Milk chocolate Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠩⠉⠉⠉⢸⣿⠉⠟⠛⠉⢸⣧⢄⠀⠙⠁⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⠀⠀⢸⣿⠀⠀⢀⠀⢸⣿⣴⠯⠄⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣬⣼⣿⣤⣤⣤⣤⣼⣯⣬⣤⣬⣥⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠈⠉⠋⠉⢹⣿⠉⣉⠉⠉⢸⣧⢩⡍⠉⠁⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠂⠀⢸⣿⠔⣿⣃⠀⢹⡟⠉⠀⠊⡀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⣤⣤⣼⣩⣴⣶⣦⣬⣼⣧⣤⣤⣤⠀⠙⠀⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠩⠉⠉⠘⠛⠀⠉⠉⠉⠙⠋⠉⢁⠅⢀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⢩⠄⠀⠀⠀⠀⠀⠑⠠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡋⢈⣴⠋⠀⠶⡀⢠⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡸⠁⠀⠀⠀⠀⠐⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡬⠀⠀⠀⠁⠀⠀⠀⠀⣠⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⢶⢇⣠⣴⣿⣿⣶⣶⢞⣁⣤⣴⡶⠒⢻⠁
⠀⠀⠀⠀⢑⠂⢤⣀⡀⢀⡠⠐⢂⠉⠀⣀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠀⠀⡸
⠀⠀⠀⠀⢸⣧⠀⠀⠈⠉⣀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢀⣩⠽⠿⠶⠾⠛⠉⠁⢸⣿⣿⣿⣿⣿⣿⡿⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠾⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣝⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣻⠢⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠒⠒⠒⠒⠒⠚⠒⠲⠶⠶⠖⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣰⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡄⠀⠀⣰⣿⣿⣶⡄⠀⠀⠰⣿⣿⣿⠏⠀⣀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⡀⠀⠙⠿⣿⠟⠀⠀⠀⠀⠀⠉⠋⠀⠘⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠁⢸⠄⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡶⢒⢔⠒⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠦⠉⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣀⠤⠒⠀⠁⠀⠀⣀⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠉⠀⠀⠀⠀⠀⠈⠋⠐⠰⢠⡚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢰⠀⠂⠀⢸⠀⠨⠘⠁⢀⡀⢀⣀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠘
⠀⠀⠀⠀⠀⠲⠒⠩⣩⢉⠆⠀⠀⠀⠀⠘⠀⠠⠀⠙⠉⡐⢕⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠂⢀⡀⢠⠀⢠⡄⠐⠀⡇
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠡⠀⠘⠋⡐⠴⢠⠘⠘⠀⠀⠀⠸⠀⠀⠀⠃⠀⠀⠄⠋
⠀⠀⠀⠀⢠⠀⠀⠀⢀⠀⢠⢰⡆⠀⠀⠀⠀⠂⢨⠀⡄⠀⢠⠀⠐⢸⠃⠀⠀⠀⠀⠉⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠈
⠀⠀⠀⠀⠀⠀⠉⠀⢸⠀⠀⠈⠀⠀⢤⠆⢂⡖⢚⡄⡀⠀⢸⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠁⡟⠀⠀⠀⠀⠀⠀⠀⠁⠂⢐⡀⠤⠐⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠠⠀⠂⠉⠀⠀⠀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⠠⠄⠊⠉⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠐⠥⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠶⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⠀⡀⠀⡄⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⠀⠀⡇⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃
⣶⣶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⠁⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠲⠀⠨⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠄⠒⠀⠀⠀⠈⠁⠈⠉⡁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠈⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠤⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⡀⠀⠠⢀⠀⠀⠀⠂⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠞⠀⠀⣀⠀⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠛⠙⠉⡀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠃⠀⠀⠀⠠⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠨⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⡀⡄⢀⡀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠈⠈⠁⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⠀⡀⠀⠀⠀⠂⠄⠈⠉⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡀⠀⢀⡤⠆⠀⠒⠊⠀⠈⠀⠠⠄⠐⠂⠛⠋⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠃⠀⠁⠀⠀⠀⠀⠀⢀
⡀⠀⠀⠈⠀⠤⠤⠀⠲⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⡀⠁⠐⠀⠀⠀⠀⠠⡄⠀⠀⠐⠀⠀⠀⠉⠀⠐⠀⡀
⠈⠀⠀⠂⠀⠀⠀⠀⠀⣀⢀⠠⡄⠐⠂⠙⠀⠀⠀⡸⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⡄⠊⠀⡂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡀⡄⢀⠀⡄⠈⠁
⠀⢃⠀⠑⠀⠀⠒⢸⠀⠀⠀⠀⠥⠤⠄⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠁⠂⠰⠊⡁⠀⠀⠃⠀⠀⠀⠀⠀⠈⢑⠀⠉⠀⠈⠀⡀
⠀⠀⠀⠈⠀⠤⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠒⠈⠐⠋⢀⢠⠀⠀⠀⠀⠀⠀⢠⣴⠟⠀⠄⠀⠀⠀⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠠⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠆⠡⠀⠤⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠠⠤⠄⠀⠄⠠⠴⠆⠀⠀⠀⠘⠚⠈⠀⠀⠀⠀⠀⠀⠈⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠴⠐⠂⠓⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠄⠀⠀⠀⡰⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⠀⠘⠀⠐⠂⠐⠀⠓⠀⠛⠂
⠀⠀⡀⠀⠀⠀⠀⠀⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠂⠀⠀⡄⠀⠀⠀⠀⠀⠀⠚⠀⠠⠤⠀⠀⢀⣀⣀⡀⠀⠀⠠
⠀⢀⡆⢀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇
⢀⠊⠀⠀⠐⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠀⠀⠰⡤⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆
⢠⠀⡀⠀⠀⣂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢈
⢨⠀⠀⣠⢀⡀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠙⣦⠄⠀⠀⠚⠀⠀⠀⠀⠀⠀⡠⠤⡀⠠⠦⠀⠀⠁⠀⠀⠀⠀⠀⡆
⢨⠐⢀⠈⠈⠈⡈⠀⠁⠀⠀⠀⠀⠀⠈⠐⠂⠤⠬⠤⠬⠤⠔⠒⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢀⠀⠀⠀⠀⠇⠀⡠⠒⠂⠈⠉⡐⠒⠤⢀
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢸⠀⡆⡀⣀⡄⢲⠂⠂⠀⠀⡇⠀⠀⠀⠀⠀⠰⢂⡆⠀⢀⠻⠁⠀⠀⠈⠀⠀⠀⠀⠠⠂⠀⣀⢈⠉⢀⠀⠁⢀⡀⣆
⢠⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠄⠀⠀⠀⠈⠀⠀⠠⠙⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⢈⣀⡈⠁⠉⠈⢀⠏
⠘⠀⠀⠒⠀⠐⠀⠄⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠓⠤⣀⣀⠤⣀⡠⠔⠋
⠀⠠⠄⠁⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⠀⠀⠀⠀⠈⠶⡄⠀⠀⠀⠀⡀⠀⠀⠔⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠐⠂⠀⠀⠀⢲⡆⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣿⡹⡄⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣥⠈⠩⣷⡩⠀⠀⠀⣀⣀⣀⣀⣻⣆⣀⣰⣶⣶⣦⡿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡫⠽⣝⠲⡬⣧⠀⣶⠿⠟⠛⠛⠋⠉⢻⡍⠁⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⡴⠷⠤⣀⠈⠁⠛⣧⢻⡀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⣴⣤⡀⠀⠀⠀⠐⠉⠓⣶⢿⣧⢷⠀⠀⠀⠀⢀⣀⡀⢻⠄⠀⠤⢖⣂⣒⣠⡄
⠀⠀⠀⠀⠻⣿⣿⣓⠀⠀⡠⠞⠓⠉⠉⠒⢮⣧⣀⢭⠭⠭⣙⣛⣓⣚⡩⠭⠴⠒⠒⠊⠔⢀⣤⡀
⠀⠀⠀⠀⠀⠈⠛⢿⣷⣴⡶⣄⠀⠀⠀⢀⠉⠉⢻⠉⠉⣩⣍⠉⠉⠀⠀⠑⢤⠀⢠⠖⠀⠈⣾⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣮⣅⠀⣀⠠⠀⢈⠠⠃⠀⢿⣯⡳⡄⠀⠀⢂⣠⡇⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣇⠉⠀⠉⠀⠀⠠⠄⠀⠙⢿⣦⠄⢠⣦⢐⣧⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠄⠚⠀⠘⠻⠛⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠛⢉⣠⠶⠳⣄⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢶⣿⡇⠀⠒⠋⠀⠀⠀⠙⠇⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⢋⣤⣤⡈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄
⠀⠀⠀⠀⠀⠀⣀⣴⡞⠉⠠⠞⠉⠀⠈⢷⡀⠹⣧⡀⠀⣀⡀⠀⠀⠀⣀⡼⣿⣦
⠀⠀⠀⣀⡴⠚⠉⠻⣧⡀⠀⠀⠀⠀⠀⠈⠓⠀⠙⣷⣄⠈⠁⣀⡴⠞⣉⣄⠘⢿⣧
⢀⡴⠚⠁⣠⠴⠛⢦⡈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡟⠁⠠⠚⠁⠈⠳⠈⡿⣷⡀
⣿⣄⠀⠈⠀⠀⠀⠀⠻⡌⠻⣆⠀⢤⣤⠀⢀⣠⡴⠛⠉⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄
⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣀⣠⠶⠋⣡⠶⠛⢷⡀⠻⣷⡄⠀⡀⠀⠀⠀⠀⢀⠽⠛⠙⠒⠢⣤⣤⣄⣀⡀
⠈⢿⣿⣦⠀⢠⣀⣀⡀⠀⢀⣼⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄⠁⠀⣀⡤⠚⠁⠀⠀⠀⢀⠀⠀⠀⠀⠉⠉⣉⡶
⠀⠀⢻⣿⣧⡀⠉⣡⠴⢚⣩⣤⣄⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢈⣩⣴⠋⠁⠀⠙⠶⠀⠀⠀⠈⠻⣤⣴⠖⠛⠋⠁
⠀⠀⠀⠹⣿⣿⡏⠁⠀⠉⠀⠀⠙⠇⠀⢹⣧⠀⠑⠖⠀⣀⡤⠖⠉⠉⠛⠒⠁⠀⠀⠀⠀⠀⣤⣴⡶⠛⢧⡀
⠀⠀⠀⠀⠘⣿⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⣠⠴⢚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠏⠁⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠈⢷⣿⣧⡀⠳⡄⠀⠀⢀⣠⣶⠋⠁⠰⢿⣿⣶⣔⣀⣢⡀⢀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⡿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⢀⡤⠞⠉⢀⣸⣧⣤⣴⡾⠋⠓⠉⠀⡙⠿⢦⣤⡀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣿⣿⣩⣤⠶⠚⠋⠉⠁⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⡌⣿⣆
⠀⠀⠀⠀⠀⠀⠀⡜⠀⢠⣿⣿⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⣠⠔⠊⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠙⣟⣊⣻⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⢿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡪⠁⡠⠊⠁⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⡠⠊⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣦⠀⠀⠀⠀⠀⢀⡴⢁⡠⠊⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣿⣷⡀⠀⠀⣠⠊⢀⠞⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣄⠀⠁⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣴⡶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣷⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⢻⡄⠀⠀⠀⠀⠀⠀⣀⡴⣻⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣿⡄⠀⠀⠀⣠⣶⡾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣆⣠⠾⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣄⡀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣤⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣩⣭⣤⣤⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣿⣿⣿⣿⡇⠀⠀⠀⢸⣿⣿⣿⣿⢿⠟⢁⣤⣤⣾⣿⣿⣿⣇⠀⠀⢸⣿⣿⣿⣿⠿⠟⠋⠠⠄⠂
⠀⠀⠀⠀⢀⢀⣀⣤⣤⣦⣴⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠸⠟⣋⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⡇⠀⠀⠘⠟⠋⣠⠄
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠉⠁
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠉




⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣛⣛⣟⣻⣭⣿⣻⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣭⣭⣿⣭⣿⣯⣭⣯⣭⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡠⣄⣤⣤⡴⢦⣶⡴⠖⠒⠛⠛⢻⣿⠉⠉⠁⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠀⠀⠤⠄⠒⠒⠈⠉⠁⠀⠈⠁⠀⢰⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠘⠂⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⢀⣀⣿⣧⣀⡤⠤⠤⡾⣿⠷⣚⣛⣫⣭⣽⡆
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣛⣉⣩⡭⠭⢽⣷⠖⠚⠓⠚⠙⣿⡏⠉⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⢈⣧
⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠀⠀⣀⣀⣀⣿⡧⠤⣤⠴⠶⠞⣟⣛⣛⣩⣭⡯⣽
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣛⣟⣋⣭⡭⠭⠶⣾⣷⠓⠒⠋⠉⠹⣿⡏⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠉⣿⡇⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⣀⣘⡇
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠄⠛⠋⠀⠀⠂⢀⣸⣿⣦⡤⠴⠶⠒⠛⠟⠛⠉⠛⠉⠉⠁
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠐⠀⠉⠈⠚⠅⠀⠂⢀⠀⠄⠀⠀⠀⣈⡦⠄⡀
⠀⠀⠀⠀⠀⠀⠠⠤⠄⠒⠂⠀⠘⠁⢀⠀⠈⠂⡀⠀⠀⠀⠐⠂⠉⣦⣀⢀⡤⠖⠚⠉⠁⠀⠀⠀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢕⠅⢀⡀⣀⣤⠴⠖⠒⠋⠉⠀⠙⠀⡈⠐⠀⡀⠀⠀⠀⣀⠄⠕⠂⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢴⠂⠋⠀⠐⠄⠀⠀⢀⠀⠀⠀⠊⢢⣀⡀⣤⢖⠉⠀⠀⠀⠀⢀⠀⠘⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠘⠀⢀⣀⠤⠐⠐⠀⠉⠑⠢⠀⠀⠂⢀⠄⠀⠀⠀⠀⡠⠊⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⡗⠸⠋⠠⠀⠀⠀⠀⠀⢀⠀⠀⠑⣄⣄⠀⠈⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢄⢀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠠⠄⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣴⣶⠶⠶⠶⠶⠾⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠿⠿⠷⠶⠶⠶⠶⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣤⣿⣧⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠾⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⣹⡟⠉⠉⠛⠿⢿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣤⡀
⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣷
⠀⢠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠟⠋⣿⡇
⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠿⠛⠉⠀⠀⠀⠀⣿⡇
⢨⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⢀⣠⣤⣶⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⢸⡇⠙⠿⣿⣿⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⣀⣤⣶⡾⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⢸⡇⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣷⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣾⣿⣶⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢸⠀⠀⢠⣿⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⢸⠀⠀⢸⣿⡄⠀⣸⣇⠀⢸⣿⣷⣦⣄⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⠀⠀⢸⣿⡇⠀⣿⣿⠀⠀⠉⣿⠿⢿⠀⣿⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⠀⠀⣼⡿⡇⠀⣿⣿⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⢠⣿⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢸⠀⠀⣿⠁⣿⢸⡏⢹⡄⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⠀⣾⡏⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣾⠀⠀⣿⠀⣿⣼⡇⢸⡇⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⢸⡇⣸⡿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⣿⠀⢸⣿⠀⢸⡇⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⢸⣧⣿⠃⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠁⠀⠘⡿⠀⠀⣿⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⠠⣶⣿⣄⡀⠀⣿⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⠀⣿⠀⠀⠀⠀⢸⡟⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠈⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣿⡆⢸⡇⢹⣇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠙⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠁⢸⡇⠀⢿⡄⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠙⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠘⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢶⣤⣄⣀⠀⠀⢹⡇⠀⠀⣀⣀⣤⣴⣶⣿⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⣾⣿⠿⠿⠟⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢉⣉⣁⣉⣉⣠⣤⣦⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⣉⣉⣈⣉⣁⣠⣴⡆
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢃⣴⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⠿⠿⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⠿⢿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣄⣀⣀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢀⣄⣀⣁⡀⣙⢛⡛⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣻⣛⣛⣻⣟⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠚⠓⠀⠉⠂⠐⠒⠖⠆⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⡙⢦⠀⠀⢀⠀⠈⠐⢄⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠉⠉⠁⠀⠊⠀⠉⠉⠉⠁⠀⠐⠀⠚⠓⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠘⠂⡀⢀⣤⣠⣄⠑⠄⡀⢀⣀⣀⡀⠳⢄⠀⠀⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠈⠠⢠⡀⠀⠀⠀⠀⠠⣀⠀⠁⠁⠀⠐⠁⠈⠉⠉⠉⢀⡸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠛⠂⠈⠰⠀⠒⠒⠒⠂⠙⡢⠀⠴⠤⠤⠄⠓⢀⠀⣠⣄⣤⡀⠢⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠲⡀⠀⠀⡀⠀⠐⢦⡀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠁⠰⣄⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠉⠉⠉⠀⠀⢁⠈⠉⠉⠉⠀⠀⠀⠀⠓⠚⠓⠀⠁⠂⠐⠒⠒⠂⠈⢱⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠌⠓⢄⠀⣠⣀⣤⡉⠢⠀⠀⣀⣀⣈⡙⢦⠀⠀⢀⠀⠈⠳⢄⠀⢀⡔⠋
⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠁⠤⣀⠀⠀⠀⠀⠈⢀⡀⠀⠀⠀⠀⠊⡀⠉⠉⠉⠁⢀⠖⠁
⠀⠀⢦⡐⠓⠒⠓⠀⠁⠄⠐⠶⠶⠦⠈⢂⠄⠠⠦⠤⠤⠙⠂⡀⢀⣄⣠⣌⠑⠄⣠⠖⠁
⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠈⠀⢠⡀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠙⢄⠉⠉⠉⠁⠀⠖⠀⠚⠒⠛⠂⠈⠐⠀⠒⠒⠒⠂⠙⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⢀⣀⣀⡁⠢⡀⠀⠀⡀⠀⠐⢦⡀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠉⠉⠉⠀⠐⠁⡈⠉⠉⠉⠀⡰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⣠⣀⣤⡉⠢⣀⡰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠴⠋

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⠶⠦⢤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠚⠉⣀⣄⣀⣀⠙⠒⠠⠄⠉⠉⠓⠒⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣠⠾⢏⣉⣉⠤⢠⣤⣓⠶⣤⣉⠙⠛⠉⠓⠀⠀⢀⣠⠴⠚⠫⢑⣈⠦⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢯⣝⣳⠦⣤⣉⠉⠛⠻⠾⣍⣁⠈⢉⣀⡠⠤⠖⠒⠋⣉⣤⡤⠖⣋⣩⡤⡖⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠠⠝⡹⡟⠓⢮⣙⣓⠲⠤⣌⣉⢉⡏⣀⣁⡤⠶⣚⡋⠭⠀⢶⢺⠁⠁⠀⣀⡤⠼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⣢⣤⣃⡐⠂⠳⠉⣿⠓⠦⣬⣍⡉⣉⠭⡖⢉⠋⢠⠀⠀⢈⣨⠴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠋⠁⠂⠬⢭⣛⡳⢦⣌⡀⠀⠘⠇⢻⠀⠒⠁⣀⣠⣤⠶⢏⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⢥⣌⣓⠦⣄⣀⠀⠀⠉⠓⠲⢭⣓⡲⠦⠼⠴⠾⣟⣛⣭⠭⠶⡚⠋⢳⡤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⣀⡘⠀⣌⠙⢦⣍⣙⠓⠶⣤⣀⠐⠤⠉⠳⡖⡊⠉⠉⢀⣀⣤⠤⣖⣿⢿⡶⠒⠋⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠞⠉⠻⣦⣄⡈⠀⠙⠉⠙⡓⢾⢿⣗⠢⠤⠥⠴⣒⣺⣋⣥⢶⠟⠋⡉⡜⠙⠋⣀⣈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡼⡜⢆⠀⠠⡉⡛⠿⢶⣤⣒⡀⠈⠛⠉⠙⢲⡞⠛⠉⠁⠟⠀⣊⣀⣠⠤⠖⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⠈⠧⡳⡀⠘⣎⠂⠒⣀⣈⣉⣛⡦⣄⣀⣸⢀⣀⣤⠶⠞⢋⣉⣸⡌⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠈⠣⡤⢱⡝⢆⠊⠟⠛⠉⠉⢁⣀⣀⣠⠭⠿⠛⢛⣓⣻⣭⡭⢥⡶⠖⠚⢻⡀⠀⠀⠀⠀⠀⡠⠂⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠉⠷⣀⠀⠀⢳⡈⠙⣎⢑⣒⣒⣚⣯⡭⠽⠖⠞⠻⠋⠹⠩⠃⠀⠀⠀⠊⢀⣠⣴⠾⠓⠀⠀⠀⠀⠎⠀⠀⣠⣤⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡀⠸⠦⣹⠂⠀⠀⠙⢆⢸⠙⠃⠘⢁⣊⣀⣭⣤⣤⣤⣶⠶⢾⣿⠿⠽⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠙⠟⢳⣾⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠚⠋⠀⠀⠀⠀⠈⠿⠾⠿⠟⠛⠉⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣆⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⣉⣳⣀⣱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⣖⣩⣏⣙⣦⠀⠀⠪⢨⣛⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⣡⠔⠳⣌⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠛⢿⣄⠈⠀⠀⠀⠈⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠔⠋⠙⣆⠙⣦⠀⢀⠀⠀⠀⢀⣽⣧⡀
⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠻⣄⠀⠀⠀⠀⠘⠀⠘⣧⡈⢁⡤⠖⣩⣄⠻⣷⡀
⠀⠀⠀⠀⢠⡞⠁⠀⠊⠉⠣⠘⣦⠀⢀⠀⠀⠀⢀⡿⢿⣇⠀⠈⠀⠈⠁⠘⢷⡀
⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠈⢷⣌⣉⡴⢚⡥⠦⡄⠻⣦⠀⠀⠀⠀⠀⠀⠳⠂⠤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠹⣿⡄⠠⣄⡠⠀⣠⠼⣿⣇⠀⠀⠀⠀⠀⠀⠹⢧⠀⢀⠀⠀⠁⠀⠀⢀⡀⠈⠉⠉⣉⠖
⠀⠀⠀⠀⠀⠀⠘⣿⣦⡤⠖⠫⠖⠲⣄⠹⣧⠀⢀⡀⠀⠀⣀⠤⠎⠁⠀⠀⠓⢀⠀⣀⣻⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀⠀⠀⠀⠀⠀⠙⢷⣀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⢀⣾⠿⠁⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⠳⠀⠀⣀⢤⡞⠁⠴⣿⣶⡄⢀⣀⠀⠀⠀⢀⡞⠁⠀⠀⠀⢸⡿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⠔⢋⣡⡴⠿⠶⠾⠋⠋⠀⠀⠈⠒⢦⣤⠏⠀⠀⠀⠀⠀⠀⠁⠹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠉⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠄⠀⢀⡠⠀⠀⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⣂⢹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠔⠁⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣄⠀⠀⠀⠀⠀⠀⢀⠔⠋⡠⠊⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣧⠀⠀⠀⠀⡠⢊⡔⢈⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⡀⠀⠜⠀⠊⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⠀⠀⠀⠀⣠⣶⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀⢀⣠⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠻⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠆⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠉⠉⠉⣿⠹⠟⠃⢰⣧⠀⠘⠉⣴⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⣰⢀⣤⠀⠀⣧⠀⠀⠉⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⠀⠀⢸⡿⠚⢠⠀⣿⠀⠀⠀⠀⠀⠀⢠⡟⠟⠷⠀⣿⢸⡷⠃⠀⣿⠘⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠿⠿⠿⣿⠶⠿⠿⢻⡟⠗⠻⠒⣟⠀⠀⠀⠀⠀⠀⢸⡗⠿⠿⠷⢿⠾⠶⠾⠖⡔⠲⠶⠶⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⡀⣷⡀⢸⡷⠋⠐⠀⡇⠀⠀⠀⠀⠀⠀⢸⡇⠊⠋⠀⢸⡇⠄⠀⠀⣇⢀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣤⣤⣤⣯⢤⣶⣤⣼⣥⣤⣤⠀⠓⠐⠄⠀⠀⠀⠀⢸⣧⣤⣤⣤⢘⣀⣠⣤⣄⢃⣠⣀⣀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠉⠀⠀⠀⠈⠁⠀⠂⠠⠀⠀⠀⠀⠀⠀⡀⢸⡇⠀⣀⠀⣾⢠⠄⠀⠈⣷⢦⠄⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⡔⠀⠀⠀⠀⠀⠈⢛⢸⡇⠐⠋⠀⢿⠈⠠⠴⠀⡟⠁⠨⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠎⠀⠀⠀⠀⠀⢀⠔⠁⠘⣿⣯⣉⠉⣮⢙⣛⠛⢱⡎⢛⠛⠓⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⠀⠈⠀⠀⠀⣠⠄⠈⠀⠀⠀⠀⡟⣿⣿⠀⢻⣼⣿⠃⢸⠃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠘⣻⣤⣾⣿⣿⣿⣯⣶⡶⠟⠉⡇⠀⠀⠀⠀⠀⠀⡷⡶⠶⠶⡸⠶⠶⠶⢮⠶⠶⠶⠶⡇⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⣤⠘⠒⠠⠂⠀⣀⣤⣶⣾⣿⣿⣿⣿⡿⠛⠛⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⣿⠀⡠⠀⢸⡆⠀⠀⠀⡇⠀⠀⠀⣀⡤⠖⠉⠁⠀⠀⠀⣀
⠀⢀⣹⣷⡤⠶⠚⠋⢹⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢰⣧⣤⣤⣤⣨⣬⣥⣤⣈⣧⣠⣤⣀⡇⠀⠀⠐⠻⢿⣦⣀⣴⡶⠟⡻⠿
⠀⠟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣷⠀⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠈⣇⣀⣀⣀⣙⠀⡀⡀⣈⣇⣀⣀⣀⡇⠀⠀⠀⠀⠀⢀⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣿⢷⣀⣀⣀⣙⣿⣤⣶⠶⠖⠶⠄
⠀⠀⠀⠀⠀⠀⠀⣀⠔⢚⣷⣶⣤⣤⣤⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢶⣟⠁⣀⢀⡀⠀⠀⠀⠀⠀⢿⣿⢋⣉⠁⠀⠈⠻⣶⢒⣀⣀⣤⣤
⠀⠀⢀⣠⣴⣀⣀⣿⣿⡟⣛⣓⣲⣿⣿⣿⣦⣀⡄⠀⠀⣀⡀⠀⣤⡶⢎⠀⠈⠓⣦⣠⢤⠶⠏⠹⢿⡃⠄⢀⣀⡀⠀⠀⠀⢿⢧⣾⣿⡿⣟⣛⡤⠭⠹⠿⠖⠁⠃
⠀⡀⠘⢿⣿⣿⣯⣽⣷⣶⣤⡤⣼⣛⠋⠉⠙⢛⣳⠖⢚⣫⡵⣀⠙⢿⣦⣖⠋⠉⠀⠙⢳⣄⣠⣤⠖⠋⠛⢭⡛⠀⢀⣀⡀⠘⠋⠉⠉
⠀⠀⠀⠀⠉⠻⢿⣿⣿⡛⠛⢳⣿⣿⣿⣳⣞⣩⡤⠚⠉⢉⣩⠥⠆⠀⠙⣿⣷⣴⡲⢿⠋⠀⠙⢶⣌⣢⡤⢴⣉⣾⣿⣿⡉
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣈⠉⠉⠙⠿⠛⠛⠋⠁⠉⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡦⢤⣶⣾⣿⣶⣶⣾⡯⠽⠟⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠿⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠛⠙⠒⠲⠤⢤⣀⣀⠀⠀⠀⣠⠴⠋⢧⣀
⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣩⠷⠒⠃⠀⠀⠀⠈⠱⠤⡀⠀⠀⣀⡀
⠀⠀⠀⠀⣤⣞⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠒⠋⠁⠀⠀⠀⠀⠀⢠⣄⣤⠖⠚⢍⠁⠔⠁
⠀⠀⠀⣸⠁⠀⠉⠙⠒⠢⠤⣀⣀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢀⡀⣠⣢⠏⡉⠉⠀⠅⠀⢅⡀⠄⠈⡄⠀⠂⡠⡀
⠀⠀⠀⠛⠬⢄⣀⠀⠀⠀⠀⠀⠈⠙⠻⡍⠉⠉⠁⠀⠀⢀⣒⢵⡿⠯⠀⡁⠉⠐⠉⠄⠂⣀⠤⠁⡉⠀⠆⠁⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠢⠤⣀⡀⠀⠓⠐⢲⡀⠀⠄⡸⠾⠋⡁⠀⠉⠀⠤⢐⢀⡰⠌⠀⠈⠑⠊⠀⠀⠀⡠⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠲⢤⠬⠃⠀⠳⣄⠀⠀⠉⠐⠀⠠⠈⡀⢀⠤⠂⠄⠀⠀⡀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠑⠘⠦⣄⣀⠀⠀⠀⠀⠀⣕⣀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠙⠦⣀⣀⣀⡀⠀⠈⢏⠓⠒⠦⢬⣿⠔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣖⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠀⠀⠀⢳⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡁⠀⠈⠑⠂⠄⠀⠀⠀⠀⣀⡤⠤⠒⠉⠁⠀⠀⠀⢀⣀⠼⠇⣈⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠓⠢⢍⡓⠢⢄⡀⠀⠀⠀⢠⠉⠁⠀⠀⠀⠀⠀⠀⢂⣉⢥⡴⠾⠋⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡍⠙⠖⠦⡁⠀⠀⢼⣤⠴⠖⢈⣁⣀⡤⠊⠉⠃⠘⠀⠁⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⠲⣤⣄⡀⠈⠀⠀⢸⡇⢠⡤⠖⠚⠋⠁⡼⠁⢀⣴⣊⣤⣴⡂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡯⢿⠿⣶⣄⡀⠐⠀⢸⠀⠀⠀⣠⡿⠤⠚⠛⠉⠉⠀⡀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠸⣆⠈⢮⡙⠓⡤⣼⠶⠖⠋⠁⠀⠀⠀⢀⡀⠠⠤⠤⠶⢛⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢤⡄⠀⢹⡄⣿⠓⣄⠀⠸⠄⠀⣀⡀⣀⣀⣀⣤⡤⡴⠶⠒⠊⣹⠏⠀⡴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠀⠀⠙⣇⠀⠈⠷⢶⠒⠛⠉⠹⠉⠁⠀⢸⡞⢁⠤⠂⠰⠃⠐⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣠⣞⣻⠖⠋⢳⢀⠈⢦⡀⠇⢸⠀⢀⠀⠀⠀⠀⣠⣏⡴⠿⠥⠴⠓⠒⠒⠋⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⣱⡦⡀⠀⢀⠛⠀⠰⢏⡀⢹⢦⠙⠦⠼⠴⠖⠒⠒⠘⠉⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒⠃⠀⠞⠀⠀⠀⠈⠳⣇⡏⠀⠀⠀⠀⠀⠀⣀⣈⣭⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠤⠠⠤⠤⣤⡄⠒⠈⠉⠉⠁⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⣇⠀⠀⠀⠀⠀⠀⡀⠁⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠩⢆⠀⠀⠀⠐⠐⠄⠀⠄⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣇⢨⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢿⣄⠀⠀⢀⣒⣢⣠⣤⣽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠚⠀⠘⠻⣆⢣⢠⣤⣤⣭⣷⣿⡶⠿⠵⠟⣍⡴⠛⠛⠋⠉⠉⠉⠁⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⡷⣄⣀⠀⠘⡆⢂⣏⠉⠁⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣏⡁⠃⠀⠏⣑⠻⡄⢺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⢩⠃⢲⠠⣍⣛⣻⡄⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠤⠤⠔⠂⠄⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠉⠐⠂⠹⠟⠛⡘⣆⠀⠀⠰⠖⠢⠘⣛⣛⣂⡪⠤⠤⠆⠒⠚⣋⣉⣉⡭⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣄⠸⣸⠖⣒⣚⣋⣉⣡⠤⠤⠴⠒⠒⠒⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⢸⡟⠀⠉⠉⠉⠀⠀⢰⠢⠀⣾⡅⡑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈

⠀⠀⠀⢀⠀⠀⠀⠀⠀⢐⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡴⠀⠀⠀⢀⡀⠀⠀⠀⢰
⠀⠀⠀⠆⡀⠈⠀⠀⠀⡜⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⣤⣀⠼⠀⠀⠀⠀⠐⠁⠀⠀⠀⠈⡙⠷⠂⠀⠈
⠀⠀⠀⣤⡉⠂⢄⠒⠠⠱⠲⠤⠤⠞⠤⢄⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠉⢻⠃⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠊
⠀⠀⠀⠀⡐⠠⢄⠀⠀⠂⠈⠙⠢⣮⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⡼⠁⠀⠀⠀⢿⠎⠀⢀⡤⠄⡂⢀
⠀⠀⠀⠀⣍⠒⠠⢤⢀⠀⠀⠀⠀⠄⠀⡈⠀⠛⠢⠀⠀⠠⠈⠒⠹⢲⠎⣅⣀⡀⢀⠎⠎⠀⠀⠈⠀⡀⠐⡌⡆⠀⠀⠀⠀⠀⠐⠀⠃
⠀⠀⠀⠀⠅⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⠀⠀⠁⠀⠀⢀⡀⠀⠀⠉⠛⢿⠌⠀⠀⠀⠳⢄⣰⣀⠤⠃⠀⠀⠀⢄⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠠⡀⠀⢀⣀⠀⠀⢀⡾⠀⠀⠀⠀⢠⡟⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣿⣁⡀⠀⠀⢀⡎⠀⠠⣪⢟⡭⣿⣿⣆⠀⠀⠀⠀⡀⠘⠐⠊
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣶⡟⠀⢀⣄⠁⠊⠀⠀⠛⢉⣄⠀⠀⠀⢇⡀⡀⠀⠀⠄
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠃⠂⠀⠉⠀⠀⠀⣤⠀⠈⠉⠉
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠰⣄⢀⣄⣀⠼⣦⡀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣾⢁⣀
⠀⠀⠀⠉⠑⠒⠀⠀⠀⠀⠒⠒⠀⠀⠀⠠⠀⠀⠀⡀⢀⠄⢀⡽⢞⣫⠝⢛⣡⣷⣀⠀⠀⠀⠰⣿⣦⣀⠈⠙⠯⣌⠙⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡿⣋⣷⡦⣻⣽⣾⡯⣭⣭⣹⠿⠀⠀⠀⠈⠻⣝⠿⠁⠀⠈⠉⠒⠠⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠃⠀⠤⠐⠀⠀⠀⠀⠀⠉⠛⠓⠉⠉⠉⠁⠉⠙⠊⠁⠁⠂⠀⠀⠀⠀⠈⠁⠁
⠀⠀⠀⠀⠀⠀⠀⣲⠀⠀⠀⢆⠠⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡎⡇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢤⡀⠀⢏⡉⠁⣀⠜⠁
⠀⠀⠐⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢀⡂⠀⠀⠀⠰⠀⢀⡉⠓⠀⠀⠀⠀⠀⠐⠒⠢
⠀⠀⠀⠀⠠⠇⠀⡀⠀⠀⠇⡀⠀⠈⠂⠚⠀⠀⠀⠀⠀⢯⠀⢀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠈⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢷⣄⠡⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⣐⢁⠀⠀⠀⠙⣣⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⢸⡆
⠀⠀⠀⠉⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠛⠯⠉⠑⠂⢊⠕⠉⠢⣄⠑⡔⣀⠀⠚⠁⠀⠐⠂⠈⠀⢀⡀⠁⢀⣴⣁⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠈⠻⠿⠉⠀⠀⠀⠀⠈⠒⠀⠄⠈⠐⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠒⠚⠉⠉⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠚⠛⢶⣏⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣄⣠⠎⠉⠁⠀⠀⠀⠀⠈⢿⡀⠀⠀⠄⠀⠀⠀⠀⢈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠚⠋⠀⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⣠⣤⣶⡾⠿⢛⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠈⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⢀⣀⣤⣴⣶⣿⠧⠐⠛⣩⠥⠒⠈⠁⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⡘⣿⣆⢀⣾⠿⠟⠋⠩⠔⠂⠰⣶⡀⠀⢡⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢣⣠⣴⣶⣾⠿⠟⣉⣊⠀⠊⠁⠀⠀⠀⠀⠀⠘⣿⡄⠀⢡⠀⠀⠀⠀⠀⠀⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⡿⠟⣋⠅⠀⠂⠉⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠳⣠⣤⣶⣾⠿⢛⣹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣦⠀⢛⣩⣤⢴⠺⣯⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⢀⣶⡾⠿⣛⣋⢭⡥⡤⣴⣿⣮⣿⡿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢀⣀⣤⣴⣶⡿⠿⣛⣎⣥⣲⣽⢷⣔⣉⣛⡤⠗⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⡀⢸⣿⣛⣩⣥⣾⠯⡩⢿⣧⡽⠾⠚⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣁⣞⢿⣿⣯⣿⠿⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠛⠉⠁




⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠾⠛⠶⣤⢀⣤⡴⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢉⠹⣇⠀⣠⡾⠛⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⢀⡴⢿⡇⢸⡟⢁⣴⣦⢹⣇⣀⣀⣀⣠⡾⢶⣾⠃⢠⡟⣸⠿⣴⠟⠀⠘⠛⠛⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⡎⠀⣴⠁⡘⢀⠈⣤⠀⣠⣉⠉⠉⠉⠉⢀⣼⡏⠀⠊⣴⣿⣤⣄⠀⣠⣶⣿⣿⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣧⣈⣡⡾⠁⣼⣦⡤⠞⠛⣿⠟⠛⢻⠛⣉⠻⠀⢠⠞⢋⠙⢙⡇⢠⡟⢋⡭⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⣿⣿⠟⠁⠀⡁⠀⠁⠸⠇⠉⢠⣃⠄⢀⡛⣀⠀⠈⠀⠟⠀⠾⠁⢸⠀⠘⣡⠏⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠈⠛⢁⣴⣃⣰⣇⣘⣄⣈⣴⣇⣘⣫⣦⣈⣵⣿⠀⠰⠴⠞⠀⠚⠓⠴⣶⣬⣥⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠉⠉⠉⠉⠉⢹⡏⠙⠛⠛⠛⠋⠉⠁⣀⡀⢴⣶⣶⣿⡷⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢶⣤⣤⣤⠶⠾⠛⠉⠻⢶⣤⣭⣤⡴⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠂⠀⠀⠀⣶⠲⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⣀⣀⡟⠀⢀⠀⠀⠀⢸⣀⠀⠀⣀⡀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠋⠉⠙⢉⡗⠛⠋⠉⠉⠉⣹⠋⠉⠉⠉⠉⢽⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢻⣿⣏⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠃⠧⣤⠤⠤⠤⢴⣧⣶⣶⣶⠶⠶⣿⡴⢶⠶⠶⠦⣾⡿⣏⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⢙⡛⠻⣷⡔⠈⠁⠀⠀⠈⠛⠓⠨⢍⡘⠁⠀⠀⠀⢉⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⠖⠚⠁⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠂


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠐⠋⠀⠠⠄⠀⠂⠉⠉⠁⠀⠰⡴⠶⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠀⢀⡀⠀⠀⠀⠀⠈⠁⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢝⡳⠶⠬⠤⠀⠈⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠷⣤⡀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⡽⠲⣶⢶⣬⣛⡿⣿⣭⠉⠀⠲⠆⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠈⡹⢦⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⢹⣟⣶⣎⣉⠟⠻⢿⣿⣻⣦⣄⡀⠀⠉⠒⠽⠒
⠀⠀⠀⠀⢠⠔⠀⠀⠀⠈⠻⢦⣄⠠⠖⠁⠀⠀⠈⠛⢦⣄⣀⣠⣴⠞⠀⠀⠀⠀⢸⣿⣟⣟⣧⡜⠛⢲⣶⡉⢉⠻⢿⣝⢿⣷⡦⢤⡐⠂⠀⠈⢠⡀
⠀⠀⠀⣤⡻⣶⣄⠀⠀⢀⠠⠊⠛⠳⣦⡀⠀⠀⠀⢀⢠⣽⠟⠋⠁⠀⠀⠀⠀⠀⠀⢻⣿⣎⢿⣳⣴⠁⢨⠟⠳⣤⠖⠙⣿⣿⣷⣤⡀⠀⠀⠀⠀⠉⣠
⠀⠀⠀⠘⠻⣮⣹⢷⣆⡉⠀⠀⠀⠀⠀⠙⢷⣤⣾⡿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣧⣝⢿⣷⣧⣠⡄⠉⡳⢯⣀⡼⢿⣿⣿⣟⣻⡭⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠹⠶⢿⣿⣶⣀⠀⢀⣠⣶⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣬⣉⠛⠿⢿⣧⣴⡛⢳⣔⢿⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣧⣯⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣷⢶⣮⣍⣹⣩⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠉⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⡆⢢⡦⣭⣞⣋⣻⣷⢎⡶⣶⡀⡤⠄
⠀⠀⠀⠀⠀⠀⠘⣤⡉⠛⠙⠷⠿⠥⠿⠿⠾⠏⢿⣶⡟⠴⠛⠋⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠈⢣⣄⣐⢀⣀⣲⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣠⣤⠞⠉⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠈⠉⠉⠉⠛⠛⠳⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢻⣧⣴⣿⣟⢳⣇⣦⡀⠀⠀⠀⠀⠀⡀⠳⠆
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡿⣿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠐⣂⢴⣮⠔
⠀⠀⠀⠀⠀⠀⢈⠄⠒⠀⠤⣭⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠒⡄⠀⠀⠀⠀⠀⠀⠀⠹⢾⣿⣾⣿⣿⣿⢿⣿⣿⣿⣴⣾⠷⣿⠗⠂
⠀⠀⠀⠀⠀⠀⠛⠒⠲⠖⠲⠶⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠫⣟⢿⠟⣩⠧⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠽⠋⠕⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡠⠄⡠⣤⣤⠀⠀⠀⠀⠀⠀⠄⠶⠶⠛⠛⠉⠉⡉⢉⡽⢣⣤⠒⢆⠀⢀⡖⢢⣄
⠀⠀⠀⠀⠀⠰⡈⠐⢄⣀⠀⢁⡤⠒⠀⢉⡟⠁⡀⠀⢀⣀⠁⠤⠄⠠⢤⣄⣲⣦⡵⠞⠋⣠⠟⣈⠆⠐⡄⡔⠀⢎⡘⢷⡀
⠀⠀⠀⠀⠀⡆⠈⠑⠂⠂⠤⠉⠀⢀⡴⠋⠀⠀⢡⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢠⡟⠂⠀⢋⠖⠁⠑⢎⠊⠀⠚⣧
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢸⠀⠀⠚⠓⢮⠀⢈⠖⠛⠂⠀⢸
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠊⠉⠀⠀⠀⠈⠉⠂⠀⠘⡇
⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⡆⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⡆⣇
⠀⠀⠀⠀⠈⠓⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢊⠀⣉⢒⠂⠀⠀⠐⠒⠒⠛⠛⠉⠉⢿⡁⠀⠀⠀⢸⠀⢸⠀⠀⠀⠐⣹⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⣠⡤⣶⣯⣶⢿⡷⢿⣿⢿⣺⠟⢋⡩⠭⠝⢛⣓⣢⠉⠛⠒⠂⠘⠀⠘⠂⠒⠒⠋⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣿⠞⣫⠾⣭⢴⡭⢖⢭⣺⣧⣴⠋⢉⣠⡏⢳⡀⠀⢠⠂⡤⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢄
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⡟⢸⠁⢰⠁⣰⢁⠎⠀⠀⠀⢉⠉⠀⢀⠔⠉⠉⢧⢳⠀⡿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⢀⡜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠳⣴⠃⠀⠀⠀⠀⠃⡾⢀⡇⠀⢀⡏⢰⠀⠎⢰⡆⠠⣸⡿⢸⠀⠈⠑⠒⠀⠀⠀⠀⠀⠀⠒⠊⠁⠀⢷
⠀⡼⠁⠀⠀⠀⠠⠤⠄⠒⠁⣀⠔⠁⡿⣇⡀⠀⠀⠀⠀⣧⡼⠀⠀⢸⠀⡇⠀⠀⠘⡇⢀⡜⠁⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢠⠀⠔⢈⣀⠀⠀⠀⠈⠉⠉⠀⣂⠜⠁⠈⠙⠓⠒⠒⠒⠒⠒⠒⠒⠶⠶⠤⠤⠴⠶⠗⠋⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠘
⣼⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡠⠴⠤⠴⢖⣒⠒⠒⠦⣄⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⡠
⣿⠁⠀⠀⠀⠀⠐⠂⠀⠀⠀⠈⠀⠀⠀⢰⠀⠀⠀⡐⣳⣤⠗⠚⠛⠓⠚⢭⣲⢞⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⠐
⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠜⠀⠀⢰⡯⠗⠚⠉⠚⠿⠭⣙⠢⡀⠑⡙⡆
⠈⠓⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣾⠊⠀⢀⠤⠒⠒⠦⣌⠑⣜⣆⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⠀⠀⠈⠳⡜⡜⡖⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠀⢳⡦⠙⠁
⣶⣶⠶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢉⣩⣭⣤⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⣉⣉⣉⣉⣉⣿⡟⢉⣉⣉⣉⣉⣽⡇⠈⣿⠸⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⢸⡇⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⠃⢀⡸⡆⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣉⢻⡇⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠁⣧⢸⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠃⢸⡇⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⡇⠀⠐⢸⣾⣿⠿⠟⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢸⣷⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣼⡏⣥⣭⣭⣭⣭⣿⡏⢨⣭⣭⣬⣥⣿⣿⢉⣭⣭⣭⣭⣽⣧⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⡇⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⣠⠟
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⡟⠀⢸⡇⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠁⢸⡇⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⡇⢀⠻⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠛⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠙⠛⠷⣶⣶⣶⣶⣶⣿⡇⢰⣶⣶⣶⣶⣾⣿⢠⣶⣶⣶⣶⣾⠷⠖⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠠⢍⡙⠻⢿⣿⣷⣾⡿⠿⠿⠿⣿⡿⠾⠛⢋⣉⠥⠆⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⣄⣀⠉⢛⠛⠾⠁⠀⠀⠤⣤⡤⣤⣀⣠⣭⠁⠀⠀⡀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠉⠉⠑⠉⠉⠉⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⣟⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⡗⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣤⠤⢤⠤⠤⠤⠤⠤⠤⠤⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⡤⠼⠃



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⠞⠁⠘⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⠞⠁⠀⠀⠀⠀⠉⢻⡦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣺⣾⣧⣄⠀⠀⠀⠀⢀⡴⡫⣪⠾⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⠞⠉⠙⢿⣿⣶⡄⢀⡴⡫⣪⠞⠁⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⠞⠁⠀⠀⠀⠀⠙⢿⣿⡫⣪⠞⠁⠀⠀⠀⠀⠀⢉⡿⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣺⣾⣧⡀⠀⠀⠀⠀⢀⡴⡫⣪⢿⣿⣶⣀⠀⠀⠀⢀⡴⡫⣪⠞⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⠞⠉⠻⣿⣿⣦⡀⢀⡴⡫⣪⠞⠁⠀⠙⢿⣿⣦⣀⡴⡫⣪⠞⠁⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⠞⠁⠀⠀⠀⠈⠻⣿⣿⡫⣪⠞⠁⠀⠀⠀⠀⠀⢙⡿⣯⣪⡞⠁⠀⠀⠀⠀⠀⢀⡼⡫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡪⠳⢨⡀⠀⠀⠀⠀⢀⡴⡫⣪⣿⣿⣦⡀⠀⠀⠀⢀⡴⡫⣪⠾⢿⣿⣦⡀⠀⠀⢀⡴⡫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡪⠊⠀⠀⠑⡙⣦⠀⢀⡴⡫⣪⠞⠁⠈⠻⣿⣿⣦⣀⡴⡫⣪⠞⠁⠀⠀⠙⠿⢿⢦⡴⡫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡪⠊⠀⠀⠀⠀⠀⠐⣸⣿⡫⣪⠞⠁⠀⠀⠀⠀⠈⢻⡿⣯⢪⡞⠁⠀⠀⠀⠀⠀⢀⡴⡃⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡪⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠞⢿⣿⣄⠀⠀⠀⠀⢀⡴⡫⣪⠾⣿⣿⣦⡀⠀⠀⢀⡴⡫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠪⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⢻⠛⠳⣄⣀⡴⡫⣪⠞⠁⠀⠈⠻⣿⣿⣦⡴⡫⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡪⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠪⣣⡿⣯⣪⡞⠁⠀⠀⠀⠀⠀⢈⡿⡻⠊
⠀⠀⠀⠀⠀⠀⠀⡠⡪⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣽⣪⡾⣿⣷⣄⠀⠀⠀⢀⡴⡫⠊
⠀⠀⠀⠀⠀⡠⡪⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡙⢄⠈⠻⣻⣷⣤⡴⡫⠊
⠀⠀⠀⡠⡪⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⢈⡿⡫⠊
⠀⡠⡪⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣴⡫⠊
⠲⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡸⠊
⠀⠈⠮⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡨⠊
⠀⠀⠀⠉⢪⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⠊
⠀⠀⠀⠀⠀⠈⠪⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⠊
⠀⠀⠀⠀⠀⠀⠀⠉⠪⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡪⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠪⡢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡪⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠮⡢⡀⠀⠀⠀⠀⠠⡨⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⡢⡀⡠⡢⠌
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣘⣪⣚⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡠⠀⠀⠀⠀⠀⠈⠈⣀⣀⣀⠀⠀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⠀⢀⣀⣠⣀⣀⠀⠀⣀⡀⢀⣠⡀⠀⣠⣄⡀⠀⠼
⠀⡔⠀⠀⠀⠀⠆⢰⠁⠀⠀⠈⢱⢸⡭⢭⢿⣿⣿⣸⠁⠀⡠⠘⣧⢸⠁⠀⠀⠀⢃⢸⠁⠈⠉⠀⡽⡾⠁⠀⠈⢳⡄
⠀⡅⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣸⢸⢠⣞⣺⣦⣼⢻⡀⠞⠁⢀⡏⢸⣀⡀⠀⠀⡸⠈⠢⣀⢀⡔⠁⠣⣀⠀⣀⠼⠁
⠀⣙⣒⣒⣂⣀⡁⠀⡉⢂⠒⠂⠁⠈⡙⠗⡿⢿⡉⠀⣭⠭⠭⠭⡀⢠⠟⠛⠒⠋⢳⢀⣶⢚⢛⢢⡀⡴⠃⠣⢄
⠀⡇⠀⠀⠀⠀⡥⠸⡀⠄⠁⠢⠀⢰⢠⠞⡡⢂⣼⣴⠇⠀⠀⠀⢧⢘⣲⣖⣲⣶⣞⢻⣇⠧⠄⢱⡇⠑⠦⡀⢀⣽
⠀⣇⠀⠀⢀⣀⣰⠀⠈⠂⠄⠑⢈⠿⢇⡔⣠⢏⡼⠛⡆⠀⠀⢀⡞⠸⣁⣸⣅⣀⣽⠈⠫⣵⠾⠛⠀⠀⠀⠈⠛⠸
⠀⢩⠭⠓⠉⣭⡁⢠⠔⠂⠀⠘⢥⢀⠆⠩⡩⠿⢦⡀⡨⠛⠉⠀⢤⢠⠴⠶⡶⡖⢶⢰⣟⠉⠁⠉⡇⣔⢻⣹⡿⣾
⠀⠃⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⢸⢸⡀⠀⠀⠀⡼⢸⠁⠀⠀⠀⠀⡿⠨⠀⠀⠄⢸⢸⡇⠀⠓⢠⡿⣿⣿⣿⣍⣿
⠀⠣⣀⡀⠀⠔⠁⢸⣀⠀⠀⠀⣠⠀⠑⢄⡀⠊⠀⠀⠣⣄⣀⠤⠎⠐⣦⣁⣀⣈⡼⠀⠧⠼⠀⠿⠇⠙⠧⠷⠞⠉⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡞⠳⢤⣀⣀⣠⣴⢿⣀⢀⣰⣤⣤⠴⠿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠿⢄⡀⠀⠈⠉⠁⠀⢢⣭⠟⠁⠀⠀⠀⠀⠈⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠈⠛⢶⣀⠀⢀⣵⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢀⠙⣷⣟⡁⠀⠀⠀⠀⠀⠀⠀⡀⢀⣤⠞⠁⠈⠛⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡍⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠈⠻⣶⣄⢄⠀⠀⡀⢀⣵⡿⠃⠀⠀⠀⠀⠀⡙⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⣠⡾⠷⣶⠟⠒⠳⣦⡀⠀⢀⣴⠿⠁⠀⠀⠀⠀⠀⠙⢿⣦⣀⣵⡿⠋⠱⠀⠀⠀⠀⠀⢀⣼⣾⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢉⣁⣀⠀⠤⢤⡄⠀⣎⠛⢿⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⣼⡿⢿⣷⡀⠀⠀⠀⠐⠀⣸⡾⢣⣽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⡛⠋⠉⠉⢛⣦⠤⠲⠄⡼⠃⠈⣿⠿⢷⡄⠀⠀⠀⠀⠐⣤⢾⠓⠀⠀⠙⠳⣼⡆⠀⢀⣾⣏⣾⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⢡⡆⠀⠀⠀⠀⠀⣻⢧⣤⡴⠞⠻⡳⣼⣀⠀⢻⢷⠶⢤⣤⣾⣝⠅⠀⡐⠄⠀⠀⠘⠟⣶⣟⣿⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⢸⠀⠀⠀⠀⠀⠀⣏⠀⠉⠀⠈⠄⢸⠛⠿⣏⣀⣀⣙⡆⠀⠀⠙⠶⠶⣶⡄⠀⠀⣠⣾⣝⡿⠋
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⡞⠀⠀⢸⡄⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⡜⠀⠀⠈⠉⠙⣿⠀⠋⢠⠶⠆⠀⠘⢷⣌⣼⣿⣷⠟⠁
⠀⠀⠀⠀⠀⣠⡞⠁⠀⢠⠇⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⡁⠀⠀⠀⠀⣾⠃⣴⢶⡄⠀⣠⣄⠀⠀⠻⢟⣿⢿⡄
⠀⠀⠀⣠⡾⠋⠀⠀⠀⢸⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠞⠁⠈⠳⡌⠁⠈⣀⡀⠀⣀⡀⠈⠻⣆
⢀⣠⡾⠋⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠶⣾⣿⣷⣿⠘⡉⠋⠀⢹⣷⣤⣼⠃
⣼⡏⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣿⡏⠀⠰⣿⡉⢸⣿⠿⠁
⠙⢷⡄⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⣠⡾⠉⠄⢠⡼⠛⣧⣀⣴⠿⢷⠾⠁
⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⣠⠾⡃⠀⢀⣴⠟⠀⠀⠈⠛⠃
⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⢸⡀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠃⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⢇⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠘⡄⠀⠀⠀⠀⠀⠈⢦⠀⠀⢀⣴⠋⠀⢀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⠀⠀⠀⠀⠀⠀⠀⠑⣠⡞⠑⠀⣰⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣆⠀⠀⠀⠀⣠⠞⠁⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⣠⡾⠁⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣴⡾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠒⠋⠉⠉⠀⠀⠀⠈⠉⠙⠒⠦⠤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠛⠒⠶⠶⣯⣬⣟⣳⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⠽⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⣹⠋⠙⢻⢿⡏⠛⠲⠦⣤⠴⠒⠊⠉⠀⠀⢀⠀⢸⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠐⣵⠋⡻⣦⣀⠀⠏⢀⣀⠤⢒⣊⣥⣤⠞⠉⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⢀⢠⣿⠁⠀⣇⣾⠷⢦⣤⠌⠒⠋⠁⠀⢸⢃⣠⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⡠⢃⡟⢸⠀⢀⣿⣇⠀⠀⠀⠀⠀⣀⣠⣴⡾⠟⠉⠱⣄⡀
⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢀⡜⣡⢿⡀⣸⡶⠛⠛⠿⠿⠶⣶⣖⡛⠹⠛⠉⠀⢀⠀⢀⡔⡿
⠀⠀⠀⠀⠀⢠⡟⠉⠓⠲⠦⢤⣀⣀⠀⠀⠀⠀⠀⣠⢎⡼⡇⠀⣡⣿⣧⣄⣀⣀⠀⠀⠀⠀⠉⡆⢀⡠⠚⣡⡖⡽⠀⢣
⠀⠀⠀⠀⠰⡿⣭⣓⡂⠤⠀⡀⠀⠈⠉⢳⡄⢀⡴⢃⣾⠀⣿⣴⡟⠛⠛⠓⠢⠤⢭⣭⣁⡀⠀⠀⢈⣴⠞⡇⢼⣡⡶⠋
⠀⠀⠀⠀⠀⠹⡀⢈⠉⢛⠳⣤⣀⡀⠀⠠⠿⠟⣡⡞⣿⢀⣾⣿⣤⣄⣀⡀⠀⠖⠉⠋⠉⠉⠉⠙⢻⡅⢀⣿⠞⠋
⠀⠀⠀⠀⠀⠀⠑⠚⠦⠬⠷⢄⡀⠙⢿⡒⠒⣾⣏⠀⢠⣿⠏⠉⠉⠉⠉⠉⠉⠛⠒⠶⠤⣴⣂⣀⢸⣧⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠴⣤⣘⣏⣢⣾⠟⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⢀⡀⠀⣀⠀⠀⠉⠉⠁⠀⡠⠊⢉⢻⣦⡀
⠀⠀⠀⠀⢀⡄⠈⣈⠹⣾⡿⢂⣡⠄⢴⡏⠷⢄⡀⠀⣰⠋⠀⠀⣸⡤⢿⣿⣀
⠀⠀⠀⠀⠀⠙⠚⠲⠾⠿⢄⣈⢀⣀⡃⣙⣤⡾⠁⠀⠣⢄⣀⣈⣉⣠⡼⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠙⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣋⣠⣀⠀⠀⢀⣌⡷⢦⡀
⠀⠀⠀⠀⠀⢀⡤⠾⣅⡼⢿⠻⣿⣆⣰⣿⣿⠙⣦⡽⠳⣄⡀
⠀⠀⠀⢠⣖⠋⠀⠀⠈⢧⣈⠳⣌⣿⣿⡷⢃⡤⠏⠀⠀⠀⠙⠦⣄
⠀⠀⠀⢸⠉⠳⣄⠀⠀⠀⣩⠟⡿⢻⣟⠻⣿⢦⡀⠀⠀⢀⡤⠞⢹⡄
⠀⠀⠀⠈⠳⣄⠀⠙⣶⡊⠁⢸⠃⢸⡝⣆⠈⣳⠉⣳⡴⠋⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠈⠳⢄⣿⠙⢶⣿⠤⠼⠇⠘⢋⣷⡞⠁⣇⣠⠞⠉⠀⣠⡾⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣸⠈⠳⣄⣀⡴⠋⠸⣇⡴⠋⠁⢀⡤⢞⡁⠀⠀⠀⣉⡷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠈⡇⢀⣠⠞⠁⠀⣀⡴⢋⣼⣿⡟⢮⣥⠾⠋⣤⡈⠛⢲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠷⠋⠀⠀⣠⠾⠃⠙⣿⣟⢛⡷⠞⣙⢷⣆⠈⣰⢷⠋⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣅⠢⠈⠊⣨⡼⠻⣄⡶⠐⣨⣬⠟⢧⣀⡑⠈⣠⡶⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠙⠦⣟⠁⠀⠀⠘⣙⣶⡋⠁⠀⠀⣉⡷⠟⠁⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠙⠮⣥⢿⣿⣿⡏⢳⣤⠞⠋⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣄⠀⠀⠀⠀⠀⠈⠙⠯⣭⠴⠋⠀⠀⠀⠀⠀⠀⣠⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⣿⠀⠀⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣿⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⣄⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡄⠀⠀⠀⣀⡀
⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⡌⠉⡀⠙⣶⣂⠀⠀⢠⣄⣀⣰⡿⠃⢦⣄⣀⣘⣿⠆
⠀⠀⠀⢻⡇⠘⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡾⠀⠀⢸⠀⣿⡏⡆⠀⠀⠉⠉⠁⠀⣤⣤⡈⠉⠉⠀⠐⢲⡄
⠀⠀⠀⠘⢷⣤⠐⠀⡀⠈⠀⠀⠀⠀⠀⠀⢀⢸⠇⠀⠀⢸⠀⣿⣿⠀⠀⠀⠰⢥⣄⣴⡾⠟⠁⠀⡀⢀⣴⡿⠁
⠀⠀⠀⠀⠈⢻⣧⣌⠐⢀⠀⢂⠄⠀⠀⠀⠈⠘⠀⠀⠀⠀⠀⢹⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠛⠁
⠀⠀⠀⠀⠀⠀⢻⣿⡦⡀⢪⠄⠐⡄⠀⠀⢀⠀⡄⠀⠀⠀⡇⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⣜⠦⠀⠀⠀⠀⣆⣷⣆⠀⢸⣷⣿⡿⠀⠀⠀⠀⢀⡀⣹⠟⢻⣿⠷⠴⣾⡅⠄⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠷⠦⠥⠀⠀⢻⣼⣿⡦⣸⣿⡿⠃⠀⠀⠲⣦⣀⠽⠃⢐⣿⡿⢶⣶⣿⣷⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⡤⡤⠄⢤⣤⣤⠄⢠⣤⢤⢍⠛⠿⠿⠛⠀⠀⠙⠲⢾⣿⣟⣶⣛⣻⣿⣷⣿⣿⡿⠟⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠁⠀⠀⠀⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⡰⠶⠂⣿⠠⠴⠆⢸⡅⠶⠦⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠀⠀⢠⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡿⠀⠀⠀⢸⠇⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⣿⠛⠓⠉⣻⡙⠛⢂⣼⡇⠀⠀⠀⠀⠄⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⢠⡄⣀⡀⠿⣄⡄⣠⣿⣧⣤⣤⢽⢷⡀⡆
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣬⡇⠀⢹⡷⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠛⠀⡤⠂⠀⠀⠀⠀⠠⠤⢦⣤⡔⠲⣶⠖⠚⠃⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣒⣶⣶⣶⣼⣥⣶⣿⠅⣀⡀⡛⠓⠶⣄⣲⣶⠶⠶⠤⣤⣄⣈⣡⣿⣿⣆⠀⣀⣤⡄
⠀⠀⣹⢦⡠⣄⣀⣾⣴⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠈⢙⠞⢿⡒⢦⣄⣈⡁⠐⠂⠚⠋⠁⠀⢀⣠⣼⣿⣿⣿⠃
⠀⠄⣠⠈⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠐⠀⠉⢺⣍⠉⠉⣛⣳⣶⣤⣀⠀⣽⣿⣿⣿⣿⣿⣿⠄
⠀⠘⠁⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠌⣱⣿⣿⣿⡿⠿⠿⠷⠿⠟⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⢀⡀⢀⣀⠀⢀⣀⠀⢀⡀⠀⡀⠀⠀⣀⠀⣀⣀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠹⠇⣿⢸⡇⣿⢹⡇⣿⠹⠇⡏⢹⡆⡇⠀⢰⣿⡆⢹⡏⢹⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⡄⣿⢹⡇⣿⢸⡇⣿⢠⡄⡇⢸⡇⡇⠀⣸⣭⣧⢸⡇⢸⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠛⠘⠃⠙⠛⠁⠙⠛⠁⠙⠛⠀⠛⠛⠛⠀⠛⠘⠃⠈⠛⠛



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠲⠤⠤⠤⠀⢀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢹⡿⡀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⡟⠀⠩⠀⠀⠀⠉⠉⠙⠒⠒⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⡞⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠂⠀⠀⠀⠈⠉⠉⠀⠈⠀⠀⠄⠜⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠥⢐⡒⠀⠀⣀⡠⠄⣀⣀⣁⢈⠞⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠫⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⠀⢃⠎⠀⢰⠫⢄⣀⡀⠉⠉⣒⠶⠠⢤⣦⠾⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠑⠁⠀⠀⠀⠀⠀⠀⢀⠊⠀⠠⢠⠎⠀⢠⠇⠀⠀⠀⠈⠁⠈⠀⠀⠠⠂⠵⠊⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠃⠤⠀⠀⠀⢰⠂⠀⠀⠙⠒⠢⠖⠻⠤⠠⠿⠁⢀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⢀⣠⠿
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠃⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⡦⠤⣤⣀⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⢤⡼⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡏⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠈⠉⠀⣀⠀⠂⢂⡀⠀⡎⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀⣉⠈⡡⢸⢁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠓⠒⠲⠦⠤⣤⣤⣀⣸⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣲⠄⠀⠀⠴⠦⠶⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠊⠉⠀⣰⠆⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⠀⢈⠋⠉⠉⠒⠂⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠠⠤⠷⠧⠤⡤⠤⠀⠳⣀⠆⠀⠀⠰⣏⡂⣖⠀⠀⠀⣀⠈⡍⠁
⠀⠀⠀⢀⡀⠀⠠⠔⠂⠀⠀⢀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠒⠒⠒⠀⠦⠤⠄⠒⠂⠀⠁⠀⠀⠀⠀⠀⠉⠉⠉⠙⠒⠈⠛⠋⠉
⠀⠀⠀⠨⡀⠲⢄⣀⢠⡴⠚⠋⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠉⠒⠈⠿⣠⣒⣦⣅⡵⡀⠨⠐⠀⠀⠀⠀⠀⠒⠁⢀⡁⣄⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣂⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢔⠀⢀⠀⠀⠀⢠⡆⠄⣤⡀⠀⠀⠀⠀⠐⡦⠈⣶⡬⠔⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⢀⠀⠀⠀⠀⠰⣌⠀⠀⢐⣀⡥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠈⠂⠁⠀⠀⠀⠀⠀⢰⡅⠠⡔⡄⠤⠁⠔⠉⠔⡀⠀⠀⠀⠘⢆⢛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠀⠀⠀⠁⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⢦⣱⡀⠀⠴⢂⡄
⠀⠀⠀⢀⣀⣀⣈⠀⢠⠥⠒⠂⠀⠀⢬⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠋⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣡⣴⢺⠿
⠀⠀⢀⠂⡴⢀⠌⠾⠃⠀⠀⢬⣴⣤⣈⠼⡦⠃⠀⠀⠀⢀⡠⠤⠢⢂⠠⠴⢊⠍⠁⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⠠⠠⡀⡀⠀⠀⠀⠙⠉
⠀⠀⠘⠶⠶⠾⣇⡀⣀⣵⠠⡶⣜⣩⠜⠀⠀⠀⠀⠀⠀⠀⡴⢘⣉⣠⠤⠚⣁⣀⣄⣀⠀⠀⠀⠀⠀⢸⡀⠉⠀⠒⠳⣄⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⠽⠛⠊⢁⢉⢀⠨⢄⢈⡇⠀⠀⠀⠀⠀⠷⢃⣀⣀⣀⣄⡀⢷⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⠤⠴⠾⠶⠒⠋⠉
⠀⠀⢠⠀⠒⡛⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠒⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠈⡀⠠⠄⠈⠾⡄⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢯⠀⠀⠀⠀⢠⡋⠀⠄⠀⠀⠂⠈⠀⡀
⠀⠀⠀⢙⠂⠀⠀⠀⠰⠀⠀⠀⠀⠀⠓⠂⠈⠀⣀⠒⠀⠀⠀⠀⠐⠒⠆⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⣸⠏⠀⠀⠀⠀⠘⡴⠀⠂⠄⠲⡑⠚⣠⠖
⠀⠀⠀⠈⣆⡀⠀⣀⠴⠣⠀⠀⠀⠀⢠⢴⢤⣀⡠⠜⠃⣀⡈⠀⣠⡶⠀⠀⠀⠀⠀⠠⣉⣀⣤⠔⢢⠎
⠀⠀⠀⠀⢙⠋⠀⠀⠀⠀⠁⠀⠀⠀⠘⡀⡀⢠⢍⠠⠶⠒⢦⠚⠘⠓⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⢧⡀⠐⠂⣀⠽⠀⠀⠀⠀⢇⠀⣠⣀⣀⡀⠤⠴⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠤⠠⡀
⠀⠀⠀⠀⠀⠈⠓⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠀⢤⡒⠚⠉⠁⠙⢧⠀⠀⣀⣸⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢴⡒⢞⠉⠁⠙⣄⠀⠀⣀⣄⣱⣀⣤⠾⠷⠾⢿⡉⠉⡉⠈⠢⡀
⠀⠄⠀⠀⠒⠂⢀⠀⠀⠀⠀⠀⢀⡄⢀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠸⢷⡀⠀⠀⣈⠳⣤⣤⣤⠶⠾⢶⠛⠛⡉⠁⢻⡀⠀⠀⢀⣀⣻⣠⠤⠴⠷⠓
⣄⠤⢄⡠⠀⠠⠘⢆⠀⠀⠀⠀⠋⠀⠀⠀⠉⠑⠁⠁⠀⠀⠀⠀⠀⡈⣷⠚⠛⠋⠉⢩⠀⠠⠀⠀⠀⠄⠀⣁⣤⡶⠷⠔⠋⢉⠁⠀⢀⡄⠠⠤⠔
⠰⠀⠤⠤⠔⠇⠐⠀⠀⠀⠀⠀⠠⣦⡅⣡⣀⣮⡀⠤⠔⠁⠀⠀⠀⠘⡇⠣⢀⣀⣠⣤⠧⠔⠚⢛⠉⠉⠁⠀⢀⣠⠾⠤⠾⠃⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠑⠄⠂⠘⢛⠁⡄⠀⠀⠀⠀⠀⠀⠹⣾⠉⠁⣀⣀⡴⠶⠄⠒⠛⠓⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣠⣄⡀⣉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⢠⠀⡄⣠⣄⢀⣤⡀⣤⣄⢠⠀⠀⣤⠠⣤⡄⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⢸⣤⡇⡇⢸⢸⠀⠁⡇⣿⢸⠀⢰⢿⡆⢸⠀⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠟⠸⠐⠇⠷⠾⠸⠶⠇⠧⠟⠸⠦⠼⠛⠇⠸⠀⠿⠤



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠒⠒⠂⠀⠒⢒⠦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠳⠒⠒⠒⠦⠤⠄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠉⠀⠀⠀⠀⢂⠀⢀⠎⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠤⣀⣀⣠⢀⠎⠀⣼⠇⠀⠀⠀⠀⠀⠀⡇⢀⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡃⠀⠀⠀⠀⠀⠀⡠⠁⠀⢀⠊⠀⡜⠓⠀⠄⡈⠁⠝⠃⠒⠷⢛⣷
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠁⠀⠀⠀⢀⠀⠀⢤⣀⢀⣠⠇⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⢘⡄
⠀⠀⠀⠀⠀⠀⠀⡯⠀⠀⠀⠀⢐⠇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⢀⠀⠀⠀⠀⠈⠀⠀⣠⠔⠋⠁
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⣤⢤⣀⣀⣀⡴⠊
⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⢤⡼⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢰⠁⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡼⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠒⠤⠤⠤⢄⣀⣀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠁⠀⣰⠏⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢶⣍⣀⣉⣉⣉⠙⠛⠒⠒⢐
⠀⠀⠀⠀⠀⣠⣾⣄⣀⣐⣀⣀⡟⢠⠍⠉⣳⣆⡤⠀⠀⠀⠀⠀⠀⣤⣀⣀⣀⠁⠀⠉⠉⠉⠳⢀⠉
⠀⠀⠀⠀⠀⢧⣦⣤⣬⣭⣍⣉⣉⣿⡷⠟⣋⠡⠒⠁⠀⠀⠀⠀⠞⠛⠻⠛⠛⠛⠛⠓⠒⠂⠒⠛⡁
⠀⠀⠀⠀⣠⣸⣻⣯⣛⢦⡴⠟⢋⣡⡴⠊⠀⠀⠀⠀⠀⠀⠀⠈⠷⢿⠿⢿⡻⠿⠛⠛⠛⢉⠉⠟⠁
⠀⠀⠀⠀⠓⠮⢭⣛⡛⠿⢷⠞⡉⠋⠰⠦⠶⠀⠀⠀⠀⠀⠀⠀⠈⢂⣰⠁⣀⠤⠐⡀⢅⠀⠠⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠚⠂⠐⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠤⠄⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣆⠀⠀⠀⠀⠈⣦⣄⣀⡀⡀
⠀⠀⠀⠀⢀⣠⡤⣼⣿⣶⣷⣄⡀⠀⠤⠄⠙⠓⠀⠀⠀⠀⠀⠀⠀⠆⠛⠻⠗⢀⣀⣤⠤⠤⠀⢰⠃
⠀⠀⠀⠀⠻⣷⣾⣦⠙⠛⢿⢿⣿⡆⢀⣠⠤⠶⣦⠀⠀⠀⠀⠀⠀⠰⣦⠤⣤⣀⣀⣀⣀⠀⠀⠀⣹⠆⠄
⠀⠀⠀⠀⠀⣈⡙⠿⣿⣷⣢⡑⠎⠉⠉⢐⡚⠉⠈⠐⡂⠀⠀⠀⢠⡀⢻⣷⣝⢿⡂⠘⠉⠛⠉⠈⢉
⠀⠀⠀⠀⠀⠉⣅⣀⠈⠛⠻⢿⣷⠂⠁⠀⠠⠐⠂⠀⠀⠀⠀⠀⠀⣄⠀⠩⡟⠈⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣯⣉⣉⣩⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣞⣧⣤⣤⡤⣟⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠉⠉⠉⠉⠉⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⢤⣄⣀⣀⣀⣤⠴⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⢀⣀⣠⣤⣀⣀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠚⠉⠻⡄
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⣠⠶⠋⠉⠁⠀⠀⠀⠉⠙⠳⢤⡀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⢀⡞⠀⢀⡞⠁⠀⢀⣤⠴⠖⠒⠶⢤⣄⠀⠀⠹⣆⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⣸⠁⣴⠋⠀⣠⠞⠉⠀⢠⢦⣠⣦⣀⡌⠙⢦⡀⠈⢳⡀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⡟
⠀⠀⠀⠀⠀⢀⡏⡼⠁⣠⠞⢁⣠⣾⣦⣿⣯⣿⣿⣿⡇⣠⣦⠙⢦⠀⠹⡜⡇⠀⠀⣀⣀⣤⣤⠤⠤⠤⠤⠤⠤⡇⠀⣸⣥⣀⣀⡀
⠀⠀⠀⠀⠀⢸⠃⠁⢠⠏⣠⡿⢿⣟⡿⠙⠋⠈⠉⠛⢿⣿⠏⡟⡌⣧⠀⠁⣷⠀⢸⠛⠲⠶⠶⠦⠤⠤⠤⠤⢤⡷⢤⡿⠴⠶⠟⣿
⠀⠀⠀⠀⠀⣼⠀⠀⣿⡤⡷⡰⡿⠈⠀⠀⠀⠀⠀⠀⠀⠛⣾⢟⠷⣸⡆⠀⢸⠀⢸⡇⠀⣶⠀⠀⠀⠀⠀⠀⢰⡇⢸⠇⠀⠀⢀⡇
⠀⠀⠀⠀⠀⣿⠀⢀⣿⠻⢷⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣯⡿⠟⡇⠀⢸⡇⠘⡇⠀⢻⠀⠀⠀⠀⠀⠀⢸⠃⣾⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⢸⡏⢳⠯⣄⣀⣀⣀⣠⢤⢤⡀⣄⣠⣄⢀⣍⣀⠀⡇⠀⢸⡇⠀⡇⠀⢸⠀⠀⢀⣀⣀⣀⣸⢀⡇⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣿⠀⠘⡇⣽⣾⢾⢹⡍⡜⡣⢘⡳⣛⡄⠿⣸⢻⣸⠟⠁⡇⠀⢸⠁⠀⣿⣴⣾⣛⠉⠉⠉⠉⠉⠻⠾⢋⣛⣲⣆⣿
⠀⠀⠀⠀⠀⢸⠀⠀⣷⠈⠙⠉⠈⠛⠃⠈⠋⠉⠁⠉⠉⠁⠈⠁⠀⢸⠇⠀⣸⠀⠀⢹⢻⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⡇⡏
⠀⠀⠀⠀⠀⢸⡆⡀⠘⣆⠘⣏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⠀⢀⡟⢀⠀⡿⠀⠀⢸⣼⡌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⣇⠹⡄⠹⡄⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⢀⡾⠀⡾⢠⡇⠀⠀⢸⡿⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹
⠀⠀⠀⠀⠀⠀⢹⡀⠹⡄⠙⣦⠈⠣⣀⠀⠀⠀⢀⡠⠞⠁⢠⠞⠀⡼⠁⣼⠀⠀⠀⠀⡇⡇⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠹⣆⠈⠳⣄⡀⠉⠉⠉⠉⠀⣠⠴⠋⢀⡞⠁⢰⠇⠀⠀⠀⠀⣧⣷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡏
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠈⢷⡀⠀⠙⠓⠲⠶⠚⠋⠁⢀⡴⠋⠀⢠⡏⠀⠀⠀⠀⠀⢿⢹⢿⠀⠀⠀⠀⠀⠀⠀⡦⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠙⠲⣄⣀⠀⠀⢀⣀⡴⠛⠁⠀⢀⡞⠀⠀⠀⠀⠀⠀⢸⢸⣈⠀⠀⠀⠀⠀⠀⠀⣇⣸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠉⠉⠋⠉⠁⠀⠀⢀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠸⣇⡈⠉⠉⠛⠛⠛⠛⢛⡏⢁⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠋⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣖⣚⡛⠛⠛⠛⠛⠛⠛⠓⠒⠒⠒⠒⠒⠒⠒⠓⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡧⠤⠤⠬⠴⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⢠⡀⠉⡞⢸⢳⠂⡸⣶⠀⢡⠎⢸⢦⢃⢢⡇⡜⣡⠠⠆⣰⣿⣷⣤⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠁⠀⠀⠀⠈⠁⠀⠈⠁⠈⠁⠁⠉⠙⠘⠘⠃⠛⠒⣠⣿⠁⠀⢙⣻⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⠷⠶⠶⠶⠶⠿⠶⠶⠶⣶⣿⠷⠾⠿⠛⠋⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣤⡴⢶⠾⠛⢁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⢸⡿⠚⠛⠛⠁⠀⢸⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡀⣰⣿⣿⣿⣿⣿⣿⣿⠟⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⢸⣿⣿⡇⣿⣿⣿⣿⣧⣿⣿⡟⣸⣿⣿⣿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢸⣿⣿⠇⢸⣿⣿⣿⣿⣿⡿⠁⣿⣿⣿⣿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡇⠀⠀⣸⣿⣿⠀⠈⣿⣿⣿⣿⣿⠃⠀⣿⣿⣿⣿⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⣠⣿⣿⣿⣤⠀⢹⣿⣿⣿⠏⠀⣠⣿⣿⣿⣿⣇⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⣿⣿⣿⡿⠀⠘⣿⣿⡟⠀⢠⣿⣿⣿⣿⣿⣿⠀⠀⣾⡇⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠛⠛⠛⠛⠃⠀⠀⠛⠛⠁⠀⠘⠛⠛⠛⠛⠛⠛⠀⠀⣿⠀⠀⠀⢀⣠⣤⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠠⠴⠶⠶⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣤⣤⣶⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠿⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣧⡦⠔⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹⣿⡷⠀⢠⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠠⢤⣄⣵⡙⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢖⣿⠿⢿⣻⡟⡉⠙⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⣁⠤⠲⣿⠀⠒⠈⣿⡃⠅⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠊⡁⠄⢲⣿⡄⢰⣫⡯⠷⢦⣺⡟⣩⠉⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣶⣿⣦⡶⣾⢛⣉⠁⣸⠀⠀⠖⣿⣧⣀⡀⡠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣼⠋⠩⣉⢻⢳⣀⣀⣀⣋⣵⣖⠚⠟⠉⡙⢿⠇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣝⣀⣀⠨⣸⣇⣿⣯⡟⠁⣤⠉⣿⠆⠸⢁⡾⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠿⢽⣟⣛⠓⠒⠲⠍⠩⢓⠚⠶⢿⣾⣿⣿⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠤⠤⣀⡀⠉⠐⠒⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠃


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⠃⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⠀⠈⠁⢀⠀⠀⠀⠀⢀⢤⠀⡆⠀⠀⠀⠠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣉⣉⡤⢬⣉⡉⠉⢉⣡⣈⡷⠁⠀⠀⠈⠒⠒⠦⠤⠦⠀⢶⡶⠤
⠀⠀⠀⠀⠀⠀⠀⠀⡂⢀⡀⠀⢀⣠⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠬⠙⣿⣁⢄⣒⢐⡄⠐⠊⠀⠀⠀⠀⠠⠄⠈⠑⣀⠀⠀⠀⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠉⠉⣭⢄⣀⡀⠀⠀⠀⠀⢠⡄⢠⣅⡬⠆⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡙⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠓⠈⠁⠀⠀⠀⠀⢠⡉⢩⠀⠠⠀⠄⢉⡐⡀⠀⠀⠀⠙⡜⡛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠉⠀⠈⠀⠈⠀⠉⠉⠀⠀⠀⠀⠀⠘⣬⣆⠀⠔⢂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢀⡠⠂⠊⡀⠀⠰⣄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢼⣴⡺⠟
⠀⠀⠀⠀⠀⠀⠀⡅⠒⢢⣀⠙⢁⠀⠐⠺⣶⢤⠚⠗⠁⠀⠀⠀⠤⠄⣪⠀⠐⢒⡩⠂⠀⠀⠀⠀⠀⠀⠠⡤⠄⢀⠐⡀⠠⣄⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠷⠤⠴⠛⠚⠛⠒⠚⠀⠀⠀⠀⠀⠀⢰⠡⣤⣴⠒⣭⠄⠲⠖⢤⠀⠀⠀⠀⠀⠇⡀⠀⠈⠙⠖⠲⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢢⣖⣀⡠⠴⠃⠀⠀⠀⠀⠈⠒⠒⠒⠒⠢⠄⠳
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠋⠉⠉⠉⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠘⠁⠀⣁⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠻⠃⠀⠀⠀⢠⠂⠀⠀⠀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⢃⠀⠀⠀⠀⠰⠈⡀⢄⡀⠤⠀⠀⠀⠀⠄⡤⠀⠀⠀⠀⠀⡐⠀⠀⠀⢠⡿⠁⠀⠀⠀⠸⡄⠀⣀⡠⠠⠀⢠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢀⠰⠆⠀⠀⠀⢀⢠⣤⡀⠉⠰⠂⣀⠀⢂⣰⠄⠀⠀⠀⠀⢀⡓⢀⡠⠴⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡓⠀⠀⠀⠀⡀⠀⠀⠈⢃⠀⢈⢉⠰⠶⠤⠄⠊⠛⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢀⣀⡌⠗⠀⠀⠀⠨⠀⢠⣤⠠⠀⠴⠆⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠠⠤⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠤⠔⠂⠲⡌⠉⠉⢀⠙⠆⣀⣀⣨⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠺⡄⠉⠀⠀⠱⣄⣀⣤⣤⠴⣴⠖⠛⠛⠙⢧⡀⠠⠀⢐⡄
⠀⠀⠀⠀⠀⠐⠀⠀⠉⠁⢰⡀⠀⠀⠀⢠⡖⠠⠀⢤⢀⡀⠀⠀⠀⠀⠀⠙⡆⣀⣠⣤⠽⡶⠖⠛⠋⠛⠉⠀⠄⠀⢙⡄⢀⡠⠴⠌⠓⠒⠛⠉⢉⡄
⠀⠀⠀⠀⠐⡈⠑⠒⢀⡌⢀⡃⠀⠀⠀⠀⢀⢠⠀⠀⢀⠀⠀⢀⠀⠀⠀⠐⡜⡅⠀⠀⠀⠰⡀⢀⣠⠤⠴⠄⠐⠚⠋⣉⢀⣤⠆⠠⠴⠚⠐⠂⠈
⠀⠀⠀⠀⠀⠁⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⡽⡙⠚⠲⢿⠆⠉⠀⠀⠀⠀⠀⠹⣠⠔⠒⠛⠉⣉⣀⢠⡦⠤⠠⠖⠂⠊⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠰⡂⠁⠀⠀⠀⠀⠀⠀⠙⠤⠐⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡿⠦⣤⡤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠢⡀⠀⠀⠁⠠⡀⠀⠀⠀⠀⣠⠖⡥⠊⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢠⡤⢈⠢⡀⠀⠀⠈⠁⠂⠒⢋⡹⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡻⠀⢠⠑⠠⡀⠀⠀⠠⠊⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠊⡛⢠⡅⢉⡑⠎⠀⠀⢀⠼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠎⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠈⠢⡃⢨⠐⠀⠦⢒⡁⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⢠⠆⠁⢀⣸⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠉⠀⠀⠀⠀⠉⠑⢎⠒⢀⠾⢉⠢⣀⠀⠀⠈⠀⠄⠀⠀⢀⠔⠁⠀⡤⣋⠐⠚⣧
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠋⠁⡴⠀⠀⠀⠀⠀⠀⠀⠀⢂⠒⣮⡀⢬⠠⠍⠑⢠⡀⠀⠀⠀⠉⠀⠀⣰⡼⠄⡄⣻⡴⠛
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⢀⠔⡡⠞⠉⢛⣿⢗⠘⠛⠤⠈⣓⡄⡀⢠⠔⣈⠃⠶⣡⠟⠉
⠀⠀⠀⠀⠀⠀⡼⠃⠁⠑⠒⠠⠤⠀⣀⣀⡀⢀⡠⠐⠉⠀⢀⣶⢚⣅⠶⢁⣤⡀⢹⠇⡴⠀⣙⠈⠉⡤⠚⠁
⠀⠀⠀⠀⠀⡼⠓⠀⢀⡀⠀⠀⠀⠀⠀⠐⠀⡄⠀⢀⠤⠊⢡⡄⣀⡵⠚⠁⠀⠉⠳⣌⡋⠰⢂⡰⠋
⠀⠀⠀⠀⠀⡇⠰⠦⠎⢡⣄⢀⡇⠠⠐⣂⠤⠟⢊⠃⠤⠴⣢⠞⠉⠀⠀⠀⠀⠀⠀⠈⠛⠷⠛⠁
⠀⠀⠀⠀⠀⠉⠉⠉⠒⠢⠭⢤⣐⣒⡀⠩⠄⡄⠚⣄⡡⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠙⠦⡀⠀⠀⠉⠳⣦⣠⡴⠚⠋⠉⠉⠛⣳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠈⠢⡀⠀⠀⠈⠁⠀⠀⣠⠤⣄⡔⠁⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⠉⠒⠒⠤⣄⡀⠀⠙⢆⠀⠀⠀⠀⡴⢃⠀⠸⡄⣀⡤⠖⠚⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠀⠀⠀⠀⠉⠒⢄⠀⠳⡀⣀⡜⡡⠋⠀⢀⢻⡅⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢹⡇⠀⠀⠀⠀⠀⣀⣀⣀⣤⣥⣴⠋⠉⢹⣯⣤⡬⠤⠾⠃⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣠⠛⣧⠀⠀⠀⠀⢸⡁⠀⠀⠤⠒⢹⣤⢶⡉⢢⠉⠳⡄⠀⠀⠀⠀⠀⡞⡟
⠀⠀⠀⠀⣠⠴⠖⢛⣛⣛⣓⡶⢦⣷⠃⠀⢻⣧⣀⡠⠔⠊⠙⡄⠀⡠⢊⡞⠀⡆⢳⠀⠂⠀⢳⡀⠀⠀⠀⡸⢱⠇
⠀⠀⢠⡞⡡⢖⣯⣽⣛⣻⣿⡭⡝⠃⢀⢊⠈⢳⡿⡀⠀⢀⠴⣇⠊⢀⠞⠀⡼⠀⢸⠘⡄⠀⡞⠀⠀⠀⡴⢡⠏
⠀⠀⢸⡞⠱⠿⠉⠤⠤⠤⠟⠛⠁⠀⠧⣏⣐⡪⠳⡙⢶⠁⠀⠈⠓⠁⠀⣸⠁⠀⡏⠠⠙⠲⠆⠑⣠⠎⣠⠋
⠀⠀⢸⡇⠀⣀⠴⣒⣻⣽⣿⡲⡄⠀⠀⠀⠠⣐⠀⢙⢮⠳⣄⠀⠀⠀⠀⣧⡴⠶⡇⠀⢃⠀⣀⠔⣁⡔⠁
⠀⠀⠸⣿⡄⢧⣎⣁⣀⣠⡴⢟⣁⣤⣤⣈⡢⠭⠐⠦⠄⠓⣌⠢⣀⠀⠀⠈⠀⠀⠀⢀⡨⠞⢁⡴⠋
⠀⠀⠀⣧⠹⢦⡈⠉⠉⠀⠐⢷⠊⠡⠊⢝⠻⡗⣦⢀⣔⣒⢿⠳⣌⠳⢄⡀⢀⡤⠖⠋⢀⡴⠋
⠀⠀⠀⠹⣄⠀⠙⠷⣤⣀⠀⠀⠙⠒⠒⠒⠒⠛⠁⠈⢯⣀⣘⠶⢨⣷⣦⡈⡇⠀⣀⠔⠋
⠀⠀⠀⠀⠈⠳⢤⣀⠀⠉⠛⠷⠶⠶⡤⣤⣤⣤⣀⣀⣀⡉⠙⠛⠋⠁⡇⠙⠓⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣤⣀⣀⡀⠀⠀⠀⠉⠉⠉⠉⠋⠙⠛⠛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠒⠶⠶⠦⠤⣤⣄⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡶⠟⠛⠋⠉⠉⠁⡄⠀⠀⢦⡈⠉⢹⣧
⠀⠀⠀⠀⢠⣶⠿⠛⣉⠀⠀⠀⢹⠀⠀⠀⣴⠏⠀⠠⠼⠃⠀⣸⣿
⠀⠀⠀⠀⢸⣿⠀⠀⢨⠇⠀⠀⣋⣀⣤⣤⡤⠶⠶⠶⠒⠒⠺⣿⡟
⠀⠀⠀⠀⠸⣿⣦⣀⣤⣴⠾⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠈⠙⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠹⣿⣆
⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠖⠒⠛⠉⠉⠀⠈⠻⣧
⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⢀⣠⡤⠶⠖⠛⠉⠉⠀⠀⠀⢀⣀⠠⣶⠖⣿⢛⡀⠀⠹⣷⡀
⠀⠀⠀⠀⣼⡏⠀⣀⣠⠴⠞⠛⠉⠀⠀⢀⣀⠀⣠⣦⠀⣧⠀⢸⣻⡆⢸⡆⢹⡏⣁⠀⠀⢹⣷⡀
⠀⠀⠀⠀⣿⠀⠛⠉⠀⠀⠠⡄⢰⠾⡄⢾⠉⠁⣇⠈⡇⢹⣀⣨⡏⢳⡀⠇⠘⠋⠁⠀⠀⠀⢿⣇
⠀⠀⠀⢀⣿⠀⣰⠖⠆⢱⠴⢧⢸⡀⣷⠸⣦⡴⠙⠚⠁⠈⠉⠁⠀⢀⡀⠀⡴⢦⠀⠀⠀⠀⠸⣿⡀
⠀⠀⠀⢸⣿⠀⢿⡀⣀⠈⡇⠸⠄⠙⠁⠀⠀⠀⢀⡀⠀⡤⣄⠀⠀⡏⢳⡼⢡⡟⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⢸⣟⠀⠈⠛⠁⠀⢀⠀⠀⢠⡖⢲⡄⢰⡋⢻⢰⡇⣿⠀⠀⡇⠈⣀⠙⢦⣀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⠋⠻⣤⠟⣼⡆⢻⡘⡇⢸⡆⣇⠹⠶⢶⣿⡈⣯⠓⢦⡽⠂⠀⠀⠀⠈⣿⡄
⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⠀⣰⣎⣰⠇⢷⠈⡇⢷⣸⡇⠻⠴⠖⠋⠉⠙⠁⣀⣀⣀⣤⠤⠆⠀⠀⢻⣇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⠀⣿⠉⠋⠀⠈⠛⠃⠈⠉⢀⣀⣠⡤⠶⠖⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⢹⣧⠀⠀⠀⠘⠶⠟⠀⠀⣀⣠⣤⠶⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠘⣿⡆⠀⠀⢀⣤⠴⠚⠋⠉⠀⠀⣴⠤⠤⠤⣀⣀⣀⠀⠀⠀⠀⠀⣠⣄⣀⡀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⢿⣷⠀⠀⠉⠀⠀⠀⠀⠀⠀⡴⠁⠀⢀⡼⡽⠃⣹⠀⠀⠀⠀⣸⠃⠀⠉⣨⢷⢶⡤⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣷⣿⢯⣿⡟⠁⣴⠃⠀⠀⢀⣼⠁⠀⠀⡸⣡⠏⣠⡇⠀⠀⢿⣇
⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠻⣍⠉⣉⣉⣧⣸⠃⣞⠆⠀⢨⣯⣽⣋⣛⣷⢃⡼⠃⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⣈⣁⣀⡀⠀⠀⠘⠷⠦⢤⣤⡧⠞⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣿⡄⠀⠀⠀⠀⠀⠀⠸⠇⠀⣰⠁⠈⠉⣴⢳⠶⡄⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣼⣁⣀⣀⣼⣱⠋⢰⠟⠀⠐⠿⠜⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⢠⠞⠒⠒⠚⠟⠁⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀⠀⠀⠀⠀⠀⠘⠛⠓⠒⠒⠖⠺⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⢿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣶⣴⣶⣶⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠋⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠉⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡷⠶⡒⠒⠲⠤⠤⣀
⠀⠀⠀⠀⢀⣀⣀⡀⠀⢀⡠⠤⠒⠊⢇⠀⠀⠀⠀⠀⠀⡼⢋⡴⠀⠘⡄⠀⠀⠀⠀⠉⠢⣄
⠀⠀⠀⢰⠃⠀⠀⠈⠙⠳⢤⡀⠀⠀⠸⡀⠀⠀⠀⠀⣰⠖⠁⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⡇⠀⠀⠀⠀⠤⠤⠄⢈⡓⢄⡠⠛⠓⢎⣀⠔⠁⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⢸⡄
⠀⢀⡴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢧⡀⠀⠈⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⡆⢰⣀
⢠⠎⠀⢧⠀⢀⣀⣀⢠⡤⠤⠴⠒⡒⠋⠙⣶⢾⠉⠒⠦⠤⠤⠤⠤⢴⡒⠯⢄⠀⠀⠀⢠⠎⠀⢸⠉⠛⣳⣦⣄⡀
⡎⠀⠀⠀⠑⠢⠤⡴⠋⠀⠀⠀⠄⠀⠀⡔⡏⠀⢣⡀⠀⠀⠀⡖⠉⣀⡠⠤⠞⠃⣀⠔⠁⠀⣠⠷⠊⠉⠈⢀⡘⠉⠲⣄
⠇⠀⠀⠀⠀⠀⡸⠁⠀⠀⠀⠈⠀⠀⠈⢰⠁⠀⢸⡉⠢⣄⠀⡇⠈⡇⠀⢀⠤⠊⠁⠀⢀⠴⠏⠀⠀⡀⠀⠀⠀⠀⠀⠘⠗
⠸⣆⠀⠀⠀⠰⡁⠀⠀⠀⠀⠀⠀⠀⠇⡎⠀⠀⠈⡇⠀⠀⠉⢓⡤⠷⠊⠁⠀⠀⣀⠴⣏⠺⢤⣀⡀⠀⠀⠀⠀⢀⣀⡀⠞⢠⢆
⠀⢂⠙⠢⠤⣀⡈⠒⢤⣀⠀⠀⠀⠀⢠⠓⠒⠤⢠⡧⠔⠒⠉⠁⠀⠀⠀⣀⠤⠚⢁⠀⠉⢦⢆⢈⣉⠟⠛⠛⠛⠯⠭⣀⢀⠞⡌⡄
⠀⠈⠢⡀⠀⠀⠀⠉⠉⠉⠑⢲⠒⢒⡪⠖⠒⠦⠼⠁⠀⠀⢀⣠⡤⠒⠋⠁⠀⠀⠀⠀⠀⣸⣤⠏⠀⠀⠀⠀⠒⠀⠀⠈⣪⣀⡃⠃
⠀⠀⠀⠈⠑⠢⠤⠄⣀⣀⣀⣈⣉⣁⣀⣀⠠⣤⠤⠶⠒⡛⠳⠦⢽⡓⠒⠐⠒⠀⠘⠛⢛⠡⣌⠀⠀⠀⡀⠀⠀⠀⠀⠀⠨⡤⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡙⡀⠀⠀⢀⡔⠁⠀⠀⠀⠂⠄⠁⠀⠑⢦⡀⠀⣀⠦⠚⠚⠓⠻⠿⢶⡦⠤⢠⠄⠴⠒⠒⠉⡰⢱⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⣔⢔⢋⡝⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠘⣉⠟⠁⠀⠀⡀⠀⠀⠁⠀⠙⢆⣸⠀⠀⠀⠀⡼⡱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠀⠈⠪⡫⣗⠶⣤⣀⣁⣀⡀⣀⣀⣠⡜⢉⡜⠀⠀⡀⠀⠄⢈⣀⠀⠀⠀⠉⣍⠑⣇⡴⣪⠞⠁⠀⡀
⠀⠀⠀⠀⠀⡠⠒⠝⠡⠄⠩⠉⠒⢤⡈⠓⢵⡢⢄⡁⠀⠅⠀⡇⠀⠹⡈⠛⠲⣤⣄⣉⣀⣂⣀⣀⡤⡤⢖⡯⣚⠭⠊⠁⠀⠀⢀⠇
⠀⠀⣀⢠⣈⣁⠀⠀⢉⠁⠀⠀⠀⠀⠙⣤⣀⠈⠑⠻⠶⢗⣤⠤⣤⣀⣷⣀⡀⣂⢀⣅⣀⡥⣴⠓⠒⠻⠕⠈⠁⠀⠀⣀⣀⢀⡜
⠀⢸⠡⣬⠀⠀⠀⠠⠄⠀⠀⡀⠈⠀⠀⢰⡤⠵⠶⠀⢤⡤⣀⠉⠉⠘⠛⠛⠛⠋⠚⠛⠃⠉⡝⠀⠀⣼⠀⢀⣤⡀⡀⡀⢀⠀⠉⠉⠉⠐⠒⠒⠒⠂⠦
⠀⠈⠆⢈⠓⠶⠶⣶⠤⢬⠥⢤⠴⢶⡟⠁⠀⠀⠀⠁⠀⠃⠈⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠛⠒⠘⠴⠃⠷⠁⢏⡛⠀⣼⢹⢒⡆⣄⡄⠀⢀
⠀⠀⠘⣆⠆⠠⠀⢀⠀⠀⠀⡜⠂⠟⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠚⡓⠢⡀⠀⠀⠀⠀⠀⢀⠁⠀⣀⠀⢀⡀⠀⣀⣀⡀⠀⣀⠀⢀⡀⠀⠡⠟⠀⠀⢸
⠀⠀⠀⠘⢮⡀⠂⠸⠀⠀⠀⣇⠙⠧⣄⣀⠁⠂⠀⠈⠁⠀⢀⣀⡤⠟⢰⣃⣀⣀⣀⣀⣀⣼⠀⠀⣿⣇⡾⡇⢸⠃⠀⢻⡀⡿⣇⡾⣿⢀⡀⡠⢦⠀⣨
⠀⠀⠀⠀⠀⠉⠛⠒⠓⠒⠒⠛⡆⢂⠀⠉⠙⠉⠉⠋⠉⡏⠉⠁⠐⢀⠏⠀⠀⠀⠀⠀⠀⡘⠀⠀⠇⠻⠃⠗⠘⠷⣴⠟⠀⣇⡻⠃⠟⠈⢏⡠⠋⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⠄⢀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠰⠦⠠⠤⠤⠄⣀⣀⣀⠀⠤⠘⠓⠐⠀⠀⠠⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢬⣄⣁⣀⣀⣰⣀⡤⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠐⠒⠒⠒⠶⠁
⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡄⠀⠀⠀⠀⢀⠂⡐⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⢀⠠⠀⠄⠚⣡⠗⣸⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢧⠀⠀⠉⠰⠒⠊⠁⢈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣴⣄⣤⣴⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢻⣿⠛⣿⡏⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢸⡧⢰⣿⠇⣽⡇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣷⢸⣿⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⣿⢸⣿⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣿⣰⣿⣨⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡛⠛⣇⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠈⠀⠀⠈⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠳⣄⣀⠀⣀⣤⣾⣆⠀⢠⣦⣄⣤⡴⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢿⣄⠀⠀⠉⠉⠉⠀⠠⣉⡿⠋⠀⠀⠀⠀⠈⠹⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠘⠳⢦⡀⠀⠀⣡⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⢀⠹⣶⣼⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠃⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡋⠀⠀⠀⠀⠀⠀⠀⠀⣨⡷⠋⠙⠿⣦⣄⢀⠀⠀⠀⠀⠐⣴⡾⠁⠀⠀⠀⠀⢈⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣴⣯⣬⣷⠤⣤⣄⠀⠀⠀⣀⣶⠋⠀⠀⠀⠀⠈⠻⣷⣆⡀⢘⣴⡿⠛⠀⠀⠀⠀⠀⠀⠀⣠⣼⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⠙⠚⠋⠀⠈⣉⣀⠀⠈⡛⠶⣦⣴⠟⠀⠀⠀⠀⠂⠀⠀⠀⠈⠝⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢢⣾⣏⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣶⠶⠶⠞⠛⠶⢦⡀⣉⣅⡀⣳⠄⠸⣿⣦⣤⡀⠀⠀⠀⠀⠀⡀⣰⣾⠍⠀⠙⢿⣄⢦⠀⠀⠀⣴⡿⣣⣽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⢡⠀⠀⠀⠀⠀⠰⣿⡅⠈⣀⣵⢶⣆⣹⠁⠈⢷⣤⣤⡀⡀⣠⡼⡏⠁⠀⠀⠀⠀⠙⢿⣧⣠⣿⣟⣱⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⡏⠀⠀⠀⠀⠀⠐⡇⠙⠛⠉⠠⠀⢪⡿⣷⡦⠈⠉⠩⣍⠙⠋⠻⣆⣀⣐⡈⠀⠀⠀⢀⣾⢿⣻⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢡⠄⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠁⢸⠀⠉⠹⠶⠶⣶⠋⡤⠄⢀⣀⠉⠙⢿⡀⢄⣰⣿⣝⡾⠋
⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣼⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⡿⠁⣀⡐⠋⠉⠀⠀⠈⢻⣾⣿⣿⣏
⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⡇⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣁⡾⠉⣷⡀⠔⠛⠆⠀⠀⠉⠻⠋⢻⣆
⠀⠀⣠⣾⠏⠀⠀⠀⠀⢰⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣁⣀⣂⣬⣝⣀⡀⡰⢦⡄⠰⣶⣄⠀⣹⡇
⢠⣾⠛⠁⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢋⣿⠟⢿⣿⠃⠠⣀⣤⡄⣹⣿⣾⠋
⢾⣟⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⢁⠀⣼⣿⠠⠀⣹⣧⡀⣿⠛⠁
⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⢀⣴⠛⠀⢀⣠⡾⠃⠹⣦⣼⠋⠙⠛⠋
⠀⠀⠈⠙⣦⡀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⡴⠛⠁⠀⢠⡾⠋⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠛⣦⣄⠀⠀⠈⣧⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠁⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠸⡄⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⣠⠟⠁⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⢳⡀⠀⠀⠀⠀⠀⠈⢦⠀⠀⣠⠾⠉⠀⢀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣅⠀⠀⠀⠀⠀⠀⠀⢁⡴⠏⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⢀⡴⠛⠀⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⣴⠟⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣴⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠹⣶⠶⠒⣶⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⡘⣦⢻⣤⠞⠁⣠⡾⠻⡆⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡶⠤⢭⣵⡟⢻⡶⠾⠛⠶⢴⡗⠛⠉⠉⠉⠙⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⣴⠟⠀⣹⡏⢦⡙⠃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⣠⠞⠁⢻⡀⠀⢀⣴⡿⢦⡀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠞⠁⠀⠀⠈⠓⠒⠋⠉⠙⠶⣝⡳⣤⡀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣝⠳⣄⣀⡴⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣬⢿⡞⢻⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣀⣠⣤⣤⠤⠶⠶⠚⠛⠋⠉⢁⣀⡤⢧⢘⡧⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣉⣁⣀⣠⣤⡤⠴⢶⣖⣚⣻⣭⠭⠶⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠗⠚⠛⠛⠋⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠋⠉⠉⠉⠛⠒⠶⠤⣄⣀⡀⠀⠀⠀⡤⠾⠃⠻⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⢉⡿⠷⠞⠁⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣠⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠴⠖⠉⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡤⠽⡒⠊⢉⠽⠁
⠀⠀⠀⠀⣼⠋⠙⠓⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡰⠖⠒⠫⠁⠂⡀⠌⢁⣀⠀⠒⢀⠠⢀⡀
⠀⠀⠀⢠⡇⠤⡀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣄⣤⠤⠤⠤⠼⠀⠀⠀⠀⢀⠤⣪⣴⠾⠚⠥⢰⣀⡠⠦⢁⣀⠁⠃⢨⠀⠤⢃⠀⢠⠐⠙⡄
⠀⠀⠀⠀⠉⠙⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠈⢉⡇⠀⠀⠀⠀⠀⠀⣠⠵⣚⣿⠍⠂⣀⠤⠀⡀⣈⠙⠂⢠⠤⠔⣃⠠⢄⠀⠋⠀⠀⠀⢘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⠤⣄⣀⠀⠉⠊⠙⣄⡀⠀⠆⡽⠺⠋⢠⣀⠀⠀⠀⠑⠂⣁⠠⣚⠢⠤⣀⠤⠋⠀⠀⠀⠀⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⡤⠜⠀⠣⠳⣄⠀⠀⠀⠉⠉⠀⠠⠎⣀⠀⢀⠭⠒⠠⠀⠀⠀⡀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠀⠀⠀⠀⠓⠘⢦⣀⡀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠔⠒⢦⡀⠀⠀⠀⠀⠈⠉⠛⡶⠦⢤⣀⡀⠰⡟⢋⠠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠚⠙⠲⠤⠤⠤⠵⠀⠀⠀⠉⠙⠋⠁




⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⡿⠛⠁⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⠟⠉
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠏⣠⣴⣶⣶⣶⣾⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⣠⣴⣶⣶⣶⣾⣿
⠀⠀⠀⠀⠘⢿⣿⠿⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠘⠿⣿⡿⠿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢰⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣼⠣⡘⠿⠀⣱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡰⡉⢔⡲⠈⢢⠘⠒⡩⠔⣉⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⢤⣀⠴⢚⢁⠈⢄⠑⣤⠴⢊⠡⡒⢌⠣⡘⢛⡠⢸⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢣⡁⠈⠂⠉⢄⠈⠉⣀⠔⣣⡄⢊⠀⠻⠇⢈⠆⠉⣵⠊⣵⡆⢑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠊⢡⠀⠀⠄⠀⠀⠳⡭⠒⡭⠄⠈⢢⠱⢄⡪⢂⣉⠳⡈⢦⡨⣔⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡂⡁⠀⠀⠀⠠⡀⠀⡀⠀⠀⠀⠙⢦⣈⡡⠔⠪⠦⡧⡀⠀⢊⣠⡷⠦⡘⣄⢣⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠋⢀⠃⣀⠀⠀⠀⠈⠢⡀⠁⠢⡀⠀⠀⠱⣎⠐⠯⠂⣸⠎⠊⡟⠡⢦⢀⠽⡸⢈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠊⠀⠀⠀⠀⢸⠀⣬⠾⢒⣆⠘⠄⠀⠀⢱⠀⠀⢀⠀⠀⠀⠈⠢⣔⡮⢚⡉⢦⠈⢦⡪⠔⠟⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣆⠀⠀⠀⠀⣘⢀⣠⠖⣏⡜⢠⣠⢤⠀⠀⡆⠀⠀⠉⠐⡀⠀⠀⠈⢦⡉⢊⣴⠗⢎⠣⡜⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢏⢧⡀⠀⠀⠈⠁⠈⢣⡄⣤⢡⠇⡸⠀⠀⠘⠦⢄⠀⠀⢁⠀⠀⠀⠀⠹⡇⠐⠯⢀⠷⢣⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⢳⡀⠀⠀⠀⠀⠀⡄⠘⠋⣠⠗⡄⠀⠀⠀⠀⠙⣆⠘⠒⠒⠲⡀⢠⠘⡦⣂⠕⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡸⣄⠀⠀⠀⠀⠓⢤⠐⢡⣊⡡⣀⠀⠀⠀⠀⢘⠀⠀⠀⠾⠁⢀⡰⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡜⣦⠀⠀⠀⠀⠘⡄⠀⢡⢔⡡⡀⠀⠀⠀⠈⣉⣵⣀⣤⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⡳⡄⠀⠀⠀⠘⡀⠈⢉⠔⠃⢀⡠⢐⣫⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡘⢦⡀⠀⠀⠙⢊⣡⡴⣺⡥⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣴⠙⣄⡤⢖⣫⠵⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡾⠒⠉





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠒⠊⠙⠿⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠶⠯⡀⠀⠀⠀⠀⠀⠀⠙⠟⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠐⠊⠉⠀⠀⠁⠀⡈⠒⢄⠀⠠⠔⡈⠄⣂⠤⠌⡙⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠿⠛⠉⠈⠢⡀⠀⠀⠀⠀⢀⠠⢓⠀⠁⠒⢹⠀⠀⠀⠀⠀⠀⠀⠄⠙⠷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⡏⠀⠀⠀⠀⠀⠀⠂⢀⠑⠄⠐⣨⡔⠂⠅⠒⠀⠂⠀⠑⠤⡀⠀⠀⢀⠠⠀⣈⣀⡼⠿⠃
⠀⠀⠀⠀⢀⡤⠦⠖⠛⠈⠐⠀⠈⠢⢀⠀⠀⢀⠠⠒⠈⠀⢀⠈⠀⢇⠀⠀⠀⠀⠀⠀⠁⣢⠈⠀⢈⣵⠾⠟⠋⢁⣠⠴⠂
⠀⠀⡏⠁⠀⠠⡀⠀⠀⠀⠀⠀⠈⣰⠄⠁⠠⠔⡾⠁⠂⠁⠀⠀⠀⢀⠁⠢⡀⠀⠠⢒⡠⣤⡤⠖⠋⢀⣀⣴⠟⠋⠁
⠀⠀⠳⣄⠈⠠⢌⠐⢄⠀⠤⢐⡡⢄⡢⠤⠄⡀⠑⢄⠀⠀⠀⠀⠀⡀⠜⠂⠀⣑⣾⣿⠟⢉⣀⣶⠶⠛⠁
⠀⠀⠀⠈⠻⢦⡀⠑⠠⡀⠂⢹⠀⠀⠀⠀⠀⠀⠐⠀⡈⠂⢀⢒⡩⢔⣪⠶⠟⠋⣉⣴⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠐⢄⠑⠤⡀⠀⠀⣀⠄⠂⡉⠀⣠⡵⠚⠋⣀⣤⠴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⠉⠢⣌⠀⠨⠔⣊⡤⠒⠋⡀⣠⡶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠑⠔⠋⢁⣢⡾⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣼⠞⠋⠉





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠿⠿⣿⣶⣲⣶⠦⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⠀⠀⠀⠀⠉⢳⣝⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠁⠈⠉⠉⠓⠒⠦⢤⢿⣷⣽⣿⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣾⣿⡿⢿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⢋⣁⣠⢤⣴⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⢣⣶⣤⣄⣀⠀⢠⡿⠿⠒⠋⣩⣶⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇⠈⠃⠘⠻⢿⣿⣿⣿⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⢠⠀⡀⠀⠉⣩⣼⠀⠀⠀⠀⠀⠈⠉⠹⡿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠋⠀⠀⠀⠁⣤⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠉⠀⠠⠄⢰⠇⠑⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣄⣒⡺⠏⠀⢠⣶⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⠀⠰⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡀⠀⠛⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠹⢻⣷⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠟⠃⠀⠀⢀⠇⢰⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠸⠤⡼⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠣⠤⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢤⣀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡀⠀⠀⠀⠀⣀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⢸⢸⣿⡿⢟⣀⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢦⣟⡬⠕⠚⠉

⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡴⠀⠀⠀⢀⡄⠀⠀⠀⢠
⠀⠀⠀⠆⡀⠀⠀⠀⠀⠼⠀⠀⠀⢸⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⠤⡄⣠⠞⢁⡀⠀⢀⠘⠁⠀⠀⠀⠈⠉⢷⠄⠀⠈
⠀⠀⠀⡄⡈⠂⢀⠒⠢⠐⠢⠤⠤⠞⠠⣄⣠⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠉⢹⢃⠂⠀⠀⠀⠀⠀⠉⠐⠀⠀⠂
⠀⠀⠀⠀⣀⠠⢄⠀⠀⠋⠈⠉⠢⣮⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⢀⡼⠁⠀⠀⢀⣣⠇⠀⢀⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣍⠓⠢⢤⢀⡀⠀⠀⠀⠄⠀⠈⠀⠚⠂⠀⠀⠠⠈⠒⠻⢶⠎⣥⣀⣀⢠⢎⠎⠀⠀⠊⠠⡀⠘⡌⡆⠀⠀⠀⠀⠀⠐⠒⠁
⠀⠀⠀⠀⠃⡀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠆⢀⠀⠀⠁⠀⠀⢀⡀⠀⠀⠉⠙⢻⠌⠀⠀⠀⠳⠤⢸⡀⠅⠃⠀⠀⠀⠤⣀⣀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⡄⠀⢠⣀⠀⠀⢀⡾⠁⠀⠀⠀⢰⠏⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠶⣿⣁⡀⠀⠀⣠⡎⠀⠀⣪⢟⡭⣿⣿⣆⠀⠀⠀⠀⡄⠉⠐⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢶⡟⠀⢀⣄⠁⠎⠄⠀⠛⢉⣄⠀⠀⠀⢦⣀⣀⠀⠀⠄
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠁⠀⠉⠀⠀⠀⣤⠀⠈⠉⠉
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠄⠂⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠃⠀⠀⠀⠀⡀
⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠰⣤⢀⣔⣺⠼⣧⡀⠀⠀⠀⠀⠀⢀⠤⠂⢩⣿⡥⣀
⠀⠀⠀⠉⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡀⢀⠄⣀⡼⢻⣿⠞⢛⣡⣾⣄⡀⠀⡀⠘⣿⣧⣄⠈⢙⠯⣌⡙⠲⣤⣀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣟⣍⣵⡆⣫⣵⠾⡿⣮⣭⣭⠟⠁⠀⠀⠈⠻⣝⠿⠁⠀⠈⠉⠑⠠⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠐⠀⠀⠀⠀⠀⠉⠛⠛⠁⠀⠉⠁⠉⠙⠈⠐⠀⠂⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠢⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡎⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⠤⡄⠀⢦⣁⣀⡤⠞
⠀⠀⠐⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡄⠈⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢠⡊⠀⠀⠀⠸⠀⠠⡈⠑⠂⠀⠒⠀⠀⠐⠚⠠⠄
⠀⠀⠀⠀⠠⠎⠀⡀⠀⠀⠧⡄⠀⠈⠀⠚⠀⠀⠀⠀⠀⢯⡂⠀⠀⠀⠀⠀⣐⡆⠀⠀⠀⠀⠈⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠳⣄⠰⢾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄⠀⢀⠀⠀⠀⢀
⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣤⣁⡀⠀⠀⠉⡳⣄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠀⢸⡆⠀⠀⡀
⠀⠀⠀⠉⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⣆⠀⠀⠛⠿⠀⠉⠢⣉⠎⠈⠱⣄⢁⣔⣠⠀⠋⠀⠀⢘⠁⠀⠀⢠⡄⠁⢀⣴⣤⠌⠐
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠛⠟⠁⠀⠀⠀⠀⠀⠑⠂⠒⠀⠘⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣤⢀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣶⣿⣷⣦⣀⠀⠀⠀⠀⢰⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⢸⣿
⠀⠀⣤⡀⠀⠀⠙⢿⣿⣿⣿⣿⣶⣤⠰⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⢸⣿
⠀⠰⢿⣿⣦⣀⠀⢀⣈⣙⣿⣿⣯⣻⣶⣿⣦⣄⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠰⠿⠗⠒⠲⠶⡿⠶⠶⠒⠒⠂⢺⡷⠒⠒⠒⠒⣺⣿⡀
⠀⠀⠈⠻⠟⢿⡟⣛⠋⠉⠉⠀⠈⠛⠿⢿⣿⣻⢿⣶⣄⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣿⣿⣥
⠀⠀⠀⠀⠀⠛⣿⣿⣷⡄⠀⠀⠀⠀⠀⢀⣨⣿⣿⢿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢿⣿⡟⠄
⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣷⡴⡶⠞⠋⠹⠿⣛⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢧⣀⣀⣀⣀⣠⣇⣤⣠⣤⣤⣤⣼⣠⣤⣤⣤⣀⣼⣿⠟⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠳⠶⠽⣷⣀⠔⠊⠉⠉⠉⠓⠤⢐⡚⠹⠂⠀⠀⠀⠛⣵⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡈⣧⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠤⠤⠔⠊⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣟⡿⣿⣶⣤⣀⡀⠀⠀⠀⢀⡼⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣾⣿⣿⡷⢾⣽⣿⡷⢶⣰⠏⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢽⡛⠻⢿⣙⡻⠿⣿⣿⣿⣇⠞⠉⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣿⣶⣤⣙⡓⣾⣿⠋⣀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⢿⢿⣛⡹⠉⠋⠛⠛⠿⠿⢿⡇
⠀⠀⠀⠀⠀⣴⣿⣿⣶⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠐⠛⠛
⠀⠀⠀⠀⢸⠁⠃⢸⠁⠈⢻⠘⣧
⠀⠀⠀⠀⡇⠀⠀⠈⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠄⠀⠙⠩⠄⠀⠈⠅⠀⠀⠀⠀⢤⣤⡤⠶
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⡇
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠶⠶⠦⢄⡀
⠀⠀⠀⠀⢡⠀⠀⠀⡄⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⢤⡀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣿⣤⣀⣀⣀⣀⣉⣦
⠀⠀⠀⠀⠈⣧⣠⠀⢰⡀⢠⣃⡏⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠘⠃⠀⢱⠀⢱⠀⠀⠂⠀⠨⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠈⢻⣦⣻⣧⣼⡟⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡁⠘⢠⠐⠄⠰⠀⢁⡼⠀⠀⠀⢀⣠⣤⡤⢀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠋⠀⠀⠀⠀⠀⠀⣀⠦⠀⠧⢀⠁⠑⠀⢈⠀⢰⡀⡶⠌⠀⠀⠀⢰⣿⣯⠀⠀⠀⠀⠀⣠⡼⠂⠀⣠⣤⠐⠀⠀⠀⣀⣸⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⠀⠀⢿⣤⡃⡁⢀⣄⣀⠆⡠⠖⠈⠉⠀⠀⠀⠀⠀⠈⠻⣿⣶⣶⣶⡾⠿⠋⠀⠀⠀⠻⠿⠿⣶⡶⠿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠠⠄⠀⠀⢀⣀⣀⣀⡀⠀⠄⠐
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠻⢿⠛⡿⠿⣿⠻⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠠⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⡀
⠀⠀⠀⠔⠊⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⣀⡀⠀⠀⠀⠀⠀⣒⣒⣀⣀⣤⣤⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠠⠄⢐⣒⣒⣀⣨⣭⣥⣤⠴⠶⠖⠒⠒⠛⠛⠛⠉⢉⡉⠁⠀⠀⠀⡀⠀⠙⢦⡀
⢰⡄⠀⠐⠒⠚⣛⣛⠉⣉⠉⠉⠀⠀⠀⠀⠀⠀⢀⣈⠻⣐⡄⢠⡤⣌⠳⣦⠹⣟⡦⢻⣳⣦⠀⠳⡄
⢸⣷⡀⠀⠀⠈⢿⡈⠓⠙⢧⣰⣆⠲⣷⢦⣻⣟⠈⡻⣕⡬⠷⠤⠟⠾⠓⠋⠛⠋⠉⠉⠀⠁⣀⣀⠹⡄
⠀⠹⣿⣦⣀⠀⠀⠙⠲⠤⠴⠛⠻⠙⠉⠓⠋⠀⣉⣀⣀⣤⣤⣤⡤⠶⠶⠶⠖⠛⢛⣛⠋⠉⠉⠁⠀⢻⡀
⢠⢴⠨⠉⠻⢿⣶⣤⣀⡀⠀⠀⠐⠚⠛⠛⠉⠉⠉⠡⠄⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⢸⡌⠳⣄⠰⠀⠈⠙⠛⠿⠿⣶⣦⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠹⣦⡈⠛⢦⣼⢰⠠⠀⠀⠀⠈⠉⠙⠛⠿⠿⠿⣿⣿⣷⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⣸
⠀⠀⠀⠙⠳⢦⣈⡉⠛⠶⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠋⢹⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠦⣤⣀⣉⡉⠓⠒⠒⠤⠤⢤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠲⠶⠦⢤⣤⣀⣀⣈⣉⣉⡉⠉⠉⠉⠉⠋⠈⠉⠉⣉⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⢰⣶⣖⣒⣶⣶⣶⣖⢶⠖⣲⡶⠶⠶⣶⣶⣖⣲⣲⣶⣷⣶⠶⠶⠾⠒⠖⢮⠻⣿⠿⢉⣤⣬⠬⠼⣍⣻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣟⣿⠁⠀⠀⠀⢹⠼⢔⡏⠀⠀⠀⠀⠈⠙⢿⣿⣸⣿⡅⠀⠀⠀⠀⠀⠀⢃⣻⢰⡿⠋⠁⠀⠀⠀⠹⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢰⡇⣿⡀⠀⠀⠀⢸⣇⡞⣇⠀⢀⠀⠀⠀⠀⠀⠘⣷⢿⣿⡀⠀⠐⠠⠀⠀⠸⣽⣺⡷⠁⠀⠀⠀⠀⠀⡿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⡏⣿⡆⠀⠀⠀⠈⣿⣷⢸⣷⣄⡑⠢⠄⠁⠀⣠⣿⣾⣿⡇⠀⠀⠀⠀⣀⣠⣿⡟⣷⣇⡀⠀⠀⢀⡼⢃⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⣧⣤⣀⣤⡤⣟⣿⣏⡿⠿⢛⢓⠲⡖⣾⣯⣵⣿⣯⢿⣤⣦⣾⣿⣿⣿⣿⡷⠌⢽⣷⡶⣿⣟⣷⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⢏⣿⠶⠶⠶⠶⠾⢿⡿⣹⡾⠛⠋⠉⠙⠻⣭⣿⡿⣿⡟⠉⠉⠉⠉⠉⠉⢹⣾⠁⣾⠏⠁⠀⠀⠉⠻⣷⢻⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠹⣧⠂⠀⠀⠀⠄⢘⢧⡏⠀⠀⠀⠀⠀⠀⠈⢳⣿⢸⡇⢀⠆⠀⢀⡀⠀⠸⣿⡇⣿⠀⠀⠀⠀⠀⠀⢹⣆⡇
⠀⠀⠀⠀⠀⠀⠀⢸⢨⣿⡄⠀⠀⠀⠀⠀⣟⣧⠀⠀⠀⠀⠀⠀⠀⠈⣿⢹⡇⢠⡀⠰⡄⠗⠀⢀⡇⡏⢿⡄⠀⠀⠀⠀⢀⣾⡏⣿
⠀⠀⠀⠀⠀⠀⠀⣸⣼⡇⠻⣄⡀⠀⠀⠀⡷⣿⣷⣄⠀⠀⠀⠀⢀⣼⢻⣾⣇⠀⠳⢤⣀⠀⠀⢀⣏⣷⣈⢻⡷⡶⣴⣶⣿⡿⣣⣿
⠀⠀⠀⠀⠀⠀⠀⢹⣏⣷⢤⣤⣤⣤⣤⢴⣇⣿⠿⠟⠛⢛⣓⡒⠋⠷⣿⣧⡛⠷⠖⢒⣒⢒⠻⢭⣥⣽⢃⣮⣭⣬⣭⣭⣍⡹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⢯⣾⠟⠛⠛⠻⢷⡜⣿⣵⡾⠛⠋⠉⠉⠉⢻⣷⢹⡏⣶⡿⠛⠉⠉⠻⣿⣮⢻⡇⣾⠉⢻⠏⠈⡏⠀⢹⡸⣇
⠀⠀⠀⠀⠀⠀⠀⠸⣿⠃⠀⠀⠀⠀⠀⠻⣖⣿⡄⠀⢀⠀⠀⠀⠀⣿⢠⡧⡟⠀⠀⠀⠀⠀⢹⣿⢎⠅⣿⠀⢸⠄⠀⠀⠀⢸⠯⣿
⠀⠀⠀⠀⠀⠀⠀⢰⢹⡄⠀⠀⠀⠀⠀⢰⡇⢿⡇⠀⠹⣄⠀⠀⠀⢻⢈⣏⣷⠀⠀⠀⠀⠀⢸⣿⡧⡇⣾⠀⠀⠀⠀⡆⠀⣸⣱⡏
⠀⠀⠀⠀⠀⠀⠀⢸⣮⣷⣄⡀⠀⢀⣠⡼⢧⡾⣧⠀⠀⠈⠁⠀⠀⣸⡂⣿⣘⣧⠀⠀⠀⢀⣾⣿⣥⡇⢾⣀⣰⣧⣤⣷⡴⣏⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⠷⠾⣭⣽⡭⣭⡭⣾⣿⣧⣝⣷⣶⣶⣶⣞⣛⣫⣱⣿⣿⣾⣿⣶⣾⣿⣿⡿⠿⠿⠤⠭⠶⠶⠶⠶⠶⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠠⠏⣀⠁⢄⠀⠀⢀⡆⡐⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠠⠀⠀⠀⣀⡄⠈⠉⠀⠀⠀⠀⠀⠀⠁⠒⠀⠐⠂⠀⠐⠈⠀⠀⠀⠈⠉⠉⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠉⠾⣥⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⠒⠂⠀⠀⠘⠆⠓⠈⠀⠀⠀⠂⠀⠀⡠⢀⠀⠀⠰⡤⠤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠘⡤⠀⢀⡀
⠀⠀⠀⠀⠀⠄⢀⠢⠎⠀⢠⣀⠳⡤⠀⠀⢀⠀⠀⠀⠁⠒⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠛⠉⠁
⠀⠀⠀⠀⠀⠓⠛⠦⠐⠓⠒⠑⠁⠀⠀⠀⠠⢢⡤⠤⠅⠠⠀⡀⠀⠀⠨⡀⠀⠑⠂⣂
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠶⠒⠊⠁⠀⠀⠀⠀⠈⠉⠁⠈
⠀⠀⠀⠀⠐⠈⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⡆⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢛⠀⠀⢀⠀⠀⠀⠁⠀⠀⣀⠀⠀⠐⡂⠀⠀⠀⡄⠀⢀⡼⠁⠀⠀⠐⠀⠂⠂⠀⠒
⠀⠀⠀⠀⠀⠘⡆⠀⠁⠀⠀⠀⢋⠁⠀⠠⠤⠄⠺⠀⠀⠀⠀⠒⠛⠚
⠀⠀⠀⠀⠀⠀⠱⠄⠄⠘⠀⠀⠐⠀⠂⠂⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠠⡔⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⠐⠀⠘⣄⣀⣬⣧⠤⠶⠒⣎⠉⠁⡀
⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠠⠂⠀⠀⠄⠀⠀⠀⠈⣧⠤⠖⠱⠛⠉⠙⠁⢀⣀⠧⠀⠐⠚⢂⠉⠉
⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠶⠦⢴⡄⠂⠀⠀⠀⢣⡀⠤⠔⢃⠈⣉⡉⠠⠀⠒⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠂⠀⠀⠀⠀⠀⠃⠀⠀⠉

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣕⣯⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⣰⠀⠀⠀⢀⣀⠀⠀⠀⢠
⠀⠀⠀⠢⡀⠀⠀⠀⠀⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⠤⠴⠃⣀⣀⣀⠄⠃⠀⠀⠀⠀⣈⠷⠀⠀⠈
⠀⠀⠀⠤⡈⠀⠌⡉⠆⠓⢒⡒⢚⠡⠤⠤⢼⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠂⠀⠀⢈⣏⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⣄⠒⢄⠀⠈⠉⠈⠉⠺⠄⠀⡀⢠⠀⠀⠀⠀⣐⢀⣀⠀⣠⠏⠀⠀⠀⡨⡎⠀⢀⠔⠐⢀⢢⡀⠀⠀⠠⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠆⠉⠐⠆⠠⣀⠀⠀⠒⠀⠀⠀⠈⠁⠀⠀⡄⠀⠉⠙⠻⠐⠦⣤⣤⡜⠜⠀⠀⢀⠈⢢⠀⠇⡇⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⢈⡏⠀⠀⠀⠈⠓⠒⠂⠂⠁⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠰⢦⣄⣀⣴⠇⠀⠀⠀⢀⡟⠀⢀⣤⠴⢶⣤⡀⠀⠀⠀⠀⠀⣤⢰⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⣠⡾⠀⠀⠠⢋⠖⠛⣻⠿⡄⠀⠀⠀⣂
⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠁⠀⠲⢦⡤⡤⠀⠀⡤⠗⠀⠀⠀⠙⠶⠦⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⣦⡀⠀⠀⠀⠀⠀⠀⠀⡀⠄⣰⠟⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠧⠤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⣣⣼⢗⣫⠼⢙⡄⠀⠀⠀⠀⣴⣆⠀⠐⠿⣊⠓⢦⣄⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢣⣴⠖⣺⣍⢶⣏⣴⣞⣛⠛⣷⡄⠀⠀⠙⢿⡻⣦⠐⠉⠹⠆⢌⡙⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠠⠄⠀⠀⠀⠈⠻⡿⠯⠒⠛⠓⠉⠍⠛⠋⠇⠀⠀⠀⠀⠀⠙⠆⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⢠⢀⡠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡆
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢌⠀⠂⢀⠵⠁
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡀⡰⠁⠉⠀⠈⠄⠀⠙⠋⠅⠀⠠⠄⠀⠠⠔⢀
⠀⠀⠀⠀⢨⠃⢀⠀⠀⠰⣄⠀⠀⠂⠰⠃⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⢤⠀⠀⠉⠀⠀⠂⢤
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢧⡈⢠⣶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣠⡁⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢨⡆⠀⠀⡀
⠀⠀⠰⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢆⡀⠀⠛⠿⠈⠑⠀⣊⠀⠉⠢⣈⢠⢀⡀⠐⠁⠀⠀⠃⠈⠀⠠⡀⠁⢀⣄⣠⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠈⠻⠋⠀⠀⠀⠀⠀⠑⠂⠒⠀⠘⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⠻⡟⡛⢻⡿⣻⢿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠚⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠉⠉⠉⠙⠓⠒⠢⠤⣀⡀
⠀⠀⠀⠀⠀⡠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⣴⣾⣿⠿⠿⣿⣿⣿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⣧⠀⢰⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⢀⣼⣿⣿⣿⣿⣀⣠⣿⣿⣿⣿⡿⠿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠸⣿⣿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣶⣶⠖⠛⠛⠛⠿⠷⠾⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⣼⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⢠⣶⣄⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡁⠀⣽⣿⣿⠿⣿⣿⣿⠟⠛⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⣴⣦⠀⠀⠙⠻⣿⣿⣿⣿⣏⠀⣨⣿⣿⣦⣤⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣠⣦⡄⠀⠀⠀⣠⣄⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⣀⠀⠀⠉⠉⠉⠉⠛⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠈⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠙⠛⠁⠀⠀⠈⠿⠟⠀⠀⢠⣤⡀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⢀⡀⠀⠙⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢸⣿⣿⣿⣿⣿⣿⡀⢀⣴⣤⠀⠀⢸⣿⡆⠀⠀⢠⣾⣦⠀⠀⠀⢾⣿⠁⠀⠀⠀⣻⣷⠀⠀⠀⠀⠀⠀⠀⣠⣄⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠈⣿⣿⣿⣿⣿⣿⣇⠀⠛⠛⠀⠀⠀⠉⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠉⠀⠀⣸⣿⡇⠀⠘⢿⡿⠃⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣶⣷⡄⠀⠀⠀⢀⡀⠀⠀⢠⣤⡀⠀⠀⢀⣠⡀⠀⠉⠀⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⠀⠙⠿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣴⣷⡆⠀⠈⠉⠀⠀⠀⠀⣿⣿⠀⠀⠙⠟⠃⠀⠀⠘⠿⠟⠀⠀⢸⣿⡇⠀⢀⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠀⠀⠈⠉⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠙⠋⠀⠀⠀⠀⠀⢀⣄⡀⠀⠻⠿⠁⠀⠀⢠⣶⣦⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠐⠒⠢⠤⠒⠊⢦⡀⠀⠻⠿⠃⠀⠀⠀⣀⡀⠀⠈⠙⠉⠀⠀⠀⣀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠸⢿⡿⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⣄⣀⡀⠀⣀⣠⡤⠖⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⣀⣀⡀⣀⢀⣤⡀⡤⣄⡴⣤⢴⠀⢰⣦⠖⣖⢲⡞⠶⣿⣶⣶⣾⡀
⠀⠀⠀⠀⠀⢸⣾⣿⣿⣅⣧⠃⣷⣹⣸⡇⣧⣷⠈⣷⢹⡼⡇⣸⣿⡆⢻⡀⢿⠒⢾⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣏⣿⣀⣿⢸⡇⣧⣿⠸⣤⠾⣼⠇⠿⠿⠇⠿⠘⠇⠘⠓⠓⣿⣿⣿⣾⣇
⠀⠀⠀⠀⠀⠀⣟⣿⣿⣿⣨⣉⣈⢠⣤⡀⢀⡒⣒⣦⢤⣄⢤⡶⡄⢠⢠⣼⡗⣶⣄⣾⠏⠝⠋⠙
⠀⠀⠀⠀⠀⠀⠉⠉⠁⠹⠟⠃⠛⠚⠥⠈⠀⠀⠉⠋⠈⠙⠋⠀⠁⠀⠁⠈⠈⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠠⣴⠎⠀⢀⠔⠢⣄⣤⠃⠀⠀⠠⣀⢀⡠⠁⠀⠀⣀
⠀⠀⠀⠀⠀⡔⠉⠐⡾⠀⠀⢀⠝⠛⢿⡏⠀⠀⢘⠾⢶⣶⠆⠀⠈⢯⣧⣤⣤⡤⢍⡁
⠀⠀⠀⣶⣟⡀⠀⢀⣘⢻⣿⠏⠀⠀⠈⠶⢶⣶⠃⠀⠀⢫⣤⡤⠤⢼⣠⠤⠖⣀⡥⠴⠒⠒⠂
⠀⠀⠴⠾⠭⠭⠭⠭⠴⠋⠛⠛⠒⠒⠛⠑⠛⠛⠂⠀⠀⠒⠀⠖⠂⠉⢠⠞⠉⠁⠀⢀⡀⠄
⠀⠀⠀⠀⠀⠀⣠⠖⠘⠉⠉⠉⠉⠉⠉⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠚⠉⠁
⠀⠀⠃⠀⠀⠀⠘⠲⠤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠔⠒⠋⠉⠉⠉⠐⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣏⠀⠉⠒⠠⠀⠀⠀⢀⣠⡤⠖⠊⠁⠀⠀⢀⣀⠼⣃⣰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠨⣍⣒⠤⢀⠀⠀⢰⠁⠀⠀⣀⠀⠀⢀⣩⠤⡶⡺⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⢀⠢⠈⡏⠂⢀⣀⠚⠖⣋⣡⢤⢤⠞⠁⣈⠀⠀⠀⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣷⣦⣀⠀⠀⡇⢸⠋⠁⠀⣤⢋⣠⠴⠿⠞⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢹⡍⠻⡷⠦⣄⣸⣤⡤⠚⠉⠁⠀⠀⠀⣀⣁⣤⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢤⠀⠹⣄⡿⠢⡈⠰⠧⠄⣀⢀⢀⣀⣠⣤⡤⠴⠒⢒⠖⢩⡽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⢀⠀⠙⢇⠀⠙⢶⠒⠛⠉⠟⠋⠀⢸⡟⣀⡔⢀⠊⠐⣀⣈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠢⠴⠯⡿⠉⣹⠂⣌⠢⡘⢸⠀⠠⠀⠀⣠⢤⠮⠚⠛⠒⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢱⣟⡆⠀⡐⠀⠀⠑⢆⡜⡇⠉⠈⠉⠉⠉⠀⠠⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⠀⠁⠈⠷⠁⠀⠀⠀⠐⠀⠒⠿⠟⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢠⢚⢼⠀⠳⠀⢾⠆⣠⣤⣶⣶⣤⣴⣦⣤⣄⡀⠀⢠⠖⠙⠠⠌⠕⢆⠀⣇⠀⠀⠀⠀⢈⡇
⠀⠐⠋⠓⠋⠛⠛⢌⡌⣄⡰⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠱⣌⣂⣁⣐⠤⡎⡔⣡⣤⣭⣭⣥⣤⣑⠆
⠀⠀⢀⠌⢩⠗⠠⠤⢉⣉⠀⢠⠖⢯⠿⢨⣿⣿⣻⣻⣟⢟⣿⠹⠿⣄⠱⣄⣀⣀⡠⠃⠉⢙⣛⣛⡛⠛⠛⠉⢩
⠀⠰⠁⡰⠁⠀⠀⠀⣀⡠⠬⠆⠓⠄⡑⠒⠡⠥⠈⠀⠁⠀⠭⠔⠊⡠⢇⡀⢄⡀⠀⠀⡘⠥⣀⣀⣈⠇⠀⠀⣠
⠀⢸⠀⡁⡔⠂⢉⣁⠠⠄⣒⡗⠀⠀⣂⢌⠉⢑⣒⠒⠒⠒⢂⡉⠁⠀⢯⠀⣀⠗⠒⢄⠫⣛⠲⠶⠶⠶⢖⡫⠇
⠀⠀⡇⡇⢈⠭⠐⣂⣈⠥⢔⣾⠀⣎⡸⠁⡴⠁⠈⠓⠒⢲⡘⢋⠤⠤⠠⠄⣘⠢⠠⠋⠐⣷⡈⠉⠉⠉⢀
⠀⠀⠸⢐⠀⣭⣛⣷⣬⠯⠟⣋⡈⠚⠃⢰⠅⠀⠀⠀⠀⠀⠃⢃⠀⠀⠀⠀⠀⠑⡢⣄⡀⢱⠳⠲⢄⡀⠺⠃
⠀⠀⠀⠙⢓⣈⢉⠀⠀⡴⠫⡑⠈⠳⡀⠸⣀⣀⣀⣀⠠⠔⠁⠈⠢⣄⠆⠀⢰⡾⠋⢻⡇⠀⠀⠐⠑⢌⠢⡀
⠀⢰⢎⠉⠙⣦⣠⡵⣄⢇⠀⠈⠀⢠⠇⣠⣤⣶⣶⣶⣶⣶⣶⣶⣶⣬⣑⢤⣘⠧⣤⡺⠗⢠⠘⡀⠀⠄⢣⢡
⠀⠀⠣⡻⡋⠉⢳⣄⣬⢦⡑⠒⠛⠁⢰⣿⠶⣭⡰⡀⢶⢆⢸⣁⢻⣼⣿⡆⠈⠉⠀⢀⣠⣤⠣⡈⢆⠀⠀⢺
⠀⠀⣠⡑⣜⢟⠋⠙⣦⣀⡸⡆⠠⡦⠀⠙⠛⠿⠿⠿⠿⠿⠿⠿⠿⠟⠋⢀⣠⣴⡾⠟⢋⠭⠰⠈⠒⠷⣤⡞
⠀⠀⠙⠁⠈⠢⣑⡨⠭⠒⠊⠁⠀⢀⡤⠒⢟⠉⢝⠉⢛⠲⣄⠀⡤⣒⠽⠟⠋⠁⠀⠀⠸⣀⠟⠉⠒⢄
⠀⠀⠏⢹⡎⠑⠆⢀⣀⠀⠸⠳⡀⡎⠁⠀⠠⣖⡚⣤⠀⡀⠈⢣⠈⠀⠔⠂⠀⢰⠒⢦⡀⠸⠀⢄⠀⠀⠑⡀
⠀⢀⠃⢸⠃⣸⠀⢀⠂⡇⢰⢠⠃⡧⣀⣀⠠⠈⠙⣛⠄⠀⢠⢺⠀⢠⠒⠒⠒⣺⠒⠒⠛⣲⠑⢄⠀⢠⡤⣁
⠀⢨⡁⢜⠀⡌⠀⠈⠦⠀⠈⠋⠀⠐⢄⠀⠱⢄⡀⠔⠐⢒⡡⠃⡎⠈⠑⢦⣄⡿⠄⠀⠠⣿⠀⣠⡌⢩⡡⠴⠃
⠀⢸⢀⡇⠐⢣⠒⢈⣉⣉⣩⣉⡁⠒⣄⡉⠐⠒⠒⣒⣊⠁⠀⠀⠈⡖⡖⠒⠀⠛⠒⡶⠴⢟⢢⡈⠀⢀⡤⡀
⠀⢸⣰⠂⣸⠈⡄⠀⠀⠀⠀⠀⠀⢠⢳⢹⠀⡴⢍⡂⠈⠫⣲⡄⢰⢠⠁⠀⠀⠀⠀⡇⠀⣨⠤⠇⢰⡁⠀⢳
⠀⠀⠉⢒⡂⠤⠵⡄⠀⠀⠀⠀⢀⣞⠥⢂⠸⡀⠀⠈⠁⠉⢀⡕⡌⠘⡄⠀⠀⢀⡴⠀⠀⠇⡤⠔⡆⠨⣍⣁
⠀⠀⠀⠘⠦⣤⣐⡻⣷⣶⣶⣾⢿⣂⣤⡤⠇⠈⠑⠢⠤⠔⠁⠀⢧⠀⠀⠀⠀⠀⠀⠀⣰⠀⠑⠤⠇⡆⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠉⠓⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠈⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢼⠀⠀⠈⠀⠀⠀⠀⠀⣰⡤⠊⡉⠑⡄⠀⠀⠉⠉⠓⠢⢄⡀
⠀⠀⠀⠀⢀⡴⠒⠲⠤⣄⣀⠤⠒⠉⠁⠀⠘⡇⠀⡄⠀⠀⠀⠀⢠⢋⡤⠊⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠉⠑⠢⣄⠀⠀⠀⢳⠀⡃⠀⠄⠀⢠⠟⠉⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⢰⠇⠀⠀⠀⠤⠄⠤⠤⠤⢀⣙⠢⣠⠞⠉⠙⢎⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⣠⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠹⣄⠀⠀⠈⣧⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⢀⡞⠘⣀
⠀⡴⠁⠸⡄⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠔⡖⠙⠳⣤⢴⠛⠲⢤⣄⣀⣀⣀⣀⣠⡤⢔⣮⡁⠀⠀⠀⠀⢀⠞⠀⢀⠟⠻⢷⣦⣤⡀
⡸⠁⠀⠀⠙⠦⣈⡉⠉⡩⠋⠁⠀⠀⢠⠊⠀⠀⡰⡟⠈⢧⠀⠀⠀⠀⠀⡠⠔⠒⠉⠁⢀⣹⠆⠀⢀⡴⠃⠀⢀⣜⡠⠖⠂⠫⠉⠹⠓⢦⡀
⡇⠀⠀⠀⠀⠀⠀⢉⠏⠀⠀⠀⠀⠠⠃⠀⠀⡐⢰⠃⠀⢸⡷⣄⠀⠀⠀⡇⠀⣴⠚⠉⠉⠀⣠⠔⠉⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀
⢳⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠁⠀⠀⢠⠁⡞⠀⠀⠀⡇⠀⠙⠢⣄⣇⠀⢹⢀⣠⠔⠋⠁⠀⠀⢀⡴⣹⠁⠀⠀⠂⠄⢀⠀⠀⠈⠈⠉⠉⣏⠑⡄
⠈⡷⢄⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⡘⢰⡇⠀⠀⠀⣿⠀⠀⠀⢀⡩⠟⠚⠉⠀⠀⠀⠀⡠⠖⠻⡆⠹⠢⢤⣄⣀⡀⢐⣂⣀⡤⣤⡤⠔⠋⢰⢳
⠀⠹⠀⠙⠲⠤⢄⣀⠙⠲⢤⡀⠀⠀⠀⠀⠁⣼⠉⠓⠢⢤⡷⠒⠚⠉⠀⠀⠀⠀⠀⢀⡠⠶⠋⢁⠀⡀⠸⡶⢦⣀⣀⠼⠙⢉⠋⠉⠿⠲⢆⡰⢠⠋⡆
⠀⠀⠳⣄⠀⠀⠀⠀⠉⠉⠉⠉⠛⢶⠶⠒⢚⡥⠖⠲⠦⠤⠇⠀⠀⠀⠀⣀⣤⠖⠚⠍⣀⠀⠀⠀⠀⠤⠀⣸⣄⠞⠁⠀⠀⠀⠀⠒⠈⠀⠀⠙⣏⡀⣷
⠀⠀⠀⠈⠑⠲⢤⣀⡀⠀⠀⠀⠀⠘⠒⠋⠁⠀⠀⢀⣀⣀⣤⠴⠶⠾⢯⣭⣙⠗⠶⡆⠤⠤⠍⢤⠶⠛⣟⢁⡜⠀⠈⢀⠀⠀⠀⢉⣀⠀⠈⢉⣹⣈⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣷⢲⠒⠊⠉⠉⠉⡡⠛⢅⠀⠀⠈⠀⠀⠅⠈⡑⣄⡁⠀⠀⠀⣀⣠⡤⡼⠤⢷⣴⣤⣄⣈⣁⣒⣀⣀⣤⢤⠤⠚⢡⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢧⢣⡀⣠⠴⡾⠁⠄⢀⠈⠐⠠⠄⠀⠈⣁⡀⠈⢷⠦⣤⠖⢉⠀⠑⠈⠂⢈⠕⠈⠳⣅⠀⢸⠀⢨⠀⠀⠀⣰⢋⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠳⡙⢄⢼⡇⠈⠐⠠⠌⠁⠒⠀⠤⠤⠀⠠⣠⡼⣶⠃⠀⠀⠁⠂⠀⠈⠀⠀⠉⢀⣈⣷⠼⣀⡈⠀⢀⡴⣡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠪⣙⢍⡓⠶⠦⣤⢤⣤⣌⡉⣤⠴⢾⡁⢤⡇⠈⠂⠤⢉⠐⠂⠤⠄⠀⣀⣀⣀⠨⣤⠈⣧⠴⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠈⠑⠭⣓⢤⣄⠀⠀⠀⠀⡆⠀⠌⢧⠀⡙⠲⠶⢤⣄⣈⣉⣁⣀⣲⡶⢶⢖⣺⠕⣊⠵⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠀⠀⠙⠒⠭⣞⣲⠤⢄⣠⣀⣘⣆⢰⡀⢁⠀⢀⣀⣀⣄⠤⠴⣖⡪⠭⠒⠉⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠚⠒⠚⠟⠯⠭⠭⠹⠻⠓⠒⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠚⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣑⣒⣒⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣒⣒⣋⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡐⠀⠀⠀⠀⠀⡠⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢦⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠘⠈⠂⠀⠀⠂⠚⠰⠰⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠳⠬⢒⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠀⠻⠶⣂⢀⠀⠀⠀⠀⠀⠀⣇⠈⢙⣿⠃⠉⣱⠀⠀⠀⠠⣦⠀⣔⡀⠒⣶⡶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣈⣉⣰⣤⢆⠀⠀⠀⢀⡟⠛⠻⣿⠛⠋⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⠘⠻⠀⠀⠀⠸⣿⣷⣾⡟⠿⠻⠿⡈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⣀⠀⠤⣤⣲⣤⣯⣽⣦⣠⣖⣀⡀⠀⠀⠀⠰⠟⠟⠋⠀⠀⠀⠢⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠂⢀⠁⠈⢋⣀
⠀⠀⠀⠀⠻⠟⡶⠶⠦⠤⣤⣤⡄⠬⢦⣵⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠁⠒⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠈⠙⠒⠀⠀⠀⠀⠀⠀⠀⣭⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀
⠀⠀⠀⠀⠀⠀⢀⣄⠠⢀⠠⠐⠀⢀⣤⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠚⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⡀⠀⠀⡀⠀⣠⡄
⠀⠀⠀⠀⠐⠛⠲⢿⣤⣴⣶⣶⣿⡿⠟⠋⠀⠀⠀⠀⠀⠂⠀⠀⠦⠄⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡄⠉⠉⠉⣔⡴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠬⠠⠔⢀⡂⢀⡀⠀⠀⢀⡀⠀⠈⣠⠍⠐⠢⣴⡺⠟⠁⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⣀⢠⡀⡂⡠⠀⠎⠁⢉⠀⡓⢂⣀⣐⠦⠶⠛⠀⠐⠻⠯⢔⣠⡄⣾⠔⠉⠀⠀⠀⠀⠀⠦⠤⡀
⠀⠘⢇⡀⠀⠑⢌⢡⠄⠢⣓⣠⡵⠶⠚⠋⠁⠀⠀⠀⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢐⡠⠄⠀⠀⠈⢣⡼⣈⠑
⠀⠀⠈⠋⣨⣀⣠⣷⠶⠛⠋⠁⠀⠀⠀⠀⢰⣴⠁⡄⠁⠀⠀⠰⠒⠂⠬⠃⠀⠀⠀⠀⣤⣀⣀⡎⠀⢀⡒⣸⢸⠆⣬⢠⣸⠾⠇
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠛⠈⠀⠀⠀⠁⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠐⢄⠀⠀⠀⢀⠄⢄⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠢⡴⡎⠀⢀⠜⠲⣤⣤⠃⠀⢀⠧⣄⣀⡰⠁⠀⠱⣀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⢀⡔⠉⠱⡾⠁⠀⢨⠟⠛⣿⣟⡒⠒⣺⠾⢶⣶⠇⠀⠈⢯⣧⣤⣤⣤⣯⣟⠩⠙⠋⠉⠀⡇
⠀⠀⠀⣶⣿⣬⠍⣥⣹⣻⣿⡏⣐⣂⡘⡷⣶⣶⠣⠤⠬⢿⣬⣭⣭⣽⣿⠦⠖⣂⣭⠴⠖⠚⠓⣦⠀⡇
⠀⠀⡴⠾⠭⠭⠭⠭⠿⠯⠛⠿⠿⠾⠿⠿⠿⠾⠷⠶⠾⠿⠾⡗⠂⠉⢠⠖⠋⠁⠀⣀⣠⠴⠚⣁⠤⠃
⠀⠀⡇⠀⠀⠀⣠⠖⠛⠛⠉⠉⠉⠉⠉⠙⠛⠲⣄⠀⠀⠀⠀⡇⠀⠀⠙⠲⠒⠚⣋⠭⠐⠊⠁
⠀⠀⡇⠀⠀⠀⠘⠳⠦⢤⣤⣤⣤⣤⣤⡤⠴⠖⠃⠀⠀⠀⠀⡇⠀⣀⠤⠐⠊⠁
⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠴⠶⠒⠚⠛⠉⠉⠉⠉⠉⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠖⠛⠋⠉⠁⠀⠀⢀⣀⣀⣄⣤⣀⣀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠹⣆⠀⠀⠀⠀⠀⢠⡴⠛⠉⠁⠀⠀⠀⠀⠈⠛⢦⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠘⣆⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠘⢧⠀⠀⠀⠈⠃⠀⢀⣀⣀⣠⣤⡤⠴⠶⠖⠒⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠈⢧⡀⠀⠀⠀⠉⠉⠉⠁⠹⣆⠀⠀⠀⠀⣠⠶⠶⠶⠶⠶⠶⠶⠞⠛⠛⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠈⢳⡀⠀⠀⠀⢀⣀⣀⣤⡼⠷⠶⠒⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⢳⡄⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠻⡄⠀⣠⠞⠋⠉⠉⠉⠉⠉⢹⠟⠓⠶⢤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢹⡞⠁⠀⠀⠀⠀⠀⠀⣠⢏⡀⠀⠀⢠⡶⠛⠛⠉⠉⠙⠓⠶⣤⣀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡴⠋⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠹⣄⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠙⣯⠙⠳⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠘⢧⡀⠀⠈⢷⠤⠴⠖⠚⠛⢉⣉⣀⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⡀⠀⠀⠀⠀⢀⣤⠞⢳⣄⣤⡤⠴⠶⠒⠛⣃⣀⠀⠀⢠⡴⠶⠚⠛⠉⠉⠈⠳⡀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠠⡞⠉⠙⣆⠀⠀⢠⡴⠶⠒⠛⠉⠉⠉⢷⡀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠙⣆⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣽⡄⠀⠘⣦⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠹⣄⠀⠘⢧⣤⠤⠶⠖⠚⠛⠉⣀⣀⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠘⢧⠀⠀⠙⢦⣤⡤⠴⠶⠒⠛⠉⠀⣀⣀⣤⡤⠴⠶⠚⠛⠉⠉⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠈⢧⡀⢀⣀⣀⣤⡤⠴⠖⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⢀⣀⣠⡤⠴⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⢸⠏⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠴⠶⠚⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣟⣀⣀⣤⡤⠴⠶⠒⠚⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶⣦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠿⠟⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣴⠿⣦⣤⣴⠿⣦⣄⣴⣶⣶⣄⣠⣶⠿⣶⣶⣶⣶⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠟⠁⠀⠈⠉⠀⠀⠈⠉⠉⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠁⠀⣹⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣦⠀⠀⠀⠀⠀⣀⣤⣴⣶⣤⣄⠀⠀⣠⡾⠛⠉⠙⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠙⠻⠷⠾⠿⠛⠋⠉⠁⠀⠈⠙⠛⠛⠋⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤
⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄
⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀
⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆
⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇
⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆
⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⣿⠃⠀⠀⠀⠀⠀⠀⢠⡿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢰⣿⠀⠀⠀⠀⠀⠀⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⣀⠀⠀⠀⠀⢸⣿
⢸⣿⠀⠀⠀⠀⢰⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⠀⠀⠀⠘⣿
⢸⣿⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡆
⢸⣿⠀⠀⠀⠀⢸⠆⠀⠀⠀⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡇
⢸⣿⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡇
⢸⡟⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡇
⢸⡇⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡇
⢸⣷⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡇
⢸⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡇
⢸⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣤⡄⠀⠀⣤⣤⡀⠀⢠⣤⣤⣄⠀⣤⣴⣶⣤⠀⠀⢀⣤⡶⠿⣷⠀⣠⣶⣤⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡇
⢸⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⣼⠉⢻⣦⡾⠉⠙⣇⠀⢹⡃⠈⣿⠀⣿⡀⠀⢿⡇⠀⢸⣯⠀⠀⢾⡿⠋⠀⣽⠇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⡇
⢸⣿⠀⠀⠀⠀⠀⣿⠀⠀⣠⡿⠀⠀⠉⠀⠀⠀⣿⡆⢸⣇⠀⣿⡀⣿⡇⢀⣼⡇⠀⢸⣿⠀⠀⠀⠀⢠⣾⡏⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⣿⡇
⢸⣿⠀⠀⠀⠀⠀⣿⠀⠀⣿⠃⢀⡄⠀⣤⠀⠀⠘⠇⢸⣿⠀⢻⡇⢿⡇⠀⠻⠿⣶⢸⣿⠀⢠⣦⡀⠈⠻⢿⣤⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⡇
⠈⣿⠀⠀⠀⠀⠀⣿⠀⢸⣿⣀⡈⠡⠖⠈⢁⣀⣀⣀⡀⣿⣄⣹⡇⢻⣇⣀⣀⣀⣿⢸⣿⠀⢸⣿⢿⣦⣀⣨⣿⠇⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿⠃
⠀⣿⠀⠀⠀⠀⠀⣿⠀⠈⠛⠉⠉⠀⠀⠀⠘⠛⠛⠛⠉⠛⠛⠛⠃⠈⠛⠛⠛⠛⠛⠘⠿⠿⠿⠟⠈⠻⠿⠟⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿
⠀⣿⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿
⠀⢿⡇⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠃⠀⠀⢸⣿
⠀⢸⡇⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⠀⠀⠀⢸⣿
⠀⢸⡇⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⣿
⠀⢸⣇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⢸⣿
⠀⢸⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⣿
⠀⢸⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢸⣿
⠀⠀⣿⡄⠀⠀⠀⠸⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠸⣿
⠀⠀⣿⡇⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠃⠀⠀⢰⣿
⠀⢀⣿⡇⠀⠀⠀⠀⠀⢸⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠁⠀⠀⠀⢸⣿
⢠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠉⠛⠻⢶⣶⣦⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⡇⠀⠀⠀⠀⠀⠈⠻⣦
⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠿⠿⠿⠿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾
⠀⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠙⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠇
⠀⠀⠀⠀⠈⠻⢿⣷⣦⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠈⠿⠿⠿⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⡿⠿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠶⠶⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠓⠒⠲⣦
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣿⣀
⠀⠀⠀⠀⠀⠀⠀⣨⣷⣤⠶⠶⠶⠶⠶⠶⠶⠖⠒⠒⠒⠛⠛⠛⠛⠛⠋⠉⠉⣽⠟⠉⠛⠿⣷⣦⣀
⠀⠀⠀⠀⢀⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠉⠛⢷⣦⡀
⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠞⣿
⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⣀⣤⡴⠾⠛⠉⠀⠀⠀⣿
⢸⠻⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⣀⣠⣴⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢻
⢸⠀⠈⠙⠻⠿⣿⣶⣶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣿⣤⡶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⠛⠛⠉⠉⠉⠉⠉⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⠀⠀⣿⠀⠀⣆⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⣼⠀⢠⣿⠀⢸⣿⠀⠘⢿⣿⣦⢰⡆⠀⠀⠀⡀⠀⠀⠀⢸⣿
⣿⠀⢸⣿⡇⢸⣿⠀⠀⢸⡇⠁⢸⡇⠀⠀⠀⡇⠀⢰⡆⢸⣿
⣿⠀⣸⠃⣇⣾⢸⡄⠀⢸⡇⠀⢸⡇⠀⠀⠀⡇⢀⣿⠀⢸⣿
⣿⠀⣿⠀⣿⡟⠸⡇⠀⢸⡇⠀⢸⡇⠀⠀⠀⡇⣼⠇⠀⢸⣿
⣿⠀⠙⠀⢸⡇⠀⣧⠀⢸⡇⠀⢸⡇⠀⠀⠀⣿⡟⠀⠀⢸⣿
⣿⠀⠀⠀⠀⠀⠀⢿⢠⣼⣇⡀⢸⡇⠀⠀⠀⣿⡄⠀⠀⢸⣿
⢿⣄⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢸⣀⣀⣀⠀⡏⣷⠀⠀⢸⣿
⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⡿⠀⡇⠸⣇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⠻⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢻⡆⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠙⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣀⡀⠀⢿⡀⠀⢀⣀⣤⣴⣾⠿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠴⠒⠒⠒⠠⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠛⠳⠤⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠐⠂⠁⠀⠀⢸⡕⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣞⡳⠤⣀⡀⠀⠉⠀⠀⢀⠴⠒⠋⠉⠀⠀⠀⣀⠤⠔⢒⣩⡴⢲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⢳⠢⢭⣑⠂⠀⠀⢸⢀⣀⡤⠄⠀⠀⣠⠖⠶⢩⠋⠋⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢤⣈⣌⠀⠸⠀⠁⢠⡄⢈⣉⣥⠴⠚⢋⡟⠁⢠⡤⣀⣀⠄⠐⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⣄⠀⠈⠁⢸⠁⠀⠀⣰⣎⡠⠶⠛⠛⠫⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡀⣧⠈⠫⡛⠲⣤⣸⣶⠶⠚⠉⠀⠀⠀⠀⣀⡀⠤⠤⠿⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢤⡀⠈⢧⣸⡗⢦⠀⠸⠥⠄⣀⣀⣀⣀⣀⣤⣤⠴⠖⠒⢹⠟⠩⡵⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠈⠻⡀⠀⢻⢶⠒⠛⠉⠙⠉⠁⠀⣷⠋⣠⠊⠀⠃⠐⠀⢀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠞⣿⠚⠉⡗⢄⠑⣄⡘⢸⠀⢀⠀⠀⢀⣀⣼⠥⠿⠯⠔⠓⠒⠊⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⡠⠊⢿⠷⡄⠀⢠⠉⠀⠘⣴⢀⢷⡌⠓⠚⠒⠒⠈⠉⢉⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠧⣀⣀⡐⠀⢻⡜⠀⠀⠀⠀⠀⠀⡤⣴⣶⢿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⢺⠋⠉⡟⠛⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⡾⠀⢰⠁⠀⠀⠈⢧⠀⢀⣀⠤⠤⠐⠒⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠓⠚⠒⢦⡀⡇⠀⢸⠀⠀⠀⠀⠘⠛⠋⠉⠉⠉⠙⠛⢯⡒⠢⢍⠲⡄
⠀⠀⠀⠀⠀⠀⠀⡾⠉⠉⢣⡀⠀⠙⡇⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠱⣽⡄
⠀⠀⠀⠀⠀⠀⣰⠙⢦⡀⠀⢳⢣⣠⣹⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⢦⣿⣆⣀⣀⣀⣀
⠀⠀⠀⠀⠀⢀⡇⠀⠀⠉⠲⠤⣧⡟⠁⠉⣷⢒⣋⠉⠉⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⡏⠉⠉⠑⠒⠲⢭⣑⠢⣄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠗⠦⣼⣯⠿⠿⠧⠤⠤⡀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠓⢲⠶⠒⠒⠲⣄⠈⠓⣌⠳⡀
⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢸⠀⠀⡟⠈⠲⢄⡀⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⢰⢻⡤⢼⠢⢤⠔⠒⠛⠲⡄⠈⢧⢱⡀
⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⡜⠀⢠⡇⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⢸⣍⠾⠶⠾⣦⣤⠤⠴⢯⡀⠈⡆⣇
⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠜⠁⠀⣼⣧⢄⣀⣠⢼⣥⣀⣀⣀⣼⠀⡇⣿
⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⢰⠁⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠊⠁⠀⢀⣼⣁⣼⠋⠉⠉⠙⣏⠁⠀⠈⢹⣠⢃⣿
⠀⠀⠀⣿⠉⠉⠐⠒⠒⠒⠒⠚⠒⠒⠓⠒⠒⠒⠒⠒⠒⠒⠒⠈⠉⠁⠀⠀⠀⣀⠴⠛⢦⡤⠿⠳⠶⡖⢊⣏⣁⠞⠛⢻⠏⡼⡿
⠀⠀⠀⢸⣄⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⢶⡞⣧⡤⡴⣾⠦⣄⣀⣤⡞⠉⠉⠉⢳⡶⢁⡜⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⠉⠛⠛⠭⠍⣛⡛⠫⠭⢽⣿⣤⡤⠤⠞⣿⣀⠀⠀⣸⠋⠉⠉⠉⣫⣉⡶⠞⣁⠴⠋⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣀⣀⡀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠒⠦⠭⢭⣝⣛⣚⣛⣧⡿⣝⣶⣖⣛⣩⠥⠖⠊⠁⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠲⠤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠢⠤⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉