Fight Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢸⣷⣤⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣶⣶⣦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣾⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⠿⠿⠻⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠟⠛⠉⠉⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢡⣤⡀⢠⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣄⠀⠀⠄⠀⠈⢿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⡏⠑⡾⠀⡇⠀⠉⣼⠀⠁⢳⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢤⡏⠁⠀⠀⠀⠀⠀⠈⣇⡸
⠀⠀⠀⠀⠀⠀⠀⠹⣴⠃⠀⠙⠢⠔⠃⠀⠀⠘⡄⢀⣀⠤⠒⠒⢉⣉⠼⠒⣪⠇⠀⠀⠀⠀⠀⠀⠀⢸⡁
⠀⠀⠀⡀⠀⢀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⠀⣀⡔⢲⣍⠀⠀⢀⡇⣀⡀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⢀⡞⠁⡴⠃⠀⡘⠀⠀⠀⠀⠀⠀⠀⢠⠖⢤⣸⡤⠊⠁⠈⠙⠮⡑⠦⣈⠉⠁⢹⢤⠖⡖⢲⢦⠀⠀⠈⡀
⢀⡞⠀⣼⠁⠀⢰⠃⠀⠒⠮⣍⣉⠉⠉⡻⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠓⠤⣉⠓⠾⣾⡧⠷⠾⠚⠀⣀⣤⠗⠀⠀⠀⠀⢄⠈⢆
⢸⠁⢠⡇⠀⠀⢘⠷⣤⣀⡀⠀⠈⠙⢲⡇⠀⠀⠀⠀⠀⠀⢷⣤⣤⣤⣄⣀⠀⠉⠒⢻⠀⣀⠤⠖⠋⢁⠏⢧⠀⠀⠀⠀⠈⠆⠘
⠈⠀⠈⠁⠀⠀⡞⠀⠀⢙⠿⣓⢦⣄⣸⠀⠀⠀⠀⠀⠀⠀⡠⢠⡀⠀⠉⠙⢿⣶⣄⣸⠋⠀⠀⠀⢠⠎⠀⠈⣇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠃⠀⠀⠈⠉⠚⠳⠤⠥⢄⣀⣀⠤⠤⠖⢋⠵⠊⠀⠀⠀⠀⠀⠻⣿⠃⠀⠀⢀⡴⠃⢀⠜⠀⢸⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣼⠀⠀⠀⠉⠉⠒⠒⡶⠤⠤⠤⠤⠴⠒⠊⠁⠀⠀⣀⡀⠀⠀⠀⢠⡇⢀⣠⠖⠉⣠⠔⠋⠀⠀⢸⡄
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠈⣉⣉⣉⣉⣁⡤⠀⠀⣀⡤⠟⣉⣤⡖⠋⠁⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠯⣀⣀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠽⠗⠚⠉⠀⠀⠈⠑⠤⣀⠀⠀⠀⢸
⠀⠀⠀⠀⢠⠃⠀⠀⠉⠉⠑⠒⠢⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣄⡜
⠀⠀⠀⠀⠺⣤⡤⢄⣀⡸⢆⣀⣀⣈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁
⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣀⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄
⣙⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣶⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣁⣀⣀⣀⣀⣀
⣿⣿⠋⡛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⢀⣶⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣯⣥⣀⣀⣀⣠⣤⣴⣶⣿⡿⠿⠃⢻⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⣀⣠⣴⣾⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠉⠁⠀⠀⠀⠀⠀⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠁⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⠐⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠏⠙⢿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠃⠀⠀⠈⢿⣿⣿⣿⣿⣧⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡆⠀⣰⣿⣿⣿⣿⡿⠋⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠟⠁⠀⣿⣿⣿⣿⣟⠁⠀⠘⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡏⠀⠀⠀⠈⢻⣿⣿⣿⣷⡀⠀⠻⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⡀⠀⠈⠻⣿⣿⣿⣿⣦
⠀⠀⠀⠀⣰⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⡀⠀⠀⠈⢿⣿⣿⣿⣷⣄
⠀⠀⠀⢀⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⠀⠀⠀⠀⠙⢿⣿⣿⣿⡆
⠀⠀⠀⠻⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠙⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣴⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⢠⠒⠰⠒⠂⡄⠀⠀⠀⠀⠀⡠⠔⠒⢂⠄⠀⠀⠀⠀⠀⠀⠀⣄⠐⠁⣀⠂⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠈⣄⠐⠈⠀⠁⠀⠀⠀⠀⣰⢠⡥⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠊⠉⠃⠶⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠉⠊⠀⠂⠀⠀⢀⣲⣾⣿⡖⣁⠋⠊⣀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠰⠲⡖⢲⡀⠘
⠀⠀⠀⠀⠀⠀⢰⠀⣤⣀⠈⢃⡒⢊⠉⣭⠐⠬⣀⣉⠍⠉⠀⢀⣤⢀⠒⠔⠁⠀⠀⠀⠀⠠⠉⢹⣾⠁⠠⡇
⠀⠀⠀⠀⠀⢀⣈⡠⢸⣿⠦⣠⡉⠠⡅⠚⣖⠶⠃⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⣠⠤⠄⠚⠛⠛⠀⠀⠙⡆
⠀⠀⠀⠀⠀⡎⡝⠉⢘⠛⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡄⡀⠀⠀⠤⠂⠀⠀⠤⠤⠤⢤⣤⣤⡀⠀⣈⣶⣄
⠀⠀⠀⠀⠀⡷⣾⠀⠸⠀⣀⠵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡶⣻⡥⠆⠈⠣
⠀⠀⠀⠀⠀⡇⣾⠈⢂⠀⠀⠀⠘⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⠁⠀⠀⢀
⠀⠀⠀⠀⢠⡇⠁⠃⢀⠉⠲⠠⣤⡤⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣹⡀⠉⣉⣒⣺⡥
⠀⠀⠀⠀⠈⠓⣠⣤⢤⣤⡤⠀⢸⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⣹⢿⣿⠿⠏⠴⠧⣄⡀
⠀⠀⠀⠀⠀⡸⠁⠀⠁⠈⠀⡀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⡴⣆⣁⠄⠀⠉⠒⠶⠯⢤⣉⣓⣄
⠀⠀⠀⠀⡔⠡⠀⠀⠀⠀⠀⠀⠀⠱⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠎⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⡀⠁
⠀⠀⠙⠓⠮⢦⣀⠀⠀⠤⢤⣀⣀⣀⣓⣐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣮⣭⣤⣤⡶⠶⠶⠶⠶⠶⠖⠶⠶⠶⠤⢤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣰⣶⣟⣳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣬⡙⠛⠲⠿⠿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡻⢷⣤⠰⡭⢤⣫⡅⣡⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣰⠀⠀⠀⡰⡐⢀⠼⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠒⠴⠛⣂⠾⣻⠛⠀⢸⡷⠶⠶⢤⡀⠀⠀⠀⠀⠈⠟⠉⣇⠀⢀⠁⠀⣨⠷⢴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣄⣸⡀⠀⠠⠝⠂⠀⣿⠀⠀⠀⠀⠻⢆⣀⡀⠀⠀⠻⡄⣿⡤⣌⣫⠶⣿⣤⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢫⠉⢙⣦⡘⠖⠀⢸⡧⠀⠀⢰⣿⠀⠀⣤⡷⠶⠶⢶⣿⣍⠛⠉⠉⠀⠀⠘⢯⠻⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⠋⠉⠈⡤⣷⣤⡴⢾⡅⠂⢒⣺⣿⡶⢤⣿⣅⣀⡀⠀⠀⠽⠄⠀⢠⠀⠀⠀⢀⡂⠀⠛⣿⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠙⠒⢛⢺⣧⣿⣇⣀⠈⠙⠿⣯⠁⠀⠙⢦⠀⠈⠋⠙⠋⠶⠶⣶⡖⠁⠀⠀⢀⢄⣼⠀⠀⠘⣧⠀⠘⢂
⠀⠀⠀⠀⠀⠀⢀⡿⡀⠀⢠⡞⠉⠉⠈⠉⠉⠀⠙⠶⡶⠼⠷⠄⣤⡀⢳⡄⠀⠀⠀⠀⠀⣬⠑⠀⠀⣀⡤⠞⠁⠀⠀⠐⠈⢻⣄⠺⢧⡀
⠀⠀⠀⠀⠀⠀⢠⣷⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠸⡇⠚⠛⠋⠉⠀⠀⠀⠀⠀⠐⠂⠀⢸⡇⢢⠻⣦⡀
⠀⠀⠀⠀⠀⠀⢈⡷⢠⢙⡆⠀⢀⢀⡀⠤⠤⣼⣭⣀⢤⣤⣤⣤⣤⠤⠴⠛⠀⠀⠀⠀⠀⢿⡆⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠑⠀⢡⡀
⠀⠀⠀⠀⠀⠀⢸⢿⣸⠈⠳⣤⡐⠉⠀⢀⣰⢿⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⢤⠀⡀⠀⠀⠠⣤⣤⣽⠃⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠟⣄⣿⡄⠀⠈⠻⠖⠒⠛⠃⠀⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠠⡀⣁⣤⠴⠾⠿⠛⠋⠙⢷⣤⡴⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠹⣿⠳⢀⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⠔⠋⠉⠈⠁⠀⠀⠀⢀⣤⣼⣿⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠆⠀⢀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡦⠀⢀⣀⣤⠖⠋⠉⠀⠈⠁⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠃⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠔⠋⠁⠁⢆⠀⠀⠀⠀⠀⢠⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢍⠙⠳⣤⣤⡤⠤⠶⣻⣽⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣞⡿⣬⣃⣀⣀⣀⣀⣂⣀⡿⣏⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠻⠇⠀⡀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣽⣥⡈⠉⢉⠙⠛⠉⠉⠙⠀⢠⠐⣕⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡞⠁⠀⠀⠙⠀⠀⠀⠀⠀⠈⠀⠐⣹⣟⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢀⡀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠦⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠟⠀⠀⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⣀⠿⠺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠦⠤⢄⣿⣿⣿⡇⣀⡿⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⠿⢿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠛⠃⠀⠀⠒⠚⠛⠋⠙⠉⠁⠀⠀⠙⠁⠀⠀⠙⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⢿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⠉⢹⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠘⠿⣿⣿⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠰⠿⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠟⠋⠀⠀⠀⠀⠉⠻⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣆⠀⠀⠀⠀⠀⠀⢀⣾⠁⠈⠑⣦⣤
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠆⠀⠀⠀⠀⠀⢀⡟⠉⠉⠉⠓⠚⠓⠲⣶⣶⣶⣶⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠙⣿⣦⣤⣿⣿⠓⠢⣀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣶⣶⣶⣶⣶⣶⡟⠣⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⣿⣿⣿⣿⢿⣷⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁⠉⠉⠙⠛⠲⠶⠤
⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⢸⣿⣿⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠛⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠹⣿⣿⣧
⠀⠀⠀⠀⠀⣸⣿⠟⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠁⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠘⣿⣿⣇
⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠙⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⡿⠁⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠘⣿⣿
⠀⠀⢀⣾⣇⠀⠀⠀⠀⠀⠀⠸⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢸⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠸⣿⡆
⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠈⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⠒⠳⣼⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣦⡇⠀⠀⠀⠀⠀⠠⢴⡶⠶⡿⠶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠠⡄⠀⢀⢻⠀⠀⠀⠀⠀⠀⣸⢧⣀⡠⡶⠀⠀⠰⠞⠙⠲⣤⡀⠀⠀⣰⠋⠀⠠⣤⠀⠀⡈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣏⠀⢀⠀⠀⠁⠀⠈⢸⠇⠀⠀⠀⠀⣉⣁⠀⠀⠀⢧⣀⠀⠀⠀⠀⠀⠀⠙⠷⣄⡇⠀⠀⠀⠀⠀⢀⠁⢸
⠀⢠⣤⣄⣠⠶⠚⠋⠉⠉⠉⢹⠟⢆⡈⠃⠀⠀⠀⣀⠞⠀⠀⠀⣠⠎⡄⢈⠟⢦⠀⠀⣸⠋⠁⠀⠀⠀⠀⠀⠀⢹⠿⣄⠀⠀⠜⠠⡽⢀⠞
⠀⢻⠏⠹⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠉⣗⣶⣶⣾⠷⠶⠶⠶⢾⢸⠀⢽⣉⡀⡸⠀⠀⡇⠀⢠⠤⠴⠲⢄⡀⣰⠏⠀⢾⡹⣖⣲⢖⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⣠⡿⠀⡟⠀⠀⠀⠀⠀⠉⠑⠺⠗⠚⠁⢀⠤⠛⠂⠀⢳⡀⠀⠀⠉⠛⢒⣲⠶⠋⠉⢡⣾⠇
⠀⠀⢀⣀⣀⡀⠀⠀⠀⡟⠀⠀⢠⠴⠊⢱⠃⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢦⡏⠀⠀⢰⢷⠀⠙⠒⢒⡏⠉⢉⠀⢀⣠⠶⠋⡾
⠀⠰⢥⠤⠋⢳⣄⣀⣠⣧⠀⠀⣮⣀⡤⠋⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⡴⠶⣶⣾⡏⣽⠟⠛⠉⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠳⢤⣀⣀⣀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠙⢮⣀⣀⣀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣀⣀⡀
⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠛⠓⠚⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠒⠒⠓⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⢀⣠⣤⣴⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⡀
⠀⠀⠀⡰⠻⢿⣿⣿⣿⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⢀⡆
⠀⠀⢀⡇⠀⣼⣿⡿⠃⠀⠀⢤⠠⠀⠀⠀⠒⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢦⡀
⠀⠀⠈⠇⠀⠈⠈⠓⠂⠀⠀⠒⠀⣄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⢐⡁⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠈⢢⠐⠄⠀⠀⠀⢠⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⢀⣾⠋
⠀⠀⠀⠀⠀⠑⡀⠀⠀⢀⣈⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠰⠋⠡
⠀⠀⠀⠀⠀⢠⣶⣤⣲⣄⠈⠉⠁⠀⠀⢸⡙⣒⠶⠶⢗⠀⢲⠀⠀⠀⠀⠀⠠⠄⡰⣄⣀⣀⣀⣀⣀⣀⡀⠀⠓⠶⠶⡄⢀⡆⢀⠄⠀⠀⠒
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣼⣏⣿⣿⣿⣿⣿⡇⠇⠀⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠛⠒⠐⠒⠒⠂⠒⢢⢽⠀⠀⣀⠲⠀⠐⠁⠘⠓⠦⠒
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⠛⠉⠉⠉⣷⠱⠀⣴⣓⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⢤⡀⢰⠸⣤⠊⠁⢀⠀⠠⠀⣀⡴
⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⢿⠸⠀⠨⠉⡉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢶⠄⠈⠆⠟⢆⠀⠂⢀⠖⠉⠉
⠀⣴⣾⣿⣿⣿⣿⣿⣿⣏⠉⠛⢿⣿⣿⣶⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠁⠀⠀⢠⡴⠀⠀⡀
⠈⠿⣿⣿⣿⣿⣿⣿⡏⠈⠀⠀⠀⠀⠉⠁⠀⢤⠤⠀⠁⠠⠤⠤⡤⣀⣒⣒⣒⣂⣀⡀⠀⠀⡀⠀⠀⠀⢀⡠⠔⠉⠀⢀
⠀⠀⠈⢏⡛⠿⠿⠋⠀⠀⠘⠓⢀⠀⠀⠀⠀⠂⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠠⡤⠖⠉⣩⠞⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠈⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⠊⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⢰⠢⠤⠥⠆⣴⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠉⠢⣄⢀⡠⠀⡌⠳⢄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠜⠀⠑⣦⡀⠀⢱⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⣠⠀⢀⡟⠉⠀⠸⠇⠐
⠀⠀⠀⠀⠀⠈⠰⡶⠴⡶⠀⠀⠀⠑⠐⣷⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠚⢁⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠰⣠⠰⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠐⠆⠐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂⠇⠂⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡏⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⣤⣀⣀⣀⣀⣀⡀⠀⣸⠀⠀⠀⠀⠀⠠⣄⣀⡀⢠⣤⣤⣤⣴⣶⣶⣾⡏⡿⢁⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣧⠹⡇⣿⡿⠟⠿⠿⠿⠿⠷⠙⠉⢀⣀⣤⣀⣀⣀⠈⠉⠁⠀⠋⠉⠉⠉⠉⣿⣿⣸⡇⣾⣿⠉⠉⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⣿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠺⠿⠛⠻⠿⠿⣿⣿⣿⣶⣦⣤⣤⣄⣀⢀⣿⣿⣿⢠⣿⣿⣶⡞⠈⠁
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣻⣿⣿⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣿⣿⣿⣿⢇⣼⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠛⠛⢳⣼⣿⢻⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣷⡿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣾⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⣶⣤⣀⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠿⠛⠻⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠙⠻⣿⣿⡿⠃
⠀⠀⠀⠀⣠⣴⣿⡿⠟⠁⠀⠀⠀⠀⠉⠙⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⢀⣤⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁
⢠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄
⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠈⠫⣎⠝⢆⠀⠀⠀⠀⢳⠰⣹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠁⠀⠆⠀⠀⢀⠂⠂⠋⠀⠀⠀⢠⡿⡳⣻⡿⠋⣠
⢄⠀⠀⠀⠈⠣⠀⠁⠀⠀⠀⠀⠡⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⢜⣿⠏⠀⠔⢀
⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠣⣳⠟⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁⠀⠀⠀⢀⢔⠫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢑⠕⡪
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠛⠳⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠲⠶⢦⡄⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⣸⠇⠀⠀⠈⠳⣤⣀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠈⠀⠀⠀⠉⠛⠶⣤⡾⠋⠉⠛⡷⠶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠛⠶⣤⣀⠀⡜⠁⠉⠀⠀⠀⢀⠀⢀⠿⠷⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡿⠁⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠈⠉⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠒⢶⡁⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠹⣿⣄⣀⣀⠀⡠⠎⠀⠉⠛⠶⣄⡀
⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠘⡟⠉⠀⠀⠁⢀⣤⡀⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠉⠓⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠉⠁⠀⠀⠀⠀⠉⠁⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⡆⡀⠀⠀⢰⡟
⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⢰⠁⠀⠀⣼⠇
⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢄⢝⢦⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠛⠿⣿⡂⠀⣠⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⢷⣀⡁⢩⡝⢿⡿⠂
⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀⣾⣿⠛⠁⠁⠀⢠⣿⣿⣿⠖⠱⠃
⠀⠀⠀⠀⠀⢀⣿⣿⣶⡟⣺⣿⡅⠈⣁⣽⣿⣿⣿⣧⡀⣠⠀⣀⡄⣀⡀
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡟⠐⢾⣿⣻⣿⣿⠃⠀⠀⠀⢀⣿⣿⣿⣷⡀
⠀⠀⠀⠀⢀⠀⣌⠛⡟⢿⣿⣿⣿⣿⣿⣿⣿⣧⣤⠀⠀⢠⣾⣿⣿⣿⣿⣇⣰⣿⡆⠀⠀⠌
⠀⠀⠀⠀⡈⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣿⣿⣿⣿⠻⣿⣿⣿⣿⠃⠠⠐⠃
⠀⠀⠀⡠⣾⣿⣟⣉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠿⣿⣿⣿⠁
⠀⠀⢰⣿⣿⣿⣭⠿⠀⠀⠀⠘⠿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣠⣤⣀⠀⠁⠀⠀⢀⣀⣀⠀⡀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡸⢿⣷⣶⣆⡀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠉⠉⠉⠉⠉⠉⠉⢿⣿⣿⡇⢴⣦⣾⡅⠀⠈⠛⠛⢿⣶⣆⣀⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣇⠀⠙⢿⣷⣄⠀⠀⠀⠀⠈⠙⣿⣿⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣶⣅⡀⠙⠻⢲⡦⢄⠀⠰⠿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠇⠄⠘⣦⣀⣈⡦⠤⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠛⠉⠀⠰⠶⠞⠋⠁⠀⠀⠀⣬⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣦⣤⣶⣦⣶⣶⠷⠦⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣷⣶⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿
⠀⢀⣠⡀⠀⠀⣀⢠⡴⣾⣿⠿⠿⠛⠋⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉
⠀⠿⠿⠿⠿⠾⠿⠿⠦⠭⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠴

⠀⠀⠀⠀⠀⠀⢠⣾⣿⣶⣀⣀
⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣇⠏
⠀⠀⠀⠀⠀⠀⡀⣶⡿⣷⣿⡋
⠀⠀⠀⠀⠀⡌⢸⠛⢿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⣀⠤⠊⢁⣀⣀
⠀⠀⠀⠀⠀⡃⢸⢀⣤⣽⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣤⠖⠋⢁⣴⣾⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⢈⢁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣠⡀⢀⣀⡠⠴⠒⠉⠁⠙⣆⠀⠀⠈⢿⣿⣿⣿⡿⠿⠓
⠀⠀⠀⠀⠀⣿⣧⡙⣿⣿⣿⣿⣿⣷⣌⣹⣿⣿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠘⣧⣀⣴⣾⣿⣽⣿⣿⣦⡀
⠀⠀⢀⣠⡶⠿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⠛⠃⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷
⢀⣴⠟⠁⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣷⣵⠊⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣻⡟
⠀⠀⠀⠀⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⢶⣶⣿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠰⢡⣿⣿⡟⠛⣻⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠟⠋⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡟⠫
⠀⠀⠀⣶⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣦⠈⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠒
⠀⣤⣴⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣇⣲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠠
⠀⠀⡅⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠴⢛⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣠⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣷
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡟⠀⠈⠉
⠀⠈⠩⠿⠿⠟⠛⠹⢿⣿⣿⠿⠟⠛⠉⢹⣛⡛⠋⠉⠉⠀⠀⠀⠛⢻⣿⡋⠀⠀⠀⠉⠉⠙⠛⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣷⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠿⠟⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠉⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⢸⡿⢠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⣀⡀⠈⢿⡶⢶⣦⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡇⢠⣤⣾⢇⣿⣿⣿⣿⣶⣤⣄⡀⠀⠀⢀⣴⠿⠋⠛⠋⣁⣀⣀⣀⣀⣴⡶⠶⠊⠉⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠈⠁⣸⣿⣿⠟⣡⣤⣭⠙⣿⡄⣠⡿⠃⠀⠀⠀⢾⣿⣿⣿⣿⣿⣥⣤⣤⣴⡶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠻⢷⣤⣾⠟⣿⡏⢸⣿⣿⣿⣿⠟⢹⣏⣰⣿⣿⣶⡄⠈⠛⠿⠿⠛⣿⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀⠀⠘⠟⠁⣰⡿⠀⢘⣿⡿⠛⠁⠀⠈⠻⢿⣿⣿⣿⣇⠀⠀⠀⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⡀⢀⣴⡟⠁⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠉⠉⠘⣿⣦⣤⣶⣶⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣯⣤⣤⣼⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⣠⣾⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢻⣷⡀⠀⢠⣾⡟⠁⠀⠈⣿⣿⣿⣿⣿⡿⠛⠉⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⢙⣿⣿⡟⢻⣿⣿⡀⠀⠀⢿⣧⢠⣿⠏⠀⣀⣤⣾⣿⡿⠋⢹⣿⣷⣄⠀⠀⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠀⢀⣴⣿⠟⠉⠀⠀⠉⠻⣷⣄⠀⠘⣿⣿⡏⠀⣾⡿⠋⠁⠀⠀⠀⠀⠀⠉⢿⣧⣄⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠁⢠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠙⣿⡄⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⡀⠈⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⢀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣄⠀⠸⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣄⠹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣧⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⡟⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠁⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠰⣿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⡿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⢸⢀⠷⠀⠀⢠⢃⡖⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢦⣀⠘⠀⠸⠃⢀⢨⡇⠀⠀⢠⠗⠁⠀⠀⠀⠀⣉⡄⠀⠀⢀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠀⠀⢀⣁⡀⠰⠀⣀⠁⡡⠢⡈⡀⠰⡀⣀⣀⠀⠊⠉⠀⠀⠐⢁⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠶⠄⠀⠀⢈⣷⡶⡶⠛⠟⠀⠀⣦⣴⣤⣈⡀⡢⣠⣤⣦⡄⠀⠘⠛⠲⡷⣶⣄⠀⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣻⠀⠁⣴⣾⡀⠀⢀⣉⣀⣠⠆⣸⠀⢢⣀⣀⣁⠀⠀⣸⣦⡄⠀⢸⡳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣼⣿⣿⣀⠈⠿⣿⡷⣋⠀⠈⡿⠟⠛⢧⠟⠛⠿⡏⠀⢈⡱⣿⡟⠏⢀⣸⣿⣾⣯⣉⣀⣀⣀⣀⣀⡀
⠀⠀⠀⣸⣿⣿⣿⠿⢿⣿⡿⠟⢛⣛⣿⡟⣼⣿⠃⠀⣸⣟⠙⠛⠷⠟⠠⠞⣀⣼⣄⡘⠦⠘⠶⠟⠛⢙⣿⡀⠀⠿⣿⡜⣿⣟⣛⠛⠿⣿⣿⠿⢿⣿⣿⣯⡀
⠀⠀⠀⣤⣤⠤⠶⠠⢤⠄⠰⠟⠛⠋⢿⣿⣿⣗⡀⣀⣿⣿⠛⠛⠛⠋⠙⢙⠛⣣⡛⢛⠙⠙⠛⠛⠛⢻⣿⣧⡀⣰⣿⣿⣿⠟⠛⠛⠷⠀⢤⠤⠰⠦⢥⣤⡄
⠀⠀⠈⠃⠁⠀⢠⢠⣀⣤⣴⣶⣶⣞⣆⣇⠻⣅⣤⣿⣿⣿⡷⣿⣶⣦⣾⣾⣶⠙⢷⣾⣾⣦⣶⣾⡷⣿⣿⡿⣧⣄⡽⢃⣇⡞⣶⣶⣶⣴⣄⣠⢠⠀⠀⠁⠋
⠀⠀⠀⢸⡶⠷⠿⠿⠟⣛⣻⣴⣶⣿⣿⣿⣏⡀⠈⠘⠙⠿⢷⣤⣀⡀⠈⢈⢃⠢⠀⠋⠈⠀⣀⣠⣴⠟⠟⠙⠈⠀⣉⣿⣿⣿⣷⣶⣼⣛⡛⠿⠿⠷⠷⣾
⠀⠀⠀⠀⠐⣶⣾⠿⠟⠋⠉⠁⠐⢂⡀⠀⢉⡽⠛⠶⠦⠖⠀⡉⡍⢛⡩⠋⡉⠑⠄⢘⡙⠛⠫⠏⠁⠐⠦⠦⠞⠛⠉⢁⠀⠀⠀⠀⠈⠉⠛⠿⢿⣶⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠚⠁⠀⠀⣀⡠⣰⠊⠀⢠⠀⠀⣼⠃⢂⣀⠁⠙⡂⢀⡆⠀⠀⢤⡀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⡴⠃⠀⠀⠈⡖⠡⡿⠀⠀⠛⠀⡄⢹⡌⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠠⣀⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠁⠀⠀⠈⠓⠄⣀⠀⠈
⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⢀⣀⠤⠀⠀⠂⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⡐⠱⠒⠀⢠⠀⠂⠤⠀⠐⠒⠂⢠⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⡐⠒⠐⠈⠲⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠔⢻⢴⡤⢄⠀⠀⢀⠴⠄⠀⠁⠀⠀⠘⡁
⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠐⠉⢲⣄⠞⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡜⠦⢴⡏⢰⠀⠈⠀⠀⠀⠰⠄
⠀⠀⠠⢀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⢁⢀⠈⠢⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⡀⢀⠀⠀⠒⠀⡄⡙⠛
⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⡀⠁⠀⢠⡤⣄⠉⠀⠇⠀⠀⠀⠀⢀⠀⡀⠀⢀⣀⠀⡄⣄⠂⠀⠀⠀⡘⣄⠀⠀⠀⠀⢀⣂⣀⣠⣆⠈
⠀⠀⠀⠀⡇⠀⠀⠀⡘⣠⢀⡀⠀⠸⠀⡀⢰⠞⢐⢀⠀⠠⠐⡢⣄⡔⠈⠀⠤⠅⠄⠈⢣⡀⢀⠌⠵⢶⣥⠦⠤⠅⠊⠥⠄⢄⠈⡇
⠀⠀⠀⠠⠁⡀⠀⠀⠀⣴⠈⣀⡤⠒⠂⠡⢭⠴⠿⠬⡌⠀⠀⢠⠀⠀⠄⠀⠀⠀⠀⠀⠒⠁⠀⠑⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠑⠚⠉⢀⠊⠀⢀⠊⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⣠⢀⢀⡀⠀⢀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⡀⣤⠔⠀⠞
⠀⠠⠀⠀⠀⠀⠀⢀⠴⠁⠀⠀⠀⡀⠢⡤⢤⡤⢀⡀⠦⠤⠔⠒⠚⠁⠀⠀⠀⠀⠈⠚⠉⢲⠦⠞⠂⠀⠈⠉⠁⠀⠀⠀⠰⠀⡧
⠀⠀⠀⠀⠀⡤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⠈⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠣⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢀⠄⣀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠀⠀⠈⠆⠀⠐⠤⠀⠀⡀⠄⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣀⡀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⡆⠐⠂⠉⠁⠀⠐⢶⡶⠶⠾⡆⢀⠄⠀⠀⠀⠀⠄⡀⢘⣄⠀⠀⠀⠀⠀⠀⢠⡄⠒⠛⠤⠀⠠⡄⢨⠟⠓⠒⠃
⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⠀⠘⡄⠀⢰⣰⠋⠘⢰⠆⢀⠃⠊⠈⢁⠀⠳⢄⡀⠀⡠⡲⠋⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⢀⢀⠴⠒⠁⠀⠀⠀⠀⠀⢀⠇⠀⠀⠉⠒⠀⠈⠢⣀⠁⠀⠀⠀⠁⢠⠊⠉⠉⠘⣤⡀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠘⠁⠈⢄⠀⠀⢀⡀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⣀⠊⢀⡠⠴⠘⠁⠈⠑⢒⡶⠤⣄⣀⡇
⠀⠄⠀⠀⠀⠀⠨⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢁⠊⠀⠈⠀⠀⠋⠀⠐⠟
⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⢀⡀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠈⠛⠉⠃⠁⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⢀⡀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠐⠂⠀⠀⠒⠤⡀⢀⡀⢀⠀⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠐⠠⠂⠀⠠⠒⠂⠀⠀⠀⠚⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠄⠀⠀⠀⠀⢠⠖⠉⠁⠀⠀⠀⠀⠀⠀⢀⠴⠰⢄⠀⢢⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠛⠷⠚⠀⠀⠀⠀⠁⠀⠀⠀⣀⠜⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠺⣄⠀⡴⠒⠲⠄⠀⠀⠀⢀⠆⡆⠀⡀⡀⠉⠉⠈⠑⢤⠇⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠈⠂⠡⡠⣀⠀⠄⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⢚⠁⠀⠑⢄⠀⠀⠀⠀⠀⢀⢀⣀⣀⣀⣀⡰⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢄⠀⠈⢠⣄⠀⠀⠣⠀⠀⠀⢨⠀⠬⠀⠀⠀⠀⠁⢸⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠦⠀⠁⠈⠀⢀⡞⠀⠀⠀⠀⠀⠀⠓⠤⠤⠤⢶⠇⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠒⣤⡤⠐⢏⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡀⢢⡀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠁⠀⠄⡀⠀⠀⢠⠇⠱⡄⠀⠀⠀⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠅⠈⠉⠩⠖⠲⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠈⠙⠒⠋⠀⠀⠙⢦⡀⠀⣀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠈⡦⠀⠀⠔⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠒⠆⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢉⠁⠀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⡤⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡠⠤⠴⢁⠀⠀⠈⢰⠦⠶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢆⠈⢴⠒⠒⠒⡄⡇
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠙⡄⠐⠁⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡠⠊⠉⠀⠀⠚⡀⢇
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠸⠀⠀⠀⣀⣀⣤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡀⡇⠀⠀⠀⠀⢀⣰⠎
⠀⠀⠀⠀⠀⠈⠉⠐⠂⠀⠀⠀⠀⠒⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⠛⢿⠛⡟⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡉⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠉⠀⠀⡲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢤⢀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⢯⠄⣬⣁⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠽⠀⠀⠠⣀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣴⠀⠀⠀⠀⠀⠒⠻⡷⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⣧⠘⠀⠀⠀⠀⡓⢉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠞⢻⣶⣤⣤⣀⠀⢶⣶⣃⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣧⡀⠁⢀⠀⡘⡗⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣐⢴⢟⠀⢀⣴⣿⣿⣿⣷⣿⣿⣿⣋⠛⠇
⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⡻⣿⣿⣷⣏⣿⣯⢿⠀⠀⠀⠂⠠⣄⠀⠀⡀⠀⣀⡾⠻⠛⠁⠀⠈⣻⠁⠀⢠⠁⠉⠹⢿⣧⡇
⠀⠀⠀⠀⠀⠀⣜⣸⣧⣤⡄⣼⣿⢻⠿⠿⠙⠉⠉⡀⠀⠀⠀⠀⠳⠾⠿⢳⠶⣅⣀⠀⠀⠀⠀⠀⠛⡀⠀⠀⠀⠀⠀⡏⢻⢦⡔⠀⡀
⠀⠀⠀⠀⠀⠈⠋⣍⠻⠏⣻⡛⣿⣟⠰⡄⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠈⠙⠲⠤⣀⠸⠀⠀⠀⠀⠀⠀⠀⠃⢸⡇⠁⠈⣁⡀
⠀⠀⠀⠀⠀⠺⣇⣿⣿⣄⣮⡿⢿⡛⣹⣧⠀⡄⠀⠀⠆⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⢦⡈⠉⠁
⠀⠀⠀⠀⠀⠀⠟⠃⠀⠉⣹⡟⠸⡇⢾⠟⢃⡄⠀⠀⠸⡀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⡇⢡⠀⠁⠀⠀⠠⠠⠠⠀⠰⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣸
⠀⠀⠀⠀⢘⠲⠄⠀⠀⣰⢿⠐⡀⠀⠀⠀⠀⠃⠀⠀⠀⠣⠀⠐⠀⠁⠄⠀⠀⠀⣰⣧⡀⠀⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⣿⡦⠀⢀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⣰⠦⡄
⠀⠀⠀⠀⠀⣹⣿⡀⣸⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣈⠐⠲⣦⣤⣀⣀⣀⣀⣀⣀⣀⡤⠆⠀⠤⠋⠙⠙⢱⡂
⠀⠀⠀⠀⢰⠝⡍⠻⢆⠦⠶⠖⠂⠀⠀⠢⠤⠴⠶⠿⢿⡅⠄⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠃⠀⠀⠐⠀⠀⠴⠂⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠜⠠⠧⠴⠮⠤⠐⠞⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠁⡀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠔⠂⠄⠀⠀⠀⢈⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢀⡀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⢀⠁⣠⡀
⠀⡠⠄⡀⠀⠀⠈⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠋⠀⠀⠀⠀⠠⠤⠠⠆⠀⠄⢀⡀⠐⠦⡠⢈⠀⢉
⠈⠡⠐⠀⠀⡠⠢⠄⠀⠀⢀⠔⠲⠀⠀⠠⠁⡐⠂⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃⠀⠀⠀⢀⡐⢀⡠⠀⠁⠀⠘⠂⠀⠈⠂
⠀⠀⠀⠀⠀⠐⠒⠀⣀⠀⠀⠂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⡀⠀⠆⠀⠀⢀⡄⠀⡀⢀⠄⠐
⠀⠀⠀⠀⠀⠀⠔⠀⠋⠀⠀⠀⠀⠀⠀⠀⡐⠠⣀⠀⠀⠀⠀⠀⠄⠰⠀⠀⠀⠀⠀⠀⠀⣄⢀⠀⡃⠀⠁⠀⠒⠁⠀⠀⠈⠁⠀⠀⡀
⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠢⢄⠀⠀⠀⠀⠀⠦⠀⢤⠀⠀⠀⠀⠁⠐⠒⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⠢⡀
⠘⡡⠆⠐⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠙⡲⠄⠐⠂⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠤⠒⠉⢢⡀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠘
⣘⡀⠀⠀⠀⠐⢆⠀⠃⠀⠀⡀⢀⡠⠁⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢤⣀⡀⠀⠀⠀⠀⠀⢀⠔
⠉⠀⠀⠀⠀⠀⠛⠀⠀⠊⠀⠈⡃⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⡉⠩⣀⠉⠉⠁⠉
⠰⢇⢀⡠⠀⠀⠴⠀⠈⠄⣀⠔⠁⠐⠒⡬⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠈⠢⢄⠁⠀⠀⡀
⠀⠀⠈⠀⠈⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⢙⡤⠴⢬⡦
⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⡀⠀⠀⠀⣀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠖⠐⠃⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢀⠐⠒⣀⡀⠂⢠⠤⣴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣬⣶⣦⠤⢶⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢱⠰⠄⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠸⠀⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠀⠀⠀⠁⣄⡈⠀⠰⣤⠀⠀⠀⠀⣠⢊⡑⠀⠃⠀⠀⠈⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⢀⠠⢄⠀⠀⠀⡀⡻⠳⡏⠀⢤⣀⠀⠀⠘⠀⠀⠐⡀⢠⠘⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⡇⣄⠠⠤⠆
⠀⣀⠀⡀⢀⣄⡀⠀⠀⡐⠁⠀⠀⠐⢄⣰⣑⠀⠀⡐⡀⠀⢄⡙⠅⠘⠀⠀⢰⠁⠀⡄⠀⠀⠀⠀⣀⠀⣠⠎⠀⠀⠀⠀⠀⢤⠦⠆
⠺⢥⣐⣀⡀⠀⠀⠀⠍⠉⠄⠀⠀⠀⠀⠀⠈⠂⢄⢡⡈⢀⡀⠀⠀⢠⠀⠀⠀⠃⠈⠀⠀⠀⠀⢰⠉⠈⡉⠛⠒⠦⢤⣤⣤⣶⣤⡤⠴⠗⠀⠐⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⠋⠀⠀⠊⠀⠐⠐⠃⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡀⢀⠀⣀⣀⠀⢀⣐⠒⣒⣒⡒⡒⠒⣒⡒⠒⢒⠒⢒⠒⣒⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣷⢸⡇⢸⡇⣿⣉⠁⣿⣉⠈⢹⡟⠉⣿⢸⠏⢻⡆⣿⣇⣿⢸⣏⡙
⠀⠢⢄⠀⠀⠀⠀⠀⠀⣿⣀⡿⢸⣇⣸⠇⣿⣉⡀⣈⣻⡇⢸⡇⠀⣿⢹⣆⣸⠇⣿⢹⣿⢀⣉⣿
⠀⠀⠀⠑⠢⢀⣀⣀⣀⡈⣹⠧⠀⠉⠉⠀⠉⠉⠁⣉⣉⣀⣈⠁⠀⠉⠀⠉⠉⠀⠉⢀⣉⡀⠉⠁
⠀⠀⠀⠀⠀⡆⠀⣚⠛⢒⡒⢒⡂⢒⣀⡂⣀⠀⡐⢀⡐⣀⣀⠀⣀⣐⠒⢂⣀⡒⠒⠚⠛⠓⠂⠀⠐⢄⡀
⠀⠀⠀⠀⠀⠁⢠⡿⡇⢸⣿⣸⡇⢿⣉⠁⢿⢸⣿⢸⠇⣿⣉⠀⣟⣹⠆⣿⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄
⠀⠀⠀⠀⠀⠀⣼⠷⣿⢸⡏⢿⡇⣈⣹⡇⢸⣿⢸⣿⠀⣿⣩⡀⡟⢻⡄⣌⣹⡇
⠀⠀⠀⠀⠐⠤⠩⢤⣬⠌⠁⠈⠁⠈⠉⠀⠀⠁⠀⠁⠀⠉⠉⠀⠁⠀⠁⠈⠩⠤⠤⢤⣤
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢸⢀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠙⠙⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⡄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡄⠒⣻⣿⣿⣿⡿⢧⣾⣻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡇⢻⠉⠙⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⠀⠀⠀⠀⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⢰⡿⢿⣿⣿⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠛⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠈⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠀⢀⣀⣠⣤⠤⠶⠖⠒⡿⡙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢁⣾⢿⠋⣹⣿⣿⣿⣿⣿⣿⣟⣥⡾⠖⠛⠉⠉⠀⠀⠀⠀⢀⠜⠀⢲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡁
⠀⠀⠀⠀⠀⠀⠀⣼⣿⡼⠀⣿⣼⣿⣿⣿⣿⣿⡿⡁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠉⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢀⠀⠀⣾⣿⣿⣟⣾⣿⣿⣿⣿⣿⣿⣿⣷⣽⣄⠀⠀⠐⠀⢀⣤⠞⠁⠀⠀⠀⠀⣠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋
⠀⠀⠀⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣤⡖⠋⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⣠⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣷⣤⣄⣀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢠⠐⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢀⣠⣾⡿⠟⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠘⠁⠚⠒⠘⢿⣿⣿⣿⣿⣿⠿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠁⠀⠉⠹⠟⠛⠉⠉⠙⣿⣿⣿⣿⣿⠛⠛⠋⠉⠁⠀⠀⠈⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⢿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣿⣿⣿⡿⡿⠿⠏⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠛⠓⠒⠚⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⢨⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠛⡁⡀⠉⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠈⠉⠒⠒⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡄⣘⠀⡀⡀⠂⠆⠛⢤⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢒⣡⣄⠀⠀⣰⠊⠁⠈⢦⡀⠀⠀⠈
⠀⠀⠀⠀⠀⡸⠇⣴⣠⠀⠀⢂⡞⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⢆⣰⣈⣀⣀⠀⢘⠀⢰⣷⣾⣿⣷⠀⣠⣄⢀⣀⠀⡀⠀⢀⡀⢀⣄
⠀⠀⠀⠀⠈⠔⣴⢻⣿⠀⣠⠞⠀⠀⢖⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠟⠋⠀⠀⠀⠀⠛⠘⠛⡛⠁⠀⠀⢦⠙⠉⢁⡄⠀⠀⠁⠈⠋
⠀⠀⠀⠐⠀⠰⠁⣠⠗⠐⡿⠀⠈⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠞⠀⠀⠀⠀⠀⠀⠅⠴⠰⠒⠒⠠⢶⣴⣛⠆⠀⠂
⠀⠀⠀⠀⠈⠀⠀⠁⠙⢘⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣀⠒⠂⠈⠀⠀⢀⣤⣤⣤⣤⣶⣬⣿⣿⣿⣷⡀
⠀⠀⠀⠀⢠⣀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠉⠙⢷⣄⡀⣰⠿⠋⢀⣛⣛⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⡎⡉⠀⠀⡼⠃⣴⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠰⢿⣏⠀⠀⢠⣶⣿⡿⠋⠙⣟⣿⣿⣿⡇
⠀⠀⠀⠀⠃⠁⠀⠀⠃⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣦⣤⣄⡀⠀⠉⠳⢦⣶⠟⠋⠀⠀⠀⠈⠙⠌⣿⡇
⠀⠀⠀⠀⠀⠈⠁⠀⠁⢀⡀⠀⠀⠀⠀⠀⣠⠴⠀⠀⠀⠀⠈⠩⣿⣿⠛⠙⢖⡢⠄⠀⠙⢄⠀⠀⠀⠀⠀⠀⢾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠈⠉⠀⠀⠀⠀⠀⣀⠈⢹⡏⠀⠀⠀⠙⣷⣦⣤⠀⠑⡄⠀⠀⠀⠺⢵⡻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢠⢠⡞⠀⠀⠀⠀⠰⣿⡿⠛⠀⣶⠃⠀⠀⠀⠘⠜⣭⡖⠛⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⠖⠈⠀⠀⠀⠀⠀⠀⢿⠀⠀⡺⠃⠀⠀⠀⠀⠀⠀⠘⢿⡶⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⣲⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⢰⠃⠀⠀⠀⣀⠀⠀⠀⢀⡀⠙⢾⣻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠤⠶⠦⢥⣤⡶⠖⣦⣄⣀⠀⠀⠢⠦⠿⣡⡟⠿⠿⠳⠿⠷⣂⣤⣀⣭⣦⡠⠉⠀⠀⠑⡖⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠺⡻⣆⣠⣀⣠⣤⠿⠿⠷⠂⠀⠒⠂⠄⠀⠀⣁⣭⣥⠤⠤⠦
⠀⠀⠀⣠⣤⡭⠶⠆⠈⠁⠀⠀⠀⠀⠐⢆⡤⢠⣔⣄⡀
⠀⠀⠀⠤⠄⠖⢀⠐⢡⢭⣿⣶⣀⣰⣿⣦⣬⣻⡿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠉⠀⢈⠉⣛⠛⠿⠿⣿⡿⠟⠛⡛⢿⣿⣯⣭⣯⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⠛⠳⠶⠿⠷⠂⠈⠹⠟⠛⠛⠣⢍⣀⣿⣷⣧⣾⠾⠟⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣶⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡋⣝⢻⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⢷⣤⡀⠀⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣴⣿⠛⠛⠓⠂⠈⠓⠀⠃⠀⠘⠃⠀⠀⠂
⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣤⠀⠀⠀⣀⣤⣤⣤⣤⣤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠹⣆⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠙⣷⡵⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠘⢷⠀⠀⠀⠀⠰⡵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠻⠿⠿⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⣴⠶⡴⢦⡀
⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣯⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢉⡄⠀⠀⠛⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⢰⣿⣿⡿⢻⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠋⡴⠆⣀⣀⡇⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄
⠀⠀⠀⣿⣿⣿⠶⢿⡿⢒⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣻⣿⡿⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣙⣯⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣦
⠀⠀⠀⣿⣿⣿⣿⣶⣷⣿⣿⣿⣿⣿⠉⠉⠠⣄⡀⠸⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⣥⣾⣘⣿⣿⣿⣇
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠟⢿⣿⠏⠀⠀⢀⣬⠁⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⣀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣧⣼⣿⣿⣿⣿
⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠀⠈⠛⠀⠀⠀⢾⣿⠀⠀⣧⠀⠀⢀⣀⡤⠤⠀⠀⠀⠀⠀⢰⣿⣿⠀⠈⠙⠂⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⣼⣿⠄⠀⠀⠀⣴⣦⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠃⠀⠀⠀⠀⢀⡴⠶⠦⣴⠏⠀⠀⠘⠛⠓⠒⠀⠀⠀⠀⠀⠀⢻⣿⠀⠙⢋⣤⠀⠀⠀⠿⠿⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⢀⡀⠈⠓⠒⢦⡟⠀⠀⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⣬⣇⣀⣀⡀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠧⣤⣀⢀⡞⠉⠓⠶⠶⠋⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠠⠤⠤⠶⠀⠈⠧⣽⣤⣈⡉⢀⣹⠶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠈⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠈⠙⠿⠽⣯⣥⠶⠚⢿⣛⡛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠰⣄⠸⡆⠀⠀⠀⠀⠀⢀⣠⠴⢋⡿⠁⠀⠀⠀⠀⠀⠋⠁⠀⢠⠖⠀⠀⢀⡴⠛⢧⣀⣠⡴⠟⠙⣧
⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠈⠻⣇⠀⠀⠀⣀⡤⣾⠁⠀⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⣼⣃⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢦⡀⠀⠈⠛⠚⠋⠁⢀⣨⠟⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⣆⠀⢹⡄
⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠉⠳⣤⣀⣠⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢻⡇⠀⠀⠀⠀⠀⠀⢿⡀⠘⣧
⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢨⡗⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⣾⡇⠀⠀⠀⠀⠀⢠⡟⠀⣼⠃
⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠛⣳⣤⠞⠁⣾⠁⠀⠀⠀⣀⣰⣟⢀⣼⠃
⠀⠀⠀⢸⣇⣀⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⠞⠁⠀⠀⠸⣧⣄⣀⣀⣼⡋⠉⣽⣿⣽⡇
⠀⠀⠀⠀⣿⠉⠉⠙⠛⠛⠒⠲⠶⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠉⠉⠙⠋⠁⠀⠀⡇
⠀⠀⠀⠀⣿⠀⠀⢀⡀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⡀⠀⠈⢷⡀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠈⣧⠀⠀⠀⢠⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠈⣷⡀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⣿⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠸⡇⠀⠀⠀⣾⣧⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⢀⡇⠀⠀⠀⡿⢸⡆⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⣿⣷⠀⠀⢸
⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⣸⠃⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⣏⢸⠀⠀⢸
⠀⠀⠀⠀⢸⠃⠀⠀⣼⠁⣿⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣠⡯⠸⣦⣤⣼⠆
⠀⠀⠀⠀⣿⠀⠀⢀⡟⢸⡇⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠇⠀⢹⠀⢸⡄
⠀⠀⠀⠀⣿⣤⣤⣼⠇⢼⣦⣤⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢀⣸⡇⠀⡼⠀⢸⣇
⠀⠀⠀⣰⠛⠛⠛⠻⢶⡾⠷⢦⡾⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠿⣚⣫⣥⡿⡿⠵⠚⣉⡼⠂
⠀⠀⠀⠘⠓⠚⠛⠛⠛⠳⠶⠶⢤⣤⣤⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠉⠀⠿⠤⠶⠚⠋⠁

⠀⠀⣀⡤⠤⠤⣄⡀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢐⡭⣗⢦⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣦⡀
⠐⣩⡴⣶⣶⣶⡶⣬⡑⠀⠀⠀⠀⣿⠛⢍⠉⠉⢿⡇⠀⠀⠀⠀⠀⠈⢣⢸⣿⡇⠀⠀⠀⠀⢸⡟⠉⠉⠉⠹⣿
⠸⣅⡀⣿⣷⣼⡟⢀⡽⠂⠀⠀⠀⢟⠐⠆⠻⣷⣌⡇⠀⠀⠀⠀⠀⢠⠏⡸⡽⠀⠀⠀⠀⠀⢸⡃⠲⠀⠰⠂⣿
⠀⠀⠉⠛⠛⠛⠋⢡⡤⠀⠀⠀⠀⠈⢇⠀⠧⢀⡜⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⣦⡆⠀⠀⠀⠀⠱⡀⠸⠄⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠁⠉⠀⠀⠀⠀⠀⠈⠛⠋⠁
⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⢸⣹⣅⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣅⠀⠀⠀⠀⠀⠀⠀⣠⣬⣟⠁
⠀⠘⣿⣿⣙⡻⣆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣀⡀⠀⠀⠀⠀⠀⢸⢿⣿⠻⣆⠀⠀⠀⠀⠀⢸⢿⣿⡟⠷⣄⠀⠀⣀
⠀⠀⣽⣿⣿⡇⣽⣦⡄⠀⠀⠀⠀⣼⠀⠻⠿⢯⣿⡀⠀⠀⠀⠀⠀⢸⡿⣇⠈⢆⠀⠀⠀⠀⠀⢸⡿⣧⢀⣤⣤⣴⡏
⠀⢯⡟⠛⠛⠓⠛⢯⡗⠀⠀⠀⠀⠘⠦⣀⡤⠞⠋⠁⠀⠀⠀⠀⠀⡾⠁⢻⠄⠈⠦⠀⠀⠀⠀⠾⠁⡿⠉⠟⠉⠹⠇

⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⣴⣾⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠂⠀⠀⠀⠀⠀⣴⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⡄
⠀⠀⠀⣿⣿⣏⠀⠀⠀⠀⠀⠀⢠⣴⣄⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⡿⣿⠀⠀⠀⠀⠀⠀⠈⠿⢿⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⣾⡟⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠸⠇⠿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠷⠤

⠀⠀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣠
⠀⣾⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢤⣀⣸⣧⡜⠉⠀⠀⠀⠀⠀⣴⣿⣷⣤⣾⣿⣦⠀⣷⠀⠀⠀⠀⢈⣿⢿⡁⠀⡀
⠀⠿⣿⣿⣿⡷⠛⠁⠀⠀⠀⠀⠀⣀⣹⣿⣿⣿⠛⠒⠀⠀⠀⠀⢿⣿⢡⢻⢟⣛⣛⡁⣋⠀⠀⠀⠀⢸⡗⢙⣿⠀⠒
⠀⠀⠛⢛⡟⠀⠀⣤⡄⠀⠀⠀⠀⠀⢠⠿⢩⡇⠉⠀⠀⠀⠀⠀⠒⠲⣿⣆⣾⠟⠁⠀⠀⠀⠀⠀⠀⢀⣽⡾⣅
⠀⠀⠀⠈⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⣴⣶⣦⣤⠀⠀⠀⠀⠀⣴⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣽⣿⣿⣟⣿⣀⣀⣠⠶⢶⢌⣽⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣷⣿⣿⣷⣼⣿⣿⣿⣿⠿⠿⠧⠸⢶⠿⢿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣿⣿⢟⣹⣿⣿⣿⣿⡿⣿⣯⡀⠀⣠⣤⣤⣙⣷⣍⣿⣿⣿⣿⡟⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣶⣿⢿⣿⣿⣿⣿⣿⡿⠗⠛⢿⣿⣶⣽⣿⣿⢁⣼⣿⣿⣿⣿⡟⢻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢠⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠈⠙⠻⠿⠋⠛⠿⡣⠏⠻⣿⣇⢾⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢿⣾⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣿⣿⣿⣿⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣼⣿⣿⣿⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠏⠟⢛⣽⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣜⠁⠀⢀⣬⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⢶⣴⡾⢛⣍⣿⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠈⠁⠀⠉⠻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠈⢿⣿⣿⣿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⣯⣟⡿⠁⠀⠀⠀⠀⠀⠙⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠘⠿⠿⠿⣿⣿⣿⣶⣦⣀⣠⣤
⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣿⡟
⠀⠀⠀⠀⠀⠐⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣄⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿
⠀⠀⠀⣠⣶⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠇⠠⠄⢀⣀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠘⠻⠻⠿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠿⠿⠿⠿⠿⠟


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡀⠀⠀⠀⢀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠘⢧⣠⡤⠞⠛⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⡶⠶⠶⠟⠀⠀⠈⠁⠀⠀⠀⠀⠸⠷⠶⠶⠶⠶⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠿⠁
⠀⠀⠀⠀⠀⠀⠀⣠⣄⡙⠛⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⢀⣀⣄⣀
⠀⠀⠀⠀⠀⢀⣼⣿⣟⠛⢿⡆⢸⣿⣿⣿⣿⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⣴⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣼⡟⠿⣿⣷⣄⡁⠀⠉⠉⢉⣠⣾⣿⡇⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢠⣿⣿⣦⡈⠻⣿⣿⣦⣤⣾⣿⡿⠟⠉⠀⠀⠀⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡀⠈⠻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣄⠙⢿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣾⣃⣤⣤⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡷⠀⣠⣌⣉⡉⠉
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠉⠉⠀⠈⢿⣄⣠⣴⠾⠛⢷⣄⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠀⠀⠀⠀⠙⠀⠀⠀⠀⠘⢋⣤⣿⣿⠟⠿
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⣀⣀⣀⣤⣤⣶⣾⣿⠿⠛⣁⣴⠃
⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⢛⣉⣉⣤⣶⣾⡿⠃
⠀⠀⠀⠀⢸⣿⣿⣿⣿⠿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠛⢿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⢈⣿⣿⣿⠇⠀⠘⢿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣶⣿⣿⣷⣦⡉⠻⣿⡿⠃
⠀⠀⠀⠀⣼⣿⣿⡟⠀⠀⠀⠈⠻⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⡄⠀⠀⠀⠀⣼⣿⣿⠟⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠟⠋⠁
⠀⠀⠀⣾⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⠀⠀⠀⢠⣿⣿⡟⢠⣿⣿⠟⠋
⠀⠀⣸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⣼⣿⣿⠁⣾⣿⣿
⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⠀⢠⣿⣿⠃⠀⣿⣿⣿
⠀⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠀⠉⠁⠀⢰⣿⣿⡟
⢰⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⠀⠀⠀⠀⠈⠿⠿⠃
⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿
⣾⣿⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣦⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⣀⣀⣀⣤⣄⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠟⠛⢞⣛⣭⣭⣭⣶⣶⣮⣵⣶⣭⡭⢛⡻⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢞⣵⣯⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣶⣥⣘⢧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⣡⣶⡟⠛⠉⣙⣛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⢷⣮⣛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢡⣼⣿⣿⣿⣿⠾⠟⢛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⣿⡎⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⣼⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⡿⢿⡛⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⡷⢸⠆
⠀⠀⠀⠀⠀⠀⠀⣠⠞⢣⣽⣿⣿⣯⣥⣤⣴⣶⣿⡿⠿⣿⢟⣛⠧⠝⠣⠂⠀⠀⠀⠀⠀⠀⣀⠔⢺⣿⢿⣧⢻⡄
⠀⠀⠀⠀⠀⠀⢰⡏⣮⡿⣿⣿⣿⣿⣏⠁⠀⠀⢠⡶⠚⠋⠈⢉⠄⠀⠀⠀⠀⠀⠄⠀⢀⠞⠁⠀⢸⣿⠘⣿⡇⢹
⠀⠀⠀⠀⠀⠀⣸⢣⣿⡇⢹⡏⢻⣿⣿⢆⣠⠖⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠈⢻⣦⣭⡇⢸⡇
⠀⠀⠀⠀⠀⠀⣇⢸⣿⣧⣼⣿⣾⣿⡿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠛⠛⠛⠳⡄⠀⠀⠻⣿⡇⣸⣧⣤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⡏⠈⢿⣿⣿⣿⠟⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⣠⠛⠛⠂⠀⠀⠀⠀⢿⣆⣥⣶⠶⢶⣬⣙⢷⡀
⠀⠀⠀⠀⠀⠀⢹⡆⣼⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠛⢠⣤⠀⠀⠀⠀⠀⢸⠟⢁⣤⡒⢤⠀⢹⣇⢿
⠀⠀⠀⠀⠀⣠⠾⢓⣼⠋⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡞⠁⡆⠀⠀⠀⠀⢬⡉⠀⠀⠀⠀⠀⠀⣰⠃⠀⠹⡆⠀⢸⣿⢸
⠀⠀⠀⠀⡼⢣⡾⠛⠉⠳⣌⠉⠉⠁⠀⠀⠀⠀⠀⣀⡠⠶⠛⣩⠞⠁⠀⢰⠀⠀⠀⠀⠀⠀⠀⢀⣀⠄⠐⢂⠙⢦⡀⠀⠀⠀⣼⢇⡟
⠀⠀⠀⢸⡇⣿⡁⠾⠉⡆⠈⠁⠒⠂⠐⠲⠶⠎⣩⣤⠔⠂⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡴⠊⠋⢁⣛⣤⠾⠃⡴⠃⠀⠀⣼⢏⡾⠁
⠀⠀⠀⢸⡟⣿⠃⣶⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢢⡄⠀⠙⢦⠜⠋⠉⠀⠀⠀⠑⢀⣠⡾⢣⡞⠁
⠀⠀⠀⠈⢷⡹⣦⡀⠂⠈⠳⣆⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠴⠴⠤⠠⠀⠈⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⡾⠟⣫⠶⠋
⠀⠀⠀⠀⠈⠳⣌⠻⣦⣀⣀⠘⠀⠻⠀⣡⡄⣄⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣠⡾⣣⡟⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠦⣭⣛⣛⡛⢿⣷⡉⣻⠌⠳⣤⡞⢉⡦⠀⠀⠀⢠⣒⣈⣶⣤⠀⠀⠀⠀⠀⠀⣠⣾⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⣎⢻⣄⠁⠀⠲⣄⡴⣏⠀⠀⠀⠘⠿⠿⠻⡿⠁⠀⠀⠀⠀⢀⣾⢟⣵⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣬⡛⢶⣤⣀⡔⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢬⣛⡻⢤⣽⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢏⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣝⢷⣤⣀⠀⠀⢀⣀⣀⣴⡿⣡⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣾⠁⣤⡉⠉⠁⣼⠙⣧⡘⠷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⣼⣇⠀⠈⣹⠖⠚⠓⣤⠹⣿⣿⣶⣭⣝⡓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣋⣴⣿⣿⠹⠀⣠⠻⣆⠀⠀⢻⡛⠿⣿⣿⣿⣿⣿⣷⡹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣩⡞⣿⣿⣿⣿⡀⣷⠉⠀⠹⣧⣀⣾⡇⠀⢹⣿⡿⣿⣿⣿⣷⡜⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢇⣿⣿⡘⣿⣾⣿⡇⠀⠀⠀⠀⢹⣿⣿⡄⠀⠀⣿⢗⣽⣿⣿⣿⣿⡈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣸⣿⣿⣷⠈⠿⣿⣧⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⢸⣿⢻⣿⢻⣿⣷⡿⡜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢻⢿⣿⣿⣧⠹⣷⣿⡀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢸⡟⣾⣿⢸⣿⣿⣶⢷⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⣿⢀⣿⣿⣿⣆⠸⣿⣇⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣽⣿⣿⢼⣿⣿⣿⣿⣎⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢸⣏⣾⣿⣿⣿⣿⣆⠹⣿⡄⠀⠀⠀⢸⣿⣿⣿⠀⠀⣿⣿⣿⣼⡿⠟⠋⠁⢻⡼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢸⣿⣿⣿⣿⣿⣿⣿⣆⢨⣗⠀⠀⠀⢸⣿⣿⣿⣤⣤⠿⠋⠁⠀⠀⠀⠀⠀⢸⡇⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡆⠀⠉⠉⠁⠸⣿⣿⣿⣆⠻⣷⣀⡀⠼⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡎⣷⣦⣤⣤⣤⣤⣿⣿⠷⠀⠻⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⣿⣿⣿⣿⣿⠅⢒⡀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠴⠖⣛⣩⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣀⣼⣦⡶⠶⠶⠶⣛⣛⣛⣯⠭⠷⠞⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣭⣛⣛⣫⣭⠴⠶⢮⣭⡵⠶⠞⠛⠛⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⣿⢻⣿⠟⠿⢿⣿⣿⣿⣿⡿⠟⠛⠛⠿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣷⠏⠀⣿⠋⠀⠀⠀⠀⠀⠀⠙⠲⣽⡄⠀⢰⣶⡀⠹⣿⡄⣿⠋⠙⢿⣻⢿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣏⣻⡛⣿⡟⢹⡇⡴⠁⢀⡼⠁⠀⠀⠀⠀⠀⣠⣴⣦⣤⣤⣭⣷⣤⣾⣿⣿⣿⣿⠃⠀⠀⠀⠙⢦⣻⡿⢿
⠟⠛⠙⠲⣍⣻⣿⣇⣹⡟⠀⠀⢿⠑⢠⠞⢀⣀⣤⠤⠄⠀⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠙⣇⠞
⠄⠀⠒⠀⠀⠉⢿⣿⠟⠻⢦⣄⣸⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⣿
⠈⠁⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⢉⣿⡤⠤⠖⠒⠂⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣇⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠸⣿⣿⣿⡀⠀⠀⠸⣧
⠀⠀⣀⣠⣤⣤⠤⢼⣿⠒⠒⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣿⣿⣿⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠈⣿⣿⣿⣿⣿⡏⠉⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⢀⣄⣿⣿⣿⣿⣿⠁⠀⠀⢸⣿⣿⣿⣿⡇⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠘⣿⡀⠀⠀⣴⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢸⣇⣿⣦⡀
⠀⠀⠀⠐⣶⣤⣄⣀⠀⢹⣿⡄⠀⠀⠀⠀⣿⣇⠀⠀⠉⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠆⢠⣤⡈⣿⣿⣿⣿⣄
⠀⠀⠀⠀⢻⣿⣿⡁⠀⠀⢿⣧⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⣿⣿⣿⣿⣤⣾⣿⣿⣿⡻⣿⣿⣿
⠀⢀⠀⠀⠸⡟⠙⠿⣄⠀⢸⣿⣀⣀⣀⡀⠀⢿⡇⠀⠀⢶⡖⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⣿⣿⣷⣿⣿⣿
⣤⣼⣧⣤⣶⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⡀⠈⠳⠀⠀⠈⠀⠠⠟⣿⣿⠛⠛⠉⠉⠈⣽⠷⠏⠀⠀⠀⣤⡙⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡓⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⡨⠒⠀⠀⢀
⠀⠀⠀⠠⣞⣿⠇⠀⠀⠀⠀⠀⠐⢿⣏⠀⠀⠀⠀⠀⠀⢴⣻⡽⠀⡀⠀⠀⠸⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⡑⠀⠀⠁⡴⣷
⠀⠀⠀⢰⣿⣿⢧⠴⠀⣀⡀⠠⢴⢿⣿⡇⠀⠀⠀⠀⠺⣽⣿⡿⠞⠁⠀⠦⠞⣿⣿⢧⣀⠀⠀⠀⠀⣠⣤⣴⣿⣿⠛⠶⠤⢾⣿⡷
⠀⠀⠀⣼⣿⣧⡀⠀⢾⣽⣿⠀⠀⣼⣿⣷⡄⠀⠀⠀⢠⣿⣿⣇⠀⠀⠀⠀⢀⣿⣿⣧⠈⠀⠀⢀⣀⣹⢿⡏⠁⠘⠶⢤⣴⣿⣿⠇
⠀⠀⠀⠀⣽⠋⣷⠀⠀⠉⠁⠀⢸⠇⢿⡀⠀⠀⠀⠀⠀⢨⡟⢹⡆⠀⠀⠀⣿⠹⣯⠀⠀⠀⠀⠉⠉⠁⢸⡆⠀⠀⠀⢸⡟⣯⡉
⠀⠀⠀⠘⠁⠀⠙⠀⠀⠀⠀⠀⠛⠀⠀⠛⠀⠀⠀⠀⠀⠋⠀⠈⠃⠀⠀⠘⠃⠀⠘⠃⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠘⠁⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢀⠀⡀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠠⣠⢀⣠⡄⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⡀⠀⠀⠀⠀⢠⣾⣥⣄
⠀⠀⠀⠀⣤⣼⣿⣤⣻⣿⣤⡄⠀⠀⠀⠀⠀⠀⢘⣿⣭⡇⠀⠀⠻⢾⣿⣥⡀⠀⠀⠀⠀⠞⣻⣾⣿⣍⣭⣥⣤⣶⠶⠀⢀⣿⣿⠏
⠀⠀⠀⢀⣾⣿⠛⠋⠛⠙⣿⣧⠀⠀⠀⠀⠀⡤⠞⢹⣿⣟⠒⠆⠀⠀⣿⣿⡃⠀⠀⠀⠰⠊⠁⠈⠙⣿⡿⠁⠀⣀⣤⢶⣾⣿⠏
⠀⠀⠀⠺⢿⡿⣇⠀⢀⣼⢿⠿⠇⠀⠀⠀⠀⠀⠀⠸⠿⣿⠳⣆⠀⣰⢿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠉⠀⣼⠋⠋
⠀⠀⠀⢠⡾⠁⢻⣀⡾⠁⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠘⢃⡟⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠐⠋
⠀⠀⠀⠈⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⡀
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣤⡌⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠨⠀⢀⡰⣾⠆
⠀⠀⠐⢦⣈⣿⣿⡏⠀⠀⠀⠲⣤⣷⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢰⢾⣷⠋⠀⠀⠀⠀⠀⠀⠀⠘⠾⣿⣿⠀⠀⠀⣿⡇⠉
⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⠉⠉⢹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⠀⢰⣿⣿⠇
⠀⠀⠀⠀⠀⣼⢻⣟⣃⠀⠀⠀⠀⣼⠻⣿⣧⡤⠀⠀⠀⠀⠤⢶⣆⣰⣆⣼⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠿⣽⠏⠀⠹⣿⠁
⠀⠀⠀⠀⠀⢹⡆⠈⠉⠁⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢤⡿⠿⠟⠿⢿⣿⠿⠿⢶⠄⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⣠⡖⡦⠶⡄⣀⠀⠀⠀⠀⣀⡤⠶⠛⠛⠛⠛⠛⠒⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡤⡤⣾⣼⣇⠀⠀⠀⠀⠀⣗⠿⣴⡖⢟⡼⣛⣦⡀⣾⡏⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠁⠀⠀⠀⠐⣆⠀⠈⠳⢦⠀⠀⠀⠻⢭⣿⡇⠋⠙⠷⣺⣼⠏⢻⣸⡔⣆⡀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⣄⠀⣿⢀⡀⠀⠈⢧⠀⠀⠀⣴⡏⠙⢶⣖⠉⠁⡾⠀⠀⠙⠗⠈⢳⠀⡴⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⣿⠀⠛⢀⣩⡷⠀⠈⢹⣤⠞⠁⠈⢳⡞⠉⠓⢦⡟⣻⠁⠀⠀⠀⠼⢿⣁⣤⡀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣀⣟⠀⠀⠀⠈⠀⣠⠖⢚⡇⠀⠀⣰⠏⠀⠀⣀⠠⣟⠀⠀⠀⠀⠀⠀⠸⠇⠀⣽⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⣿⠉⠉⠀⠀⠀⠀⠀⠃⠀⡼⠁⣠⣞⣁⡀⣾⠛⠛⠳⡜⣿⠓⠦⠀⠀⠀⠀⠀⢺⡅⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⢀⣈⣿⠖⠀⠀⠀⠀⢀⣠⠞⣡⠞⡿⠋⠛⠙⣯⣤⣤⣄⣽⣈⣳⣦⣤⣤⠴⠶⠛⠛⠙⠓⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣏⣉⣽⠷⠒⠒⠓⠲⠿⠶⠾⠷⠶⣧⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣹⡶⠖⠳⠦⠤⢤⡤⢤⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠶⣶⠒⠚⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠿⡄⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠚⠉⠀⠀⠀⠙⣆⠀⠀⣀⣠⡤⠖⠋⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣤⣤⠴⠚⠳⠶⠦⠴⢶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⣀⣠⡤⢿⡿⠋⠉⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢠⠞⠋⠉⠁⠀⡰⠊⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠸⣷⣄⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣽⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⢰⡇⠙⠳⣄⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⡇⠀⠀⠀⡟⠀⠀⠀⠀⣴⠛⠁
⠀⠀⠀⠀⠀⢀⣤⠟⠁⠀⠀⢀⡼⠁⠀⠀⠈⠳⡄⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⣾⣓⣶⠤⣼⠀⠀⠀⢀⡇⠀⠀⠀⣧⠀⠀⠀⠀⢧
⠀⠀⠀⢀⡴⠋⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠹⣿⣍⠓⠮⠷⢤⣤⡬⠇⠀⠀⠀⠸⡆⠀⠀⠀⠈⢧
⢀⡤⠶⣯⡀⠀⣀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⢀⠀⠀⠀⠈⠺⢷⣆⢄⡀⢸⠁⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠘⢦
⣾⣇⠀⢈⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣧⠴⢯⣉⣿⠀⠀⠀⠀⠀⠈⠓⠶⠟⠀⠀⠀⠀⠀⠀⠸⣇⣀⣠⣤⠖⠻⣄
⠈⢿⣦⠸⡄⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⡤⠾⠷⠖⢋⣽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠏⣀⠴⠃⠀⣠⠼⡇
⠀⠈⠻⣷⣿⣟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⠀⣠⢴⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣉⣽⣋⣥⠶⣚⡩⠖⠋
⠀⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⠓⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣺⣿⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿⠿⠿⣿⣿⣿⡿⠿⠿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡅⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠤⣤⣀⡀⢠⣀⣤⠤⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃⠀⠉⠉⠀⠀⠀⠁⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠀⠀⢤⠀⠀⠀⢀⣤⡤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⡶⠚⠿⣿⣧⠀⠀⠀⠄⠒⠀⠚⠁⠀⠀⠈⠻⣍⠉⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠉⠀⠀⡠⠊⠀⠀⠀⠈⠙⣧⡀⠀⠀⢀⣾⡀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⢨⡏⢿⣿⠏⠁⠈⠑⠦⣀⣦⣄⡀⠀⠀⠙⠢⡀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣠⠞⠁⠀⠀⣀⣤⣾⣤⡞⠉⠀⠀⠛⠀⠀⠀⠀⢠⣿⣿⣿⡟⢶⣆⠀⠀⠙⢦⡀⠉⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠷⢀⠜⠁⠀⢀⣾⡟⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡀⢻⣆⠀⠀⠀⠙⢄⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⡔⠁⠀⠀⠀⣼⠃⢠⣿⣿⣿⣿⣿⣿⣦⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣧⠀⢿⡆⠀⠀⠀⠈⠳⡀⠈⣧
⠀⠀⠀⠀⠀⠀⢠⠏⡠⠊⠀⠀⠀⠀⣼⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⡄⠀⠀⠀⠀⠘⠄⠘⣧
⠀⠀⠀⠀⠀⢀⡟⡘⠀⠀⠀⠀⠀⣰⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⢠⡟⠀⠁⠀⠀⠀⠀⣰⣿⡿⠈⢿⣿⣿⣿⣿⣿⠿⠿⣛⣛⣛⣭⣭⣵⣶⣿⣿⣿⣿⣿⣿⠟⠁⠹⣿⣿⣄⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⣴⣿⡿⠃⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⠿⣿⣦⣤⣤⣀⢀⡾⠁
⠀⠀⠀⠀⠈⢧⣀⣠⣤⣤⣾⡿⠟⠁⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⣉⣩⣽⣿⣟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⢱
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⡼⠁⣠⠴⠊
⠀⠀⠀⠀⠀⠀⠀⣞⠀⠈⢳⡀⠀⣧⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢄⣧⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⣒⣚⠛⠉⠉⠉⠉⠉⠙⠓⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣯⠉⠙⠳⢦
⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠑⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⡀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠈⢳⡀⠀⠀⣠⠤⠶⠒⠒⠲⣄
⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⣧⠴⠋⠀⠀⠀⠀⡴⠚⠻
⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠻⣄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⠃
⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠈⠓⢶⡄⠀⠀⠀⠀⠀⠀⣠⠏
⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⢀⣼⠃⠀⠀⡞⠛⠛⠋⠁
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁⠀⠀⢠⡇
⡇⠀⠀⠀⠀⠀⠀⢀⣴⢲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⡇⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⢹⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⢳⣀⣀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠰⡄⠀⠀⢀⣀⣀⠤⠤⢤⠤⠄⠒⣒⡿⠛⠁
⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢹⡈⠇⠀⠀⠃⠀⠀⣸⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⣀⣈⣇⣹⡀⠀⠀⠀⠀⠀⠀⢸⣧⡴⠤⠴⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠳⣄⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠙⢦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡀⣀⡄⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠀⠈⠁⠈⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠌⢀⠀⠀⢀⠀⠀⠀⠀⠀⠠⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠈⠀⠀⡀⠀⠈⠢⣀⠂⠐⠄⠣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠈⠀⠀⡀⠄⠘⠀⢀⠊⠀⠀⠀⢀⣀⠀⠀⡀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠁⠀⠀⠀⠰⠁⠀⠴⣤⡤⠀⠀⠀⠐⠉⠀⠑⡀⣸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⢌⠀⢀⡤⠤⣄⠀⠀⠀⢀⠀⠄⠀⠀⠐⠐⠒⠂⢄⡏⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠑⠘⣀⡀⠀⠄⠔⠀⠊⠀⠁⠈⠈⠀⠀⠀⠀⠸⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠐⡋⠀⠑⢄⠀⠀⠀⠀⠀⣀⢀⣀⣀⣀⣠⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠤⢄⠀⠰⣤⡀⠀⠱⠀⠠⢀⡥⠠⠇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠘⡤⠊⠀⠁⣀⡞⠀⠀⠀⠑⠊⠚⠒⠶⠒⢲⠋⠈⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⡀⠀⠀⠀⠀⠈⢳⢶⠀⠻⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠻⢄⡱⢄⣀⡠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠤⣀⣀⠟⠀⢣⡀⠀⠀⠛⣆⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⢘⡍⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⡀⠀⠀⠀⠂⠀⠀⠀⠀⠙⢦⣤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⡗⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠄⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⢸
⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⢠⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠙⣠⠤⠤⢤⢸
⠀⠀⠀⠀⠊⠀⠀⠀⠑⡄⠀⠈⠀⠀⠈⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⢎⢸⡀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⡇⠀⠀⠀⠀⢀⡤⠁
⠀⠀⠀⠀⠀⠉⠁⠂⠀⠀⠀⠀⠚⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠒⠊⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⣀⣀⣀⣀⣀⣠⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⣣⣿⣿⣿⣬⣼⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠻⠿⠿⠿⠿⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⣀⢄⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣂⡎⠀⠀⠑⠍⠁⠇⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠉⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠈⠁⠀⠉⠐⢤⠀⠀⠐⠀⠀⠀⠀⢀⣆⣀⣀⡔⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢪⢇⡠⡤⠔⢧⢀⡀⠀⠀⠀⠀⠀⠘⠃⠛⠠⢊⠤⢠⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⠄⠒⢉⣉⡍⢃⠐⡬⠀⠀⠠⠤⠤⠤⠀⣶⣥⠀⡸⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⣎⣵⠟⠉⣖⣊⣀⢀⣀⡀⣀⠀⣀⠴⠈⠑⠒⠒⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠌⠀⢰⣠⠋⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠄⡀⠀⡐⠉⠉⣴⠄⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⡆⠔⠉⠈⡦⠤⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠑⢄⠀⠀⠀⠈⠉⢀⡀⠔⠃⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠠⠤⠊⠀⠀⠊⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠁⠐⠒⠂⠈⣠⡀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢸⠃⠀⠀⢀⡠⠒⠒⠒⠒⠪⠁⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⡀⠤⠒⠒⠂⠀⠒⠥⣀⠀⡇⠀⠀⡔⠉⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⡕
⠀⠀⠀⣀⠠⠴⠃⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⢀⢔⡡⠔⠁⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⣔⠁
⠀⠰⢅⣀⡀⠀⢀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⣅⣀⣀⡠⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣀⣀⣀⣉⡲

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠒⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⢀⠀⠀⠚⡂⠘⠥⠘⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣘⠀⠀⠀⠀⠀⠂⠀⠀⠀⡀⢠⡀⢀⡐⠀⠘⠃⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠄⠀⠀⠀⢀⠠⢰⠀⠠⢐⡀⠘⠻⡈⠑⠱⠀⠀⠀⢀⠀⡁⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢄⡰⠒⠤⢀⠀⡀⠀⠄⠀⠀⠁⠀⠈⠀⠀⠈⡂⢄⠀⠀⠀⢀⢁⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠤⠒⠂⠀⠀⠀⠀⠠⠔⠂⡀⣀⡂⠂⡁⠀⢰⠄⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⡆⠀⠀⠀⠀⠘⠀⠀⠈⠀⠤⠀⠀⠤⠐⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣀⣀⣀⡀⠆
⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠠⠀⠀⠀⠠⠀⢠⡀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢀⣤⣤⣔⡤⣤⣤⡀
⢰⠇⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠈⠈⠐⠀⠀⠀⠤⠚⠀⠈⠁⣀⠀⠀⢀⠀⠀⠀⢻⡵⠞⠡⣄⣀⣉⣺⣿⣿⠶⡄
⢀⠀⠀⠀⠀⠤⠂⠀⣱⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡀⠀⠒⡔⠀⠀⣤⠀⣀⡧⠀⠀⠀⠘⢦⠀⢠⠂⠒⠒⡍⠉⡯⡸⠃
⠀⠉⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠈⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠴⠋⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢖⡊⠀⢩⠟⠃⠀⠀⠀⠀⣶⠀⠀⠀⠀⣝⡠⣄⣾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡵⠲⢼⡆⠀⠀⠐⣖⠚⠀⠳⣤⡄⠘⠋⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠂⠀⠀⣸⡴⢦⡏⠁⢀⡄⠀⣀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣄⠀⠀⠀⣄⠀⠁⠀⢀⣠⡤⠤⠭⠤⣬⣅⡀⠀⠀⠀⣤⡤⠞⠘⢓⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⡍⣀⢩⠟⠋⠀⠀⠀⢀⡞⠋⠙⠒⠶⢤⣄⣀⣠⠽⠷⣄⠀⢀⣏⠴⣜⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠉⠻⠀⠠⠄⠀⢠⠞⠉⠓⠦⣄⣠⠴⠋⠉⣀⣤⠷⡛⢦⡈⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⢀⡟⠒⣦⡤⠞⠉⣀⡤⠖⠋⠁⠀⠀⢉⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⣞⣁⣤⡴⠿⠥⠤⠴⠶⠶⠶⠶⠶⠶⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⣒⣩⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠻⣄⣁⣤⣤⣤⣤⠤⠤⠤⠶⠖⠛⠉⠁⠀⢸⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠒⣤⠀⠀⢀⣤⣴⠂⠀⠀⠀⠈⢻⢲⣄⠀⠀⠀⡴⠂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⠂⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠱⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠲⡆⠀⠀⠀⠀⠀⠐⠛⠓⠀⠀⠀⢠⡆⠀⢀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠈⠃⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠖⠛⠉⠉⠉⠉⠃⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢲⣤⣄⣀⣀⣀⣠⠞⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⡌⠴⢋⡩⢋⡽⢋⠞⣹⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢦⠖⠛⢧⠻⣄⠀⠀⠈⠠⠎⡴⢣⠞⠵⣠⠏⣹⠓⡶⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠳⣎⡌⠳⣌⡓⠦⢤⣄⣀⣤⠤⠶⢚⣡⢾⣡⠞⠁⠀⠀⠉⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠈⠙⠻⣤⣝⣛⡶⢲⡶⠶⡶⣚⣿⠵⠋⠁⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⢠⠖⣀⠄⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⢀⠀⢀⠀⢀⠔⢀⡴⠀⡠⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣠⠞⢁⠔⢁⡔⠁⣠⠆⣠⠎⣠⠞⢁⡴⠋⡴⠃⡰⠋⣠⠊⣠⠎⣠⠆⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠴⠃⡴⠋⠀⠞⠁⠞⢁⠞⠁⣠⠋⢠⠞⢀⡞⠁⡼⠁⡰⠃⡴⢁⠔⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⢒⠒⠲⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠬⠭⠍⠉⠙⠂⠀⠡⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠰⠡⠴⠒⠒⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠴⠁⠃
⠀⠀⠀⠀⠀⠈⠙⠓⠀⠀⠀⡆⠀⠀⠠⠄⠀⠀⠈⠻⣆⠀⣠⠞⠁
⠀⠰⢅⣢⣀⠀⠀⠀⠀⠀⢀⡃⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢈⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠨⠀⠀⠀⠀⠀⢈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠢⢀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠐⢄⡀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⡄⠀⠀⠀⢠⠀⠀⢡⠆⠀⠀⢈⣂⠈⠁⠉⠑⠰⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠄⠀⠀⢘⠄⠀⠀⠐⠓⠀⠀⠀⣀⡠⠉⠀⠀⠀⠀⠀⠈⡄⠐⠁⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠛⠒⠒⠚⠉⠀⠁⠀⣃⡠⢊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠄⠀⢀⣀⣠⠤⠖⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣅⠀⡀⣀⣠⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⡿⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⢠⠤⣀⣠⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣦⡄⠀⠀⠀⠀⠢⠄
⠀⠀⠀⠀⠀⢠⢿⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⢸⡘⠿⠿⠿⠟⠛⠁⠀⠈⠻⣿⣿⣿⣿⣿⠷⢄⡴⠟⠀⠈
⠀⠀⠀⠀⠀⠈⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⢁⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣦⠀⠀⠀⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⢹⡶⢿⡀⢠⠚⣟⣀⠀⣯⡿⢀⣞⣶⠀⣄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠰⠂⠀⠀⠈⠧⠘⠃⠈⠉⠉⠁⠘⠇⠀⢸⠇⠀⢀⢉⡟⠀⠀⠀⠒⠐⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⢀⣄⠀⣠⡆⠀⠀⣤⣄⢀⡀⠀⠀⠈⠉⠀⠀⠀⠀⠁⠰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢻⣄⣿⡄⢀⡞⣧⣠⠉⠹⣤⠀⠻⠶⠈⠷⠟⠀⠷⠶⠇⢰⣯⠇⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⡏⠓⠀⠈⢿⡈⢷⠀⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⠟⠀⣾⡗⠀⠀⡀⠒⢀

⠀⠀⠀⠀⠀⠀⢤⡘⠒⠁⠀⠀⠀⠈⠁⠀⢀⡤⡄⠀⠀⠀⠠⠀⠀⠀⠀⡄⠤⠒⠀⠀⣀⡀⡀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⢀⠀⠀⠀⠀⡎⠀⠁⠀⠀⠀⠀⠀⠀⣀⠀⠤⠀⠀⠃⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠑⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠤⠂⠂⠁⠀⠀⠀⠙⠀⠀⠀⢀⠐⠈⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠈⠉⠂⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠁⠀⣀
⠀⠀⠀⠀⠀⡆⠃⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⢀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠀⢀⠤⠀⢒⡒⠢⠠⡀⠀⠀⠀⠠⠐⠤⠓⠠⠂⠁⠀⠈⠂⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠈⠀⠈⠈⠉⠆⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡐⠔⠀⠄
⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⡀⠠⠀⠀⠀⠀⠒⠄⠀⠀⡇⠀⠀⠘⠃⠄⠠⠆⠀⠀⠇⠀⠀⠀⠀⠤⢢⠀⠀⠀⠀⠀⠈⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠃⢀⠀⡅⠈⠀⠀⠀⢈⠐⠀⠀⡚⠀⠀⠘⠄⠀⡀⠀⠀⠀⡀⠀⡰⠁⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣑⠂⠊⠀⠀⠀⠀⠀⠀⠉⠈⠀⠚⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠑⢇⢀⣠⢠
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠒⠂⠈⠂⠀⠀⠀⠀⠁⠁⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠱⠄⠀⠀⢰⠀⠆⠀⠀⠂⢐⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠐⢪⠃⠀⠀⠀⢀⢀⠀⢐⡎⡆⠀⠀⠀⢀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⡁⢇⢱⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⢂⠀⠀⠀⠀⠃⠁⠁⠀⠀⠀⡄⡳⣴⣦⢟⠢⡀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢆⠀⠀⠀⠀⠀⠀⠀⠀⠨⢬⢴⣩⡎⠦⠧⠇⠀⠀⠀⠀⠀⠁⡀⠀⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠘⡔⠄⣷⠚⣣⡂⠆⠀⠀⠀⠀⠀⠀⠑⠉⠈⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠂⠁⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠉⠉⠙⠒⠦⣄⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠁⠀⠀⠀⠀⠀⠠⢬⣻⣦⣝⢶⣶⣶⡖⠚⠉⠁⠈⠉⣉⡓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠒⠊⢋⠘⠛⣉⡄⠀⠀⠀⠀⠀⠀⠾⣿⣿⣿⣿⡋⠀⣀⣠⢂⡤⠂⠀⠀⠀⠨⠙⠻⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠠⣻⣿⣿⡏⠀⠀⠀⠀⠀⠀⠕⠪⠙⠎⠙⠁⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⢀⣒⡠⠼⣯⣳⣄
⠀⠀⠀⠀⠀⢀⣀⠠⠤⠒⠁⠀⠃⣌⢆⠄⠀⠀⠀⢝⣿⡟⡖⢀⣀⠀⠀⠀⠢⠈⠀⠀⠀⠀⣰⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⣦⣽⣿⣆
⠀⠀⢀⡴⠚⠉⡀⣀⣠⣢⢠⣮⠀⠏⠀⠀⠀⠠⣒⠌⠻⢷⣷⣼⣏⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣧⠄⠀⠀⠀⠀⠒⢒⣂⣀⣉⣲⣿⣿⡇⢻
⠀⢠⠟⠀⢰⣿⣾⢟⡿⣡⣿⣿⡤⠀⠀⠀⠀⢀⡂⢍⠀⠀⢹⣿⣿⡄⠀⠀⠀⠀⠀⠀⣐⣺⣿⣿⣿⣿⡵⠒⠂⠀⠀⠀⠀⠒⠬⣍⣛⡿⣿⣿⠈
⢠⡏⠀⠀⠀⠈⣱⢟⣼⣿⣿⣿⡇⠀⠀⠀⠐⠂⠈⡓⢽⣦⣸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣤⣽⣿⣿⡿⢛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣧
⣼⠀⠀⠀⠀⠈⠀⣸⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠈⢧⡹⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⣉⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷
⣏⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠠⣑⠝⢮⣻⣿⡆⠀⠀⠀⠀⠀⠀⠨⢿⣿⣿⣿⣿⡵⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟
⣿⠀⠀⠀⠀⠀⠀⡞⣽⣿⣿⣿⣿⠁⠀⠀⠀⠀⣀⡁⣲⣄⡠⣽⣿⡇⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣯⠆⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿
⡇⠀⠀⠀⠀⠀⢀⠜⣽⣿⣿⣿⡏⡄⠀⠀⠀⠀⠀⣈⡙⠻⢝⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣷⢋⠴⠒⠛⠋⠑⠒⠀⠀⠀⠀⠀⢞⣿⡿
⡇⠀⠀⠀⠀⠀⠀⠘⡱⣿⣿⣿⡏⡀⠀⠀⠀⠀⠀⠀⠍⣓⢤⣽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⣯⣴⣶⠄⠀⠀⠀⠈⠉⠉⠀⠀⠀⣸⣿⠇
⣷⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⡅⠁⠀⠀⠀⠀⠐⠢⡉⠊⠙⢿⣿⣿⡖⠀⠀⠀⠀⠀⠀⠋⣨⠿⣻⣿⣿⣿⣥⣀⣀⣀⣀⠀⠀⠀⠀⠀⣿⣿
⢸⡀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡇⠆⠀⠀⠀⠀⠀⠀⠠⠅⠈⢺⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣯⠭⠥⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⠠⠀⠀⠀⠀⠀⠨⠥⢤⡀⢲⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⢀⣉⣹⣿⣿⣿⣟⠻⠦⠀⠀⠀⠀⠀⢀⣴⡟⣿
⠀⠸⣆⠀⠀⠀⠀⠀⠀⠈⢋⣿⣿⡅⡀⠀⠀⠀⠀⠈⠁⠀⢴⣶⣿⣿⣿⣿⣿⣶⣤⣖⣤⣶⠟⠋⣛⣿⣿⣿⣿⠭⠥⠤⠀⠀⢀⢠⣴⡿⠟⢹⡄
⠀⠀⠻⣷⣆⡒⠀⠀⠀⠐⣛⣫⣿⣷⡁⠀⠀⠀⠀⢐⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣭⣭⣽⣿⣯⣭⣾⣿⣿⣿⣤⣤⣤⣤⣶⣿⡟⢁⠙⣆⣧
⠀⠀⠀⠈⠙⠿⣷⡒⠀⠉⢭⣿⣿⣿⣿⣶⣤⣀⣀⣠⣼⡿⢟⣻⠿⠛⠛⠉⠉⠉⠀⠀⠈⠉⠛⠅⠀⠀⠉⠉⠙⣿⣿⣿⡻⠛⠋⠉⠀⠀⠱⡜⣿
⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⢀⣈⣀⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢬⣝⢯⡉⠢⡀⠀⠈⢆⠀⢹⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢮⣝⡛⠿⣿⣿⣿⠋⠀⢠⠋⠐⠀⠐⠀⠙⠏⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⢻⡄⠱⣦⣵⢸⡄⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠾⢿⣏⡄⢀⡏⠀⠀⠐⠂⠄⠒⡀⠀⠉⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢹⣿⣾⢇⣾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡁⣸⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⡟⠀⠀⢒⠦⣴⣤⡀⠀⠀⢰⡏⡰⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰⣿⣷⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡿⠀⣀⣀⠉⣻⣿⣦⣄⢀⡾⣰⣷⢢⢴⢠⢀⡄⡀⢀⣼⠇⠀⠀⠀⠀⣰⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣬⣍⣙⣛⡛⠛⠛⠋⠚⠟⠱⠫⠯⠏⠞⣴⡟⣼⣿⡇⠀⠀⢀⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠶⠶⠦⣤⣥⣽⣾⡷⠤⠖⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠃⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀⠀⠀⠛⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢀⣠⣼⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣶⣶⣶⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⢸⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠈⠿⠇⠀⢸⣿⠉⠉⠉⠙⠛⠛⢿⣦⣄⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢶⣦⡾⠁⠀⣿⡿⠟⠙⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠸⣿⠁⠀⠀⠈⠉⠛⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣥⣤⣤⣤⣤⣤⡀⠀⠉

⠀⠀⠀⠀⡠⡀⠠⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡈⠀⠢⣴⡋
⠀⠠⡀⠀⡠⠀⠐⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠈⠁⠀⠈⠁
⠠⡈⠀⠀⢠⠀⠒⠈⡁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢄
⠈⡄⠀⠀⠀⡀⢀⣠⣔⡉⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⢉⣻⠇⡠⠃⠈⠢⠀⠠⠒
⠀⠀⠁⢀⠣⡄⠻⢹⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⡠⠁⢨
⠀⠀⠀⠀⠀⠀⣅⢀⡨⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⣡⠓⠂⠚⢄⠄⠀⠀⠀⠀⠄⡈⠖⣀⠀⡆
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠐⠤⠁⣐⡀⢤⡤⡈⣂⢢⡇⠀⠴⢮⣸⣠⡄⠲⠒⠂⠁⡀⠘⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⢨⠀⠅⣂⠀⡈⠑⠛⠋⢡⠤⢀⠔⠀⠀⠉⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠈⠃⠐⠀⠊⠀⠀⠁⠀⢇⠀⠀⠀⡸⠀⠀⠀⠀⠘⠀⠒⠐⠒⢺
⠀⠀⠀⠀⠀⠀⠈⠲⠀⠐⠒⠃⠀⠀⠀⠀⠀⠀⠀⡊⠑⡆⢈⡇⠀⠀⠀⠠⡀⠀⠀⠀⠀⣈
⠀⠀⠀⠀⠀⠀⠀⠀⠱⠁⠀⠐⠄⠄⠀⠀⠀⠀⠀⠉⠈⠈⠉⠀⠀⠀⠀⠀⢈⡓⠒⠲⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢶⠀⠈⢈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡱⠛⠀⠅⢂⠀⠀⠀⠀⠀⠀⢀⠄⠺⡗⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣅⣠⣤⣤⡼⠛⠀⠀⠀⠀⠀⠀⠙⠄⠀⠤⠊


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠔⢲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣷⣿⣇⣀⣏⡸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣿⡇⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢨⠇⠀⠀⡀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⢸⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣏⣌⠥⠀⠈⠀⠀⢰⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠈⠀⢸⣿⣿⡿⠿⠿⠛⠛⠉⠁⠀⣀⣠⡤⠀⠀⠀⢀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣆⣀⣤⣤⣶⣾⣿⣿⡿⢃⣗⠀⠄⢼⡄⢃⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⠀⢀⣄⣾⠀⠈⠁⣤⡀⣀⡭⠴⣙⡻⣿⣿⡿⡟⢿⠿⣿⡟⠋⠁⢸⣿⠀⠂⣿⡇⢠⡄⠈⠑
⠀⠀⠀⠀⠀⠀⢀⣿⡀⣼⠿⠓⠁⡠⠟⠪⠴⠀⠩⠈⢁⣄⢂⡡⠈⠉⠉⢠⠀⢀⡄⠁⠊⠲⠄⢄⣠⠈⠙⠛⠻⣀⡀⠄
⠀⠀⠀⠀⠀⠀⠸⡟⠁⠡⠀⠀⢊⠑⢠⡆⡀⠠⣀⠀⠈⠁⠀⠀⡠⠐⠈⠀⡄⢸⣇⠀⠀⠀⠀⠀⠘⠩⢂⠀⠀⡉
⠀⠀⡀⠀⡀⠀⠀⠀⠉⠀⠀⠐⠀⠀⠸⡧⠓⠀⡀⠀⠀⠀⣸⡆⣀⠄⠀⣰⣷⣾⠿⠄⠲⢂⠀⠂⠀⠄⢸⠀⠀⠇
⠀⠀⠃⠠⠀⠀⠤⠈⠐⠒⠀⠾⢿⣿⠿⠆⠀⠈⠉⠀⠚⠃⠾⢧⠈⣉⠈⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠁⠲⠄⠀⢰⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠁⠀⠒⢂⡤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠖⠈⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠈⠁⠀⠀⠄⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣭⣿⣿⣿⣷⣶⣦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⢰⣿⣇⠘⢿⠟⠁⢸⡟⣿⣿⢻⣟⠻⢿⣷⣶⣤⣄⣀⡀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠾⣿⣷⣼⣇⠛⣣⣾⡟⢱⣿⢋⣿⢏⣭⢻⣿⣿⣶⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢈⠉⠛⠛⠿⠿⣷⣿⣿⣼⣧⠙⠿⣰⣿⣃⠸⠟⣻⣿⣿
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢸⡆⢻⣷⠈⣴⡆⠀⣦⣍⠉⠛⠻⠿⣾⣿⣧⣿⣦⣼⣿⣿⠇
⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠛⡷⢀⡎⢀⡞⠛⠀⣠⠀⢀⡉⠛⠛⠿⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡄⠀⣤⡀⠀⠀⠀⠈⠻⠶⠢⠿⠷⢾⠇⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡉⢠⣇⢀⠁⣤⠀⢰⠄⢠⡶⣀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢀⣟⠃
⠀⠀⠘⠀⠀⠀⠀⠀⣤⠀⠈⠀⠀⠉⠉⠀⠻⠶⠃⠀⣶⣦⡟⠃⠀⠀⠀⠀⠀⠀⠈⠑⠞⠉⠀⢀⠀⣄
⠀⠰⣆⡀⠀⠀⠀⢠⡷⢦⡾⠁⣾⣛⡉⠀⢀⣀⠀⠀⠁⠘⠓⠀⢠⡜⠃⣤⠀⡆⠀⠀⠀⠀⢀⡘⠁⠀⣙
⠄⠀⠈⠁⠐⠒⠀⢀⣀⠘⠁⢰⣭⣍⠁⢀⣾⣿⡀⠐⣶⣄⠀⠀⠈⡇⠰⠂⡀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠉
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠉⠁⠀⠤⠀⠉⣀⠹⠇⢠⣁⣘⡇⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢲⣤⣉⠉⠁⠀⠀⠀⠀⠦⠀⠀⠀⠸⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠀⠹⡦⠈⠁⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠈⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠈⠟⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣡⣼⠷⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠉⢀⡰⠆⠀⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠈⠁⠀⠀⠦⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⢰⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢇⠀⢀⣠⠆⠙⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣏⠉⠁⠘⠁⠈⠁⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⢀⣤⣀⣀⣀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⢀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡇⠀⠀⠀⠀⠀⠐⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇⠀⠀⠀⠀⠀⠘⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡷⣀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶
⣿⣿⣿⣿⡟⠛⠻⠟⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣁⣀⣀⣀⣀⣀⣀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠒⠒⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⡀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⢠⣴⢀⡔⢢⡙⣆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⡰⠛⠛⠉⠀⠀⠃⠛⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠤⣶⢺⠀⠀⠒⠤⠀⢀⠀⠂⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠤⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡄⡏⠠⢹⣼⠀⠀⠀⠀⠀⢸⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣳⡘⠈⠍⠀⠀⠀⠀⢀⣸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡜⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣹⠇⢠⠀⠀⠀⣀⣈⣉⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⢱⡀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠁⠀⠈⠣⡀⠀⠓⠒⠊⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠲⠘⢆⠀⠀⠀⠀⡆⠀⠀⠀⠀⡀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠈⢧⡀⠀⠀⠀⠈⢱⠒⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⡗⢲⠀⢀⡇⠀⠀⠀⠀⢷⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡝⠀⠀⠙⠦⡀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⢀⡼⠀⣸⠁⠀⠀⠀⠀⢸⡀⢸
⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠛⠛⠉⠉⢗⢹⣰⠠⢽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⢤⠀⠀⠀⡇⢠⠇⠀⠀⠀⠀⠀⢸⡇⢸
⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡏⡸⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡎⠀⠀⣠⠇⡞⠀⡴⠀⠀⢰⡆⢸⠇⢸
⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠇⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⡝⢸⠁⢸⠃⠀⠀⣸⠃⡼⠀⣸
⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠸⡄⢸⡀⢀⡴⣣⠜⠁⡠⠃
⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠂⠉⠚⠉⠀⠀⠈⠉⠙⢄
⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⢀⡀⠤⠐⠒⠂⠐⠒⠠⠄⣀⠀⠀⠀⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠀⠄⠀⠉⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠊⠁⠀⠄⠠⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡈⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⣾⢧⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⢀⣀⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄
⠀⠀⠀⠀⠀⠀⠀⢺⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇
⠀⠀⠀⠀⠀⠀⠀⠘⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢤⡤⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⣀⠀⠀⠠⢤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠁⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠒⢄⠀⠀⠑⠒⠒⢄⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⡆⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠑⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⢡⠀⢠⠁⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⢸⡠⠃⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠀⠀⠀⢀⠎⠀⠀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠀⠀⠀⠠⠤⢄⣀⡀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢀⠤⠚⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠒⠂⠐⠒⠈⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣷⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠋⠉⠉⠛⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠋⠉⠉⠛⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⢹⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⠀⠀⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢀⣠⣄⠀⠀⠀⠀⠀⢀⣤⣀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⡀⠀⠀⠀⠀⣠⣿⣿⠏⠀⠘⣿⣿⣆⠀⠀⠀⢀⣾⣿⡟⠀⠈⢿⣿⣧⡀⠀⠀⠀⠀⣠⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⣶⣾⣿⣿⡿⠋⠀⠀⠀⠘⣿⣿⣆⠀⢀⣾⣿⡟⠀⠀⠀⠈⠻⣿⣿⣿⣶⣶⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣭⣽⣛⡛⠉⠁⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠉⠙⣛⣫⣭⣅⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡿⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡟⠉⠀⠀⠀⠀⠙⢿⣿⣷⣄⠀⢀⣴⣿⣿⢿⣿⣿⠟⠛⢿⣿⣷⣄⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠈⠙⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣾⣿⡟⠁⢸⣿⣿⡀⠀⠀⠙⣿⣿⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠋⠀⠀⢀⣿⣿⣿⣆⠀⠀⠈⠻⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⣰⣿⣿⠟⢿⣿⣷⡀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣤⣀⣀⣾⣿⡿⠃⠀⠀⠹⣿⣿⣆⣀⣠⣴⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠸⣿⣿⡛⠻⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⡿⠛⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠨⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡯⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇
⠀⠀⠀⠀⠀⠀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄
⠀⠀⠀⠀⠀⢰⣿⣿⠃⠀⠀⠀⣴⣿⣷⡄⠀⠀⠈⢻⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠋⠀⠀⠀⣰⣿⣷⡄⠀⠀⠀⢻⣿⣷
⠀⠀⠀⠀⢠⣿⣿⠇⠀⠀⠀⣰⣿⣿⣿⣿⣆⠀⠀⠀⠹⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠁⠀⠀⢀⣾⣿⣿⣿⣷⡀⠀⠀⠀⢿⣿⣧
⠀⠀⠀⠀⣾⣿⡟⠀⠀⠀⢰⣿⣿⠃⠘⢿⣿⣷⡀⠀⠀⠈⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣴⣿⣿⠏⠀⠀⠀⣰⣿⣿⠟⠀⢻⣿⣷⠀⠀⠀⠘⣿⣿⡆
⠀⠀⠀⣼⣿⡿⠀⠀⠀⢠⣿⣿⠏⠀⠀⠀⠻⣿⣿⣆⠀⠀⠀⠹⣿⣿⡄⠀⠀⠀⠀⣼⣿⡿⠁⠀⠀⢀⣾⣿⡿⠃⠀⠀⠈⢿⣿⣧⠀⠀⠀⠸⣿⣿⡄
⠀⠀⣰⣿⣿⠁⠀⠀⢀⣿⣿⡏⠀⠀⠀⠀⠀⠘⢿⣿⣧⠀⠀⠀⢻⣿⣧⠀⠀⠀⢠⣿⣿⠃⠀⠀⢠⣿⣿⠟⠀⠀⠀⠀⠀⠈⣿⣿⣇⠀⠀⠀⢻⣿⣷⡀
⠀⢠⣿⣿⠇⠀⠀⢀⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣇⠀⠀⠸⣿⣿⡄⠀⠀⣼⣿⡿⠀⠀⢀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣆⠀⠀⠀⢿⣿⣧
⢀⣾⣿⡏⠀⠀⠀⣼⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⣿⣿⣇⠀⢀⣿⣿⡇⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡄⠀⠀⠈⣿⣿⣆
⣼⣿⡿⠀⠀⠀⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢸⣿⣿⠀⢸⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡄⠀⠀⠸⣿⣿
⣿⣿⣇⠀⠀⣰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣀⠀⣠⣿⣿⠃⢻⣿⣷⡀⢀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⠀⢀⣿⣿
⠘⢿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⠋⠀⠈⠻⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⢀⡀⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠘⢡⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠤⠄⠀⠀⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠙⡌⠀⠀⡜⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠛⡍⢀⡰⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠈⠀⠀⠐⠋⠉⠰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠉⠙⠃⠀⠀⠀⠤⠀⠀⠀⡠⠶⠀⣀⣀⣀⣀⣀⡠⠤⠄⠀⠒⠒⠛⠛⠚⠒⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠐⠒⠢⢄⣀⠀⣀⣔⣀⣂⣱⡄⠀⠀⠀⠀⠀⠈⠳⢀⠀⡝⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⣀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⠒⠒⠊⠉⠁⠁⠀⠉⠉⠉⠳⡄⠀⠀⠀⠀⠀⠟⠉⠙⠇
⠀⠀⠀⠀⠀⠀⠀⢀⡜⢃⠀⠀⠀⠈⠁⠀⠀⠠⠏⠀⠀⠀⠀⠉⠉⠉⠙⠓⠒⠤⠤⣀⣀⣀⣀⠀⣀⠆⠘⠀⠁⣂⣸
⠀⠀⠀⠀⠀⠀⠙⠁⣀⠀⡝⠃⠀⠠⠄⠀⢀⠂⠀⠀⠀⠀⠀⢀⡀⠠⠤⠀⠒⠒⠂⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⢂⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠏⠀⠙⠂⠀⠀⠀⠀⠀⠘⠀⠐⢀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠠⠰⠀⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣣⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠦⣴⠶⠖⠓⣞⠳⠺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢀⣤⠰⡎⠛⠫⢾⡱⢄⠈⠲⣕⡤⠀⠈⠳⣄⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⠀⠀⠀⠀⠀⠀⠀⣠⠄⡺⢏⠍⠃⠴⠀⠈⣠⠚⠝⢦⣐⠀⠈⠑⠠⣄⠀⠀⠀⠀⡑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⣀⠔⠊⠉⠁⢠⡚⠗⣀⣊⣠⠔⠋⠀⠀⠀⠀⠈⠷⢦⡀⠀⠀⠙⠢⣔⠤⣠⠱⡘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⡠⠞⠁⢀⠠⣔⠊⠃⢁⠞⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠨⡓⢄⠲⣼⡀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⡠⠊⠁⢀⠤⠊⠐⣋⡁⠀⠀⠀⠀⠀⠀⠀⢀⣉⠉⠁⠒⠂⣌⠳⡀⠀⠀⡔⢀⠱⣩⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢀⠎⡠⣐⠕⢁⠐⣵⢛⡽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⢛⣷⣤⡀⠈⠀⠱⠀⠐⢠⠀⠆⢡⠚⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡎⠰⣉⠊⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⠀⠀⠀⡇⠀⡇⠠⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢇⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⠀⡀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠸⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⡇⠀⡀⠀⠰⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠄⠀⣞⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡇⠀⠁⢠⢣⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⣷⢽⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠄⠒⠒⠒⠒⠢⠀⠀⠀⠀⢠⣿⠀⠀⠀⡸⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⢸⡅⠚⣷⠀⠀⠀⠀⠀⠀⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢻⡗⡄⠀⣧⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⢸⡂⠝⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢲⡭⣻⢱⠀⠘⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⡘⡥⢚⡵⠂⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡥⣛⠭⣋⣿⢸⣿⡇⢸⡈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⡇⡃⢛⡡⢚⠴⢪⠖⢛⠛⠲⣦⣄⣀⠀⠀⠀⢀⣀⢤⡶⡟⢣⡗⠊⢕⠺⠵⠟⡐⠛⠓⠀⡇⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢠⠃⡇⠀⠔⡡⠒⡡⠒⣩⡆⠀⢠⠈⡩⠋⡰⠋⠙⠉⠔⠄⡐⢲⣋⠁⡈⠔⠛⠀⠹⠀⠄⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⢠⠃⠀⢊⠄⠊⠔⠉⢐⡇⠀⠀⠈⠀⠊⡠⠊⠔⡁⠀⠊⡄⢪⠖⠩⠐⠀⠀⠀⠂⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⡈⡄⠀⠠⠖⡡⢊⠀⣈⠇⠀⠀⠀⠀⠈⠁⠊⠔⠄⢀⢂⠄⠘⠃⢐⠌⠀⡀⠀⠀⡀⠁⢀⠃⠄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠠⠎⣴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠉⠒⢤⡤⣄⡈⡔⣀⠀⡌⡸⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⡠⠊⠀⠀⠈⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠙⢶⡇⠀⡰⡝⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠠⠄⠀⠀⢀⠀⠀⢠⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠑⢆⠘⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡀⠃⢀⠠⢂⡀⠐⣀⠄⢀⡀⠀⡀⠀⡀⠀⡀⠀⣀⠀⠀⠄⠀⡠⢂⠄⡀⠀⡀⠈⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠈⠐⢊⠠⠂⢁⠔⠊⡠⠒⠁⠔⢈⠔⢊⠔⢉⡴⠊⡠⠊⢀⠔⡡⠊⡡⠊⡡⠊⡤⠂⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠐⠈⠠⠊⠠⠂⠡⠀⠁⠔⠁⡠⠊⠀⠖⡡⠊⠠⠊⡀⢈⠴⢁⠄⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⣴⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣟⠁⠀⠀⠀⠀⣀⣀⣤⣴⣶⣿⣿⠰⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁⢀⣠⣿⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⠉⠉⠁⣠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠟⠛⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⠛⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣇⢘⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠏⠈⠻⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠋⠀⠀⠀⠹⣿⣿⣿⣿⣿⣆⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡄⠀⣰⣿⣿⣿⣿⣿⠏⠀⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠟⠀⠀⣿⣿⣿⣿⣿⠃⠀⠀⢻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠏⠀⠀⠀⠘⢿⣿⣿⣿⣷⡀⠀⠘⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡄⠀⠈⠙⢿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡄⠀⠀⠈⠻⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⢾⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡆
⠀⠀⠀⣴⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷
⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⢿⣿⣦⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠁

⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠛⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠈⢷⡀⠀⢀⡴⠟⠛⠛⢶⣄
⠀⠀⠀⢀⣤⡶⠶⠶⠶⣄⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠸⡇⢠⡟⠀⠀⠀⠀⠀⠙⣧
⠀⠀⢠⠟⠁⠀⠀⠀⠀⠈⢷⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣠⡶⠶⠶⢦⣤
⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⠏⠀⠀⠀⠀⠘⣷⡄
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠸⣷
⠀⣿⠀⠀⠀⠀⢀⣀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠛⠛⠲⠶⠶⢦⣤⣿⡀
⢰⡇⠀⠀⣠⠶⠋⠈⣿⠀⠀⠀⣤⣀⣤⣀⣠⣄⣀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⣲⠀⠀⠀⢹⡇
⢸⡇⠀⢰⡏⠀⠀⠀⠉⣷⠀⠀⢉⠉⠉⠀⠛⠁⠉⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⣤⣉⣉⣀⣀⣀⣸⡇
⢸⡇⠀⠀⠻⢤⠶⢦⡤⠋⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⣀⣀⣤⡤⠴⢺⡇⠀⠀⠉⠉⠉⠉⠉⢹⣧
⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠛⠉⠉⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠶⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠃⠀⢀⣠⣼⣇⡀⣀⠀⡄⠀⠀⠀⠀⣿⡀
⠀⣿⠀⠀⠀⠀⠀⣾⡖⠻⡷⠚⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣤⡤⠖⠛⠉⠁⢸⡏⠙⣿⠛⡿⠖⠀⠀⠀⢹⡇
⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠀⠀⠀⠀⠀⠀⢸⡇
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⣧⣠⠤⠴⠚⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢀⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⢰⡟⠁⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠁⠀⠀⠀⠀⠈⠙⢶⣾⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠋⠉⣹⠿⢦⣄⣀⣠⣤⠤⠴⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠰⡄⠀⣸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣽⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠐⣦⣀⣠⣿⡶⠖⢿⠋⠘
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠚⠋⠹⠇⠀⠈⠃
⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⡄
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⢻⡆⢀⡴⠞⠳⣤⣤⠞⠁⠹⣦⡀
⠀⠈⢿⡏⠀⠀⠀⠀⠀⠀⠀⢀⣨⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀
⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠉⠻⠷⣶⣾⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠘⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⢠⡶⠛⠿⠀⠀⠛⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⣿⠀⢀⡀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⠳⠤⠿⠳⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣦⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣴⠶⠟⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡟⠉⠛⠛⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣶⣦⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡠⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⢄⠀⠀⠀⠀⠀⢗⡀
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⠀⠀⡂⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠈⢶⠄⢄
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⡁⠀⠀⠀⠘⠂⡄⠀⠀⠀⠈⠀⠄⠀⠠⠀⡁⠀⠀⠀⠄⣀⣀⣀⡀⠁
⠀⠀⠀⠀⠊⠤⠂⠄⠢⠀⠀⠀⠀⠀⠉⠁⠀⠈⠁⠀⠆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⢀⠒⠂⠀⠂
⠀⠀⠀⠀⠐⠀⠀⠀⠃⠀⠀⠀⠀⠀⡈⠀⠀⠈⠀⠼⠅⠈⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠱⠀⠌⠀⠀⠀⠀⠀⠀⠀⠂⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠊
⠀⠀⠀⠀⡀⠔⠂⢀⠀⠀⠀⢸⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠂⡀⠀⠀⠀⢀⡄⠀⠀⠀⢠⡀⠀⠀⠘⠋
⠀⠀⠀⢄⠀⠀⢀⠠⣀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠃⠄⠀⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⠰⠠⠂⠁⠀⠑
⠀⠀⠀⠀⠠⠀⠂⠀⢸⠀⠀⠀⠀⠂⢀⠀⠀⡀⠀⠂⠀⠀⠀⠀⡀⠀⠀⠀⠇⠀⠀⠀⠠⠂⠀⠀⠁
⠀⠀⠀⠈⠄⠀⠀⠠⠃⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢆⠐⠄⠠⠀⠀⠄⠐⠢⠄
⠀⠀⠀⠀⢐⠄⠀⡀⠀⠀⠀⠀⠀⢁⡀⠀⠈⠀⣀⠀⠀⠀⠀⢄⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢠⢃⡸⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣐⢅⡪⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡊⠅⡂⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠆⠒⠒⠛⠚⠓⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⠀⠀⠀⡨⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠖⠒⠉⠉⠉⠀⠉⠉⢉⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠒⠒⢲⠤⠤⣍⣀⡂⠄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠒⠈⠀⠀⣠⠔⠋⢍⢻
⠀⠀⠀⠀⠀⢀⢆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⡠⠤⠒⠉⠉⠉⠉⣑⢺⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢱⠤⠏⠀⢀⠸⠦⣤⠀⠀⠀⠀⠀⠀⠀⠀⣗⣒⡻⠟⠛⠉⠛⠛⣲⠾⠀⠀⠀⠀⠀⣀⠈⢒⠶
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠉⢲⠦⣧⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⣤⠴⠒⠭⣑⡇⠀⠀⠄⠀⠀⠨⠖⠺⠄
⠀⠀⠀⢀⡔⠑⢲⠂⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⣀⣀⡠⠓⡋⠻⡀⠀⠉⠀⡀⠀⠅⠀⠀⠐⠂⠀⠀⢠
⠀⠀⠀⠀⠨⠎⠘⠂⠀⠁⠂⠀⡴⠊⡏⠉⡇⠈⣇⠈⠣⡀⡞⢄⠈⠢⣄⠀⠀⠲⠀⠀⠀⠠⠄⠐⢆⠁⡱⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⣼⠘⣄⣸⠞⡽⡄⠘⢄⠀⠙⡇⠈⡧⡀⢈⠓⢍⣠⠀⠀⢄⠀⠀⠀⠚⠉⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠘⢄⡜⠁⡜⠀⡟⢄⠈⠳⣔⡇⠀⡇⠈⠢⡑⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⢳⣼⣠⣴⣤⣇⣵⣾⠬⢷⡥⢷⡭⠴⣚⠫⢋⠠⢑⠢⢐⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⣴⣮⣿⣥⣦⡀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠸⣿⠟⡿⢿⣿⣿⣿⣇⡀⡠⣴⢵⡦⣠⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⣀⣴⣤⠚⠻⣷⠂⠸⣿⡿⠸⠣⠴⠿⣿⡛⢷⣿⣿⡷⣇⣾⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠚⢫⣤⠹⠿⣿⡿⠂⠒⡋⠀⠀⣠⡔⣲⣌⢛⣯⣿⣋⠿⢎⢿⡋⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢠⣾⠯⠄⠀⣠⣴⠿⠛⠷⣦⣔⣛⢷⣿⡇⣼⣿⡿⣌⣀⣼⠃⢹⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠿⡄⠀⠀⢠⠞⠀⠀⠀⠀⠈⠉⠛⠷⠊⠘⠻⢋⡰⠉⣹⣻⡀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢇⡙⣻⣭⡳⣶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⠿⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢊⣯⡿⣿⣥⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢀⣽⠛⢻⣂⠴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⢠⡿⢸⣷⡄⣥⣮⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠁⠊⣋⡴⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⡄⣝⢷⣾⣿⣷⣶⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⢀⡀⣡⣪⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⡇⣯⣶⣿⣿⣿⣿⣿⡿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⣴⠔⣘⣻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣵⣿⡇⠘⠋⠉⠛⠿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠽⡀⠸⣋⣍⣴⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡬⢻⡿⣿⠃⠀⠀⠀⠀⠀⠹⣿⣝⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣷⠀⠉⠻⢿⠿⢲⣶⣶⣶⡀⣀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡾⣴⣴⡿⠃⠁⠀⠀⠀⠀⠀⠀⠀⠘⠿⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠈⠉⢙⡋⠀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠌⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠗⠄⠀⠀⠀⠀⠀⠀⠤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡹⣇
⠀⠀⠀⠀⠀⠀⣸⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⣁⠀⠐⢀⠀⠀⠀⠖⣨⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⡘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠁⣀⣄⣠⣶⣿⣿⠆

⣶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣷⣼⣷⣮⣿⣶⣬⣾⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣯⣤⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⢉⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢉⡽⠋⠉⠓⢤⡀⠀⠀⠀⠀⠀⢻⣾⣿⠶⠃⠀⠀⠀⠀⣠⠴⠶⠶⠷⢯⣉⠁
⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⡼⠀⠀⠈⢳⣤⣳⡀⠀⠀⠀⠀⠘⠟⠁⠀⠀⠀⠀⢠⠎⢁⡠⠄⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⢰⠇⠀⠀⢀⡇⠀⠀⠀⠘⠛⠋⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⣾⣿⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⣾⠀⠀⠀⢸⠀⠀⠀⣠⠴⠖⠲⠼⠀⢀⠀⠀⠀⠀⠀⠠⢄⣀⠺⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⡇⠀⠀⠀⡿⠀⠀⢾⡀⠀⠀⢠⠠⠤⠤⠤⠀⠀⠀⠠⠴⠶⢀⡄⠀⠀⢉⡆⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⢠⡇⠀⠀⢰⠇⠀⠀⠀⠉⠉⣻⠟⠉⠉⢀⣀⠀⠀⢀⡀⠀⠊⠁⠀⠸⣏⡉⠀⠀⠀⠀⢀⣠⠖⠁
⠀⠀⠀⠀⢸⠇⠀⢀⡞⠲⡤⠤⠴⣖⣋⡥⠤⠶⠒⠿⣈⡇⢰⡋⢉⡦⣄⣀⡀⠀⠀⠉⠛⠓⠒⢻⡉
⠀⠀⠀⠀⣸⠀⢠⠞⠀⢰⠿⠯⠭⠥⠤⢤⣤⣄⣀⡤⠤⣀⠀⠉⠉⠀⠀⠈⠉⠙⠓⠲⠦⠤⢲⡏⢧
⠀⠀⠀⣰⣧⠖⠁⠀⢀⡟⣆⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠈⡇
⠀⠀⠀⠉⠀⠀⠀⠀⣸⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⡼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣰⠃⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠦⣤⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀⡅
⠀⠀⠀⠀⠀⢠⠇⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢹
⠀⠀⠀⠀⢠⠏⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠈⡇
⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⢿
⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⢸⡄
⠀⠀⣞⣀⡀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⣇
⠀⠀⢠⠏⠉⠉⠛⠛⠒⠒⠒⡶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠘⢦⡀
⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠳⣄
⠾⠤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣚⣉⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢚⣛⣉⣛⡛⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠐⠒⠒⠂⠈⠉⠁⠀⠁⣄⠀⠀⠀⠀⠀⠀⡠⡀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⠎⢴⣒⠚⠒⠀⠀⠀⡀⠀⠀⠀⠘⡆⠀⠀⠀⡠⠎⠐⠁
⠀⠀⠀⠀⠀⠈⠛⠓⠒⠀⠀⣾⠀⠀⠲⠯⠅⠀⠀⠈⠻⣆⠠⢠⠶⠃⠀⠀⠈
⠀⢦⣒⣀⣀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠀⠀⢦⠃⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠳⡀⠒⠀⠀⠀⠀⠀⠀⡀⠀⡄⠑⣈⡀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⡔⡥⠠⠀⠬⡉⠁⡇⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠂⠡⠄⠤⡰⠈⠁⢠⠇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠁⠀⠈⠀⠀⠀⠀⣀⡀⠀⠐⡡⠀⠀⠀⢓⠀⠐⠒⠢⠤⢀⠔⠛⢃⢉⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⡀⠀⠈⠆⠀⠀⠀⢸⣆⠀⠐⠃⠀⠀⡰⠖⠂⠀⠀⠀⠀⢸⡀⢀⡼⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠊⠀⠀⡠⠚⠉⠁⠈⠀⠀⠀⠀⢀⡖⠒⠁⣐⣄⣀⣀⣤⠴⠶⢯⣀⣥⡬⢃⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢤⠀⠃⡌⠀⠀⠀⠀⠀⠀⢀⡠⠞⢡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠔⢚⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢡⠜⠃⠓⠲⠖⠒⢛⣉⡤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣤⣰⢠⡤⠖⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⠀⠀⢠⠤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠐⢢
⠀⠀⠀⠀⠈⡇⢿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠁⡰
⠀⠀⠀⠀⠀⢿⠘⠿⠿⠿⠿⠛⠋⠀⠀⠙⢿⣿⣿⣿⣿⣿⡿⠄⣠⠟⠁⠀⠁
⠀⠀⠀⠀⠀⠈⠳⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡟⠁⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠤⠗

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢿⡌⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠘⣷⡌⢿⣹⣇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡴⠒⠒⣻⡗
⠀⠀⠀⠀⠀⠀⠀⡀⠹⣷⣄⠈⢿⣾⣿⣿⣦⡀⠀⠀⠠⠶⢉⡀⠀⢤⣶⣄⠀⠀⠀⠈⢁⣤⡶⢾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠹⣧⣌⠻⣷⣤⡙⢻⣿⣿⣷⣤⠈⢠⡆⢈⣠⣀⠀⠈⠁⡀⠀⣤⠖⢋⠀⣨⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠠⣤⣈⠙⠷⣦⣽⡿⢷⣿⣿⣿⡇⠀⠸⠋⠙⠛⠁⠀⠀⠀⠀⠈⢁⡴⣫⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠶⢾⣿⣿⣿⣿⣿⣆⢀⣿⣤⢃⣼⠂⠀⠀⠀⢘⣷⣿⣷⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠶⢶⣶⣶⣾⣿⣿⣿⣿⣾⣿⣷⣾⣿⣶⡄⠀⠀⡜⢻⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⣉⡛⣷⠶⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⢸⣼⣿⣿⣿⣟⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠤⠈⠻⢿⢷⣿⣿⣿⡿⠟⣸⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠝⡼⠟⠁⠀⠈⣻⣿⣿⣿⣿⣿⣿⡿⣿⡿⠷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⠁⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣫⡿⣿⣿⣿⡿⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣶⣿⢿⣼⣟⡳⣠⣾⡿⠁⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠿⠯⠛⣛⣿⣿⣿⠟⢹⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⠙⠻⠖
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢁⣠⡴⢾⣽⣿⣿⣻⣆⣿⡿⣿⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⡴⠋⣡⡶⣻⣿⣿⣿⣿⣿⣿⡇⠘⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦
⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠾⣩⡾⢋⣿⠯⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⣷⣀⣾⣷⣾⣷⣅⠀⠀⠀⣸⣧⣿
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢰⡿⠀⣾⣿⠀⢸⣿⡇⠀⠁⠀⠀⢰⣶⣶⣿⣿⣷⣿⣿⣿⣿⠟⠀⠀⢠⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠐⣿⡿⢧⡌⣿⡇⠀⠀⠀⠀⢺⣿⣿⣧⣾⣿⣿⣿⣿⣦⠄⠀⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠿⣧⠈⠿⠎⠉⠀⠀⣀⡿⣿⡝⢿⣿⣿⣿⣿⣿⣿⣄⢀⣼⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠈⣿⡇⢀⠘⠛⣷⣿⣿⣿⣿⡁⣸⣿⣿⣿⣿⣵⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠘⠳⠂⠀⠀⠘⢹⡷⢼⡟⢾⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⣀⣠⣄⠘⣧⡼⣷⡀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢋⣹⣾⣿⣿⣿⣦⠘⢿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠉⣭⣭⣭⣽⣿⣿⣿⣿⣭⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠿⢿⣿⣭⡿⠷⢛⣫⣽⣿⣿⣿⣿⣿⣿⣿⢻⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠐⠛⠛⢟⣩⣿⣹⣯⣼⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟⣽⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣴⣿⠿⢃⣾⣯⡿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠙⣴⣿⣿⣿⣵⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⣿⢻⣿⣿⣿⠁⠀⠀⠀⢠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢠⡿⠁⣿⡿⢹⡇⠀⠀⠀⠀⠀⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⢸⡿⠁⢸⣷⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢸⡇⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⣄⣤⡄⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣷⡟⣹⠃⠀⠀⢠⣤⣤⣾⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡲⠀⠀⠀⡙⠤⢤⢡⡄⢈⣉⡉⠛⢿⣿⡁⠀⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣁⠲⢐⠊⠀⡀⠄⠁⠐⠈⠛⠿⡶⢼⠻⠿⠂⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣡⡏⠄⠘⢄⠀⠀⠖⡀⢀⡄⡍⣁⠀⢠⠀⠀⡾⣻⣯⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⡁⢴⣞⣻⣤⡦⠀⠰⠈⠀⠈⠀⠉⠓⢌⠀⠐⠛⢿⡮⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⢀⣀⠀⠬⡹⠛⣍⡀⠁⠢⡐⢂⣈⡅⢀⢀⠐⠂⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢘⣄⢐⡀⣀⠜⠛⠋⠀⣎⣸⠛⡑⡃⢄⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠠⣄⠈⠀⠀⡀⠃⡔⠀⡀⣀⣈⢫⠑⡦⢀⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡩⠷⠈⣁⣠⡅⠀⠀⠀⠁⢉⡁⠀⠖⠀⠸⠏⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⣭⡀⠉⠉⠁⠀⠰⠐⠀⣘⣁⣠⣀⠀⠠⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠟⠀⠀⠀⢠⣴⣦⡀⠀⠘⠿⠿⠃⠀⢀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣤⡀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣇⠀⠀⠀⠀⣠⣤⣄⢀⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀
⠀⠀⠀⠀⠀⠀⣰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄
⠀⠀⠀⠀⠀⣰⣿⡟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄
⠀⠀⠀⠀⢠⣿⡟⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷
⠀⠀⠀⠀⠸⠋⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⡆⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠟⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡎⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⢰⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡄⠈⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣷⣿⣿⣹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣆⠻⠃
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣈⣛⣷⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⣀⣀⣁⣀⠀⡘⣻⣯⡻⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠁⠁⠈⣉⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⡧⠂⠀⠈⠀⠁⠀⠀⢠⣀⡈⣌⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⡌⠀⠀⠀⠀⠀⠀⠀⢀⣤⠽⠛⠉⠀⠀⠀⠐⢀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠙⣳⡀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⢈⠻⣿⣶⣦⠂⠀⠀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡧⢧⣻⣧⣷⠀⠀⠀⠀⠀⠉⠂⢄⢀⢄⣾⣧⡽⠷⣿⢿⡅⠀⠀⠀⢻⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡻⣿⣮⠳⣄⠀⠀⠀⣷⣆⢺⣿⣿⣿⡿⠃⠀⠉⠈⠀⠀⡀⠀⠀⢸⡇⠀⠂⠰⠂⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢠⡀⠀⣴⣜⣻⣮⠿⣶⡎⢩⣲⣦⣾⣿⣿⣿⣿⣿⣷⠀⠠⣧⣄⣀⣰⣧⠌⠀⣺⣧⠀⣠⣿⢀⣼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⣸⣿⣶⣿⣿⢦⣾⣿⣿⡿⢾⣿⣿⡷⠴⡿⣟⢻⣿⣿⣿⣿⣯⣀⣴⣿⣿⣿⣿⣿⡀⢶⣿⢿⣿⡿⠿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⢠⣶⠋⠀⠀⠙⠹⠁⠈⠙⣿⡏⠁⢸⣷⢹⣿⢯⣷⠾⠚⢻⣼⣿⣿⣿⣿⣿⣿⡿⠟⠋⣿⡿⠉⠐⠿⣿⣿⣿⡄⠀⠙⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠙⠿⣿⠀⠘⠀⠀⢸⣿⠟⠉⠉⣾⡟⠉⠀⠀⣄⢿⣿⠀⠀⠀⠀⣽⡿⠃⠀⠀⠙⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⡀⠀⠘⣧⣿⢀⠀⠀⢰⡿⠇⠀⡄⠀⠀⢸⣿⣀⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢠⣦⠙⣗⡞⢳⡆⢘⠀⠰⠐⠘⠀⠀⠊⠹⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠚⠈⠉⠀⠀⠀⠉⠀⠀⠠⠖⢀⣸⣶⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⢒⠲⠶⣤⡀⠀⠀⠀⢀⣠⣤⣤⣴⣶⣟⡀⠀⠀⠀⠀⣀⡤⠶⢒⠒⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠉⢦⠀⠙⢷⡤⠚⠉⠉⠁⠀⠩⠽⠛⠛⠿⢦⣤⠞⠉⢠⠖⠁⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⣀⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢺⣯⡀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣤⡀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠶⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠆⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣾⠃⠀⠀⠀⢀⣤⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣄⠀⠀⠀⠘⢷⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⣿⣿⣧⣼⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣤⣿⡆⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠧⠀⡀⣀⠀⠀⠙⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠟⠀⠀⢀⠀⡀⠨⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠉⠐⠒⠂⠠⠀⠀⠠⡖⠛⢒⡆⠀⠀⠠⠀⠀⠂⠈⠁⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠒⠒⢐⣿⠁⠀⠀⠀⠀⠉⠉⠉⢉⡉⠁⠀⠀⠀⠈⢳⠋⠀⠀⠀⠈⠉⣉⠉⠉⠉⠉⠁⠀⠀⠀⢻⡇⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⢸⣯⡖⠀⢀⡀⠄⠒⠀⠉⡀⠄⠂⠀⢀⠀⠀⣸⠀⠀⠀⠀⠀⠂⠄⡀⠉⠐⠂⠄⣀⠀⠰⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠚⣿⣿⡏⠁⠀⠀⡀⠐⠁⠀⠀⠀⠀⠈⠓⠒⠉⠓⠒⠃⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠉⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣾⠃⠉⢷⣄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠏⠀⢿⡀
⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠙⠻⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠾⠛⠁⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠒⠒⠶⠶⠶⠶⠶⠶⠒⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠻⣄⣀⠀⠀⣰⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣷⡀⠀⢀⣤⡾⠁⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠟⠋⠉⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠤⠶⢶⣶⣶⡟⡀⢀⠀⡀⣿⣿⣿⣶⣶⣶⣶⣤⣴⣶⣶⣶⣿⣿⣿⡃⡄⢀⢠⠙⣷⣶⡶⠶⠦⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⢀⣠⣤⣴⣾⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⡀
⠀⠀⠀⡰⠻⢿⣿⣿⣿⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⢀⡆
⠀⠀⢀⡇⠀⣼⣿⡿⠃⠀⠀⢤⠠⠀⠀⠀⠒⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢦⡀
⠀⠀⠈⠇⠀⠈⠈⠓⠂⠀⠀⠒⠀⣄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⢐⡁⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠈⢢⠐⠄⠀⠀⠀⢠⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠄⢀⣾⠋
⠀⠀⠀⠀⠀⠑⡀⠀⠀⢀⣈⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠰⠋⠡
⠀⠀⠀⠀⠀⢠⣶⣤⣲⣄⠈⠉⠁⠀⠀⢸⡙⣒⠶⠶⢗⠀⢲⠀⠀⠀⠀⠀⠠⠄⡰⣄⣀⣀⣀⣀⣀⣀⡀⠀⠓⠶⠶⡄⢀⡆⢀⠄⠀⠀⠒
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣼⣏⣿⣿⣿⣿⣿⡇⠇⠀⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠛⠒⠐⠒⠒⠂⠒⢢⢽⠀⠀⣀⠲⠀⠐⠁⠘⠓⠦⠒
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣟⠛⠉⠉⠉⣷⠱⠀⣴⣓⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⢤⡀⢰⠸⣤⠊⠁⢀⠀⠠⠀⣀⡴
⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⢿⠸⠀⠨⠉⡉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢶⠄⠈⠆⠟⢆⠀⠂⢀⠖⠉⠉
⠀⣴⣾⣿⣿⣿⣿⣿⣿⣏⠉⠛⢿⣿⣿⣶⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠁⠀⠀⢠⡴⠀⠀⡀
⠈⠿⣿⣿⣿⣿⣿⣿⡏⠈⠀⠀⠀⠀⠉⠁⠀⢤⠤⠀⠁⠠⠤⠤⡤⣀⣒⣒⣒⣂⣀⡀⠀⠀⡀⠀⠀⠀⢀⡠⠔⠉⠀⢀
⠀⠀⠈⢏⡛⠿⠿⠋⠀⠀⠘⠓⢀⠀⠀⠀⠀⠂⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠠⡤⠖⠉⣩⠞⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠙⠲⢤⣀⠀⠀⠀⠀⠈⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⠊⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⢰⠢⠤⠥⠆⣴⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠉⠢⣄⢀⡠⠀⡌⠳⢄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠜⠀⠑⣦⡀⠀⢱⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⣠⠀⢀⡟⠉⠀⠸⠇⠐
⠀⠀⠀⠀⠀⠈⠰⡶⠴⡶⠀⠀⠀⠑⠐⣷⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠚⢁⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠰⣠⠰⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠐⠆⠐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂⠇⠂⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢃⠀⢀⡄⠀⠀⠀⠀⠀⠀⠄⡀⢄⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣂⡊⠀⠀⠑⡍⠉⠇⠀⠀⠀⠀⠀⠀⠔⠉⠀⠀⠉⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠈⠁⠀⠉⠒⢤⠁⠀⢰⠀⠀⠀⠀⢠⣇⣀⢀⡔⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢪⢇⡠⡤⠜⢯⢀⡀⢘⠀⠀⠀⠀⠘⠃⠛⠠⢊⠤⢀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠤⠒⢉⣁⡍⢃⢰⡬⠀⠠⠀⠀⠤⠤⠀⣦⣥⠀⡼⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡄⠀⠀⣎⣽⠟⠉⣖⣊⡀⢀⣀⡀⣀⠀⣀⠴⠈⠐⠂⠈⠐⠈⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⣲⠁⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⡌⠀⢰⣰⠋⠉⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡀⠀⡐⠁⡀⣤⠄⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⡅⠖⠉⠈⡦⠴⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠑⠀⠀⠀⠀⠈⠉⢀⡠⠔⠃⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠤⠤⠊⠀⠀⠊⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠁⠒⠒⠒⠉⣨⡀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠢
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢹⠁⠀⠀⢀⡠⠒⠀⠐⠐⠪⠁⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⢀⡠⠤⠒⠒⠂⠀⠒⠥⣀⠀⡆⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡗
⠀⠀⠀⡀⠠⠔⠃⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⢀⢊⠡⠔⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⣔
⠀⠰⢁⣀⣀⠀⢀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⣅⠀⢀⡠⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⣀⣀⣀⣉⠲

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⡠⢆⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⢣⢠⠛⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘⡄⠀⠀⠀⠀⠀⣄⠀⠀⠈⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣿⣷⣄⣀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡒⠒⠠⠤⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠒⠒⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠉⠉⠉⠁⠐⠒⠃⠀⠀⠀⠀⠀⢀⠤⠂⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣔⡈⠁⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⣤⣼⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣴⢦⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⣿⣷⢒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⣷⡿⣇⣨⡿⠛⠀⠀⣤⣄⠀⠀⠀⠀⢡⠝⣸⠿⡃
⠀⠀⠀⠀⠀⠀⠀⢬⠁⠀⡀⠘⠙⠿⠶⠖⠛⠶⣯⣻⣃⠀⠰⡆⠰⡞⠷⡘⠁⠀⠤
⠀⠀⠀⠀⠀⠀⠈⣾⠃⠂⢻⡆⣀⠀⠀⣴⣠⣖⣶⢦⠈⠙⠛⠻⣦⣨⣿⡃⠃⠐
⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠈⠉⠉⢩⡁⢸⣿⣿⣿⠀⠀⠀⠀⢸⣭⣿⣟⡣⢀⣴⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢏⣷⣦⡶⠶⡚⠁⠈⠛⢦⣐⢦⣤⡀⠀⠀⠀⠉⠛⢀⠀⣉⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⣾⡿⠬⠋⣩⣿⣯⣉⠀⠀⠀⠀⠘⣿⣿⣿⠆⠀⠀⠀⠀⠈⠙⠛⠿⣿⣧⢁
⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠉⠉⢙⡏⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠈⠉⠀⣀⣨⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⣹⠃⠀⢀⠠⠂⡀
⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠏⠀⠀⠀⠠⠚⠁
⠀⠀⠀⠠⠟⠃⢠⠀⣠⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠠⣀⡀⠀⣰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⢀⣠⣤⡄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⠀⠀⣰⣄⠀⠀⠀⠀⠀⠀⠀⠂⠘⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢺⡇⡀⠀⠀⠀⠀⠈⠉⢳⠂
⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⢨⣆⠀⠀⠀⠀⠀⢀⠀⠀⠀⣾⠐⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⣀⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⣼⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⠃⠀⠀⠠⠀⠀⠀⠀⣰⣿⣿⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠈⠉⠀⠀⠰⢧⡀⠀⠀⣰⣿⣿⣿⠧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣰⣿⠟⠋⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠒⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠿⠇⠠⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠁⠀⠐
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠛⠦⠄⣠⡀⣠⠀⠀⠀⠀⠀⠺⢿⣿⣿⠶⠀⠀⠀⠀⠀⠀⠈⢿⣿⡆
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠙⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠃⠀⢀⣀⡀⠀⠀⡠⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡛⠃⠀⠀⠀⠀⢀⡀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣏⠉⣹⣛⣛⣟⣛⣻⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣿⣻⣿⣛⣛⣛⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣝⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠈⡋⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡶⢦⣆⠰⢾⢻⡿⠄⠀⠀⠈⡵⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢺⡏⠀⠀⠁⠀⠀⠀⠀⠀⡇⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣄⣠⠔⠀⠀⠀⠀⠀⠀⡇⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣔⣒⠒⠀⠀⠀⠀⢀⡼⠁⠀⠘⠃⡄⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠀⠀⠀⠀⣠⠞⠁⠀⠀⣰⠀⢁⠔⠁⠀⠠⢄
⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⢀⣾⣿⣷⣶⣷⡶⠟⠁⣤⠀⣀⠔⣡⠊⠁⣠⠞⠀⠀⢀⣥⠀⡀
⠀⠀⠀⠜⠠⠄⣀⢨⡆⠀⠀⣿⠘⡇⠘⠛⠃⠀⠸⠸⠧⠊⢁⠴⢿⠴⠋⠁⠀⡤⠀⠈⢉⠀⠙⡄
⠀⠀⢣⠀⠤⢀⣀⣹⠋⢠⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣆⠀⢀⡤⠊⠀⠀⠠⢾⠆⠀⠘⣆
⠀⠀⢡⠀⠐⠀⠀⢽⣠⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣞⠉⠀⣠⠔⠀⠀⠈⡄⠀⠀⠘⡀
⠀⠀⠘⡄⠠⢔⣂⣼⡿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⠚⠁⠀⢀⣤⡾⠂⣀⠀⠀⡇
⠀⠀⠀⠀⠀⠐⠛⣿⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣤⣶⡿⠟⣿⣿⠯⠂⠀⢹⡀
⠀⠀⠀⠀⠠⠀⠀⠡⡹⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡇⠀⠀⢸⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⢧⠀⠀⠀⠙⡶⠤⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠀⠸⠇⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠈⠀⠈⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡁⠀⡐
⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠁⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⢀⣿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆⣤⠴⠋⠁⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀
⠀⠀⠀⠀⠀⠀⢐⣿⣃⣀⠀⠀⠀⠀⢶⣆⣠⠀⠀⠀⠀⠀⠀⠀⢻⣿⣴⠶⠶⠀⠀⢀⣀⠹⢾⣟
⠀⠀⠀⠀⠀⠀⣿⡿⠋⠀⠀⠀⢀⣰⣿⡏⠁⠀⠀⠀⠀⠀⠀⠰⠋⠈⢻⣧⠀⠀⠛⠛⠙⢷⣿⣿⠂
⠀⠀⠀⠀⠀⣰⡟⢷⡄⠀⢀⣼⢻⡟⠁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀⠀⠸⣯
⠀⠀⠀⠠⠾⠋⠀⠼⠃⠀⠈⠁⠘⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⠀⠀⠹⠆