Drunken Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣦⠀⠀⠀⠀⢀⣴⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠃⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⠂⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡖⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣬⣶⣿⣿⣿⣋⡀⣀⣀⣀⣈⠻⣿⣿⡯⠞⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠿⢿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣿⠿⠛⠉⠀⠀⠿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣿⡿⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠄⠦⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⡿⠛⣿⣿⣿⣿⣿⣿⠙⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢈⣠⣴⣾⣖⣦⣶⣾⣿⣿⡿⠟⠋⠁⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⢻⣿⣿⣿⣟⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⢹⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⡿⠛⣽⣿⣿⡿⠁⠀⠀⠀⣿⣿⣿⡏⠉⠻⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠿⠋⠁⢠⣾⣿⣿⠟⠁⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠈⠻⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠟⠁⠀⠀⢠⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠈⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠁⠀⠀⠀⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠋⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⠃⠀⠀⠀⠀⠀⠸⣿⣿⠏

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣛⣻⣛⣟⣟⣛⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣽⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡺⠿⠟⠛⠛⠿⠿⣶⣢⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⡾⢁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣿⠃⠌⠩⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⢀⡠⣤⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⡴⡵⠃⠀⡤⠜⠀⠀⠀⠀⠒⠻⣦⠀⠀⠀⢠⣾⣿⣦⣹⣷
⠀⠀⢠⣮⣾⣿⣿⣿⣆⠉⠉⠘⠛⠛⠻⣖⢄⣼⡿⠁⠀⡘⠋⠉⠀⠀⠀⠀⢀⡀⠘⠀⠀⠀⣾⣯⣾⢿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣷⢾⣁⣀⡀⢇⠀⠀⠀⠀⠀⢿⡁⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⢿
⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣄⣇⠏⣌⣄⡑⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡩⢂⠀⡂⡷⡇
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣿⠟⠉⠉⠉⢉⡩⠽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣪⣾⠟
⠀⠀⠀⠙⠿⠿⢿⡿⣛⣿⣿⣿⣿⣿⣿⠁⢠⡤⣶⢎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⡯⠟⠊⠁
⠀⠀⠀⠀⢀⣔⣽⣿⣿⣿⣿⣿⣿⣿⣿⣇⢀⣿⠉⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣾⠿⠛⠁
⠀⠀⠀⠀⠘⢟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣦⣴⣫⣷⣄⠀⠀⠀⠀⠠⣾⣽⠋
⠀⠀⠀⠀⠀⠈⠻⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡈⠐⢀⠤⠲⢌⣯⡳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢟⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡜⢄⠺⣄⠀⢸⢹⣿⣮⣢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠛⠿⢿⣻⣿⣿⣿⣿⣿⡇⠀⠀⠘⢷⡿⠈⣿⣿⣿⣝⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣇⠀⠸⣿⣿⣿⣯⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⠀⠀⣿⣿⣿⣿⣷⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⡇⠀⢹⣿⣿⣿⡫⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⡇⠀⠈⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢝⣿⢿⣿⣿⣿⣿⡇⠀⠀⠀⢸⣟⡯⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠚⠛⠛⠓⠒⠒⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠉⠀⠀⠠⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠢⣀⣄⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣤⢶⣶⣶⣿⣿⣿⣿⣷⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠈⠀⠉⠿⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠸⣿⡇⢦⢟⠄⠁⠐⠒⠢⠤⣀⡀⢠⢤⠤⠤⠤⢤⣤⣄⣀⡜
⠀⠀⠀⠀⢀⠀⡄⠀⠀⡇⠀⠀⠀⢀⣐⣻⣿⣿⣿⢠⣊⡀⠀⠉⠉⠁⠀⠉⡽⠋⠉⠉⡆⠀⠉⡆⠀⠀⠉⠃⠈⡄⠀⠀⠀⠀⠀⢀
⠀⠀⢠⠀⠐⠒⣃⣀⣀⣁⠤⠤⣄⠀⠙⢿⣹⠋⠉⢰⠀⠠⠤⣀⡀⠀⠀⢠⠇⡠⠀⠀⡇⠀⡴⠁⠀⠀⠀⢀⡔⢣⡀⠀⠀⠀⠀⡞
⣅⠀⠀⢀⠠⠎⠁⠡⠀⠤⠴⠀⠘⡆⡴⠋⠙⠀⢤⢸⠉⠒⠲⠀⡙⠂⠐⠿⡮⠒⠶⡀⠷⠏⠀⠁⡀⠤⠒⠁⣀⡤⣋⡕⠀⠀⢠⠃
⠈⠓⣄⠳⠴⢖⣀⣀⣀⣠⡤⠤⠖⠙⠶⠀⠀⢩⡓⠊⠀⠀⠀⠈⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣹⣶⡞⣿⡿⠿⠃⢀⠇⠀⠐⢾⡀
⠀⠀⠀⠂⠑⠢⢄⡁⠀⠀⠀⠀⠀⠀⠀⠑⠀⠊⠁⠀⠀⠀⠀⠀⠀⢀⣀⣠⡆⠀⠀⡖⢸⣿⣿⠿⠋⠀⠀⠀⣠⠴⠵⠶⠖⠒⠻
⠀⠀⠀⠄⡆⠀⠀⠉⠓⠦⣄⣠⠀⠀⠀⣀⣀⣀⠤⣤⡔⠒⠚⠉⣭⣿⣿⣿⣗⠀⠀⡗⢈⠔⠁⠀⠀⣠⠔⢋⣤⠄⠐⠒⠒⠛
⠀⠀⠀⠉⡇⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⡁⠀⠀⠀⢿⡇⠀⠀⢠⠏⠹⢭⡯⢸⠀⠀⣃⡀⠀⠀⠛⣻⣽⠇⣾⣿⠃⠀⠀⠀⣿⡟
⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡇⠀⣠⠃⠀⢠⠎⠀⠸⠀⠀⠉⣌⣣⣄⡀⠀⠙⠷⣿⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⡈⠲⣼⡧⠰⢁⠀⢀⡞⠀⠀⠀⠢⠤⠤⢟⣨⢟⣹⠶⣄⡀⠀⠉⠓⠀⢀⠀⠇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⢌⠢⡈⠋⠻⡗⢕⡿⠀⠀⠀⠀⠘⢦⣀⢀⣀⡈⢸⠀⢸⢹⣇⠠⠊⣀⣠⠃⢁⡀
⠀⠀⢀⡓⠈⢀⠀⠀⡠⠀⠀⠀⠀⠀⠀⣷⠀⠀⠱⢜⣄⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⢿⠉⠁⠀⠚⠀⡘⠜⠛⠆⢀⠟⠁⠀⠉
⠄⠀⠿⠇⠉⠿⠀⠈⠉⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠙⠗⠓⠒⠒⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠓⠒⠐⠒⠊⠁
⠀⠀⠀⣀⣀⡀⠤⠄⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⣸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋⠙⠛⢿⣦⡀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣠⣶⠿⠛⠉⠙⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⣀⡤⠿⠛⠟⠉⠍⠀⠀⠀⠀⠀⠀⠀⢀⠭⠙⠻⠻⠧⢤⣀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣴⣿⣿⣿⡿⠶⣶⣿⣷⡀⠀⠀⠀⠀⠀⡔⣡⣾⣿⣶⠾⢿⣿⣿⣷⢦⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣯⣴⣿⠋⠀⠀⠀⠀⠙⢻⣿⠀⠀⠠⡄⢠⢰⣿⡟⠁⠀⠀⠀⠈⠻⣿⣬⣽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡧⠀⠀⠀⠀⠀⣤⠨⣿⠀⠀⣀⣀⢸⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠛⠿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣼⣿⢠⣯⣉⣉⣿⠸⣿⣖⠲⠖⠒⠒⠒⣲⣿⣿⡿⠟⠁⠢⡄
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠉⠛⠻⠷⠶⠤⢶⣿⠿⠁⠈⠿⢿⡿⠟⠀⠙⢿⣷⡶⠦⠶⠾⠛⠋⠁⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠲⡆⠀⠀⠀⠀⠀⠀⠈⠀⠀⠖⠀⠀⡀⠈⠒⡦⠥⠼⠤⠄⠀⠂⠁⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⠀⠙⠒⢲⠒⠢⢤⡀⠀⠀⠀⠘⠢⢄⣀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⢲⡖⠒⠃
⢠⠊⣹⣿⣿⡷⠒⢦⣄⡘⡃⠀⠀⠈⠑⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠋⠁⠀⠀⢸⠁
⠀⢺⣿⣿⡿⠁⣴⣿⣿⡿⢃⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⠀⠀⢀⣀⣀⣀⠀⢀⠀⠀⠤⠒⠊⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠙⠏⣠⣾⣿⣿⠟⠀⡍⢦⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠤⠄⠠⠤⠤⠤⠠⣄⡀⠀⠀⠀⠀⠀⠀⢀⡞⡱
⠀⠀⠀⠀⠀⠉⠉⠉⠈⠁⢸⠚⠑⡤⠀⠀⣄⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢀⡀⠀⠀⣴⠋⠺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠼⣾⢠⠀⠀⡿⠤⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⠤⠴⣇⢀⢀⣈⡷⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠂⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠄⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠱⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⠿⢿⣟⣓⣚⣒⣀⣀⣀⣀⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡛⠉⣴⣿⣿⣿⣟⡉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠻⠿⣿⣿⣿⣿⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⣹⣿⠓⠒⠀⠀⠀⠀⠀⣀⠀⠀⠀⠢⠀⠀⠏⠻⣿⣿⣟⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡦⢟⡻⢷⠶⣟⢦⡄⠀⢀⣻⣵⣶⣶⣄⠀⠀⠄⠀⠙⢛⣿⣼⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣼⣷⣿⡾⢻⣧⡷⢻⠴⢿⣶⡶⢹⡎⡬⠐⡊⢁⣤⢽⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣓⣳⣻⣿⠁⠈⢧⣘⠢⠸⣦⠅⠀⠀⠀⢳⡄⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣏⡽⣻⡏⠀⠀⠈⢯⡙⠉⠁⡄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠀⠀⠀⠈⠿⠿⢷⡟⠿⠒⠀⠀⠀⠙⢦⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣾⡀⠁⠀⠀⠀⠀⠰⠀⣾⡿⠃⠀⠀⠀⠙⢆⠁⢀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠅⠘⠠⠤⠀⠀⠀⠀⠀⢰⣦⣇⠀⠀⠀⠀⠀⡀⠀⠀⠀⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣤⣴⢶⣦⣤⣤⣤⣤⣤⡆⣼⣿⣿⣤⣼⣧⠖⢻⡿⠃⠀⡆⢸⣿⣿⣷⣦⠠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡷⠀⠿⠿⢿⣿⣿⣿⣿⢇⣿⣿⣿⣿⡿⣿⡀⠈⠁⠀⢰⠇⢸⣿⣿⣿⣿⣧⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣤⣤⡀⡀⠸⠛⠋⢼⡇⠘⢿⣿⡇⢹⡇⠀⠀⣰⡟⠀⢸⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠾⠷⣦⣤⢥⣤⣴⣿⢠⣶⣍⡁⢈⠓⣀⢼⣩⡄⠀⢸⣿⣿⣿⣿⣿⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣄⣠⣺⣿⣿⣿⣿⣧⠉⠙⢿⠻⠚⠋⠉⠻⡄⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠾⣿⣿⣿⣿⠀⠀⢀⡇⢀⠀⠀⠀⠀⢹⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠂⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠋⠓⠦⠶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⡤⢤⣀⣀
⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠧⠀⠀⠁⠉⠳⡄
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠲⡄
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢀
⠀⠀⠀⣏⢀⣤⣠⣤⣤⣠⣤⣤⣆⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⡀⠀⠀⡸⠁⠀⠀⠀⡀
⠀⠀⠠⡏⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠙⠶⠤⠼⠋⠧⣄⣀⣤⠞⠁⠈⢹⠁⠀⢀⡇
⠀⠀⠀⢙⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣸⠀⢠⠋
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⢣⣤⣤⣄⣀
⠀⠀⠀⢠⣿⢠⠓⢦⠠⢀⠀⠒⣆⣀⣠⠐⠂⢲⣄⠀⢀⣀⠤⢤⡤⠔⠢⠐⠆⢸⡇⠄⢸⠁⠀⠈⠉⠳⣦
⠀⠀⠀⢸⣿⢸⠀⢈⠀⠀⠀⠀⠘⠿⠋⢰⡄⠘⠿⠿⠋⠀⠀⠀⡆⠀⠀⠀⠀⢸⡇⢀⡿⠒⠲⢦⡀⠀⠈⠳⣄
⠀⠀⠀⢸⣿⢸⠀⠘⢄⡀⠀⠀⠀⢀⡴⠃⠳⡀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢀⢸⡇⣸⠁⠀⠀⠀⠙⢦⡀⠀⠘⢧⡀
⠀⠀⠀⡚⣿⠀⠀⠀⠀⠈⠁⠁⠉⠁⠀⠀⠀⠈⠓⠀⠀⠔⠚⠁⠀⢲⣦⠀⢸⢸⡇⢿⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠳⡄
⠀⠀⡠⠋⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⢸⠈⣧⠈⠳⡄⠀⠀⠀⠀⠀⠹⣆⠀⠀⠹⣆
⠀⣸⠁⠀⡇⠀⢠⡾⠋⠙⢲⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠁⠀⠀⠀⠈⠀⣿⠀⠀⢧⡄⠀⠀⠀⠀⠀⠘⣦⠀⠀⠙⣆
⠀⢻⡀⠀⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡆⣿⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠸⣆⠀⠀⢹⡄
⠀⠘⢦⢰⡇⡆⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠃⢿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢻⡀⠀⠘⣇
⠀⠀⠀⢰⡇⡇⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡿⠿⠛⠛⠁⠀⠀⠈⠑⠢⣄⢠⢸⡇⠀⣀⣴⠃⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⡿
⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣸⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⢸⡇
⠀⠀⠀⣸⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠏⠀⠀⠂⠱⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣷⢀⣤⠶⠶⣤⣤⣤⣤⡴⠞⠁⠀⢀⣾⠁
⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢄⠀⠀⠀⠀⠀⢀⡜⢡⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⢀⡴⠛⠁⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⣤⣶⠃⠀⠑⠲⠤⠤⠖⠋⣀⡴⠈⠻⢶⣄⠀⠀⠀⠀⠀⠀⣀⣴⠟
⣼⠁⠀⠀⠀⠀⠈⠑⠂⠤⠄⢀⡀⢀⣀⣀⣀⣀⣉⠉⠁⣀⠀⠀⠤⠄⠒⠊⠉⠀⠀⠀⠀⠀⢹⡆⠀⢀⣠⣴⠾⠋
⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠓⠛⠛⠉
⠀⠙⠷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠁
⠀⠀⠀⠀⠉⠻⣷⡶⢦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣴⣶⣶⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⢦⣬⣭⣭⣍⣭⣍⣭⣭⣭⣭⣤⠾⠿⠟⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⠀⠀⠰⣖⣃⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⡀⠄⠂⡁⠀⠠⠀⠀⠀⠀⠀⠀⠀⢸⠿⠋⠉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⢿⣇⣤⣄⡁⣀⣀⣠⣤⣄⡀⠀⠀⠀⠀⣀⠀⣈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢋⣤⠰⠿⠆⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣼⣿⣼⡇⠀⠀⠀⠈⠉⣽⣿⣿⣿⠃⠈⠉⠻⢣⣦⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⣿⣭⡣⡇⣀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⠀⣴⣿⣿⣷⣄⠀⠀⡀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⡄⠀⠀⠉⠛⠇⠋⠀⠀⠀⣰⣿⣿⣿⡇⣀⣴⣾⣻⣽⢾⣿⣿⡗⠀⢁⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⢿⣿⠁⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⠋⠀⠀⠀⠀⠀⠀⢸⣷⣇⠀⣀⣀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⣭⣽⣛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣾⣿⡟⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⢿⣿⣿⣿⣷⣄⠀⠀⠈⠹⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⢢⣾⣿⡟⣀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠙⢿⣿⣿⣿⠆⠀⠀⠀⠘⢿⣟⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣼⣿⡿⣁⠟⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠙⠟⠁⢶⣿⣶⡄⠀⠀⠹⣷⣝⢿⣿⣧⠀⠀⠀⠀⠀⠈⠉⠉⠁⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠟⢻⣤⠀⠀⠈⣛⣃⣙⣿⣧⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠐⠠⠀⢀⣼⣿⣿⣿⡿⠋⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠁⠂⢠⣾⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡤⠙⢿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠸⠷⣤⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣿⣿⣿⣿⣿⣿⣶⠄⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠟⠋⠉⠀⠀⢀⣤⣶⣿⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⣿⡟⠡⠶⣀⠤⠀⢺⡟⠀⠀⠀⠀⠀⣤⡶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⢻⡆⠀⠀⠉⠀⠀⠀⠑⠀⠀⠀⠀⠀⠈⢳⡈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⢻⣄⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣻⡄⠀⠁⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠤⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣢⡞⢿⠋⠙⠷⠀⠀⠀⠀⠀⢠⣧⠀⠀⠀⠀⠀⠀⠀⠀⢲⣤⡔⠀⠀⠁⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠈⢃⠀⠀⠀⠀⡀⠁⠀⠈⠷⡀⢄⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠀⠀⠀⠀⠀⠀⢀⡞⠋⠛⠸⠉⠻⠁⡌⠀⣄⠀⠌⠀⠀⠀⠀⠀⠹⣄⠃⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⡠⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⡤⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⢀⣀⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⣄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠵⡯⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢹⠦⣤⠀⠀⠀⢘⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠘⠀⣿⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠐⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡶⠀⠀⠀⢸⠀⠠⠀⢀⣀⠠⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⡧⠀⠀⠀⠈⠀⠀⢀⠀⣀⣀⣤⣤⡀⢀⡠⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⣤⢀⣀⣀⣠⡴⢦⠾⠿⠛⠛⢿⣷⣤⡾⠁⠀⠀⠈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⢸⣧⣼⣧⣁⣼⣦⡃⠀⠀⠀⠀⢿⢿⡇⠀⡀⠀⠀⠮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠈⠛⠛⠋⣿⠛⠛⠧⠤⠤⠤⠒⡿⠀⠀⠀⠀⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠋⠙⠋⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣾⣿⣿⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⡄⠀⠀⡄⢤⣄⣀⡀⠀⠀⣀⣀⡀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⢀⣀⣀⣀⡀
⠀⠲⣼⡇⣿⣆⣇⣼⣿⣿⣾⣾⣾⣿⣿⣷⠀⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣶⣖⠀⠀⠀⠀⣷⣾⣿⣿⣿⣿⢸⣿⣿⣿⣷
⠀⣷⣿⡇⣿⣹⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣄⣿⣿⣭⣿⣿⣿⣿⣿⣿⡭⠅⣀⠀⠀⡀⠀⠠⢿⣻⣿⣿⣿⣿⢸⣿⣿⣿⣿
⠀⢿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⣿⣟⣛⡛⣿⣿⣟⣛⣛⠛⡒⠒⠶⢠⣿⣶⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿
⠀⠨⢸⡇⣿⠏⣿⡿⣿⣿⣿⣏⣿⣿⣿⣿⡏⡟⢯⡉⠛⠘⢿⣿⠏⠋⠁⠀⠁⠀⣰⢃⢳⣾⣿⣿⣿⣿⣿⢿⣸⣿⣿⣿⣿
⠀⠀⢸⡗⣿⢃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⣶⣾⣿⡶⢆⣸⣿⣶⠀⠀⠀⣤⠾⠶⠀⠸⠟⢿⣿⣿⣿⢥⣾⣿⣿⣿⣿⣿
⠀⠀⢸⡟⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣿⣿⠟⠁⠆⠻⣿⣿⠀⠀⠀⢠⠆⠶⢴⢠⡆⢿⣿⣿⣿⢚⣿⣿⣿⣿⣿⣿
⠀⠀⢸⣷⣿⠀⣿⣿⣿⣹⣿⡿⣿⣿⣿⣿⠀⠋⠉⢠⠄⡄⠆⢹⣿⣆⣀⠲⣼⣀⣰⣷⣦⠀⢸⣟⡻⣻⠨⣿⣿⣿⣿⣿⣏
⠀⠀⢸⣿⣿⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⣧⡄⣠⣶⣄⣴⣿⣿⣿⣿⣿⡾⣿⣿⣿⣷⡞⠈⣿⢘⣿⢈⣿⣿⣿⣿⣿⡇
⠀⠀⢸⣿⣿⠂⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣤⣿⣾⢿⣿⣿⣿⣿⡟
⠀⠀⢼⣿⣿⠂⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣉⠉⢿⢿⣿⣧⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠛⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⣿⣿⣿⠖⠉⠀⣠⠀⠈⠙⠿⣿⣿⣿⣾⣿⣧⠈⡀⠨⠿⠿⣿⡿⢿⠿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣿⡏⣻⣿⣿⣿⡇
⠀⢰⡼⣿⠏⣠⣾⡿⣿⡳⠄⠀⠀⠈⠿⣿⣿⣿⣿⡇⢉⠁⣙⠢⠤⠁⠐⣉⠌⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣯⢹⣿⣿⣿⡇
⠀⢸⣗⡁⠰⣿⣿⢣⣇⠁⣤⢉⣶⡄⠀⠈⠉⠙⠛⠻⠚⠈⣽⣆⣀⠑⠓⠒⢀⣾⠟⣿⠂⠠⠍⡙⠻⢿⣿⡏⣹⣿⣿⣿⡇
⠀⢸⣏⡽⣰⣿⣏⣿⠁⠀⠃⢊⣺⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠢⢬⣿⣷⣿⣷⠀⠀⠈⠀⠀⠉⠁⢻⣿⣿⣿⡇
⠀⢾⣿⣿⣷⣿⣿⣿⣿⣷⣶⡾⠃⠀⠂⠀⠀⠀⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠻⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡇
⠀⢘⣛⣻⢿⣿⣿⣿⡿⠛⠅⠀⠀⠄⠐⣄⣠⠖⠄⠀⠃⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀⢿⡛⠂⢀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣧
⠀⠈⠉⠻⠀⢻⣿⠋⠁⠉⠑⣽⣄⢀⣗⡈⢿⣷⣄⠀⠀⠀⠀⢀⣿⣧⠀⠀⠀⠀⠀⠈⠣⡔⠋⠛⠓⠠⣄⣠⣬⣿⣿⣿⡏
⠀⠀⢶⣠⣴⣾⣿⣶⠁⠀⠀⠀⠙⣻⣿⣷⣼⠿⠿⠿⣤⣀⡀⡈⣿⣿⣶⣄⠤⠀⠀⠀⢀⡉⠃⣠⣴⣴⣬⣿⣿⣿⣿⣶⡇
⠀⠀⠋⠙⠛⢹⣿⣿⣆⠀⠀⠰⠚⠁⠀⠙⠉⠂⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⣀⣀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⢀⡠⠐⠻⣿⣿⣷⣀⠀⠀⡀⠀⠀⢀⣠⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠐⠈⠉⠀⠀⡀⢹⣿⡿⠿⣦⠾⠶⠖⠛⠛⠛⡿⢿⠿⢿⣿⣿⣯⣿⣿⣿⣿⣷⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠃
⠀⠀⠀⠀⣀⣠⣗⡋⠉⠁⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠙⠛⠛⠟⠛⠻⠿⠿⢿⡿⠛⠛⢻⠥⠾⢬⣡⣤⢲⣤
⠀⠀⠐⠂⠈⡉⠀⠀⠀⠀⠈⠉⠑⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⢒⣶⣶⣶⣤⡀⢀⡀⠠⠠⠶⠦⠔⠙⣭⣽⣿⣦⠆
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠟⠉⠀⣩⠴⠂⠀⠀⠀⠈⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣶⢟⣫⡭⠷⠶⠖⠲⠶⠾⢭⣝⣛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⠸⢿⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡓⢮⣙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠹⠿⣿⣶⣦⣤⣄⣀⣲⢷⣦⡉⠀⠙⢷⡝⣷⡀
⠀⠀⠀⠀⠀⠀⢠⡿⣱⠆⢀⡶⠀⠀⠀⠀⠀⠀⠙⢻⡟⠛⣩⡅⢈⣝⠉⠀⠀⠀⠙⣎⢿⡄
⠀⠀⠀⠀⠀⢀⡿⣱⠃⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡰⠛⢚⣡⣿⣷⣄⠀⠀⠀⠘⣎⢿⡄
⠀⠀⠀⠀⠀⣸⢇⡏⠀⠀⠀⢠⣶⣶⣤⣤⣀⠀⣸⢿⣿⣾⣿⡿⠟⠙⢿⣿⣦⡀⠀⠀⢹⡸⣇
⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠸⣿⣿⠿⣿⣿⣿⣿⣆⢭⠋⠁⠀⠀⠀⠀⠙⢿⢟⣤⠀⢸⡇⣿
⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⢻⣿⡿⠿⢿⣿⣿⣿⡆⠀⣆⠀⠀⠀⠀⠀⠀⠙⠿⣦⡸⡇⣿
⠀⠀⠀⠀⠀⢹⡏⣇⠀⠀⠀⠀⠈⣿⡇⠀⠀⠈⣿⣿⠇⠀⣿⠀⠀⠈⠀⠀⠀⣀⠀⢋⢹⢆⠏
⠀⠀⠀⠀⠀⠈⣷⡹⡄⠀⠀⠀⠀⢹⡇⠀⠀⠈⠙⢛⣀⣤⡛⠁⣤⣤⣶⡻⣿⣿⣿⢆⢏⣶
⠀⠀⠀⠀⠀⠀⠘⣷⡹⣄⢀⣀⣠⣾⣿⠀⠀⠀⠀⠀⠙⢟⣷⣼⣿⣿⡿⠟⠾⠛⣡⢏⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣌⢻⣟⠋⠁⠀⠀⠀⠀⠠⠶⣿⣿⣿⣯⣿⣷⣿⣿⣷⠼⣣⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣍⡳⢤⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣮⢻⣿⣯⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣯⣝⣓⡶⠶⠾⠿⠷⢖⣋⣥⣥⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢬⣖⢂⠁⠀⠀⠄⠀⢀⠀⣠⠄⡉⠁⠂⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠆⠀⠐⠓⠻⣈⠀⢁⡀⡄⠈⠁⠎⢁⠀⠞⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠤⠄⠈⠉⠂⠀⠘⢁⡄⠀⣀⡉⠁⠀⢠⠃
⠀⠀⠀⠀⠀⠀⢀⣤⡐⣄⠀⡀⠀⠀⠀⠀⠀⠁⢾⠁⠔⠁⢁⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡀
⠀⠀⠀⠀⠀⢠⣿⡏⠁⠀⠀⠀⠉⠁⡀⠀⠀⠀⠃⠀⠄⠀⣼⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢺⣿⣿⡇
⠀⠀⠀⠀⢰⣿⠟⠅⠀⠀⠁⠀⠀⠀⠀⠐⠀⠘⠁⠐⣀⠀⠀⣔⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣼⣿⣿⡄
⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠒⠀⠛⠁⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉


⣶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣏⠉⠉⣉⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⣿⣿⣿⣿⣿⣿⣿⣿⡂⠀⠨⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣯⡉⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠦⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠿⣟⣛⣛⣩⣭⣥⣤⣴⣶⣶⣶⣶⣶⣶⣤⣿⣷⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣾⣿⣿⣷⣶⣿⠿⠛⠉⠉⡉⠤⠀⠀⠀⠀⢷⠈⠛⠿⢿⣿⣿⣿⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣼⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⠀⢀⢀⠁⠀⠀⣀⠀⢀⠀⠀⠀⢻⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢻⣿⣾⣿⣢⣠⣼⣆⠀⢠⣾⣷⣶⣥⠶⠀⠀⠸⣟⣓⡶⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡟⣿⣿⣿⣿⠇⣿⢿⡟⠻⢿⣆⡄⠀⡀⣯⣹⣿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣌⠻⣿⣿⠀⠉⠀⠙⠚⠫⠁⠀⣼⡇⢋⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣾⣿⣿⡀⣠⡼⠳⣤⣜⠿⠹⢻⣷⣎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣡⣤⣤⣽⣯⣠⣤⣄⡉⣼⠁⢸⣿⣿⣿⣿⣿⣟⣳⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣷⣿⣿⣿⡏⠙⠁⠀⠸⢁⣧⣴⠉⣿⣿⣿⣿⡗⠀⣀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣇⣿⡇⠀⠀⠀⣦⣼⣿⢇⢠⣿⡏⣿⣿⣁⠀⠙⣏⣉⡙⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠓⣧⣀⣠⣶⣿⣏⣁⠈⢸⣿⡇⣿⡟⠋⣠⠐⢛⣉⣉⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣧⠄⠨⣟⣉⣥⣬⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢻⣿⡿⠿⠟⠛⠛⠛⠛⢛⣿⣿⣿⣿⢠⣤⡀⠀⣹⢻⣤⡆⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡰⣿⣷⢸⣿⣿⣄⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣾⣿⣶⣾⣵⣾⡷⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⡼⣿⣿⣞⣿⡇⣿⣿⣿⣧⣄⠛⣴⣿⣿⣿⣿⣿⡿⣳⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣧⣿⣿⣿⣿⣧⢸⣿⣿⣿⣿⣿⣟⣹⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠖⢀⣲⣦⡀
⠀⠀⠀⢀⣤⡄⠀⢤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠹⢿⡇
⠀⠀⢀⣿⠉⠀⣀⠈⢹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⣾⠃⠐⠛⠓⢺⡇
⠀⠀⢸⣷⠄⠀⠤⠴⢼⣿⡇⠀⣠⣤⣶⠂⠀⠀⠀⢢⣾⣿⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠤⠄⠰⠆⢀⣠⣤⣤⡉⠀⠀⣿⠋⠀⠀⠻⣿⣧
⠀⠀⢸⣿⠀⠀⢠⠀⢈⣿⡇⠀⣿⣋⠉⠀⠐⠒⠒⣾⣿⣿⣿⡟⠇⠀⣠⣤⠄⠀⢤⣤⡀⠈⢻⣏⠀⠀⠀⣀⣼⣿⣿⣿⠧⠀⠀⣿⠀⠀⠀⣠⣸⣿
⠀⠀⠘⣷⠀⠀⠀⠀⣼⣿⠃⠀⠈⠙⣶⠶⠴⠾⣷⣿⠟⠉⠀⠀⠀⢸⠇⠀⠤⢻⣎⠻⣿⠀⠀⠙⠿⡁⠠⣘⣻⠟⠙⠀⠐⠀⠀⢻⡆⠀⠀⢁⣿⡏
⠀⠀⠀⠈⠷⣄⣸⣦⡿⠁⠀⠀⠀⠀⠻⢤⣤⣦⡾⠟⠀⠀⠀⠀⠀⡿⠃⠦⣐⣢⣼⣿⣿⡆⠀⠀⠀⠐⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠉⢲⣿⡟⠋
⠀⠀⠀⠀⠀⠸⣿⠇⠀⢀⡀⠀⠀⠀⠀⠘⢦⡿⠃⠀⠀⠀⠀⠀⠀⢳⡀⠺⠟⠿⣎⣽⡿⠃⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⢀⣠⢀⣸⠀⢀⠋⠁⠀⠀⠀⠀⠀⠈⡇⠀⣠⠀⠀⠀⠀⠀⠀⠈⠉⠲⣿⠋⠉⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⠀⠀⢀⡀⠀⠀⠀⣼
⢀⢠⡷⠟⠋⠉⣻⠀⢨⠒⢟⡷⢶⡶⣄⠀⠀⡇⠀⢿⣁⠉⠄⠠⢤⣄⠀⠀⠀⣿⠀⠀⠀⡀⠒⢶⠠⠀⢰⠇⢰⣤⣿⠆⠀⠻⣾⣤⠆⠀⢹⠀⠀⠰⢦
⠻⠂⠁⠰⡖⠐⠙⠃⠈⢹⡿⠇⠈⢳⣿⠐⠈⢻⣶⣦⠀⠀⠀⠀⠀⣿⠂⣤⠐⠙⣦⣤⠐⡄⢀⡟⢠⣻⠚⢷⣦⡄⠀⠐⢊⣽⡧⣤⡄⠒⣹⣷⣶⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠈⠈⠁⠀⠀⠛⠛⠋⠀⠀⠀⠀⠀⠀⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢂⣴⠏⠀⠀⠈⠉⢀⡒⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⣿⣷⡋⠁⠀⠀⠀⠀⠀⠀⠙⣦⠛⠛⠷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠁⠀⣿⣿⣧⣀⡀⠀⠀⠀⠀⠀⢀⢈⣷⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠉⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⡀⢧⠀⠀⠀⠀⠈⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⢀⣤⣴⣶⣚⣋⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣭⣭⣭⣭⣤⣀⠐⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⢿⡟⠛⣿⣿⠋⢹⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠉⠛⣿⣿⠧⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠉⠒⢎⣍⠀⢸⠀⣱⡶⢤⡀⢀⣤⣓⠓⠆⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⡜⡟⡏⠐⠋⠁⣰⣧⠀⠻⠏⠀⠀⠀⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢻⣄⠀⠉⡁⠿⠀⠀⠄⡉⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡇⡞⠙⠁⢤⠀⠀⠙⠀⣤⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⣠⣴⣶⣿⡟⢹⣿⣏⡶⠚⠀⠀⠈⠙⠀⡆⠘⡄⢹⢻⣷⠤⣄⠐⠇⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⢿⡆⣀⢴⣯⡈⢟⡟⠻⣿⠃⠀⢿⡙⢷⣦⣤⣤⣤⡄⠀⣿⠀⠀⢸⣏⠁⠀⠀⠀⠀⡀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡖⠫⠀⠑⣜⡆⠀⡛⠀⠀⢸⣧⠀⠈⠻⣏⡜⠀⠀⢿⡀⠀⢸⢿⣿⣶⣦⡂⠀⢨⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠈⣿⠀⡁⠀⠀⠈⣿⠀⢀⣠⣯⣴⣦⡀⢸⡇⠠⣾⣄⡀⢠⣿⡅⢠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀⠀⢸⡇⣿⣶⠀⠀⠛⠀⠉⢻⣿⣿⠃⠁⢸⡇⠀⠈⠿⢷⣾⣇⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣘⣷⢹⠋⠀⠀⠐⠀⠀⠀⣿⣿⣆⠀⢸⠀⠀⠀⢀⣀⣽⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⣄⡀⠀⠀⢇⠀⢰⣿⣿⣿⠀⡟⢀⣀⣤⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢶⣾⣶⣾⣿⣿⣿⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠄
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠂⢄
⠀⠀⠀⠒⠉⠘⠀⠀⠀⠰⢄⣀⠈⠀⠠⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⢠
⠃⠀⠁⠐⠤⢀⠁⠀⠀⢀⠠⠏⢀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢠⠀⠀⡄⠀⢠⠀⠀⠡⠜⢉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠐⠃⢂⣴⡀⢄⡀⠀⠀⠀⠀⠀⠄
⠀⠀⠰⠀⠈⠀⠀⠀⠀⠀⠀⠀⠐⢂⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠒⠀⠈⠉⠉⠀⠒⠠⣤⢀⠀⠀⠐⡶⠣⣤⡄⢫⠀⠀⠀⡠
⠀⠀⠀⠀⠄⠀⠀⠄⠀⠠⠀⠀⠀⠈⠁⠑⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠙⠃⡶⠋⠈⠙⢷⠀⢈⠶⠂⠤⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠳⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠒⠈⠁⠁⠶⡀⣸⠑⠁⠀⠀⠀⢆⣁⠀⢑
⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠂⠤⠎⣅⠈⠁⠈⠢⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡖⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠆⣀⡀⠀⠀⠀⢀⣠⡖⠊⠀⠀⠠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣤⣿⡿⠁⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⡠⣄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠓⡁⢀⡉⠂⢄⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠒⢸⠀⠀⠀⠀⠀⠀⡀⠀⠄⣀⢀⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⢀⠈⠀⡸⠂⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠐⠉⡉⠹⠿⠿⠋⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⢠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⢊⢀⡀⠀⠊⢃⡀⠔⠈⠆⠘⡊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⣄⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢤⠀⠀⠠⣄⠀⠀⠀⠀⠀⢠⡀⠀⠀⢄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⣀⠈⢀⠀⠀⢧⠀⡁⠊⠳⡀⠀⠀⠈⠲⢄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠂⠘⠄⠀⠀⠘⡄⠀⠀⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠜⣛⠀⠀⠀⠈⣓⡤⠤⠒⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡁⢙⠁⠀⠀⠈⢒⣀⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⢄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠎⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠂⠠⣶⠒⠀⠀⠀⠀⠉⡀⠀⠠⠀⠀⠀⠀⠀⠀⣚⡅⠀⠀⢈⣱
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡿⢟⣀⡀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠂⠀⠩⣀⣀⠀⣀⠰⠁⠀⠀⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⢱⢿⠃⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠑⠦⣀⡉⢙⠋⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⡖⠒⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠙⠀⠀⢆⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏⡴⠊⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⡟⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣼⣿⣿⡏⠙⠀⠀⠈⢻⡶⣄⠀⠀⠀⠀⠀⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⢿⣹⣦⣶⣔⢀⠀⠀⣽⠛⢮⣧⡀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡿⠛⠛⠻⢿⣿⢀⢰⠏⠀⠀⠉⢷⡀⠀⠀⣿⠋⠀⠀⠀⢀⣀⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠋⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⢻⡀⠀⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢃⠀⣿⡆⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⢀⣠⣾⠀⠀⠀⠀⠀⢹⣶⣤⣀⠘⢇⣻⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡏⠀⠀⠀⡴⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠈⣿⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⣀
⠀⠀⠀⠀⠀⠀⠀⣊⡻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠸⣢⡀⣠⠀⠤⠘⣿⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠨⡙⠻⣿⡇⠀⡄⠜⢢⣀⣊⠁⠀⠀⠀⠀⠐⡿⡒⠂⠀⠈⣿⡇⠀⠀⠀⢸⠀⢀⠠⠐⠊⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡌⠻⢀⠀⠈⠚⠀⠁⠀⠀⠗⠀⠀⠀⠀⠰⡀⠁⠀⠀⣿⡇⠀⠀⠀⠀⢐⠀⢱⡄⠘⢀⠠⣞
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⣠⡏⠀⣄⡓⠒⠊⠀⠀⠀⠀⠀⠀⣀⠘⢧⡀⠀⠀⢹⡇⠀⠀⢀⡠⡘⠢⠌⠒⠉⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣿⡄⠀⠈⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠀⠹⡄⠀⢿⣧⠀⠀⣎⠀⢸⠀⠀⠀⠀⣀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⣦⣄⣀⣀⣀⣀⠟⠛⣻⣿⠀⠀⠈⢳⠂⢺⡛⠛⠋⠉⠀⡟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⣿⢻⣇⠀⠀⠸⢤⣼⣁⣀⣈⡀⢼⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣍⡙⠷⠶⠦⠼⠦⣅⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠉⠉⠉



⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣀⣀⣀⣄⣘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠄⠀⣀⢀⣊⣀⠀⢅⠀⣸⠀⡀⠀⡀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠆⢲⣤⣾⠃⣔⣰⠘⠱⣄⡀⠈⠣⡀⠄⠀⢀⠀⡌⡠⢀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠙⣏⠎⡞⠏⠀⠀⡷⠎⠀⠘⢿⠆⠀⠀⠂⠙⠀⠀⠊⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣼⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠸⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡤⠥⠛⣖⠂⠠⢀⠀⠈⠁⠇⠀⠀⠠⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢡⡆⠀⡖⠁⠀⠀⡨⠃⠀⠀⠄⠀⢰⠀⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⠃⣰⠇⣀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠑⠚⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠀⠀⠀⠀⡀⠈⡕⠄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠘⣄⣧⠖⠂⠀⠀⠀⠀⠈⢁⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣀⣠⣤⡼⠀⠀⠀⠀⠀⠀⠀⡄⢈⡄⠥⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠚⠟⠠⠀⠉⠛⠀⠀⠀⠶⠶⠆⠀⠁⠀⠀⡀⠠⠄⠂⠉⠀⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠚⠓⠒⠂⠀⠀⠀⠀⠀⠐⠀⣀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠂⣄⡀⠀⠀⠀⠀⠀⡆⠀⡶⠖⠛⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣀⣶⠏⣀⢆⡁⠠⡀⠀⠀⠀⠀⠘⠁⠀⢇⠀⠙⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⡄⢷⡶⠊⢁⠤⠀⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡖
⠀⠀⠀⠀⠀⡀⠀⠀⠀⡎⢀⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢻⣏⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠜⠂⠲⠿⠓⠶⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⠔⠛⣈⡗⠐⢢⠒⡚⢦
⠀⠀⠀⠀⠀⡀⢒⣿⢤⡅⡀⠤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠐⢆⠉⠣⡤⢄⠁⢸⠋
⠀⠀⠀⠀⠀⠀⡎⠀⣸⡁⢀⣄⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠈⢿⣀⠀⢡⠀⣁⠸⢂⠍⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠶⠚⠓⠀⠀⠉⠉⠁⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠆⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠿⠷⠀⠀⠀⢠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⣀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠈⢣⠀⡠⠒⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⣟⢁⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⢿⠀⠀⠀⠀⠀⢤⠄⡇⠈⠁⠀⠀⠀⢸⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠈⢧⡀⠀⠀⠀⢀⡜⠹⡄⠀⠀⠀⢠⠏⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠠⢆⠀⠀⠀⠙⠲⠶⠚⠉⠀⠀⠈⠓⠶⠞⠋⠀⠀⠀⡦⠀⠈⠳⣄
⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⢨⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⡤⢄⠙⣆
⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⢇⠀⢀⠝⠉⠉⠈⠁⠀⠀⠀⢀⠔⠊⠉⠉⠁⠀⠀⠀⠈⠦⠜⠀⠘⡄
⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠈⠂⠀⠀⢱
⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⡆
⠀⠀⠀⢠⡇⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⢸⡇⠀⠀⠸⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠈⡇⠀⠀⢠⠊⢑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⣀⣴⣷⡀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡧⣄⡀
⢀⡞⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡠⠔⠒⠒⠂⠀⠀⣸
⠀⠙⠒⠶⠦⠤⢤⣄⡀⠀⠀⠀⠀⣀⣀⡀⠀⠐⠤⠤⠤⠤⠄⠀⠀⠀⣠⣀⡀⠀⠀⠀⠀⣀⣤⠤⠤⠴⠖⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠉⠉⠀⠙⠲⠤⣤⣀⣀⣀⣠⡤⠴⠚⠁⠈⠉⠉⠙⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⠿⣿⣿⣷⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢠⣴⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢻⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡘⢛⢻⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡎⢉⣀⡀⠀⠀⠀⠀⠀⠀⣾⣿⠁⣠⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣤⣴⢄⡀⠀⠀⠰⠆⠉⠀⠀⠀⠙⢻⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⣿⠉⢈⡁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠰⠆⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣼⣧⡆⢀⡴⠁⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣼⣷⡄⢸⡇⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠈⠀⠀⠰⡄
⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⢞⣴⠟⡿⠁⠄⣼⣿⡇⠀⣰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠞⢁⡞⢀⠀⣰⡿⠃⠀⣴⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠈⠰⣏⠁⠀⣼⣿⠟
⠀⠀⠀⠀⢀⣴⣶⣦⠆⠸⠏⠀⠘⠃⡀⢿⢠⣾⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⢀⠗⠀⢷⠀⠸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⢀⣾⣦⣄⣸⣆⣀⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡏⠠
⠀⠀⠀⠀⠀⢠⡞⣡⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⢀⡞⣹⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⢸⡏⠙⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⢸⡇⠀⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⡇⠀⠛⠛⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠈⠁⠀⠀⠀⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣶⡞⠋⣤⢁⣼⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄⠲⢁⠞⢹⠿⡙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⠐⠟⠰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠶⣮⣿⣿⣿⣷⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢸⣧⠀⠀⠠⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠁⠀⠀⠀⠀⢀⣬⣿⣿⣿⣿⣷⡀⠀⠀⠀⣼⣇⡀⠀⠀⠀⠐⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡀⠀⠀⣠⣀⣨⣿⣿⣿⡿⣿⡿⠁⠀⠀⠀⢿⠋⠁⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠉⠻⠟⠀⠛⢵⡿⠿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡟⠋⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣴⣤⣦⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⢁⣀⠄⠀⠀⠀⠀⠀⠀⣛⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣾⣿⣶⣾⣿⣿⣿⠶⠀⠀⠈⡘⣻⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣬⣍⣻⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣿⣿⠃⠙⠈⠳⣍⠉⠙⠛⠛⢛⣽⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⣿⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⣹⣤⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢰⡛⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣯⣽⣿⣿⣯⣿⠻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⣀⣭⣿⣿⣿⣷⣬⡆⣻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⣠⣴⣿⣶⣶⣶⣤⡄⠀⠀⠀⠀⠈⠉⠁⠀⠙⡿⠿⣿⡇⣼⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⣸⣤⣴⣶⣶⣾⣷⣶⣤⣹⣿⡿⢻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⢸⣯⢸⣿⠏⢿⣛⣛⣻⣿⣿⣿⡆⠺⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢱⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠈⠛⣾⠛⣿⢿⡟⢹⣿⣿⠁⠀⢸⣿⣏⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠀⠀⠀⠀⠈⠐⠈⢁⡿⠛⡏⠀⠀⣿⣿⣏⡙⠛⠋⣸⣿⣿⣿⣿⡷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣻⣿⣿⣦⠉⠛⠻⢿⣛⣿⣿⠇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣿⣏⡀⠁⠀⠀⠀⠀⣹⣿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀⠄⡀⠀⠀⢠⡞⠁⠀⠀⠀⠀⣸⣿⡟⣷⡄⠀⢀⣤⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠁⠘⠀⠀⣿⠷⣶⣤⣀⣠⣴⣿⣿⣴⣿⡇⣶⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⣿⡶⠄⠈⠛⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⣀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡄⠀⠀⠀⠀⠸⢀⠀⣼⣏⠠⠤⠤⠤⠤⣤⣤⣄⣈⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡀⠀⠀⠀⠀⡼⢿⣭⡟⠁⠀⠂⢤⣤⣤⣤⣄⣠⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡄⢀⣄⠁⠀⠀⠀⠀⢐⠃⠀⠙⠳⣤⢀⣀⠀⠀⣼⣍⢿⣿⣿⣿⣿⣿⠁⢻⣇
⠀⠀⠀⠀⢀⣀⠀⠀⠀⠉⠛⠀⢤⣤⣴⣶⣾⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⢻⣾⠈⠄⠀⠀⠉⣺⣿⣿⣿⣿⠇⠀⢈⡏⢷⣄
⠀⠀⠀⠀⠀⠙⠛⠳⠶⠾⢷⣿⣄⣈⣿⣿⢿⣿⠇⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠙⠿⣷⣶⣶⣿⣿⣿⣿⣿⠇⠀⠀⠰⠇⠀⠙⠦⢤⡀
⠀⠀⠀⠀⠲⢦⣤⣄⣀⣠⣇⡀⣈⡉⢹⡇⣸⣿⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠟⠁⠀⠀⢰⡟⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢀⣀⡀⠀⠉⢉⡉⣉⣙⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⡀⠀⠚⣿⡿⠛⠁⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠙⠛⢷⡄
⠀⠀⠀⠀⣈⠉⠛⠿⣿⣿⣛⠋⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⣸⡏⢀⣦⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠂
⠀⠀⠀⠀⠈⠛⠲⠾⠿⠿⢿⠟⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⠀⢠⠿⢧⣶⣤⡤⢐⣿⠏⠁⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠿⠟⣠⡾⢁⡄⠀⣠⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠐⣿⡟⣱⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⠛⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣴⣾⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠛⣩⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣴⣾⡿⠟⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⣩⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⣁⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⣡⡾⠻⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠊⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⠿⠿⠿⠿⠻⢿⠟⠙⠿⢿⠿⠟⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣿⣛⣛⣻⣟⣿⣿⣿⣟⣛⣛⣛⣛⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⠈⠁⠉⠄⠀⣠⣶⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠿⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⠀⠀⠀⠀⣴⠋⠘⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡰⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⢣⠀⢠⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣆⠀⠰⠁⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⢸⣠⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⠼⠣⠂⠀⠠⠷⢄⠀⠀⢀⣴⠒⠒⠁⠀⢠⡟⢃⠈⠟⠘⣾⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⢠⠀⠓⠦⠘⡆⠀⢸⠿⠇⠰⠋⠹⠛⠃⠀⡆⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⣸⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠐⠁⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡁⠀⡀⢀⣎⠠⠀⠀⠀⠁⠚⠋⠁⠀⠀⠀⢀⣠⠆⠀⢹⠀⢸⠀⢀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢀⠀⣸⣿⡄⠀⠀⠀⠀⠒⠒⠂⠀⠀⠀⠀⠁⠀⢀⣬⠀⡾⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠞⣧⠾⠋⠁⠀⠀⠠⠀⠉⠉⠁⠀⠀⠀⠀⢀⣰⢿⡟⡰⠃⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣾⡄⠀⠀⠀⢠⠀⠠⢀⣀⣴⣶⡿⣿⣨⠟⠁⡠⠃⠐⠟⠀⠠⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣠⡄⠀⠀⠈⠻⣿⣇⡀⠀⠀⠀⠒⣿⠟⢻⠛⠉⣷⠟⢁⠔⢋⢸⠀⠀⠀⠀⠀⠀⠀⠠⠴⠆⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⠀⠁⠀⡀⠀⠀⠀⠈⠫⡧⣀⣀⣠⡼⠁⠀⠀⠉⠀⠉⠀⣷⡟⠠⣿⠇⠀⢨⡆⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠈⠉⠁⢲⠀⠀⠀⠀⠀⠘⠁⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⢱⡆⢀⡞⠀⠀⢿⣟⡄⠀⠀⠀⠀⢨⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣠⢀⠀⠀⠀⢠⠀⣀⢤⣄⡉⠃⠀⠀⠀⠀⠀⢈⡴⠚⢀⡞⠀⠀⠀⠀⠋⠙⠀⠀⠀⠀⡈⢁
⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠀⠀⠆⣸⠃⠈⠳⣄⠀⠈⠁⠄⢠⠃⠀⠁⠀⠀⠀⠀⣠⠏⠀⣠⠏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠂⠀⠑⠄⠀⣰⣲⡀⠀⠀⠀⠀⠀⠀⡏⠀⡰⠃⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⣳⠀⠀⠀⠀⠀⠀⠁⠀⠁⢀⡞⠁⡜⠀⠀⠀⠀⠀⠀⠀⠀⠉⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⡆⢰⠀⠀⠀⠀⠀⠀⠀⠀⡰⠣⠤⢠⣠⣤⣀⣀⣀⣤⠀⣼⠁⠄⠁⠀⢀⡀⠀⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⣇⠈⠀⠀⠀⠀⠀⠀⠀⢠⡷⠖⠲⠦⠤⠤⠤⠤⠀⠀⠀⠛⣤⠀⠀⠀⣈⠁⠀⠀⡇⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⢬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌

⠀⠀⠀⢀⣄⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⣠⡄⠀⢀⣄
⠀⠀⢀⣼⠷⠛⠘⠺⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠤⠄⠰⠦⢼⡇⣄⣨⣧
⠀⠀⠸⣿⡀⠀⠀⠀⣸⡇⠀⠀⠀⠰⣀⣾⣿⠻⠯⡼⠴⣦⠤⠀⠀⠀⠹⣿⡀⠀⠀⣴⣾⠷⠀⢸⡿
⠀⠀⢀⡿⣷⠀⠀⢸⣿⡄⠀⠀⠀⠀⡟⠛⠿⡇⠀⢈⢶⠁⠀⠀⠀⠀⠀⢹⡏⠀⠘⠋⢿⠀⠀⢸⣇
⠀⠀⠘⠁⠋⠀⠀⠘⠁⠉⠀⠀⠀⠀⠀⠀⠀⠋⠀⠁⠀⠁⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠘⠂⠀⠘⠙
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠰⢦⣼⣿⠼⠀⠀⠀⠀⢘⣿⡟⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣻⣷⡖⠒⠀⣀⣀⡘⢾⣏
⠀⠀⠀⠀⢺⣇⠀⠀⠀⠀⠀⠸⣻⣇⠀⠀⠀⠀⠠⣾⣿⣿⠟⠀⠀⠀⠘⠁⠈⣿⡄⠀⠉⠉⠙⣿⠟
⠀⠀⠀⠀⣼⢻⡆⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⢠⡟⠋⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠁⠈⠁⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠰⢦⣿⡂⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⣠⣀⣀
⠀⠀⠀⠀⡿⢷⣤⡀⠀⠀⠀⠀⣹⣷⣄⠀⠀⠀⠀⠀⢉⣿⣻⣗⡀⠀⠀⠀⠀⣿⣧⣤⣴⣿⣇⣀⡇
⠀⠀⠀⠀⠀⢸⡇⠻⠀⠀⠀⠰⠏⣿⣿⡄⠀⠀⢀⡀⠬⠋⠙⠋⠁⠀⠀⠀⠈⠋⠉⢻⠍⠉⠉⠉⠋

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠴⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⠄⠄⡀⠀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠸⠌⠀⠀⠐⠉⡀
⣿⣿⣿⣿⣿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠨⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⡀⠀⠈
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠃⠀⠀⠡
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⡿⢿⣿⣿⠁⠀⠑⠄
⠀⠀⠀⠀⠀⢠⣿⠏⠉⠉⠀⢀⠀⢈⠛⣿⡄
⠀⠀⠀⠀⠀⣿⣿⣷⣶⣷⣾⣿⣷⣾⡇⠼⠁⠀⣀⣄⡀⡀
⠀⠀⠀⠀⠀⣿⣿⣿⠿⣿⣿⣿⣿⣿⠟⠀⠀⠘⠹⠿⣏⠁⠀⠀⢀⠔⡸⠀⢦⣀
⠀⠀⠀⠀⠀⣿⣿⡇⣗⢮⡙⣿⣿⡁⠸⣧⠀⠀⠀⠀⢈⣡⠴⠢⠃⣴⣷⡀⠀⠈⢳⢤⡀
⠀⠀⠀⠀⠀⠹⣿⣿⣮⠺⢯⠈⠿⠋⠀⠀⠀⠀⠀⠀⠀⠡⢲⡖⠚⠛⠛⡂⠀⡄⠈⠃⠛⢆
⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⣤⣴⣄⠀⠀⠀⠀⠀⠀⠀⠄⠀⢈⠉⠢⠜⡁⠈⠻⡟⡈⠰⢦⣌⡑⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠡⣄⠐⠒⠿⢷⣮⢾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠸⠃⢿⡇⠙⠛⠷⢶⠆⡴⠒⠛⠉⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠈⢣⣹⠟⢩⠄
⠀⠀⠀⠀⠀⠀⢀⠏⠳⡄⠀⠸⣷⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⢠⣢⠀⠀⢸
⠀⠀⠀⠀⠀⣀⠞⡄⠀⠙⠷⣄⣽⣆⠀⠀⢀⡞⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣆⣠⠴⣇
⠀⠀⠀⠐⠋⠁⠀⠘⢆⠀⠀⠈⠙⠛⠤⣀⡜⠉⢢⠈⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠷⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⡜⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⢀⠔⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣥⣭⣭⣿⣿⣿⣦⠀⠀⢠⠀⠀⠈⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⢳⡄⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠡⢸⣦⣸⡿⢿⢿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠭⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⢀⡿⠋⠉⠀⠘⠯⢛⣿⡿⣟⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⣼⠃⠀⢠⣄⠀⠀⠀⠀⠉⠉⠉⠉⠀⠁⠂⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠂⠀⠉⠀⠀⠈⠻⠷⠆⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣿⡏⠁⠠⠀⠀⠀⠀⠀⠐⠂⠀⠀⣌⠙⠀⠀⠐⠆⠄⠀⠀⠀⠓⠀⠀⢘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⠀⠀⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⢰⣦⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣄⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡍⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⡆⠀⠀⢠⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⣱⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣯⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠈⢹⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⢸⣿⣿⣿⠇⣠⠀⢄⢀⠀⣀⠀⢸⡿⠻⢿⣿⣿⣿⣿⣿⣿⠿⢆⡀⠀⠀⠀⠀⠀⢸⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣼⣿⣿⣿⣄⣉⠀⠘⠣⠀⠈⠂⣼⠃⠀⠀⠙⠿⣿⣿⡿⠁⠀⠀⠈⠢⢄⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⣿⣝⢿⣿⣿⣷⣶⣶⣶⣾⡟⠀⠀⠀⠀⢀⡨⠭⣁⢀⣄⠀⠀⠀⠀⠉⠲⢄⣘⠀⠀⠀⢠⠤⠖⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠸⠿⠿⠿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣇⣀⡠⠖⠊⠁⠀⠈⠉⣀⡗⠛⠓⠢⢄⡀⠀⠀⠘⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⢀⣸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣋⣉⠤⢄⡀⠀⠀⠀⠀⠀⣲⠀⠀⢀⣀⣈⠁⠒⠐⠒⠒⠉
⠀⠠⠖⠒⠚⠋⠉⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠈⠛⠁⠀⠀⠉⠓⠒⠶⠤⠤⠟⠀⠀⢸⢰⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴

⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢠⣶⣿⣿⣿⣶⣿⣿⣿⠟⠻⠃
⠀⠀⠀⣰⣿⣿⣿⣿⣿⣻⣟⠋⠏⠇
⠀⠀⣸⢿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠶⣤⠄
⠀⠀⣿⣿⣷⣶⣶⣾⣿⣿⠋⠀⠀⠀⠀⠀⠉⠀⢀⡀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠘⣿⣿⣿⡏⠫⡍⠛⠀⠀⠀⠀⠀⠀⠀⠀⣉⡀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⢃⢀⣎⡁⡹⡤
⠀⠀⠀⠈⢿⣿⣧⣤⠳⠄⠀⠀⠀⠀⠀⠀⠀⠈⡙⠚⠁⠐⠢⢼⠿⠀⣤⣤⣤⡠⠈⣠⣤⣏⣿⣇
⠀⠀⠀⠀⠀⠙⣿⡟⠀⠐⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⢔⠧⠤⠥⠞⠁
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠙⠀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⠄
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⢰⠇⡀⠀⠀⠀⠀⠀⢀⡿⡆⠱⠒⠒⠒⠉⠉⠂
⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠈⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⢀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡆⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀
⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠢⣀⠀⠀⠀⢡⠘⡷⣀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠈⠑⠢⣠⣌⢆⠻⣮⣓⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠈⠛⠶⣌⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢸⣿⣿⠀⠀⠀⠀⢰⣶⣿⣶⣶⣤⣤⣀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⢀⣠⣤⣴⣶⣶⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣾⣿⣿⡆⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢰⣿⣿⣿⣿⡄⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢀⣾⣿⣿⣿⣿⣷⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣟⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠶⠶⠶⠶⠶⠶⠶⠶⠶⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠛⠛⠿⠿⠿⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⠶⠶⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⣿⡗⢲⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠁⠀⠀⠀⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⣷⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⢷⣝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⢰⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠟⠋⠛⠛⠛⢋⠤⣒⣶⠗⠀⠀⠀⠀⠈⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⣀⠀⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢲⣾⣿⣿⣿⣿⣾⣿⣿⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠋⠀⢀⣸⣿⣿⡀⠀⠘⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣠⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⢿⠿⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣠⣤⣶⣾⣿⣿⣿⣟⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⠃⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⡀⢠⣾⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣷⣿⣿⣙⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠟⠛⠻⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢀⣠⠆⠀⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⢤⣴⡁⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⡴⢎⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠟
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣹⣯⣿⣩⣿⣵⣏⣹⣿⣩⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣽⣿⣿⣿⣿⣽⣭⣭⣭⣽⣭⣭⣭⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠠⠶⢿⣗⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⠀⠲⣿⠟⠁⠈⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⡴⣠⠶⠖⠒⠓⠐⠀⢤⢶⣿⣽⣿⣄⡀⠀⠀⣤⡉⢢⡀⠀⠀⠀⠠⠰⣿⣿⣿⠇⣴⡄⠀⠀⠀⠀⠀⠀⣳⡀
⠀⠀⠀⠀⢀⣀⣲⠾⣽⠑⠂⣰⣷⢄⢠⣤⣴⣺⠛⠋⠁⠀⠀⠉⠲⣄⠈⢷⡀⠻⡀⢠⣤⡀⠑⠈⠁⠀⣀⣼⣯⠀⡄⠀⠀⠀⠀⣼⡇
⠀⠀⠀⣶⣏⠀⠣⢀⣼⡇⠈⣿⣿⣿⠸⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠨⠂⠀⠙⠦⡘⣮⣿⠷⡀⠀⠀⠀⠹⣿⣿⣷⠗⠀⠀⠀⢀⡃⡟
⠀⠀⠐⡇⠈⣤⣴⣶⣿⣝⣂⣻⡾⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡙⠳⢶⣀⢠⣁⢀⡿⠃⠀⠙⠛⠛⣩⣦⣀⣙⣻⡇⠀⠀⢸⡏⢴⠇
⠀⠀⠀⠁⣠⣿⡿⠏⠻⢉⡍⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠀⠀⠻⠛⠁⠀⠀⢠⣶⣿⣿⣿⣿⣿⡿⢷⣤⣤⣿⢓⡟
⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣳⣄⣁⠈⢛⡼
⠀⠀⠀⠀⠀⠀⠂⠈⣀⣉⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠉⠒⠲⠤⠤⣿⢿⣷⠽⠿⣿⣿⣿⣿⣟⣻⠵⠋
⠀⠀⢀⣚⣣⣖⣾⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⣷⠻⣦⠄⠀⠛⠛⠉⠉
⠀⠀⢸⡿⠋⣩⣽⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢄⡀⠀⠀⢀⠀⣀⠀⠠⣀⣼⣿⡷⠂
⠀⠀⢸⡷⠀⠾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠡⣶⢾⣛⣯⣭⣥⠚⠋⠀⠘⣛⣫⣽⣿⣆
⠀⠀⣸⠀⠀⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣠⠖⠋⠉⠀⠀⣸⣣⣾⣿⣻⡿⠁⣠⣄⠀⠿⠛⠛⠉⣼⣿⣷⣄⡀
⠀⠀⣿⡀⠀⣾⣿⣿⣿⡇⠀⠀⢀⡴⠋⡁⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠁⢐⣿⢿⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣶⣦⣤⣄
⠀⠀⣿⠀⢀⣽⣿⣿⣿⢷⣤⡴⢏⣠⣾⣿⣾⣴⣿⣿⣿⣿⡿⢿⣿⠁⢠⣾⣷⠘⠀⠀⠀⢠⡿⠈⠘⠋⠛⠟⠿⡻⣿⣿⣇
⠀⠀⣿⠀⠀⣿⣿⣿⠏⣼⠃⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⣾⣿⣿⠀⠀⠀⣠⣿⣧⡀⠀⠀⠀⠀⡄⠁⠘⠙⣿
⠀⠀⢿⣶⣾⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣼⣿⣿⡏⠀⠀⣰⣿⣿⣿⣿⣷⣶⣿⣾⣷⣆⣦⠀⢸⡇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⣿⣿⣿⣿⣿⠇⣸⣿⣿⣾⡃⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣷
⠀⠀⠘⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠉⠁⠀⠀⠀⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⢸⣿
⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠋⡅⣼⣿⣿⣿⡇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡿⠁⠚⠙⠳⢿⣿⣿⡿⡿⠿⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣶⣶⡶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢸⠃⢊⠃⢺⠏⠀⠀⠀⠀⢀⣀⠀⣠⣾⣷⣦⡀⠦⠀⢀⣀⣀⡀⠈⠀⠀⠀⠰⠐⠂⠲⡄⡀⠄⢰⠄
⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠈⠂⠙⠁⠸⠀⠀⠀⠀⠀⢸⣿⢿⣿⣿⢿⠙⡁⠀⠀⠸⣿⣿⡇⠀⠀⠀⠀⠈⠀⠰⢤⡄
⠀⠀⠀⣾⣿⢟⡁⢀⣀⠀⠀⠈⠀⠐⠀⠀⣀⡓⠀⠀⢀⣼⠙⠻⡙⠛⠻⣾⠋⠀⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⣠⡿⠃⠈⠀⠀⠀⠀⢠⣤⡈⠙⢳⣄⣩⠅⢀⠀⠘⣿⣄⣟⣁⡀⠀⠶⠐⠀⣠⠀⢸⣿⣿⡗⠀⠀⠀⢀⠀⠀⢸⣁⢟⠂
⠀⠀⢘⠁⠀⡄⠀⠀⠀⠰⠈⡹⠓⠤⠼⠋⢩⡄⠑⠀⠟⣹⣷⡉⠀⠀⣰⠆⣤⡄⣿⠀⢸⣿⣿⣿⠀⠀⠀⠈⠀⡄⢸⡌⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣀⢾⡇⠀⠒⠈⢸⡇⡍⠄⠀⣿⣿⣿⣶⣷⠀⣾⣿⣿⡎⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠁⢸⣏
⠀⠀⠀⠀⠀⠀⡤⢠⣥⣾⠛⠺⣝⡶⠀⠈⢸⡋⠉⠉⠀⣻⡟⣹⣯⣉⣾⣿⣿⣿⣹⣦⠀⢻⣿⢿⣷⠿⠀⠀⠀⠀⠘⠇
⠀⠀⠆⠐⣀⣭⣶⡞⣿⣷⡌⠙⠘⠛⠒⠠⢾⣧⣖⡆⡀⠸⣏⡄⢹⣿⣿⣿⣿⣏⣾⡟⢿⡌⡿⠙⡉⠀⠀⠀⠀⢀⡈⠀⠀⢄⠀⠠
⠀⠀⣸⣦⣤⠈⠀⠀⠈⣿⡇⠀⠀⠀⠀⢀⣼⣿⡷⣇⠡⠀⢹⡟⠄⣿⣿⣧⠙⣼⣿⣿⣶⣿⡜⢺⡇⠀⠀⠀⠀⠛⠑⠶⠶⠈⠀⣤⡀
⠀⢻⢿⣿⠹⠀⠐⠒⠈⠉⠀⢰⢾⡧⣷⣾⠏⢹⡟⣿⠀⠀⣄⠀⠀⠉⠀⠈⢶⣿⡿⠹⣻⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢳⣖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⢈⣠⣇⡿⠀⡴⠋⠀⢠⣦⠀⠛⠈⠀⢱⠄⠘⡏⠙⢛⠁⠀⠀⠀⣀⡤⠤⠤⣠⣶⡶⣿⣿
⠀⠀⠀⠀⠀⣲⣶⣄⡋⠀⠀⠀⠀⠀⣠⣴⣿⠟⠟⠀⢀⠁⠀⢸⣿⣿⣿⣆⣀⠀⠀⠃⠀⡼⢀⠈⠄⠐⠒⠉⠀⠀⣠⣜⣋⣽⣿⣿⡏
⠀⠀⢀⣴⣿⣿⣿⣿⠛⠀⠄⣠⣴⣾⣿⣋⡀⠀⠀⠀⣸⡆⢰⣿⣿⡇⠻⣿⣯⠀⠀⠘⠶⣖⣦⣄⣀⠀⠀⠀⠀⠉⣽⣿⠓⣸⣴⡟
⠀⠰⠋⠁⠀⠘⠿⠟⣧⣾⣿⣿⣿⡿⡿⠟⠂⢀⣠⣶⣿⣷⣿⣟⣿⣅⣰⣿⣿⣄⡀⠀⠀⠈⠻⣿⣿⣷⣄⠀⠀⠿⠝⣇⡶⠛⠃
⠀⠀⠀⠀⠀⣀⣤⣾⠿⡿⠁⠈⠃⠀⠀⢰⣶⣿⠾⣿⣿⣿⣿⢿⡿⣿⣿⣻⣿⠪⣧⠀⠀⠀⠀⠘⣿⢿⡦⢀⠀⠀⠉⠂⠁
⠀⠀⠀⠀⠺⠛⠵⠓⠘⠀⠀⠀⠀⠀⢀⣶⠋⠀⠀⠈⣴⠛⠻⣶⠖⠉⣻⢸⣿⡷⠶⠖⠀⠀⢀⣀⠋⣐⣢⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢹⣄⠀⢡⣶⣾⢻⡎⠁⠀⢀⣠⣤⣾⡿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠀⣿⢠⣶⣶⣿⣿⣿⣦⢸⣿⣧⣶⣷⣾⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣿⣼⣿⣿⣿⣿⣿⡏⣾⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠛⠛⠛⠛⠙⠋⠚⠀⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠆⠠⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⠛⠛
⠀⠀⠀⠀⠀⠀⠀⣶⣛⣿⣿⣿⡌⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠴⣒⠮⢀⣩⣳⠀⢄
⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⡿⠀⠀⢈⠭⠝⠀⠀⠀⠀⠀⢊⣤⣶⣶⣮⠛⢿⣿⣿⣤⣌⠆
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⣻⡛⠧⠀⠀⠀⠀⢠⡐⡂⣀⣰⠷⠿⣿⣻⡿⠷⠒⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⣑⠧⠀⠀⠀⠀⠀⠀⠉⢜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢿⠛⠀⠡
⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⣷⠺⣆⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡟⠀⠀⠈⠉⠉⠋⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢣⠀⠀⠀⠀⠀⢠⠁⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠑⠤⣀⣀⠀⠘⢦⣶⠄⠀⠀⠑⠄⠠⣀⣀⣀⡀⠀⠀⠀⡀⡜⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⡠⠊⠀⠈⠢⣄⠀⠀⠀⢨⡿⣮⣿⡇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠚⢄⠱⣄⠀⠀⠀⢸
⠀⠀⠀⣀⠤⠋⠀⠀⠀⠀⠀⠀⠑⠒⠤⠼⠙⢦⣽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠓⠤⡤⢼
⠀⢀⠜⠁⠀⠀⠉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣄⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⢄⠪⠍⠐⡒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⢠⣾⣖⣛⣁⣀⡀⠤⠤⠤⠄⠩⠖⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⡆
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣧⣤⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢸⡇⠚⢳⡄⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣉⠛⣋⣠⠎⠀⠀⠀⠀⠀⣀⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠙⠢⠜⠀⠀⠀⠀⢾⣃⡆⠀⠀⢀⠖⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠑⠂⠀⠀⠀⢀⣤⣤⠰⠶⠶⠒⠒⠒⠒⠶⠦⣤⣀⠀⠀⠀⠀⠀⠀⢀⠒⠢⡄⠀⠉⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⣠⠶⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⡀⠀⠀⠛⣄⣠⠗⠀⠀⡰⠆⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⠀⠀⠙⠦⠴⠂⠀⢀⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⢀⡤⣄⠀⠀⠀⣀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠤⠤⠴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠙⠃⠀⠀⣎⠉⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠉⠀⠀⠀⠀⠉⠱⣄⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣷⠀⠐⠿⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠁⠀⠆⣀⡀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠘⢦⣀⡀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⣽⣿⠗⣦⣄⣀⠇⢀⡶⠟⠛⠛⠳⢤⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠈⠛⠛⠋⣡⡟⢠⡟⠃⠤⣄⡀⠀⠀⢡⠀⣸⠀⢠⡶⠛⣛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠒⠀⠤⠀⠀⠚⠉⠀⢸⡇⠀⠀⣿⣟⣳⣦⣼⠀⡿⠀⡟⢰⠎⠩⡉⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠁⠀⠀⠀⠀⠉⠉⠁⠒⢢⣄⠀⠀⠀⠀⠲⣆⡀⠀⠀⣱⡄⠀⠈⠉⢉⣴⠏⣴⠁⠀⠳⣌⠓⠒⢋⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠉⠀⠈⠉⠀⢰⠇⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⠴⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠙⠉⠉⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠶⠀⠀⠀⠀⢠⠞⠁
⠀⡔⠀⢠⡞⠁⠀⢀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁
⠀⠁⠀⡎⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠘⡟⠲⣤⣄⣀⣀⡀⢀⣀⣀⣀⠀⣠⡤⠐⠂
⠀⠀⠀⡇⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢻⡄⠀⠀⣉⠉⢹⠋⠉⠉⠉
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠈⢷⡀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠻⣤⡋⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡛⠛⠛⣶⡀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠈⠻⢷⣄⣀⠀⠀⠀⠀⠀⠀⣴⠞⢻⣷⠤⠾⣯⡀
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⡀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠚⠛⠁⠘⠋⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⠋
⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡰⠏⠉⠒⠲⢦⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⢀⣽⠆
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⢹⣧⡀⠀⠀⠀⠀⠙⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠙⠲⠶⠤⠴⠾⢧
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⠛⠛⡀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⢀⡿⠀⠀⢀⣤⢀⣀⣀⡀⢘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⢸⡆⠀⠙⣆⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⣸⠃⠀⠀⣼⠁⠀⠉⠁⠉⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠸⡇⠀⠀⠘⣆⠀⠀⠀⠀⠘⣇⠀⠀⢰⡇⠀⠀⢀⠏⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠘⣇⠀⠀⠀⠀⠙⣦⠀⣼⠁⠀⠀⣾⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⢹⡄⣿⠀⠀⠀⠙⠓⠶⠦⣀⣀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢋⡀⠀⠀⠀⠈⢳⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢹⠈⠻⢶⣦⣀⡀⠀⠀⠀⣀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⣧⠀⠀⠀⠉⠙⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠛⠛⠉⠉⠲⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠰⠿⠤⠤⣀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⢶⣤⣤⣤⣤⣠⣤⡴⠶⠞⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣯⣭⣭⣍⣉⣩⣭⣭⣄⣩⣍⣿⣉⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣶⣶⣶⣶⣤⣾⣿⣿⣴⣤⣧⣼⣷⣦⣼⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠰⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠈⠀⠐⡏⠁⠀⠀⠀⠰⠀⠀⣀⠀⠀⠀⠀⡆⠀⠇
⠀⠀⠀⠀⠀⠀⡄⠀⢤⡄⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠘⠀⠀⠀⠈⠂⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠃⠀⢛⠁⠀⠀⠀⠀⠀⠸⣿⡗⠀⠀⠀⠀⠂⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⡖⠀⠀⢀⣽⣿⣧⠀⠀⠀⠀⠀⠀⠀⡀⡀⣰
⠀⠀⠀⠀⠀⠀⢀⣀⣈⠀⠀⠀⠀⠀⠀⣸⣿⣇⠀⠀⠀⠀⠴⣀⠀⡀⠆⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⡾⠟⠛⠻⢷⡄⠀⠀⠀⠀⢀⡾⠟⢿⡀
⠀⠀⠀⠀⠀⣀⠜⠛⠙⣄⡀⠀⠀⢀⣤⣇⣿⣿⣦⠀⠀⠀⢀⣀⠀⢀⣠⣰⠀⢐⠀⠀⠀⢰⠆⠀⣎⠀⣀⡀⡀⠀⣿⠀⠀⠀⢀⣤⣤⣤⣤⣽⣶⡄
⠀⠀⠀⣶⣿⣷⣴⡶⠶⢿⣿⣷⡆⢀⠺⠟⠛⠻⢿⡇⠀⠐⠿⠲⠟⠋⠀⣿⠀⠐⠀⠀⠀⠀⠁⠀⣿⠾⠛⠛⠿⠷⣿⠀⠀⠀⣜⠋⠀⠉⠉⠙⠿⠃
⠀⠀⠀⣀⠤⠀⠠⠤⠰⢰⣀⢸⠇⠈⣤⡀⠠⠀⣼⡇⠀⠀⣀⢤⣠⠄⡀⢹⠀⠀⠀⠀⠀⢀⡁⠀⡏⠀⠀⠀⠀⠀⣿⠀⣾⢸⠃⠀⠠⠀⠄⠤⠈⣿⡆
⠀⠀⠀⠹⣶⡍⠛⠋⢰⣿⣿⣿⠀⢀⡇⠀⠀⠀⢸⡁⠀⠀⠈⠀⠀⠈⠁⠀⠀⠸⠀⠀⠀⠸⠇⠀⣧⣀⣀⣀⣀⣀⣿⠀⢩⣼⣧⣀⠀⠀⢀⣀⣴⣿⡇
⠀⠀⠀⣼⣿⣿⠟⠓⢬⣯⣾⣿⡄⠀⠗⠶⠶⠶⠾⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠤⠀⠻⠿⠿⢿⠿⠿⠏⠀⠀⠙⠻⠟⠏⠀⣽⣿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠂⠁⢠⡶⢶⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠋⠀⠀⠀⠀⠀⠿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡤⠤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⢀⠉⠀⠀⠀⠀⠀⢀⢀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⣠⣶⠿⢟⡃⣠⣴⡶⠀⠉⢉⡻⣷⣄
⠀⠀⠀⠀⠀⢠⡟⠀⣄⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⣾⣿⣿⣿⠟⠀⠀⠀⠘⣿⢿⣿⡆
⠀⠀⠀⠀⠀⢾⠀⠀⡜⠶⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠘⢿⡟⠉⢹⣿⣿⣿⠀⠀⠀⠀⠀⠘⠋⢹⣷
⠀⠀⠀⠀⠀⢸⡄⠸⡷⠤⠀⠀⠀⠋⠙⠀⠀⣯⡄⠀⠀⠀⠀⠀⠀⣇⠀⠀⠽⣿⣿⠀⣠⣄⡀⠀⠀⢀⣼⣿
⠀⠀⠀⠀⠀⠈⡇⠀⡴⠀⠀⠀⠀⢤⡼⠇⠀⠙⡅⠀⠀⠀⠀⠀⠀⢸⣀⡀⠀⠈⠹⠂⣼⡌⠁⠲⣦⢺⣿⣿⡀
⠀⠀⠀⠀⠀⢸⡇⠀⢳⠀⠀⠀⠀⠀⠀⠀⣠⣼⠁⠀⠀⠀⠀⠀⠀⠈⢫⠷⠂⠀⠀⠀⣼⡇⠀⠀⠈⠁⠀⠘⠇⣀⡀
⠀⠀⠀⠀⢀⣾⠃⠀⢺⣶⡾⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⠔⣫⣶⣿⣿⣦⣀
⠀⠀⡀⠐⠛⠁⠀⠀⠀⠈⠀⠀⠀⠙⠲⠶⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣧⡷⠄⠀⠀⠀⠀⠀⣰⣯⣾⣿⣿⣿⣯⡄⠁
⠀⣸⡇⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⢀⣀⣴⢷⡀⣰⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠷⠀⠀⠀⢀⣽⡆⠀⠀⠀⠀⠀⣼⠁⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠟⡟
⠀⠘⠂⠐⠶⠛⠋⠀⠀⠀⠀⠀⠀⠿⠈⠉⠉⠈⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠋⠀⢹⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⢀⡠⠶⣂⡞⢡⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣄⡀⡴⠂⠀⢈⡀⠀⠀⠀⢀⣶⡯⡾⡻⢹⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣟⣻⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⠛⠰⢋⡀⠈⠇⢀⡴⠚⠉⠀⣀⡬⠒⠈⠀⢠⣼⣿⣿⣿⣿⣿⣟⣿⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠐⠛⠁⢀⣠⠷⡄⠙⠛⠻⡅⣀⡀⡆⠐⣿⣿⣿⣿⣿⣿⣿⣽⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⢫⣏⠀⠀⠀⡰⢁⡿⠋⠀⡇⠀⢸⣿⣿⣿⣿⣿⡟⠃⠀⣛⣿⣿⣂⠤
⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⣠⠚⠁⢀⡞⠀⠀⢀⠞⠁⣸⠀⠀⣸⠃⠀⢸⣿⣿⣵⣟⢋⡔⠁⠀⢻⣯⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⢠⡞⠁⠀⢀⡞⠀⣀⡴⠃⠀⣰⠏⠀⠀⠇⠀⢠⣿⣿⣿⣿⣇⠎⢀⡀⠀⠀⠙⣿⡿⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⢠⠏⠀⠞⠁⠀⠀⣼⠇⠀⠀⠀⢀⣴⣿⣿⣿⡿⢽⠏⠀⠀⠙⢦⡀⠀⠈⢻⣞⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢀⣾⣿⣿⣟⡟⣣⠏⠀⠀⠀⠀⠈⠻⣄⠀⠀⠹⣭⢛
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⠠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣾⣿⣿⣻⡞⢠⠏⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⣿⣿⣷⣿⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣤⣦⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⣿⣿⣿⠿⢡⣞⣷⠨⡄⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠿⠾⠇⣩⡼⡴⣧⣾⡉⢉⣉⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⣷⣿⢤⡄⠈⠿⣿⣄⣼⠹⠟⢧⣌⡀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣺⣿⢛⠛⠲⠊⡍⣿⢛⢿⣧⠐⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣿⣿⣿⡆⢠⡀⣯⠈⢦⠠⠙⠻⣤⣀⠀⠀⢀⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣳⢷⠄⠰⣸⣿⣿⣿⣿⣮⣙⠘⢦⣸⠀⠀⠀⠈⠛⠻⠲⠦⠴⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⡏⠀⠐⢁⡛⣇⠿⢿⠾⣿⣿⢥⡄⣱⠀⠀⠠⣐⠢⣄⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠫⣄⡝⠀⠘⣿⣿⣿⣿⢟⣻⠏⠀⠠⠈⣌⣹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠴⠒⠿⢽⣿⡿⢿⡟⠀⠒⣄⠀⠀⠚⠿⠽⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣭⣶⣿⠀⠁⠀⠘⠓⠒⠾⠷⡶⣬⣉⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡿⢿⣭⡁⢤⠄⢀⠄⠀⠀⠀⠀⡈⠻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠾⠏⠥⠀⠀⠀⠀⠀⠀⢲⡎⡰⠐⠀⠀⠀⠈⠀⢉⡿⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡔⠈⠈⠉⠐⠀⠀⠀⠐⠒⠒⠤⣬⣙⣻⣧⠆⠀⠀⠀⠀⠀⠈⣆⣤⣴⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⡀⠀⠀⣠⣄⡤⠤⣶⣶⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠻⢏⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠐⢶⡺⣯⣤⡿⠶⣿⣋⣡⣴⣶⠿⠛⠻⣷⣆⠀⠀⠀⢰⣴⡆⣷⣾⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠘⡇⠈⢻⣆⠸⡟⠋⠉⣿⣿⡶⠀⠀⠈⠹⣷⡀⠀⠐⠂⠊⠿⠻⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⣠⡼⠃⠀⠈⣿⡆⠻⠀⠀⠸⣿⣿⠀⠀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠈⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠤⠀⡽⠀⠀⠀⠀⠸⣷⠀⢀⠀⠀⢻⣿⣧⠀⠀⠀⠀⠀⠈⠉⠻⣷⣶⣥⣀⠀⠀⠘⢳⡄
⠀⠀⠀⣀⡀⠀⠀⠀⣼⡇⠀⡾⠁⠀⠀⠀⠀⠀⢻⡆⢰⡄⠀⠐⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢻⣿⡻⢿⣶⣤⡀⠀⠙⢦
⠀⠀⠈⢿⣯⣶⠔⠶⣿⠁⣰⣇⣠⣤⣠⣤⡄⣤⣼⣧⠀⢷⣤⣴⣾⣿⣷⣤⣤⣤⣤⣤⣤⠄⠈⣿⣷⡀⠙⠟⢻⣶⣎⠸⣶⡄
⠀⠀⠀⠀⠙⠻⣿⣷⣌⠁⣻⣶⣾⢶⣿⣿⣶⣿⣿⣿⡇⠸⣿⣿⣿⣿⣿⣿⣿⣾⣴⣶⣦⣤⣤⣬⣁⣀⡀⠀⠀⠉⠻⣷⣞⣍⠓⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠻⢿⡟⣁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢿⣿⣿⣿⠾⠿⠿⠿⠟⠿⠛⠛⠛⠛⠛⠛⠛⠻⢿⣿⣷⣽⣿⠙⠀⡤⠋
⠀⠀⠀⠀⣀⣠⣶⣿⣿⠿⠿⠏⠉⠉⠉⠀⠈⠉⠉⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⢿⣟⡴⠃
⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠒⠀⠀⠀⠀⠐⠂⠐⠐⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⠈⠀⠂⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠆⠀⠳⠀⢃⠀⢀⣠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⡀⠀⠀⡄⠀⠚⢇⠀⠀⢇⡀⣠⠄⠂⠈⣠⠞⠙⠀⠀⠀⠀⠀⠀⢠⡀⠀⢠⡄⠀⣤
⠀⠀⠀⠀⠀⢘⣤⠴⠚⢆⠀⠸⠗⠀⠀⠉⠁⢐⣦⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⣲⣶⡞⠛⠛⠋⠉⠁⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣶⡄⠘⠇
⠀⠀⠀⠀⠀⠠⣤⣀⣠⡴⠚⠁⠀⠀⠀⠀⠀⠄⡀⣀⣬⣷⣤⣤⣄⠀⠀⠀⠀⠀⠈⠁⠠
⠀⠀⠠⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⡀⢠⠸⠛⠿⠿⢿⣿⠿⢟⡐⠢⡆⠀⠀⠀⡀⠠⣶⡄⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠓⠲⠥⣂⠀⠘⢷⠞⠻⣼⠀⠀⠈⠙⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠌⢀⠀⠀⠘⠓⠂⠑⠤⠀⢻⡆⢐⡢⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣀⠀⡀⠚⣁⡀⠡⠐⠒⠈⠀⠀⠀⠀⢐⣿⠳⠇⠛⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠁⠈⡁⠀⠀⠀⠀⠀⣴⡟⠙⠀⠈⢁⣀⣠⠞⠡⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠓⢀⣀⠙⠁⠀⠀⢀⠀⣷⡏⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡸⠿⣶⣤⣄⠀⣿⡀⠉⢩⠀⠀⠀⣸⣿⡷⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢠⣟⣙⡿⢻⣯⣍⠫⡁⠀⠀⠀⡛⣛⣛⣛⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢀⠈⠈⢒⣿⣛⣿⠁⠈⠉⠉⠀⠌⠀⠀⢰⢩⣁⢉⣉⣥⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠆⠀⠀⢀⠘⠋⠙⠗⠀⠀⠀⠀⠁⢀⡀⠀⢠⣬⣯⣶⣾⣼⣖⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠁⠚⠳⠪⠴⢄⢀⠐⣂⠠⢚⡤⠀⣾⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⡄⠀⠀⠀⣴⣾⣧⡄⠧⢶⣿⣿⣟⠗⠤
⠀⠀⠀⠀⣀⡀⢀⢀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠿⠟⠐⠁⢢⠐⣡⣿⠉⡜⠀⠀⢀⣀⠀⢀⣀⣀⣀⣠⣀⣀⣀⣀
⠀⠀⠀⠀⣇⠀⣾⣷⣷⣿⣿⣿⡿⣶⣶⡦⣤⣀⣤⠀⠉⠓⠂⠬⠅⠊⠀⠈⠀⠁⢀⣴⣾⠟⠳⣿⢯⣼⣷⣿⣿⣿⣿⣿⡿⣿⣶⡆⡀
⠀⠀⠀⠀⡷⡆⢿⣿⣏⢿⣿⣿⣿⣤⢼⠧⠞⠛⠛⢷⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠙⠾⣿⣿⣿⣿⣿⣾⣯⣿⣿⣿⠇
⠀⠀⠀⠀⠡⠁⠸⣿⠿⠨⠍⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠻⠿⡿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢄
⠀⠀⢸⣷⠏⠀⠀⣿⣺⡁⠀⢘⣶⣆⡦⠀⢀⣿⣂⣤⣤⣄⣻⡀⠀⢀⣺⢃⡀⠀⠸⣇⠀⠀⠘⣶⣆⡦⢀⣈⣿⡎
⠀⠰⢻⡇⠀⠀⠺⣿⣧⠀⠀⢸⣿⣀⠀⠀⢸⡿⡅⠀⠀⠈⣹⡿⠀⠸⡟⠋⠁⠖⢊⣿⠇⠀⢸⣿⣀⠀⠃⢠⣿⣧
⠀⠀⣸⠟⣆⠀⠀⣿⣿⠀⠀⢀⡟⢹⠀⠀⠀⡇⠀⠀⠀⠀⢸⡅⠀⠀⡿⠀⠀⠀⠀⣯⠀⠀⢀⡟⢹⠀⠀⠈⡧
⠀⠀⠁⠀⠉⠀⠀⠈⠉⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠁
⠀⠀⢠⣤⣤⠂⠀⠀⠀⢀⡾⠆⠐⢻⣄⠀⠀⢀⣴⡖⢛⠀⠀⠀⢀⡴⣄⣠⣗⣤⠀⠀⢀⣶⣀⡀⠀⠀⣰⣆⣠⡄
⠀⢀⡾⣿⣯⣄⣀⠀⠀⢺⣟⡲⣭⠍⣽⠂⠀⠀⣹⠞⢸⡆⠀⠀⡞⡟⠛⠛⠛⢻⡄⠀⢻⣿⣿⣿⡀⠸⣿⣿⣿⡇
⠀⠈⠀⠉⠉⠉⠉⠁⠀⠈⠉⠁⠉⠈⠉⠉⠀⠀⠉⠀⠈⠉⠀⠀⠉⠁⠈⠁⠈⠉⠁⠀⢸⣿⣿⡏⠁⠀⣿⡟⣿⠁
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⣀⡠⠀⠀⢀⣄⠀⠀⠀⣠⣄⠀⠀⠀⣀⢀⠄⠠⣣⡤⢀⡈⠁⠉⠁⠀⠀⠉⠀⠈
⠀⢀⣼⣿⠃⢤⣀⠀⠀⢠⣿⣟⠁⠀⠠⣾⣿⠿⠀⠻⢿⣷⡄⠀⠘⣿⠗⠀⠀⣻⡏⠉⠁⠀⠀⠀⠀⠀⡤
⠀⠈⢼⣿⠄⡿⠿⢷⠀⠀⢽⣿⠀⠀⠀⢽⣿⠄⠀⠀⣼⣿⠁⠀⢰⣿⡍⠀⠀⠛⣿⠀⠀⠀⣀⣴⣶⣦⣤⣀
⠀⠀⠸⠿⠀⠀⠀⠈⠀⠀⠸⠸⠀⠀⠀⠸⠸⠀⠀⠀⠘⠿⠀⠀⠼⠁⠧⠀⠀⠀⠿⠀⠀⠉⠉⠁⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠄⢀⠀⢀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡡⠤⠐⢂⣶⡤⠄⠈⠻⣿⢦⠀⠀⠈⠙⠳⢆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠠⠁⠋⠀⠀⢀⠄⣀⡈⠳⡆⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠠⠁⠀⠀⠀⢀⡖⢫⠏⢀⠀⠀⠀⠉⠉⠉⠉⠀⠂⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣄⣈⠃⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢰⣷⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⣶⣷⢿⠀⠀⢠⢀⡖⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣶⠀⠂⠀⠀⠀⠀⣄⣿⡏⡎⠀⡰⢃⡞⠀⢀⠀⣤⠴⠒⠀⠀⣬⣭⠟⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢠⡇⢰⠀⠀⠀⣤⣾⣿⣿⠃⡇⡰⢡⠎⠀⠀⠔⠀⠛⠀⠀⠀⠀⠈⠁⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠂⢀⡇⠘⠀⠀⠸⢿⣿⣿⣿⠀⢱⣵⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⡈⠀⠘⠃⠀⠀⠀⠀⠀⠸⢿⣧⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⣻⣾⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠸
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⢠⠃⣆⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢠⠋⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⢿⣿⠘
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⢰⡿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠠⠁⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢀⣿⡇⠀⠀⠘⡇⠀⠀⡀⠀⢀⠃⠠⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡋
⠀⠀⠀⠀⠀⠘⠀⠀⠰⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠀⠳⠀⢃⠀⠀⡀⠀⠀⠀⠀⠀⢠⠀⣤⡄⢴⠃⠜
⠀⠀⠀⠀⠀⡆⢠⠁⣃⢾⣿⠇⠀⠀⠀⡆⠀⠀⠀⠀⠀⡇⠀⠀⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠾⠟⣡⣎⣜⣀
⠀⠀⠀⠀⠀⣀⢆⡼⢁⣾⣿⠁⠀⡆⠀⡇⠀⠀⠀⠀⠀⢳⠀⠀⠘⣀⠀⠈⠀⠁⠀⠀⠠⠀⠀⠀⠚⠁⠸⠁
⠀⠀⠀⢀⣴⠃⠞⢠⡟⣻⠇⠀⢰⠀⠀⣇⠀⠀⡄⠀⠀⠈⠗⠀⠀⠘⣠⠎⠀⢀⣴⠁⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀
⠣⠤⠒⢉⠄⣠⠔⠊⠉⠁⠀⠀⡎⡌⠀⢸⠀⠀⡐⠀⠀⠀⢇⠀⠆⠀⡆⡆⠀⠀⠁⠀⠀⠀⠈⠀⣰⢃⠀⠀⠀⠀⠀⠀⣰⣿⡟⠁
⠀⠀⠀⠁⡰⠃⠀⠀⠀⠀⠀⣼⡔⠀⠀⠀⠀⠀⡇⠀⡦⠀⢸⢰⡄⠀⠿⠃⠀⠀⠀⠀⢀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⢰⣿⠃⢹
⠀⠀⠀⢰⠁⠀⠀⠀⠀⣠⢞⡑⠀⠀⠀⠀⠀⢸⡇⠀⡇⠀⠈⣸⠇⠀⠀⠀⠀⠤⠀⣀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢸⡣
⠀⠀⢀⠃⠀⠀⡤⠖⠋⠁⡞⠁⠀⠀⠀⠄⢀⠆⠁⢰⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠇
⠀⠀⡜⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡆⡰⠀⠌⡘⢠⡟⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠇⡘⢠⢁⣾⠁⠀⠀⢸⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡠⢁⢃⢪⠃⡔⢁⠄⡾⠃
⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢻⡗⢁⡾⢡⢃⠌⢀⠎⠜⢡⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢃⠾⣠⠟⣠⡗⠀⣠⠋⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠐⠁⠳⢋⡴⠋⣠⠞⠁⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⣀⡩⠴⠛⠒⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠈⢹⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢁⣤⣠⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣋⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠛⠋⠉⠛⠛⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⣿⠿⠀⠴⠿⠶⢰⣶⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠄⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣧⡤
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⡏⠀⠀⠀⠀⠶⠾⠇⣸⣷⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⢀⣿⣷⣞⣤
⠀⠀⠀⠀⢀⣤⡶⠉⠻⠶⢟⠆⠀⠀⠀⢠⡄⠘⢿⣿⣿⣿⣿⣿⣿⢦⣤⢄⣀⣠⣴⣿⡇⠀⢸⡷⠈⢻⡷⠳⣄
⠀⠀⠀⣰⡹⢆⡁⢤⣠⡖⠀⠐⠆⠘⠛⠻⠆⠀⠈⣿⣿⣿⣿⣿⣿⣏⣱⣿⣿⠋⣾⣘⣇⠀⢀⣷⣀⠀⠁⢀⣘⣦⡀
⠀⠀⠀⣿⠀⢨⣿⣿⣿⣷⡶⠀⠒⣠⠀⠀⢈⡀⠀⢸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣶⣿⡿⠛⢀⢦⡝⠉⣈⣷⣄
⠀⠀⠜⠿⠀⠸⣿⣿⣿⣿⡄⠁⢦⡀⢧⡀⠈⠁⠀⠀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠁⠀⠈⢣⣴⣶⠙⢿⣿⠆
⠀⢰⡆⠂⠠⠆⣿⣿⣿⣿⣿⣷⣄⢻⣿⣿⣆⠀⠀⠀⢹⣿⣿⣿⡆⠈⠙⢿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠙⡝⢿⣶⣿⡿⠃
⠀⣾⠃⠀⢳⣶⣾⣿⣿⣿⣿⣟⠹⠿⣧⣌⣻⣷⣄⡀⣾⣿⣿⣿⣄⡀⠀⠀⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠉
⢀⠖⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣶⡦⣄⡋⠉⠛⣿⣿⣿⣿⣿⣿⣿⣷⡀
⣼⣦⣤⡤⠛⣿⣿⣿⣿⣿⣿⢿⡟⠓⠈⢁⠤⣄⣻⣿⣿⣿⣿⣿⣿⣿
⠙⠛⢯⣇⠇⠙⢻⣿⣿⣿⣿⣿⡀⣀⣀⠶⣄⢠⣼⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠛⠓⠳⠤⢽⣿⣿⢿⣿⣿⣿⣿⣷⣶⠑⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⢾⣿⠹⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣧
⠀⠀⠀⠀⠀⢠⣾⣿⠀⠀⠘⠻⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⣯⣿⣿⠿⢿⣷
⠀⠀⠀⠀⠀⠾⣿⣧⠈⠳⠶⣄⠀⠁⠘⢹⣿⣿⣿⣿⣨⣄⢹⣿⣷⣿⣷⣿⠳⣦⡝⢣⡀
⠀⠀⠀⠀⠈⢠⣿⠄⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣏⣿⣬⣿⣶⣿⣻⣿⣿⡟⣶⣿⠛⣿⣏⠢⣀
⠀⠀⠀⠀⣦⠼⣿⣦⣀⠐⠀⠀⠀⠀⢀⣾⣿⣿⣿⡼⣯⣽⣿⣿⣿⣿⣿⣷⣿⡿⢿⣏⢘⠿⣌⣦⣄
⠀⠀⠀⠀⠋⠀⠈⠻⣁⠈⠃⡀⠀⢠⣿⣿⣿⣿⣿⣇⠈⣄⠹⠎⢻⣿⣿⡿⣉⡽⢧⣈⣿⣄⣨⡟⢈⣥⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢦⣁⣠⡏⢹⣿⣿⣿⣿⣟⢫⣈⢧⡐⢎⠛⠛⠶⣿⣍⣶⡞⢷⣤⣻⣄⠸⠇⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠹⣿⣿⣿⣿⡎⢩⣀⢡⡄⠃⢀⠀⠀⠉⣿⣿⣿⡽⣧⢿⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⠀⠻⣄⢡⡄⠛⠀⠀⠀⠹⣌⣉⠛⢛⡀⣾⣿⣧⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⢇⠙⣀⠰⣤⠖⠀⠀⠀⢻⣿⠟⠛⣅⢙⣿⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣾⣇⠙⣄⠁⣄⣰⠃⠀⠈⢻⡉⣋⠹⣏⣹⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣹⡿⢿⣿⣇⣹⣭⣿⡷⠀⠀⠀⠀⢿⠟⠆⠘⣯⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢀⡟⢳⠎⣠⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⣶⡰⡔⠷⠉⣦⣿⣿⣆⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡈⠀⠄⢠⣟⣨⡭⠁⠀⠀⠀⠀⠀⠀⠀⠘⣤⣰⣬⠳⣍⣿⡿⢍⣷⣄⣠⣤⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢀⠃⠴⣠⣴⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠘⣣⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⢶⠶⢻⣏⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡷⢛⣉⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⠀⢀⣾⣤⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠎⠀⠲⢷⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡓⠻⣿⣦⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡦⠀⠙⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢿⣟⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⣻⣿⣿⣿⡦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣴⣤⡔⠂⠀⠀⣶⣤⡖⠂⠀⠰⣇⣤⡀⡀⠀⠀⠀⣶⡄⢀⡀⡀⠀⣶⡄⠀⠀⠀⢠⣶⠀⠀⠀⠠⣶⠄⠀⠀⠀⢯⣠⡄⢀⠀⠀⠐⣶⣮⠇
⠀⠀⢠⣾⡶⠃⠀⠀⡴⣾⣿⠛⠀⠀⠀⣿⣿⠛⠛⠀⠀⣾⡧⠖⠛⠃⠛⠳⠴⣷⡄⠀⢠⣿⣦⠶⠤⣀⣀⣼⣷⠀⠀⠀⣸⣿⠗⠋⢃⠶⠶⣻⣏
⠀⠀⠋⢿⣇⠀⠀⠀⠙⢿⣿⡄⠀⠀⠘⣿⣧⣄⠀⠀⠀⢻⡝⠆⠀⠀⠀⠀⢰⣿⠃⠀⠘⣿⠀⠀⠀⠉⠁⣴⡿⠀⠀⠀⢻⡿⣤⠀⠀⠀⢰⣿⠿⠆
⠀⠀⢀⣼⠏⣷⠀⠀⠀⢸⣿⠃⠀⠀⢀⣼⠃⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣰⠟⢸⠃⠀⠀⢈⣷
⠀⠀⠘⠁⠀⠙⠀⠀⠀⠈⠉⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠋⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⡄⠀⢴⣦⠀⠀⠀⠀⠀⢀⣤⣰⡶⠀⠀⠀⠀⠀⢀⡀⠀⠀⣆⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⣸⣿⣽⡅⠀⠀⠀⠀⠀⣶⣯⡁⡠⣤⣼⣿⡄⠀⠀⠰⣿⡿⡄⢀⠀⠀⠀⠀⢴⣟⣿⣴⣾⣧⣾⠆⠀⠀⣴⣿⣷⣴⣆⠀⠀⣴⣿⣧⣾⣷
⠀⠀⣸⢻⣿⣷⣶⣄⣀⡀⠀⠀⣿⣭⡙⣴⣦⢀⣿⣃⡀⠀⠀⣸⠟⠁⣸⣄⠀⠀⢰⣫⡏⠉⠉⠉⠉⢩⣷⠀⠀⢻⣿⣿⣿⣿⡀⠀⢻⣿⣿⣿⣿⡀
⠀⠀⠁⠀⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠁⠉⠁⠈⠉⠉⠁⠀⠀⠉⠀⠀⠉⠉⠀⠀⠈⠈⠁⠈⠉⠁⠉⠉⠁⠀⠀⢸⣿⣿⣿⡏⠁⠀⢸⣿⡏⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⣀⡀⠀⠘⠋⠙⠛⠃⠀⠀⠘⠋⠁⠙⠃
⠀⠀⠀⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⣾⣗⡿⠀⠀⠀⢰⣿⣲⣤⠀⢠⣴⣻⣟⡀⠀⠀⣰⢿⣲⠋⠀⠈⢿⣿⠥⠔⢆
⠀⠀⡮⢿⣿⠇⢘⣗⢲⡀⠀⠀⠺⣽⣿⠀⠀⠀⠐⢯⣿⡏⠉⠀⠈⠋⣿⣿⡇⠀⠀⢈⣿⣏⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆
⠀⠀⠀⢾⣿⠇⢿⠿⠿⢿⠀⠀⠀⢿⢿⡇⠀⠀⠀⠸⡿⣿⠀⠀⠀⢰⡟⣿⠀⠀⠀⢾⡿⡆⠀⠀⠘⠛⢻⡇⠀⠀⢀⣀⣰⣾⣿⣶⣶⣄⣀⡀
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠸⠀⠀⠀⣿⠸⡇⠀⠀⠀⢸⠇⢿⠀⠀⠀⠀⠹⣿⠀⠀⠀⡾⠁⢻⠀⠀⠀⠀⢻⡇⠀⠀⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠚⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⠍⠁⠀⢀⠀⠀⢀⠀⠀⣠⡀⠀⠀⠀⡀⢈⣈⠃⠀⠀⠀⠙⠛⠆⢀⡴⠶⠀⠀⠀⠀⠀⣥⣾⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣧⣤⡄⡤⠀⣿⡏⡀⠀⠀⠀⡧⠀⠉⠑⠀⢹⣿⣿⡇⠀⢹⣿⡇⠀⠀⢰⣄⡐⡆⠀⠀⣀⣀⣀⣄⠀⠀⠀⡟⢛
⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠹⣿⠎⠀⠀⣿⣷⢁⠀⠀⢲⣶⣶⣶⠀⠀⢺⣿⣿⡰⠀⢸⣿⠀⠀⠀⢸⡛⡃⡇⠀⣰⣿⣿⣿⣿⣧⠀⢰⡏⣻⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠂⠀⠀⢸⣿⣿⣿⠀⠀⠀⠙⠋⠁⠀⢨⣿⠀⠀⠀⢸⣉⡇⡇⠀⢺⣿⣿⣿⣟⡿⠀⠀⠙⠛⠁
⠀⠀⠀⠀⠄⠢⠀⠀⠀⠀⠠⠂⠄⠀⠀⠀⠠⠀⠀⠀⠘⠻⠿⠓⠁⠀⠀⠀⠠⠀⠀⠈⠉⠀⠀⠀⠸⠿⠇⠇⠀⠈⠻⠿⠿⠟⠁⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⣀⣀⣤⡄⠀⠀⢀⣄⠀⠈⠀⠀⠀⡀
⠀⠀⢀⠀⠀⠀⡀⢰⣿⣿⣿⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣿⢹⠀⠀⢸⣿⣿⡟⠄⢾⣿⡿⠀⢠⣤⣤⣤⡉⠀⠴⠋⣷⢿⣿⠆
⠀⠀⢸⣿⣿⣏⡇⠘⣿⣿⣿⢸⠀⣤⣤⣤⣀⠀⢰⡦⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⢸⠀⠀⢸⣿⣿⡇⠀⢸⣿⡯⠁⢸⣿⣿⡏⠀⠀⢹⡾⢽⢸
⠀⠀⠀⠉⠙⠉⠀⠀⣿⣿⣿⢸⠀⠉⠛⠛⠉⠀⠈⡃⠀⢸⣧⣌⣍⡇⢸⣿⣿⣿⢸⠀⠀⢸⣿⣿⡇⡄⠀⠻⠇⠀⢸⣿⣿⣇⠀⠀⢸⣿⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠘⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⠀⠀⠁⠀⠁

⠀⠀⠀⠀⢠⣶⡶⢀⣀⣀⣀⣀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄
⠀⠀⢀⣴⣷⣿⠁⣘⠛⠛⠛⢛⣛⠈⢛⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠘⣿⣿⣿⠃⠿⠿⠿⠿⠿⠿⠇⠻⠇⠀⠀⠀⠀⠀⣾⣿⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⣤⡄⠀⠀⡄⠀⠀⣾⣧
⠀⠀⠀⠈⠛⠁⢠⣿⣿⣿⣿⣿⣿⡇⢸⡇⠀⠀⠀⠀⠀⣿⣿⡇⠀⣠⣤⡤⡄⠀⠀⣠⠀⠀⠀⠀⡇⠀⣿⡇⠀⠀⡇⠀⣸⡟⢻⡆⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠃⠠⡈⣛⣛⣛⣛⣛⣛⡃⢘⡃⠸⣿⣿⡿⠃⣿⣿⡇⠂⠹⣿⡷⠁⠀⠀⠘⠀⠀⠀⠀⡇⠀⢿⠇⠀⠀⠀⠀⣿⣷⣿⡇⠀⠻⠿⡿⠟⠁
⠀⠀⠀⠀⠀⢠⠈⢛⠛⠛⠛⣛⣛⠃⣛⠃⠀⠈⠉⠀⠀⣿⣿⡇⡄⠀⠨⠀⠀⠀⠈⠀⠀⠀⠀⠀⡇⠀⠸⠀⠀⠘⠀⠀⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠁⠀⠘⠛⠛⠛⠟⠛⠐⠟⠀⠀⠀⠀⠀⠀⠛⠛⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠐⠀⠀⠀⠀⠀⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠞⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠀⢀⡤⠔⠒⠛⠛⠛⠓⠒⠦⣄⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠙⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡁⠀⡠⣒⣤⠀⠀⠀⢠⣖⠢⡀⠀⣹⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⢸⠈⠉⠁⠀⠀⠀⠀⠀⠀⠉⠃⢸⠀⣈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣷⢸⡀⠀⠙⠁⠤⠀⠠⠀⠙⠁⠀⣸⢰⡇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢿⠀⠙⠒⠒⠧⢄⣀⣀⠤⠗⠒⠚⠁⢸⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⡲⠤⣤⣤⣤⠤⠖⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⡿⡄⠀⠀⠑⠔⠁⠒⠂⠀⠀⠀⠀⠀⡼⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⡘⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠀⠀⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢀⠃⠀⠀⠀⠀⠉⠛⠒⢲⠒⠚⠋⣥⠄⢒⢂⢤⡆⠀⠀⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢀⡴⡾⠀⠀⠀⠀⠀⠀⠠⠢⢸⠀⠀⠀⡇⠀⠀⠀⠀⣿⡶⠒⢒⡆⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣸⠀⡇⠀⠀⠀⠀⠀⠀⢀⢀⢸⠀⠀⠀⡇⠀⠀⠀⠀⣯⣏⣉⠩⡷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⢰⡇⠀⠀⠀⠀⠀⠀⢀⠄⢸⠀⠀⠀⡇⠀⠀⠀⠀⣟⣿⣔⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠒⠒⠺⡄⣇⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⠀⠓⠒⠒⠒⠒⢃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠰⣏⠸⡷⢤⣀⣀⠀⠀⠈⠈⢸⠀⠀⠀⠀⣀⣀⡠⠴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠚⠁⠀⢳⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠈⢹⠉⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠉⠉⠉⠉⠉⢻⠛⠉⠉⠉⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠤⠤⠤⠤⠤⠤⠾⠦⠤⠤⠤⠤⠤⠼⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢸⡇⠘⠛⡄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠙⠒⠚⢃⡼⠇⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠉⠁⠀⠀⠀⠀⠀⠀⠻⣤⣼⠀⠀⠀⠀⢠⡶⢆⠀⠀⠀⢀⡴⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠲⣄⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡤⠶⠶⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠈⠙⠋⠀⠀⠀⠛⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⣀⡠⠶⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⣦⣀⠀⠀⠀⠀⢾⡁⠀⣳⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀⠀⠀⠙⠚⠁⠀⠀⠸⣇⡀⣹⠄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢸⣭⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⢾⣭⠀⠀⢀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠸⣇⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠄⠀⠠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⢀⣤⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠉⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢿⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠉⠀⠲⢤⣄⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠘⠶⣤⣄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣼⣿⠟⣶⣤⣀⣿⠀⣰⡾⠛⠛⠛⠳⢦⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠈⠛⠛⠛⢉⣽⠇⣸⠏⠠⢤⣀⠀⠀⠀⢱⡄⢸⡇⠀⣴⠞⢛⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠤⠤⠀⠤⠐⠛⠁⠀⣿⠀⠀⢸⣿⡟⣷⣤⣼⠇⣾⠀⣾⠁⡼⠋⣍⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠁⠀⠀⠀⠐⠒⠒⠒⠒⠲⣤⡀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠘⣇⠀⠀⠙⠛⠋⣠⡟⢠⠟⠀⠻⣄⠻⠆⠜⢂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠉⠓⠲⠒⠉⠉⠉⠰⠶⠶⠚⠉⢠⡟⠀⠀⠀⠈⠑⠶⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣀⣀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠶⠶⠶⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠉⠉⠉⠛⢦⡀⠀⠀⠀⠀⠀⠐⠇⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⣰⠟
⠀⢀⠀⠀⢀⡄⠀⠀⠀⢠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣠⠚⠁
⢠⡎⠀⢰⠏⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠲⠋⠁
⠀⠁⠀⡇⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⢻⡌⠛⠳⠶⠦⠀⣤⣤⠄⢤⡶⠶⠖⠛⠋
⠀⠀⠀⡇⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠻⡀⠀⠀⠀⠀⠈⢷⡀⠀⠀⣶⠀⣽
⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠈⣧⠀⢀⠟⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠈⠳⣾⡀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡍⠉⠉⣷⠄
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⡀⠀⠀⠀⠀⠈⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀⣠⠾⠛⣻⡷⠶⠾⣧⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠛⠋⠀⠛⠁⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⠋
⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡸⠋⠓⠒⢦⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠄
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⣷⡀⠀⠀⠀⠀⠀⢻⡏
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠛⠶⣤⣀⣀⣀⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⢠⡶⢶⡄⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⢀⡀⠉⠉⠉⠀⠹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢰⡆⠀⠰⣆⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⢰⡟⠀⠀⠀⡟⠉⠒⠒⠒⠢⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠸⡇⠀⠀⠙⣆⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⣼⠁⠀⠀⣸⠃⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠸⣇⠀⠀⠀⠀⠈⢷⡀⠀⢸⡇⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⣸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠸⣦⠀⠀⠀⠀⠈⢷⠀⣼⠃⠀⠀⢸⣇⣀⠀⠀⠀⠀⠀⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠉⠉⠙⠛⠒⠤⣴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢸⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠘⡄⠙⠻⠶⣦⣄⡀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⠙⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠻⠷⠶⠶⠶⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⢀⣿⣀⣀⡀⣀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⢫⡍⠁⠀⠉⠉⠙⠳⣤⡀⠀⠀⠀⣴⠋⠉⠁⠀⠉⠉⠉⣙⣻⣶⣦⣶⣖⠚⠛⠛⠛⠛⠓⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⢻⡄⠀⠀⣀⡤⠖⠛⠉⠁⠀⠀⠀⠉⠛⠶⣤⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣀⡾⣷⡀⠀⠀⡴⠖⠲⣄⠀⠈⣧⠀⠀⢹⣶⣟⠉⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠙⠳⣤⣀⡼⠃
⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢸⡏⠁⠈⢹⠄⠸⣟⠛⢛⣿⠀⠀⢸⡇⣴⠋⠀⠙⠳⣤⣴⠛⠉⠁⠀⠀⠀⠀⠀⠀⢹⣆⣤⠞⠛⣦
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⢸⠅⠀⠈⠙⠋⠁⠀⠀⢸⡇⢿⣀⠀⠀⣰⠏⠉⠛⠶⣤⣀⣀⣀⣤⡴⠖⣿⠋⢷⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠲⢾⡷⠶⠶⢾⠷⠆⣠⡤⢤⡀⠀⠀⣸⠃⠀⠉⠛⠲⡿⠶⠶⠶⠒⠛⠛⠉⠛⠶⣦⣾⣧⣤⣸⣧⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠘⠳⡶⣶⠞⠁⢸⡷⠶⠶⣿⠀⣰⠏⠀⠀⠀⠀⠀⣧⣴⠒⠒⠒⠒⠒⠒⠛⠛⠛⠒⠒⢲⣬⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠚⠛⠛⢒⣀⠀⠙⠶⠞⣡⠾⠃⠀⠀⠀⠀⠀⣼⠋⣿⠀⠀⣠⣤⡀⢠⡞⠋⠙⢷⡀⢸⡏⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡶⠛⠉⣍⠙⠳⣶⠛⠁⠀⠀⠀⠀⢀⣀⣀⣘⣦⣿⡀⠀⠿⡴⠇⢸⣄⠀⠀⣸⠇⣸⡧⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣿⠀⠀⠈⣧⠀⢀⡴⠛⣉⣉⣉⣉⣉⣉⣉⣷⡀⠀⠀⠀⠀⠉⠛⠛⠁⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠋⠀⠀⠀⡿⢠⡞⠀⡼⠉⠉⠁⠀⠀⠀⠀⠀⠙⢶⣤⠴⠶⠶⢤⣴⠞⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠃⠀⣠⣾⢡⡟⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣀⣤⣄⡀⠈⠳⡄⠹⣆⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢿⣥⣸⡟⠀⠸⠷⠶⠶⠶⠶⠶⠶⠶⠶⣾⠁⢀⡾⠷⠶⠶⠿⡆⠀⢻⡀⠹⣟⣠⡼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⡼⠃⠀⠀⠀⠀⠻⣤⡼⠁⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡟⠉⠙⠓⠶⢦⡄⠀⣠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⡀⢀⡴⠶⠞⠋⠉⢹⡎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⡀⠀⠀⠀⠀⢷⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣼⠃⠀⠀⠀⢀⣼⠃⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠉⠛⠛⠓⠲⠾⠃⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠷⠖⠚⠛⠛⠋⠁⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⡉⠉⢉⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢻⡉⠉⠉⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣯⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠿⠏⢹⣿⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⠋⡄⢀⣄⣬⣡⣾⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢪⠟⢛⠛⠻⡝⠉⠀⠿⣦⣼⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣳⠅⠈⠀⠀⠀⠙⡠⠰⠄⠺⢻⠷⡲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢱⠏⠀⠀⠒⠁⠀⠀⠀⡠⡆⣰⣮⡜⠁⠀⠀⠀⠀⠀⠠⣀⣀⣀⣀⠀⢀⡤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣴⡋⣀⡟⠈⠀⠈⡸⠄⠐⠄⣴⣡⣵⡙⣾⣀⠶⣆⠀⠀⢠⠀⠰⠀⠀⠈⣴⠏⢠⡀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⣟⢁⣤⣹⢷⡒⠀⠉⢨⣯⣿⣄⡂⢀⡸⠆⢀⡐⣌⢻⢻⡿⠋⠉⠁⠀⠈⠉⠉⠃⠰⠶⠤⠾⠿⢾⣿⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠲⢷⣼⣿⣶⣷⣾⣿⡯⢭⡉⣙⣳⣄⣬⣿⡟⢾⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⣉⡭⠋⠀⢀⡞⠘⡟⠈⠳⣮⣛⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣶⠒⠻⢻⠃⠀⠻⣤⣐⣯⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⣀⢸⡀⠀⡤⠀⠉⣿⣟⣿⢿⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠠⢤⡘⡆⢧⠘⠁⠀⠀⠙⡈⣿⣼⣿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠉⣷⣼⠀⠀⠀⠀⢀⡙⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢙⣿⠀⠀⠀⠀⠀⠹⡟⠻⣽⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⣤⡎⠀⠇⠀⠀⠀⠀⣸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠠⠴⣦⠞⠀⠀⠈⣦⠀⠀⠀⣇⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⢀⣴⡞⠉⠀⠀⠀⠀⣧⠀⠀⠐⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⢈⣽⠇⠀⠀⠀⠀⠀⠈⠳⠄⠀⣼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⡀⠰⣿⡀⠀⠀⠀⠀⠀⠀⠈⡂⠄⢹⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡅⠄⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠇⠀⠙⣟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠈⣆⡀⣹⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡀⠀⢵⣟⠀⠀⠀⠀⠀⠀⠀⠀⠩⡉⠹⡇⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠘⢿⡀⠀⠀⠀⠀⢸⣶⣴⣤⣏⣰⣯⡀⢤⣀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠐⢿⡄⠀⠀⠀⢰⣶⣿⣿⣿⣿⣥⡈⣻⡁⣿⣧⣶⠧⡖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠊⣀⣽⣾⣷⣤⣶⢿⡿⠿⠿⠛⠛⠋⠙⢷⣌⢻⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠐⠚⠥⠄⠘⠛⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠤⠀⠀⠀⠠⠀⠠⠠⠀⠠⠰⠀⠀⠠⠠⠠⠀⠀⠀⠀⠀⠀⠀⠰⠀⠆⠄⠀⠀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋⠀⠀⠀⠈⠣⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄
⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⢸⠀⣠⢀⠀⡠⢀⢄⣀⠀⣀⣤⡀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠛⠾⠖⠧⠘⠴⠛⠋⠛⠶⠛⠆⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⣀⣀⣀⣓⣒⠶⠤⣤⣤⣤⣤⡤⠄⢸
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢹⣿⣿⢿⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠖⠋⠉⠉⠹⣿⠁⠀⠀⠀⠉⠛⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⢻⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢻⣿⣿⣄
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⢿⣿⣿⢽⠠⠾⠳⢤⡀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⢹⣧⠀⢀⣀⣀⣠⣤⣤⣿⣿⣿⣦⣀⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⢹⠀⠀⠀⡀⠳⡀⣰⣟⣀⣠⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⡦
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠀⠀⣼⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣼⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣻⣭⣭⣿⣍⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢹⢠⡀⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠿⣿⣿⡞⣿⡿⠇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢺⠀⢻⠿⠿⣴⠶⢶⣟⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⣿⣿⣧⣤⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣻⠀⠀⣾⣿⣿⣦⣼⣿⡇⢿⠿⠋⠉⠉⠉⠉⠉⠉⠁⠀⠈⠻⣿⣿⣿⣿⡿⠋
⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⠿⠿⡿⠿⡿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⣩⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠜⠀⠀⢀⣠⠤⠴⠖⠲⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠘⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡁⢀⣔⣲⠄⠀⠀⢠⣖⣢⡀⣈⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡄⢸⠈⠁⣀⠀⠀⠀⠀⣀⠈⠁⡇⣠⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⠸⣄⣀⣁⠐⠂⠐⠀⣈⣀⣠⠃⣟⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠀⠀⠀⣈⠛⠒⠒⠛⣁⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠀⠀⠀⢏⠝⠉⠉⠉⠀⠀⠀⢀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠡⠃⠳⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠙⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⡀⠀⠀⠀⠉⠓⠲⠶⠶⠖⢚⣉⠀⠀⣠⣄⠀⠈⠳⢤
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣠⢾⠁⠀⠀⠀⠀⠀⠔⠤⠀⠀⠘⡇⠀⠀⠀⢻⡶⠒⢒⡄⡧
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡇⡾⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⡇⠀⠀⠀⢸⣯⠭⢴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣀⡇⣇⠀⠀⠀⠀⠀⠀⢔⢰⠄⠀⠀⡇⠀⠀⠀⣸⡿⠢⠜
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠉⠉⣱⠸⣄⠀⠀⠀⠀⠀⠄⢸⠀⠀⠀⠉⠉⠉⠉⣡⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠤⠼⠀⢳⠉⠓⠒⠶⠶⠤⠼⠦⠤⠶⠶⠒⠚⠉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⢲⡖⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣀⣀⡀⠀⢸⡇⠀⢀⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠉⠈⠉⠉⢹⡏⠉⠉⠉⠉⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠒⠒⠚⠓⠒⠒⠒⠒⠒⠋
⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠉⠀⠀⢠⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⣀⡀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣠⣤⣶⣦⣿⣿⣿⣿⣷⣆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠋⠝⠉⠛⢿⢻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠥⡵⢀⠒⠂⠤⠤⣄⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠴⣶⣶⣿⡟⢩⠛⠀⠀⢒⠒⠂⠀⠙⢳⠞⠛⠓⢄⠀⠐⢆⠀⠈⠉⠲⠁⠣⠀⠀⠀⠉⠉⠉⢉⠁
⠀⠀⠀⠀⢘⠤⠴⠀⠀⠘⠀⣃⣀⠀⠘⢿⡿⡿⠛⠓⡌⠘⢀⠀⠀⠀⠀⠀⠀⡏⠀⡀⡀⢸⠀⢀⡌⠀⠀⠀⠀⠀⡰⡄⠀⠀⠀⠀⠀⡌
⡄⠀⠈⠀⠀⡴⠒⠛⠉⢉⣉⡅⠈⢧⠀⣠⠟⣧⢀⡀⠹⠢⠤⣬⠙⢲⡀⢠⣾⣅⡡⢤⠀⣾⡴⠫⠀⠂⠀⣀⠴⠊⠀⣸⠖⡀⠀⠀⢀⠃
⠑⠄⡀⢴⣉⣩⠀⠀⠁⠀⠀⢀⣀⡘⢞⡅⠀⠀⠀⠯⠄⠀⠀⠀⠠⠂⠀⠀⠀⢩⠀⠈⡉⠀⠀⠀⠐⣮⣭⢤⣶⣶⣟⠒⢛⠀⠀⣀⣸
⠀⠀⠉⡀⠠⢈⠓⠒⠛⠋⠉⠉⠁⠀⠀⠉⠄⠀⠜⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⣥⠤⣤⣶⣶⡿⠋⠀⠉⠉⢀⡠⣊⣀⣠⣤⣼
⠀⠀⠀⢀⠀⠀⠉⠲⢤⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡤⠤⠴⣶⣾⣿⣿⠀⠀⢧⠀⠟⡻⠋⠀⠀⠀⡠⠔⠉⣉⣉⣀⡠⠤
⠀⠀⢠⠸⢀⠀⠀⠀⠀⠈⠙⠲⠇⠤⠤⠰⠖⠒⠋⠉⣿⡀⠀⠀⠀⡷⢿⠿⣿⠻⠀⠀⢺⠀⠉⠀⢠⣠⡔⠋⠀⡞⣿⠀⠀⠀⠀⡀
⠀⠀⠨⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢀⡜⠀⠈⣹⠟⠀⡄⠀⢸⠰⣄⠀⠀⠐⠳⢄⠀⡇⡇⠀⠀⠀⠀⠃
⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄⢢⡀⢿⡇⢠⠞⠀⠀⣰⠃⠀⠀⠃⠀⠀⢸⡄⢽⣦⣄⠀⠀⠙⠳⢧⡀
⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡜⢄⠉⠻⣇⣮⡢⢄⣰⠃⠀⠀⠀⠨⡉⠉⠙⠞⠊⠇⡏⠙⡶⣄⡀⠀⡠⠀⢲
⠀⠀⠀⣀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠢⡑⣄⠀⠙⢮⠑⠋⠀⠀⠀⠀⠀⠙⢢⡤⠤⠖⢀⠇⠀⡇⣿⣔⠋⢠⢤⠞⠀⠤
⠀⠠⣠⡄⢠⣠⡂⢀⣴⡂⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⡩⣲⣀⠆⢀⣀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⣀⠀⠂⠁⢉⣀⠜
⠁⠀⠛⠁⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠉⠉⠉⠈⠉⠀⠀⠀⠀⠀⠀⠘⠣⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠠⠤⠄⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡉⠁⠀⠀⠀⠀⡀⠀⠀⢰⣿⣤⣶⢿⡿⢿⢿⣶⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢀⣇⠀⠀⠀⠀⢀⣧⠀⠀⢸⣿⠿⠿⠿⠷⠾⠿⠿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣼⣿⠂⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣀⣀⣠⣤⣼⣿⣤⡄⢸⣿⠀⠛⠃⠀⠀⢰⣇⠀⣿
⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣧⣭⣿⣿⣿⣿⣿⣷⣼⣿⣶⣶⣾⣿⣷⣾⣿⣴⣿⣦⣶⣶⣶⣶⣴⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⠟⠻⣿⠛⠋⠉⠉⠉⠉⠉⢹⣿⠉⠉⠉⠉⠉⠉⠉⠉⣿⠉⠉⠙⠛⣿⠟⠻⡿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣀⣀⣀⣀⣀⣀⢀⣿⡀⠀⠀⢀⡏⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠒⠒⠺⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢸⠗⠒⠒⢺⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⠉⠉⠉⠉⠉⠉⣿⠀⣿⣶⣿⡀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠒⠒⠒⠒⢻⡄⠀⠀⠀⠀⠀⢸⣿⢀⣀⣀⡀⠀⠀⠀⢀⣿⣿⣿⣠⡟⠒⠒⠒⠒⢻⡄
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣄⠘⣇
⠀⠀⠀⠀⠀⠀⠀⣿⠤⠤⠤⠤⠤⠤⣿⠀⠀⠀⠀⠀⣸⣿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠤⣿
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⣀⣼⣿⡟⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟⠛⣋⣡⣶⣿⣿⣿⠟⠋⠁⠉⠉⠁⠻⠿⠿⠀⠙⠻⠿⢿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠈⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠀⠏⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠈⠃⠀⠀⠀⠀⢠⡤⣄⠤⣀⣤⡀⠀⠀⠙⡀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠚⠀⠀⠀⠁⠀⠷⠦⣄⠈⠀⠉⠀⠀⢀⡤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⠔⠑⢄⠈⢳⡀⠀⠀⠀⠯⣄⠙⢦⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡄⠠⠖⠀⢀⡞⠀⠀⠀⡠⠐⠀⠈⠁⠉⠀⠀⠀⠀⠑⡀⣷⠀⠀⠀⠀⡼⠀⠀⠀⠀⠑⢄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠰⡄⠀⢸⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠏⠀⠀⠀⠰⡇⠀⠀⡀⠄⡀⠈⢩⡷⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⢄⠀⠱⣉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⢠⠋⠉⠂⠀⠀⢀⠀⠀⠈⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠣⠀⠀⠀⠀⠀⠀⠐⠦⠊⠀⠀⣠⠃⠀⠀⠀⠀⠀⢘⠀⠀⠁⡄⠂⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠂⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢳⠀⠀⠀⢀⡰⠁⠀⡼⠋⠙⢆⣀⡠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⣠⠴⢦⣄⡀⠀⠀⠉⠀⠀⠀⠀⠁⠀⠠⠀⠛⠲⠶⠒⠉⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⢄⣸⠀⠀⡎⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠤⠤⠤⠤⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠤⠄⠉⠀⠰⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣃⣀⠀⢀⡜⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠤⠔⠋⠀⠀⠀⠀⠀⠀⠈⠳⡖⠒⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⢰⠚⠙⠳⣄⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠸⠀⠀⠀⠈⠳⡄⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⢹⠀⠀⢀⡠⠷⠶⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠧⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠘⢷⠋⠁⠀⠀⢀⠀⠐⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠂⢾⡁⠀⠀⠀⠀⠀⠀⠀⠸⣤⣄⡠⠴⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⠀⠀⠀⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠤⣂⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⡊⠉⢙⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣍⡄⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠶⠶⠶⢾
⢀⣠⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠴⠶⠚⠛⠋⠉⠉⣉⣠⠴⠚⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸
⡎⠀⠀⡀⠄⠘⠓⠀⢀⠀⠀⢀⣠⠴⠚⠋⠉⠀⠀⠀⢀⣀⣠⠴⠖⠛⠉⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⡇
⠈⠉⠉⠀⠀⢀⡴⠛⡏⠀⠠⣯⠤⠤⠤⠤⠶⠶⠚⠛⢉⠡⠄⠀⠀⠀⢈⢭⣭⡙⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⣇
⠀⠀⠀⠀⢰⠋⠀⣸⠃⠀⠀⠹⣦⡀⠀⠀⣀⣤⡶⣯⡀⢀⣤⠴⠶⣦⢀⣀⣬⢿⠌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢻⡀
⠀⠀⠀⠀⢿⣄⣴⠏⠀⠀⠀⠀⠘⢿⣤⣾⣟⣁⣀⣨⣵⣯⡴⠶⠖⢛⣩⢥⣄⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠀⠈⠳⣄⡀
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⢻⣯⠉⠉⢉⣵⠞⠛⠶⠶⣆⢻⠀⠀⢹⡧⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠋⡏⠀⠀⠀⠀⣿⠀⠀⣐⡚⠁⠀⣿⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⠀⠀⠰⠶⢶⠇⣴⠋⠉⠉⣋⡴⣿⠀⠀⠀⠀⠀⡴⠋⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣀⣀⣀⣁⣤⣥⡴⠶⠛⢉⣠⠟⠀⠀⠀⠀⣼⠵⠒⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠚⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⠉⠉⢉⣀⣠⡤⠔⠚⠉⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠤⠒⠒⠒⠲⢤⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠈⠉⠉⠉⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⠦⣤⡾⠚⠛⠻⢦⡀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⢹⡄⠀⣀⣀⣀⡴⠞⠉⠀⠈⣷⠀⠀⠀⣠⠞⠻⠷⠊⠀⣿⠀⣠⠤⣄⠀⢻⡄⠀⠀⡇
⠀⠀⠀⢠⣶⢨⡇⢸⡏⠉⠉⠀⠀⠀⠀⠀⠘⠷⠤⠖⠁⠀⠀⠀⠀⠀⣿⠎⠀⠀⠘⡆⠀⡇⠀⠀⡇
⠀⠀⠀⠛⢋⡜⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡇⠀⡏⠀⠀⢻
⠀⠀⠀⢠⠋⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡼⠀⣸⠁⠀⠀⢸
⠀⠀⠀⠃⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢀⡼⠁⡴⠃⠀⠀⠀⢸
⠀⠀⠈⢧⣤⣤⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡖⠋⣠⠞⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤
⠀⠀⠠⠖⠀⠂⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠞⠁⠀⠀⠀⠀⠀⠀⠀⡷⠶⢦⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣤⣤⡤⠶⠶⠛⠋⠁
⠀⠀⠀⣠⣤⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉
⠀⠀⠀⠿⠋⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⢸⡿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴
⠀⠀⠀⠀⠸⣧⠈⠙⠒⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠉⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⢶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⠶⠶⠞⠛⠉
⠀⠀⠀⠀⠀⠈⠻⠶⣦⣤⣀⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⠶⠚⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣀⣀⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠋⠉⠉⠉⠉⠙⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠒⠒⠒⠒⠦⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⡀
⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠄⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠤⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⠀⠀⠀⠀⠀⢀⡤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠤⠔⠊⠁



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

⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠀⠀⡀⡐⠀⡀⠀⠀⡔⢋⣲⣄⣀⣀⣴⠒⠀⠀⠀⠀⠀⠀⠀⠼⠆⠀⠀⢰⣤⣶⣦⣆
⠀⠀⡴⢾⢒⡆⡆⡀⡀⠀⠀⢀⣷⡾⣶⣇⠀⠀⠳⢬⠿⣿⣿⠿⠋⠀⠀⠀⠀⠀⣠⡶⠉⠂⠀⠀⠀⣿⣿⣟⣿⣭
⠀⠀⡇⢸⢸⡇⡇⡇⡇⠀⠀⠸⣿⠇⢿⡿⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⢀⣴⣝⡟⠁⠀⠀⠀⠀⠀⣿⣿⡽⣿⣿
⠀⠀⠙⠺⣬⣇⣇⣇⡇⠀⠀⢠⡆⠀⠀⣥⠀⠀⠀⠀⠀⣸⣄⠀⠀⠀⠀⠣⡸⠋⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣯⠀⠀⠀⢰⣿⣟⡴⠢⡀⠀⠀⢰⣿⣿⣿⣿⣆⠀⠀⠀⢸⣤⣀⣼⠀⠀⠀⢸⢩⣭⣭⣩⣍⣭⢹
⠀⠀⢠⣀⣀⡄⣿⣿⡇⠀⠀⠀⢸⣭⣭⡗⠃⠀⠀⢻⣿⣿⣿⣿⡟⠀⠀⠴⣿⣿⣿⣿⡿⠆⠀⢸⢩⣍⣭⣩⣍⣭⢹
⠀⠀⠀⠻⡟⠁⣿⠀⠀⠀⠀⠀⠸⣿⡿⠇⠀⠀⠀⠀⠉⢹⡏⠉⠀⠀⠀⠀⢹⣿⣿⣿⡇⠀⠀⢸⣩⣭⣭⣩⣍⣭⣹
⠀⠀⠀⠰⠇⠀⠿⠿⠇⠀⠀⠀⠀⠼⠤⠀⠀⠀⠀⠀⠠⠾⠷⠄⠀⠀⠀⠀⠘⠿⠿⠿⠀⠀⠀⠸⠉⠉⠉⠉⠉⠉⠹

⠀⠀⠀⣄⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⢀⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⣠⠤⠤⠤⠤⠤⣄
⠀⠀⠛⣦⣼⣧⣤⣤⡄⠀⠀⢀⣀⡀⠀⣿⣇⠀⠀⠙⢻⣿⣿⡟⠋⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣳⡴⠴⠤⠦⢦⡞
⠀⠀⠀⠈⠙⠿⠿⠋⠁⠀⠀⢸⣿⡇⢸⣿⣿⡆⠀⠀⠈⢻⡟⠁⠀⠀⠀⠈⣿⣧⣿⣷⣄⠀⠘⢇⢸⡇⡆⡆⡆⡎⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡏⠀⣸⣿⣿⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠆⠀⠈⢻⡅⠇⠇⠇⠇⡇
⠀⠀⠀⠀⠘⠛⠛⠃⠀⠀⠀⠀⠛⠀⠘⠛⠛⠁⠀⠀⠐⠛⠛⠂⠀⠀⠀⠀⠛⠉⠙⠛⠉⠀⠀⠀⠈⠛⠛⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠲⠀⠖⡆⠰⢲⠀⠀⢰⣖⣒⣒⣲⡆⠀⠀⣰⢶⡖⠒⢶⢲⡀⠀⢀⣀⠀⠀⠀⢀⡀
⠀⣠⢠⡄⣤⢠⣀⠀⠀⠀⣞⠉⣳⠁⢱⡋⢈⡆⠀⣼⠛⠛⠛⠛⣧⠀⢠⡟⣿⠛⠛⠻⡟⢧⠀⢺⣗⢀⠀⣀⣸⡇⡇
⠀⣿⢸⡇⣿⢸⣿⣤⡀⠀⡁⠄⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⣿⠀⢸⡄⣧⠀⠀⢀⡇⣸⠀⢬⡧⠀⠀⠀⢸⡇⡇
⠀⠛⠘⠇⠿⠘⠋⠉⠁⠀⡉⠍⠉⠉⠉⠉⠍⡇⠀⢸⣿⣿⣿⢿⡇⠀⠀⢿⣹⣏⣉⣿⣻⠇⠀⠼⣗⠀⠀⠀⢸⠧⠃
⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣶⣦⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠛⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣩⣭⣻⣿⡟⠈⠀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠁⠀⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡅⣀⠙⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣮⢠⡀⠀⠀⠀⠀⠐⠳⠻⠿⠟⣺⣿⡛⣯⣧⣬⣥⡌⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠙⣦⣤⣀⣀⣀⡀⠀⠀⠀⠈⠙⠙⠻⠿⠿⢿⠻⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠇⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⠀⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠛⠵⣄⠀⠀⠀⠈⢣⣄
⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠀⠓⠦⡀⢰⠙⢺⠈⠀⠀⠀⠀⠀⠀⠁⠒⠤⣀
⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⡄
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠻⢿⣷⠄⠀⢠⣀⣀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⡟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠒⠘⠁⠉⠉⠁
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⣏⣀⣤⠤⠀⠀⢀⣀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⡇⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⡗⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠟⠉⠙⠛⠛⠙⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠋⣣⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢀⣀⡀⠀⠀⣀⣤⣄⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣧⡿⠿⢻⣿⠈⠿⠳⠆⠂⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⠀⠀⠉⡁⠀⠀⠀⠀⠀⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⣣⢀⡖⠙⠛⠉⠳⠀⠀⡔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠘⠷⠀⠂⠀⠘⠁⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣀⠈⠉⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣷⣄⣀⣀⣾⠟⢸⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠛⣿⡟⠋⠋⠀⣸⠇⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡹⣧⠙⠃⠀⢀⡴⠋⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢿⣿⣿⠿⢠⡽⠳⠀⢻⣆⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠋⠁⠀⠀⠹⣟⢷⣈⣿⡄⡿⢢⡿⠶⠋⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠙⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⣷⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡞⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣞⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡿⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⢰⠂⠉⠀⠀⢈⡁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⢀⣀⣀⠀⠀⠀⠀⠀⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠈⣉⡀⠀⠀⠀⣌⣠⠍⣦⡤⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣏⡵⠚⠂⠀⣀⠀⠀⠀⢸⢿⠁⠄⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⡉⠉⠒⢄⠀⠀⠉⠀⢹⡆⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠐⠂⠀⢠⡞⠀⠀⠀⠀⣸⠀⠀⡀⠀⠀⣀⣀⣀⡀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠘⣁⠒⢚⣠⣴⠁⢠⣿⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣟⠀⣈⢀⢀⣾⠁⢀⣀⣀⣀⣟⠀⣀⣵⣾⠛⠀⠂⠤⡄⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠍⠓⡀⡴⠛⠏⠀⠀⣸⢷⠀⠀⠀⠀⠀⠀⠀⣿⣿⣯⡀⢩⣼⡾⠃⠀⠈⡯⠉⠉⠉⠛⠉⠉⠉⠐⠒⠤⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠄⣀⣤⠞⠁⢸⠀⠀⠀⠀⠀⠀⠀⡿⣱⣿⣿⡄⠀⢳⣤⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢁⣛⠛⠉⠁⠤⡼⠿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠇⠀⠀⠀⠀⠀⠹⣿⣀⣁⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠄⠀⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⣤⣤⡄⢀⣀⣄⣤⣤⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠘⠻⣿⣟⠟⠁⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣴⣿⣶⣦⣜⠛⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣀⣀⡀⠀⠀⣀⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢻⣿⣿⠇⢹⡿⠿⠛⠋⠈⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⡶⠲⢀⣤⣶⡆⠀⠀⣶⣶⣆⠲⡀⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣿⣿⣿⡿⢈⡑⣱⣿⣿⣿⡇⠀⠀⣿⣿⣿⣷⣌⢸⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣺⡿⠛⠋⠙⣿⣿⣤⡍⢼⣿⣿⣿⣽⣷⣶⣤⣿⠿⣿⣿⣿⣾⣹⡿⣛⠋⠉⠛⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡟⠸⢧⣶⣼⣿⣏⣿⣿⣿⣿⡿⣿⣿⣿⣿⣯⣽⣿⣾⣽⣻⣟⡻⣿⣿⣶⡆⠀⠈⢷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣀⣀⢘⣣⣤⣾⣛⡛⢻⣯⣿⣿⣷⣿⢿⡋⠑⠀⠈⠀⠀⡉⠙⢿⣿⣿⣏⣷⣴⢿⣯⣤⣴⡟⠂
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠈⡉⠜⠉⢡⡾⠋⢩⣿⣿⣿⣿⣿⣿⢿⠀⣿⣿⣷⡄⡆⢠⣶⣶⣶⡿⣿⣿⣿⣿⡿⣿⡊⠁⠙⠛⠛⠛⠁⢄⠁
⠀⠀⠀⠀⠀⡠⠾⠉⢙⡄⠀⠊⠀⠀⣠⣿⣷⣤⣴⣿⣿⢻⣿⣿⣿⢸⠀⣿⣿⣿⡇⠁⢸⣿⣿⣿⣧⠻⢹⣿⣿⣿⣷⣽⡦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠛⢗⣾⢛⣾⠛⠁⠀⢩⣿⠛⡾⠘⣿⣿⡟⢺⡆⢿⣿⣿⠇⠀⢘⣿⣿⣿⡇⠀⢘⣿⣿⡛⠙⠻⣆⢱⣤⣤⡤⡀⠀⠀⢀⣄⣤⣄
⠀⠀⠀⠀⠀⣠⠞⢠⠔⠀⠈⠳⠶⠋⣀⣤⣾⣿⣿⣦⠃⣰⣿⣿⣷⡼⠃⣼⣿⣿⣆⠀⢸⣿⣿⣿⣿⡀⣨⣿⣿⣣⠀⣸⣿⣿⣦⣀⠙⢿⣟⣢⡼⢿⣿⠟
⠀⠀⠀⠀⣾⡃⢀⠄⠀⣤⡶⠞⣾⣿⣿⣿⣿⣿⢿⢿⣷⣿⣿⣿⣿⠷⢺⣿⣿⠿⡿⣶⣿⣿⣿⣿⣿⣿⡻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣋⣰⣿⣟⣷⠏⠉
⠀⠀⠒⢠⣻⣤⣬⠁⠐⠛⠉⠘⣿⣿⡿⠓⠉⠀⠀⠀⠀⠀⠈⠃⠙⠈⠀⠁⠈⠀⠀⠀⠸⣇⠉⠉⠁⠀⠀⠺⠷⢬⣬⣙⡋⠉⠉⠙⠛⠿⢿⡽⠟⠻⠧
⠀⠀⠀⠈⣬⠯⣿⣤⣴⡶⠠⣶⣿⣿⡶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠘⡈⠄⠀⠀⠀⠀⠀⠀⠀⠀⡠⢈⣩⡉⣕⢦⡀⠸⠀⠀⠀⠲⣄⡀
⠀⠀⠀⠀⢻⣷⣶⣿⡾⢿⠿⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⡀⠀⡀⠀⠀⣼⣿⡡⠚⠃⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡻⢄⡀⠀⠀⠀⠘⢷⣆⢠
⠀⠀⠀⠀⢼⣿⢁⣤⣤⣈⣀⠩⠹⣿⡀⠀⠀⠀⠂⠠⠀⠀⣾⣻⣿⣾⠃⠀⠀⠉⠀⠀⠐⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠂⠀⠠⠀⢸⡟⣿
⢰⠶⣾⣷⣿⣿⣿⣿⡛⣹⣿⡧⠀⣿⡇⠀⠀⡠⠠⠛⠛⢷⣿⣿⣋⡁⠀⠀⠀⠀⣆⢀⣤⠆⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠀⠙
⠘⠓⠉⠆⣿⣹⣿⣿⣿⠿⢫⠁⣠⣿⣇⡄⠈⠂⡀⠀⢀⡜⢫⡴⠾⡏⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠠⢀⣀⠀⠀⠀⠀⡀⠀⠈⠙⢿⠄⠀⢠⣤⣦⡀⠀⠐
⠀⠀⠀⠘⣷⣿⣿⣿⠧⢺⣽⣿⣿⠿⣿⡇⠀⠀⠉⠤⠆⡿⠿⣦⢾⡇⠀⠀⠈⠁⠀⠀⠀⠐⠀⠠⠆⢀⣿⠓⡶⠖⠀⣈⠀⠀⡀⠀⠀⣠⡏⣿⣟⣿
⠀⢠⣾⢾⣿⣿⡿⠁⣽⣿⣿⣟⣿⣷⣷⡄⠀⠀⠀⢸⡷⠀⠀⠈⠉⢁⠀⠀⢙⠢⡀⠀⠀⠀⠀⠀⣤⠏⢈⣤⣀⠒⠀⡈⠉⠀⠀⠀⠀⣀⣀⢠⣿⠉⠁
⠀⠀⢿⢿⣿⣿⡇⠀⣿⣿⣿⡟⠙⠿⣿⣷⣆⠀⠠⠀⠀⠀⠀⠀⢀⣜⡢⠄⡃⣸⣷⡄⠀⠷⠠⣌⠛⣾⣿⣿⣿⣷⣦⣀⡀⣀⡀⣀⠀⣀⠁⡹⣟⢾⡄
⠀⠀⠈⠀⢻⣿⠃⣾⣿⣿⣿⡫⣄⠠⠉⡿⢻⠀⠀⢀⣤⣦⡴⠶⠢⠮⠥⠌⠠⡉⠈⠁⠀⢀⣀⣒⡂⠸⣛⣻⣿⠛⠉⠛⠁⠁⠘⠁⠔⡥⠪⣚⠿⠁⠄
⠀⠀⠀⠀⢄⣿⣧⣿⣿⣿⡏⢈⣿⣳⣶⡷⣾⣤⠐⢾⡛⣯⡄⠀⠀⠂⢘⣂⣀⣘⣠⡴⠶⢼⣿⣿⣟⠋⠉⠉⠁⠀⢀⣤⣀⡨⠟⠓⠮⣦⠔⢡⠀⠄⢄⡀
⠀⠀⠀⠀⠀⠻⣿⡟⣿⣿⣟⡀⠰⢿⣿⣧⣿⡿⢳⣺⡇⣿⠃⠒⠛⠛⠋⠉⠉⠀⠀⣀⣀⡄⠈⢻⣿⡀⠀⠀⠀⢀⣿⣿⡿⠁⢠⣦⡄⣭⡴⣀⠀⡀⠈
⠀⠀⠀⠀⠀⠀⠹⣷⡼⢻⣶⣶⠞⣠⣾⣿⣿⣿⣿⣯⣙⠛⠂⠀⡀⠀⠀⠀⣤⣶⣿⣿⣿⣷⡄⠸⣿⣷⡆⠀⠀⠀⢀⣿⣇⣠⣾⣾⠖⠿⠆⢬⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⣿⣃⣾⣿⣿⣈⣛⣨⣿⡛⢾⣦⣶⠶⠾⠀⠀⠀⡈⣿⣿⣿⣿⠿⡏⠁⢹⡿⣧⠀⠀⠀⢾⣿⣿⡟⢛⣿⣷⣶⡶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣷⣌⣍⠉⠁⠙⠿⣶⣽⣿⣶⣤⣴⡀⠀⠈⢹⣿⣿⣏⢴⣿⡀⣸⣿⠻⣆⣰⣿⣿⣿⣿⣤⣤⣽⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣤⣤⠤⢤⡄⠉⠻⠿⠁⠈⠠⣤⡤⡞⢩⣿⣿⣷⣿⣩⣿⣿⣻⣾⣯⢿⡁⠉⠳⠇⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠴⣷⠆⡠⠄⠠⠥⠉⠈⠉⣉⢸⡟⢹⣼⣿⣿⣿⣿⡿⠟⠛⠓
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣁⣉⣬⣼⣿⣿⣿⣟⣛⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡏⠉⠋⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣦⣴⣾⣿⡇⠀⠀⠀⠀⠀⣠⣾⣿⣦⣴⣆
⠀⠀⣴⣿⢿⣿⠋⠀⠹⠿⠿⠟⠛⠛⠋⠉⠉⠉⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⣠⣾⣿⣿⣿⣿⣿⣿⣆
⠀⠀⢿⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠻⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠉⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣷⡄
⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣄
⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣆
⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡆
⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢿⣿⣷
⢸⣿⣿⣿⣿⣇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿
⢸⣿⣿⣿⣿⣿⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠁⠀⡀
⠈⣿⣿⣿⣿⣿⣿⡄⠀⠀⠹⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿
⠀⢸⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠛⢛⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿
⢶⣿⣿⣿⣿⡿⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡏
⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⣽⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⡟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⠀⠀⠀⠀⠀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣶⣯⣶⣶⣶⡄⠀⠘⠻⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣶⣭⣽⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠿⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠑⠀⠀⠀⠈⠉⢫⣹⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣯⣿⣿⣽⡟⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⢀⣀⣀⣀⠀⠀⠀⠀⠰⠶⠿⠿⣿⣷⣷⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡇⣰⣿⣿⣿⣿⣿⣦⠀⠀⣄⣠⣤⣤⣯⣭⡋⣿⡿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⣹⠇⣿⢟⣿⣟⣻⣿⣿⡇⠚⣿⣿⡿⢿⣿⣿⣿⣿⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠉⠟⠙⣛⢏⣽⣿⠃⢀⣿⣧⣶⣾⢿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠘⠁⠈⠀⢸⣿⣿⡄⠤⣾⣿⣿⣿⠏⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣉⠁⠀⠀⢈⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠄⠠⠀⢠⡎⠀⠀⠀⢀⣿⢿⣷⠀⣠⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣃⠀⠀⢸⡟⠻⢶⣶⣿⣿⣿⣿⣼⣿⣿⡇
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⢀⣎⡀⠤⠠⣤⣤⣈⣙⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⡼⢿⣽⠁⠀⠀⠴⣴⣤⣤⣿⣿⣿⡿⣄
⠀⠀⠀⠀⠀⠀⠀⠤⡄⠀⣀⣒⣰⣦⠀⠀⠀⢠⡇⠀⠈⢻⡤⠀⠀⠻⠧⣿⣿⣿⡿⠀⠻⣦⡀
⠀⠀⠀⠘⠳⠦⠤⣴⣴⣈⣹⣿⣿⣿⠀⠀⠀⢸⡇⠀⠀⠈⠻⣦⣤⣶⣾⣿⣿⡿⠁⠀⣼⠈⠳⣤⡄
⠀⠀⠀⠒⠦⠤⣄⣼⣀⣉⣉⣿⣸⡇⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠁⠀⢸⡇⠀⠀⠀⢠⣀
⠀⠀⠀⠰⢤⣤⣤⣭⡤⢼⣿⠿⠟⠁⠀⠀⠀⠀⠘⠂⠀⠀⣠⠄⢈⡿⢋⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠉⢻⣄
⠀⠀⠀⠐⡤⢬⠿⡷⡶⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⢼⢃⣀⣘⢣⣾⠃⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠈⠿⣡⡞⣡⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣭⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣫⣵⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣾⠟⣫⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣵⣿⠟⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⢋⡵⠟⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣾⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢰⡆⠀⠀⠂⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡎⠀⠈⠋⠓⠉⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢠⡀⠀⡀⠀⠰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠈⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠾⠟⠈⠛⠛⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠾⠟⠀⠈⠟⠻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⣤⣤⣄⠀⢠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⢹⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⠀⠈⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⢀⣠⡶⠁⠀⢸⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡿⠿⢿⠟⠛⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⡿⠿⠆⢠⣿⣿⣿⣿⣿⣷⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢳⣤⠀⡀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⡿⢿⣿⣿⣧
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠙⠛⠁⠀⠈⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠸⠇⠂⡀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡀⣸⣿⣿⣿⣿⣿⠛⠿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣤⣤⣄⣀⣤⡀⡈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⢻⣿⣿⣿⣿⡇⠀⠀⠀⠀⣀⠤⠶⠂⢡⣄⠐⠶⢀⣀⡉⠘⠄⢄⡀
⠀⠀⠈⣹⠀⠀⠉⠋⠉⠂⢀⣀⠀⠘⠂⠀⠀⠀⠐⠀⠀⠀⢸⠆⠀⠀⠰⣄⣠⣽⢻⣿⣿⠃⠀⠀⣠⠞⠁⠀⠀⢤⣀⠉⠙⠶⢦⠉⠁⠀⠀⠀⠑⠄
⣶⣴⣦⣿⠁⠄⠀⠀⢠⡀⠈⢡⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠻⢿⣿⡿⠋⠀⠀⣰⠋⠀⠀⠂⠀⠈⢻⣶⣶⠀⠀⠁⠀⠀⠀⠀⠄
⣿⡏⣿⣟⣦⡴⣳⣶⡾⠁⢠⣦⣤⣼⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⡏⠀⠀⠀⠀⠀⣀⠀⠀⠘⢿⣶⠃⠀⠀⠀⠀⠀⠀⢰⡄
⣿⣧⢻⣿⣿⡷⢉⣻⡄⣀⣰⣿⡄⣼⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⡇⢰⡀⠀⠀⠘⠻⣄⡀
⠻⣿⠿⣿⣷⣿⣿⣿⣿⣿⣿⣧⣇⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠰⡇⣸⡇⠀⠀⠀⠀⠀⠱⣄⣀⠀⠀⠀⠀⠠
⢶⣴⡆⢹⣿⣿⣿⣿⣿⡟⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣼⣿⡏⣆⣀⢠⡀⠀⠀⠀⠉⠁
⠀⠀⠁⠀⢻⣯⣉⣉⠙⠛⠻⠿⠿⣿⣧⡀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢠⠈⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠙⠉⠉⠈⠛⢺⠗⠂⠛⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠻⠏⠛
⠀⡀⠀⠀⠀⠀⠸⣶⣶⣶⣶⣤⠶⠶⠦⠈⠉⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⠀⠀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠉⡁⠀⣩⣄⠀⣴⡶⠀⠀⢠⣿⣶⡆⠈⠀⠀⠀⠀⠀⣀⠈⠀⠈⠀⢀⣾⣿⣿⣿⣿⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢙⡀⠙⣃⢀⣠⡤⠀⠀⣿⣿⣿⡧⠀⣷⣼⣿⠀⠀⠙⡇⠀⠠⣠⣿⡿⠋⣼⡿⣙⠓⠈⢁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠊⢻⠀⢨⣇⠀⢰⡟⣿⣿⡇⢸⣿⠸⣿⡇⠀⠀⢁⣴⡶⠛⠋⠀⣾⣿⣿⡧⠀⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣸⣷⣴⠟⢰⡟⠁⢸⣿⡇⣾⣿⡇⣿⣿⡄⠠⠛⠁⠀⠀⢠⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠰⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡁⣩⠿⣆⣰⣿⠀⠀⠈⢿⣷⣿⣿⡇⢻⣿⠇⠀⠀⠀⠀⣴⠟⠘⣿⠇⡟⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⣄⣤⣴⡿⠟⠃⠀⠀⠀⠈⢿⣾⣿⣫⣾⡿⠀⠀⠀⠀⡜⠁⠀⠀⠃⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡄⣰⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⢸⡆⠀⠈⣷⡛⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢸⡇⠀⠀⠘⠇⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⢉⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⡿⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣤⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢸⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⣀⡀
⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣉⠀⠀⠉⠉⠙⠳⢦⡀
⠀⢀⡼⠃⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣼⠃⠀⠀⠀⠀⢀⣠⠖⢻⡄
⣴⠿⠶⣶⣴⡿⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡟⢶⡶⠶⠖⠛⠋⢻⡄⣼⠃
⣿⣀⣙⣻⠍⣻⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢼⣧⠀⠈⢁⣴⠀⠲⠂⠸⣷⡏
⠈⣿⠉⠉⠀⣻⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠷⣤⣿⣇⣀⣀⣠⣶⡿
⠀⠹⠶⢶⣶⠿⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⢤⣌⣉⡉⠉⣹⠇
⠀⠀⠀⠀⣿⠀⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣈⣉⣠⡶⠋
⠀⠀⠀⠀⠸⣧⠀⠀⠙⠷⣤⣀⡀⠀⠀⢀⣤⣴⡶⣾⠋⠉⣿⡶⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠳⠟⠻⠟⠳⠟⠳
⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠉⠙⠛⠛⠿⠃⠈⠀⢸⣧⣤⡿⠀⠀⠀⠻⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⣤⣄⣤⣄⣠⣄⣠
⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⡀⠀⠈⠙⠛⠶⢦⣤⣄⣀⣀⣀⣀⣤⣴⣿⣿⡿⠀⠀⠀⠈⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠶⠦⣤⡄⠀⠀⢸⡇⢸⡇⠀⠀⢸⡟⠷⣤⣄⣀⠀⠀⠀⠈⠉⠉⠉⠉⠹⣷⠀⣿⣷⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⢸⡇⠀⠀⠈⣷⠀⠀⠈⠉⠛⠛⠳⠶⠶⠶⠶⠦⢤⣿⣿⣛⣿⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢸⡇⢸⡇⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣦⣤⣤⣤⣤⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⣤⡄⢸⡇⢸⡇⢀⣤⣤⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠁⢸⣇⣸⡇⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣻⠶⠶⣤⣼⡏⢹⣧⣤⠴⠶⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⢀⣤⡶⢶⣄⡀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⣴⠟⠁⠀⠀⠈⠻⣦⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣿⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⣿⢻⡇⠀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⢹⣆⠀⠈⣷⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣼⠃
⠀⠀⠀⠀⠀⣴⠟⠘⢷⡄⠀⠀⠀⠀⢻⣄⠀⠘⣧⡀⠀⠀⠀⣰⠟⠀⢀⣼⠋
⠀⠀⠀⠀⢸⣿⠶⢶⡆⣿⠀⠀⠀⠀⠀⠹⣦⡀⠘⢷⡄⢠⡾⠋⠀⣠⠟⠁
⠀⠀⠀⠀⢸⣇⠀⣸⡇⣿⠀⠀⠀⠀⠀⠀⠈⠳⣶⣛⣿⠋⣀⣴⠟⠁
⠀⠀⠀⠀⢸⡟⠛⠛⠁⣿⠀⠀⠀⠀⠀⠀⠀⢰⣟⠉⠙⡿⣿
⠀⠀⠀⠀⠀⠻⠶⠶⠾⠃⠀⠀⠀⠀⠀⣠⡾⠋⢻⡄⠈⠛⠻⣆
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⢙⡂⡉⠑
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⣦⡙⠛⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⣀⣀⠀⡀⢀⢘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡤⢀⡀⠀⠀⠀⠋⠁⢉⠰⣷⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠢⠀⡸⢷⡆⠀⠁⣀⠀⢠⡟⣀⠼⠀⠀⠄⠀⠀⢀⣀⠀⣤⡀⠠⠊⠁⠠⢀⠂⡜
⠀⠀⠀⠀⠀⠀⢠⡄⢠⡴⠤⣄⣰⡟⢛⠁⠀⡉⢙⣀⠸⠗⠄⠀⠀⠀⠀⠀⣠⠏⠀⠟⠉⠁⠀⠠⡀⠀⡞⠁
⠀⠀⠀⠀⠀⠀⠹⠀⠀⣤⣤⠒⠩⠈⠙⠛⢳⠀⠘⢷⣲⡞⠱⠀⠀⠀⠉⢀⠄⡀⠀⠂⢀⠞⡀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠡⠐⠀⠀⠠⡠⠟⠁⠀⠀⠁⠀⠀⠀⠀⠄⢘⢇⡤⠓⠚⠁⠨⠆⠁⠆⣆⠀⠙⢲⢤
⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠄⠀⠀⠈⠀⠀⠀⡾⠟⠃⠄⢄⠀⠀⠐⠊⠀⠉⠀⠁⠀⠁⢄⠆⡀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⣞⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠼⠀⡈⢆⣀⠀⠴⠆⠀⠀⠀⠀⠀⠀⡶⠁
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠉⠉⣰⠀⠀⠀⠀⢠⠐⠀⠀⠀⠠⠔⠉⠀⠁⠀⢸⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠃⡀⠠⠀⠀⠀⠀⠈⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠆⣸⡇⠀⠀⠀⠀⠀⠀⠄⡈⣠⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⡋⠀⠀⠀⠀⠀⠀⠈⢡⡀⠀⠀⠀⠀⢀⠐⡂⠀⠀⠀⠀⠀⠀⠀⢢⡈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠌⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⠂⠀⠀⠀⠀⣁⠀⠀⢀⡀⠀⠀⠀⠀⠀⠙⢷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠃⡀⠀⠈⣁⢰⠂⠀⠀⠀⢰⠄⠀⠈⠻⠄⠄⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠰⠀⠀⠀⠀⠀⡍⠀⠀⠈⡠⠀⠀⣠⠔⠈⢀⠀⠀⠀⠀⠈⠀⠱⡔⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⢄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⣀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠊⣁⡖⢃⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⠖⠀⢀⠀⠀⠶⢰⣏⠅⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡀⠘⡀⣀⠀⠀⠀⠀⠐⠀⢂⠀⠀⠀⠀⠀⠈⠀⢰⠞⣋⠂⠀⢙⣄⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢰⠟⠀⠁⠀⠀⠀⠀⠀⢠⡈⠄⠀⠀⠀⠀⠀⠠⣼⡾⠀⠶⠆⠉⠚⢉⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⢠⣉⠀⠰⠀⠘⠚⠀⠀⠀⠀⠀⢀⣠⢾⡶⠶⣃⣀⣀⣀⣀⡀⡀⠐⠚⠂⠀⠀⠁⠤⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠁⠐⠋⠒⠂⠂⠀⠀⠀⠀⠀⠈⠉⠈⠀⠀⠉⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠨⠭⠤⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⣄⠀⣴⣦⠀⢠⣶⣦⣄⢰⣦⣶⡦⣤⡀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠦⢄⠠⠤⠤⣤⡴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠀⣿⠀⣿⢻⡆⢸⣇⢀⣿⠀⢸⡇⠀⠸⣇⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢢⠆⠀⠀⠲⡶⠣⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠛⠋⢰⣇⣸⡇⢸⡟⠻⣧⠀⢸⡇⠀⠀⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠃⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⢼⠏⠙⣿⠸⡇⠀⣿⠀⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⠒⠒⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡄⣤⡄⢠⣤⡄⠀⢠⣤⡄⢠⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⠉⠀⣿⡇⢸⣿⣷⠀⣼⣿⡇⢸⣿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⣿⡇⢸⣿⣿⠀⣿⣿⡇⢸⣿⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠷⠤⠶⠶⠾⣮⠿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⢸⡇⢹⣷⡏⢸⡇⢸⣿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠒⠉⢀⠀⢀⣀⣀⠐⢷⠶⠤⠭⢒⠒⠤⣀⠀⠀⠀⠀⠀⢸⣧⠀⠀⣿⡇⢸⡇⢸⣿⡇⣿⡇⢸⣿⣤⣤⡄
⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⠑⣄⠀⠀⠀⠈⠁⠀⠀⠉⠁⠈⠁⠀⠉⠀⠈⠁⠀⠉⠉⠉⠁
⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠘⡆
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠄⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠜⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠀⠁⠀⡆⠀⠀⠀⠀⠠⡆⠀⠀⠁
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣾⠀⠀⢀⠀⠀⢠⠜⠛⠀⠁⠐⠄⠀⠀⡄
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡏⠀⠀⠀⠀⠀⠈⡶⠀⠀⢀⡠⠂⠠⠴⠃
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⡟⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠆⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡼⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠘⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠂⠊⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠦⠤⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠴⠶⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠉⠁⠑⢦⡈⠹⡕⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠐⠈⣿⡆⠀⢸⡏⠉⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠐⠲⢤⠠⠲⢤⠠⠞⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠢⠤⣤⠤⠤⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡠⠤⠀⠒⠀⠀⠀⠁⠒⠒⠒⠒⠀⠀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡏⠒⠶⠤⠤⠤⠤⠤⠄⠀⠀⠀⠒⡈⣇⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠉⠑⠲⠶⠶⠶⠶⠂⠁⠀⡸⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠟⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡉⢳⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡸⠤⠒⠉⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣨⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢁⣄⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠢⣤⣀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠼⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⡿⣄⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⡠⠁⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢐⠄⠀⠀⠀⠀⢸⠈⠳⢄⡀⠀⠀⠀⠀⠀⢀⡠⠂⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⢫⠀⠀⠀⠀⠀⣞⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠄⠀⢠⠀⠀⠀⠀⠀⣧⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠀⠀⠀⠀⠀⢸⠀⠀⢸⠀⠀⠀⠀⠠⡇⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠀⠷⠂⠀⠘⠀⠀⠀⠀⠀⠘⡇⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⢀⠃⠀⠀⢀⢤⡄⢤⡒⠚⠀⠈⡆⠈
⠀⠀⠀⠀⠀⡎⠐⠐⠒⢀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⢇⠀⣸⠀⠀⠀⠀⠀⢧⡀⠀⡘⠀⠀⠀⢠⡀⠊⠄⣛⠡⠖⣂⢀⠀⠀⠢⡀
⠀⠀⠀⢠⠰⠀⠀⠀⠀⠀⠑⠦⢤⣀⡈⠀⠃⢠⡄⠘⢀⡀⠤⠤⣼⡔⠀⠀⠀⠀⠀⠀⠀⠙⡀⣧⠀⠐⠒⠢⠉⠒⠉⠀⠀⠠⡅⢂⡀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠈⠀⠀⠀⠀⣈⠁⠒⠂⠒⠒⢀⣤⣈⣀⣈⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠚⠛⠋⠁⠀⢠⣴⣄⣍⣥⣤⠄⠦⠝⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠱⣀⣀⠤⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠦⠀⠀⠁⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦⣀⡄⠀⢀⠀⠀⠀⠀⠱⠊⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠚⣥⣄⡷⠤⢄⣁⠀⠀⠀⠀⠀⠀⠉⠉⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⡠⢺⣽⠚⠒⢤⣘⠈⢲⠻⡀⠄⠀⠀⠀⠀⠀⠸⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠉⠉⠉⠁⠒⠒⠾⠤⣮⠃⠀⠀⢀⠼⠤⠮⣀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠉⠉⠢⡀
⠀⠀⠀⠀⠀⠀⣎⠉⠐⠢⡜⠦⣀⠀⠀⠀⠀⠀⠀⠀⠘⣀⠀⡨⡕⠀⠀⠀⠀⠉⢫⡤⠀⠀⠀⠀⠀⠀⠰⣤⠤⠅
⠀⠀⠀⠀⠀⠀⠀⠉⠐⠲⣜⠤⣀⢉⡶⠦⢤⣄⣀⣀⡀⠀⠀⠀⠈⠒⠠⠤⢄⡤⠔⠁⠀⠀⠀⠀⠀⠀⣀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⢀⠟⢉⡽⣯⣸⠠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠘⢤⠀⠀⠀⠀⠀⠀⠀⠐⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⢠⠃⡠⢯⡔⠋⠁⠀⠀⣀⠼⣲⠀⠀⠀⣠⡠⠦⡨⢆⠀⠀⠀⠀⠀⠀⡤⠔⠃
⠀⠀⠀⠀⠀⠀⠀⡰⠉⣇⢀⠇⡰⠓⠠⣉⠖⠒⠚⠛⣾⡾⠁⢀⠔⠋⡀⠉⡾⡁⠀⢀⢠⠦⠄⠤⠤⠊
⠀⠀⠀⠀⠀⠀⢰⠁⣼⣭⣾⢀⡇⢅⣷⠏⠀⠀⢢⣼⡿⢁⡴⠃⠀⢏⠈⠺⡄⠸⡦⢮
⠀⠀⠀⠀⠀⣀⣼⡾⢻⠁⠈⠳⠷⢿⡏⠀⠀⠀⠸⠜⡡⠊⠀⠠⠛⠒⣓⠆⢱⠀⢳⣀⡆
⠀⠀⠀⠀⡜⢝⠁⢣⠀⢣⠀⠀⠀⢸⠀⠀⠀⠀⢀⠜⠀⠀⣠⠒⠊⠁⣀⠤⠅⠒⠊
⠀⠀⠀⣤⡿⠒⠁⠈⢆⠀⢇⠠⡚⣇⣀⣀⣀⠤⣯⠶⠀⠀⠘⡄⡞⠁
⠀⠀⣞⢏⣀⣀⠀⠀⠈⢢⠀⠣⠧⢄⣀⣀⡀⢏⠀⠀⠀⠀⢴⠣⠜⡑
⠀⠀⠀⣨⡷⠋⠀⠀⠀⠀⠳⣠⠃⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⣇⠀⢡
⠀⠀⠀⠻⠢⣴⣶⠶⠀⠀⢠⡏⠀⠀⠀⠀⠀⢘⠑⠤⡈⠑⠤⣸⠀⠸
⠀⠀⠀⠀⢰⠱⣁⣠⣄⡄⠀⠉⡗⠀⠀⠀⠀⢸⡀⠀⠈⠒⢄⡁⠀⠀⡇
⠀⠀⠀⠀⠀⠁⠈⠉⡟⠥⢔⣲⡇⠀⢀⠀⠀⠀⢦⠀⠀⠀⠀⠙⠢⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠑⠵⠺⡻⡁⢀⠠⣒⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠉⠉⠕⠠

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠂⠉⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣰⣦⣾⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣴⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡏⢉⣠⣀⢀⣨⣿⡟⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡋⠁⠈⠉⡉⢈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣱⡆⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣽⠏⠀⠀⠀⣠⣴⡏⣰⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢙⣿⣧⣆
⠀⠀⠀⠀⣀⣤⡚⠿⣶⠶⠀⠀⠀⢀⡀⠰⣿⣿⣿⣿⣿⣷⣦⣀⢀⣀⣠⣶⡇⠀⢺⡏⠻⣯⠷⣄
⠀⠀⢀⡞⢧⣀⢠⣠⠆⠀⠲⠈⠓⠻⠇⠀⠘⣿⣿⣿⣿⣿⣏⣴⣿⡟⣹⣍⣷⠀⢈⣧⡠⠈⢀⣈⣦⡀
⠀⠀⢸⡇⠀⣿⣿⣿⣿⠖⠀⠳⡀⠀⢠⡄⠀⢻⡻⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣶⣿⡏⠁⡴⠼⠉⣠⣷⡄
⠀⢀⠛⠃⠀⢿⣿⣿⣿⣄⠘⢧⣹⣄⠀⠀⠀⢸⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⠋⠉⠀⠀⠀⢶⣿⣎⠻⣯⣂
⠀⣼⠋⢀⢋⣸⣿⣿⣿⣿⣷⣮⣿⠻⣧⡀⠀⠀⣿⣿⣿⠇⠀⠈⢻⡿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠣⣻⣿⡿⠋
⠀⣇⠠⢀⣿⣿⣿⣿⣿⣿⣇⣉⠙⠷⠾⢿⣷⣼⣿⣿⣿⣷⣆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢸⣀⣀⡰⢿⣿⣿⣿⣿⣿⣿⠭⠙⠂⢀⡈⢿⣿⣿⣿⣿⣿⣿
⠻⠿⣻⠰⠸⢿⣿⣿⣿⣷⡏⠀⣀⢤⣀⢉⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠘⠷⠲⠤⢽⣿⣿⣿⣿⣿⣿⣷⣮⠑⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠚⣿⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣯⣿⣿⣿⡄
⠀⠀⠀⠀⢠⣼⡿⠠⡀⠈⠉⠿⠿⣿⣿⣿⣿⡿⠿⢿⣿⡟⣿⡿⣿⡛⢿⡆
⠀⠀⠀⠀⠈⣸⡟⠀⠈⠛⠂⠀⠀⠸⣿⣿⣿⡗⢶⣌⣿⣿⣿⣿⣇⣹⣷⣸⡦⡀
⠀⠀⠀⢠⢀⣿⡃⠂⠠⠈⠀⠀⠀⣰⣿⣿⣿⢿⣟⣿⣿⣾⣿⣿⣴⣿⣧⣼⠳⣾⠢⣀
⠀⠀⠀⠸⠃⠙⢿⡋⠱⠄⠀⠀⣴⣿⣿⣿⣿⡉⢋⠹⡟⢿⣿⡿⡟⢛⣦⠙⢶⡁⢹⠏⢳⣀
⠀⠀⠀⠀⠀⠀⠀⠙⠦⣌⠁⣰⠛⣿⣿⣿⣿⡗⣊⢡⡀⠌⠛⠿⢴⣟⣢⣼⢿⣉⣻⣀⢿⢹⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⠀⠙⣿⣿⣿⣷⠉⣄⠡⡌⠃⣀⠀⠈⢻⣿⣿⡽⡷⠟⢠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣇⡉⢆⠠⡄⠃⠀⠀⠈⢮⣍⣉⣡⢸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡛⡈⣤⠰⡖⠃⢀⠀⠸⣿⣛⣙⣦⡽⣏⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷⡄⢦⠰⣶⡏⠀⠀⠘⣦⣶⠙⣦⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢱⣿⣙⠛⣷⣾⣿⠟⠁⠀⠀⠀⠙⡉⣀⢸⡿⣟⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠚⢀⠉⣸⢛⠿⠋⠀⠀⠀⠀⠀⠈⠻⡉⣄⢷⡜⣿⣿⡓⣄⠀⡀⣠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢦⣄⣤⣭⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⡉⢳⣿⣿⢧⣼⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡴⢞⡏⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠞⣋⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣇⠂⢴⣧⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣿⣿⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⣀⡐⢻⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠍⠛⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢗⣤⣼⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣾⢿⣿⣷⣤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣷⣾⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣙⣿⣿⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣦⣠⣄⠀⠀⠀⠀⢀⣴⣿⣿⣿⡇⢿⠿⢃⣾⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⢿⣿⣿⣦⣀⢠⣿⣿⢻⣿⣿⣇⣾⣆⣾⣿⡿⠛⠻⢿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⡿⠁⠈⣿⣿⣿⣿⣿⣿⣿⡁⢀⣠⣤⣽⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣅⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡇⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡏⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡇⠀⠀⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠘⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡏⠁⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡾⢿⣿⠄⣤⣤⣴⠿⣿⡧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡾⠟⠛⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⢀⠀⠀⣘⡈⠀⠼⠋⠀⠀⠣⢸⣿⣯⣿⣿⣟⣿⣦
⠀⠀⠀⠀⢤⣄⢀⣚⡇⠀⠀⠀⠀⠢⠀⠯⣿⣙⣿⠿⢿⣿⣿⣿⣿⣄
⠀⠀⠀⠈⠮⢻⣾⣍⠃⠀⠀⠠⣶⣾⣷⣆⢻⣋⠁⣘⡂⣽⣿⣿⣿⣿⣷⡀
⠀⠀⠀⢀⣷⣼⣷⣿⣇⡀⠀⠀⣺⡿⠟⢛⢀⣽⣽⣿⣿⣷⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠠⠛⣿⢿⣿⣿⣧⠀⠀⠉⠀⣠⠳⠿⣟⣿⣿⠛⣹⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠃⢙⣯⢿⣿⣿⣧⡀⠀⠀⠾⠆⠀⡟⣯⣶⣾⠿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⣧⣻⣯⣿⣿⣿⣴⡤⠀⠄⠀⠀⣹⡿⣧⣼⣿⣿⣿⣿⣿⣿⣗
⠀⠀⠀⠀⠀⠠⡍⠻⢾⣿⣟⣿⣿⣷⣶⣄⢦⣄⣻⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⢉⠀⣉⣻⢻⡿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠙⣢⣽⡍⢿⣿⣿⣿⣿⣿⣏⠀⠀⠀⠉⠾⢛⣿⣿⣿⣿⣿⣿⣷⣦⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡊⠕⠂⡈⣿⢻⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠜⣧⣿⣿⣿⣿⣿⡿⢿⠻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⢉⢈⣍⢂⡘⣫⣿⣯⣿⣿⠃⠀⠀⠀⠀⢀⣨⢿⠟⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠊⢀⠐⠨⣡⠓⣝⡻⢿⡿⣿⠄⠀⠀⠀⠄⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠔⣀⡐⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⠐⣄⡉⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠐⣄⡀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠀⡾⠃⢀⠤⠒⠠⢤⡀⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⡴⠥⠘⢧⠔⠁⠀⠀⢀⡀⣷⣶⢯⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡰⠶⠟⠉⠁⠀⠀⠀⢀⠀⠀⠈⠀⠁⠀⠘⣁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⢸⣾⠁⠀⠀⢀⠀⠀⢠⣾⡁⠆⢰⠁⠀⠀⠀⠐⡮⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠨⠉⠉⢀⠀⢰⣿⢦⡀⡾⠉⢙⡸⠀⡀⠀⡆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣞⣱⠀⠸⡀⣿⠁⣈⠻⢧⡀⠀⠀⢡⠘⢾⣇⡤⠖⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡠⠄⡇⢧⠀⠀⠁⡀⠁⠀⢀⣠⣴⣈⠫⠧⠐⠦⢸⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣨⣿⣦⣸⣮⣗⠀⢀⣰⣄⠙⠁⠛⠉⠁⠀⠀⣄⣴⠃⠀⠀⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠛⡿⣿⢎⠙⡟⠋⠀⢰⠁⠀⠀⠀⠀⣧⠀⠉⠢⡀⠀⢸⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠃⠀⠋⢹⡜⣧⠤⠖⠁⠀⠀⠀⠀⠀⡏⠀⠀⠀⣨⢆⢸⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠏⡘⠀⡎⢰⠎⢀⠇⠀⠀⠀⠀⠄⢼⡇⠛⣰⣟⢆⠀⣞⠃⣄⢿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠠⡔⠀⠐⠀⡐⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⡿⢸⠂⠀⠑⠀⢸⡇⠀⠐⠀⠰⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡶⣀⠠⣀⠃⠀⠈⠓⢦⣥⢄⡀⠀⠀⢀⡼⠋⡖⢹⡄⠀⠄⡀⢸⡇⢸⠀⢀⢄⠌⢁⡶⠂⠀⠠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠘⠢⢴⡈⢦⠀⠀⠀⠀⢹⠲⡍⠛⠉⠁⠀⠀⣠⠞⠙⣆⠀⠈⣺⡇⠚⠀⢠⠋⡰⠋⠀⠈⡁⠠⠀⢀⠉⢢⡀
⠀⠀⠀⠀⠀⣀⠤⠒⠚⠧⣀⠀⠀⣀⡿⠀⠀⠀⠀⢀⡼⢀⡱⣆⠦⠖⠚⠉⠀⠀⠀⢸⡄⣸⠃⠁⣹⠂⡟⡴⠁⢀⠔⠁⠀⠀⠀⠀⠈⢀⡇
⠀⠀⠀⠀⡸⢁⠀⠀⠀⠀⠀⢙⡾⠏⠀⠀⠀⢠⡔⡃⢠⡞⢳⠈⠳⢦⣀⠀⠀⠀⠀⢸⣃⣟⣊⡁⠉⢦⣼⠇⢠⠁⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⢀⠗⠁⣠⠴⠒⠂⠒⠏⠀⠀⠀⠀⣰⣯⠀⣉⡟⠀⠈⠀⠀⣀⣈⣉⣒⢴⠈⠁⠀⠀⠀⠀⢹⡆⣙⣶⣇⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⢠⠃⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣿⢋⠔⠀⠀⠀⠈⠛⠉⠁⠀⠀⠀⢈⡀⠀⠀⠀⠀⣀⡼⠓⠁⠀⠈⠃⠀⠀⠀⠀⠀⢀⡞
⠀⠀⢸⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢣⠟⡠⠖⠚⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⢈⠀⠀⣠⡈⠉⠁⠆⠀⠀⠀⢀⡴⠋
⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠃⡷⠚⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⢴⣢⢀⠤⠐⠀⠀⠀⠀⠀⠆⠀⣴⠾⠿⠤⠴⠶⠶⠶
⣀⣀⣀⠙⣷⠀⠀⣀⣔⣩⡴⠾⠯⠤⠚⠓⠛⠛⠛⠋⠉⠉⠉⠛⠛⠂⠀⠉⠉⠉⠉⠀⠹⡆⠀⠀⠀⠂⠈⢀⠀⢀⡞⠁
⠀⠀⠀⠀⠈⠓⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠳⠶⠴⠖⠋⢀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣤⣤⠌⠀⢂⠀⠤⠤⠄⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⣀⣀⡐⠁⠀⠀⠀⠀⠄⠖⠈⠀⢠⠀⠀⠀⡜⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡆⠉⠀⠀⡀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠼⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠊⠀⠒⠈⠡⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠂⠀⠈⠉⠉⠉⠉⠉⠉
⠂

⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⡛⢿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣷⣶⡽⠃⠉⠙⠻⢷⠗
⠀⠀⠀⠀⠀⠀⠀⣿⡟⢿⠃⠀⠀⠤⠤⢸
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠁⢸
⠀⠀⠀⠀⠀⠀⣠⠔⠃⠸⣄⠀⠀⠠⢄⠁⠀⠀⣤⣐⣐⡒⢢⡀
⠀⠀⢀⡠⠂⠀⢷⠀⠑⣄⠘⢿⣦⠤⠄⠀⠀⠀⣧⠀⠀⠀⢸⠽⡆
⢀⠞⠁⠀⠀⢄⠘⡆⠀⣈⠳⡘⢉⣧⠀⠀⠀⠀⢸⠀⠀⠀⠈⣯⡇
⣾⠀⠀⠀⠀⠈⢷⡙⠚⠁⠀⠁⠈⠐⢦⠀⠀⠀⠈⠓⢤⡤⠀⠑
⢻⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⢠⠀⢳⡀⠀⠀⣰⢣⡑⡼⠁⠀⠀⠀⣀
⢸⢷⡄⠀⠀⠀⢀⣀⣈⢦⡀⠀⠀⢸⢀⣤⣛⣦⡠⠛⢄⠙⠣⠀⠀⠀⡀⠁⢀⣈⢣⠀⠀⠀⢀⣀⣀⣀⣀⣀
⢸⠇⠙⢦⡀⠀⠀⠉⠉⠁⠉⠑⠲⠼⠭⢀⣀⣞⡁⠀⠀⠩⠏⢀⡀⠀⡏⠉⠉⢁⡨⠖⠚⠉⠨⡅⠀⠀⠀⠈⠙
⣸⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠹⡆⠀⠀⠀⢐⣮⠀⠑⠂⠐⢅⠀⠈⠁⠢⠄⠀⠀⠀⠀⠠
⣏⠀⠀⠀⠀⠀⠉⠒⠤⠤⣄⣀⣀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⠀⠀⠀⠀⣀⣭⣶⣦⡤⠐⠀⠀⠀⠀⢀
⠈⢣⡰⣄⠀⠀⠀⡤⠤⠤⠤⠤⠤⠤⠤⠤⠬⠥⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠭⠭⠭⠤⠤⠤⠤
⠀⠘⢿⣾⣷⢢⣤⣗⡒⢲⣒⣒⣒⣒⣒⣒⣒⣒⣒⡒⠒⠒⢒⣒⣒⣀⣀⣉⣉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢄
⠀⠀⢸⣷⡏⠀⠀⣿⣺⡁⠀⢘⣶⣆⡦⠀⢀⣿⣂⣤⣤⣄⣻⡀⠀⢀⣺⢃⡀⠀⠸⣇⠀⠀⠘⣶⣆⡦⢀⣈⣿⡎
⠀⠰⢻⡇⠀⠀⠺⣿⣧⠀⠀⢸⣿⣀⠀⠀⢸⡿⡅⠀⠀⠈⣹⡿⠀⠸⡟⠋⠁⠖⢊⣿⠇⠀⢸⣿⣁⠀⠋⢠⣿⣧
⠀⠀⣸⠟⣆⠀⠀⢸⣿⠀⠀⢀⡟⢹⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⢀⡟⢹⠀⠀⠈⡧
⠀⠀⠁⠀⠉⠀⠀⠈⠉⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠀⠁
⠀⠀⢠⣤⣤⠂⠀⠀⠀⢀⡾⠆⠐⢻⣄⠀⠀⢀⣴⣖⢛⠀⠀⠀⢀⣴⣄⣠⡗⣤⠀⠀⢀⣶⣀⡀⠀⠀⣰⣆⣠⡄
⠀⢀⡾⣿⣯⣄⡀⠀⠀⢸⣟⡲⣭⠍⣽⠂⠀⠀⣹⠟⢘⡆⠀⠀⡞⡟⠛⠛⠛⢻⡄⠀⢿⣿⣿⣿⡀⠸⣿⣿⣿⣇
⠀⠈⠀⠉⠉⠉⠉⠁⠀⠈⠉⠁⠉⠈⠉⠉⠀⠀⠉⠀⠈⠉⠀⠀⠉⠁⠈⠁⠈⠉⠁⠀⢸⣿⣿⡏⠁⠀⣿⡟⣿⠉
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⣀⡠⠀⠀⢀⣄⠀⠀⠀⣠⣄⠀⠀⠀⣀⢀⠄⠠⣣⡤⢀⡈⠉⠉⠁⠀⠀⠉⠁⠈
⠀⢀⣼⣿⡃⢤⣀⠀⠀⢠⣿⣿⠁⠀⢠⣾⣿⠿⠀⠺⢿⣷⡄⠀⠘⣿⠗⠀⠀⣻⡏⠉⠁⠀⠀⠀⠀⠀⡄
⠀⠈⢸⣿⠄⡿⠿⢷⠀⠀⢽⣿⠄⠀⠀⢽⣿⠄⠀⠀⣼⣿⠁⠀⢰⣿⡍⠀⠀⠛⣿⠀⠀⠀⣀⣴⣶⣤⣤⣀
⠀⠀⠸⠿⠀⠀⠀⠈⠀⠀⠸⠸⠀⠀⠀⠸⠸⠀⠀⠀⠘⠿⠀⠀⠼⠁⠧⠀⠀⠀⠿⠀⠀⠉⠉⠁⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⣶⡶⠶⠆⣶⡆⢰⣶⡴⠚⣶⡄⣴⡶⠓⢶⡔⣶⣆⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇⢸⣿⠃⢠⡿⠃⢿⣧⣀⠚⠁⠘⣿⡾⠁⠀⠀⠀⢾⣿⣾⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡇⢸⣿⠶⠋⠁⠀⠀⠈⠛⢷⡄⠀⢸⡇⠀⠀⠀⠀⠀⠙⠟⠁⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⣿⡇⢸⡿⠀⠀⠀⠀⠲⣤⣤⡾⠋⠀⢸⡇⠀⠀⢀⣤⣤⣄⠀⢀⣴⠋⠉⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⠁⢠⣿⠇⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡄⠀⠻⡄⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣦⣿⣿⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⠻⣆⠀⠙⠀⠀⠀⠀⣾⡏⢻⣿⡇⠀⠀⠙⠋⠀⠀⣠⣤⡄⠀⠀⠀⠀⢀⠀⢸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣄⡀⠘⢆⠀⠀⠀⠀⢀⣿⠇⠸⣿⣿⠀⠀⢀⣤⣄⡼⢹⣿⣿⠀⠀⣴⣿⠋⠉⢾⣿⡇⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠐⠶⢦⣄⡀⠀⠙⠢⠀⠀⣀⣤⣤⣼⣿⣀⠀⣿⣿⡀⠀⢸⣿⣿⠁⢸⣿⣿⠀⣼⣿⡏⠀⠀⢸⣿⡇⠀⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠀⠀⠀⠚⠋⠉⠙⣿⡿⠿⢿⣿⣿⣷⠟⢸⣿⡏⠀⢸⣿⡟⠀⣿⣿⡇⠀⠀⢸⣿⡇⠀⠸⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⢸⣿⣷⠀⢸⣿⣇⠀⠸⣿⡇⠀⡿⣿⣧⠀⠀⢘⣿⣷⠀⠀⠈⢽⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠖⠲⣤⡀⠀⠀⠀⣿⡏⠀⠀⠀⠀⢿⣿⣧⠀⠙⠋⠀⠀⠈⠛⠛⠀⠙⠿⠦⡴⠞⠛⠋⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⢘⣿⡄⠀⣼⡿⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠿⠷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣤⣾⣿⠃⣰⡿⠁⢀⣄⢀⣤⡀⠀⣠⢀⣠⣀⢀⣄⠀⣀⣠⣄⡀⢀⡄⠀⢀⡄⢀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠈⠉⢁⣴⠟⠁⠀⢸⣿⠋⠈⣿⠀⣿⡏⢠⡿⢸⡇⣰⡟⢁⣨⠇⢸⡇⠀⢸⡇⠈⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠖⠛⠁⠀⠀⠀⢸⡿⠐⠾⣅⠀⣿⣴⠛⠁⢸⡇⢿⡇⠰⠖⡦⢸⡟⠛⢻⡇⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⢤⣤⠿⠁⠿⠙⠷⠆⠸⠇⠈⠿⣦⠴⠃⠸⠇⠀⠸⠇⠀⠸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣹⢿⣿⠂
⠀⠀⠀⠀⢀⣴⣿⠿⠟⣋⣽⣿⡿⣧
⠀⠀⠀⢀⣩⣀⣤⣾⣿⣿⣿⣿⣷⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⡟⠀⠀⠴⣦⡄⠀⠀⠀⢤⣴⣶⢾⣥⠔⠟
⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠈⠁⠀⠰⠟⠛⠆⠀⠀⠀⢀⣘⣿⣿⣿⣏⢴⠇
⠀⠀⠸⣿⣿⣿⡟⣛⡻⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⣦⣄⣤⣶⠛⢿⢿⠋⠼⢊⡀
⠀⠀⠀⢿⣿⣿⣇⠁⣩⡄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠟⠉⠉⠀⠈⠁⠀⠀⠀⠁
⠀⠀⠀⠘⢿⣿⣿⣦⣀⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢏⠀⠀⠀⠀⠐⠀⠲⠶⢾⣅⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠙⠿⣿⣿⡟⠹⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠹⡇⠀⠀⠉⠓⢶⡶⢦⠀⡄⠐⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⣼⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⢀⡠⠤⢀⠀⠀⠀⠙⢥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠻⢅⣀⡀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠉⠀⠀⠀⠀⠙⠑⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⢀⡠⠤⠼⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠐⠁⠀⠀⠀⠑⢦⢤⣄⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠜⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠤⠤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⣀⠤⠤⠔⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠃⠄⣀
⠀⠀⠀⠀⢀⠞⡀⠀⠀⠀⠀⠀⡑⠤⡍⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠳⠽⢢⣀
⠀⠀⣠⠤⠞⠉⠀⠙⢆⡠⠲⠅⢂⠄⠀⡀⢠⠄⠀⠀⠀⠀⠀⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡈⡃⠀⠑⠐⠉⠢⡀
⠀⠀⢇⣀⠄⠀⠀⠀⢊⢀⡔⠀⡀⠹⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠣⠀⠀⠀⡀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠧⠱⣌⡁⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠚⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠈⢤⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠸⣀⠟⠉⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠊⠁
⢀⡰⢄⡀⠀⠀⠀⠀⠄⠀⠀⠙⣦⣀⠀⣀⣀⣠⠰⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⢙⣄⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠹⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠠⠂⠘⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠻⢿⠟⠓⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠃⠐⢂⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡄⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠁⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠀⠀⠀⠀⠠⠃⠀⠄⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠈⠁⠁⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠢⠖⠆⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⠄⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠙⠀⠀⠀⡀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠄⠀⠈⠀⠀⠀⠁⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠈⠉⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠉⠉⠉⠙⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⣧⣧⣴⣦⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⢴⣞⡻⢿⠿⢿⣿⣿⣿⣿⣿⣧⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠉⠁⠆⠈⠉⡹⠍⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⣄⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢆⡼⠠⠀⠐⠒⠒⠦⢤⣀⠀⠀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢸⠀⢀⠀⠀⠀⠠⠶⣶⣷⣿⣿⠁⡭⠋⠀⠈⠓⡒⠒⠀⠀⠛⣷⠟⠛⠑⢢⠀⠈⠒⡄⠀⠀⠉⠓⠄⠘⠄⠀⠀⠀⠀⠀⠀⠉⡁
⠀⠀⠠⠀⠀⣃⠠⠥⠀⠀⠸⠓⠘⠄⠀⠀⠙⢿⡿⢿⠿⠿⠤⡑⠛⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⣀⣀⢸⠇⠀⢠⠃⠀⠀⠀⠀⠀⢀⢆⠀⠀⠀⠀⠀⠀⢰⠁
⡄⠀⠀⠃⠀⢃⡤⠖⢖⠒⠛⠉⢩⠉⠹⡄⠀⣀⠵⢾⠀⠀⠈⡧⢄⣉⣉⠓⠦⡀⠀⣠⣾⡠⣊⣀⠀⢸⣀⡔⡁⠤⠂⠀⠀⣠⠔⠁⠈⣷⠤⡀⠀⠀⠆⡏
⠧⡀⢠⢀⡄⠚⠂⠀⠐⠒⠈⠉⠉⠀⠀⣷⡴⠃⠀⣉⣈⣹⠂⠇⠀⠀⠙⢀⡘⠁⠀⠈⠉⡏⠁⠘⡒⠈⠉⠀⠀⣤⡐⣚⣉⣠⣤⣴⡮⠵⢾⠀⠀⠀⢰⠃
⠀⠈⠰⠤⠓⠚⠫⢤⣤⡤⠤⠤⠶⠒⠛⠀⠙⢗⠀⢀⢐⣏⡉⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⡇⠀⢀⣀⣀⣠⣿⡿⠚⠿⠟⠛⠁⢀⠞⠀⠉⠉⢛⠄
⠀⠀⠀⠐⠀⡍⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡇⠀⠀⡟⠉⣽⣿⣿⡿⠋⠀⠀⠀⢀⡠⠶⠵⠶⠖⠛⠛⠻
⠀⠀⠀⠀⡄⡇⠀⠀⠈⠓⠦⣄⡀⢠⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⠔⠒⠒⠋⣩⢽⣿⣿⣿⡇⠀⠀⢹⠂⢩⠔⠁⠀⠀⠀⣠⠖⣉⣠⡤⠤⠔⠒⠒⠛
⠀⠀⠀⠀⠃⡇⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠒⠉⡏⠁⠀⠀⢸⣿⠀⠀⠀⢀⡞⠹⣟⣹⡏⢹⠀⠀⢸⠀⠁⠀⠀⠤⠶⡍⠅⠀⡇⣿⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⢸⣿⠀⠀⢀⡞⠀⠀⢠⠟⠁⢸⠀⠀⠸⡀⠢⣀⠀⠀⠈⠑⢦⡀⡇⣿⠀⠀⠀⠀⠀⠁⡄
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⡇⠰⣄⠈⣿⠀⢠⠎⠀⠀⢠⠏⠀⠀⠈⠀⠀⠀⢘⡇⠮⣷⣤⣀⠀⠀⠉⠳⢿⣄⠀⠀⠀⢸⠀⠁
⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⡎⢆⠈⠓⣿⣃⣏⠢⣀⢠⡟⠀⠀⠀⠀⢩⠉⠉⠛⠣⠓⢹⢺⡏⠓⡦⣄⡀⠀⢀⠄⠐⢦⠸
⠀⠀⠀⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢦⡙⢦⠈⠈⠻⣍⠢⠿⠀⠀⠀⠀⠀⠀⠑⢤⣀⣀⡤⠄⠸⡇⠀⡇⢻⣥⠔⠉⣠⣠⠎⠀⣠⠄
⠀⠀⠀⣈⠁⡉⢀⠤⠄⢀⠄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠙⠦⣣⢄⠀⡌⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠑⠀⣀⠡⠚⠛⠃⢀⡗⠉
⠄⠀⢰⠿⠀⠱⣿⠀⠜⠉⠉⠉⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⠨⠻⠾⠥⠒⠖⠂⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠓⠠⠤⠤⠒⠒⠉
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠉⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠀⡼⠃⢀⠤⠐⠠⣄⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⠰⠦⠀⠧⠜⠁⠀⠀⢠⢸⣷⡼⢧⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠞⠛⠉⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠩⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣀⣷⠃⠀⠀⢀⡄⠀⢠⣮⣅⢂⠘⠀⠀⠀⠀⠱⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡦⣂⠀⠀⡄⢰⣿⠷⣄⣾⢀⠨⠜⠀⢄⢰⡃⠀⢄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣽⡆⠀⠃⢸⠁⠤⠙⠻⡄⠀⠀⠠⠈⢻⣧⠒⠋⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡂⢹⡸⣄⠀⠀⢀⠀⣀⡠⣴⣾⠬⠛⠓⠘⢃⠗⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠛⣷⣦⣿⣿⣀⣠⣼⣦⠀⠠⡁⠀⠀⠀⢸⠖⠫⡀⠀⠀⠸⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣇⠿⢹⢵⠤⡇⠀⢀⠌⠀⠀⠀⠀⢸⡇⠀⠈⠣⡄⢰⡇⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠞⡇⢀⠀⡁⠜⣇⠛⠋⠁⠀⠀⢠⢀⣤⢸⣇⠀⠀⡴⠛⢸⡇⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠐⠀⡀⠀⠁⣰⠇⠀⠀⠀⠀⠁⠙⠃⢠⠿⡎⣧⠘⠢⡘⠊⡇⠀⠀⡘⢂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢉⡀⠀⠀⠸⠀⠹⢦⣀⠄⠀⠀⠀⠀⠀⢸⠴⡡⡇⠀⠀⠀⠀⣧⠀⠀⠀⡈⠙⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠘⣝⣂⡑⢆⠀⠀⠀⠈⢿⣑⠢⢤⠄⠖⠁⠘⢀⡾⢄⠀⠀⢤⡇⢸⠆⠀⡱⢁⡴⠉⠠⠀⠘⠒⠀⢤⡀
⠀⠀⠀⠀⠀⠀⣀⡀⣼⡁⠀⠀⠈⢻⠄⠀⠀⠀⠀⣸⠈⢧⣄⣀⡤⠴⠖⠋⠀⠈⣆⠀⡶⠓⠐⡄⣼⢠⠏⠀⡠⠐⠂⠉⠀⠀⠀⢹⡄
⠀⠀⠀⠀⡰⠋⠀⠀⠀⠉⠓⢄⡴⠋⠀⠀⠀⣠⡞⠁⣼⠆⠳⢦⣀⠀⠀⠀⠀⠀⡿⢸⠥⠒⠘⢄⣡⡟⠀⠌⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⢀⡥⠋⢀⣠⠤⠤⠴⠋⠀⠀⠀⢀⡼⠁⠲⡼⠁⠐⠀⠀⠉⠑⠢⢄⣠⠒⠉⠉⠉⠉⢐⡄⠻⣅⡎⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⢠⠊⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠠⠉⠁⠀⠀⠖⠒⠋⠉⠉⠁⠃⠀⠀⠀⠀⠀⣀⠷⠛⠉⠙⠢⠀⠀⠀⠀⠀⢀⠎
⠀⠀⢯⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⡼⢂⠤⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⣿⢺⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢸⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠐⠋⠁⠀⠀⠀⠀⣠⣴⣯⠀⠤⠤⠤⠤
⢀⣀⡈⠛⡆⠀⠀⣠⣐⣡⡴⠾⠥⠤⠟⠒⠚⠓⠒⠒⠒⠚⠟⠓⠒⠂⠀⠈⠉⠃⠘⢧⠠⠄⠀⠒⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠙⠒⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠤⠶⠊⠁⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡤⣤⡤⠁⠀⠄⠠⠤⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠈⠀⠀⠀⠀⠃⠰⡂⠀⢀⠀⠀⠀⡘⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⡆⠀⠀⢀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠼⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⠉⠉⠈⠢⣢⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣹⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁