Cartoonist Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⢀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⣤⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢺⡀⠀⠀⠀⠀⠀⢀⡤⠂⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⢤⡀
⠀⠀⢠⡅⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢄⡀
⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⡆⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢀⠞⠁⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⡀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⡇⠀⣶⣶⣶⣶⣿⡿⠟⠀⠀⠀⠀⠘⠿⠿⠛⠛⠛⠗⠠⠀⠀⡰⠁⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠰⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣶⣶⠶⠶⣼⠀⠀⠀⠀⠀⠰⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠈⠒⢶⠀⠀⠀⠀⢰⡇
⠀⣀⣤⠤⢴⣶⠶⣾⢟⡛⠛⢷⣀⣀⣸⡁⠀⠀⠘⠶⠃⠀⠃⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢻⣦⡀
⠀⠛⢟⠀⠀⠁⠀⠈⠋⠁⠀⠈⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢻⣷
⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⢀⠀⠲⡞⠛⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⠟⠂⢸⡆⠀⠀⠀⣸⢿
⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢸⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⢴⡏⢸
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡠⠀⢀⡄⠀⠀⠀⠀⠀⠐⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢰⠋⠘⢧⡟
⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠐⠀⠀⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢸⠈⢄⠀⠈⣧
⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠔⠁⠀⠀⣇⠀⠀⣿⢻⡀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠔⠋⠉⠑⠀⠀⠀⢀⡄⡀⢠⣷⡄⡇⠀⢱⡾⠙⡄
⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⢠⢣⡀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⣼⠯⢾⠃⣾⠉⠀⠀⣷
⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠑⠒⠒⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠙⠍⠻⣄⠀⠀⠀⠀⠀⠀⠠⣄⣀⣀⡀⠀⠀⠀⠀⠀⢠⡇⠐⠁⠀⡿⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠵⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣤⠤⠔⠋⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠠⠂⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⡀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡠⠉⠁⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠐⢊⠀⠀⠀⡄⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⣠⠂⠈⢳⡄⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠙⠀⠀⠀⠀⠁⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⡛⠀⠄⠀⠼⣇⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⠀⠀⡀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⢷⡄⠀⠀⡀⠀⠀⢀⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠆⠀⠁⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠁⢤⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠁⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠙⠦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣟⣧⣀⣤⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢀⣤⣄⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡟⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠹⡂⣀
⠀⠀⣴⠋⠋⡱⡀⠀⠀⠀⠀⠀⠀⠀⠈⣻⠏⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠂⡀⢀
⠀⠀⠘⣧⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠷⠋⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣤
⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠢⠤⠄⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⣤⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠢⢤⣴⡿⠟⠋⠀⠀⠀⠐⣄⡠⡀⠀⠀⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡠⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠸⣷⣕⡌⢀⣿⣧⣤⣄⣴⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⣧⠀⠀⠀⠀⠀⠀⠀⢘⠃⣀⣶⣆⣾⣿⡆⠀⠙⡟⠛⠿⡿⠉⠉⠀⠀⠈⠲⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠔⢴⡇⢀⣻⣷⡰⣔⠦⡀⠀⠀⠈⠑⠈⢿⡿⣿⣼⡇⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣿⣿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⢨⣿⠿⢿⢋⠐⠁⠀⠀⠀⠙⠀⠈⣷⢹⡟⠧⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠦⠀⠁⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢝⢢⡀⠀⡀⠀⠀⠀⠀⣄⣿⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠠⠀⠀⠁⣉⢀⡈⠢⣀⠠⣤⣌⣿⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣈⠢⡀⠸⣆⢈⠲⣤⣽⣿⡟⢃⡀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣝⣻⣷⣮⣶⣿⣿⣿⣿⣿⠿⠯⠉⠁⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡺⢿⣯⣿⣿⣿⡿⠿⠿⢿⣟⣓⣶⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢡⣿⠟⠁⠀⠀⠀⠀⠈⠙⠛⠿⢷⣀⣒⠂⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⣴⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢦⣥⣠⣤⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣆⣩⣿⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢹⡋⠃⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣉⣹⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣶⣿⣀⣴⣿⣄⠀⠀⠀⠀⠀⠀⢹⣅⣇⣤⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠷⠶⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠇⠀⠀⠀⠀⠀⠐⠒⠓⠒⠒
⣿⣿⡟⠻⠻⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣟⠳⠀⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠀⠀⠀⣀⣤⣤⡀⠙⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠛⠓⢦⡀⢀⡴⠛⠁⡀⣈⠻⣆⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⡼⠛⠓⣦⠹⠞⠁⣰⠟⠉⠙⢷⡸⡆⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣼⠁⠀⣀⠈⣇⠀⣸⠃⣠⣤⡀⠈⣧⢻⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡇⢀⣾⠛⢧⢸⠀⡿⢰⣿⠀⣷⠀⣿⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⢸⣿⡀⢸⣸⡆⡇⣾⣿⣀⡟⢀⡏⢸⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢷⠘⣿⣷⣾⣿⡇⣇⣿⣿⣿⠇⣼⠁⡞⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣌⢧⡙⣿⣿⠟⠿⢛⣻⢿⣏⡾⢁⡞⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⢶⡍⡿⠁⢀⣠⡾⡏⣅⠝⠰⡏⠀⠀⠘⠷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣸⠙⠛⠛⢹⡿⡾⣹⠁⠀⠀⠹⡄⠀⠀⠀⠀⠉⠛⠛⠳⠶⣶⠾⣳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⣧⣿⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⠀⢹⡄⢤⣄⣀⡀⠀⠐⢚⣋⣥⠞⠋
⠀⠀⠀⠀⠀⢀⣤⡤⠶⠛⠁⠀⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⣯⣩⡽⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠈⠻⣝⣒⠆⣀⣠⡾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢉⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⡀⠀⠀⠀⢀⣀⣴⠿⠿⠥⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⣫⠍⠙⠛⣻⠛⠻⣏⠀⠀⣌⣉⠓⢲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⢀⠞⠁⣰⠏⠀⠀⠈⠳⣦⣄⣉⡷⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠞⠁⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠄⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣯⣿⣫⣭⣿⣿⣶⢶⣅⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣟⣛⣭⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡤⢤⡼⣿⣿⣿⣽⣿⣿⣟⣻⣿⣽⣿⣿⣿⣿⣿⣇⡇
⠀⠀⠀⠀⢀⠀⠁⠀⢀⣠⣤⣶⣄⣤⣄⡀⠀⠀⠀⠀⠀⠀⠔⣂⣤⣴⣶⣶⣾⣟⣛⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡱⠁
⠀⠀⠀⠀⠂⢀⣴⣾⣿⣿⣿⣿⣿⣮⣿⣿⣦⡀⣀⠴⢊⣵⣿⡿⣿⣾⣿⣿⣿⣭⣧⣾⣿⣿⣿⣯⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⡡⣾⣿⣿⣿⣿⠿⣟⣿⣿⣿⣵⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⠂
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣯⣻⣷⣿⣏⣿⡟⢛⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⢍⣿⢹⣿⣿⣷⡄
⠀⠀⠀⠀⣾⢿⣿⣟⣿⣿⣯⢿⣿⣿⣿⣿⣯⣽⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣾⣿⡏⣿⣿⣿⠉⠆
⠀⠀⠀⡎⢻⡿⡿⣿⣷⡿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⢷⣿⣿⣿⣿⣿⣿⠽⠇
⠀⠀⠀⠇⠈⢧⣿⣾⣿⣧⣿⣿⣿⣿⣿⣯⣦⣤⢭⠛⠻⣿⢻⡋⠉⢦⣀⠹⡯⡋⠻⣻⣽⣿⣿⣯⣿⣿⣿⣿⠃⣾⣿⣎⣹⡟⡀
⠀⠀⠀⠠⠀⠈⠻⣿⣿⣿⣿⣿⣿⣷⣿⠟⠁⡐⢀⡀⡾⠃⠀⠑⠦⠔⣈⣑⠲⢦⣀⠈⢽⡻⣿⣿⣯⢾⣿⡟⢼⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⠍⠁⢸⣿⡏⣰⡿⣷⠋⠘⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠛⠛⠻⠯⣭⢥⢴⣿⣿⣵⣿⣿⣷⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⣿⡿⠋⢘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣻⡛⠿⢿⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠟⠋⠁⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠟⠋⣁⣀⣀⣤⣤⠄⠀⠀⠀⠀⠀⠁⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠷⣶⣤⡤⠀⠀⠀⠀⠀⠙⠋⠁⢀⠴⢻⣿⣿⣩⠟⠁⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣟⢿⣿⣖⡄⠀⠀⠀⠀⠀⠀⠘⠐⠒⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣛⣩⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢹⣿⣿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⣀⡀⠀⠀⢸⣿⣿⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⣾⣿⡇⢀⣶⣿⣿⣿⣷⣴⣿⣿⣿⣿⠋⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠟⠀⣾⣿⣿⣿⣿⣿⡿⠿⠿⠛⠁⠀⠀⣀⠈⠉⠁⠈⢿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⣼⠟⠋⠀⠀⢻⠿⠟⠿⠿⣿⠃⠀⠀⠀⠺⣿⣿⡿⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠼⠛⠛⠛⠀⠀⠄⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣾⣧⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣀⣴⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠙⣿⣷⣶⣤⡐⢆⣀⢀⣀⣿⣸⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⢿⣿⣿⣿⣿⣾⣿⡿⢿⣿⣿⣿⣿⣿⠟⠹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠀⠀⠉⠙⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢰⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣦⣤
⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⣠⣾⣿⣷⣦⡀⠀⠉⠉⠀⠀⠠⠄⣀⠀⠀⠀⣀⡀⡈⠍⠉⠻⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠄⢀⠁⠀⠀⠀⠀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⣴⠀⠀⠀⠀⠀⣶⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠀⠀⠀⠀⠀⠛⠛⠛⠛⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⢲⠀⠀⠀⠀⣠⠄⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣗⡣⠀⠀⠀⠈⠀⠉⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠈⢹⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣼⠂⠀⠀⢀⠐⠳⠦⣤⣤⠠⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣠⢠⡛⠡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠐⢄⣀⣠⠀⠀⠀⠀⠀⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢁⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠜⠃⢀⠀⢀⢠⠊⠚⠐⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠐⠄⢈⠄⢀⠂⡰⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⢀⠀⢀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠈⠉⠁⣃⠔⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠁⠀⠁⠀⠀⠋⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠄⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠘⣷⣤⣀⢀⣀⠀⠀⢦⣦⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠿⠄⠐⠊⢉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢹⡀⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⡶⠒⠿⠃⠀⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⢓⢤⡲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢣⠀⣠⢌⡀⠌⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢀⠖⡻⠛⠉⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠂⠙⢄⡨⢀⣠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⠒⠂
⠀⢈⠈⡉⠀⠐⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⡄⡙⡺⢈⢉⠀⠀⠀⠀⠀⠀⢀⠂⢀⠨⠆⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⠆⠀⢸⢠
⠀⠎⢰⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢈⠀⠀⠀⠀⠀⠀⠀⠀⡈⠢⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠄⠀⢸⣿
⠀⢄⢠⢏⡀⡹⢃⣳⣀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠌⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢸⣿
⠀⠂⠀⢡⠥⠐⠉⢡⡉⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣦⣤⣶⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⣄⠀⢼⣀⠀⠔⢉⡽⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⣿⣿⡇
⠀⢿⡀⠀⡀⠄⠂⠀⢀⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿
⠀⠸⠈⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⣿⣿
⠀⠀⠡⣦⣀⠀⠀⠀⣿⣅⡹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡟
⠀⠀⠀⠙⠻⠿⣷⣾⣿⣿⣿⣿⡿⠿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣻⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡟⠉⠣⣀⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡄⠋⠠⠭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢄⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣤⣤⣤⡤
⠀⠀⣰⡅⢀⡀⢠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⡀
⠀⠀⠈⠁⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⢺⣾⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⠓⠀⣸⠃
⠀⠀⠰⡆⠀⠀⠀⠀⠈⠀⣠⣶⡆⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⣀⣈⣇⣀⣀⣀⡀⠀⠀⡡⠀⠀⠀⠀⣷⡄
⠀⠀⠀⠀⠀⢀⣀⠰⣿⣄⠙⣿⠀⠀⠀⠀⣀⣠⣿⣶⠶⠋⠉⠉⠙⢻⣿⣿⣿⡿⠿⣿⣷⣤⣀⡀⠀⣿⡇
⠀⠀⠀⠀⠀⠘⢿⢿⣿⣿⣦⣈⣤⣴⠎⠜⢻⣿⠏⠀⠀⠀⠞⠂⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠉⠛⠻⢿⡁
⠀⠀⠀⠀⠀⠀⡀⢼⣧⣼⣿⣿⣿⠁⡴⢲⡿⠿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠋⠰⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦⠟⠁⠀⠀⢀⠀⣠⣾⣇⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⣰⣶⣄⠙⠛⠁⠀⠀⠀⠀⠀⣾⣿⣿⣿⡀⠀⠀⢀⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄
⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⠀⢀⣤⡀⢹⣿⣿⣿⣇⠀⢀⣾⣿⣿⣿⠇⠀⠀⠀⠉⠁⢀⣀⡖⠩⡀⣷⠁
⠀⠀⠀⣼⠟⠋⠓⠦⡄⠀⠠⠀⠘⠛⠃⠘⣿⣿⣿⠋⠀⠸⣿⣿⣿⠏⠀⢀⡀⠀⢀⠀⠆⠀⣂⣠⠀⠋
⠀⠀⠀⣿⣾⣿⠲⣦⣔⠓⢀⠩⠌⣻⠃⠢⢩⢻⡃⠀⠀⠀⠀⠉⠋⠀⠀⠘⠁⢎⢀⠤⠂⠀⣉⣥
⠀⠀⠀⠉⣿⣿⡀⣿⣿⣷⠀⠀⠀⠀⠀⠂⠀⠳⠀⢡⡀⠀⠀⠀⠀⠀⠀⣐⡀⠚⢋⠀⠀⠀⠉⠁
⠐⠀⠀⣠⡿⢿⣌⣾⡿⠛⠃⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠁
⠀⠀⢠⡀⣠⣼⣿⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣾⣷⣴
⠀⠀⠀⢠⣿⣿⠏⠀⣴⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛
⠀⠀⠀⠀⠈⠁⠀⡘⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⣀⣀⠀⠀⠀⠀⠈⢀⡀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠙⠒⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠓⠀⠀⠀⠀⠀⠉⠻⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠶⢶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢰⡏
⠀⢤⣄⠀⠀⠀⠙⠒⣶⠟⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣠⣴
⠀⠀⠻⢆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠋⠁⠀⠀⠄⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿
⠀⠀⠀⠚⢱⣄⠀⠀⡔⠝⠃⠀⠀⠶⢶⠀⠀⢀⣼⡿⠟⠻⠿⣷⣶⣤⣤⣴⣴⣶⣶⣾⣿⣿⣿⡿⠿⠛⠁
⠀⠀⠀⠀⣿⡟⢷⣄⠠⠀⠀⠀⠀⠀⣸⠀⠠⠞⠁⠀⠀⡶⠆⠀⠉⠙⠛⠛⠛⠛⠛⠻⠛⠉⠀⠄⠈⠀⠂
⠀⠀⠀⢸⣿⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⢀⣤⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠄
⢀⡀⠀⢸⣿⣀⡀⠀⠀⢰⣿⣷⠀⠀⠀⠈⠸⠿⠂⠀⠘⣿⠓⠲⠶⠦⢤⣤⣤⠤⠴⣶
⠙⠃⠀⠼⠿⠿⠛⠀⠀⠘⠛⠉⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣

⠀⠀⠀⣾⢿⣿⢂⣀⡀⠀⠀⠘⢿⡆⠘⠿⣷⢸⣥⣦⢀⣤⣶⣿⣿⣿⣿⣀⣿⣿⣀⠀⠀⣿⣿⣿⡗
⠀⠀⠀⣴⣾⣿⣿⣿⣿⣧⡄⣤⣤⣻⣾⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⠛⠛⠀⠻⠟⣿⡇⠰⡟⣋⠁⣶
⠀⠀⠀⢸⠛⠻⠿⢿⣿⡿⠇⢛⠛⡏⢩⠡⠆⠐⡀⣳⣧⣿⠿⠿⠁⠀⠀⠀⠀⠈⠉⠀⢠⡀⠀⢀⣿
⠀⠀⠀⢸⠃⠀⠀⢀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢇⠠⠃⣸⣿
⠀⠀⠀⢨⡐⠊⠉⠁⠀⢀⣿⡄⠀⠀⢀⣠⣴⣶⣶⣶⣶⣷⣶⣭⣿⣭⣽⣭⣿⣧⠐⡿⠁⠀⢐⣛⣋
⠀⠀⠀⣠⣄⡀⣶⣶⣶⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠁⠀⠉⣿⣿⡿
⠀⠀⠀⠈⠉⠈⠙⠋⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠸⣶⠶⣶⣶⣷⣾⠒⠾⢶⡀⡟⠻⣿⣿⡄⢾⢿⡗⠿⢿⣿⣿⣿⡿⠿⢿⣟⢚⣿⡛⣿⣰⡗
⠀⠀⠀⢲⣿⠀⣿⣿⣿⠟⠓⠓⢦⠀⢢⠺⡿⠉⠀⢀⠸⣷⠇⠰⢿⠉⢻⢃⡄⢺⣿⣎⡟⢑⣿⡿⢇
⠀⠀⠀⣾⢿⣤⣿⣿⣿⡀⠀⠀⢸⡆⠈⢠⡀⣴⢠⡄⠀⢸⠄⣠⠾⠀⠈⢻⡅⢸⣿⢯⣧⣴⠙⣷⣿
⠀⠀⠀⣿⣾⣿⣿⠁⢸⡇⠀⠀⣨⠁⠀⠈⠁⢹⣎⠃⡀⢀⣴⣿⠀⠀⠀⠀⠁⠀⣿⠈⣿⣿⡀⢸⣿
⠀⠀⠀⢿⣷⣿⡿⢀⣿⣗⢰⢐⣿⡀⣤⣭⠀⢸⡿⢫⠁⢸⣿⣿⡄⠀⠀⢠⢠⣴⣿⢿⣿⣿⣅
⠀⠀⠀⣾⡿⠛⠓⠚⣻⠟⣿⢸⣽⡇⣿⣿⢸⣼⣇⢸⢀⢸⣽⣿⢳⣿⡀⣸⣿⣿⣿⣸⣿⣿⣿⣆⣤
⠀⠀⠀⢹⡇⢀⣛⣛⡷⠀⣛⣉⣛⢃⣙⣉⣙⣛⣛⣘⢚⣛⣛⣛⣓⣛⣛⣛⣛⣛⣛⣛⣋⣋⣛⣛⣋
⠀⠀⠀⢹⣫⣜⠛⠛⢋⣈⣫⣥⣤⣬⣯⣯⣭⣽⡍⣭⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣬⣭⣭
⠀⠀⠀⣾⣹⣟⣆⠈⢑⢟⣻⣿⣿⣿⣿⣿⣿⣿⡏⣿⡿⠉⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣿⣿⣿⠐⢋⢹⣿⣿⣿⣿⣿⣏⠶⠈⡁⠿⣃⠀⢀⡀⠀⠀⡄⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣼⣿⡿⠁⠀⣎⣬⣿⣿⣿⣿⡇⠀⢻⣯⣾⡻⢀⣌⠛⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢹⡾⣼⠁⠀⠀⠠⠻⠷⠟⣿⣿⠑⢠⣶⡇⣿⣷⣷⢹⣬⡇⢠⢭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢸⣷⣿⡀⠀⠀⠘⣷⣶⣿⡿⣿⣇⣾⣿⣿⠛⠉⠁⠀⠉⠀⠀⠈⠰⠂⣶⣏⣻⣿⣿⣿⣿⣿
⠀⠀⠀⣼⣿⣿⠇⠀⠀⣴⣼⡿⠀⡁⣼⣿⢹⠟⠁⠀⠰⣄⠀⠀⠀⠀⠀⣼⡇⢠⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣿⣼⣿⠀⠀⠀⡿⠇⠀⠀⠁⢹⡟⠈⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⠉⠁⠈⢩⡉⠉⠉⠉⠉⠉
⠀⠀⠀⢻⣿⡿⠋⠀⢰⣇⠀⠀⠀⠁⢸⡇⠀⠀⠀⠀⠈⠀⠀⠤⡤⠀⠀⠀⠀⢴⡶⣧⠄
⠀⠀⠀⣼⠏⠀⡐⢂⠀⠀⠀⠰⠾⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣠
⠀⠀⠀⠀⢀⠊⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⣾⡀⢶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠈⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⡂⠀⠀⠀⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠔⠃⠐⠀⠐⠁⠀⠀⠉⠁⠈⠁⠀⠀⠀⠤
⠀⠀⠀⠈⠀⠒⠒⠀⠈⠑⠒⠾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠈⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠠⡒⠆⠐⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⡠⠤⡀⠀⠄⠀⢀⣀⣀⡀⣠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠀⠀⠀⡁⠚⠈⠁⠀⠀⠀⠀⠀⠀⠀⠰⢶⠁⠀⠀⠀⠙⠛⠛⠃⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠁⡠⢞⠁⠀⠉⠀⠠⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⢀⠀⠀⠀⠉⡠⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠄⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠃⠀⠁
⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢤⠆⠰⡀⠀⠀⠐⠄⡀⠀⠀⠔⠁
⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣀⡠⠀⠠⣁⢀⠀⠀⠀⠀⢀⠀⠀⠀⠁
⡀⢁⡠⠀⠣⠀⠔⠊⠑⠀⠀⠀⠀⢸⢀⠁⠀⠀⠀⣠⣧⠤⡀⠀⠀⠀⠀⡀⠴⠈⠀⠈⠤⠠⠤⠿⠏⠓⠀⠀⠀⠈⠗⣤⣼⡤
⠀⠀⢠⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠈⠑⠈⠑⠠⢎⢉⠻⡂⡅⣀⠀⠒⠉⠀⠀⠁⠀⠂⢃⠈⠢⣀⠐⠀⠀⠀⠀⠀⠀⠛⢻⣇
⠁⠀⠀⠀⠀⠠⠀⠴⠂⠸⠀⠀⠀⠀⠄⠀⠈⠀⠐⠎⠉⣡⢘⠀⠀⠁⠁
⠈⠂⠄⠀⠀⠀⠀⠀⠀⡜⠠⠀⠀⢈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠡⡐⠀⠀⠄⠀⠀⠜⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⢀⡀⠄
⠀⠀⠈⠢⠀⡀⠄⠊⠀⠀⠀⠀⠀⢄⣀⣀⣀⣀⣀⣀⣠⣤⣴⡞⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠍⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠠⠤⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⠀⠄⠄⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠀⠘⠁⠐⠒⠠⠀⠀⠀⠐⠂⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣦⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡿⣿⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣴⡿⠀⠀⠈⠻⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢳⠃⢰⣿⡇⠀⠀⠀⠀⠙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⠀⢸⣿⢣⠀⠀⠀⠀⠀⠸⣿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣵⡷⠶⢾⣶⣾⣄⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⠁⠀⢀⣡⡙⡟⠀⠀⠀⠠⠶⠿⠿⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣶⢶⡖⠯⡇⣷⠀⠀⠀⠀⠀⣀⣀⢳⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣸⠇⠀⠈⠀⠃⣿⣿⠀⠀⠐⠿⠉⠟⠋⠈⣧⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢡⠟⠀⠀⠀⢀⣼⣳⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡡⠋⠀⠀⠀⣠⣾⡿⠋⠀⠀⡄⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⢀⣀⣤⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠛⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⢴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⠂⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠐⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⡀⠀⠀⠀⠀⠀⠀⠁⠰⠀⠀⠀⢀⡄⢀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠒⠀⠀⢸⡄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⠂⠛⠉⠉⢣⢄⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⢠
⠀⠀⠀⠀⠀⠀⠠⡍⠀⠀⠀⠘⠒
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠙⠃⠲⠦⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠠⠠⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠂⢠⣄⣀⠀⠰⣶⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⡠⠤⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠘⢄⠤⠒⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣤⠼⠟⠛⠉⠉⠉⠉⠀⠉⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠠⣄⣀⠀⠀⠀⠀⠀⠀⣀⣠⠴⢿⡁⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⣾⡟⠉⣩⣿⡛⠛⠉⢉⣀⡀⢀⡷⠛⠁⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⣠⢴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣤⡤⣤⠘⢿⠇⠀⠠⠆⠀⠀⡀⢀⡄⠀⡾⣀⠀⠀⠀⠀⠀⠀⠳⡌⢧⡤⠔⠉⣴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⣤⣈⡦⠀⢰⡖⠋⠀⠀⠀⠀⠀⠀⠀⣿⢠⣎⠩⠄⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢳⡀⠀⠘⢧⣒⣒⣲⠖⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢳⠖⠂⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⢦⠿⢿⠿⣷⣄⡀⠈⠉⢉⣠⡤⠖⠋⠀⠀⠀⠀⢀⣠⡴⠞⠉⠈⣦⠚⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠋⠉⠁⢾⣳⣿⡶⣿⠤⣿⢽⣶⣟⣸⣟⣲⣶⠶⠒⠚⠋⠉⠀⠀⠀⠀⠀⣸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⠀⠀⠀⠀⠸⡟⣿⡤⣿⣶⣿⡾⡶⣯⣷⣿⣹⠇⠀⠀⠀⠀⢀⣀⣤⡴⢾⣋⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⢀⣠⣴⡒⠀⠀⠉⣡⡾⢿⢿⣿⡹⠇⠈⠳⠾⠃⣴⣠⠾⠗⠛⣩⣵⠜⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⢀⡴⠋⠈⣇⠁⠀⠀⠘⠷⣿⠏⢸⢸⣷⡴⠀⠀⠀⠀⣿⠁⣠⣴⣟⣋⣤⣄⣲⣯⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠧⣤⣤⠤⣟⠀⣀⠤⠿⣦⡀⠀⠀⠀⠀⠀⢸⢠⡄⠀⠀⠀⢀⣠⣿⡿⠿⠟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⢀⡔⢩⣶⣢⠀⠈⢳⡈⣏⠀⠀⣠⣤⡑⣄⠀⠀⠀⠀⢸⠀⠀⠀⠈⠉⠉⠉⣽⠁
⠀⠀⠀⠀⢀⡞⠀⠀⠙⠁⠀⠀⠀⠳⠾⠂⠈⠻⡿⠃⢸⠀⠀⠀⠀⢸⠐⠆⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢸⡇⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠘⣷⡈⠀⢀⡤⢤⡀⠀⢠⣾⣭⡆⢀⣠⠟⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠘⠷⣦⣜⣷⡷⢃⣀⣀⣉⣥⣴⣿⣿⣿⣷⣶⣶⠖⠒⡏⠀⣀⣀⣠⣤⣤⣶⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠉⠀⣸⣿⣿⣿⣿⣿⠃⠀⠀⠉⠉⠉⠉⢿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣶⡲⠶⠿⠿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⠦⣴⠒⢚⡥⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠖⠋⠳⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠙⠳⠾⠉⠛⠋

⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⢰⣤⠿⠷⢂⡀⠀⠀⠀⠀⠀⠠⣿⣿⣿⡇⠀⢰⡆⠂⣿
⠀⠀⠀⠀⠀⠚⠀⠸⢇⣶⣿⠿⠿⠀⠀⠀⠀⠀⠀⠈⠻⠟⠀⠀⠈⠁⠀⠉⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠁⠀⠀⠀⠻⠟⣡⣶⠿⠁⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠈⠀⠄⠈⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠈⠁⠀⠀⡀⠀⠀⠐⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠱
⠀⠐⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠓⣦⣀⣀⣀⣀⣠⡆⠀⠀⢀⡀⠀⠀⠀⢀⣀
⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠦⡀⠠⢸⣾⣿⣿⣿⣿⣿⣿⣿⡆⠀⠘⠟⠃⠻⠃⠛⠛
⢠⣶⢰⡷⣒⠀⢲⡆⠀⠀⠀⠜⠉⡀⢀⣀⠰⠆⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⣙⣛⠙⠛⠃⠈⣷⠀⢀⠄⡀⠀⠉⠈⠋⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⡠⢀⠀⠀⠀⠀⠀⠀⣤⣤⡆
⠀⢭⣉⡀⠀⠀⠀⠉⠐⠢⡀⠈⠂⠀⢀⡀⠀⡀⠈⠠⡤⠈⠹⢿⡋⠙⣿⣿⠑⠀⡀⠠⠙⠀⠀⠀⠀⠀⠰⠿⣿⠿⠂
⠀⠀⣬⠑⠊⠀⠀⠀⠀⠀⠈⠀⠀⠀⡃⠫⠂⢡⠄⠀⠀⠀⠀⠀⠈⢀⣿⣿⡎⠀⠀⢀⠀⠸⠈⠒⠀⠁⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠴⣄⠀⠀⠀⢀⣀⣨⡦⠈⣼⠆⠀⠶⠄⢤⠄⠶⠄⠘⠁⠀⠀⠀⠀⢴⠀⠀⢀⠀⠀⠀⠀⠀⠈⢈⠄
⠀⠀⠀⠀⢀⠀⠀⠈⢃⣠⣾⣿⡿⠻⣷⣄⠛⠀⠀⠀⠀⠛⠃⠀⠀⢀⡀⠀⠾⠀⠀⣀⢣⠀⠈⠀⠐⠂⠀⠤⠀⠈
⢠⡀⠀⠡⠤⡀⠀⠀⢨⣏⠠⢹⠇⠂⢸⣿⠀⠘⢆⠄⠀⠀⠀⢀⡔⠈⠉⠀⠀⠀⠐⣿⣿⡥⠄⠀⠀⠀⠀⠀⡀
⠀⠉⠢⠉⡄⠀⣀⣤⣤⣻⡦⠄⠀⠡⠾⠿⠈⠀⢈⣀⡀⠀⠐⠂⠁⠂⠈⢁⠀⠀⠤⠋⠁⠈⠀⠀⠠⢹⣿⡿
⠀⠀⠀⠐⣧⣾⣿⣿⠿⠿⣧⡀⠀⠀⠀⠀⠀⠀⠈⠐⠁⠀⡄⠀⠀⠀⠀⠀⢀⡠⠂⠀⠀⣰⡶⠀⠀⠈⣟⠁
⠀⠀⢰⣾⡛⡿⠉⠏⠀⣴⣿⣷⡄⠀⢀⠀⠀⢀⡀⠀⠀⠄⠁⠀⠀⠀⡀⠀⠈⠁⡀⢀⠀⠉⠃⠀⠀⠀⢰⡥
⠀⠀⠸⣿⣿⣧⣀⣀⣠⣿⣦⣼⡇⠀⠈⠁⠒⠈⠁⠀⡀⠀⠙⠀⠀⠀⠃⠀⢤⣔⠉⠙⢠⣄⣠⡤⠔⠁⢪⡀⠄⠑⠄
⢀⡐⡐⡜⠛⠿⢿⣿⣿⠿⠟⠋⣠⣁⡰⠀⠀⠀⠄⠈⠁⠀⢀⢀⠀⡀⠐⡂⠸⣿⠁⡺⠦⣨⠿⠇⣶⡶⢡⠁⠀⠒⠐
⠀⢒⠌⠲⣤⣦⣀⡀⢀⣰⣦⠀⣁⣿⠁⠀⠀⠀⢨⠀⠀⡠⠂⠀⠀⢈⡀⡀⠔⣿⡇⠀⠀⠀⠀⢨⣿⡇⡈⠀⠀⠀⠊
⠀⠈⠀⡀⠀⢸⣿⣿⣿⣿⡟⠉⢹⠗⠦⢄⠠⢀⠄⢥⡸⢀⠄⣀⡄⡠⠻⡀⠢⣿⡇⢸⣦⢀⣴⢸⣿⠀⠉⢉⡤
⠀⠀⠀⠈⠂⠚⠠⠜⠗⠐⠣⠄⠊⠀⠂⠘⠃⠔⠢⠜⠃⠰⠤⠚⠤⠞⠀⠃⠀⠉⠁⠘⠛⠘⠛⠸⠟⠀⠀⠀⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⢀⠂⠀⣰⠄
⠀⠀⠀⢀⡀⢢⠀⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡈⠉⠛⠃⢈⠡⠂
⠀⢀⠀⠈⠳⡀⠂⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠟⣀⠈⠓⠲⠶⡄⠈
⠀⠈⢄⠐⢦⡐⡀⠰⠃⠀⡀⠀⠀⠌⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⡇
⠀⠀⠀⠐⠦⠈⠁⢠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⢤⠀⢀
⠀⠀⠁⠀⠀⠲⡀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠂
⠀⠀⠀⠀⠀⠀⠉⠒⠀⡀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠋⡸⢛⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡀⠀⠀⠀⠀⠀⠀⣠⠤⣀⡀⠤⠤⠤⢷⣄⣤⡀⠠⠤⠤⠤⠐⠛⠋⠉⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠐⡀⠀⠀⢀⡄⠶⠁⠀⠀⠀⠀⠀⠀⢀⠈⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠱⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⡆⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠉⠠⠁⠀⠀⠀⠀⠀⠀⣀⣀⠤⠞⠁⣠⣿⡀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⡆⠀⠻⡃⠀⠈⠉⠉⠀⠀⢀⣤⣾⣿⣿⡇⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⣄⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⡇⠀⠀⠹⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠫⡐⠒⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠘⢿⣿⣿⡿⠋⠛⠉⢻⣿⣿⠁⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠈⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠙⠻⣀⡄⠀⠀⢀⡴⠃⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⢄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠉⠉⣥⠔⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠻⠦⣤⠄⣀⠤⠤⠖⠋
⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠢⠤⢤⣤⠤⠖⢻⠋⢤⡀⠃⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠃⢸⢆⠀⠸⠀⠀⠀⠉⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠂⠤⠤⠤⠄⠐⠊⠁⠀⠀⠀⡈⣴⠃⠀⠀⠀⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠈⠻⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢋⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⢀⡴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠚⠉⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠸⠁⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⡀⠀⠀⢰⠈⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢊⣠⠾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡑⠦⠴⠃⡦⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢐⣊⡥⠞⠋⠙⣦⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⠾⠁⢠⣾⣀⣀⣀⡠⠠⠦⢶⠋⠁⠀⠀⠀⠀⠀⠘⢧⠀⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠣⡀⠀⠀⠀⠀⠀⠀⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠐⠤⣀⠀⠀⢀⡼⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣉⠛⠛⠋⣀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠑⠊⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⡎⡴⠒⢆⠀⠤⣄⠉⣱⠄⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢂⣀⣈⠀⡏⠀⠀⠻⢀⣀⡀⣂⠴⠒⠛⠁⠀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⢠⠞⠉⢀⠀⠀⠁⠀⢠⡞⠉⣠⠎⠁⠀⢀⡀⠀⡜⠀⠀⢀⠤⠀⠀⠀⠸⣸⡀⣸⡜
⠀⠀⠀⠀⠀⠂⠁⡔⠀⠘⣤⠖⠋⠉⡿⠠⡏⠈⠂⠀⠀⠀⢌⠙⢧⠀⠀⢀⡤⠒⠀⠀⠀⠈⡏⠙
⠀⠀⠀⠀⠐⠉⢓⣧⢠⡂⣀⡀⠀⠀⠇⠀⡠⠒⡁⠀⠀⠀⢘⡆⠘⡆⠀⢏⠀⠀⢰⡄⠀⠀⠃
⠀⠀⠀⠀⠀⡰⠋⢀⡜⠉⡁⠀⠀⠀⠀⢰⠁⢸⠀⠀⠀⠀⠉⠀⠀⠁⠀⢸⢀⠔⢁⢠⡀⠀⠀⠀⠀⡀⠠
⠀⠀⠀⠀⢀⡥⠄⣼⠀⢸⠀⠚⠉⠉⠂⠸⡀⠀⢧⠈⠒⠤⠤⠀⠀⠀⣠⠎⠀⡔⠁⠘⢡⣤⣤⣤⣤⣶⠾⠂
⠀⠀⠀⠀⢸⠀⠀⠸⡀⠈⠓⠰⠉⠉⠉⠙⠓⠀⠀⢧⠀⢰⡀⢀⣀⠈⠅⣀⣈⣁⣈⡀⠘⠉⠉⠉⠤⠶⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠁⠈⠒⠚⠂⠀⢀⡀⠀⢠⠀⠀⠀⠀⢜⣀⠼⠓⠋⠁⠒⠛⠛⠛⠻⠿⠿⠿⠿⠿⣿⠷⠒⠀⠄⠰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠙⠁⠀⠋⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠀⣀⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⣉⣀⣒⣀⣈⡉⠁⠐⠒⠀⠀⠀⠤⠐⢀⣠⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠐⠉⠉⠉⠙⠛⠛⠛⠛⠚⠉




⣏⠉⣻⣛⣛⣛⣛⣿⣛⣛⣛⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣿⣛⣻⣟⣛⣛⣻

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⠟⡟⣿⠟⠻⠿⠿⢿⣿⢿⠟⠛⠛⠻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⡿⠃⢠⠟⠁⠀⠀⠀⠀⠀⠙⠲⢧⡀⠸⢧⣄⣻⣧⣸⠃⠉⠻⣟⢿⣿⣿
⣿⣿⣿⠿⣿⣿⡼⣽⡿⠁⢿⣜⠁⣠⠋⠀⠀⠀⠀⠀⠶⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠙⢮⣏⢻
⡁⠀⠈⠙⠲⣿⣷⡿⣇⠀⠘⣇⡴⠁⠐⠚⠋⠉⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⢹⠋
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠉⠓⣿⣀⣀⡤⠤⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠘⣿⣿⣷⠀⠀⠀⣷
⠀⢀⣀⣤⡤⠤⢼⣷⠒⠂⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣽⣿⣿⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠀⠀⢿⣿⣿⣿⡿⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⢹⣇⠀⠀⢀⣠⣶⣿⣿⣿⡿⠁⠀⠀⢸⣿⣿⣿⡇⠀⠀⣿⣠⣄
⠀⠀⠀⢠⣀⡀⠀⠀⣿⣧⠀⠀⠀⠈⣿⡀⠀⠸⠛⠛⠛⠛⠉⠀⠀⠀⠀⢸⣿⣿⣿⡆⢀⡀⢸⣿⣿⣷⡀
⠀⠀⠀⠸⣿⣿⡋⠀⠸⣿⡀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣇⣼⣿⣷⡿⢿⣿⣿
⠀⢀⠀⠀⣿⠛⢷⣄⠀⢿⣇⣀⣀⡀⠀⣿⠀⠀⢰⡶⠀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣾⣿⣿
⣤⣿⣶⣶⣾⣶⣶⣿⣿⣿⣿⣿⣿⣷⡀⠘⠃⠀⠈⠁⠰⢛⣿⡟⠛⠉⠉⠈⠿⠚⠀⠀⠀⣤⣹⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠀⠀⠀⠀⡀⢰⡄⠀⠀⠀⠀⠀⠀⢠⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠈⠳⢇⠄⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⢸⣧⡀⠴⣿⡿⠚⠚⣛⡯⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣌⠂⠀⠀⠀⠀⠀⢁
⠀⠀⠀⣿⣿⡧⢤⡼⡂⢽⠯⢅⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⣲⠆⠀⠀⠀⠀⠀⠀⠛⠳
⠀⠀⠀⣿⠿⣷⣿⣿⣧⠻⢷⠿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡌⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⡀
⠀⠀⠀⠘⣆⠙⠋⣿⣜⢳⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠐⢀⠀⠀⠠⠈⠗⡄⠀⠔
⠀⠀⠀⣴⣿⡷⣤⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠢⣄⠀⢀⣴⣾⣤⡿⢠⣥⠇
⠀⠀⣾⣿⣧⡉⢲⣼⣇⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⡀⣀⠈⠉⠻⠿⠗⠰⠛⠐⠊
⠀⠀⣿⣿⣿⣿⡌⢻⣇⢻⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⢉⣠⠤⢤⣤⣶⡖⠁
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⢈⠻⣿⣷⣦⢬⣋⠈⡀⠐⡄
⠀⠀⢿⠿⠿⣿⣿⠿⡿⣿⠿⠿⠿⠿⠿⠿⠷

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣵⣶⣶⡌⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡘⠿⠿⢃⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠉⠙⠛⠛⠉⢹⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢸⣟⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⣀⠀⠀⠀⠀⢠⣀⠻⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣼⡏⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢛⡿⠀⠀⠀⠀⠀⣿⡇⠙⣿⣿⠇⠀⠀⠀⠀⠀⠀⣿⡇⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣿⠀⠀⠀⠀⢀⠻⣿⠆⢀⠉⠀⠀⠀⠀⠀⠀⠀⠛⢃⠀⠻⠃⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⠐⠒⠒⠚⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠦⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣆⠁⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢀⣴⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⢀⣴⡿⢉⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⡀⠀⢀⡀⠀⠀⠀⢀
⠀⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠁⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠁
⠀⢀⡀⠀⠀⠀⠘⡄⠀⣄⠠⠄⠀⠀⠑⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠠⠄⠀⢘
⠀⣨⣀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣀⣸⠗⠐⠀⠀⠀⣄⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠘⠁⠀⠈
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠈⠀⠒⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⣩⡆
⣄⡀⠀⠀⠀⠀⠉⠀⠀⠐⠛⠢⢤⠀⠀⣤⣀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠙⠋
⣿⣿⣧⣄⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣄⢀⣧⠘
⣷⣬⣝⠿⣧⣤⣀⣑⣄⡀⠀⠀⠀⠀⠀⠀⠀⠐⠆⢉⣻⣿⣬⡁⠀⠀⠀⠈⠿⢶⣶⣶⣶⡄
⠀⠉⠛⢿⣿⣿⣟⣛⣛⣻⣿⣻⡆⠀⠀⠀⠀⠀⠀⠈⢿⣿⡏⠙⢷⡦⠀⠀⠀⠀⠈⠏⢉⡄
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⢷⣝⡻⢿⣦⣄⡀⠀⠀⠀⠓⠈⠃⠀⠀⠀⢀⠀⠀⣀⠀⠹⡆⠀⢠⡄⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⣷⣽⣿⣿⠲⣆⣱⣄⣶⣤⣦⡠⠃⠉⠀⠀⡀⠄⠀⣇⠀⠈⢶⣶⣶⠀⠰⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣽⣿⣿⣷⣿⣿⣿⣿⡷⣘⢄⠀⣴⣠⡾⠂⠀⠀⠀⢠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣇⣰⣿⣿⡤⠐⠀⠀⠀⠀⢫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡿⠉⠿⣿⣿⣿⣛⠀⢰⣄⡀⠘⢟⠢⡀
⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⠿⣿⣿⣿⣾⣷⣿⠋⠉⠉⢩⣾⣯⡁⠀⠀⠱⣼⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣿⣿⡇⠀⠀⢀⣾⣿⣷⡅⠀⠀⠀⠘⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣾⣿⢿⣿⣿⣍⣿⣷⠄⢀⣾⣿⣿⡟⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⣤⣤⠂⠴⢆⣀⣠⣶⣶⣿⣿⣿⣿⣿⠈⣿⣿⢻⣿⣿⠀⣾⣿⣟⣋⠁⠂
⠀⠀⠀⠀⠀⠀⡲⣒⣶⠛⠃⢾⠙⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⡟⣋⢸⣿⣿⣿⣯⠌⠀⠡
⠀⠀⠀⠀⠀⢀⠨⣿⣿⡶⠖⠋⠉⠉⠉⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⡯⠟⣾⢀⠀⢸⣿⣿⣿⡅⠀⠀⠘⣇⠀⢀
⠀⠀⠀⠀⠀⣄⡸⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣿⣿⣿⣿⣷⣷⡿⣿⡅⣸⣿⣿⣿⡇⠀⠀⠀⢸⡀
⠀⠀⢀⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣿⣿⣿⡿⠿⠟⠛⠁⣿⡇⠛⠛⣿⡿⣿⢻⣆⠀⠀⢛⡆⠰⢄
⣤⡶⠊⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣄⠈⠀⠀⣠⣄⣴⡾⣟⡀⠀⠀⠙⢿⡿⢸⠏⢠⡀⠘⠓⠲⣤
⣿⡑⠡⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡶⠀⠀⠙⣿⠿⢽⣿⠀⠀⢠⣤⣶⠶⠂⠀⢀⣿⣄
⢏⠙⣶⠀⠀⠴⣾⣦⡀⠀⠀⣤⣀⣤⣤⣄⣀⣤⣾⣿⠟⣇⠀⠀⠄⠀⠀⠀⠉⠑⠒⠛⠉⠀⠀⠀⠀⠀⣍⠉⠉⠱⠶
⠞⠃⢁⠀⠀⠀⠈⢻⣷⣾⣿⣿⣿⣿⣿⣿⣻⣿⡿⠃⢠⡟⠷⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣀⣀
⣤⣄⠺⢖⣤⠀⠀⣠⣿⣿⣿⣿⣿⡿⣿⣿⡿⠋⠀⠀⣾⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠙⠻⠟⠁
⠀⣀⢀⣬⡍⠻⠀⢈⣿⣿⣯⣝⣻⡶⠏⠁⠀⢀⣴⣪⣿⣿⣧⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⡀⠀⢈⠻

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⠶⠶⣤⣤⣀⡀
⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣥⣴⣶⣶⣶⣶⣤⣌⡛⢿⣷⡀
⠀⠀⠀⢰⣿⣿⡿⠛⠛⠻⢿⣿⣿⡿⢿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠛⢿⣿⣿⣿⣿⣿⣶⣿⣧
⠀⠀⠀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿
⠀⠀⢀⠿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⢟⣣
⠀⠀⢘⠋⡎⠉⠀⠀⠀⣦⠀⠀⠀⠀⢰⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠇⠀⠀⠀⠀⠶⠀⠀⠀⠀⠚⡉⠀⠀⡀⡀
⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠆⠀⢀⠀⠀⠀⠘⣲⠺⠂⠀⠀⠀⠀⠀⣸⡇⠘⠂⠻⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠀⠈⠡⠀⠋⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⠟⢋⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠀⠰⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠈⠑⢄⠙⠻⢿⣷⠀⢰⣿⠿⠛⢉⣠⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠑⠒⣠⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣀⠀⠀⠀⠀⣠⣴⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢀⠒⢄⢀⠆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⠀⠀⠸⠿⠗⠙⠛⠂
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠰⠮⣹⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⠀⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠐⠀⠀⠁⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠁⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣄⣀⠀⠀⠐⠲⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠴⠈⠄
⠀⠀⠀⠀⣠⠀⡠⠀⠀⠀⠀⠀⠠⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⢁⣠⠼⠀⠃
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣍⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⠀⠀⠀⠀⠀⣰⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⢸⡇⢠⡇⠀⠀⠀⠀⠘⣇⣄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡗⠶⢶⠀⠀⠀⠀⣿⣷⡀⠀⠀⠀⠀⢸⠃⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⢄⣠⠱⠀⠀⠀⠀⢻⡿⣿⣦⣀⠀⠀⢸⠀⠘⠀⢀⡄⠀⠀⠀⠀⠀⠀⢀⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣿⡇⠈⠻⢿⣷⣦⣬⣄⣥⣴⣿⣷⣄⣀⣀⣠⣴⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠇⠀⠀⠀⠉⠙⠛⠛⠛⠉⠈⠙⠛⠟⠛⠋⣿⣿⠁⠀⣤⠤⠴⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⣶⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣿⣧⣀⠀⢻⡀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⣆⣠⠞⠉⠀⠀⠀⠀⠉⢻⡿⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠖⠋⠀⢀⣿⣇⣀⣀⠀⢠⡶⢶⡀⠀⠀⠀⡏⠀⠘⣿⡅⣴⡾⢛⣻⣷⠶⠿⢶⣿⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢶⣶⣶⡾⠛⠉⠁⠀⠉⠙⢾⣿⡧⠙⢦⡀⢰⡇⠀⠀⠹⣷⣏⠀⢿⠀⠀⠀⠀⢸⣿⣆⣀⣸⡓⠂
⠀⠀⠲⡶⠺⡄⠀⠀⠀⠀⠀⢹⣿⡠⢀⣤⣴⣦⣄⡀⠀⠙⣯⢂⠈⠳⣼⠀⠀⡀⠀⢻⣟⠦⣼⡷⠟⠁⠀⣼⠹⡏⠀⠈⣷⣤⣤⣀⡀
⠀⠀⠸⠓⢴⠆⠀⠀⠀⠀⠀⣾⣿⣏⣾⠋⠀⠀⠉⢷⠀⠀⢸⡷⣄⠀⠈⠀⢠⣧⠀⠀⢿⣄⠀⠀⣀⣤⡾⣣⠾⠷⠶⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣷⣷⡀⠀⠀⠀⣸⠃⠀⢸⣯⣿⣷⡄⠀⢸⠙⣧⣠⣬⡿⠻⠛⠛⠉⠰⡏⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⣀⡤⠶⠾⠿⠿⠿⢿⣿⣿⣯⠻⠦⠤⠞⠁⠀⢀⣾⣿⣿⡈⠻⡶⠟⠀⠉⠉⠁⠀⢄⣑⣄⣀⣀⣹⣄⠀⠀⠀⠠⢎⢀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⡹⢿⣿⣧⣀⡀⢀⣀⣴⣿⣟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠳⡌⠳⣄⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⣠⠞⠁⠀⢈⠿⠛⠛⠛⠋⠁⠈⠻⣧⠀⠀⠀⢀⡴⠞⠛⠓⠲⣄⡂⠀⠙⢦⠈⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⣰⠋⠀⣠⠴⠶⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠤⠔⢃⡀⠀⠀⠀⠀⠀⣿⣰⠃⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣃⡀⢰⠊⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠛⠀⠀⠀⠀⠀⠀⠟

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣄⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠚⣻⣿⡿⠛⠣⠾⢧⣴⠾⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠿⠟⠛⠿⣦
⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠋⡤⢤⣄⠀⠀⢀⡤⠤⢄⠘⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⠇⣶⣶⠀⠀⠲⣾⣧⡄
⠀⠀⠀⠀⠀⠀⣾⡇⠈⠤⣶⠍⠀⠀⠈⢱⣶⠄⠀⣹⠿⠁⠀⠀⠀⠀⠀⠀⢰⣿⠀⠉⠁⠀⠀⠀⠈⠉⠴⣄
⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠰⡙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⣀⣀⣤⣤⣤⣀⡀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠤⠶⠆⠀⠀⠀⢠⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢿⣷⣴⡿⠛⠛⠉⠛⠛⣿⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⡄⠀⠀⠀⠀⢠⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣤⣿⣿⣷⣶⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⣦⣀⡀⠘⠁⢾⣿⢇⠀⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⢳⡀⠈⠿⠛⠄⠀⠀⠀⠈⠁⢸⡇⢸⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣵⣿⣿⣄⢤⡀⠀⠀⠀⠀⠀⠀⣾⠁⢨⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣼⡇⡀⠀⠀⠀⠀⢸⠃⢠⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇⠀⠀⠀⠀⠀⠀⠘⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣶⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣆⡀
⠀⠀⠀⠀⠠⢀⡿⠛⠉⠉⠉⠙⠛⠛⢿⣿⣿⣟⣻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⢉⣏⠙⣿⣿⣿⠋⠻⣿⣦
⠀⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣿⣿⠿⠟⠛⠁⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡟⠆⠀⠀⠀⠀⠀⠀⣚⣿⣿⣿⣿⡿⣏⠀⠀⠀⣀⣀⠀⢸⣟⠃
⠀⠀⠀⠀⠘⣉⢿⡆⠐⠛⠛⣏⡛⠀⠀⢿⣿⣿⠿⣿⡿⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠁⠰⢶⠈⠀⠀⠀⢩⠤⠄⠸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⢁⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣹⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣷⠀⠀⠀⠀⠀⢀⣾⣧⣋⣿⣦⡀⠀⠁⠀⠀⠈⠁⠀⣠⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⣀⡉⠀⢀⡀⠀⠀⠀⠀⠀⢻⣿⠃⣿⣇⠀⠀⠀⠀⠀⣿⡟⣿⡇⢈⣿⡆⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣇
⠀⠀⠀⠀⣠⣾⣦⡟⠀⣰⣾⣧⣤⠀⠀⠀⠀⠈⢻⣿⢿⣿⠀⠀⠀⠀⠀⢸⣷⡈⢿⣄⣿⠃⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿
⠀⠀⠀⠘⣿⣿⣟⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣼⣿⠿⣮⣽⠇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠛⠛⣿⣿⣾⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⣿⠏
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣤⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⠻⠛⠛⠛⠛⠿⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣆
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠁⠀⠀⠁⠀⠀⢹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣀⣀⡀⠺⣿⣿
⠀⠀⠀⠀⠀⠀⢼⣿⣟⣀⣤⣄⣀⠀⢀⣀⣀⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⠀⢈⣉⣁⣀⡀⠻⣍⣩⠤⣄⣹⡿
⠀⠀⠀⠀⠀⠀⣼⣿⠉⠿⣿⣿⡿⠀⣿⣿⣿⡟⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠋⠈⠉⢇⠀⠙⠁⠀⠉⠈⢳
⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⢈⠀⠀⠈⠉⠉⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠈⢻⣇⠰⣤⣼⣦⣤⠈⢀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄⠉⠈⠁⠀⠈⠋⠁⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣶⣄⣀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠈⠀⠀⠀⢀⣼⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣾⣿⣿⠃⠀⠂⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠀⠀⠀⠀⠀⠾⠿⠟⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠄⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠐⠒⠁
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠠⣄⣠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠄⠀⢁⡀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠞⡛⠀⢀⠁⠒⠒⠖⠀⠀⠀⠶⠀⠠⡎⠀⠀⠉⠲⢄⣀⣀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠧⣄⣀⣀⡨⣮⠀⠀⢰⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠣⢄⡀⣀⠴⠊⠀⠀⠀⠀⣈⠄
⠂⢀⡦⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⡄⠀⠐⠂⠁
⠈⠠⠠⠈⠁⠀⠀⠀⠈⠁⠒⠰⠬⢔⡀⠤⢙⣦⣤⣀⣀⣀⣀⣠⠴⠊⠀⠀⠀⢀⡢⠴⠊⠘⠦⠄⣠⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠂⠌⠑⠐⠊⡤⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⡲⠀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠶⠤⣤⣀⣀⡀⠀⢀⣀⡤⠞⠁⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠉⠉⠉⠁⠠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⣀⠄
⣿⣿⠛⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⠀⣀⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢠⣶⣿⠉⣷⣄⠀⠀⠀⠀⡧⣿⢯⠷⡾⡿⢭⠂⠀⠀⠀⢾⡟⠉⠉⠉⣯⡆⠀⠀⠀⢀⣂⣂⣉⠈
⠀⠀⣿⣤⣿⣻⣏⣸⡆⠀⠀⠀⢈⣿⣯⣤⣼⣿⣁⠀⠀⠀⠀⡱⠆⢸⡷⠀⠶⡇⠀⠀⠀⣾⣿⣿⣿⣿⣿⡆
⠀⠀⠹⢧⣼⣏⣨⠟⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠻⠀⠀⠀⠀⢾⣧⣀⣀⣠⣟⡇⠀⠀⠀⢿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⠀⣰⠁⠀⢘⡄⠀⠀⠀⢸⠙⠋⠋⢳⠃⠋⠋⢻⡇⠀⠀⣼⣛⣛⣛⣻⡄⠀⠀⠀⡠⠴⠟⠙⠋⠹⢶⣄⡀
⠀⠀⡼⡌⠀⠀⠀⡿⣆⠀⠀⢸⢀⣀⡀⣰⡀⣀⣀⣸⡇⠀⠀⠀⠙⣤⡜⠁⠀⠀⠀⠀⣿⣿⣿⣷
⠀⠘⠚⠒⠒⠒⠒⠚⠚⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠙⠁⠀⠀⠠⠊⠀⠈⠢⠀⠀⠀⠀⠃⠀⠀⠀⠐⠀⠂⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣀⣀⢀⡀⠀⠀⢀⢀⣀⡀⠀⠀⠀⠀⣀⡠⠤⣲⣷⠀⠀⠀⣴⠤⣤⢦⡤⢶⠀⠀⠀⠀⠀⠀⣾⡆
⠀⠻⡇⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⣿⣭⣶⣾⣿⣿⣿⠀⠀⠀⢹⠀⣿⢸⡇⣾⠀⠀⠀⠛⢷⣾⢫⡙⣶⠟⠃
⠀⣴⡇⠀⠀⠀⠀⠀⠀⣷⡄⠀⠀⠋⡟⠻⢿⣿⣿⣿⠀⠀⠀⢸⡆⣿⢸⡇⡿⠀⠀⠀⠀⢀⣿⡿⢿⣧
⠀⠉⠉⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠉⠉⠁⠀⠈⠉⠀⠀⠀⠘⠧⠿⠼⠶⠇⠀⠀⠀⠀⠚⠁⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠦⠤⠤⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠄⢀⡀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⡦⢄⡀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⢀⡀⠀⠀⠀⢀⠔⠈⠀⠠⠈⠀⢀⠜⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢀⠸⠀⢆⠀⠄⠀⡀⠐⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠘⠻⠒⡽⠃⠈⠂
⠀⠀⠀⡠⠂⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠤⠤⠤⠤⢄⣀⠈⠁⠀⠀⠀⠄⠦⠤⠤⠤⠀⠀⡀
⠀⠀⢀⡁⠀⠀⠀⠂⢩⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠀⠀⠀⠀⠐⠠⡀⠀⠈⠑⠢⣄
⠀⠀⢼⠀⠀⠀⠂⠐⠋⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠈⢦
⠀⠀⠘⡀⠀⠀⠀⠈⢼⠁⠀⠀⠀⠀⠀⠀⠁⠈⠀⡈⠍⠛⠀⠀⠈⠀⠁⠈⠉⡉⠉⢉⠉⠉⠉⠁⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠂
⠀⠀⠀⠳⠀⠀⠀⣀⠙⠀⠀⠀⠀⠀⠀⠄⠈⠢⠠⠤⠂⠡⠔⠠⠀⠠⠀⠀⢄⡀⠐⠢⠤⠀⡀⡀⢤⣶⠀⠀⠀⣀⠤⠄⠒⠈⢀
⠀⠀⠀⠀⠉⠂⠀⢀⠀⠀⠀⠀⠀⡃⠀⢀⢬⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠒⠀⠀⠈⠁⠈
⠄⠀⠤⠁⠀⠐⠂⣁⣀⡀⠀⠀⠀⠁⠊⠁⠀⠉⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠁⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠠⠄⠈⠍⠉⢀⡀⢀⣐⣒⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⡠⠘⠣⣀⢀⣈⡍⠁⠈⠀⠀⠀⠀⠀⢰⠂⠐⠒⠒⠊⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢷⠀⡀⠀⡔⠋⡀⢀⠀⡬⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣀⠔⠂⠈⠒⠑⠊⠀⠀⠣⠘⠒⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡨⠄
⠀⠀⢀⠂⠤⠀⣀⡀⠀⠘⠀⡠⠔⣊⠤⠊⠀⠀⠀⠀⡀⠀⡀⠀⠐⠉⠉⠉⢨⡂⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡠⠊⡠⠊
⠀⠀⠀⠈⠑⠒⠦⠬⣉⣹⣁⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠠⠐⣐⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡠⠊⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠄⠀⠜⠀⠰⠤⢀⣉⠐⠒⠠⠤⠤⣸⡄⠊⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠢⠤⠆⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡐⡀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢂⢀⢤⠊⠀⠩⠐⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢿⠀⢀⠀⠀⣠⠐⠱⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠹⡨⠄⠉⠁⠀⠀⠀⠄⢠⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠆⠀⠈⠁⠀⠀⠀⠄⠀⠀⠀⠨⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⠠⡀
⠀⠀⠀⠀⠀⢀⡠⡀⠀⠀⠀⠀⠀⠃⠌⠠⠀⠀⣀⣀⣀⢠⡀⠀⠤⠆⢒⠀⠀⠀⠀⠔⡀⠌⠀⠀⠁⠘
⠀⠀⠀⢀⡌⡄⠀⠀⠀⠀⠂⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀
⠀⠀⡠⠁⠐⠤⠀⠀⠀⠂⠀⠀⠠⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀⠄⠀⠊⠐⠠⡀
⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠘⠀⠀⢂⣠⡀⢠⣀⠂⠀⢸⠀⡐⠀⠀⠄⠀⠀⢀⠈⢂
⠀⢜⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠇⠐⢩⣆⠀⠀⣶⡙⠀⡈⠀⠡⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⢃⠀⠀⡀⠀⠀⠀⠰⡦⠀⠀⠀⠀⢀⠀⠈⠉⠀⠀⠉⠁⢀⡃⠐⢤⠄⣀⣀⣀⣀⣀⣀⡠
⠀⠀⠀⠆⠈⠛⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⠑⢤⣀⣀⣀⣀⠴⢋⠀⠀⢸⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡆⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠑⠒⠒⠀⠀⠉⠀⠀⠀⠀⠀⠐⠤⠤⠤⠤⠤⠔⠁⠀⠀⠀⠉⠁⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣴⡄⠀⠀⠀⠀⠴⢿⣆⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⡿⠤⠠⠀⠄⠀⠀⠈⠉⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢈⢁⡤⢏⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢠⠃⠀⠀⠈⠳⢄⠠⠤⠄⠆⠀⢂⡈⠁⢢⡀⠈⢧⡀⠀⡀⠠⣀⠁⡀⠀⠡⠤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠤⠀⠀⡀⠁⢈⠀⠀⠀⣂⢀⠂⠀⠀⠀⠒⠦⡀⠀⠀⠀⠀⠑⡌⢀⠊⠀⠀⠈⠀⣀⣀⠀⠀⠁⡄
⠀⠀⠀⠀⠀⡐⠁⠀⠀⠠⢀⠂⠐⡰⠇⠄⠀⠀⠈⠱⡀⠀⠀⠀⡀⠀⠀⣀⡀⠀⠀⢰⠀⠀⠀⡠⠤⠀⠠⣄⠑⢆⠀⠰
⠰⣄⡆⠀⠀⡅⠀⠀⠀⢀⡤⡄⠀⢤⡄⠀⠀⠀⠀⠀⡆⠀⠀⠚⡅⠀⠀⡄⠀⠀⠀⡄⠀⠀⠰⠘⠲⠠⠄⠉⠀⢸⠀⡘
⠚⠻⣿⠋⠀⠁⠀⠀⠀⠀⣤⡄⠀⣄⡌⠀⠀⠀⠀⠀⠃⠀⠀⡈⠀⠀⠀⢊⡀⠀⢰⢤⡀⠈⢠⣀⠀⠉⡡⠀⠀⠃⡐
⠀⠀⠈⠳⠦⠴⡀⠀⠀⠈⠘⠀⠐⠒⠀⠄⠀⠀⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣤⠿⠀⢰⣦⣤⡼⠁⡀⢡⡇
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠤⢒⣿⠀⠀⠀⠀⢠⢷⠀⠀⠡⢄⠀⡠⠄⢀⣼⣿⣾⢇⠀⠘⠒⠊⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⣴⣵⣤⡄⠀⠈⠋⠑⢀⡤⢄⡠⢴⣋⣿⠀⠀⠀⠀⣀⠀⠀⠀⣠⠋⢀⣨⠦⢀⣀⣀⡠⢒⡏⣀
⠀⠀⠐⢦⣤⣀⣻⠀⠉⠉⠒⠦⢖⠒⠉⡇⠀⠀⠀⠞⠟⠓⠂⠰⡎⡼⠁⠒⠈⠀⠰⠯⠥⠤⣤⡄⠀⢳⠈⠳⠟⠃
⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢠⡟⢧⣰⡇⠀⠀⠀⠀⠀⠀⠀⣠⠿⠴⠶⢲⡆⠀⠀⠀⣀⣴⠟⠁⠀⠈⠷⠤⠤⢤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠁⠀⠀⠀⠀⠀⢠⣾⣥⣤⡀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁

⠀⠀⣀⣤⠤⣄⡀⠀⠀⠀⠀⢠⣺⣭⠷⣠⣚⣯⡷⡄⠀⠀⠀⢀⡤⡤⠤⠤⢤⢤⡀⠀⠀⠀⠀⡀⡀⠄⠄⠀⠂
⠀⣼⠛⣿⣤⡾⠻⡆⠀⠀⠀⠘⠯⣯⠝⠉⢯⣿⠽⠁⠀⠀⠀⠠⣛⠀⢠⣀⠀⣛⡇⠀⠀⠀⢰⣶⣶⣦⣦⣦⣤
⠀⣿⠟⢻⡾⠷⣶⡇⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣴⠀⠀⠀⠀⠐⣭⠀⠘⠉⢨⣭⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿
⠀⠈⠳⠾⠷⠴⠋⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠉⠀⠀⠀⠀⠈⠒⠒⠒⠒⠒⠒⠃⠀⠀⠀⠛⠛⠿⠿⠿⢿⡟

⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⣬⠀⠀⠀⣣⠀⠀⠀⠀⡇⠁⠁⠁⠑⠁⠁⠁⠁⡇⠀⠀⠠⣯⣭⣭⣭⣽⠄⠀⠀⠀⡤⣶⣿⣁⠍⠠⠿⠷
⢀⣞⡇⠀⠀⠀⢨⢳⡀⠀⠀⡇⡀⡀⡀⡠⡀⡀⡀⡠⡇⠀⠀⠀⠀⢑⣴⡋⠀⠀⠀⠀⠀⢺⣿⣿⣿
⠘⠚⠒⠒⠒⠒⠚⠓⠃⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠔⠁⠀⠉⠢⠀⠀⠀⠀⠓⠒⠒⠂⠉⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⣶⠀⠀⠀⢠⡬⣥⡤⣤⡬⣦⠀⠀⠀⠀⠀⠀⢰⣧
⢿⣿⠀⠀⠀⠀⠀⠀⢹⡿⠀⠀⢰⣖⣫⣥⣶⣾⣿⣿⠀⠀⠀⠘⡇⢸⡇⣸⠀⣿⠀⠀⠀⠲⣶⣶⠟⡟⢶⣶⠶
⣠⣿⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠘⠻⡿⢿⣿⣿⣿⣿⠀⠀⠀⠀⣷⢸⡇⣿⠀⡏⠀⠀⠀⠀⠀⣽⣾⣿⣾⡁
⠛⠛⠀⠀⠀⠀⠀⠀⠚⠛⠀⠀⠀⠈⠓⠒⠋⠉⠙⠻⠀⠀⠀⠀⣿⣸⣇⣿⣰⡇⠀⠀⠀⠀⠰⠟⠁⠈⠙⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣾⣆⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡇⢩⠖⠤⡀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠧⢍⡓⠀⢸⣗⢦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⣿⡏⢘⣛⣿⡤⣀⣉⣓⠰⣿⣶⠦⡭⠏⠅⠐⣂⠀⠐⠂⠀⠂⢠⠀⠀⠀⡤⣤⣤⣶⣄
⠀⠀⠀⠀⠀⠀⢠⣿⠁⢘⣝⣿⠀⠋⠉⠰⣦⣿⣿⡆⠀⠀⢀⠰⣷⠄⠁⠀⠀⠒⣼⠨⠅⠛⣷⠶⢸⣻⡏⠧⡤⢄⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣴⡿⣾⣿⠀⢘⣵⠀⣯⣹⣿⡇⠀⠉⠭⠓⠿⣞⠆⢀⠀⡞⠶⢭⠉⠭⢴⡄⣾⣽⣇⣰⣾⡖⡆
⠀⠀⠀⠀⠀⠀⢸⣿⠹⠟⣻⣿⠆⠸⠇⠸⢷⣿⣿⣧⣬⣿⣷⣆⣒⣶⣀⣸⣿⣿⣟⣛⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⢸⣿⣶⣾⣿⠁⢒⣈⣨⣥⣾⣿⣿⡿⠻⠛⠿⠿⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠇
⠀⠀⠀⠀⠀⠀⠸⡼⣇⢽⣿⡿⠟⠛⠉⠉⠀⠀⣿⡇⠀⠀⠀⠀⣠⣾⢿⣿⣿⡞⠯⣿⠿⠟⠛⠛⠛⠻⠟⠋⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠳⣧⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⣴⣿⢏⠞⣿⣿⣿⣿⡶⠟⠀⠀⠀⢰⡀⠳⢶⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣶⣾⡿⠃⢸⣾⣿⣿⠃⣿⠃⠀⠀⠀⣀⣀⣻⣦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣍⠉⠁⢀⣟⣭⣭⠇⣼⠃⣠⡴⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⣾⣷⣿⡝⢰⡏⠸⣯⣶⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⠿⠁⢿⣿⠿⠟⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠄⢤⣤⠴⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡈⢣⢸⢇⠎⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣢⣿⣿⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣵⣿⣯⣽⡳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢧⣟⡿⡾⢾⠶⣟⣹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠙⡾⢽⣭⣟⣹⡏⢹⣅⡼⡆⠀⠀⣠⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣏⣹⠓⡿⢤⣯⡼⣯⡽⢧⡤⢷⢀⡴⢋⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⢧⠀⠀⣸⠦⣯⣹⣿⣾⡟⠚⣟⠶⢻⠒⠛⡏⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠳⣄⣟⢺⠧⢼⡇⠙⣏⢛⣏⠓⣻⡓⢚⣧⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢹⣍⣽⠓⢺⡇⠀⢹⣏⣿⣙⣹⣏⣉⣼⢰⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⢦⣻⡀⢼⠢⣿⣝⣽⠇⠀⠈⡯⢾⣍⣉⣿⣭⢼⣾⡏⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠻⡇⣾⣉⡿⢤⡟⠀⠀⠀⡷⢺⡯⡭⢿⠦⠾⡿⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠹⡷⢭⣽⣾⠁⠀⠀⢰⣟⣹⡗⠶⣿⡓⣾⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⡖⢿⡏⠀⠀⠀⢸⣧⣤⣏⣋⣹⣿⠏⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠈⢿⣹⠇⠀⠀⠀⢸⠶⠾⣧⣉⡽⠋⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠈⢿⠀⠀⠀⠀⢸⣓⢚⣷⠏⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠸⡇⠀⠀⠀⠸⣯⡟⠁⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⢻⡀⠀⠀⠀⢻⡀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⢳⣄⠀⠀⠘⡇⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣍⣷⣤⣼⡧⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣀⣸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠚⠛⠛⠛⠛⠛⠓⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠁⠀⣀⣠⠤⠤⠤⠤⣄⡀⠀⠀⠈⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡾⠃⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⠙⣧⣴⣾⡥⠶⠶⠶⢤⣤⣀⡀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣠⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⢀⡇⠀⠀⢠⡄⣸⠿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣼⣷⢠⣷⣸⡟⠛⢷⡘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⠇⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠒⠾⠷⠶⠞⢡⠿⠋⠈⠟⠀⠀⠈⣧⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⢀⣴⠾⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⣤⣴⣶⣶⣶⣶⣤⡄⠀⠀⢹⡄⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣿⠀⠀⠀⠈⢁⡤⠶⠖⠶⢤⡀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠦⣤⡀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡶⠛⠁⠀⠀⠀⢰⠏⠀⠀⣀⣄⠀⠙⣆⠀⠀⠀⢀⡞⠁⣀⣄⠀⠀⠙⣆⠀⠀⠘⠳⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡃⠀⠀⠀⠀⠀⣿⠀⠀⢸⣿⣿⣶⠀⢹⠀⠀⠀⢸⡇⢸⣿⣿⣶⠀⠀⢸⠀⠀⠀⠀⣿⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣸⡇⠀⠀⠀⠀⠀⠘⠦⣤⣀⣙⡛⠁⣠⠟⠀⠀⠀⠈⢧⡈⢙⣛⣁⣀⣤⠏⠀⠀⠀⢀⣿⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣽⣷⠀⠀⠀⠀⠀⢰⣶⡶⠦⠭⣍⣉⣁⡀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⣸⣯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⡹⢳⡀⠘⣧⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⠉⠙⠛⠒⠶⠦⢤⣄⣀⡀⠀⠀⠀⠀⠀⢰⡏⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡇⣄⢧⠀⠘⢧⡀⠀⠀⠀⢻⣿⣿⣷⣶⣶⣤⣤⣄⣀⣀⡀⠀⠀⠀⢨⣿⡟⠀⠀⠀⣰⠏⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣧⣿⢸⠀⠀⠈⠳⣄⠀⠀⠀⢿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣶⣿⠟⠀⠀⢀⡾⠃⠀⠀⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢹⣽⣸⠀⠀⠀⠀⣿⠳⣤⡀⠀⠻⢿⡁⠀⠀⠀⠁⠀⠀⠙⣿⣿⠟⠁⢀⣠⣾⠋⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⣱⠃⠀⠀⠀⢀⣿⢀⣸⣽⣷⢶⣤⣉⡓⠶⠤⠤⠤⠴⢚⣉⣠⣴⣶⠛⠳⠿⢦⣄⣀⣀⣀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⣻⡿⠟⠋⠉⢀⣸⣷⠉⢿⠙⢿⣍⣛⣿⠿⠉⠉⣿⡒⢻⣷⢦⣤⣤⣈⡉⠻⣯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠶⡶⠋⠉⠿⠶⠿⢷⡀⣀⣥⣤⡀⠀⢸⡉⣉⠉⠁⠀⠘⣯⠉⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⢸⡇⠀⠀⠀⢰⢒⣾⠳⣿⣿⣿⣿⠀⠘⣧⢼⠀⠀⠀⠀⣿⣀⣀⣀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⣶⠾⣧⣀⣀⣀⣬⡼⠇⠈⠻⢿⠿⠟⠀⠀⠙⢿⣷⠶⢴⡶⠋⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⢸⡉⢹⣏⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣾⠉⢛⡿⠿⠖⠒⠒⠛⠛⠛⠛⠛⠉⠉⠉⣧⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠷⢾⠃⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⡟⠳⢽⣀⣿⠀⠀⠀⠀⣼⠋⠉⠉⠹⣆⠀⠀⠀⢀⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡼⠁⠀⢰⡏⠉⠙⠛⠛⠛⢻⡆⠀⠀⢰⡟⠛⠛⠋⠉⠉⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠺⣧⣤⣤⣤⣤⣠⡿⠀⠀⠀⠀⣷⣀⣠⣤⣤⣤⡾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠷⣤⡿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢿⡴⠿⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠁⠀⠀⢀⡠⠔⠒⠈⠉⠉⠁⠒⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠻⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⢣⠀⠀⠀⢀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠑⢄⠀⠀⠂⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡆⠠⠂⠀⠀⣠⣈⣀⣤⠶⢉⠀⠀⠀⠀⠀⢀⠤⠀⠷⣤⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈⠀⠀⠀⠉⠉⡹⠉⠉⠀⢠⠊⠀⠊⠀⠈⢄⠀⠀⡰⠁⢀⡑⠀⠈⢿⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⡀⠀⠀⠀⢠⠃⠀⠀⠀⡆⠀⢠⠊⠉⣢⠈⠀⠀⠃⡜⠡⠈⣂⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠡⢌⣙⠳⠶⠋⠒⠒⠒⠐⠇⠀⠀⣶⣿⣾⢀⠒⠒⡆⣗⢿⣿⡿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠘⢄⠈⠳⠭⢋⠂⠀⠀⢘⢌⠓⠓⢁⠔⢹⡓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠑⠦⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠈⠁⠀⢀⠠⠎⠀⠈⠉⠀⠀⡸⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠊⡟⢦⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡀⠀⠀⠀⠀⠀⠀⣴⠷⢮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠁⠘⡀⠈⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⣠⢾⠁⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠈⡁⣒⣤⠄⠀⠀⠀⠀⢀⠀⣀⡠⠤⠶⠈⠁⢀⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⡏⠉⠉⠉⣀⠴⢻⠑⢄⡀⢀⡸⠧⣄⠀⠀⠀⠀⠇⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡔⠀⠀⠀⡜⠁⠄⠂⡃⠠⠘⠃⠀⠃⠄⠑⣄⠀⠀⠘⣄⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡜⠀⠀⢸⠀⡅⠀⠀⠀⠀⠀⠁⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⢸⡗⡈⠀⠀⠀⠀⠀⡆⠰⠂⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡟⠀⠂⠐⠎⣈⡈⢄⢀⡀⠠⢤⡦⠤⢀⡀⡠⠋⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡖⠓⠤⣀⡀⠀⠀⢡⡼⠎⠁⠁⠈⠲⠦⠤⢼⠁⠀⠀⠀⠀⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠙⢆⡀⠀⠀⠉⠙⠖⠛⠻⠀⠀⠀⠀⠀⠀⢀⠀⠰⢄⠀⣀⡀⠀⠈⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⢹⢄⠐⢶⠂⠀⢈⠀⠠⠄⠐⠂⠈⠈⠲⠀⠀⠀⠂⠉⠀⠀⠀⠀⣀⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢠⠙⢪⠢⡑⢄⠀⠁⠂⠠⢒⡀⠀⢀⣀⡀⠠⠤⠤⠐⠒⠒⠈⠉⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢢⠀⠀⠑⢌⢢⡑⠒⠒⠂⠉⠉⠁⠀⠀⠀⠀⢀⣀⣀⣠⠤⠤⠐⠒⢲⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡑⢄⠀⠀⠈⠉⢢⢤⠤⠄⢒⠶⡂⠈⠉⢹⠁⠀⠑⢬⡒⢄⠀⠀⢸⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠳⡀⠀⠀⠸⠘⣂⣀⡎⠸⠆⣤⣤⡇⠀⠀⠀⠀⠈⠢⡑⢤⡀⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢌⢢⡀⠘⠀⣄⣹⢛⡄⠻⠦⠴⠃⠀⠀⠀⠀⠀⠀⠈⠓⢌⠃⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡙⢤⡅⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠂⠁⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣴⣦⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⣴⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢸⣧⣄⠀⡀⠀⢀⣶⣿
⠀⠀⠀⢠⣴⣾⣿⠿⠛⠿⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⠀⠀⠀⣾⣿⣯⠋⠉⡁⠈⠹⣿⣿⠃⠀⠀⢀⠔⠛⠻⣆⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠃⠀⠀⣿
⠀⠀⠀⠘⢿⣿⡄⠐⠛⠆⢦⡿⠋⠀⠀⠀⠊⢠⡀⢠⣻⠀⠀⢠⣴⡞⠉⠙⠛⠙⠃⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣌⠟⠁
⠀⠀⠀⠀⠀⠉⣷⢉⢦⣼⣥⠀⠀⠀⠀⠘⠀⠀⢤⠿⣸⠀⠀⢺⣿⡇⠀⠀⠀⠀⢀⣿⣿⠆⠀⣀⡤⠤⠤⢦⣄⠀⠀⠀⠀⠠⠖⣨⡿⠉⠟⠃⠀⠈
⠀⠀⠀⠀⢠⣿⣿⣿⣆⠺⣴⣶⣶⣦⡀⠀⠀⠐⠒⠁⠇⠀⠀⠀⠻⠇⢀⡀⣀⠀⠸⠿⠋⠀⣼⠏⠀⠀⠀⠀⠹⣆⠀⠀⠀⢀⣬⣥⡤⠚⣞⣶
⠀⠀⣠⣾⣿⣿⣿⣿⣷⣄⠝⣻⣿⣹⣵⢲⡀⠲⣶⡆⠀⢀⡀⠀⡃⠰⡀⣒⠀⡄⠀⠈⠀⡀⣿⠢⢤⠀⢠⠤⠀⠟⠁⠀⣿⡇⣿⣿⢷⡶⣿⣿
⠀⢸⣿⠟⢋⢓⣾⣿⣿⣧⣤⣿⠟⠋⠁⠸⣿⣦⣽⣏⡀⠘⣷⡀⠀⢀⠀⠭⠀⠀⠖⠀⡠⠻⣜⣷⣾⣤⡄⠀⠀⠀⠀⢰⢁⣼⣋⠿⣤⡽⠿⢾⡇
⠀⠈⠛⠳⣤⣿⣿⣿⣻⣿⡿⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣿⢷⡤⣀⡙⢸⣋⣡⣀⡔⠁⠀⠈⢿⣿⣟⡛⠀⠰⠀⠀⢸⣾⣿⣿⡒⢂⣠⣐⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⠁⠀⣄⣄⣰⢿⣿⣽⣿⡿⠿⠋⠉⠀⠀⠀⠙⠁⠁⠀⠀⠀⠀⠺⢿⣻⡿⠿⠀⠀⠐⠈⠁⠀⢹⠿⣿⣿⣿⣿⣿⡿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣿⡽⠖⠚⡎⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠹⣿⣭⣿⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠂⡠⠶⠭⠭⠭⣉⡵⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⡇⠂⡆⢀⠔⢤⡇⠀⣇⠀⠀⠀⠀⠀⡞⠿⠀⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡉⠀⠀⠁⠁⡇⠀⢸⠀⠀⠀⠀⠀⣧⡘⠒⡡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⠬⣖⣊⡯⠇⡧⠄⢸⠀⠀⠀⠀⣰⡑⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⣶⢲⠶⠶⠷⠊⠁⠀⠀⢀⡼⣑⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠔⠒⠻⠶⠓⠒⠒⠦⣤⣄⣠⠮⣱⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⡅⠈⠉⠉⠉⠉⠒⠒⡎⢹⡗⣉⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠲⡇⠀⡩⢩⠉⠉⢱⡀⡇⠸⠭⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⢲⣷⠀⡍⣉⠀⠀⢸⡃⡇⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠑⢺⢸⠀⢟⣒⣁⣀⣸⠇⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡏⠸⡄⠀⠀⠀⠀⠀⠀⣇⡠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣈⡷⡀⠧⠤⣤⠭⠭⠭⢭⣷⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣰⠁⢂⣱⢠⣉⡇⠀⠀⠀⠀⡦⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠀⠈⠉⢸⠒⡇⠀⠀⠀⠀⣏⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢬⠃⠀⠀⠀⠀⡗⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢼⣺⢦⠀⠀⠀⡐⠫⡼⠒⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣀⡡⢼⠀⠀⠀⠹⣒⠠⠤⠤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠊⠁⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⢿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣾⣿⣿⣿⣿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠘⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠛⠋⠉⠉⠉⠙⠻⠟⠋⠉⠀⠀⡏⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠟⠋⠉⠉⠉⠉⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⡀
⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⣠⠞⠩⢀⡤⠶⣾⣷⠶⣄⠀⠀⠀⠀⠀⢀⠀⠌⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⡾⠁⠀⣰⠋⠀⠀⠈⠻⣷⡌⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠉⣼⠃⠀⠀⠀⠀⠀⠘⣿⡌⢧⠀⠀⠀⠠⠀⢀⠀⠀⢀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⡇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠸⣷⢸⡄⠀⠀⠀⠀⠀⠑⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢸⡇⠀⠀⠀⢰⣦⡀⠀⠀⣿⢸⡇⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⠈⣧⠀⠀⠀⢸⣿⡝⢦⡀⠏⢸⠇⡁⠀⡁⠀⠀⠐⠀⢸⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢹⣄⠀⠀⣸⠘⣷⡀⢹⡇⢹⠀⠈⡊⠀⠀⠈⠀⠀⠘
⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠹⣎⣡⠙⢦⡀⡟⣶⣿⣧⣼⠀⠸⡆⠀⠀⢆⡀⠀⠀⠀⠀⠈⠐⠢⢀
⠀⠀⠀⠐⡆⠀⡀⠀⠀⠀⠀⠀⠈⣻⣷⣤⣉⣓⣟⣉⣵⡇⠀⠀⢧⠀⡓⠒⠒⡄⠀⣀⡀⠀⠀⠀⠀⠙⢀
⠀⠀⣰⣇⠈⡏⠀⠀⠀⡐⠈⠀⣤⣇⠼⣟⣿⣯⣿⡋⡜⠀⠀⠀⠘⣆⠀⠀⠀⡇⠉⣄⠙⠋⠐⠒⠲⠄⠤
⠐⢠⠇⠸⡄⣇⠥⡀⠇⣘⠀⠐⠿⠿⣽⣧⣟⡗⣏⠟⠁⠀⠀⠀⠀⠘⣆⠀⠀⡇⠀⠀⠀⠀⠀⣌⡉
⣠⡏⠀⠀⢹⡇⠃⠐⠀⠄⠾⠂⢼⡆⣼⣙⡮⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⡁⠀⠀⠉⠈⠒⠂
⢸⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠃⠈⠋⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗⢂⡡
⠈⠓⠤⠔⠊⠀⠀⠀⠀⠀⠐⠆⠠⡶⠖⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⢶⣤⡼⢃⠈
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠁⠉⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣀⣀⣀⣀⣡⣤⣔⣀⣤⣤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⢧⣼⣿⣿⣿⣿⣧⣼⡿⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠆⠰⠀⠐⠀⠆⠄⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠁⠀⠀⠄⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠘⠁
⠀⠀⡈⠀⠀⠀⠀⠀⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠁⠀⡠⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⡀⠀⠀⠀⠀⠠⠂
⠀⠀⠐⠂⡀⣄⣤⡄⢠⣄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠁⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⢴⡄⠀⠀⠀⣲⠂
⠀⠀⠀⠀⡀⠈⠐⠀⠀⠈⠉⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⠉⡔⡁
⠀⠀⠀⠀⠁⠖⣀⠶⢄⡀⠦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠲⠆⢸⡆⠀⡼⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⢀⠉⠐⠒
⠀⠀⠀⠀⠀⠂⠀⠙⠉⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⡆⢰⠁⠀⠀⡬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⠐⠒⠠⢄⠄⠀⠈
⠀⢰⠋⠃⡇⣔⠀⡀⡀⢤⢠⠀⢆⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠘⠆⠀⠙⠂⠀⠉⠁⠀⠻⠐⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣄⠀⡀⠀⠛⠛⣤⣀⠀⣀⢴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠠⠀⢀⢀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⢀⡀⢆⠀⢀⠈⠉⡀⠐⠃⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣼⣦⡀⠀⠀⢀
⠀⠀⠈⠀⠀⠀⠈⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡀⢿⠀⡀⡞⠀⠉⢠⠸⢃⠗⢠⣀⡴⠀⠀⠀⠀⠀⢸⣷⠒⠋⢸⣧⠈⠒⣲⣿⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠘⢀⡀⠈⠀⠁⠀⠠⠄⠀⠀⠀⠀⠀⢐⣞⠠⠯⠬⠅⠡⠌⠋⢅⣲⠚⣄⡠⡴⠃⠀⠀⠀⠀⠀⢻⠙⠀⠀⠀⠀⠀⠀⠈⠀⢣⡀
⣧⣄⣀⠀⡀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠠⠠⠤⠀⠀⠀⠀⢀⠈⠉⠚⠁⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠄⠠⠠⠀⠀⠄⠀⠱
⠙⢿⣿⣤⢿⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⢀⠁⢂⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣌⢑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⣄⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣊⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣴⣲⡿⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⢠⣾⢿⣯⣷⣦⣀⣀⣤⣄⡀⠀⠻⣄⣠⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠟⠻⠿⠟⠀⠀⠙⢿⣿⡿⣭⣷⣿⣁⣀⣼⣿⣿⣦⣿⣄⡀⠀⠀⣀⣾⣦⣄⡀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠉⢻⣿⣿⣟⣽⣿⣿⡇⠀⠀⠀⠀⠛⣿⣿⣿⣭⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠙⠙⠻⣿⡍⠑⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣹⡆⡀⠀⠏⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣿⡛⢿⣿⣿⣿⣿⣿⠁⠀⠀⢀⣤⣀⣔⣿⣿⡿⠃⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠛⠋⠀⠀⠀⠀⠉⠻⢿⠿⠖⠶⠿⠿⠛⠉⠛⢿⣿⣷⣶⡾⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⠁⠉⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⣾⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣷⣾⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠰⠠⠞⢃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⢁⠀⠀⠀⠀⢀⡞⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢾⣿⠀⢴⣶⣶⣹⠇⢿
⠀⠀⠀⠀⠀⠀⠀⠀⣲⣀⠀⡀⠀⠀⡰⣷⣶⣿⠀⡖⠀⠀⠌⣰⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⣿⣿⣿⣿⠿⠘⠇⢠⣗⠀⣀⣠⣭⣿⣷⣷⣶⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠁⠀⢀⣤⡾⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣵⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣾⣶⣤⣤⣿⣿⢀⡀⣹⣯⣉⣹⣿⣿⣿⣿⠟⢉⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⡟⠙⣿⣿⣿⡍⢿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣁⣤⣬⡿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢨⡘⠁⠀⣿⣿⣿⣿⣿⣿⡃⠐⣿⣿⣿⣿⣿⣿⣯⣥⢈⣿⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣤⣤⣤
⠀⠀⠀⠀⠀⢀⡀⣠⠜⠳⢀⣠⣿⣿⣿⠿⣏⣿⣿⣧⣼⣿⣿⡟⠈⣉⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⣀⣤⣰⣿⣧⣴⣤⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠒⠏⢋⡁⢀⣼⢿⡿⣿⣿⡛⠁⢈⠉⠿⣿⣿⣿⣿⣿⣶⣿⡁⠉⠀⣀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠹⠿⠿⣿⢨⣏⣉⣿⣧⡤⢿⠁⢰⣿⣿⣿⣿⡙⣿⣿⣷⣶⣶⣯⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠺⢻⣛⣿⣿⢿⡿⠁⠀⠀⡿⣿⣿⣿⣿⣷⣿⣿⣿⣿⢏⡁⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣛⣿⠀⠀⠀⢀⢖⣴⣿⣿⣿⣿⣿⣿⡿⣿⣿⣎⣠⣴⣿⣿⣿⣿⣿⡿⠿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⣀⠠⠿⣿⡟⣻⣿⣿⣿⣿⣿⣿⣬⣿⣿⣿⡿⠟⠋⠉⠀⠀⠀⠀⠻⠄⢀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠠⠄⠀⠀⣤⢸⣾⡿⣿⡟⣹⠛⣿⣶⠟⢈⡟⠙⣛⣿⠛⢿⣿⠃⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣄⣠⠾⠿⡇
⠀⣀⠀⠀⡠⠆⠀⠀⣬⣿⠐⢿⣿⢁⠀⠙⢼⠀⠀⠀⠄⠁⢾⠁⠀⡿⠀⠀⠠⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⡀
⠶⠛⠛⠚⢡⡆⠀⠀⠻⡆⣶⠀⢻⣷⣆⠀⣶⢂⠀⠀⠀⠀⠀⠀⢹⠗⠀⠀⠀⢻⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⠇
⠀⠀⠀⠀⠈⠀⠶⠂⠀⠀⠉⠓⢻⣿⣿⡆⠀⠈⡷⠀⠀⠀⠰⠀⠈⠀⠀⠀⡀⠈⠉⢹⣿⠷⠶⣤⣤⣤⣀⣴⣶⣷⣦⣤⣄⣀⣴⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⠀⠀⠙⠉⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠑⠀⠀⠀⠀⠀⠉⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠒⠉⠁
⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⣀⠔⠈⡾⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣀⣀⠠⠀⣤⣤⠴⠤⣄⡀
⠴⠊⠀⠀⢘⠁⠀⠀⣉⣳⡄⠀⢧⠀⠀⣠⠡⢀⣜⡀⠀⠠⠀⢀⡴⡿⠟⠂⢀⡴⠋⠀⠀⠀⠀⢭⣢⡀
⠁⠀⠀⡢⢃⠐⠋⠉⠉⠁⠀⠀⠚⢠⡾⠟⠋⠉⢉⠹⠀⠀⣰⣫⡶⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⡠⣝⢿⡄
⢀⡤⣾⠱⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣰⠃⡋⠀⠀⡼⣋⡀⠀⠀⠀⠀⠀⣵⣌⢿⣷⣇
⢴⣾⢧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠂⠉⠋⠀⠀⠀⠀⠀⠀⠈⠢⡀⣦⠀⠈⢿⣷⣻⣿
⠹⣿⡀⠁⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⣀⡜⠀⢀⣠⠀⢀⡀⠀⠀⣤⠤⠄⠀⠹⡜⣷⡀⠈⢿⠻⢻
⠠⢹⠟⣷⣠⡶⠚⠒⠒⠛⠿⠿⣶⠄⢀⣴⡾⡿⠧⢤⣈⡏⢠⣬⡉⠀⠀⢰⣦⣤⡀⠀⠘⢮⢷⡀
⢀⢸⡀⡆⠉⣇⠀⠀⠀⠈⠻⠃⡸⠉⠹⡿⠀⠁⠀⢸⡟⣹⠞⢷⣿⠀⠀⠸⣷⣿⠇⠀⠀⠀⢷⣧
⠈⢢⠑⠄⡀⠘⠢⢤⣤⣤⠤⠖⠁⠀⠘⠷⠴⡧⢴⠿⢹⠁⠀⠈⠁⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⣹⠄⢀
⠀⠀⠀⠘⡇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠔⠁⠀⣢⠎⠀⣿⠀⠀⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢸
⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠑⠄⣀⠠⠇⠀⠀⡿⠀⣤⣿⡄⠀⠀⡀⠒⠀⠠⠐⠊⠀⠀⠀⠀⢠⣶⠏⣼
⠀⠀⠀⠀⢸⠑⢄⠀⠀⠀⠀⢀⣀⣠⠜⢀⡔⠁⠀⠟⠊⣧⠀⠀⠁⢀⣀⠔⠁⠀⠀⠀⠀⢠⡾⠋⢰⣿⣤
⠀⠀⠀⠀⢸⠀⠀⠉⠒⠢⡤⣀⣆⣀⣠⣧⠖⠀⣧⠀⣄⢂⣱⣄⠀⠀⠁⢀⠀⠀⠀⢀⠴⡿⢰⣶⣾⣿⣜
⠀⠀⠀⠀⡜⠀⠀⠀⠀⡼⢰⠂⠈⠁⢱⣁⡀⠀⡩⢎⣿⣿⣜⣿⢷⣦⣙⣉⣀⡴⠊⠁⠀⡇⢸⣿⣿⣿⣯
⠀⠀⠀⢠⠇⠀⠀⠀⠀⠇⣠⡤⢶⡖⠛⠿⠃⠀⠀⠐⢛⣙⡉⠉⠨⣿⣿⣿⣿⠂⠀⢀⠀⡱⡈⠋⠐⠻⣛
⠀⠀⠀⡞⠀⠀⠀⠀⢠⠟⠽⡷⡌⠁⠀⠀⠈⠉⠀⠉⠉⠉⠀⠀⠀⠀⠀⠹⣟⢲⣶⣵⠟⠁⠀⠐⠚⠉
⢀⣠⠞⠀⠀⠀⠀⠀⠘⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠈⠉⠀⠀⠀⠀⠀⠀⢠⡾
⠠⡇⠀⠀⠀⠀⠀⣀⠆⢠⡆⠀⣄⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠱⡀⠀⠀⠀⢸⠁⠀⢸⠇⠸⡿⠀⠈⠀⢀⡀⠀⠀⠀⠀⣤⣄⡀⠀⠸⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠈⠓⠢⠄⠚⠀⠀⡾⠀⡐⠁⠀⠀⣴⣯⣿⡆⠀⠀⢸⣾⣿⡈⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢸⡇⣴⣇⠀⠀⠈⠉⠛⠟⠀⠀⠠⡈⢉⡉⠁⠀⠀⠀⢸⣓⣀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢀⣠⠀⠀⠀⣛⠿⣎⣆⠀⠀⠀⠀⠈⠑⢛⡫⠭⠉⠀⠀⠀⠀⣠⣟⡱⡏⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠐⠢⠼⠷⠦⠜⠭⣷⣌⡝⠳⠦⣤⣤⣤⣀⣀⣤⣶⠿⣾⠟⠻⣫⠀⠀⠈⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠐⠂⠀⠀⠉⠉⠉⠁⠈⠉⠁⠀⠀⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣠⣴⣀⡁⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣽⣿⣿⠿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⢟⣿⡿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⢟⣿⣟⣹⣿⣿⣻⣿⡤⠂⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⣿⣯⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣳⣿⣿⣿⣿⣯⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠔⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⣏⡛⣛⣽⢿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠈⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠁
⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠠⠤⠀⠄⠀⢀⠀⢠⡄⠤⠄⠒⠉
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⢠⣄⣀⣠⣴⣶⣷⣞⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠋⠁⠀⠀⠀⠁⠀⠀⣠⠊
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠚⠛⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⡄⠤⠛⠉⠀⠀⠀⠀⠀⠈⢧⣄⣀⡀⠀⢀⣀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠤⠤⠶⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠁⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠚⠀⠀⠀⠀⠀⠠⠄⠤⠤⠤⠭⠀⠀⠀⠶⠶⠶⠶⠴⠦⠀⠀⠀⠀⠀⣤⠴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⢶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣦⣞⣠
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠐⠒⠒⠒⠒⠒⠒⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡇⣀⣀⣰⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⣖⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⣴⠃⢀⡴⢖⣶
⠀⠀⠀⠀⠀⠀⣿⡀⢸⡅⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤
⠀⠀⠀⠀⢀⣠⣬⣿⣦⣝⣶⣦⣴⣶⣾⣿⣿⣶⣾⣿⣿⣿⣯⣤⣤⣤⣀⣀
⢀⠀⢀⡴⢋⣴⣶⣿⣿⣿⠿⠛⠉⠁⢠⡿⠋⠀⠀⠀⠈⠻⣧⠀⠈⠉⠉⠛⠛⠷⢶⣦⣤⣀⡀
⠙⠶⠋⣰⡿⣻⣿⣿⠟⠁⠀⠀⠀⠀⣿⡇⣾⡆⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷⣦⣄⡀
⣀⣀⣴⠟⣱⢿⣿⠋⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢷⣤⡀
⠀⠀⣠⠼⠁⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢶⣶⡶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⡄
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡆
⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⢀⣤⣿⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⠀⢰⣿⠏⠁⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠰⣶⣦⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡿⠃
⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠉⠉⠉⢻⡿⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠉
⠀⠀⠻⣿⣶⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⡀
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠠⠤⠶⠾⠛⠋⠻⣦⣀⠀⠀⠀⣠⡆⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠏⠉⠉⠉⠛⢿⣦⡀
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠛⠋⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣀⣀⡄⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠀⠀⠀⠀⠀⢈⣿⣴⣶⣶⣦⣤⣀
⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠉⠻⣷
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⣿⣷⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⡶⠾⠿⠛⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⡠⢫⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿
⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⡐⡱⠁⠀⠀⠀⠀⠀⠀⢀⣠⣴⠿⠋
⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⡀⠀⠀⠀⠀⠀⢴⣦⣈⠏⡴⣤⣤⣤⣤⣤⡶⠶⠞⠛⠉⠁
⠀⠀⠀⢰⣿⠁⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠹⢿⣦⡀⠀⠀⠀⣠⣿⠋⠊
⠀⠀⠀⣸⡟⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠙⠿⣷⣶⣿⡿⣷⣷⣤⡄
⠀⠀⠀⣿⠇⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⢿⣟⣾⣷⣯⣭⡶
⠀⠀⢠⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⢠⢊⠟⠿⣾⠏⠉
⠀⠀⢸⣿⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠁
⠀⠀⢸⣿⣤⣤⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣾⠿
⠀⣀⣨⡍⠉⠉⣿⠋⠉⠉⠉⣿⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡏⠁
⠀⠻⣿⣯⣤⣤⡿⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠉⢉⣡⣤⣤⡤⠤⠤⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣧⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⢰⡏⠁⠀⡄⠀⢀⣀⡄⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠉⣤⣀⠀⠀⢰⠀⠈⣻⡆
⣀⣀⣀⣈⣻⣶⣶⣷⣚⣋⣉⣷⣶⣛⣀⣀⣀⣀⣀⣀⣀⣀⣘⣷⣶⣏⣙⣛⣷⣾⣶⣾⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠈⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⠔⠁⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠠⢀⡐⠂⢤⢀⡀⠀⠉⠀⣠⠊⠀⠀⠀⠀⠀⠀⠘⣆⠀⢀⡠⠤⠐⠈⠅
⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢂⠀⠈⠐⠢⢄⠀⠁⠢⣸⠃⠀⠀⠀⠘⠀⡀⠀⠀⢩⠖⠁⢀
⠀⠀⠀⠀⠀⠀⡆⠑⠠⢀⡀⢃⠀⠀⠀⠀⠉⠢⣄⣿⠀⠀⢀⠀⠀⠘⡗⠀⡰⢁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠈⢻⡀⠀⠆⠀⠀⠀⠘⣴⡥⠂⠀⠀⡆⠀⠀⢰⣆⠠⠒⠂⢩⠊
⠀⠀⠀⠀⠀⠀⢠⠀⡄⠀⠀⠘⣷⠀⡆⠀⠀⠀⠀⠀⢳⣆⡀⠀⠀⠀⢀⣿⠁⠀⠀⠀⡇⠀⠀⡜⠁⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⢸⠀⢃⠀⠀⠀⠘⣷⣴⡀⠘⣦⡀⠀⢸⠏⢳⡀⠀⠀⣸⣿⠀⠀⢀⡾⢃⣠⠞⠀⢀⡏⢀⡞⡀⠄
⠀⠀⠀⠠⠀⠀⠌⣇⢸⣆⠀⠀⠀⣿⣿⢷⣦⣄⣽⣷⣿⠀⠀⢹⠶⢶⡿⠿⠶⠶⠟⠛⣿⡥⢴⢂⣼⠣⠊⠁⠀⠆
⠀⠀⠀⠀⢡⠀⠀⠹⣦⡙⣷⣄⣰⣿⠛⠄⠈⠉⠉⠀⠈⢧⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⡾⢡⠚⠀⠀⠰
⠀⠀⠀⠀⠀⠣⡈⡉⠻⣿⢿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⣠⡤⠋⠁
⠀⠀⠀⠀⠐⠂⠙⠛⢦⣹⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢿⣾⣿⣥⠴⠋⠊
⠀⠀⠀⠀⠀⠘⡀⠀⠈⣿⡟⠀⠀⠀⠉⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⢀⣀⣀⠀⠀⠀⠀⠘⡟⠉⣠⣀⣐⣀
⠀⠀⣀⡀⠀⢠⣨⣄⣶⣿⠇⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣆⠀⠀⠀⣧⠞⠉⠀⢠⠐⠉⠁
⠀⠀⠀⠀⠑⣄⠀⠈⠻⣿⠀⢠⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⢻⣿⣿⣿⣿⡆⠀⠸⠁⠀⠀⢠⠛⢦
⠀⠀⠀⠀⠈⠈⢢⠀⣀⠸⠆⢸⡃⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣼⣿⣿⣿⣿⡇⠀⠀⡰⣻⢶⠃
⠀⠀⠀⠀⠀⠀⠈⡳⣝⠂⠀⠘⣷⣾⣿⣿⣿⠃⢀⡀⠀⠀⠀⠀⠀⢀⣀⡈⠻⠿⢿⠿⢟⠕⠀⠀⠀⢀⣃⠜
⠀⠀⠀⠀⠀⠀⠀⢠⡈⣀⠀⠀⠈⠋⠭⠑⠁⠀⢸⣿⣦⣤⣤⣤⣶⣤⣿⠃⠀⠀⠀⢈⠁⠀⠀⠀⢀⡻⡷
⠀⠀⠀⠀⠀⠀⠀⡀⠈⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠻⣿⠟⠋⠉⠉⡹⠋⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⢉⠁⠀⠂⢍⡛⠶⢦⣴⣤⣀⣀⣀⠀⠀⠒⠒⠈⠀⢀⣀⣀⣠⣤⡶⠷⠛⠉
⠀⠀⠀⠀⠀⢀⠤⠠⢷⡄⠀⠀⢱⣀⣠⣾⣿⠿⣿⠿⠿⠿⠿⠿⠿⣿⡿⠿⠿⣿⡷⢦⣔⠁⠀⠂
⠀⠀⠀⠀⠐⠁⣀⠠⠄⣈⡙⢷⡾⠋⠀⠀⣸⣆⠈⠉⠀⠀⠀⠀⠈⠀⠀⠀⠐⣿⡀⠀⠀⠑⣞⢁⠀⠀⠀⡀
⠀⠀⠀⠀⠋⠁⠀⠀⠀⢀⢘⣿⣷⣤⣤⠛⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⢳⣤⣤⡾⣧⠈⠁⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⠉⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⣀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⡈⠉⠙⣿⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡏⠉⢠⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠿⠿⠷⢶⣶⣶⣶⣤⣶⣶⡶⠶⠾⠿⠟⠛⠚⠛⠛

⠀⢀⣀⣤⠄⢇⡒⠀⠠⠁⠀⠐⠀⠀⠠⠀⠤⠀⢠⠀⠀⠀⠀⠀⠀⢰⣾⠄⠀⠀⠀⠀⠀⠀⠄⠰⠁⠀⠀⠓⠈⢒
⠈⠉⠁⠀⠀⠀⢈⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⣩⠹⢀⡴⠀⠠⠚⠀⠀⠂⠈⠉⠉⠁
⠀⠀⠀⠀⢤⡀⠢⠀⠀⠞⠀⠀⠀⢄⣆⣀⣤⠴⠂⠀⠀⠀⠀⠀⠀⠁⠒⠛⠃⣰⠀⡄⠀⠀⠀⠀⠀⠸⠂⠀⠀⣠⠄
⠂⠀⠀⢀⠘⢂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⣈⠀⡐⠀⢾⢧⡞⠃⠀⠀⠀⠀⠀⠀⢀⣠⣾⠋
⠒⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢀⡀⢄⠀⠈⠀⠀⠀⠀⠴⠶⠄⠀⠀⠉⡟⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⠀⠀⠳⢦⣄⣄⡦⠅⠁⠀⡀⠀⠀⠀⡀⠈⠀⢀⡀⠀⠀⠀⠰
⡀⠐⠀⠀⠐⠃⠁⠀⠀⠲⡄⠀⠀⢀⠧⠤⠙⠧⠼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢱⠀⠀⠀⠈⠀⠐⠇⡼⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠎⠀⠀⢀⠀⣀⠱⠀⠀⠀⠀⣄⠘⡶⠀⠈⢸⡀⠀⠀⠀⠀⠀⣠⠦⠌⠁⠀⠀⠐
⠀⠀⠉⠀⠀⠠⠾⠼⠛⠀⠀⠴⠂⠀⠀⠚⠛⠁⠈⣻⠀⠀⠀⠀⠀⠉⠓⠀⠀⠀⡁⡀⠀⠀⠂⠀⠀⠀⠀⠀⢀⢐⡄
⠀⠄⠀⣠⠤⡤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠂⠒⠄⠀⢠⠀⠀⠀⠁⠀⠀⠀⢒⠂⠀⠐⡀⠈⠉
⠀⢀⠞⡁⠀⠀⢿⣷⠀⠀⠂⣰⠀⠀⢤⣆⠀⠀⠘⣆⡀⣀⡴⠌⠴⢺⡀⠀⡄⡁⠀⠀⠈⠀⢀⠟⢂⡄⠈⠀⠀⠀⠈
⠀⠸⠀⠀⠀⠠⢑⣽⠀⠱⢤⠏⠀⠀⠀⠙⠧⠀⠀⠁⢊⣡⡤⠴⠕⣋⣧⠀⠈⢮⢦⡀⢀⡀⠁⠈⢀⠀⠠⠄
⠁⠸⣄⡀⡀⢀⡴⠃⠀⠀⠀⢀⢴⠄⠀⠀⠀⠀⠀⠀⢎⣡⠴⢞⠟⠋⠁⠐⠀⠀⠁⠁⠀⠀⢆
⠀⠀⠐⢩⠍⠉⠀⠀⠐⢿⠀⠉⠉⠃⠈⢀⡼⠁⠀⠀⠉⣆⠠⠀⠂⠀⠀⠐⠒⠈⠁⢔⡮⠇⢤⠊⠀⠀⠁⠀⠀⠀⠁
⠁⠀⠀⠂⠀⠀⠀⠀⠀⠘⠊⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⡀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⢐⣀⡀
⠀⠠⡌⠀⠀⠀⠐⠄⠀⡴⠀⠀⠀⠀⢐⡉⢳⣰⠀⠀⠀⠀⢠⠃⠀⡀⠀⠀⠀⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡙
⠀⢀⠃⠀⠀⠙⠃⠀⠀⢘⠊⠀⠀⠀⠉⠋⠠⠋⠀⠀⠀⢠⠃⠀⠰⠀⠀⠀⢀⡞⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⡄
⠀⠊⠀⠀⠀⠀⢀⡶⠶⡋⠉⠀⡀⠀⠀⠀⠐⣲⡄⠀⢄⡏⠀⠀⠀⠀⠀⠀⡂⠇⠀⠀⢠⣬⣀⠄⠠⠀⠂⣀⠃
⡤⠖⣿⣆⠀⠀⠀⠀⠀⠀⠀⠢⣄⣀⠀⣀⠀⠀⢀⠀⠀⠃⠀⠠⠄⠀⠀⠢⡃⠀⠀⠀⠀⠉⠓⠢⠤⠤⠖⠋
⢀⡀⠜⠋⠀⡄⢠⠀⠀⠀⠀⡄⠊⠉⠝⠓⠨⠭⠄⠠⠀⠀⠰⠀⠀⠀⠑⠀⠈⠂⠀⠀⠈⢄⠀⠄⡀⠀⠀⠀⠰⠛⠉
⠁⠀⠀⠀⠐⢂⠝⠂⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠂⠀⠣⢄⢠
⠀⠀⠀⠀⠀⣠⠖⠂⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⢂⣀⣀⠠⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⡷⢦⡀⠀⠀⢀⣠⡤⠤⠶⠶⠶⠶⠶⠤⣤⣀⡀⠀⢀⣤⠞⡟⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⢦⡉⠓⠾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠝⠛⠉⣠⠞⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠊⠁⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⡀⠀⠉⠑⠀⠀⠀⠀⠰⠊⠁⠀⡀⢠⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠐⠤⠘⢁⣁⣐⠀⠀⠀⠀⠀⠀⠀⠠⠐⣈⣥⣍⡀⠃⢀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡄⠐⠎⠀⣼⣯⣈⣿⣷⡌⠀⠀⠀⠀⠰⠁⣾⣿⣧⣠⣿⡆⠈⡄⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⡀⠀⡀⠀⢿⣿⣿⣿⣿⠇⠀⣠⠖⢄⠀⠀⢿⣿⣿⣿⣿⠇⠀⡄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠐⠀⠀⠙⠛⠋⠁⡀⠘⣇⠠⢸⠊⢄⠀⠉⠛⠋⠁⠀⠐⠀⢢⠏
⠀⠀⠀⢀⡞⣹⡄⠀⠀⠀⠀⠀⠈⢧⡑⢄⠀⠐⠀⠀⠀⠀⡠⠞⢻⣀⡞⠑⠦⣀⠂⠀⠀⢐⡠⠔⣡⠏⠀⠀⠀⡜⡆⠀⢀⣤
⠀⢀⠀⠈⢦⢞⠤⢤⡄⠀⠀⠀⠀⠀⠙⣦⢄⡁⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⢁⣀⢴⡎⠁⠀⠀⠀⣰⢁⣧⠞⠁⢻
⠀⢿⣍⢣⡈⣿⠶⠚⠀⠀⠀⠀⠀⠀⣼⣁⣀⣈⠉⠒⠲⠦⡄⠤⣤⣄⢤⣤⠤⠆⠖⠈⠉⢣⠠⡹⡄⠀⠀⠀⢳⣼⣏⠄⢀⡟
⠀⠀⠙⢷⡹⢿⡇⠀⠀⠀⠀⠀⣠⠞⢉⠄⠉⡩⠉⠈⢢⠀⠈⢁⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⡄⢣⣿⡀⠀⠀⢀⡏⣟⣚⣁⡤⠶
⠀⠀⠀⣀⣻⡄⠳⣄⠀⠀⠀⡼⠁⠠⠁⢀⡜⠀⡀⠀⡘⠢⠤⠊⠢⠴⠉⠲⠚⠙⠂⠊⠀⠂⣃⢸⣟⣷⡴⠚⠉⣀⣤⣤⣤⣤⠞
⠀⢰⠋⠠⢀⡿⣦⠈⣧⠀⢸⠃⢀⠂⢠⡊⠈⠁⠀⠒⡃⢀⢆⡀⡰⢄⢀⠴⣄⣀⠔⢄⡠⠋⠁⢸⠀⣿⠀⢠⣾⣩⠤⠤⣄
⠀⠛⠛⠛⠋⠀⠈⢷⡘⣆⣸⠂⠈⣠⠃⣀⠀⠀⠀⢸⡍⠁⢀⡍⠀⠀⣅⠀⠀⡄⠀⢀⣄⢀⡇⡌⢰⡏⣴⠏⠀⠈⠳⠶⠞⠁
⠀⠀⠀⠀⠀⠀⡀⠈⢷⡈⢿⣀⡞⠁⢀⡀⠀⡈⢠⠇⠈⠒⠊⠈⠒⠊⠀⠑⠊⠈⠁⠁⠈⢠⣿⠀⣾⠿⠁
⠀⠀⠀⠀⠀⣨⠟⢦⡈⣷⣞⠉⢀⣠⠞⡸⢫⢡⡟⠀⠁⠀⠈⠀⠀⠁⠀⠀⠀⠈⠀⠀⣰⣿⣾⠞⠁
⠀⠀⠀⠀⠀⢿⠀⠄⣷⣷⡉⠉⢉⡰⢏⣠⣧⢿⡀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⣡⢾⡿⠃
⠀⣶⠲⠦⢤⣌⡳⢴⡇⠻⡟⠛⠉⠀⣨⠟⠉⠳⢽⠷⡶⢦⢤⣀⣀⣀⣠⣤⠶⡿⡷⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠻⡄
⠀⠙⠳⡶⢤⣄⡈⠉⠛⠒⠛⠛⠚⠛⠃⠀⠀⠀⢲⡞⡇⣼⢧⡏⠉⠉⢧⣿⢠⡇⣿⡞⠒⠦⣄⣀⠀⠀⣀⣀⣀⠀⣾⠀⠀⣿
⠀⠀⢠⠷⣄⠈⠉⠛⠶⠶⢶⠄⣀⣤⠴⠶⠶⣤⣤⣤⣬⣡⣬⣄⣄⣤⣤⣥⣥⣼⣤⣤⣀⣀⠀⠉⠉⠉⠉⠍⣫⡝⢿⣤⠖⠃
⠀⠀⠘⣆⣸⠀⠀⢀⠀⣠⢏⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⢀⡤⢛⣉⣤⡴⠶⠶⠶⠶⠒⠶⢶⣄⣉⠓⠦⠄
⠀⠀⠀⠀⠁⢠⠞⡽⠿⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡴⢫⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⠦
⠀⠀⠀⠀⣠⣞⡼⣷⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠯⣄⣤⢟⡴⠋
⠀⠀⠀⠀⠈⠁⠀⠈⠓⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⠕⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢩⢇⠾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠒⠁⣎⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⣤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠿⠟⠛⠛⠛⠛⠛⠛⠿⣶⣄⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⣰⣿⠏⠀⠀⠀⣴⣾⣿⣦⠀⠀⢠⣾⣿⣧⠀⠀⠀⠀⠀⠀⠘⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢰⣿⡏⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠸⠿⠿⠛⢀⠶⠄⠘⢿⣉⠀⠀⠀⠀⠀⢠⠃⠀⣿⡟⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⢀⣼⡿⠁⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠁⠈⣿⠿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⠀⠐⡡⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣴⡟⠋⠀⢀⣤⠟⠀⠹⣿⣿⣿⣶⣶⣶⠆⠀⣰⠀⢀⡷⠀⢸⣶⣶⡾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⢿⣶⠿⠋⠉⣿
⠀⠀⠀⠀⢀⣠⣿⡋⠉⠀⢠⣾⣿⣄⣀⣠⣀⡙⠻⠿⠿⣿⣿⣦⣤⣿⣤⣼⣿⣤⣾⣿⡋⠀⢀⣀⣠⡾⠿⣦⡀⠀⠀⠀⠀⠀⣴⡿⣿⠀⠀⠀⠀⠀⣰⡟
⠀⢀⣴⠾⠛⠉⠉⠉⠻⣆⣸⡟⠀⠉⠉⠙⠛⢿⣦⡀⢀⣼⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⡿⠿⠿⣧⠀⠘⢷⣦⣤⣤⣤⣰⣿⠀⠘⠷⠶⣶⡶⠟⠋
⠀⣾⡇⠀⢀⣤⣤⡀⣀⣿⠟⠁⠀⠀⠀⢠⡄⠀⠙⢷⣿⣟⠛⠛⠛⠻⣿⡟⠹⣿⣛⣉⣀⣀⣠⣤⣶⣿⣶⣦⡄⠉⠁⢨⡿⠟⠃⠀⣠⣶⡾⠟⠀⠴⠂⠄
⠀⠈⠛⠛⠋⠉⠈⠙⡛⠁⡀⠀⠀⠀⠀⠀⠀⠀⣴⡶⠿⠿⠿⠷⠶⣾⣿⠃⠀⣿⡛⠉⠉⠉⢉⣉⣉⣿⠇⠹⣿⣀⣴⣿⣦⠀⢀⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠁⠀⠀⠀⢠⠀⠻⢷⣦⣤⣄⣠⣤⣴⣿⠀⢸⣿⣟⡛⠛⠻⠿⣿⣿⡁⢀⠆⠙⠛⠋⠀⠹⣷⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠉⠉⠉⣉⣽⣿⡄⢸⣿⡛⠿⣿⣷⣶⣤⣽⣿⢠⡇⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⡿⠟⢋⣩⣿⣷⣿⣿⣿⣦⣄⡙⢿⣯⡉⠀⠈⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⣯⣴⡾⠿⣿⣿⣁⣠⣿⣿⡿⠿⢿⣷⣿⡇⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠿⢿⣶⣤⣶⠟⠙⠷⣦⡤⡈⠙⣿⠟⢁⣤⣶⠟⠉⢙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡷⣦⡀⠀⠀⠈⢀⣀⡀⣠⡿⠀⠀⣠⣿⠀⠈⢻⣇⠀⠀⢼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠟⠛⠁⢸⣿⣤⣤⣾⠿⠛⠛⢿⣤⣴⠾⠋⠙⠷⣦⣤⣿⣦⠀⠈⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠈⠻⣿⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⠈⢻⣧⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣦⠀⠈⠙⢻⣦⣤⣄⡀⠀⠀⠀⠘⠟⠀⠀⠀⠀⣿⡷⠾⢿⣷⣾⡏⠀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⡾⠛⣿⠛⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⢈⣩⣿⠆⡼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢿⣿⠃⢰⣿⣶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⣾⠟⠁⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⠁⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡙⢷⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣧⣤⣄⡀⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠉⢳⡄⠈⢹⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⢿⣧⣀⠀⠙⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠷⠿⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣦⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⣿⢿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⡟⣏⣵⣿⣯⣭⣥⣦⣭⣽⣻⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣛⣷⡿⠿⠛⠋⠉⠉⠛⠻⣷⣨⣉⡛⠻⣿⢿⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢴⣾⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣉⣛⢦⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣏⣵⣿⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠿⠈⢿⣳⣄
⠀⠀⠀⠀⠀⡠⣶⣾⣿⣿⡿⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡃⠀⢀⣿⣟⠷⡄
⠀⠀⠀⠀⣾⣾⡿⣿⣿⣿⣿⣶⣶⠦⠀⠀⠀⠀⠀⠀⠶⢶⡶⠶⢄⠀⠀⠀⠀⠀⠈⢩⡒⠚⣿⣿⣦
⠀⠀⠀⠀⠿⣿⣧⣿⣇⣿⡏⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⡄⠀⠀⠀⠀⢜⣥⣚⢻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⢠⡾⢻⣿⢦⢻⠀⠀⠀⠤⡤⢞⣿⣿⡇⠀⠻⠀⠀⠀⡀⢹⡏⣯⣍⡻⣿⣷⣿⣦
⠀⠀⠀⠀⠀⣿⣿⣿⣾⣿⡴⢿⣾⣭⢾⣾⠀⠀⠀⠀⢔⠸⠿⠿⠅⠄⠀⠀⠀⢠⣌⡡⣿⣿⡟⣾⣳⣻⣿⣿⣷
⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠓⠉⠉⠀⣼⠏⠀⣠⡀⠀⠀⠀⠀⠀⠈⠐⠀⠀⣠⣲⣿⡟⡿⠈⣻⣾⣅⠙⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠘⢿⣿⡇⠀⠀⠀⢰⡃⠀⠀⠈⠗⣄⠀⠀⠀⠀⠀⠀⠀⢰⣽⣿⣿⠙⠃⠀⠀⠏⢻⡺⠰⣿⡹
⠀⠀⠀⠀⠀⣀⣠⣾⣿⡇⡀⠀⠀⡻⣷⣤⡄⠔⠀⠼⠀⠀⠀⠀⠀⠀⠀⢠⣷⣽⣿⠃⠀⢀⢓⣆⣼⢷⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠉⠙⣿⡇⡇⢀⠌⠃⢀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣿⢿⡟⠀⢐⣿⡓⢞⢁⡄⢐⣿⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣧⠙⢷⣶⣼⣶⣴⣶⣶⣾⣦⣤⡄⠀⠀⠀⠀⢸⠇⣼⣟⠀⠉⠉⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡌⠀⠀⢹⠋⠉⠉⠉⠀⣼⣿⠛⠁⠆⠀⠀⠀⠞⢠⣿⣿⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⢸⡆⠀⠀⠀⢠⣿⠟⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⠈⢷⠀⠀⢀⡾⠁⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡌⠷⡶⠏⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣶⣤⣤⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣡⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠶⠶⠶⣦⣀⣠⠴⠶⠶⠶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠉⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣠⡀⢀⡤⠖⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⣠⠟⠹⣶⠋⠀⠀⠀⠻⣄⠀⢀⠀⠀⢠⡴⢰⣾⣇⡼⢧
⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⢰⡄⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⡧⢠⣌⠳⠖⠋⠁⠀⠀⣦
⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⢠⠟⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣿⠏⢀⡀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢠⠟⠀⠀⠀⢹⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⣿⣧⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⣇⠸⡀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⣤⣤⣀⡀⠀⠘⠛⡇⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⢷⣿⡄⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠈⠙⠿⠁⠀⠀⢀⠇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡄⢻⣆⠀⠀⠀⠀⠰⣤⡀⢀⣠⡄⠀⠀⠀⠀⢠⣾⣿⡆⠀⠀⠀⠀⠀⢳⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠙⢷⡀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⣀⠀⢠⣀⠀⢉⡻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⣙⣳⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⣾⣇⠀⠀⢿⣷⣤⣽⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡟⠉⠉⠛⢳⡶⠤⠶⠚⠛⠉⠀⠀⠘⣏⠀⠴⠤⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣤⣀⣀⣼⣧⣀⣀⣀⣀⣀⣀⠤⠚⠉⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⣿⠃⠀⠀⣿⡉⣹⠏⠉⠉⠉⠉⢁⣀⠀⣼⠿⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣼⠏⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⢰⡏⢉⣿⣿⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⣼⢋⡴⠲⡄⠀⠀⣠⠖⠲⡄⠀⠀⠀⠉⠊⢹⡟⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⠃⠈⠳⠞⠃⠀⠀⠛⣤⠾⠁⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠲⣄⠀⠘⢷⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⣼⠋⢙⡆⠀⠀⠀⠀⠀⠀⠘⢧⡴⠇⠀⠀⠀⢳⡀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣀⡀⠀⠀⠙⠓⠋⠀⠀⠀⢠⠶⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡅⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠳⣆⡸⠃⠀⠀⠀⠀⢀⣀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⢀⡷⠀⠀⢀⣼⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢴⣶⠀⠀⠀⠀⠀⠀⣤⠶⣄⠀⠉⠉⠀⠀⠀⠺⣅⣿
⠀⠀⠀⠀⠀⠀⢸⡿⢠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⠿⠀⠀⠀⠀⠀⠀⢀⣀⢼⡇
⠀⠀⠀⠀⠀⢠⡟⠀⠙⣿⡽⣟⠓⣂⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣤⣤⣤⣤⣤⣤⣤⣶⠾⣿⠛⠊⢳
⠀⠀⠀⠀⢠⡎⠀⠀⢰⡟⠀⡏⠀⠀⠀⠀⠈⠘⡿⢻⡄⠈⠉⠉⠉⠛⠛⢻⣿⠹⠉⢻⠀⢹⠀⠀⠘⡆
⠀⠀⠀⠀⠘⢧⣄⡀⠸⡇⠀⠁⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⢸⡏⠀⢃⢸⡇⠈⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣤⣀⣀⣀⠀⠀⠀⠀⠹⠀⠇⠀⠀⠀⠀⠀⠀⠘⠁⠆⠀⠀⠀⣀⣠⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠿⠛⠿⠶⠶⠶⠶⠾⠿⣶⣶⣶⣶⣶⣶⣶⠶⠾⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢀⡀⣠⡀⢻⣄⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠙⠁⠀⠈⣻⠃⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⣺⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣄⣀⣀⡜⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⢀⣨⠟⠛⠷⣤⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣅⣀⣀⢀⣀⣈⣉⣉⣬⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠉⠉⠉

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⠿⣿⠿⠿⡿⠿⠿⢏⠹⠿⢿⡿⠿⠿⠿⣿⣿⣿⣿⡟⣻⣛⠛⠛⠛⣛⡛⣛⢻⣿⣿⠛⠛⠛⠿⠿⠟⢻⠛⠛⠻⣿
⣿⣷⣿⣶⣶⣷⣾⣶⣾⣶⣾⣶⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣀⠤⠁
⠀⠀⠀⠀⠄⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⡀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⣠⣾⠂⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠁⠀⣀⠀⡀⠀⠀⠂⠲⠉⠂⠀⢠⣀⣼⠀⠀⣤⣛⠄⡀⠀⠞⡄⣦⡄⠀⠀⡤⠄⠀⠐⢩⣘
⠀⠀⠀⠚⡅⠀⢐⣀⡄⠂⠀⠀⠀⠀⠀⠛⠛⠂⠀⠿⠿⠈⡀⠀⠈⣀⣿⡋⠀⠀⣳⣠⠈⠀⠈⣿⣶⡄
⠀⠀⠀⢠⡿⠆⠘⣿⡿⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠐⠀⠉⠁⠀⠀⠻⠛⠀⠀⠈⠻⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⢀⣀⣀⣀⣧⣤⡄⣤⣤⣤⣴⣶⣶⣶⢤⣾⣴⣶⣶⣶⣰⣶⣶⣶⠤⣤⣾⣦⣤⣤⣄⡀⠀⡀
⠀⠀⠈⠙⠏⠉⠛⠛⠏⠉⠿⡟⠉⠛⠻⠏⠘⠋⠀⣿⠏⢀⡿⠟⠁⢰⣿⠋⠀⠹⣿⠋⠀⠉⢻⣿⣿⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⠀⣾⠏⣀⣤⠞⠋⠉⠉⠉⠉⠉⠛⠛⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠞⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⢿⣄⣀⣀⠀⢻⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⣿⣀⣿⣤⡟⠿⠁⢼⡟⠛⠛⣧⣀⣿⣆⠀⠀⠀⠀⢵
⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⣃⣼⠻⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠛⠛⠻⠟⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⡀⠀⠀⠀⠀⠀⠀⠀⣾⡂⢠⠟⢸⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣴⠄⠀⢸⠃
⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣷⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠙⡄⢀⡎
⠀⠀⠀⠀⠀⢹⣸⣇⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⣼⠆⣸⠃
⠀⠀⠀⠀⠀⠀⣿⢸⣇⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡴⠋
⠀⠀⠀⠀⠀⠀⢹⣆⠹⣦⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠹⣧⠈⠀⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣀⣠⡾⠃⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⠼⣷⣄⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠳⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣿⣦⣤⣄⣀⡀⠀⠀⢀⣀⣠⣤⠞⠛⣿⡀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠟⠙⢿⣄⠈⠉⠙⠛⠚⠉⠉⠁⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠛⠿⠶⢶⣤⣀⣀⣀⣤⡶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⣠⡛⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⣾⣿⡿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠻⠶⣄⣀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠋⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠟⠶⣦⣬⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⢾⡷⠆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⣿⣧⣄⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢀⣀⡀⢠⣴⠀⢶⣾⣿⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣴⣶⣶⣦⣾⡿⠿⠛⠉⠁⣿⣿⣟⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠈⢻⡃⢸⡇⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠶⠄⢦⣤⠤⠴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣤⠶⠶⠶⢶⣤⡀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⣠⣤⠚⠛⠛⠛⠛⢳⣄⣼⠋⠁⠀⠀⠀⠀⠈⠙⣶⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢾⣧⣄⠀⠀⠀⠀⠀⠀⣨⣿⣤⣤⣀⣤⣤⣤⡤⠶⢛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⢿⣿⣶⣶⣾⡛⠾⠉⠈⠙⠛⠋⠶⠶⠶⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⣄⡀⢠⡀⠀⣠⡄⠀⠀⠀⠀⠀⣶⡦⢀⠀⠀⠀⠀⠀⢀⣤⣾⣦⣄⠀⠀⠀⠀⠠⠐⠒⣄⡒⠀⠄
⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⣼⣿⡗⣲⡄⠀⠀⠀⠀⠛⠛⢻⠛⠛⠃⠀⠀⠀⢃⢠⡦⢐⣴⡆⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣯⠀⠀⠀⠀⠀⣐⣀⣸⣀⣐⡀⠀⠀⠀⠨⢑⡨⠤⢂⡰⠁
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⣾⡟⠛⠛⠛⣿⡆⠀⠀⠀⢸⡏⠉⠉⢹⡇⠀⠀⠀⠀⣴⡺⡽⣖⢄⠠⠀⠀⠀⢀⣤⣤⡄⣤⡤⣄
⠀⠀⡟⠀⠰⡇⠀⠙⡇⠀⠀⠀⢸⡷⠤⠤⢼⡇⠀⠀⠀⢸⢞⢎⢏⣎⣾⠀⠀⠀⠀⢸⣿⣿⣷⣿⣤⣿
⠀⠀⣿⣲⣴⢳⣴⣾⡇⠀⠀⠀⢸⣇⠀⠀⢸⡇⠀⠀⠀⠈⣯⢗⣷⣮⣎⠀⠀⠀⠀⠻⠟⠃⠀⠈⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠉

⠀⠀⣦⣬⣀⣀⣥⣴⡄⠀⠀⠀⢠⣶⣾⣷⠂⠀⠀⠀⠀⠀⠀⢀⣒⣒⡀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣷⡄
⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⠱⢆⣾⣿⠀⠀⠀⠀⢀⣿⡿⣿⣷⠄⠀⠀⠀⢸⣿⡏⣄⡌⣿⣿
⠀⠀⠿⠿⢿⡿⡿⠿⠃⠀⠀⠀⠈⠀⣾⣿⠿⠃⠀⠀⠀⠀⣼⣿⣷⣶⣶⣆⠀⠀⠀⠀⠉⢡⣟⣣⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢉⠉⠃⠀⠀⠀⠀⢠⠖⢻⠛⠲⡄⠀⠀⠀⠀⠾⠮⠴⠧⠷⠇
⠀⠀⠀⢸⡁⠀⠀⢀⡀⠀⠀⠀⠀⠀⣹⠶⠀⠀⠀⠀⠀⠀⡟⠑⣾⣷⠊⣻⠀⠀⠀⢠⠀⢴⠄⢴⠄⢠
⠀⠀⣀⣀⣙⣲⣒⣋⡀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠘⠾⣅⣨⠶⠃⠀⠀⠀⠈⢶⣾⣶⣾⣶⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠠⣀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠋⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢈⢁⠜⠀⡤⠈⢈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠂⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠸⢲⠛⠊⠂⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⡀⡀⠄
⠀⠀⠀⠠⠄⠀⠀⠨⢨⠅⠀⢠⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠂⢯⡤⢄
⠀⠀⢀⢈⠆⠀⠀⠀⠁⠋⠃⠉⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠌⢒⣄⠀⠀⠁
⠊⠛⠃⢀⠄⠀⠀⠀⠀⠀⠏⠂⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠀⠀⠀⡹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠞⠶⣶⡅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠐⠚⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠄⡀⠈⠉⠀⠀⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⡤⠀⠀⡀⠀⠀⠸⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣀⠀⠀⠰⣠⠉⢉⡤⠄⠀⠀⢀⡠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠡⠄⢨⢹⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂
⠀⠀⠀⠀⢠⠀⠂⡐⠰⢀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠠⠀⢄
⢀⡄⠀⠀⠀⠀⠐⢷⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠
⠀⠀⠀⠀⠀⢰⣄⠀⡀
⠀⠀⠀⠀⠀⠀⠟⠋⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠲
⠀⠀⠀⠀⠀⠀⠀⢄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⠈
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣶⣶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣴⣶⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠿⠿⠿⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⢑⣰⠇
⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⠂⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠂⡀⢀⠀⠐
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠠⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣶⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡏⠙⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⢂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠠⡀⠈⢧⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠⡞⠑⠠⣀
⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⣰⡁⠀⡉⡆⠀⢘⠀⠁⠂⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠘⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢴⡀⣀⠀⣢⠀⠈
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠷⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡠⠤⣄⢤⣀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡷⠀⠠⠹⠇⠙⢦⠀⠀⠀⠀⠀⢠⣤⡾⠛⠛⠳⠿⠗⠀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡈⠇⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⣼⠽⠁⠀⠀⠀⠀⠀⠀⠀⠹⢿⢲
⠀⠀⠀⠀⠀⠀⠀⡜⢹⣿⡥⢶⣶⣿⣷⣿⣶⣶⣿⣷⠀⠀⠠⢿⡀⠀⠀⠀⠀⠀⠀⠀⢀⡈⢂⢸⠀⡀
⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⢷⣶⣿⡿⣿⡟⣿⣷⣿⣿⡀⠀⣾⣮⣷⡦⠶⣤⣞⠋⠢⠀⠾⠇⢸⣎⣸⠇
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠉⠀⣾⢁⠀⢸⣿⡿⢃⣼⡏⠀⠉⠀⠀⠛⠸⠛⠂⠀⣼⢧⡧⡊⠙⡦
⠀⠀⠀⠀⠀⠀⠈⢿⣧⣬⠑⠂⠀⠈⣿⡟⢀⡾⠋⠀⠀⠙⢿⠀⣀⣀⣤⡄⠀⠀⠀⠀⠻⣿⣿⠇⣿⡤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢉⣟⡀⣤⣤⡄⠟⢠⡎⠀⠀⠀⠀⠀⣸⣜⣿⡃⠀⢇⠀⠀⠀⠀⣶⣉⣿⡇⠛⠁
⠀⠀⠀⠀⠀⠀⡀⠀⡼⣟⢰⣀⣸⠿⡷⢦⠄⠀⠀⠀⠀⢀⣿⡹⠿⢦⡐⠊⠀⢀⣠⣰⣿⡟⣷⣱
⠀⠀⠀⠀⠀⠈⠀⠸⢰⡟⣿⣿⣿⣿⣿⡟⠀⣄⠀⠀⠀⠀⠙⠦⡀⠀⣀⣀⢀⣾⣛⣿⡟⠠⣿⣿⡀
⠀⠀⠀⠀⠀⡴⡃⠊⢸⠁⢿⠿⡄⠀⠙⠁⠄⠸⡆⠀⠀⠀⠀⢠⣇⠉⠡⠀⢿⣽⣾⠏⢀⣴⡿⣿⠃
⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⡸⢛⠂⠀⠀⠀⠀⠀⡲⠉⠀⠀⠀⠘⡿⠳⢴⣶⣶⣾⣶⣶⣿⣿⡇⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠉⠀⡀⣿⠃⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠛⠛⠉⠻⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⢠⣜⣿⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣄⣆⡀⣈⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠉⠛⠿⠛⣿⣿⠏⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⡄⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢸⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠉⡀⠁⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠂⠀⠀⣦⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⡇⠁⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢈⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⣄⠀⠀⢠⣼⠃⠐⠦⣄⡀⢠⣤⠀⠘⢷⣦⡀⠀⠀⣸⡇⠀⣀⣀⢻⠏⡜
⠀⠀⠀⠀⠀⠀⠀⠁⠠⠘⣿⣗⡄⠀⠈⠙⢻⡟⠂⠤⠀⠉⢿⣦⣴⣿⣿⠀⠈⠉⠳⠶⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠂⠀⠀⠀⠀⠁⠒⠀⠀⠀⢸⣙⢃⠜⠉⠀⠀⠀⠀⠈⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⣤⣭⣿⡶⢾⡿⠾⡟⠛⠻⢶⠿⠶⣦⣤⣠⡟⠛⢷⣿⡛⠛⠷⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⢀⣴⡾⠟⠉⠉⠑⢄⠑⠄⠘⠀⠀⠁⠀⠀⠀⠈⠙⠿⣦⡀⠙⢿⣄⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⢻⣆⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠈⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠚⠉⠙⠳⢄⠀⢠⠀⢀⠔⠊⠁⠀⠙⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⣠⣄⡀⠈⠑⠎⠟⠁⣠⣤⡄⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡀⠀⠀⠀⠀⠀⢉⣻⠷⠄⠀⢴⠿⠋⠁⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠛⣿⣶⣄⠀⣴⠟⠛⠛⢷⡄⠀⢠⡶⠛⠛⢷⡆⠀⠀⣀⣴⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢠⡾⢛⣿⣿⣯⠙⢿⣏⠀⢰⠄⢸⣧⣤⣿⠀⣤⠀⢈⣿⠶⠟⣽⣿⣼⣟
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠸⢃⣼⣿⡇⠈⢿⣦⣀⣠⣾⣯⣾⣿⣦⣀⣠⡾⠃⠀⣼⡿⢿⡌⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠺⡿⢈⣿⡀⠀⠉⠉⠉⢻⣦⣴⠟⠉⠉⠉⠀⢀⣼⢏⣿⠄⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠛⠙⣷⣄⠀⠀⠐⢿⣿⡿⠷⠀⠀⠀⣠⡾⠻⢿⣥⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣄⣉⣉⣉⣁⣤⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡿⠿⠿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣇⠀⣶⠀⢀⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⣿⣤⣾⣿⣿⢙⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣠⣤⣴⣿⠋⣿⣿⣿⣧⢿⣿⣿⣿⡟⣏⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠦⠛⠉⠀⠀⢹⣿⣿⣿⣸⣿⣿⡿⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣧⡄⠀⠀⠀⠀⠈⣿⠛⠛⡿⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡃⠀⠀⠀⠀⣼⠃⠀⣸⣇⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠰⣶⣤⣼⣧⣤⣴⡟⠙⠻⠿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⡄⣤⢠⢶⡀⡄⡄⢴⢠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⡀⠀⠀⢀⠰⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡀⠌⠀⢸⠿⢻⢸⢸⡇⣿⠇⢸⢸⡇⠸⠓⡀⠰⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠢⠔⠀⢁⠀⠀⠆⠈⠠⠀⠠⠉⠁⠒⢠
⠀⠠⣐⣦⣤⣄⡢⡌⠁⡀⠀⠘⠀⠘⠈⠛⠁⠘⠀⠚⠈⠓⠀⠀⠀⠁⠀⠀⠈⠀⠀⠃⠐⢤⠀⠈⠂⠀⠀⡠⠃⠈⠇⠀⠀⢐⡀⣥⠀⣀⠴
⠀⠌⠛⠛⠋⠉⠀⠃⠀⠈⡆⠀⠈⠄⠀⢀⠄⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠆⡠⠃⠀⣬⠆⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠈⢀⢐⡀⣀
⠀⠄⠀⢿⣿⡗⠀⡬⠀⢂⣀⠀⠀⡼⠰⠄⠀⡀⣀⠀⠀⠃⠀⠀⠠⠞⠀⠀⠀⢀⠑⠐⡂⠡⠄⣀⠀⠀⠣⠀⡔⠉⠢⡀⠀⡰⠊⠁⠀⠀⣄⠑⡄
⠀⠈⠂⠠⠭⠀⠊⠀⡈⣤⣴⣶⣶⣶⣶⣦⣤⠀⠀⠈⠀⠃⠀⠀⢀⢀⡀⠀⠀⠀⡄⠙⠤⢄⠀⣻⠈⢈⠁⠸⠀⠀⠀⠓⡀⣄⠀⢁⠀⠌⠠⢀⠇
⠀⢀⠄⠠⠠⡀⠀⠀⡇⣿⣿⣷⣿⣟⣿⣿⣿⠀⠀⠀⡆⢰⠀⠀⠙⠺⠹⠈⠠⠀⠰⠀⠀⢛⠒⠚⠀⠂⡃⠘⡐⠀⠀⣈⠃⠈⠐⠀⠀⠀⠀⠁
⠀⠊⠀⠀⠀⠈⢂⠀⡇⣿⣿⡟⡿⣿⡿⢿⣿⠀⠀⠀⠆⠀⣤⠆⠂⠐⠒⠒⠒⠒⡖⠀⠀⠸⠀⠀⠀⠨⠁⠀⢱⠀⠀⡄⠀⠀⢠⢴⣯⡀⠀⠈⠢
⠰⣅⣀⣀⢀⣀⠃⠀⠇⠛⠿⠿⠿⠿⠿⠟⠣⠀⠀⢀⠀⠀⠉⠀⢀⡠⠄⠐⠀⠤⡀⠀⠀⠀⠆⠀⠀⡠⠀⠀⠈⠒⠒⠁⠀⠀⠁⠀⠈⢿⣄⠐⡰
⠀⢽⠔⠛⢸⡇⠀⠀⠸⠋⠉⠉⢉⣉⡉⠉⡈⠉⠻⠅⡠⠐⡠⢤⣌⡰⢄⠀⠀⡠⠄⢹⠒⠄⡀⠀⠀⡴⠒⠒⢠⡀⠀⠐⠄⠀⠐⢀⠀⠸⠿⠋
⠀⢺⢤⡄⢾⠀⠀⠀⠀⢸⠉⠀⠀⣠⡤⠀⠃⠀⢀⡐⠀⠠⡀⠀⠀⠀⢀⠀⢸⠀⠀⣘⠢⠱⠈⢄⠀⠀⠀⠒⡆⣶⠐⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠙⠲⠧⠟⠂⠀⠀⠀⠈⡄⠀⠠⡤⠛⠀⠸⠀⠑⢄⠀⠖⡱⠆⢩⠀⢊⠐⢚⡁⢎⠠⢊⠜⢀⠒⠀⠢⠄⠤⠬⠤⠤⠤⠊
⠀⠀⠀⢀⣤⣶⣶⣦⣀⠀⢃⠀⠀⠶⠐⠂⠀⡆⠀⠀⠑⠠⢀⠀⠀⠉⠉⠀⠀⠀⠀⢁⠠⠐⠁⠀⠀⠀⠀⢀⠠⢀⠀⠀⣿⣻⠏⣿⡟⣿⡏⡉⣿
⠀⠀⣴⢟⣭⡶⣶⣭⡻⣆⠘⠒⠒⠈⠉⠉⠀⠀⠀⠀⢀⣀⡤⡀⠀⠀⠀⠀⠀⢀⢠⠶⠤⠤⠀⢄⠀⠀⢠⠁⠀⠀⢑⠀⠟⠛⠛⠃⡀⠈⠛⠛⠛
⠀⠰⠿⠟⠁⠀⠈⠙⢳⢿⠀⢠⣴⣶⣶⣶⣶⣶⣶⡄⠈⢥⠜⠁⣀⡤⡄⠀⠼⢁⣄⡀⠀⠘⠃⠃⠀⠀⢸⠀⠀⠐⠘⡄⠀⠀⢘⠀⠉⠈⠈
⠀⢃⣀⡀⠀⠀⠀⠀⣄⣠⠀⢸⡏⠁⠸⠀⡏⠠⢸⡇⢠⣀⢶⡄⢈⣀⠀⠀⠄⠈⠛⢀⠔⠒⠤⣀⡸⠀⠈⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠄
⠀⠀⢹⣷⣄⠀⢀⣼⣿⠀⠀⢸⣇⠀⡀⡄⠃⠰⢺⡇⠈⠁⠀⢠⣼⣙⠃⠀⠈⠒⠒⠁⠀⣀⠀⠀⢀⡀⠀⠑⢰⡶⠒⠁⢐⠀⠀⠀⠐⠈⠀⠐
⠐⠂⠘⠋⡻⠀⠘⢋⡙⠀⠀⢸⣿⢾⣷⣿⣾⣤⣾⣿⠀⠀⢀⠀⠈⡉⠀⠀⠀⠀⠀⠀⢺⠁⠋⠙⠛⠛⣿⣆⠘⠷⠇⠀⠺⣶⣿⣛⣓⣚⣻⣷⣾
⠀⠈⣠⣉⠤⡀⠀⠀⣈⡄⠀⣰⣿⠀⡇⡆⢀⠘⢸⣿⠀⢰⠓⠲⠾⠶⢾⠄⢄⠀⠀⠀⠇⠀⣘⢀⡀⠀⠈⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⢀⠿⠏⢀⡠⣿⣿⠿⠷⠀⠉⢿⣶⡷⠶⠿⠶⠾⠟⠀⢸⠀⠀⠄⠠⠀⠀⠀⠀⢀⡞⠋⡧⠰⠎⠀⡤⠢⡇⠀⠀⠀⢀⠀⠀⠀⠀⠀⢈⠅⡇
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⡀⠀⠀⠀⠀⠀⢸⠀⠐⠀⠀⢠⠆⠌⠀⠸⡄⠀⡀⠀⠀⠀⠃⠀⢸⠀⠂⠀⠞⣀⣀⡀⠙⠀⠈⠀⠁
⠀⢀⡀⠤⠤⠤⠀⠀⠀⠀⠀⡘⠀⠀⠀⠘⠀⠀⢀⣀⡀⠀⠑⠀⠀⠀⠊⠀⠀⠰⠀⠘⠒⠁⠀⠀⠀⠧⠴⠃⠐⠀⠀⢼⣿⣿⣿⡗⠀⡠⠀⠐⠄
⠀⠂⠀⠀⠀⠀⠀⣳⠀⠀⡖⠃⠀⣀⠀⠀⠑⡄⢸⠀⠀⠉⠐⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢠⠄⠀⠀⡄⠀⠀⠙⡍⠉⠀⠘⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠇⠀⠈⠿⢿⠀⠀⠃⠈⡀⠀⠀⠀⠀⠀⡥⠐⠭⠂⠀⠀⠀⢀⠄⠠⣀⠀⠀⣀⠀⢀⠇⠀⠀⢠⠇
⠀⠀⠀⠀⢶⠂⠀⢸⡀⠀⠀⠀⣀⠀⢀⣀⡀⠀⠀⠇⠀⠀⢀⠔⡨⢔⠁⠀⢀⠀⠀⠐⣵⡿⢷⡌⡆⠀⠜⠀⠣⡀⠀⢔⠺⠂⡄⠀⢸⠀⠘⠃
⠀⡀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠰⠟⠣⠞⠃⠈⠀⢀⠀⠀⠈⠁⠀⠸⠀⠀⠀⠠⡊⠀⠙⠾⠋⠈⠀⢸⡀⠀⠀⡄⠀⠀⠀⣤⡆⠀⠈⡄
⠀⠑⠚⠚⠛⠛⠛⠋⠀⠀⠑⠆⠀⠀⠀⠀⠀⠐⠃⠀⠉⠑⠒⠒⠢⠤⠆⠀⠀⠀⠈⠢⠠⠊⠀⠀⠀⠈⠑⠀⠊⠁⠀⠀⠀⠈⠁⠀⠀⠐⠀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣷⣦⡀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⢀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⡄⢀⣠⣼⣿⣿⣿⣿⣏⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡟⠁⠀⠈⢦⣠⠒⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠁⠂⠀⠀⠈⠀⠀⢏⡻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⢻⠈⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠉⠃⠀⠀⠈⠙⠲⣄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢿⣷⣶⣿⡿⠋⠁⠀⠉⠻⡇⠀⠀⠀⢀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡀⠀⠀⣠⣾⣦⣄⣀⡀⠠⢿⣷⡀
⠀⠀⠀⠀⠀⠁⠬⡀⠀⠈⢰⣿⣿⡿⣇⠀⠀⢰⠂⠀⠀⠀⠀⠀⠛⣠⡞⣠⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠉⠀⠘⣿⣿⣿⣿⠃⠀⠀⠈⠻⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠻⠛⠁⠈⠢⡀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠁⠒⠂⠤⡀⠀⠀⢸⡋⢇⠀⠀⠀⠸⠟⠛⠛⢄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠀⠀⠀⠱⡀⠙⣦⣀⠀⠀⠀⠀⠀⣀⠹⠁⢀⡀⠀⠤⠄⠀⠀⠀⠀⣇⠈⢄⣀⣀⡀⠀⠀⠀⠈⣢⣤⣶⡁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠈⡉⠈⠛⠛⠓⠂⠂⠙⣃⠜⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⢸⣿⣿⣧⣀⠀⢀⣠⣿⣿⡿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⣀⣀⡩⠭⣄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⢶⣶⣶⣦⣄⠀⠀⠀⠀⠙⢽⣻⣿⠉⠀⠀⢀⣨⠿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢒⢾⣿⡁⠀⠀⢄⠀⠊⠀⠀⠀⠀⢀⠔⠁⠀⣠⣾⠟⠋⠉⢉⡉⠣⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⣤⣤⣿⣷⣄⣀⣀⡐⠁⠀⢠⣾⠏⣰⣦⠀⠀⠛⠟⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠒⢳⡞⠋⠀⣙⡿⢿⡿⠋⠌⠀⠀⣰⡿⠁⠀⠀⠁⠀⠀⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠐⠁⠊⢡⣦⣽⣿⣿⠀⣁⠀⠀⣠⡾⢿⡀⠀⠀⠀⠀⢀⠄⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⣀⣅⡀⠀⡈⠛⢿⣿⡿⠀⠈⠙⢶⡟⢰⣶⠍⣓⡠⠤⠀⠁
⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⣙⠛⠉⣻⣖⠂⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠈⣷⡀⠈⠙⣷⣤⣈⣃
⠀⠀⠀⠀⠀⠀⠐⠿⣷⣄⣰⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⣠⠄⠀⠀⠁
⠀⠀⠀⡀⣀⠀⠀⠰⠁⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠍⣶⠐⠆⠀⠀⠘⡄
⡔⠈⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡄⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⡈⠁⠀⠀⠀⠀⡅
⠑⠄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡶⢿⠆⠂⠀⢴⠀⠃
⠀⠀⢆⠀⠀⠀⢸⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⢈⠣⠀⢀⣀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠀⠀⠈⠤⡀⠀⠀⠀⡌⠀⠄
⠀⠀⠀⠄⠀⡀⠘⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠰⠀⢀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠐⡄⠀⠀⠀⠢⠤⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⡀⠃⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⡀⠀⠀⠀⠀⠀⢀⡠⠞
⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠤⠀⠉⠑⠒⠒⠀⠋⠭⠀⡁⢀⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣔⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⡄⠘⠚⠓⠂⠀⠀⠀⠀⠀⠈⠂⠀⡀
⠀⠀⠀⠀⢠⠈⢀⣀⣀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡤⠀⡀
⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠅⠀⠀⠀⠀⠀⢀⡦⠘⠁⠀⠀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⡆⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⣇⠀⠀⢀⣴⡶⡊⠀⠊⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⡀
⠀⢀⢀⠃⠠⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢹⠀⢀⡿⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⢂⠈⠀⠀⠀⠈⢆
⠀⣏⢀⢱⡇⠀⠀⠀⠀⢠⡄⠀⡀⠀⠀⢤⣤⠀⢼⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢂⠀⠀⠀⠀⠘⡆
⠀⠹⡄⠀⠁⠀⠀⠀⠈⠉⠀⠀⠁⢸⠀⠒⠊⠀⠡⡀⢰⢇⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠈⡀⠂⠀⠀⠀⢻
⠀⠀⢧⠀⡆⠀⠀⠀⠀⡀⠀⠀⠀⠐⠄⠀⠀⠀⠀⢱⡿⠀⢤⣴⡒⠒⠂⠀⠀⠐⠿⠀⠈⠉⠀⠃⠸⠀⠀⠀⢸
⠀⠀⠀⠀⢻⠀⠀⠠⣀⠙⠲⣄⣀⡀⠤⠀⠀⠀⢀⢾⡇⢀⠞⠉⠀⠀⢀⠇⠀⠀⢀⠀⠀⠀⠀⢸⠀⡆⠀⠀⢸
⠀⠀⠀⠀⠘⡇⠀⠀⠘⡗⠢⠤⠠⢤⡄⠀⠀⠀⡜⠸⡇⢞⠀⠀⠀⢠⡀⠀⢀⠠⠈⠀⡀⡴⠀⢸⠀⠁⠀⡄⣾
⠀⠀⠀⠀⠀⠻⡀⠀⠀⠈⢦⠀⠀⠀⠀⠀⢀⡜⠀⠀⢧⠈⢦⠀⠀⣀⡉⠉⠀⠀⠀⠁⠀⠇⠀⢸⠀⠀⠀⢣⡏
⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠒⠄⠀⣠⠎⠀⠀⠀⠈⢆⠈⢆⠀⠈⢧⡀⠀⢀⡀⠄⠈⠀⣠⠚⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡅⠂⠠⢄⣀⠠⠇⠀⠀⠀⠀⠀⠈⠢⡀⠢⡐⢤⣥⠥⠀⠀⢀⣤⠞⡁⠀⠈⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠦⠽⡀⠀⠀⠎⣠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣷⢤⡀⡠⢴⠚⢩⠆⠀⠷⡄⠀⠀⠀⣶
⠀⠀⠀⠀⠀⡰⠋⠘⠠⠀⠁⠀⠀⢼⣈⡟⢶⠠⢀⣀⠀⠀⠀⠀⠀⠈⣻⠶⣀⡞⠀⠇⠐⣄⠀⢳⠀⠀⢠⡏
⠀⠀⠀⢠⠞⠀⡀⠀⠀⠀⠑⠓⠄⡶⡞⠓⠞⠙⠀⡀⠐⠂⠛⠁⣋⠱⠃⢀⡜⠀⡼⠀⠀⠘⡆⠋⠀⢀⡞
⠀⢀⡴⠃⢀⡜⠁⠀⣀⠀⠄⠈⢲⢱⠃⣶⢀⠃⣨⠁⢰⠘⡄⠈⠇⠀⠠⢸⠴⠊⠀⠀⠈⢶⢹⠄⣠⠏
⠰⠋⢠⠀⡞⣿⠫⣥⡄⣶⣀⡤⣌⠈⠐⠃⠈⠐⠘⠂⠌⠠⣈⠓⠀⠠⠄⡈⠀⠀⠀⠀⠠⣪⠏⠀⡇
⠘⢆⡆⠀⡇⢸⠠⡈⠱⣐⠀⠀⠀⢹⣶⠤⠤⠀⠂⠀⠀⠀⠈⠓⠴⠃⠀⠖⠀⠀⠀⠃⠞⠁⠀⠈⠁
⠀⠀⠙⠄⠹⠄⠣⣑⠂⢼⠃⠀⠀⠈⢟⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⡤⠀⠀⠶⠎⠱⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⡆⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠘⡆⠀⠁⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠶⢶⠣⠀⠀⠀⠀⠀⠀⠁⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣷⠲⠙⠓⠉⠓⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠉⠀⠀⠀⠀⠀⠀⠀⠉⡻⠛⠲⢤⡀⠀⠀⠀⠀⠀⠠⠤⠀⢀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⠑⠀⡎⠀⢀⣀⣀⣀⠤⣤⣤⠤⢂⣁⣀⡀⠀⠹⡄⢠⠦⠀⠀⠠⠀⠈⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡗⢉⣉⠀⣤⣤⡄⠀⠀⠀⣤⡀⠀⣉⡑⠂⡗⠀⠋⠀⡀⠀⠑⠨⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⡚⢡⣿⣿⣿⣷⣶⣤⡄⢠⣤⣶⣾⣿⣿⣿⡆⠙⡄⠀⠞⣡⠀⠀⠀⠀⠀⠀⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠧⠀⠻⣿⣿⣽⣿⡿⠀⠀⢿⣿⣯⣿⣿⠟⠠⢚⣷⠀⠀⠁⠀⠀⠀⠔
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡐⣚⠁⠈⠛⠛⠛⠑⠛⠚⠊⠛⠛⠋⠁⠀⣐⠃⡼⢂⡠⠀⠀⠀⠀⠀⠮⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠉⢧⡀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⣠⠏⠈⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⣀⠞⢉⠉⠒⠤⡙⢦⣄⣀⣀⠀⠀⠀⣀⣀⣤⠞⠁⠀⠀⠀⠊⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢀⡀⠀⠀⠀⡍⠀⡀⠀⠀⠀⠈⣦⠤⠽⢿⣉⣉⣹⠿⠷⠦⢤⠀⡀⠤⢄⠄⡀⠀⠀⠀⢀⠀⠤⠤⠒⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⢀⠤⠄⠀⠀⠀⠀⠐⠋⢹⠀⠀⠀⠉⠉⠁⠀⠀⠀⡞⠘⠀⠠⠀⢀⠈⠆⠀⠀⠀⠳⣤⡀⠀⠀⠐⠴⠇
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠠⠀⠀⠀⠐⠁⠠⠒⢄⠀⠀⣸⡀⠀⠀⠀⠀⡀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠋⠀⠀⠠⢹⣦⣌⠛⠿⠶⢶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⡀⠀⠀⠀⠰⠀⠀⠀⠁⠐⠙⡇⠀⠀⢀⠘⠄⠀⠀⢠⡇⢀⠀⠀⠀⠂⠀⠀⠀⠁⠌⢉⡙⠁⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⢀⣄⠤⢤⣿⣄⣀⡴⠛⣄⢠⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣤⠀⠀⢀⠢⣀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⠘⠁⠀⠀⠀⠀⠉⠑⢄⠀⠘⣾⠇⠀⠀⠀⠀⠀⠀⠀⢸⡇⡞⣿⠃⠉⠁⠀⢬⠀⠀⠀⠀⣀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠊⣾⠁⠈⠉⠉⠉⠉⠀⠀⠘⣿⣿⣉⠀⠀⠀⢀⡴⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⡷⠀⠀⠀⢠⣴⠀⠀⠀⠀⢿⠈⠻⢃⠂⠤⠞⠁⠀⠀⠤⠀⠴
⠀⠀⠀⠀⠀⡴⠊⠉⠉⠙⠺⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⢸⢹⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⡂⠀⠀⠄⡀⠀⠈
⠀⠀⠀⠀⢸⠀⢀⠀⠈⠐⠄⣸⡆⠀⠀⠀⠀⠀⢀⣠⠊⣿⠀⠀⠀⠀⣾⠘⡆⠀⠀⠀⠀⢷⠘⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢄⣸⣀⣀⣨⠉⠑⠉⠉⠀⠀⠉⡇⠀⠀⠖⠋⠀⢧⣤⡀⠤⠄⡞⠅⠀⠀⠀⠁⠘⠁⠀⠘⠀⡄
⠀⠀⠀⠀⠀⠈⠻⠤⣄⣠⠶⣹⠋⠉⣹⠉⡁⠀⠰⠀⠀⣠⣖⣠⠀⡄⠀⠀⠀⠀⠀⠀⠄⣴⡒⠀⠀⠀⠀⠀⠀⢀⡠⠈⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⢀⠈⠠⠴⠃⠠⠁⠀⠀⢀⣴⢋⡽⠁⠀⠀⠀⠀⠀⠀⡲⠘⠻⠶⠻⢦⣄⠀⠀⠃⠉⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠐⠀⣀⣷⡏⠀⠀⠀⠀⡀⠀⡜⠉⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠙⡆⠀⠀⠀⠐⠂⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠣⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠡⠀⠀⠂⡠⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⣷⣶⣶⣾⣧⣔⡠⣶⠶⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠛⠛⠟⠻⣿⣿⣖⠛⢀⣀⣠⣌⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⢨⠉⠛⠿⠿⠿⣿⡟⡿⣯⣶⡤⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⢸⡿⢷⡌⢻⡷⣤⣤⣤⣽⣷⣆⠀⠀⠀⠀⠐⣿⣿⣷⣆⠐⠂⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠁⣿⣷⣿⣿⣿⣹⣿⣿⣿⣿⣿⣶⣤⣤⣿⣿⣿⣿⣷⣦⣶⣾⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⡀⡠⠒⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⢿⡉⢹⠧⠀⠹⣿⣿⣿⢿⣿⣿⣿⣿⣿
⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠁⠈⣧⢸⠀⢃⠀⠈⢰⣟⠀⣿⣿⣿⣿⣿
⠀⢠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⣏⣿⣿⣯⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠂⢀⠀⠀⠠⠀⠒⠈⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛
⠃⠈⠙⢶⣦⡀⠂⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠇⣀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣏⢽⣿⣿⣿⣿⣿
⣤⣀⣀⣾⠡⣷⣎⢷⣮⣱⡄⠀⠀⠀⠀⣶⠈⠉⠁⠀⠈⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⠋⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡆⣉⠉⢠⣻⣿⣷⣴⣦⣴⠀⢴⢦⣿⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⣨⣽⣿⣿⣿⣿⣛⡀
⠋⠉⠙⠛⢷⣾⣷⠘⣿⣿⣿⣿⣯⣶⡇⠨⣾⠂⠙⠆⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣶⣿⣿⣿⣏⣠⡜⠿⠁⣤⣤⣀⣀
⣷⣤⣄⡀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡄⣸⣗⠀⢈⡵⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡇⠈⠀⠀⠉⢸⠀⠿
⣄⠀⣌⠁⣄⢸⣿⣿⣿⣿⣿⣷⣿⣿⢿⣿⡟⠻⢟⣿⣿⠋⠓⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠘⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘
⣿⣨⣿⢰⣷⣼⣿⣿⣿⣿⠿⠿⣿⣿⣟⠛⠛⠛⠻⣿⣇⣤⠀⠀⢸⣿⣿⣿⣿⣿⡿⡿⣿⣿⠁⠀⠀⡄⣸⣿⣿⣿⣿⠀⠀⠀⠀⠀⡀
⣶⢮⣿⣾⣿⣿⣿⣿⣿⣏⠀⠀⢿⣿⣿⠁⠴⠀⠀⢿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣦⣿⣿⣿⡀⠀⢰⣇⣿⣿⣿⣿⣿⣤⣤⡆⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣿⣿⣆⣐⠀⠀⣻⣻⣿⣿⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⡿⠧⠀⢸⣿⣿⣿⣿⣿⣿⣏⠀⠻⣄
⣿⣿⣿⣿⣿⣿⣿⣟⠉⠉⣿⣿⣿⣿⣿⡟⢩⡌⠛⠉⣿⣿⣯⡄⠀⣼⣿⣿⣿⣿⡿⠟⠁⠀⠀⡀⣾⣿⣿⣿⣿⣿⣿⣿⡄⢲⣿⡆
⣿⣿⣿⣿⣿⣿⠿⣛⠷⠺⣿⣿⣿⣿⣿⡇⠀⣀⠀⠀⢻⣿⣿⣿⣶⣿⣿⣿⣿⣿⡃⠀⣀⣀⣤⣿⣿⣿⣿⣿⣿⡿⣏⡿⠇⠀⣿⡁
⣿⣿⣿⣽⡿⠦⠚⠉⠀⢠⣿⣮⢿⡿⢿⣧⠀⠉⠀⠀⠸⣿⣿⣷⡹⣿⣿⣿⣿⠏⠁⣰⣿⣿⣿⣿⣿⣿⠋⠉⠉⠀⠈⣵⠃⠀⠛⣿
⢸⣿⣿⣿⠀⠛⠀⠀⠀⠀⠀⢁⠚⣿⣿⣿⡀⠚⠃⠀⠀⣿⣿⣿⣇⠈⠙⠉⠛⢀⠀⠛⠻⡿⢿⠟⢅⠠⠀⠀⠀⠀⢠⣭⠶⠲⣶⣿⡆⠀⢀
⣼⣿⡿⠇⠟⠀⠀⠀⠀⠉⠀⠀⠀⢙⢩⣿⣇⠀⠀⢺⡧⢸⣿⣿⡿⠀⠀⠀⠀⠀⠂⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠱⠤⠴⢿⣿⡇⡀⢸
⣿⣿⠃⢰⠀⠀⠀⠀⠀⢴⡄⠀⢤⢸⠘⣿⣟⠓⠒⠿⠟⢋⣿⣿⠷
⣿⣿⣒⢸⠀⣷⠀⠀⠀⠀⠀⠀⢰⣿⣇⣿⣿⣿⣷⣤⡶⠿⠟⠛
⢿⣿⣯⣶⣦⣿⣴⡄⠀⠟⠃⣀⣸⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠈⠉⠙⠋⠈⢫⡼⠟⠚⠾⠿⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣀⢀⣀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⡄⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠐⠀⢀⠀⢄⠀⠀⠀⠀⠀⢀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠨⢀⠌⠃⠀⠀⠀⠁⠀⠀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⡄⢀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢠⣤⣤⣤⠀⠀⠀⠀⠀⠀⢣⠀⠀⠈⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢡⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠐⠂⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠂⡀⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄
⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡠⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⢄⠁⠀⠠⠈⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀
⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠐⠀⢀⠔⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠤⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢄⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠈⠀⠀⠀⠀⠉⠙⠀⠀⠀⠁⠀⠀⠂⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠢⠋⠀⡠⠊⠈⢐⡄⠀⢄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡀⠰⡄⠀⠀⠀⠀⠀⠀⡀⠀⢸⠄⠈⠜⠀⠀⠀⠀⠀⠀⠉⠐⠠⠄⠀⠀⠠⠄⠀⠀⠀⠄⠿⢀⣆⢠⠎⠀⠀⠀⡜⠀⠀⠀⡅⡀
⠀⠐⠀⠀⢃⠀⠈⢆⠀⠀⢀⠀⠀⡟⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢣⡀⠀⢀⡌⠀⠀⢀⡜⠀⣸⠂⠐⠐⠒⠂
⠀⠀⠀⠀⠀⠐⠤⠸⠦⣀⠜⠁⠈⠀⠀⠀⠀⠀⠀⢀⠀⠄⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠉⠉⠁⠑⠤⠤⠋⠔⠚⢁⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊⠁⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣽⣭⣭⣯⣵⣭⣽⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣶⣷⣶⣶⣾⣿⣼⣿⣶⣶⣶⣿

⠀⠀⢀⣴⣾⣿⣿⣿⣿⣶⣄
⠀⢠⣿⢻⠇⠀⠀⠀⠈⠉⢻⡇⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠘⠀⠀⠀⠀⢀⣴⣶⣶⣶⣦⡀
⠀⠸⣿⣾⣶⣶⣤⣴⣶⣶⣬⣇⠀⠀⠀⢠⣿⣿⣿⣯⣽⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠛⠉⠉⠉⠙⢿⣆
⠀⢰⣟⠛⠛⢻⡇⣿⠛⠿⡟⣿⠀⠀⣶⠊⠀⠀⠀⠉⠋⠙⠛⣿⡄⠀⠀⣠⣴⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⢀⡀⠀⢀⣀⡈⣿⡄
⠀⣿⡟⣶⣾⣿⣷⣿⣿⣿⡇⣿⡇⢀⣥⣤⢀⣶⣶⣦⣴⣶⢷⣿⣷⠀⢸⡭⠭⠛⠛⠻⣿⡀⠀⠠⠤⠂⠀⠤⠤⠀⠀⢀⢠⣿⣿⠚⠿⠿⡶⡾⠿⠛⣿⡇
⠀⠈⠉⠛⣿⣯⣉⣹⣿⣻⠃⠉⠀⢸⣇⠈⠁⢀⣀⠃⠸⣇⣈⣽⠏⣰⡟⠀⠀⠀⠀⣀⢸⡇⠀⡀⠀⣀⡀⠀⠀⠀⠀⠀⣿⣿⡿⠁⡀⠌⣁⠈⢁⡈⢿⡇
⠀⠀⠀⠀⠻⠻⠿⢿⡿⠋⠀⠀⠀⢸⣿⡀⠀⢰⡏⠀⢹⣿⠰⠋⠀⢿⠀⠸⠿⠀⠘⠓⢀⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣿⣿⣧⠀⠙⢯⣉⡨⠋⠀⣼⣿
⠀⠀⠀⠀⠀⣰⣾⣿⣅⠀⠀⠀⠀⠈⣽⡄⠀⠀⠀⠀⠘⣻⠄⣀⠀⠀⣄⠠⣆⡀⢀⡔⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣷⣤⡀⣀⢀⣠⣾⣿⡿
⠀⠀⠀⡀⠈⠻⣿⡿⠋⢀⡀⠀⠀⠀⢉⠀⠀⢾⣦⣶⡈⠁⣿⣿⠀⠀⣈⣤⣌⣀⣈⣄⡀⠀⠀⠀⠀⣠⠀⢠⣄⠀⠀⠈⣿⣿⣿⣿⣿⡏⢿⣿⣿⣿⣿⡗
⠀⠀⠘⡇⣠⡄⠈⢠⣤⣾⠛⠀⠀⠀⠀⢢⣼⣷⣿⡋⢹⣶⠈⠛⠀⠐⣿⣿⣿⣿⣿⣿⣿⠀⠀⣴⣿⣿⣶⣿⣿⣿⣦⠀⠈⢻⣿⣿⣟⣁⣼⣿⣿⣿⠿⠃
⠀⠀⠘⠁⠛⠋⠀⠛⠋⠉⠉⠀⠀⠀⠀⠈⠉⠉⠉⠉⠈⠉⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠋⠀⠀⠛⠙⠛⠛⠛⠛⠛⠛⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠠⣄⣄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡄⢠⠀⡂⠀⠀⠀⣀⣤⣠⡈⡆⠀⠀⠀⠀⢰⠀⡄⠀⠀⢀⣴⠿⢿⣦⠀⠀⠀⠀⠀⡜⢃⠀⠀⠀⠀⠀⠀⣀
⠀⢸⣿⠻⠏⣿⡇⠀⠀⠀⣈⠀⠶⠀⠀⠀⣿⣿⠛⣿⡆⠀⠀⠐⣻⡏⠁⠁⠀⠀⢰⡇⢸⢀⡇⠀⠀⠘⣿⣤⣴⡿⠀⠀⠀⠀⠋⠠⠋⠀⠀⠀⣿⣫⣿⣻⡇
⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠁⠈⠀⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⣒⢴⣲⠀⠀⠀⣠⣴⡞⢿⡆⠀⠀⠀⠉⠸⢃⡀⠀⠀⣾⢷⣶⡶⣶⠀⠀⢠⡤⡤⢠⢤⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⣠⣄⣄⠀⠀⠀⠀⠴⣷⡄
⠀⠀⢶⣿⣾⣿⠀⠀⠀⣷⣴⠿⠟⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣿⣿⣿⣿⣿⠀⠀⢸⡆⡇⢠⣾⠀⠀⠰⣷⠀⠀⣾⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⢰⣿⡇



⠀⠰⠶⠆⠰⠆⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⣀⣠⣞⣟⡷⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⢠⡄⠀⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⢀⠀⠀⡀⠀⠀⢠⠤⠤⠤⠤⢤
⠀⢀⡀⠰⢆⡰⠆⠀⠀⢠⣄⢠⣤⠀⠀⠈⢿⡾⠾⠁⠁⠀⠀⣶⣦⣶⣤⣤⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⢺⣧⣼⠇⠀⠀⠀⢸⢡⡆⡟⠀⠀⢸⠹⠀⠇⠳⢸
⠀⠈⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠁

⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⣐⡿⢣⣤⡄⠀⠀⠀⠄⠛⣿⡆⠀⠀⣀⣀⣤⣄⡀⠀⠀⠠⠀⠀⢂⠀⠀⠀⠀⠀⢠⣮⠛⠀⠀⢠⠊⡉⣳⣀⡀⠀⠀⠀⢰⣦⡤⠀⠀⠀⣄⣰⡀⡄
⠀⠘⠿⢣⣾⠍⠀⠀⠘⣿⣦⡄⠈⠀⠀⠀⣿⡏⣶⢎⣿⠀⠀⠀⠱⣖⣻⡆⠀⠀⠀⡴⠟⠁⠀⠀⠀⠘⢄⣀⠜⠉⠁⠀⠀⠛⢻⣿⠟⠀⠀⠘⡘⢤⢼⡘
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⠉⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠈


⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⠀⣼⣿⣿⣧⠀⠀⢸⢾⡯⡭⡿⠇⠀⢀⣾⣶⣶⣾⣷⠀⠀⠠⠤⢤⠤⡄⠀⠀⢠⣼⣟⡷⣤⠀⠀⠀⠀⡖⠿⠀⠀⠀⠀⠀⡠⠚⠁⡀⠀⠀⣤⣶⠀⠀⡀
⠀⠀⠘⠾⠷⠃⠀⠀⠈⠀⠀⠁⠁⠀⠀⠈⠻⠟⠉⠻⠟⠀⠀⠠⠤⠦⠹⠄⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠶⠀⠚⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠛⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠐⠠⠢⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢠⡄⠀⠀⠀⠀⣿⠁⣿⠀⠀⠀⠀⠘⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠄
⠀⢸⣿⡇⠈⠁⠀⠀⢰⣋⣟⣹⣏⡇⠀⠀⠘⠁⠀⠁⠀⠀⠀⠀⡏⠀⢹⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⢸⠀⠀⠀⠀⡇⠀⠀⠦⢀⢀⠂
⠀⠈⠉⠁⠀⠀⠀⠀⠀⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠈⠁


⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣼⣿⣿⣼⣷⣶⣧⣼⣧⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣷⣶⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠖⠛⠛⠉⠉⠙⠛⠓⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⣯⠄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⢀⠞⠁⢠⠎⢠⠃⠀⠀⠀⠀⠀⠀⡆⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⣠⡴⢚⡋⠉⠉⠙⠛⠶⣤⡀
⠀⠀⠀⢠⠏⠀⠀⡏⢀⡇⠀⠀⠀⠀⠀⠀⠀⡇⠘⣏⠳⢤⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣴⠛⠉⠀⣀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⣟⣀⣀⣀⣇⣸⣀⠀⠀⠀⠀⠀⠀⠀⢹⡀⣸⣦⣄⠈⠑⠲⠤⣄⣀⣀⣸⡏⠙⣧⣞⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠉⠉⠁⣏⠹⣿⣿⣍⣿⡟⢻⠛⠛⢻⣿⣿⣟⣹⡏⣣⠀⠀⠀⠀⠈⠉⡙⠋⢻⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⢘⠦⣈⣉⡩⡞⠁⠘⢦⡀⠘⠿⣿⣿⢟⡵⠁⠀⠀⠀⠀⠀⠀⢷⡴⠞⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⢠⡤⠀⠀⠀⠝⠲⢦⡤⠶⡋⠁⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠈⠳⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢁⠀⢰⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠠⡀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⠀⢸⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⡼⠀⡜⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⣀⠀⠀⢀⣀⣀⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⢀⠇⢠⠃⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠤⠭⠝⠛⣛⠏⠙⠃⠤⠤⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡌⢀⠎⢀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⢦⡄⡀⢀⠤⣀⡠⠢⠴⣅⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⡀⠆⠀⡄⢸
⠀⠀⠀⡀⠀⠀⠀⠀⠀⣸⣍⠀⡼⠀⠈⠁⠀⠀⠀⠸⡆⠈⢙⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣇⣧⠀⢡⡈⢆
⢀⠀⠴⠀⠠⡀⠄⣐⠭⠒⠉⢻⠃⠀⠀⠀⠀⠀⠀⠀⢿⠛⠙⣕⠦⣀⠀⠀⠀⢀⠒⡀⢀⡀⠀⠀⠀⠀⠀⠙⠿⢦⣄⣉⣒⣿⡶
⢁⣚⢀⠀⠠⠂⠁⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠙⠪⢍⣒⡖⠁⠌⠰⣪⠄
⠀⠉⠀⠂⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠘⠢⠤⣐⠑
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣴⣋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⣄⣀⣀⣀⣤⣤⣤⣀⣀⣀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣸⢸⠇⠄⠂⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⡘⠓⠀⠌⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢐⠅⠀⣠⠆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢤⣀⣈⣉⣋⡩⠇

⠀⠀⠀⠀⠀⠀⣴⣦⡤⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠀⣠⡤⠤⠤⠂
⠀⠀⠀⠀⢸⣿⣿⣽⣧⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⠞⣡⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠘⢛⣭⣷⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⣾⠛⡩⠭⠭⣙⠻⣷⡄
⠀⠀⠀⠀⠀⠈⠙⢻⡏⠀⠀⠀⠀⠀⠀⠐⢷⣦⣀⠀⢿⣿⣧⣎⡤⠒⠢⣌⠳⣌⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣀⣀⣤⣤⣤⣶⣶⣶⣾⣿⣿⣾⣿⣿⣷⣬⣁⣉⢎⠣⠈⢦⡙⢿⣦⡀
⠀⠀⠀⠀⠀⣠⣴⡾⠿⠛⠛⠉⠉⠀⠀⠀⢠⡾⠋⠁⠀⣈⡙⢿⡉⠙⠛⠿⣷⣵⣄⠙⢦⠙⣿⣄
⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠿⠍⣼⠇⠀⠀⠀⠈⠙⣷⣗⡄⢳⢸⣿
⠀⢠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣦⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠈⢿⣾⣸⢸⣿⡄⢀
⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡸⣧⠙⠛
⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠴⣦⣤⣀⠀⠀⠀⠀⢻⣿⣷⣽⣷⡄
⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣷⠉⠀⠀⠀⡾⠟⠻⣿⣿⠿⠊
⠀⠀⠀⠈⠙⠛⠿⠶⠶⣶⣶⣶⣶⣶⣶⡶⠶⠿⠆⠀⠀⠀⢀⣼⠋⠀⢸⡆⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⢀⣀⣀⣠⣤⠶⠛⠁⠀⢀⣼⡇⠀⠀⠀⢿⣦⣶⡿⠋⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠹⣯⠀⠀⠀⣠⣴⣿⣿⠃⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⣀⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠹⣿⣿⡿⠛⠁⣰⠟⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⢠⣶⣦⣤⣾⣧⣾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠈⠛⠶⠶⠞⠋⢀⣾⠀⠀⠀⢀⣿⠁⠀⠀⠀⠈⠉⢉⣿⣿⣿⡿⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠋⠁⠀⠀⠀⣸⡟⠀⠀⠀⠀⣀⣴⡿⠋⠉⠉⠀⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣍⣉⣛⡓⠒⠒⠶⣆⠀⣠⠤⠦⠴⠶⠶⠶⠲⣿⡃⣀⣤⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠈⠉⠉⠉⠉⠛⠛⠛⠛⠒⠒⠒⠶⠶⠶⢾⣿⠛⠋⠉
⠀⠀⣠⣶⣄⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣸⡇⠀⣹⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⣿⠀⢀⡟⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣤⠿⠆⣼⠁⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠿⠴⠞⠛⠛⠿⢶⣦⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠈⠿⠷⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠻⠷⠶⠶⢶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢤⣄⣀⣀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⣤⠈⢿⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⠀⢸⡇
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣷⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡏⠉⠋⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠴⠖⠒⠦⠤⢤⡀⠀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⣴⠶⠯⣭⣤⣤⣄⣀⣀⣠⠴⣲⣿⣛⣋⣉⣀⣀⣀⣀⠉⠉⠉⠉⠉⠛⠒⠒⠲⣤⡄
⠀⠀⠀⠀⡇⡐⠒⠒⠒⠒⠒⠠⡀⡿⢸⡇⠀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣉⡉⠉⠛⠓⢲⡏⠀⡇
⠀⠀⠀⠀⡇⡨⠭⠭⠭⠭⠉⢉⠀⡇⢸⠀⢀⡇⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⡷⠀⢸⠁⢸⠟⡆
⠀⠀⠀⠀⡇⠑⠒⠒⠒⠒⠒⠊⢠⡇⢸⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡾⠀⢸⠀⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⡇⠀⡟⢰⠇
⠀⠀⠀⠀⣧⠀⠘⠋⠒⠒⠂⠀⢸⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠃⢀⡇⣸
⠀⠀⠀⠀⢻⠀⠀⠀⣀⠀⠀⠀⡿⠀⢸⡀⠘⠒⠒⠶⠶⠦⠤⠤⠤⠤⠤⣤⡼⠀⣸⠀⣸⠖⠃
⠀⠀⠀⠀⢸⡀⠀⠀⠒⠁⠀⠀⣇⡴⠋⠛⠓⢲⢖⡶⠒⣶⡶⠶⠤⢤⡤⢤⡤⣤⡿⠞⠁
⠀⠀⠀⠀⠀⠉⠉⠙⠛⢛⣛⡛⠉⠀⠀⠀⡊⠁⠸⣧⣤⣀⣉⣉⣉⣉⣤⡾⠀⠈⠒⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡼⡩⢭⢭⠭⡭⢭⢉⡉⣛⣓⡒⠛⠻⠿⠯⠭⣭⣁⣀⠀⠀⠀⠀⠀⠀⡡
⠀⠀⠀⠀⠀⠀⠀⡼⡰⢥⠯⡯⣹⣩⣏⣞⣱⡓⡞⢺⢡⢮⠏⣴⣰⠂⡰⣹⠀⠀⣠⠖⣻⠟⠙⣆
⠀⠀⠀⠀⠀⠀⢸⣥⣍⣉⣚⡒⣓⣒⡒⠀⠧⠼⠥⠃⠎⢞⣲⣲⢃⢜⡴⠁⠀⡼⠉⠉⠉⠒⢤⡟
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠒⠒⠾⠿⠭⠭⢤⣄⣒⣲⡾⠋⠀⠀⠀⢷⣄⣀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⢀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⣀⡀⠀⢀⠤⠒⡤⡀⠀⢀⡠⠤⣀⠀⢀⡀
⠀⠀⢸⠏⢳⣝⣿⣦⣙⣷⣌⠻⣿⣕⡄⠈⣁⠤⠐⠒⠉⠁⢡⡁⡇⠀⠘⠻⠅⠀⡓⢓⣈⣅⢡⠔⠡⡄⢖⡄⠱⡈⠉
⠀⠀⡾⢄⣀⣦⣤⢀⣀⠀⠈⠉⠉⠉⠁⢂⢀⠀⡀⠀⠀⠀⠘⠞⡇⢸⠲⠤⣔⣒⠽⣼⣧⠔⠉⡇⠉⡥⡠⣒⢂⠇
⠀⢠⠁⠉⠙⠃⠶⠾⣛⣩⣵⡶⠦⣤⡄⠀⠉⡏⡝⠉⣀⡒⠒⠓⠁⠘⠚⡲⠢⢌⡉⠑⠺⣿⠒⠸⢦⣭⡡⠴⠊⢀⡀
⠀⡌⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠛⠫⠃⠀⢀⠑⠃⠀⠉⣁⢀⡀⠀⠀⢠⠃⠀⠀⠀⠉⠡⠀⠀⠀⠀⠀⠈⢳⠀⠛⠃
⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠽⢿⠃⡤⠂⠉⠀⢀⠈⠉⠢⣌⠒⡦⠤⣀⡀⠀⠀⢀⠀⠀⠀⢀⠎⠉⠁⡹
⠀⢀⣍⠁⠒⠠⠤⢁⣀⠀⠀⠀⠀⡇⠀⠀⢀⠎⠀⠀⢆⠀⠸⠁⢀⡠⠈⢣⠈⠁⡒⢩⡝⡒⠤⢌⡀⠀⣜⡀⠀⢰⠁
⠀⠘⠉⣀⡤⠔⠊⠠⣀⣈⠉⠒⠒⠀⠀⣠⡿⠀⣀⣀⠠⠆⣘⠂⠁⢀⡀⠈⡆⠹⣛⣀⣉⠐⠚⠓⢡⣌⠀⠈⠲⠃⣤
⠀⢠⠊⡀⠀⠐⠑⠂⠀⠌⢳⠀⠲⠖⠛⠁⢠⡀⠀⢀⣠⢴⡀⠺⡁⡡⠁⢀⠇⡴⠇⠤⢈⠓⡄⠀⡠⡔⠂⠀⢲⣄⠉
⠀⢹⣦⠤⣀⣁⣀⣀⣀⣀⣼⠀⢠⠿⠴⣄⢄⢢⡀⠉⠒⠰⠇⠀⠑⠁⢀⠜⠀⣇⢐⡒⢡⡅⡇⢔⠑⠒⠒⣂⡭⡊
⠀⠸⣿⠀⣿⠀⣿⠇⣿⢸⠇⢀⡖⢔⣒⠨⡉⠃⠙⠢⢄⣀⣀⣀⡠⠔⠃⠰⠀⣿⢨⠬⢸⡇⢱⠀⢷⢋⣴⢟⣴⢷
⠀⠀⣿⡄⣿⠀⣿⢰⡏⡞⠀⡾⢁⡨⠙⠃⡉⠀⡀⠖⠠⢀⠶⠰⣖⠀⠉⣿⠀⢫⠃⠫⠄⡧⢸⠀⠘⣟⣵⠟⣡⠾
⠀⣤⠙⠓⠻⠶⠿⠾⠓⠁⣸⠐⢌⠛⣣⡐⠀⡾⠂⡖⠄⡘⠄⠀⣿⠆⠀⢻⡆⠘⢄⡀⣓⣠⠚⢠⡄⠘⣥⢞⣥⡾
⠀⣉⣤⣀⣠⣄⣠⣒⣂⣄⡈⠐⠀⠀⡰⡠⠊⠀⠠⠛⠂⠌⣃⣄⢩⣇⣀⣸⣇⡀⠀⣍⠉⠀⠀⢠⡀⠀⠀⠉⠀⢤
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⣠⠀⠘⢠⣤⢄⠀⠀⠀⠀⠉⢉⠾⣿⣴⣟⣻⢆⢀⣸⣧⠰⠆⢠⣀⣀⡀⠀⠀⣠
⠀⠉⠢⠠⠠⠂⠒⠤⠤⠔⠊⠘⠛⠁⠘⠠⠀⠀⠈⠑⡇⢀⠔⠁⢦⢆⠀⣤⠈⣿⠀⠀⢿⡄⢰⣽⡃⠀⠀⠀⡀⣹⠢
⠀⠐⠂⠒⠂⡆⠀⠀⠀⢀⠀⠀⠀⠐⠈⠐⠐⠉⠁⠀⠉⠁⡀⢴⠟⢢⠠⠁⠀⠶⡇⠀⢹⡇⢰⣏⢁⣀⠀⢤⣠⠀⣽
⠀⠀⠀⠀⠀⠀⠀⣤⣶⠿⠐⠦⡀⠀⠀⠀⠀⠐⢿⢶⠶⠥⢐⠡⠀⠠⠱⠑⡀⢸⣥⡀⠸⠗⣀⡙⢦⠑⣷⡺⢃⡴⠁
⠀⢰⠀⠀⠐⠀⣸⣿⣷⣿⣬⣀⣵⠄⠃⠀⠀⡄⠈⢢⠣⠀⠀⠰⢐⡂⡂⠱⠝⠀⠀⣠⠚⠁⠐⡵⡌⢻⣟⢻⣟⠐⠗
⠀⢸⣄⡠⠂⠀⠸⣄⡜⢛⣻⣿⠏⠀⠈⢀⣀⡇⠀⠀⢣⠑⡈⠚⣉⠡⠌⣁⠂⠀⢸⡠⠉⢀⢀⡤⣧⠋⡹⢧⡑⢷⡀
⠀⢸⠻⣄⠀⠀⠀⠈⠉⠸⠋⠁⠀⠀⠀⣠⠟⡇⠰⣿⡇⠛⠊⠀⢈⢦⣤⣤⠚⢥⠺⠓⠭⠔⡉⠀⢡⡜⠁⠀⠳⣾
⠀⠈⠓⠚⠓⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠒⠂⠁⠀⠈⠙⠂⠀⠘⠋⠀⠊⠉⠉⠉⠁⠙⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠒⠀⠉⠉⠉⠉⠄⠂⠈⢉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⠀⢀⡀⠀⠠⠄⠀⠀⢀⠀⠀⠀⠀⢀⡛
⠀⠀⠀⠀⠀⠀⠀⠰⠋⢀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠠⢄⠈⠀⠰
⠀⠀⠀⠀⠀⠀⢠⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⢢
⠀⠀⠀⠀⠀⢀⠞⠀⢀⡒⢉⡁⠀⠀⠀⠀⠀⠀⠐⠋⢑⠂⠀⠀⠀⢀⠀⠀⢃
⠀⠀⠀⠀⠀⢸⠀⢠⠋⣁⣈⣙⣄⠀⠀⠀⣠⣊⣁⠀⠈⠑⠀⠀⠀⢨⠀⠀⠸
⠀⠀⠀⠀⠀⡇⠀⠻⠋⠿⣿⢬⠃⠀⠀⠀⢋⠀⣿⣿⣋⣿⠃⠀⠀⠀⠈⠀⢣
⠀⠀⠀⠀⠀⡇⠀⠀⠉⠀⠀⠁⠐⡇⠀⠀⠘⠶⣬⣭⠟⠃⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉
⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠄⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠱⣤⡀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢀⡴⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢦⣤⣀⣀⣀⣀⣀⢤⣤⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⠄⡠⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠂⡀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⢤⠀⠀⠀⠀⠣⣄⠀⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⢀⡼⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡀⠀⠀⠀⣠⠃⢠⡤⠀⠋
⠀⠀⠀⠀⠀⠀⡼⠁⢠⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠀⠀⠰⣄⠀⡄⠛⢦⠋
⠀⠀⠀⠀⠀⡸⠀⠀⡎⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢦⠀⠀⠘⠞⠀⠀⢀⠇
⠀⠀⠀⠀⠀⡇⠀⠀⢱⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢳⡀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠣⣄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠹⢦⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠗⠒⠂⠀⠀⠀⠀⠀⢤⣤⣀⡀⣤⠤⠐⢶⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣰⠟⠉⢳⡄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⣰⠃⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⣳
⠀⠀⠀⠀⠀⣺⠤⣤⠤⠤⠤⠠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡖⠒⠒⠀⠉⠃⡀
⠀⠀⣠⠄⠛⢄⠲⠀⠆⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠠⠀⠠⠈
⠠⠊⠀⠈⠠⡀⠈⠀⠀⡠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠉⢀⠀⠀⠉⠑⢄
⡆⠀⠀⠀⠀⢰⣠⠼⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡐⠂⠀⠀⠀⠀⢀⡄
⣉⣫⣤⣌⣛⣋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣐⣠⣤⣤⣤⣬⣁⣀⣀⣀⣀
⣿⣿⣿⡿⠛⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣥⣤⣤⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰⣄⠀⣠⡄⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣘⣦⣾⣷⣾⣿⣿⣿⣿⣿⣿⣧⣾⣃⣼⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢆⣸⣖⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠛⠛⠻⠿⣿⣿⣿⣿⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢬⣲⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣽⣶⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣧⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢻⣿⣿⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⣾⣿⣿⡿⠁⠀⣀⣤⣤⣤⣄⣀⠀⠀⣀⣤⠖⠛⠉⠉⠉⠙⠻⣶⣄⠀⠀⢻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡿⠁⣠⣾⣿⠟⠋⠁⠀⠀⠉⠉⠉⠀⠀⣀⣀⣀⣀⠀⠀⢹⣿⣧⠀⠀⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢴⣿⣿⣿⠁⣼⣿⡿⠃⠀⣠⣴⠾⠛⠳⢶⣄⣠⠞⠉⠁⠀⠉⠻⣆⠀⠙⠛⠀⠀⠸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⣿⡇⠀⠛⠋⠀⢠⡾⠋⠀⢀⣀⠀⠀⢻⡏⠀⠀⢠⣤⡀⠀⢻⡆⠀⠀⠀⠀⠀⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⠿⠃⠀⠈⣿⡀⠀⠈⠉⠀⠀⢸⡷⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⢀⣼⠛⢿⣦⣄⡀⢀⣠⣾⠃⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠈⠻⣦⣤⣤⣴⣾⣿⠁⠀⠀⠹⣿⣿⣿⣏⣁⡀⠀⠀⠀⠀⠀⠘⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠨⢾⡿⠋⣏⠀⠀⠀⠀⠹⣿⡙⠳⠦⠀⠀⠀⠀⠀⠀⠆⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠋⢀⣠⣿⠀⠀⠀⠀⠀⢻⣏⠳⣄⠀⠀⠀⠀⢀⠈⠁⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⣿⡀⠀⠀⠀⠀⣼⡿⠀⣿⠀⠀⢀⠂⠀⠐⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠾⢷⣤⣀⣤⣾⡿⠻⠿⠛⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⢀⠀⠰⠀⠠⠀⠀⠨⢙⣟⢻⠁⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⢀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⣨⣷⣾⣧⠀⠀⠀⠐⠀⠂⠀⢀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⠀⠠⣿⣿⣿⣿⣧⠀⠀⠠⠀⠀⠀⠀⠀⢀⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣿⣿⠏⠂⠀⠀⠀⠀⠀⢀⢀⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀⠀⡄⠀⢀⠀⠂⠀⠀⠉⠀⠈⠙⠛⠳⣦⠀⠀⠀⠤⠄⢀⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣥⣀⠁⠄⡀⠀⠀⠀⠀⠄⠀⠘⠄⠸⣷⢀⣠⣤⣶⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠻⠿⠷⠶⠶⠾⠶⠿⠿⠟⠛⠋⠁


⠀⠀⡀
⠀⠁⠀⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠢⠶⠰⢀⣀⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣰⠖⠒⠢⢄⣀⡰⠉⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⣠⠒⠀⠀⠠⡅⠀⡀⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠲⠅⠀⠀⠀⠃⠀⠀⠀⠘⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢴⠒⢒⠐⠣⡆⠀⠀⠀⠈⠉⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠄⢀⣶⣀⢀⢠⣦⠀⠉⠀⢸
⠀⠀⠀⠀⠀⠀⢀⠼⠀⠉⠁⠀⠀⠀⣐⠐⠃⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠃⠙⠛⠁⠀⠀⠉⢀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠸⡀⠃⣄⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢒⠈⠀⠀⣤⣀⠀⢀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠲⡌⣷⣦⣤⠤⠒⠁⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⢸⡿⢿⠇⠀⠀⠀⢀⡠⠋
⠀⠀⠀⠀⠀⢠⢴⠶⢯⡇⠉⠁⡡⢒⣒⠂⢲⡒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠐⢧⠀⢀⡀⢰⠂⠂⠁
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠋⠠⢼⠋⠀⠀⠁⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠳⣀
⠀⢠⠔⢲⣌⡓⣇⣀⡴⠀⠀⢖⡀⠀⠢⣀⣠⠞⠀⣀⢤⡖⠒⢦⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠑⠢⢄⠀⠀⠀⡀
⡔⠃⠀⠏⠀⠹⡖⠖⠀⠀⠀⠈⢆⠁⠀⠀⢀⢓⠏⠀⠠⠃⠀⠸⢦⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣙⢢⢀⠉
⣇⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠁⢢⠀⠀⡞⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠠⠃⢂⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡗⠊
⠘⣄⠀⠀⠀⠀⠀⢐⡀⠀⠀⠀⠀⠀⠀⠱⠀⡇⠀⠀⠀⠀⠀⣰⠃⠀⠀⡀⠂⠀⠁⢄⠀⠁⠐⠀⠀⠀⠄⠓⠀⣀⠀⢀⠜
⠀⠈⠓⠤⠤⠴⠋⠀⠑⠤⣀⡀⠀⠀⠀⡠⠦⢧⡀⠀⠀⣠⠜⠁⠀⠀⠀⠈⠂⠦⠀⢠⣀⠀⡀⠀⢆⣴⡁⠀⠀⠘⢘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⢿⣿⣿⡿⣱⣟⣼⣿⣿⣿⣿⣿⢿⠿⠿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣿⣿⣿⣹⣿⣿⣿⣶⡾⠃⠀⠈⠻⣿⣟⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⢄⣷⠈⢿⡆⠹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣻⡟⠻⠿⣿⣿⣿⡿⠿⣿⢿⣿⡻⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠸⣷⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⡟⠀⠀⠀⠀⠀⠈⠻⠶⠇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢺⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢢⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⠘⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⣿⣿⣿⣿⢀⠀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡆⢳⣿⣿⡀⠀⠀⠀⠀⠀⢠⡀⠀⢠⣾⣟⣡⣤⣤⣶⣶⣶⣿⣿⣿⣿⣄⠀⠀⣿⣿⣿⡏⢀⣴⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣼⣿⣿⣷⣶⣶⣶⣶⣦⠀⢹⣀⣉⣤⣹⣿⣿⣿⣿⣿⣿⣯⣭⣥⣙⣿⣿⣿⣛⣿⡿⣠⣿⣿⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠉⣿⣿⣿⠛⠛⢛⣛⣻⣿⣿⡿⢿⣿⣿⠿⣿⣿⣿⠁⣼⣿⣹⣿⣿⠿⢟⣿⣿⣿⣿⠛⠉⣴⠿⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⣤⡿⢶⣿⡿⣿⠃⣴⡿⣿⣿⣿⣿⢿⣷⣬⣿⣿⠀⠉⣿⣿⡈⠉⠀⠶⢶⣶⡿⠿⠟⠉⠻⣿⣿⠀⣼⡶⠁⡌
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⣿⡇⢍⡻⢿⣷⣯⣭⣿⠴⠂⠀⢀⣿⣿⠀⠘⠀⢧⠷⡀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⣿⠖⠉⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⠀⠀⠈⠉⠁⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠈⠳⣌⣳⠴⠦⢀⣀⣤⡶⠛⠁⠀⣿⡇⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⣶⣤⣤⠀⠀⠀⣠⡾⢫⡟⠀⠀⠀⠀⠀⠀⠈⡙⣝⠻⠿⠿⢿⠄⠀⠀⠀⢽⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠑⠒⣲⣶⡶⠟⠁⣴⠋⠀⠀⠀⠀⠀⡀⢀⣬⡿⠛⠀⠠⣄⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠘⠟⠋⣠⠄⠀⠈⠛⠻⣶⣤⣴⣾⡿⢟⣥⣾⣶⣦⣀⣬⣿⣶⣄⡀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣴⣿⣶⣶⡦⠀⠐⣬⣟⣛⣯⣷⣿⠟⠛⠙⠛⠛⠿⢿⣿⣿⣿⡆⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⣿⣿⣟⡉⠀⠀⣀⣉⣙⣿⣿⣿⣶⣿⣿⠿⣿⢷⣶⣾⣿⣿⣿⠃⠀⢀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠙⢿⠙⢿⣿⡿⣿⠿⠟⠻⡿⠛⠛⠀⠈⠀⣠⣼⡿⠋⠁⣾⣏⢀⣠⣾⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⡀⠀⠀⠈⢳⡀⢽⣷⣄⠀⠀⠀⠀⠀⠀⣶⣾⡿⢿⣯⡞⠁⢸⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣾⣦⣄⣰⣧⠈⢷⣌⠙⠳⠶⣾⡾⠛⠋⢁⣴⡿⠋⠀⠀⣾⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡇⠈⠻⣷⣦⡀⠀⢀⣠⣴⣿⠟⣡⠀⠀⠀⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⡄⠀⠀⣉⣛⠛⢛⣛⣩⣴⣾⠇⠀⠀⠀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⠀⠀⠈⠻⣿⣿⣿⡿⠟⠁⠀⠀⠀⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⣄⠀⠀⠀⢀⣀⣴⣾⣿⣿⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏⢛⡛⣻⣿⣿⠟⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢙⣿⣿⣿⠏⠀⠀⠀⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⣹⣿⠀⠈⢿⣿⠃⠀⠀⠀⠀⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⢹⣿⣾⣿⡏⠀⠀⡿⠁⠀⠀⠀⠀⠀⣿⣿⡟⣿⣯⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠁⠀⠀⣾⣿⣿⣿⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡄⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣫⡾⠋⠀⠀⠀⠀⠀⣿⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⣿⣿⣿⣿⣧⠀⠢⣀⠀⠙⣿⡶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠁⠀⠙⣦⡤⠐⠉⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣟⣛⣻⣭⣿⣿⣿⣿⣿⡄⠀⠈⠳⢾⡋⠀⠈⠙⠦⣄
⠀⠀⠀⠀⠀⣀⣠⠴⠋⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠙⢷⣄⠀⠀⠈⠳⣤⣀⡀
⠀⠀⠀⠀⡞⠀⠛⠀⠀⠀⠀⠀⠀⠻⣤⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⣸⠏⠙⢷⡀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣋⣉⠉⠀⠈⢉⠙⠿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠟⠀⢰⣿⣿⣿⣿⣿⣿⡿⢻⡾⣿⠋⠁⣰⣿⠀⢞⣤⣤⠘⢿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠉⠙⠛⠛⠛⠋⠀⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⢰⣏⡀⢰⡿⠉⠁⠘⣿⡀⠀⠘⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠀⠀⠰⠾⠛⠃⠻⣷⠞⢣⣶⣾⠇⠀⠀⢹
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡟⠀⠀⣠⡶⢿⣧⢸⡇⠀⣿⠂⠀⠀⠀⠀⠀⠸
⣿⣿⣿⣿⣿⣿⡿⠛⠃⠀⠀⠘⠃⠀⠀⠀⠐⠂⠀⠀⣾⣿⣿⣿⠟⠀⠀⠀⢀⣤⣾⡏⣼⡇⢠⣿
⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠛⠁⠀⠀⣀⠠⣿⣡⡿⠃⠸⢷⠜⣿⡄
⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⣾⣿⣿⣶⣶⣦⣄⠘⢿⣆⠈⠉⠀⠀⢶⡄⠀⠀⣠⠀⠀⠀⠀⣠⡀
⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣻⣿⣿⣿⣿⣿⣿⣧⢸⣿⣤⣄⠀⣠⣌⣷⣴⡄⠛⠀⠀⠀⠀⣾⡇
⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⣿⣿⣿⣿⢸⣿⠁⣽⣾⡷⢫⡿⣸⢇⡇⡾⣿⣴⠾⡿⢰
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⢸⣿⣿⣿⢸⣧⠾⠁⠻⣷⠘⠃⠛⠘⠓⠃⠋⠙⠛⢁⣾
⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⢿⣿⣿⡇⠀⠀⢸⡇⠀⣸⡇⣰⠶⣆⣴⠀⣦⠀⢀⣾⣿
⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⢿⣿⡇⠀⠀⠈⠻⠿⢿⡟⣿⣰⠟⣿⡼⠃⢠⣾⣿⣿
⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⣴⠟⣠⡿⠃⠈⠉⠀⠀⢀⣴⣿⣿⣿⣿
⡇⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣦⡀⠛⠛⠋⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿
⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣇⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⢀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⠀⠀⢸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣸⠀⢸⣿⣿⣿⣿⣿⣿⣿⣯⣍⡋⠁⠀⠙⣿⣿⠋⠻⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠀⢙⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀⣠⣿⡟⣰⣶⣿⣿
⣿⣿⣿⣿⣿⣿⠻⣿⣿⠿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣦⣀⣿⣷⣿⣿⣿⣿⡏⠁⡙⠻⡿⠿⠷⠀⠀⠋⠉⣁⣿⣿⣿⣿
⣿⣿⡛⠿⠿⠏⠀⠹⠋⠀⠻⠃⠘⣿⠟⢹⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣾⣿⣦⣠⣤⡄⠀⠀⠀⣼⣿⣿⣿⣿⣿
⣿⣿⡿⠆⠰⣶⣀⣿⣿⡋⠁⣰⣧⣤⣶⠞⠁⠘⡿⠋⠹⡿⠀⠙⠟⢋⣥⣾⣿⣿⣿⣿⡿⠇⠀⠀⠀⠛⠛⠋⣿⣿⣿
⣿⣯⣤⣤⠀⣿⣿⣿⢼⠋⠡⠋⠏⠻⠟⢠⣠⣶⡶⠂⣦⣶⡏⠀⣾⣿⣿⣿⣿⣿⡍⠀⣀⣀⣠⣶⣤⣴⡖⢰⡟⠻⣿
⣿⣿⡿⢁⣀⡟⠀⠉⠸⢻⡟⣠⢰⣞⠀⠟⠋⢹⡟⠀⠋⠉⣭⣤⣼⣿⣿⣿⣿⣿⣿⡀⢽⣿⣿⣿⣿⣿⣇⣠⣤⣤⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⡟⠻⢿⢸⣇⠀⠀⠀⠀⠉⢠⣤⣄⣸⣿⣿⣿⣿⣿⣿⣏⠉⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣤⣶⣿⠁⠘⣡⣤⠈⣠⣧⠀⣠⣄⠀⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣾⣿⣿⣶⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡏⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠠⣷⠆
⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⣄⣀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤
⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠉⠉⠁⠀⢺⣿⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠆⠀⠀⠀⠀⠻⠿⠿⠿⠿⠿⠿⠷⠄⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠻⠿⢟⠻⠿⠿⠿⠿⠿
⠈⠀⢀⡀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⢋⡀⢸⠅⠎⠠⡺⠀⠀⠀⠀⠀⠀⠀⠈⣀⠈⠠⠀⠀⠀⠀⠀⠓⠆⠊⠈
⠀⠀⠀⠰⠀⠐⠀⠀⠠⠘⠀⠀⠀⠀⠈⠆⠘⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠀⠀⠀⠀⠐
⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠂⠀⠖⠒⠀⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠄⢀⡀
⠀⠀⠀⠀⠐⠂⠂⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠠⡀⣠⡀⠀⠀⠀⠀⡀⠀⣠⠤⠉⠁
⠀⠀⠔⡐⠊⢐⣩⠀⢔⠀⠀⣤⠀⢀⠀⠀⠠⠀⠀⠀⢠⡀⠀⡀⠀⠀⠀⠀⠁⠀⢀⠀⠲⠂⠂⠀⢤⠉⠀⠀⠐
⠀⠀⠀⠊⢃⠀⣰⠀⠂⢀⡁⢀⠈⠘⠀⠀⠰⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠉⠃⠀⠀⠤⡀⠐⠀⢂
⠀⠀⠀⢀⡀⠤⠁⠀⠐⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠄⢌⡀⢀⠀⠐⡀⠀⠀⢠⠀⠀⠐⠂⠚
⠈⠁⡄⣀⠂⠀⠀⠂⠤⠀⣀⡀⠀⡀⢀⠀⠀⠀⠀⠀⢀⠴⡀⠀⠀⠀⠀⠀⠨⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠂⠀⠀⠂⠀⠠⠤⡀⡀⠙⢀⠂⢀⠀⠀⠀⠀⠀⠠⠔⠁⢀⠈⠁⠀⠀⠀⠀⠀⠀⢀⠀⣀⠂⠀⠀⠀⠀⠤
⠠⠄⠀⠀⢀⠀⠈⠀⢀⠉⠉⠉⠀⠰⠐⠀⠀⠠⢀⠂⠀⢀⡠⠐⢀⣀⣄⠈⢀⠀⡀⠈⠀⠈⠀⠑⠐⠂⠒⠚⠢
⠀⠀⠀⠀⠀⠂⠂⠀⢂⠄⠀⠀⠁⠀⠀⠠⠄⠀⠂⢠⠀⠀⠀⠀⠂⠀⠘⠡⠬⠀⢩⢉⡈⠠⠀⠀⠀⠀⠈⠁
⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠈⠐⠁⠀⠀⠀⠀⠈⠀⠁
⣶⣶⣶⢾⣶⣿⣶⣶⣶⣶⣾⣿⣷⣶⣶⣿⣿⣾⣿⣶⣾⣷⣿⣷⣾⣿⣿⣷⣶⣶⣿⣿⣷⣾⣿⣷⣶⣶⣷⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⡡⠞⠁⠛
⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠀⠡⠀⠀⢸⣯⣿⡇
⠀⠀⠀⠿⠿⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣶⡏⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠛⠷⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠐⠶⠷
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠲⠂⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠘⣿⠛⠛⠛⣿⠀⠄⠁⠄⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⠀⠀⣿⡀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠠⠀⠀⠀⠛⠋⠀⠻⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣨⣠⣤⣍⢥⠀⠐⠐⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣠⡄⠀⠀⡄⠀⠈
⠀⠀⠀⠁⣠⣤⣤⣀⡀⠀⠀⠓⠊⠀⠐⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠇
⠀⠀⠀⠀⠋⠉⢙⣿⡗⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣤⢀⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠰⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢛⡻⡟⡛⣛⡛⣻⠿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣠⣤⢀⣀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣉⣁⣤⣤⣤⣀⣉⡙⠻⢿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠄⠀⠀⠀⠀⢀⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣹⣿⣧
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⣼⣿⡿⠿⠛⠉⠈⠛⠻⠿⠛⠛⣿⣿⣿⣿⣿
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⠟⠻⢿⣿⢿⣿⣿⣿⣿⣿⣯⠉⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⣿⣿⣿⡿
⠀⠀⠀⢸⣿⣿⣿⡿⠋⠀⠀⠀⠀⠉⠀⠉⠃⠈⠃⢹⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢋⠅⡀
⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠻⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠘⠈⠁⠀⢀
⠀⠀⠀⠀⡕⢢⠙⠃⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀⠀⢱⠿⠠⠂⠀⢀⠀⠀⠀⠀⢒⡶⢶⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⡗⠚⢾⡔
⠀⠀⠀⠀⠠⢈⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠈⠃⠀⠀⠆⠀⠁⢄⢀⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⠟⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠙⠁⡙⠿⣷⣦⣤⣄⠀⢀⣴⣶⣾⡿⠟⢉⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠁⠂⣀⠉⠙⠋⠀⠜⠙⠋⠀⢠⣴⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢂⠀⠀⡐⢂⠀⠄⠀⠀⠐⠀⠀⠀⠀⠀⠀⢹⣶⡄⠀⠀⠀⠀⠰⣾⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠃⠀⠀⠘⠁⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠹⣿⣿⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⢡⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠃⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠊⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⣀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢤⠀⠥
⠀⠀⠀⠄⡀⠑⠂⠀⠌⠀⠀⠠⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡉⠂⠂
⠀⠀⠈⠁⠜⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⠁⠐
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠁⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠙⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠦⠄⢀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣀⡀⠀⡄⠀⠄⡈⠀⠀⠀⡐⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⣶⡌⡌⠀⠀⠀⠘⢂⣤⡈
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠘⠛⠃⠃⠀⠀⠀⠀⠌⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠘⠈⠠⠀⡄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠁⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠄⠄⢀⠀⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣀⣀⠄⠄⢀⠄⡀⠀⢀⠠⠤⠀⠄⠊⠄⠄⠈⠀⠁⠀⠀⢀⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⡀⠀⠀⠀⠉⠉⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠨⠀⠀⠀⠠⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣛⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡟⡾⢏⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⡇⠁⡼⠛
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿