Confectionery Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣷⠀⠀⠀⠀⢀⣴⣾⣿⢿⣿⣦⠀⠀⠀⠀⠀⢠⠶⠿⣿⣿⣿⡀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣦⡄
⠀⠀⠀⡯⣝⣫⢿⣿⣿⣿⡿⠀⠀⠀⠀⣬⣟⣿⣾⣿⣻⣽⡇⠀⠀⠀⢀⡞⢶⣶⢼⣿⣿⣷⠀⠀⠀⠀⢸⣿⣿⣿⡿⢿⡇
⠀⠀⠀⠯⣓⢺⠿⠟⠋⠁⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠉⠓⠦⢬⡿⠛⠁⠀⠀⠀⠀⠺⣿⣿⣿⡿⠿⠃
⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⣀⣀⣀⣀⣤⣶⡀⠀⠀⠀⠀⠀⠀⢀⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠠⠤⢴⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⡚⢻⣦
⠀⠀⠀⢸⣿⣿⣿⣿⣿⢟⡁⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢰⣿⢿⣷⡹⣷⠀⠀⠀⠀⠀⠀⠋⢿⣷⠘⣿⡆
⠀⠀⠀⢰⣯⣽⣯⣽⣶⡿⠁⠀⠀⠀⠀⠸⡿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠸⣿⣷⡝⣧⢻⡇⠀⠀⠀⠀⡘⠀⢸⣿⣶⠿⠃
⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⠓⠻⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠀⠀⠀⠀⠀⠀⠈⠐⠠⠋⠁

⠀⠀⠀⠀⠀⣤⣤⣤⣄
⠀⠀⠀⠀⠀⣻⣿⡏⣿⠀⠀⠀⠀⠀⠀⢀⡤⠤⣤⡤⠠⣄⠀⠀⠀⠀⠀⠀⢀⡠⣦⡄⣀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣷⣦⡀
⠀⠀⠀⠀⠀⢿⣿⣟⣿⠀⠀⠀⠀⠀⠀⢰⣯⣶⣒⣒⣦⣵⠀⠀⠀⠀⠀⣰⣮⢿⡎⣿⣼⡄⠀⠀⠀⠀⢨⣟⢿⣿⢿⣻⡅
⠀⠀⠀⠀⠀⣿⣿⡷⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⡸⢏⣿⣧⡶⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⣾⣿⣯⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠉⠁⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉
⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⣴⢦⣳⡄⠀⠀⠀⠀⢀⣴⢦⡰⣄⠀⠀⠀⠀⠀⠀⠀⣠⣾⣶⣷⣦⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠇
⠀⠀⠀⢀⣀⣔⣶⣿⡟⣷⡽⠿⠀⠀⠀⢰⣿⠱⠂⣿⡝⣷⡄⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⢸⣿⡿⣿⣿⣿⡃
⠀⠀⠰⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠹⣿⣷⣾⣿⡿⡿⠃⠀⠀⠀⠀⠘⣿⡿⣸⣿⡿⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠈⠋⠛⠛⠋⠛⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⢀⠀⠀⠐⢆⠐⠀⢀⡍⠀⠀⢁⠔⠀⠀⠀⠘⠯⣽⠆⠀⠀⠀⢀⠀⢴⡦⠄⠀⠠⠆⠀⠀⠀⡀⠐⠻⢶
⠀⠀⠌⠙⢙⣿⣭⠇⠀⣿⡿⠿⢧⣠⡆⠀⠀⢄⠀⢀⢀⣸⡦⠀⡀⠸⠷⣶⣿⠿⢠⡿⠀⠀⠀⢰⡿⠉⠈⠉⢰
⠀⠀⠢⠄⣭⡵⢖⡃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠀⠘⣿⣷⠇⠀⠁⠀⠀⠛⠃⠀⠈⠛⠀⠤⠂⢸⡿⠷⡆⠀⢾
⠀⠀⠀⠀⠚⠋⠁⠀⢀⠈⠁⠀⠀⠀⣀⣴⣀⣀⡀⠀⠉⠉⠀⠀⠈⢀⡀⢤⡤⡄⠀⠲⠲⠶⠂⠸⣧⣤⣄⠀⠤
⠀⠀⠀⠀⣤⣥⣀⠂⠤⠂⠀⠀⠀⠞⠻⠮⠭⣯⣄⠀⠀⠀⠀⠀⠀⠒⠂⠘⠊⠙⠙⠛⠛⢋⡁⢀⣀⣀
⠀⠀⠀⠀⠸⣾⡽⣿⣏⣷⢦⡀⠀⠈⣁⣀⡒⠠⢿⠀⠀⠔⠋⠀⠑⢛⣿⡇⠀⠀⠀⠀⠠⠬⡥⠍⠉⢩⣥⢾⠃
⠀⠀⠀⠀⠀⠙⠛⠓⠻⠮⡾⠁⠀⠉⠒⠢⢈⣑⣶⠀⠀⠀⠀⠀⠀⢻⡿⠀⠀⠀⠐⢶⣤⠒⠄⠐⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢂⠐⡀⢂⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠛⠀⠀⠀⠀⠀⠀⠠⠀⠄⠠⠀⠰⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⠐⠀⢀
⠀⠀⠀⠀⠨⠀⠀⣤⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠂⠀⠀⡀
⠀⠀⠀⠀⠐⠄⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠄⡀⠀⠀⠀⠀⠰⡱⠭⠆⠀⠀⠁
⠀⠀⠐⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠐⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠁⠠⠀⠀⠀⡀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠃⠀⠀⠀⠀⠈⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⡠⢐⡂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⡀⢐⠀⠀⠀⡁⡣⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⢰⣿⡏⢀⠀⠀⠀⠑⠬⠅⠁
⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡐⠂⡀⠀⠉⠀⠀⠀⠀⠂⠀⠈⡀⠀⠂⠀⢠⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠁⠐
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⢀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡄⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣬⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢰⣦⡀⠀⠀⢀⠈⠛
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⠚⠛⠒⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡏⠀⠀⠀⠀⠀⠂⠀⠀⡀
⠀⠀⢦⣀⣀⡠⠢⣀⠀⢀⡠⠶⣄⣀⣠⠇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡆⠀⠀⠀⢐⠐⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠠⣶⣾⣷⣬⣭⣵⣶⣷⣶⠮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠈⠙⠛⠿⠿⠟⠛⠋⠁⠀⠀⠀⢀⠤⠒⣒⡙⠹⢢⢀⠜⠨⢤⠂⠑⡄⠀⠀⠘⠿⠶⣤⣤⣀⣀⣀⣠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡄⣼⣿⣿⣶⣤⠁⣠⣤⣴⡖⣖⠓⢦⠀⠀⠀⠀⠈⠀⠉⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⠹⢿⣟⣿⡼⠀⢻⣿⣿⣿⠏⣰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣠⡆⢨⣡⠄⡗⣠⠈⢩⡁⣰⠆⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠃⠉⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠶⠄
⠀⠀⠀⠀⠀⠀⠘⠋⠂⡄⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠒⢀⣌⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⣃⠲⠈
⠀⠀⠀⠀⠀⠈⠒⠠⠒⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣀⣀⣴⣤⣴⣿⠆⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣷⣤⣤⣴⠟⠓⠲⠶⢿⣿⠿⠟⠛⠁⡸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠟⠛⠋⠁⠀⠀⠀⠀⢠⠀⠀⠠⠀⠀⢀⠉⠀⠀⠐⠃⠀⠂⠀⠐⠀⠀⠀⠀⠄⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉



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

⠀⠀⠀⠀⠀⠀⢀⢠⠤⠤⢤⣄⡀⢐⠋⠒⠐⢆⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⡔⢱⠤⣀⡴⡁⠈⠀⠒⡦⠉⠙⢎⣢⠇⠠⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠈⠆⣰⠚⢍⢍⠙⡉⠉⡝⣧⡷⠉⡝
⠀⡹⠐⠉⠉⠐⣼⡦⠀⠉⢠⠀⢺⢻⣅⠄⠒⢊⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠇⠘⠒⢆⡀⢸⡜⠀⣇⠀⡁⣿⡦⣀⠸
⡎⠀⢀⣤⠒⠪⢀⣁⠤⠀⠄⢁⢁⡼⢏⠙⢀⠇⠉⠀⠀⠀⣀⡀⠀⡀⢀⣀⡀⠀⠀⠸⠴⡆⣜⠷⠎⠢⠼⠴⠤⠿⠔⠓⠃⠘⠃
⠈⠐⠉⠀⠱⠤⠜⠣⢇⣒⣱⡥⠚⠀⠀⠉⠉⠀⠀⢀⡒⠃⠄⢈⡶⡶⠭⣄⠬⣙⡆⠀⠘⠷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠑⠒⠂⠀⠖⠀⠒⠗⠊⢻
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠀⡇⠀⠀⡇⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⡠⠤⣀
⠀⠀⠀⠀⢀⢠⠔⠁⠀⠀⠀⠀⠉⢢⠀⠀⠀⠀⠀⠈⠠⢀⡇⣀⣀⣇⣀⣀⡧⠔⠃⠀⠀⠀⠀⠀⠀⠀⢀⠞⠅⠀⠀⢰⣉⡈⠣
⠀⠀⠀⠀⣀⠈⢆⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠠⠂⠠⣈⠆⠀⠀⢆⠃
⠀⠀⠀⠀⢘⠢⡀⠑⠤⣀⠀⠀⠀⣠⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠂⠄⣀⡀⠀⠀⠀⠀⠀⠀⢣⠠⡀⠀⠠⠀⣀⠹⢀⠁
⠀⠀⠀⠀⠈⢦⡈⠑⠂⠤⢈⣉⣉⡤⠊⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠁⠀⠀⠀⣠⠖⠂⠈⠁⠒⢢⡄⠀⠀⠑⠆⡈⣉⢀⣤⠴⡃⢤⡀
⠀⠀⠀⠀⠀⠀⡝⠒⡤⠤⠠⠴⠊⠀⠀⠀⠀⠀⢀⠤⢦⣊⠀⠀⠈⠀⠱⠂⠀⣀⣀⠀⢀⠄⠂⠁⢰⠀⠀⠀⠀⠀⢠⠩⠤⡰⠹⡉
⠀⠀⠀⠀⠀⢠⠃⡰⠁⠀⠀⠀⠀⠀⠀⠀⣀⠄⠓⠒⠂⠬⢲⡤⡀⠀⠀⠀⢀⠀⡠⠊⡄⠀⢀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠱⡀
⠀⠀⠀⠀⢠⠏⡰⠁⠀⠀⠀⠀⠀⣠⠖⢉⠀⠀⠀⠀⢀⠔⠀⠊⠉⠑⠒⡶⡉⠓⡄⠀⡧⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠱
⠀⠀⠀⢠⠏⢠⠃⠀⠀⠀⠀⠀⠀⢈⠑⠢⢅⠂⠠⢴⠐⠓⢢⠤⠀⠴⡄⠀⠉⠀⡶⠈⠀⠀⠀⢀⡠⠖⠋⠉⠙⠙⠢⡄⠀⠀⠀⠈⠉
⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢸⠄⠄⣠⠀⠀⢼⡠⠄⠤⣇⠠⠂⠉⠁⠀⠀⠀⣠⠋⠀⠀⢀⡤⢤⣀⣀⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢐⣀⡜⢁⡤⠄⣻⠀⠊⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢰⣧⠈⠦⡀⠀⠀⠀⠀⠀⠈⣆⠀⠸⡀⢀⡦⠔⢋⢆⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠖⠚⢍⠡⠀⠉⣧⡤⠀⡆⠀⠀⠀⠀⠀⠀⠈⠣⣌⡙⢧⣀⣀⣼⠞⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⡤⠒⠘⠃⢉⠢⠀⠀⠀⢃⢁⡠⠛⠳⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠠⡈⢆
⠀⠀⠀⠠⠠⣤⣀⠀⡔⠉⠭⡉⠢⡐⡀⠀⠀⣂⣣⠤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠳⡀
⠀⠀⠀⢠⢄⡘⢄⣉⡉⡠⠀⠁⠀⣸⠼⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠘⡆
⠀⠀⠀⣼⠀⢠⢦⠤⠋⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠄⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⡶⠀⠀⠀⠀⠀⠀⠀⢀⠀⠬⠉⠉⠁⢀⣀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠠⠴⠄⠀⠀⠀⠀⠀⠀⠠⠈⣀⣀⣀⣉⡑⠚⣉⡀⠡⠀⠀⠀⠓⠦⠧⠤⢀⠢⣴⠤
⠀⠀⠐⠂⢄⣀⢀⣤⠶⠂
⠀⠀⠀⠀⠐⠈⠻⢤⣢⣥⡤⠀⠉⠀⠀⠀⠀⠒⠀⠈⣄⠀⠀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⢂
⠀⠀⠀⠀⠀⠁⠠⠄⠀⠐⠆⠴⠦⠀⠀⠀⠈⢆⡰⠶⠊⠀⠀⠀⠠⠤⠀⠀⠀⡠⠀⠀⠀⠈⢦⣀⣤⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠜⠴⠎⠂⠀⠀⠀⢡⣠⠀⠀⡀
⠀⠀⠀⠀⠀⡀⢀⠄⠒⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣡⣤⡶⠏
⠀⠀⡆⠖⣀⠛⠃⠀⠀⢵⡦⡄⠳⠃⠀⠀⠠⠄⢂⠂⠠⣒⠍⠁⠀⠀⠀⠀⠀⡤⢀⠀⢀⠤⠀⠀⠀⠈⠁
⠀⠀⠉⠉⠙⠦⠐⠚⠘⠃⠒⠁⠀⠀⠀⠀⠠⠆⣤⠶⠖⠥⠒⠖⠢⠀⠀⠀⠀⢣⡀⠀⠈⠑⠒⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⣀⣠⠴⠤⠔⠚⠁⠀⠀⠀⠀⠁⠉⠉⠉⠀⠙
⠀⠀⠄⠒⠊⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣤⡄⠀⠀⠀⣀⠀⠀⠀⠠
⠀⠀⢠⡐⠀⠈⠆⠀⠀⠀⠀⡠⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣼⠆⠀⠀⠀⠅⠀⠀⢀⣀⡀⢀
⠀⠀⠀⡆⠀⠀⢀⡄⠀⠀⠀⣀⣀⡀⢁⠤⠀⠀⠀⣠⠁⠀⠀⠀⠀⠂⢀⣠⢀⠏⠀⠀⠀⠀⠉⠀⠈⠈⠀⠀⠉
⠀⠀⠀⢹⠂⠈⠀⠀⠀⠀⠀⢃⠁⠉⢁⠤⠬⢥⠊⠗⠀⠀⠀⠀⠀⠉⠙⠒⠃
⠀⠀⠀⠈⢧⠀⣀⠤⠃⠀⠀⠈⠄⠠⠤⠤⠰⠒⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⠤⠐⠐⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡠⠄⠠⠀⠒⠀⠘⠄⠀⣀⣌⣣⡤⠦⠞⠂
⢀⠀⠀⠤⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠈⠳⣀⣀⣤⠽⡴⠶⠛⠛⣏⠉⠁⢀⠹⣄⣀⡤⠥
⡀⠤⠤⠀⠀⠣⠀⠀⠀⠈⠀⢁⠉⠑⠀⠀⠀⠀⠀⢈⣷⠚⠛⠉⢉⠀⠀⠀⣀⡀⠠⠴⠞⠂⠊⡉⠁⣀⠄⠤⠄
⠐⠀⠒⠊⠀⠀⠀⠀⠀⠐⡖⠂⢦⣶⠄⠂⠁⠀⠀⠀⢧⣀⠤⠶⠒⢃⠉⣩⣀⡀⠤⠀⠚⠃⠋⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣀⠀⠰⠀⠀⠀⠀⠀⠀⠈⠫⠀⠒⠒⠉⠁
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠀⢠⡾⠁⠉⠀⠀⣀⡀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠴⠂⠀⠘⠁⠀⠀⠚⠉⢀⡀⡀⠀⠀⠐⠉⠀⠀⠀⠀⠀⣠⡀
⠀⠀⡌⠀⠀⣴⠄⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡀⠘⠁⠀⡤⠀⠀⠀⠀⣨⠏⠀⢀⣆⠀⠚⠁⠀⠀⠀⣤
⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⠈⠀⣀⠤⠐⢀⣀⠿⠒⠈⠀⠀⠀⠘⣇
⠀⠀⣇⠀⠀⠀⠀⠺⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠐⠛⠂⠀⠀⠶
⠀⠀⠙⠀⠀⠴⡄⠀⠀⠀⣠⠀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⠀⠀⠀⠀⠀⠀⠈⠂⣀⣀⠀⠐⢶⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⣠⡶⢛⣷⠀⣾⠿⠿⠶⣦⣾⠷⠋⠤⢀⣀⣞⡆⠀⠀⠀⠈⠛⠀⠤⠴⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢡⣿⠃⣠⠶⡀⡶⢲⣰⣿⣸⢧⡟⣿⢈⣜⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠙⣰⡿⢤⠿⣟⡾⠻⠟⣧⣈⡯⠭⡅⠻⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⣠⠜⠉⠛⠫⣤⣬⣴⡶⠞⠋⠙⠲⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠴⠀⠐⠛⠃⣀
⠀⠀⠀⠴⣀⠀⠤⠀⠀⠈⠉⠀⠀⣤⡄⠀⠀⠀⠀⠀⣠⠖⠒⣀⠃⠈⠙⠂⠀⠀⠀⠀⠀⢰⣧⠶⠒⠉⠁⠉⠂⠀⠀⠒
⠀⠀⢰⡄⠉⠃⠀⠀⣀⠘⠋⢀⡀⠀⠀⣀⠀⠀⡰⠀⡅⠀⠈⠉⢤⠀⠰⠖⠀⠦⠀⠀⠀⠘⢃⠰⡷⠤⠤⠤⠤⢖⠀⠀⠢
⠀⠀⣼⣿⣦⣈⣉⡈⢙⣁⠀⠋⠉⢀⣰⠁⠀⢘⡇⠀⠲⠀⠀⠀⡀⢠⡀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⠲⠀⠀⠀⠈⠘
⠀⠀⠻⣿⣉⣩⡉⠹⠟⠛⠉⠉⣽⣧⣡⡆⠀⠘⠂⠀⠀⠀⠀⠀⠀⠐⠁⠀⠐⠀⠀⠀⠀⢈⠁⠀⠛⠀⠀⠀⠀⠉⠀⠀⠐
⠀⠀⠰⠿⠿⠗⠒⠶⠶⠶⣾⠛⠛⠉⠉⣠⠀⠀⠀⠀⢠⠀⠀⠀⠀⠤⠀⠐⠀⢠⠠⠀⠀⢸⡔⠂⠀⠀⠀⠲⠆⠀⠀⣄
⠀⠀⠘⣿⠗⢲⡶⠶⢶⡾⢯⠶⠶⠞⠛⢃⠀⠀⠀⠀⠀⠀⢀⡤⠤⠄⠀⠀⠀⢀⠀⠀⠀⠈⢧⠀⠛⠀⢠⠀⠀⠀⠃
⠀⠀⣾⡟⣲⠶⣥⣤⣤⡤⠬⠴⠖⣒⠉⠍⡄⠀⠀⠀⠈⡁⠀⠀⠠⣤⡄⠀⠀⠘⠁⡤⠀⠀⠈⠲⠄⢀⠀⠀⠤⢀⠤
⠀⠀⠐⠳⠿⠧⠤⠛⢂⣀⣠⣤⣤⠭⠗⠊⠀⠀⠀⠀⢀⠈⢤⡀⠀⠀⠀⠠⡄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⡿⠲⠆⢤⡀⢀⣀⡀⠀⠀⠀⠀⢀⠀⣀⣠⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠿⣿⢿⡿⠿⠶⢯⣄⠀⠀⠀⠀⠀⠁⠢⠌⠀⠂⢶⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⡄⠀⠀⠀⠊⠹⣿⣿⣦⣄⣀⣀⠀⠀⠀⠈⠀⠀⠁⠀⠉⠈⡀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣄⣠⠀⡁⠉⠛⢻⣛⣿⣿⣿⣿⠛⠉⠋⢈⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣟⣿⣿⣿⠿⠿⢿⣟⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢾⣿⣿⢻⡆
⠀⠀⠀⠀⠀⢘⣄⡀⠀⠀⠀⠀⠛⠿⣿⣤⣍⣉⡙⠛⠛⠛⠓⠚⠛⣛⣛⣿⡿⠃⠰⣿⣶⣿⣿⢧⡨⠝⣄
⠀⠀⠀⠀⠀⣸⠧⠭⠕⠂⠀⠤⢀⠀⡀⠈⠉⠉⠉⣿⣿⣻⣿⣟⠉⠉⠉⠁⠀⠀⠀⠘⢿⣿⣿⣦⠑⢄⠈⠳⢤⡀
⠀⠀⠀⠀⠀⢻⣕⠒⠤⠤⢤⢀⣁⣀⣀⣀⣤⣀⣌⣹⣿⣟⣟⠛⠧⠀⠀⠄⠄⠀⠒⠀⠀⠿⢿⣿⣷⡌⠳⣄⠀⠐⠰⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠶⠤⠤⠤⠤⠤⠤⠤⠴⠞⠛⠻⣿⡛⠲⠲⠦⠶⠤⠀⠀⠠⠀⠤⠬⢽⣿⡇⠀⠨⡙⠢⣄⡈⠀⢯⣼⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠲⠆⠤⠤⠤⠤⠤⠦⠒⠋⠁⠀⠀⠀⠈⠙⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣷⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣬⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣾⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⣙⣛⣛⣃⡀
⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⡄⠢⣀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⡈⠉⠉⠉⠉⠁⠀⠀⡔⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢠⠓⠦⣌⣉⡛⠛⠛⠛⠉⢁⣠⡇
⠀⠀⠀⠀⢢⡀⠀⠀⠉⠉⠉⠁⠀⠀⣠⠇⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣶⣾⣿⣿⣿⠟⠀⠀⠀⠀⠀⠈⢄⡀⠀⠈⠉⠉⠉⠉⠉⢁⣴⠃
⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠖⠒⠋⠰⠀⠀⠀⠀⠀⠀⠈⣷⣾⣯⣭⣭⣭⣭⣽⣾⠇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣶⣶⣶⣾⣿⡇
⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⠀⡀⢠⠁⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠘⣄⣇⣡⣸⣀⣅⣬⣸⠁⠀⠀⠀⠀⠀⠀⠀⠈⠿⠻⠿⠟⠿⠿⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⢀⣀⢀⣀⢀⠀⠤⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠴⠀⢈⣄⠀⢀⡄⠀⢡⡀⠀⠀⠀⠀⢀⠀⠀⠀⠙⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠁⠀⠀⠀⢰⡆⠀⠀⢀⠀⠀⠈⠓⠀⠀⠀⠀⢀⣄⢀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡃⠀⠀⠀⠠⠀⡠⠊⢀⠀⠀⠈⠀⠀⢀⢈⠉⠋⠉⠛⠋⠉⠀⠀⠀⠀⠀⠠⠜⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡂⠈⠃⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠇⠀⠀⠁⡼⡀⠀⠀⠀⠀⡀⠀⠄⠀⠀⡤⠔⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⠶⠀⠀⣤⡄⠀⠘⠃⠀⠀⠀⡀⠊⠀⣼⠇⢡⢀⡀⢰⢘⠥⠀⠠⠒⠉⡠⠐⠁⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠓⠀⠀⠀⠀⣀⡠⠔⠉⢀⡤⠛⠓⠒⠤⠤⠬⠥⠤⠤⠒⠒⠉⠁⠀⠀⠠⠤⠀⠁
⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠅⠐⠒⠢⠄⠀⠂⠈⠀⡀⠠⠂⠫⢅⡀⠉⠐⢄⠀⢀⠤⠀⢀⣀⠀⠀⠀⠊⠁⢀⠀⠈⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠑⠂⠠⠄⠀⠀⠀⠀⠤⠭⠀⠀⠀⠈⢀⣠⠤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠃⠠⠄⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠠⠤⠤⠖⠒⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠈⠀⠀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⡀⠑⠀⠀⠀⠀⠀⠀⠀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠸⠀⠘⠀⠐⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⢈⢩⡙⠘⠒⠁⠀⠀⠆⠈⠀⠀⠁⠁⠢⡀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠘⣄⠢⡑⠀⠀⢠⠀⠀⠀⠂⠈⠀⠀⡆⠀⠀⠈⢆⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠈⠑⠀⠩⡥⠀⠀⠀⠀⠁⢈⠀⠀⠸⡀⠀⠀⠀⢣⠀⠡⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⣁⣨⠀⠀⢄⢡⠀⠀⢕⢄⣇⠀⣁⠀⠄⠑⣇⠠⠀⠀⠀⢀⠂⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡠⢀⠔⠼⠢⠠⠀⠊⠀⢣⠀⠀⠦⢻⢀⢀⠠⠌⠦⠧⢀⠀⠀⠀⠀⠀⡠⠜⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠈⢲⠒⣦⣀⠀⠒⠐⣬⠡⡆⢤⡾⢠⣌⣒⣐⣒⠶⡊⠭⠩⠉⣁⣠⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠑⠒⠒⠳⠤⠤⠜⠋⠉⠉⠀⠀⠈⠉⠉⠁⠀⠀⠀⠈⠠⠀⢀⡀⠐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⢂⠀⠁⠀⠀⠐⠀⡰⠂⠀⢀⣀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠤⢀⡀⡑⢄⠀⠀⠈⠹⠀⠀⠀⠀⡏⠁⠀⠀⢀
⠀⡎⠀⢴⡁⠉⠉⠉⢇⣀⣀⠀⠀⡁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠰⠁⠈⠀⠈⠀⠀⡀⠉⡀⠀⢀⡀⠁⢠⠀⠀⣠
⠀⠈⠒⠤⠤⣀⡴⠀⠀⠀⠀⠉⠉⠉⠒⠀⠀⠰⠤⠄⠀⠀⠠⡚⠀⠀⠠⢀⠁⡀⠉⠁⢠⠀⠀⠈⠐⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠐⠧⢄⣀⠴⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠆⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠈⣠⠂⠀⠂⡀⠀⠀⠀⢠⠀⠍⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⠀⠀⠀⠀⠀⠀⠂⠈⠤⠬⠉⠉⠉⠤⠸⠂⠀⠀⠙⠚⠂⠂⠀⠶⠆
⠀⠀⠀⠀⠀⠀⠁⢂⠤⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⣚⣀⣀⠀⠀⠀⢀⠀⣀⡰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁⠉⠀⠀⠀⠠⡈⠅⠀⠀⠀⡡⠄⠀⠀⠙⡜⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⣀⣨⡄
⠀⠀⠀⠀⠀⠐⠤⣀⠓⠂⠀⠰⣤⡌⠷⠂⠀⠀⢠⠀⡀⠀⢄⡢⠁⠀⠀⠀⠀⢀⢀⠀⠀⠀⡀⠀⠈⠋
⠀⠀⠀⠀⠀⠈⠉⠙⠢⠐⠓⠛⠒⠂⠀⠀⠀⠀⠰⢠⠤⠢⠍⠀⠒⢠⠀⠀⠀⠰⡄⠀⠉⠒⠒⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠴⠖⠒⠉⠀⠀⠀⠀⠀⠈⠉⠉⠀⠁
⠀⠀⠀⠀⠀⠂⠈⠁⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠶⡆⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠐⠆⠀⠀⠁⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⢀⠀⠀⠀⣰⠃⠀⠀⠐⠄⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⢱⡀⠀⠚⠀⠀⠀⢰⠒⠢⠄⣁⢀⢀⢴⡃⠀⠀⠀⠨⠥⠶⠼
⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⡰⠀⠀⠀⡂⢀⣀⡀⠠⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡄⠠⠀⠐⠄⠉⢀⣙⣄⢤⠬⠆
⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠠⡄⠀⠈⠧⣀⣀⣬⢦⠴⠖⠛⢎⠉⠉⣙⣦⣐⣠⠤
⠀⠀⠀⠀⠀⠤⠀⠀⠢⠀⠀⠀⠁⢀⠈⠁⠀⠀⠀⠀⠀⡽⡞⠋⠁⢉⠀⣀⣀⣄⠨⠴⠞⠂⣉⠀⢀⠤⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠙⠓⠒⠾⠊⠀⠀⠀⠀⠘⣤⠐⠒⢋⣀⠀⠤⠄⠐⠀⠊⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠨⠂⠀⠀⠀⠀⠀⠉⠀⠉⠁

⡀⢀⡀⢀⠀⠀⢀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠀⡠⠂⠀⢀
⠀⠀⠀⠀⠀⠐⢦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠐⠁⠀⠀⠁⠃⠋⠐⠐⠐⠡
⠀⠀⠀⠀⠀⠀⠀⠳⡍⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⡈⠛⣋⡄⠄⠀⠀⠀⠀⠀⣿⣀⣈⣿⣁⣀⡗⠀⠀⠀⠰⠆⠰⠬⠈⠻⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⠴⠷⣗⡄⠀⠀⢠⣟⡉⢉⣿⣉⣁⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠈⠙⠈⠉⠂⠀⠀⠈⣻⣿⣿⠋⠛⠙⠻⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⣀
⠀⠀⠀⠠⣄⣐⢒⠺⠷⠞⠶⠛⠦⠾⠧⠤⡀⠀⠀⠈⠋⠉⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣀⠀⣀⣩⣤
⠀⠀⠀⠀⠙⠋⠍⣛⡛⠛⠒⠒⠒⠛⠚⡿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣄⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⢀⣤⣰⣆⠁⢐⣀⣠⣤⣶⣿⠟⠀⠀⠀⠀⡀⠀⠀⠀⠘⢢⣤⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⠀⠰⠤⠴⠃⠀⡄
⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣧⣤⡀⠀⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⡉⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⢀⡀⢀⣤⣶⠀⠀⠀⠀⠀⠈⠛⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡐⢀⡨⠐⠎⠡⣉⠀⠒⣐⣀⡤⠀⠠⣖⡴⣀⢚⠁⣤⡨⠗⠉⠀⠀⠀⢀⡀
⠀⢰⡔⠀⡘⢂⠐⠁⠠⠀⠄⠡⣌⣤⠷⠞⠉⠁⠀⠀⠀⠀⠈⠉⠚⠇⠋⠀⠀⠀⠀⠀⠀⠀⣈⠑⠀⠀⠤⡠⡄
⠀⠀⠑⠆⠀⠀⠑⣍⣤⠼⠞⠋⠉⠀⠀⢀⣀⠄⢀⠒⠀⠀⢠⡄⡀⡢⠄⠀⠀⠀⢀⡀⠀⢉⠌⠀⠠⠀⡔⣏⠙⢂⡠⣄⡖
⠀⠀⠀⠀⠚⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠛⠀⠀⠰⠦⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠛⠶⠄⠓⠘⠉⠃⠽⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠶⢰⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠁⠀⠁⠀⠐⠄⠀⠀⠀⠀⠂⠀⢇
⠀⠀⠀⠀⣰⠢⠄⠀⠀⠀⠤⠀⠀⠀⠀⠀⠃⠰⠀⠠⠀⠀⠀⠂⢃⠄⠀⠰⣄⢀⠀⣠⠕⠀⠀⢀
⠀⠀⠀⢰⣫⣀⣀⣀⣠⢔⣒⡋⢱⠀⠀⡀⠳⠀⠀⠀⠀⠐⣒⠭⠿⠀⠀⠀⢩⣆⣽⣧⡠⢄⣤⣬
⠀⠀⠀⠑⠚⠤⠠⠤⠄⠊⠍⠀⠀⠀⠀⠈⠐⠤⠤⠄⠠⠤⠤⠤⠒⠁⠀⠀⠀⠀⠀⠈⢯⣽⣭⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢀⠰⣤⣀⡀⠀⠀⡀⠉⡦⢢⠀⠀⠀⠀⠀⡐⠀⠁⠂⠀⠀⣼⠀⠀⠀⠀⡠⠔⠁⠊⠉⠀⢒
⠀⠀⠀⢤⣄⣀⣀⣀⣀⣀⣀⣤⡔⠀⠀⠀⣤⡂⠀⠀⠀⠀⢄⡴⠁⠀⢀⡤⠈⠀⡄⠀⠀⡀⡠⠁⠄
⠀⠀⢀⢀⠠⠈⠉⠉⠉⢉⡡⠞⠀⣠⠀⠀⠉⠑⢧⢀⣀⠤⠋⠀⠀⠀⠑⠳⠄⠉⠀⣀⣀⠆
⠀⠀⠀⠀⣴⠒⠀⠌⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⡢
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡳⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠘⡤⠋⠀⠤⠄⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⢀⣤⡖⢋⢥⠀⠀⠀⠀⠀⠀⠀⠂⠀⠸⣦⣠⠏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠰⠞⠋⠁⠀⠀⠠⣱⣤⡀⠀⠀⠀⠀⡇⠀⠠⢙⣛⡀⡇
⠀⠀⠠⠀⠑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣝⠀⠀⠀⠘⠀⠦⠃⠉⠩⠵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠙⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⡀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡼⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠹⢷⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣶⠶⣦⣼⡇⠸⠃⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⡋⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠋⠀⠀⣠⡴⠖⠁⢀⣀⣤⢤⡄⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠁⠈⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠔⠚⠉⢁⡠⠖⠃⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣇⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣈⣀⣤⡶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠋⠀⠀⠀⠀⠀⠀⠹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡏⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠺⣆⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢶⣤⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠶⠾⠷⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⣀⣤⠤⠖⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢦⣤⣄⣀⣀⣴⠏
⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠚⠉⠀⠀⠀⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⡽⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⢸⣶⠶⠶⠶⠶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣤⣤⣄⡀⠀⠀⢸⠃⢠⠇⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⡄⠀⠀⠀⣾⠀⣸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⣏⢠⡇⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠙⠋⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

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

⢎⠑⢄⠀⠰⢈⠀⠀⠀⠀⠀⠀⠖⠤⠀⡀⡀⠁⠀⣀⠀⠀⠀⠀⠀⠀⠡⠆⠀⠀⠄⢀⠄⠀⠀⠀⠀⠀⠀⠀⠁⢀⢇⡐⡀⣀⢀⡩⡀⠀⠀⠀⠀⠀⡃⠴⡁⠠⠈
⠠⠓⢄⠑⣤⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠃⠀⠀⠀⢀⠂⠀⠆⠐⠀⢂⠄⠁⠀⠄⣄⢠⠀⠀⠀⠀⢠⠐⠄⠐⢀⠐⠂⠀⠠⠀⠀⠀⠐⠀⠐⢤⠊⡠⡈
⡐⡢⠠⠐⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠘⠈⠀⠒⡁⠐⠁⠀⠀⠝⢀⠁⠈⢳⠀⠀⠀⠊⠒⠐⠂⠂⠒⠐⠂⠂⠂⠀⠀⠀⠀⠢⠀⠂⠄⢔
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠥⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠒⠀⠠⢀⠀⠀⠄⠀⠐⠠
⠀⢀⢐⠆⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⠣⠀⡈⠂⠐⠄⠀⠀⠀⠀⠀⠀⢀⠤⠦⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠔⠀⠀⠀⡔⠁⡠⠀⠀⠀⢀
⠂⠉⠣⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠜⠀⠀⠘⠀⠱⠊⠁⠀⠉⠉⠑⡀⠂⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁
⠀⠀⠘⠂⠀⠀⠀⠀⠇⢀⠀⠀⠀⠀⡠⢂⠀⠀⠁⠀⠀⠀⠀⠈⠂⣀⠀⠀⠀⠀⠀⠀⠁⡐⠀⠀⠀⠀⢁⠀⠀⠀⠀⢀⠤⠃⢀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠐⢋
⠤⠊⠀⠀⠀⠀⠀⠀⠌⠂⢀⠂⠄⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠘⠄⠀⠒⠀⠄⢃⠌⠀⠄⠀⠀⠀⠀⠀⠀⠑
⠠⡀⠀⠀⠀⠀⠀⠀⢡⠐⠀⠈⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⠑⠀⠀⠀⠀⠐⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⠀⠄⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⢀⠀⠀⣠⠔⠄⠀⠀⠀⠀⢀⠔⠁⠁
⠈⠉⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⢀⡀⡅⠈⣄⠀⠤⠀⡄⠠⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠉
⠀⠀⡀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠰⠒⠈⠁⠘⠃⠁⡀⢢⠀⡙⠀⠀⢀⠦⠂⠁⠀⠀⠀⠀⠀⠀⠀⡆⢢⠰⡀⠀⠀⠀⠀⠀⠁⠀⠀⠄
⠀⠀⠠⠀⢈⡀⠀⠀⠀⠀⣤⠤⠤⠀⠄⠠⠄⡄⠀⠀⠀⠀⢀⠨⡀⠘⢀⠚⣀⠁⢠⠀⡃⡠⢐⠅⠀⠈⠠⠀⠀⠄⠀⠀⠀⠐⠀⠀⠂⠀⠤⡀⠀⠀⠃
⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠠⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠌⠐⠠⠄⣠⠐⠉⠀⠀⠈⠀⢠⠀⡠⠊⠀⠀⠀⠀⠀⠈⠁⠁⢀⡀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠊⠀⡐⠀⠀⠀⠀⠀⠐⠒⠒⠒⠚⠀⠀⠀⠀⠀⠀⣈⣩⠋⣁⣝⡉⣡⡋⣉⡜⡉⣨⠋⣉⡝⣉⣩⡋⡱⠀⠀⠀⠤⠐⠀⠀⠀⠊⡠⠀⠀⠀⠠⡀⠀⠀⠄
⠀⣀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠠⠤⠼⠄⠠⠀⠠⠀⠤⠠⠤⠄⡇⠠⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⢰⠀⠐⠀⠐⠀⠆⠀⠀⠀⡇⠐⠀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢈⠠⢀⡀⢄⠁⠂⢄⠀⠀⠀⠀⠙⠣⠸⣁⣈⣁⢉⡀⣁⣀⣁⣀⠁⠘⠁⠀⠀⠀⠀⠀⠀⠀⡀⣐⠁⠑⠐
⠠⠀⡀⠂⠀⠀⠀⠀⢀⠈⠀⠁⠀⠠⠈⠁⢀⠀⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠉⠐⠂⠈
⠀⠊⡠⠂⠄⠀⠀⠀⠂⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢂⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠍⠀⢓⠂⠓⠆⠰⠀⠀⠀⠀⠀⢀⠐
⠀⠐⢀⠍⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀⠂⠉⠐⠀⠀⠀⠀⠂⠉⠐⠂⠀⠀⠀⠀⠀⠆⠐⠂⠐⠒⠐⠒⠠⠄⠀⠀⠀⠊⡰
⠈⡀⠁⠀⠀⠀⠀⠀⠄⠑⠀⠆⠀⠀⠀⠀⠀⠀⠁⠀⠂⠠⠀⠀⠀⠀⠠⡙⠄⠄⠀⣠⠄⠠⢤⢀⠠⢠⢋⠄⠀⠀⠀⠦⠀⠠⠄⠠⠄⠀⠄⠂⢴
⠔⠁⠀⠀⠀⠀⠀⠀⠈⢄⠀⢀⠁⠠⠀⠚⠀⠀⡠⠀⡠⠁⠀⠀⠀⠀⠐⠁⠀⠀⠉⠁⠀⠀⠈⠉⠀⠀⠈⠂⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠁⠐⠀⠀⠀⠐⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⠀⡄⡀⢈⠠
⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⢁⡕⠀⠠⠀⠡⠀⠀⠀⠀⠀⢀⡀⡀⢀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠐⠀⠐⠅⠀⠀⢀⠀⢀⡀⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⡄⠀⢢
⠁⡈⠂⡠⠒⢄⠀⠀⠀⠀⠀⠀⢀⢀⠈⠱⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⢀⠔⠁⠀⠈⡀⠀⠠⠁⠀⠀⠀⠀⠀⢠⠄⠨⡄⢠⠀⠀⠀⠀⠀⠀⠀⠀⠒⢄⠐⢅
⠂⡠⠂⢈⠰⢈⠀⠀⠀⠀⢐⠂⠀⠁⢀⣐⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠈⠇⠀⠀⢀⠔⠀⠀⠀⠀⠀⡡⠀⠸⠄⠤⠇⠼⢄⠀⠀⠀⠀⠀⠀⡁⠖⢁⠑⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡬⠥⠴⠶⠶⠶⠶⠶⠶⠶⠶⠤⢤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⠉⠉⢀⣴⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢫⡀⣀⣴⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣀⣀⡸⠣⠴⠒⠒⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠉⠛⠻⠯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠞⣛⠩⠀⠀⣀⣀⣄⣀⠀⠉⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠭⠭⠅⠐⠒⠂⠉⠁⠀⠀⠀⢸⠁⠀⠀⠀⠙⡆⢂⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⢀⡇⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⣠⣴⠟⢁⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠾⠟⠛⢉⡠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠳⡀⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣆⣀⣠⠤⣔⠊⠉
⠀⠀⠀⠀⠀⢀⠔⠋⠁⠀⠀⠀⠀⠙⢦⡙⢅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠂⢄⠀⠉⠓⢄
⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡦⠤⣀⣀⣀⠀⠀⠀⢀⣀⣀⣤⢴⠖⠉⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⢳
⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠢⠤⠬⠭⠭⠭⠭⠴⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠈⠲⢄⡀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠒⠀⠀⣀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠤⠤⣀⣈⠁⠒⠂⠠⠤⠄⠀⠤⠠⠤⠀⠠⠤⠀⠐⠒⠈⢁⣀⣠⠤⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠓⠒⠒⠒⠒⠒⠒⠒⠒⠛⠉⠉⠉

⠀⠀⣀⣀⣤⣤⣤⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣶⣶⣤⣤⣤⣤⣀⡀
⠀⣾⣟⡯⠍⠓⠒⠒⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠭⣽⣿⣧
⠀⣿⠈⠉⠻⠓⠒⢶⣶⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⢴⣶⣶⣶⡶⠟⠛⠉⢸⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣀⣠⣤⣤⣀⡀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠿⠟⠋⣉⣉⣉⣙⠻⣷⣄
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣴⠟⠋⠉⠉⠛⣷⡌⢿⣆
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⠃⠀⠀⠀⠀⠀⠘⣿⠸⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠃⠀⠀⠀⠀⠀⠀⢀⣿⠀⣿
⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⡟⢸⡿
⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⢀⣼⡟⢠⡿⠃
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⣠⣾⠋⣰⡿⠁
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢀⣠⣴⡾⠋⣡⡾⠋
⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠿⠛⠋⣁⣴⡿⠋
⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣦⣴⡾⠛⠁
⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠋⠁
⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿
⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠈⠻⣶⣦⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣴⡾⠟⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣿⣿⣿⣿⣿⣿⣯⣭⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣽⣭⣬⣽⣭⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠖⠒⠒⠒⠒⠒⠒⠒⠒⠲⠤⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣚⡭⠵⠖⠒⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠓⠲⠤⣍⣓⠲⣄⡀
⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⠀⠀⢀⣀⣠⣤⠤⠤⠶⠒⠒⠒⠒⠒⠒⠶⠤⢤⣄⡀⠀⠉⠛⢦⡙⢦
⠀⠀⠀⠀⠀⢠⡏⡏⠀⢀⡤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢤⡀⠀⠀⠀⠉⠙⠲⣄⠀⣿⢸⡆
⠀⠀⠀⠀⠀⢸⣇⢣⡞⠉⠀⠀⠀⠀⠀⢀⡤⠴⠒⠒⠒⠋⠀⡤⠤⡄⢹⡀⠀⠀⠀⠀⠀⢀⡿⣡⢾⡇⣀⣤⠤⠤⠤⢤⣀
⠀⠀⠀⠀⠀⢸⡈⠳⣌⡳⢤⣀⡀⠀⠀⠸⡄⠀⠀⢰⠖⠒⠚⠁⠀⢹⢸⡇⠀⢀⣠⡴⢞⣡⠞⣡⠞⠋⠁⠀⣀⣀⣀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠘⡇⠀⠀⠉⠓⠮⣍⣛⠒⠶⠿⠦⢤⣬⣷⣤⣤⣤⠤⠿⠾⠒⢋⣩⡤⠖⠉⠀⠀⣧⣀⡤⠖⠋⠁⠀⠉⠙⣦⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠶⠶⠶⠶⠶⠶⠶⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢧⣄⣀⣀⣀⣀⡤⠞⠁⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣨⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡀⠀⠈⠉⠉⠁⣀⡠⠔⠋
⠀⠀⠀⠀⠀⣠⠞⠉⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠛⠻⣍⠛⠋⠉⠉⠁
⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⢸⡷⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡏⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠙⢦⣌⡙⠲⠦⢤⣄⣀⣀⣀⣀⣀⣀⡤⠤⠖⠚⣋⡥⠞⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⢻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠶⠤⠤⠤⠤⠤⠤⠴⠶⠒⠋⠉⠀⠀⠀⠀⢀⣠⣾⠟
⠀⠀⠀⠀⠀⠙⠪⣝⡲⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⢴⣚⡭⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠺⠭⣍⣓⣒⠲⠦⠤⠤⠤⠤⠤⠤⠤⠴⣖⣒⣻⠭⠷⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⡪⢋⠻⣿⢄⡒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠶⠾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⢤⡀⠀⠀⠀⠀⡎⢠⠋⢠⠃⠀⠀⢡⠘⢆⠃⠀⠀⠀⠀⠀⠀⡸⣤⣰⣀⣀⣠⡼⢇
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢤⣆⣊⠜⣣⠄⠀⠀⡼⠺⡤⠜⠠⠤⠥⠐⠂⠒⢳⡀⠀⠀⠀⠀⢠⠁⠀⠀⠰⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⢠⠊⢤⠀⠀⠉⢳⠉⠀⠀⠀⠘⡃⠒⠰⠖⠒⠒⠒⠒⠐⠈⢁⠃⠀⠀⠀⠐⠯⠿⠶⡶⠶⠶⢶⠟⠋⡏
⠀⠀⠀⠀⠀⠀⠨⠀⠀⡀⠐⠆⡐⠀⠀⠀⠀⠀⠇⠀⢠⡄⠀⠀⠀⠠⠦⠀⡜⠀⠀⠀⠀⠀⠘⢄⠈⠁⠀⠀⠈⠀⡰
⠀⠀⠀⠀⢀⡔⡸⡦⣄⣀⠠⠔⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠉⠀⠀⡴⢀⠢⡀
⠀⠀⠀⠀⠀⠙⠺⢼⣏⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠈⠑⠒⠒⠒⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⡜⠁⠂⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠙⣿⡿⠿⠀⠀⡸⠁⠠⠆⠀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣤⣀⡠⠏⢢⣀⠠⡀⠀⠀⠀⠀⠀⢀⠜⠂⠀⠒⢅⠀⠀⠀⠀⠢⣀⢄⣈⣡⣴⡾
⠀⠀⠀⠀⠀⠀⠐⢸⠒⠂⡙⠢⡀⠀⠀⠀⠀⠀⠸⣀⣄⠵⠘⠉⠀⠀⣸⡄⠀⠀⠀⠠⢁⠀⠲⠀⣀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢏⡉⠉⣉⣃⠀⠀⠀⠀⠀⢸⠁⠀⢀⡠⠔⠊⠁⠀⠈⡆⠀⠀⢸⡍⢧⠶⣠⡄⡠⠃⠀⠀⠀⡠⢔⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡤⠤⠤⢈⡆⠀⠀⠀⠀⠀⢗⠉⠀⠀⠀⣄⠤⠒⠀⢡⠀⠀⣸⠻⡀⢶⡹⠋⠀⠀⠀⠀⠾⠄⣠⣏⣨⡋⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣀⠲⠇⠀⠀⠀⠀⠀⠘⠤⠐⠊⠁⠀⣀⠠⠔⠊⠀⢀⡿⣎⣱⠎⠀⠀⠀⠀⠀⢸⠤⠐⣆⡸⠷⢛⣄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⠤⡀⠀⠈⠢⠔⠊⠁⠀⠀⠀⠀⠀⢸⢛⡽⠃⠀⠀⠀⠀⠀⠀⠘⣤⠋⡬⠓⠶⠻⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⡀⢮⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⠤⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠂⡀⣪⡸⠋⠶⠲⠤⠤⣄⣀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⣠⡤⢦⡄⠀⠀⠀⠀⠈⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠙⠁⠀⠀⠀⠀⠀⠀⣀⣤⢆⠔⠒⠲⡠⣄
⠀⠀⠀⠀⠀⠀⣿⣇⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⣿⠀⠀⢀⡀⠀⠀⠀⠀⡴⠍⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠂⠀⠻⣷⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀⣾⡇⠀⠀⠏⢈⡷⠀⠀⢸⠃⠀⠈⢡⠄⠛⢄⠉⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⣼⡟⠀⠀⣴⣳⢀⡴⠀⣠⡶⠀⢸⣿⠓⠒⠒⠒⠋⠀⠀⠀⢰⢄⠀⠀⢣⡀⠀⢀⠇⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⢀⣿⠃⢠⡄⢈⢇⣾⠁⢰⡿⠁⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⡀⠀⠀⠉⠈⠁⠀⠀⢠⠏
⠀⠀⠀⠸⢤⣀⡀⠀⣀⣼⡿⠸⣿⣀⣼⣿⡌⢸⡏⠀⢼⡇⢀⠜⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣠⡀⣀⣀⡠⠞⠉
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠉⠉⠀⠉⠀⠀⠁⠀⠀⠁⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⢤⣄⣀⣠⠴⠒⣒⣒⠒⠶⢤⣀
⠀⠀⠀⠀⠀⣀⣤⠤⣤⡴⠋⠛⠋⠉⠁⡴⠋⠀⠈⠉⠉⠉⠙⠓⠦⣌⠳⣄
⠀⠀⠀⠀⣼⠱⠂⠀⢸⠁⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣈⣧
⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠉⠙⠯⢽⡲⣄
⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⢠⠪⠀⠀⠀⠀⠀⢀⣠⣤⣬⣷⡀
⠀⠀⠀⠀⠀⠀⠈⠛⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠁⠀⠀⠀⡠⠚⠁⠀⠀⠈⠻⠝⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠂⠀⠀⡠⠴⠖⠒⠶⢾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⠠⠤⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠙⠛⠋⠓⠒⠛⠲⢤⣤⣀⣠⡾⠵⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠤⠶⠖⠒⠒⠒⠚⠛⠛⠛⠒⠒⠲⠶⠦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⢀⣠⠴⢖⠚⢻⡟⢿⡓⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⣷
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢧⣸⠇⠀⠀⣀⡿⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⢸⡇
⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⠤⠶⠶⠖⠛⠛⠉⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡴⠟
⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⣼⠉⠁⠉⢹⡇
⠀⠀⠀⢸⣿⠆⢠⠶⠤⣄⣄⠀⢀⠀⡔⠚⠛⡆⠀⠀⠀⢰⠉⡆⢸⠀⠀⠀⢆⢀⡴⣿⠀⠀⠀⣾
⠀⠀⠀⠀⢿⣆⡾⢠⠀⠈⠫⡁⢀⠤⡿⠀⠀⣧⠀⠀⠀⣸⠀⠙⠞⠀⠀⠀⠘⠦⠾⠃⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠈⠁⠀⢧⠀⠀⠈⠓⠚⠁⠀⠀⠘⢦⣠⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⣠⡤⠶⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠒⠒⠶⠖⠒⠒⠒⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠂⠀⠀⢲⡄⠀⠀⠀⠀⠀⣤⠄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢸⡟⠛⠛⠛⠋⢰⡏⢰⠇⣰⢂⠀⣠⡄
⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⢹⠀⠀⠀⢰⠇⡼⢣⡾⢱⡆⢀⣿⢀⡿⢸⢳⡟⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣿⠈⠀⠸⡷⠊⠀⢸⡇⣼⢁⡟⠘⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀⠿⠀⠈⣷⣀⡀⠀⠀⠀⠁⠘⠇⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠤⠀⠀⠠⠟⣸⡤⠖⠚⠛⠛⠛⠶⢼⢃⡶⢰⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣯⠁⡀⡆⢸⡆⢰⡆⢀⡿⠃⠛⠛⠁⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⠀⣴⠃⢸⡆⣿⠸⣇⠇⣿⠀⣾⠁⣾⠃⣼⢠⡆⢀⣤⢀⣀
⠀⠀⠀⠀⠀⠀⢠⡆⠁⠲⣄⠀⠘⣇⣿⠀⣼⠀⢿⠘⣇⠰⠏⢸⡇⣾⡃⣼⠃⣼⠋⣹⢻⡏⢰⡇
⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠈⢷⡄⡏⢿⡄⠙⠂⠘⠇⠉⠀⠀⠀⠀⠈⠁⠙⠺⠃⣼⠃⣼⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢻⠇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠘⠓
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠸⢿⣦⡀⠀⠀⠉⠒⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡐⠀⠀⠈⠉⠻⣶⣄⠀⠀⠀⠀⠁⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⢸⣦⣶⣤⠞⠉⠙⠃⠀⠀⠐⠀⠺⢿⣷⣄⠤⠒⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⣿⢻⣷⣤⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢐⣦⣄⠀⠀⠀⠀⠀⠀⢶⣶⣤⣿⣮⣿⣿⣿⣦⡀⠀⠀⡆⠀⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⠀⠀⠀⢀⡀⣀⠀⢉⠤⠈⠁⠈⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠘⠀⡀⠀⠀⠄⠨⣿⣨⠶⠆⠂⠀⠀⠀⠀⢸⣿⣦⣅⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠀⠀⠘⢿⠀⡄⠀⢀⡄⠁⠰⣞⣏⡻⠀⠀⠀⡾⠻⠝⢿⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠘⣷⠀⣤⠁⣀⠀⠀⢺⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠐⠆⠀⠀⠰⠏⠀⠀⠄⣸⣆⠀⠘⠏⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⡀⠈⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠾⠃⠀⠀⠀⠰⣿⣏⠈⠙⠲⣦⢄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠷⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠀⠀⠀⠟⠀⠀⠀⠀⢀⣀⡀⡿
⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠐⢠⣤⡴⠂⠀⠀⣿⠁⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠃⠀⠋⠀⠀⠰⡾⠏
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⡀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⡗⢚⠉⢋⡡⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠰⠞⠂
⠀⢀⡀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣀⣀⣠⣴⣶⣾⣿⣶⣶⡶⠄⠀⠀⠀⣠⠀⠀⠀⡠⠉
⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠻⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢠⡏⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣼⠁⠀⡾⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣰⠇⠀⣸⠃⠀⢠⠏⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢠⡟⠀⢰⠇⠀⢠⠏⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠖⣾⠀⢸⠃⠀⡿⠀⢠⡟⠀⢀⡏⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣛⣭⠴⠒⠀⠀⡏⠀⣿⠀⢸⡇⠀⢸⠁⠀⣼⠀⠀⠠⣌⣙⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠏⢾⣿⣶⣞⣋⣥⣤⣿⣤⣿⢠⣼⡇⣤⣼⢠⣤⣿⣀⡀⠒⠦⣭⣛⠆⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠶⠈⢉⣠⠟⢑⣶⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣍⠓⠂⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠋⠉⠉⣉⣀⣤⡴⠾⣛⣵⡆⣚⣛⠧⣄⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣝⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⢋⣉⣉⣭⣴⡶⠿⣛⣭⠀⠉⠉⠙⣾⡇⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠛⠃⢸⣟⡳⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣉⣉⣉⣥⣴⡶⠿⣛⡅⠈⠑⣂⡴⣻⡣⢠⡏
⠀⠀⠀⠀⠀⢀⣤⠞⣋⡥⢒⡠⠄⠀⠀⢻⣟⠲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣉⣉⣉⣩⣭⣴⠶⢟⡋⢡⣞⣛⣽⣾⢟⣵⠟⢶⣄
⠀⠀⠀⠀⣰⠟⣡⡞⢡⡞⢉⡴⠊⡀⠀⠈⢿⣟⠒⠄⠀⠀⠀⠀⠀⠀⠀⣀⣉⣉⣉⣉⣭⣭⣴⡶⢿⡛⢡⡿⢿⣛⣭⡶⠛⠁⣀⢢⡈⢷⡄
⠀⠀⠀⠀⣿⠀⣿⠀⣿⠀⣿⡀⢾⡀⠀⠀⠀⠻⣯⡒⠀⠀⠀⠀⠀⠀⠀⠈⢉⣉⣭⣥⣤⠴⠶⣞⡛⣱⣿⣿⣿⣿⣿⢿⡌⢳⡈⣆⢳⠈⡇
⠀⠀⠀⠀⠻⣆⠹⣧⣌⠳⢮⣛⠶⣬⣁⠀⠀⠀⠈⠻⣥⣄⣀⠀⠀⠀⠀⠀⠤⠤⠶⢶⣶⣾⣿⣿⣿⣿⣿⢸⣿⡜⣿⢎⡇⢸⠇⡏⢀⡼⠃
⠀⠀⠀⠀⠀⠈⣳⣮⣙⠷⣦⣍⣙⠓⠦⠄⠀⠀⠀⠀⠈⠙⠻⢯⣿⣛⣛⣛⣛⣛⣯⣽⡿⠿⢛⣫⣵⡿⢋⣾⠟⣰⠟⠘⠁⢋⣠⣶⣿⠤
⠀⠀⠀⠀⠀⠀⠀⠨⠽⠿⠶⢮⣭⣙⣓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠭⠽⠷⠶⠶⠶⣚⣛⣋⣭⡵⠾⠛⢁⣈⣡⣤⣶⣾⣿⣿⠿⠭⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣉⣉⣹⣿⣿⣷⣶⣶⣶⣤⣤⣤⣤⣤⣤⣭⣭⣭⣭⣭⣭⣭⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣛⣉⣉⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠶⠶⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠶⠶⠶⠶⠶⠶⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⣛⣛⣛⣛⣛⣛⣛⣛⣻⣟⣛⣛⣛⣛⠛⠛⠛⠛⠛⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢉⣉⣩⣭⣭⣭⣭⣭⣭⣉⣉⡉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣄⠀⠀⠀⠀⠀⠀⠀⠠⢾⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣦⣄⣀⠀⢀⣤⣄⠀⠀⠉⠛⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠛⠛⠛⠋⠉⠀⢠⣿⣿⠁⠀⠀⠀⠀⠈⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣧⣀⠀⠀⠀⠀⠀⠀⠙⠻⣿⠁⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⡀⠀⠀⠀⣩⣿⡿⠉⠉⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠴⠾⠟⠋⠀⠀⠀⠘⣧⠀⠀⠀⢨⣿⣿⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⣼⣿⣿⡄⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣄⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠛⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢀⣀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣦⡀⠀⠀⠘⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⢻⣿⣿⣿⣿⣸⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢸⠏⠹⡇⢸⣿⣿⣿⣿⣿⡇⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡜⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠸⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠸⡉⢄⠀⢷⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡟⠀⠀⠀⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠈⠻⣿
⠀⣶⠀⠀⠀⠀⠀⠻⣼⢦⠘⡇⠀⠒⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⣠⣿⣿⣿⣿⣿⣿⣿⡁⠁⠀⠀⢸⣿⣇⠈⠉⢛⣫⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿
⠀⠘⣧⠀⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣾⠀⠘⣿⣿⣆⠀⠈⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿
⠀⠀⠹⣷⣦⣀⠀⠀⠀⠀⠈⢻⣿⣦⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠟⠋⠉⠀⠉⢻⣿⣿⣿⣿⡆⠀⢿⣿⣿⡆⠀⠈⢿⣿⣿⣿⣿⣿⣧⠀⠀⢸⣿
⠀⠀⠀⠹⣿⣿⠁⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠱⢦⣀⣠⣤⠀⠀⠈⠛⠿⣿⣿⣇⡜⡘⣿⣿⣿⡄⠀⠘⣿⣿⣿⣿⣿⣿⠀⠀⣸⣿
⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⣄⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣥⣄⠀⠀⠩⠿⢿⣶⣶⡇⠀⠀⠀⠙⢿⡼⣷⢿⣿⣿⡷⠀⠀⠘⣿⣿⣿⣿⡿⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠻⣿⣿⣿⣧⠀⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠈⣿⣹⣤⣿⠿⡥⠃⠀⠀⠸⣿⣿⣿⡇⠀⣸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣤⣤⣿⣿⣿⣿⣿⣿⣷⣶⣤⣤⣈⠻⣷⣦⣤⣴⣿⣿⠟⠁⡆⠀⠀⠀⠀⣰⣿⣿⣿⡇⢠⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢀⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡹⣿⣿⣿⣿⣿⠀⠀⠄⠀⠀⠀⠀⢸⣿⣿⣿⣧⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⣼⣷⣼⣿⣿⣿⣿⣿⣿⣿⡿⢡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣹⣿⣿⣿⣿⡇⠀⢰⣾⡟⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣼⣿⣷⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣰⣦⡀⠀⠀⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⡴⠛⠿⣿⣿⣿⣿⣿
⠀⢠⣿⣿⣿⣦⠀⠀⠀⠀⠀⠲⣌⠻⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠈⢻⣿⣿
⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠹⢶⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⣀⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠏⢀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⡿⠯⠥⢤⣱⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣸⡄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⣀⡀⣀⠀⡀⠀⣶⠀⠲⠀⠐⢁⡠⡀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⠀⢲⠀⢷⠀⢸⠀⠀⡆⠀⠀⢨⢸⡁⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡏⠒⠈⠚⠈⠊⠈⠊⠀⠉⠀⠈⠋⠑⠁⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣤⢤⣖⣒⣛⣛⣛⣛⣛⣛⣛⣒⣶⢤⡄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡇⠀⠀⢸⣤⣒⣒⠉⠛⠛⠛⠉⠑⣒⣒⣦⣼
⠀⠀⠀⠀⠀⠀⠀⡇⠠⠭⠍⠀⡇⠀⣠⠖⠉⠉⠲⢤⣤⡤⠖⠋⠁⠀⠀⡇⠀⠀⢸⡀⠀⠉⠉⠉⠉⠉⠉⠉⢉⡁⠀⡾
⠀⠀⠀⠀⠀⠀⠀⡇⠈⠥⠖⠀⡷⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⢀⣒⠒⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⢇⣀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⣧⣄⣀⣀⣀⣀⣀⣀⣀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠲⠧⠤⠶⠶⠶⠶⠶⠶⠒⠒⠒⠒⠒⠒⠒⠃⠀⠀⠀⠀⠈⠛⠒⠲⠶⠶⠖⠚⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣵⣾⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⢿⣻⣿⣿⣿⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠋⣀⡼⣿⣹⣿⣿⡆⠀⠈⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⣽⣿⣿⣿⣧⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣭⣿⣿⣿⣿⣿⣿⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣿⣿⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣾⣿⢿⣿⣿⣾⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡝⣯⡇⠈⢻⣿⣿⣿⣿⣿⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣡⣼⣷⢸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣱⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧

⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡠⡄
⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⡠⡜⢄⠉⣇⣀⠀⠀⠀⠀⡠⡀⠀⠀⠀⠀⠀⡠⠚⠢⢠⠀⠀⠀⠀⠀⠀⠐⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢍⠳⢘⡌⠢⡨⠊⠀⠀⠰⠝⠊⢀⠀⠀⠀⠊⠈⢃⡀⠤⠆⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⡏⡭⡢⡀⠙⠢⠅⢀⡴⢊⠁⠀⠰⠇⠀⠈⠀⠀⠀⠀⣠⡄⠀⠀⢀⠀⠀⠀⠰⡹⠁⠹⠂
⠀⠀⠀⡖⠢⡀⠘⢄⡚⡀⠀⢀⠔⠉⠀⠣⠐⠀⠀⠀⠀⠀⠐⠂⠀⠄⠻⢀⡠⠐⠁⠀⠀⠀⠛⠃⢀
⠀⠀⠀⠘⢄⠑⠄⡄⠀⠀⠘⠀⠀⠀⠀⠀⣠⡾⢑⢄⠀⠈⠐⠁⠀⠐⠂⠁⠀⠎⠐⠀⠀⠀⠀⠀⠃⠁
⠀⠀⠀⠀⠈⠒⠊⠀⠀⠀⠀⠀⠀⠀⣰⢯⣲⠃⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀⢀⠀⠀⠄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⠞⢛⣼⠃⡐⠀⢀⠀⡰⡡⢀⠀⠀⠀⠀⠛⠀⠀⠈⠀⠀⠀⠐
⠀⠀⠂⠀⠀⠀⠀⠠⡒⠁⠀⠀⠀⠉⢤⡾⠋⢉⠔⠀⠀⠈⢄⣔⢲⠇⠀⠂⠂⠢⡀⢀⠾⠆⠀⠞⢂⠄
⠀⠀⠀⠀⡀⢄⡀⠀⠈⠈⠁⠀⠀⢀⠀⠀⠀⠁⠀⢀⢤⡀⠀⠉⢻⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠁⠀⠀⢀
⠀⠀⡄⠊⡤⠊⠑⡀⠀⠀⠀⠀⠒⠀⠆⠀⠀⠀⠰⡟⠋⡰⠀⠀⠈⢇⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠈⢎⠀⠀⠅⠅⠀⠀⠀⠀⠀⠆⠐⠄⠀⠀⠀⣵⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⡁
⠀⠀⠀⣊⡇⠀⠀⠀⠀⢀⠊⠀⠉⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠊⠉⠉⠀⠀⢠⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⣀⠀⠀⣈⠀⠀⠀⠀⠂⠀⠀⠠⠒⢀⠀⠀⠒⠀⠀⠠⡀⠀⠀⠀⡞⠂⠂
⠀⠀⠀⠀⠀⢶⣀⠀⢀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠐⠀⠀⠐⢄⣀⣶⣠⡔⠁⠀⠀⠀⠁⠀⠘
⠀⠀⠀⠀⠄⠄⠌⠍⡒⠀⠀⠀⠀⢀⠴⣗⢄⠀⠀⠀⠀⠀⠀⠀⠌⠍⢿⡇⠀⡃⠀⠀⠀⣀⣀⡀
⠀⠀⢠⢆⠀⢊⠈⠌⠀⠀⠀⠀⣰⡁⠀⠈⡪⠇⠀⠀⠄⠀⠀⠀⡂⠀⢺⣇⣀⡁⠀⠸⠛⠃⠉⢁
⠠⠀⠀⠀⠁⠆⠆⠀⠀⠀⠀⠀⠀⠀⢠⢊⠀⠀⠀⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢆⠄⠀⠘⠃⠀⠀⠂
⠀⠀⠄⠆⠶⠲⠀⠀⠀⢀⠀⠀⠀⠀⠈⠈⠀⠀⠘⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⢀⣤⣾⣸⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠰⠟⠙⠾⣷⣶⣮⣾⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⠶⠀⠀⠀⠈⢿⣿⡟⡘⠂⠀⠀⠰⢀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣋⡭⠀⠀⠀⡀⠀⠀⢠⣠⣀⡄⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣠⠚⣽⡁⣴⣿⠏⠁⠀⠀⣠
⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠹⣿⣭⣽⠁⣠⠔⢩⡇
⠀⠀⠀⠲⣄⠀⣀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣯⣿⠋⠀⢀⡨⠃
⠀⠀⠀⠀⠘⠷⠟⠛⢷⣤⡄⣢⡀⠀⣀⠀⢀⡜⢁⡔⠀⢀⠀⢰⣶⢬⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⢇⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠿⠿⠿⠿⠛⠚⠿⠿⠞⢧⣀⣏⣠⡦⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⡉⠤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠠⢤⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀⠁⠀⠀⠈⠓⢄⡀⠀⠀⠙⠀⠒⢦⠀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠁⠈⠒⢤⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢡⡀⠉⡐⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠉⠀⠠⢀⠀⠉⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠈⠸⣧⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⢠⡀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣧⠀⡀⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠠⠀⠈⣳⠀⢿⠀⠀⠀⠀⠀⢠⠀⠀⢠⠀⠀⠀⣷⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠸⡄⠀⠀⣹⡆⢀⡀⠀⠠⠀⠀⣸⠀⠀⡎⠀⢀⣼⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣠⡟⣰⡇⠀⠐⣿⠁⠀⡇⠐⠁⠠⣰⠇⢠⣿⣧⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠻⠷⠷⠶⣿⣶⣾⣷⢂⣀⣴⣏⣠⣾⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠤⠤⠴⠶⠦⠤⠤⣀⡀
⠀⠀⠀⠀⠀⢀⡄⢀⡤⠖⠋⠉⠀⢀⡠⠴⠒⠚⠛⠛⠛⠒⠀⠉⠛⢦⣄
⠀⠀⣀⢶⡒⠈⡷⠉⠀⢀⠀⠀⠈⠁⠀⠀⣀⣠⠤⠴⠒⠒⠀⢀⣀⣠⠽⢚⡥⣰⠃
⠀⠀⠉⢢⠄⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣀⡤⠶⠊⠉⠠⠒⣩⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣤⣤⡤⢤⣤⣀
⠀⠀⣰⠃⠄⠀⠀⠀⠀⠐⠂⠤⠤⠤⠤⠤⠤⠐⠒⠉⠀⠀⠀⠀⣠⡴⠞⠁⡌⣇⠀⠀⠀⠀⢀⣀⡠⠔⣉⠤⠒⠉⠀⠀⠀⠀⠀⠀⢉⣲⣄⣀⡴⠋⡙⠛⢶⡄
⠀⢰⠃⡜⠀⢠⠂⠀⠀⠀⠀⡀⢀⣀⣀⣀⣀⣀⣤⣤⠤⠶⠚⠋⠁⠀⠀⠀⢱⣹⠀⠀⣠⠞⠩⠎⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⢿⣀⡠⠀⠹⡄
⠀⡟⢠⡆⠀⡇⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⣼⠃⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⣆⢷⡠⠔⠀⡇
⠀⡇⢸⡇⠀⢀⠄⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢸⠆⠀⡇⢰⢻⠸⡀⠀⠀⠀⠀⠀⢈⣉⣉⠉⠑⠒⠤⣄⡀⠀⠀⠀⠀⣠⠟⡾⠇⠀⣸⠃
⠀⣧⠀⠇⣠⠋⣠⣤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⡇⢸⠸⢀⠓⢦⣄⣦⠤⣄⣀⠀⠈⠙⠲⢤⡀⠀⠉⠓⠶⠶⠾⣫⠀⡷⠴⠚⠁
⠀⢻⡀⠀⡏⣾⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣱⠀⠀⣸⠁⠘⣇⣸⠰⠀⠀⣤⠀⠀⠉⠙⢦⡀⠀⢀⠙⣆⠐⠀⠀⠀⠊⠁⡔⡇
⠀⠘⣷⠀⠀⠙⢮⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡼⣰⠃⠀⠀⠈⢿⠀⡄⠀⠈⠀⠀⠀⠀⠀⠃⢸⡍⢱⡈⠀⠀⠀⢀⠄⡼⢡⡇
⠀⠀⠸⣧⡀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⣠⢞⡵⠃⠀⠀⠀⠀⢸⡘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠈⢬⠼⠁⠀⠀⠂⣡⠞⢁⣾⠁
⠀⠀⠀⠈⠳⣄⡙⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⢉⡴⠋⠀⠀⠀⠀⠀⠀⠀⢷⣄⣀⡤⠎⠀⠀⠀⠀⠀⠀⢠⠀⠀⠐⠒⠉⠀⣠⣿⠋
⠀⠀⠀⠀⠀⠈⠙⠓⠺⠷⠦⢄⣀⡀⠀⠀⠀⠀⢀⣀⣀⡤⠖⠋⠀⠰⠿⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠂⠤⠤⠖⣋⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢳⡄⠈⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠙⠒⠤⣄⡀⠀⠀⣀⣠⣷⣤⠤⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠓⠤⠍⠓⢤⡀⠀⠀⠀⠀⠀⠀⣠⣶⣷⣦⣀⣀⠀⠀⠀⠀⠀⢀⡨⢆⣀⢎⡀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡟⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠰⡄⠀⠀⠀⠀⢡⠈⠧⠀⠀⠀⠀⠹⣿⣿⣿⡿⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠇⠀⠀⠀⠀⠀⡆⠣⢄⡀⠀⠀⠀⠀⠙⠛⠁⠀⠀⢀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠛⠃⠀⠀⠀⠀⠀⠀⢡⠀⠀⠉⠙⠒⠶⡶⠜⣦⠤⠴⠚⠉⢈⠀⠀⠀⠀⠀⠀⠸⣄⣠⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⠊⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠳⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⡞⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⠲⡄⠀⠀⢀⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⢠⠇⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠦⠤⠿⠗⢒⠋⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢑⣠⠀⡀⠀⣀⣠⣼⢰⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⢀⠞⠉⢂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠙⠾⢦⢰⣴⡉⡿⠾⠛⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠃⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⠤⣤⣄⣀⣤⡤⠤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣄⡤⡀⠀⣏⠋⡢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢮⠀⢀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠤⠜⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠈⠰⠩⠽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠛⠉⠉⠁⠀⠀⠀⠀⠉⠉⠙⠳⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣡⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣟⠓⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠟⠛⠛⠿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠁⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠈⣧⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢾⡏⢳⡀
⠀⠀⠀⠀⠀⠀⠀⣾⢁⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣾⡇⠈⣧
⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠈⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⣠⣿⠀⣰⡟⡇
⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠉⠻⣿⣻⣧⠀⠀⠀⠀⠀⢹⣿⣷⠀⠀⠀⠀⠀⠀⣀⣼⡿⣷⣤⣴⣾⣿⣷⣾⣿⣠⠇
⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⣾⣿⢿⣦⣶⣤⣶⣾⣿⠟⠛⠛⠛⠛⠉⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⢸⣇⣀⣤⣶⣶⣤⡀⠀⠀⢸⣿⣿⣶⣶⣾⡿⠟⠛⠛⠛⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠈⢻⣿⠋⠉⠙⠻⣷⣤⣾⡿⠋⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠘⣿⣄⡀⣀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠴⠶⠒⠒⠒⠒⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣇⣀⡀⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠈⠉⠓⢦⡀⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢿⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣸⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢀⣀⣀⠀⠠⢤⡀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⡿⠀⢀⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠋⠉⠉⠙⠳⢦⡉⠳⡄⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⢀⡼⠃⢀⡼⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠙⣦⠙⠆⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⣾⣥⣤⡤⠴⠛⠓⠛⠻⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⢀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⣸⣧⣄⣠⣤⣤⠴⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⡴⠶⠦⢭⡀⠀⠀⢀⡿⠦⠤⠴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠀⠀⠀⠀⢹⣦⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⣀⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⢶⠶⠶⢶⣶⡶⢶⠶⠶⠶⠶⠶⠶⢶

⠀⠀⠀⠀⠀⣠⡤⠤⠤⢤⣤⣤⠤⠤⠤⣄⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣰⢀⡒⣎⠜⣁⠦⣤
⠀⠀⠀⠀⠀⣿⡂⠀⠀⢸⣿⣇⣀⡀⠀⣿⠀⠀⠀⠀⠀⢠⡿⠿⠿⠚⣿⣶⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⡿⠿⠿⢿⣿⡾⢷⣦⣌⣔⠁⡸
⠀⠀⠀⠀⠀⣿⡿⠿⠿⢿⣿⡿⠿⠛⠛⣿⡀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣿⣿⣀⣀⣀⣀⡶⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⢸⣿⡇⠀⠀⠉⢹⡇⣘⠋
⠀⠀⠀⠀⠠⣿⣀⣀⣀⣸⣿⣇⣀⣀⣀⣿⠂⠆⠀⠀⠀⢠⡿⠿⠿⠛⣿⣷⡿⠿⠿⠿⡇⠀⠀⠀⠀⠀⠐⣶⣿⠿⠿⠿⢿⡿⠛⠿⠿⢿⢿⡇⢉
⠀⠀⠀⠀⠈⠿⣿⣿⠿⣿⡏⢛⠛⠛⠛⠿⡡⢘⠂⠀⠀⠸⣇⣀⣀⣀⣿⣿⣀⣀⣀⣀⡿⠀⠀⠀⠀⠀⠐⣯⡵⠀⢀⡠⠸⡄⠀⠀⠀⠀⢠⠀⡶
⠀⠀⠀⠀⢠⣾⣿⣿⠿⠛⠀⠀⠀⠀⠠⠄⠳⡇⠀⠀⠀⢀⡿⠛⠛⠛⣿⣿⠿⠿⠿⠿⡇⠀⠀⠀⠀⠀⠀⠛⠛⠉⠉⠘⠓⠀⠀⠀⠀⠀⣟⣰⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠸⣇⣀⣀⣀⣿⣿⣀⣀⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠛⠛⣿⣾⠟⠛⠛⢻⡄⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⣄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⣇⣀⣀⣀⣿⣷⣀⣀⣀⣸⡇⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢠⣾⠋⠁⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⢰⡟⠛⠋⠙⣿⣿⠛⠛⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠤⠀⢀⣴⣿⣅⡀⣸⠏
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢒⡒⠛⠙⠀⠀⠀⠀⠀⠸⠧⠤⠤⠤⠿⠿⠤⠤⠤⠼⢇⣤⡴⠓⢄⠀⠀⠀⠁⠀⠀⢀⣼⣿⡟⠙⠻⣿⡏
⠀⠀⠀⠀⠀⣇⡀⠀⢀⡀⣀⣐⠤⢩⡿⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⣿⠟⠁⣠⠼⠃⠀⠀⠢⠀⢴⣋⣾⡟⠀⣠⣰⠏⠘
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⡶⣾⣿⠏⠙⢾⣻⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢤⣱⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣿⡇⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⠞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣡⠶⠋⡹⠋⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⣠⠞⠂⠀⣼⠁⢠⠀⠀⠀⢈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠛⠀⠀⣴⢃⣠⡦⠄⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠈⠂⠀⠚⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⡤⠚⠀⣠⣦⠰⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⢾⠆⠀⠀⠀⠀⠀⠀⠌⠃⠀⠁⠈⠉⢒⡆⠀⠙⣿⠀⡆⠐⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠳⣤⢀⡉⠻⠀⢇⠀⠀⠁⠀⠀⠀⠀⠀⠀⣸⠇⠀⢸⡿⠀⠀⢠⠗⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠱⣤⠦⠈⠢⣀⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠏⣰⡿⠚⠁⠰⠟⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⢀⡤⠃⠀⠀⠉⠻⠆⠐⠶⠚⠾⠃⠀⠀⠶⠀⠀⠒⠛⠉⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠠⡟⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⣦⡀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠁⠀⠀⢠⠀⠀⠀⠈⠁⠀⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣅⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡿⣧⠀⠀⠶⣦⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡤⠶⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣷⠉⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣧⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠘⠀⠀⠀⠀⠀⠀⠐⠒⠲⠚⠀⠀⠀⠀⠀⠀⢀⣤⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⢠⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡟⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢤⣿⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡜⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠀⠀⠘⠀⠀⠀⠀⠀⠀⠤⠠⠀⠀⠀⠀⠀⠘⠀⠀⢸⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⠇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠘⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣶⣶⣶⣶⣶⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘






⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣾⣶⣶⣶⣾⣶⣾⣶⣿⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣟⣻⡟⢿⡿⢿⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣷⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⣳⣦⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣄⣀⣤⣶⠟⠃⠀⢿⣿⣿⣿⢻⠻⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈⣿⣿⣿⣇⣷⢹⣿⣽⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡀⠀⠀⠀⠀⣿⠿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⢹⣿⣦⢠⣤⢀⡀⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⢠⠦⣠⣶⣦⣤⣤⣤⣵⣦⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣏⣾⣿⣿⣶⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⢠⣀⣴⣿⣿⣿⡿⢉⠀⠀⠀⠰⣦⣤⣄⣀⠀⠀⠉⢩⣀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣾⣧⣶⣴⣸⣿⣿⣿⣿⣶⣶⣿⣿⣿⡿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠛⠇⠀⠁⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠠
⡄⠀⠀⠀⠀⠀⠀⠀⠉⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣼⣿⣿⣿⣿⣿⣿⡇⣹⡁⢀⣴⡀
⣿⣶⣄⣠⣾⣿⣿⣿⣾⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠛⠉⠿⣿⣏
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⣿⣿⣯⣷⣿⣷⣿⣿⣦⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⡶⠶⢶⣶⡶⠶⠾⠿⠿⢿⢿⡿⠿⠿⠿⣷⢶⠶⠶⠶⠶⢶⣶⣦⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢸⠸⡇⠀⠀⠀⢿⢸⠀⠀⠀⠀⠀⣿⢸⡀⠀⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⡏⡇⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣀⣀⣀⣧⣷⣀⣀⣀⣀⣸⣠⣇⣀⣀⣀⣸⣿⣀⣀⣀⣀⣀⣿⣸⣀⣀⣀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠉⠉⠉⠉⠛⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⢸⡿⣤⣀⡀⣀⣀⣀⡤⡞⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠳⡄⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣬⡉⠉⠉⠉⣁⣠⣶⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠹⣄⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠙⣦⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠈⢧⠈⣿
⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠈⢳⣽⡇
⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⢀⡤⠖⠛⠓⢦⠀⠀⠀⠀⢀⣠⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿
⠀⠀⠀⠀⠀⢠⣿⡀⠀⢀⡞⠁⠀⠀⠀⣸⠃⠀⠀⠀⡟⠀⠀⠀⠹⣄⠀⠀⠀⣴⠖⠒⢦⡀⠀⠀⠀⣿⠷⠦⣄⠀⠀⢠⠶⠒⢦⡀⠀⣿⡆
⠀⠀⠀⠀⠀⢸⡟⠙⠛⠉⠀⠀⠀⠀⠀⠻⣄⠀⠀⣠⠇⠀⠀⠀⠀⠙⠲⠤⠞⠃⠀⠀⠀⣇⠀⠀⢸⡏⠀⢀⡟⠀⠀⢸⠀⠀⠀⡇⢀⣼⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⣻⡇⠀⢸⣇⠀⣀⡼⠀⠀⠀⠉⠉⣿⠃
⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢀⣿⢿⣆⣴⣾⡆⠀⣀⠀⠀⣿⠇⠀⣿⠀⠀⣀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠘⣿⠈⠛⠁⢸⣇⠀⣩⡀⠀⣿⠀⠀⣿⣴⣿⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠹⠇⠀⠀⠸⣿⠀⢿⠇⠠⡿⠀⠀⣿⠉⠻⣦⡀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣠⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠶⣶⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣿⣀⣤⡶⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⣄⣼⡿⣷⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣶⡏⢟⡇⠻⢿⠿⣇⠊⢳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠁⠋⡿⡿⠿⢶⢷⡌⢀⣼⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⠶⠿⡏⠂⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠙⣻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⡿⠂⠁⠀⠀⢠⡀⣀⢂⠀⠀⠀⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣬⡙⢋⠇
⠀⠀⠀⠀⠀⣠⣶⡿⠿⢫⠙⠿⠶⠒⢂⠐⠛⣄⠻⠿⠻⠁⠀⠀⠠⣆⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡂⢦⢢⣦⣼⡇
⠀⠀⠀⢀⣾⣷⣮⡀⣠⣀⡄⣀⠀⣰⣺⣠⣀⢿⠋⠀⠀⠡⠀⠀⠀⠈⠝⠀⠀⣿⡛⠶⣤⠀⠀⠀⣼⣿⣶⣿⣿⡿
⠀⠀⢀⣾⣿⣿⡟⠁⠈⣛⣾⡿⠒⠺⣿⣿⣉⠀⠀⠀⢀⡴⡆⠇⢠⠀⠀⠀⠀⠈⠛⠂⠈⠁⠀⢸⡿⢿⠿⢿⡿⠁
⠀⠀⢸⣿⣿⣟⠂⠀⣼⢿⡿⠁⠀⢠⣿⣿⡇⠀⠀⢀⠊⢠⠇⠀⠠⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⢹
⠀⠀⢸⣾⣿⡏⠀⠀⢻⣸⣄⣼⠯⠛⢱⣶⣬⠀⠀⠈⠀⠁⠀⠀⠄⠈⠒⠦⠄⠀⡀⠀⠀⠀⠀⠀⠒⠃⡠⠂
⠀⠀⠘⣿⡜⡿⠁⠀⠸⣷⡜⣿⡷⠀⢘⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠁
⠀⠀⠀⢿⡷⣘⣴⣦⢀⠀⣤⣿⠃⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠘⠬⢀⡀⣀⢀⡀⠤⠄⠐⠊
⠀⠀⠀⠘⣿⡹⣿⣷⢀⢸⣿⣇⠀⠀⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⣀⠇
⠀⠀⠀⢀⠈⢀⠘⣿⣷⡍⢻⣶⣿⡉⠑⠚⠁⠀⠀⢀⣠⠤⠖⠊⠁
⠀⠀⠈⣾⣶⣿⡇⣾⣿⣽⣿⣿⡿⠇
⠀⠀⠀⠙⠝⠟⠿⣿⣦⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⠶⠶⠶⠞⠛⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠶⠞⠛⠛⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⢸⡆⠀⡇⠀⡆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⣾⠀⠀⢸⠀⠀⣿⠀⢸⡇⠀⢸⣀⣀⣧⣤⣧⡤⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⣸⣀⣠⣽⣤⠶⠷⠛⠛⠉⠉⠁⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢷⡖⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠹⣄⠀⠀⠐⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⢀⡼⠃⢀⣀⣤⡤⠴⠶⠚⠛⠉⠁⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⢠⡿⠷⢿⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⢀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠶⠿⣦
⣿⠁⠀⠀⠀⠈⠉⠛⠒⠦⠤⣄⣀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠴⠖⠛⠋⠉⠁⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠦⢤⣀⣘⠆⣀⣀⣤⠤⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⠀⢸⡇
⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⣴⡄⠰⡟⣷⠞⣹⠆⠸⡇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⢸⠀⠀⢰⠲⡆⠀⣾⣆⠈⣏⢿⢻⡘⡇⠀⣷⠀⢠⣏⠀⠀⣿
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⡆⠀⢸⠀⠙⢶⠇⠹⡆⢻⢸⣼⡇⣿⣀⣽⠀⣶⣝⢦⡀⢿
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⢀⠀⢀⡀⢹⣼⡎⣿⣧⣈⣠⣿⣧⡽⠘⠾⠁⢸
⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⠀⡟⣧⢘⣿⣦⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⠚⠃⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⠀⠠⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⣿⠀⠀⣒⠦⣭⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⠀⢠⣭⣟⡒⠦⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣿⠀⠈⡇⠀⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⢹⡀⠀⢇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠘⣧⡀⠈⠳⢦⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠞
⠀⠀⠀⠀⠀⠉⠙⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⣀⣤⡴⠶⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢶⣤⣄⣀⠀⣸⣤⡶⠞⠋⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⠁⠉⢉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠆⠸⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢲⡼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡄⣤⣶⣶⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣷⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠁⠙⢿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠛⠛⠉⠀⠀⠀⠀⠀⠀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣷⡄⠀⠀⠀⠀⠀⢀⡀⠀⠸⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣦⣗⢀⣀⣴⡏⠁⠀⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣟⢀⣾⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢿⡏⢻⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⡀⣀⣈⣡⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣸⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⣬⣉⠉⣉⢁⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢹⡏⠀⢫⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸⡇⠀⠘⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣇⡀⠀⠀⠀⠀⣠⣁⣴⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣷⣦⣴⡦⢞⣱⣿⡿⣀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣶⣤⣍⠛⠛⣯⣿⡽⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠦⠐⠒⠂⠉⠉⠀⠀⠐⠢⠤⣄⡀
⠀⠀⠀⠀⢀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠈⠒⢆
⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⢠⠀⠄⠀⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠑⠂⡀
⠀⣴⠁⠀⠀⠀⠊⠀⡀⠀⠀⠠⠠⠔⠀⠀⠀⢀⠠⠄⠀⠀⠀⠀⠀⠀⠀⢰
⢀⠟⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢀⣀⠠⠐⠊⠁⠀⠉⠉⠓⠂⠤⢀⣀⣀
⡇⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠓⠄⠀⠀⠀⢠⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠢⢀
⢈⠀⠀⠀⠀⠁⠀⠀⠀⠠⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠜⠀⢀⠔⠁⠀⠀⠀⠀⡈⠈⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⢲⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠙⣄
⠈⣄⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠎⠀⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡔⠁⠀⠀⠀⠠⣁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡆⠉⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠳⣌⠂⠄⡀⠀⠀⠀⠀⠀⠀⢀⠈⠈⠀⠀⠤⠤⠤⢀⣀⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒
⠀⠀⠀⠀⠙⢆⡀⠀⠉⣉⡠⠜⠋⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠟⠁⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂
⠀⠀⠀⠀⠀⢀⡩⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠤⠔⠀⠀⠀⠀⠀⠀⢀⠊⠁⠀⠀⠀⠀⠈⣀⡠⠀⠀⠀⠀⢰
⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⢦⡑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠈⠀⢀⠀⠀⠀⣇⠀⠂⠤⣀⠀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⢠⠊⠁⠀⠀⠀⠀⠀⢀⠎
⠀⠀⢠⠃⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠷⣄⣀⠀⠉⠂⠄⡀⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢠⠟
⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⠈⠉⠉⠢⣀⣀⠀⠀⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠈⡏⠉⠉⠑⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁
⠀⠀⢰⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠹⡀⠀⠀⠀⠀⠀⠙⠒⠤⠴⠒⠊⠉
⠀⠀⠀⠣⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠂⠀⠀⠠⠤⠘⠀⠀⠀⠰⠀⠃⠀⠀⠀⠂⡀
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⡸⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡰⠃⠀⠀⢠⠀⡂⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠃⠌
⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⣈⡠⠤⠐⠊⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠲⢌⣀⡐⠀⠀⠊⠁⢀⡠⠤⠤⠴⠚⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣶⣶⣶⣶⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣉⣉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⢶⠶⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⠋⠁⠀⠀⠈⢡⣶⣿⡎⡳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠉⣷⣴⣿⣿⡇⠀⠀⠀⠀⠉⠋⠑⠃⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢃⡀⠀⠀⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠳⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⢳⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢀⡠⣄⠀⠀⠀⠀⠀⠀⢸⣿⣿⠯⠖⠀⠀⡀⣼⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢠⣿⣿⠉⠀⠀⠀⣴⣶⡄⠀⠉⠁⠀⠀⠀⠐⠇⠃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡄⠀⠉⠁⠀⠀⠀⠀⠨⡝⠁⠀⠀⠀⠀⠀⠀⢀⣴⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀⠀⠀⠀⠀⢀⠀⣀⣀⡀⠀⠀⠀⠠⢞⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣦⡀⠀⠀⠚⠸⢿⣿⡿⠀⢐⣣⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠶⠶⠶⠒⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠚⠉⠉⠉⠙⠒⠒⠒⠒⠒⠒⠒⠒⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁⠈⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠱⡄⣀⣀
⠀⠀⠀⠀⠀⠀⢀⠴⠚⠉⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠁⣀⠴⠉⠀⠀⠉⠲⣄
⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠈⡆⠘⠀⡀⡂⠀⠀⣠⡳⣸⠞⠁⠀⠀⠀⠀⠀⠀⠈⠑⠦⢤⣀
⠀⠀⠀⢀⠎⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⠀⠀⠀⠀⠀⣰⢣⡟⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢆
⠀⠀⢀⠞⠊⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠃⢸⠀⠀⠀⠀⡸⢁⠏⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠐⠒⠋⠉⠑⠲⢌⣇
⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⢃⠎⠀⠀⠀⠀⠀⢀⡠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢢⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⡜⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀
⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⢣⠀⠀⠀⠀⢿⠀⡀⠀⢸⠃⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⣄
⡇⠀⠀⠀⠀⠀⠀⠀⠄⠄⡀⠒⠈⢯⣆⠀⠀⠀⢸⠘⡡⠀⢸⠀⣠⠀⣰⠃⠀⠀⠀⠀⠀⠈⠠⠠⠄⠀⣀⣀⠀⠀⠀⠉⠣⠀⠀⠘⣆
⢧⠁⠤⣔⡒⡛⠛⣡⣠⠤⠖⠛⠚⠚⠛⠛⠶⠤⣬⣦⣘⣇⣼⠀⠁⢀⠃⠀⠀⠀⠀⠀⢀⣤⠶⠒⠋⡩⠩⠍⠉⠭⠝⠛⠻⣄⡀⠀⠸
⠈⠓⠤⠤⠔⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣸⠇⠂⠀⠀⠀⢠⠖⣩⠤⠒⠚⠉⠉⠉⠐⠓⠒⠢⠤⣀⡀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠄⡀⡄⣴⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣸⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡈⢺⣹⠋⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣾⠇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡸⠴⠖⠒⠒⠲⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠉⠁⠀⠀⠀⠀⠀⠒⠦⣄⠙⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠃⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄⢘⢧⠀⠀⠈⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⡀⡇⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⡀⠐⠀⠂⠔⠠⠈⠐⠠⢀⠀⠀⠀⠀⢠⠇⢠⠇⠀⣠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⣊⣠⠾⠖⠋
⣶⣶⡶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣦⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣲⢬⣽⣯⣿⣿⣿⣷⠆⠁⢀⠀⠀⠀⠐⠄
⠀⠀⠁⠀⠀⠀⢀⡴⠞⠩⢛⣩⣽⣾⣿⣿⣿⡿⣿⣇⠀⠀⠠⣓⢤⡀⠑
⠀⠀⠀⠀⠀⣶⣟⡵⢣⢘⡵⠟⠁⠉⠀⠀⠀⢠⡾⠋⠀⠰⣾⣯⡻⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠒⢲⣄
⠀⠀⠀⠀⢰⠏⠏⠀⠰⠋⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠘⢿⣿⣿⣿⡄⠀⡠⢶⠶⠆⠀⠈⠀⠀⠀⠀⠉⠀⠠⠤⣤⣄
⠀⠀⢠⡆⠀⠀⠀⠀⠀⢸⡟⠁⠲⢦⣄⣼⠟⠀⠀⠀⠀⣀⠀⠀⠙⣿⣿⡿⣄⠃⠀⠀⠀⣀⠀⠀⡇⠀⠀⠀⣀⠀⠀⠀⢸⣧
⠀⢀⢸⡇⣁⢀⡉⢡⡏⣿⠃⣰⣦⡀⠉⠉⢀⠀⠀⠀⣸⣿⠇⠀⠀⣨⣿⣉⠛⠀⠀⠀⠀⠐⠛⡏⠁⠀⠀⠰⣿⡇⠀⠀⠀⠉⢀⡀
⠀⣼⠀⢰⣧⣾⣿⢸⡇⢿⠀⠙⣿⠇⢀⡄⠈⠳⣦⡀⠀⠁⠀⠀⠰⣿⠇⢙⡆⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⢲⡄
⠀⢏⠀⢸⣿⢿⢻⠸⣧⡘⣷⠀⠀⠀⣸⠁⠀⢰⣄⠙⢦⣀⠀⢀⡇⣿⠀⢸⡟⠀⠀⠀⠀⣸⣦⡀⠀⠀⠀⠐⠀⠀⠀⣠⣿⡆⠀⠀⢠⡇
⠀⠸⣆⠀⢻⡎⠇⢧⡟⡱⠘⣧⣀⠀⠋⠀⠀⢸⣿⣷⣄⠙⠳⠾⡁⢹⣆⠀⠃⠀⠀⠀⢼⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠻⣿⠛⠀⠀⠈⣿⢶⣄
⠀⠀⠈⠀⢾⠙⠚⠚⠀⠛⠂⡉⡁⠈⣁⠀⠀⠿⣿⣿⣿⡇⠀⡜⠁⠀⠈⠀⠀⠀⠀⠀⠀⠹⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢈⣠⡴⠾⠀⠚⠾⣿
⠀⠀⠀⠀⠈⠁⢷⠀⢠⢲⠀⠻⣜⣎⠁⠀⠀⠀⠀⠙⣿⠁⠈⠀⠀⠠⠀⢠⣄⠀⠀⠀⠀⠀⠈⠰⠀⠀⠀⠠⠀⠀⡀⠀⡉⠀⠀⢠⠗⠳⠦⠤
⠀⠀⠀⠀⠀⠀⠀⠌⡄⢆⢣⡀⠙⢿⡓⠀⡀⠀⠀⠀⠀⣄⠀⠀⡐⠁⠀⣿⣿⣷⡄⠀⠀⠉⠀⠀⠀⠀⠀⠀⣀⣀⡤⠀⠀⠎⢈⠷⣶⠐⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠈⢞⣌⢦⡳⡀⠈⡷⠠⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠙⠻⣿⠇⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠒⣀⢠⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠈⠀⠈⢫⣢⠑⡬⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠄⠒⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⡀⠀⠄⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢠⡄
⠀⠀⠀⠀⠀⠀⠈⣠⣄⡀⣈⠲⡌⠣⡀⢤⢀⠀⠊⢧⠐⠁⠀⡰⠴⠄⠒⠦⠍⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠘⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠐⢎⡸⣿⣋⠈⠓⠈⢓⡻⣯⡀⢸⣧⠀⣀⠀⣤⡾⠀⠉⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠰⠀⠀⡀⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠠⠀⠀⠀⠀⠠⣿⣟⢆⠸⣆⠨⣤⣷⣶⣤⡶⠚⢴⣦⣱⠎⠀⠈⠀⠀⠀⠀⠀⠀⠠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠈⠲⢾⣶⣦⣿⣿⣈⢦⡘⣴⣻⡿⠏⣯⠀⠀⡉⣴⠇⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠂⠼⠀⠹⣎⣷⠸⠁⠀⠀⣁⡀⠀⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡽⣇⠀⢀⣾⠉⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢻⡄⠈⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠂⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠐⠒⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢁⠈⠀⠀⠒⠂⠈⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠒⠂⠀⠈⠐⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠠⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠒⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠒⠢⡀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠶⢺⡀⠀⢁⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⢂⣹⠀⠀⣏⠉⢵⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⢋⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡠⠒⠡⠐⢧⠀⠱⣀⡀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⣀⡀⠀⡈⡗⢤⡈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⡜⢀⢊⠐⠁⠀⠀⠀⠑⢤⡈⠑⠂⠷⠤⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⠴⠊⠉⠀⠀⠀⢀⠻⠲⡐⠄⠑⡀
⠀⠀⠀⠀⠀⠀⠀⡇⠆⠀⠀⠀⠀⠀⠀⠀⡼⠉⠑⠂⠠⠀⢤⡀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠡⠁⠀⠀⠀⠀⠀⣠⠞⠀⠃⠀⢨⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢱⡈⠀⠀⠀⠀⠀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠙⢒⠉⠀⠀⠒⠀⠀⠀⠀⠀⠀⢀⣁⠤⠖⣒⠼⠶⠶⠦⠤⠶⠚⠁⠀⠀⠀⠠⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠠⠆⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⣠⠴⠶⠒⢉⣡⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠊⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠂⠌⡁⠂⠠⢀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠉⠀⠀⠔⠊⠁⠀⠀⠀⠀⢀⣀⣀⣤⣤⡤⠴⠒⢈⠠⢐⡮⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠄⣀⠀⠀⠀⠈⠉⠁⠒⠒⠀⠤⠤⠤⠤⠤⠤⠠⠤⠤⠶⠶⠾⠛⠛⠓⠊⠉⠉⠠⠀⠂⢀⠠⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠠⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠐⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠃⠐⠒⠒⠒⠒⠒⠒⠒⠂⠋⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⣠⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⣤⡴⠋⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣸⠀⠀⢻⣏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣧
⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣫⣷⣿
⠀⢸⡿⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⡿⢟⣭⣴⢿⣿⢿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣿⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣿⠿⣻⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⢽⣶⣿⣿⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⣏⣽⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⣠⣤⣀⠀⠀⠀⢀⣄⣀⠀⠀⢀⣀⡀⠀⢀⣀⡀⠀⠀⠀⠀⢀⣀⡀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⢀⣾⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⠀⠀⠀⠀⢸⣿⡇⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣿⣿⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⣿⣿⠻⣷⡀⣼⡟⣿⣿⠀⠀⣿⣿⡇⠀⢸⣿⣿⠀⠀⠀⠀⢸⣿⣷⣾⣿⡋⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣹⣿⣿⣿⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⣿⣿⡄⢻⣶⣿⠁⣿⣿⠀⠀⢿⣿⡇⠀⢸⣿⣇⠀⠀⠀⠀⢸⣿⣿⠛⢿⣿⣄⠀⠀⠀⠀⠀⠀⢸⣿⡇⣿⣿⣿⣿⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿⠇⠈⠻⠃⠀⣿⣿⠀⠀⢼⣿⡇⠀⢸⣿⣿⣶⣶⣶⡆⢸⣿⣇⠀⠈⢻⣿⣆⠀⠀⠀⠀⠀⢸⡟⣿⣿⣿⣿⣿⣿⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠁⠀⠈⠁⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢸⣧⣧⣿⣿⣿⣿⣿⣿
⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣽⣿⣿⣿⣿⣿
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏⠙⠉⢉⣭⣍⡙⠿⢶⣶⣶⣶⠶⠋⠉⠻⢿⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠯⡭⠤⠤⣤⣀⡘⠻⣿⣇⠀⠈⠛⠛⠋⠠⣿⣆⢠⡀⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠀⠈⠉⠀⠀⠀⠀⠀⠀⠈⢡⣿⠇⢠⠁⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣠⣄⠀⣿⣀⠀⠀⣀⣠⣤⣤⣀⡀⠈⢆⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⢻⣿⣿⣿⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡄⣿⠀⠀⠉⠁⠈⠛⠛⠛⠙⣦⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⣿⣿⢻⣻⣿⣿
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢡⠟⡀⠀⠀⠀⠀⠀⠀⡧⠞⠀⡿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢻⣿⣾⣿⣿⣿
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣤⣤⣤⣤⣿⣧⣼⣿⣥⣤⣤⣤⣤⣤⣼⣿⣥⣤⣷⣏⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣵⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠹⣧⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⢸⣷⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⠀⠀⢠⣾⣿⣷⣶⣶⣶⣶⣿⣿⣿⣷⣶⣴⣶⣾⣿⣿⣿⣦⣤⣴⣾⣿⣿⣿⣶⣤⣤⣤⣶⣿⣷⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢸⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⢸⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢸⣿⣿⣿⣿⡿⠋
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠁

⠀⠀⠀⠀⠂⠀⠀⠉⠉⠀⢠⡀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠉⠉⠀⢠⡄⠀⠀⠉⠉
⠐⠄⠄⠀⠀⠀⠀⠀⠀⡤⠔⢇⠀⠀⠘⠀⠀⠀⠀⠀⠐⠄⠄⠀⠀⠀⠀⠀⠀⡤⠔⣇⠀⠀⠘
⠀⠀⠀⠀⣄⠐⠂⠀⠀⠓⠲⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠐⠂⠀⠀⠓⠲⠎⠀⢀
⠒⠀⠀⠀⠈⠙⠂⠀⠀⢀⠄⠀⠀⠄⠈⠉⠁⠀⠀⠀⠒⠀⠀⠀⠈⠙⠂⠀⠀⢀⠄⠀⠀⠄⠈⠉⠁
⠀⠀⠀⠘⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠖⠋⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠖⠋⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠘⠄⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠈⠄⠀⣀⠆
⠂⠀⢐⠘⠙⢢⠄⠀⠀⠈⠀⣀⠀⠀⠀⠀⡀⠰⠙⢢⠆⠀⢘⠘⠉⢢⠀⠀⠀⠈⠀⣀⠀⠀⠀⠀⡀⠰⠙
⠀⠀⠈⠓⠒⠉⠀⢠⡄⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠙⠒⠉⠀⢠⡄⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣤⣴⠆⠀⠉⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⠆⠀⠉⠀⠀⠀⢠
⠀⠀⠀⠀⠢⠀⠀⠉⠉⠀⢠⡀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠉⠉⠀⢠⡀⠀⠀⠉⠉
⠐⠄⢄⠀⠀⠀⠀⠀⠀⡬⠔⣃⠀⠀⠘⠀⠀⠀⠀⠀⠐⠄⠄⠀⠀⠀⠀⠀⠈⡭⠔⣂⠀⠀⠘
⠀⠀⠀⠀⣄⠐⠂⠀⠀⠓⠲⠆⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣄⠐⠂⠀⠀⠓⠲⠊⠀⢀⠀⠄
⠒⠀⠀⠀⠈⠙⠂⠀⠀⢀⠄⠀⠀⠀⠈⠉⠁⠀⠀⠀⠒⠀⠀⠀⠈⠙⠂⠀⠀⢀⠄⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠖⠊⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠖⠋⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠈⠄⠀⢀⠆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⡀⠀⠀⠈⠄⠀⢀⠆
⠀⠀⢈⠘⠙⢢⠀⠀⠀⠈⠀⣀⠀⠀⠀⠀⡀⠰⠙⢀⠄⠀⢐⠘⠉⢢⠀⠀⠀⠈⠀⣀⠀⠀⠀⠀⡀⠰⠙
⠀⠀⠈⠑⠒⠉⠀⢠⡄⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠙⠒⠉⠀⢠⡄⠀⠀⣿⡄
⠀⠀⠀⠀⠀⡀⢠⣤⣴⠆⠀⠉⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣤⣴⠆⠀⠉⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⡴⠊⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⠀⠙⣼⠀⢀⣼⡞⠀⠀⠀⣀⡤⠤⠶⠶⠦⣤⣄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⠀⢸⣽⣦⡀⢹⣷⣌⣽⣇⢀⣢⡾⠉⠀⠒⠈⠙⠒⢦⣻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⠶⣌⢻⣿⣧⣠⣿⣿⣿⣿⣿⣿⣷⣶⣞⣭⠄⠀⠀⠀⠈⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠠⢾⣷⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣫⣴⡖⠀⠀⠈⣒⢌⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣉⣁⠀⠲⣿⣿⡟⠚⠋⠉⠁⠀⠈⠙⠛⢿⣿⣿⡟⠀⠀⠀⢀⣸⣷⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⢿⠤⠀⡸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠻⠀⠀⠒⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠟⠐⣄⠀⠀⢀⣠⡄⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢸⣦⢠⢟⣳⠿⠛⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⠀⠀⠜⠛⠉






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣀⡀⠀⢀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢀⡴⠀⠀⠰⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡎⠀⠀⠀⢀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⡂⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠠⠀⡘⢡⡷⢤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢤⡄⢖⠀⣠⣴⣶⣶⣿⡿⢷⣼⣿⣿⣿⣿⣻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠷⢂⢹⣧⣤⣬⠍⠉⠉⠁⠉⠉⠉⠁⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠑⠻⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠀⠠⠐⠞⠻⣦⡀⠀⠀⠀⠀⠀⢀⣤⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⠷⣤⣍⣓⣶⣶⡤⠴⡋⠁⠀⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣌⠻⣿⣿⣿⣿⣦⣌⣉⣉⣉⣁⡀⠔⠁⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠈⠀⠀⠀⢠⡴⣿⣿⣿⣿⣷⣿⣿⣿⣿⡟⠋⠉⠉⠀⠀⠀⣀⣀⣤⡔⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣟⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡿⠿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠈⠉⠁⠀⠈⠁


⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠶⠛⠛⠛⠛⠋⠛⠛⠛⠛⠛⠛⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡋⠓⠐⠒⠲⠤⠖⠒⠲⢤⠴⠒⠒⠒⠊⠉⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠗⠀⠀⠀⠐⠲⠶⠶⠶⠶⠒⠒⠒⠒⠀⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⣀⠀⠀⠀⠀⠀⠀⣤⠒⠛⠻⣦⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⢱⠀⠀⠀⠀⠀⠀⢰⠋⠁⠀⠀⠉⢧⡀⠀⠀⠀⢨⠁⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠈⢶⣄⠀⠀⢀⡰⠃⠀⠀⠀⠀⠀⠀⠳⢦⣀⡰⠎⠀⠀⠀⠀⠀⠀⠘⢷⡄
⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠹⣆
⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⡙⢇⠀⢠⠻⡆⠀⠀⢸⠋⡇⠀⠀⡇⢸⠀⠀⠀⠀⠀⢸⡉⡇⠀⣀⡤⢶⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠸⠃⠈⢷⡎⠀⠻⡀⠀⠘⠀⠇⠀⠀⡇⢸⠀⠀⠀⠀⠀⢸⡆⠰⠞⠁⣠⠏
⡇⠀⠀⠀⠀⠀⠀⠇⣠⢦⡀⢀⣤⡀⢣⡀⠀⡆⢠⠀⠀⡇⠀⠀⠀⠀⠀⠀⠸⡇⠀⠠⣞⠁
⡇⠀⠀⠀⠀⠀⢰⢀⡉⠀⠳⠎⠀⢳⠈⢧⠀⣇⢸⠀⠀⡇⠀⡆⠀⠀⠀⠀⠀⡇⢸⣧⠘⠦
⣿⠀⠀⠀⠀⢀⡇⡜⠁⠀⠀⠀⠀⠀⢧⡈⡇⣿⢈⠀⠀⣇⠀⠛⠛⠛⠂⠒⡄⠃⠸⠈⢧⠘⢣
⡇⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠈⠳⠇⠈⠛⠀⠀⠘⠓⠒⠲⠖⠒⠋⠀⠙⠃⠀⠈⠳⠞
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⠄⠀⠀⠀⠐⠒⠒⠲⠶⠶⠶⠶⠆
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠒⠒⠒⠒⠒⠂⠀⠈⠉⠉⠉⠉⠉⠉⠁
⡇
⢣
⢸
⢸⡆
⢸⡇
⢸⡇
⢸⡇
⢸⡇
⢸⡇
⠘⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢻⣆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠟
⠀⠀⠻⣷⣶⣤⣤⢤⢤⣤⢤⣤⣤⢤⣤⣤⣤⣤⣤⡤⣤⡤⠤⣤⡤⠤⠤⢤⡤⠲⠲⠖⢶⠖⠒⣩⡟⣻⠟⠁
⠀⠀⠀⠈⢿⣀⣳⣀⠀⠳⠀⠈⠃⠀⠘⠃⠀⠉⠀⠀⠈⠀⠀⠘⠁⠀⠀⠀⠁⠀⠀⠀⠀⢀⣞⣡⡞⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠋⠀⠀⠀⠘⠻⠿⠛⠛⠻⢿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠁⢹⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡇⠀⢈⣙⣛⠀⠀⠀⠠⠶⡟⠷⠀⢿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠛⠙⠃⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⣀⣀⣠⡤⣤⠄⠀⢀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣦⠀⠀⠙⠻⠶⠖⠛⠁⠀⠀⢀⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠠⠃⠀⢸⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠓⠂⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⣠⣾⣿⣿⡟⠂⠀⠀⣸⣿⣿⡟⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢀⣿⣿⣿⣿⣇⣀⣀⣴⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⣠
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉

⢸⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⢸
⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣦⡄⠀⠀⠀⢀⣀⣀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⣀⠀⣿⣿⣿⣿⣿⡇⠀⠀⢰⣿⣿⣿⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⣿⣿⣿⡷⠀⣦⢸⣿⣿⣿⣿⣿⣿⣶⡄
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⣀⣹⣿⠟⠋⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣀⡀⢀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⢀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣤⣤⡀⠄⣄⡀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣷⣤⡄
⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣯⣽⣷⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠙⢿⣿⣿⣿⣿⡄
⢸⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣡⡌⠁⢈⠙⢋⡽⢿⠰⠾⣿⡛⣛⣿⡃⠀⠀⠀⢹⡍⠻⣿⣿⣿⣷
⢸⠀⠀⠀⠀⢀⣨⡿⣩⣾⠿⣿⣿⣿⣿⡟⠀⣠⡿⣯⣤⡶⠿⠋⠛⠁⠀⠀⠀⠈⠓⢿⣿⣷⡀⠀⠀⠀⢩⠀⠸⣿⣿⡏
⢸⠁⠀⠀⠀⣼⣟⣱⣿⣿⡶⣛⣠⠞⠡⠞⢠⣿⠞⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠿⣿⠷⣤⣶⢠⣤⡀⠘⣿⣀
⢸⠀⠀⠀⣼⣿⣿⣿⣿⣿⡟⣿⡏⠀⠀⢠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⢾⣶⣿⣷⡇⢘⢈⠀⣶⡊⠿⣿⠿⠇
⢸⠀⠀⠸⣿⣿⣿⣿⣿⣿⡎⠁⠀⠠⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⣿⣷⣶⡩⠴⣷⣿⣿⣶⡦
⢨⠀⠀⢰⣿⣿⣿⣿⣿⣿⡷⠀⠀⢀⣾⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢈⣧⣼⣷⣿⣸⣿⣼⡿⠁
⢸⠀⠀⠰⣷⣿⣿⣿⣏⢻⣷⣤⣾⠛⠿⠀⡀⠀⠀⢀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣼⣿⣿⠛⣿⣿⢿⣿
⢸⠀⠀⠀⢻⣿⣿⣿⣿⠟⢻⣯⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⡿⣿⣣⠟⠉⣿⢿⡇
⢸⠀⠀⠀⠀⠹⣿⣿⣧⠀⢘⠎⢩⠑⢦⡤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢰⡿⢁⣿⣿⡼⣷⣿⣿⣿
⢸⠀⠀⠀⠀⠀⠹⣿⣟⠂⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠑⣠⣿⣏⢳⣾⣿⣿⣿⡆
⢸⠀⠀⠀⠀⠀⠀⠛⣿⣆⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠋⠀⠀⢁⣿⣿⣼⣟⢹⣿⣿⣅
⢸⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢸⣿⣿⣷⢹⣿⣿⣿⡇
⢸⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠈⠱⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⣿⣿⣼⣿⣿⡿⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡇
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⣻⠶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣟⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣧⣛⣿⣷⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣯⣿⡏
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣵⠞⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠾⡿⠿⠋⠻⣿⣿⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣾⣿⣄⠀⠀⠀⢀⢀⡤⠁⠀⠐⢨⠇⣤⠀⠀⠀⠱⣰⣿⠁
⢸⠀⠀⠀⠀⣿⡟⢿⣿⢻⣷⠸⣿⡀⣿⡇⠀⠀⠀⠀⠀⠈⠉⠓⠼⣶⣉⠉⣀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣀⣹⡟
⢸⠀⠀⠀⠀⣿⡇⢸⣿⢸⣿⠀⣿⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⠿⣼⣧⣴⣿⣄⠠⠄⣆⣸⣿⣿⠁
⢸⠀⠀⠀⠀⠿⠇⠺⠿⠸⠿⠀⢸⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠉⣿⣧⣴⣯⣿⠿⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⢸⠀⠀⠀⠀⣾⡟⢿⡦⣾⡇⢸⣷⢸⣿⢠⣾⢻⣷⡀⣼⡟⢿⣧⠸⣿⡟⢸⣿⢻⣿⡆⣴⡟⢻⣦⢠⣾⠟⣿⡆⢺⣿⡷⢿⣿⠗
⢸⠀⠀⠀⠀⠙⠿⣶⣄⢸⣿⣿⣿⣿⡟⢸⣿⠛⣻⠁⣿⡿⢛⡟⠀⣿⡇⢸⣿⢈⣿⡇⣿⡿⢛⣟⢀⣼⡾⣿⡇⣼⣿⠀⢸⣿⠄
⢸⠀⠀⠀⠀⠻⣧⣾⠟⠘⣿⡏⠹⣿⠇⠘⢿⣶⡿⠃⠻⣧⣾⠟⠀⢿⣧⠸⡿⠠⣿⠇⠻⣷⣼⠟⠘⢿⣦⣿⠇⢽⡿⠀⠸⢿⣦
⢸
⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡶⠿⠿⠿⠿⠿⠿⠷⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢷⣦⣀
⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣤⡀
⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⢠⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⣼⡟⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⣼⡟⠀⠀⠀⠀⠰⣿⣿⡇⠀⢠⣶⣦⡀⠀⠀⠀⢠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣹⣿⣀
⢰⣿⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠻⠛⠁⠀⠀⠀⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⠿⠿⠛⠛⠛⠛⠛⠻⠿⢷⣶⣦⣄⣀
⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣦⣄
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣤⡀
⣿⡇⠀⠀⠀⣴⣶⣄⠀⠀⠀⠀⠀⣰⣶⣄⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣄
⢿⡇⠀⠀⠀⠙⠿⠋⠀⠀⠀⠀⠀⠙⠿⠋⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀
⢸⣿⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠀⠀⢻⣷⡀
⠀⢻⣧⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠈⢿⣆⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⣀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠈⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠙⢿⣆⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠃⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⠛⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢷⣦⣄⣀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢷⣶⣦⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣄⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠛⠉⠉⠉⠉⠙⠻⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣤⣼⡟⠀⠀⠀⠀⢾⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠟⠉⠉⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣀⠀⠀⠀⠀⠀⠀⢠⣿⠏⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣶⣤⣀⡀⠀⣾⡏⠀⠀⠀⠀⠈⠻⠿⠷⠀⠀⠀⢀⣶⡄⠀⠈⠙⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠤⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠂⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠀⠀⠚⠆
⠀⠀⠀⠀⠀⠀⠀⠐⢁⠄⠀⡀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠐⠀⠄⠀⠀⠀⠐⠀⠀⠀⠀⠐⠄
⠀⠀⢀⡀⠄⠄⠀⠀⠂⠀⠁⠀⠀⠀⠀⠁⠀⠀⠑⠀⠀⠀⠈⠀⠀⠀⠀⠈⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⢀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣐⣠⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠂⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡈⠀⠀⠀⠀⠈⠁⠀⠀⠉⠁⠀⠀⠀⡈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠄⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢁⠤⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠐⢄⠊⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠓⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠛⠦⣍⣘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠀⣸⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠉⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⣠⠔⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠓⢄⡀⠀⠀⠀⠀⠀⢀⢤⣶⠿⠛⠉⠀⠀⢀⢠⠃
⠀⠀⠀⠈⢇⠀⣈⣉⠐⠠⣀⢮⠢⡐⠄⠀⠀⠀⠀⠀⠙⠓⠲⢦⡴⢒⡵⠟⠁⠀⠀⠀⠀⢄⡴⠃
⠀⠀⠀⠀⠀⠑⠄⡀⠁⠲⣈⣧⠦⠬⠱⡾⣽⡴⡦⡄⣀⣰⣯⣥⣔⣉⡀⡀⠠⢀⡂⠬⠒⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣉⣗⣾⡿⣿⠬⡯⢑⢔⡉⣀⠛⣧⣶⡖⡖⠒⠂⠀⠀⠉
⠀⠀⠀⠀⠀⠤⠠⡿⠿⠹⣞⣛⢯⡉⣯⣽⣿⣘⢣⢻⣯⢏⣿⣾⣤⢀⡠⡀
⠀⠀⠀⠀⠀⠀⠜⠀⢘⢐⣝⡭⠨⣽⢛⠖⢚⣿⣓⠾⠏⠉⠉⠉⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠠⠤⠂⠈⠑⠋⠉⠒⠃⠘⠯⠄


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⢀⠉⢉⠱⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣠⣆⢴⣏⣀⣀⣠⣨⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡾⢿⠻⠿⠃⠁⠝⠉⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠛⠻⠟⠁⠀⠀⠀⠀⠑⢐⠀⠀⠀⢀⡈⠳⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠉⣆⠦⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢂⠀⠀⠒⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡗⣤⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣾⢿⣿⡁⠬⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠈⠲⣶⡀⠀⠀⠀⠀⠀⠀⢺⣤⠋⠀⠀⢀⢻⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡇⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣦⡝⠁⠀⠀⠀⠸⠘⠋⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⡇⠀⠀⠀⠀⠀⠢⢹⡄⠀⠀⢀⡤⠃⠀⠀⠀⠀⠀⢀⣾⡄⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠁⠀⠀⠀⠀⠀⠀⠻⢷⡀⠀⠉⠀⠀⢀⠀⠀⠀⠀⣠⠟⠛⢾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠠⠖⠛⣳⠀⡤⠀⠀⠀⡀⡤⠔⣻⠟⠰⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠁⣤⠶⠉⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢄⣀⠀⠀⠀⠀⢀⣀⣤⣾⠃⠀⠠⠀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠉⠛⠛⠛⠋⢻⣿⣏⠀⠀⠗⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⣿⣾⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠁⡄⠀⠀⠉⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⠿⠉⠛⢿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⠏⠁⠀⠀⠀⢸⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠁⠀⠀⠀⠀⠀⣼⣧⢸⡆⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⡀⢸⣿⠘⣇⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢻⣿⡀⣿⠀⠀⠀⠀⠀⠀⢸⡇⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢩⠂⠀⠀⠀⠀⠘⢻⡇⣿⠀⠀⠀⠀⠀⠀⢸⠃⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠸⡇⠿⠀⠀⠀⠀⠃⠀⠀⠀⠈

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⢿⠟⢻⠿⡿⠟⣿⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢺⠇⠠⠀⠀⠀⠀⠀⠀⠐⠢⡠⠄⠗⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣞⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢶⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠄⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣀⢸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⣯⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⣀⠀⠀⠀⠀⣀⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣄⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠁
⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡀
⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠉⠉⠀⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⣟⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣾⠟⠁⠀⠀⣠⣿⢃⣾⠃⠀⣾⠇⠀⣠⡿⣧⣼⡿⠛⠁⠀⠀⠀⠀⠀⠀⢠⡾⠃⢀⡜⠁⠀⠀⢠⣿⣧⣃⣤⢾⡟⠀⢀⡆
⠛⠁⠀⢀⡴⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⠀⣠⡾⠛⠻⠟⠁⠀⠀⢿⣤⡾⠋⠀⠀⢻⣀⣀⣴⠖⠀⠀⠀⠀⢀⡿⢁⡴⠋⠀⠀⢀⡴⣿⣏⡟⠉⠀⣾⠁⢠⠚⠷⣴
⣀⣀⡴⠞⠀⠀⠀⠀⠀⠀⠸⣿⡀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⣾⡷⠋⠀⠀⢀⡴⠋⠀⠻⠛⠀⠀⠀⠿⠖⠁⠀⠀⠸
⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⡤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡄
⠀⠀⠀⢠⡾⠛⣦⠀⢀⣠⣾⠆⠀⠀⠀⠀⠀⣴⡶⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁
⠀⠀⢀⣿⣿⣰⣿⡶⠿⣿⡏⠀⢀⡄⠀⢠⣾⠋⢠⣾⠇⠀⠀⠀⠀⠀⠀⣠⡟⠁⢀⡼⠁⢀⠄⠀⠀⠀⢴⡆⠀⠀⢀⡀⠀⢀⣴⢿⡆⢠⡀⠀⠀⠀⣠⣿⣿⠁
⠀⣴⣿⣿⢋⣿⠋⠀⣸⣿⠀⢀⣾⡇⢠⣿⣃⣴⠿⠃⠀⠀⠀⠀⠀⢀⣾⡿⠁⣰⠟⠀⣠⢷⣠⡤⠊⣠⠏⠀⠀⠀⣼⠃⣠⣞⡡⠋⠀⢸⠃⠀⠀⣰⣿⡿⠁
⡾⠋⢿⣇⡼⠃⠀⠀⣿⡇⢠⣾⠉⠓⢾⡿⠋⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣡⡞⠁⢠⢾⣏⡠⠀⠀⢠⠏⠀⠀⣠⠎⠻⣴⣿⠋⠀⠀⣠⡟⠀⠀⢠⣿⡿⠁
⠁⠀⠀⠉⠀⠀⠀⠀⠻⢷⠿⠁⠀⠀⠸⣇⣀⣀⣤⡴⠂⠀⠀⢀⣿⣿⠟⠃⢀⡴⠋⠈⠉⠀⠀⠀⣏⠀⢀⡼⠁⠀⠀⢾⣿⣀⣠⣾⠏⠀⠀⢠⣿⡿⠁⠀⠀⢠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢸⣿⣟⣀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠿⠶⠋⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⣼⡿⠁⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⣠⠟⠀⠀⡠⣄⠀⠀⡀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀
⡆⠀⢸⡆⠀⠀⠀⠀⠀⢀⣾⣿⢃⡾⠋⠀⣠⣶⡇⠏⣠⣾⠏⠀⣴⠂⢠⣾⣿⣿⠋⠀⠀⡀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⢠⣿⢻⡆⠀⣠⣿⠃⢀⡀⠀⣠⡿⠋
⠀⠀⣸⠇⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⢀⣴⣿⣏⡟⠋⣹⡟⠀⡴⣿⣤⣿⡿⠋⠁⠀⣠⠎⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⣼⡿⣿⣧⣾⣿⠃⠀⣸⡇⢰⣿⣡⣾
⠀⣴⠏⠀⠀⠀⠀⠶⣾⣿⡏⠀⢀⣴⠏⠸⠿⠟⠀⠀⢿⣧⠞⠁⠀⠹⣿⣄⣀⣤⡾⠃⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠛⢹⡏⠀⣰⡟⠙⣿⠟⠋⠁
⡾⠋⠀⠀⠀⠀⠀⠀⣿⣿⣥⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⣠⣿⠛⢿⠟⠀⠀⣿⡇⣴⡿⠁⠀⢿⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠙⠻⠛
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⢀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⣠⡖⢶⡄⠀⢀⣴⡷⠀⠀⠀⠀⠀⣠⣾⠟⣶⡀⢠⡏⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⢠⣿⡇⣼⣧⣶⢿⣿⠃⠀⣀⠀⠀⣴⡟⠁⣴⡿⠀⢸⡇⠀⠀⣠⣾⠟⠀⠀⠀⣠⠖⠀⣸⠁⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀
⠁⣶⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⣰⣿⡿⢻⣿⠉⠀⣾⡏⠀⢠⣿⠀⢰⣿⣠⡾⠛⠀⠀⠀⠳⠶⠿⠋⠁⠀⠀⢠⣾⠏⢀⡼⠁⣠⠈⠀⡠⢀⡟⠁⠀⢀⡖⠀⣰⢏
⢠⠇⠀⢠⣿⡿⠃⠀⠀⠀⢠⣾⠟⣿⢃⣾⠃⠀⢰⣿⠃⢠⡿⠉⠳⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⢏⣴⠋⢀⣴⠋⡙⠋⢀⡞⠀⠀⣠⢾⣇⣼⡿⠋
⠏⠀⢀⣾⣿⠃⠀⠀⢀⣴⡟⠁⠀⠉⠛⠁⠀⠀⠈⢿⣴⠟⠁⠀⠀⠹⣇⣀⣠⣴⠖⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠁⣴⠋⠘⠛⠀⠀⡼⠀⢀⡴⠁⠀⢸⣿⠀⣀
⠀⠀⣸⣿⠃⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢁⣠⠟⠁⠀⠀⠀⠀⠀⠿⡶⠋⠀⠀⠀⠈⠛⠛⠋
⠀⠀⣿⡏⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠛⠁
⠀⠀⠻⢧⠾⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⣠⣾⠟⠁⢠⣤⣄⠀⠀⣠⣶⠄⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⢷⠀⠀⠀⢀⡀
⢀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⣠⣾⡟⠁⠀⢠⣿⣧⣿⠶⢻⣿⠃⠀⢠⡄⢀⣔⢋⣼⠃⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⣠⠏⠀⠀⢠⡏⡃⠀⠀⣠⡟

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠒⠒⠦⢄⡤⠖⠚⣛⣉⣉⡉⣉⣉⣉⠉⠙⠛⠒⠲⢤⡀⣀⣀⣀
⠀⠀⠀⠀⠀⢀⡴⣋⠤⠒⠀⠀⠀⠀⠀⡞⠀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡠⠖⠊⠉⠁⠐⠊⠭⢝⡒⠤⣀
⠀⠀⠀⠀⠀⡞⠘⠁⠀⠀⠀⠀⠀⠀⢀⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠪⠙⠢⣄
⠀⠀⠀⣠⠖⡇⢸⠀⡀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⢀⡞⠁⠀⢻⠈⡆⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⡀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⢀⡎⠀⠀⠀⠸⡄⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢀⢎⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢂⡠⠤⢔⣒⣉⣭⠤⢤⣷
⣼⠀⢀⠀⣀⡀⢧⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⢀⢠⢣⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡪⢔⣪⠵⠒⠋⠉⠀⠀⠀⠀⠀⠀⠙⣄
⡇⠀⠔⢋⣠⠴⠚⢦⣀⣠⡤⣤⣀⣧⠀⠀⠀⠀⢰⢧⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⡭⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠳⠤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⣄⠀⠀⠈⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠚⠹⣄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢕⣦⣔⡀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠫⢭⣓⣂⣀⣿⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠤⠤⠤⠤⠄⣒⣒⡒⠠⢚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⢀⠔⣡⠤⠖⠒⠒⠛⠉⠉⠉⠉⠉⠉⠉⠙⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠈⠓⢤⡀⠀⠀⠀⠀⢀⡴⢃⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠈⠳⣄⠀⠀⣉⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⡠⣠⠞⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠠⣤⣦⣶⠿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡖⠚⢻⠛⠉⢹⠉⠉⠏⠉⢹⠀⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⣤⠼⠦⠶⠾⠖⠒⠛⣛⣋⣉⠙⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢋⠽⢦⡀⠀⠀⠀⠀⠀⣾⡏⠀⠙⡆⠀⠈⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡯⠚⠁⠀⠈⠳⣄⠀⠀⠀⠀⠻⣿⣦⠾⠁⠀⠀⢀⣈⣽⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠛⠁⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⣀⣠⡤⠶⠚⠛⠉⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠛⠛⠛⠛⠒⠶⠶⠿⣶⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡤⠤⠶⠶⠖⠒⢹⡇
⠀⠀⠀⢠⣟⣛⠓⠒⢶⣄⠀⠀⠀⠀⠀⠀⡷⠤⠤⠤⠤⠤⠖⠒⠒⠢⠤⣀⣀⣇⣀⡠⠞⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⢧⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡜⣷⠿⠿⠿⠿⠿⢿⣿⣶⣶⣶⣤⣄⠀⠀⠀⠀⢀⡇⠀⣄⣀⣀⠠⠄⣶⢸⣿⡁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡾⣿⢿⡶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣯⢾⡇⠀⠀⠀⢸⡇⢸⡏⠉⢹⡜⠇⠙⠈⠁⠉⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢹⡌⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⣀⣧⣹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣠⠤⡀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠉⠉⠉⠉⠙⠒⠒⠒⠊⠉⠉⠉⡏⣿⠀⠀⠀⠀⢸⡇⠀⠀⢠⠖⠳⣄⡰⠃⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡿⠉⢆⠀⡴⢺⡏⢦⣀⠜⠀⠀⠈⠀⣀⠀⢆⡿
⠀⠀⠀⠀⠀⠀⠀⠀⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢰⡇⠀⠀⠉⠀⢸⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⢸⠀⠀⢀⣠⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢏⡟⠉⠓⠶⢤⣄⣸⣤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣭⣒⣒⣒⣤⡤⢤⣔⣚⣥⠞⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⢀⡠⠤⠒⠉⡉⠉⠒⣄
⢠⠄⢀⠀⡀⠄⠈⠀⠄⠐⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠲
⡇⢀⠈⠀⡀⠀⠈⠀⡀⠀⠐⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢠⢅
⢣⠀⢀⠀⠀⠈⢀⠀⢀⣀⠀⠀⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢰⡃⠐⠛⠁⡃
⠀⢆⢠⠀⡠⢄⡀⢠⠃⠀⢣⡀⢰⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠓⠤⠤⠴⠑⢦
⠀⠘⡄⠀⡇⠀⠈⠁⠀⠀⠀⠉⠁⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠈⠀⠀⠐⠀⢀⠀⣱
⠀⠀⠱⡤⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⣀⣤⡖⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡇
⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠴⡪⢋⠎⠀⡟⢄⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠜⠁⠎⠀⠀⠱⡀⠉⠓⠮⣙⣄⣀⢄⠀⡀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⣀⠏⠀⠸⠀⢸⠀⠀⠀⠀⠈⢆⠀⠀⠈⢆⢑⠎⢸⠭⢦⡤⠖⢢⣀⠇
⠀⠀⠀⠀⠀⠈⠓⠤⠤⠤⠰⡖⠉⢹⡀⠀⢠⠀⠈⢆⠀⠀⠀⠀⢈⠀⠀⢀⡮⡉⠒⠚⣄⣀⡙⣦⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢄⣱⣀⡆⠈⠒⠈⠢⢄⣈⠷⠄⣀⠤⠊⠐⠊⠁⢹⠉⠫⡉⠀⠑⡴⠁
⠀⠀⠀⠀⠀⠀⣔⣑⣊⢉⣹⡉⠐⠪⠢⡔⠁⠑⠔⠉⠙⠤⠊⠙⡖⠉⠳⠔⢚⢺⣉⠩⠯⠽⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠋⠉⠗⠒⢳⠀⠀⠇⠀⠀⡇⠀⠀⠇⠀⣸⠤⠊⠁⠀⠐⠐⠀⡀⠀⠂⢉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠸⡀⠸⡀⠈⡆⠀⢸⠀⠀⡇⠀⢸⠀⡠⠋⡀⢈⢀⠀⡐⢠⣊⣙⠢⢄⠠⠀⠀⠑
⠀⠀⠀⠀⠀⣀⡀⢰⠀⠀⠀⣀⣣⡠⠗⠠⢸⠀⠈⡄⠀⡇⠀⡈⢠⠁⠀⠠⠀⠸⡜⠉⠀⠀⠀⢉⡟⢐⠀⠁
⠀⠀⠀⢠⠋⠀⠈⠿⠉⠉⠻⠀⠈⠁⠀⠀⠈⡇⠀⠇⠀⠇⠀⠇⠸⣀⡄⢀⡀⠐⠈⠒⠖⠒⡂⠡⠐⠀⣰⠉⠑
⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⡰⠉⠉⠁⠈⠀⠉⠈⠉⠙⢌⠁⠈⢆⡠⠔⢄⠁⡠⠢⠤⠋⠁⢀⠜
⠀⠀⠀⠀⠑⠢⢄⣀⣀⠴⠋⠒⠂⠄⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣀⠀⠀⠀⠉⠀⠀⣀⡠⠒⠁
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⢦⠹⡌⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠘⡄⣿⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⢰⠃⣿⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢀⠏⣸⠇⠀⢰⢿⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⡟⠀⠀⡞⢈⡇⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣾⠁⠀⡼⠁⣼⠃⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⣰⠏⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⡶⠶⠖⠚⢻⡀⠈⠁⣿⠀⠈⠀⠀⠀⠤⠤⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣟⣋⣥⣤⠴⠶⠶⠒⠈⠻⠦⡘⠙⢧⡘⠛⠳⠶⠶⠤⢤⣀⠉⢻⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢿⣿⣥⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⠾⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠻⠟⠛⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⣀⣼⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢁⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⡇⠀⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢹⡇⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠖⢋⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣡⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⣶⠶⠾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢰⡁
⠀⠀⠀⢀⣀⣤⣶⠾⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡀
⠀⢀⣴⡿⠋⠉⠀⠀⠀⠀⣀⣀⣤⣤⣴⣶⡶⠶⠖⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡄
⠀⢸⣿⠀⠀⠀⠀⣠⣶⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⢤⣄⠀⠀⠀⠀⠀⣹
⠀⠈⢿⣦⡀⠀⠀⢿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠙⠿⣶⣄⣈⠙⠿⢷⣶⣦⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠴⠞⠋⠁⠀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠿⠶⣶⣤⣬⣉⣉⡙⠛⠛⠛⠻⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠛⠛⠋⠉⠉⠁⣀⣀⣠⡤⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠻⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠛⠛⠋⠉⠉⠉⠁

⣦⣶⣶⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣽⣭⣭⣿⣵⣮⣽⣯⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣾⣿⣶⣶⣾⣷⣶⣶⣶⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⢀⣴⠦⠳⡤⠷⠀⠀⠀⠀⠀⠀⠀⢀⣤⣷⡾⣤⡀⠀⠀⠀⠀⠀⠀⠀⣘⠡⢲⢎⢳⢢⢱
⠀⠀⠀⠀⠀⡠⢸⡁⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⡎⡀⠀⠀⢇⢱⠀⠀⠀⠀⠀⠀⠀⠰⡰⢞⣮⡛⢎⡜
⠀⠀⠀⠀⠀⠑⢤⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣓⣓⣒⣒⣚⣒⠆⠀⠀⠀⠀⠀⠀⠘⠕⠋⠭⠜⠢⠇



⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠠⠤⣀
⠀⠀⠀⠀⠀⣠⣣⣜⣒⣢⣄⡀⠀⠀⠀⠀⠀⠀⠀⡠⠼⠌⠡⠧⢄⠀⠀⠀⠀⠀⠀⠀⢰⣁⣠⠔⢄⠈⢧
⠀⠀⠀⠀⠀⣷⣦⣴⣳⣦⣴⣟⠀⠀⠀⠀⠀⠀⠀⠑⡆⠀⠀⢰⠊⠀⠀⠀⠀⠀⠀⠀⠸⡀⠘⠢⠊⢉⡏
⠀⠀⠀⠀⠀⠋⠛⠋⠀⠛⠋⠃⠀⠀⠀⠀⠀⠀⠀⠮⣀⠖⠢⣀⠵⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠒⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣀⡤⡖⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠒
⠀⠀⠀⠀⠀⠀⠠⡓⢝⢮⣲⠃⠀⠀⠀⠀⠀⠀⠀⢸⠭⠝⠫⠭⡇⠀⠀⠀⠀⠀⠀⠀⢰⠉⠉⠉⠉⣓⢢
⠀⠀⠀⠀⠀⡠⢖⡝⠢⠓⠃⠀⠀⠀⠀⠀⠀⠀⢰⠭⠕⠭⠭⠪⠭⡆⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⢀⡵⠃
⠀⠀⠀⠀⠘⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠒⠃⠀⠀⠀⠀⠀⠀⠰⠭⠥⠬⠭⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣄⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠉⢹⡏⠉⠁⠀⢈⡽⡅⠀⠀⢿⣯⠉⠉⠉⢉⡟⡏⠛⠛⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢸⣿⠀⠀⠀⠀⡇⡇⠀⠀⢸⣿⠀⠀⠀⢸⡇⡇⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣼⣿⣤⣤⣤⣴⣷⣧⣤⣤⣼⣷⣤⣤⣤⣼⣷⣧⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⢀⣴⠞⠛⠛⠛⠛⢶⡄⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⣿⢦⣄⣀⣀⣤⠴⡎⣿⠀⠀⠀⠀⠀⠀⠀⣼⢳⡀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠘⠶⣤⣤⣤⣴⠶⠛⠁⠀⠀⠀⠀⠀⠀⢰⠇⠀⠱⡄⠀⣷
⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠙⣆⢹⡆
⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠘⢮⣷
⠀⠀⠀⠀⢠⡏⠀⠀⣠⠖⠋⠙⣆⠀⠀⠀⡤⠤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⢸⡧⢤⠴⠁⠀⠀⠀⡇⠀⠀⢸⠃⠀⠀⠹⣄⣀⣠⠋⠉⠑⡄⠀⢀⡟⠉⢳⠀⠀⡞⠉⢱⡄⢸⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠒⠒⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠓⠤⢼⡇⠀⣏⠀⢀⡇⠀⠈⠓⢺⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠈⠉⠉⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⣴⣦⠀⣠⡄⠀⠀⠀⣶⠀⢠⡀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⣿⠘⠟⢹⡇⠐⣃⠀⣿⠀⢸⣤⡾⠃⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠙⠃⠀⠀⠿⠀⠟⠀⠟⠀⢸⠏⠻⣆⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⡴⠋
⠀⡀⠀⠀⠀⠀⠀⠀⠸⣦⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⣀⣤⠶⠟⠉
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠛⠛⠛⠒⠶⠶⠶⠶⠶⠾⠛⠋⠉
⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠒⠲⣦⣄⡀⠀⠀⣠⠚⠉⠉⠉⠙⠲⡄⠤⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⣠⠞⠋⠉⠉⠉⠁⠺⠗⠛⠉⠉⠙⠒⢤⡀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⣼⠁⠀⠀⠀⠀⡖⡖⡴⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⢀⠔⠚⠉⠙⠛⠲⣄
⠀⠀⠀⠀⠀⣠⠾⠚⠛⠓⠲⢤⡇⠀⢀⣄⣠⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠋⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠘⡇⠀⠈⠉⠁⠃⠋⠛⠸⠅⠀⠀⠀⡠⠂⠁⠀⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⢀⡟⠀⠀⣀⠉⠊⢷⠠⢀⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠉⠀⠀⢀⣾⠃⠀⠀⠀⠀⢀⢀⡀⡄⠀⠀⢸
⠀⠀⢸⡇⠀⠀⠑⠙⠳⢂⠄⢈⠛⢳⡀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⣟⠁⠀⠀⠀⠀⠘⠈⠚⠈⠁⠀⠀⡾
⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠹⣄⡀⢀⣀⣀⣤⠴⠖⠛⢿⣿⠁⠀⠉⠉⠐⠀⠀⠀⠀⠀⠀⠀⠈⢠⠇
⠀⠀⠀⢳⠈⠒⠀⠀⠀⠀⠀⠀⠀⠐⠂⠉⠻⣿⣿⡿⠁⠀⠀⠀⠀⠙⠲⠤⣄⣀⡀⠀⠀⠀⢀⡠⠤⠶⠶⢿⣄
⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠭⠭⠭⠟⠉⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⢀⢠⠀⡒⠢⠄⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠐⢤⠪⠂⠛⠉⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠈⠑⠒⠂⠀⠀⠀⠀⠀⠀⠀⠁⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⢤⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠋⠀⠀⠀⢀⣴⣶⣄⠀⣀⣀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣾⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣷⣦⣄⠀⠀⠙⠛⠋⠁⣠⣴⣾⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣦⣤⣄⡀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢀⣠⣤⣴⣦⣤⣄
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣦⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣴⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⡿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣏⣀⣀⣿⣿⣿⠃⠀⠀⠀⠀⠘⣿⣿⣿⣀⣀⣹⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⡟⠋⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠉⠙⢻⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠐
⠀⠀⠀⠀⢀⣀⣀⠌⠀⠀⣀⣀⡀⠉⠙⠛⠿⣿⣿⣿⣟⡁⢄⠀⣾⣷⠀⠀⠀⠀⠀⠀⣾⣷⠀⡠⢊⣻⣿⣿⣿⠿⠟⠋⠉⢀⣀⣀⠀⠀⠡⣀⣀⡀
⠀⠀⠀⠀⠉⠙⠋⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠂⢸⣿⡷⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠻⠟⠀⠀⢸⣿⡇⠔⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠋⠙⠖⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⣀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢅⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠑⢐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠤⠐⠢⣀⠀⠀⠀⠀⠀⠈⠓⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠔⠒⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄
⠀⠀⠀⠀⡀⠤⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢄⡤⠠⡄⠀⠀⠑⢄
⠀⠀⠀⠀⢇⠀⠈⠀⢠⠂⠀⠀⢀⡠⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⣠⠂⠀⠀⠀⠀⠑⢤⠀⠀⠀⠀⡔⠂⣄⠄⢤
⠀⠀⠀⠀⠈⠢⡀⡰⢃⠤⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠌⠀⠀⠀⠀⠀⠀⠀⠘⠦⠖⠁⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⢣⠀⠀⠀⡰
⠀⠀⠀⠀⠀⣀⠜⠊⠀⠀⠀⠀⠀⠀⠀⡠⠀⢤⠔⠂⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠳⣀⠜
⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠈⠳⡀
⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⢀⠇⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⠆⠀⠀⢀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠈⠲⠉⠑⠄⠀⠀⠀⠀⠀⠈⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄
⣘⡠⠖⠉⠀⠀⢀⡀⠀⢀⡀⠈⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠁⠀⠀⠀⠀⠰⡀⠈⠛⠀⢹⠀⠀⠀⠀⠙⠢⡀⠀⠠⠲⠖⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣀⠀⣀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠑⢄⠀⣠⠃⠀⠀⣀⠠⠂⠁⢉⣢⡈⠢⡞⣀⣀⠤⠀⠀⠀⢠⡄⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠁⢀⠜⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠁⢀⡠⠊⣡⠔⠚⠉⠈⠀⠙⠂⠉⠉⠀⠀⠀⠀⠀⡐⠀⠠⠍⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⡐⠀⠀⠀⠙⢇⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠠⠁⠀⠀⠀⠀⠀⢣⠈⢢⡀⠄⠒⠀⠈⠁⢀⠀⠀⠈⠁⠐⠒⠤⣀
⠀⠰⡂⠒⠐⡆⠀⡘⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⡄⠰⠂⠀⠚⠀⠀⠀⠀⠀⠀⠀⢣⠀⢂⠀⠀⠀⠀⠀⠉⠉⠒⠒⢢⠀⠀⠀⠀⠑⢄
⠀⠀⠑⡤⠊⠀⢠⠁⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠠⠀⢀⢀⡏⠀⢨⡁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠆⠀⠀⠀⠀⢣⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠱⡀⡘
⠀⠀⠀⠀⠀⠀⡆⢀⡃⠀⠀⠀⠀⠀⠀⢠⠊⠁⠈⠑⢧⡀⠀⠀⡀⣿⠀⠀⠃⣨⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠘⡀⠀⠀⠀⠀⠱⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⢀⡡⠊⠉⠉⠁⠐⠢⢄⡀⠈⠠⡀⢀⠔⠀⠈⠢⠎⢠⠁⠀⣰⢂⠡⠐⠂⠉⠉⠁⠀⠈⠉⠘⠣⡀⠃
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⡄⢀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⢀⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡇⠘
⠀⢀⢀⣀⡀⢸⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⡇⢰
⠀⠘⢄⡠⠃⠈⡀⢰⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡈⠀⠑⠶⠠⠄⠀⠀⠀⠀⠤⠔⠊⠁⠀⠀⠀⠀⠇⢸⠀⠀⠋⠁⠒⠉⢰
⠀⠀⠀⠀⠀⠀⢃⠀⠆⠀⠙⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡄⠀⠀⠱⡀⢀⡰⠃
⠀⠀⠀⠀⠀⠀⠈⡄⠘⡄⠀⠀⠀⠈⢓⡒⠂⠠⠄⠓⠒⠁⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠃⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠘⡄⠀⠀⠀⠀⠉⠂⠤⣀⣀⣀⣀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠒⠉⠀⢀⠌
⠀⠀⠀⠰⡀⠒⠂⡰⠆⠀⠈⠢⣀⠀⠉⠐⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠂⠀⠉⠉⠉⣀⣀⠀⠤⠤⠔⠒⠁⠀⠀⠰⢍⠐⠂⡠⠆
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠲⡒⠒⠒⠒⠒⣒⠶⠒⠒⠒⠂⠈⠉⠙⠥⣀⣀⣀⣀⠠⠔⠁⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣚⣽⡶⠾⣷⣶⣬⣍⠓⢤⡤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢚⣉⣀⣀⡀⠀⠈⠉⠻⣿⣦⣝⢦⡉⠲⢤⡄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠚⠉⠉⠀⠀⠉⠙⢿⣶⣄⠈⠙⢿⣧⣳⡄⠀⢳⡀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⣃⠀⠐⠶⣤⣀⡀⠀⠀⠈⠻⣷⣦⡀⠙⣿⣿⠀⠀⢷⡄⠀⢿⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⣴⠾⠋⠙⠛⠶⣿⣿⣻⣧⡀⡈⠱⡄⠈⢻⣿⣦⠸⠟⠀⢠⢸⡇⠀⣸⣧⢀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣗⠍⠋⠁⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣶⣷⣿⣿⡿⣿⣶⣌⠀⣈⣀⣿⣼⡾⣿⣷⡽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡵⠓⠛⣓⠶⢶⣤⣄⠀⢄⣀⠀⠈⣿⣿⣿⡞⢖⣯⣷⣻⣿⣿⣿⣿⣿⡿⠃⣠⣏⣡⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠛⠉⠉⠙⠳⢾⣿⣷⣬⣛⣹⣷⣾⣿⣿⣿⣾⣽⢯⢿⡿⢟⣿⣿⡿⠶⠏⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⣠⣲⣽⣿⣿⣾⣿⡻⡟⣿⣿⠙⠖⢛⣸⣿⡿⠏⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡣⠖⠛⣉⣉⣙⠺⣷⣿⢻⢿⣿⢟⣟⣀⣿⣷⠶⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣴⣶⡶⣾⣿⢿⣺⣷⣯⣴⡾⠿⠝⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣙⠿⠞⣛⣵⣾⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠄⠀⠀⠀⠀⠀⢀⣀⠠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠄⣀⠀⠀⢠⡅⠐⠀⠉⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠉⠀⠀⠀⠈⠑⢤⠀⠀⠠⢊⠀⠀⠀⠀⠀⠀⠑⢄⢀⡠⣛⡆⢀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⡢⡀⠱⡀⠁⠀⠀⠀⠀⠀⠀⢀⢔⣫⣵⠊⢁⢁⠅⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠁⠀⠀⠀⠀⡀⢔⡬⠒⠉⢁⠸⠀⠈⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⡥⠚⠁⠀⠀⠀⢐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠈⢆⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢆⠆
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠨⢁⠊
⠀⠀⢀⠄⣒⠃⣿⣶⣤⠄⡪⠜⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠖⠶⠁⠀⠀⠀⠐
⢔⣪⣿⣛⣽⡿⢞⣩⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢀⡀⢈⠕⠉
⠀⠈⠉⠻⣵⠚⠅⠀⠞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢑⠠⠂⠁
⠀⠀⠀⠀⢱⠆⣆⠠⠊⠁
⠀⠀⠀⠠⠌⠊
⠀⠀⠀⠀⠀⢠⠀⠀⡠⠠⡀⡠⡢⠀⠀⡰⠂⠀⢀⢄⠀⠀⡀⠀⢀⠐⢀⠀⠀⡀⡀⡀⢀⢀⢀⢀⠀⢀⠀⢄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠤⠤⠤⠤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⠤⠼⠤⢠⣄⣠⣰⡀⡇⣰⣶⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣦⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⣻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠿⠛⠁⠉⠢⡀⠀⠀⠀⠀⠀⠀⠐⠔⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠗⠋⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠈⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠈⠳⣄⣀⠠⠤⠖⠒⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⢀⣠⡠⠤⠔⠒⠈⠀⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠒⠀⠀⠈⠉⠉⢉⡍⢹⠀⢀⡀⠀⡄⠀⡟⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣶⣀⡀⢀⠀⢀⠀⢸⠀⢸⡇⣼⠁⠀⠇⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡿⠀⠸⠁⠃⢸⠀⣿⠀⢸⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⠀⠀⠀⠀⠈⠀⠛⠀⢸⠋⢷⡄⢀⡀⠀⣠⡠⠴⠚⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠄⠒⠒⠒⠒⠒⠒⠒⠀⠁⠀⠀⠬⠭⢼⠗⠉⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠛⠓⠒⠒⠒⠒⠶⠤⠤⠤⠤⠤⠤⠼⠛⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠿⠛⢛⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣃⣀⣀⠀⠰⣶⣶⣆⠈⢻⣿⣿⣿⣿
⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡋⠉⠁⠀⠀⠀⠀⠀⠈⠙⠀⡀⢻⣿⣿⣿
⣿⣿⠟⡡⠂⠑⠀⠀⠄⠀⠢⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠘⠲⠤⣄⣿⣿⣿
⣿⣏⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⠔⠀⠙⠒⠤⢄⣀⠀⠠⣤⢠⠴⠓⢏⠻⠿
⡟⠁⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡶⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠈⣥⣤⣴
⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿
⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⢀⠠⠘⠁⠀⡉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⣀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠄⠈⢻⠟⠿⡿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠠⠤⠤⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡏⠀⢀⢄⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠛⠻⢿⣿⣿⣿⣿⡏⠀⠐⡀⠒⠠⠀⢸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣟⠁⠀⠐⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡠⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢛⠿⠿⠻⠀⠀⡄⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠁⠀⠐⠀⠀⠀⠘⠠⠄⠐⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡘⠂⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠈⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠀⠀⠀⠠⠀⠀⠀⢀⡀⠀⠀⢀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⣥⣤⣵⣢⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠠⠀⠀⠕⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⠃⠀⠀⠠⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣹⣶⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢰⣶⠊⠀⠀⠀⠀⠀⠀⢸⣶⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣶⣌⣀⣠⣿⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠠⠄⠀⠤⠀⠸⠀⠀⠀⠀⠠⠜⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠈⠀⢀⠄⠣⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣦⣄⣀⠀⠀⠀⣈⣁⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣴⡀⠀⠀⠀⠀⢀⣨⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡞⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣿⠀⡇⢀⠀⠀⠀⠉⠛⠛⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡖⠛⠉⠉⠉⠉⠙⠀⠀⠏⠀⢀⡤⠔⠀⣀⣀⣀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠉⡡⠴⠊⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢷⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⠴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢤⡀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠈⠳⣄⠀⠀⠀⠀⠈⠛⠦⣄⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠈⠙⠳⢦⣾⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⣛⡙⠁⠀⠀⠀⠀⠀⠙⠶⣤⣀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⣠⠞⠁⠠⠒⠉⠁⠠⠖⠂⠀⠀⠀⠀⠀⠀⠀⠉⠙⢛⣿⠟⠁
⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢶⡶⠤⠶⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠶⢤⡀⠀⠘⠀⡆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠁⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠘⠚⢁⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡾⠁


⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣿⣻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣄⡀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⠋⠀⠀⠀⠀⠀⠀⠘⠛⠉⠁⠈⠛⢦⡀⠀⠀⠀⠀⠀⣀⡴⠶⣤⠴⠶⠶⠶⣤⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠋⠉⠀⠈⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⣤⠴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠐⠃⣠⠞⠛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠖⠢⡀⠀⠀⠀⠀⠀⠀⣰⣲⡌⣧⠀⠀⠛⠛⠒⠋⠀⠀⠀⠀⢀⡴⠛⣦⠀⠘⡇
⠀⠀⠀⠀⠀⠀⢀⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠴⠋⠀⣼⠃
⠀⠀⠀⠀⠀⢠⡟⠁⠈⢳⠀⠀⠀⠀⠀⠀⣀⣀⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠃
⠀⠀⠀⠀⠀⢘⡷⢦⡤⠞⠓⠀⠀⢀⣠⠎⠁⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⣞⡦⠀⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠈⠉⠈⠳⠤⠴⠚⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡀⠀⠀⠠⢤⣤⣴⠖⠾⣏
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⣀⡤⠶⠋⠁⠀⠀⠀⠉⠳⠦⣄
⠀⠀⠀⠀⠸⣦⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠦⢤⠞⠀⠀⠀⠀⠀⢀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⢠⡏⠀⠀⠈⠉⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⣸⠀⠀⠀⠀⡴⠒⢢⡀⠀⠀⠐⠢⠀⠀⢺⡄
⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⢠⡏⠁⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠊⢠⡞⠁⡀⠀⠀⠘⠳⠶⠖⠃⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠘⢳⡆⠀⠀⠀⠈⠳⠤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠋⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣀⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⢠⢴⡞⠁⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⠴⠖⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⢠⡀⢠⡀⠀⢸⠁⠀⠀⠀⢹⠔⠒⠊⠉⠀⠀⢀⡴⠛⠲⠶⠶⠚⠓⠒⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⢧⡀⠀⠀⠀⠉⠁⠈⠙⠛⢦⣤⣤⠶⠋⠀⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⣤⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⠴⠶⠶⠶⠶⠶⠦⠤⠤⠶⠋⠉⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠾⢧⣤⡼⠇⠀⠀⠀⠀⣠⣤⠀⠀⠀⢰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉




⣿⡟⣋⡿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠒⠀⠀⠀⠀⣀⡀⣀⣀⣀⣀⣀⣀⣀⣀⠃⠀⠀⠀⠀⢠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠠⠆⠉⠈⡈⠉⣁⠉⠀⠀⠀⠀⣼⣿⣿⠿⣽⣶⣶⣶⣮⣉⠙⠁⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠴⠀⠀⠀⠀⢀⠀⢲⣂⣀⣤⣤⣶⠂⠀⡀⠀⠁⠘⠛⣩⠉⠿⣿⣿⡆⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠄⠀⣸⠃⠀⠀⠀⠀⠀⢈⡀⠁⣙⡂⠐⠛⢿⢷⣄⡀⠈⠃⣬⣿⡿⠁⢘⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠠⢌⣙⠀⠤⣄⣀⠀⠈⠉⠀⠩⠁⣠⡀⠀⢐⠛⢛⣛⡻⠞⠋⣤⡞⢾⣏⣀⣄⣈⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠻⣶⣶⠄⠀⠀⠀⡀⠐⠓⠛⠓⠂⣙⡋⠩⣷⣴⡀⢠⡿⣧⣿⡟⠁⠀⠙⣯⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠛⠁⠀⠀⠉⠄⠈⢸⠏⣿⠇⠀⠀⣠⡿⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠻⠶⠶⠛⠉⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⠷⠟⠛⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣿⣿⣷⣶⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⡴⣿⣗⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⢀⣶⣿⡿⢟⣳⡄⠈⠉⠛⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⢘⣿⣉⣻⣷⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠘⠀⠀⣛⡾⣿⣟⣩⣿⣥⡀⠀⠱⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⢁⣯⣽⡟⠉⣻⠏⣿⣾⣧⣤⣀⣀⠀⣀⢀⠀⣀⣁⣠⣶⣿⣫⢊⡽⣒⣿⣿⣷⠞⠀⠀⠀⢘⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢛⣥⡀⣌⠉⢙⠛⠻⠿⠿⠿⠿⠿⡿⠿⠿⣿⣟⢍⣯⣱⣝⠋⠁⠀⠀⠀⢀⢰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠞⠁⠰⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠛⠉⠉⢁⠀⢀⡮⢶⡋⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠰⠤⠦⠤⠤⠤⣄⣢⣤⣄⣤⡐⠿⠯⠁⠘⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠉⠁

⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠾⠋⠈⠻⣷⡾⠟⠀⠀⠈⠿⣶⣶⡿⠋⠀⠈⠿⣦⣴⠾⠛⠁⠀⠀⠀⣀⣴⣶⣶⣶⣤⣾⣿
⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣠⠶⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠁⠀⠁⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣤⣶⡄⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿
⠏⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠻⣷⣄⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣴⠟⣹⡆⠀⠀⠀⠈⢿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠛⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣾⠃⣠⡿⢀⣀⡀⠀⠀⣠⣤⣀⠀⠀⠀⠀⠀⢠⣾⠟⠛⢻⣷⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⣤⣌⠻⣿⠃
⠀⣀⣀⣠⣤⣼⣿⠾⠋⣴⣿⠛⠿⣷⣾⠟⠙⣿⡆⠰⣿⣷⣶⣿⣷⣶⠿⠟⠋⠀⢀⣤⣴⠶⠶⠂⠀⠀⠀⠀⣴⠟⠛⠋⠈⣿
⠀⠉⠉⠉⠁⣿⠁⠀⣼⣿⡇⠀⢰⣿⠏⠀⢸⡿⠀⠀⢘⣿⢸⣯⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⣼⡟
⠀⠀⠀⠀⠀⣿⣤⣾⠟⢿⣷⣠⣾⡟⠀⠀⢿⣇⣀⣠⣾⠏⠈⢿⣄⣀⣠⣴⠟⢁⣤⣤⣄⠊⠛⣷⠀⠀⠀⠀⠀⠀⠈⠿⠏
⣤⣠⣤⣄⠀⠈⠉⠀⠀⠀⠉⠋⠉⠀⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠉⠋⠉⠀⠀⢸⡇⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⣿⣿⣿⡟⠀⠀⠀⣠⣤⣤⣤⠶⢶⡆⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠈⠻⣦⡀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣿⣿⠋⠀⠀⠀⠀⣿⡍⠉⠃⣠⣾⠇⠀⠀⠀⠀⠀⠀⣰⡿⢡⡿⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠃⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⠀⠈
⠈⠉⠀⠀⠀⠀⠀⠙⠿⣦⣼⡟⠉⠀⠀⠀⠀⠀⠀⣰⡏⣠⡾⢃⣠⣄⣀⠀⣠⣶⣦⡀⠀⠀⣀⠀⢀⣾⡟⢉⣉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⣤⣤⣴⢶⣿⠟⠋⢰⣿⠏⠉⢻⣾⡟⠀⢸⣿⠀⠻⣿⡷⣿⡿⠿⠟⠛⠉⠀⢀⣴⡶⠟⠛⠋
⠶⠿⠷⠶⣦⣀⠀⡴⠛⠛⣷⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⣿⣿⡀⠀⣾⡿⠀⠀⣿⠇⠀⠀⣽⡇⣿⡇⠀⠀⠀⢀⣴⠿⠁⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠸⣷⡾⠟⠙⢿⣧⣾⡿⠁⠀⠈⢿⣤⣤⣾⠟⠁⠘⢷⣤⣤⡶⠟⠃⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⣠⣴⣶⣤⣴⣶⣦⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠉⠉⣀⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹
⢷⣤⣀⠀⠀⠀⠀⢀⣴⡿⠁⠀⣿⣅⠀⠿⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣾⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠉⠻⢷⣆⠀⢠⣾⠋⠀⠀⠀⠈⠻⣷⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⣾⣿⣾⣿⣿⣿
⠀⠀⠀⠀⠻⣷⣿⠃⠀⠀⠀⠀⠀⠀⠈⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠁
⠀⠀⢀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠸⠿
⠀⢰⡟⠉⠉⢙⣿⠀⠀⠀⠀⠀⠀⠀⣼⣏⣴⡿⣡⣤⣦⣄⢀⣴⣾⣶⣄⠀⣀⣤⡀⢠⣾⣏⣀⣤⣿⠇⠀⠀⠀⠀⢀⡀
⠀⠈⠻⣦⣴⡿⠋⠀⠀⠠⠶⠶⠶⢺⡿⠛⠁⣸⣿⠇⠈⢻⣿⠏⠀⣸⡿⠀⠹⣿⡿⣿⡿⠟⠛⠉⠁⠀⣠⣶⠟⠛⠛⠉
⣤⣤⡀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣴⣿⣿⡀⢀⣿⡟⠀⠀⣿⠃⠀⢀⣾⡇⣿⡇⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠾⠛⠛⠛⠛⠛⠻⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠟⠛⠛⠛⠛⠻⠷⣶⣄⡀
⠀⠀⠀⠀⠀⢀⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣄
⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣾⣄
⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣇⣶⣶⡀
⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⣿⣿⣷⣿⣯⣥⠄
⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡾⠽⢿⣿⣿⣥⠄
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣄⠀⣀⣹⣶⣦⣿⣿⣿⣟⡥
⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣐⣾⡞⠁⢹⣿⣿⣿⣯⢾⠏
⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣩⠴⢿⣾⠞⣯⢻⣸⣧⣯⣤⠄
⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⢤⣰⣿⢻⣀⣰⣿⣋⠙⣿⣿⢿⣿⡿⠆
⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⢁⣏⣓⣿⣿⣿⣿⠛⢾⡿⠴⣿⠋⣩⠽⣇
⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠳⢾⣍⡿⠛⢿⣽⣿⣌⣿⡛⠙⣧⣾⣷⣤⠈
⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣤⣴⡷⢋⣹⣯⡤⠿⢶⠤⣿⡙⠛⣿⢧⢞⣙⠻⣿⣷
⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣯⡏⣸⣿⡁⡞⢽⠳⡍⢳⣸⡄⢸⡝⢦⢸⣟⣉⠉⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⠻⣿⣴⠻⣄⡙⣷⣮⠷⢛⡫⠋⡇⢸⠀⢨⢿⡁⣠⣾⡅⣩⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣿⡏⠙⠒⡾⠻⣄⠈⠫⣭⣭⣟⣋⡤⣾⣴⠋⡰⠋⢀⣿⢁⣀⢻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⡀⠀⠀⠀⠀⠀⠀⡞⢆⢀⡄⣈⠉⢳⣙⣤⣹⣇⠀⢻⡓⠲⠾⠶⠤⠴⠚⢁⡼⠋⢀⣤⠿⣿⠈⣉⣠⣽⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠶⣷⣿⣸⣇⣿⢶⣋⣉⠤⢬⡟⠓⣤⣉⣓⣲⣶⡦⠴⠒⠛⢒⣫⢿⣯⣅⠘⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⡀⠒⠶⢿⣿⣿⡛⠛⢉⢩⣿⡿⠂⢲⠞⢳⠤⠽⠓⢤⣤⣤⣔⣋⣁⣀⣁⣈⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣉⠛⣹⠿⣿⠗⣺⣿⢻⡇⠀⠉⠀⣀⣠⠴⣾⡉⠉⠗⣨⠏⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄⣰⠃⢈⡵⢿⣨⡷⠛⢛⣯⠤⠶⠛⠁⠉⠳⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡾⠋⠀⠘⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⠰⠶⢤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡠⠖⣊⣉⠭⡤⠤⢤⠤⠬⢭⣙⡒⠦⣀⠀⠻⠷⣀⣀
⠀⠀⠀⠀⠀⡰⣡⣶⣋⣭⣥⣴⣶⣶⣶⣶⣧⣔⠀⠈⠑⠪⡻⣄⠀⠀⠈⠑⣄⣀⣠⠄⠀⠤⠄⠠⢄
⠀⠀⠀⠀⢀⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣺⠗⠀⠀⠀⡹⣏⣹⠦⠤⠚⡁⠀⣀⡴⠂⠈⠀⠠⠊
⡴⢊⡭⠭⣙⣿⣌⠻⢿⣿⣿⣿⣿⣿⣿⣿⢿⡇⢀⣠⠤⣚⣹⡟⠋⢀⠄⣸⣷⣚⡉⠉⠀⠀⣠⣆
⣇⢸⡀⢀⡼⣿⣿⠀⠀⠈⠉⠉⠛⠛⠛⠛⠉⠉⣍⣴⣿⣿⣿⢧⣤⡷⢞⣉⠁⠀⠀⠀⣴⣉⣠⣄⣙⡢⢄
⠘⢦⡙⠯⣄⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⣿⣿⣿⣿⠀⣌⢧⡀⠭⠀⢠⢶⡉⠻⠀⠉⠈⠉⠂⢘
⠀⣼⠙⡷⠦⣽⣟⠣⠀⠀⠀⠀⠀⠀⠀⠀⣌⠙⣿⣻⣿⣿⠇⢀⡿⣧⢿⣯⣭⣓⢦⣉⣀⣠⠤⠤⠶⠋⠉
⠀⢿⠠⠂⠀⠀⠙⢦⡀⣠⣄⣀⣄⣠⣀⣦⣿⣼⣿⣿⣿⣿⣶⣄⣠⡿⣻⣧⣩⣿⠟⠁
⠀⠘⢆⠠⠀⠀⠀⠀⠙⠺⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣶⠤⠆⣱⣿⣍⣧⣽⣀⡀
⠀⠀⠈⠓⢤⡀⠀⢀⡀⠀⠀⠈⠙⠛⠿⠟⠿⠿⠟⠛⠉⠉⢀⣠⣾⣿⠛⢽⣿⣭⣿⢿⡆
⠀⠀⠀⠀⠀⠈⠓⠲⠤⣍⣁⣀⣀⣀⢀⣀⣀⣀⣠⣤⣶⣞⣩⣿⣿⣿⢀⡘⠿⠤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠛⠉⠉⠉⠈⠿⣯⠭⠶⣿⢿⣝⢧⣀⣾⣯⣽⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣎⢿⣼⠏⠳⠬⡅⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⡿⠿⠿⠿⠿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⡄⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠁⠀⠀⣰⣾⣷⣦⠀⠀⠀⠀⣿⣿⣿⡿⠀⠀⠀⠀⢠⣾⡿⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠻⣿⣿⡿⠀⠀⢀⠀⠈⠉⠉⠀⠀⠀⠀⠀⣿⡟⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧⠀⠀⠛⠃
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣸⣿⠋⠀⢀⣴⣶⣦
⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢰⣿⣿⣿⡄⠀⠀⠀⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠘⢿⣿⠿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠈⠻⠿⠟⠁⠀⠀⣤⠀⠀⠛⠿⠟⠁⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⠀⠀⣶⡆⠀⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠀⠀⢀⣤⣦⣤⠀⠀⠀⢀⡀⠀⠀⢀⣠⣀⠀⠘⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀⠀⢸⣿⣿⣿⠇⠀⠀⠙⠁⠀⠀⣿⣿⣿⣷⠀⢸⣿⡇⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠁⠀⠀⣻⣿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣷⣶⣶⣶⣶⣿⡿⠿⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣀⣃⣀⣚⣃⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠯⠯⠿⠽⠇