Time clock Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠒⠒⠚⣛⡛⠓⠒⠒⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⣉⡤⠴⠒⠋⠉⠉⠉⠉⠉⠉⠙⠒⠦⢤⣉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⣡⠔⠋⠁⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣌⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢁⠞⠁⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡾⢷⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠳⡈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡞⢠⠏⠀⠀⠀⠀⠀⢀⡎⠉⢷⠀⠀⠀⢀⡇⢸⠀⠀⠀⠀⡞⠉⢱⡀⠀⠀⠀⠀⠀⠹⡄⢳⡀
⠀⠀⠀⠀⠀⠀⠀⡼⢠⡏⠀⠀⠀⠀⠀⠀⠀⠧⣤⠞⠀⠀⠀⢸⠃⢸⡇⠀⠀⠀⠳⣤⠼⠀⠀⠀⠀⠀⠀⠀⢹⡀⢣
⠀⠀⠀⠀⠀⠀⢰⠇⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⡆
⠀⠀⠀⠀⠀⠀⣸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡼⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣇
⠀⠀⠀⠀⠀⠀⣿⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣹⣏⣉⣉⢈⣉⣉⣻⠶⠶⠆⠀⠀⠀⠀⠀⢸⠆⣿
⠀⠀⠀⠀⠀⠀⢹⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡏
⠀⠀⠀⠀⠀⠀⠸⡆⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢠⠇
⠀⠀⠀⠀⠀⠀⠀⢣⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⡜
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⣖⠒⠒⠒⠒⠒⠒⣲⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠙⢮⣓⠶⠤⠤⠔⣚⡵⠋⠀⠀⠀⠀⠀⠀⠀⢀⡴⢁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⢋⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣉⠓⠲⠤⣄⣀⣀⣀⣀⣀⣀⣠⠤⠖⠚⣉⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠤⠤⠤⣬⣥⡤⠤⠤⠖⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠙⡆
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠉⠉⠓⣦⠀⠀⠀⠈⢳⡞⠁⠀⠀⠀⣴⠚⠉⠉⠉⠛⠲⢤⡀
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣀⣀⣰⣇⣀⣀⡀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⣠⠞⢁⡤⠖⠋⣉⣡⣤⠤⠤⣤⣌⣉⠙⠲⢤⣈⠳⣄⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⣠⠞⣧⠞⢁⡤⠖⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠲⢤⡈⠳⣼⠳⣄⠀⠀⠀⠀⣇
⠀⠀⠀⠀⢹⠀⠀⣠⠞⢁⡞⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡈⢳⡈⠳⣄⠀⠀⡟
⠀⠀⠀⠀⠈⠷⠞⠁⢠⡟⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠹⡄⠈⠳⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡾⢀⡟⠀⠀⠀⠀⣠⡤⣄⠀⠀⠀⠀⠀⢀⣤⢤⡀⠀⠀⠀⠀⢹⡀⢳
⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⠁⠀⠀⠀⢰⠃⠀⠈⢧⠀⠀⠀⠀⡟⠀⠀⠹⠄⠀⠀⠀⠈⡇⢸⡆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠸⡆⠀⠀⠀⠀⠀⠀⠀⡞⠛⠛⠛⠛⡧⠀⠀⠀⠀⠀⠀⠀⢠⠇⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢳⡀⠀⠀⠀⠀⠀⠀⠻⣖⠚⠓⣶⠃⠀⠀⠀⠀⠀⠀⢀⡞⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠳⡄⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁⠀⠀⠀⠀⠀⠀⢠⠞⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠘⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠙⢦⣈⠙⠲⢤⣄⣀⣀⣀⣀⣠⡤⠖⠋⣁⡴⠋⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠈⠙⠲⠦⢤⣤⣀⣠⣤⡤⠴⠖⠋⠁⠀⠀⠀⠀⠘⢦


⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠓⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛
⠀⠀⠀⠀⠀⠀⢠⡄⢠⠄⢄⠠⢰⠄⢠⡄⢤⣠⢠⠀⣤⠀⠀⡔⠀⢴⠀⡄⡄⡤⠢⡠⣠⠄⡄
⣀⣀⣀⣀⣀⣀⣈⣥⣸⣤⣎⣥⣸⣀⣋⣣⣬⣽⣸⣤⣿⣥⣀⣬⣇⣸⣀⣏⣇⣣⣴⣱⣙⣦⣯⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⡇⠀⡞⠃⣾⢹⠀⢺⠀⣖⡆⢰⢳⠀⡞⡆⣾⠢⢰⠂⢰⢻⠠⠻⠀⡏⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠒⣇⣷⠒⣇⡗⢺⣼⠘⣿⢷⣧⣷⢺⣼⡚⣇⣷⡻⡜⢻⣸⣻⣼⣛⣼⣏⢧⣿⠉⠉⢹⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⠀⠢⢀⠖⠐⡆⢀⠖⠒⠰⡀⠀⠏⠉⠑⠢⡀⠀⢀⠔⠢⠀⢰⠉⠃⢸⠉⡇⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠈⠀⢠⡡⡄⠀⠃⠨⠀⣄⠀⢡⢰⠀⠘⠀⣠⠂⢀⠇⢰⣊⣀⣸⠀⢐⣚⠀⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢀⣀⡼⠀⢇⣀⡇⠃⣠⢄⠀⠈⣲⡆⠀⣤⣀⣑⡜⢦⣀⣠⠞⠡⠤⠼⠸⠤⠇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⠀⡀⢀⠀⡀⠀⠤⢄⠠⠠⠀⠤⢠⠀⠀⠂⢠⠀⢲⠠⠄⢠⢀⠠⠄⠠⠤⠄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠠⠀⠅⠠⠤⠄⠠⠠⠜⠒⠐⠀⠄⠔⠘⠒⠃⠘⠄⠐⠸⠤⠜⠠⠤⠄⠠⡀⠄⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡆⢰⠀⠂⠂⢠⠒⠄⠔⠰⡄⠖⢤⠀⠄⢠⠀⡔⢢⢠⠀⢄⠠⠄⢤⠠⠒⠆⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠑⠚⠈⠂⠂⠘⠂⠂⠈⠚⠁⠃⠊⠀⠂⠘⠀⠣⠞⠘⠂⠊⠈⠂⠂⠘⠒⠃⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠒⠀⠒⠒⠄⡊⠱⠀⡎⠂⢘⠉⡆⠐⠉⡆⡒⢒⠀⠒⢲⠀⡒⢢⠀⠒⠂⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠈⠚⠁⠉⠉⠁⠉⠈⠁⠁⠁⠈⠉⠁⠈⠉⠀⠉⠁⠀⠉⠁⠀⠉⠁⠀⠁⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⣄⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠬⠭⠍⢁⣚⣛⣓⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⣒⠒⠒⠒⠒⠀⠀⢉⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣂⣐⣂⣀⣀⡀⠀⠄⠒⠒⣒⣛⣛⣛⣛⣛⣒⣚⣓⣀⡀⠀⠀⡠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠒⠒⠒⠒⠒⠒⠒⠒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠒⠛⠓⠲⠞⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⡄⣠⡀⢠⢠⣤⣤⣠⢠⡄⠀⢀⡀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢻⣿⣿⠿⡿⡿⢿⣿⣿⠿⢿⢿⣿
⠀⠀⠀⠀⠀⠀⠓⠛⠓⠚⠊⠛⠛⠛⠚⠃⠀⠀⠛⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣴⣿⣿⣾⣷⣶⣾⣿⣿⣿⣶⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⢀⡀⠀⠀⠀⣀⡀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣏⣈⣷⣀⣼⣉⣙⣆⣀⣾⣁⣹⣆⣠⣏⣉⣳⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢠⠟⠀⠀⠀⣤⠇⠀⠀⢀⡼⠃⠀⠀⢠⡞⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠁⠀⠈⠁⠀⠈⠁⠀⠉⠀⠀⠉⠀⠀⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⠆⠀⠠⠄⠀⠠⠄⠀⠴⠀⠀⠤⠀⢀⣀⣤⣄⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡀⠀⢀⡀⠀⢀⡀⠀⢀⠀⠀⣠⠞⠉⠀⠰⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠁⠀⠈⠁⠀⠈⠀⠀⠈⠀⢰⠃⠀⠀⠀⢰⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⠂⠀⠐⠂⠀⠐⠂⠀⠒⠀⣿⠐⠂⠀⢀⡼⠀⠀⠀⠒⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣆⠀⠀⠈⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⡘⣀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢲⠀⢸⢳⡆⠀⢰⠛⡆⠀⢰⠒⡆⢰⠓⡆⢸⠓⡆⢰⠛⡆⢠⠖⡆⢰⠟⡄⣾⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠤⢼⣈⠤⢼⠰⠧⠄⠸⡁⡷⠐⠾⡀⡳⠰⣂⡗⠺⣀⡗⠺⣀⡷⠲⡀⡗⢺⣀⡓⢻⢘⡛⠋⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠈⠙⠁⠘⠋⠀⠀⠀⠉⠁⠀⠈⠃⠁⠀⠉⠁⠀⠀⠁⠀⠁⠁⠀⠃⠃⠀⠁⠁⠈⠈⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠂⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢰⠋⠙⢐⠁⢐⠀⠁⠈⠀⡁⠈⠀⡏⠀⡅⠊⠀⠀⠈⠀⠈⠰⠁⠈⡀⠈⠀⡆⠉⠀⠁⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠀⠈⠀⠁⠀⠀⠉⠉⠀⠀⠀⠁⠈⠉⠁⠈⠁⠀⠈⠁⠀⠀⠈⠈⠀⠙⠒⠋⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠉⠁⡂⠀⠂⠈⠉⠂⡋⠉⠁⠈⠁⠆⢸⠁⠱⠐⠂⠐⠀⠂⠒⠀⢘⠐⠂⠈⠉⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠉⠀⠑⠒⠀⠈⠀⠁⠈⠀⠀⠈⠉⠁⠈⠀⠀⠈⠀⠚⠀⠓⠒⠀⠈⠀⠁⠈⠀⠂⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡖⠀⠆⠘⠀⠐⠰⠉⠉⠀⠏⠙⠀⠉⢹⠀⠋⠉⠃⡊⠉⠀⠘⠉⡀⠐⠂⣂⢰⠀⠒⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠀⠃⠈⠀⠈⠁⠉⠀⠁⠈⠉⠀⠁⠚⠀⠉⠉⠁⠈⠉⠀⠈⠉⠁⠈⠁⠀⠈⠁⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⠠⠤⢤⠄⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠀⣀⠀⠐⠒⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⣠⣤⣤⣤⡤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠤⠤⠴⠴⠦⠤⠭⣭⡭⠭⠥⠤⠖⠁

⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠂⠀⡀⢀⠤⠤⠖⠺⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣻⣭⣔⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⢸⡇⠀⠀⠀⣿⠀⢸⡇⠀⠀⠀⣾⠀⠀⣷⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⢸⡇⠀⢹⡆
⠀⠀⠀⠀⠀⢰⠶⠶⠶⠶⢾⡇⠀⢸⡷⠶⠶⠶⣿⠀⢸⡷⠶⠶⠶⣿⠀⠀⣿⠶⠶⠶⢾⡅⠀⣿⠶⠶⠶⢾⡇⠀⢸⡷⠶⠶⠶⠶⡆
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣸⡇⠀⢸⣇⠀⠀⢀⣿⠀⠸⣧⠀⠀⢀⣿⠀⠀⣿⡀⠀⠀⣸⡃⠀⣿⡀⠀⠀⣸⡇⠀⢸⣇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡿⣇⠀⣸⢿⡆⠀⣿⣿⡀⣸⣿⡇⠀⣾⢿⡀⢀⡿⣷⠀⢸⣿⣇⢀⣿⣿⠀⢰⡿⣇⢀⣸⢿⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠻⢮⣭⣥⠟⠀⠀⠙⢮⣭⣭⠞⠁⠀⠘⠷⣭⣭⠾⠃⠀⠈⠳⣭⣭⡵⠋⠀⠀⠻⣬⣭⡵⠟⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⢸⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡇
⠀⠀⠀⠀⠀⢸⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⢸⠁⠉⠉⠀⢹⠀⠀⣿⠉⠉⠉⠁⣿⠀⠀⣿⠉⠉⠉⠉⣿⠀⠀⣿⠀⠁⠀⠉⣿⠀⠀⡏⠀⠉⠉⠈⡇⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠘⠓⠒⠒⠒⠚⠀⠀⠙⠒⠒⠒⠒⠛⠀⠀⠛⠒⠒⠒⠒⠛⠀⠀⠛⠒⠒⠒⠒⠋⠀⠀⠛⠒⠒⠒⠚⠃⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⢰⠛⠛⠛⠛⢻⠀⠀⣾⠛⠛⠛⠛⣷⠀⠀⣾⠛⠛⠛⠛⣷⠀⠀⣾⠛⠛⠛⠛⣷⠀⠀⡟⠛⠛⠛⠛⡆⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⢸⣤⣤⣤⣤⣼⠀⠀⢿⣤⣤⣤⣤⣿⠀⠀⣿⣤⣤⣤⣤⣿⠀⠀⣿⣤⣤⣤⣤⡿⠀⠀⣧⣤⣤⣤⣤⡇⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⢠⣤⣤⣤⣤⣤⠀⠀⣠⣤⣤⣤⣤⣤⠀⠀⣤⣤⣤⣤⣤⣤⠀⠀⣤⣤⣤⣤⣤⣄⠀⠀⣤⣤⣤⣤⣤⡄⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠘⠛⠛⠛⠛⠛⠀⠀⠙⠛⠛⠛⠛⠋⠀⠀⠙⠛⠛⠛⠛⠋⠀⠀⠙⠛⠛⠛⠛⠋⠀⠀⠛⠛⠛⠛⠛⠃⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⠶⠦⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡡⠖⠛⠉⠉⠙⠲⢬⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡇⠀⢀⣀⣀⣀⣀⣀⣀⣀⠀⢸⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠹⡄⢸⣿⣿⣿⣿⣿⣿⣿⢀⡞⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣜⠻⣽⡏⠉⠉⠉⣯⠽⢋⡼⠁⠀⢠⠖⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢾⣇⣀⣀⣀⡷⠚⠁⠀⠀⢠⣏⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠚⠋⠉⠉⠉⠉⠉⠉⠙⠓⠒⠤⣤⣯⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⣀⣀⡤⠤⠤⠤⠤⣤⣀⣀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⣠⡴⠚⠋⠁⠀⠀⠀⢸⡇⠀⠀⠀⠈⠙⠓⠦⣄⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⣠⠋⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠙⣄⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⢯⡽⣻⣿⣭⣭⣉⣭⣭⣭⣭⠇⠀⠀⠿⠇⣿⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠋⠉⠙⠛⠿⢿⣶⣤⣄⡀⠀⠀⠀⠀⡇⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠖⠀⢸⠃⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠹⣄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣠⠏⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠈⢦⡘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢃⡴⠁⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠉⠲⣄⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠉⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠉⠒⠦⣤⣀⣀⣀⠸⠇⣀⣀⣀⣤⠴⠒⠉⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⢤⣀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⣀⡤⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠶⠶⠶⠶⠒⠒⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣯⣭⣽⣗⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣀⣤⣤⣤⣤⣄⣄⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⣩⡿⠟⠛⠛⠛⠛⢿⣯⡛⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠳⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⢰⢁⡏⠀⠂⠀⠀⠀⠀⠀⣠⠔⠀⠀⠙⡆⢡
⠀⠀⠀⠀⠀⠀⢰⣿⠀⣿⣿⣿⣟⣛⣛⣛⣻⣿⣿⣿⠰⣿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠒⣦⡎⠁⣴⣲⠀⠀⣽⠘⣯⡇
⠀⠀⠀⠀⠀⠀⣼⣿⡦⢟⡿⣿⣿⣾⣷⣶⣿⣯⢟⡻⣼⡿⡇⠀⠀⠀⠀⠀⢠⢸⡄⠀⠀⠀⢀⠀⠀⢀⡀⠈⠀⠀⠀⡾⢸⠛⠃
⠀⠀⠀⠀⠀⢠⡗⠋⣪⠗⠋⠁⠀⠀⠀⠀⠀⠉⠑⠪⣗⠝⢿⡀⠀⠀⠀⠀⠈⢎⢷⡄⠀⠀⠈⠁⠈⠉⠉⠀⠀⢀⣾⢇⣿⠇
⠀⠀⠀⠀⣠⠋⣠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠳⣖⣦⠀⠀⠀⠈⢯⣿⣦⣄⡀⠀⠀⠀⠀⣠⣴⣿⣷⠋⠈
⠀⠀⠀⢠⠃⣰⠃⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠹⡄⢹⡿⠂⠀⠀⠀⠘⣿⢻⠿⢿⣿⣿⣿⡿⠿⠟⢻⡏
⠀⠀⠀⡞⢀⡏⠀⠀⠘⠲⠤⣀⡀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⣷⣤⡄⠀⠀⠀⠻⠼⠀⠀⠀⠀⠀⠀⠀⢠⠼⠁
⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⣀⣀⣉⠻⣷⡄⠀⠀⣏⣹⠀⠀⠀⢸⠀⣿⣷⡇
⠀⠀⠀⢧⢸⡇⠀⠀⠀⣾⣿⣿⣿⣧⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⡿⠛⠃⠀⠀⠀⣴⢲⠀⠀⠀⠀⠀⠀⠀⠐⢲⡀
⠀⠀⠀⠘⡌⣿⡄⠀⠀⠻⣿⣿⣿⡟⠀⠀⠁⠀⠀⠀⠐⠀⣰⡿⣰⢷⠄⠀⠀⠀⢠⣿⡼⣶⣾⣷⣿⢿⣿⣶⡦⣾⣇
⠀⠀⠀⠀⠙⣜⢿⣄⡀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⡱⠿⠏⠀⠀⠀⢀⡞⢡⠞⠉⠀⠀⠀⠀⠀⠉⠛⢆⠹⡄
⠀⠀⠀⠀⠀⠘⡦⣟⢿⣦⣄⡀⠀⠀⠀⠀⠀⣀⣠⣴⡿⣫⣾⠁⠀⠀⠀⠀⢀⠎⡴⠁⠀⠄⠂⢁⠀⠀⠈⠂⠀⠀⠳⡘⡆
⠀⠀⠀⠀⠀⠀⢻⣿⠗⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢻⣷⡇⠀⠀⠀⠀⠀⠸⢰⠁⠀⠈⠀⠀⠈⡄⠀⠀⠀⠈⠀⠀⢣⢸⣤⡄
⠀⠀⠀⠀⠀⠀⠸⣿⠀⣿⣿⣿⣯⣭⣭⣭⣽⣿⣿⣿⠰⡿⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠐⠻⠃⠐⠐⠀⠂⠀⢸⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠊⠁⠀⠀⠀⠀⠀⠀⠸⡸⣆⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡟⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡻⣦⡀⠉⠂⠀⠀⠀⠐⠀⠀⣠⡾⡵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣶⣤⣄⣀⣀⣤⣴⣾⣿⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣽⣟⣛⣻⡯⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢨⠉⠙⠛⠛⠛⠛⠉⠁⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠀⠀⠀⠀⠀⠀⠀⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀⣤⣤⣄⣀⣤⣤⣤⣀⣠⣖⣦⣄⣠⣤⣤⣀⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⣰⠚⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡹⣯⢽⣦
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⡇⢱⢻⡇
⠀⠀⠀⠀⠀⠀⠙⢦⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣿⣫⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣀⠀⣉⡀⢀⣀⡀⣀⡀⢀⠀⡀⢀⣠⡀⢀⣀⢀⣉⡉⠉⠉⠈⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢿⡼⠀⣷⡀⠸⣤⠀⢿⡄⢸⠟⢿⢸⣗⡇⢸⣂⢸⠷⡏⠀⠀⠀⡏⣿
⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢰⢒⣶⢲⠤⣤⠤⡤⠤⠤⣤⠤⠤⠤⣤⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣷⡿
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠁⠒⢺⠒⠒⢲⠗⠛⠏⡦⠬⠭⠤⡇⢐⣒⣸⣀⣒⣈⡋⠯⢹⠇⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣸⢀⣀⣜⣀⡀⢸⠀⠀⢀⠇⠀⠀⢸⠀⠀⠀⡆⠀⠀⠸⠀⠈⣹⠀⢸⢿⠇
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⡇⠀⠀⡇⠀⠀⡏⠉⠉⢸⠓⠒⠂⡞⠒⠒⢲⠇⠤⠤⡧⠤⢤⡇⠀⢸⣾
⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⡧⢄⣰⣁⣀⣀⠃⠀⠀⡇⠀⠀⢠⠃⠀⠀⢸⠀⠀⢀⠃⠀⠀⡇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢰⠃⠀⣸⠀⠀⡎⠀⠀⡜⠉⠉⢉⠋⠉⠉⡻⠀⠒⠒⠗⠤⠤⢼⠤⠤⢤⠇⢰⣿⠃
⠀⠀⠀⠀⠀⠀⡞⠀⠀⡗⠂⢰⠧⠤⠤⡧⠤⠤⣼⣀⣀⣀⡇⠀⠀⢸⠀⠀⠀⡇⠀⠀⣸⠀⢸⣿
⠀⠀⠀⠀⠀⣸⠁⠀⢸⠀⠀⠸⠀⠀⢰⠀⠀⠀⡇⠀⠀⢸⠉⠉⠉⡝⠉⠁⢸⠓⠒⠲⡇⠀⣿⡏
⠀⠀⠀⠀⢀⡇⠀⢀⡏⠉⠉⡏⠀⠀⡞⠒⠒⢲⠧⠤⠤⡦⠄⣀⣠⣇⣀⠀⡘⠀⠀⢸⠁⢠⣿⡇
⠀⠀⠀⠀⢸⠀⠀⣸⠀⠀⢸⠀⠀⢰⠁⠀⠀⡜⠀⠀⢠⠃⠀⠀⢸⠀⠀⠈⡏⠉⠉⡟⠀⣸⣿
⠀⠀⠀⠀⢿⣄⣀⡈⠉⠉⠛⠒⠒⠚⠒⠒⠒⠧⠤⠤⠼⠤⣄⣀⣌⣀⣀⣸⣀⣀⡰⢃⡤⣿⡏
⠀⠀⠀⠀⠀⠳⢶⣿⣭⣭⣽⣶⣒⣒⣒⣒⣒⣒⣲⣦⣤⣤⣄⣀⣀⣀⣀⣠⣤⡤⠔⠋⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠭⠭⠿⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠶⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⣠⣤⣤⣤⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⢀⡿⠛⢶⣄⠀⣠⣤⠶⠛⠛⠉⠉⠉⠉⠉⠉⠛⠻⠶⣤⣀⠀⣠⠾⠛⢯⡀⠈⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⡴⠋⠀⠀⢀⡹⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢧⡀⠀⠀⠙⢄⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⠀⠀⢀⠔⠁⠀⠀⠀⠀⣀⡠⠄⠐⠒⠒⠒⠒⠶⠤⣤⣀⠀⠀⠀⠀⠙⢦⡀⠀⠀⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡤⠃⠀⠀⠀⡠⠔⣉⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣬⣉⠢⢄⠀⠀⠀⠑⢤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⢀⡴⣫⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡑⢤⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⣰⢋⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡻⣄⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢀⡼⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢦⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡼⣱⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⡌⣧⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⢣⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡸⡆⠀⣿
⠀⠀⠀⠀⠀⠀⢠⡇⠀⡏⣼⣿⣿⣿⡇⠀⣴⠶⢢⡀⠀⣴⠶⢢⡀⡴⠶⢀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⣷⠀⢻⡄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠁⣿⣿⣿⣿⡇⠀⡋⠀⠘⠋⠋⡋⠀⢘⠁⠃⠀⠈⠀⠀⠀⡀⠐⣆⠀⢸⣿⣿⣿⣿⢸⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⣿⣿⣿⣿⡇⠀⢿⣀⡸⠇⠋⢗⣀⡸⠇⢇⣀⠸⠀⠄⠀⠤⣀⠄⠀⢸⣿⣿⣿⣿⢸⡇⣸⠇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⣿⣿⣿⣿⠃⠀⠀⠉⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⠀⢀⣿⣿⣿⣿⢸⠁⣿
⠀⠀⠀⠀⠀⠀⠀⢹⠀⢃⢸⣿⣿⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣿⣿⣿⠇⡈⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⠁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠹⣌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣠⠃⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠘⢧⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⠞⠁⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠉⠳⣍⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣛⡥⠞⠁⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠉⠛⠲⠬⠭⢉⣛⣛⣛⣛⣛⣛⡉⠩⠴⠖⠛⠉⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣉⡉⣷⣿⣿⡟⣹⣭⣥⣤⣤⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡾⠿⠿⠛⠛⠛⠃⢻⣿⣿⠇⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠻⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⣷⣶⣶⣦⣤⣤⣤⣄⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠤⠄⠀⠀⠠⠀⠀⠄⠄⠂⠄⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⢀⠀⠰⠐⠆⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⡶⠿⠿⠿⠿⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⣵⣶⣶⣾⣿⣿⣶⣶⣶⣭⣽⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣻⣭⣭⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣭⣭⣟⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠿⠿⠿⠛⠛⠛⠛⠉⠉⠉⢉⣿⣿⡉⠉⠉⠉⠛⠛⠛⠛⠿⠿⠿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⠤⢄⣀⣀⣀⣀⣀⣀⣈⣻⣟⣁⣀⣀⣀⣀⣀⣀⡠⠤⠤⠖⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡶⠾⠟⠛⠛⠛⠛⠲⠶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠟⠋⠉⠀⢀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠙⢀⡀⣠⠀⠀⢸⡍⢉⣩⠗⠀⠀⠀⢠⡀⠁⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⣴⣿⠏⠁⠀⠀⢸⡇⣿⠀⠀⠘⠓⠛⠛⠓⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠻⣧⡀
⠀⠀⠀⠀⢀⣾⡿⠃⠀⠀⠀⠀⠘⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⣀⣀⡀⢀⡀⠘⢿⡄
⠀⠀⠀⢀⣾⡟⠁⢸⡇⣾⠛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⡿⠀⠀⠀⠈⣿⡀
⠀⠀⠀⣼⡿⠀⠀⠸⠇⠻⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠀⠀⠀⠀⠘⣧
⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢻⡄
⠀⠀⢸⣿⡀⢰⣞⣛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣏⠀⡀⠀⢸⡇
⠀⠀⢸⣿⠁⠠⢯⣽⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⠶⠟⠀⠀⠀⢸⡇
⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⢿⡆⠀⠀⢠⣖⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠘⣧⠀⡀⢾⣭⣭⡷⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢿⡆⠀⠀⠀⠀⠀⠘⠿⢾⡷⠀⠄⠀⠀⣾⠁
⠀⠀⠀⠀⢜⣧⠀⠀⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⠀⣿⡇⠸⣷⠀⢠⣤⣤⡄⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⣠⣿⣷⠄⠀⠀⢈⣛⣛⣷⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠄⠉⠀⠀⠀⠀⢿⣿⣿⡷⠀⠀⠈⠉⠉⠡⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣀⠀⠀⠀⠀⠀⠀⢹⠋⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⢤⣄⣀⣀⣀⣀⣀⡤⠤⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣀⠀⢀⣀⡀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣒⣦⣰⣋⣳⣤⡮⠭⡦⠾⠭⡷⠿⢿⡷⠿⢿⡿⠚⠓⣺⠗⠓⢲⠞⠛⢒⡾⡆
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣏⠩⠞⠀⠀⠚⠀⠀⠚⠁⠀⠉⣀⡀⢉⠀⡀⣨⣄⠀⣤⡀⡤⣄⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⣸⠀⣿⣿⠀⠀⠀⠀⢰⠋⢠⡿⡄⣇⡀⢿⡄⢹⠓⠇⠳⠜⠐⠛⠃⠛⠙⠀⠀⠀⣀⣀⠈⡇
⠀⠀⠀⠀⠀⠀⡏⠀⢻⣿⡇⠀⢀⣀⣀⣩⢤⡤⠤⠤⠤⢤⠒⠒⠒⢲⡒⢒⣚⣻⣉⠉⢽⡭⠭⢽⠭⠭⡇⢹
⠀⠀⠀⠀⠀⣸⠁⠀⠸⣿⣿⠀⠸⡖⠒⠒⠒⠗⠒⠈⠉⢹⣉⣉⣉⣉⣇⣀⡠⢸⡤⠤⠤⡦⠤⠤⡦⠤⢿⠈⡇
⠀⠀⠀⠀⠀⡏⠀⠀⠀⣿⣿⡇⠀⢷⠒⠊⠉⢹⠉⠉⠉⢀⣇⣀⣀⡀⢥⠤⠤⠤⡧⠤⠐⢷⠒⠒⢻⠊⠙⡆⢹
⠀⠀⠀⠀⢸⠃⠀⠀⠀⢸⣿⣿⠀⠸⡖⠒⠈⠉⡏⠉⢀⣀⣹⣀⠠⠤⠼⡤⠤⠄⢲⠒⠒⢺⡂⣈⣙⣏⣉⣱⠈⡇
⠀⠀⠀⠀⡞⠀⠀⠀⠀⠘⣿⣿⡆⠀⢷⠒⠒⠈⢹⠉⣁⣀⡬⡦⠤⠔⠒⢗⠒⠒⠚⡏⠉⠉⣏⢉⣀⣣⣀⠬⡇⢸⡀
⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⢻⣿⣷⠀⢸⡊⠉⠉⢉⣅⣀⣀⣀⢸⠤⠤⠤⢺⠒⠒⠒⢻⠉⣉⣹⣀⡠⠼⠤⠤⠞⠀⣇
⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠘⣿⣿⡄⠀⠏⠉⠉⠁⣣⣀⣀⣠⠤⠦⠴⠖⠚⠓⠋⠉⠉⠉⢀⣀⣀⣠⡤⠤⠤⠴⢶⠛
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢻⣷⣇⠀⠘⠚⠉⠉⠁⠀⢀⣀⣀⣀⡤⠤⠴⠖⠒⠚⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⢘⡇
⠀⠀⢰⠃⣀⣀⠤⠤⠖⠒⠒⠙⣿⡼⠤⠶⠖⠒⠒⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠤⠴⠖⠒⠒⠋⠉⠉
⠀⠀⠈⠙⠓⠶⠤⣄⣀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠤⠴⠒⠒⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠾⠦⠖⠒⠚⠉⠉⠁


⣶⣶⠶⣶⠶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⠀⠀⠉⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠒⠉⠀⠀⠀⢦⠾⠃⠀⠉⠁⠠⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⣴⡀⠀⣀⣀⢀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠻⠋⡏⡏⡏⠍⠋⢀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣤⣤⣤⣤⣤⣤⠤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣂⣀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣟⣚⠓⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠶⠻⠛⠛⠛⠿⠶⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠛⠁⠀⠀⠀⠀⢀⠰⠂⠀⠐⠄⠀⠰⠖⠄⠀⠀⠀⠀⠀⠀⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⣏⣸⡃⠀⠀⠀⢠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠾⠇⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⡀⠀⠂⣶⡄⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢲⡄⠠⠀⡠⠀⠀⠀⢡
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠐⠀⠀⠀⠛⠑⠊⠀⠀⠀⠄⢀⡤⢸⢁⠠⡀⠀⠀⠀⠀⠀⠀⠿⠆⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠈⠀⠀⠀⠀⡠⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠉⠀⠀⠀⣥
⠀⠀⠀⠀⢸⣿⠀⡠⢄⠀⠄⠺⢸⠀⠀⠀⠀⠠⠖⢡⠆⣤⣞⣻⣆⠀⣱⣤⡀⠀⠀⠀⠀⠈⢤⡀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠸⣿⠀⠁⢀⠀⠀⠀⠀⠐⠒⠚⠛⠙⠀⠂⢀⠀⠈⠉⠀⠸⠷⡽⡧⡀⠀⠀⠀⠁⠈⠀⠀⠀⠁⠀⠀⣿
⠀⠀⠀⠀⠀⣿⡇⢰⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠁⠛⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠃⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠹⣿⡄⠆⠀⠠⠀⠀⣼⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠌⣯⠀⡀⠠⠘⠂⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⢻⣷⡀⢂⠀⠤⠀⠈⠀⠀⠀⠤⠄⠀⠀⠀⠰⡆⠀⠀⠀⠀⠤⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠐⡀⠀⠀⠀⠀⠀⢀⡎⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⡈⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠃⠀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠙⠢⣄⡀⠀⠀⠀⠀⠈⠀⠀⣄⠀⠀⠀⡀⠤⠚⠁⣠⡴⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠈⠉⠒⠒⠂⠘⠧⠒⠐⠒⠈⠁⣀⣠⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠶⠴⠴⠤⠤⠴⠶⠶⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠛⠛⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⠋⠛⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⣀⣠⣤⣤⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⠁⠀⠈⣇⠀⠀⠀⡀⠠⠐⠂⢐⠄⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠪⣁⣀⣉⠉⠁⠀⠀⠀⢸⡀⠀⠀⢀⡟⠀⠀⠀⠀⠐⠒⢊⣁⣤⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⣤⣤⣤⣤⣤⣤⡤⠶⠚⠋⣹⠟⠛⠻⢿⡛⠛⠛⠻⢿⣉⠻⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⣠⠞⠁⠀⠀⣠⠞⠁⠀⠀⠀⠀⠉⠳⣄⠀⠀⠈⠳⣌⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢠⡞⠁⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⢀⣙⣎⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣯⡤⢤⠀⢠⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⣿⠀⠁⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠈⣧⣼⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⡁⢀⠀⣀⠀⠀⠀⠘⠇⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠻⣆
⠀⢀⣀⣠⡶⠶⠛⠋⠁⠀⠀⠰⠶⠀⠂⠀⠀⠠⢀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠁⠀⠀⢠⣤⠁⠒⠀⠹⣦
⢀⡾⠉⠉⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠁⠀⠀⠀⠊⠁⠀⣸⡆⠀⠀⣤⠀⡀⠀⠀⠀⠁⡀⠈⠁⠂⢠⡌⠀⠀⠂⠙⢷⣄⡀
⣼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠮⡀⠀⢈⠀⡽⣷⠀⠀⠀⢴⠄⡉⠀⠀⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⣦⣤⣀⡀
⠈⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢹⠀⠈⠀⠂⠰⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠄⠒⠂⠈⠉⠉⠉⠉⠉⠉⠉⢻⡄
⠀⠀⠀⠈⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤⠔⠐⠒⠒⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠤⠒⠊⠉⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⢦⣤⣀⡀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⢀⡠⠔⠂⠉⠀⠀⠀⠀⢢⡀⠀⠀⠀⡠⠃⠀⠀⠀⢀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣶⠟⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠉⠀⠀⢀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣯⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣤⣀⣀⣀⣀⣀⣀⣤⣤⡴⠶⠞⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠖⠛⠛⠛⠛⠛⠛⠻⠶⢶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠋⠁⠀⠀⠀⠀⢶⢲⢺⢲⠂⠀⠀⠀⠀⠀⠈⠙⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⣠⣴⠂⠀⠀⠀⠀⠀⠀⠘⡞⢨⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠉⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠰⠻⣽⡈⢧⠀⠀⠀⠀⠀⠀⠀⣧⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠈⢳⣌⢳⡀⠀⠀⠀⠀⠴⠿⠚⠛⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⣯⡷⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⢀⣾⠋⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢷⡀⠹⣆
⠀⠀⣾⠇⢠⠿⢬⣧⣄⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⢞⡯⠖⠋⠉⠀⠹⣆
⠀⣸⠇⠀⠀⠀⠀⠀⠈⠻⣽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠞⠁⠀⠀⠀⠀⠀⠀⢻⡄
⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠟⠛⠁⠀⠀⠀⠀⠀⠀⢹
⣿⠀⢠⡀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀⣀⣀⣤⠤⠶⠚⠋⠉⠉⠉⠉⠀⠀⢠⣀⣀⣀⣀⣀⣠⡄⢸
⣿⠀⢸⡯⠿⠓⠛⠛⢽⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣓⣒⣐⣒⣒⣺⡄⢸
⣿⡄⠸⠟⠛⠉⠉⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⢸
⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠘⣧⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⢻⡆⠀⠀⣀⡤⢖⡯⣚⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢟⡮⣝⡦⣄⡀⡀⠀⡾⠁
⠀⠀⢳⡀⠘⣵⣪⠵⡋⢥⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⢯⣗⢯⣳⡟⠀⣼⠃
⠀⠀⠈⢷⡀⠘⢗⣩⠴⠋⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠏⠀⣼⠃
⠀⠀⠀⠈⢳⣄⠈⠃⠀⠀⠀⠀⠀⠀⣠⢿⠷⣀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⢰⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣰⢣⢋⢸⠏⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⠀⢻⡳⣄⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⢼⣵⡡⢃⡟⠀⠀⠀⠀⠀⠀⢈⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢧⠈⣳⠶⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠉⠓⠾⠁⠀⠀⠀⠀⠀⠀⣸⢹⠋⣇⠀⠀⠀⠀⠀⠀⠀⠚⠋⢀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢶⣤⣀⡀⠀⠀⠀⠀⠀⢿⠸⣄⣿⠄⠀⠀⠀⢀⣀⣠⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠶⢶⣦⣤⣤⣤⣤⠴⠶⠶⠛⠋⠉⠁
⣿⣿⠟⠟⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠛⠛⠾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⢀⣀⡀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣐⡀⢀⣿⣯⣽⡆⢈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⢻⣿⣿⣿⣿⣿⠇⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣸⡇⡃⠘⣿⣗⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣥⣥⣤⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠇⠤⠭⠿⠧⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠠⠐⠂⠀⠀⠀⠀⠀⠀⠀⠐⢦⣄⡀⠀⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⢀⠔⢈⢠⠀⠀⠀⢀⢸⠀⠀⠀⠀⠀⠙⠻⣦⣄⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡆⠔⠉⠀⠀⠙⣧⠀⠀⠘⠛⠀⠀⠀⠎⠀⠀⠀⠈⠿⣷⣄⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⠋⠀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣢⡤⠀⠻⣿⣿⡌⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠈⠁⠀⠀⠀⢻⣿⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⢤⡔⠋⠀⠀⠀⠀⢀⡀⣀⡀⢸⣿⣿⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣟⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠻⡾⠃⠀⠀⠀⠀⠀⠈⠉⠉⠁⢸⣿⢼⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⣧⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣼⣿⣟⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠸⣟⣆⠀⠾⡫⠋⠀⠀⠀⠀⠂⢰⡇⠀⠠⠀⠀⠀⠙⠻⠿⠆⣰⡿⡿⢃⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⣟⢟⣈⠁⠀⠀⣰⡗⠀⢠⢸⡦⠀⠐⠂⢄⠀⠀⠀⢀⣴⣟⡕⠈⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠎⢿⣷⣿⣷⣄⠘⠃⠀⠀⠀⠀⠀⠀⠠⠂⠈⠁⣠⣼⣿⣫⠞⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢼⣿⣿⣯⣳⣖⠂⠀⠀⢀⣉⣀⣠⣤⣶⠿⣛⣥⠞⢁⡴⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣶⣦⣬⣭⣭⣽⣷⣶⣿⣫⠵⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠿⠛⠻⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡶⠶⠶⠶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣾⡾⠶⣶⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣇⣀⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⠛⠋⠉⠀⠀⠀⢴⣶⡆⠀⠀⠀⠈⠉⣻⠿⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠈⢳⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣰⠏⠀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠁⠀⠀⠀⠀⠙⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⢈⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠛⠶⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⣠⡴⠋⠁⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠖⢳⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠈⠀⠀⠀⢸⣿⣇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⡀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣾⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠇⢿⣿⣷⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠛⠛⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⢀⣿⡿⠀⠘⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣆⢀⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡁⠀⠀⠀⠀⢀⣴⠄⠀⠀⢠⣤⡄⠀⠀⠀⠀⠰⣆⠀⠀⠀⢀⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⡀⠀⣠⠞⠁⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠙⣦⣀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣶⣯⣀⠀⠀⠀⠀⠘⠛⠃⠀⠀⠀⢀⣀⣤⣾⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣷⣶⣶⣶⣶⣶⣶⣾⣿⡿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠂⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠂⠀⠐⠀⠀⠀⠀⠀⢀⣀⣀⣾⣄
⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣻⣧
⠀⠀⠀⠀⠀⠀⢠⣿⣶⣶⣶⣦⣤⣤⣤⣶⣶⣾⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⡀
⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⣿⡿⣽⣿⣏⣽⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⣼⡃⠘⢿⣿⣿⣄
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣅⠚⠙⠓⠑⠚⠻⣿⣿⡡⢽⠿⢙⠽⢛⠟⣻⠃⠈⢸⣿⡇⠁⡀⠈⢿⣿⣿⣆⣠⡄
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣄⣀⣀⣀⣈⣻⣠⣤⣤⣤⣦⣶⠶⣇⡄⢠⣽⣿⣇⡀⢷⣄⡞⣿⣿⣿⣿⣿
⠀⠀⠀⠈⠉⢩⣿⣿⣿⣿⣿⣿⣥⡾⠟⣋⣥⣾⡿⠋⠛⠿⣿⣿⣿⣿⢸⣏⣴⣿⠁⠀⠀⠁⠀⢿⡴⣿⣿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣧⣶⣿⣿⣿⡿⣲⣒⣲⣶⣶⢿⣿⣿⣾⣿⣿⣷⣶⣤⣤⣤⣶⣾⡗⣝⣏⣽⡿⠿⣿⢛⣻⣿⡇⠀⢀⡀
⠀⠀⣠⡄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⢿⠟⣻⣿⡛⡿⢛⣿⠀⠉⣿⣿⣿⣿⣿⢻⣿⣿⣿⣴⣿⣧⡄
⠀⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢹⡇⢽⢣⣿⣿⣧⣿⠸⣿⠀⠀⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣏
⠀⣯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡗⢹⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣇⣟⣿⣿⣿⣿⣿⡤⣿⠆⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⡟⣯
⠀⣷⡶⡟⣿⣿⣿⣿⣿⣿⣿⣿⠀⡇⢸⢸⣿⢾⣿⣿⣿⣿⣿⣿⣿⣿⢸⡏⠛⠋⠉⠉⠉⢩⣅⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣽
⠀⡿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣷⣮⣌⣹⡟⠛⢻⣿⡟⠛⠛⢻⣿⣸⣇⡶⣀⣀⡀⣀⣀⣀⣘⣇⣲⣟⣉⣉⣉⣉⣹⣿⣿⣿⣿⡶⠾⠷
⠀⡗⠒⣾⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣭⣉⣉⣁⢠⣾⣿⣿⡦⠤⠀⠀⠀⢈⣯⠉⠉⠉⠉⠛⠛⠛⢻⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⠶
⠀⠀⢈⡑⡌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠈⢱⡄⠀⠀⠀⠀⠀⠀⠀⠙⠛⠦⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠈⠛⢛⣛⠛⠿⠋⢛⣛⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣀⣀⡒⡉⠙⠂⠈⠉⠉⠋⠉
⠀⠀⠀⠀⠀⠤⠤⠶⠛⠛⠛⠛⠋⠉⠗⠛⠁⡿⠿⣿⠿⠛⠛⠿⠛⠛⠿⠛⠻⠿⠿⠿⠛⠻⠿⢿⡿⠿⣟⡿⣿⡻⠿⠿⣟⠳⠶⠂⠤⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣤⣬⣭⣥⣴⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⠿⠟⠋⠉⠉⠉⠉⠉⠛⠻⢿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣀⣼⣧⣴⣿⣤⣀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⠀⢸⣷⣷⣷⣧⣿⣿⣿⡀⠀⣠⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣾⣏⣉⣻⣿⣿⣿⣟⣥⣿⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⡿⠿⠛⢛⣛⣛⣛⣛⣛⡛⠉⢿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⠿⠛⣉⣥⠶⠞⠛⠋⠉⠉⣉⡉⠉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⣡⡴⠟⢉⡀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⡀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⠁⠀⠀⠀⢠⠐⠁⣀⠀⠙⠿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⢀⣾⣿⡟⢁⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠒⠀⠀⠀⠀⢸⠀⣠⠊⠁⡀⠀⠙⢿⣿⣿⣿⣷⡀
⠀⠀⠀⢀⣾⣿⡟⢀⡾⠁⠰⡄⢁⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⠞⠀⠀⠀⠀⢂⡠⠈⢻⣿⣿⣿⣷
⠀⠀⠀⣾⣿⡿⢁⡾⠁⠀⡐⠀⠀⠇⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⣰⡿⠃⠀⠀⠈⠠⠇⠀⢁⠀⠀⢿⣿⣿⣽⡇
⠀⠀⢠⣿⣿⠇⣸⠃⠀⢰⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠀⠀⠀⠀⠀⠒⠂⠀⠀⠂⠀⠘⣿⣿⣿⣿
⠀⠀⢸⣿⣿⠀⣿⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⡺⠋⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⢸⠀⠀⢿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⠀⣿⠀⠰⠆⠘⠇⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣏⡀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢠⡤⠀⢸⣿⣿⣿⡇
⠀⠀⢸⣿⣿⠀⣿⠀⠀⣇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣿⣟⡁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣾⣿⣿⣿⡇
⠀⠀⠈⣿⣿⡄⢹⡄⠀⠸⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡤⠔⣶⠾⠿⡋⠛⠟⢦⡀⠀⠀⢀⡀⠀⢀⠄⠀⢀⣿⣿⣿⣽⠁
⠀⠀⠀⢻⣿⣷⣌⣷⠀⠀⢁⡀⡘⢦⠀⠀⠀⠀⠀⣼⡁⠀⠀⢉⠀⠀⢈⣦⠀⠀⠈⠑⠄⠈⡇⠀⠄⠀⠀⣼⣿⣿⣯⡏
⠀⠀⠀⠈⢿⣿⣿⣿⣧⡀⠋⠡⡁⠈⠀⠀⠀⡀⢸⠈⠀⠀⠀⣨⠀⠀⠀⠈⣇⣀⠀⠀⠀⠀⢁⠸⠓⢀⣼⣿⣿⢿⡿
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣷⣄⠀⠈⠀⠀⠀⠀⡩⠻⣀⡀⠀⠀⠉⠀⠀⢀⣀⠏⢠⠀⠀⢀⠐⠃⠀⢠⣾⣿⣿⢫⡿⠁
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠃⠀⠙⠄⡀⠀⣀⠀⢀⡨⠉⠁⠈⣀⠐⠀⠀⣀⣴⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠊⡏⠂⠀⠀⠀⠀⠀⠈⣁⣤⣾⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣀⣈⣁⣀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠰⣶⣶⣶⣤⣤⡤⠆⠄⠀⠀⠛⠛⠛⠛⠛⠛⠛⢿⣿⣟⡛⣛⠛⢛⣛⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄
⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣷⣤⠤⠤⠀⢠⠀⠀⠀⠀⠈⠭⢉⣠⣦⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⣿⣿⣿⣾⣾⣾⣶⣶⣶⣶⣾⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣼⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⣰⠟⠉⠀⠀⠀⠀⣸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡀⠀⠀⠀⠈⠙⢷⡀
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠣⣉⡡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣉⡡⠃⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿
⠀⠀⠀⠀⠀⢸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⠖⠶⠲⡆⠀⢠⠖⠶⠖⢦⠀⠀⡄⠲⠖⢦⠀⠀⡴⠲⠒⠲⡄⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⢸⠀⠀⠀⢸⠀⠀⡇⠀⠀⢸⠀⠀⡇⠀⠀⠀⡇⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠃⠀⠘⠓⠒⠒⠛⠀⠀⠓⠒⠒⠚⠀⠀⠛⠒⠒⠚⠁⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⣠⠤⠤⢤⡄⠀⢠⠤⠤⠤⡄⠀⢀⡤⠤⠤⣄⠀⠀⡤⠤⠤⢤⠀⠀⣠⠤⠤⢤⡀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⣇⠀⠀⠀⡇⠀⢸⠀⠀⠀⡇⠀⢸⠀⠀⠀⢸⠀⠀⡇⠀⠀⢸⠀⠀⡇⠀⠀⠀⡇⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠓⠖⠶⠒⠃⠀⠘⠶⠶⠶⠃⠀⠘⠒⠶⠖⠞⠀⠀⠳⠶⠶⠞⠀⠀⠓⠲⠖⠖⠃⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⣀⣀⣀⣀⡀⠀⢀⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⡏⠀⠀⠀⡇⠀⢸⠀⠀⠀⡇⠀⢸⠀⠀⠀⢸⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠘⣧⠀⠷⠤⠤⠤⠇⠀⠸⠤⠤⠤⠇⠀⠸⠤⠤⠤⠼⠀⠀⠧⠤⠤⠼⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠙⢷⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠶⠶⠶⠶⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⠛⠛⡿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠶⢦⡀⠀⠀⠀⠀⣀⣸⣀⣀⣇⣀⠀⠀⠀⠀⢀⡴⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⣀⣿⠶⠖⠛⠋⠉⠉⠉⠉⠉⠉⠙⠛⠲⠶⣿⣀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣤⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⢀⣠⡴⠶⠛⠋⠉⠉⠉⠉⠙⠛⠲⢦⣄⡀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠙⠷⣄⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⠀⠀⠀⠀⣼⠁⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣼⠃⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠙⠳⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠞⠋⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠈⠉⠛⠓⠶⠶⠶⠶⠚⠛⠉⠁⠀⠀⠀⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠲⠶⠶⠶⠶⠶⠶⠖⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠠⠦⣄⣉⣉⣛⣉⣉⣉⣉⠀⠶⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⣌⣷⣼⡿⠿⠟⠙⠋⠉⠉⠉⠉⠿⢿⣿⣦⣄⠉⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣑⣾⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣄⠈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢱⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠙⡆⠀⠀⠀⠀⢠⣶⠾⢿⣷⣶⣶⣶⣤⠀⠀⠀⠀⡀⢃⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣤⡈⠳⡄⠀⢀⣼⡇⠀⢸⣸⣿⣿⣿⣛⢠⡀⣀⠚⢠⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣼⣯⣀⣸⣷⣤⣼⣿⢿⡿⢿⣛⣀⣤⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⡿⠶⠶⠶⠶⠶⠾⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠒⣶⡶⣾⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⢈⣿⣿⣿⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠷⣬⣿⣿⣶⠖⠻⠓⠛⠷⠄⣨⡿⠿⠿⠟⠛⠳⣶⣤⣤⣤⣀⢠⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣀⠤⠘⠛⠁⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠁⠐⠒⠉⠽⢛⡻⢶⣤⣌⡓⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⡋⠁⠊⠁⡀⢠⡀⠢⠈⠉⠒⠀⠄⠀⠠⠤⠠⠤⠔⠒⠋⣉⠤⠖⣀⡤⠘⡻⠶⣹⢿⣶⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡉⠀⠀⢀⡠⣔⠲⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣴⡆⠀⠀⠀⠀⠀⠉⠁⠚⣣⢄⡈⠸⣋⢜⡽⣿⣶⣅⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠑⠋⠀⣠⠶⠓⠉⠀⣀⢶⣄⠀⠀⠀⠀⠀⢀⠀⢠⠀⢠⡄⠀⡀⠀⡀⠀⠀⠀⠀⠀⢀⡉⠙⠫⣦⡉⠺⣿⣽⡽⢿⣷⣄
⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⢀⡨⠂⠀⠁⠀⠀⠉⠆⣈⠀⠠⡄⠘⠂⠈⠀⢀⣀⣈⣁⡀⠀⠀⠁⠘⠃⠰⠆⢀⡘⠃⠀⠀⠈⠻⣷⡌⠻⣿⣷⡽⣿⣧
⠀⠀⠀⠀⣰⢋⠄⠀⠀⡰⠋⠠⠀⠀⠀⠀⠀⢠⡀⠙⠃⣀⡀⠀⠀⠀⠀⠀⢻⠈⣿⠀⠀⠀⠀⠀⠀⠀⢀⠙⠃⢀⠀⠀⠀⠀⠈⠻⣷⡘⢻⢿⣞⣿⣧
⠀⠀⢀⡴⢡⠆⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠻⣿⢧⠀⠀⠀⠀⠀⣞⣦⣿⠀⠀⠀⢠⠀⠀⢠⠟⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠻⣦⢫⢻⡾⣻⣧⡄
⠀⠀⣼⠃⠀⠀⣠⡞⠀⠠⣆⡄⠀⢠⠈⠃⠀⠀⠀⠀⠀⠙⣧⡦⠄⠀⠀⠀⠉⠁⠀⠀⠀⢀⡞⠀⢴⠏⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⣀⠙⢷⡋⠾⣣⢿⣎⡄
⠀⣾⡇⠁⠀⢰⡿⠀⠐⠶⠷⠀⣤⡄⢀⡄⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠰⠆⠘⠋⠀⠈⣿⡜⢩⡞⣿⣤
⢠⣿⠀⠀⢀⠻⡄⠀⠀⠀⠀⢤⡀⠀⠾⠷⢦⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⣀⡴⢊⡽⠆⠀⠀⠂⠀⠀⠀⢸⣷⠋⣿⢹⣿⡆
⢸⡇⠀⠀⡘⢠⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠱⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢙⡿⢂⠀⠀⠀⠀⠀⠀⠀⠻⠞⠉⠀⠀⠀⠀⠒⠂⠀⠀⠀⣿⡞⠛⣿⣿⣧
⣾⠃⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢸⣷⢸⣿⣿⣿
⣿⠀⠀⠀⢿⠀⣄⣸⠏⠉⠉⠙⣶⣶⢶⣶⣶⣶⣦⣤⣼⣯⣁⣀⣀⣀⣀⠀⢀⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡄⠀⠀⠀⠀⠀⠀⣿⡄⣿⣿⣿
⣿⠀⠀⠀⢳⠀⠐⠲⠆⠙⠃⠀⣿⠭⠭⠷⠆⠀⠁⠀⠸⣏⡍⠙⠻⠿⣿⣿⣯⣶⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⣓⣾⡇⠀⠒⠀⣭⠿⠀⣿⡇⢿⣿⣿
⣟⣹⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⣿⡇⣾⣿⣿
⢻⡏⠀⢀⡿⠀⠀⠀⠀⠈⣁⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣿⢷⣼⣿⣿
⢹⡇⡆⠀⢡⡶⠀⠀⠀⠀⣠⡄⠀⣿⣻⡞⣛⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢆⣤⢀⡀⠀⠐⠂⠀⠀⠀⢸⣇⣸⣿⢿⣿
⠈⣿⠀⠀⠈⣰⠆⠀⠀⢠⡀⣠⠄⠈⣧⡜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⣈⣔⡿⠁⠀⠀⠀⠀⠀⢀⣿⣉⣿⡛⣾⡿
⠀⢹⣇⠀⠀⢡⠞⡀⠉⣩⠆⠀⢠⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠸⠷⢀⣛⡦⠀⣼⣏⢻⣞⣿⣿⠃
⠀⠀⢻⣆⠀⡀⠚⡱⠂⠀⠀⠀⠀⢠⡄⠀⠀⠀⢀⣼⠍⣩⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠈⠐⠀⣼⠇⣼⣿⣽⣿⠏
⠀⠀⠀⢻⣦⣉⠄⠰⣫⢆⠀⠀⠀⠀⠰⠆⠀⠀⠻⢮⣰⠋⠀⠀⠀⠀⠀⠀⡦⢠⡀⠀⠀⠀⠀⠀⠘⡷⣀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⢀⣾⢃⣰⣾⣿⣿⠛
⠀⠀⠀⠀⢻⣷⣻⢆⡀⢀⢁⠀⠀⠀⠀⠀⠋⢀⣤⠀⠋⠀⠀⠀⠀⠀⠀⠀⣷⡸⠃⠀⠀⠀⠀⠀⠀⠰⠍⠃⠀⠠⠄⠈⠀⠀⠀⢀⣴⡿⢡⣿⣟⣿⣿⠃
⠀⠀⠀⠀⠀⠹⣷⣾⢦⡄⠲⡝⢦⡀⠀⢸⡅⡠⠀⠀⠆⢀⡀⠀⠀⠀⠀⠀⠷⠥⠶⠀⠀⠀⠀⠀⠀⢀⡀⠸⠆⢀⠀⠀⠀⢀⣤⡾⢋⢔⣵⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠘⢻⣷⣽⣦⡈⠀⣙⠔⣈⡐⠁⠀⠀⠀⠈⠁⠀⠿⠀⢀⡄⠀⣤⠀⢀⠀⠀⡀⠐⠆⠀⠁⠀⠶⣬⠀⢀⣴⠿⠋⠔⣵⣿⣿⢟⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣽⣦⡠⠂⢈⠟⢢⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣁⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⢏⠉⣢⣴⣿⣿⢿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣮⣕⡣⣎⡳⢮⡽⠻⣶⠶⣀⣤⣀⠀⠀⠈⠉⠓⠀⠀⣀⣠⣤⣴⡶⢿⠛⢏⡡⣜⣶⣿⣯⣾⠛⠕⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠩⣿⣿⣿⣣⡶⣍⡐⠚⠋⠥⠿⠟⠛⠛⠛⠛⠛⠛⠛⠶⢄⣉⣓⣦⣽⣾⣻⣿⣿⡿⠯⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠻⠟⢿⣿⣷⣿⣿⣶⣶⡾⣿⣿⣿⣭⠷⠶⠿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣛⣩⣵⡶⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠴⠖⠒⠚⣊⠉⣻⣏⣛⡓⠒⠒⠢⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠒⢉⠡⠀⠀⠈⠉⠉⠀⠀⣤⠄⣠⠤⣄⠈⠉⠁⠒⠢⢌⣉⠒⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢊⡩⠓⣨⡄⢀⣄⠀⠀⠀⠀⠀⠀⣿⠀⠉⣡⠟⠁⠀⠀⠀⠀⠀⠀⠉⠀⠾⡛⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⡡⠐⠁⠀⠀⢹⡇⠈⣿⠀⠀⠀⠀⠀⠀⠿⠆⠞⠷⡦⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠑⢄⠑⢦⡀
⠀⠀⠀⠀⠀⠀⣠⠞⡠⠊⠀⠀⠀⠀⠀⣸⣇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠢⡙⢦
⠀⠀⠀⠀⢀⡞⢡⠞⠁⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⠀⠀⠀⢠⣿⡴⣷⡦⢠⡖⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢤⡀⠁⠸⣦
⠀⠀⢠⠏⡼⠁⢸⡇⣿⡁⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⡼⠃⠀⠘⠛⢧
⠀⢠⠏⡼⠁⠀⢼⡇⠸⣧⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⣦⡴⠀⠀⠠⠈⣧
⠀⡞⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠘⡆
⢸⠃⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢻
⣾⢠⠃⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢸
⡏⢸⠠⡞⠁⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣤⠀⠘
⡟⢻⠀⣝⠛⣻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠐⢳⣄⠀⠶
⣷⢸⠀⠙⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠥⠼⠋⢰
⢹⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢰
⠘⡇⢣⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣸
⠀⢱⡈⡆⠀⠰⣿⡀⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⠀⠀⡰⢠⠇
⠀⠀⢷⠈⡀⢠⣿⠉⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠥⣿⠤⡆⠰⢁⡞
⠀⠀⠈⣷⡶⡄⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⣰⣧⡞
⠀⠀⠀⠈⠳⡈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢡⠏
⠀⠀⠀⠀⠀⠙⢆⠱⣄⠀⠀⠀⠀⣠⣤⣄⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠀⠀⠀⣠⢊⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠱⢌⠓⣄⠀⠀⠈⠁⢨⡏⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⢦⡀⠀⠀⠀⣠⠞⡡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡑⠦⡀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⣼⠟⣀⠴⢊⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢾⣟⠧⢄⣀⠀⠀⠀⠀⠀⠀⢿⡃⢸⢷⡄⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⣾⡥⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⢬⣉⡒⠲⠤⠤⢀⣈⢳⣺⣟⣁⣀⡀⠤⠤⠖⢒⣉⡥⠖⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣺⡯⠭⠭⣗⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⢋⣠⣤⣤⣤⣤⠙⡞⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⢸⠀⠀⠀⠀⢸⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡻⣿⡟⠛⢻⣻⣞⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠲⣄⠀⠀⠀⣀⣠⠴⠖⠛⠛⠛⠛⠛⠛⠳⢤⣄⡀⠀⠀⠀⣠⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⢀⡼⣅⡴⣚⠅⣀⡤⠶⠒⠚⢛⠛⠒⠲⠦⣤⣀⠉⠳⣄⣘⢧⡀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠴⢯⡴⡫⣊⠴⠋⠱⡄⠀⠀⠀⡘⢀⠀⠀⠀⢠⠍⠳⣤⡀⠹⣄⣱⣤⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢌⡴⢃⠀⠀⠀⣲⣲⠀⠀⠓⠓⠀⠀⢰⢀⡄⠀⠈⠳⣄⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢌⡞⠐⠢⢠⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⢀⡠⠠⢖⠘⣆⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠐⣼⠀⠂⠀⠘⠉⠁⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠈⠙⠀⠀⠂⢹⡄⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⣀⠀⣀⢤⠀⠀⠀⠀⠀⠀⡠⣴⠋⠀⠀⠀⠀⠀⡠⡄⣀⡀⡇⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠉⠁⠈⠉⠀⠀⠀⠀⠀⣠⠟⠃⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⡇⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢻⠀⠀⠀⣀⣠⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⢠⡠⠀⠀⠀⢸⠃⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠈⢧⠠⠄⠈⠙⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠑⠦⢠⠏⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠈⢳⡌⠀⠀⠀⠇⠇⠀⠀⣄⡤⠀⠀⠇⠙⠀⠀⠂⣰⠋⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠙⠶⣄⡰⠃⠀⠀⠀⢨⠉⠀⠀⠀⠈⣂⡴⠚⠁⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡈⠙⠓⠦⢤⣤⣬⣤⣤⠤⠖⠛⠩⣐⡵⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠤⣤⣤⣀⣠⣤⡤⠴⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣶⣶⣟⣢⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠈⣏⡛⠻⠿⣿⣷⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠛⠃⠀⠀⠀⠈⠉⠛⠿⢿⣿⣷⣶⣤⣄⣠⠤⢤⡀
⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠘⡶⠦⠀⣀⠀⠀⠀⠉⠛⠻⣿⣿⣟⣷⣷⣤⣀
⠀⠀⠀⠀⠀⢀⠏⢀⣤⣀⠀⠀⠀⠐⠒⠃⢠⠾⣽⠀⣰⣆⠀⡀⠀⢹⡦⠈⠉⠛⠻⢿⣿⣆
⠀⠀⠀⠀⠀⡞⠀⡜⠙⢺⠯⣷⣲⠤⣄⡀⠀⠀⠈⠀⠃⠘⡾⠁⠀⠀⠀⠀⠀⠀⠀⣼⠏⢸
⠀⠀⠀⠀⢰⠃⢰⠉⢑⠗⠤⣠⡏⠙⠳⣼⣉⣖⢢⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠈⣇
⠀⠀⠀⢀⡏⢀⣏⡉⡾⠤⢄⣜⠈⠙⢲⠧⢄⣈⠟⠚⠦⣽⣓⡶⢤⣀⡀⠀⠀⢰⣿⠁⠀⠀⢹
⠀⠀⠀⡼⠀⡼⣄⣸⠓⠲⣼⣉⠉⢒⠧⢤⣀⡎⠉⠒⣴⣅⡈⠉⡞⠺⢭⡇⢀⣿⠏⠀⠀⠀⠈⡇
⠀⠀⢰⠃⢰⠧⢄⣏⠙⢲⠧⢄⣉⡟⠢⢤⣜⠉⠑⢲⢧⣀⠈⡝⠓⠤⡼⠀⣾⡟⠀⠀⠀⠀⠀⢹
⠀⠀⣞⠀⠘⠒⠼⣁⣉⠟⠢⢄⣼⠉⠒⡾⢥⣉⢓⠾⢤⣀⣹⠓⠦⣤⠃⢸⣿⠃⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠻⢽⣓⠦⢄⣀⠉⠑⠲⠤⣇⠉⢲⠧⢤⣀⡝⠓⠢⢤⣏⠑⢲⡎⢠⣿⣏⣀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠉⠓⠺⢽⣒⠦⣤⣀⠉⠛⠢⢄⣸⠉⠒⢢⠯⣀⠉⡞⠀⣾⣿⡀⠈⠉⠒⠦⢄⣀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠯⢽⣳⣦⣤⣀⠉⠓⠺⠤⣀⣹⠁⣼⣿⡇⠈⠑⠒⢤⣀⣠⠤⠭⠷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠫⢽⣓⠦⣤⣀⠀⢠⣿⡿⠀⠀⣠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠺⢽⣛⣻⣧⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⢤⣶⣤⣤⣼⣦⣤⣤⣤⣤
⠀⠀⠁⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⡆⠀⠀⠀⠀⢀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⣹⠀⣀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠁⠀⠀⠿⠶⠶⠶⠤⠶⠶⠶⠶⠶⠶⠶⠶⠿
⠈⢅⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⠀⠀⡄
⠀⠀⠑⠢⠤⠤⠤⠆⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⠉⢉⣀⠀⠀⠀⠀⠀⠀⢀⡴⢿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⠤⠀⢀⡀⠀⠀⠀⠀⣀⣈⣀⣼⠁⠀⠀⠀⠀⢀⡤⠒⠉⢸⡀⠈⠙⢆
⠀⠀⠀⠀⠀⣇⢠⢄⡠⠀⠘⠀⠀⠈⠦⡄⠀⠀⠈⡇⠀⠀⠉⠀⠀⠀⠀⠀⠜⠁⠀⠀⠘⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠉⢠⠋⢰⣄⠀⢀⡀⠀⠀⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠁⠀⠀⠘⠁⠉⠁⠀⣿
⠀⠀⠀⠀⠀⠀⢺⠐⠀⠈⠓⠋⠀⠐⠈⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠨⣀⠀⠀⠀⠀⢀⣀⣔⠇
⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠉⠈⠀⢀⠀⠀⠀⠀⠀⠈⠚⠶⢾⢿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠑⠀⠀⣀⡀⠀⠀⠀⠀⠀⣆⢀⡄⠀⠀⠀⠀⠀⠀⠀⠑⠀⠄
⢠⣠⣀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡜⠃⠈⠉⠳⡄⠀⠀⢠⣿⠋⠀⠀⠀⣀⣤⣬⣤⣾⣜⣂⣐⣒⣢⣀
⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⣧⣀⠀⠀⠀⠘⣆⢀⣾⡏⠀⠀⠀⠀⠈⠥⢤⣤⣤⣤⣤⣤⣤⣬⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⢹⣾⠋⠀⠀⠀⠀⠉⡉⠡⠉⠉⠁⠀⠉⠉⠙⠉
⠀⠀⠀⠀⣀⠄⢂⠄⠀⠀⠀⠀⠀⠀⢴⡈⣿⣷⣄⣠⠾⠁⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠂
⠀⠀⡀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠰⠊⠀⡠⠉⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠁⠈⠁
⠀⢈⠀⠀⠀⠈⠀⡂⠀⠀⠀⠀⡜⠀⠀⢴⠀⠐⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢀⣀⣂⣀⠂
⠀⠂⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡇⠀⠀⢦⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢸⠀⢃
⢠⠆⣶⣔⡐⠚⠒⠐⡆⠀⠀⠀⠁⠌⣀⣤⠶⠗⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣶⠂⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣿⣗⠀⠻⢧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠿⠁⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣵⣶⣾⣶⠤⠦⠤⣤⣤⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣣⣿⣿⠿⠟⣉⣉⣉⠉⠛⢒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢭⣿⣿⣿⣿⣿⡋⠀⠀⠀⢦⡛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠁⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠰⢿⣟⣛⣫⣭⣭⣭⣥⠤⠤⣄⣘⣃⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣳⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⡀⠒⠂⠈⢽⣷⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡿⢿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣦⣤⣄⣐⣿⣿⣌⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⣟⣽⣶⣿⡿⠋⠉⠈⠻⣿⣿⣿⣿⣦⡄⠄⠈⢹⣿⣿⣿⣟⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⣾⣿⣿⣿⣿⣧⡀⠀⠀⢀⣿⣿⣿⣿⣿⠶⠀⢰⣿⣿⠿⣟⡥⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠗⣴⣶⣿⣿⣿⣿⣿⣿⣛⣭⣿⠿⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣴⠏⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡠⢤⣾⠿⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⢉⣤⣀⣠⡾⠟⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣏⣁⣠⣤⠔⠾⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠲⠾⣿⣿⠟⢫⡉⣁⢀⣠⡞
⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠀⢀⣿⣿⠿⠋⢙⠋⠉⢁
⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⣸⣿⣷⠾⠿⠛⠟⠉⢁
⠀⠀⠀⡤⠚⠟⠀⠀⢀⣤⣾⣿⣿⠿⣿⣾⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠘⢿⢿⣿⣽⣥⣿⡿⠛⢻⡗
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠟⠋⠀⠀⠀⣷⠆
⠀⠀⠀⠀⠀⣠⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⢠⣯⠁
⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡫⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣝⣦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢋⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣀⡴⠟⡿⠀⠈⠉⠉⠉⠛⠛⠓⠲⠶⠶⠶⠦⢤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⢠⡏⠀⢠⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢸⣧⣾⣿⡷⠶⠤⠭⠭⠭⣍⣉⣙⣒⣒⣒⣒⣒⣒⣒⠲⣶⣤⣤⣿⠀⠀⠀⠀⣀⣤⡴⠶⠚⠛⠋⢷⡀
⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⡤⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠶⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣼⠿⣷⡀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⣿⠀⠀⢿⠀⠀⠀⠀⢀⣤⣶⠿⢻⡿⠀⠀⠀⠉⠀⠹⣷⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠘⣇⠀⠀⠀⠀⠁⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⣼⣿⠾⠛⠛⢷⣄⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠙⠷⣄
⠀⠀⠀⠀⠸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢿⡆⠀⠀⠀⠈⠻⡧⠀⠀⠀⠀⠀⠈⠛⠶⠶⡶
⠀⠀⠀⠀⠀⣿⢹⡟⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⡀⠀⠀⠀⣿⣿⣷⢏⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⣤⣤⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⣿⡟⣿⣹⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⣿⣧⢻⡜⣿⣽⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⠉
⠀⠀⠀⠀⠀⢹⣼⢹⢱⢇⢧⣷⣬⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣄⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠚⠋⠁
⠀⠀⠀⠀⠀⠘⣇⣎⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠙⢷⣄⣠⣤⠶⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠹⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣴⣦⣤⣦⣴⣴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⣿⣿⣿⠿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⠀⠀⠀⣀⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠀⠀⢰⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠇⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠠⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⣴⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⢀⣀⡀⠀⠉⠙⠻⣿⣿⣿⣿⣷⣄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣦⣀⠀⠙⢿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⡄⠀⠻⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢰⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠏⠀⣠⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠛⠁⢀⣴⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠈⠛⠋⠉⠁⢀⣠⣶⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣷⣶⣶⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠈⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠶⠶⠿⠶⠶⠶⣶⣤⣄⡀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⢀⣴⠟⠛⠓⠒⠒⠒⠒⠒⠒⠒⠒⠤⠤⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠒⠒⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠐⣿⠖⠒⠺⢿⣓⠒⠒⠶⠶⠶⠤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⣀⡀⠀⢹⣧
⠀⠀⠀⠀⠙⠿⣦⣄⡀⠈⠉⠑⠲⠤⢄⣀⠀⠀⠀⠉⠉⠉⠛⠓⠲⠶⢤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢽⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⣦⣤⣀⡀⠀⠉⠙⠒⠲⠤⠤⣄⣀⡀⠀⠀⣾⠀⣿⠙⠓⠶⠦⣤⣀⡀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠷⣶⣤⣤⣄⣀⡀⠀⠉⣽⠟⠋⠉⠛⠲⣤⣤⣤⣀⣈⣉⣛⣲⣤⣀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⣿⠁⠀⠀⠀⠀⠀⠘⣧⣀⠀⠀⠀⠀⠁⠀⠈⢙⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⡿⠛⠛⠛⠛⠿⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉
⠀⡀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣄
⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄
⠀⠀⠀⢀⣾⣿⠟⠀⠀⠀⠠⣦⠀⢠⡄⠀⣴⠀⠀⣦⠀⢠⡆⠀⢰⡄⠀⣤⠀⠠⣦⠀⠀⠀⠘⢿⣿⣆
⠀⠀⢀⣾⣿⠏⠀⠀⠀⣾⣾⣿⣶⣾⣷⣶⣿⣶⣶⣿⣶⣾⣷⣶⣿⣷⣷⣿⣶⣾⣿⣾⡆⠀⠀⠈⢿⣿⣆
⠀⠀⣼⣿⡏⠀⠀⠀⠀⣿⣿⣿⣿⠛⠛⢻⡟⠛⠛⡟⠛⠛⡟⠛⠛⣿⠛⠛⢻⠛⠛⢻⡇⠀⠀⠀⠈⣿⣿⡄
⠀⢰⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣄⣀⣠⣇⣀⣠⣧⣀⣠⣧⣀⣀⣧⣀⣀⣼⣀⣀⣼⡇⠀⠀⠀⠀⢸⣿⣷
⠀⢸⣿⡏⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⢸⡇⠀⠀⡇⠀⠀⡇⠀⠀⣿⠀⠀⢹⠀⠀⢸⡇⠀⠀⠀⠀⠈⣿⣿
⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⠖⠒⢺⠖⠒⢺⡗⠒⠲⡗⠒⠒⡷⠒⠒⣿⠒⠒⢾⠒⠒⢾⡇⠀⠀⠀⠀⠀⣿⣿
⠀⢸⣿⣧⠀⠀⠀⠀⠀⣿⣀⣀⣸⣀⣀⣸⣇⣀⣀⣇⣀⣀⣇⣀⣀⣿⣀⣀⣸⣀⣀⣸⡇⠀⠀⠀⠀⢠⣿⣿
⠀⠘⣿⣿⡀⠀⠀⠀⠀⣿⠉⠉⢹⠉⠉⢉⡏⠉⠉⡏⠉⠉⡏⠉⠉⣏⠉⠉⢹⠉⠉⢹⡇⠀⠀⠀⠀⣸⣿⡟
⠀⠀⢻⣿⣧⠀⠀⠀⠀⣿⠤⠤⢼⡦⠤⢼⡧⠤⢤⡧⠤⠤⣧⣤⣤⣿⣤⣤⣾⣤⣤⣼⡇⠀⠀⠀⢠⣿⣿⠃
⠀⠀⠀⢿⣿⣧⠀⠀⠀⣿⠀⠀⢸⠀⠀⢸⡇⠀⠀⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢠⣿⣿⠇
⠀⠀⠀⠈⢻⣿⣷⡀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⣰⣿⣿⠋
⠀⠀⠀⠀⠀⠙⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣷⣦⣤⣀⣀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣠⠶⠚⠛⠳⢦⡀⠀⢀⡴⠖⠛⠛⠲⣤⠀⠀⣠⠴⠚⠛⠓⢦⣄⠀⠀⣤⠖⠛⠛⠲⣦⡀⠀⢀⡴⠚⠛⠛⠶⣄⠀⠀⣠⠖⠛⠛⠳⢦⡀
⣼⠃⠀⠀⠄⠀⠀⢹⣆⡞⠀⠀⠀⠀⠀⠈⣷⣰⠋⠀⠀⠀⠀⠀⠹⣆⡾⠁⠀⠀⠀⠀⠈⢳⣰⡏⠀⠀⠀⠀⠀⠘⣇⣼⠁⠀⠀⠀⠀⠀⢻
⢿⠀⠀⠀⠁⠀⠀⢸⡟⣇⠀⠀⠀⠀⠀⠀⣿⢻⡀⠀⠀⠀⠀⠀⢠⡟⣧⠀⠀⠀⠀⠀⠀⣸⢻⡆⠀⠀⠈⠀⠀⢀⡿⣿⠀⠀⠀⠁⠀⠀⢸
⠈⠷⣄⣀⣂⣀⣴⠟⠀⠙⢦⣀⣐⣀⣠⡾⠃⠈⠳⣤⣀⣀⣀⣤⠟⠀⠘⢧⣄⣀⣀⣡⡴⠋⠀⠻⣦⣀⣀⣀⣠⠞⠁⠈⢷⣄⣀⣂⣀⡴⠏
⠀⢀⣨⠽⠿⢭⣄⠀⠀⠀⣀⡭⠿⠯⣥⡀⠀⠀⠀⣠⠭⠿⢭⣄⠀⠀⠀⢀⣬⠽⠯⣥⣀⠀⠀⠀⣠⡭⠿⠯⣅⡀⠀⠀⢀⣨⠽⠿⢭⣄
⢠⠏⠀⠀⠀⠀⠈⢷⡀⡼⠋⠀⠀⠀⠀⠙⣦⢠⡞⠁⠀⠀⠀⠈⢳⡄⣴⠋⠀⠀⠀⠀⠙⣧⢀⡞⠁⠀⠀⠀⠈⠻⡆⣰⠏⠀⠀⠀⠀⠈⢷
⣿⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣿⢾⠀⠀⠀⠀⠀⠀⢀⡷⣇⠀⠀⠀⠀⠀⠀⢸⢿⡅⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠄⠀⠀⢸
⠘⣦⡀⠀⠀⠀⣀⡾⠁⢳⣄⠀⠠⠀⠀⣰⠏⠘⢧⡀⠀⠀⠀⢀⡼⠃⠻⣄⠀⠀⠀⠀⣠⠟⠈⢷⡀⠀⠀⠀⢀⣼⠃⠹⣆⡀⠀⠅⠀⣠⡾
⠀⠈⢙⣳⣶⣛⠉⠀⠀⠀⠉⣛⣶⣞⡛⠁⠀⠀⠀⢙⣓⣶⣛⡋⠀⠀⠀⠈⢛⣳⣞⣛⠁⠀⠀⠀⠙⣛⣶⣞⡋⠁⠀⠀⠈⢙⣳⣶⣛⠉
⢀⡶⠋⠁⠄⠉⠛⣦⠀⣠⠞⠉⠀⠈⠉⢳⡄⢀⡴⠋⠁⠀⠉⠙⢦⡀⢠⠞⠉⠁⠀⠉⠳⣄⠀⣴⠋⠉⠀⠈⠙⢶⡀⢠⡞⠋⠁⠀⠉⠻⣦
⣾⠀⠀⠀⠀⠀⠀⢸⣧⡏⠀⠀⠀⠀⠀⠀⣿⣼⠁⠀⠀⠀⠀⠀⠘⣧⡟⠀⠀⠀⠀⠀⠀⢹⣼⡇⠀⠀⠀⠀⠀⠈⣷⣿⠀⠀⠀⠀⠀⠀⢸
⢻⡄⠀⠀⠂⠀⠀⣼⠋⢧⡀⠀⠐⠀⠀⢀⡿⠹⣆⠀⠀⠀⠀⠀⣰⠏⢷⡀⠀⠀⠀⡀⢀⡾⠙⣇⠀⠀⠀⢀⠀⣠⡏⢻⡄⠀⠀⠀⠀⠀⣼
⠀⠙⠶⢤⣤⠴⠞⠁⠀⠈⠻⠦⣤⡤⠶⠋⠀⠀⠙⠳⢦⣤⡴⠞⠋⠀⠀⠛⠶⣤⣤⠴⠛⠁⠀⠈⠳⢦⣤⡤⠾⠋⠀⠀⠙⠶⢤⣤⠴⠞⠁
⠀⣠⠖⠛⡛⠛⢦⡄⠀⢀⡴⠚⠛⠛⠳⣦⡀⠀⣠⠶⠛⠛⠛⠶⣄⠀⢀⡴⠞⠛⠛⠳⢦⡀⠀⢠⡴⠛⠛⠛⠲⣄⠀⠀⣠⠞⠛⠛⠛⢦⡄
⣼⠁⠀⠀⠀⠀⠀⢹⣆⡟⠀⠀⠀⠀⠀⠈⣷⣰⠃⠀⠀⠀⠀⠀⠹⣆⡾⠁⠀⠀⠀⠀⠀⢻⣰⡏⠀⠀⠀⠀⠀⠘⣇⣼⠁⠀⠀⠀⠀⠀⢹
⢿⡀⠀⠀⠁⠀⠀⢸⠟⣇⠀⠀⠀⠀⠀⠀⣿⢻⡄⠀⠀⠀⠀⠀⢠⡟⣧⠀⠀⠀⠀⠀⠀⣸⢻⡆⠀⠀⠀⠀⠀⢀⡟⢿⠀⠀⠀⠁⠀⠀⣸
⠈⠳⣤⣀⣀⣀⡴⠏⠀⠙⢦⣄⣀⣀⣠⠾⠃⠈⠻⣦⣀⣀⣀⣴⠟⠀⠘⢷⣄⣀⣀⣡⡼⠋⠀⠹⢦⣀⣀⣈⣤⠞⠁⠈⠷⣄⣀⣀⣠⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠐⢈⣵⣶⣶⡶⢒⡶⠦⣴⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡶⣞⡻⠯⢩⠩⠍⠭⠉⠛⠛⠒⠶⠤⣄⡀⠀⠀⠀⢻⣶⣬⡿⢼⣷⣇⣼⡇⢺⠉⣽⣶⣌⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⣿⡿⠿⠛⠛⠋⠉⠉⠉⠉⠉⠉⢉⠋⠓⠒⠦⢄⣀⠉⠛⠢⣄⣀⠿⡛⢦⡀⡇⠈⠻⣿⣿⣾⣡⡿⢹⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢪⣿⡷⠛⠁⠀⠀⠀⢀⡀⠐⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠉⠒⢄⡈⠙⢆⢨⣾⣷⣿⣾⣿⢋⣛⣻⣟⡃⣀⡀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠫⢱⡿⠋⠀⠀⠀⠀⠳⣦⢄⠙⢶⣄⡀⠀⠀⠈⠁⠀⠀⠀⠄⠴⠖⠀⠀⠀⠙⢆⢸⣿⣿⣿⠛⠻⠿⠿⠯⣿⣿⣯⠥⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⢇⣿⠁⠀⠀⠦⢤⠤⠤⠀⠀⠀⠀⠹⢯⣿⣄⣀⡀⣀⣴⢶⡾⠋⠀⠀⣀⡀⠀⠀⢹⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⢸⡀⣇⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠨⣿⣿⣿⡿⣯⠁⠈⠁⠀⠉⠁⠀⠀⠀⠀⠈⣿⡇⣿⣏⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠘⣇⠹⡄⠀⢀⡖⠒⠀⠀⠐⠂⠀⡲⠌⠁⠐⠶⠖⠛⠁⠀⠀⠀⠀⠂⠐⠲⡆⠀⠀⢀⡿⢰⣿⠹⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢤⢱⠀⢀⠙⣦⡀⠀⠄⣀⠀⠀⠀⢠⡤⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡐⢦⣀⠀⠀⠀⠀⣠⠞⣱⡿⢧⠘⡌⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡆⢣⡘⢀⢈⠛⢶⣤⣀⠑⠢⢀⣰⠀⠀⠀⢀⡜⠀⠀⠐⣦⠒⡆⠀⠀⠐⢋⡁⠤⠒⣋⣥⡾⠋⡅⢈⡜⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡙⢆⠱⣄⠈⠀⠀⠈⠛⠿⣶⣤⣈⡁⠒⠒⠠⠧⠤⠤⠤⠮⠦⠛⠒⠂⣉⣡⣤⡶⠟⠋⠀⠠⠞⣠⠎⣰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⠳⢬⡓⢤⣀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠶⠶⢶⣶⣶⣶⠶⠾⠿⠛⠋⠉⠰⢀⡴⠓⢈⡴⢚⣡⠞⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣄⡙⠲⢬⣕⡲⠤⣀⡀⠀⠀⠀⠀⠄⠰⢠⣖⠀⣤⡔⡀⠺⠢⠘⠶⢃⣠⣴⣚⣽⡾⠋⣡⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣀⠀⠉⠙⠷⢿⣭⣍⣙⡓⠒⢶⡶⠶⢶⡶⠶⢶⡶⣶⣶⣾⣿⣿⠿⠟⣋⠁⣠⣴⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣤⣀⠀⠀⠈⠉⠙⠋⠙⠛⠛⠛⠛⠛⠛⠛⠛⢋⣉⣡⡴⢖⣫⣵⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠶⣶⣭⣭⣭⣄⣀⣀⣒⣒⣂⣛⣹⣭⣭⣶⣾⡿⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉⠈⠁





⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⡟⣉⣿⠿⠿⠿⠿⠻⠟⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣀⣴⡟⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠋⠙⢳⡀
⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⣰⡏⠀⢸⣿⣸⣆⠘⣿⡇⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⡸⠃
⠀⠀⠀⠀⠀⢸⣿⣏⠀⠀⠹⣿⣤⣈⣿⣿⣟⡸⠟⠋⠉⢹⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣷⣾⡁
⠀⠀⠀⠀⠀⠈⠻⠿⣷⡶⠶⠶⣻⣿⠙⠛⣋⡶⠀⡀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣿⠿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⣰⡾⢻⡟⣥⠀⠀⠹⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣶⣶⠀⢰⡅
⠀⠀⠀⠀⠀⠀⢀⣀⡴⠋⢀⣾⣿⠃⣾⡟⢿⣷⡀⠀⣠⣵⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠈⠛⠤⡀⢿⣿⣇⣸⣿⠃⢸⣟⣵⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣇⠈⣧⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠿⣿⣿⠀⢘⣾⣿⠋⠙⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣛⡛⠛⣋⣉⣉⡉⠙⠛⣋⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠛⠛⠓⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⠹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⢀⠀⠀⣼⡆⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢠⣟⡀⣠⣾⣧⢀⣿⡇⢀⣶⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⢀⡙⠻⠷⣯⣿⣿⠿⢷⣿⣿⣷⣶⣶⠶
⠀⠀⠀⠀⠀⠀⢸⡇⠠⣤⣤⣾⡿⢿⡾⢿⣿⣿⡿⠂⣠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡅
⠀⠀⠀⠀⠀⠀⠈⣿⣇⠻⠟⠋⣴⡿⢿⡄⠈⠙⣠⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣿⣷⣶⣦⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⢸⣧⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠸⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢙⣻⣿⣿⣿⣿⣿⣋⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣲⣾⣿⡂⠀⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠦⣤⣤⣽⣯⣭⠯⠼⠿⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢤⣿⣿⢿⣿⣷⣶⣿⣿⣿⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⡿⠿⢿⣤⣤⣤⣤⣶⣶⠾⠿⢿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢠⡴⠒⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⢀⡤⠶⠶⠶⢤⡞⠋⠉⣉⣙⣯⡤⠴⠒⢻⠏⢧
⠀⠀⠀⠀⠀⢀⡴⠛⠉⠉⠉⣹⣿⣠⣤⣤⣶⠾⣿⠛⠋⠉⢁⡿⠀⠀⠰⡿⠀⠈⢧
⠀⠀⠀⢀⣠⠼⠷⢒⣚⣛⣭⠭⠞⣟⠉⠁⠀⣀⡟⠀⠀⠀⠘⠃⠀⠀⢀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⣸⢠⠖⢻⠟⢻⡅⠀⠀⣴⣏⠀⠀⠀⠛⠁⠀⢀⣤⡀⠀⣷⢦⣸⣆⠀⠀⠀⠈⢷⡀
⠀⠀⠀⡏⢸⠀⢸⠀⠀⡇⠀⠀⠉⠁⠀⠀⠴⠶⣿⠋⢸⣯⡿⣄⠹⡆⠉⠛⠀⠀⢀⣀⡈⢳⡀
⠀⠀⢰⡇⢸⡇⠸⡇⠀⢻⠀⠀⠀⠀⠀⠀⠀⢀⣹⠀⠸⠇⠀⠉⢀⣀⣤⡴⠒⣻⡩⠄⢹⡄⠻⡄
⠀⠀⢸⡇⠸⡇⠀⣧⠀⠘⡇⠀⠀⠀⠀⠀⠀⠉⠁⢀⣠⡤⢶⠚⣙⣅⠄⢳⣈⠥⠿⣎⠉⠙⣆⠙⣆
⠀⠀⢸⡇⠀⡇⠀⢸⡀⠀⢹⡀⠀⠀⣀⡤⠶⡖⢋⡉⢧⠒⣊⣧⠴⠚⣏⠁⠙⣆⣀⠼⢶⡊⠉⢧⡈⢧⡀
⠀⠀⢸⡇⠀⣇⠀⠀⣇⠀⠀⢷⠀⠈⢇⠰⠒⣱⣬⠴⠚⢏⠁⠈⢧⣀⠼⢶⡊⠉⠣⡀⢀⣱⣤⠒⠛⣄⠙⢦
⠀⠀⢸⡇⠀⢻⠀⠀⢹⡄⠀⠈⢧⠀⠘⣞⠉⠁⠹⡄⣀⡬⢶⠚⠉⠳⡀⠀⣱⣤⠖⠛⢏⠀⠈⢣⣀⡬⠷⡀⠳⣄
⠀⠀⠘⡇⠀⢸⡄⠀⠀⢷⠀⠀⠈⢧⠀⠘⢦⠴⠚⠹⡅⠀⠈⢣⣠⠤⠛⢏⠁⠈⢢⣀⡨⠷⣞⠉⠙⢦⡀⢙⣦⡈⠳⣄
⠀⠀⠀⡇⠀⠀⣇⠀⠀⠈⣧⠀⠀⠈⢧⡀⠈⢧⡀⣀⡼⢶⠚⠉⠙⣄⠀⣈⡷⡔⠋⠙⢦⡀⠈⣳⣤⠔⠛⢯⡀⠙⣦⠈⠑⢄
⠀⠀⠀⣿⠀⠀⢹⠀⠀⠀⠘⣆⠀⠀⠈⢳⡀⠀⠻⡄⠀⠈⢣⣠⠴⠚⠻⡁⠀⠈⢲⣄⠤⠛⢯⡁⠈⢲⣤⠴⠛⠋⠁⠀⢀⣠⠗
⠀⠀⠀⢸⠀⠀⠘⡇⠀⠀⠀⠘⣆⠀⠀⠀⠹⣄⠀⠙⢶⠊⠉⠙⢦⡀⣀⡼⠶⡚⠉⠈⠳⣄⡠⠽⠚⠉⠀⠀⢀⣠⠴⠚⠉
⠀⠀⠀⠘⡇⠀⠀⢳⠀⠀⠀⠀⠘⣆⠀⠀⠀⠘⢦⡀⠀⠳⣄⡤⠖⠛⢧⡀⠀⣈⡷⠖⠋⠁⠀⠀⠀⢀⡤⠖⠉
⠀⠀⠀⠀⣷⠀⠀⠘⣇⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠙⣦⠀⠈⠑⢦⣠⠴⠚⠉⠁⠀⠀⠀⢀⣠⠴⠊⠁
⠀⠀⠀⠀⢸⡄⠀⠀⢹⡄⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉
⠀⠀⠀⠀⠀⣧⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⢀⣹⢦⣠⠴⠚⠋⠁
⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⣣⠀⠀⠀⣀⡤⠴⠚⠳⣤⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠳⠒⠛⠉⠉⠳⠚⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣷⡼⠂
⠀⠀⠀⠀⠀⠀⠀⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣶⣒⣛⠷⢄⡀
⠀⠀⠀⠀⠀⠀⠸⣿⠿⣦⣄⠂⠄⠴⡤⢄⠀⠀⠀⠀⠀⢀⣾⠋⡀⠠⠀⠄⠉⠑⡍
⠀⠀⠀⠀⠀⠀⢰⡇⣰⣯⢁⢛⣤⣤⣌⢘⣷⠀⠀⠀⠀⣾⡇⢀⠉⢲⡄⠀⣀⡤⠈
⠀⠀⠀⠀⠀⠀⣸⡃⣧⣽⡀⠨⠤⢽⠈⢧⠄⢌⡀⠀⠀⣿⡇⠰⠀⠀⠛⠉⠁⠐⠀⠄
⠀⠀⠀⠀⠀⠀⢹⡇⢻⣧⣀⡠⠀⡠⠤⠞⡀⣼⡇⠀⠀⠘⣷⣄⠘⠠⠄⠠⠈⠀⠈⠀⠀⠀⠀⣀⢀⠀⠀⠀⣼⣙⠢⡀
⠀⠀⠀⠀⠀⢠⡞⠀⠀⠻⣿⣿⣾⡥⣬⣤⣾⡷⠃⠀⠀⠀⠈⠙⠿⢶⣶⣶⠶⠏⠀⠀⣠⠖⠉⢡⠀⡤⠁⠀⣿⠿⣶⡃
⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠈⠙⠛⠿⠿⠟⠋⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢣⣌⠃⠀⡄⠀⠘⠃⢉⢧⠙⣧
⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠖⠛⠋⠉⠉⠙⠛⣦⠀⠀⠀⢀⣄⠀⠀⣯⢈⡁⠀⠀⠷⠄⣀⣈⣈⢸⠀⢸⡆
⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⢀⣠⠴⠋⠉⠀⠀⠀⠀⠀⢀⣀⣤⠟⠀⠀⠀⠸⣿⣿⣄⣿⣎⢡⡀⠀⠀⠀⢠⣄⡹⡾⢀⡞⠁⢀⡴⢦
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢉⣰⠖⠛⠛⠛⠛⠛⠓⠛⠉⠀⠀⠀⠀⠀⠀⠀⠘⢌⠻⣯⣻⣶⣄⣀⣈⣛⣀⣼⠟⠁⢼⣁⣀⡜⠁⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⢐⡋⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢽⣻⣿⣍⠉⠛⠉⠉⠀⠀⠀⠀⠉⠉⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠟⠃⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠶⠚⠒⠲⠦⠤⠦⠤⠤⠴⠶⠖⠖⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠿⣤⣀⣠⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⣀⣼⣍⢉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠉⠉⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣉⣝⣫⣍⣉⣏⣹⣟⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢞⣩⠵⠖⠲⠮⣍⡳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⡱⠋⠀⠀⠀⠀⠀⠀⠙⢎⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢰⠃⢀⣠⣤⣤⣤⣤⣄⡀⠘⡆⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢸⡄⢸⠀⠀⠀⠀⠀⠀⡇⢀⡇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠳⣸⢤⣄⣤⣠⣤⡠⢇⠞⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠲⣄⠀⠀⠀⠀⠈⠳⢌⣻⡇⠀⠀⢸⣟⣡⠞⠁⠀⠀⠀⠀⣠⠖⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⢀⣼⠀⠀⠀⠀⣀⣠⡤⠽⠷⠶⠶⠾⠯⢤⣄⣀⠀⠀⠀⠀⣧⡀⠀⠈⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⡴⠋⠈⣳⡴⠚⣉⣡⠤⠖⠒⠒⠛⠛⠒⠒⠲⠤⣌⣉⠓⠦⣞⠁⠙⢦⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢈⡶⠊⣡⠔⠋⢁⣠⠤⠖⠒⠚⢛⡛⠓⠒⠲⠤⣄⡈⠙⠢⣌⠑⢶⡁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢋⡴⠋⢀⡤⠚⠉⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠉⠓⢤⡀⠑⢦⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣠⠎⢀⡴⢫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡝⢦⡀⠱⣄⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣰⠃⢠⠏⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠋⠀⠀⠹⡄⠘⣆⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢰⠃⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠸⡄⠘⡆⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡏⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢹⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⡟⢸⠃⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣒⣲⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠘⡇⢻
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⢸⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⣿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⡇⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢷⠸⡆⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠛⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢰⠇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢧⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⡼⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⣆⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣶⣶⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⣰⠃⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠘⣆⠈⢧⡀⢀⡴⠀⠀⠀⠀⠀⠳⣄⠈⠁⣠⠞⠀⠀⠀⠀⠀⢦⡀⢀⡼⠁⣰⠃⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡈⠳⡀⠙⢮⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⡵⠋⢀⡞⢁⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⠢⣄⠉⠳⢤⣀⡀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⡤⠞⠉⣠⠔⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣌⡙⠦⣄⣀⠉⠛⠒⠲⠶⠶⠖⠒⠛⠉⣀⣠⠴⢋⣡⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣌⣉⡛⠒⠒⠒⠒⠒⠒⢛⣉⣡⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⣠⡶⠶⠲⠶⣦⡀⠀⠀⠀⣠⡴⠶⠛⠶⢦⣄⠀⠀⠀⢀⣤⠶⠞⠳⠶⣤⡀⠀⠀⠀⣠⡶⠶⠓⠶⣦⡀
⠀⢠⡾⠁⠀⠀⠀⠀⠀⠹⣆⠀⣼⠋⠀⠀⠀⠀⠀⠙⣷⠀⢠⡟⠁⠀⠀⠀⠀⠈⢻⡄⢀⡾⠁⠀⠀⠀⠀⠀⠹⣦
⠀⢸⡇⠀⠀⠀⠖⠁⠀⠀⣿⢰⡏⠀⠀⠀⠰⠒⠀⠀⢸⡇⣿⠀⠀⠀⠠⠤⠄⠀⠀⣿⢸⡇⠀⠀⠀⣤⡀⠀⠀⣿
⠀⠘⣧⡀⠀⠀⠀⠀⠀⣠⡟⠀⢿⡀⠀⠀⠀⠀⠀⢀⡾⠁⠹⣇⠀⠀⠀⠀⠀⠀⣰⠇⠘⣧⡀⠀⠀⠀⠁⠀⣠⡟
⠀⠀⠈⠻⢦⣤⣤⣤⠾⠋⠀⠀⠀⠛⢶⣤⣤⣤⡴⠟⠁⠀⠀⠙⠳⣦⣤⣤⣴⠞⠋⠀⠀⠈⠻⢦⣤⣤⣤⠾⠋
⠀⠀⠀⠀⣀⣠⣤⣀⡀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⣀⣠⣤⣄⡀
⠀⠀⣰⠟⠉⠁⠀⠉⠙⢷⡀⠀⢠⡾⠋⠁⠀⠈⠙⢳⣄⠀⢀⣴⠟⠉⠀⠀⠉⠻⣦⡀⠀⣰⠟⠉⠁⠀⠉⠙⢷⡄
⠀⢸⡏⠐⠀⠀⡀⠀⠀⠈⣷⢀⡟⠀⠀⠀⠀⠀⠀⠀⢹⡆⣼⠃⠀⠀⠀⠀⠀⠀⠘⣧⢰⡏⠀⠀⠀⡀⠀⠀⠈⣿
⠀⢸⡇⠀⠀⠀⡧⠀⠀⠀⣿⠈⣧⠀⠀⠀⡟⠀⠀⠀⣸⠇⢻⡄⠀⠐⠚⠁⠀⠀⢀⡟⢸⡇⠀⠈⠉⡁⠀⠀⠀⣿
⠀⠀⠻⣦⣀⠀⠀⢀⣠⡾⠃⠀⠙⢧⣄⠀⠀⠀⣀⣴⠏⠀⠈⠳⣄⡀⠀⠀⢀⣠⠞⠁⠀⠻⣦⣀⠀⠀⢀⣠⡾⠃
⠀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉
⠀⠀⢀⣤⠶⠞⠛⠶⢦⣄⠀⠀⠀⣠⡴⠞⠛⠳⢶⣄⠀⠀⠀⢀⣴⠶⠛⠛⠶⣦⡀⠀⠀⢀⣤⠶⠟⠛⠶⢦⣄
⠀⢠⡾⠁⠀⠀⠀⠀⠀⠹⣆⠀⣼⠋⠀⠀⠀⠀⠀⠘⢷⡀⢰⡟⠁⠀⢀⠀⠀⠈⢻⡆⢠⡾⠁⠀⠀⢀⠀⠀⠹⣧
⠀⢸⡇⠀⠐⠲⠆⠀⠀⠀⣿⠰⡏⠀⠀⠈⠢⠀⠀⠀⢸⡇⣿⠀⠀⠀⠘⠆⠀⠀⠀⣿⢸⡇⠀⠀⠀⠏⠀⠀⠀⣿
⠀⠘⣧⡀⠀⠀⠀⠀⠀⣠⡟⠀⢿⡄⠀⠀⠀⠀⠀⢀⡾⠁⠸⣇⠀⠀⠀⠀⠀⠀⣸⠇⠘⣧⡀⠀⠀⠂⠀⠀⣠⡟
⠀⠀⠈⠻⢶⣤⣤⣴⠾⠋⠀⠀⠀⠙⠷⣤⣤⣤⠶⠛⠁⠀⠀⠈⠳⢦⣤⣤⡴⠞⠁⠀⠀⠈⠻⢶⣤⣤⣴⠾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⢀⣀⠀⠀⠀⠀⡴⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠺⢍⠀⠀⡄⠀⣀⡈⠃⠀⢀⢿⣦⡆⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢇⣀⠙⠓⠀⠉⠀⠛⠀⣤⡀⡩⡏⠻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣾⠃⠼⠟⠀⠀⠀⣼⠀⠀⠀⠉⠁⢑⢽⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⢄⠐⣿⡰⣶⠂⠀⠀⠀⠟⠦⣀⡠⠈⠉⢹⢸⡇⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⢿⣧⡱⣿⣧⠁⢔⠀⠀⠀⠀⠀⠈⠉⠺⠗⡌⣸⠀⠀⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⢿⣷⣜⢿⣷⣍⠀⢴⠀⣤⣤⠐⠿⣢⠞⣹⠃⠀⡶⠋⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠻⣿⣦⣻⠷⣵⣢⡤⣭⣍⣐⣬⡴⠛⠁⢀⡿⠁⠀⠀⣴⠏⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣬⡿⣿⣦⠀⠉⠙⠛⠋⠉⠁⠀⠀⠀⠈⣷⣦⣤⡾⠁⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠻⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⢠⣤⠿⠝⠛⠛⠺⢶⣦⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠋
⠀⠀⠀⢠⣿⠁⠀⠀⣖⠛⠓⢦⡀⠉⠉⠙⠓⠿⠿⠷⠧⠶⠶⠶⢶⡶⣶⠶⠽⠟⠛⠋⠁
⠀⠀⠀⠀⠻⠷⣾⣿⠿⣷⣀⣼⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢦⡀⠀⠀⢀⡴⠶⢦⡀⠀⠀⠀⣠⡤⣄⠀⠀⠀⢀⣤⠤⣄⠀⠀⠀⢀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣾⣷⣶⠶⠿⠶⠶⣿⠶⠶⠾⠷⠶⠶⢾⠿⠶⠾⠷⠶⠶⣿⠷⠶⢾⣷⣶⣶⣿⣥⣤⣽⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠘⢷⠄⠀⠀⠀⠀⠹⠦⠀⠀⠀⠀⠀⠘⢷⠄⠀⠀⠀⠀⠙⢶⠀⠀⠀⠀⠀⠳⣤⠀⠀⠉⢹⡿⣷
⠀⠀⠀⠀⠀⠀⠀⢸⣧⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠤⠤⠤⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣸⡇⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⣄⢠⠤⠤⠤⡄⡤⠤⠤⢤⢀⠤⠤⠤⢄⡠⠤⠤⠤⣀⠤⠤⠤⡄⠀⢸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⡿⢤⠀⠀⢀⡇⣇⠀⠀⢸⠠⡀⠀⠀⡸⢇⠀⠀⢀⢿⡀⠀⠀⡧⠀⢸⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⡎⠉⠀⠐⣴⠉⠉⠉⡇⠘⠉⠉⠙⡆⡎⠉⠉⢹⢠⠋⠉⠉⢱⡖⠉⠉⠙⣶⠋⠉⠉⡇⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠧⠤⠤⠤⠛⠤⠤⠤⠇⠰⠤⠤⠤⠃⠣⠤⠤⠼⠀⠦⠤⠤⠜⠣⠤⠤⠤⠛⠤⠤⠤⠇⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⡏⠀⠀⠈⣾⠉⠉⠀⡇⠈⠉⠉⠈⠃⡁⠈⠉⢹⢰⠁⠉⠉⢱⡏⠉⠉⠈⣾⠉⠉⠉⡇⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⡵⠶⠶⣖⡹⠶⠶⢶⢃⠴⠶⠶⡔⢁⠧⠴⠶⡞⣨⠦⠶⢶⠊⡱⠶⠶⡔⡹⠦⠶⢴⠃⠀⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⢸⡀⠀⠀⣿⡇⠀⠀⢸⢸⠀⠀⠀⣸⢠⠀⠀⠀⡇⣇⠀⠀⢰⢸⠀⠀⠀⡯⡇⠀⠀⠸⠀⢀⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⣼⡟⠀⢠⠊⠙⠋⡋⡔⠛⠛⢻⢥⠒⠛⠛⢫⡔⠒⠛⠛⡯⠔⠒⠛⢳⠁⠀⠉⠉⠉⠀⠉⠉⠉⠁⠀⣼⢹⣿⣿
⠀⠀⠀⠀⢠⣼⠏⠀⠀⠳⠤⠤⠤⠃⠧⠤⠄⠼⠸⠤⠀⢀⠜⠅⠀⣀⡠⠇⠄⣀⣀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢸⣿⣿
⠀⠀⠀⠀⠈⠉⠛⠛⢳⡶⠲⠶⠶⠤⢤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣇⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⣉⣉⣉⣉⣉⣉⣀⣠⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣛⣿⣿⣭⣭⣭⣭⣭⣭⣽⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣀⣀⣀⠀⢀⣤⣤⣄⠀⣠⠤⠤⣄⣠⠤⠤⣄⢠⠶⠶⢦⡀⢠⠖⠛⠲⣄⣰⠚⣛⣳⣄⣞⣋⣙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⣉⣉⣙⣦⣾⡥⠤⢼⡷⠿⠶⠶⣾⠷⠛⢒⣚⡟⠛⠛⣛⡟⠋⠉⣩⡿⠋⠉⠉⢉⣽⠋⠉⠉⢩⡟⠉⠉⢉⣽⠋⣧
⠀⠀⠀⠀⠀⠀⣠⣴⡟⣿⡉⢡⡴⠃⠀⠀⠰⠟⠀⠀⠀⠛⠃⠀⠀⠘⠁⠀⠀⠀⠉⠀⠀⠀⣈⣀⡀⠀⣤⡀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⢀⡏⠸⣧⣿⣇⠀⠀⠀⠀⠀⠀⣠⠴⠆⢀⣶⡄⢰⡆⠀⢸⣯⠅⠀⣿⢦⣹⠀⣯⢈⡷⢰⡧⢿⠀⣷⠾⣇⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⢸⠇⠀⣿⣾⣿⠀⠀⠀⠀⠀⠀⢿⣀⡄⢸⠛⠷⠈⠧⠤⠘⠓⠒⠀⠛⠀⠙⠀⠙⠋⠁⠈⠀⠈⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⡀⢸⡆
⠀⠀⠀⠀⠀⡿⠀⠀⢹⣿⡟⡇⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⠤⠤⠤⠴⠶⡶⠖⠒⠒⠛⠛⣿⠛⠛⢉⣉⣹⣉⣉⣉⣭⣯⠤⠤⠤⢽⠤⠤⠼⡇⠀⣷
⠀⠀⠀⠀⢰⠇⠀⠀⠘⣿⣷⢻⠀⠀⢸⣍⣡⣤⡤⠤⠼⡦⠤⠴⠶⠒⠒⢻⠒⠒⠒⠒⠛⢻⠉⠉⠉⠉⠉⡇⠀⠀⠀⣸⣀⡀⣀⣘⣆⣀⣀⣻⠀⢸⡄
⠀⠀⠀⠀⡿⠀⠀⠀⠀⢿⣿⡿⡇⠀⠀⣧⠀⣀⣀⣀⣀⣷⣀⣤⣤⠤⠤⠼⡧⠤⠶⠒⠒⠚⡗⠒⠛⠋⠋⢻⠉⠉⠉⠉⡏⠉⠉⠉⣿⣉⣁⣘⡆⠀⣧
⠀⠀⠀⢸⠇⠀⠀⠀⠀⢸⣿⣿⢿⠀⠀⢸⡍⠉⠁⠀⠀⠸⡆⠀⠀⠀⣀⣀⣷⣀⣀⣠⡤⠤⢿⠤⠴⠶⠖⠺⡖⠒⠒⠛⢻⠉⠉⠉⠹⡍⠁⠀⢻⠀⢸⡄
⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⣿⣿⡿⡇⠀⠀⣷⠴⠒⠒⠒⠚⢿⠉⠉⠉⠉⠉⠸⡀⠀⠀⠀⢀⣸⣄⣀⣠⣤⠤⣧⠤⠤⠴⠾⡖⠒⠒⠚⢿⠉⠉⠙⣇⠀⣷
⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢹⣿⣧⣷⠀⠀⢹⣀⣀⣀⣀⣠⢼⡤⠴⠒⠒⠒⠛⣟⠉⠉⠉⠉⠀⣇⣀⣀⣀⣀⣸⣤⠤⠤⠤⢷⠒⠒⠒⢻⡖⠛⠋⢻⡀⠸⡆
⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠸⣿⡿⣾⡆⠀⠈⣏⠉⠀⠀⢀⣀⣧⣀⣠⠤⠤⠶⠺⡖⠚⠉⠉⠉⢹⡉⠀⠀⠀⠈⣇⠀⠀⣀⣸⣀⣠⣤⠤⣧⠴⠶⠞⣇⠀⢷
⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⣇⣧⠀⠀⢹⡛⠉⠉⠉⠁⢹⠀⠀⠀⠀⢀⣀⣧⣀⣤⠤⠤⠼⠷⠲⠒⠒⠚⢻⡋⠉⠁⢸⣇⣀⣀⣠⣽⣤⣤⣤⠿⠄⢸
⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢸⡄⠀⠈⡷⠶⠶⠖⠒⠚⡏⠉⠉⠉⠉⠀⢹⡀⠀⣀⣀⣀⠶⠤⠴⠶⠶⠾⠓⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⣀⣀⣀⣤
⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡎⣇⠀⠀⢻⠀⢀⣀⣀⣤⡽⠤⠴⠶⠒⠒⠛⠉⠉⠉⠀⠁⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⠶⠶⠶⠚⠛⠛⠋⠉⠉⠉⣧
⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⢻⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⡤⠤⠶⠖⠒⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⢸⠁⠀⠀⠀⠀⢀⣀⣀⣤⠤⠴⠖⢿⣿⡼⣇⣀⣀⣤⣤⡤⠤⠶⠶⠒⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡤⠤⠶⠖⠚⠛⠉
⣿⣤⣶⠒⠛⠉⠉⠁⠀⠀⠀⠀⠀⠸⡟⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⠤⠶⠖⠒⠛⠋⠉⠉
⠀⠀⠉⠙⠓⠲⠦⣤⣀⣀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⠤⠶⠖⠚⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⠤⣼⣧⡤⠤⠶⠖⠚⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣸⡇⡏⢹⢸⡇⡏⢹⢸⣇⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⢹⣇⣧⣼⣸⣇⣧⣼⣸⡏⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣷⡄⠀⠀⠀⢉⣉⣩⣿⣿⣍⣉⡉⠀⠀⠀⢠⣾⣿⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠻⣿⣤⣶⣾⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣷⣦⣤⣿⠟⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⠟⠛⠉⠁⠀⠀⢀⡀⠀⠀⠈⠉⠛⠻⢿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠋⠀⣀⠀⠀⢹⡄⠀⢸⡇⠀⢠⡇⠀⠀⣀⠀⠙⠻⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁⢀⠀⠀⠘⢦⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⡴⠃⠀⠀⡀⠈⢿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠟⠀⠀⠈⠳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠰⠞⠁⠀⠀⠻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⡟⠀⠐⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⣠⠴⠂⠀⢻⣿⣷
⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠈⠉⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠁⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢀⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⢀⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⡀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⠀⠐⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠂⠀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⣼⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣷⣄⠀⠀⠀⣠⠏⠀⢀⡄⠀⢀⡀⠀⢠⡀⠀⠹⣄⠀⠀⠀⣠⣾⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣷⣄⡀⠁⠀⠀⠼⠁⠀⢸⡇⠀⠈⠧⠀⠀⠈⢀⣠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠁⠀⠀⡀⢀⣀⠀⠀⠉⠉⠓⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣋⠀⡀⠀⠀⠀⠀⠀⠈⠿⠠⠯⠀⠀⠀⠀⠀⠀⢀⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠻⠈⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⣠⠏⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⡀⠈⢧
⠀⠀⠀⠀⢠⠇⠸⠗⣯⠇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢨⣟⠀⠈⢧
⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⣾⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢸⡄
⠀⠀⠀⣿⠀⠈⠿⠃⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣀⡤⠤⠾⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠇⠀⢸⡇
⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠿⠉⠉⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⢷⠀⠀⠀⣀⠀⡠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡀⢀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠈⢧⠀⠠⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠇⠀⣰⠏
⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⣀⣀⠊⠀⠀⠀⠀⠀⠲⡷⠂⠀⠀⠀⠀⠈⢂⣀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠨⠽⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⢤⣤⣄⣀⣀⣀⣤⣤⠴⠶⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⠛⠋⠉⠉⠉⠉⠛⠛⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⣀⣤⣥⣶⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣴⣇⡀⣤⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠟⠛⢛⣿⣿⣿⠿⠃⠲⠶⠶⠆⠀⠈⠛⢿⣿⡛⠛⢿⣿⣿⣥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣶⣿⡿⠛⠉⠀⠀⣀⣀⣄⣀⣀⣀⣀⠀⠀⠈⠑⢲⣾⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠋⠁⠘⣷⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣞⠁⠉⠛⠿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⣿⣿⣿⠿⠿⠻⠛⠋⠛⠻⠻⠻⠿⣿⠿⣿⣷⣦⡀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⠿⠛⢡⠀⡀⠀⠀⡃⠀⠃⠀⠀⠀⡄⠉⠀⠉⠻⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠟⠁⠀⠀⢸⠀⡇⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡻⠇⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠇⠁⠀⠀⠇⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠶⠀⠀⠀⠀⠀⠀⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡇⠠⠀⠆⡄⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡷⠛⠛⠉⠉⠀⠀⠀⠀⠀⠆⠰⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣇⠀⡀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠄⠀⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀⠀⠆⠀⠀⠀⢰⡏⡀⠀⠀⠀⠀⠈⠀⠀⠀⣠⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⢀⣠⣾⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠟⠻⣿⣷⣦⣤⣄⣀⣀⣀⣀⣀⣀⣤⣴⣾⡿⠿⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⠿⠿⠿⠛⠛⠉⠁⠀⠀⠀⠙⠆





⣿⣿⣿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣴⣄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⣒⣈⣉⣉⣠⣄⣀⣀⣈⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⡿⠟⠛⠋⠉⠉⡁⢀⡀⢀⠉⠉⠉⠓⠒⠤⣄⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠟⠋⠁⢠⠀⠲⠀⠃⠀⠃⠘⠃⠘⠀⠸⠀⠴⠀⡄⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡿⠋⠀⢄⠘⢇⠀⠀⡀⠀⠀⠀⢸⠀⠀⠌⠀⠀⠀⠀⠀⠁⡸⠃⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⣀⠘⠦⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠰⠃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠏⠀⢄⡈⠃⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠁⡠⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⠶⠄⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⠶⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⠓⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠒⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡟⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢈⣉⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⣉⡁⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⢈⣉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣉⡁⠠⣟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢸⡇⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧⠀⢀⡤⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡛⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⣼⠧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀⠀⠤⠄⢠⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠤⠀⣰⣿⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠀⢰⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡀⠀⠊⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠓⠀⣰⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡄⠀⠁⢠⠆⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠒⡄⠈⣠⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣽⣶⣄⡀⠀⠋⢠⡆⠀⠀⠀⠀⠀⠀⠀⡎⠢⠀⠀⠀⠀⠀⠀⠀⢰⡀⠑⠀⣠⣶⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⣄⡈⠀⠘⠀⠖⠀⡆⠀⡄⢠⡄⢠⠀⢠⠀⠲⠀⠃⠀⣠⣴⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣶⣦⣄⣀⣀⡀⠁⠈⠁⠈⣀⣀⣀⣤⣴⣾⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉



⣿⣿⡿⠿⣿⡿⢿⣿⡿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣶⣾⣶⣾⣴⣿⣷⣿⣴⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠛⠛⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣉⣉⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⣻⡆⠀⠀⣠⣴⡶⠟⠛⠛⠉⠉⠉⠉⠛⠛⠻⢶⣦⣄⠀⠀⢰⣟⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠐⢿⣅⣠⣾⠿⣷⣴⠟⠋⢁⣠⣴⡶⠿⠟⢿⡟⠻⠿⢶⣦⣄⡈⠙⠻⣦⣾⠿⣷⣄⣨⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⣾⠟⠁⣠⡾⠿⣿⡀⠀⠀⠀⠘⠃⠀⠀⠀⢀⣿⠿⢷⣄⠈⠻⣷⡟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⣠⡾⠋⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⢷⣄⠘⢿⣄
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⣰⡿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⢠⣼⢿⣆⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠃⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠘⣿
⠀⠀⠀⠀⠀⠀⢸⣿⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⣿⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡿⠷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣅⣨⣿⠀⠀⠀⠀⠀⠀⠀⠀⠾⢿⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠸⣿⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢿⡆⠘⣿⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣿⠃⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠘⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠃⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠈⢿⣦⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣴⡿⠁⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠙⠻⣶⣿⣁⠀⠀⠀⢰⡆⠀⠀⠀⢈⣿⣶⠟⠋⣀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⠉⠛⠻⠷⢶⣾⣷⡶⠾⠟⠛⠉⣀⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⣦⣤⣤⣤⣤⣤⣤⣴⡶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢰⣇⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢺⠄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⠼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠞⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠒⠂⠈⠑⠀⠀⠀⠢⠀⠉⠙⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⢰⠰⡇
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠐⢸⡇
⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠘⠀⠀⠈⠁⠀⠀⠸⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⡁⢸⡇
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⢄⠀⠀⠀⢀⠀⠀⠠⢀⠀⠀⠀⡀⠀⠀⠄⠁⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠁⠀⠀⠈⠁⢸⡁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⢀⠀⠀⡂⣀⠀⠀⢂⠀⠀⠐⢠⠀⣀⡐⣀⠀⠀⢆⠀⠀⠀⢀⡀⢸⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠴⢀⠀⠀⠂⣀⢀⣐⡨⠤⡀⢠⠄⠀⠀⠤⡄⠀⠠⢌⠀⠀⠀⠤⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠠⠀⠀⠀⠁⠀⠀⠀⡄⢈⢁⠴⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⢰⡇
⠀⠀⠀⠀⠀⠀⢀⠄⠀⠐⢀⠀⠀⠒⡀⠀⠀⢊⡀⠀⣀⣚⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⡀⢸⡇
⠀⠀⠀⠀⠀⠰⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⢈⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⢸⡇
⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⠶⠶⠤⣤⣀⡀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠀⠀⠀⠈⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠈⠉⠳⢦⣤⢤⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⡴⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠛⢦⣀⡀⠀⠀⠀⠀⠀⢀⣸⣧⣼⣅⣀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⣀⡤⢖⡿⠛⠉⠀⠀⠀⠈⠙⠲⣤⣀⠀⠀⠀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠖⠋⠁⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⠉⠙⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠛⠒⠦⢤⣄⣀⣀⣀⠀⠀⠀⣀⣀⣀⣠⡤⠴⠛⠛⠲⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠲⠶⣤⢤⣤⣤⣤⣤⣤⣤⣤⡤⠤⠤⠶⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠀⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⢀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⠛⢿⠛⡟⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠉⠉⣀⣀⠉⠉⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁⠈⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠛⠲⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢁⣀⠤⠤⠐⠒⠒⠒⠂⠀⠀⠀⠀⠐⠒⠂⠤⠤⣀⡈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠒⠒⣂⣉⣉⣉⣉⠀⠀⠀⠀⣀⣉⣉⣉⣐⠒⠒⠠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⢀⣴⠛⠒⠀⠒⠀⠠⠄⠀⠤⠤⠀⠤⠤⠤⠤⠀⠤⠄⠠⠤⠤⠄⠠⠤⠄⠀⠒⠒⠒⠛⠀⡀
⠀⠀⣀⠘⠋⠀⠈⠉⠀⠉⠁⠈⠁⠀⠀⠂⠀⠒⠀⠒⠒⠀⠒⠂⠐⠒⠒⠀⠀⠉⠉⠀⠉⠉⠉⠁⠀⠙⠃⣀
⠀⣾⠓⠦⠤⠤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⠤⠤⠴⠚⣷
⠀⠙⠲⠦⣤⣄⣀⣀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⣀⣀⣠⣤⠴⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣂⠭⠉⠉⠩⡲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⢸⡐⣲⣙⣹⣗⣼⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠿⣉⡙⣉⡭⠷⢽⠿⣆⣀⠀⠀⠀⣀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⣥⠀⠀⠈⠛⣿⣉⣷⣯⡿⠷⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠚⠻⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⢓⣬⣿⡐⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠄⣂⠈⠩⢭⠁⣒⠀⠀⠈⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢔⡠⠂⠁⠀⠀⠀⣎⠁⠀⡌⠰⢅⠢⡀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⢢⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠗⢄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠄⠀⠌⠃⠀⠀⠁⠀⠀⡀⠴⠞⠋⠈⠁⠠⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠁⣄⡀⠠⠤⠤⠤⠴⣾⠛⠐⠀⠀⠀⠀⢘⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠄⢃⠘⠀⠀⠀⠀⣀⠀⠙⣇⠀⠀⠀⠀⢀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡈⡌⡇⢸⡇⠀⠀⠀⠀⠀⠘⢷⠀⠀⠀⣯⢀⠁⠁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡕⢌⠪⣁⠀⢲⠆⠀⣠⡄⠀⠙⢇⢀⡴⡡⡁⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡙⢮⡒⢆⠤⠀⡙⠃⠠⠈⣁⣈⠊⠊⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣬⣁⡉⠀⣀⠀⠨⢝⠒⠡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡶⠾⠿⠿⢿⡿⣿⣿⣿⣉⡉⡉⣉⠒⡒⠂⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠍⡉⢉⢁⢀⡐⠒⠒⠂⣀⣀⡤⠐⠀⡈⠅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠂⠐⠀⠐⠊⠁




⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⢢⠀⠀⠀⣰⠂⠀⠀⠀⠀⠀⠱⡄⠀⠀⢠⠎⠀⠀⠀⠀⠀⠐⣆⠀⠀⠀⡔⠀⠀⠀⠀⠀⠈⢢
⠀⠀⢸⠁⠀⠀⠀⠄⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠄⠀⠀⠀⣷⠀⠀⣾⠀⠀⠀⠠⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠠⠀⠀⠀⠈⡇
⠀⠀⠈⢇⠐⠀⠀⠀⠀⠀⣰⠃⠀⠀⢳⡀⠀⠀⠀⢀⠐⢠⠇⠀⠀⠸⡄⠂⠀⠀⠀⠀⢀⡜⠀⠀⠘⢆⠀⠀⠀⠀⡀⠀⡸⠁
⠀⠀⠀⠈⠓⠦⠤⠤⠤⠚⠁⠀⠀⠀⠀⠙⠢⠤⠤⠤⠖⠁⠀⠀⠀⠀⠈⠲⠤⠤⠤⠔⠋⠀⠀⠀⠀⠈⠓⠤⠤⠤⠴⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠢⡀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠂⢄⠀⠀⠀⠀⢀⠄⠂⠀⠀⠐
⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⡜⠀⠀⠀⠀⠀⠠⠈⡆⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⢣⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠸⡄⠂⠀⠀⠀⠀⠀⢀⡇⠀⠀⡇⠀⠀⠀⠂⠀⠀⠀⡽⠀⠀⢿⠀⠀⠀⠐⠀⠀⠀⢸⠀⠀⢸⠀⠂⠀⠐⠀⠀⠀⢠⠇
⠀⠀⠀⠳⣀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠹⣄⠀⠀⠀⠀⢀⡴⠁⠀⠀⠈⢦⡀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠣⡀⠀⠀⠀⠀⣀⠞
⠀⠀⠀⠀⠈⠙⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠙⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠋⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠋⠁
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⣠⠂⠀⠀⠀⠀⠑⢄⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⢢⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠠⡀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠑⣄
⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⡏⠀⠀⠀⡀⠀⠀⠀⣧⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠘⡆⠠⠀⠀⠀⠀⠀⢠⠇⠀⠀⢇⠀⠀⠀⠀⠀⠠⠀⡏⠀⠀⢹⠀⠄⠀⠀⠀⠀⠀⡸⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠘⠦⣀⡀⢀⣀⡴⠋⠀⠀⠀⠈⠣⣄⡀⠀⣈⡠⠞⠀⠀⠀⠀⠳⢄⣀⠀⢀⣠⠜⠁⠀⠀⠀⠙⢦⣀⡀⢀⣁⠴⠃
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠈⣿⠲⡀⠀⠀⠀⢰⠋⠀⢹⢧⠀⠀⠀⠀⡜⠁⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣘⡆⠀⢸⣀⣳⣀⣀⣀⣸⠀⠀⣞⣈⣇⣀⣀⣰⠃⠀⣼⣁⣇⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠼⠥⠥⢿⡀⢸⡽⠥⠼⠬⠧⢿⠀⢠⡯⠧⠬⠥⢤⡏⠀⡼⠥⢼⡧⣤⢤⣤⠀⡏⠈⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⣇⠈⣧⠀⠀⠀⠀⣸⠀⣼⡀⠀⠀⣠⣼⠁⡼⠁⠀⠀⡇⢸⠘⡟⣷⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠸⣿⣶⣿⠇⠀⠀⠐⣿⣷⣿⠇⠀⠀⢿⣿⣿⡇⠀⠀⠀⡇⢸⡆⡇⡏⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⣷⢸⡇⡇⡟⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⡇⡿⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⡇⣇⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢀⣇⡏⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⣸⢸⢻⢣⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡏⣼⣼⣾⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢰⢃⣇⣿⠇⡇⠀⡇
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡞⣸⣹⡟⢰⡇⠀⡇
⠀⠀⠀⣠⣀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢰⢃⣇⣿⢁⡟⡇⠀⡇
⠀⠀⠀⢷⠈⠙⠳⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢀⡏⡼⣼⠃⡾⠁⡇⠀⡇
⠀⠀⠀⠈⢳⣄⡀⠀⠀⠉⠙⠒⠦⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡼⣰⣳⡏⣸⠃⢠⡇⠀⡇
⠀⠀⠀⣠⠏⠀⠉⠙⠓⠒⠲⠶⠤⠤⢤⣬⣉⣛⣒⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⢠⠏⣸⢡⢧⣿⢡⡏⢠⢏⡇⠀⡇
⠀⠀⠐⠓⠒⠒⠒⠒⠒⠒⢲⡖⢲⡖⠒⠒⣶⠲⠚⢻⢛⠛⣿⠛⠛⠛⣻⠓⣶⢻⠒⠓⠛⢻⠇⡞⢠⢏⢀⡇⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠖⠒⠉⠉⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠤⣤⣤⣤⣤⡖⠀⠀⠀⠀⠀⠙⠷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠘⣿⡟⠃⠱⡄⢀⡀⠀⠀⠀⠀⠀⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠲⣿⣿⣿⡿⠖⣚⣉⣭⣉⣛⡒⠾⣿⣇⣀⣀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠁⠀⢸⡟⣡⠖⣩⠁⠀⠒⠀⠀⢩⠓⢬⡻⣿⣿⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣷⣀⣠⣾⡞⣁⠀⠀⠀⠀⣾⠀⠀⠀⠀⢀⡱⡌⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠡⠀⠈⢯⡼⠀⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠀⢹⢽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⣸⡇⠲⠀⠀⠀⠀⠰⣿⠇⠀⠀⠀⠀⠰⢸⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⠶⠶⢻⣷⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣸⢸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸⡿⢻⣿⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⠀⢸⣿⠳⡁⠀⢀⠀⠀⠀⠀⠀⢀⠀⠈⡴⢣⣿⠿⠿⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢡⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⡴⠋⠛⣷⣝⠢⢍⣀⠀⠰⠀⣀⣨⠴⢋⣴⠟⠀⠀⠀⠀⠉⠉⠀⠀⠀⡀⠀⠀⣠⡟⢀⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⣿⣿⣿⣶⣬⣭⣭⣭⣭⡴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⣸⠁⢀⣴⡟⠀⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠛⠛⠋⠉⠉⠛⠿⢿⣿⣷⣦⣤⣀⣀⣀⣀⣀⡀⠀⠀⠀⡘⠰⠃⣠⣾⠏⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠻⣶⣄⡀⠀⢀⣴⣿⠏⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣿⣿⠋⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠃⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⢀⣠⣴⠶⠞⠛⠛⠛⠛⠛⠛⠶⢶⣤⣀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⢀⣤⡾⠋⢉⣠⣴⠶⠟⠛⢛⠛⠛⠷⢶⣤⣀⠙⠻⣦⣄⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣴⠟⢁⣤⠾⠋⣅⠀⠀⠀⠀⣿⡅⠀⠀⠀⢀⡍⠻⢦⣄⠙⢷⣜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠃⣠⡟⠁⠀⠀⠹⠇⠀⠀⠀⢿⠇⠀⠀⠠⠿⠁⣀⡀⠙⣦⡀⠻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⣼⠏⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣠⡌⢿⡄⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⣸⠏⠀⠈⠙⠃⠲⣦⣀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠛⠉⠀⠈⢿⡀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣀⣀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠸⣿⠛⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠰⣿⠰⠶⠶⠶⠆⠀⠀⠀⠀⠈⢹⣏⣿⠁⠀⠀⠀⠀⠰⠶⠶⠶⠶⢸⡇⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⣿⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢹⡆⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⢀⣾⠁⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⢻⣄⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢃⣾⠃⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠹⣦⡀⠀⠀⣰⡆⠀⠀⠀⣾⡆⠀⠀⠐⣶⡀⠀⠀⣠⡾⠁⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠻⣦⡈⠻⢶⣄⡋⠀⠀⠀⠀⣿⡇⠀⠀⠀⠘⣃⣴⠾⠋⣠⡾⢫⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠈⠛⢶⣄⡉⠛⠳⠶⣤⣤⣬⣤⣤⡶⠶⠛⠋⣁⣴⠞⠋⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠉⠛⠻⠶⣦⣤⣤⣤⣤⣤⣤⡶⠾⠛⠉⠁⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠞⠛⠛⢻⡟⠛⠛⠳⠶⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡞⠋⠉⠀⠀⠀⠀⠀⣶⠰⠒⣲⠀⠀⠀⠀⠀⠉⠙⠳⣦⣀
⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⢱⡆⢶⠀⠀⠀⠀⠀⣿⣠⣞⣥⠀⠀⠀⠀⠀⠀⣶⠘⠀⠙⠳⣦⡀
⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢸⡇⣸⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⣰⠿⣴⠀⣠⠴⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢦⠠⠿⣆
⠀⢰⡏⠀⢸⢰⡁⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⣋⠀⠀⢹⡆
⢀⡟⠀⠀⠈⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⢿
⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣿⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⣿⠶⠐⠧⠴⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢾⡅⠶
⣿⠀⠀⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠋
⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠈⣧⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣾
⠀⠸⣇⠀⠀⣮⡤⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣋⣇⠀⠀⣸⠇
⠀⠀⠹⣶⠒⠧⠴⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠇⠐⣶⠏
⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠉⢩⠏⠀⠀⠀⠀⠀⠀⠿⡿⠀⠀⠀⠀⠀⠀⣯⣭⣅⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⡀⠞⠀⠀⠀⠀⠀⠀⢠⣞⣭⡀⠀⠀⠀⠀⠀⠦⠴⢋⠀⣀⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢧⣄⣀⠀⠀⠀⠀⠀⠸⣥⡴⠃⠀⠀⠀⠀⠀⣀⣠⡼⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠶⢦⣤⣤⣼⣧⣤⣤⠴⠶⠞⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣿⡆⢀⣀⣀⣀⣀⣀⣀⠀⣿⡆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⠁⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣾⣿⡐⠿⢃⣿⣿⣿⣿⣿⣿⣿⡄⠿⢃⣿⣷⡀⠀⠀⠀⢸⣿⣿⣿⣿⠋⠀⢸⣀⣸⠀⠀⠀⠀⠀⠀⠀⢸⣄⣸⠇⠈⢻⣿⣿⣿
⠀⠀⠀⠀⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠿⠿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠀⣀⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⡀⢸⣿⣿⣿
⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⣷⢸⣿⡇⢸⣿⡇⣾⣿⡇⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠀⣿⣿⣿⣿⠀⠀⣯⠀⠈⡏⠀⢸⡇⠀⢸⡇⢸⣿⣿⣿
⠀⠀⠀⠀⣿⢠⣤⣤⢠⣭⣥⢨⣭⡅⢨⣭⡅⣨⣭⡅⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠀⣿⠛⠛⣿⠛⠛⣿⠛⠛⡟⠛⢻⡟⠛⢻⡇⢸⣿⣿⣿
⠀⠀⠀⠀⣿⠘⠛⠛⠘⠛⠛⠘⠛⠃⠘⠛⠃⠛⠛⠃⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠀⣿⠤⠤⣿⣤⣤⣷⣤⣤⣧⣤⣼⣧⣤⣼⡇⢸⣿⣿⣿
⠀⠀⠀⠀⣿⢸⣿⣿⢸⣿⣿⢸⣿⡇⢸⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⠀⣷⠀⠀⣾⠀⠀⠷⠀⢸⣿⠀⢸⣿⣿⣿⡇⢸⣿⣿⣿
⠀⠀⠀⠀⠻⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠿⠁⠀⠀⠀⢸⣿⣿⣿⣿⣆⡉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⣁⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠑⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠔⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠉⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠧⠤⠤⠤⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆
⠀⣧⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠱⣄⡀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠁⣹
⠀⠀⠀⠙⠲⢤⣀⡀⠉⠒⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣀⡀⣀⣀⣸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠚⠉⠀⣀⡤⠚⠁
⠀⠀⠀⣀⠴⠚⠁⠈⠉⠑⠒⠒⠒⠚⠛⠛⠓⠒⠒⠒⠊⠉⢉⡽⠃⠀⠀⠀⠀⠈⢯⡉⠑⠒⠒⠠⠤⠶⠶⠶⠮⠭⠥⠤⠤⠒⠒⠚⠯⣀
⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠿⠶⠖⠒⠒⠒⠲⠶⠼⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀
⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⡸
⠀⢓⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⡇
⠀⠸⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⢀⣀⣀⡠⠤⠤⠤⠤⠄⠒⠒⠒⠒⠒⠒⠒⠒⠒⠠⠤⠤⠤⠤⢀⣀⡀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⡰⠋⣀⠠⠴⠒⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠠⠈⣦⡀
⠀⠀⠀⠀⠀⢠⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣄
⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡄⠤⣤⠤⠤⠴⠶⠶⠶⠶⠶⠶⠶⣤⠤⠤⠤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⡼⠁⠀⠀⢀⣀⠤⠔⠒⠂⠉⠉⠁⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠈⠉⠉⠒⢲⡤⢄⡀⠀⠀⠀⢷
⠀⠀⢸⠇⣀⡴⠊⠉⠉⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠈⠙⠢⣄⠈⣇
⠀⠀⣯⠞⠁⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠦⣠⣄⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⣤⡤⠶⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⣾
⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠱⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣤⣀⡀⠀⠀⢀⣀⣤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠙⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠂⠤⠤⢄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠠⠤⠤⠔⠒⠊⠉⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⢁⢈⣈⣈⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡠⠖⣉⠥⠄⠤⢉⡐⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠊⠀⠀⠀⠀⠀⠈⠲⡘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠂⠀⣴⠦⢤⣀⡀⠀⠀⠹⠈⡂
⠀⠀⠀⠀⠀⠀⠴⣄⠀⠀⠀⠀⠀⢀⡠⢴⡀⠀⠀⠀⠀⢸⠀⡀⢰⡷⠁⠀⠀⢉⡗⠀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⢺⡁⠀⣈⡷⠀⠀⠀⠀⠈⢧⠀⢩⡿⠶⢤⣄⡼⠁⣠⠂⡰
⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢏⣉⣽⠴⠶⠒⠚⠛⠿⠿⢾⣧⣄⣠⣟⣑⣈⡤⠞⠁
⠀⠀⠉⠛⠲⠤⠀⠀⠀⠀⠀⠀⣀⡴⠟⠉⠀⡀⢠⠤⠤⠤⠤⣤⣀⡀⠙⠻⢿⣯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⡠⠼⠉⠳⢦⡀⠉⠻⣦⡀⠀⣤⠶⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⣠⠂⠈⠀⠀⠀⠀⠀⠄⠀⠀⡄⠀⠀⢣⠊⠙⢷⡀⠈⢻⡞⠛⡄⠀⢘⡀⠀⠠⠤⠖⠚⠃
⠐⠶⠦⣤⠀⠀⠀⠀⣼⠏⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⡔⠁⠀⠀⠀⠙⡆⠀⢻⡖⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⣀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⡀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠙⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⠞⠋⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣀⠉⠓⠶⠤⣤⣤⣤⣤⠷⠶⠛⠉⢀⣠⡶⠋⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣤⣄⣀⣀⣠⣤⣤⠶⠞⠋⠁⠀⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠉⠉⠉⠉⠉⠉⠙⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⣀⡤⠴⠒⢚⣉⣉⣉⣉⣉⣉⣉⣙⠒⠲⠤⣄⡈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⢁⡠⠖⢋⡡⠔⠚⠉⠉⠀⠀⡄⠀⠤⣄⠀⠈⠉⠙⠒⠤⣉⠓⠦⣀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠋⣀⠔⢉⡴⠊⡅⠀⣀⠀⠀⠀⠀⠀⡇⠀⠀⠃⠀⠀⠀⠀⠀⢠⡄⠉⠲⣌⠑⢤⡈⠻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠋⢀⠜⢁⠔⠁⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠑⢄⠙⢆⠈⠻⣿⣿⣿⣿
⣿⣿⣿⡟⠁⡰⠃⡴⠁⠀⠀⠀⠀⠃⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠱⣄⠳⡀⠙⣿⣿⣿
⣿⣿⡟⠀⡼⢁⠞⢠⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠘⢆⠹⡄⠘⣿⣿
⣿⡿⠀⡼⢁⠎⠀⢸⠀⣯⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⢆⠹⡄⠸⣿
⣿⠃⢠⠃⡞⠀⠀⠈⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠀⠘⡆⢳⠀⢻
⡿⠀⡞⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣖⢲⠶⠀⠀⠀⠀⢳⠘⡆⠘
⡇⠀⡇⢸⠀⢀⠄⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⢀⣀⣠⡤⠴⠒⠚⠉⠉⠀⠈⠁⠀⠀⠐⠦⠀⢸⠀⡇
⡇⠀⡇⢸⠀⠈⢃⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⢘⠀⡇
⡇⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⠀⡇
⣷⠀⢧⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠇⢠
⣿⡄⠘⡄⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠃⡼⠀⣼
⣿⣷⠀⢱⡈⢇⠀⠀⢦⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠗⢀⠏⣰⠃⢰⣿
⣿⣿⣧⠀⠳⡈⢦⠀⠇⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣰⠃⢠⣿⣿
⣿⣿⣿⣧⡀⠱⣄⠳⡄⠀⠀⠀⠀⠠⠤⡄⠀⠀⠀⠀⠀⠀⣸⣅⠀⠀⠀⠀⠀⠀⠀⠀⣖⠂⠀⠀⠀⡴⢃⡴⠁⣠⣿⣿⣿
⣿⣿⣿⣿⣿⣄⠈⠢⡈⠢⣀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢣⡎⠀⠀⠀⠀⠀⠀⠀⢀⡀⠃⢀⡠⠊⡠⠊⢀⣴⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣄⠈⠢⣌⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢥⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⢋⡤⠊⢀⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡈⠑⠢⣌⡑⠲⠤⣄⣀⡀⠀⠀⠃⠘⠀⠀⣀⣀⡤⠴⠒⣉⡤⠖⠉⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠉⠑⠒⠤⠤⣍⣉⣉⣉⣉⣉⣉⡥⠤⠔⠒⠉⢁⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⠉⡩⠕⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⢀⠤⠂⠁⢀⡠⠔⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠠⠂⠁⣀⠤⠒⠁⢀⠠⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠳⡔⠈⢀⠠⠐⠉⠀⡠⣴⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⢹⣎⣀⡀⢄⣒⣥⣮⠶⠦⠤⠽⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⡁⠉⡺⠽⠃⣀⡤⠄⠀⠲⠤⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡅⡼⠃⣠⠊⠀⠁⠀⠀⠆⠀⠀⠀⣀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠃⢠⡅⠀⢠⠀⠀⢸⠀⠀⠀⠈⠉⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠑⠒⠿⠀⠀⠀⠀⣀⠄⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠈⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠄⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢗⢌⠢⢄⣤⣀⣀⡀⠦⠔⠊⣠⠊⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣞⠢⠤⠤⣤⠤⠔⣒⠩⠕⠚⠉⠁⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣀⡔⠅⠂⠁⠀⢀⣀⠤⠒⠈⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠣⣤⠤⠒⠈⠁⢀⠀⠄⠒⠉⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠈⠦⡔⠂⠉⠀⡀⠤⠒⠊⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠙⡖⠈⠀⠀⢀⡠⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣼⣁⣈⡩⠥⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⣠⣧⣀⣀⣠⣼⣄⣀⣀⣀⣬⣄⢠⣭⣄⣀⢀⣬⣥⠀⢰⣽⣀⠀⣀⣠⠞⠦⣄⣀⢼⣥⡀
⠀⠀⠀⠀⠀⢺⣤⠠⠒⠁⠨⠥⠁⡛⠋⠙⢹⠜⠁⡇⠀⠙⠃⣿⠀⠀⡼⠀⠈⠀⠉⠀⠂⣶⠁⠄⢿⣟⣿
⠀⠀⠀⠀⠀⠈⠈⢦⣄⡐⠛⠂⡀⠟⠂⠁⠈⢷⠀⣹⠀⠄⠀⣿⢀⣰⠃⠀⠀⠀⠐⠀⠈⡿⠀⠀⠙⣿⣿
⠀⠀⠀⠀⠀⣸⠀⠀⠺⠟⠟⡆⠙⠚⠛⣁⠀⠈⣆⠘⢀⣠⣤⣿⣀⡟⠘⠻⡦⠀⣀⡀⢀⡻⠀⠀⢾⣿⣿
⠀⠀⠀⠀⠀⣼⢀⠀⢀⡀⠰⣁⠀⢁⣿⣿⣿⡷⢘⣸⡜⡇⠸⠇⢿⢏⠳⣄⣉⣛⠛⠁⣉⡷⠠⠀⢾⡍⣿
⠀⠀⠀⠀⠀⢠⠀⠀⠀⡀⠑⠁⠀⣸⣿⠿⠿⠇⢼⣆⣸⡇⠉⣿⣤⣼⠃⣯⠻⣿⣆⡀⣟⡛⠀⠀⣻⡧⠉
⠀⠀⠀⠀⠁⣾⣉⡂⢀⣄⡀⠐⢲⠏⠀⠀⠀⢀⠀⠋⠻⠇⠀⠇⠉⠀⠀⠓⠚⠟⠛⢿⣯⣛⠀⠀⣭⣷⣶⠻⠃
⠀⠀⠀⠀⠀⣼⣯⣭⣦⣉⡀⣚⡏⢀⡀⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢠⣤⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠃⠨⠼⡭⠭⠥⠤⠩⣀⢡⡄⠶⡶⠲⠛⠰⠻⠎⠛⠛⠻⠛⡃⣶⡶⠀⢈⡂⠫⣩⠩⠭⢹⡬⠽⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⠶⣗⣒⣺⡟⠉⣯⠈⢹⠉⡉⠙⣏⣛⣻⡿⢯⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢽⣯⡭⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠭⠉⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⠿⢿⢷⢿⣼⣯⡇⣷⠇⠙⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣛⡇⡀⠀⡘⢻⢻⣉⠿⣷⡎⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡌⠁⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠮⠁⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠠⠚⠍⠙⠷⢆⡀
⠀⠀⠀⠀⠀⡀⢀⣶⣯⢿⠴⣧⣤⡐⡀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⢍⢂
⠀⠀⠀⠀⠸⢽⣭⣽⣿⣿⣭⣭⣭⣬⣄⣤⣀⣀⣀⣀⣀⣼⣧⣄⣀⣀⣀⣀⣠⣤⣥⣤⣭⣬⣭⣿⣽⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡿⢿⣇⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡷⠞⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠥⠇

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠋⠀⢀⣀⠀⠀⠀⠀⠀⣿⣿⣶⣶⣤⣄⡀⠀⠙⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⠀⠀⠀⢿⡿⠆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠈⠻⣿⣷⡀
⠀⠀⠀⠀⠀⢠⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠙⣿⣿⡄
⠀⠀⠀⠀⢠⣿⣿⠃⠀⢰⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠘⣿⣿⡄
⠀⠀⠀⠀⣼⣿⡏⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢹⣿⣧
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿
⠀⠀⠀⠠⣿⣿⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣿⣿
⠀⠀⠀⠀⢻⣿⣇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣸⣿⡟
⠀⠀⠀⠀⠘⣿⣿⡄⠀⠸⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⢠⣿⣿⠃
⠀⠀⠀⠀⠀⠘⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⣠⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀⠀⠀⠀⣾⣷⠆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⢀⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣄⠀⠈⠉⠀⠀⠀⠀⠀⣿⣿⠿⠿⠛⠋⠁⠀⣠⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⠒⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⣴⠞⠛⠻⣦⠄⣻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠙⠢⠄⠤⠎⣠⣳⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡧⠀⠀⠀⢴⣾⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠴⠒⠛⠓⠉⠈⠙⠛⠛⠛⠲⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢊⢅⠐⠖⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⣖⠤⢀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠅⣊⠭⢒⡈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⡩⠖⣊⠥⠆⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡋⠔⢋⠠⠒⠊⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢊⠤⣊⠤⢈⡡⠄⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⡥⢊⠴⢊⣡⠤⢒⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⢚⡥⢚⡩⠒⣊⠭⠄⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⡡⢚⡥⢒⡩⠴⢒⡁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡡⢊⡥⢚⡡⢔⣋⡥⠄⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡡⢞⡥⢚⡥⣒⠭⢖⡺⠭⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠸⠀⡻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣡⢖⡥⢂⠵⣊⠵⢊⡥⢖⣪⠄⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢊⠔⡡⢊⡵⢊⠵⣪⠵⣊⢥⣲⣷⡀⡆⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠤⠴⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡛⡚⢓⠚⡒⠓⠚⠓⠚⠷⠮⢾⣭⣆⣱⡀⠈⢦⡑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡾⡒⠒⠒⠒⠒⠈⠉⠉⠉⠉⠉⢉⣈⡙⢛⡉⣉⠿⣛⠛⢓⠓⠓⠲⠶⠦⣬⣍⣳⡀⠀⠁⠀⠣
⠀⠀⠀⠀⠀⢀⠔⠊⠀⠊⠈⠈⠁⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠴⣺⠕⡨⢔⡬⢐⣪⠕⣪⠍⣒⠣⠴⣒⠮⣝⡛⠦⣀
⠀⡀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣊⢔⡩⠐⡡⠒⠩⠔⡩⠖⢉⠥⢒⡭⢓⡨⠝⣛⠥⠈⠳⣄
⡜⠀⠆⢰⠃⠀⢀⠀⣀⢀⢤⡤⢀⣀⣀⣐⣖⣶⣶⣶⣶⢶⣶⣶⣚⣖⡀⠀⠀⠀⠠⠤⣜⣁⣊⡁⠚⠡⢖⡩⠖⣪⠕⢂⠘⣇
⡇⠀⣀⡟⣨⠷⠶⡲⢲⢪⢋⢏⡝⡜⡸⠿⠿⢉⡡⢿⣮⡜⡸⡱⢣⠏⡜⡽⣩⢫⢏⠞⡶⣲⢒⠞⡿⣿⢿⣶⣞⡰⠯⣼⣂⠸⡄⠀⠰
⠃⠀⠻⠳⣌⡛⠳⣧⣃⡃⠎⡘⣸⠟⠀⠀⠈⠑⣊⠤⢒⣻⣅⢡⠇⡞⡜⡰⡡⢣⢋⠎⡜⠡⠃⠞⠐⠱⠃⠎⠼⠩⣻⢓⣮⠙⡇⣤⢰
⠀⠀⠀⠀⠀⠉⠓⠲⠬⣝⣻⣿⢿⡀⠀⠀⠀⠀⢐⡊⡭⣶⣯⢇⡜⡜⡼⡰⠑⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⢞⣉⠴⢡⠇⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡹⡍⢧⠀⠀⠀⣉⡡⠔⣊⣴⢟⣾⣷⣓⣓⣓⣒⣒⣒⣒⣒⣉⣉⠉⠩⠭⠭⠙⠒⠒⠚⠉⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⠀⠓⠦⠌⣴⡛⠭⠞⠁⠞⡱⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⡀⠀⣀⠀⣀⠄⢀⠤⣀⠄⢀⡀⠀⣀⠀⣀⠀⣀⠀⣀⠀⢀⠀⣀⠀⣀⠀⡀⢀⡀
⠀⠀⠀⠠⠲⠟⡮⢇⡵⢊⡥⢒⡡⠖⣉⠔⣊⠤⣊⠥⢊⠥⢂⡡⠔⡈⠔⣊⠵⢊⠵⣊⠤⢊⠵⢊⠠⣊⠕⡨⢖⡡⣖⠥⣪⢞⠕⡢⢢⢖⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣄⣤⣴⣤⣤⣤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣮⡿⠞⠛⠉⠉⠉⠉⠙⠛⠻⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡇⠀⠀⠀⢀⢀⣀⣀⣀⣀⢀⡀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⢰⣿⣮⣽⣯⣿⣧⣿⣿⠀⠀⢔⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⠛⠉⠉⠉⠛⠙⠫⢿⣷⣷⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣶⣴⣤⣤⣤⣷⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠿⣻⣻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⣀⠀⠠⠤⠠⠘⠒⠛⠒⠻⠤⠄⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠛⠉⣁⠤⣤⣒⣶⣶⣼⣼⣤⡭⣤⣶⣄⣢⣤⣞⣣⠄⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣂⣴⣶⣧⡶⠿⠛⠋⠉⠉⠀⢠⣆⣠⢲⡄⠈⠉⠉⠛⠻⠿⣿⣦⡌⠑⠶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⡡⢞⡭⠟⣭⠁⠀⠀⠀⠀⢀⠀⠠⠀⠉⠌⠈⠄⠀⡀⠀⠀⠀⠀⡀⡽⠿⢶⣀⠀⠙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢊⣴⣿⠟⠋⢻⣤⡴⠞⠀⠀⠈⠀⠀⠀⢲⡆⠒⡗⢰⡆⠀⠀⠈⠀⠐⠀⡿⠋⠀⠀⠙⠳⣄⢀⡙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⡠⢊⡷⠁⠀⠀⠀⡅⠀⣡⠰⣆⠀⠀⠀⠀⠀⣿⠀⡇⢸⡇⠀⠀⠀⠀⢀⡶⠂⠐⠀⡀⠀⠀⠈⢢⡹⣯⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⣾⣷⠏⠀⠀⢀⠀⠂⠠⠾⢤⡆⠈⢧⡀⠀⠀⣠⠇⠷⠷⠸⠇⠀⢀⠁⢀⡞⠁⠀⠀⠀⠀⠄⠀⠀⠀⣹⡜⣷⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠸⣽⠃⣔⣦⠀⠄⠀⠀⠀⠀⠀⢙⢳⠾⠛⠀⠀⠀⠀⠀⠀⠀⣀⣰⠇⠐⠻⠀⠀⠀⠀⠀⠀⢀⡈⠐⠚⣉⢄⡀⢿⡻⣆
⠀⠀⠀⠀⠀⠀⠀⠢⣰⣽⠷⠤⣲⠀⠂⠼⠄⠀⠀⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣡⡍⠐⠀⠀⠀⠀⠀⢀⣠⠴⢋⣵⡈⠘⠓⠉⠀⠘⣧⢿⡄
⠀⠀⠀⠀⠀⠀⡈⢢⣧⠏⠀⠀⠁⠀⠸⠛⠛⠷⠶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢲⣤⣄⠀⠀⠀⠀⠀⠈⢻⡵⠞⠉⠀⠀⠀⡄⠀⠀⠐⠸⣿⣷
⠀⠀⠀⠀⠀⠀⢃⣹⣽⠀⠀⠀⠈⠀⠀⠀⠀⠀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣎⠔⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⡇
⠀⠀⠀⠀⠀⢘⠀⡈⡟⠀⢀⡀⠁⢠⡀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠰⢸⣟⡷
⠀⠀⠀⠀⠀⢸⠀⠃⣏⠙⣀⢃⠀⢰⠶⠛⠛⢙⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠰⣯⣭⣭⣭⣭⠀⠈⠏⢛⡃⢸⣟⡷
⠀⠀⠀⠀⠀⠸⠀⣤⣿⠀⠉⠁⠀⢲⠖⠒⠓⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠙⢏⡘⠳⣄⠀⠀⠀⠀⠐⠟⠛⠛⠓⠛⠀⠈⠛⠉⠁⢸⣉⡿
⠀⠀⠀⠀⠀⠀⡴⢸⢸⡄⠀⠀⠀⠀⠀⠀⠀⣀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠩⢤⣑⣄⢀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⡯⢽⠇
⠀⠀⠀⠀⠀⠀⢰⡼⡏⣧⠀⠀⠈⡀⠠⣔⣫⠵⣺⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣑⠦⣄⠀⠀⢀⠁⠀⠀⢀⢠⠳⣿
⠀⠀⠀⠀⠀⠀⠈⡴⢻⡹⣆⢠⢤⡄⠄⠩⠞⠋⣡⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠿⣽⡺⣽⣦⡝⠃⢀⠀⠀⠀⢀⡎⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣥⠱⣹⡟⢉⣶⡀⠄⠀⢶⠋⠀⠀⢀⡼⣳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠙⠶⠟⠀⢀⡛⡠⠀⢀⡞⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠑⡦⢳⡟⣎⠉⠀⠀⠂⠀⠀⠀⣠⠞⡴⢁⡾⠀⠀⠀⢲⠂⣦⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠑⠝⠠⣠⠟⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠻⣮⣧⡀⠀⠀⠀⠀⠀⠉⠺⢥⢀⡇⠀⠀⠀⢸⠀⢹⡄⠀⠀⠀⠠⠙⣦⠄⠀⠤⠀⠀⠀⠀⡀⢀⡤⢉⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢳⣍⢢⡀⠀⠾⠓⣀⠀⠀⠈⡁⠀⠀⠀⠾⠠⠀⠷⠀⠀⠀⠈⠀⠆⣨⠀⠀⠀⠀⡀⢈⡴⢏⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢘⢷⣾⣿⠇⢠⣅⠁⠀⠀⠀⠈⠀⠀⣀⠂⢀⠀⠀⠀⠁⠀⢴⡊⠹⡄⠀⠀⣠⡴⢋⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⣝⡳⢂⢤⢂⠤⢄⣀⠀⠀⠀⠁⠚⣍⠀⠀⠀⠀⣀⠀⠛⣂⣥⠖⣟⣧⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣦⣭⣛⣛⠶⠖⠺⠠⣭⣤⣉⣩⣭⡍⠒⠶⣂⣻⣭⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠶⠶⠶⠿⠶⠶⠞⠛⠛⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣧⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣼⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠿⠛⠉⠉⠉⣡⣌⠉⠉⠙⠛⠿⢿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⠛⠉⣶⡄⠀⠀⠀⢀⠌⡡⡀⠀⠀⠀⢠⣶⠈⠛⢿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠋⠀⠀⠀⠨⡂⢔⡀⠀⠘⠜⠡⠃⠀⠀⠀⢆⠀⠀⠀⠀⠙⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⣁⡀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣈⢻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠀⠙⠃⠘⠄⣉⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠩⢸⡁⠘⠋⠀⢻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⡀⠀⢀⢀⠄⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⢀⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⠘⠟⠀⠙⠀⠅⠀⠀⠀⠀⠀⠀⠀⠯⠾⠀⠀⠀⠀⠀⠀⠀⠀⠇⠹⠀⠻⠃⣼⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠀⠀⣠⡄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⠂⠀⠀⠀⢸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠾⠇⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠸⠷⢠⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⠀⠀⠀⠀⠀⡆⠰⡀⠀⠀⡀⢀⠀⠀⢀⠒⠲⡀⠀⠀⠀⠀⣰⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣷⣄⠀⠀⣤⡅⠈⠀⠀⠀⠇⠣⠇⠀⠈⠀⢨⣤⠀⠀⣠⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣦⣍⡀⠀⠀⠀⠀⢴⡦⠀⠀⠀⠀⢀⣩⣴⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠿⠿⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠤⠒⠊⠉⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣤⣄⣀⣀⣴⠀⠀⠀⠀⠀⠙⠳⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⢿⣿⠏⠙⣄⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⡀
⠀⠀⡠⠶⠶⣶⣶⣿⣿⠶⠖⣚⣛⣛⣓⠲⢮⣾⣿⣀⢀⣀⠀⠀⠀⠀⠀⠘⣆
⠀⢸⡑⠂⠀⢸⡿⢋⡵⢚⡉⠁⠰⠄⠈⢉⡓⢬⡙⢿⣿⡇⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠘⣷⡀⢀⣼⡷⠋⠀⠈⠁⠀⢰⡆⠀⠈⠁⠀⠙⣎⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⡴⠋⡉⠙⢿⣹⠁⠉⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠉⠘⡞⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⣷⠠⠀⠀⢸⡟⠠⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⠀⠠⠄⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣌⠳⣤⡀
⢨⢧⣤⣤⢾⣿⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⡏⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠈⢻⡾⢶⣶⣦⣤⣀
⢸⠀⠀⠀⢘⣿⢧⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡜⣰⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢁⣿⣿⣿⣿⣿⣿
⠈⢧⣀⣀⠼⠿⣦⡑⢤⡘⠂⠀⢠⡄⠀⠐⢂⡴⢊⣴⠟⠁⠀⠈⠙⠓⠒⠀⠀⠀⠀⠀⠀⢠⡿⢁⣾⣿⣿⣿⣿⣿⣿
⠀⠀⢸⡇⠀⠀⢹⣿⣶⣬⣙⣒⡒⠒⣒⣋⣥⡶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⣰⡟⠀⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠻⠤⠴⠿⠿⠟⠛⠿⣿⣿⣿⣿⣍⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⣰⠃⢀⣾⡟⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠷⠶⠶⢶⣦⣀⠀⠘⠀⠀⣴⣿⠏⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣤⣾⣿⠏⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⠋⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣄⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣽⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢀⣀⠀⣾⡆⣀⣀⡀⣾⡆⣀⣀⡀⣾⡆⣀⣀⡀⣾⣦⢀⣀⠀⠀⠀⢀⣀⢠⣾⡆⣀⣀⡀⣾⡆⣀⣀⡀⣾⡆⣀⣀⡀⣾⡆⣀⣀
⠀⢸⣿⡇⣿⡇⣿⣿⡇⣿⡇⣿⣿⡇⣿⡇⣿⣿⡇⣿⡧⣿⣿⠀⠀⠀⢸⣿⡿⣿⡇⣿⣿⡇⣿⡇⣿⣿⡇⣿⡇⣿⣿⡇⣿⡇⣿⣿
⠀⢸⣿⣷⣶⣾⣿⣿⣿⣶⣾⣿⣿⣿⣶⣶⣿⣿⣿⣶⣶⣿⣿⠀⠀⠀⢸⣿⣷⣶⣾⣿⣿⣷⣶⣾⣿⣿⣿⣶⣾⣿⣿⣿⣶⣶⣿⣿
⠀⢸⣿⡟⠛⠛⠛⠛⣛⣛⠛⢛⣛⡛⢛⣛⡛⠛⣛⣛⠛⢻⣿⠀⠀⠀⢸⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⣿
⠀⢸⣿⡇⠀⠀⠀⢸⣿⣿⠀⣿⣿⡇⢸⣿⣿⢸⣿⣿⡇⣸⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⣀⣤⣤⣤⣀⠀⠀⠀⠀⣠⣤⡄⠀⠀⣿⣿
⠀⢸⣿⡇⣠⣤⣄⢠⣥⣥⠀⣬⣭⡄⢨⣥⣥⢀⣭⣭⡀⢹⣿⠀⠀⠀⢸⣿⠀⠀⠀⠾⠿⠟⠉⣿⣿⡇⢀⣤⣾⣿⣿⡇⠀⠀⣿⣿
⠀⢸⣿⡇⠿⠿⠿⠸⠿⠿⠀⠿⠿⠇⠸⠿⠿⠸⠿⠿⠇⣼⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⣾⣿⣿⡁⠸⠛⠉⣿⣿⡇⠀⠀⣿⣿
⠀⢸⣿⡇⣶⣶⣶⢰⣶⣶⠀⣶⣶⡆⢰⣶⣶⢰⣶⣶⡆⢼⣿⠀⠀⠀⢸⣿⠀⠀⠀⣀⣀⡀⠀⢹⣿⣿⠀⠀⠀⣿⣿⡇⠀⠀⣿⣿
⠀⢸⣿⡇⠛⠛⠋⠘⠛⠛⠀⠛⠛⠃⠘⠛⠛⠈⠛⠛⠃⣼⣿⠀⠀⠀⢸⣿⠀⠀⠀⠙⠿⣿⣶⣿⡿⠋⠀⠀⠀⣿⣿⡇⠀⠀⣿⣿
⠀⢸⣿⡇⣿⣿⣿⢸⣿⣿⠀⣿⣿⡇⢸⣿⣿⠀⠀⠀⠀⢿⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⢸⣿⣧⣬⣭⣥⣤⣭⣭⣤⣭⣭⣥⣬⣭⣥⣤⣤⣤⣤⣿⣿⠀⠀⠀⢸⣿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣿
⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠿⠟⠛⠛⠉⠉⡏⠉⠛⠛⠻⠿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠫⡀⠀⠀⠀⠀⠀⡤⢤⠀⠀⠀⠀⠀⠀⡝⠻⢿⣿⣦⡀
⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⢰⢰⠀⠀⠀⠀⠁⠛⠀⠀⠀⠀⠀⡆⠀⠀⠀⠙⢿⣿⣦⡀
⠀⠀⠀⠀⢠⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡄
⠀⠀⠀⢠⣿⡿⠉⠓⠠⡤⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⠒⠉⢿⣿⡄
⠀⠀⢀⣿⣿⠁⠀⠀⠈⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠈⣿⣿⡀
⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⣼⣿⣇⣀⠀⣔⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡄⣀⣸⣿⣷
⠀⠀⢿⣿⡇⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁⠀⢨⣿⡿
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠈⣿⣿⡀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⢀⣿⣿⠁
⠀⠀⠀⠸⣿⣷⣠⠄⠀⠛⠀⠀⠀⠀⠀⠀⠀⢠⡟⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠠⢄⣼⣿⠇
⠀⠀⠀⠀⠙⣿⣷⡄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠁⠀⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⣾⣿⠏
⠀⠀⠀⠀⠀⠈⢿⣿⣦⡀⠀⠀⠀⠰⠁⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠈⠿⠂⠀⠀⢀⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣄⡜⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⢱⣤⣶⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣷⣦⣤⣄⣀⣀⣀⣇⣀⣀⣠⣤⣶⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⢿⣿⣿⣿⠿⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⣛⣻⣛⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡶⠶⠶⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⢐⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠈⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⠀⠀⢀⣤⡿⠟⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⣀⠀⠀⠀⠀⠀⢀⣀⣤⣀⣀⣠⣴⡾⠋⠁⠀⠀⢀⣀⣤⡶⠞⠋⠁⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⢀⣾⠉⠉⠁⠉⠙⠳⠶⠦⣤⣤⣀⣀⣀⣀⣀⣬⣽⣿⣿⣷⣶⡾⠋⠉⣿⠉⠻⣿⣿⠷⠿⠟⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⢐⣿⡇
⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⣼⡇⠀⠀⣼⣷⣾⣿⣯⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣼⣿⣿⣦⣼⣿⣁⣴⣿⣿⣿⡿⠶⠶⠶⠤⠤⠤⠤⠴⠶⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣉⣭⠟⠋⠀⢨⣿⣯⣿⠿⣿⡃⠀⠈⠙⠳⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠁⠀⠀⢠⡿⠁⠀⠙⠷⣌⠙⢦⡀⠁⠀⠈⠙⠻⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⣤⠴⠶⠛⠉⠁⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⢷⡀⠙⢷⣦⡀⠀⠀⠀⠀⢉⠍⠛⠛⠛⠛⠛⠛⢛⣽⠟
⠀⠀⠀⠀⣀⣤⠶⠚⠛⠉⠉⠉⠉⠁⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⠀⠀⠀⠀⠈⠀⠀⠈⢷⡀⠀⠙⢻⣶⣄⡀⠠⠄⠀⠀⠀⠀⢤⣶⠞⠋⠁
⠀⢀⣤⠞⣉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⡇⠀⠀⠀⠈⠙⠿⣷⣄⠀⠀⠀⠀⠀⠉⠛⠶⠦⣤⣤
⡠⠞⠛⠋⠉⠉⣻⡷⠖⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⠞⠋⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⡇⠀⠀⠀⠀⠀⠀⠈⠙⣿⠲⢦⣤⣤⣤⣤⣤⣤⠶⠛
⠀⠀⠀⠀⢀⡾⠋⠀⣀⣠⡴⠶⠛⠛⠋⠉⢡⡟⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⣾⣡⡴⠟⠉⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⢳⣦⣄
⠀⠀⠀⢰⠟⠉⠀⠀⠀⠀⠀⠀⢀⣤⡶⠟⠃⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠠⡁⠀⠀⠘⢸⣇⣤⡤⢀⣀⣠⡤⠶⠖⠛⠛⠛⠛⠟⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⢿⢛⠻⠛⠛⠓⠶⠶⢶⣮⣝⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⣵⢿⣿⡟⠉⣻⠀⠀⠀⠀⠀⢀⡠⣺⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⣳⢅⠀⠀⠀⠀⠀⠀⢸⣿⠋⠙⣻⠶⢦⣄⡀⠀⠀⢀⣸⡏⠁⠈⠻⠷⠶⠋⠀⠀⠀⢀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⣀⠀⠀⠀⠀⠈⠻⠶⠶⠋⠀⠠⠈⠙⠳⢦⣄⡹⣧⠀⠀⠀⠀⠀⣀⣤⡴⠞⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣦⣄⣀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⣴⠶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⢶⣤⣤⣤⣀⣰⣶⣶⣾⣿⠏
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢔⣒⣢⣤⣭⣭⣥⣤⣖⣂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣣⠞⠉⠀⢀⣀⣀⣀⣀⣀⡀⠈⠙⢶⣥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⠀⠀⢾⣭⣹⣬⣭⣽⣯⣿⠃⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⣆⣠⠄⠻⡿⢛⣿⣿⡿⠗⠢⣤⣮⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⡶⢶⣶⣿⣶⣶⠾⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢿⠶⣿⡿⡟⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⣶⣤⣿⣷⣷⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢖⣢⠭⠖⠚⠿⠿⠿⠿⠯⠿⠯⠑⠒⠯⢕⣲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣪⠕⠊⢁⣠⣤⠶⠞⠛⠛⠛⡉⠙⠛⠛⠳⠶⣤⣄⡀⠙⠺⢕⡦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢔⠵⠋⣀⡴⠞⡋⠁⠀⠀⠀⠀⠀⣀⠄⣄⠀⠀⠀⠀⠀⠉⢙⠷⣦⡀⠙⢮⡳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠔⡵⠃⣠⠾⠋⠀⠀⢡⠀⡄⠀⠀⠀⠀⡇⠵⠉⠀⠀⠀⠀⠀⡆⠉⠀⠈⠙⢦⣄⠙⢮⡳⡀
⠀⠀⠀⠀⠀⠀⢠⢏⠞⢀⡼⠃⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠙⢦⡀⠱⣝⣄
⠀⠀⠀⠀⠀⢠⢧⠏⢠⠟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢈⠳⡄⠹⣞⣆
⠀⠀⠀⠀⢠⢇⡟⢠⡟⠀⠁⢸⡞⠉⡆⠀⠀⠀⠀⠀⠘⠀⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠀⠀⠘⠀⠟⠀⠀⠹⡄⢹⡿⡄
⠀⠀⠀⠀⡼⣼⠁⡾⠀⠀⠀⠘⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢻⠀⣿⢷
⠀⠀⠀⢠⡇⣿⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢹⣿⡄
⠀⠀⠀⢸⣿⣿⢸⡇⠀⡤⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⣆⢀⡀⡇⢸⡗⡇
⠀⠀⠀⢸⡟⣿⣾⡇⠁⢈⠜⠁⠀⠀⠀⣀⣀⣀⣠⣤⠶⠖⠛⠻⠿⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠈⠁⡇⢸⣷⡇
⠀⠀⠀⠘⡇⣿⣿⡇⠀⠀⠀⠀⠀⠤⠖⠳⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⣾⣿⠇
⠀⠀⠀⠀⢻⢹⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⢀⡀⠀⠀⠀⡜⣾⣿⣾
⠀⠀⠀⠀⠈⣏⣿⣿⣄⠀⠀⣘⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡀⠀⠀⠈⢏⣦⠀⢤⣸⡇⢀⠀⡰⣸⣿⣿⠇
⠀⠀⠀⠀⠀⠘⣞⣿⣿⣄⠁⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡄⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠈⡰⣱⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠘⢎⢿⣿⣦⡀⠀⠀⠀⠀⠀⠂⠂⠀⢀⠀⠀⠈⢛⠁⠀⠀⠀⠀⠠⢦⡀⠀⠀⠀⠑⢀⢞⣼⡿⣻⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠣⡹⣿⣿⣦⡀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⢁⠀⠀⢀⢔⣵⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠮⡛⢿⣿⠷⢄⡁⠀⠀⠀⠀⠀⣀⣀⠁⠁⠀⠀⠀⠀⠀⠀⢈⣥⣾⣷⣿⢟⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢭⣳⢦⣌⡑⠒⠤⢄⣀⣀⠀⠈⠀⢀⣀⢠⣤⣶⣾⣿⣿⢿⡯⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⢽⣟⣲⣶⣤⣤⣤⣭⣤⣤⣤⣴⣶⣿⡿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⢐⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⠖⠉⠀⠈⠉⠲⡈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⣊⠡⡀⠀⣽⠁⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠰⣌⠈⠣⠶⠿⣞⠔⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡪⠠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠇⣠⣠⣏⣉⡁⢀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠠⠆⣞⠣⣀⡀⠀⠀⢀⣠⠔⠊⠀⠈⠉⠀⠉⠉⠁⠈⠉⠀⠀⢅⣂⠠⢀⠀⠀⢐⠁⠈⠲⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠺⣤⡴⠞⠉⢀⣀⡤⠴⠶⠟⠛⠘⡛⠒⠻⠴⢶⣦⣄⣈⠁⠢⢄⠢⣀⣕⠆⠡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠫⠀⡠⡘⠝⣈⠀⠀⠀⠀⠀⢀⢃⠀⠀⠀⠀⠀⢈⠙⠳⣦⣄⡉⠪⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⡠⡪⠊⠀⠀⠈⠆⠄⠀⠀⠀⠨⠍⠠⢄⡀⠀⠀⠀⡠⠍⠀⠙⢻⣦⡈⠢⡑⠄
⠀⠀⠀⠀⠀⠀⠀⢀⢂⠂⠀⠜⡌⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⢀⡰⠊⠙⡄⠀⠀⠁⣠⠞⠀⠀⠙⢞⣆⠘⡄
⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⢐⡉⠀⠓⠲⠆⠄⠀⠀⠀⠀⠇⠀⠀⠿⠃⠀⠀⡅⠀⣠⠖⠁⠀⢀⢀⣀⠄⠈⢗⠘⢎⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣤⣀⣀⠠⢎⢔⡱⠋⠀⠀⠀⠀⠁⠀⠐⠀⠈⡆⠈⣯⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⡵⠋⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠠⢱⠀⢹⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠂⠒⠺⠥⠀⠀⢀⠐⡀⠀⠀⠀⠈⢭⡥⡚⠀⠀⠀⢀⠄⠀⠀⠀⠀⠒⠃⠶⠀⠀⠂⢸⡗
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⢀⡐⡱⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠴⡗
⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠰⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢂⢶⠆
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡐⡀⠆⠋⠁⠀⠀⠀⠀⠀⠀⠉⠉⢀⠈⣤⠍⠁⠀⠀⠀⠀⢠⣶⢦⣄⡐⣴⣾⡳⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠡⠠⡀⠐⢜⢄⠀⠀⠀⠀⠀⠦⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠉⠰⠿⠳⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠠⡀⠀⢕⠢⡀⠀⠞⠀⠀⠀⠀⢰⣤⠀⠀⠀⠀⠘⠋⢡⡀⠀⠂⠡⣺⠞⡺⣟⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢭⡲⣄⠁⠦⢅⡂⠄⢀⠀⠀⠀⢒⠀⠀⠀⠀⠀⠀⡈⠅⣂⡄⢆⠤⣻⠕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠰⢿⡶⡤⣌⡑⠒⠢⠡⠠⠄⠀⢤⡤⠠⠉⠰⠚⣉⡥⣞⠜⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠐⠩⠥⣳⡶⡴⣤⣤⣤⣰⣴⣖⡾⠯⠗⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⢀⠀⢀⠠⠐⡈⠄⠂⠁⠐⠀⠀⠀⠀⠠⠀⠈⠀⠈⠀⠀⢀⠀⠀⠄⠀⠀⠁⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣴⣤⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⡟⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠃⢫⣿⠙⢮⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⣉⣋⣡⣤⣤⣈⣈⠑⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣫⠶⠛⠋⠉⠉⣀⡀⠉⠉⠛⠷⣦⣌⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⣵⠟⠁⠀⢶⡀⠀⠀⢿⠇⠀⠀⣠⠂⠀⠙⢷⣄⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⡞⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⠹⣧⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡞⠀⠀⠈⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⠀⠹⣇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠈⠉⠈⠀⠀⠀⠀⠀⠀⠛⠋⠁⠀⠈⠉⠀⠉⠉⠉⠀⢾⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⣀⡤⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠈⠉⠊⠀⠀⡠⠀⠀⢀⠀⠀⠘⠄⠀⠈⠙⠟⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⢀⡞⠓⡀⠀⠈⠀⠀⠀⠑⢄⠀⠀⠀⣰⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣦⣤⣤⣤⣤⣤⣤⣶⣾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠉⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢻⡇⠠⠞⠛⠛⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⣠⣤⠀⣠⣄⠀⠀⠀⠀⠀⢸⡇⠀⣠⠶⠶⠛⠁⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣗⠀⠀⠀⠀⠀⠸⠃⠸⠷⠶⠶⠶⠆⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿
⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿
⣿⣿⣿⠃⠀⠀⣠⣤⠀⠀⣠⡤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡀⠀⠀⠘⣿⣿
⣿⣿⠃⠀⠀⠀⠀⣿⠀⢸⠋⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣀⣨⡿⠀⠀⠀⠘⣿
⣿⡏⠀⠀⠀⠀⠀⣿⠀⠘⢧⣀⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣛⣉⣁⣀⠀⠀⠀⠀⢹
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉
⡇
⠃⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄
⠀⠀⣿⣁⠀⣈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠠⠤⠀⠀⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣠⣠⣼⠃
⠀⠀⢈⣉⠉⣉⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⣹⡇
⡄⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⢠⡴⠶⠶⣤⠀⠀⠀⠀⠀⠀⠀⠀⢴⠟⠋⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤
⣿⣇⠀⠀⠀⠀⢘⣷⠤⠴⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣿⠀⠀⠀⠀⠀⣸
⣿⣿⡄⠀⠀⠀⠿⣤⣀⣠⡼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠶⠶⣿⠶⠀⠀⠀⢠⣿
⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⣿⣿
⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿
⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⢋⣉⣉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡛⠉⠉⠉⣷⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⣉⣉⣙⠃⠀⠀⠀⠀⠀⠀⠙⠛⠓⠛⠋⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣟⠉⠉⢙⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡗⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡈⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⢏⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣾⣿⣧⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⣹⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣏⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠛⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⠀⠠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡏⠀⠠⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣧⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⡀⠀⢻⣟⠳⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢸⣿⣷⣮⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢹⣿⣷⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠘⣿⣿⡀⢹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣇⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⢹⣿⣿⠀⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⡀⠀⠀⠀⢻⣿⡆⠈⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⡇⠀⠀⠀⠈⣿⣷⡀⠸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⢸⡇⠀⠀⠀⠀⢸⣿⣇⠀⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢠⣿⣧⠀⠀⠀⠀⠀⢻⣿⡆⠘⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⠀⠀⠀⠀⠀⠈⢿⣿⡆⠘⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡟⠁⢸⣿⣿⡆⠀⠀⠀⠀⠀⠘⣿⣿⡀⠈⢻⣿⣄
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣽⠆⠀⠺⣿⣿⡧⠀⠀⠀⠀⠀⠀⢸⣿⣷⡄⠀⠻⣿⣦⡀
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣾⣿⡿⣿⠶⠶⠶⠶⠶⠶⠶⠿⣿⣿⣶⣶⣿⣿⣿⣶⡄
⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⡿⣶⠖⠒⠒⠒⠒⠒⠒⠚⢿⣿⣿⡛⠛⠙⢻⣿⣿⡄
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⠀⠀⠀⢿⣿⣿⡀
⠀⠀⠻⠟⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⠷⠶⠖⠒⠒⠒⠒⠒⠖⠿⠿⠿⠷⠒⠲⠾⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⢂⣿⡐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⡗⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣌⣛⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣌⣛⣣⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣤⣤⡄⠀⣤⣤⡄⢠⣤⣤⠀⣤⣤⡄⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣀⣀⠀⣈⣉⡁⠀⣉⣉⡀⢈⣉⣉⠀⣈⣉⡁⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠘⠛⠛⠀⠛⠛⠃⠀⠛⠛⠃⠘⠛⠛⠀⠛⠛⠃⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣶⣷⠀⢾⣶⡇⠐⣷⣾⠆⢰⣶⣷⠀⢾⣾⡇⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢠⣤⣤⠀⣤⣤⡄⠀⣤⣤⡄⢠⣤⣤⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠉⠉⠀⠉⠉⠁⠀⠉⠉⠁⠈⠉⠉⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠯⠽⢧⢭⣭⡽⣼⠤⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠴⣶⣖⣒⡖⣒⣒⣶⡶⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⣺⣭⣿⣾⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣶⣯⣽⣲⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢞⣭⡼⣿⣿⣿⣿⣿⣿⣿⣿⠟⢹⣿⣫⣭⢻⣿⣿⣿⣿⣿⣿⣿⡿⣨⣝⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⣾⣿⣿⡿⢻⣿⠟⢻⣿⣿⣿⣿⣿⢸⣿⡿⢋⣼⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣮⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⣾⣿⣿⣿⣿⣾⢸⣷⡗⢸⣿⣿⣿⣿⣿⣼⣯⣘⣛⣻⣿⣿⣿⣿⣿⣾⢸⣿⣿⣿⣿⣿⣿⣮⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢟⣾⣿⣿⣿⣿⣿⣿⣿⣰⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣎⢧⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣋⠿⣿⡿⢿⡿⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⠻⣿⡿⢇⣳⡀
⠀⠀⠀⠀⠀⠀⣰⣳⣿⣿⣿⣶⢸⢸⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿⣿⣿⣿⣷⣿⠗⣼⣿⣿⣷⣳⡀
⠀⠀⠀⠀⠀⢠⣧⣿⣿⣿⣿⣿⢸⡜⠿⢣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⢠⣿⣿⣿⣿⣿⡟⠱⠾⣿⣿⣿⣿⣿⢷
⠀⠀⠀⠀⠀⡿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡞⡇
⠀⠀⠀⠀⢰⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿
⠀⠀⠀⠀⢸⢹⣿⣿⡟⣩⣭⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⣭⢻⣿⣿⣿⢸
⠀⠀⠀⠀⢸⢨⣭⣿⣧⣙⣛⢸⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⢸⣿⣯⣭⢹
⠀⠀⠀⠀⢸⣸⣿⣿⣿⣍⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣫⣼⣿⣿⣿⣸
⠀⠀⠀⠀⠘⡯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿
⠀⠀⠀⠀⠀⢷⢻⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢷⠇
⠀⠀⠀⠀⠀⠘⣟⣿⣿⣿⣿⣇⠺⠇⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⠀⣿⣿⣿⣿⣟⡞
⠀⠀⠀⠀⠀⠀⠸⡜⣿⡿⣿⡇⣾⡷⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅⣍⡁⣿⡿⣿⡿⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠙⣄⢾⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢀⣿⣿⣿⣿⣿⣿⣿⡇⣾⣿⣿⣿⣿⣿⣿⡟⠰⢶⣿⣿⣿⣿⣿⣿⣿⣿⣯⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣝⢿⣿⣿⣿⣿⣿⣿⢃⣿⣿⣿⣿⣿⣿⣿⡟⡁⣉⣿⣿⣿⣿⣿⣿⡷⣾⣷⢹⣿⣿⣿⣿⣿⢟⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢜⡻⣿⣿⡿⣿⣼⣿⣿⣿⣿⣿⣿⣿⡀⣤⡌⢻⣿⣿⣿⣿⣿⣷⣮⣴⡿⣿⣿⡿⣛⠵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⣝⡱⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣍⣥⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣙⡽⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠮⢽⣛⡿⠿⣿⣿⣿⣿⡏⣿⣿⣿⣿⡿⠿⣟⣻⡯⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠚⠿⠷⠾⠟⠒⠚⠛⠉⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠿⠛⢿⠛⡿⢿⡿⢛⡿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠦⠤⠤⠠⠤⠀⢂⣩⡆⡤⠤⠶⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⣵⣞⣿⣿⣿⠶⣌⢣⡈⢲⡘⣆⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⡾⣽⣿⣿⡿⣟⣿⣞⣧⢵⡀⣁⣨⡶⠾⠿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⣨⠴⠐⣗⣿⢿⣷⣁⣷⣞⣿⢸⣞⣷⣽⡧⠆⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢬⢏⠂⢇⢻⡽⣿⣿⣻⣟⡷⣏⣾⣿⡟⠉⣀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠡⠈⢎⢆⠈⢣⡙⢿⣿⣽⣯⣷⣿⣿⣫⣴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢀⣼⡶⣟⣩⠤⠴⠿⢶⣶⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣾⣏⡒⣁⣠⣤⡶⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠉