶⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠴⣬⣌⡀
⠀⠘⢷⣎⠄⠀⢦⢰⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠛⠿⠳⠦⢤⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀
⠀⠀⠀⢻⡆⢼⡼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡀⢛⠑⠀⠀⠀⢀⡀⡐⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠈⣧⣄⣀
⠀⠀⠀⠀⠁⠀⠀⠀⣀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢳⠘⡅⠘⢧⢉⠀⠙⠟⠟⠈⠉⠀⠀⠀⠀⠀⢫⣄⢀⠀⠘⠀⠀⠸⣯⠿⡿⣷⣶⡆⢠⣄
⠀⠀⠀⠀⢠⣤⣄⡀⠙⢿⣷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⣀⣤⣤⡶⣾⣾⣷⣦⣄⠀⠀⠙⢿⡄⡀⠀⢠⣶⣿⣄⠸⠇⢸⡟⢿⡿⣠
⠀⠀⠀⠀⠈⠳⣯⣟⣷⢮⡙⠆⠀⢀⣶⣶⣶⣤⠀⠀⠀⠀⠀⠀⠈⢻⣿⣟⠋⠻⣮⠻⣿⠝⣻⠆⠀⠀⠀⠙⠁⠀⢘⡻⢿⡖⠂⠀⠘⠀⠞⢡⠏
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⠟⠂⢤⣄⣉⡉⠉⠁⠀⠀⠀⠀⠀⠀⣠⣤⣽⡷⠖⣚⣶⣦⡆⠁⠉⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣯⣙⡀⠀⠈⠐⠋
⠀⠀⣴⣶⡶⠶⢷⠖⠂⠀⠀⠘⠳⣶⣿⣛⠲⡄⠀⠀⠀⢀⠴⢿⣿⢯⣭⠄⠀⠈⠙⠉⠄⠀⢀⠀⠀⠀⠀⠁⠀⠈⠻⢿⣿⣽⣥⡄⠀⠰⡀
⠀⠀⢈⣙⣛⣛⣛⡛⠃⠀⢤⡙⢷⣤⡀⠉⠙⠉⠀⠀⣠⣾⡛⣛⣫⣤⠴⢀⣀⣴⣤⡾⠂⣀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠉
⠀⣾⣿⣿⣯⣿⣯⡅⢀⡐⢦⡙⠳⣽⣻⣆⠀⠀⠀⠀⠉⠛⠟⠿⣿⣿⣿⠟⣻⣿⡏⡅⣴⣟⣰⣿⠇⠀⠀⠀⠀⠀⠀⢦⣶⡆⠀⠀⣠⡄
⠀⣈⣭⣭⣽⡶⠄⠠⣌⣳⣦⡛⢷⡌⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣾⢳⣿⣿⠿⠏⠀⠀⠀⠀⠀⢰⠤⢹⣙⣤⡞⣽⢟⡏
⢼⣯⣿⣿⡿⠟⠀⠸⣿⡿⣿⣟⠿⠿⠀⠀⠀⢀⣠⣤⠤⢦⠀⠠⣤⣤⣀⠀⠈⠉⠁⠁⠁⠀⠀⠀⠀⢠⣶⠀⢀⡶⣢⣾⡿⠋⣻⣿⣆⣋⡜⢳⡀
⠀⣤⡶⠟⢛⡯⢠⣷⣬⡻⢿⣿⡆⠀⢀⣤⡾⠿⡛⠣⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢸⣤⡌⠀⠛⠙⠳⢚⢉⣭⡸⣟⣿⡯
⠘⠻⠟⠛⣩⣧⡌⢻⣿⢿⡄⠀⠀⢠⡾⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠁⠀⠀⠀⠀⣀⠄⠤⠚⠀⠉⢀⡈⢠⣥⣈⡘⠻⣷⣾⣥⣿⣧
⠀⠀⠀⢸⣿⣿⡇⠀⠙⠻⠃⠀⣠⣏⠀⠀⠀⠀⠀⠀⢠⢂⢂⣾⣶⡾⠁⠀⠀⠀⠀⠀⠊⠁⣀⣠⠴⢤⣯⠉⠙⠿⣿⣿⡛⢦⣬⣽⣣⡌⠉
⠀⠀⠀⠘⢿⠟⠁⠀⠀⠀⠀⠈⠉⠉⠙⠓⠀⢠⣤⣤⣷⠶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⠀⠀⠀⠀⠀⠘⠛⠛⠂⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢆⣠⡄⢦
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠿⠿⠟⠛⠻⠷⣶⣤⡀⠀⠀⠀⠀⣠⣴⠾⠟⠻⠿⢿⣽⣿⣾⣷⣀⣠⡀
⠀⠀⠀⠀⠀⢀⣴⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⣠⠛⠉⠀⠀⠀⠀⠀⠀⠉⠁⠙⢿⣿⣿⣿⣄
⠀⠀⠀⠀⣄⣾⣿⣿⠉⠀⠀⠀⠀⠆⠀⠀⡀⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡄
⠀⠀⠀⠰⢻⣿⣿⠇⠀⠀⠀⠀⢰⣀⠴⠈⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠃
⠀⠀⠀⢠⡟⣿⣿⡖⠀⠀⠀⠀⠈⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦
⠀⠀⠀⠀⣩⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢀⣀⡠⠀⠴⠒⢐⡩⠋⠀⠀⠀⠀⢠⣿⣿⠫⡉
⠀⠀⠀⠀⠈⣻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠔⠒⠊⠉⠀⠀⠀⠀⠔⠋⠀⠀⠀⠀⠀⠀⣰⣿⣿⠾⠃
⠀⠀⠀⠀⠀⠿⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠎
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⢀⡀⢀⡀⠀⣶⣿⣿⠏⠈
⠀⠀⠀⠀⠀⠀⠀⠺⠿⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠠⣞⣁⡀⠤⠄⠒⠂⠈⠉⠀⡔⢀⣼⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⢿⣿⣶⡄⠀⠀⠀⠀⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣌⣴⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠜⠻⡾⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡶⡀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠀⠀⣠⡼⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠉



⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀
⠀⠄⠀⠘⠱⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠶⠀⠀⠀⠓⠛⢁
⠀⠀⠀⠀⠁⠓⡀⠀⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⢀⡚⢠
⠀⠠⠀⠈⠀⢠⢁⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢌⡉⡸⠀⡀
⠀⠀⠀⠀⠀⡤⠀⢤⠀⡻⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠀⠐⠀⠀⠀⠀⠀⠀⠐⠲⠤⡀⢀⠜
⠀⠂⠀⠀⠈⠀⠠⣀⠆⡴⢎⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠀⠀⠀⠀⠀⠀⠀⠐⠆⠄⢀⠀⠠⠒⠁
⠀⠀⠀⠀⠨⠀⠀⢠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⡠⠀⠁
⠀⠈⢥⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁⡀⠀⠀⢨⠟⢃⠀⠂⠤⠄⠀⠊⠐⡀⠀⠀⡤⢄⠀⠀⠀⠀⠀⡄
⠀⠀⠸⡁⠀⠀⠀⠀⣴⠂⠀⠀⠀⣉⣁⠤⠀⠀⠀⠀⠘⢅⢁⠂⢀⠄⢄⠀⣤⠘⠂⠀⠀⠀⠀⠀⢀⠢⠤
⠀⠀⢘⡇⠀⠀⠀⡶⢗⠀⠀⠀⣀⣀⠀⠀⠄⠀⠀⠀⠖⠂⠠⢤⠞⠀⢀⠈⠁⠀⣀⠄⠀⠀⠀⢤⠀⠑
⠀⠀⢸⠁⠀⠀⠢⣭⠵⠀⡀⠀⠀⠀⠁⠀⢀⠄⠀⠀⠀⠐⢃⣬⣄⠛⢆⠲⠷⠢⠀⠀⠀⠀⠠⠀⠀⢈⣤⡀
⠀⠀⡎⠀⠀⠙⠦⠶⠍⡉⠀⠀⠲⠄⢀⠠⠡⠀⠀⠀⠀⠀⠘⠀⠀⠫⠀⠆⠠⡀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠉⠲⢶⠾⠛⠁⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁
⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠂⡀⠀⠄⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠁⠀⣰⠏⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⢠⣷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢰⣴⡿⠋⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠄⠀⠀⠃⠀⠀⠀⣼⣿⠟⠋⠁⠀⠀⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⣠⣶⡿⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣿⠷⡿⠿⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⣥⠀⠀⠀⣰⣿⠆⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⢳⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣠⣾⡿⠋⠁⠀⠀⠠⢴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡯⠤⠤⠄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠈⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠏⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⢠⡄
⠰⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠠⡀⠀⠀⠀⠀⠁⢀
⠀⠐⢆⢀⡐⠠⡀⠀⠀⠀⠀⠀⠀⠘⢦⡰⣄⠀⣠⣤⠀⠚
⠀⠀⠀⡀⠑⢦⠈⠑⠦⢄⣀⠀⠀⠀⠀⠐⢚⣟⣵⡿⢦⡀
⠀⠀⠀⠐⠀⠠⠀⠈⠂⠀⣙⠫⢿⣶⣶⢤⣌⣉⠙⠛⠲⠷⣄⡀
⠀⠀⠀⠀⠠⠀⠀⠀⠐⢤⡈⠠⠄⠉⠑⠀⠀⠙⣶⠁⠒⠤⢉
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠻⣄⡀⠀⢷⠀⠀⠀⠙⠀⠀⡀⠀⠀⠛⠂⣄
⠀⠀⠀⠀⠀⠈⠀⠠⡀⠘⡄⠘⢟⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠳⡀
⠀⠀⠀⠀⠀⠀⡅⠀⠄⠀⠀⠀⠈⠳⡀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣦⢡⡄
⠀⠀⠀⠀⠀⠀⠃⠀⠴⠂⠀⠐⠀⠀⢈⠣⢂⣅⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠘⢷
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠠⠒⠉⠀⣄⡡⠙⣄⠀⠀⠀⠀⠂⠀⠀⠀⠀⢷⣀⣨
⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠠⠃⠈⢫⣦⣄⠀⠀⠀⡀⠀⠈⢀⠀⠈⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⡢⠉⠀⠄⠀⠀⠈⠹⡄⠀⠀⠀⠀⠀⠚⣠⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠉⠀⠐⠊⠉⠁⠉⠛⣄⣄⠀⠀⠀⠄⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⡹⣄⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠐⠀⠠⠤⠀⠃⠀⠀⠀⠀⠀⠐⠿⣦⡀⡂⠀⠀⡀⠚⠀⢤⣄⣌⣄⣤⣴⠓⠂⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⡀⠀⠀⠀⠀⠠⠖⠖⠒⠾⠙⠁⠀⠐⠽⠕⠀⠈⠅⠀⠀⠃⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⣀⡀⢻⡘⠃⠒⠂⠀⠤⠈⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠝⠉⡀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢁⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣶⢂⡶⠀⠀⠔⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢄⠀⢸⠀⠀⠀⣖⢦⠀⠀⠀⢈⠀⠀⠀⠀⣏⠳⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠋⠀⠀⠀⡤⡀⠀⠀⠀⡄⠀⠀⠀⢉⡁⠀⠀⠀⢸⠀⠀⠀⠀⠈⠄⠁
⠀⠀⠀⠀⠀⢀⡠⡆⢀⠀⠀⠀⠘⠓⠀⠀⠀⠀⢱⢠⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂
⡀⠀⠀⢠⠎⡠⠗⠉⠀⠣⡀⠀⠀⠀⠁⠀⠀⠀⡈⢣⡑⠤⢀⣀⡀⢴⠏⢈⠐⠤⠤⠤⠐⢒⣶⠞⠁
⠃⠀⠀⠀⣘⢀⣠⡄⠀⠀⢱⡀⠤⣀⣀⣀⡠⡴⠁⠀⠉⠒⠒⠒⢂⠁⠀⠈⠙⠉⡩⠉⠉⠉⠀⠀⠒⠀⠀⠄⠀⠀⠀⡀
⠀⢠⡀⠀⠈⠑⠛⠁⠀⠀⣰⠉⠒⠤⠤⠴⠚⠀⣀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠣⡈⠂⠤⡀⣀⠀⠤⢒⠟⠀⠠⠀⠀⠀⠀⠰⢌⠳⢄⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⠬⢍⣉⡉
⠀⠀⠈⠑⠒⠠⠄⠐⠒⠁⡄⠀⠀⠀⣤⡀⠀⠀⠂⠑⢄⠑⢤⡀⠀⠀⠀⠆⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠐⢀⠂⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠰⠀⠀⠀⠑⠦⠘⠀⠀⠀⠄⠀⠀⠄⠀⠀⠀⣤⣤⣶⠶⠀⠀⠆⣘⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠘⠀⠂⠀⠀⠀⠀⠉⠉⠉⠉⠀⠘⢯⣭⠽⣳⠶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⠀⢀⠀⠀⠀⠈⣀⡠⢤⠀⡀⠒⠒⠒⠤⠤⢄⣀⡀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡎⠀⠀⠀⠴⠷⠒⠃⠀⠙⠒⠒⠐⠢⠤⠔⠀⠀⢰⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠒⣚⡭⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠭⠗⠋

⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢦⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⢀⣴⠟⠁⢀⡀⢸⠀⠀⠀⣠⣴⡶⠶⠶⢄⡀⠀⣸⢡⠏⣼⢃⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃
⠀⠀⠀⠀⠀⣾⡏⠀⢰⢫⢇⡞⢀⣠⣾⠟⠁⠀⠀⠀⠀⠙⢶⣷⠋⢰⣧⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠃
⠀⠀⠀⠀⢸⣿⠀⠀⡸⠓⠋⠀⠀⢈⡀⡀⢀⣠⡀⢀⣤⢤⣾⠃⢠⣿⣃⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠘⣿⡄⠊⠀⣴⣿⡀⢴⡟⢀⠟⡟⢂⡶⣿⠁⣼⡏⢠⣾⠁⣽⣻⠏⣠⣾⢠⣾⠩⢃⠄⠀⢰⡟⠁
⠀⠀⠀⠀⠀⠈⠛⠒⡫⢻⡏⠀⠘⠖⠋⠀⠓⠊⠀⠙⠋⠈⠓⠁⠙⠚⠁⠙⠋⣼⠇⠀⠛⠚⠁⠀⢀⠈
⠀⠀⠀⠀⠀⠀⢠⠞⢡⡿⠀⠀⠀⠀⢠⣤⠀⠀⠀⡤⢲⡄⠀⢀⣤⠄⠀⡠⢢⡟⠀⠀⠀⣼⡿⠀⠿⠃
⠀⠀⠀⠀⠀⠀⢯⠴⠋⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⣧⢈⡇⠀⠘⠋⠀⠸⡤⠏⢠⣤⣤⣴⣿⡧⠄⠀⠀⠀⢰⠊⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⣤⡄⠈⢻⠷⣤⡄⠀⣴⣷⠀⣠⣄⠀⢀⣾⣿⠀⠀⣴⡶⣆⠘⣦⣃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⣼⣿⡇⠀⡸⣸⣿⠁⣸⣿⣿⡞⣿⡟⠀⡼⣿⡏⠀⣰⣿⣣⠇⡰⢁⣾⡟⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣶⠻⣿⣇⡴⠁⣿⣏⡼⠃⣿⡿⠰⣿⣇⡾⠀⣿⣧⡴⠻⣿⣧⠞⠁⢸⣿⣁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠈⠉⠀⠀⠙⠋⠁⠀⠉⠀⠀⠉⠉⠀⠀⠈⠉⠀⠀⠈⠁⠀⠀⠀⠉⠉







⡶⣶⢶⢶⡶⠶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⣶⡶⣶⣶⢶⣶⠶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⣦⠀⢀⣴⡿
⠀⢀⣀⡀⠀⠀⠀⠀⢠⡾⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠆⠀⣰⣿⠋⢠⡏⢠⣿⡟⢡
⠀⣼⣿⡟⠀⢀⡀⠀⣿⣇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⣼⠟⣷⠀⠀⠀⠉⠀⣴⣿⠃⣠⠟⢠⣿⡟⣠⡟
⢰⣿⣿⠃⢰⣟⡿⠀⠸⣿⠇⠀⣠⣶⡿⢷⠀⠀⠀⢠⣿⡟⢀⣤⡀⠹⣷⡟⠀⣼⣿⠂⣸⣿⣯⠞⠁⢠⣿⣿⠟⠋
⣾⣿⡟⠀⣾⡿⠁⠀⣰⡿⢧⣰⣿⣿⣡⠟⠀⠀⢀⣿⣿⢁⡾⣿⡇⣠⣿⠛⢻⣿⡟⢀⣿⡿⠁⠀⠀⣾⣿⠃
⣿⣿⡇⢀⣿⡇⠀⣴⡟⠀⠀⢻⣿⠃⠀⡤⠀⠀⠘⣿⣧⣾⠃⣿⣷⣿⠃⠀⢸⣿⢁⣼⣿⡇⠀⣠⣾⣿⡟⠀⢠⡆
⠻⣿⣤⡾⠙⢷⣾⠏⠀⠀⠀⠈⠛⠶⠟⠁⠀⠀⢀⣈⡛⠃⠀⠈⠋⠁⠀⠀⠀⡙⠛⠁⠻⣧⡾⠋⠘⣿⡇⣠⡟
⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠸⠿⠃⠀⣠⡶⣄⠀⠀⢠⣿⠟⣷⠀⠀⠀⠀⠀⠀⠙⠷⠋
⠀⠀⠀⠀⠰⣄⠀⢀⣴⣶⡄⢀⣾⢋⣿⡇⠀⢠⣶⣦⠀⠀⣿⣧⡟⠀⠀⢸⣿⡴⠋⠀⣀
⠀⠀⠀⠀⣰⣿⣄⡾⢡⣿⣧⣾⠃⣼⣿⡇⠀⣾⣿⡏⠀⠀⣹⣿⡄⠀⣀⡴⢿⣷⣠⠞⠁
⠀⠀⠀⢀⣿⣿⣿⠃⣾⣿⣿⠃⣰⣿⡿⠀⢰⣿⣿⠀⢀⣴⠋⢹⣿⡞⠁⠀⢨⣿⣧
⠀⠀⠀⢸⣿⣿⡟⠀⠙⠿⠏⢀⣿⣿⡇⢠⡾⣿⡇⣠⡞⠁⢠⡞⣿⣇⠀⢠⡟⢹⣿
⠀⠀⠀⠀⠻⠟⠁⠀⠀⠀⠀⢸⣿⣿⣰⡟⠀⠈⠛⠋⠀⠀⠺⣷⣿⠏⠀⢺⣇⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⠟⠀⠀⠀⢀⣤⣄⠀⠀⢈⣁⡀⠀⠀⠉⣉⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⣠⡄⠀⠀⢀⣴⡾⣇⢸⡇⢀⣾⣿⡇⠀⢀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⣰⣿⡇⠀⢠⣿⣿⠁⠈⣿⡿⢾⣿⣿⠀⢀⣾⣿⡿
⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⣰⠏⣿⡇⠀⣾⣿⡏⠀⣼⡿⠁⢸⣿⡇⣠⡿⣿⣿⡇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣼⡟⢀⣿⣷⠞⢿⣿⣇⣾⣿⠃⠀⠀⠙⠿⠟⠁⢿⣿⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⢠⣾⣿⡇⠀⠈⠛⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⢰⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣿⣿⠏
⣶⣶⠾⠶⠶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⡰⠇⠠⠐⠂⠀⠀⡢⡗⢄⠀⠀⠑⢄⠀⡇⡆⠀⡄⠡⠀⢸⠆⠌⠂⠀⠰⠈⠂⠈⣄⠀⠀⠀⢀⠂⠀⠼⠐⠄⠀⠀⠀⠈⢃⠀⠀⠁
⡗⠀⢀⠈⠀⠀⡐⠄⡦⠀⠱⠄⠀⠀⠑⠏⠀⠰⡀⢂⠁⠱⠀⠔⣁⠀⠀⠀⠀⠀⠹⡆⠀⠀⠨⠀⢀⠏⢐⠃⠀⠀⢀⡀⠀⠠⡀
⠀⠀⠈⠀⠀⢸⠀⠀⡳⠀⠀⠘⠀⠀⠀⠁⠀⠀⠀⠀⠀⡖⠀⢀⠄⢀⣤⠀⡀⠀⠀⠘⠄⠀⢨⠀⡜⣀⠊⠀⠀⠀⣞⢇⠀⠀⠐⠀⢀
⡠⠄⠤⢀⠀⠀⠀⠀⣹⠀⠁⠀⠀⢀⠤⠶⡏⠀⠀⠀⢸⠧⠀⠈⠀⢸⠸⡀⠈⠳⡀⠀⠀⠀⠀⠋⠉⠁⠀⠀⡠⠁⣸⢈⢄⠀⠀⠠⠊
⠙⢤⡀⠀⠳⡄⠀⠀⡸⠀⢀⠤⠊⢡⠋⢨⠁⠀⠀⠀⡆⠀⠀⠀⠀⠨⡀⠺⡄⠀⢖⠀⠀⠀⠀⠀⣠⠀⠀⡌⠀⠀⣽⠀⠈⢦
⠡⣄⠙⢤⡀⠈⡄⠀⠃⠀⠈⠀⡰⠂⠀⣙⠀⠸⠆⡈⠀⠀⠀⠀⠀⠀⠙⠤⡙⢦⣸⠀⠀⠀⠀⡜⠋⠄⠀⠠⡀⠀⣲
⢀⠈⠑⠀⠊⠟⠓⠀⠀⠀⠀⡴⠁⠀⠠⠃⠀⠀⡙⢦⠐⠢⠤⡀⠀⠀⠀⠀⡉⠈⠉⠀⠀⠀⡜⢨⠅⠱⡄⠀⠀⠀⠹⠁⠀⠀⠀⢱⢦
⢤⠈⠒⢄⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⢀⠂⠈⢣⠀⡀⠈⠀⠀⠀⡐⣿⠠⢀⠀⠀⢘⠀⠰⠂⠀⠰⠀⠀⠀⠀⠇⠀⠀⠀⠀⢇
⠀⠓⡄⠈⠀⠀⠀⠀⠊⠀⡠⠊⠹⠟⠂⠀⠀⠀⠄⠀⠀⠹⣤⠄⠀⠀⠰⠀⠸⡄⠀⠉⢠⠀⠀⢨⡅⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠺
⠀⠀⠘⢆⠀⠀⠀⠀⠀⡘⠁⢀⡜⠀⡃⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⡀⠂⠀⡀⠶⠀⠀⠀⠆⠀⠈⠁⠀⢀⢧⠀⠀⠀⠎⢣⡀⠙⠢⡀
⠀⠀⠀⠀⠑⠠⠀⠀⠀⠊⠀⡰⢁⡐⠀⠀⣀⣀⡀⢤⣰⠂⠀⠀⠀⠀⠈⡀⠈⠰⡄⠀⠀⠀⠀⠀⠀⠀⠌⢏⠀⡀⠀⠸⡈⠳⡄⠀⢱
⠀⠀⠀⠀⢀⡀⠈⠀⠀⡱⠮⠔⠊⢀⠀⠁⠉⢁⠰⢨⠁⠀⠀⡰⣶⠂⢄⠉⠀⠀⢷⠁⠀⠀⠀⠀⠀⠎⠀⢻⠀⠈⢆⠀⠑⠂⡈⠢⢄
⠀⠀⠀⢐⠹⠏⠱⡀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠈⡠⠃⠀⠀⠀⠂⠹⡀⠀⠱⠀⠀⠀⢢⠀⠀⠀⠀⠘⠀⠀⠈⡄⠈⠈⠀⠀⠀⠀⠁⠉
⢀⠀⠀⠅⠨⡅⠀⠠⠀⠀⠀⠀⡠⠘⠉⠀⠠⠖⠁⠀⢠⠇⠀⠰⡀⠑⡄⠀⠇⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠹⣇⠂
⠀⠱⡄⢱⡀⣧⠀⠸⠀⠀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠰⠹⠎⢄⠀⠈⠢⢌⣢⣜⠀⠀⠀⠀⡠⠒⢃⡵⣓⠀⠀⠈⢦⠀⠀⠀⡄⠙⠧
⠀⠀⠀⠀⠑⢄⣧⡎⠀⠀⠀⠀⢀⠄⣿⣂⠀⠀⠰⠁⠘⡆⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⡌⢠⠔⠁⠀⡜⠀⠠⣄⠀⠀⠀⠀⠂⠠⠀⠳
⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⢠⡆⠀⠆⠈⠢⡀⠈⣇⠀⡀⠃⠀⠀⠀⡄⠀⠀⢐⢰⠋⠀⡠⠊⠀⠀⠀⡇⣯⠒⢄⣀⠀⠂⡀
⠉⠱⣄⠀⠀⢀⠀⠀⠀⠰⠀⠀⠀⠰⠈⠀⠊⠀⠀⠀⠀⢷⠀⠀⠀⠀⢀⠞⢷⠀⠀⠈⠇⠂⠉⢠⡀⠀⠀⠀⡆⠐⢆⠀⠀⠰⠀⠈
⠀⠀⠈⠁⠀⡜⡡⡀⠀⠀⠀⠄⠀⡖⠀⢀⠅⠀⡦⡀⠀⠘⡄⠀⢀⠶⠁⣘⠩⠀⠀⠀⠀⢀⠐⣿⠡⡀⠀⠀⡇⠀⠈⣇⠀⢀
⡩⠻⠀⠀⠠⠁⣇⠉⢆⠀⠀⠀⣾⠅⠀⠉⠀⠸⢰⠑⢄⠀⠀⠀⠉⠀⠠⠄⠀⠅⠀⠀⠄⠀⠀⠏⠀⠡⠄⠀⠁⠀⠀⠸⡆⠁⠀⢀⠠
⠀⢀⠁⡰⠁⠀⢧⠀⠀⢰⠀⢠⠃⠀⠀⠀⢠⠁⢰⠆⠈⠐⡀⠀⠀⢀⡏⠄⠰⠁⠀⠀⠂⠁⠰⠂⠀⠀⢘⠀⠀⠀⠀⠀⢃⠀⢀⠊⢀
⡠⠊⠀⠀⠂⠀⣶⠀⠀⠀⠀⠁⠀⠀⠀⠀⠇⠈⢀⡃⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠐⠂⠀⡳⠀⠀⠀⠋⠀⣷⣄⠀⠀⠀⠀⢠⢀⠇
⠀⠀⢀⡀⠀⠀⡙⠀⠀⠀⠀⢀⢶⠤⢀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠐⠿⠠⠀⠀⠀⠀⢃⠰⠁⢢⡀⠀⠈⢾⠴
⠤⠂⡿⡇⠀⠠⠃⠀⠀⠀⠀⠨⠀⠣⡀⠡⠀⠀⠀⡇⠀⠀⣀⠀⠀⠂⠀⠠⠹⡜⢠⠀⠀⠀⡄⠀⠀⠀⠀⠀⡞⠀⢉⡄⠈⡆
⠀⠸⠂⠠⡀⠀⠀⢠⠀⠀⠀⠰⡀⠀⢳⠀⡃⠀⠈⠀⡀⠎⡟⠄⠀⠀⢀⡓⠀⢷⠀⠈⢢⠀⠉⢀⠠⢶⢦⠀⠑⠀⠀⢂⠀⠀⠀⡐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣦⣴⠆
⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡴⠶⠶⠶⢶⣤⣄⣀⣀⡀⢀⣀⣀⣤⡴⢞⢏⡥⣶⡿⠟⠋
⠀⠀⢸⣯⣻⣆⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⢋⠥⠀⠀⠀⠀⠀⣀⠤⠌⢉⠉⠛⠛⡩⠉⠀⣰⡷⠋⣠⡟
⠀⠀⠀⠈⠙⠻⢷⣤⣀⠀⢀⣠⡴⠟⡡⠖⠁⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⡠⠔⠊⠀⣠⠖⠉⣀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠙⣿⡿⣯⣭⣔⠋⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⢀⠔⠉⢀⣠⠴⠋⠉⠈⠉⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠉⠹⡓⠲⠶⠮⣥⣤⡤⠴⠖⠚⠓⠚⠛⠛⠤⣀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠑⢄⠀⠀⠀⠀⠉⠒⠤⣀⡀⠀⠀⠀⠀⠀⠈⠉⢂⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠁⠀⠉⠢⣄⠀⠀⠀⠀⠀⠈⣑⣢⣀⣀⣀⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⡀⠀⠀⠉⣒⣠⡴⠞⠛⠋⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢠⣄⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣤⣿⠻⠏⣀⣀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⢀⠘⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠞⢡⡾⠃⠀⠈⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⡼⠃⣠⠄⠀⠀⠀⠀⠀⠀⠀⠲⠛⠋⢠⡀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠈⠀⠀⢀⠉⡀⢨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡷⠂⠠⡀
⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠻⠇⠀⠟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠱⡄
⠀⠀⢀⠄⠉⠀⠀⠀⠀⠀⠀⠀⣋⣠⣀⠀⢀⠁⣠⠇⠀⠋⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⡠⠊⠀⠀⠸
⠀⠀⠈⠶⣅⠀⡀⠀⡀⠀⠀⠶⠋⠈⠉⠠⢀⣼⠏⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠺⠋⠁
⠀⠀⠀⠀⠀⠑⢷⣤⣨⡄⠀⠀⠀⠀⡄⠀⣾⠃⡄⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠴⠀⠘⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠛⢶⡄⠀⠀⠈⠙⢶⣄⠀⠀⠀⡇⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠛⣡⣦⠄⠁⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠈⠀⠁⠀⠀⠀⠀⠀⢠⡔⠋⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⣿⣾⡟
⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠄⣠⣦⣹⡆
⠀⠀⠀⠛⠋⢀⢀⣠⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⢠⡿⠀⠈⠉⠉⠁⠙⠆⣀⣀⣉⣉⣤
⠀⢰⣼⡷⢀⡘⣿⡋⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⢿⡟
⠀⢀⣤⣀⢺⡕⠟⠁⠀⠀⠀⠀⠀⢸⠂⠀⣀⠀⠀⠀⠀⢒⡂⠀⣤⣤⡄⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⢳⣾⡟⠉⢳⣐⣦⠀⢀⡀⠀⠀⠈⠁⠠⠀⢀⣤⠶⠞⠋⠉⠀⠀⠀⠀⠀⠉⠰⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⢤⣅⣴⠿⡿⠋⢰⣤⣼⠇⢀⣤⣠⣴⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿
⠀⠀⠈⠉⠁⠀⠁⠐⠉⠉⢉⣤⣿⣽⡟⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟
⠀⠀⣾⣡⣷⣤⣦⡐⠟⠒⢚⡷⠀⢩⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀
⠀⠀⠈⠉⠉⠛⠟⠓⣄⣀⣘⡗⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠘⠁⠀⠀⢸⣯⡛⠋⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡏⠀⠀⡀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏⠀⣠⠿⡿⠓
⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠃⠀⠀⠈⠓⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⠀⠀⠸⣷⠚⡏⠐⠂
⠀⠀⠀⠄⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠶⠀⡀⠀⠀⠀⠀⡰⠋⠁⠀⠀⠀⠀⠀⠀⢰⠀⠀⣼⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠠⠛⠃⠀⠀⠀⢀⠀⠰⠃⠰⠀⠀⠀⠙⢳⡄⠀⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠁
⠀⡀⠀⢀⣰⠆⠀⠀⠀⠂⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠋⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⢁
⠀⣧⣤⡿⡇⠀⠀⠠⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⠄
⠀⢿⡋⢸⠃⢠⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠲
⠀⠀⠃⣠⠀⠀⠀⠀⠀⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠱⠀⠀⠐⠋
⠀⠀⠀⠘⡀⠀⠒⠀⠀⢒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⠀⠙⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠠⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⣿⣿⣧⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⠀⠙⠛⠁⢀⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢾⠷
⡰⠂⠀⠐⠀⠀⣀⢤⣤⡄⠉⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⣤⣀⣀⣀⣀⣘⣶⣤⡀⢀⣀⠀⠀⠈⠓
⣤⣾⣶⠀⠀⠀⠸⠿⡿⠃⠀⠈⢦⡀⠀⠀⠀⠀⢀⣠⣤⠞⠁⣠⣾⠿⠛⠛⠈⣉⠉⠙⠛⠛⠛⠻⠷⠀⠀⠀⠀⠒
⠉⠛⠛⢧⣤⣬⠀⠀⠀⠀⠀⠀⠴⠛⣀⡠⠤⠚⠋⣯⠀⠀⠊⠉⠀⠀⠀⠃⠀⠀⠀⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦
⠀⠀⠀⠿⢶⠿⠂⠘⠀⢀⣠⠔⢂⣼⠛⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠛⠻⢦⣀⠙
⠀⠀⠀⠀⠀⢀⣠⡄⠂⠙⠁⢀⣿⠃⠀⠀⠘⠀⠀⠀⠀⢿⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿
⠀⠀⠀⢠⣄⠘⠁⠀⠀⠀⢠⣿⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀
⢀⣾⡾⠛⠁⠀⠀⡀⠀⣠⠿⠿⡽⠂⠀⠀⡟⠀⠀⠀⠀⢁⡘⠀⣿⡇
⣤⣧⣤⣤⣤⣤⣤⣤⣤⣬⣴⣤⣤⣤⣤⣴⣧⣤⣤⣤⣴⣿⣽⣦⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡿⠋⠹⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣤⣴⣦⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⣶⠓⠓⠒⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠒⠚⠛⠒⠲⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⣿⡴⣾⠁⠀⠀⠉⠳⣄⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠈⢳⡄⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⢀⡀⠀⠀⠀⠀⠹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢠⡟⠀⣠⠶⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⢀⣾⡴⠞⠁⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠜⠋⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⣀⣀⣤⡤⠶⢒⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡤⠴⠖⠛⠋⠉⠁⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⠀⣀⣀⣠⡄⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣚⣡⣤⠤⠶⠖⠛⠋⠉⣡⠏⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣁⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⢈⡭⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⢀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣝⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣌⠻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⢡⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⡜⢿⣿⣧⠀⠀⠀⠀⠀⢀⣾⣿⢃⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣆⠹⣿⣷⡀⠀⠀⠀⣼⣿⡏⣸⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⡘⣿⣇⠀⠀⢠⣿⣿⢁⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣶⣤⣤⣀⠀⠀⠀⠙⢿⣷⡜⣿⡀⠀⢸⣿⡏⣸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣷⣶⣭⣍⣙⠛⠿⣿⣿⣷⣤⡀⠀⠉⠻⣿⣇⠀⠘⣿⡇⣿⣿⠋⠀⠀⠀⠀⢀⣤⣶⠿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣶⣦⣍⣙⠻⣿⣦⡀⠀⠀⠹⣧⠀⣿⣷⣿⠏⠀⠀⠀⢀⣴⣿⡟⣡⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣷⣦⣍⡻⣦⡀⠀⠹⣇⢸⣼⠋⠀⠀⠀⣰⣿⣿⢋⣼⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠿⠶⣄⣹⣿⠁⠀⠀⠀⣰⣿⡿⢡⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⢶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⢰⣿⡿⢡⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣷⣬⡛⢿⣿⣷⣤⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣼⡿⣰⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⣌⠛⢿⣿⣦⡀⠀⠀⠀⠀⣿⠀⠀⣿⢱⣿⠟⠁⠀⠀⠀⢀⣠⣴⡶⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣦⡙⢿⣿⡄⠀⠀⠀⢸⡇⢠⣽⠟⠁⠀⠀⢀⣤⣾⡿⢟⣵⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣦⡙⢿⡆⠀⠀⠸⣷⠟⠁⠀⠀⢀⣴⣿⡿⢋⣴⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⣀⡀⠀⠀⠀⠈⠙⠻⣿⣦⣻⡄⠀⠀⣿⠀⠀⠀⢠⣾⣿⠟⣠⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣭⡛⢿⣷⣦⣄⠀⠀⠀⠀⠈⠉⠛⢦⡀⣿⠀⠀⢀⣿⡿⢣⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⣍⠻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠙⣿⠀⠀⣼⡟⣱⣿⣿⠟⠁⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⣌⠻⣿⣿⣆⠀⠀⠀⠀⠀⣿⠀⢰⣟⣾⡿⠛⠁⢀⣠⣴⡾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣌⠻⣿⣧⠀⠀⠀⠀⣿⣠⡾⠟⠋⠀⣠⣾⣿⠟⣩⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠈⠛⢿⣿⣷⣌⢿⣇⠀⠀⠀⣿⠏⠀⠀⣠⣾⣿⠟⣡⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡻⣷⣦⣀⠀⠀⠈⠛⠿⣦⣿⡄⠀⠀⣿⠀⠀⣴⣿⡿⢃⣾⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⡹⣿⣷⣄⠀⠀⠀⠈⠙⠻⣦⢀⡿⠀⣸⣿⠏⣴⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣌⢻⣿⣷⡀⠀⠀⠀⠀⠈⢻⡇⢀⣿⢋⣾⣿⠿⠋⠀⠀⢀⣀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣦⠙⣿⣿⡄⠀⠀⠀⠀⢸⠇⣸⣷⣿⠟⠁⢀⣤⣴⣾⡿⢟⣯⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡘⣿⣷⠀⠀⠀⠀⣾⣶⠟⠉⠀⣠⣶⣿⡿⢛⣡⣶⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡘⣿⡇⠀⠀⢀⡿⠁⠀⢀⣾⣿⡿⢋⣴⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡘⣧⠀⠀⣸⠇⠀⢠⣿⡟⣣⣶⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⠀⠀⣿⠀⢀⡾⢫⣾⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣸⡏⢀⣿⡷⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴⢒⣋⣨⡥⠈⠥⠬⢤⣤⣤⣑⡳⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠜⣋⠄⠀⠉⠁⠀⠀⠀⠀⢀⣀⠀⠀⠉⠙⠳⢦⣝⡲⣆⡀
⠀⠀⠀⠀⠀⠀⠀⣠⢟⣵⠏⠁⠀⠀⢴⣦⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⢀⡀⠈⠛⢮⡓⣦
⠀⠀⠀⠀⠀⢀⡖⣡⠟⠁⠀⠀⠀⠀⠀⣠⡤⠖⠒⢒⠲⠀⠒⠤⣄⠀⠚⠟⠀⢀⣬⣿⣎⢻⣀
⠀⠀⠀⠀⢀⡟⣴⠃⠀⢰⣶⠀⢀⠴⠉⠀⠀⢠⠸⠈⡀⡆⠃⠀⢀⣹⣶⣶⡟⢻⣿⣿⣿⣧⢹⡄
⠀⠀⠀⢀⡜⢰⠃⠀⠀⠀⠀⣰⢹⠀⠀⠀⠀⠀⠀⠂⣁⣤⣼⠞⠋⣻⡀⢿⣷⡀⢿⣿⣿⣿⡇⢳
⠀⠀⠀⢰⢃⡟⠀⠀⠀⠀⢰⠉⡀⠆⠃⢀⣠⣴⡾⠻⡏⠻⡈⣇⠘⠛⣷⠈⢿⣷⡈⠛⠻⣿⣿⡜⡇
⠀⠀⠀⢺⢸⡇⠀⢰⢶⠀⡇⣂⣥⡶⠟⠿⡍⢠⣾⡆⠑⠀⠁⠸⣆⠸⠿⢧⣈⣡⣷⠶⠛⠉⢸⡇⣏
⠀⠀⠀⢻⢸⡇⢀⣀⣤⠶⣟⠉⢻⣆⠐⠆⢹⡀⢡⣼⣦⠀⠀⠀⣻⣤⣶⠾⠛⣻⠀⢰⡦⠀⢸⡇⣯
⠀⠀⠀⢹⡜⣿⣿⣯⠀⢴⣿⡄⢀⠹⣆⠠⡄⢱⡀⢉⣹⣷⡾⠏⠋⢱⠘⠀⡄⡏⠀⠀⠀⠀⢸⢃⡧
⠀⠀⠀⠀⣧⢻⣿⣿⣧⠀⣤⣧⠈⣀⠘⣆⣽⡶⠿⢛⠹⠀⠀⠀⠀⠀⠀⢇⡟⠀⠀⠀⠀⢀⡟⡸⠂
⠀⠀⠀⠀⠸⢆⢿⡿⢿⣦⠘⣿⣦⠿⠟⠋⠅⢠⠘⠈⡀⡆⠃⢀⠀⣀⡤⠋⠀⠼⠆⠀⢀⡾⣱⠋
⠀⠀⠀⠀⠀⠘⣦⠹⣆⠚⠋⠁⣀⣄⠈⠓⠦⢤⣄⣆⣁⣠⡸⠴⠚⠉⠀⠀⠀⠀⠀⣠⠟⣵⠉
⠀⠀⠀⠀⠀⠀⠈⠳⣜⠷⣄⠀⠘⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠰⡷⠀⠀⠀⣀⡄⣩⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢬⡛⢦⣄⣀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⣀⣠⡴⢛⡥⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠱⠮⣭⣛⡳⠶⠶⠶⠶⠶⠶⢞⣛⣩⡵⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠛⠙⠋⠙⠁⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⠀⣼⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡇⢰⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣀⡿⢿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠶⠶⠶⠾⣿⣵⠟⢳⡟⣦⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣍⠀⠀⠠⠄⠂⠀⠸⣿⣷⢂⣼⣿⠏⠁⠀⢀⡀⠤⠾⠧⠀⣄⠀⡄⠀⠈⠟
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠣⠾⠋⠀⠀⠀⠀⠉⠀⠀⠁⠀⣿⠙⠃⠀⠄⠒⠉⠁⠀⠀⠀⠀⡏⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢡⠀⠀⠀⠀⠀⠀⢀⣠⠓⣷⣠⠀⠀⠀⠀⠐⢄⡀⠲⠷⣶⠋⢀⡴⠃
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⠈⠀⠀⢀⡠⠖⠛⠁⠀⠀⠀⠀⠀⢤⣄⠀⠀⠉⠓⠒⣴⠂⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⣠⠖⠉⠀⠀⡀⠀⠀⢈⣠⡆⠀⠘⠈⠑⡄⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⡟⢉⠀⠀⠀⠀⠀⠠⣰⡖⣻⢭⣿⣀⠂⠀⠀⠙⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠤⠀⠀⠀⠀⠀⠙⠻⠇⢀⣿⣸⡟⠋⠀⢰⣀⡀
⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠊⠉⠉⠀⠀⠀⢸⡟⠳
⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠂⠀⠤⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠀⢀⡎⠀⠀⠊⠀⠀⢐⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠂⠀⢀⡞⠀⠀⠀⢀⠕⠄⣘⣹⠟⣦⠠⠤⣄⢁⣈⠃⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⡞⠀⠀⠀⣠⡴⡀⢀⠍⠉⠉⢲⠀⠀⠀⠈⠉⠛⠀⠶⠧⡀⠄⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠀⠀⣼⠁⠴⠒⠋⠁⠀⠈⠂⠀⠈⡀⠀⠳⡀⠀⠀⠀⠀⠀⠄⠲⠀⠈⠁⠈⢬⠤⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠐⠀⠠⠀⠄⠂⠀⠤⠤⠤⠀⠤⠔⠬⠦⠤⠬⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢈⣷⣦⠀⡀⠀⠀⠀⠀⠀⠀⢀⣴⣤⠁⠀⠀⠀⢀⡠⠀⣾⣦⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣠⡄⠀⠀⠀⠀⢀⡇
⠀⠀⠀⣠⣪⠞⣿⣶⡾⢤⠀⠀⢸⣿⣦⡿⣿⣾⡄⠀⠀⠀⢈⠈⠰⡽⢻⠆⡀⠀⠀⠀⠀⣼⣿⣦⣾⣿⣿⡄⠀⠀⠀⢀⡁
⠀⠀⠀⠛⢁⣴⣿⣷⣶⢬⡃⠀⢸⣿⣿⣧⣿⣿⡆⠀⠀⠀⠀⠀⠀⣷⣔⡼⠃⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠀⠀⠠⢿⣄
⠀⠀⠀⣿⠉⣿⣿⣿⠦⡘⣟⠀⠘⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣌⣟⡿⠃⣅⠀⠀⠀⢸⣿⣿⣿⣹⣿⣿⣿⠀⠀⠀⢨⡯
⠀⠀⠀⡣⢾⣿⣽⣯⡀⢿⠛⠀⠀⢻⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⣹⣿⡁⠀⠄⠀⠀⠀⢸⣿⣿⣿⣝⣿⣿⣿⠀⠀⠀⢸⡟
⠀⠀⠨⡶⢋⣡⣿⣏⠉⠶⠆⠀⠀⠈⢿⣿⣿⠇⠀⠀⠀⠀⠀⠐⢸⡯⠀⠁⠀⠀⠀⠀⠘⢿⣿⣿⣗⣿⣿⡇⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠴⢾⣯⡐⢠⡄⠀⠀⠀⠀⠈⠛⡟⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠏⠀⠀⠀⠀⠀⢹⠂
⠀⠀⠀⠈⣠⣾⣟⢣⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠃⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⣠⢄⣀⣀⣴⡾⠷⠀⠀⠀⠀⢀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢋⣿⢙⣿⣿⠀⠀⠀⠄⠀⠀⢸⣿⣾⣿⠀⠀⠀⢠⣾⣷⡄⠀⠀⠀⠀⠀⢾⠞
⠀⠀⠀⠐⢀⣄⣀⠀⠀⠀⠀⠀⠀⢱⣿⣿⣋⣿⣇⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⡐⡿⠂⢀⡄
⠀⠀⠀⢀⢰⣿⣿⣼⡷⠀⠀⠀⠀⠀⢿⡟⢁⡚⢣⢠⠰⠤⠁⠀⠀⠘⣿⣿⠃⠀⠀⠀⢸⣿⣿⠏⠀⠀⠀⠠⣟⣇⣠⡾⠁
⠀⡀⠀⠀⠈⠉⠀⠈⠉⠁⠀⠀⠀⠀⠈⠉⠊⠧⡄⠃⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠑⠈⠻⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠄⠀⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢠⠇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠤⠐⠤⠐⠓⠒⡉⠁⠐⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠁
⠀⠀⢘⠃⢀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠠⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋
⠀⠀⡬⠂⠁⠃⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⢀⠤⠔⠛⠁⠀⠀⠀⠠
⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡐⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠀⠀⠀⠀⠀⠂⠀⠁
⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⢀⡷⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁
⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢁⡇⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢀⠀⠠⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠁⢠⡄
⠀⠀⠀⠀⠀⠀⣀⠀⢔⠀⠀⠁⠀⠀⠀⠀⡴⠀⠰⠀⠀⢁⡀⢠⡄⠰⠦⡚⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⡀⠂⠀⠀⠀⢠
⠀⠀⠀⠤⠈⠓⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⣀⠜⠂⢈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⡀⠀⣠⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⠀⣀⠵⠿⠁⡁⠉⠐⠂⠈⠁⡄⠀⠀⠀⠀⠀⠁⠆⢡⢘⣁⠁⠰⢀⡀⠰⠆⠸⠇⠀⠀⠁⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠀⠁⠀⠀⠀⠀⠆⠀⠀⠀⠁⠁⠀⠀⠀⠠⠀⠀⠈⠉⠀⠀⠀⠁⠈⢣⠀⠃⠀⠀⠁⠀⠀⡀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⢀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⡂⠐⠈
⠀⠀⠀⠈⠀⠀⠀⠂⣀⠠⢌⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠢⠂⠐⠢⠀⠀⠀⠀⠀⠀⢀⠒⠀⠀⠐⠀⠁⠀⠀⠀⠀⠤⠀⠀⠠⡀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢤⡀⠀⠀⠀⠀⡀⠀⠀⠀⠢⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠐⠀⠓⠈⠂⠈⠀⡀⠀⠀⠔⠀⠁⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠈⠈⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⡠⠀⠁⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠄⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠃⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠰⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠈⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⢩⣇⠖⠛⠲⣤⠖⠲⣼⠉⠉⠙⣦⣀⣀⣀⡤⢿⠀⣀⠉⣷⠋⠳⠴⠒⡛⢛⡻⠦⡇⢸⠶⢤⡀
⠀⠀⠀⠀⠀⣀⣤⣼⠁⠀⡄⠼⣿⡀⢠⡄⠘⠠⡄⠘⠀⠶⠀⡸⠈⠢⠤⠃⢸⠀⣄⠘⠇⠑⡆⠰⠊⠃⣬⠇⠀⠓⠒⠀⠀⠘⣦⠤⠤⠤⣄⡀
⠀⠀⣀⡤⠾⠁⠀⠈⢆⡀⠁⠀⠀⣇⣀⡠⠜⠤⠤⠜⠂⠐⠊⠁⠀⠀⠀⠀⠠⢀⣀⡠⠂⠀⢥⡬⠀⢅⣀⣸⠀⠪⠆⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⢀⡞⠁⠀⠀⠀⠀⠀⠀⠨⣁⡸⠉
⡞
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⢨⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠈⠓⠦⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠙⠓⠒⠒⠒⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠒⠒⠚⠉⠁⠀⠀⠉⠓⠦⢤⣄⣀⣀⣀⣤⡤⠴⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣶⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣴⣶⣶⣦⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣠⣴⣾⣿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠣⡄⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣈⠀⠀⠶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⢈⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣈⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠋⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡼⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠀⠀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⠿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠻⣿⣿⣏⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣧⡀⠀⠙⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁⣠⣾⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⢴⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⢸⣿⢿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠇⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡄⠀⣶⣦⠀⠀⢰⠀⠀⠀⠀⣾⡖⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⢸⣿⡄⠀⢸⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠘⣿⡇⠀⢸⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⠀⠸⠀⠀⠀⠀⣿⡏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⢸⢻⣿⡀⡆⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⡆⠈⣿⣇⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢻⣿⡇⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢸⣿⡇⠀⢀⣀⡀⠀⠀⠀⠀⠙⠃⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⡠⢾⣷⠀⡄⠀⣾⣿⡇⡐⠁⣼⣿⡄⠀⠀⢰⣶⡄⠀⠀⠀⡈⠹⣿⣷⡀⠀⠀⠀⡠⠘⢿⣿⣆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠀⢸⣿⣦⠀⠀⣿⣿⡷⠁⠀⣿⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠈⢿⣿⣦⠂⠁⠀⠀⢀⠽⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⢿⣿⠇⠀⢸⣿⡿⠀⠀⠀⠺⣿⠃⠀⠀⠀⠀⠀⡠⠊⢿⣿⣇⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠛⠀⠀⢸⣿⡇⠀⢀⠂⠀⠹⠦⠀⠀⠀⠀⢰⠀⠀⠸⣿⣿⠀⠀⠀⠠⣀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⣸⣿⠏⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣤⣴⣶⣶
⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠦⠴⠄⠀⠀⠘⢿⣿⣿⣿⣿⠟⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠦⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡆⠀⣴⠀⠀⠀⠀⢀⣴⠆⢢⡀⠀⠀⠀⠀⢰⣶⡆⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢀⡏⠀⠀⠀⠀⣾⡿⠀⠀⢧⠀⠀⠀⠀⢸⣿⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠁⠀⠀⠀⢠⣿⡇⠀⠀⢸⠀⠀⠀⠀⢸⣿⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⢸⣿⡇⠀⠀⢸⠀⠀⠀⠀⢸⣿⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⢸⣿⡇⠀⠀⡸⠀⠀⠀⠀⢸⣿⡆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣇⠀⠀⡇⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠸⣿⣀⡴⠀⠀⠀⠀⠀⠈⢿⣧⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁



⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⢀⣀⣀⣀⡀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿