Digestion Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⠀⠈⠑⠂⠄⡀⠀⠀⠀⠘⣇⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠀⢘⣄⣀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠈⠉⠙⠚⠓⠄⣀⡀⠀⠐⠲⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣟⠀⠀⢀⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡠⠤⠤⡴⠊⠉⠉⢁⡤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⣀⣤⣶⡾⡟⠉⢉⡼⠋⠀⡀⣀⣀⠤⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⣠⣾⣿⡿⠋⠀⠙⠖⢋⡵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⣿⣿⠟⠀⠀⠀⠀⠀⠸⠁⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣁⠤⠠⢤⠀⠐⠢⣤⣀⠀⡎⠀⠀⠱⣤⣀⡀⠀⠀⣀⡀⠀⠀⠀⢀⣀⣠⣤⣶⣴⠞⠣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠙⠒⠄⠀⠈⠳⢄⡠⣴⠋⠈⠉⠛⢿⡟⠉⠙⠻⠛⠛⠛⠉⠛⠁⣉⣀⣴⢞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⣦⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⢷⣄⣀⡀⠀⠀⠀⠀⢀⣀⣴⣤⠶⠶⠿⠉⠉⠁⣀⣨⡵⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠻⣿⣿⣷⣦⣦⠀⠀⠀⠀⠀⢄⠀⠈⠉⠀⠉⠋⠙⠛⠉⠛⠁⠀⠀⢀⣀⠠⠐⠒⠋⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠈⢹⡏⣹⠏⠳⢤⠦⡀⠀⠀⠁⠀⠀⠀⠀⠄⠀⠠⠤⠶⠀⠐⠊⠉⠀⠀⠀⠀⢀⣄⣀⣠⣦⣀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢠⡏⠀⣽⠀⠀⠀⠀⢉⡶⠛⠂⠤⣤⣄⠀⢀⣀⠀⠀⣀⡀⠀⣠⡄⣠⣴⠟⣻⣿⡿⠟⠿⠟⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⢸⡇⠐⣧⢠⡄⠀⠀⠉⠀⠀⠀⠠⠁⢈⡿⠛⢻⠟⠚⢻⠏⠉⠁⠀⠀⠐⠊⠁⢹⣧⠀⢀⡇⠀⠚⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⢠⡏⠀⠛⠦⢤⡤⠀⢰⠋⠀⠀⠎⠀⠐⠋⠀⠀⣼⠀⠀⠀⠀⠀⣀⣠⡤⠾⡇⠀⢸⡆⠀⢀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢸⠁⠀⣿⠀⠀⠠⠋⢀⡴⠁⠀⠀⢠⡀⠀⠀⠀⣠⠎⠀⠁⠂⢒⡾⠋⠁⠀⢀⣰⡇⠀⠀⡇⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⢸⡇⠈⣷⠀⢀⠃⠀⠈⠁⠀⠀⡰⠁⣈⠐⠒⠊⠁⠀⠀⠀⠀⡟⠀⠀⠀⠊⠉⢙⠇⠀⠀⠳⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢸⣇⠰⣿⠀⠈⢧⠀⠀⢀⠀⢈⣠⣎⡀⠀⠀⠀⠀⠀⣀⡤⠶⢳⣄⣀⣀⣀⣀⢘⠇⠀⠀⢸⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠈⡇⠀⣸⠇⠀⢀⡤⠤⢤⡞⠉⠀⠀⠀⠉⠢⣀⠈⠁⠀⢀⡴⠛⠉⠉⠉⠉⠛⣿⠀⠀⠀⢸⡀⢀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⣿⠀⢹⡆⠀⢨⠀⠠⣼⠀⠀⠐⠶⠤⢤⣤⣤⣭⣤⡼⠟⠁⠀⠀⡀⠀⠀⢸⠃⠀⠀⠀⢸⠁⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠘⣆⠘⣧⠀⠀⢦⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠼⠃⠀⠀⠀⡼⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⣿⡀⣾⣠⠤⠊⠀⠀⡼⠉⠓⠦⢤⣤⣤⡤⣤⣤⣤⢶⡆⣀⠀⠑⣴⠟⠀⠀⠀⠀⣸⣀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⣽⣧⣼⠋⠉⠁⠒⠋⠁⠀⠀⡆⠀⠀⢹⡀⠈⣧⠀⢸⡟⠉⠉⢺⡇⠀⠀⠀⠀⣴⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⠀⠀⢀⣰⡿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢸⠀⠀⠀⡀⠀⠀⠁⠀⠀⢀⣾⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠟⠛⠋⠀⠀⠻⣦⡄⠀⠀⠀⠀⠀⠀⢣⠀⠀⢸⠇⠀⠀⠲⠶⠒⠿⣿⣷⣶⣶⣶⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠈⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣡⠶⠒⠒⢍⠙⢢⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⢂⡈⠛⠡⡀⠀⠃⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⣁⠀⠀⠘⠀⠀⠀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠀⠀⢰⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠐⠊⠉⠀⠀⠀⡇⢸⠀⠀⠀⠉⠐⠢⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⢨⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠸⠆⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢀⡠⠤⠄⠤⠼⠤⠶⠄⠀⡄⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠶⢄⡀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡆⠀⠀⢰⠒⣆⠠⠒⠈⠀⠀⠀⠙⡀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠧⢤⠦⢬⣻⣀⠔⠁⠀⠀⠀⠀⢠⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡆⠀⠀⠀⠈⢀⠝⠉⠀⠀⠀⠀⠀⣀⢴⢥⡀⠀⠀⠘⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⡆⠔⢻⣃⠖⠀⠐⠈⠀⠀⡠⠊⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡇⠀⠀⡠⢄⣠⠤⢸⡬⠲⣢⡶⠶⡾⠅⠠⢄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢐⠉⠐⠢⠤⢀⠤⠤⠤⠬⠂⠤⠔⠒⠂⡊⠉⡄⢀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡜⠀⠀⠢⠤⠢⠤⠔⢢⠔⠒⠒⠎⠑⡆⢱⠀⢱⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠱⠀⢨⠀⢇⠀⢳⠀⢘⠀⡟⠀⢀⠖⡗⢨⠀⢆⠸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠱⠀⢸⠀⠏⠀⣘⣄⣈⡠⢳⠤⠼⢴⠇⠨⠀⠌⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⠄⠸⠀⣆⡠⠀⠈⡎⠂⢸⣦⣤⠴⢠⠂⢀⠄⠀⡃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠐⣄⡀⢀⡠⠄⠠⢚⠖⠒⢃⣀⠁⠔⠂⢀⡸⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⡀⠀⠀⠀⠀⠈⡏⠀⠀⠀⡇⠀⣀⣁⡠⠄⡠⠎⠁⠀⠀⠀⡇⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢡⣀⠀⠀⠀⠀⠁⠀⠀⠀⠱⡀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⣇⢃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠖⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠙⠛⠛⠛⠲⠶⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣯⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⣽⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣿⢸⠈⢹⠉⠉⣻⠛⠛⠛⡟⠛⠛⢿⠛⠛⢻⠛⠛⢻⠛⠛⢹⡏⠉⡏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠙⢾⣦⣼⣄⣀⣽⣀⣀⣠⣇⣀⣀⣼⣀⣀⣸⣀⣀⣸⣄⣀⣼⣄⣤⣧⠾⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠧⠤⢤⣉⣉⣉⣉⣉⣉⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣉⣁⡠⠿⣆
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⣼⠷⠦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣼⠇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠁⠀⠀⠀⠀⠘⠛⠛⣶⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⣷⠀⠀⠀⠀⣴⠟⠛⠃⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⠶⠶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠘⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡏⠀⣼⠋⠉⠉⠉⡏⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣄⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣴⠟⠀⠀⢿⣤⣤⣤⣤⣿⣤⣤⣤⠾⠁
⠀⠀⠀⠀⢀⣤⠶⠶⢶⣤⣤⣭⣍⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⡴⠶⢶⣤⡀
⠀⠀⠀⠀⣟⠀⠀⠀⡼⠀⠀⠀⠈⠙⣦⠀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠛⠁⠈⢹⣧⠀⢀⡼⠛⢶⣄
⠀⠀⠀⠀⠙⢦⣄⣀⣳⡀⠀⠀⢀⣰⠟⢀⣀⠀⠀⣿⠁⠀⠀⠙⣳⣦⣀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠙⢦⣠⡾⠋⠳⣮⡀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⢛⣻⣷⠞⠋⠉⢻⡄⠹⣦⡀⢠⠞⠁⠀⠙⢷⣄⠀⠀⠀⢿⡀⠀⠀⣠⡾⠋⠀⠀⠀⠈⠻⢦⣄⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠈⢧⠀⠀⣠⠟⠀⠈⠻⣧⡀⠀⠀⠀⠀⢹⡇⠀⠀⠈⠛⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⣀⣼⠷⠛⠁⠀⠀⠀⠀⠈⠻⢦⣀⣀⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣄⡀
⠀⠀⠀⠀⠀⠀⢠⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣶⣶⣶⣶⡶⠶⣶⣶⣶⣶⡆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⡿⠿⢰⣇⠸⠿⣿⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣇⣛⢻⡿⢛⣃⣿⣿⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⣿⣿⣿⣘⣃⣸⣿⣿⣿⡇⠀⠀⣿⡴⠖⠛⠳⢦⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣡⣴⣾⠉⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣧⡴⠶⠶⠶⠶⣿⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠘⠷⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠹⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠙⠳⠶⠶⠦⠴⢿⣿⣿⣿⡿⠟



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⣀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⠀⠈⠓⠀⠉⠟⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣀⠀⠈⡌⢿⣦⣐⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⣾⣿⡿⣦⣤⠀⠀⠀⠀⠑⢦⡈⠻⢿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⠀⠀⠈⣿⡷⣼⡟⠀⠄⠀⠀⠀⠱⣄⠈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡻⣶⡤⡿⣿⡟⠎⠉⢾⣷⣠⡀⠀⠀⠘⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣿⡿⠷⠶⣴⡌⠠⣅⠀⠀⠀⢹⣿⣿⡆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⣿⡆⠀⠀⠀⠋⠹⠶⢋⣀⣤⣤⡈⢳⠀⢉⣷⢧⡶⣺⣹⡿⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠀⣀⣴⣿⣷⣿⣆⡿⣦⡹⠿⣿⣧⢹⡿⠾⠛⠁⢀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⡀⠀⠀⠘⠀⠀⠀⠾⠟⠉⣸⠛⠛⠋⢰⣽⣯⠈⠋⠙⠋⠀⠀⠀⠀⠈⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢠⣴⢆⡄⠘⠁⠀⠀⠀⠈⣿⡿⠀⠀⠀⢀⣀⡦⣀⣴⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡙⢦⡀⠀⠀⠟⣀⡀⠀⠀⠀⢀⡼⠛⠠⣄⠢⢴⣿⣿⣧⡿⡟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⣷⠀⠀⠐⣌⠻⢶⣤⣀⣘⠁⠀⠀⢀⣀⣨⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄⠸⣷⡀⠀⠉⠙⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠪⢒⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠊⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠈⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠁⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⠀⠀⠐⠒⠶⣶⣄⡀⠀⠀⠀⠀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⢽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠉⠻⢷⡂⠤⠒⠋⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⢼⡇
⢀⡄⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣃⢸⣦⡀⠀⠀⠀⠀⢀⡠⠛⠲⣄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⡈
⡟⠁⠀⠀⠘⡄⠀⠠⠄⠀⠀⠀⠀⣻⠀⠈⠳⡀⠀⢠⠔⠁⠀⠀⠀⠀⠙⢄⢀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠁
⢹⡄⠁⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⢳⣤⣶⣷⣦⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠁
⠀⢹⡄⢰⣄⢤⣼⡄⠀⠀⠀⠀⠀⣸⣽⡄⠀⣀⢀⠆⡶⣄⡀⢐⡤⠀⣀⣀⣨⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠃⠀⠀⠀⠀⠀⣰⠄
⠀⠀⢻⣿⣷⡈⢿⣿⡆⠀⠀⠀⣠⡿⠻⠃⠚⠉⠉⠈⠐⠋⠻⡿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡴⠿⠟⢋⣡⣤⣶⠄⠀⢀⣠⡴⠞⠋
⠀⠀⠀⢿⣿⣷⡈⢻⣿⡄⠈⠈⠍⡁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠉⠉⠣⠛⡄⠀⠀⠀⠀⠀⠘⣧⣴⣾⣿⣿⣿⡿⠷⠛⠉
⠀⠀⠀⠈⢿⣿⣷⣼⠛⡇⢀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢼⠇⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠙⠛⠛⠀⠀⢸⡉⠀⠀⠀⠠⡙⣶⣤⡀⠀⠀⠀⣀⣀⡀⣠⡴⠔⠋⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⡀⢢⣼⠿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⣿⠈⣷⡄⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⣠⡀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡱⠂⠈⠛⢿⣿⣤⣌⠻⢿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⠀⠈⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠚⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⢆⠀⠙⠻⣿⣧⣄⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠁⠀⠀⠀⣸⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠀⢀⢂⢀
⠀⠀⠀⠀⢺⢆⡀⠀⠀⠀⠀⣀⢀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⠀⠈
⠀⠀⠀⠀⠀⠢⣍⣿⣷⣏⣍⣇⡴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠒⠚⠉⠛⠉⠙⠛⠉⠳⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠃⠀⠀⠀⣀⠀⢀⣤⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠘⠲⡀
⠀⠀⠀⠀⠀⠀⠀⡤⠃⠀⠀⣀⡴⠚⠉⠉⠉⠀⠀⠀⠈⠉⠋⠙⢦⣤⣄⡀⠀⢀⣧⡀
⠀⠀⠀⠀⠀⢀⡴⣇⣀⡶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠻⡀⢹⡀
⠀⠀⠀⠀⠀⢸⢀⡞⠁⠀⠀⠀⠀⠀⠀⢀⠤⠄⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⢳⡀
⠀⠀⠀⠀⢠⠏⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡞⠁
⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣆⠀⢀⡰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⢀⡤⣤⣤⣤⡶⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⢸⣿⣿⣟⣻⡇⠀⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⣸⠛⠛⠓⠚⣇⣀⣠⠤⣶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⡾⠶⠭⣦⡀⢀⣜⣉⣠⡤⠴⢿⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⢠⡇⠀⠀⠀⣹⠋⠀⠀⠀⠀⠀⠘⡇⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢠⣼⣀⡤⠖⠚⣇⣸⡀⠀⠀⠀⠀⠀⢹⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⡟⠀⠀⠀⠉⣩⡿⡄⠀⠀⠀⠀⠘⡇⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠘⣇⡀⠀⠀⠀⣇⠀⠀⠀⠀⣤⣶⣅⠀⠀⠀⠀⠀⢹⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⢹⡖⠒⣛⣶⠒⠲⡖⣇⣀⣸⠷⢶⣶⣶⢤⣈⣇⡴⢻⢷
⠀⠀⠀⠀⡴⠒⠒⣲⡾⣭⣿⣿⠽⠋⠙⠤⠴⠃⠀⠉⠁⠀⢯⠀⣸⡇⠈⢿⡷⣿⠾⣷⡒⠒⠒⢦
⠀⠀⠀⣸⠃⣠⠞⠁⢠⣾⣷⣛⣦⡤⢖⣦⠀⠀⣠⣤⣄⠀⢈⣭⣭⣤⠖⢋⣴⡿⠓⡆⠙⢢⡀⠈⢧
⠀⠀⣰⠃⠀⢻⡀⠀⠘⢯⡙⠻⢭⣛⣛⣛⠓⠛⠓⠛⢋⣉⣉⣠⡤⠴⠚⣩⣾⣳⠋⠁⠀⣰⠃⠀⠘⣆
⠀⢠⠇⠀⠀⠀⠙⠲⢤⣀⡉⠓⠶⠤⣬⣉⣉⣉⣉⣉⣉⣉⣥⠤⠴⠒⠋⠁⠀⣉⣠⠴⠚⠁⠀⠀⠀⠸⡆
⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠲⠶⠤⠤⠤⠤⠤⠤⠤⠴⠶⠒⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠀⠈⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠻⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⣀⡤⠖⢒⣶⣾⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠘⠁⢀⠤⠚⣛⡛⢟⣟⣻⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⡄⠀⠀⠀⠁⡰⠟⢛⣿⣮⣭⣧⣤⣤⣝⡲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢰⢱⣤⣆⡴⢊⠔⢺⣿⣏⡙⣿⣿⣿⣿⣿⣿⢦⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠛⢿⡴⠁⠀⠀⢻⠀⠀⢹⣿⣿⣿⣿⣿⡇⡟⢶
⠀⠀⠀⠀⢀⣠⡤⠶⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡷⠺⠤⠈⠷⡦⠾⠆⠀⣠⣿⣿⣿⣿⣟⡏⢱⣾
⠀⢀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⣤⣤⠄⠀⠄⠀⠘⠻⣿⣿⣿⣿⡟⠀⣾⡟
⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⣉⢿⣿⣀⠀⢀⠀⠀⡀⠀⠈⠙⣿⣿⣷⡦⠉
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢂⠆⠀⠀⠀⠀⠀⠀⠻⢆⣿⡿⠋⠉⠁⠉⠁⢀⠀⠀⠘⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⢈⠳⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠈⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈
⠈⠳⣦⣌⡉⠙⠛⠛⠛⠛⠛⢉⡉⠤⠀⡾⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠀⡀⠀⠀⠀⠐⡆⠀⠀⠀⢹⡤⡤⠐⠁⠀⠀⠀⣆⡀⠀⠀⠀⢸⠤
⠀⠀⠈⠙⠒⠷⠠⠀⠠⠈⠄⠄⠚⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠄⠀⠀⠀⢀⣧⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠤⢴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣦⣤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠐⢶⠶⠆⠀⠠⠀⠀⠀⠀⠙⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠂⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢢⡀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⣀⡠⢐⡲⠿⣇⠀⠀⢱⡀⠘⡦⣤⠄⠒⠀⠐⠂⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⢀⣠⢴⡏⠀⠀⢀⡎⣰⠉⠈⢁⣹⢦⡀⠀⠁⠀⠟⠀⡠⠴⠛⠂⠀⣀⣴⠷⢦⣤⣀⡔⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢶⠏⢩⠀⠽⢿⡓⡠⠼⢧⣀⡇⢠⠊⠀⡤⢹⣶⢤⠀⠀⠀⠀⢀⣠⣴⠞⠁⠉⠳⡔⠂⠹⢁⢂⣮⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⢀⡈⠀⠈⠀⡈⠸⢯⠀⠀⠀⠙⢢⡁⣠⠋⡠⠊⣌⠜⡑⢛⢟⠟⢻⡶⠋⠀⠀⠐⡄⠇⠈⠃⡞⠘⠃⣻⡳⣄⡠⠀⠄
⠀⠀⠀⠀⠀⢸⠉⠀⠀⠈⠳⣄⠑⣄⠀⢀⣴⣧⡀⠑⣤⠶⠒⢛⡿⣯⣩⡤⠊⡖⠚⠛⠛⢆⡠⠊⠀⠀⠀⢰⠁⠳⠤⢤⡴⠃⠰⣋⠆⠁⡸⠁⢠⠆
⠀⠀⠀⠀⠀⠘⣆⠀⠀⣄⠠⣎⠀⢈⢞⠏⠁⠀⢹⣦⡇⣀⣄⡛⠀⠴⢀⠘⠐⠉⢢⣄⣤⠞⠵⣂⣀⠁⠄⢉⠃⡀⠀⠀⠱⠄⢲⠟⠀⢈⠅⠴⢇
⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠘⠚⢽⡏⡜⠠⢠⡀⠈⣷⡾⠀⠠⠂⠠⠃⣸⡲⡀⠼⡱⠋⠀⠀⠀⠈⢻⣠⠞⠁⠀⠀⣀⡀⠀⣧⢀⡠⠖⠂⢀⣀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⢸⡟⣷⡦⢤⣼⢱⡇⠀⢀⡀⡆⢻⡁⠀⡀⠀⢠⠀⠀⢰⣷⡠⣷⣟⠀⣀⡤⠖⠋⠀⠀⠀⠀⠀⣌⠀⠀⣿⠋⠁⠀⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⠻⢶⣼⡄⢷⠰⡀⣀⠀⢌⢿⠋⠇⣀⣀⣠⠞⠃⠭⣉⠉⠛⣾⡁⠀⡎⠁⡅⢀⡀⠰⠄⢀⠀⢀⡟⠛⣩⡿⡋⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠉⠛⠾⣧⣱⣀⠠⠀⢻⢻⠉⠁⠑⣾⠀⠀⠀⠈⡗⠉⢩⣷⣦⣙⠦⢤⣤⣤⠤⠔⣉⣤⠿⠖⡋⠕⡊⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠈⠉⠙⠒⠳⠶⠧⣤⣤⣿⣄⣀⣀⣸⣃⣠⣏⣈⣧⡭⠿⠶⠶⣒⣚⡭⠥⢒⡪⠅⠒⠁⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣒⣒⣒⣛⡭⠭⠕⠒⠺⢍⡓⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣑⢄⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣬⡛⠷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢍⡓⠶⢬⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢒⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠤⢌⣉⡙⠓⠒⠒⠒⠒⠒⠒⠒⠒⠛⣉⣉⠤⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉⠉⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⢲⡤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡀⠘⠀⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠴⠆⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⡀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢄⠀⠘⡣⠤⠔⠂⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠂⢴⡈⠐⡄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠁⠀⠉⠀⣍⠉⠀⠀⠀⠀⠀⠀⡠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⢈⣦⠁⠀⠀⠀⠀⠀⣀⠄⠲⠼⣠⠋⡐⠠⠄⡀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣻⡖⠈⠀⠀⡀⠀⠀⠀⡀⠀⠀⡈⠁⡓⢴⠉⠑⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠁⠀⠿⠀⠀⠐⠀⠰⠔⡌⢡⡄⠠⠅⠀⡀⢅⠀⡈⠁⠀⠀⠀⠀⠀⠦
⠠⠄⠐⠀⠀⠀⠀⠀⠀⠀⢔⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠁⠐⠒⡆⠀⠀⠁⠀⠀⠑
⠀⠈⢠⢈⠤⡀⠀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠂⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢕⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢄⠀⡰⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⠒⡃
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠤⠦⠄⡈⠀⠀⢀⠙⠻⡀⠀⠀⠀⡰⠁⡁⢴⢔⡄⠀⠀⠀⠀⠘⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠂⠀⠀⠹⣄⢀⡔⠁⠀⠀⢐⢊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⡀⠄⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⢴⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠤⠴⠄⠠⠤⠴⠴⠦⠤⠴⠤⠤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⡾⠑⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡤⠈⠚⠉⠉⡷
⠀⠀⠀⠀⡼⠈⠓⢲⠤⠖⢚⣄⣥⣀⣱⣴⣶⠒⡷⠲⡔⠒⠈⢉⡀⠀⡷⠦⠒⠶⠚⢧⣶⡦⣤⠾⡄
⠀⠀⠀⠀⣣⠀⠀⠘⡿⢸⠥⠒⠤⠖⠓⡏⢈⠛⣄⢃⠷⠔⢊⣩⡿⢋⢧⡲⢤⣄⡮⢶⣎⡃⣠⠀⡇
⠀⢀⡠⠼⢇⠁⠌⠄⠉⡦⠒⠒⣒⡩⡖⢻⡌⠀⢘⠿⢲⠶⠟⢭⡜⠁⠄⠀⠠⢾⣃⠀⠀⡟⢀⡱⠓⣄
⠀⠸⣄⣈⠉⠓⠒⠒⠠⠿⠭⠥⠀⠹⠷⠾⠭⠤⠮⡴⠓⣈⡀⠠⠜⠈⠀⠉⠉⠉⣉⣉⣉⣤⠤⢀⡴⠃
⠀⠀⠀⠈⢣⡀⠈⠉⠉⠐⠒⠒⠒⠒⠒⠲⠶⠂⢰⡡⠊⠁⠒⠒⠒⠒⠚⠋⠉⠉⠉⠀⢀⠀⢠⠏
⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠑⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠲⠦⠤⠤⠤⣤⣀⣀⣀⣀⣀⣠⡤⠤⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⣿⣉⣉⣉⣉⣉⣉⣉⣉⣉⣛⣛⣛⣲⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠞⠻⢦⣤⣀⣉⣉⠉⠉⠉⠉⠉⠉⠉⣉⣉⣁⣬⠟⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢻⠶⣶⣤⣬⣭⣭⣉⣉⣉⣉⣉⣉⣉⣉⣩⣥⣤⣶⡾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⠀⢸⡇⢸⡏⢹⡏⢹⡏⢹⡏⢹⡏⠉⡏⠉⡇⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣾⣄⣸⡇⢸⡇⢸⡇⢸⡇⢸⡇⢸⡇⠀⡇⢀⣇⣠⣧⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡟⠙⠛⠛⠻⠿⠷⠾⠷⠾⠷⠾⠿⠿⠛⠛⠛⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⢷⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⡾⠿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣴⣦⣤⣤⣀⣀⣀⣀⣤⣤⣤⡄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢠⣤⣤⣤⣀⣀⣤⣤⣄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢀⣉⣉⣉⣛⣛⡋⠉⠉⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡇⠀⠀⠀⠀⠀⠀⢀⣴⠶⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡏⠛⠿⢿⣶⣶⣤⣤⣤⣤⣤⣴⣶⣶⠿⠟⠛⢻⡇⠀⠀⠀⠀⢀⣴⣟⡱⠋⠀⣽⡇
⠀⠀⠀⠀⠀⠀⠀⢰⡿⠋⠛⠻⡿⠷⠶⣦⡀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢸⣷⣄⠀⠀⢰⡿⠃⠈⠹⣦⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⡀⣠⡇⠉⠛⢸⡇⠀⠀⢻⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⡇⠀⠸⣧⣀⣠⣾⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⢿⣿⣷⣾⠟⠁⠀⠀⠀⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠈⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⢟⣛⡛⣟⠛⠙⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠉⣀⣿⣀⣀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠿⠿⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠀⠀⠀⠠⠖⡡⠐⠒⠒⠠⡙⢦⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄
⠀⠀⠀⠀⠀⠀⡠⢂⠥⢂⠈⠌⢁⠠⠤⢀⠀⠀⠀⡀⠀⠀⠈⠂⢃⠀⢀⡀⢞⠃⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⡠⡪⢚⠕⠈⠀⠐⢊⡔⠂⠀⢨⡇⠢⠀⠀⠐⠄⠀⡀⠈⠀⠀⠹⡄⢣⠁⠀⠳⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢀⠌⠔⠔⠑⠀⠀⠀⡀⠈⠂⢊⠔⠋⠈⠓⠀⠀⠈⢆⠀⠡⠀⠀⠀⠀⠰⠀⠃⠳⡘⣆⣄⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠶⠂
⠀⠀⡌⠀⠀⠀⠀⠀⠁⠀⠙⢄⡉⠀⠀⠀⠆⠀⠆⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⢣⠀⠀⠈⠀⠁⠀⠀⠀⠒
⠀⠀⠀⢁⠀⣤⠀⠛⣀⡀⠀⠀⠉⠀⠀⠀⠁⠀⠈⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⡀⠙⠀⠘⠉⢼⣻⡆⠀⠀⠈⠀⠀⠀⠀⠈⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢴⢼⠰⠔⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤
⠀⠀⡀⠂⠀⠀⠀⠀⠀⢠⣻⠛⠀⠀⠀⠀⠀⠀⠒⢄⠀⡄⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠⠀⠈
⠀⠀⢀⡀⠀⠄⠀⠀⠀⠈⠠⡄⠀⠇⣞⠄⠀⠂⠁⠀⠁⠐⢀⠀⠂⠐⠀⠆⠱⠠⠈⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠘⠀⠀⠀⠀⢄
⠀⠀⡜⠱⠀⢄⠀⠀⠀⠀⠀⠠⠖⠚⣿⢲⡦⢀⡄⢀⠄⠠⢂⠀⠀⠀⠀⡄⠃⠀⡀⠀⠀⠂⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠠
⠀⠀⡇⠀⠈⠀⠁⠀⡀⠀⠀⠀⠀⠀⠉⢋⠉⠅⢀⠠⢊⠔⠁⠀⠀⠀⠀⢟⠀⠰⡇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡄⠀⠀⡈
⠀⠀⠐⠀⠀⠀⠀⠀⠀⡄⢀⠀⠀⠀⠀⢒⣀⠠⠐⠈⠀⠀⢀⡀⠀⡀⠀⢀⣀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠌
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⢿⠀⠇⠈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠂⢉⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠇⠀⡆⠀⢀⠈⠀⠀⢈⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠐⠢⢤⠂⠐⢄⠀⠀⠀⠇⠄⠀⠀⠂⠃⠀⠘⠂⠃⠀⠛⠀⠀⠇⠀⠀⠀⠀⠀⢀⡤⣤⢤⡤⠄⣲⠶⡄⣀
⠀⠀⠀⠀⠀⢀⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⢀⠆⠀⠀⠀⠀⠀⠐⠐⠠⠒⠀⠔⠂⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⡀⠀⠀⠀⠈⠢⢬⣎⡢⠄
⠀⠀⢀⠄⠢⠎⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠈⠈⠄⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁⠀⠀⠀⠀⠀⣠⠎⠀⢢
⠀⠀⠠⠀⠀⡄⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⢢⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⡇⠀⢣⠀⠀⠀⠀⠀⠙⠲⣄⢸⡇
⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⠤⠄⠀⠀⠀⠀⠀⢠⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠑⠊⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⢂⡵⢶⠒⢦⠀⠀⠀⠈⢹
⠀⠀⠀⠀⠀⡂⢡⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠰⠦⢴⣒⣐⠀⡠⠶⠆⠀⠄⠀⠀⡐⡀⣄⣘⠶⢞⡴⠀⠑⡄⠀⣠⠇
⠀⠀⠀⠀⠀⠘⠉⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡜⣯⠍⠄⠀⠀⠀⠃⠁⠀⠀⠀⠀⠀⠺⠀⠀⠏⠀⠀⠀⠈⡁⠀⠀⠀⡼⠜⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⢀⢼⠀⠀⠀⠀⠀⠀⢰⠄⠉⡄⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⢄⠞⠁
⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠛⠄⠀⢌⠀⠀⠀⠀⠀⠀⢸⠀⠀⡁⡼⠇⠀⠀⢀⡠⠒⠉⣀⠤⠀⠀⠀⠀⠀⠉⠀⠀⠚⠛⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠔⠒⠒⠶⠤⢀⠀⠄⠀⠀⠀⠀⠀⢸⠀⡏⠁⡇⠀⠠⠚⠁⠀⢀⠄⠃⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢀⠃⢀⠈⡊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠺⠄⡰⠃⡀⠰⠅⠒⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡴⠴⣾⣲⠴⡲⣆
⠀⠀⠀⠀⠀⠀⢠⠚⠳⠵⠲⣆⠀⠈⣥⣼⢏⣿⡇⢉⠌⠉⢡⣿⠐⠦⠀⠀⠀⣠⣤⣴⡤⠿⠿⢆⢀⡀
⠀⠀⠀⢀⡴⠚⠛⣤⣄⣠⡇⠉⢻⣿⡧⢠⡈⢸⣿⣿⣠⠄⠈⢉⣿⣿⣷⣶⡟⠁⠈⠋⡀⢰⣠⡾⢛⠟⣳⠄
⠀⠀⠀⢘⣧⠀⠰⣾⣿⠟⠿⠲⣿⣇⣐⢦⡹⣼⣿⣿⣵⡶⠂⠈⢿⡟⠁⠄⢀⠀⣳⢴⣥⡘⠛⠛⢃⣀⣻
⠀⢀⣴⣿⡏⠀⣶⡏⠉⣀⣦⡆⢸⢿⣿⣤⣿⢟⡿⠙⣿⣿⢁⣰⣿⣁⣦⡼⢿⣾⣅⣾⣿⣿⣷⠦⣼⣿⣯⡄
⢠⡟⣿⣿⣷⡶⠿⢷⣏⣿⣼⡇⣀⣘⣿⠋⡴⠋⣤⢯⣿⣿⡿⢟⣿⣟⣩⠤⣤⡀⠜⠻⠿⢍⣻⣿⣿⣿⣿⡿⣦
⣾⣿⣿⣧⠀⠠⣀⡆⠈⣿⡿⢿⣿⣿⣡⠞⡁⡾⣫⣾⣿⣫⠖⣛⣉⠉⠻⡛⠿⠹⣿⢿⣿⣿⣇⣈⠁⢈⣿⡇⢹
⣿⢿⣿⣿⣤⣍⡛⠳⣴⡇⠀⡄⣿⣿⣧⣬⣼⣾⢿⣿⣿⣶⣾⣿⡿⢷⣦⣶⣾⣶⠈⠣⠈⠛⠿⠏⣠⣾⣿⣇⣼
⣿⠈⠻⢿⣿⣿⠡⠤⢼⣧⣼⠀⣸⡿⠙⠿⣿⣶⡾⣿⣄⣰⣋⣀⣤⣾⣯⣽⡿⣿⣿⣶⣾⡟⠻⢿⣿⣿⣿⢟⣹
⢸⡈⣷⣤⡉⠻⢷⣦⣄⣹⣿⣿⠿⠞⠲⣾⠛⠻⣖⣻⡿⢷⣦⣇⠀⢣⠉⢿⣧⡘⢿⣻⣿⣿⣦⡽⢟⣫⣴⣿⡿
⠀⢧⠹⣿⣿⣷⡦⠤⠉⠛⠛⠷⠶⣶⣦⣤⣦⣴⣈⣁⣴⣀⣉⣿⣷⣮⣧⣼⣿⠿⢾⣛⣛⣭⣵⣾⣿⣿⡿⣽⠃
⠀⠈⢧⠹⣿⣿⣿⣯⠄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣱⠃
⠀⠀⠈⢳⡘⢿⣿⣿⣽⣒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣭⣽⣿⣿⣿⣿⣿⣿⣿⣟⡽⠃
⠀⠀⠀⠀⠙⢦⡙⢿⣿⣷⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢒⣛⣿⣿⣿⣿⣿⣿⡿⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠙⠦⣝⠻⣿⣯⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣽⣶⣿⣿⣿⣿⠿⣫⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣌⣛⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢭⣿⣿⡿⠿⣛⣭⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣤⣭⣭⣵⣶⣾⣿⠿⠃

⢀⣴⠟⠻⣆
⣼⠇⢀⡾⠃
⣿⠀⣿⠁
⢻⣆⣿⣀⣀⣀
⢀⣿⠋⠉⠉⠙⠻⣦⣀
⢸⡇⠀⠀⠀⠀⠀⠀⠙⠷⣤⣄⣀⣀⣀⣀⣠⡴⣷⡀
⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⣠⡿⠁
⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡖⠒⠒⠒⠛⠻⣦⣀
⠀⠘⣷⡀⠀⠀⣾⠲⠶⠤⢤⣤⡽⠆⠀⠀⠀⠀⠀⠙⠷⣄⡀
⠀⠀⠈⢷⣄⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠙⢷⣄⡙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠉⠻⣮⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⢶⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠶⠶⢶⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣤⣤⠿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣿⣟⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣭⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠋⠉⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡓⠂⠀⠀⠀⠚⡉⠂⠀⠀⠉⠉⢉⢩⡅⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠿⠆⠀⠀⠸⠿⠃⠀⠀⠀⠀⢱⡆⠃⣀⠔⢸⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⣈⢴⠊⠀⠐⠋⠉⢉⠍⣠⠞
⠀⠀⠀⡀⣤⠀⠀⠀⠀⠀⠀⢧⠀⢤⠤⠤⢀⡠⠄⠀⠀⠀⡀⠡⡼⢶⠶⠿⠭⠄⠒⠈⠁
⠀⠇⠀⠄⠋⠓⣦⢤⡀⠀⣠⣤⣷⡄⠻⠉⠹⠁⠀⠀⢀⡔⣀⣴⣿⣷⣤⣤⣀⡀
⠀⡄⠀⠀⠓⠀⡌⠀⢰⣾⣿⣿⡏⢹⡄⠒⠃⠀⣠⣴⡫⢕⡫⡾⠃⣿⣿⣿⣿⣿⣿⣷⣶⣄
⠀⠈⢦⡀⠈⠠⢁⣴⣿⣿⣿⣿⣿⣿⣿⣶⢖⣋⠉⡀⠀⠁⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠄⠊⠙⠻⣿⣿⣿⣿⣿⣿⣿⣍⠽⠳⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣾⣿⣿⣿⣿⣿⣿⣦⣙⠿⣿⣿⣿⣿⣿⣿⣿⣿⡹⣿⣿⣿⣿⣿⣷⡄
⡀⠀⠀⠀⠀⡇⠀⠀⣠⠶⠟⠋⠨⠟⠛⠛⠛⠛⠛⠛⠛⠳⣬⣙⠿⠿⢿⡿⠟⠛⢷⣽⣿⣿⠟⠋⠉⠙⢄
⡇⠀⠀⠀⢠⢂⠴⠋⠀⢀⠤⠤⣀⣈⣀⣤⡀⡠⣤⣠⣤⣾⣿⣿⣷⣿⠛⠀⠀⠀⠀⠈⠉⠉⠀⠂⠀⠀⠀⠙⠢⢄
⠱⠤⠤⠄⠊⠁⠀⠀⠀⢸⣿⣿⣿⠿⣿⠿⡿⢿⣿⣟⣿⣟⡁⠉⠉⠙⢼⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯⣭⣿⢿⣿⣽⣿⣿⣿⣿⣟⣳⣆⠀⠀⢀⠊⠐⠤⠐⠀⠂⠉⠀⠉⠒⠤⡀
⠀⠀⠀⠀⠀⢄⠀⠀⢼⠛⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⡿⠿⠁⢈⡡⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠉⠐⠒⠦⠤⠭⠭⠉⠭⠭⠽⠯⠥⠜⠂⠲⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣆⠀⠀⠀⠀⠀⠀⠀⢸⡴⠋⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠳⡇⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢠⠞⣧⠀⠀⢀⣀⡤⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠉⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⣀⠀⠀⣠⠋⠀⠘⠚⠉⠉⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠈⠙⠲⢤⠞⠉⠉⠙⠣⡀⠀⠉⠳⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⡞
⣀⣀⣀⣀⣀⣀⣀⣀⣀⡈⣧⠀⠀⠀⠀⡰⣋⣞⠉⣱⣄⡀⢸⡄⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⡼⠁
⠙⣄⠀⠈⠉⠉⠉⠀⠈⠉⠉⠀⠀⢠⡾⣽⠣⣼⠃⢌⣇⡜⡸⠀⢀⡤⠲⡈⠳⣄⠀⠀⠀⠀⠘⠧⠤⠤⢤⣤⣀⣀⣀
⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠒⠲⢧⡦⢴⠛⣬⣶⠁⡰⠛⢢⠰⢇⣠⠟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠈⢾⣠⣿⠏⠻⣅⣀⠼⣀⡠⠃⢱⠛⡆⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⣨⠆⠀⠀⢠⡇⠀⠀⠀⠀⠠⠁⠀⣼⠟⠁⠀⠀⠘⠷⣤⢼⠒⠒⡇⢀⠇⠀⠀⠀⠀⠀⠐⠛⠲⠤⣄⣀
⠀⢀⡠⠖⠋⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠈⠛⠳⠿⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡨⠽⠗
⠶⣉⡀⠀⠀⠀⠀⠀⠀⠀⠙⠤⣀⣀⣤⠞⠉⠀⠀⠀⠀⠀⠀⣀⣤⣤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉
⠀⠀⠉⠙⠒⠤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢶⡛⢏⣙⡦⢵⣈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀
⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠉⢫⠈⣇⣸⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⡏⣧⣞⡁⠀⠀⠀⠀⠀⢀⣀⣠⣀⣀⣀⣀⣀⣈⣶⡄
⠀⠀⠀⣴⣁⣤⠤⠤⠶⠒⣶⠂⠀⠀⠀⡠⢿⡀⠀⠀⠀⢀⣠⠴⠋⠁⠀⠉⠙⠲⢤⣀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣠⠔⠋⠀⠀⠙⠓⠒⠚⠋⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⠑⠢⢌⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⡠⠞⠁⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡽⠃⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⠀⢀⡴⠋⠸⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠦⣄⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢨⣇⡀⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠂⢀⡀⠀⠀⠀⠀⠀⠀⢴⠒⢣⡦⠔⢘⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠖⠀⠀⠐⠠⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠙⠀⢀⠁⠠⡾⢸⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠒⢻⠊⠀⣠⠀⡠⢰⠀⠈⠀⠈⢲⡀⠀⡠⠀⠀⢉⣽⣷⣶⣴⢂⡴⠒⠲⡄
⠀⠀⠀⠀⢄⠀⢄⠀⢀⡀⡀⡂⠀⠀⠀⠀⠲⠀⡐⠁⠀⠀⠁⠀⡀⡀⠄⠀⠀⠀⠀⠀⣠⣿⣮⡵⢭⣿⡌⢠⠄⣀⡟⠀⢠⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠠⠶⠯⠅⠀⠾⠃⠈⣆⡀⠀⠀⠀⠀⠀⠈⠣⡤⠂⠸⡏⠉⠇⠀⠀⠀⠀⠀⠀⠉⠷⣟⣧⣾⡼⡗⠡⠂⠈⢳⣤⣤⢤⡄⠀⠀⠀⠸⢀⣴⣃⡀
⠀⠀⠀⠀⠀⡶⢀⡀⠶⠁⠀⠀⠁⠀⠀⠀⠂⠀⠀⢠⡽⠷⡆⠀⠁⠀⠀⠀⡰⠂⡤⠀⠀⢀⠀⡿⠤⠀⠑⠨⠀⢀⣋⠈⠂⢀⣾⣟⡭⢿⣯⣀
⠀⠀⠀⠀⡀⠀⠀⠀⢉⠵⠀⣠⣶⣾⣷⣤⡀⠀⠀⠀⠁⠐⠀⠀⣈⠂⠀⠀⡁⠄⠁⠄⠁⡄⡞⠀⠀⠀⠀⠀⠈⠁⢀⣤⠤⠾⢏⠣⣀⡔⣻⣷
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⣱⣿⡟⢘⢿⢽⡀⠀⠀⠀⠀⠐⠀⠀⠀⣀⣠⣈⡀⢰⠃⢈⠸⠀⠀⠀⠄⠠⠊⠐⠐⠈⡓⢦⠘⣌⠮⠤⣴⣡⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣸⣿⢯⡉⣁⠞⡽⠉⠲⣄⠀⠀⠀⢀⣦⠈⠋⠉⠉⠑⠠⠍⠈⢠⡇⠐⠠⡺⠁⠔⠑⠶⠖⠾⢠⠀⠀⠉⠋⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⠉⠓⠋⠀⠰⠞⠛⡟⠷⡒⣁⣀⣀⠰⠀⠀⠀⠊⠀⠀⡆⢁⠀⢀⡞⠒⠠⠌⠫⠄⠀⠘⠈
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠁⠀⠀⠈⠉⠀⠁
⠀⠀⠀⠀⢀⣴⣿⣿⣿⡟⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢸⣿⣿⣿⡿⠁
⣀⣀⣀⣀⣘⣿⣿⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠉⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣛⣭⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠻⣿⣿⡿⠿⠿⢟⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⢀⣀⡀⡀⠈⠛⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⠀⢻⠿⡤⠀⠀⠀⠟⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⠀⠀⠀⠀⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣑⡒⠊⢀⡀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⡓⠀⠉⠀⠀⢀⣤⠂⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠤⢶⠿⣿⣧⣀⣀⣠⣴⠟⠁⢀⠀⢸⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢿⡇⠙⣿⡍⠁⢀⡄⠀⠀⡎⠀⠈⣏⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣠⠟⠀⠀⢀⠀⠀⠀⠀⡀⠸⠇⠀⠈⣧⣤⠈⠀⠀⢸⠃⠀⠀⣿⠀⠀⠉⠓⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⡁⠀⠀⠀⠀⠀⠉⠀⠺⠁⠀⣾⠠⠞⣿⣿⠢⡀⠀⡌⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠋⠑⣄⠀⠀⠰⠀⠀⠀⡄⠀⠀⠐⠀⠀⢿⡄⢀⣿⣷⡀⠀⢰⠃⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠼⠃⠀⢀⠀⢠⡇⠀⠀⠀⠀⠀⢸⡇⢸⣿⣿⡇⠀⡎⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢹⠂⠀⠈⠀⢸⠃⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⣿⢰⠃⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠈⠘⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠇⣄⠉⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡟⠀⠀⠀⡜⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⣞⡼⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠃⠀⠀⡼⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠀⠀⡰⠁⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇⠀⠰⠁⠀⠀⠀⠀⣧⠀⣀⣀⣤⣤⣄⡀⢻⡀
⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢠⡏⢠⣿⣿⣿⣿⡋⣁⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⣀⣠⡼⠟⣿⠀⠀⠀⢰⡿⠀⠀⠀⠀⠸⠟⢠⡴⢀⣠⡄⠀⠀⢸⡇⠈⣿⣿⣿⡟⣼⡿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣛⣉⣀⣀⣀⣿⠀⢀⠀⠈⠁⠀⠀⠀⠀⠀⠰⣿⣅⡉⠁⠀⠀⠀⡼⠧⠤⠬⠷⢤⡾⠿⠦⠴⠷⠶⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢧⣀⡈⠓⠶⠶⠶⠶⠒⠀⠀⠀⠊⣉⣁⡤⣤⠤⠊⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠷⠿⠿⠿⠿⠛⠛⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣖⢀⣖⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠶⠶⢦⣄⠀⠀⢀⡀⠀⠀⠀⢰⣿⣦⣴⡇⣥⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢱⠁⠀⠀⠀⠀⠀⠀⢰⣾⣶⡆⣾⢫⣶⡿⠛⢿⣷⣝⣷⡀⣿⡇⠀⠀⠀⢸⣿⣿⢡⢳⣿⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⣾⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⢸⡏⣿⣿⣧⠀⣾⣿⣿⢸⡇⢻⡇⠀⠀⠀⠈⣿⣿⢸⠸⣿⣇⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⣿⡹⣿⣿⣆⢻⣿⢟⣾⠃⢸⡇⠀⠀⠀⠀⠘⣿⣼⡀⠈⠿⣾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠻⣮⣭⣟⣯⣵⠿⠃⠀⠈⠁⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠈⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⢠⡰⡄⣎⡦⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢰⠼⣰⣠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣶⠆⡦⡖⠂⢀
⠀⠀⠀⠀⠀⢀⡾⠃⠁⢀⠠⡄⠈⠈⢳⡄⠀⠀⠀⠀⠀⠀⣴⠜⠚⢁⡠⢆⠉⠒⠡⣆⠀⠀⠀⠀⠀⠀⢠⠙⠟⠁⣀⠤⡉⠀⠋⢥⡀
⠀⠀⠀⠀⠀⣾⠀⠀⠀⣿⣿⠟⠀⠀⠀⢻⡄⠀⠀⠀⠀⣸⠃⠀⠀⢸⣿⡟⠃⠀⠀⠸⡇⠀⠀⠀⠀⢠⡏⠀⠀⠀⣿⡿⡇⠀⠀⠈⣷
⠀⠀⠀⠀⠀⣧⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢻⠀⠀⠀⠘⣿⠠⠀⠀⠀⢀⡟⠀⠀⠀⠀⢸⡇⠀⠀⠀⢻⣷⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠹⣧⠀⠀⢠⡟⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠘⢿⡄⠀⢀⡼⠁⠀⠀⠀⠀⠀⢻⡄⠀⠀⠈⢻⣆⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⣀⣨⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣤⣀⣀⣥⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣄⣀⣡⡴⠞⠁



⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣿⣷⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣷⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣶⣶⣄⡀
⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⢟⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢀⣾⣿⡿⢟⢿⡿⣛⣿⣿⣧⡀⠀⠀⠀⠀⠀⣴⡿⢟⢿⡿⣛⣿⠿⡻⣿⡄
⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⣼⣿⣿⣿⣿⡆⠀⠀⠀⠀⣼⣿⣿⡇⠀⣼⡀⠠⣾⣿⣿⣇⠀⠀⠀⠀⢰⣿⡇⠀⣼⡄⠠⣾⠀⣠⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⡀⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢻⣿⣿⣷⡀⢿⣧⠘⣿⣿⣿⡇⠀⠀⠀⠀⠸⣿⣷⡀⢿⣧⠐⣿⣆⠻⣿⣿
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣷⣬⣿⣿⣿⠏⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣬⣿⣷⣼⣿⡟⠀⠀⠀⠀⠀⠀⠹⣿⣿⣬⣿⣷⣼⣿⣦⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⠿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⡐⠉⠠⠀⠀⠀⠀⠀⠀⡠⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡈⠓⠔⡡⠀⠐⡘⠃⢐⡀⣨⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠜⠀⠀⠓⡄⠀⠀⠀⠎⠒⠓⠢⡤⠀⢤⢀⠗⠈⢱⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠤⡀⠂⠀⠀⠀⣂⡈⠁⠀⠀⢠⠖⠈⠉⠍⠣⠀⠾⡗⢀⠖⠚⢼⠄⢄⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠬⡄⠄⠘⡀⠻⣤⠴⠆⡙⠛⠓⢄⠀⠀⡇⠀⠀⢀⡠⠄⣦⣈⣁⡉⠀⠀⣰⠀⠈⠁⠀⠥⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⡄⠐⡘⡀⠡⡴⠅⡘⠀⠀⠀⠀⣸⠤⠒⣇⢀⡰⠉⠁⠀⠀⠀⠈⢅⡱⠜⠾⣷⡀⠀⠔⢢⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣠⣄⠔⡪⠉⣛⡛⠣⡀⠈⣦⡤⡕⡼⠁⡀⡴⠛⡐⠅⠀⠀⠀⠀⠀⠀⣃⠔⠁⣠⠏⠱⠎⠀⢸⠀⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⣠⣢⣎⡔⠉⠄⠌⢷⠑⡤⠉⠀⡙⢀⣬⡊⢈⡀⢰⣌⠙⡳⠂⣶⠴⢦⠋⢀⡾⢁⣀⠀⠁⠀⠌⢈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⡀⠀⠱⣀⠜⠙⡬⠆⠗⠠⣀⣡⠊⠀⠈⠁⠉⠁⠘⠷⠉⠀⠈⠑⢦⠔⣡⡤⠤⡈⠻⣀⣀⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢶⡀⠀⡂⠀⠙⠲⠀⠀⢸⠁⠀⠄⢤⠵⠤⠤⡔⠀⠀⠀⠀⠀⢠⠹⠋⠀⠑⠌⢤⠋⢰⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡮⡣⢄⡇⠀⠀⠀⠄⠀⠸⠰⠁⣰⠁⠀⠀⡰⠇⡄⠀⠀⠄⠀⠈⢀⠃⠘⠐⢢⡸⢔⢵⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠁⠒⠤⢀⡺⠄⢠⣂⡇⠀⠙⡀⠈⠈⠁⢡⡀⢀⣀⣀⣴⢡⠮⠀⡒⠄⠒⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠉⠀⠒⠐⠈⠈⠩⠦⠤⠬⠥⠍⠁⠁⠂⠒⠀⠉⠀⠀⠀⠀⢀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠤⢀⣀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠔⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠒⠶⠋⠙⠚⠉⠙⠚⠋⠙⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣀⣠⠦⠤⠴⠞⠲⠶⠛⢦⣄⣠⢤⡀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⢀⣤⠞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠲⣄⡀⢀⣸⠷⣄
⠀⠀⠀⠀⠀⠀⢀⡤⢿⣀⣰⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢧⡀⢹⡄
⠀⠀⠀⠀⠀⠀⢸⠃⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠹⡄
⠀⠀⠀⠀⠀⢀⡟⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡦⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣴⠃
⠀⠀⠀⠀⠀⠸⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠧⣤⣀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣴⣤⣴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢸⡾⣿⣿⠿⣿⠃⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣄⡀⠀⠀⣼⢿⣿⣿⣯⡽⡇⠀⠀⠀⣀⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣟⠲⠾⡀⠀⠀⠀⣰⠷⠖⠛⠉⣩⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⢹⠋⠙⠓⠻⢦⢀⡾⠧⠶⠶⠒⠋⠉⢿⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⡿⠀⠀⠀⠀⢸⢸⡀⠀⠀⠀⠀⠀⠀⠸⡆⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢠⣼⣇⣠⠴⠖⠛⢻⢸⡇⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢸⠇⠀⠀⠀⠈⢋⣩⣇⡀⠀⠀⠀⠀⠀⠸⡆⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢈⣉⣼⠃⠀⠀⠀⠀⠀⠀⢷⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⣀⣸⣇⣀⣀⣀⣀⣼⠋⠉⢳⣄⠀⢀⣀⡀⠀⠸⡆⢀⣤⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣰⣇⣨⣭⡽⣏⠀⠈⣿⠙⠦⠤⠞⠉⣩⠟⠻⢯⠛⢶⣷⣞⢁⡟⢳⡀
⠀⠀⠀⠀⢠⡟⠉⠛⣉⡿⠿⣶⠿⣿⡖⠋⠀⠙⠒⠚⠃⠀⠀⠀⠀⠀⢻⣄⣀⡼⠀⠀⢹⠞⢻⣟⠻⢿⣝⠉⠉⠙⢧
⠀⠀⠀⢀⡞⠀⣠⠞⠁⠀⣴⣾⣿⣉⣧⣤⠴⢛⣧⠀⠀⣠⣤⣤⣄⠀⠀⣠⣴⢤⣤⠟⢋⣠⣿⠟⢒⡆⠈⠳⡄⠀⠘⣇
⠀⠀⠀⡾⠁⠀⢿⡀⠀⠀⠻⣍⠛⠯⣝⣓⡛⠻⠿⠶⠾⠿⠒⠚⠛⠛⠛⢁⣀⣠⡤⠖⢋⣴⡛⣶⠋⠁⠀⢀⡿⠀⠀⠸⣆
⠀⠀⣼⠁⠀⠀⠀⠛⢦⣄⡀⠈⠓⠦⣤⣉⣉⠛⠛⠓⠒⠒⠒⠒⠛⠛⠛⢉⣉⣤⠴⠞⠋⠀⠙⠛⠀⣠⡴⠛⠀⠀⠀⠀⠹⡄
⠀⣰⠃⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠦⣤⣌⣉⣉⣛⠛⠛⠓⠚⠛⠛⠛⠉⠉⣁⣀⣀⣠⣤⠴⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⢻⡀
⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣶⣦⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡏⠉⠉⠙⠛⠛⠻⠿⢿⣿⣿⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣄⠀⠀⠉⠻⣿⣦⣄⣠⣤⣤⣴⣶⣶⣶⣾⡿⠿⠿⠿⠟⠛⠻⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠙⠻⣿⣯⣍⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣤⣽⣿⣷⣄⡀⠀⠀⠀⠙⠻⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣟⡛⠛⠋⠉⠉⠉⠙⠻⣿⣶⣤⣀⠀⠀⠀⠉⠛⠿⣿⣷⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⣻⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠀⠈⠙⠻⣿⣷⣤⣀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣦⣄⣀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣿⣷⣶⣶⣶⣶⣿⣿⠁
⠀⠀⠀⠀⠀⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣦⣄⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣶⣤⣄⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢉⣿⠃
⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⣿⣶⣶⣤⣤⣤⣤⣤⣤⡾⠋
⠀⠀⠀⠀⣼⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠉⠉⠉⠉⠁
⠀⠀⠀⠀⣿⣿⡿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣷⣦⣄⣀⣠⣾⠟⣿⣿
⠀⠀⠀⠀⠘⣿⣧⡈⠙⠻⣿⣿⣶⣦⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣿⣿⣿⠟⠋⢠⣿⣿
⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠈⠉⠙⠛⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠋⠀⠀⣠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣷⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣴⣶⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠢⢀⡀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠁⢄⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⢄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠙⢟⢦⡀⠀⠦⠀⠀⠑⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⡙⢄⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠢⠥⠀⠀⢀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⠀⠀⠀⠠⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠂⠀⠀⠀⢀⣤⣾⣿⣿⣿⣷⡄⢀⡀⠀⠀⠀⠑⠢⠀⣀⣁⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢋⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⡰⠆⠐⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡅⢉⠷⠦⡀⠀⠀⠀⠀⠁⢸⣿⡀⠉⠉⣿⣿⣿⣿⡿⠀⠀⠀⠀⡀⢄⠀⠠⡚⢾⢌⠑⠦⠀⠀⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠐⢇⠸⠁⣤⠀⣄⠀⠀⠀⠀⠆⠀⠿⢷⠀⠘⣿⡿⠻⠛⠃⠀⠀⠀⣠⣮⠎⡡⡀⠘⠂⠋⢵⢆⠂⢵⡀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⠘⣱⠂⣡⡈⠳⠢⢀⠀⡠⠒⢢⠊⠉⢣⠀⣿⡠⢐⡒⢄⠀⢀⠔⠀⠰⣾⠀⠀⠀⠀⠀⠂⠉⠘⠙⠉⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠡⣴⡇⠀⠀⠙⠀⠀⢨⠀⠀⢀⠀⠙⠀⢁⣠⡾⠶⠊⢀⡠⠂⠔⠀⠀⠀⠀⠀⠀⠀⠁⠠⢀⡈⠂⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⣀⣠⣀⣤⣤⡤⠔⠒⠠⢀⡴⠂⠈⠉⠈⠳⠤⠌⠀⠀⠈⣿⠦⠀⢠⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠸⢿⣿⣿⡏⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣰⣦⣤⣀⡀⠀⢩⡐⠘⠁⢛⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡤⠖⠠
⠀⠀⠠⠄⠀⠀⠀⢀⣞⣠⣄⠀⠙⢄⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⢀⡠⠚⢿⣿⣿⣿⣿⣶⣼⣇⡇⠡⡀⠙⣧⠀⠀⠀⠀⠀⠰⡁⠈⡎⡆⠀⠀⡀
⠀⠀⠠⢤⡄⠐⠂⠈⠃⠀⠨⠁⠀⡌⠁⠀⠚⠂⠤⠶⢆⣠⢀⣀⢉⢀⡠⠊⠙⠛⠿⣿⣿⣿⣿⣿⣄⠘⠄⠈⠻⠗⢄⡀⠀⠀⠈⣵⢠⠠⠀⠀⡄
⠠⠞⣀⠄⠀⠰⠦⣀⠀⠀⣘⡆⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠛⠈⠑⢠⠋⢹⠿⢿⣿⣷⣌⠽⠃⠀⠑⡿⠆⠀⠀⠣⠄⠣⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠋⠁⢀⠈⠑⢢⡴⡄⢀⣀⣀⡤⣴⠀⠀⠀⠀⢠⣄⡀⠠⠎⠀⡸⡀⠶⣷⠀⠉⠈⠢⠠⠀⠸⠿⠷⠄⣶⠄⠀⢀⠄⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⠀⠀⣸⠀⠀⢸⠀⢠⣠⠤⢷⠀⠀⣠⠲⠤⡄⣠⠊⢀⠀⠀⢠⠇⡄⣶⣼⣄⣀⡀⠀⠀⠀⠀⠀⠀⠮⠤⣄⠀⠈⠧⠢⡀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠠⠀⠀⣸⠀⠀⡤⠂⡛⠀⢀⠃⠈⠤⢁⡌⠔⠁⠀⣴⣿⠾⠠⠆⠤⣇⠀⠀⠀⠂⠀⢄⠀⠰⠀⢠⡄⠑⠊⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⣴⢏⠠⠊⠀⠀⠝⠁⠀⠳⣀⡀⠀⠀⢀⣤⠊⣡⣴⣾⠋⠈⡐⢾⠀⠀⠀⠀⠄⠀⠹⡘⢂⣟⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠙⠿⣦⣆⠘⢡⢂⡀⡄⡲⢶⣼⠂⠁⠀⠀⠀⠀⠀⠈⠁⣏⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣞⣣⢸⠷⣮⣝⢰⣘⣂⣂⡅⠷⢶⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠂⠒⠒⠒⠒⠒⠒⠒⠶⢤⣦⣶⠶⠠⢒⡆⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠘⠧⣄⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⣶⡆⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⡀⠀⠀⠀⣠⠞⠀⠀⠈⠓⣦⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⠏⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡿⠀⠀⠀⠓⣄⠀⠀⠀⣖⠋⠀⠀⠀⠀⠀⠀⠀⡞⠀⠈⢀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⡄⠀⠀⠀⠤⠞⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⢰⠇⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢀⣀⣀⠀⠀⠀⠀⠀⠋⠁⣀⣀⣀⠀⠀⠀⡼⠀⠀⡼
⠀⠀⠀⠀⣤⣤⠤⠤⠶⠶⡶⠋⠁⠈⠙⣖⠒⠒⠒⢲⠎⠁⠀⠈⠳⡖⢲⠇⠀⣸⠷⠶⠤⢤⣤⣄
⠀⠀⠀⠀⡏⠉⠉⠉⠉⠙⠛⠛⠃⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⢹
⠀⠀⠀⠀⡇⠀⡴⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢦⡀⢸
⠀⠀⠀⠀⣧⠘⣇⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⢀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠸⣆⡀⣠⠇⡟
⠀⠀⠀⠀⢹⡀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠈⠋⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣸⠃
⠀⠀⠀⠀⠀⢳⡀⠀⡤⠶⣄⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⣠⠋⠀⠀⠀⠀⠀⠀⡤⠶⣄⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠳⣄⠳⡤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⠀⠀⠀⠀⠣⡤⠞⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠠⣄⠀⠀⠀⠀⡖⢲⠀⠀⠀⠀⠀⠀⠀⠀⡔⢲⡄⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣀⡤⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣏⣉⣉⣉⣉⣉⣉⣉⣉⣹⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠋⠉⠙⠛⠲⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠛⠛⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⡾⠥⠤⠤⣀⡀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⠏⠀⠀⠀⠀⠀⠉⠓⣄⠀⢀⡼⠁
⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⡞
⢀⡴⢏⠉⠋⠉⠙⠓⠦⣄⠀⣷⣀⣀⣀⣀⣀⣤⡤⠤⠤⠶⠒⠚⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⣾⡇⠀⠑⢦⡀⠢⡀⠀⠈⠙⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁
⣯⠱⡀⠀⠀⠙⢦⡈⠢⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠹⡄⠱⣄⠀⠄⣀⠙⠢⡘⢦⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠰⠐⠀⢀⡾⠁
⠀⠙⣆⠈⠣⣄⠀⠀⠀⠈⠢⡙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡴⠏
⠀⠀⠈⠛⢦⣀⠉⠒⠦⠤⠤⢾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠶⠴⠶⠚⠉⠀⠀⠀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠛⠉⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢀⣠⠴⠚⠋⠉⠁⢀⡠⠞⠋⣻⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⢀⣴⠋⠁⠀⠈⠁⡠⠖⠉⣠⠔⠋⠁⢀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠈⠛⠲⠶⠶⠒⠋⠁⠀⠀⠀⠀⣼⠃⠀⠀⣠⠔⠁⢀⡴⠊⠡⠀⠀⢀⢼
⠀⠀⠀⠀⣠⡞⠻⢭⣀⠀⠀⠀⠀⠉⠛⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠦⣴⠋⠀⣀⠔⠁⠀⢀⣀⠤⠞⢁⡾
⠀⠀⢀⡾⠉⠙⠲⢤⣈⠉⠒⠤⣀⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠘⢧⣀⡉⠉⠉⠋⠉⣉⣉⣀⡤⠶⠋
⠀⠀⢸⣧⣀⠀⠀⠀⠈⠙⠲⢤⣀⠉⠒⠤⣄⡀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⢿⡈⠓⠦⢄⡀⠀⠀⠀⠈⠙⠲⢤⣀⣉⣳⠖⢻⡆
⠀⠀⠀⠈⠳⣄⠀⠀⠈⠉⠑⠒⠒⠒⠒⠚⠋⠉⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣿⣶⣶⣶⣶⣾⣯⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣩⣭⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡓⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠒⠷⠞⠉⠛⢻⡆
⠀⠀⠀⠀⠀⠀⣾⠛⣆⣀⣀⠀⠀⣠⣤⡇⢳⡀⠀⢧⡀⠀⣀⣀⣠⣄⣀⠀⠀⣀⡀⠤⠔⠚⢩⠹⡇⠀⢀⣀⠀⣀⡾⠃⣀⡀⠀⠀⣠
⠀⠀⠀⠀⠀⢴⠛⠀⠈⠀⣸⢋⡋⢀⡤⠧⡴⠷⠴⠶⢿⣿⢿⡉⡡⠛⡍⢻⡁⠆⠂⣀⣤⣄⣀⣸⠉⠙⠋⠈⠋⠉⣙⠻⣿⣏⠳⠶⠉⢷
⠀⠀⠀⠀⠀⢘⣆⠀⠀⠀⠉⣿⠉⣻⠴⠚⢦⡴⠚⠉⢲⡇⢀⠉⠳⡌⢇⣹⠷⠒⠋⣉⣴⣾⠇⡹⢖⣚⡤⢤⢄⣮⣴⣶⣮⣹⠀⣤⠀⢸
⠀⠀⠀⢀⣀⣿⠉⠃⢈⣆⠀⠙⢶⣁⡤⠴⢤⠴⢚⣥⠾⣧⠐⢇⠀⢻⣿⣤⣤⣴⣮⣗⢋⡵⠋⠀⣈⠀⠀⣩⢽⠗⠀⠀⠈⣿⠊⠈⢧⡾⣤⡀
⠀⠀⡜⠉⠠⢤⣷⣄⣀⣈⠣⠀⢸⣧⠤⠴⠒⠒⢯⣠⡀⣹⢣⡀⢁⡼⢋⣤⣊⡩⠄⠈⠉⢧⣤⣬⣤⣤⠤⣭⠽⠶⠦⠤⠴⠧⠀⠒⠊⠀⢨⡇
⠀⠀⠳⠤⢤⣀⠀⠀⣉⡉⠉⠉⠛⠛⠒⠒⠒⠒⠒⠛⠛⠓⠒⠛⠚⠓⡿⠋⣁⡤⠤⠒⠒⠋⠀⠀⠀⠀⣀⣀⣀⣀⣤⡤⠤⠶⠖⠋⣠⠔⠋
⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠈⠉⠉⠉⠑⠒⠒⠒⠒⠒⠒⠶⠶⠖⠂⣼⢠⠞⠁⠀⠐⠒⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⢀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠁⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠶⠦⠤⢤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡀⠄⠀⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢌⡔⠊⣠⣶⠷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰⠏⠀⢘⡕⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠈⠲
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠘⠁⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠐⡄⠀⠀⠀⠰⠀⡠⠄⡠⠐⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠀⣰⠃⣠⠈⢢⠀⠀⠀⢲⠀⠠⣅⠀⠀⣠⢃⠠⠄⠒⠒⠈⠁⠀⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠙⠐⠀⢈⢹⣧⠀⠀⠀⠂⡼⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠠⠄⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣀⠀⠀⠀⠀⠀⡠⠞⠀⠀⠔⡒⢆⡉⢰⡄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠠⠂⠈⡀⠀⢠⠒⠖⠠⠤⢤⠠⣄⢀⡈⣙⣋⡉⠉⠀⠀⠀⣀⠰⠇⡾⠟⠣⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠓⠶⠤⠴⠄⠤⠄⠥⠠⠃⠀⠀⣀⡤⢎⣀⣀⣀⣀⡀⣀⣀⣀⡀⣀⣈⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠘⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡪⠥⠠⢍⡹⠯⠸⣁⡆⢺⡟⠳⠿⣿⡉⠶⢂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢻⣮⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⢤⡤⠶⠚⠛⠛⠉⠙⠚⠾⠭⠶⣶⣿⣽⣣⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠘⣿⣇⣃⡀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠐⠀⣤⣀⣀⣀⣀⡀⠠⠄⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢩⠈⠀⠀⠋⣨⠁⢃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡸⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠈⡆⢰⠉⢤⠌⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠘⡀⠘⡁⢡⠌⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⡜⢡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠣⢄⡉⢳⠀⠑⠊⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⡠⠊⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠈⠐⠣⢀⡀⠀⠀⡐⠤⠀⠠⢄⡀⠔⢊⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠄⡀⠈⢹⢂⣍⠈⠁⠀⠈⡖⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⠒⠼⠀⠛⢃⠀⢠⡄⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢐⡀⠀⠀⠀⠀⠀⠘⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡒⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠄⠠⠐⣄⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠰⠴⠂⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡰⢁⠀⠀⠀⠀⠀⠀⠒⢺⠞⠀⠀⡀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠁⠉⠿⠀⠐⠒⠒⠒⠒⠂⠀⠘⠒⠒⠾⠿⠽⠧⠤⠤⠤⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⠀⠂⡆⢰⢰⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⣘⣀⣁⣃⣘⣘⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⣀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢸⠉⢉⣉⣉⣉⣈⡀⠀⠀⠀⡴⠊⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⢨⡇⠀⢀⠎⠈⠢⡀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠘⣀⠤⡄⠒⠒⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⠤⠤⠤⠤⠤⠤⡇⢠⠊⠀⠀⢱⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢀⡇⠣⢀⣀⣀⣀⠠⠔⠊





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⠓⠚⠚⠻⠴⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡼⢆⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠄⠐⠀⠈⠻⣝⠒⠛⣚⡚⢧⡄⠀⠀⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡏⢀⡤⢤⣉⠈⢷⡀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣔⣦⡀⠀⠀⠀⠀⠀⠀⢸⠹⠏⢱⠁⣾⣷⠈⣧⠈⣱⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢣⠁⠙⣄⣄⠀⠀⠀⠀⢨⠟⠚⠿⢄⡻⠏⣀⠟⠀⡿⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣗⠛⠧⠉⠀⢷⢄⠈⢦⣦⠀⢀⣀⣱⠦⠀⠀⠈⠉⠀⠤⡚⠓⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠶⣆⠀⠐⢦⡤⠌⠁⠑⠿⠝⠒⠒⠦⣀⠀⠀⠀⠈⢉⡠⠃
⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠒⢲⠛⡖⡦⢤⡨⡙⠦⠤⣉⣀⡀⠻⠀⣀⢳⡢⠄⠈⢳⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠈⣳⠤⢤⣘⣖⣢⠣⣼⡠⢷⡀⠀⠀⠉⠉⡍⣖⣈⠂⠀⠀⢀⡜⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣯⣑⠦⠤⠲⣤⣜⡉⢉⡟⠀⠀⠀⠀⠀⠳⣄⠈⠉⠉⠉⢉⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⣉⣉⣁⣐⡢⠖⢋⠀⣀⣒⠀⠀⠀⢀⠜⠉⠉⢹⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠸⠤⢤⠤⠤⠤⠔⠲⡃⢀⡠⠞⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⣎⣠⠀⠀⠀⠀⠈⠁⠀⠀⣇⠀⠲⠤⠤⢶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⣟⣒⠒⠢⣌⠆⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠀⠀⠀⠀⠀⠀⢀⠤⣄⣰⠟⠉⠈⡇⠀⡟⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⣤⣀⣠⠏⠀⠀⢠⡞⣛⣚⠁⠞⠙⣦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠈⠱⡀⠀⢾⣸⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡠⠞⢅⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠈⡇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠂⠀⢀⠀⠂⠁⢀⠀⠀⣇⠀⠀⠉⢁⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⢢⡔⠈⠀⡀⠰⣎⡹⠖⠈⠀⡀⠄⠊⠁⠰⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢨⠀⠀⠁⢠⣀⠁⢀⠠⠐⠀⢀⡠⢤⢀⠸⠀⠀⠀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⡄⢼⠀⢻⠁⢀⠤⡆⠹⠔⠊⠁⢀⠠⠂⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⣀⢼⠀⢸⠀⠰⠒⡟⢤⣤⠔⠈⠀⡠⡄⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢨⠀⠀⠀⣸⠀⢸⠀⠰⠂⡇⠈⡏⠀⡔⢩⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢴⣦⠀⠁⢸⠀⢸⠀⠀⠐⡇⠀⡇⠀⣋⠀⠐⠛⢢⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⡀⢸⠀⠀⠀⡇⠀⡇⠀⠇⢀⠠⠂⠁⢀⠰⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠊⠀⠀⡇⠀⡇⠀⠉⠀⡀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄⣇⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡶⢾⣟⣻⡿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠁⣤⣦⣿⣿⣿⣿⡦⣿⡙⠛⢻⠻⣿⡿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠉⣅⣽⡟⡻⠿⣿⡓⠙⣛⣷⣜⣦⣍⢷⣾⣿⣜⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣵⠀⣶⣿⣿⣃⣙⣿⣿⡿⣿⣿⣿⣝⣿⣿⣧⢻⣿⣿⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡟⠛⠻⠖⠻⢿⣿⣟⢺⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⢡⡿⠀⠀⠀⠀⠐⠀⢹⣿⣾⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣁⣾⣁⠠⣤⠄⠒⠈⠀⠀⠘⣧⢹⡙⢿⣿⣿⣯⣿⣿⣿⣏⣿⣿⣿⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣿⣟⢦⣼⡄⠀⠂⠀⠀⠀⠉⠀⠈⢹⣆⢻⡘⢿⣿⣿⣿⣿⣿⣿⣿⣏⣹⣿⣭⡧⠁⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣇⠤⣾⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⢷⣜⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣽⣿⣽⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣆⣻⣧⡤⠀⡀⠀⠀⢠⡁⢀⣀⣸⣷⠈⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⢿⣯⣼⣇⠀⠀⠇⠀⠀⠀⠐⡉⢑⡩⠿⣿⡀⢹⣿⣿⣿⣮⡳⣭⣙⣋⣯⣅⣸⣷⣲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣧⣽⡿⢿⣤⣶⣤⠤⢠⡶⠛⠊⠁⠀⠀⠈⠛⠞⢿⣿⣿⡿⣿⢶⣽⣿⣿⣿⣿⣻⣿⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣿⡆⠀⠈⠈⡟⠀⠀⠧⢀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣮⣿⣛⣛⣯⢿⣿⣿⣿⡽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣱⣿⣷⠀⠀⢰⣷⣤⣴⣶⣼⠃⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣦⣭⡭⣡⣴⣝⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣿⣿⣿⣷⠀⠀⠋⢀⣀⣀⣀⠀⡀⠀⠀⠀⠀⠀⣿⣿⣿⣯⣿⢛⣫⣷⣟⣿⣿⣿⣿⣯⣽⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⣧⡀⠰⠟⠛⠛⠛⠛⠻⠀⠀⠀⠀⣼⠻⢿⣿⣽⣿⣿⣿⣿⣽⣿⣿⡶⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠘⠋⢼⣾⡟⣷⡀⠀⠛⠛⠛⠀⠀⠀⢀⣤⠞⠁⠀⠛⠻⢿⣿⢿⣿⣿⠏⣷⣭⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠾⠾⠻⣦⣀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠁⠀⣿⡇⠀⠈⢻⣼⡟⠛⠦⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠙⠛⠛⢻⣇⠀⠀⠀⠀⠀⠀⠀⣠⢧⠃⠀⠀⠀⠈⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⣠⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣀⣠⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⢿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡀⠠⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⢀⠠⠂⠁⠀⠀⠀⠀⠀⠈⠐⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢬⣄⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⡠⠋⠀⠀⡄⡀⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⡑⠀⠀⠀⠠⠀⠀⠁⠊⠉⠛⠳⠶⢶⣦⠤⢤⡀⠀⢒⠍⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⠁⠀⠀⢀⠐⠁⠈⠉⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠠⠀⠀⠌⢂⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠁⠀⠀⠀⠀⠁⠀⠀⢀⠄⠄⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⢡⠀⠀⠀⠡⡐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⡳⠀⠀⠀⠔⢃⠀⠀⠀⠀⠀⠐⠗⠂⠀⠀⠀⠠⠸⢂⠅⠀⠀⢸⣀⠖⢄⠀⠐⣬⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠑⢢⠀⠀⠀⡀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡘⠀⠀⡠⠖⠁⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⣀⠀⠘⢄⠀⠀⠈⠂⠘⡀⠀⠀⠀⠀⡏⠉⠀⠀⠈⠉⡀⠀⠀⠀⠀⡐⠀⠀⠁⠀⢀⠅⠀⠀⣀⢄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⠌⠀⠑⢄⠀⠁⠢⡀⠀⠀⠐⠄⠀⠀⠀⠐⠤⠄⢀⢠⠔⠀⠀⠀⠀⡐⠀⠀⠀⡠⠀⠁⢀⠄⠁⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠡⡀⠀⢈⠖⠈⠢⡀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣀⠂⢤⠊⠀⢀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡲⢁⠔⠈⠀⠈⠢⡀⠁⠀⡤⠠⠠⠄⡄⠀⠁⡠⠊⠀⠑⢄⠀⠤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢁⠀⠀⠀⠀⠀⠀⠁⠈⡇⠀⠀⠀⢽⠁⠈⠀⠀⠀⠀⠀⠑⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⢀⠀⠀⠀⠀⠀⠃⠐⠐⠨⠊⠀⡶⠦⢀⡀⣠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢰⣦⠐⠀⠒⠀⠂⠎⠀⢦⣑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠠⠐⠈⠁⠀⠀⠀⠀⠀⠀⢻⡄⠁⠸⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠠⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠄⠀⠱⣖⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⣴⠀⢶⡄⠀⢸⡆⠀⠠⠹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⠒⠈⠙⠀⠉⠙⠠⡀⠀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠊⠉⠉⠛⠈⠀⠈⠠⠀⠀⠀⠈⢄⠀⣿⣧⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠒⠠⠀⣀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢻⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠉⠡⡀⠀⠀⠀⠈⠁⠐⡄⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⠀⢸⡗⠀⠈⠑⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠈⠺⢦⣀⠀⠀⡠⠊⠀⠀⠀⣂⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⣠⡀⢀⣬⠏⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⢀⡀⠉⠙⠓⠤⠤⠀⣠⣄⠁⠀⣄⣀⢀⣀⣠⣄⣀⡠⠤⠶⠛⠋⠉⠁⡀⠠⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⣟⣻⡿⣿⠿⠿⠿⣿⡿⢿⣟⣻⢿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠶⢮⣭⣭⣭⣭⣭⣭⣭⣭⡵⠶⠛⠿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢠⡶⠛⠛⢶⡞⠉⠀⠈⠉⢉⣭⣭⣿⣿⡛⠉⠉⠉⣴⣶⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣼⣷⡀⠀⠀⠹⢦⣤⣤⣤⣴⣿⣿⣿⣿⣇⣀⣀⣤⣿⡿⣿⠟⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠁⠀⠻⢶⣄⣠⣶⣽⣶⡉⠁⢻⣿⣿⣿⡟⠉⠉⠀⣨⣽⣿⣷⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢰⣀⠀⠀⠀⠀⣩⣛⣿⣿⣇⣠⣴⠿⠿⢿⣻⣿⣶⣤⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⣙⠻⠶⣦⣤⣿⣿⣿⣿⡟⠉⠀⠀⠀⢻⣿⣿⣿⠇⠀⠉⣉⣽⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣌⣉⡙⠛⠋⣄⣀⣠⣤⠶⠟⢛⣉⣀⣤⣶⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠟⠋⠋⠉⠙⠓⠷⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⢏⣤⣀⣠⣀⣀⡀⠀⠀⠙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠃⠈⠀⠀⢽⠎⠁⠐⠦⠙⣇⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⠀⠀⠀⠀⠀⠀⠀⡠⣶⠾⡤⢪⣭⠒⡄⠸⢆⠀⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡛⠓⡄⡀⠀⠀⠀⠀⢳⠭⢴⣇⢻⣿⠁⡸⠀⡟⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⡴⠷⡖⠃⢰⣌⠙⢆⣄⠀⠀⠘⣤⡀⠈⠑⠒⠊⢁⠴⠣⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⣤⡀⠈⢤⣅⡈⠋⠲⠿⡛⠦⠤⣀⠀⠀⠀⠐⠛⡠⠃
⠀⠀⠀⠀⠀⠀⠀⡔⠒⠒⢴⢳⠦⡤⣄⣙⠲⢄⣉⣀⡀⠲⠀⡀⢶⠤⠀⠑⡄⠀⡼⠉
⠀⠀⠀⠀⠀⠀⠀⢱⠦⠤⢼⣞⣶⣣⣎⠼⡆⠀⠀⠉⠉⡭⢶⣙⠈⠀⢀⡰⠃⡰⠁
⠀⠀⠀⠀⠀⠀⠀⡸⢍⣒⡒⠳⠤⠯⠉⡹⠃⠀⠀⠀⠀⠱⣄⣀⠉⠉⢉⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠬⠭⠭⡝⠋⡆⠠⠭⠄⠀⠀⢠⡊⠀⠈⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠑⢲⠗⠒⠒⠋⠙⠤⠤⠚⢱⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣚⡴⠂⠀⠀⠀⠀⠀⠀⠘⠦⢬⣍⣉⡚⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠒⢦⠈⡁⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⢄⣀⠀⠀⢀⠎⠉⠛⢩⠤⠤⠇⡠⠧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠸⠞⠑⠲⡀⠀⣻⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⠿⡁⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⢀⣀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠉⠉⠁⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⣀⣤⣶⡶⣶⣶⣤⣔⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠁⠀⠀⠀⣀⣽⠻⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠆⠰⢰⡿⠁⠀⠀⢀⣤⠾⠁⠀⠀⠀⢹⣧⠀⠐⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢉⠋⠀⢠⡿⠓⠘⠁⠑⠀⠀⠀⠀⠀⠂⠠⢀⢹⡆⠀⠑⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⠀⢸⡇⡰⠁⢠⣤⡄⠀⠀⠀⣤⣤⠀⠀⠘⡇⠀⠀⠈⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢆⡁⠀⠀⠀⠁⡗⠀⠀⠘⠛⠀⠀⠀⠀⠛⠋⠀⠀⢸⡇⠁⠀⠀⠀⢻⠗⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢅⠀⠀⠀⡀⠀⠀⠠⠴⡀⠀⠀⠀⠰⠖⠒⠢⠀⠀⠀⠀⠸⠄⠂⠀⠀⠀⠂⠀⢀⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠑⢄⠈⠐⠄⠀⠀⠐⡀⠀⠀⠀⠳⠖⠃⠀⠀⠀⠔⠀⠀⠀⠠⠂⠀⠔⠁⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠑⠄⡠⠋⠀⠐⢌⠂⠄⣀⠀⠀⢀⠀⠐⠀⡠⠐⠁⠙⢀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⠀⠀⠀⠀⠁⠀⠂⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⡀⠀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⢀⣀⠠⠐⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠀⠀⠀⠉⠠⡀⠀⠈⠆⠀⠄⠀⠈⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠂⠐⢤⡀⠀⠁⠢⠀⠠⠀⠐⠀⢀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢬⠀⠀⠈⣷⠀⠀⠀⠀⢀⠂⠀⢀⣀⡥⠖⣀⠄⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⡐⠚⠛⠿⠿⠒⠌⠀⣤⠂⠠⣄⣹⣇⠀⠀⠀⢀⠀⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠐⠀⠀⢀⠀⠀⠀⠈⠞⡁⢰⣤⣿⣿⣏⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⡉⠆⠀⠀⠀⠀⠀⠈⡄⠔⠂⠀⠉⠀⠀⠀⠀⠀⠀⢑⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠌⠀⢠⡴⣶⡶⢆⠀⡀⠀⠀⠀⠃⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⡄⢁⠀⠐⠂⠠⠾⠚⠉⠀⠀⠞⠛⠛⠁⠀⢀⠀⠀⡠⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢄⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠀⠢⢀⠌⠀⠨⢤⠄⠄⠀⡄⠚⠁⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡂⠀⠸⡄⠁⠁⢠⡾⠴⠥⣀⠀⢀⠀⡧⠐⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⡀⠀⠀⠀⢤⠐⠛⠀⠀⢀⠆⠂⠀⠚⡀⠸⡞⠒⡤⠦⣥⠠⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢤⠡⠈⠄⠳⡠⠴⢂⠚⠚⠆⠀⠀⡆⠀⠀⣀⠤⢼⣈⢃⡈⠀⠀⡄⠀⠁⠀⠡⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠰⠀⣄⣄⠀⡼⠅⡀⠈⠀⠀⣸⠄⠒⣇⢀⡎⠉⠀⠀⠀⠀⢥⠱⡚⠽⣆⠀⡀⠂⢔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠧⠲⠔⡨⢂⡩⣍⡑⣄⢸⡶⢒⡘⠁⢔⢟⠉⠝⢄⣀⡀⠀⠀⠀⣡⠊⢀⡞⠉⠒⠀⢸⢄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡓⠀⠘⠚⢴⠀⢠⣀⢹⠈⡆⠀⠠⢁⠞⠆⡠⢆⠜⢘⣨⡉⠸⢟⡳⢁⠴⠓⠠⢤⡀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢄⠀⠒⠆⠈⢿⣀⠁⠑⡶⠀⠀⠀⢇⠀⠀⡀⠁⠀⠀⠀⠙⢧⡶⠉⢑⠄⢡⢖⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠧⡀⠀⠀⠀⠘⠀⠀⡃⡐⠁⠜⠉⠉⢉⠅⠀⠀⠀⠀⠀⠈⠆⢠⢀⠈⣃⢘⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠂⠅⡠⠀⣰⠀⣠⢀⠀⠘⡀⠐⠒⡉⡀⠀⠀⠀⢀⠌⣐⠀⡀⠄⠫⠑⠨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠈⠀⠒⠉⠉⠀⠠⠗⠤⠤⠲⠟⠦⠉⠉⠉⠈⠂⠈⠀⠀⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠤⠄⠀⠀⠀⠀⠠⠤⠐⠂⠉

⠀⠀⠀⠀⠀⠀⠀⢼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⡀
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠚⠁
⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⡐⠒⣡⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⠀⠀⠀⠀⠀⠀⡐⠒⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤
⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠇⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⢀⣿⠉⠁⠀⠀⠀⠀⠨⠤⠾⠛⠁⠀⠀⠀⣀⡀⢀⠀⠀⠀⠀⠀⠀⣿⠉⠁⠀⠀⠀⠀⠨⠤⠾⠛⠁⠀⠀⠀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⠇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⠇
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶
⢦⣬⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⡼⢦⣬⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠁
⠀⠉⠉⠀⠀⠀⠀⢀⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢀⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⡀
⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠁
⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⣐⠒⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣤⠀⠀⠀⠀⠀⠀⣐⠒⣠⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣤
⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠇⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦
⠀⠀⠀⣿⠉⠁⠀⠀⠀⠀⠨⠥⠾⠛⠁⠀⠀⠀⣀⡀⢄⠀⠀⠀⠀⠀⢀⣿⠉⠁⠀⠀⠀⠀⠨⠤⠾⠛⠁⠀⠀⠀⣀⡀⢀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣼⠇
⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶
⢶⣮⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⡼⢦⣬⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁
⠈⠉⠉⠀⠀⠀⠀⢀⣤⣼⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⢀⣤⣴⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⢀⠘⠓⠀⠀⠀⠀⡀⠀⠀⠀⠀⡏⢸⡄⢻⠄⠀⠠⣎⠀⠀⠀⠀⠀⢀⣼⡵⣿⡶⠀⠀⠀⠀⠀⢀⣀
⠀⠘⠛⠙⠈⠼⠓⠇⠀⠼⠧⠴⠖⠀⠀⠀⢿⠈⠁⢀⡇⠀⠠⠰⠆⠢⡀⠀⠰⢣⣟⣿⠞⠀⠀⠀⠀⠀⢸⣇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠋⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠈⠁⢀
⠀⠀⢠⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠀⠀⠀⠠⣤⣤⣦⠄⠀⠀⡀⠒⠀⠁⠀⠀⠀⢠⣤⣤⣴⡀
⠀⠀⠈⠂⡀⠀⠀⠀⠀⠔⢰⡮⠃⠀⠀⠀⠶⠉⢀⠜⠁⠀⠀⠀⠉⠁⢀⠀⠀⣤⠞⣀⡈⠳⠀⠀⠈⢉⡻⠏⠁
⠀⠀⠀⡀⠃⠀⠀⠀⠘⠀⠤⠤⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠜⠃⠈⠡⢤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠋⠉⠂⢀⠀⢠⡄⠘⠓⢠⠀⠀⠀⠉⠙⠀⠀⠀⠀⣀⡀⠀⠹⠀⠀⠀⠀⠀⠀⠀⣙⡧
⠀⠀⠀⠀⣾⢴⡄⠀⠛⠀⢀⡀⠀⠘⠀⠈⠀⠀⠈⠀⠀⠀⢦⣤⣤⣤⡆⠀⠀⠐⠁⡠⡄⠀⠀⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠁
⠀⠀⣠⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠄⠀⠀⠀⢠⠐⢄⣡⠀⠀⠀⢀⠀⢀⠀⠀⢀⣤⣤⣤⣀⡀
⠀⢀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢂⡀⠀⠀⠀⣀⠀⢀⡀⡃⠀⠤⡥⢬⠖⠋⠀⠀⠅⡠⠀⣀⠀⠀⠀⠨⢉⠉⠁⠶⠋
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡤⠀⠀⡤⠄⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡇⣀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡙⠁⠀⠘⢀⡐⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠠⠀⠀⢼⣵⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠐⠁⠀⠀⠀⢀⠀⢱⠀⠀⠀⠀⠀⠀⠀⢶⣴⣄⡇
⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠈⠀⠀⠀⢠⣴⢶⠶⣦⠀⠀⠀⢀⣀⠀⠀⠀⠠⠶⠀⠀⠴⠆⠀⠀⣠⠀⡛⡀⠀⠀⠀⢠⣤⣤⡄⠰
⠀⠳⢶⣶⣶⠶⠃⠀⠈⠛⠾⠿⠛⠀⠀⢄⡈⠀⣀⡄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠁⢚⠟⢑⣇⣱⠀⠛⠣⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠉
⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠶
⠀⠀⠀⠁⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠐⠓⠲⠂⠀⠀⠀⠙⢿⡉⠋⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⣄⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠙⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠠⠾⠥⠀⠀⠀⠀⠰⣦⣄⣤⡾⠃
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⠄
⠀⠀⢁⡐⠀⣨⠀⠀⢀⡠⠀⣤⠐⠀⠀⠀⢶⡌⠑⠄⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠸⠶⠂⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠈⠐⢎⠹⠀⠀⠀⠁⠈⠀⠁⠀⢀⣹⢿⡟⣿⡄⠀⠀⠠⠸⠠⡔⠁⠀⠀⠶⠆⡀⢠⡀⠀⠀⡘⠁⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠐⠂⠐⠁⠀⠀⠀⠀⠘⠃⠈⠁⠀⠀⠠⢀⣠⣀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⠟⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⢴⡄⠀⠀⣠⡀
⠀⠀⣩⣤⣦⠀⠀⠀⠀⠀⠀⠇⠀⠀⢠⡶⠟⠋⠁⠀⠀⠀⠀⠀⣦⡉⠀⠀⢀⠀⠀⡅⢠⠡⠀⠀⠀⠐⠀⠸⠃⠿
⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠤⠀⠋⠀⠀⠠⡿⠟⠛⠛⠃⠀⠀⠀⠀⠎⢀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⡿⢿⡿⠻⡿⢿⢿⠿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣷⣾⣶⣾⣷⣾⣿⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡞⠀⠀⠀⠀⠀⠀⢋⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⢀⡇⠀⠀⠀⠀⠀⠀⢸⡀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⢤⡇⠀⠀⠀⠀⠀⠀⢸⡤⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⣄⠢⠄⠀⠀⠠⠔⡠⠃⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠄⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠹⢀⠂⠀⠀⠰⡄⠏⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠂⠀⠀⠀⠀⠀⡠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⠀⠀⠀⠀⠀⠐⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠘⠄⠀⠀⠀⠀⠀⠀⠚⠁⢠⠂⠀⠀⠐⡄⠈⠃⠀⠀⠀⠀⠀⠀⠠⠃⠀⠰⠁
⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⡁⠀⠀⠔⠈⠀⠀⡁⢠⠀⠀⡄⢈⠀⠀⠁⠂⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢆
⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⢄⠀⠀⡠⠔⠈⠀⠀⠁⠈⠁⠀⠁⠀⢀⠀⠀⡠⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡁⠒⠒⠀⠀⣠⠖⠊⠑⠲⣄⠀⠁⠒⠒⢉⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠂⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠛⠒⠒⠒⠉⠀⠀⠀⠀⠀⠀⠉⠒⠒⠒⠻⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠐
⠀⠀⠀⠀⢈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡁
⠀⠀⠀⠀⠈⠓⠄⠀⠀⠀⠀⠀⢀⠠⠒⠁⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠈⠒⠄⡀⠀⠀⠀⠀⠀⠡⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠤⠤⠤⠤⢤⢤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⠀⠀⣀⣸⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠉⠉⠉⠉⠈⠹⢿⣇⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠟⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠠⠤⠤⠤⠤⠶⠾⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠏⠁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣴⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⢻⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡰⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⣀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⣇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢾⠛⡌⠐⢲⡶⠲⠂⠒⠒⢒⣾⢻⠀⠀⠀⠀⠀⠀⠀⣧⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣄⡔⠺⣾⡟⢀⣦⣀⡸⠟⡀⣸⠀⠀⠀⠀⠀⠀⠀⣥⣿⡆⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⢈⣿⡋⢁⣼⡁⣀⣴⠟⠀⠀⠀⠀⠀⠀⠀⣽⣿⡇⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠘⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢀⣀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠓⠲⣶⠶⣾⠟⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠃⠀⠀⢤⣧⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢙⡆⠀⠀⣞⠉⣷⠀⠀⣚⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢀⣀⣀⣠⣤⣬⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠈⠋⠁⣀⡀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⢸⡇⣼⣿⣿⣿⣿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡄⢀⠀⡤⠠⡄⠀⠀⣠⠒⢠⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠹⠉⠉⠉⠉⠉⠉⢸⠰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⠼⠃⠀⠀⠢⠴⠃⠀⠀⠙⠶⠞⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣋⣸⡇⠀⠀⢨⣀⣵⠀⠀⠺⣤⡿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢾⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡈⠐⠀⠀⢠⣤⣤⣤⣤⣤⣶⣶⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢰⡄⠀⠀⣔⠀⣆⠀⠂⢠⡁⣰⠄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⢹⠙⠛⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠙⠛⠃⠀⠀⠈⠛⠋⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⣀⣈⣀⣀⣼⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠉⠁

⣷⠛⠛⣶⢶⡶⣶⠶⠶⣾⠶⢶⠶⠶⣾⠷⠶⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⢶⡶⡶⣾⢿⣿⣿⠾⠿⠷⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠘⠋⠀⠀⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣶⣿⣇⣤
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠐⠂⠈⠁⠙⠟⠿⠿⠀⠀⠘
⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⣄⣤⣀⣀⡀⠀⠀⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣄⣻⣳⠀⠀⠀⠀⠀⠀⠀⠚⠉⡹⢻⣿⣧⣿⣿⣷⣦⠼⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⡦⠀⠀⠀⠀⠀⠀⢀⣨⣠⣾⣿⣿⣿⣫⠔⠛⠿⠆⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢀⣴⣶⣶⣷⣄⢾⣿⣿⣿⣿⣿⣿⣷⡀⠄⠀⠀⠀⠁⠀⠈⠛⠻⣿⡿⠋⠀⠀⠀⠀⣤⣄⣄⣀⠀⢁
⠀⠀⢸⡳⣿⣟⢻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠙⠻⠾⣽⣛⣻⠿⣿⠷⢿⣿⣿⣿⣿⣿⣧⣶⡦⡀⠀⠀⠀⠈⠉⠁⠀⠀⣀⣤⣴⣾⣟⣻⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠻⠷⠿⠿⠥⠤⢼⣭⣯⣷⣭⣶⠤⠀⠴⠷⠾⠿⠟⠛⠛⠉⠉⠉
⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣻⣿⣻⣟⣛⣻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⢦⣤⣤⠄⠀⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡉⣵⢠⣴⡏⣴⠿⢁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠋⠜⠃⠂⠈⠆⠦⠑⠌⢳⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠳⠷⠤⠤⢦⣤⣤⣤⡶⠿⢋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⠲⠄⠀⠀⣀⣠⣴⣶⠆⢴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⡰⠄⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⠀⠀⠀⠀⠀⢰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⢀⣾⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠟⡄⠀⠀⠀⠀⠈⠁⢀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠨⣧
⠀⠀⠀⠀⠀⠀⠺⢧⣤⡄⠀⣀⡀⠀⣀⢀⠀⠠⠬⠠⠤⠟⠀⠀⠀⠀⠑⠚⠛⠛⠓⠂⠀⠤⠤⠄⠈⠛⠓⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠇⡀⠙⡀⠒⠲⠈⠁⠒⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢠⢠⠖⡆⣶⠰⣄⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠐⠷⠶⠬⢄⡃⣘⡀⣀⣀⢀⡅⣶⡌⢹⠀⠀⠀⠀⠀⠀⠀⣠⠞⡿⢀⡞⠈⠀⠈⢣⠘⢆⢁⠹⡄
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⢰⡇⢀⠡⠊⠐⠀⠀⠀⠈⠳⡀⠈
⠀⠀⠀⠀⠀⠀⢹⣶⠞⠷⢦⡀⠀⠀⠀⢀⣠⣤⠄⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠁⠀⠁⢀⡇
⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠁⠀⠈⠀⠛⠉⠀⠈⠙⠀⠀⠀⠀⠀⠀⢰⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠘⢃⡀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠸⡇
⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠢⠒⠛⠒⠦⠄⠀⢀⠠⠀⠸⠷⠦⠤⠜⠃⠀⠀⠀⠀⠀⠀⠀⠙⠗⠒⠒⠛⠛⠛⠒⠒⠒⠚⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠀⠀⡀⡀⠄⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⠂⡀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠈⠳⢄⠀⡀⠀⠀⠑⠂⠉⠁⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡆⢀⢜⠀⠑⣶⠒⣦⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⡀⡠⠀⠀⠀⠀⠀⠘⢇⢸⠁⡰⡀⠎⡇⠐⢂⠀⠀⠀⠀⠂⠱⢄⠀⠀⠁⠀⠸⠀⠰⢖⠢⢤⣀⣀
⠀⠀⠀⡠⣂⠵⡂⡉⢢⠄⠐⠒⠈⠉⠉⠉⡽⠄⡢⠰⢁⠄⠎⠢⣀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠖⡑⠠⡀⢱⣤⡀
⠀⢀⡾⡎⠁⠆⡈⡾⠁⠀⡠⠒⢐⢄⡠⢊⠜⠑⢦⠒⠂⢍⡀⢒⠨⠉⢡⠀⠀⠠⠤⠤⠤⡀⠀⢠⠀⠠⡀⠶⠀⠁⢸⠇⡅
⠀⠰⠀⠛⣈⣁⡜⠀⠀⢊⡀⢳⣼⣾⢗⡃⢅⠢⣡⡄⠧⠎⢥⣀⣠⢀⢠⠢⡀⠀⠀⠀⠀⠈⠢⡇⠀⠈⠠⡐⣤⢞⠍⡰
⠀⠀⢧⠀⠢⡀⠻⠀⠀⠢⣩⢛⡟⣁⠻⠂⠈⠁⢀⠄⣀⡀⠀⢡⠭⢡⠰⠑⢄⢹⢀⠁⢀⢱⢀⠐⢄⠀⢠⠀⡠⠊⡔⡃
⠀⠀⠰⠐⠠⡈⠉⠂⠠⠎⡸⠋⢌⣡⠶⣖⠒⠚⠍⠉⣉⣀⡠⠂⣭⡈⢰⡀⠱⡜⡇⡔⢀⡟⡎⣥⠂⡴⠇⠊⡠⠊⢀⠃
⠀⠀⠀⢀⠀⠈⠐⠢⠄⡀⠀⠁⠀⠐⠀⠈⠰⠖⠀⣀⠀⣅⠒⢛⣐⣲⣂⡱⠅⠤⠌⠙⠋⠐⠃⠉⢀⡠⠔⠊⠀⠀⡜
⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠉⠐⠒⠀⠄⠤⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠤⠄⠒⠉⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠤⠄⠀⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⢰⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣊⡀⠘⠄⠱⠀⠀⡀⠀⠀⠀⣠⠊⠁⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸⠴⠴⣌⠀⠑⢄⡌⠉⠉⢲⢃⡆⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢀⠀⠀⠀⠀⢀⠤⠤⣽⡇⠀⠀⢡⠀⠀⠾⡆⡁⠤⠊⠀⠀⠀⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠠⢀⣂⠑⢤⠀⠀⠐⠌⣩⠈⠁⠀⠀⠀⠑⠀⠘⠓⢒⡒⠈⠉⠉⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠈⢢⡰⠁⠀⢀⠔⠁⠀⠀⣀⠤⣀⡖⡰⠂⡤⣈⡁⠂⠀⠀⡤⠒⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠺⣗⡤⠐⠁⠀⢀⡤⠊⢀⠀⠀⠈⠑⠚⠤⢆⡨⠓⢤⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠹⣇⠀⠀⢠⠿⢦⣀⠄⠺⣀⢀⡐⠀⠘⠀⠟⠀⠤⠠⡀⢄⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠋⠁⠀⠀⠀⢃⠢⡀⢗⠈⠦⠔⢨⣠⣋⠀⠈⠠⠒⠉⠑⠄⠣⠀⠀⠉⠁⠀⠈⠁
⠉⠤⢀⠄⢒⡤⠛⢉⡹⠔⠚⢆⠀⠀⠀⠀⠀⠀⠀⢂⠙⠦⡑⠛⠫⠧⠇⠚⡤
⠀⠀⠒⠐⠙⡀⡴⠋⠀⠀⠀⠀⠑⢄⠀⠀⢠⢄⠀⠈⠑⠒⣬⠒⠀⠀⣠⢎⠑⠒⡰⣆⠀⠀⠀⢰⡡⣬⡂⣤
⠀⠀⠀⠀⠀⠣⣀⡀⠀⠀⠀⠀⠀⠀⠉⠢⢀⠀⠈⠢⣀⣮⠁⠀⠀⠀⠀⠸⢅⠼⠳⡀⠀⠀⠀⠘⠐⢮⠥⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠘⠓⠂⠄⣀⡀⠠⠌⣈⣄⠀⠀⠀⡠⠁⠰⠀⣕⡹⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠄⡀⠈⢦⣀⠤⠤⠤⣤⠀⠭⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⡄⢀⡀⠔⢹⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠁⣀⡴⡿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⠤⠤⠦⠀⠤⢤⠦⠴⠦⠤⠤⡤⣤⠤

⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣶⠶⣶⡚⣿⣿⣿⡿⡿⠙⠃⠀⠀⣀⠤⠲⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠘⠉⢤⡀⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣤⣤⣴⠿⠿⠳⠦⠀⢀⠔⠈⠀⠀⢀⣼⣷⠄⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡲⠿⣿⣿⣽⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⣾⡿⠿⠘⠋⠁⠀⢀⠔⠁⠀⡠⠀⠀⠀⠀⠀⠀⠰⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠃⠀⠀⠀⠀⢀⣰⣶⣯⡏⠀⠐⠁⠀⢀⢴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⡾⠛⡿⠛⢋⠀⠀⠀⠀⢈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⠟⠀⠀⠁⠊⠀⠄⠈⢀⢴⡁⠀⣸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣽⠀⠂
⠀⠀⠀⠀⠀⡠⡾⠿⠉⠀⠄⠂⠁⠀⠀⠀⠀⠀⠢⣶⡝⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣟⡍⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠐⠉⠠⠐⠀⠀⠀⠀⠀⠀⢀⠠⠔⠀⠀⡍⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢟⡿⠁⣿⡗⢂⠀⠀⣃⣤⣦⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢥⣔⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⠟⠀⢰⠯⣼⣧⠀⣼⣿⣿⡋⢁⡀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢰⣿⡄⠀⣼⣶⣾⣧⠊⠉⠻⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢸⣿⠇⣼⡟⠷⠻⣧⣶⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣤⣾⡟⠀⠉⠀⠀⠀⢀⠠⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢿⣛⣹⣷⣶⣶⣶⣀⢠⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠈⠉⠉⠛⠛⠛⠿⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⢢⢠⢤⠀⠀⠾⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠄⡠⠃⠤⢀⣦
⠀⠀⠀⠀⠀⡸⠁⠋⠰⢆⠀⣉⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⢈⣶⡆⢰⠾⡏
⠀⠀⠀⠀⠀⢁⣯⠁⠀⡀⠀⠁⠀⠒⡨⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠛⢀⣠⣈⠈⠉⠀⡅⢈⠘⠁⠁
⠀⠀⠀⠀⠙⠴⠄⠀⠂⠀⠡⠘⠒⠞⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡴⠀⠡⠄⠘⠚⣀⡄⣡⠋
⠀⠀⠀⠀⢠⣐⢄⠨⠄⡤⠂⠢⢉⠀⠉⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡕⠀⠂⢀⣤⣤⣤⣈⣁⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⢀⠈⠀⡱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⣹⠀⡤⠰⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣻⡤⡀⠱⡅⢄⣨⠼
⠀⠀⡀⡀⠀⠴⠀⠁⡀⠊⢀⡀⢀⠄⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠞⠠⡈⠙⠖⡂⠮⢑⠀⢠
⠀⠘⠀⠑⠈⠀⠀⠅⠙⠂⠠⠝⠁⠀⠉⠠⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠁⠁⠐⠀⠀⠀⠀⠀⠁⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈

⠀⠀⠀⠀⠀⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠢⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢰⡇⠀⠀⠀⠀⠉⢳⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⡐⡇⠀⠀⠀⠀⠀⠞⠁
⠀⠀⠻⣤⡀⠈⠳⣶⣤⣈⠻⢿⣶⣤⡀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⡥⠀⠀⢀
⠀⠀⠀⠈⠙⠷⣾⣿⣿⣿⣷⣦⣉⣻⣟⠂⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣼⣷⣔⡁⠀⠀⠀⢀⡸
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣟⣋⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣟⣿⠡⣓⣤⡻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣷⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⣴⠇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢜⠁⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠
⣀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠒⠉⠁⢀⣤⠏⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢷⠀⢀⠀⠀⢀⠀⣀⣴⣿
⣿⣶⠦⠄⠀⠂⠀⠈⠀⠀⣀⡠⠴⠚⠋⠁⠀⠀⠀⠀⢠⣄⣀⣀⣀⣤⣆⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⢉⣻⣿⣿⡿⠃
⠙⠻⠶⣤⣤⠤⠤⠖⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠷⠶⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠂⠄
⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠒⠐⠚⡆⠀⠀⠀⠀⠀⠀⢠⣾⣿⠞⠓⠂⠐
⠀⠀⠀⠉⢁⢤⠁⠀⠀⠀⠀⠀⠀⠘⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣟⡽⠁
⠀⠀⣾⡤⠴⠐⢦⠀⠀⠀⠀⠀⠀⠀⢻⡧⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⠀⡀⢸⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⣿⢳⡴⠀⠚⠇⠰⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠸⡇⢹⠀⠀⠀⠀⠀⢸⣿⡏
⠀⠀⢹⣿⢀⣄⣄⣰⡶⠀⠀⠀⠀⠀⠀⢹⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣿⢸⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠻⣏⡭⠵⢿⠃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆⣭⣿⡇⠀⠀⠀⠀⠀⢻⣿⡆⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣀⡠⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠶⠦⠴⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠑⠖⠋⠉⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠑⢦⠀⠀⠀⠀⠀⠀⢀⣀⡸⠀⠀⠀⠀⠀⠀⠘⠦⣄
⠀⠀⠀⠀⠀⠀⡠⠤⠔⠂⠁⠀⠀⠀⢈⠇⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠤⠂⠀⠀⠀⣀⣀⡇⠀⠀⠀⠀⠀⢠⠖⠉⢙⡤⣄⢀⡴⣺⣕⢦
⠀⠀⠀⠀⢀⠎⠀⢀⠤⣤⡀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⢸⡄⠀⠔⠁⠀⢀⣤⣀⣘⠅⠀⠀⠀⠀⠀⠀⠀⠈⡳⢒⡽⠊⠹⣾⠏⠀⢸⢸
⠀⠀⠀⠀⢸⠀⠀⣿⠀⢀⡷⠀⢸⠁⠀⠀⠀⠀⠀⢀⡴⠋⢀⣠⣄⣀⣀⡏⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⠀⠀⠀⠙⣄⠀⣸⢸
⠀⠀⠀⠀⠈⢢⡀⠈⠛⠛⠁⢀⠏⠀⠀⠀⠀⠀⠀⠸⣀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢀⣈⠢⣽⢸
⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠐⡁⠀⠑⠌⣙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⡞⠁⠀⠈⣇⠤⢤⠀⠀⠀⠀⠀⠀⢸⠀⠄⠀⠀⠀⠀⢱⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢄⡀⠀⡠⠖⠋⠉⠹⠶⣄⡤⠶⢼⡇⠘⡰⠊⡁⠀⡼⣀⣀⣀⠀⠀⠀⢸⠀⢄⠀⠀⢀⠠⢂⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠸⡟⠁⠀⠂⠀⠂⠀⢘⡏⣀⢉⡇⡞⠠⠊⡠⢾⠟⠁⠉⠈⠦⡄⠀⠘⢆⠀⠉⣉⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⡿⠁⠀⠀⡇⠀⠀⠹⡏⢉⣿⡫⢍⡲⡏⢉⣈⡉⠳⢧⣔⡋⣴⠛⠀⠀⠀⠀⢠⠇⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢹⠣⢤⣀⡀⠀⠐⠀⣠⠟⠧⣴⠛⢖⠋⠍⢿⡴⣫⠟⠅⢈⡿⠀⠀⢀⣀⡠⠔⣻
⠀⠀⠀⠀⡼⠻⠷⠈⢳⡀⠀⠈⣇⠀⠀⠉⠉⠓⠒⠓⠲⠶⠷⠦⠤⠷⠤⠼⠶⠾⠾⠖⠚⠓⠚⠉⠉⠀⠀⢀⡇
⠀⠀⠀⠀⠸⡄⢀⢂⠀⢻⡄⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠹⡄⢂⠀⢀⠙⣆⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⢀⣠⢴⡲⡄
⠀⠀⠀⠀⠀⠀⠹⡔⠀⠐⣆⠘⣦⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠃⠀⠀⣠⠴⠚⠉⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠹⡔⠔⢌⢦⡈⢷⡀⠀⠀⠈⠓⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠚⠁⠀⠠⡖⣏⠀⠀⠀⠀⠀⡰⢣⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⠢⡁⢵⣌⡇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠙⠮⣑⠲⠤⠖⣊⠵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠮⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣳
⢰⣩⡤⣌⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢧
⠀⠀⠀⠈⢳⡀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠘⣆
⠀⠀⠀⠀⠀⢳⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠙⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠳⠤⣤⣀⣤⠤⢧
⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⢀⡴⠋⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⢸⠦⣄⣠⣤⠴⠫⢀⠔⠂⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⣉⣳⠀⢠⠓⠐⣶⠁⡂⠐⡄⠀⢸
⠀⠀⠀⠀⠘⡄⠀⠀⡁⠰⠀⠈⡆⠃⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢁⠎⠀⠀⠀⠰⡀⠀⣸⠤⠀⠔⢁⡄⢸
⠀⠀⠀⠀⠀⠱⡀⠠⣔⢂⠀⠊⠘⠀⢈⣷⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⢸⠀⠀⠀⠀⠀⢸⠛⠒⠒⠂⠉⣀⡆⢸
⠀⠀⠀⠀⠀⠀⠹⡀⢡⣀⠉⠉⠉⠁⣁⣀⠀⠀⠀⠀⠀⠀⡴⠚⠁⠀⠘⢆⠀⠀⠀⠀⠀⢻⠃⠀⠈⠀⠐⠁⢸
⠀⠀⠀⠀⠀⠀⠀⢣⢸⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⡜⠳⠤⣄⣀⣀⣸⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⢸⠈⢯⠀⠀⠀⠇⠀⢩⠀⢠⠊⡉⠉⢣⡤⠒⠠⢄⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡆⠀⠀⠀⠀⢸⠀⠰⡀⠀⠀⣈⠀⠀⠁⢈⠀⣰⠁⠢⠀⠀⠀⠀⢹⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠣⡀⠀⠀⡠⠂⠁⠀⠈⠉⡏⠉⠒⠄⠔⣊⢰⠃⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡼⠉⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⣤⣀⣈⣀⣤⠄⢹⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⡾
⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠟⠙⠋⠛⡿⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⣰⠃
⠀⠀⠀⠀⠀⣾⠀⢀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⠴⠚⠁
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢄⣈⠽⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⠄⠀⠀⠰⠄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠐⠀⠒⠂⠉⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⠼⠄⣀⡀⠀⠀⣤⣀⣀⣀⣀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠁⠀⠀⠄⠀⡄⠀⡠⠈⠑⢢⡘⠿⠿⡿⠟⠛⠿⠖
⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠠⠀⠒⢘⠄⠀⠀⠤⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴
⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠁⣀⡰⠉⠢⡀⠀⠀⠀⠀⠀⠀⢎⢹⠄⣀⠤⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠀⡜⠁⠈⠀⠄⠀⠀⠀⠠⠤⠒⠉⠀⠀⠀⠂⠀⣎⠙⠼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁
⠀⠀⠀⢰⠁⠀⠀⠀⠀⡀⠀⠀⡀⠀⡀⠀⠈⠀⡔⠐⢦⢈⣧⢾⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠖⠋⠁
⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⢀⠜⠀⢀⡤⠋⠁⠀⠈⠙⠒⠒⠒⠒⠚⠉⠉
⠀⠀⠀⠀⠉⠻⣅⠉⠂⠤⠒⠁⠀⠀⠉⣉⠥⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠀⠒⠒⠈⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⢠⡄⠦⢀⠊⠀⠀⠂⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠦⢤⣄⣈⡉⠙⠓⠲⠦⣤⣄⣀
⠀⠀⠀⠀⠂⠀⠈⢡⠀⠎⠀⠀⠁⠁⠚⠃⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⢀⣀⠀⠀⠀⠀⠈⠉⠛⠓⠶⠤⣤⣄⣈⠉⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠲⠀⠀⠀⠀⠀⠀⠀⠈⡏⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒
⠀⠀⠀⢀⠆⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠁
⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠑
⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶
⠀⠳⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠞⠹⠡⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠐⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡄⠀⠀⠀⠇⠸⠀⠀⠀⠀⠀⠠⠔⠂⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⣴⠟⢻⡆⢠⡾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠻⠶⢾⣧⡟⠁⣴⢲⡶⢠⡞⠶⣰⠞⣶⠂⣾⠟⣰⠇⣴⠛⣦⢰⡖⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠘⠛⠀⠀⠛⠛⠛⠘⠛⠒⠙⠛⠛⠚⠛⠂⠛⠓⠛⠛⠃⠛⠀⠛⠂
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠂⠰⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠀⠀⠀⠀⠀⠀⠀⠀⡂⡀⡀⠤⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠠⠀⠀⠀⠶⢤⠀⠀⠀⠀⠀⠀⢀⡀⠠⡄⠀⣠⢌⠀⠀⠉⠂
⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⣀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠘⠈⠑⠃⠀⠁
⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠛⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⢀⡶⠋⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠁⠀⠀⢈⠀⠸⡆
⠀⠀⠀⢠⣤⣶⣶⠀⣠⣄⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⠁⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡄
⠀⠀⣀⣄⠉⠀⠀⠀⠈⢛⣉⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠻⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠻⢿⣷⠆⠀⠐⢾⣿⠟⠁⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣾⣿⠆
⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠆⠀⠀⠀⠀⠙⠁⢠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⡅⣠⡔⢀⠄⠀⠀⠀⢀⡴⠋⠀⠀⠀⢠⠀⠀⠀⠈⠻⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠀⢀⢸⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⠀⠈⠀⠃⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡇⠈⠀⣀⣀⠈⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⣀⠀⠀⠄⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⡀⠐⠰⣦⡀⠀⣁⠈⢧⣀⣉⡈⣴⠋⠘⠀⠀⠉⢰⡢⡄⢸⣁⠒⠧⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠷⠽⠾⣆⡙⠿⣷⡤⠉⢀⡉⢉⠓⠔⠐⠒⠂⠀⣌⣴⡷⢎⠺⠷⢶⢸⡏⠉⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡦⠈⠄⣠⣤⡤⢠⣽⣦⡤⣤⠶⠔⠀⠍⠠⠀⠀⡂⠀⢀⠈⠙⠿⣤⡀⣁⣠⠞⠁⠀⠉⠀⡙⠄⠤⡀
⠀⠀⠀⠀⠀⡰⠀⠘⠁⠀⠀⠀⠉⠀⠀⠀⢘⣿⣷⡄⠟⠒⠓⢮⣀⠰⠶⢿⣞⠉⠁⠈⠒⠶⢤⣝⡁⠀⠀⠐⠀⠐⡂⣠⠆⠴
⠀⠀⠀⠀⠀⢆⣠⡈⠐⠒⠚⠓⣤⣀⣀⣤⣾⣿⠟⠁⢀⠀⠀⠈⣿⡄⠀⠈⠻⣷⡄⠀⠀⠐⠀⠙⣿⡆⠀⠑⠒⢖⡧⠃⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠑⠙⠩⡛⠓⠋⠉⣿⠿⠿⢭⣴⣎⠀⢀⣽⡧⣿⠃⠀⠠⣸⣿⠀⡀⠄⠀⠀⠀⣸⢟⣄⣀⡗⢥⢶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠪⠶⠄⠀⠀⡨⠛⡿⠿⠿⣿⣅⣀⣴⠟⣋⣏⣩⣲⡖⡒⠚⣉⡭⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠀⠈⠉⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠈⠳⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠞⠀⢠⠀⠈⠀⠸⠓⠲⣄⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠹⣤⠴⢦⣀⡤⠗⠀⠀⣀⣀⣗⣁⠔⠊⠉⠒⢋⠅⠀⠀⢸⣃⡤⡄
⠀⠀⠀⠀⠀⣠⠶⠾⠁⠀⠀⠀⠀⠀⠉⠑⠀⢀⢶⠻⡈⡇⡟⡆⡶⣪⠕⣏⠉⠉⠻⡀⠀⠀⠛⠖⠒⢲⡀
⠀⠀⠀⠀⢀⣸⠦⠀⠢⠄⣄⡠⠔⢀⡤⢚⠒⣚⢧⠻⠅⣻⠮⠧⣅⡟⢡⠛⠀⢒⠤⡀⠀⠀⠀⠀⠈⢿⠛
⠀⠀⠀⢠⡏⠀⠀⢄⠀⡠⡺⡒⣄⠈⠫⠆⣏⣂⢳⡗⠞⣵⠁⡨⢮⣧⢋⠄⠶⢜⢤⡌⢯⢤⣍⢢⠤⣾⡤⠖⢦⡀
⠀⠀⠀⠀⢙⡇⢠⢶⢻⣌⡓⠞⣌⠖⠊⢁⡄⣀⣉⢳⣇⠱⣝⡍⠡⡛⢋⣮⡢⣘⠀⠀⡰⠒⠹⠶⠒⢋⠄⠀⠀⣷
⠀⠀⢀⣠⣾⡟⠃⠈⣮⡑⠷⠊⡎⠀⢙⡅⣤⣖⢒⣬⡣⣑⠀⡝⡏⠘⣿⢵⣌⣲⣝⡫⠔⠉⠑⢂⠈⣉⠥⡤⡶⠃
⠀⠀⢺⡀⠀⠈⠛⠚⠛⠻⡛⡏⢳⡄⢀⡀⣡⡴⣪⢎⣿⡟⢿⡕⡿⣦⢤⢋⢆⡸⢨⢷⣦⠕⠂⢛⠀⡨⡆⢇⡇
⠀⠀⢰⠃⡠⠒⠉⠀⢳⢤⠸⣒⡭⠋⢠⠖⠁⠠⢸⠚⡷⠾⠭⢊⠗⠒⡽⡀⠑⠵⠁⣪⢆⣀⠀⠉⡳⣘⢝⣾⠃
⠀⠀⢻⣀⣠⡄⠀⣤⣤⡄⡙⠢⡇⠸⠁⠀⠈⠞⣁⠤⠘⠒⠺⡿⣛⢭⠫⠙⡔⢒⡈⣝⣁⡈⠛⠭⢔⡵⠋⣸
⠀⠀⠀⠀⠀⣧⡅⠀⠙⠺⢾⣢⠿⣐⡗⣤⣈⠋⠰⢦⠻⡤⠄⣼⡉⢔⡇⠁⠸⠇⣄⠈⠀⠙⡖⠀⢠⠶⣦⡏
⠀⠀⠀⠀⠀⢹⣄⠀⠫⠂⠀⣈⡉⠓⠺⠯⠽⣴⣒⣛⣀⣰⣊⣚⣛⣁⣲⡭⠬⠿⠓⡤⠀⠰⠇⣴⣆⠗⣹⠁
⠀⠀⠀⠀⠀⠀⢧⠉⠂⠤⣀⡘⠁⠀⠪⠆⠀⢠⡆⠀⢀⢤⠀⠀⣤⡀⠀⢔⡄⠀⢻⡁⠀⠐⠀⡨⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠉⠑⠒⠂⠤⠤⠤⠤⠀⠉⠀⠠⠬⠠⠤⠄⠒⠒⠉⠙⣄⣀⠜⠁⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠐⠲⠤⠤⠤⠤⢤⠤⠤⠴⣶⢶⢾⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠸⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢄⡽⠦⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣴⣾⣟⣲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠁⠀⠀⠀⠉⠉⠉⠙⠛⠛⠛⠉⠉⠉⠛⣛⣿⢿⣿⠑⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢻⣙⡎⣰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠠⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⠿⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠹⠀⡆⡆⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⣱⢳⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢼⣟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⡆⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠦⠴⠶⠞⠳⠻⠛⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡖⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠤⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇⢰⡆⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢻⡼⠇⠸⣤⣄⣄⣀⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣤⣤⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣮⠉⢧⠀⠀⡎⠘⢿⣿⠉⠉⢏⠉⠉⠉⠉⢩⠉⣴⣦⡶⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⢀⣡⡀⣷⠀⣸⣿⡖⠀⢈⢄⠀⠀⠀⣸⢴⡿⠈⢅⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣿⡀⠉⠻⣿⡻⣿⡇⣠⢞⣺⣧⣤⡰⠣⠋⠁⡐⠕⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣄⠀⠈⠻⣾⣿⡿⠋⠁⠀⣨⡧⠁⠀⡰⠋⣴⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣟⣷⠤⣠⣿⣿⣀⡠⣤⣾⢟⣷⣀⣠⣦⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠿⠿⠶⠾⠿⠛⠛⠛⠉


⡿⠿⠿⠿⡿⡿⢿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣻⣿⣛⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⢠⠆⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣷⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⢀⠩⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⠳⢄⡀⠀⠀⢤⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠂⠊⠁
⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠒⢀⣀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠊
⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠲⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣇⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠃⠉
⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⣀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢄⠄⠀⠰⠂⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢢⣄⠀⠀⠁⢀⠀⠴⠆⠁⠀⠀⠀⠀⠀⠀⣀⡀⢀⡀⠐⠈
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⡀⠀⠀⠀⠀⠀⠔⢀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢘⡂⠤⠀⠀⣀⠀⠁⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢠⡤⢀⡈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⢠⠈⠐⠋⡓⠦⣄⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠈⡄⠀⠀⢀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡟⠉⠁⠀⡄⠀⠀⠀⠀⠀⠀⢡⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠅⠀⣀⠁⠀⠀⠀⠀⠀⣠⠂⠰⠟⢂⣴⠒⠀⠀⠀⠀⠀⠀⠀⢘⣀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣀⣤⠖⣩⡏⠀⠘⠁
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢄⠁⠀⠄⠀⠀⠀⠰⠁⠀⠀⠀⠠⠘⠉⠒⠐⠂⠤⢤⠈⡁⠙⠟⠛⠒⠾⠉⠉⠈⠉⠉⠉⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⡠⠔⠁⠘⠢⠄⠨⡌⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⡀⠁
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠒⠀⠀⠂⢠⠊⠀⠀⠀⠀⢀⡴⠣⠀⠀⢀⠩⠀⠀⠀⠀⠀⠄⢠⠊⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⢀⢐⡠⢤⣤⣾⣄⠈⠀⡄⡐⠁⠀⠀⠌⠀⠐⠄⠀⠀⠀⠀⠀⣀⡆⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⣀
⠀⠉⠁⠁⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⣁⠈⢳⢾⣯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣇⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣠⡤⠄⠒⢺⡟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠣⠈⠁⠉⡳⢄⡀⠀⠀⠀⠄⠀⢀⡄⠀⠄⠠⠽⠶⢦⣤⡀⠀⡤⠖⠂⠀⠀⠈⠁⠀⠀⠀⡘
⠐⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡞⠀⠐⠂⠀⠀⠀⠀⠀⠜⠳⠤⢤⠶⠈⠀⠅⠀⢠⠠⢦⣄⠢⢬⣴⣶⣤⣤⢢⣶⢤⣤⣤⢤⡤⢠⣧⣤⣤⡄
⠤⠀⠀⡤⠀⠀⠀⢀⠀⢤⠀⠀⠀⠀⠀⠀⡜⠁⡦⠀⠀⠀⠈⠐⠄⢀⠀⠄⠁⠀⠀⠀⠀⣄⡀⢀⡀⢀⠺⠛⣷⣿⠯⣮⢽⣿⠿⠾⡷⠶⢶⣤⣼⣿⣼⣟⣻
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠔⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠤⠀⠀⠀⠠⠄⠀⠄⠀⠄⠈⠁⠉⠈⠸⠧⠿⣿⠾⠿⢿
⠂⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⡀⢀⢀⣀⠀⡀⡀⠀⠀⠀⢀⠀⢀⡀⠀⣀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢀⡠⠞
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢀⠀⠀⠒⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠈⠈⠈⠁⠀⠀⠀⠀⠀⡏⢘⠀⢀⣅⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠁⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠂⠒⠀⠀⠀⠀⠂⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⡀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈⠀⡔⠁⡀⠀⠀⠄⠀⠁⢀⠌⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠁⠀⠀⠀⢀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⢈⡠⠔⠊⠁⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⢀⡤⠤⠤⣶⡌⢥⠈⡢⣠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠀⠈⢣⡀⠶⣅⠙⠦⠌⣠⢆⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠐⣤⠐⠟⠁⢉⠉⠁⠂⠀⠊⣉⠢⡄⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠈⡄⢠⡀⠀⠘⠀⠀⠀⠄⠀⡓⠀⠀⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠀⠀⢀⠀⠀⠀⠀⠀⢰⠁⠀⠰⠋⠙⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⡩⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢈⢀⠀⠊⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠠⠄⠲⠎⠀⠀⠀⠀⠀⠀⠘⠆⠀⠓⠄⡠⠀⠀⠀⠀⠀⡀⠀⠀⠐⠂⠒
⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠠⠤⠀⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢠⠐⠠⠀⠀⢀⠀⠀⠓⡀⠀⠀⠀⠦⠐⠊⠁⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠂⣉⣆⠀⢀⠄⠰⢤⡀⠀⠀⠸⡀⠀⠀⠀⠐⢰⢔⠋⢤⡄⢀⡹⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢠⡢⠐⡉⠠⢨⡗⠁⢀⠴⠈⠀⠀⠀⠀⠳⡀⠀⠀⡀⠀⢀⡤⠐⠁⢠⡇⠈⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠒⢰⠋⠐⠁⠀⢠⠔⠁⢰⠁⠠⠂⠀⠀⠀⠀⠀⢱⡀⠀⠑⠒⡁⠈⠑⣀⠈⠦⣼⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀
⠂⠀⠀⠀⠀⠀⠈⠀⠀⠄⠠⠈⠀⢀⠊⢀⡔⠀⠀⠇⠀⠀⠀⠀⠀⢀⠊⠉⠈⠁⠘⠂⠙⠁⠁⠀⠀⢹⠹⠒⠠⢤⣀⡀⠀⠀⠀⠣⠀⠀⠀⡀⠀⡈
⠀⠀⠀⠀⠀⠀⣀⠐⠀⢁⠀⠠⠾⠛⠰⠛⠀⠀⠀⠄⠀⠀⠀⠀⠀⢠⡀⠂⠀⠂⠒⠒⠀⠀⠀⠀⠀⠈⣆⢀⠀⠀⠘⠉⠙⠦⣄⠁⠐⠄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠑⢄⡀⡀⠀⠀⢠⠔⠊⠀⠀⠀⠀⠀⡴⠁⠀⠑⣀⠀⠒⠒⠀⠀⠀⠀⠀⠀⢈⠇⠑⢄⠀⢀⠀⠀⠙⠦⣀
⠀⡀⠀⠀⠀⢀⡀⠀⠀⠃⠀⠀⠰⠛⠒⣀⠴⠃⠀⠀⠀⠀⠀⣬⠀⠀⠀⠀⢱⠤⣉⣉⣁⣀⣤⠴⣶⡒⠃⠀⠀⠀⠀⠀⠁⠲⣞⠀⠈⠲⢤⣄⡀
⠀⠁⠀⠔⠀⠀⠀⠀⡈⠀⠀⠀⠀⢠⠄⠀⠀⠆⠀⠀⠀⣠⠎⠉⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠙⠢⣴⠂⠀⠀⠀⠀⠀⠀⠙⠲⠶⠒⠚⣛⣳⡄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⢀⠔⡁⢦⡀⢴⠀⠀⠀⠀⢦⠀⠀⠀⡄⢀⠀⠀⠀⠀⠀⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢻⡄
⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠖⠁⠀⢿⣳⣤⢴⠀⠀⠀⠀⠸⡆⠀⠜⢀⠎⠀⠀⠀⠀⠀⠀⠰⠉⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠈⢢⠀⢸⠟⠁⢸⠀⠀⠀⠀⠀⠹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣠⣿⡇⠈⠙⠦⣄⡀⠀⢀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠈⠀⢠⠀⠀⠀⠀⠀⠸⡰⠋⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠟⡇⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⢀⠴⠁⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠔⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⢠⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠩⣍⠽⠝⠻⡲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠑⠃⠀⢀⠸⠈⠀⠀⡁⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠀⢀⠂⠰⠀⢠⠀⠐⠐⠂⠜⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⡀⢄⡀⠐⢰⠀⠐⠀⠸⠠⣳⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⣴⠛⠿⣿⢻⡿⣿⣦⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠛⢲⠖⢿⠖⠒⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠐⡂⢰⠆⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣎⣁⣨⡅⢸⢍⣉⡳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⢋⣀⠠⠄⠒⡃⢰⠂⠤⠤⡤⠝⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠭⠐⡀⡉⣀⠀⣀⣞⡏⢨⣁⣠⣀⣀⠉⣲⡇⠀⠨⡑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡫⠀⠁⠀⡉⢋⣀⡤⣞⣛⠠⡇⢨⠤⠄⠬⢤⣤⠄⢂⣈⠀⠒⣄⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠈⠑⠒⠊⣁⠴⠚⣁⣐⠢⠄⣈⡇⢰⢚⡩⠖⠢⣉⠩⠂⢄⠈⠒⡦⠁⠸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠁⡀⠀⣀⡀⡝⢸⢍⡀⠀⣀⠀⠀⠇⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢄⣩⠄⠀⠒⡃⢸⡒⠦⠈⠩⣀⠄⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠡⠖⠀⠤⠀⠖⣃⣣⢸⣍⡀⠀⠐⢤⡂⠀⢻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠚⠀⠰⠁⠀⠉⡋⢸⡂⠈⠉⣛⠂⠉⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠄⠀⠀⠒⠀⠍⢱⢸⠤⠀⠀⠨⠖⠀⠡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠠⢈⡤⠐⢂⣩⢸⣍⠲⢌⡙⠊⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠄⢀⠤⢀⡩⠗⢰⢄⡉⠂⢍⡐⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠂⡠⠔⢉⡡⢊⢸⡢⣽⡐⠢⡁⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢃⡜⠀⣠⣺⢗⢵⢸⠮⡺⠔⣄⠈⠖⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡗⡡⠀⣰⢭⡗⠀⣹⢸⡁⠈⣇⠨⡌⠚⠦⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢁⠁⠼⠃⣿⠤⠊⡴⠰⢌⡂⢨⡔⠌⠢⠀⡌⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢀⠈⠠⢁⡤⠐⡀⠜⢀⡢⠉⠐⠳⡄⢀⢂⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢀⡎⠀⢁⡎⢠⠀⠙⠐⢿⠇⠠⡘⠄⢰⠈⠢⣄⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠁⠆⡠⢨⠀⠈⢆⠼⠀⢘⠀⡆⠃⠘⠀⢳⣄⠠⠙⠼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄⢸⠃⣘⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⢸⠀⠐⣄⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠃⠈⠸⡉⠆⠀⠀⠀⢠⠃⢣⠀⠀⠀⡠⢟⠀⠀⠈⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡿⢤⢤⣀⣀⣀⣀⣀⣀⣀⣠⡽⡇
⠀⠀⠀⠀⠀⠀⣀⠴⠚⠙⢧⡀⠻⣤⣀⣀⠀⠀⠀⠁⢈⣀⣀⡴⠃
⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠙⣆⡧⢀⣈⡉⠉⠉⠉⠉⠁⠀⣶⣛⣉⢉⣙⣦
⠀⠀⠀⢠⣶⠋⠙⢫⡳⡀⠀⠀⠘⡇⠀⠀⢩⢭⠉⢹⠀⠀⢸⡷⠤⠤⠤⠤⢾⣀
⠀⠀⠀⠇⡇⠀⣠⠤⣷⢹⠀⠀⠀⣷⠀⠀⠘⡫⠆⢸⠀⠀⢸⠀⠀⠀⠀⠀⠈⡇⠉⠓⠢⢄⡀
⠀⠀⠀⡇⢧⡠⠗⣶⣹⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⣾⠑⠒⠲⠶⠒⠊⡇⠀⠀⢀⠔⠉⡆
⠀⠀⠀⠘⢾⣤⣞⣡⡧⠏⠀⠀⠀⢸⠉⠒⠦⠤⠴⠚⠀⠀⢻⠀⠀⠀⠀⠀⠀⡇⡌⡀⡜⢰⠁⢩⣦
⠀⠀⠀⠀⠀⠈⢉⣈⣱⡦⠤⠤⠴⠚⠓⠤⣄⣀⣀⣀⡤⠔⢻⡄⣀⣀⢀⣀⣠⠏⠙⠓⠷⠞⠛⠛⠉⠑⠢⢄⡀
⠀⠀⡠⠤⢤⠴⢅⣀⡤⠟⠀⠀⠀⠀⠀⡴⠶⠶⣆⠀⠀⠀⠀⠉⠛⠛⠚⠛⠁⠀⢠⠤⠖⠢⠤⢤⡀⠀⠀⠀⠀⠁
⠀⠀⠑⠲⠦⠤⠤⠃⠀⠀⠀⡆⢉⠉⣹⡯⠭⢭⡿⠶⡉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠄⣤⡤⠤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠭⠭⠟⠁⠀⣎⠀⣀⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣬⣭⣬⣭⣯⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⡀⠀⢿⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠠⡄⠀⢀⠘⣇⣠⣤⣀⠀⠀⠀⠀⣇⢼⠆⡇⠀⢸⣇⣀⡾⠋⠉⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠹⡄⢡⠀⠛⠁⠀⢹⡄⢠⡴⠶⠿⠊⠁⡇⠀⠘⢩⡟⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⣰⠖⠲⣄⠀⢀⣬⢷⡄⠹⠇⠹⡄⠀⠀⠀⠀⠸⠛⢻⣤⣄⡀⠀⠀⣴⠟⠳⣾⠁⠀⢀⡇⠀⠚⢻⡆⣀⣠⣀⠀⠀⠀⣀⣤⣤⡀
⠀⢠⡶⠲⢶⣿⢠⠄⢹⡾⠋⢳⣄⣀⠈⠉⠀⠉⣠⠾⠛⠉⠳⣴⠏⠀⠈⢷⡀⢸⡇⠀⠀⡀⣄⠀⡼⠀⠀⠀⣼⠟⠋⠀⠈⣧⠀⣾⠋⠀⠀⢹⣤⠶⠛⠳⡆
⠀⢸⡇⠀⠀⠉⠐⢂⠀⠀⠀⠘⢃⣹⡷⠶⠖⠲⣏⠀⢠⡀⠀⠙⠀⢠⣾⠋⠙⣛⠳⢦⣄⠉⠀⢰⠇⠀⡆⠀⠀⠀⠀⣠⠶⠿⠾⠇⠀⡆⠀⠘⠁⠀⠀⠀⣿
⣴⠶⠿⣦⠀⠀⠀⣁⣀⡀⢀⡴⠛⠁⢠⢒⡆⣠⠿⠆⣀⡙⠢⠈⠀⢸⡎⢣⡀⠣⡵⠀⠉⠳⣄⠈⠀⠈⠀⠀⠀⠀⢰⡇⠀⠀⢤⡐⢠⡇⣘⠀⠀⠀⠀⢠⡏
⣿⠀⠤⡤⠀⣰⠟⠩⡍⢻⡟⢁⣴⡦⠈⠉⣠⢿⣄⠀⠀⠋⠀⠀⢀⡀⠻⣆⠙⢦⡀⠀⢯⡷⠘⣧⣠⡴⠶⢒⡶⠛⠛⠛⢠⢠⡄⠁⢸⠀⢠⡠⠄⠀⠀⠙⠳
⠘⢷⣈⠓⠀⣿⠀⠀⢳⢸⣁⣀⣉⣀⠴⠚⠁⢀⡽⠗⠀⢀⡴⠚⠉⠉⠳⡌⠳⢦⣈⠓⠲⠤⠤⣿⠁⠀⠀⢸⡇⠀⠀⠲⣄⡈⠁⠀⠿⠀⠀⢁⣠⠖
⠀⠰⣟⣓⢀⣻⣄⣀⣘⣎⣿⣭⣭⣤⣤⣤⣾⣿⣤⣤⣤⣾⣤⣤⣤⡤⡤⠿⠤⠤⠭⠿⠷⠶⠶⠿⠤⠤⠴⣯⣿⣦⣤⣤⣤⣝⣂⣀⣀⣀⣐⣋⣀⣀⣀⣀⣠
⠀⠀⠘⣿⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⢉⡿⠃
⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠻⣟⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⠟⠁
⠀⠀⠀⠀⠀⠀⠙⣷⡶⠶⠶⠶⠶⠶⠖⠒⠒⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠛⢻⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⣐⣲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠐⠦⠭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣠⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢁⡞⠁⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣼⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠁⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⢿⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⣾⣿⡟⣾⡿⡁⣈⠺⣿⣿⣿⣿⣦⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⣼⠆⣰⣅⡹⣿⣿⢟⡙⢹⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠉⠈⠀⠙⠚⠿⢏⡷⢂⠬⢈⣽⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⡟⢿⠿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⣼⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣞⠀⠀⣳⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠏⡳⣿⣦⣢⡆⠀⠀⠀⠀⠀⠀⠀⠈⢻⡾⣶⣳⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢟⢰⡷⢿⠿⢿⣡⢄⣀⠀⠀⠀⠀⠀⠀⠀⢛⠔⠁⠋⡉⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠂⠀⠀⠀⠀⠀⠀⠀⣿⡇⡸⠸⠀⠀⠀⠀⠉⢿⣟⣃⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⡇⠀⠀⠀⠀⠀⠀⠈⡋⠀⠀⠀⠀⠀⠀⠀⠀⣁⣒⣶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⡇⡀⠀⢰⣷⣿⣏⣴⣇⠀⠀⠀⠀⠀⠀⠀⠀⣮⠍⠉⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⠀⠁⠀⠀⠀⠀⠂⠀⠀⢘⣿⣷⡇⡀⠀⣿⣿⣿⣿⠿⢿⠇⠀⠀⠀⠀⠀⠀⢰⡓⠅⠀⠄⣙⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠋⠀⠀⠀⠀⠀⠀⠀⣠⣠⠆⣿⣿⣧⡅⣿⡿⠛⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡝⢾⣶⣿⣾⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢺⣷⣦⣻⣿⣿⣷⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠋⢿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠘⠷⣾⣿⣿⣯⣿⣾⢸⣿⣿⣿⡆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠃⠀⢰⣤⣤⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡠⡠⢌⢌⣿⣿⣿⣿⣿⣽⡎⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣴⣇⡀⠀⠀⠀⣻⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⣦⣸⣿⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⣄⣀⢀⡠⣄⢒⠈⠁⠹⣿⣷⣦⣴⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⣿⡸⡌⡈⠎⣿⣶⡄⠀⠀⣻⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡇⢁⣤⢿⣿⣷⣷⣮⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠿⣿⣿⣿⣿⣿⣾⡾⢿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠈⠳⣄⢀⣠⣤⣴⣦⣤⣶⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⢀⡼⠋⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣶⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣥⣤⣤⣴⣾⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣯⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢹⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣆⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣿⡟⢿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠈⠻⣿⡈⠻⣿⣿⣧⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠀⠀⠀⠀⠈⠁⠀⠀⠉⠙⠃⠀⠀⢸⣿⣿⡏⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠏⢿⣿⡇⠀⠀⢀⡴⠶⢤⠀⠀⠀⠀⠀⠀⣠⠶⠦⣄⠀⠀⢸⣿⣿⠁⠈⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⢀⡞⢹⣧⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⣯⠙⡆⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠿⣿⣿⣿⡇⠸⣇⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢀⡇⠀⠀⣿⣿⣿⡿⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⣿⣿⣿⡇⠀⠈⢻⣿⣷⡀⠀⠀⠀⠀⣤⣤⣤⣠⣤⣤⡤⠀⠀⠀⠀⣸⣿⣿⠋⠀⠀⠀⣿⣿⣿⣿⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢻⣿⣇⠀⠀⢸⣿⡇⠳⣄⠀⠀⠀⠘⢧⣀⣀⣀⡽⠃⠀⠀⢀⡴⠃⣿⡟⠀⠀⠀⠀⣿⣿⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⣿⣿⠻⢶⣴⣿⡀⠀⠈⠳⢤⣀⠀⠀⠉⠉⠁⠀⢀⣠⠴⠋⠀⠀⣿⠇⠀⠀⠀⢰⡿⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠟⣋⣉⣭⣉⣛⣶⡀⢀⣬⣽⣛⣒⣒⣚⣻⣯⣄⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢉⣉⣉⣉⣭⣽⣿⣿⣦⣄⡉⠉⠉⠉⠁⠀⣈⣳⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠠⠤⠤⠴⣶⡿⠉⠉⠛⠿⣿⣷⣦⣠⠖⠻⢉⢁⠬⠬⠕⠠⠲⢭⡩⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣇⠀⠀⠀⣲⠞⠋⣽⠁⠀⠀⠀⠀⠀⠉⣹⢃⢃⠖⠉⠀⠀⠀⠀⠀⠀⠀⢹⡞⢚⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠉⠉⠛⠛⣷⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠹⡜⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⣹⠦⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡿⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣥⣂⣄⣀⣀⣀⣠⣤⣲⡴⡾⢋⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣸⡧⠞⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠦⣍⣉⠉⠉⣉⣡⣴⡯⠴⢋⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠶⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠷⠻⠶⠶⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠈⠻⠿⣿⣿⡿⠿⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢀⣀⣀⠀⠀⢀⠁
⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠁⠀⠀⠀⣿⣿⣷⡎
⠂⠀⠐⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣤⣶⣵⣿⣿⠀⠀⠀⠀⠹⣿⣿⠇
⠈⡄⠀⠀⠈⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠘⠿⣿⣿⣿⣦⠀⠀⠀⠀⠉⢿
⠀⠈⢄⠀⠀⠀⠀⠁⠂⠤⢀⠀⠀⠀⠀⠀⡀⠠⠐⡸⠁⠀⠀⠀⠀⠀⠈⠉⠛⠛⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠈⠐⢄⡀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁
⡄⠠⢀⡀⠀⠀⠀⠀⠀⠈⠐⠠⣀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠠⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠑⡀⠀⠀⠉⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠈
⠀⠀⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠁⣀⡀⠀⠀⠀⠀⣀⡀⠀⠤⠐⠈⠁
⠀⠀⠀⠀⠀⠉⠒⠠⠄⠀⣀⠀⠀⠀⠀⠀⢀⠀⠠⠄⠂⠁
⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡉⠙⢦⠀⠀⢀⠀⡠⣠⠴⢦⠐⠀⠀⢠⠶⢤⡠⡄⢀⠀⠀⢀⡞⠁⣁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡄⣹⠆⡸⠀⣀⠒⠦⢰⠃⣀⣛⡲⠂⠰⣞⣋⡀⢱⡀⠖⠂⡀⠸⡇⢸⡁⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠞⠉⢘⣁⣘⡭⠇⠀⢣⠞⠁⣆⣽⠀⠼⣇⣤⠙⢧⡁⠀⠿⣭⣀⣙⠢⠙⠲⠦⢤⣄⡀
⠀⠀⠀⠀⡀⠀⠀⠐⢉⡠⠶⠶⣍⠂⠔⣉⢍⡐⠒⢛⠴⢣⠞⣠⢋⡤⡄⡠⢌⠛⡈⠣⡑⢌⠓⠒⣊⢭⡙⠆⢎⡵⠶⠦⣌⠑⠄
⠀⠀⢰⡏⣭⠑⡄⠀⠋⢀⠞⠳⡌⣀⡞⠡⢞⡎⠀⡨⠙⠲⢲⠠⠹⢖⠣⠙⠶⠡⢠⠢⠚⠫⡀⠈⣟⡳⠙⢆⠌⡴⠛⢗⠈⠣⠀⡔⢉⡍⢳
⠀⠀⠀⠉⠁⣐⣒⠀⠃⠀⠪⠴⠃⢞⣀⡉⠭⠶⠂⠠⢪⢱⠀⠀⠠⢒⡀⢠⡒⠀⠀⢐⢩⢢⠀⠐⠦⠍⢉⣈⠣⡹⠤⠇⠀⠂⢐⣒⡂⠉⠉
⠀⠀⠀⢠⢞⡥⢒⡦⢄⠀⠠⡀⠀⠸⣀⡟⠇⠀⢀⢐⠉⠤⠾⠀⠎⠱⠃⠲⠌⠆⠸⠦⠈⢑⡂⡀⠀⠇⣯⡸⠃⠀⡠⠀⢀⠤⣴⠲⣍⢦
⠀⠀⠰⢸⣸⡀⠃⣹⢠⢞⣃⣨⠙⠫⠉⠒⠠⠀⠀⡡⢞⡙⠁⠈⠀⠈⠁⠙⠀⠀⠀⢘⢈⠦⡉⠀⠀⠐⠆⠩⠙⢩⣄⣛⢢⡸⡇⠇⣸⢸⠇
⠀⢠⠰⣌⣓⣿⠏⠁⠛⠏⠺⢋⡴⡰⠁⢼⡁⣖⢄⡀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁⣀⣄⡆⢹⠄⠱⡰⣌⠻⠎⡇⠁⠉⢻⣗⣋⡴⢂
⠀⠀⠀⠲⠋⠚⠚⠉⠁⠄⠀⠉⠚⠁⠀⠲⠻⠄⠈⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠨⠿⠊⠀⠉⠊⠉⠀⠄⠉⠙⠊⠃⠱⠆
⠀⢀⠀⣘⣦⣳⠺⠤⠄⠠⠀⠤⡲⡄⠀⢚⠿⢁⣠⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢤⣄⡨⢾⠂⠀⡴⣢⠄⠠⡀⠠⠴⢳⣇⣜⣋⢀
⠀⠀⠘⢡⢞⡿⠷⣄⢶⢧⣺⣧⠙⠘⠄⠘⠤⠐⠀⡈⢡⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠍⠀⠑⠣⠜⠁⠜⠐⢣⣾⣣⢇⡄⡴⠾⣟⢦⠘⠂
⠀⠀⠘⢼⠸⡀⠧⡼⣈⠳⠆⡨⢶⠦⢤⡫⠀⠀⢐⢀⠑⠼⠄⠀⠀⠠⡄⠰⠀⠀⠀⠸⠔⢋⠐⡀⠀⠸⣁⡤⠶⠦⡁⠶⠋⡸⣧⠇⣸⢸⠇⠂
⠀⠀⠀⠈⠳⢭⣋⠉⢉⠀⠀⡀⢁⠸⣤⡟⠇⠀⠀⢒⢤⢉⠹⠀⠵⢼⡆⣺⠥⠃⠰⠍⢡⢔⠃⠀⠀⠇⢧⣸⢂⠀⣀⠀⢀⠉⠉⣋⡵⠋
⠀⠀⢠⠴⣄⠒⠒⠁⠆⢠⣪⠙⡮⣳⡀⠴⢭⡙⠂⣈⠩⠜⠀⠀⠈⢒⠀⠐⠂⠀⠀⠐⠬⠉⡀⠘⣩⠽⠦⣰⡏⡾⢉⣃⠀⠃⠈⠒⢂⡤⢦
⠀⠀⠈⠣⠭⠔⠁⠀⠢⣐⠳⠚⣡⠀⠻⣌⠳⡧⠀⢈⠔⠊⠚⣀⢭⡑⡏⣕⢫⢅⡈⠊⠓⢢⣀⠠⠗⢞⡴⢃⢡⡙⠲⠓⣠⠎⠀⠐⠦⠥⠞
⠀⠀⠀⠀⠀⠀⠀⠐⠠⣌⣙⡋⠡⠂⠑⠦⣥⣔⣒⠲⠙⢮⠳⠠⣦⣍⠀⠈⣡⣆⠠⢏⠜⠡⠒⣒⣢⡭⠴⠃⠓⠍⣛⣉⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⡓⢦⠐⣄⠰⡭⠇⠀⢎⠳⣤⣁⡼⠈⠹⣇⣩⡴⢋⡔⠀⠻⡵⠀⡴⢂⡴⣛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣏⣁⡼⠀⣸⠀⠀⢒⠋⡘⢦⡐⢒⡚⠂⠈⢓⠒⣀⡞⡀⢙⡂⠀⢸⡇⠸⣤⣉⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡴⠋⠀⠀⠀⠀⠈⠀⠉⠉⠘⠀⠀⠈⠉⠉⠈⠁⠀⠀⠀⠀⠳⣤⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢷⡈⣻⠷⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡤⠾⠟⠁⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠿⠦⣤⣌⣉⠛⠶⣦⣄⠀⠀⠀⢀⣠⣤⡤⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠈⠙⠻⢶⣄⠉⠛⠶⠶⢿⠁⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠻⢦⣼⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠲⠶⠒⠒⠒⠒⠲⠶⠶⠶⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡾⠃⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⡀⠀⣀⣴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣄⡀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⠶⠶⠶⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠦⣤⣄⣀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⣤⡟
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠢⠀⡀⠀⡀⠀⣀⠀⠀⢀⠲⢄⡀⡠⠄⠀⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠠⡆⠁⠠⣄⠀⢘⠀⠼⠖⠀⠑⡆⢀⡀⠀⠉⠠⣶⣤⡝⠐⠃⠰⢃⣾⠑⠤⢄
⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⡀⠀⠠⠤⠀⣀⣀⣜⡀⠉⠀⠀⠘⠉⠀⠀⠀⠀⢲⣦⠀⡀⠀⡠⢜⡁⠀⠀⠀⠂⠚⠙⠁⠀⡀⣄⠀⠁⠀⢀⠀⠄⡀
⠀⠀⠀⠀⢀⠀⠀⠂⣠⡊⠀⠀⠁⣈⠀⠋⠉⠁⠀⠰⣆⣴⣤⣤⣀⠀⠠⠉⠀⠀⠉⠁⠀⠐⠂⠤⣀⢀⣶⣻⣿⣷⣦⡠⣈⠿⠒⢈⡀⠀⠒⢢⣾
⠀⠠⠃⠀⠀⠄⠀⠀⠀⠑⠄⠃⠄⠀⢀⠐⠄⠀⢀⣴⣿⣿⣿⣶⣿⣀⠀⠀⢈⡀⠀⠤⠀⠀⢀⠀⢄⠉⠙⣿⣿⣿⡿⣋⠀⠀⣈⡃⢈⠒⠊⡆⡀⢰⣆⣀
⠱⢆⢔⠈⢉⠀⠒⠀⠀⡁⠀⠚⠢⠂⠆⢰⣤⠔⠁⠄⠀⠐⡀⠒⠂⠀⠀⠲⡀⠈⠂⠀⡡⠀⠀⠂⠈⠀⠰⠈⡋⢧⠀⠃⢐⣤⠝⠐⡚⠃⠀⠀⠑⣢⡄⣤⠂
⠀⠈⠀⢁⠄⣅⠐⡠⢎⡀⢂⠀⠀⠀⢀⠹⡵⠂⠀⠀⠁⠄⠈⠁⠀⠀⠀⠲⣴⠀⠄⣀⣧⣤⣄⣈⠍⠈⠀⡆⡾⠓⠦⠀⠈⠃⠀⠆⠀⠀⠀⠀⠀⠀⡂⠁⣬
⠀⠀⠀⢨⡘⠞⠲⠀⠘⢀⡸⣄⠉⣀⠀⠄⡂⠀⠠⠀⠂⠀⠀⠀⠀⢖⠠⠰⠿⣦⠾⠿⣿⣷⣧⣼⠁⠌⢉⠛⠻⠀⠀⠉⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣸
⠀⠀⠀⢧⠀⠂⠀⠀⢠⣼⠃⡿⡀⣠⣧⢶⡏⠀⢠⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠈⠁⠂⢾⡻⠟⢉⠠⡀⣦⣼⠆⠀⠀⠀⢀⠀⠹⡆⢀⣤⣴⣤⣄⠀⠀⣞⣱
⠀⠀⠀⢰⣄⠈⠠⡀⢀⡀⠉⠀⠀⠙⢧⠀⠀⠀⣸⢀⣤⣤⣾⣷⣤⡀⠐⠂⠀⠲⣂⠁⠀⢁⡤⡀⠩⠤⠄⠂⡐⢧⠂⠀⠁⠀⣢⢽⢿⣿⣿⣾⣧⡷⠚⢁⡏
⠀⠀⠀⠈⡿⢿⣦⣀⠀⡁⢰⡈⠁⠀⠈⠀⠀⠀⢉⣿⣿⣿⣷⣷⣾⣷⢠⡁⠀⠀⢀⣼⣀⠇⠂⠡⣶⡄⠲⠀⣶⢀⡅⠁⠀⡻⠋⠀⠘⡋⠝⠋⠁⣠⣴⣿⠇
⠀⠀⠀⠀⠸⡀⠙⠻⣿⣷⣧⣌⡀⠁⠈⠣⠔⠦⠮⠁⣀⣿⣿⡏⠁⡌⠉⠃⡀⠈⠀⠌⠀⢀⡀⠀⢨⠀⢀⠀⣉⠀⠠⠤⠐⠂⠈⠀⠀⣀⣤⣶⣿⠟⠉⡘
⠀⠀⠀⠀⠀⠹⡄⠀⠀⠍⡛⠿⢿⣿⣶⣦⣤⣀⣀⠀⠀⠀⠀⠀⠁⠁⠉⠉⠉⠀⠁⠈⠉⠀⠉⠉⠈⠁⠀⠀⠀⠀⣀⣀⣠⣤⣶⣾⣿⠿⠛⢉⡄⠊⡰⠁
⠀⠀⠀⠀⠀⠀⠙⢆⠈⠀⠰⠅⠀⠈⠉⠛⠛⠿⠿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣾⣿⣿⡿⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠈⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠙⠒⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠚⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠤⡉⠑⠒⠢⠤⢄⣀⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠤⠒⠚⠉⠁⠀⠂⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠵⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠀⠤⠤⠠⣤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠖⠒⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢸⣿⠀⠀⢸⡇⠀⠀⣿⡇⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣸⣿⣀⣀⣸⣇⣀⣀⣿⣇⣀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡏⠉⠉⠉⠉⠉⠉⠉⠉⢹⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⠾⠷⠶⠶⠶⠶⠶⠶⠶⠶⠾⠷⠶⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⣀⣠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣴⠟⠋⠉⠉⠉⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⠶⣶⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣀⣀⣀⣿⠀⠀⣿⣀⣀⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠉⠉⠉⠀⠀⠉⠉⠉⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠿⠶⠶⣶⠀⠀⣶⠶⠶⠿⠀⠀⠀⠀⠀⣿⣷⠀⠀⢀⣀⣀⣤⣤⣴⢾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⡿⠛⠛⠋⠉⠉⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣿⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⠀⣿⡀⢶⡄⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⢸⣧⠈⠻⣦⣤⣤⡀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⠟⠁⠀⠀⠙⢷⣤⣀⣀⣀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⣠⡀⠀⠀⠀⠀⠀⡄⠠⠀⠀⠀⠀⠀⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢧⢰⢻⡇⣾⣩⠆⣶⠙⡇⢰⢠⡎⠁⢐⣩⡆⢹⠋⢷⢠⠎⢱⡄⡖⠙⡆⢾⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠃⠘⠃⠙⠒⠂⠙⠒⠃⠘⠀⠓⠒⠙⠒⠃⠘⠂⠙⠈⠓⠚⠁⠃⠀⠃⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣦⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠉⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡏⠀⠀⠀⣀⠀⠀⠀⣀⡀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡆⠀⠈⠁⠀⠀⠀⠈⠁⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⣿⣿⠁⠀⠀⠢⠂⠀⢠⡅⠒⠀⠀⣷⠀⠀⢰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡐⢎⠻⠆⠀⠀⡀⠀⢤⣸⠇⠀⠀⠀⣿⠀⠀⣼⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⡆⠀⠀⠐⢧⡀⠀⠀⠀⣠⠀⢀⡏⠀⠀⠹⡟⠁
⠀⠀⠀⠀⠀⠀⠰⠾⣉⡉⠓⣻⣄⠀⠀⠀⠈⠉⠉⠉⠀⠀⣼⠁⠀⠀⢀⣿⢲
⠀⠀⠀⠀⠀⠀⢠⠾⣉⣩⠿⠁⡏⠳⢤⣀⡀⠂⢒⣂⡠⣾⡁⠀⠀⠐⢹⡟⡻⣄⡤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣉⣀⡀⠇⠀⢠⡟⢹⠉⢹⡀⠑⠸⡝⢦⠀⠀⢣⡻⠖⣨⠟
⠀⠀⠀⠀⠀⠀⢠⠿⢻⢩⢨⡛⣧⣠⡟⠀⠊⠀⠈⣁⢦⢠⡹⣌⣳⡄⠀⡇⣾⠁
⠀⠀⠀⠀⠀⢀⣿⡄⢸⢸⢸⡇⡇⣿⠀⠀⠘⡝⣤⠁⠛⢪⣃⠙⢏⠀⢠⠃⢸
⠀⠀⠀⠀⠀⡞⢽⢸⣼⠘⢸⡇⣅⡶⠃⠀⡆⢰⠀⢀⣠⡼⠚⠀⣸⡀⡎⠀⢸
⠀⠀⠀⠀⢠⣇⢸⢸⢿⣨⣴⠛⠁⢰⣄⣠⢷⡌⢠⣏⣠⢶⠳⡖⠃⠙⠃⠀⣸
⠀⠀⠀⠀⢸⡟⢸⢸⢸⠉⠻⣆⠀⠀⢧⣠⠏⢀⠋⢩⣵⡟⠀⠈⢢⠄⣚⠈⠉⠑⠂⠠⣀
⠀⠀⠀⠀⢸⣧⣼⣸⢸⠀⠀⠙⣦⠀⠈⠁⠀⡼⠀⣌⣿⠇⢀⣀⣶⠠⠤⠄⠒⠒⠉⠀⡿⣿⣿⣶⣶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⡏⠉⠙⠛⠛⠻⠷⠿⢷⡀⢀⣼⢶⣿⣿⣿⣿⣿⣏⠈⠦⣀⢀⢀⣀⡤⠞⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣬⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⣀⣠⣤⣄⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⣿
⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠈⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠳⣌⠙⢻⣿⣿⣿⣿⣿⣿⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠦⣤⣤⣤⣤⣤⣿⣄⣀⠀⠀⠈⢧⠈⣇⣨⣽⣿⠋⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠙⢳⡄⠀⠈⣷⣿⣿⣿⣿⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠹⣦⣾⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⡿⣋⣶⣤⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠙⠛⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠠⣄⣀⡀⠀⢀⠀⢀⣴⢶⡚⠳⠀⢀⣀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠲⠾⢶⣦⣽⠀⠈⠉⠙⠁⠂⠉⠁⢱⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠠⠐⢢⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠱⠀⠀⣸⢳⡖⠀⠀⠈⠠⠤⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠃⠀⠀⠀⠀⣠⠞⣁⠀⠀⠀⠀⠀⢀⠃⠀⠀⡿⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡤⢺⠁⠉⠙⠛⠁⠀⠀⢀⡎⠀⢠⠴⠃⠀⢉⠓⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⢠⠀⠛⠛⠟⠀⠀⠠⣀⠄⠀⠀⣸⠃⠀⠀⠀⠰⠋⠘
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⡀⠀⠠⢟⡧⣀⣀⣀⠰⡄⠀⠀⠀⠀⠐⣾⠶⠴⠛⠈⣳⢄⡀⡄⣀⡠⠂
⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⡿⠇⠀⠀⢱⣌⣹⠋⠈⠙⠄⢰⣶⣄⣀⣅⠀⢀⣠⣴⢧⠀⠀⠈⠁
⠀⠀⠀⠠⢄⠀⠀⠀⠀⢀⠀⠀⠐⠤⡄⢶⠾⠛⠛⠀⠀⠀⠈⣟⠉⠉⢽⣛⣛⣯⡅⠀⢣⠁⣠
⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢻⣋⠙⠻⠿⢿⡄⠀⠈⠒⠁⠀⠀⡀
⠀⠀⠀⠤⠴⠂⠀⠀⠀⡠⠐⢢⣄⠀⣀⠀⠀⠀⠹⣀⠀⢠⠾⣿⢽⣯⡷⠄⠀⠀⠉⡄⠀⢠⣄⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠹⠀⠈⠀⠒⠒⢂⠀⠉⡁⠈⠀⠀⠀⡳⠳⠾⠛⠋⠀⠉⠀⠈⠀⠀⠈⠁⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠁⠀⠀⠀⠀⠀⢀⡴⠀⡠⡗⠀⠀⢁⡀⠀⡄⠀⠀⠀⠀⠀⢀⠄⠀⠀⢠⡔⠊⠀⠀⡀
⠀⠀⠀⠠⠂⠀⠀⠀⠹⠿⠄⠀⠀⠀⠀⠀⠀⠜⠀⠀⡁⠁⠀⠀⠀⣠⡴⠀⠀⠀⠐⠂⠀⠀⠀⠀⠐⠁⠀⠠⡀
⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠋⠔⠉⠀⢠⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡶⢿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⣀⡷⠾⠛⢹⡄⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⢇⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠒⠒⠉⠉⠩⠖⠒⣦⠊⢾⢤⣤⣤⣀⣀⣠⡶⠒⢒⣶⡀⠦⡐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠈⠀⢀⠀⠀⢰⠗⡤⢒⣉⠉⡉⠉⠉⣤⢴⡀⠐⠚⠒⠖⠂⠈⠦⣄⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡅⢠⣷⠖⠂⠘⠁⢀⡀⣨⣾⠃⢸⠱⠎⠀⢊⠁⢀⣄⣀⠀⠁⣨⣷⣿⠻⣦⠀⠀⠸⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⢤⣧⠟⠁⠀⠀⠀⠀⠀⠀⣅⣀⡴⣟⢀⡀⠀⢁⡀⠀⠀⢉⣬⡾⡁⠔⠋⠀⢻⡇⠀⠀⢼⠤⡀
⠀⠀⠀⠀⠀⠀⣀⠆⠝⢿⣿⣿⠏⡄⠀⠀⢰⠂⠈⠁⠀⣿⠙⣇⠈⠁⠼⣈⠀⡤⠂⠀⠉⠁⣠⡸⠢⠉⠠⠀⢹⣦⢲⡏⠀⢘⣀⡀⡀
⠀⠀⠀⠀⡐⠋⠀⠀⠉⢻⣿⣿⠈⠣⠤⠐⢙⣄⠀⠀⠁⠙⢧⡌⠀⠀⠀⠈⠓⠀⠐⠀⣠⡖⠈⢠⡆⢟⡛⠛⣛⣿⡿⠃⠀⢠⠟⡂⢅⡉⠱⣓⠂
⠀⠀⠀⢠⠀⠀⠀⠠⣀⣽⣿⢿⠃⠀⠹⡄⠀⣻⡀⠀⠀⠀⠀⠑⡄⢀⠀⣠⠤⠤⣄⣀⣿⣿⠂⠀⠰⠾⢋⣽⡿⠋⢀⣀⣴⣿⣾⣽⣿⢅⣸⠟⣵⡄
⠀⠀⠀⠈⡀⠀⠀⠀⢺⣿⠁⠈⣂⠀⠀⠳⡀⠀⠉⠋⠉⠀⠁⠙⠛⠁⠀⠀⠀⠀⠀⠙⢧⡀⠟⠚⠳⢶⣽⣷⣶⣶⣟⣿⣋⢿⡿⠿⢿⣋⣍⡆⣩⠇
⠀⠀⠀⡇⠃⠀⡀⠴⣾⣧⠀⠀⠸⣄⠀⠀⡿⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⢰⣿⣿⣿⣿⡟⢿⣿⣿⠀⡛⣆⡀⠙⠧⣤⠋
⠀⠀⢠⠃⠀⠠⢈⣻⣿⡏⠀⠀⠀⠛⣻⣷⠀⠀⠀⠀⠠⠀⠀⡿⠀⠈⠀⠀⢀⡄⡀⠀⠀⡄⢷⣰⡾⢻⣿⣿⣟⣱⡿⠟⠁⠀⠡⣿⣿⣷⣤⠀⡱
⠀⠀⠘⡃⠀⠀⢀⠰⢿⣷⠀⠀⢀⠈⣼⡇⠀⠀⠀⠁⠀⠃⠐⣣⡾⠀⢠⣤⠞⢛⣅⢀⢼⡇⠾⣿⣿⣷⣿⠿⠋⠁⠀⠀⠀⣴⣾⣿⣼⢿⠗⠁⠀⠘
⠀⠀⠀⠑⡌⠀⠐⠬⣠⠿⠳⣄⠀⢄⣉⣧⣠⣀⣀⠀⠳⠀⢠⣬⡀⢰⣿⠇⣂⠛⣾⡟⣏⣛⣡⣿⡿⠿⣥⣀⣠⣶⣤⣤⣴⣿⢟⡯⠁⠀⠒⠀⠠⠄⣇
⠀⠀⠀⠀⠳⠄⣀⡵⠁⠀⠀⠻⣆⠀⠙⠙⠛⠛⠳⣷⡾⣤⢮⡾⣥⠹⢿⣞⣿⣿⣿⣯⡿⠋⠀⠀⠀⠀⠈⠉⠉⢿⡿⢿⣿⣷⢮⣁⠀⠀⠀⠀⠸⡔⣥
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠈⠉⣳⣶⣤⣄⣘⣀⡉⠋⠉⠹⣹⠿⣫⡖⠻⠉⡀⠀⠀⣜⣤⠀⠀⠀⠀⠄⠀⠐⠆⣠⣿⣯⣽⢤⠷⠚⠦⠖⠂⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⡀⠈⠛⠺⠿⠿⣿⣿⣶⡦⣤⣷⡿⠋⠠⠀⠀⠀⠿⠀⠈⠻⠆⢦⢸⠃⢀⣠⣴⣾⣷⠻⠋⠁⠀⠀⢀⣀⣠⠄⢀⠰
⠀⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠦⢿⣿⣿⡀⠀⠀⠀⠈⠀⠀⡄⠀⠀⠘⠀⠀⠀⠈⣠⣾⡿⢟⡯⠋⠀⠀⠀⠀⠀⠀⢈⡉⠀⢐⠋
⠀⠀⠀⠀⠀⠀⠀⠱⠄⠲⠄⠀⠀⠁⠀⠀⠀⠀⡰⠛⢿⣷⣶⣦⣴⠶⠲⠤⢤⣤⣀⡀⠤⠖⠒⢿⣿⠍⠊⠉⠀⠀⠀⠀⠀⠀⠄⠈⢁⡀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠠⡀⠀⠀⢀⣀⣤⣭⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠂⠒⠒⠶⠶⠖⠒⠒⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠖⠒⠚⠛⠛⠛⠛⠛⠛⠒⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⠲⢤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⢿
⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠫⣉⠀⠸⣄⠀⠀⠀⠈⠈⠉⠉⠉⠉⠉⠉⠀⠀⣀⠟
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⠳⡄⢸⠙⠛⠒⠒⠶⠦⠴⠤⠶⠶⠖⠚⠛⡃⣠⡤⠤⠤⢤⣄⡀
⠀⠀⠀⠀⣜⣀⣤⣀⡀⠀⠀⠀⠀⠹⣼⡇⠂⠤⢤⣄⣀⣀⣀⡀⠀⠀⠀⢰⣿⠧⠤⠤⠤⠤⠴⢿
⠀⠀⡴⡿⠋⠉⠙⢦⡹⣄⠀⠀⠀⠀⢹⡇⠀⠀⠀⡤⠤⡄⠀⣿⠀⠀⠀⢸⡿⠶⠤⠤⠤⠴⠶⣏⣀
⠀⡼⢰⡇⠀⠀⢀⣈⣧⠘⡆⠀⠀⠀⠀⡇⠀⠀⠀⠷⢮⡤⠀⣿⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠈⡏⠉⠓⠦⢤⣀
⠀⣇⢸⡇⠀⢾⣁⣈⢿⡄⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠉⠀⢸⠀⠀⠀⣿⠤⣀⣀⠀⠀⢀⣀⡤⡇⠀⠀⠀⠀⠈⣹⠦⡄
⠀⢹⡀⢧⠔⠋⢩⠿⣼⢡⡏⠀⠀⠀⠀⣧⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣿⠀⠀⠉⠉⠉⠉⠁⠀⡧⠀⡀⠀⠀⡞⢁⡀⣿⡀
⠀⠀⠳⣜⡦⢴⣋⣴⣣⠞⠀⠀⠀⠀⠀⢿⠈⠙⠓⠶⠶⠶⠖⠋⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣇⢰⠁⡄⣸⠀⡏⠀⢀⣽⡆
⠀⠀⠀⠈⠉⠉⠉⠉⠳⢤⣀⣀⣀⣀⡤⠾⠦⣄⣀⠀⠀⠀⠀⠀⠀⣀⡤⣿⡀⠀⠀⠀⠀⠀⠀⢀⡟⠛⠲⢧⣿⣤⠽⠳⠾⠋⠙⠲⢤⣀
⠀⠀⠀⠀⠀⠤⠒⠻⠉⢹⡄⠉⠉⠀⠀⠀⠀⠀⣉⣉⣉⡛⠛⠋⠉⠀⠀⠈⠳⣭⣓⣒⣒⣒⡪⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠄
⡞⠋⠉⡛⠛⠓⢦⡴⠒⠋⠀⠀⠀⢀⣀⣀⡀⡾⣒⣂⣉⣹⡆⠀⣀⣀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡖⠉⠉⠉⢹⠉⠓⢦⡀
⠉⠒⠲⠧⠤⠤⠼⠁⠀⠀⠀⢠⡎⠁⡸⠉⢉⡷⠦⠭⠭⣾⠖⠫⡁⢀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣤⣼⡤⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣙⣛⣛⡩⠇⠀⠀⡼⠁⠀⠀⣰⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⢄
⠀⠀⠀⠀⠀⠀⣠⠀⢐⣒⠿⣿⣮⣱⡂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢐⣎⣵⣿⠿⣒⡂⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣮⠻⣫⣥⣬⢳⣄⠀⠀⠀⠀⠀⠀⢠⡤⢠⣄⠀⠀⠀⠀⠀⠀⣠⡞⣥⣬⣝⠟⣵⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢻⣿⡏⠤⣻⡆⡀⠀⠀⣠⡄⠿⣰⣆⠿⢠⣄⠀⠀⢄⢰⣟⠤⢹⣿⡟⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⡟⣠⠏⡜⠁⢠⣷⡘⣥⢠⣿⣿⡇⢠⠁⣶⡄⠀⢳⡹⣄⢻⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡙⢰⡟⣸⠃⠀⣾⣿⠇⠏⠘⣿⣿⠃⠘⠘⢿⣿⡄⠀⣧⢻⡆⢋⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠦⠁⢻⡇⣀⣀⣀⣤⣄⣀⡸⢏⣀⣀⣤⣀⣀⣀⢀⡿⠈⠴⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡿⠀⣀⣤⣽⣦⣀⠈⢉⡛⠚⡉⠁⣀⣤⣾⣧⣄⠀⢸⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣱⠀⣠⡄⢉⣛⡻⠿⠟⠁⠈⠻⠿⠿⣛⡉⢀⣄⡀⣦⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠛⡿⠀⠻⣧⣀⣩⣥⠖⢰⡂⢀⡆⠰⣬⣍⣁⣴⠟⠁⢿⡛⠶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢞⡥⠀⣦⣈⣩⣤⣴⣤⡀⠁⠈⢁⣤⣦⣤⣍⣁⣴⠄⢮⡻⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡷⢁⠙⠿⢿⣋⣁⠀⠀⠀⠀⠀⠀⣈⣙⡿⠿⠛⠀⢷⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⣹⣷⠏⠀⠀⣯⣀⡈⠈⠙⠒⠒⠋⠁⢁⣀⣽⠀⠀⠸⣶⣿⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⣿⡾⢡⡗⣌⡃⠤⠤⠖⠒⠒⠲⠦⠤⢘⣣⢊⡆⢷⣿⡟⠷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠟⠀⣼⣬⣛⣛⠷⣒⣲⣦⣴⢖⣒⠾⣛⣛⣥⣧⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠿⠇⠸⠿⠿⠿⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠛⠓
⠀⠀⠀⠀⠀⠀⠀⢾⣽⢿⡁⠀⠀⠀⠤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠙⣦⠀⠀⠀⠀⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠸⣧⠀⠀⠀⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣿⣆⠀⠀⠹⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⣸⣿⣄⠀⠀⢠⣿⣿⣷⣄⠀⠘⢿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⡀⣿⣿⣿⣿⣿⣆⠀⠀⠹⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⢹⣿⣿⣿⣿⣿⣆⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡄⢻⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡀⠹⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠈⠙⠛⠿⠟
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⡄⠈⠻⢿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡄⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣷⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⠿⠿⠛⠛⠃
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⡿⠿⠛⢉⣡⣶⣾⣿⣿⣿⡆⢠
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉⠀⢀⣠⡴⠟⠉⠁⠈⣉⣉⣉⣀⠈⠂
⠀⠀⠀⠀⠛⠻⠿⣿⣿⠿⠿⠿⠿⠿⠟⠛⠛⢉⣩⠴⠶⠶⣶⣶⣶⣾⣿⠟⢁⣠⣤⣶⣿⣿⣿⣿⣿⣷⡀
⠀⠀⡀⢢⠀⣶⡿⠛⠛⠿⢿⣶⣦⣤⣴⣶⠾⠋⠁⠀⠀⠀⣀⣠⣭⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠸⡄⠁⠀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠁⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀
⠠⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⣠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠈⠁⠀⠀⠤⠀⠀⠤⠀⠀⠈⠁⠂⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠠⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠄⠀⠀⣠⠄
⡀⠐⠛⠀⣤⠀⠀⠀⠈⠁⠰⠆⠀⠰⣶⠄⠀⣀⡀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⣀⠀⠠⣶⠆⠀⠘⠆⠈⠁⠀⠀⠀⣤⠀⠛⠂
⠙⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠋⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠙⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢠⣄⠀⠀⠀⠀⠠⠦⡤⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢤⠴⠀⠀⠀⠀⠀⣠⡄
⠀⠀⠈⠀⠠⣤⠀⠀⠀⢀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⠠⣤⠄⠀⠁
⠀⠀⠀⠀⠀⠀⠰⠶⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠶⠆

⠀⠀⣀⣀⠀⠀⢀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀
⠀⠺⣿⣧⠀⠀⠻⢿⡄⠀⢀⣀⣤⠀⠀⣀⣤⡀⠀⠀⢾⣿⡁⠀⠀⢶⣟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠺⢿⣯⡀⠠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠇⠀⠘⠿⠿⠄⠀⠀⠀⠈⠁⠀⠀⠀⠙⠃⠀⠀⠀⢶⣿⡛⠀⠀⠀⠼⣿⣶⠆⠀⠀⠀⠈⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃

⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⡔⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢂⣶⠆
⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄
⣤⣤⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠺⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠗⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⣤
⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠄⠀⠀⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠀⠀⠠⣤⡀
⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠤⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣷⣦⢤⢤⣴⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⢠⡼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣼⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⠀⠁⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⣿⣿⠿⠿⠿⣼⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⡷⢶⣦⢉⡉⡋⠉⠁⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠸⡧⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠈⠉⠓⢥⡀⠄⣪⣽⡄
⠀⠀⠀⠀⠀⠀⢸⣿⠶⠴⡶⢶⠒⣻⠂⠀⠀⠀⢀⣹⡥⡀⠀⠀⠹⡿⠿⠿⠿⢿⣶⣶⡶⢶⣤⣤⣇⡀⢸⠉⠙⠓⠒⢲⠀⠀⢱⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣀⠸⠀⠿⡂⠀⢠⣾⡿⠛⠿⣖⢄⠀⣠⣷⣄⠀⠀⠀⠀⠈⠉⠲⡄⠈⠙⣿⣿⡄⠀⠀⠀⢸⠀⠀⢸⢸⣿⣿⣇
⠀⠀⠀⠀⢀⣤⠟⢳⣯⡿⠯⢿⣄⣶⣛⣦⣼⣿⣦⣤⣤⣾⣿⣟⢋⣡⣾⡁⠀⢀⣹⣿⣿⣷⣷⣦⣶⣿⣿⠁⠀⠀⠀⢸⠀⠀⢸⣼⣿⣿⡟
⠀⠀⠀⠀⡿⢥⣀⣀⠈⠉⠉⠉⢡⣿⣤⣤⣠⡤⣼⣟⣭⢫⡉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⣽⢫⣿⡏⢸⠀⠀⠀⠀⢸⠀⠀⢸⣿⣿⣿⣷
⠀⠀⠀⠀⡇⠀⠀⠈⠉⠉⠉⠉⢹⣿⣿⡆⡇⠀⢸⡟⣸⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⣿⡇⠸⠀⡀⠀⠀⢸⠀⠀⢸⡟⣿⣿⣿
⠀⠀⠀⠀⡇⠀⡏⠓⠒⠒⠒⠒⠚⣿⢛⣿⠻⠛⣿⡇⣿⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠻⣿⡇⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⣿⣿⣿
⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⣠⣾⣛⠋⣘⣃⢨⡳⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣜⠂⠉⠉⠉⠀⠒⣦⡀⠀⠀⠀⠀⡇⣿⣿⣿
⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⣞⣿⣿⣿⣾⣿⣿⣗⠙⡘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠛⠛⠛⠒⠚⠋⢹⡇⠀⠀⠀⠀⡇⣿⣿⣿
⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠳⠤⠤⢤⣤⠤⠴⠚⡇⠀⠀⠀⠀⡇⣿⣿⣿
⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⡇⠀⢉⠉⠉⠉⢉⣉⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡉⠛⠒⠤⠶⠶⠶⠖⠙⢙⣆⡠⠤⢤⣧⣿⣿⣿
⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⡇⠀⠘⢒⡶⠻⣟⠛⠀⠀⣿⣝⡢⢤⣄⣀⣀⣀⣀⣀⡤⣿⣝⣲⠲⠤⠤⠤⠤⠒⣎⣭⡏⠀⠀⠀⠀⠈⠉⠙⠓⠲⠦⢤⣄⣀⡀
⠀⠀⠀⠀⣧⠀⠓⠤⠤⠤⢤⡇⠀⢰⡋⠀⠀⠈⣱⠆⠀⣿⣿⡿⠋⠓⠓⠒⠒⠒⠒⣋⣿⠀⠉⠉⠛⠒⠛⠋⠉⠁⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠽
⠀⠀⠀⠀⠙⠦⣄⣀⣀⣀⢀⡇⠀⢀⠙⢦⣤⠞⢁⠀⠀⢿⣿⡇⠒⠢⢤⠖⠂⠛⢿⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⡇⠀⠈⠙⠋⠛⠋⠋⠀⠀⣸⠿⣇⣀⡀⢸⣶⣶⣲⠷⡳⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣦⣤⣀⣀⠴⠊⠁⠀⠀⣀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣷⣶⣦⣤⣤⣴⣶⡆⢹⣿⠀⠀⠈⢉⡹⣻⡉⢈⠇⢱⣿⣄⣀⠀⠀⠀⠀⠀⠀⣀⡤⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⡤⠞⠉
⠀⠀⠀⢠⠶⠶⠖⠒⠒⠒⠒⠛⠉⠉⠉⠙⣿⣟⣛⣡⠴⠃⣴⣆⣢⠿⠿⣿⣏⣁⣠⣿⣽⠀⠉⠙⠛⠒⠒⠛⠋⠁⠀⣿⠉⠙⠻⠿⢿⣿⣿⣇⡤⠞⠉
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠄⠀⡄⠀⡈⠉⠛⠂⠀⠼⠈⠉⠉⠀⠘⠧⣄⣀⣀⠀⠀⢀⣀⣠⠴⠃⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣗⠺⢿⡶⠦⠛⠲⣎⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉
⠀⠀⠀⠸⡧⠤⠤⠶⠒⠒⠒⠒⠒⠚⠛⠋⠉⠉⢻⠀⠈⠳⠖⠚⠉⠁
⠀⠀⠀⠀⣧⡤⠤⠤⠤⠴⠶⠶⠒⠒⠒⠒⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠠⠤⠄⠀⠐⠂⣡⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠒⠒⠒⠒⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢳⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠤⠤⠒⠒⠒⠚⠉⠉
⠀⠀⡀⠀⠀⣀⣀⣤⠮⠤⣘⣆⣀⡠⠴⠒⠉⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠘⠓⠛⠛⠉⠉⠀⠀⠀⠀⣀⡀⠠⠚⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠐⠒⠒⠒⢀⡢⠏
⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠋⠉⢣⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡤⠶⠚⠉