Beach holiday Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⡀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⡀⢀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⢺⣡⠴⠂⠒⠒⠦⢄⠀⢠⠀⠀⠑⠀⠀⠀⠀⠀⠀⠢⠘⠃⡁⠐⠒⠃⠒⢤⣣⠐⠀⠞⠘⠋⠉⠉⠁⠐
⠀⠀⢀⠸⣄⣸⡀⠐⠋⠉⠙⢺⣋⣀⡀⢠⣄⡀⢀⠀⠑⠄⢈⣡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⢤⣾⣀⣀⣻⡿⠔⠚⠳⠏⣴⠃⣴⠦⠀⠀⠹⢄
⠀⠁⠀⡴⣯⡟⠁⠀⠀⢀⣾⣭⣿⠉⢾⣋⣻⠈⣤⢀⠄⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢠⣱⡷⣾⠿⢿⠾⡿⣿⣄⡤⠖⠀⠈⠡⠈⠠⠐⢃
⠀⠀⢠⡧⣽⠀⠀⣌⠥⠀⠈⠃⢩⣧⣄⠳⠇⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠗⠉⢁⣄⣨⡞⠁⢻⣨⡧⣴⣂⠀⠀⠀⠀⠀⠐⠔⣣
⠀⠀⠘⠃⠀⠀⠀⠈⠃⠀⠀⢀⡼⢿⠈⡀⣄⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠉⢉⡛⠀⠀⣘⠷⠆⢫⡥⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠹⠂⠀⠀⠈⠛⠛⠓⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠛⠃⠀⠀⠤⠀⠀⠀⣴⠟⡩⠊⠑⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠠⣆⣔⣤⠆⠀⠀⡛⠀⠀⠀⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠉⠡⠀⠊⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠴⢀⡀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠉⢉⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⣷⢀⣠⡀⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⡀⠀⠀⠀⠀⠀⠠⠤⣤⠠⠤⠄
⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠁⠀⠁⠠⠀⠠⠐⠒⢿⣿⡄⠡⣷⣤⡀⠀⠀⠀⠀⠀⠀⠁⡐⠃⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠁⢐⣤⠀⠀⠀⠀⠀⠈⠘⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⣤⡀⠁⠂
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⢄⡀⢄⠀⠈⠓⠈⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠣⣀⡙⠅⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⢀⠀⠐⢀⠀⠀⠀⠃⠋⠀⠀⠀⡀⠀⠒⢬⣶⡴⠒⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⣤⠄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠦⡀⠀⢂⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡘⠆⢀⡴⠃⠀⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠈⠀⠸⠏⠂⡈⠀⠀⠀⢤⡀⠀⠀⠀⠀⡤⠀⠀⠀⠀⡰⠸⠇⠀⠀⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠒⠒⠀⣀⠤⠤⠈⠀⠀⠀⠠⡤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⡀⠃⠠⡤⢀⡀⠒⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠂⣠⡭⠏⠀⠀⠸⣇⠀⠲⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡴⠖⠂⢸⡇⠀⠀⠙⠭⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠴⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠲⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡀⠀⠀⠘⠃⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠃⠀⠀⠀⣀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠤⡄⠠⠣⠀⠤⠤⢤⡀⠀⢰⠊⠉⠀⠃⠈⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⢹⡆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠱⡘⡀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠸⠧⠀⠃⠄⠀⢀⣀⣀⣠⣀⣼⡃⠐⡄⠀⠀⠀⠊⠉⠂⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠿⠿⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣤⡀⢸⠀⠠⡀⠀⠀⠘⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⢠⣿⡇⠀⠀⣀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠉⠉⠻⣿⣷⠈⠣⠤⠩⠠⠴⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠟⠁⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠀⠀⢸⣿⣧⡀⠀⣠⣿⡿⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡿⠟⠁



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⣼⣿⣿⡿⠟⢁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⠀⠻⣿⠟⢁⠼⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⣼⣿⡿⠋⣻⣿⣿⡟⠻⣿⣿⣿⡿⢁⣤⣶⣶⣤⡈⠀⢠⣴⣶⣶⣄⠙⣿⣿⠏⢻⣿⣿⡏⠙⣿⣿⣧
⡿⠛⠁⠀⣿⠿⠋⠀⠀⢿⠟⠁⠀⣾⣿⣿⣿⣿⣷⠀⣿⣿⣿⣿⣿⡆⠸⡿⠀⠀⠙⠿⣿⠀⠈⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡟⢋⣁⣤⣉⠙⢿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⣄⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡈⠛⣀⡿⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢉⣠⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠘⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⡈⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⣆⠸⣿⣿⣿⣄⡙⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡛⠛⢻⣧⠀⠀⠀⠀⠀⠀⢸⣿⣆⠘⢿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣸⣿⣿⣷⡈⠻⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣦⣀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣛⣉⣉⣉⣉⣁⣀⣀⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣯⣉⣽⣿⣿⣿⣿⣿⣿⡿⠿⠿⠀⣿⣿⣿⣿⣿⣿⠃⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣤⣤⣈⣉⣁⣀⠛⠛⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂
⠀⠠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡿⠻⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢖⢦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⢤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠑⡌⠢⡀⠀⣠⠖⠋⢁⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠘⡄⡷⡺⠁⠢⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠴⠂⣉⣉⢉⡙⠓⠶⣧⡘⣳⠁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣛⣋⣩⡴⠶⠶⣏⠳⣚⠓⠶⣢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⣡⠔⠋⣁⣀⣤⢼⠃⢰⡘⢧⡀⠈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢎⡡⠔⠊⢁⢟⠔⢻⠠⣘⢇⢸⡏⠓⣆⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠕⠉⠀⠀⠀⢸⠎⠀⠰⠀⠹⠈⣼⠀⠀⠈⠳⡀⢟⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⢣⡇⠀⠃⠀⠀⠀⠀⠈⢾⠑⣽⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⢤⠠⠤⠥⢤⣀⣀⡀⠀⠀⠀⠀⠀⠈⠳⣹⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⡶⠋⠀⢠⠃⠀⠀⠑⢄⠀⠀⠈⠑⠮⡉⠒⠦⢄⡀⠀⠀⠘⢾⢱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⡠⠋⠀⠀⠀⠎⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠈⠳⣄⠀⠈⠒⢄⡀⠀⠻⣈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⡜⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⢀⣀⡈⢢⠀⣀⠄⠝⢦⡀⠙⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⡸⠀⠀⠀⠀⠀⠆⠀⢀⡠⢤⢤⠤⠤⡀⣦⢖⡩⠲⣄⣈⠉⠷⠹⢩⠱⠴⠒⣄⣜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠒⠢⠤⣀⣃⠤⠒⠂⠒⠤⣐⡰⠊⠀⠈⡜⡀⠀⣈⠵⠉⠩⠤⠀⠈⠻⣏⠱⡀⠚⠒⣿⣿⣓
⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠋⠐⠒⠐⠂⢀⡸⠷⠖⠂⠐⠂⠀⠈⠐⠂⠒⠀⢳⢱⠚⠒⠒⠒⢂⣒⠒⠒⠒⠒⠒⠚⡒⠒⠛⢃⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⣁⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠆⠀⠀⣠⣿⢠⢻⢉⠏⡙⢉⡿⠋⠀⠀⠈⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢐⡢⠀⠀⠀⠀⠀⠀⠀⠘⡸⣀⡼⠫⢣⢢⠆⠜⡰⢡⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠆⠒⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⣿⢕⡵⡡⢃⠎⡴⣱⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⠠⠤⢜⡫⠔⡩⢊⠔⣡⢎⡼⠃⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣰⡞⠃⠖⢭⣖⣡⠞⢡⡞⠁⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⠆⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⣃⣯⣶⠿⠲⠦⣤⣤⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠓⠦⣤⣄⣀⠀⢁⣼⠃⠀⠀⣀⢤⣌⡉⠙⠋
⠀⠀⠀⠀⠀⠀⢠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠙⢻⡿⠁⠀⠀⡞⡽⡺⠯⡙⡄
⠀⠀⠀⠀⠀⠀⠣⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠻⣀⡇⠀⡱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠐⠒⠒⠆⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⢤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣀⠀⠰⢮⡒⢺⠟⠊⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣫⠳⠛⢉⣿⣁⡀⠀⠿⣓⣲⠖⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢠⡤⣤⣀⢶⠺⠯⣥⠀⠀⠀⠠⢴⠒⠷⠀⠀⠈⠁⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⡤⠛⠆⠈⠘⢉⣙⣷⡆⣰⡞⡛⢲⣿⡚⠦⣤⡶⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⢩⢋⡤⢦⣄⢦⢍⡶⢧⡏⡇⡷⠯⣬⠉⠀⠁⠋⠒⣤⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠘⠋⠀⣿⡿⠞⠀⠉⠈⢰⢱⠁⠺⠕⣲⣶⡀⣌⢻⡉⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⢱⠀⠀⠀⢀⡏⡸⠀⢀⣔⡝⠉⣇⠏⠹⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠘⣈⣆⣠⡤⠼⢠⣇⣴⣫⠎⠀⠀⠉⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⡠⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⣤⠤⠼⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠽⣤⣤⣤⣤⣤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⣭⠭⠥⠤⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣉⣉⣀⣛⣳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠭⠭⣭⠭⠤⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠭⠭⢭⡭⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢯⣭⣤⣤⣤⠀⠀⠀⠉⢩⣭⠭⠽⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠚⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠚⠷⠶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡀⠐⠀⠀⠌⠙⠻⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠂⠀⠠⠭⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⣫⠇⢈⠠⠄⠀⠈⢻⣤⠚⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠰⠆⠃⠀⠀⠀⠘⠳⡀⣈⠁⣀⢤⠀⠀⠰⠓⠀⢀⠀⠀⠀⠀⢀⡀⠶⢀⠀⠀⠞⠉⠁⡤⢨⡄⠀⠀⡠⠟⣷
⠀⠀⠀⠀⠀⠀⠆⠩⠁⠀⠀⠀⠄⠀⠒⣀⡤⠿⢥⡨⠀⠛⣶⡃⠀⠈⠿⠂⣴⠐⠋⠘⠁⠀⠀⢀⠀⠀⠀⠀⠸⠃⠰⢀⣙⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣼⠛⠀⠀⠀⢹⠄⠀⠀⠀⢀⠀⠐⠀⢄⠀⠀⠀⠐⢀⡀⢀⡀⠤⠀⠀⠠⢉⡐⠂⡀⠃⠂⣠⡀⡠⠾
⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⡀⠮⠛⠗⠀⠰⣲⠦⡬⠖⠀⠀⠀⠀⠀⢀⠀⠀⠆⠀⣀⠤⠈⡐⠉⡀⡀⠀⠀⢀⠐⠁⠀⠙⣤⠬⠠⠁
⠀⢀⣄⣠⢌⣰⠀⠁⠀⢐⣁⣀⣴⠂⠛⣁⠀⠀⣙⡘⠄⠀⠀⠀⠀⠀⠀⢰⢠⠒⠄⠡⢣⠌⠡⠀⠀⠀⠨⠀⠄⠂⢀⠐⠛⠁⠀⠀⠁
⠀⠂⡀⠀⠀⠁⢁⡀⠐⠌⠀⢋⠁⠀⠘⠟⠀⠘⢛⠧⠁⠀⠀⡀⠀⣀⣀⠀⠁⠀⠀⠀⠀⠲⡄⠀⠀⠀⠀⠠⡄⠀⠄⢀
⠠⠀⢐⡀⠐⠒⡘⠁⠀⠀⠀⠐⠑⠀⢀⠀⢁⠀⠁⠀⠀⠀⠐⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠑⢀⣶⣅⡠⢌⣤⣒⣤⠄⣐⣧⡀
⠐⠀⠌⠀⠉⠀⠂⠀⠀⠀⠀⢀⠀⠐⠾⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠄⠀⠀⠀⠘⠛⠋⠈⢿⣿⣙⣛⣩⢥⡇
⠀⠁⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⣀⠀⠈⠀⠹⠄⠲⠤⣄⡀⠀⢀⠀⠀⠀⠀⠠⢀⠁⠀⣀⣠⢰⡞⠒⠀⠀⠀⠀⠀⠀⠘⢇⠐⠐⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠊⠉⣻⡉⠀⠀⠀⠀⠀⠀⠀⠈⢳⡦⣤⡴⣄⠀⢈⠀⠘⠣⡤⠁⠀⢄⠠⠀⠈⠤⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠠⠀⠀⠀⠑⠒⠤⠤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠌⠐⣎⠠⣀⠀⠀⠀⠠⠖⣊⠓⠂⠰⠐⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⢀⠀⠀⠡⠈⠄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠐⠀⠠⠈⢃⡜⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠠⠃⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢸⠀⡇⢀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠃⣸⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⢈⠀⠣⠈⡃⠀⠀⠘⡄⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⡾⢠⡁⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣜⠀⢼⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈⠢⣽⠀⠀⠀⢰⠀⠀⠀⠀⡆⠀⠀⠀⡀⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠸⠀⠀⠀⠘⡀⠀⢠⠀⠇⠀⠀⠈⠂⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⡠⠀⡠⠂⠀⠀⠀⠀⡇⠀⢸⢸⠀⠀⠀⠀⠂⠀⠆⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠓⠁⠈⢄⠀⠀⠀⠀⠀⣇⠦⡴⠼⠀⠀⠀⠀⠈⡰⠀⠻⢶⠄⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⢸⡀⠀⠀⠀⠀⡁⠁⢸⢛⠀⠀⠀⠀⠈⠁⠘⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⣠⠞⠂⠀⠀⠀⠀⠛⠀⠁⠉⠁⠀⠀⠀⣨⣦⣤⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⢠⠂⢸⠀⠀⠀⠀⢀⠀⠘⠁⢀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⡀⠀⡀⡀⠀⠀⣀⠀⠀⠈⠓⠄⡟⡀⠈⠀⠀⠀⠀⠘⣥⠠⠒⠁⠀⣀⢀⡀⢀⠀⢀⢀⡀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠷⡀⠀⠀⠀⢰⢁⠁⠀⠀⠀⠀⢀⣀⣡⠀⠀⠀⠐⠉⠋⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠤⢀⡤⠤⠀⢠⣄⣐⡂⠠⣴⠦⠀⠈⠲⡂⣀⡈⡛⠀⠀⠀⠀⠀⠉⠈⠉⣠⣄⠔⠀⠀⠄⢰⠆⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠀⠀⠀⠈⠉⠐⢅⡀⠀⠙⠇⡁⠀⠀⠀⠀⠀⠀⠀⠀⡏⡀⠀⡠⠖⠀⠀⠀⠑⠀⠛⠦⠀⠄⠠⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠶⠷⡇⠀⠀⠀⠐⢸⠀⠀⠀⠀⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠴⠸⠖⠂⠀⠀⠻⠀⠰⢧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠀⠆⠀⠀⠒⠂⣦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠊⠀⠀⠀⠀⠀⠀⠀⣤⠒⠰⢷⣄⣴⠂⠠⢤⣀⡀⠾⠀⢀⣄⠀⠀⠀⠀⠀⠙⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠋⠀⠀⠀⠀⠀⠀⢸⠄⠋⠀⠀⠀⠀⢠⠃⠄⠑⠀⠠⠀⠀⠀⠀⠈⠑⠀⣠⠀⠀⠀⠀⠀⠘⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⠁⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢠⣀⠁⡀⠀⠀⠀⠀⠀⠈⠂⢆⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⢢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢃⡀⠀⠐⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⡠⠈⡁⠄⣊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢻⠡⢀⠁⠰⠀⠈⠈⠱⢤⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⠃⠀⣽⠠⠄⠠⠄⠀⢠⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠓⠠⠀⠸⠄⣀⡀⠤⠤⠤⠘⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣴⢶⣿⣿⣿⣿⣿⣿⣿⣶⣦⣄⡀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠤⠄⠄⠄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⡀⠾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡑⠢⠍⠭⢽⣿⡟⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⢀⣶⣿⡇⠀⣼⣿⡆⠀⢀⣠⣬⣿⣷⣾⠻⠿⣿⣿⣾⣿⣿⣿⣷⣄⣀⣄
⠀⠀⠀⠀⠀⣾⢏⣿⣿⣾⣿⣿⠅⠀⢺⠋⠉⠙⢿⣴⣤⣄⣈⣿⣿⣿⣿⣿⣿⣿⣼⣿⣧⣦⣄
⠀⠀⠀⠀⠀⠋⠀⠃⣿⣿⣿⣿⡄⠀⠈⢇⢰⡿⣳⣿⡿⣟⣿⣍⣉⠍⠉⠙⠻⢿⣿⣿⣿⣿⡟⣧
⠀⠀⠀⠀⠸⠆⠀⢸⣿⣿⣿⣿⠁⠀⠀⣾⡟⢿⣷⣭⣼⣿⡿⣻⣿⡷⣦⣄⠀⠀⢹⣿⣿⣿⣿⣿⣆⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣉⠙⠁⢀⣤⣤⣙⣳⣴⠟⠙⣛⣿⣾⣿⠏⣼⣿⢿⣿⣷⣾⣿⣿⡟⢹⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢸⣤⣾⡟⣻⣭⢠⣾⣿⣿⣿⣿⣿⠿⢞⡾⠟⠛⢿⣿⣿⣏⣼⣿⣿⣿⣿⣿⣷⣿⣅⣻⣿⣷⡀⠀⠀⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠙⠻⣧⣤⣷⣿⣿⣿⣭⣭⠇⡼⣦⣿⠁⠀⠀⢰⡏⠹⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠸⡛⠤⠀⠀⣾⠀⠀⢸⡇⢙⣉⠻⠟⣿⢻⣿⣿⣿⣶⣿⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠿⢂⣠⣾⠠⠄⡀⢀⡀⠠⠀⣿⠿⢿⣿⣿⣿⡟⢻⣷⣤⣤⣦⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠹⡟⣻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣴⠶⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡤⢒⡿⠉⡁⡀⠈⡆⣠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠐⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣮⣿⠽⣛⠿⢛⠀⠀⠀⠙⣄⠄⣶⢀⡇⠟⠾⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⢀⣀⡀⢀⣞⡩⠽⣿⣷⡟⠁⠀⠀⡀⠁⣨⣥⣿⡤⠁⣼⣁⣤⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢣⠋⠙⠉⠈⣹⣿⣷⠟⠁⠀⣀⡼⠟⣆⠀⣚⣴⣿⣟⢛⣩⣷⣾⣿⣏⣄⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⢻⣧⢀⣿⣤⣴⡲⠾⢿⣿⠇⠀⠠⠾⣩⣤⣿⣿⣿⡟⠟⣷⣴⣿⡟⠛⠒⠛⢺⡻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⣴⣿⠿⠸⠛⠉⠁⠀⢀⣘⠟⠀⡤⠀⣲⣿⣻⣿⣿⣧⣿⡾⠿⢿⡿⠓⠒⠲⡞⠀⡟⠃
⠀⠀⠀⠀⠀⠀⠀⡴⢿⢏⠁⢀⡴⠾⣿⡏⠀⠀⠀⠀⠀⠀⣬⠧⠀⢼⡆⠈⣟⡉⣭⣼⣿⡿⡛⢲⣤⠀⠀⠉⣿⡴⠧⣼⠁
⠀⠀⠀⠀⠀⠀⣼⣿⠇⣠⣿⣿⡇⢀⣿⠃⠀⠰⡀⠀⠀⣐⠛⡤⣥⣤⣶⠋⠉⠁⠈⣿⣿⡍⠀⠈⣻⡆⣠⣢⣟⣀⣴⠃
⠀⠀⠀⠀⠀⢠⣿⣿⣰⣿⠁⠀⣧⣾⠏⠀⠀⠀⠘⢓⣾⣯⣾⠏⠉⠉⠁⠀⠀⠀⠀⠀⠻⣿⣀⠨⣦⡟⠙⠁⠈⠁
⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⡤⠖⠁⠀⠀⠀⠀⡴⢋⡞⠁⣿⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡼⢿⢿⣿⣇⡤⠔⠒⠠
⠀⠀⠀⠀⠀⠀⠹⣯⣿⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⢸⠀⠀⠈⠱⣤⣤⣖⡲⢛⡹⠶⠛⠛⠙⠁⢨⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⣛⣉⣉⣋⣙⣿⠛⠁⠀⠀⠀⣀⣴⡿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠛⠛⠛⠉⢉⡽⠟⣀⠀⠀⣠⣶⣽⡟⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⢤⡀⠀⠀⠀⡀⠤⠐⠀⠈⠃⢀⣩⣿⠿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠹⠵⣤⣴⣦⣤⣦⣤⣴⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢻⣿⢿⡟⢿⢿⡿⡿⢿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣾⣷⣿⣶⣷⣷⣿⣷⣿⣼⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⣶⣶⢿⡶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠛⢿⣷⡦⣄
⠀⠀⠀⠀⠀⠀⢠⡾⣁⣴⠏⣵⠋⢠⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣇⠘⡏⣻⡌⢳
⠀⠀⠀⠀⠀⣰⣿⣴⡟⢠⡞⢀⡔⢃⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠨⣆⢸⡄⢻⡎⣧
⠀⠀⠀⠀⢠⣿⣯⠴⠄⢸⡖⣋⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣤⣈⣾⡅⣘⢻⣿⡀
⠀⠀⠀⠀⣾⡿⠄⠀⠻⣮⠛⣛⣿⡋⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣯⡉⣽⠖⠀⢛⣿⡇
⠀⠀⠀⢸⣿⠿⠤⠋⠉⠈⢸⣿⣿⡇⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⣠⠖⠈⠀⠀⠀⣹⣿⣿⠁⠙⠉⣄⣹⣿⡇
⠀⠀⠀⠸⡹⣮⠀⡡⢰⣶⣿⣿⡯⠀⠀⠀⠀⠀⠘⡄⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠈⠻⣿⣷⠢⡈⠄⣠⢿⠇
⠀⠀⠀⠀⢿⣿⡟⠻⢿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠟⢳⣾⡷⠁
⠀⠀⠀⠀⠀⢻⣷⠈⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣀⠇⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠏⠁⣾⡏
⠀⠀⠀⠀⠀⠘⢿⡂⢼⣟⣿⣿⣶⣀⣴⠾⢻⣦⠀⠀⣿⣿⠀⠀⣴⡟⠷⣦⣀⣶⣿⢿⣓⡷⢐⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠺⣭⣉⡽⣻⣿⣧⣀⠀⢻⣷⡾⢿⡿⠿⢾⡟⠀⣀⣼⣿⣟⢫⣉⡭⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⣷⣿⣿⣿⣶⣿⡅⣼⠀⢁⡻⣶⣿⣿⣿⣼⣿⡾⠋
⠀⠀⠀⢀⡀⠠⢤⣤⣤⡤⢄⣸⡃⠀⠉⠙⢿⣿⣟⣥⠁⠀⢠⣻⣿⡿⠋⠉⠀⢘⣇⡠⢄⣤⣤⡤⠄⢀⡀
⠀⢀⣴⣿⠟⠛⠋⠉⠙⠛⢿⣿⣵⣢⣀⠀⠀⣿⣿⣧⡟⢤⣼⣿⣿⠀⠀⣀⣀⣾⣿⡿⠛⠋⠉⠛⠛⠻⣿⣦⡀
⣰⣿⢋⣠⣴⣲⣶⣿⣯⣵⣾⡧⣄⡉⠛⢿⣶⠟⣫⠭⢭⡭⠭⢛⢿⣶⡿⠋⠉⣠⢼⣗⣪⣽⣷⣶⣖⣦⣄⡙⣿
⠉⣑⣭⡿⠋⠉⠀⠀⠉⠙⢻⡿⠶⢮⣷⣄⡽⣸⣿⡀⢸⠀⢀⠆⣄⣯⣰⣾⡽⠶⢻⡿⠋⠉⠀⠀⠉⠙⢿⣭⣊
⠞⠽⠋⠀⠀⠀⢀⢀⣠⣤⣿⣦⣤⣄⣈⣙⡇⣿⠃⢱⠠⠀⡆⠀⠿⢻⣋⣀⣠⣤⣴⣷⣤⣄⣀⡀⠀⠀⠀⠙⠯
⠀⠀⠀⠀⢀⣾⣷⠟⠋⠉⣿⠉⠉⠉⠉⠙⡇⠆⠀⠀⠀⠀⠀⠀⠐⣸⠋⠉⠉⠉⠙⣿⠉⠙⠻⢿⣷⡀
⠀⠀⠀⢠⣾⡟⠁⠀⠀⣠⣿⣶⣾⠶⠾⠻⣷⢨⣖⣀⣀⣀⣀⣀⠅⣿⠟⠶⠶⣿⣶⣿⣄⠀⠀⠀⢻⣷⡄
⠀⠀⠀⠋⠀⠀⠀⢠⣾⣿⣿⠀⠀⠀⠀⠀⢸⡿⣿⣿⠟⠛⠻⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣷⡄⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⢀⣿⠋⠀⡿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣶⣤⣾⣿⣿⠃⠀⠀⠀⠀⠀⢻⠀⠙⣿⡀
⠀⠀⠀⠀⠀⠀⢸⠁⠀⢸⡇⠀⠀⠀⠀⠀⠠⣿⣿⣟⣀⣀⣽⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣉⡉⣿⣿⣏⠀⠀⠀⠀⠀⠀⢸⡇
⠤⠤⠤⠤⠤⠤⠤⢄⠤⣾⠇⠠⠤⢠⠤⠀⠄⣿⣿⣟⠛⠛⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣷
⠁⡀⠀⠀⠀⠀⠀⢀⢀⣇⡀⠀⠀⠀⠀⠀⠀⣿⣿⡿⠛⠻⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢻
⣉⠀⣀⢀⡀⣀⣀⣀⢨⡇⣀⢀⣀⡀⣀⠁⣂⢻⣿⡷⠶⢶⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⣸⣿⣇⡀⠀⣹⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⡠⢶⣿⢿⣿⡉⠛⣿⡿⣿⣷⢄⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠞⢁⣿⠁⠈⣿⣧⢰⣿⠀⠈⣿⡀⠳⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠀⠀⠀⠀⣧⣾⣿⣴⣶⡿⣿⣿⠿⣶⣦⣿⣷⣼⠀⠀⠀⠀⠀⠀⠀⠣

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⣾⡀⢹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣿⠇⠀⠀⠀⠀⠀⠀⠀⢹⣷⣾⣿⣿⣷
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠠⠀⠀⠀⠀⠀⠘⢻⣿⣇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣾⣿⠟⠁
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⢺⠉⠗⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸⡌⢿⣿⣆⠀⠀⠀⣸⣿⡀⠀⠀⠀⣼⣿⠏⣸
⠀⠀⠀⠀⠄⠢⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠰⠂⠄⠀⠀⠀⠀⠘⣆⠛⣦⡹⢿⣿⣦⣼⣿⣿⣿⣦⣶⣿⠿⢋⡼⢋⡼
⠀⠈⠀⠀⠁⠀⣀⠊⠀⠀⠀⠀⠀⠀⠀⠘⣀⡀⠀⠁⠀⠂⠀⠀⠰⣌⠳⣬⡙⠶⣬⣹⣿⣿⣿⣿⣿⣉⡥⠞⣋⡴⢛⣱⠂
⠀⠀⠀⠀⠁⠐⠤⢀⣀⠀⠀⠀⠀⠀⢐⡀⠤⠔⠀⠡⠀⠀⠀⠀⠀⠙⠳⢦⣍⣓⠶⢼⣿⣿⣿⣿⣿⠷⢖⣛⣩⠶⠛⠁
⠀⠁⠀⠀⠄⠈⠁⠀⠐⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠁⠈⠲⣤⣄⣀⣀⣉⣉⣽⣿⣿⣿⣿⣿⣍⣉⣉⣀⣀⣤⡤⠞
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⣿⣿⣿⣿⡇⠀⠈⠁⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣽⣿⣿⣿⣵⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠟⠻⠿⠛⠿⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠄⠒⠂⠀⠒⠒⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⠤⢄⣀⣀⠉⠁⠀⠀⠀⠀⠀⣈⣉⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡻⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢙⠦⣈⠛⢦⠀⠀⢀⠴⣶⠶⢤⣀⡀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠑⠁⡎⣸⣿⣿⣆⠙⣿⣞⡾⣥⣿⣍⣉⣙⣒⠲⢤⣤⣄⢂⡤⠄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣿⣿⣿⡆⢫⠙⣿⣟⠛⢋⢿⣝⢿⣿⣶⣌⠙⢷⣶⣖⠚⠓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠃⣹⢿⣿⣷⠘⢧⡀⠛⠃⣸⡼⣯⡼⡟⢻⣿⣿⣦⣮⡻⣿⣃⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢤⣱⣾⣃⣏⣻⣿⣇⢀⣹⣧⠀⢡⠄⡏⠃⣿⠇⠟⢉⣿⣿⣿⣮⡻⣤⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⡀⠀⠴⠶⠶⠦⢬⡻⠿⢿⣶⡶⠚⡈⠀⣼⣿⡿⠄⠀⠉⢹⣿⣷⣽⣾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢾⣤⣒⠢⡀⢀⡀⢄⠒⠤⠄⡴⢺⣿⠟⠋⠀⢀⣴⢻⡿⢻⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣌⡑⠛⠦⠕⠒⠊⠀⠀⠈⠓⠂⠒⢫⡍⣨⢁⣾⢻⣿⣯⢢
⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣷⢱⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢈⡏⣼⢿⣿⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡞⢆⠰⣤⣄⣀⠀⠀⠀⠀⠀⣉⣾⣿⡎
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⢧⡀⠳⣜⠿⣮⠙⢶⣄⠀⠀⢈⢻⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⠋⣻⣷⣦⡈⣆⣼⣿⣷⣬⡛⠿⣄⢼⣿⣷⡄⠈⣺⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠈⠿⢿⣿⣿⢿⣿⣿⣿⣾⡿⡟⠿⣹⣷⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠄⡀⢀⡀⠀⠀⠛⣦⣹⣿⣷⠻⣿⣿⡈⠁⠉⢀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢶⣷⠀⠀⣿⣿⣿⣿⣯⠈⢉⣟⣿⡶⠒⢹⠻⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀⢀⣮⣿⠀⣷⣿⣿⣿⢿⡟⢰⠿⣫⣟⣡⣤⣼⣶⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣿⣿⠏⣼⣿⢇⣿⡟⣼⡠⠴⣺⢿⣻⣿⣿⣿⠻⣿⣟⠀⠙⠆
⠀⠀⠀⠐⢶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶⡶⠶⠀⠀⠀⣠⣴⣶⣿⣿⡿⠋⣰⡿⢋⣾⠟⡼⠉⠀⢘⣵⢿⣿⣿⠿⠏⠙⠈⠛⣿⡄
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠻⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠶⢂⣼⡿⣛⣽⣾⣿⠁⡈⠉⣴⡿⠃⠈⠀⠀⣰⠟⣵⠿⠟⠉⠀⠀⠀⠀⠘⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠫⣾⣿⠿⠋⠛⠛⠁⠸⠋⠀⠀⠀⠀⠈⠁⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡝⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠘⣆⠀⠀⣿⡀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⡄⠀⠀⢀⠜⠀⠀⠀⣄⠀⠀⠀⠘⣆⢀⡇⠱⠀⢈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠈⠢⣄⠎⠀⠀⠀⢀⠛⡄⠀⠀⠀⠸⠞⠀⠀⢧⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠘⡄⠀⠀⠀⠀⠀⠀⠘⣴⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⣸⠀⠀⣄⠀⠀⠀⠀⢰⠃⠀⠀⢱⠀⠀⠀⢰⡆⠀⠀⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠙⠀⠀⡏⠱⣄⠀⠀⡎⠀⠀⠀⠈⡇⠀⡰⠃⢱⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⢀⣄⡇⠀⠈⢣⡀⡃⠀⠀⠀⠀⣧⠊⠀⠀⢸⠀⣠⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠈⡏⠃⠀⠀⠀⠙⠇⠀⣷⠀⠀⠁⢀⣶⠀⠘⠋⢸⠟⡈⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠹⡄⠀⠀⢶⣀⠀⣰⠁⢣⣠⠞⠁⢸⠀⠀⡰⠧⣪⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡹⡄⠀⢸⠈⠳⠇⠀⠘⠁⠀⢀⡼⢀⡴⢥⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡽⠻⠤⠬⠦⣤⠔⠒⡒⠒⠲⢾⠒⢭⡰⢄⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⢀⡴⠊⠀⠀⣠⠔⢑⣦⡈⠳⠄⠀⠀⠰⢍⠂⠉⠲⠌⣓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣷⡦⡜⢁⠄⣠⠔⠋⠀⣠⠵⠚⠉⠲⢄⡐⢦⡀⢄⠙⠆⡴⢊⠵⡌⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⣟⠷⡜⠀⡠⢖⡩⠖⠉⠀⠀⠀⠀⠀⠀⠉⠲⣌⠳⠁⡞⡰⣟⡼⢱⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠮⣒⣱⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣧⣠⠭⠒⠁


⣿⣿⢛⢿⢛⠟⣿⢟⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠀⠀⡂
⠀⠀⠀⠀⠀⠠⠖⠀⠐⠀⢸⠁⠀⠄⠀⠀⠀⠀⠈⠂⢀
⠀⠀⡀⣀⠈⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢀⣀
⠀⠀⠱⠀⠀⠀⠀⠀⠀⢰⠀⠀⣤⠀⢀⣟⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠉⠁⢀⣾⡿⠟⠁⠀⣴⠿⠂
⠀⠂⢀⠀⠀⠀⠀⣀⢀⠀⠀⠀⣴⠋⣁⣶⣤⡂⠀⠛⠂⠀⢀⣀⡀⢈⡛⠀⠀⠠⣤⣷⣤⡀
⠀⠀⢀⠋⠀⠀⠀⠈⡈⠈⠐⠀⠘⠀⠸⠋⠛⢫⣽⣶⣎⡀⠠⣾⠿⡿⠄⠐⠀⠀⠘⠉⠛⢀⣰⣄
⠀⠀⢾⠀⢇⠀⠀⠾⠇⠰⠄⠀⠀⠀⠀⠀⠸⠀⠉⡉⠁⠀⡰⠃⠀⠁⠀⠀⠀⠀⠠⠞⠀⠀⠛⠋
⠀⠀⠀⠂⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠇⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠠
⠀⠀⠀⠀⠀⠡⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⣸⠀⡤⠇⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠤⠤
⠀⠀⠀⠀⠀⠰⠀⢈⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⠟⠙⠛⠛⠒⠚⣋⠉⠉⠙⠋⠛⠛⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠂⡠⠀⠀⠀⢠⣴⣾⣿⣿⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠰⠀⠃⠘⠛⠟⢉⣙⡛⠁
⠀⠀⠀⠀⠂⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠁⠐⠠⠄
⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠁⠒⠂⠂⠐⠀⠀⠀⠀⠈⠙⠶⠄
⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⢀⣀⠀⠀⠈⠀⢀⡀
⠀⠀⠀⠀⠒⠦⠀⠀⠀⠀⠀⠈⠉⠁⠈⠁⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⡀⡀⠀⠶⠦⠀⠀⠀⠀⠀⣀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣄⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣻⣧⢻⡄⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣻⣾⣿⣿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣻⣾⣿⣿⡿⠿⠿⢃⣀⣀⣀⣀⣤⠴⠶⡄⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣾⣿⢟⣩⣴⣶⣶⣾⣿⡿⣻⣿⡟⠡⡜⢿⣼⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣶⣤⣀⠸⣿⣿⠟⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣀⢷⢹⢸⡿⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣷⣮⡉⣸⣿⡿⣿⣿⣿⣿⣿⣿⡟⠛⠀⡟⠀⡟⡾⡇⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣇⢹⣿⡇⣿⣿⣧⣈⣉⡙⢿⣷⣶⣤⣀⡀⠀⢙⣦⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⣛⣛⣻⣽⡔⢮⣅⣈⣛⣛⣫⣥⣾⣷⣮⣝⠻⢿⣿⡿⠿⠛⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠛⠿⡿⣦⣝⡛⠿⠟⠛⢋⣛⣿⣿⡿⠿⠿⠟⠁⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠈⠉⠉⢉⣴⠟⠉⠉⠀⠙⠃⠀⠀⠀⠐⠳⣶⣶⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠀⠀⣰⣿⠃⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⣼⣿⡏⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⣼⡿⠿⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⣿⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣶⣤⣤⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⡤⣤⣤⢀⣤⣤⣤⣤⢠⣤⡄⣤⣤⡤⣤⣤⢠⣤⣄⢠⣤⡄⢀⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡌⠁⢸⣿⠘⢿⣷⣬⣉⠀⣿⣦⣼⣿⠀⣿⡇⢸⣿⣿⣦⣿⠀⣿⡏⢈⣛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⣾⣿⠼⡿⢶⣿⠿⢰⣿⡆⢼⣿⠤⣿⣧⢼⣿⠌⠿⣿⠀⠻⣿⡶⢿⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢻⣿⠷⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣽⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⣼⠏⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠑⣇⠛⢻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠁⠀⠀⠈⠩⠀⠐⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⢿⡀⠘⠃⢻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⢈⡁⢀⠀⡜⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠁⠀⠸⡰⣦⣠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣀⠀⣻⣞⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠀⠀⠀⠀⡷⣻⢛⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠃⠛⣿⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⢙⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⣀⢻⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣄⠀⡆⠀⡘⣟⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢀⣀⣰⣿⢃⡀⠀⠾⠀⠀⠀⠀⢀⠀⣄⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠘⣣⣷⠀⢿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢸⣿⠿⠟⣁⠈⠟⠊⠀⠀⠀⠀⠀⠘⣂⠘⠣⣔⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣭⣟⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣇⠈⠀⠉⠙⢀⡀⠀⠀⠀⠀⠀⢐⣏⠀⠀⣩⡀⠀⠀⠀⠀⠀⠀⣠⣤⣀⠠⣤⣿⣟⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣿⠖⢤⡤⣀⠀⢨⡅⠀⠀⠨⢋⣶⡀⠀⣄⣀⣌⢿⣿⣿⣾⣿⣿⡏
⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠘⢿⡷⠞⠛⠋⠀⠈⣷⠿⣦⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣧⣽⣿⠿⠿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢀⠀⠀⠀⢀⣧⣀⠀⠑⢤⣸⡏⠀⢹⡄⠀⠀⠀⠀⢨⣿⡟⣾⣿⡿⠟⠋⠉⠀⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⡷⠆⠀⠀⠃⡙⠳⣄⡀⠉⡁⠀⣸⠀⠀⠀⠀⠀⣸⣿⡇⣿⣧⣤⡄⣠⣶⡴⢛⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠒⣄⠈⠑⠊⠉⣿⠃⠀⢸⡀⢀⡀⡄⣰⣿⣿⡟⣿⣿⠿⠟⠋⢁⣠⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠬⣻⢦⣀⠀⠈⡆⠀⠸⣷⣶⣾⣧⣿⣿⡿⣱⣿⣿⣄⠀⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠀⠉⠀⠭⠿⣿⡇⠀⠀⠙⠋⠙⢫⠉⠋⣼⣿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣿⣿⠀⠀⠀⠀⣀⣤⣤⣤⡶⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠢⠤⠀⢀⡀⣟⠀⠀⠀⠀⠀⠀⢈⣾⣿⣿⣿⡟⠀⢀⣰⣾⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠿⠉⣿⣠⣤⣤⣤⣀⣤⣿⣿⣿⣿⣿⣷⣶⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠘⣻⣿⠋⠉⢉⣙⣛⣉⣭⣿⣿⣿⣿⣅⣴⣶⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠋⠁⠉⠉⢉⡟⠁⠈⠉⠉⠉⠉⢿⣿⣿⣿⡟⠉⠉⠀⠸⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠟⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⢀⣰⣿⣿⣿⣿⣇⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠈⠉⠉⠉⣹⣿⣿⣿⣿⠀⠀⠀⠀⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⢨⣦⡄⢠⣤⣀⣀⣤⣿⣿⣿⣿⣇⠀⠀⠀⠀⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⢽⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠆⠤⠤⣤⣠⣤⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⢰⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠒⠛⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⡀⠀⠀⣨⣿⣿⣿⣟⢳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⣿⡿⢿⣶⣿⣿⣿⣿⡟⢧⣌⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⡀⢸⣷⣾⣧⣄⣸⣿⣟⣀⣼⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠚⠛⠉⠛⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⣿⡇⠀⢰⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⢸⣇⠀⠈⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠈⠻⣶⣴⣿⠃⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠘⣿⡄⠀⠀⠁⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡇⠀⠀⠀⢻⡇⢠⡀⠀⠀⣼⡇⢀⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢻⣇⠀⠀⠀⣸⡏⢸⡟⠶⠞⢹⠇⣸⣿⣿⠏⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠘⣿⡄⠀⢀⣿⠇⣸⠁⠀⢠⠏⣰⣿⢹⡿⢰⣆⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠘⠿⡶⠿⠋⣰⠏⠀⠀⣾⠀⢿⣷⡿⠃⡾⢹⡄⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⡿⢦⣤⠴⠞⠁⠀⠀⠀⢻⡄⠀⠀⢀⡼⠃⠈⡇⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⢻⡄⠀⠀⠀⠀⠀⢀⣀⠀⠉⠓⠚⠋⠀⠀⢸⠇⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠆⠀⢁⣀⡤⠶⢒⣾⠉⠉⣿⣄⡀⠀⠀⠀⢠⡟⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⡩⠥⢤⡾⢫⢻⡄⡸⣸⣏⢏⢻⠲⠦⣤⣀⡉⠃
⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠯⠭⢤⠤⠀⢸⣠⠯⣔⠥⢛⣧⣽⠁⣿⠻⢷⡯⢶⢤⣬⣍⣹⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⢸⡏⠛⠲⣄⠀⢰⣖⣰⣿⡳⠞⠢⣀⡞⣿⣷⠋⢹⡆⠠⠛⢶⣖⣒⠒⠢⡿⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠸⠧⢤⣤⣽⡴⠟⣹⡟⠥⠀⠤⣠⡟⠀⢹⣿⣀⣈⣷⣇⢰⠉⠉⠻⣝⠓⠷⠶⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠷⠶⠦⣄⣠⠏⠀⠀⢸⡿⠉⠉⢻⠙⢶⣠⡟⢉⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣤⡤⠾⠋⠀⠀⠀⠀⠓⠒⠛⠛⠀⠈⠻⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣠⣀⣀⣠⣤⣤⣤⡄
⠀⠀⠈⠉⠉⢉⣀⣀⣖⣒⣤⣄⣀⣤⣤⣤⡤⠈⡍⠍⡙⢍⣉⣙⣛⢩⠭⠭⠭⠴⠒⠶⠦⠤⠥⠤⠄
⠀⠀⣀⣚⣛⣋⣉⣉⣈⣉⣉⣍⣉⣁⠂⠐⠀⠤⠀⠠⡤⠤⡴⠶⠴⠮⠍⠭⠤⠤⠤⠤⠤⣖⣶⢶⡶⠄
⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⢳⠀⣀⣀⣀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠐⠀⠀⠂
⠀⠀⠀⠁⠀⠀⠀⠀⡀⠺⠀⠈⠂⠐⠉⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡈⡉⠀⢠⣷⡂
⠀⠀⢀⣴⣄⣀⡁⠀⠈⣷⣼⣄⣲⣿⣴⣧⢸⣤⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣿⣿⡿⡾⣿⣿⠄
⠀⠃⠋⢉⢿⠟⠃⠀⠂⠛⠛⠛⠛⠻⠻⠛⠛⠛⠀⠀⠙⠁⠀⠀⠀⠀⠀⠈⢉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⢒⢤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠈⠉⠐⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⠄⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⡿⢤⡀⠀⠀⠀⠀⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢼⣆⣀⠀⣀⣤⣶⣿⣟⣛⣿⣿⣿⣿⣿⡟⢿⣷⣶⡅⠀⠀⠀⠀⢀⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⢀⣼⣷⡘⢷⣽⡿⠿⠿⣛⡋⡉⠛⠛⠻⣾⣿⠏⣴⣿⣶⣄⠀⠀⠓⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣞⠉⠀⣴⣿⣿⣿⡿⠈⠁⠀⠀⠀⠀⠀⠈⣉⣉⣉⣡⣄⣜⣷⣿⣿⣿⣷⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⡁⢈⣧⣾⣷⣾⣿⡯⣄⡀⠀⠀⣠⠴⡒⡋⠉⠉⠀⠈⠠⠀⠀⣉⣻⣿⠿⢿⡿⢿⡿⣿⡿⢟⣻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢍⣉⣿⣿⡿⠋⠀⠀⠉⣽⠟⠉⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⠀⠀⠞⠐⣛⠛⠈⢀⡼⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡅⢠⠀⣱⠟⠇⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣅⠀⠠⣄⡈⣿⣦⣾⣥⣇⣤⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢫⠀⣒⠿⡈⠠⠂⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠙⣛⠶⣄⠈⠁⠉⠀⠀⠀⢀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡷⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢦⣄⡠⠀⠀⠀⣤⠀⠀⣰⡦⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡷⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠰⢖⣛⣿⡦⠖⢻⣿⣿⣿⠦⠂⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⡿⠉⣹⠃⠀⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣄⠀⠀⠀⠀⠀⡀⢰⢖⡓⢲⠶⠚⠁⠀⢰⠇⣰⠏⢇⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠙⣿⣿⣿⣷⣀⠀⡀⡠⠚⠙⡟⡇⡿⠀⠀⠀⠀⢸⢞⣅⣴⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⢻⣿⣿⣿⣷⣾⣄⡜⡇⢀⣿⠇⠠⣀⠀⣀⡄⠀⢻⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡀⠀⡱⢄⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣆⠀⢹⠃⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⡐⠀⡄⡌⠙⢻⣶⣯⣿⠿⢿⣿⡿⠿⠿⣿⣿⣿⠿⠛⡿⠲⠁⠀⡠⡀⠡⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢳⠮⠥⡘⠃⠀⠀⠀⠙⢿⣷⣆⠈⠚⢿⣿⣿⣿⡿⠁⠀⡰⠃⠀⠀⠀⠈⠛⣀⠭⢶⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠐⣤⠀⠀⠀⠀⠙⢻⡄⠀⠈⠹⣿⣿⠀⠐⡏⠀⠀⠀⠀⢀⡔⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⣥⠀⠀⠀⠀⠀⠀⠿⠒⠦⣤⣿⢟⠁⠀⣧⠀⠀⠀⠀⢤⡁⠒⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠻⣄⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⣠⣤⣴⣬⢛⣿⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⢿⠯⠀⠀⢀⣀⠀⡀
⠀⠀⠀⠁⣾⠻⠟⡻⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠘⠇⠀⠀⠛⢧⠚⠻⠁
⠀⠀⠀⡠⠁⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠄⡀
⠀⣀⠔⢁⡴⠁⠀⠂⠒⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⢤
⠀⠉⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀
⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣿⣿⣿⣯⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⣠⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡄⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⢸⡀⢸⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣤⠀⢸⠀⣸⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠳⠜⠀⠈⠃⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠉⢂⠀⠀⠋⠀⢘⠴⠃⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⠀⠀⠀⢀⡀⠀⠊⠀⠀⠀⠂⠄⠀⣀⠀⠀⢠⠎⠀⠀⠈⠃⠀⣀⠀⠀⠀⢀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠘⠐⠏⠀⠀⠀⠀⠀⠀⢀⣀⣔⣻⡄⠈⣜⠀⠀⠀⠀⠀⠀⠈⠗⠈⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠠⠀⠀⢐⠔⠹⠃⠿⠘⠃⠀⠀⠀⠀⠀⠈⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠊⠁⠀⡀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠙⠂⠀⢀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠃⠀⠀⠠⠤⡞⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠂⠀⠀⠀⠀⢊⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⣀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁⠈⣁⠀⠀⠀⠀⠀⠀⠀⢈⡁⠉⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠁⠀⠊⠉⡄⠀⠀⠀⠀⠀⢀⡌⠉⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠠⠁⠀⠀⠀⠀⠁⠨⠂⠀⠠⠀⠠⠆⠈⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠲⠀⠸⠤⠄⠤⠄⠀⣄⠀⠰⠣⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠁⠀⢄⡀⠀⠀⠀⠀⢀⠄⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⠀⠀⠀⠀⠓⠀⠤⣤⡤⠄⢊⠀⠀⠀⠀⠀⠛⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠀⠠⠠⠄⠀⢚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠉⠀⠄⠀⠀⠀⠤⠽⠉⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠸⠀⠀⠀⠀⠀⠀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⠐⠳⠄⠺⠤⠤⠤⠄

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⣠⠖⠀⠀⠀⢠⣦⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢼⣟⣿⡀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠙⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡷⠀⠀⡉⠀⠀⠀⠓⡄⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣤⣀⠁⠙⠁⠶⠀⠀⠀⡇⠀⢠⣤⠀⢈⢠⡄⣉⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠠⣤⣠⠀⢤⢴⢦⠄⠀⠀⠁⠉⠙⠋⠐⠘⠠⣶⡤⠾⠿⢿⣿⣿⡿⢣⠦⠼⢷⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠐⠂⠸⠄⠀⠀⡈⢰⣶⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣤⣧⠖⠂⢛⢻⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠸⣏⠿⠏⠙⠋⡉⡏⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⣈⣿⣿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⢂⡠⢀⣿⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦⣹⣿⣿⣿⣯⣿⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠙⠛⣿⣅⣤⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⡄⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⢶⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠡⠊⡈⠀⠀⠀⢀⡆⠀⢀⡀⠀⠀⡠⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⢀⣀⣼⠀⢰⡁⠉⠀⠎⠰⣋⡈⢪⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡅⢳⢸⢸⣿⠀⡌⠳⢦⡀⢄⠸⣿⠷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠂⠣⡱⡌⢆⢣⠻⣷⡙⡄⠀⢻⡌⣆⠈⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄⠀⠈⢀⢩⠑⣌⢻⣾⣷⣇⠹⣷⢹⣴⣼⡿⢸⢀⠀⠈⡇⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢑⡏⣝⡳⣿⣿⣿⣶⡿⢸⣿⣟⡵⠋⡈⠀⣸⠇⠀⠙⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠠⠓⠂⢀⡇⠘⣿⣿⣿⣧⣿⣿⡋⣰⠾⠷⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢊⣀⣀⡀⢐⡄⠸⣧⠰⡘⣿⣿⣿⣿⣿⣿⣷⣷⢄⡀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡴⠀⠟⠹⢭⠏⠛⢿⣿⠿⡿⠋⠉⠁⠀⠀⠀⠃⠈⠈⢉⡶⡲⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣉⣠⠇⠀⠀⣀⠴⠊⠉⠀⠀⠀⢀⡀⠀⠀⠉⢀⣦⡄⣾⢰⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠉⠙⠛⠂⠙⡟⠲⢖⢦⡀⠀⢠⣰⣯⣦⢀⠏⠙⠋⢹⣿⠾⢦⡵⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⣿⡅⠀⠀⣧⠀⡌⣿⣇⣤⠞⠛⠈⢿⣾⣄⣉⣀⣿⠻⡇⠌⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⣷⣀⣨⡥⢴⣿⠟⠛⢲⢿⣿⢿⣧⣈⣠⡼⠏⡉⠫⠁⠀⠀⠂⣀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠷⠀⠐⠈⠁⠀⠙⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⣲⣾⣿⣗⡀⠀⢠⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠁⠷⠀⠙⠀⠼⠃⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣄⡀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠲⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡝⠟⠛⠀⠀⠀⠀⠀⠃⠀⠀⢠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⢤⣀⣤⣤⣸⣦⡴⣻⣿⣿⣶⣵⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠓⠛⠚⠛⠛⠛⠛⣛⣻⣛⡻⠿⠿⠿⠿⠿⠿⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠀⠀⢀⣀⠠⠄⠀⠀⢀⣀⠩⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣶⡶⠶⠶⠶⠴⠶⠶⠶⠖⠚⠋⠁⠐⢀⣀⠀⠀⠂
⠀⠀⠀⠀⠀⠒⠊⠉⠉⠉⠁⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⠤⠤⠴⠶⠖⠋⢉⠇⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣀⣀⣀⣠⡤⠴⢖⣛⣋⣭⣤⣤⣤⣤⠤⣤⣤⣀⣀⣀⣀⣀⣠⣤⣴⠒⣫⠀⠀⡀⠀⠀⢁
⠀⠄⠤⠀⠀⠶⠶⠒⠒⠂⠈⠉⠉⠉⣀⣀⠠⠌⠀⠠⠖⠒⠉⢁⡉⠀⠒⠁⠀⠀⠈⠉⠁⢰⣀⣄⡠⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡩⠄⠀⠀⢀⣀⠠⠀⠀⠐⠏⠀⠀⠀⠀⢀⠠⣠⣴⢶⣪⡟⠉⣙⡑
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠉⠁⠀⠠⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠚⠀⠈⠁⠀⠉⠈
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣲⣾⣿⣖⡂⠀⠠⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⠉⣷⠀⠙⠆⠹⠛⠉⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢰⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡽⡿⠯⠁⠀⠀⠀⠀⢂⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⣀⣀⢸⣤⣠⢼⣶⣷⣦⣖⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣦⠶⠴⠾⠷⢾⢿⠿⢿⠿⢿⣿⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣉⠉⠁⠐⠀⠀⠀⠀⠄⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣠⣤⡤⠶⠋⢉⠀⠀⠀⠐⢞⠉
⠀⠀⠀⠠⠄⠠⠤⠤⠐⠒⠒⠛⠛⠛⠉⠋⠉⠉⠉⠁⠀⠀⠀⠁⠀⠀⠀⢀⣀⣀⣨⡿⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠶⠒⠒⠚⣛⡛⠛⡛⠛⠑⠒⠚⠉⠉⠉⠉⢀⣀⠴⠃⠀⠀⠀⠀⠤⠊
⠀⠀⠀⠀⢀⣒⣒⣒⣒⡋⠩⠭⠶⠖⠛⠛⠉⠋⠛⠋⢉⣛⡛⠷⠒⠒⠒⡒⠞⠋⠙⠃⠾⠆⢀⠒⠈⠀⠀⣢
⠀⠉⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠤⠤⠔⠒⠒⠉⠁⠀⠈⠁⠀⢀⠴⠂⠁⠀⠀⠀⠀⠀⢀⣀⡈⣷⡞⠾⣅⡀
⠀⠀⠀⠀⠀⠠⠄⠠⠀⣀⣀⣤⠤⠖⠋⠁⣀⡤⠔⠒⠈⠁⠀⠀⠁⠠⠀⠀⠀⠠⢨⠖⢳⠛⠲⠿⠀⠴⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠉⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⣀⣀⣀⣀⣀⡤⠄⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⠤⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢀⣠⠶⠖⢿⠉⠉⢹⡏⠀⢸⡿⠉⠉⠉⠁⠀⠸⣁⠀⣀⠄⠀⠀⣲⠍⢁⣉⡁⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⣠⣾⠋⢀⡤⠇⠀⠀⠉⠷⢴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁⡀⢤⡾⡯⠀⠓⠚⠛⠒⠀⠉⠉⠀⠀⠀⠁⠐⠂⠄⠀⠘
⠀⢸⢇⢨⡟⠯⡀⢑⣀⡀⠀⠀⠸⣟⠡⢀⠀⠀⠀⠀⠀⢀⣠⡀⣠⣿⢋⡇⣢⠴⠖⠒⠂⠀⣀⡀⠂⣶⣋⣽⣿⡯⠯⢽⢀⣠
⠀⢸⡈⠙⠒⣤⠾⠍⠡⡄⢸⠆⠀⠉⢿⠓⢾⠶⣾⠒⠲⣛⣪⢹⡛⠿⠽⠥⠾⢥⣤⠔⢲⣾⡟⠀⠀⠀⠉⠁⠁⠒⠒⢈⡡⠃
⠀⠘⣿⠃⠘⠃⠉⠚⠂⠙⠀⠀⠀⠀⠀⠂⠈⠦⠈⡛⡄⢠⡉⠉⣓⡐⠒⠒⠒⠚⠲⠾⠿⠓⠿⠯⠶⠶⠶⠶⠶⠞⠊⠇
⠀⠀⠈⠣⣄⠀⠐⠒⠠⢤⡀⢠⡀⠀⠀⠀⠸⣆⠀⠨⢷⡈⠐⢦⡉⠙⠁⣢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠘⢦⣀⠀⠀⣸⠃⠘⠀⠀⠀⠀⠀⠘⠀⠀⠈⡇⠀⠀⠙⣶⢄⠀⠐⢽⠶⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⣀⠀⠀⠀⠀⠈⢣⣷⡀⠈⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡝⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⠔⢡⠔⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢁⠎⡐⢁⠞⡠⣊⢔⡁⢒⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣰⣘⣃⣃⣊⣐⣡⣊⣊⠕⡰⠲⠕⡀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢀⣀⣴⣲⠟⢹⣿⡿⡪⠋⠛⣽⣽⡝⡟⠹⣷⣷⣯⣀⣠⡾⠪⣂⢐⢌⢂⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂
⠀⠀⠀⢀⣤⠔⠛⠿⠱⠑⡀⡢⠙⣿⡇⡄⠜⣾⣿⣟⣄⣜⣿⣿⣻⡟⠊⠻⣿⣷⡶⢵⣯⡇⠀⠀⠀⠀⠀⠀⣠⣶⣫⡂
⢀⣠⠖⣁⠣⠖⠇⠀⠀⠀⠀⠍⠉⠎⢅⢄⠌⢜⣿⣞⢀⠈⠜⣿⣽⡟⠔⠴⣽⣽⣟⣔⢜⣿⣿⢁⣦⣿⣷⣘⡮⣿⣥⠂⢀
⠫⣁⠑⢬⡁⣧⢠⠆⠀⠂⡙⠂⠃⣀⢂⡎⠊⠊⠻⠏⠔⠐⡠⣻⣿⠏⡊⡀⣾⡿⣫⠎⠨⠛⠋⠉⣉⢉⢩⣉⡡⣿⣆⠡
⢀⠈⣢⢤⠳⡈⠜⣠⠤⠈⠀⡠⢠⡾⠛⠇⠀⠀⡐⠄⡸⡈⢀⡿⠋⠈⢁⠁⠙⠈⢄⢠⣢⣥⢾⣉⠀⠀⠀⠀⠙⠯⣍⠒⡠
⠀⠀⠈⠁⠉⠐⠲⠤⢤⡄⠀⠐⠰⡋⠅⠲⡀⠄⡠⢑⠀⠀⠎⡈⣖⣱⣕⡤⠴⠚⠻⠛⠈⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢺⣷⠖⣚⣒⠛⠒⠓⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠑⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣲⡽⡟⢌⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡤⢤⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⣶⡀⣰⡿⠉⢠⣽⠿⣿⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⣋⣴⣾⣷⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠘⢷⢿⡅⢠⡿⡛⠀⢈⣙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣷⡿⠛⢻⣿⣿⣗⣶⣶⣏⢾⡷⠶⠋⠀⠀⠀⠀⠀⣠⣤⣴⣶⠖⠀⠀⢀⣬⡶⢶⡌⢀⡠⣄⡀⠄⣠⣀⠤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⢋⡴⠖⢒⣛⣿⣿⣿⣯⣿⡭⢀⠀⠀⠀⠀⠀⠰⠚⠚⠉⠋⡵⠀⠀⠘⠋⣿⠀⢨⣿⡈⠓⠄⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⣠⡎⢿⣿⣿⣿⣿⣿⣿⠿⣆⠉⠒⠄⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠠⠃⠀⢸⠈⢷⠀⠀⠀⠀⠀⠀⠀⡰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢿⣵⠛⠁⣿⠋⡿⠉⢿⡇⠀⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⠘⢀⡄⠀⠀⠰⠀⡜⠀⠈⢇⠀⠀⣠⠀⠀⠀⣷⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⢰⣿⡴⠁⠀⠈⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⢨⡇⠀⠀⠘⡀⠀⠁⠈⠀⢸⠃⠡⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡮⠃⠀⠀⠀⠘⠛⠁⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣧⠀⢘⠀⠃⡞⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠸⠀⢰⠃⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⣼
⠀⠀⠀⠀⡄⠀⣶⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢿⡀⠀⡏⠀⠀⠤
⠀⠀⠀⡠⣏⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠛⠖⡾⢳⡦⠴⣶⣟⣇⠠⡇
⠀⠐⣴⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣊⢚⣉⢊⠰⢓⣣⠔⢪⣉⣼⣷⢸⣇⡀
⢀⣈⣹⣯⣿⣷⣷⣦⠄⣀⠀⠀⣀⡀⠀⠀⠀⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡷⠚⠑⠣⣏⡉⠄⠛⢅⡒⢂⣰⣾⣿⣿⣿⣷⣆⡤⠄
⠀⢨⣽⣷⣿⣟⣿⣟⣗⣺⣿⣿⣿⣿⣷⣄⡄⢠⡏⠏⠇⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣷⣾⣖⣬⣥⣬⣤⣞⣋⣭⣿⣿⣷⣿⣿⣿⣿⣿⡶⠖⠂
⠀⢸⣿⣿⡟⠀⠈⠉⠩⣤⣿⣿⣿⣟⣿⡏⠀⢸⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠉⢛⣻⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣁⣙⢛⣷⡈⠷⣦
⠀⣀⣿⠟⠤⡴⣶⣶⣾⡿⢿⠉⠽⢿⠣⠀⠀⠸⠀⡄⠘⠀⠀⠀⠀⠀⠀⠀⠤⠰⠶⠌⣩⣿⣿⣿⣿⠿⢿⣟⢋⣿⣿⠿⠽⠿⠿⠿⠙⣷⠀⠐⢦
⣀⡵⠋⠀⠀⠀⠐⠚⠋⠤⣗⠐⠀⠠⡶⠈⠁⢸⢀⡇⡧⠀⠀⠀⠀⢀⣀⣀⣠⡴⢴⠖⣛⣛⣛⡿⢶⣶⣶⡍⣉⠁⠀⠀⠀⠀⠀⠀⠀⠛⠳
⠈⠁⠀⠀⠀⠀⠀⠒⠂⠐⠒⠘⠃⠔⠦⠤⠀⢸⢾⠇⡇⠀⠀⠉⠉⠉⠁⠈⠛⠛⠛⠻⠛⠻⠿⠭⠞⠛⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣾⣶⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣟⣩⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡴⠌⢅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⠑⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠂⠀⡝⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢫⠀⠐⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⢈⠀⡰⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢂⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⡖⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢲⠁⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠸⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠇⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⢀⡀⠠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠤⢀⡀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢊⠁⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠈⠱⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠈⡄⠀⠀⠀⢆⠀⠀⠀⠀⢀⡴⠺⠚⠻⡖⢦⡀⠀⠀⠀⠀⡰⠀⠀⠀⢠⠁⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢃⠱⡈⢄⠀⠀⢀⡦⢄⠀⣠⠎⡠⠋⠉⠉⠛⢄⠱⣄⠀⡠⢶⡀⠀⠀⡰⢁⠎⡘⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠑⡈⢢⡬⠲⣗⡉⠉⠀⠀⡝⠃⠌⠀⠀⠀⠀⠀⠀⢣⠘⢫⠀⠀⠉⢉⣺⠔⢅⡔⢁⠊⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠡⡈⢢⣕⢄⡈⠪⣕⢠⣎⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⢱⡄⣪⠕⢁⡠⣪⡐⢁⠜⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⠢⣘⠯⡀⠑⠬⣺⣀⡍⠒⠬⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠒⢩⡀⣗⠥⠊⢀⠽⣃⠔⡩
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀⡱⠦⢕⠤⣋⡙⠐⠠⢴⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠄⠀⢋⣙⠤⡂⠱⢎⡠⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠑⠠⠀⢈⡸⠋⠖⠲⢴⡅⠀⠀⠀⠀⠀⠀⠀⠀⢨⡦⠔⠲⠙⢇⡁⠀⠄⠊⠁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⠂⠄⠀⣀⡀⠀⠈⠉⠐⠒⠒⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠒⠒⠀⠉⠀⠀⣀⣀⠀⠤⠐⡙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠼⣀⣈⣉⣉⣋⡁⠠⠄⠲⡀⣀⣀⣀⣀⣀⢀⣀⠖⠠⠄⢉⣹⣉⣉⣁⣀⠧⠀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠂⠤⠤⠤⠤⠤⠐⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⢀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠒⠒⠒⠈⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠤⠀⣀⣀⣀⡀⠠⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠉⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⡦⠤⠄⠀⠀⠠⠤⣖⠠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠀⢀⠎⠱⠀⠀⠀⠀⠀⢀⠉⢢⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠼⡀⠀⣣⡀⠀⠀⣠⡎⠀⢀⠦⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠁⠈⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⢀⡄⣚⠿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⡄⠁
⠀⠀⠀⠀⠚⢙⣿⣿⣯⣜⡟⠊⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣿⠩⣦⠁⠁⠀⣴⣗⢂⣠⣦⠄
⠀⠀⠀⠀⠀⡾⠁⠋⢡⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠝⠀⡀⠈⠀⠙⢇⠉⠘
⠀⠀⠀⠀⡐⠁⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⠀⡀⠑⠠⡀
⠀⠀⣠⠞⠀⣠⠊⠀⠐⠀⠴⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⢄⡀
⠀⠘⠁⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⢰⡐⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⢲⣄⠀⠘⣬⡀⠀⠀⠀⠀⠈⠣⡀⠀⣠⣤⣤⠄⠶⠤⠠⠠⠀⠠⢄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠓⠛⠒⢢⣌⠙⢶⡀⢹⠧⠀⠀⠀⠀⣀⣤⣹⣾⠋⢴⢉⠑⠁⠀⠁⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠘⢋⣉⣉⣉⣑⣄⣀⣈⣧⣀⣷⡀⢾⡀⠀⣠⣒⠞⢛⣡⠻⡖⢦⡥⣀⣐⡂⣨⣄⡉⠈⠉⠛⠀⠀⠀⠀⣿⠃
⠀⠀⣰⣶⣶⣢⣀⣠⣤⣴⣶⣗⣿⣿⣿⣿⣿⣯⣿⣿⢿⣿⣿⣿⣿⣿⣿⠷⣶⣾⣘⡶⠚⠁⠀⢱⠀⠈⢀⠌⠈⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⣿
⠀⣸⠷⠆⣛⠱⠽⠟⢯⠿⠉⡟⠘⢏⠉⣸⠏⢙⡞⢹⡿⠿⢛⣿⠿⣿⠟⢿⣷⣾⣭⣿⣿⣶⣶⡿⣀⣴⠡⠐⡚⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⣿
⠀⢣⡤⠁⢤⣤⡶⡦⠈⣇⠀⣮⠀⢸⡀⢠⡇⠁⢧⣾⠟⠠⣀⠁⠈⠹⠈⠈⢿⣻⣿⣿⣿⣩⣿⣿⡭⠤⠒⠊⡠⣠⣞⡍⡡⢂⠔⠀⠀⠀⠀⣿
⠀⠘⢷⣀⡀⠊⢹⡝⠴⠻⠄⠙⠷⠈⠓⠚⠷⣄⣼⡟⠀⠐⠀⠂⠀⠀⠀⠀⠀⣿⡿⣛⡩⣿⣟⡟⡏⠑⠒⠨⣴⣯⠫⣜⠐⠁⠀⠠⠀⠀⠀⣿
⠀⠀⠘⣟⢃⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣥⣀⣀⣀⣀⣀⣀⣠⡶⠟⠛⠛⠉⠻⡏⢿⠇⠀⠰⠀⠀⠙⢷⣭⡆⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⣶⡆⡟⢺⠯⡙⣄⢀⡨⠛⣤⠀⢩⣞⠁⠀⠂⠀⠀⠠⣻⢯⣥⡆⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠊⠁⢙⣾⣯⠝⣿⠙⢾⣧⣤⡂⣠⠏⠀⠀⠀⠀⠀⣠⣶⡡⠮⠉⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣴⡶⠊⠁⢀⣤⣾⢽⡿⠁⣸⡇⠀⠀⠀⠘⢻⠯⠌⠻⠲⡠⠰⠂⠗⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⠖⠋⡽⣇⡞⠁⠀⣽⠇⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠁⠀⠀⣼⣿⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⡬⢼⠋⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠐⣁⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛

⠀⠀⠀⢰⣾⣖⡀
⠀⣤⠆⠈⠛⠈
⣕⢾⢃⣼⠀⠀⠟⢠⠀⢲⠆
⠉⠉⢉⠿⢧⣐⠂⠀⠠⢀
⣶⣄⢸⣷⠀⠘⠷⣄⢘⡀⣁⣤⣤⣄
⣿⡈⣿⠿⠦⠤⠦⠌⠉⠁⠀⠀⠀⠀⠀⠀⠄⣀⣀
⠉⠙⠛⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠐⠐⠐⠠⠄⢤⣀⣀⣀⠀⠀⠀⠀⢀⢀⣀⣀⡀
⠀⢲⣿⣶⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠲⣤⣤⣤⣉⣉⡉⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⢿⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠛
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠂⠀⣻⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠠⠀⠐⠄⠀⢉⡃⠀⢾⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣏⠀⠀⠀⠀⢸⡆⠀⠀⠁⠀⣺⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠀⠀⢼⣷⣀⠀⠀⠀⣸⡇⠀⠀⡀⠈⣽⣏⠀⠀⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⢀⡾⠁⠐⠀⠀⣴⡿⠁⠀⠀⢸⡄⠁⠙⠦⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡁⠉⣰⠄⠀⡆⢸⡿⠁⠀⠀⠀⣾⡇⣾⠀⠀⢨⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠦⠚⠁⠀⢰⠇⢸⠇⠀⠀⠘⠀⣿⠁⢸⡄⠠⣴⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣧⡐⠀⠀⣿⠀⠈⠇⠀⡆⠀⠀⢹⡇⠸⣿⠀⡀⣸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣿⣏⠀⠀⠟⣿⠀⠀⠀⠀⠱⣦⠀⠋⠀⢸⡿⠀⠀⣿⡅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢽⣿⡇⢀⠀⠀⢻⡀⠀⠄⠀⠀⢹⣇⡠⠀⢸⠁⠀⡀⢸⡧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣚⣿⣟⢸⡆⠀⠀⠁⠀⠀⠰⠀⢸⠋⠀⠀⠀⠀⢠⡇⣽⣓⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⢿⠿⠾⢿⣄⠸⣄⢰⡇⠀⣴⠀⠀⣸⠀⠀⣠⣾⠷⢿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⣬⢻⣷⣿⣶⣿⣶⣿⣷⣶⣿⣾⣿⠟⠁⠀⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣏⣹⢟⢁⡽⠋⢛⠉⢻⡋⠙⢯⡈⣻⣿⣥⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡤⣿⣧⡶⠉⢂⡠⠊⢷⠀⠑⢌⡀⠈⢶⣼⣇⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢈⣿⢷⣤⠮⣤⣄⡼⢦⣠⣤⣵⣦⣾⠏⠉⢻⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⣷⣤⡿⠃⠀⠉⢳⣾⠿⢦⣶⡟⢉⠉⠙⣇⠀⠀⣸⠃⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣦⠈⠛⢯⣤⣤⡔⠛⠡⠀⢀⠉⣣⣀⣁⣠⣾⣶⡶⠋⠀⢴⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡄⠀⠀⠀⠙⠶⠶⠶⠾⠛⠋⠉⠙⠉⠉⠁⡀⠴⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠖⠄⢠⡄⡄⡄⡀⠀⡄⠀⠤⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⠿⡒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⠉⠀⠁⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⡯⠋⢃⣠⣴⣾⣿⣿⣿⡿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣦⣤⣀⢰⣸⣟⣿⠿⢳⣴⣿⣿⣿⣿⠿⢯⣛⠻⠌⢻⠳⠹⢿⣧
⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⡄⢾⣛⣿⣿⣶⣶⣿⣿⣥⣶⣞⡥⠷⠀⠀⠹⡇
⠀⠀⠀⠀⠀⠀⠐⡿⢋⠟⠿⢉⣫⣯⣿⣖⣿⣿⣏⢿⣾⣿⣿⣿⣿⡻⡟⣽⣿⣿⣿⣾⣿⣥⣄⣀
⠀⠀⠀⠀⠀⠀⠈⠀⢀⣴⣾⣿⣿⢻⣷⣿⣿⣇⣿⣯⢿⣿⣿⡟⣿⣿⣿⣛⣻⡿⣿⣿⣿⣿⡉⠁
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡟⢏⣿⣿⣿⡻⢿⣿⣿⡥⢿⣏⠿⢻⣿⣿⣿⣿⠆⡇⠿⢿⣿⣷
⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⣟⠗⣾⣿⣿⣿⡷⣼⣿⣿⣿⠭⣷⠀⠈⠃⢸⣿⣿⡶⢄⠀⠀⠛⠈
⠀⠀⠀⠀⠀⢰⡟⠻⠙⠌⠈⢸⣿⣿⣏⠳⠽⠸⣿⡿⣍⡁⢸⣧⠀⠀⠇⠯⠻⡏
⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⢸⣿⡟⣟⠦⠀⠀⣿⣿⣄⠀⢘⣿⢀⣤⣀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠙⠈⠀⠀⠀⠘⠿⢈⣥⣶⣿⡝⢿⣿⣿⢶⣤⣤⡤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⠖⣫⠾⣏⣿⡇⠀⠁⠹⡆⠙⡷⢤⡀⢀⡉⠳⣶⣒⣲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠶⠶⠾⠿⢶⣶⣶⣥⠤⣤⣀⡈⣿⡷⠖⠶⠶⠅⠶⢤⣤⡶⣤⣍⢽⣶⣭⢯⣽⣿⣿⠿⠿⠿⠶⣶
⠀⠀⠀⠀⠰⠖⠲⠦⠤⠤⠤⠶⠂⢀⣀⣉⣉⠙⠋⠛⠫⠽⠥⣿⠇⠒⠂⢧⡆⠈⡉⠛⡀⠴⠿⠾⣍⣉⣡⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠽⠋⠉⠉⠉⠁⠀⠀⠀⠀⢸⣿⠁⣴⢡⣿⡇⣸⣡⢞⡁⠈⢉⣛⣓⣲⣶⣶⣒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣆⠾⠇⠐⡯⢼⠘⢱⠿⣱⣏⣧⠆⠀⠀⣉⣻⡷⢿⣿⠿⠷⠶⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢶⡿⣿⣿⡟⠀⢸⢣⢿⡇⣎⠳⢤⣿⣿⣿⡶⣤⣴⣿⣭⣭⣁⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠠⠚⠁⠀⠀⠀⠈⠈⠘⠀⠈⠁⠀⠀⠉⠉⠉⠛⠛⠉⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⣀⣀⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⠠⡀⠀⠑⠀⠀⠀⢀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⡟⠉⣶⣄⣻⣯⣿⠿⢟⣻⡦⠀⠀⠰⡆⠀⠄⠀⢨⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⡇⠀⢿⣿⣿⣏⠀⢸⣽⣽⠇⠀⠀⠀⠀⠀⠸⠀⢸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⡰⣿⣿⣦⣀⣬⣙⣛⣷⠿⠋⠁⠀⠀⠀⠀⠀⠀⠐⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠖⠙⣻⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠻⢿⣿⣿⠟⠛⠋⣀⣤⠞⠋⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⣀⣤⠤⠴⢶⣯⣵⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⢿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢪⣿⣿⣿⣷⡕⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠰⣿⣿⣿⣿⣿⡟⣻⠷⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡹⣿⣿⣿⣿⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠏⢁⣼⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠖⠙⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡏⠀⠀⡌⠀⠹⠁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆⠐⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣼⣷⣆⣶⣶⣶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠻⣧⠺⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠻⣿⡓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖⠒⠀⠉⠁

⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⡇⡟⡝⠉⣫⡏⡯⡏⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⣷⢇⢇⣀⣷⣗⡷⣇⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢀⡴⠋⠁⠀⠀⠙
⠀⠀⠀⠀⠉⠉⠉⠉⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡀⡄⠅⠀⢼⡦⠚⡤⢄⣠⠞⣛⠡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⡀⠀⠄⠂⠀⠀⠄⠈⠀⢇⠀⠀⠀⠀⠀⢠⣤⣶⣿⣿⣷⣿⢷⣶⣦⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠄⠀⠀⢸⠀⠀⠀⠁⠀⠀⠈⠀⢀⠤⢴⡾⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⢠⢂⠀⠰⠀⠀⠀⡀⡀⣄⡞⠈⠳⣤⣀⣀⣠⣤⡴⢾⠀⠀⠀⣀⣤⠤⠤⣮⣭⣉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠠⠺⢤⣹⣦⣾⡐⠊⠈⠉⠀⠀⣀⣾⣲⡶⠈⠻⣍⠀⠑⠀⢿⠟⠁⠀⠐⠐⠂⠉⠻⡆⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠄⠀⢸⣿⣿⣿⣿⡆⠀⣀⡴⠚⠍⠉⣿⠅⠀⠀⠊⠙⠳⠦⡈⠳⣄⠀⠀⠀⠰⠀⠈⠳⡶⠶⠒⠒⠒⠒⠒⠢⡄
⠀⠀⠀⠀⠀⢸⠃⢐⣾⣿⠿⠿⠛⠀⢐⠀⠀⠀⠀⢀⣟⠀⠀⠀⠀⠀⠀⠁⢿⠀⠈⠙⠶⣤⣀⠀⠀⠀⠈⠒⠄⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠛⠖⠊⠀⠀⠀⠀⠀⠄⠈⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢺⡇⠀⠀⠀⠀⠉⠙⠲⠶⠤⣤⣀⣀⣁⣀⡠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒


⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠠⠄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡈⠅⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⢠⠝⠐⠋⠉⠀⠦⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢜⡁⠤
⠀⠀⡀⠂⠀⠂⠐⠂⠀⠀⣿⡄⠀⠀⠂⡀⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡆⠄
⠀⠈⡄⠀⢀⠒⠀⠀⠀⠀⠡⠀⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡁⠀⠀⠀⠈⠀⠀⠀⡴⠉⢀
⠀⠀⣀⠀⢀⠀⠗⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⠂⠀⠠⠀⠀⠀⢠⣿⡐⠂⡀
⠀⠀⠟⠀⠈⠙⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢻⠀⠀⠀⡇⠀⠀⢀⠎
⠀⠀⢰⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇⠀⠀⡎
⠀⠀⠸⡄⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⣷⢀⣸⣤⣤⣤⣶⡦
⢀⣠⡄⣧⡠⣤⣀⣿⠃⢄⡠⠤⢤⣤⣤⣤⣤⣤⢤⡤⣤⣀⠤⣤⣤⠤⡤⣤⣤⣤⣤⠤⠄⡀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠁⠀⣠⡀
⢀⢎⣇⣿⣃⠌⡀⣿⡆⠀⠀⠀⣀⡀⠈⠉⠁⠀⠀⠀⠀⠀⠦⠒⣠⡤⠀⠀⠀⠀⠀⠒⣂
⣏⣾⣿⣿⣿⣿⣿⣿⠁⣷⠅⣀⡀⠀⠐⠀⠀⠙⠷⠶⠦⢤⣤⣿⣿⣿⣾⣦⠰⠾⠶⠿⠿⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣧⣪⣮⣜⣿⣿⣿⡿⢠⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠿⠛⠻⠟⠉⠀⣿⡉⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡆
⠀⠀⠀⠀⠀⠐⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠔
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⡈⣀⠀⠀⠀⠄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢠⠀⢀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠀⠀⠸⠀⡀⣷⠱⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⡔⠘⣣⠀⠄⠀⢹⠐⠐⢿⠢⣁⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢱⠀⣤⣦⣠⠀⠀⠐⠐⠟⠿⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣼⣦⠄⠀⠂⠛⠀⠇⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠀⠁⠀⠀⠀⠀⠀⣀⠀⠄⠀⣠⠀⢀
⠀⠤⠤⣤⣤⣤⣠⣤⣤⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠋⣤⠼⣿⢘⡹⠿⡄⠐⡿⠇⣈⡿
⠀⠀⠀⠀⠀⠈⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠄⠚⠘⢷⠀⠱⡶⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠈⠃⠀⠰⠰⠅
⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠀⠒



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣉⣭⣫⣌⣩⣯⣻⣟⣿⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠁
⠀⠀⠀⠀⢀⡁⠀⠀⠀⣀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⡀
⠀⢠⠀⢀⠄⠀⠀⢠⢿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣄⠀⠀⠀⠐⢂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣤⡤⠀⢉⠐⢦⠤⠄⠀⠀⠰⡀
⠀⠀⠀⠈⠁⠀⠀⠀⡄⠀⠑⠀⠀⠀⠀⡄⠀⠠⠀⠋⠿⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡠⠀⢹⠦⢀⡄⢙⠆⠃⢀⠐
⠀⠀⠀⠀⠀⠀⠊⠸⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠡⠞⠀⠀⠠⠢⠌⠉⣿⠒⢊⡼⠉
⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣠⠶⠂⣠⣈⠙⠆⠀⠀⢀⠀⠈⠉⡷⠄⡄
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀⣤⣠⡄⠀⠀⠀⠀⠀⠀⠄⡀⠊⠹⠈⠠⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⡿⠋⠻⠒⢏⠗⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⢆
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠠⣥⠰⠀⣠⣤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⠘⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠐⢀⠀⢠⢠⠀⠁⢐
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠘⠒⠀⠠⠀⠀⡀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠐⠂
⠀⠀⡉⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⡀⠈⠉⠡⠤⠄⠀⠀⢀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠
⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠓⠀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠁⠀⠀⠀⠀⠠⠀⠀⠀⠤⣄⣀⡀
⠀⠠⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⡘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠤⠄⠀⠀⠀⠀⠉⠀⠂
⢀⣀⡄⠀⠀⠀⠀⠐⠶⠂⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠉⠉⠙⠂⠀⠀⠀⢀⠄⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⢠⣀⣀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠀⠀⠁
⣤⣤⣤⣤⣼⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣇⣀⣈⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣴⣆⠈⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣟⠿⣿⡿⠿⠿⢯⣭⣿⣿⣾⣿⣮⣜⡿⣆⠀⢉⣦⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⢾⣒⠚⠓⠈⢀⣀⣀⡼⢥⣿⣿⠼⠋⠛⠻⢿⣼⡄⠀⢀⣧⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⢠⣾⣷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠒⠒⠒⠢⣤⣤⠰⢿⣿⡦⠌⠛⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣤⣤⣤⣤⡾⠙⠏⢀⣼⠅⠀⠀⠒⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣧⣀⡔⢿⣿⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠀⠀⠉⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢴⣶⠷⡶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⢿⢶⡦⣀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⢉⣴⠏⣱⠏⢀⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢣⠈⣇⢹⡌⢳
⠀⠀⠀⠀⠀⠀⢀⣾⣵⡟⢁⡾⢁⡔⢁⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠈⢇⠸⡄⢻⡊⣇
⠀⠀⠀⠀⠀⢀⣾⡿⠔⠆⢰⣟⣉⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣌⣶⠄⣤⢻⣿
⠀⠀⠀⠀⠀⣼⣿⠲⢀⣘⡧⠉⣩⣿⡁⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣈⣵⠚⠀⣩⣿⡀
⠀⠀⠀⠀⢀⣿⡟⠓⢀⠈⠀⢨⣿⣿⠇⠀⠀⠀⠈⠄⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⢨⣿⣿⡀⠈⠀⣤⣽⣿⡇
⠀⠀⠀⠀⠀⢣⣷⣌⣠⣀⣷⣿⡿⠟⠀⠀⠀⠀⠀⠈⡀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠙⢿⣿⣀⡀⢂⡴⡻
⠀⠀⠀⠀⠀⠘⢿⣿⠉⣛⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣟⠉⢹⣿⠟
⠀⠀⠀⠀⠀⠀⠈⣿⠃⢈⣻⣿⣆⠀⠀⠀⢀⣀⠀⠀⢸⣄⣼⠀⠀⢀⣀⠀⠀⠀⣠⣾⡟⡉⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠙⢧⣘⡿⣿⣿⣿⣴⡿⠋⠹⣧⠀⣸⣿⣿⡀⣰⡟⠉⠻⣦⣼⣿⣿⣭⣟⡠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣾⣸⡟⣿⣦⣄⢹⣿⠉⣿⠛⢹⡟⢁⣤⣾⡿⣿⣸⡶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠻⠿⣿⣿⣿⣷⠠⠏⠀⢠⣽⣿⣿⡿⠿⠿⣯
⠀⠀⠀⠀⣠⣴⣤⣤⡿⢿⣧⣴⣾⣇⠀⠀⠈⢹⣿⣵⢃⡀⠀⢶⣿⣿⠁⠀⠀⢀⣿⣆⣤⣿⠷⣦⣤⣴⣄⡀
⠀⠀⢀⣼⠷⢋⡀⢀⣠⣤⠨⣹⡟⠛⠾⣶⣤⣘⣿⠿⢿⣥⣻⢿⣿⡇⣠⣴⠾⠟⢛⣯⡭⢤⣤⣀⡀⣈⠻⢷⣄
⠀⠐⠿⠣⢶⣿⠷⠛⠛⠻⠷⣿⣯⣅⣢⣄⠙⣿⢡⡖⠀⠙⠀⠀⠈⠻⠟⣁⣄⣪⣽⣿⡶⠿⠛⠛⠶⢿⣷⢌⠻⠃
⠀⢀⡖⣾⠟⠁⠀⠀⠀⠀⣀⣸⣇⠉⠙⠛⢿⡇⡿⡟⡄⢠⢀⠀⢨⣾⡷⠟⠛⠉⣁⣯⣀⡀⠀⠀⠀⠀⠙⢿⡷⣄
⠀⠀⠈⠁⠀⠀⢀⣴⣬⡾⠟⣿⠿⠿⠿⠷⢶⡇⠁⠀⠃⠀⠈⠀⠀⠐⡷⠶⠿⠿⠿⣿⠟⠷⣮⣶⣄⠀⠀⠀⠉
⠀⠀⠀⠀⠀⣠⣾⠏⠁⠀⠀⣿⣄⣀⣀⣤⣼⡇⢀⡠⠀⠀⠀⠀⠀⢸⣧⣤⣄⣤⣀⣿⠀⠀⠀⠙⣿⣆
⠀⠀⠀⠀⠰⠋⠉⠀⠀⣴⣾⣿⠋⠉⠉⠀⠀⢿⣾⣿⣿⡿⠿⣿⣶⣾⠁⠀⠈⠉⠉⢻⣿⣦⡀⠀⠈⠉⢣
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠋⣿⠀⠀⠀⠀⠀⢸⣿⣿⣣⣄⣀⣼⣿⡿⠀⠀⠀⠀⠀⢸⡍⠻⣧
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⡟⠀⠀⠀⠀⠀⢨⣿⣿⡟⠉⠉⣿⣿⡇⠀⠀⠀⠀⠀⢸⡇⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠈⣿⣿⡟⠛⠛⣿⣿⠃⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⣿⣿⠟⠛⠻⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠶⢶⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⢺⣿⡧⠤⣤⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣀⠀⢈⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⡠⣶⡿⢿⣏⠉⢻⣿⢿⣶⠦⡀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠞⢀⡿⠀⠘⣿⡄⣼⡏⠀⢹⡇⠙⡀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⣦⣾⡷⠶⠾⠿⠿⠿⠿⠶⠾⣿⣦⠇⠀⠀⠀⠀⠀⠀⠣
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⢀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣆⠀⣰⡿⠉⢀⣙⠿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⡉⣤⣾⣶⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠸⣧⣿⠁⢀⡿⡻⠀⠈⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⢾⡰⠛⢿⣿⣿⡆⣤⣴⡆⢴⣤⡴⠖⠂⠀⠀⠀⠀⢀⣠⢄⣤⡤⠖⠀⠀⠀⣀⣬⣤⡈⠀⠀⣀⠈⡉⠁⡀⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⢋⣤⠶⠾⢿⣿⣿⣿⣟⣥⣊⠁⠀⠀⠀⠀⠀⢀⠴⠫⠞⠫⠋⡅⠀⠀⠲⠋⡏⠀⠘⣷⠘⠃⠈⠁⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣠⠰⡿⣷⣿⣿⣿⣿⡿⣷⡄⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢠⠃⠀⢰⠘⣇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⣟⣴⠟⢹⣿⠛⡟⠙⣻⡄⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠇⢀⠀⠀⠀⡀⠀⠸⠀⠘⡆⠀⠀⢀⠀⠀⠀⢼⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠟⠁⠀⣸⣯⣸⠃⠀⠘⡡⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠸⡀⠀⠀⠸⠄⠀⠈⠀⠂⠀⡾⠘⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠃⠀⠀⠀⠿⠿⠁⠀⠀⢈⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⢧⠀⠰⠀⠄⢸⠃⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠘⠄⠀⡞⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⢀⡜⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⢀⣺⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸
⠀⠀⠀⠀⢣⢀⣾⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣈⣲⣄⠀⠀⢀⣹⣇⠀⣿
⠀⠀⠀⣀⣿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⣠⣎⠠⢡⣏⠜⢛⡉⠭⢣⣿⠀⣿
⠀⠠⢽⡿⣿⡟⣻⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣒⣬⢆⠤⡄⠤⠉⣤⠔⡉⠐⢖⢾⣿⣣⣿⡦
⠠⠤⢼⡿⣿⣿⣿⣶⣃⠢⣄⣂⣤⣦⣄⡀⠀⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠸⡉⣀⡬⠽⠤⠐⣈⣈⠤⣌⣱⣾⣽⣿⣿⣿⣿⣓⣚⡂
⠀⢰⣾⣿⣿⠟⠾⠿⣭⠭⢿⣿⣿⣿⣿⣿⠦⠀⢸⠃⠃⠃⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⡿⢿⣿⣿⠿⣟⠋⠁
⠀⠸⣿⣿⠏⠀⠀⠀⠀⣺⣿⣿⣿⣿⡩⠟⠀⠀⢸⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠩⠽⢭⣿⣿⣿⣿⣻⣿⡿⣿⣿⣿⣿⢿⣧⣤⣬⣉⣿⣇⠙⠻
⠀⡤⢟⠋⠐⠎⠻⠿⣿⠿⠛⠆⠐⠒⠏⠀⠀⠀⠘⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠛⠋⢠⣴⣿⠿⣿⠿⠛⠿⣭⣡⢿⠿⠛⠚⠛⠛⠛⠈⢻⣆⠀⠙
⣠⡼⠁⠀⠀⠀⠀⠉⠉⠀⠺⠁⢀⠀⠐⠂⠀⠀⢸⢸⡆⡇⠀⠀⠀⢀⣀⡤⠤⣤⣰⣲⡏⣉⣉⣭⣽⡛⣟⡻⢷⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂
⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⠂⠉⠒⠛⠒⠒⠀⢺⢻⠃⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠉⠙⠛⠒⠊⠁⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣾⡾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣎⣍⣬⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠤⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⢰⣿⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡟⠀⣼⣿⣿⠀⣸⡇⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⡿⢠⠿⠏⢸⠟⠘⣷⠀⢰⡟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⠛⠋⠀⣠⠋⠀⠀⠈⠀⠀⣹⡇⠾⠃⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡴⠏⠀⠄⠀⠋⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢼⣷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡾⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠠⣾⣀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣭⡟⣧⠀⡄⠀⠀⠀⠀⠰⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢀⡴⣊⢃⣿⣿⡸⣿⠁⠀⠀⡀⠀⠀⡀⣤⣰⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣶⠿⠁⢡⠎⠘⣿⡇⣹⡀⠀⢠⠃⠀⠀⠀⣿⣿⢦⡖⠐⢤⣄⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⢴⣿⡏⠁⣠⠋⢁⡆⠀⡄⠀⣠⠏⣷⠋⣷⡀⢸⡆⠀⠀⠀⣧⡈⠣⡙⢷⣿⣇⠀⣼⣥⠽⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢒⣁⣀⠀⠀⠀⠈⣿⣿⠞⢁⣾⣿⣿⠎⠀⢰⣿⠀⣿⠀⠘⣿⣾⣇⠀⢀⣼⣷⢍⠀⠈⠐⡙⢿⣴⡟⠁⠀⢀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣽⣥⣱⡄⣀⣤⡿⢃⣴⣟⣿⢣⠏⠀⢠⣿⡇⠀⡇⠀⢸⣿⣈⡎⣷⠻⢿⣿⡎⢳⣄⠀⠈⢲⣹⣁⡀⠀⡆⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠸⢋⠀⠀⠈⠙⠛⠻⣿⣵⣿⣋⣾⢣⡟⠀⢀⣿⢙⡇⣸⠁⠀⠀⣿⣏⣿⢸⡀⠈⢞⣿⡈⣿⣷⡶⠖⠿⣧⣈⠰⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠈⠀⠀⠀⠀⠀⠌⣱⣾⠛⣙⣙⠛⢳⠖⠚⠛⠛⠓⣿⢾⣁⡥⠿⠿⠿⡧⠿⠄⠺⠿⣿⡋⠁⢀⣀⣠⠄⠘⣶⡄⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡌⢀⣻⡇⠊⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢸⡟⠀⢀⣀⡀⠀⠀⠀⠀⠀⠹⡇⠀⠏⠁⠀⠀⠀⢹⣷⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⠀⠀⠀⢠⠁⠀⣻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⡇⠸⠏⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⣀⡀⠀⠀⠀⣸⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⣾⣤⣤⣏⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⣽⡇⠈⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⡼⠋⢱⣦⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠙⠓⠦⠤⠤⠤⠄⠤⠤⠤⠧⠤⠛⢇⣄⣀⣀⣤⣤⣀⡤⣴⠁⠀⠀⣼⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠒⠒⣲⡉⠒⠚⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠥⠥⠤⠭⠟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⣠⣤⣤⡄⠄⠀⠰⡆⠰⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⣶⣀⣄⡰⠋⠀⢦⠀⣀⣤⢤⠒⠶⠉⠈⠁⠁⠀⠰⡄⠀⠀⠀⣧⠀⢀⡋⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠛⢁⣠⣼⣿⣿⣿⣿⡦⣠⡾⠟⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠻⣾⣥⣄⢻⣿⡌⣷⡆⣏⢑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠁⢀⣰⣾⣿⣿⡿⢠⠛⣥⠞⡹⠁⠀⠀⠀⠀⠐⠈⢦⣄⡶⣦⣿⣿⣷⣝⣿⣯⣸⣿⣧⡿⣣⣟⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⢠⣤⢿⣿⣿⡿⠟⠁⠐⢸⠟⡔⣡⣼⣔⠁⠂⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣻⣧⣶⣶⣭⣾⣿⠟⠑
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⢠⣶⠟⣡⣿⣿⠏⠀⠀⠀⠀⣁⣼⡁⠍⣥⣡⣬⢲⣆⠀⢠⣿⣿⣿⣿⡿⢿⡉⠋⢉⡽⢿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢠⣾⢿⣾⡟⢡⣾⣿⡟⠁⠀⠀⠀⠰⣊⣿⣿⣟⣽⣿⣿⣿⡿⣿⡳⡾⢿⣿⡋⠉⢶⣄⠹⠆⠸⣧⡈⢙⡭⠋
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠋⣴⣿⡿⠋⠀⠐⠒⠒⠒⢺⡿⠿⠟⠛⠉⠛⠛⡛⠚⣛⣻⣧⠀⠙⣇⠀⢈⡿⢈⡇⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⣿⡟⢣⣾⡿⠋⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⡆⢠⡏⠀⣸⠇⢸⠁
⠀⠀⠀⠀⠀⠀⠀⢿⠴⠛⠁⠀⠀⠀⣀⣀⣀⣀⠀⠁⠀⣤⡀⣰⠄⣤⠀⣶⣶⣿⣿⣿⣿⠃⢸⠇⢠⡅⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠛⠙⢉⠉⠛⠻⣿⣿⡿⠀⠀⠀⠀⠀⠙⢿⣯⢻⣿⠟⢠⠟⠀⡸⠁⠀⠁
⠀⠀⠀⠀⠀⠀⢀⣴⣩⣥⣶⣶⣶⣶⣷⣿⣿⣿⣿⠿⠛⠁⢠⣀⣠⡤⡲⠏⠘⡿⠟⠉⡴⠋⠀⠀⠁
⠀⠀⠀⣤⢀⠀⠟⣉⢉⡁⠠⠄⠻⠭⠬⠛⠛⠋⠁⢀⣤⣿⣿⣿⣿⡟⠷⠎⣸⠃⠀⠃
⠀⠄⠀⢿⣄⣁⠈⠁⣀⢀⢀⣀⣄⣤⣤⣤⣤⣤⣶⣿⣿⣿⣿⡿⢃⢁⣠⠞⠁
⠀⠁⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⡽⠧⠴⠚⠉
⠀⠀⠀⠀⠈⠛⠟⣻⢿⣿⣿⣿⣿⣿⣻⡛⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣀⠠⢄⡀⠀⡀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠻⠛⢉⠙⠳⣿⣾⠟⠁⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢂⣴⠟⡩⠄⠒⢿⣷⣿⣿⡯⢅⡈⢀
⠀⠀⠀⠀⡀⠀⢠⠆⢀⡀⠀⠟⡙⠡⡈⢀⣾⡾⣿⡿⣟⢶⣄⠻⣬⡀
⠀⠀⣀⣤⣼⣿⣿⡿⢦⣤⠀⢀⠊⢰⣷⣿⢿⢳⡟⢧⠸⡖⢿⣷
⠀⢰⠏⢠⢈⣼⠻⢵⣎⢿⣦⡆⠐⡿⢫⡟⣼⣼⠀⠈⠀⡰⠮⣿⠆
⠀⠘⠀⠀⢸⣿⡘⠘⠏⠀⠋⠈⠀⢠⡟⠀⠃⠸⠀⠀⠈⠀⠀⢸⠂
⠀⠀⠀⠀⠈⠘⣷⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠻⢆⠀⡀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⠈⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⢀⣀⣀⢀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡏⡇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⢀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢰⢣⠀⢀⣀⠈⣀⣋⣈⣉⡉⣋⠀⡀⣋⣈⣉⣃⡉⣁⣙⠈⢛⣉⣉⣐⣠⡀
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢸⢸⠀⠀⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⣿⠟⠛⠛⠛⠉⠙⠙⠋⠉⠉⠁
⠀⠀⠠⠀⠀⠀⢸⡧⠀⠀⣾⢸⠀⠀⢀⡄⢀⡠⢀⢄⠀⠀⠀⠀⢠⡏⠠⠠⠤⠀⠀⡀⠀⠀⠀⠄⡠⠀⠄⠀⠀⠄⠀⢤⢀⡄⠄
⠀⠀⠐⢠⠄⠀⢸⡇⠐⠄⣗⢸⠴⣞⣂⣐⣭⡭⠤⢒⡀⠈⣁⣀⡹⡇⠍⣉⣩⣤⠤⠀⣀⣈⠉⠧⠄⠒⠒⣛⣩⣤⡒⢒⣠⣤
⠀⠀⠐⠒⠒⠀⢻⡟⠛⠛⡟⢸⠃⠀⠒⠒⠀⠉⠓⠣⡈⠉⢂⠬⠽⣧⣴⣶⣾⣿⣭⣍⣽⣷⣶⠶⠶⠖⠈⠉⠛⠓⠠⠤⠤⠦⠄
⠀⠀⠀⠀⠀⠢⣜⠃⠀⠀⢡⢸⡀⠀⠀⠀⠀⠀⠀⠀⢣⠠⠀⠚⢡⡟⢦⡀⠈⢆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣸⣧⡦⠀⠀⠀⠀⠀⠀⠀⣣⣄⣘⣯⡇⠈⣷⠹⡞⣮⡁⡀⠔⠚⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠘⠛⠛⠋⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠉⠙⡇⠐⢺⣧⣼⣾⣿⣶⠞⠋⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠠⡤⠀⠀⠧⠀⠉⠀⠀⠈⠙⠉⠒⠲⢤⣼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠁⠀⢤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠀⠀⠀⠀⠀⡜⠀⡀⠀⠑⠀⠀⠀⢀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠄⠁⠠⡈⠐⢄⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠄⠀⢬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠠⢠⠀⡀⡆⠀⠀⠀⠀⠰⢄⠀⠀⠈⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠑⠌⠀⡠⠁⠀⠓⠀⠀⠀⠁⠀⠡⡐⠀⠀⠀⠘⠄⠠⠊⠀⠀⠀⠀⡐⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠠⠀⠀⠦⠀⠒⠈⠂⠘⡡⠀⠀⠀⠀⠌⠢⡀⠀⠀⢈⠢⡁⠀⠁⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⡐⠈⠃⠢⡀⠀⠀⠀⠀⣀⠀⠀⠀⡞⠀⠀⢻⠀⡄⠠⠀⡀⠀⠐⠀⢀⠀⡠⠌⠢⡀⠚⡘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⠀⠀⠈⠢⢀⠁⢦⠏⢦⡀⡙⠀⠀⠀⢸⠀⢰⠁⠨⡝⡆⠀⠀⠀⢨⡆⠊⠁⠀⡀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠉⠀⠙⡀⠶⠀⠀⠑⡇⠀⠀⠀⢸⡀⠀⠀⡜⠀⢸⠀⠞⣀⡜⠀⣄⠀⠀⠀⠁⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠊⡤⡁⠀⢸⠀⠀⠀⠙⠀⠀⠀⠘⡄⠀⠼⠁⠀⢸⢀⠀⠌⠠⠀⡸⠀⠀⡀⠀⠁⢰⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⡇⠈⠓⢼⡀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠁⠀⠀⢸⠁⠂⠀⠀⡰⠃⠀⠀⠐⠒⠒⠂⠂⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢱⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠀⠘⢦⠀⠀⢰⠃⡞⠔⡮⢻⠅⡤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠈⠂⡠⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⢠⠖⠋⢀⠞⢀⠈⠐⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⡀⠉⢀⠀⠀⠀⠀⠰⠄⠀⠴⠀⠀⠀⠀⠀⠀⡠⠇⢤⠀⠀⠘⠃⠄⠀⠊⢀⠟⠐⡠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣠⣨⣅⡂⠀⠀⠐⠀⠀⠄⡙⠠⠀⠂⠖⡄⠀⢀⠀⠁⠠⠔⡂⠀⠀⢀⠤⠶⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠠⡦⢷⣒⣒⠒⠈⣉⣭⡤⠐⠒⠂⠀⠀⣠⣀⣀⢁⡀⣴⢡⢄⣱⡀⠤⢄⣀⡀⠀⠀⠴⣾⢾⣶⣶⠄⡀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⢯⣧⣩⣯⣭⡤⢾⣁⡇⣀⣽⣤⡾⠿⡏⠑⣢⠈⣹⠇⡧⢅⡄⠀⢿⡆⠄⠽⠄⡷⠂⠀⢠⣤⡯⣖⣛⣐⣨⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠑⠒⠚⠛⠋⠉⠁⠚⢻⣧⠼⠫⠁⠻⣄⣡⣠⣞⡛⢦⣖⣸⣛⡛⠳⠾⠾⠤⠟⠉⠉⠉⠉⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⡿⠖⠾⢿⡖⢤⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡿
⣿⣿⣿⣿⣿⣿⣿⣿⣍⣿⣿⣿⣿⣷⣶⣶⡤⣾⠤⣶⡷⠀⠗⠀⣲⣿⣿⣿⣿⣷⣿⣿⣿⣿⣉⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣨⣿⣭⠿⠿⠟⠃⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣿⣿⣿⡏⣥⣀⠀⠀⠨⠰⠀⠀⠀⠈⠙⢯⡿⢽⣟⣿⣿⡿⠿⠿⠿⠿⠟⠃⠋⠘⠋⠉⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣯⣁⠀⡐⢩⠑⠉⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣶⣶⣿
⠿⠿⠘⠛⠉⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣯⣿
⠯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⣀⣀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣴⣶⣶⣾⢿⡿⢻⢿⣿⡛⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣤⣤⣤⣀⣄⣠⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣶⣿⣿⣿⣿⣿⣿⣧⣞⣷⠾⢿⠁⣇⣰⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣽⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⢿⣿⣿⡿⢻⣿⣿⡿⣿⣿⣿⣿⡟⢿⡿⣿⣿⣿⣿⣿⢿⣿⣿⣟⠋⡛⠋⠉⠿⠟⢿⣿⣩⣿⣉⡙⠙⣛⠛⠛⠛⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿
⣻⣿⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⠛⠿⠭⣿⣿⣿⣮⠿⣿⡕⠻⡽⣤⣴⣶⣆⣀⣀⠀⠀⠁⣶⣶⡍⠙⠙⠛⠿⢦⣤⡉⣰⠦⠀⠀⠉⣉⠙⠛⠿⠿
⠉⣿⡿⢛⣓⠛⠙⠁⠋⠁⠤⡦⠤⢬⢴⡆⠀⠀⠉⠉⠛⠿⢛⡛⠻⠿⢿⢿⣿⡾⠋⠵⣶⣖⣂⡐⠀⠀⠀⠀⠀⠀⠐⢀⠙⠻⠿⣶⣴⣀
⠈⢉⠙⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⠀⠔⠂⠃⢶⣶⣾⣾⣼⡏⣶⠦⡙⢿⣷⣖⡰⠂⠀⠀⠖⠀⠀⠀⠀⠄⠀⠉⠻⣷⣆⡆⣤
⠀⡀⠀⠈⠁⠀⠀⠀⢀⣠⣤⣴⣶⣶⣿⣿⣿⣟⠥⠔⢊⡏⠀⠀⠄⢝⣋⣭⣼⢟⣩⠎⡠⠤⣿⣿⣿⡿⡜⠃⠁⠀⣀⣴⡆⠀⠀⢰⡤⣀⣼⣷⣉⡉⠁
⠀⡂⠀⠀⠄⢀⠀⠀⠈⠁⠀⠀⠈⠻⣛⣛⡿⢋⣄⡤⠶⠶⠆⠸⣿⣯⣭⣩⣽⢋⠁⢈⣭⣶⣿⡿⠛⣤⣵⣾⣿⡀⢉⡉⠀⠀⠀⠉⠀⠀⢹⡟⠛⠒⠈
⠀⠀⠀⠀⠘⢓⠂⠀⠒⠀⢐⣾⢛⣛⣏⣩⢬⡳⠋⣾⠏⣴⡼⣫⣽⣿⣿⣃⣽⣷⠞⠿⠛⠷⡾⠲⠰⠶⠃⠀⡀⠀⠚⠓⠀⢀⠀⣂⣴⡿⢛⠉⠓⣀⡃
⢀⣠⣈⢉⡙⠛⢋⣬⣥⣾⠗⠲⣿⣶⣶⣛⡛⢿⡿⢟⣉⣿⣿⣿⣿⣍⣹⡶⣇⢀⠀⢀⡀⢈⡈⢤⡔⣂⠰⠐⠆⠀⠐⠛⣡⣤⡾⠋⠭⢛⠛⣻⣭⡈⠆
⠈⠁⠁⠀⣀⣄⡈⠛⠡⣥⡤⠶⢿⣿⣿⣿⣯⣿⣯⢿⣿⣿⢿⣿⣽⣟⠿⠿⠴⠙⢯⡍⢩⣭⠉⡄⠜⠀⠀⠜⢶⣶⣶⢟⡩⣿⢿⣇⣂⣤⣌⢋⢋⣁⡀
⠜⠣⠤⢩⢏⣭⣿⡟⠲⡜⡷⣛⡺⢙⣩⣽⡆⢨⣥⣦⣼⡦⠨⡟⡛⢻⠗⢆⡙⣳⠦⣤⡈⠂⠀⣥⣤⣨⠟⢻⠛⢦⣛⠺⢥⠒⠀⠘⠋⠻⠁⠈⠉⠀⡀
⣀⣂⣄⣀⣤⣑⣚⣀⣙⣂⣐⣒⣃⣼⣯⣛⣛⣟⣛⣛⣋⣐⣁⣐⣀⣒⣂⣀⣀⣀⣀⣀⣁⣸⣂⣙⣉⣐⣀⣀⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠠⡀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠄⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⡎⢠⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠃⠠⠀⠀⠀⠀⢀⠀⠀⠐⠀⣀⠤⠀⠀⢀⠀⠀⠀⠘⠄⠀⡀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠾⠀⠉⠠⠀⠘⠓⠁⠀⠀⡐⠂⠾⡐⢄⡀⠀⢠⡘⠀⠄⢼⣷⡤⠅⢷
⠀⠀⠀⠀⠀⠠⠄⢰⡀⠀⠂⠠⠀⠀⠀⠀⣰⡿⣣⣾⣧⣁⣈⠀⣇⠉⠀⠀⠀⡀⠱⡄⠈
⠀⠀⡆⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⢀⠀⠈⠆⠠⠄
⠀⠀⢳⡀⠀⠈⠛⠿⠿⠷⠾⠲⠶⠶⠶⢶⣶⣒⣛⣛⣛⣛⣛⣉⠉⣿⠀⡸⠃⠀⠀⠀⠀⠂
⠙⠛⣉⣉⣐⣛⣛⣛⣋⣁⠀⠀⠈⠛⠿⠯⠭⢥⣤⠀⠀⠀⠀⠀⠀⢹⡗⠰⠀⠀⠀⢱⠀⠀⠁⠀⠀⣠⡀
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢀⣦⣬⣭⠉⠁⠀⡀⢠⠀⠀⠀⠬⣤⣴⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠀⠘⡉⠀⡀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣧⠀⠀⠀⣿⡇⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠃⢰⡀⠀⠀⠛⠁⠀⠀⢰⡀⠐⠠⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⣄⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡼⠁⠠⠄⠀⠀⠀⠀⠀⠀⠁⠐⢷
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡓⠀⠀⠀⠄⠈⠛⠉⠓⠄⠀⠠⠀⠀⠐⠊⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠽⠿⠿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠐⣀⣀⣤⣤⣶⣦⣀⣀⣀⣓⣠⣤⣤⣤⡀⠀⠀⠶⠿⠿⠛⠛⠉⣉⣀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠿⠿⠿⢿⡿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠆⠀⠉⠉⠙⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠉⠉⠳⠒⠦⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣶⣄⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠘⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠟⢱⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠁⠀⣸⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠁⠀⠀⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣸⠇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡇⠀⠀⠀⢻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⢠⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠁⠀⠀⠀⠀⢻⣿⣿⣦
⠀⠀⠀⠀⠀⢀⣾⣿⠉⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠙⢿⣿⣧⡀
⠀⠀⠀⠀⣰⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣤⡀
⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⠟⠁
⠀⠀⠀⠀⣿⠃⠀⢠⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣄⢀⣄⠀⢁⣤⣄⡀⠀⣤⡀⢠⣄⠀⣤⡀⢠⣄⠈⢩⡍⠁⢀⣤⣀⡀
⠀⠀⠀⢰⡟⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠋⠀⣿⠀⣿⠀⠘⠇⠀⣿⠀⢸⡇⠀⣿⠁⠸⣿⡄⢸⡅⢠⡟⠀⠘⠇
⠀⠀⠀⠸⡇⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⣴⠀⠀⣿⠀⢿⣦⣀⠀⠀⣿⣀⣸⡇⠀⣿⠀⢀⡻⣇⢸⠇⣾⡷⣆⣀⣀
⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠛⠀⠀⣿⠀⠈⠙⢻⣷⠘⣿⠉⢹⡇⠀⣿⠀⠰⡆⢻⣼⡅⢿⡇⠀⢸⡏
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⣆⠀⠀⣿⠀⣿⠀⢸⡇⠀⣿⠀⢰⡇⠘⣿⠀⠸⣇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣛⣃⡀⠀⢐⣟⣀⠛⣳⣖⠁⢀⣿⣆⢸⣷⡀⣿⣇⣸⣧⡀⢹⡀⠀⠙⣳⣞⢿
⣿⣿⡿⠿⣿⡿⠿⠿⡿⣿⠿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣾⣶⣾⣶⣿⣷⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⢠⠇⡄⣰⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡟⠀⣠⠏⠀⠀⢿⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡇⡇⢿⠀⢠⡇⢸⡇⠰⡄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⠀⣼⠃⠀⠘⡀⣿⡇⠘⠀⠀⠉⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⠃⡀⢻⡄⠀⠀⠁⣻⠏⣠⠆⠀⠀⡇⠂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⠀⣧⠈⠇⠀⠀⣰⡏⢰⡏⠀⠀⣼⠃⢸⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡈⡇⠹⢀⢠⠆⠀⢹⡁⢸⠀⠀⢸⡇⢠⠟⢀⡇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠃⢀⠎⠋⠀⠀⢸⠃⠈⠀⠀⣸⣼⡏⠀⡞⠠⠃⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠘⣠⠀⢠⠎⢠⠇⠈⠀⠀⠀⠀⠀⠘⠀⡀⠇⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⢠⡇⠀⡟⠀⣿⠀⠀⠄⠀⠀⠀⠀⠀⠀⠱⠸⡎⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⣧⠀⢁⠀⢹⡄⠀⣷⠀⠀⠀⠀⢀⠀⠀⢠⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠶⠤⠍⠢⠀⢧⡀⠃⢸⡇⠀⢀⠆⣠⠏⢠⢠⠯⠶⠶⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠿⠿⠟⠳⠟⠓⠊⠁⣸⣷⡄⣼⠧⣀⣾⡴⠿⠃⢬⣼⡘⡛⠛⠋⠹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⠆⠀⢠⣄⣀⣤⠖⠋⠀⠉⣹⢁⠀⠘⣿⡀⡀⠀⠀⠈⣝⠻⠷⣶⣤⣶⡗⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢏⣠⣾⠿⠛⠱⠂⡀⠀⢀⣼⡃⠙⠀⠁⠙⠻⣦⣶⠂⠀⠩⢀⢀⠄⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠂⢰⣾⢿⠋⠙⠂⣤⢀⠀⠀⢸⡇⠊⠀⠘⠋⠘⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠋⠀⠈⠠⣴⠀⠘⠁⣈⡴⠉⠳⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⢀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⡦⡀⠀⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⣠⢋⠼⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠰⡄⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠠⡣⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢆⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⢀⡿⢁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠑⣰⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢼⣥⠃⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠰⡄⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠺⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠈⠀⠀⠀⠀⠀⢀⠀⢾⡇⠀⡀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⣇⣠⠒⡎⠁⠀⠀⣔⡁⠀⡔⠛⣦⡄⢠⡶⠛⡄⠀⠀⢶⡄⠀⠑⠦⠤⣀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢛⠀⠈⠂⢠⡞⡟⢀⠎⠀⠸⠿⠀⠸⠟⡄⠈⠆⠀⠈⢻⡽⠀⠁⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠀⢀⣿⣤⠊⠀⢰⠀⠀⠀⠀⠀⠘⡀⠈⣦⠴⣏⣀⢀⣀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⣋⣠⠃⠑⢤⡇⠀⠀⠀⠀⠀⠀⣷⠂⠉⢆⣈⣹⠏⡁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⣹⠟⠦⠤⢼⠣⠀⠀⠀⠀⠀⢀⢻⠦⠀⠞⣯⠃⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡃⠀⠀⠄⣾⠀⠙⠇⠀⠀⠛⠁⢸⡶⠀⠀⢀⣷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠠⡄⠀⠠⠴⣾⠀⠀⠀⠀⠀⠀⠀⢸⠷⠠⢒⠜⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠆⣀⠀⠀⠠⢾⡄⠀⠀⠀⠀⠀⠀⣸⠦⠐⡁⠚⡀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠘⠀⢈⡒⠀⠠⠶⢷⣶⠒⠒⠒⢾⣿⠿⠒⠀⠀⠀⠉⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠐⠀⢸⠁⠀⠈⠁⠀⠀⠀⢰⡿⠦⠌⠉⠿⣿⠀⠀⠀⠀⢀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⡀⠀⠀⠀⢸⣄⣀⡀⠀⣠⣼⠃⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠀⠀⢸⡉⠉⠀⠀⠀⣱⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠂⠀⠀⠘⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠄⠀⠀⠰⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡄⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⣤⣳⣆⡀⢀⣴⣧⡄⠀⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⣠⠂⠀⢹⡈⠉⠁⣘⠁⠀⢢⡀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣄⣀⣀⣧⣄⣠⣇⣀⣠⠼⠛⠚⠁

⠠⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⢠⡤⠄
⣶⣆⣄⠴⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢲⠴⠄⣤⣶⡅⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠈⣿⣧⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠐⠀⢤⣿⠁
⢀⣾⣷⠞⠉⠀⠤⠑⢾⣿⡁⣲⠀⠄⠀⢀⣂⣰⣶⠿⠂⠠⠀⠈⢳⣼⣿⠍⠀⠠⠴⠤⠴⣶⡀⠄
⢈⣿⣟⠁⠀⡀⣀⠀⠀⠙⠻⣽⡄⠀⠀⣻⡿⠗⠚⠁⣀⡄⡀⠀⣹⡿⢿⠉⠀⠀⣀⠀⠉⠓⢿⣷⠀⠀⠀⠐
⣏⣶⣺⣧⣶⡮⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⠀⠁⢨⣶⣶⣿⣶⣠⣿⣾⡦⠀⠀⠀⠀⠀⠈⠁
⣿⠃⢠⣻⠷⢅⢄⢀⢀⠲⣄⠀⠀⠀⠀⠀⣀⠔⢂⢠⢄⣴⣿⣿⣿⠀⣿⡿⣿⠳⢄⢠⡀⠀⠲⣄⠀⠀⠀⠀⠀⠐
⣿⢡⠸⣿⠀⠀⠁⠁⠋⠷⣉⠿⣆⡀⢠⡾⢣⡢⡞⠋⠉⢺⣿⡟⢻⡄⡿⠛⢸⡇⠀⠁⠉⠞⠢⣚⢷⣄⣀⠀⠀⠀⡴⠄
⠁⡸⠒⣯⠀⠀⠀⠀⠀⠀⠉⠈⢈⣷⠏⠀⠀⠀⠀⠀⠀⢀⣿⠀⢸⠀⠁⠀⢸⣇⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠄
⡔⠁⠐⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡔⠀⠀⠸⣿⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⡇⡦⠶⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠤⢸⡇⡄⠀⢀⡧⣿⡧⠀⠀⠀⠀⠀⠀⣀⡀⠄⠀⠀⢀⢠
⣿⢁⢾⡏⠀⠀⠀⡎⠀⡢⢤⡀⠐⡄⢰⢁⠝⠃⣤⣀⣅⠀⠀⢰⣼⡇⡧⠆⠚⡇⠿⡀⠀⢀⢤⠒⠐⡊⠁⣠⠋⡑⠠⣆⣲
⠸⣜⠀⡅⠀⣀⠠⡍⠈⠤⠃⠐⠉⢳⢈⠁⠖⠁⣀⡁⠙⠏⠋⢉⢸⡃⣷⠀⢸⢃⠦⠉⠈⠀⢰⠄⢁⡁⠀⢳⢆⡀⠀⣀⠁
⠀⣿⠀⡇⠷⠀⢀⡄⠀⡧⠀⠘⠁⢀⡃⢴⢁⠀⢈⠀⠐⠆⠀⠉⣹⠀⠶⢨⠃⠎⢕⠀⠉⡁⢨⣇⠀⣠⠠⠞⡼⠧⣀⡆
⡴⡇⠀⡁⠀⡀⠀⠤⠤⠋⠂⠓⠎⠈⢀⠆⠀⠈⠈⠈⠀⠀⠉⠈⣽⡌⠤⠌⢠⠀⠀⠷⠴⠈⠁⠀⢄⣁⠀⡼⢁⣀⡈
⠀⠁⠠⠄⠀⠉⠈⢁⣀⠀⠀⠈⠈⠉⠁⠀⠀⠀⠀⣀⠐⠒⠂⠀⣿⠀⠈⠀⣾⠀⠀⠀⠀⠀⠈⠀⠀⠐⠒⣀⣀⣀⣀
⠀⢀⠈⠦⠁⠀⠀⣐⠂⠀⠀⠀⠀⠉⠀⡀⠐⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⡇⠒⠒⠒⢦⣁⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⡠⠥⠮⠅⠀⠰⢒⣋⠁⣀⡀⣖⡒⠂⠀⠈⠛⠀⠌⠉⠐⠚⠀⣈⠀⢰⠀⠀⠠⠄⠤⠤⠤⢋⠈⠉⠤⡄⠀⠀⠀⠈⠭
⠒⠈⡠⠂⠒⠀⠠⡄⠀⠀⠂⠀⠀⠈⠉⠁⠂⠤⠀⠀⠁⠀⢨⣁⠂⠀⠐⡍⠁⠀⠐⠀⠀⠄⣀⠂⠀⠀⠀⠢⡄⠁⠚⠉⠍
⣉⣁⠀⡃⠠⠀⠂⢁⡀⠠⠤⠬⠀⠂⠂⣈⠀⡀⡀⠀⠄⠀⠀⠂⠨⠉⠅⠚⠀⢀⡢⠀⠀⠔⠁⠀⠀⠀⡄⠐⢁⢀⠠⠐
⠀⠁⠍⢄⡀⠀⠐⢐⠒⠒⠒⠀⡒⠈⠀⠠⠄⣐⣀⠀⠀⠈⢢⠐⠀⠒⠀⠅⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠤⠤⠤⠀⠐⠂
⠀⠠⠀⡘⠂⣀⣀⣐⢒⣈⠭⠥⠭⠩⠭⣐⠬⠁⠀⠰⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠥⢐⠀⠀⠠⠭⠤⠀⢀
⠓⠒⠊⠓⠀⡀⢂⠀⠐⠀⡀⠆⠀⠀⠉⠉⠀⠈⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠚⠐⠚⠒⠒⠒⠒⠒⠒⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣶⢦⣀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣤⣄⡤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⣿⣟⣷⣼⣿⣿⣿⡿⢟⣯⣽⡟⠟⡴⢋⣴⣷⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣛⢷⣶⣿⣿⣿⣿⡿⠋⠑⢋⡽⢛⡅⣠⢿⠟⡉⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠻⠿⣿⡘⣿⡇⡄⠀⠀⠀⢉⡞⠟⢸⣴⣷⣦⣿⡤⠄⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣾⣿⣿⠀⣘⣶⣶⣝⠻⡧⢳⣄⣀⢀⣼⣤⡄⣨⡭⠭⣂⣀⡨⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡄⠀⠽⣿⣿⠀⢷⣆⠛⠛⠛⢛⡭⠀⢰⣶⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷⣤⣤⣶⣾⣷⣤⠙⠿⠶⣟⣫⣴⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠩⢭⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⠉⠁⠀⠀⠀⠀⠀⣠⠴⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣾⣣⣸⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢹⣿⣿⡿⠃⠀⠀⠀⠀⢀⣾⣿⢿⣿⣿⡏⠉⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠈⢿⣿⣧⠀⠀⠀⠀⠀⠈⣿⡇⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣄⠈⠻⣿⣦⡀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣿⡇⠀⠈⢻⣷⣄⠀⠀⠰⠿⣧⣀⠀⠀⠀⢀⣀⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⡇⠀⠀⠀⢿⣿⣷⣦⡀⠀⠀⠉⢿⣿⡟⠋⣉⣤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢸⡇⠀⣦⡄⠈⠿⠟⠙⠻⣷⣤⣤⣾⣟⠳⣌⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣧⠀⣿⡇⠀⠀⠀⠀⠀⠀⠙⢿⢻⡝⢳⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⢷⡙⢦⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣮⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋

⣀⣐⣶⣶⣦⣤⣶⣿⣿⣯⣶⣿⣿⣷⣶⣶⣦⣿⣽⣉⣥⣄⠲⠶⢆⣐⠓⣲⣒⣒⣲⣶⣲⣶⣶⣦⣄⣰⠶⠞⢶⣶⠶⢶⠶⣶⣒⣷⣞⣻⣶⣶⣶⠶⠶
⠒⣒⣚⣛⣍⣭⣭⣭⣭⣿⣶⣶⣶⣿⣿⣿⣷⡶⡶⠶⠾⡿⣿⠟⣻⣿⣿⣿⣿⣯⣭⣿⣿⣿⣿⣿⣶⣷⣶⣿⣿⣿⠿⠿⢿⣿⣿⣿⣶⡿⡿⠭⠿⠿⣛
⡨⠩⠿⣛⣛⠛⠛⢒⣲⡿⣿⣿⣿⣿⠿⠿⣷⣾⣿⢿⣿⣻⣿⣏⣋⡿⠭⠉⠿⣭⣿⠻⠿⠿⣿⣿⣉⠉⠙⠻⠇⠀⡖⠶⠟⠻⠷⠒⠀⠀⠤⠤⠌⠉⠉
⠛⠛⠖⠂⠈⠋⠨⠭⠭⠭⠤⣀⠉⠉⠀⣷⣶⣿⣛⣉⠉⠉⠉⠀⣀⡀⠈⠉⠋⣀⣤⣀⠀⠀⠀⠀⠉⠴⠦⠀⠀⠀⠀⠉⠉
⠿⠆⠀⠀⠀⠀⠀⣀⠀⠀⠠⠶⠶⠶⣤⠀⠀⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⢀⣀⣀⣀⣴⠂
⡀⠀⠀⠐⠀⠀⠀⠀⠉⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠡⠖⠴⠠⢶⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⣀⠊⠁
⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⣿⣿⣷⣦⣄⣠⣀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠂⠀⠀⠀⠀⠀⢀
⢿⣿⠿⠿⠿⣯⣄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣈⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿
⢀⡀⠀⠁⠚⠿⠿⠛⠀⠀⢀⠁⠶⢀⠀⣬⣴⡴⠀⣀⠉⠙⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⢷⣦⣤⡀⠤⠀⣀⠀⠈⠉⠋⢀⣴⣦⣤⣤⣄⠀⠿⠛⠉
⠘⠛⠛⠃⠀⠛⠃⠀⠀⠐⠿⢿⣦⡤⠀⠙⠛⠁⠀⠀⠀⠀⠠⠀⠀⠶⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠼⢷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠓⠠⠶⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠄⠀⢀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠰⠌⠡⠈⠁⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠃⠀⠀⠀⡀⠤⠖⠀⠩⡯⡄⢰⠦⠄⠌⠄⠐⠠⠀⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠐⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⡀⢀⡈⠀⣸⡀⠠⣤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⣇⠙⠀⠀⠂⠈⢨⢲⢑⣁⣀⠀⠀⠡⢠⢪⠀⠀⡀⠌⠿⠗⠠⠨⣗⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠈⠘⠡⣿⢄⡁⠀⠀⠈⠉⢹⣘⠋⢁⣀⡄⠀⠀⠴⠀⢸⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⡿⠻⠆⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⠀⠀⠀⢀
⢀⡄⠀⢠⡾⠛⠁⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠠⠀⠀⣀⠀⠀⠀⣸⠀⠀⢠⣅⠀⠁⠀⣀⣴⡀
⠀⠀⠀⠈⠀⠂⠀⠂⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⢀⡿⠀⢼⢷⠀⡄⢛⠟⠲⠿⠛⠛⣝⢀⠆⡽⠽⢻⡾
⠀⠀⠀⠀⢀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⡉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠠

⠁⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⣿⣶⣶⣾⣷⡀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠟⢋⡄⠀⠀⠀⠀⢲⡴⠋⠀⠀⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⣠⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠘⢃⠀⠿⢿⣿⣿⣦⡾⠁⠀⠀⢠⡶⠋⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠻⣿⣿⡥⢾⠀⢠⣶⡇
⠀⠀⠀⠀⠠⠀⠀⠸⠀⠀⠀⠀⠀⠈⠳⠀⠘⠟⠁⣿⠇⠀⠀⠰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⠀⠀⠀⠀⠀⢀⠀⡀⠈⠙⠻⢿⣧⠀⠀⠀⠀⠀⢠⠀⠀⠉⠉⠙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⣿⣷
⠀⠀⠀⠀⣰⠿⠁⠀⠈⠉⠀⠀⠀⠀⠈⠈⠓⢀⡀⠤⠤⠄⠻⠀⠀⠀⠸⠹⡤⠀⠀⡐⠀⠔⠈⡇⠀⠀⠀⠀⠀⠲⠈⠀⢀⣀⡀⢻⡆
⠀⠀⠀⢠⠏⠈⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⢰⡆⢛⠶⠄⠀⠀⠀⠀⢀⠑⠀⠀⣶⣄⠀⠁⡠⠂⠀⠀⠀⠀⠀⠀⠠⣍⠡⣦⡁⣀
⠀⠀⠂⠈⢢⡈⠛⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠰⠋⣠⡎⠀⠀⠀⠘⢿⡀⡠⠖⣁⡠⣴⠊⠀⠀⠀⠀⠀⠀⠙⢶⣾⣿⣶⣶⠟
⠀⠀⠐⠗⠤⣅⣀⣛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠋⠀⠀⠀⠀⠀⠀⠀⠻⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠉⠛
⠀⠀⠀⠀⠀⠀⠈⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣭⣭⣽⣯⣯⣭⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣽⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⢀⠠⣤⣤⣤⣤⠤⠤⠤⢴⣄⠀⠀⠀⣾⣿⣷⣶⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀⠀⠀⠀⠀⢀⣀⣠⢤⠈⠉⢹⣿⠟⠛⠉⠁⠀⠈⢉⠟⠀⠀⠀⠀⠠⣿⣦⣤⣤⣬⣋⣉⡀⠉⢉
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢻⠁⢹⣷⡢⣤⣀⢠⠂⠀⠀⣼⡤⠴⠞⠋⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠙⠈⠛⠿⢿⣭⣿⣷⡿⠶
⢀⡀⣠⣤⣤⣤⠀⣨⣿⣷⣉⣤⣶⣿⢇⣼⣿⣾⣀⣀⣸⠁⣀⣀⣀⣠⣤⠴⠖⠒⠚⠛⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠸⣷⣬⣿⣿⡇
⢀⣀⠀⣀⡐⣛⣛⣿⣿⣿⠿⠿⠿⠟⠛⠿⠿⣿⣿⣿⣯⣿⣿⣀⡀⢠⡶⣀⡔⠀⠀⠀⢹⣿⣿⣿⡄⢠⠄⣠⣀⠀⠀⣼⡏⠉⠻⢿⣥
⢸⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⠶⠺⠷⢶⣦⣘⣉⠉⠩⢍⣛⡛⠿⢿⣿⢿⣿⣿⣿⣿⡿⠿⠿⢿⠟⠿⠿⠿⣿⣿⣿⣅⣀
⢸⣿⡛⣛⠟⡛⠘⠛⠘⠻⡿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣿⣿⣿⡿⠿⠿⠶⠶⢦⣞⣿⣿⣿⣀⣀⡀⠘⣇⡀⠀⠀⣯⡉⠉⠙⣍⠛⠶⣶
⢠⣤⣤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⢫⣤⣭⢿⣿⣿⣿⣿⣶⣦⣄⣩⣿⠓⠢⠬⣭⣉⡉⣛⠛⠻⠿⠿⢷⣄⣀⠈⣳⣄⡀
⠐⠂⣀⡒⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⠻⠿⠭⠿⣟⡿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠜⢹⣷⣄⣀⠀⠈⠉⠉⠛⠛⠿
⢸⣿⡿⠭⠩⠅⠠⠤⠤⠤⠤⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⡿⣿⡿⣿⣿⣿⣷⣻⣿⣿⣿⣻⣿⣶⣬⣙⢳⣶⡦⣄⣀⡀
⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠠⠀⣤⣥⡴⠶⠿⠿⣿⡷⠼⣿⣿⣿⣯⣥⣎⣻⡿⣿⣿⣿⡿⣿⣿⣷⣶⣭⣿
⠸⠷⠶⠖⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠹⣿⣧⠤⠼⠿⠛⠻⣿⣿⣭⣟⣙⣷⡷⢿⣽⣽⡾⣽⢿⣻
⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠻⠟⠿⠿⠿⠷⠛⢻⡃⠀⠀⠀⠀⣾⣿⣿⣇⣩⣟⣙⣿⣿⣿⢶⣏⣽⣞⣷
⠰⠶⠶⠶⠶⠶⠶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠶⠶⠶⠶⠟⠛⠛⠛⢿⣿⠃⠀⠈⠈⠙⢿⠿⠟⠟
⠐⠒⠒⠀⠀⠀⠀⠐⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⣶⣼⣄⠀⠀⠀⢀⣏⣀⡀⡀
⠘⠓⠀⣀⣠⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡔⠀⠀⠀⠙⠓⢤⠀⠀⠑⢤⣀⣼⣯⣇⣱⡟
⢠⣤⣤⠤⠤⠤⠀⠨⠿⠿⠿⠿⠿⠿⠿⠷⠶⠤⠤⠤⠤⠤⠄⠐⠒⠒⠶⠶⠶⠶⣶⣶⣷⠀⣀⣀⣤⢄⣠⢳⢦⡄⠀⡙⣿⠟⠛⠋
⣴⣴⣤⣤⣤⣤⣤⣤⣤⣤⣥⣤⣤⣤⣴⣶⣶⣶⣿⣭⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣬⣭⣿⣿⣽⣭⣽⣯⣿⣭⣥⣥⣤⣥⣧⣤⣤⣤⣤
⣿⣿⣤⣬⣤⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠚⢿⣿⣶⣦⡀⠀⠀⠀⡀⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⣾⢿⣯⡉⠑⠀⠀⢠⣬⣿⣿⣿⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠂⠙⠂⠀⠀⠀⠙⢻⠻⠋⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⡀⠠⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠙⠃⠀⠀⢀⠀⠀⠀⠀⣄⠐⡔⣼⣷⡤⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⡀⠀⢀⠀⠀⢀⡘⣁⡀⢀⣄⣱⣶⣿⡿⣿⣿⣫⣴⣾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢵⣶⡞⣿⣻⢟⣽⣿⠟⣿⣛⣿⡿⣟⡿⣾⣿⡷⠾⡛⢽
⠷⠟⠒⠀⠉⠁⠉⠀⠀⠈⠁⠉⠉⠙⠛⠛⠛⠛⠛⠋⠉⠉⠛⠛⠋⠙⠉⠋⠉⠉⣉⣉⣉⠍⠩⢉⣩⠥⠖⠒⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣀⣀⣀⣠⡤⠶⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠐⠂
⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠒⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡤⢛⣽⡿⢻⡏⠈⢹⠁⠈⢈⣿⣷⢶⠤⢄⣴⡵⡗⣠⠀⢀⣴⣾⠟⣳⠤⢤⣀
⠀⠀⠀⠀⠀⣠⣺⠟⢿⠋⢡⠀⣡⡀⣼⠀⠀⣾⠟⠁⠊⠁⠀⠈⠀⢿⣟⡷⢉⢙⣈⡴⢯⡄⠀⠈⠑⠢⡀
⠀⠀⠀⠀⢀⡿⠋⡤⣒⣀⠿⣿⣿⢻⡛⣦⣾⠇⠁⠀⠀⠀⠀⠀⢠⠄⠉⠳⢾⠿⡋⠀⠈⢻⣦⣄⠀⢀⡈⠢⡀
⠀⠀⠀⠀⢺⠖⠊⣠⠏⠀⠀⠋⠘⠈⠃⢸⣿⡀⠀⠀⠀⠀⠀⢰⡃⢆⠀⠀⠀⠙⠪⡀⠀⠀⠈⠛⢤⣮⠻⣦⡘⣦
⠀⠀⠀⠀⠀⠓⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢌⣳⡀⠀⠀⠀⠙⢧⣄⡁⠀⢰⢆⣠⣿⣤⣤⠀⠀⠀⠉⠳⣝⣝⢾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⣪⠏⣹⠖⢲⡤⠀⠠⢤⣍⡲⠤⠥⣈⢿⠿⢿⣷⣄⠀⠀⠀⠀⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⠤⣴⣷⣊⢤⢴⣿⠤⠾⡿⡚⠛⠛⢿⡛⠻⡓⠛⢋⣉⣀⣀⣉⣤⣤⡤⠤⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡇⠀⠀⢸⢿⠀⠀⢀⣧⠀⠀⠸⣷⠀⢈⣙⣃⠉⠀⠀⠀⠳⠶⠖⠐⠉⠃⡱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠀⠀⣾⠀⠀⠈⢘⣄⠀⠀⠙⢇⣯⣁⣀⡄⣄⣒⡁⣀⡀⣠⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠙⠒⠆⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣔⣾⡐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠣
⠀⠀⠀⠀⠀⠀⠀⠀⡙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠐⠀⠰
⠀⠀⢢⢸⡆⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡄⡀
⠀⠀⠀⠰⠀⠀⠀⠸⠀⠀⣤⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠙
⠀⠀⠀⠰⠀⠀⠀⠂⠀⠀⠁⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢰
⠂⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠠⡀
⠈⠁⠐⠂⢤⡙⠁⠄⠀⠀⠀⠀⠰⠶⠶⠴⠶⢶⡴⠖⠶⣶⣶⣶⣤⠴⠶⠶⠶⠖⠒⠠⠤⢄⠀⠤⠘⠛⠓
⠀⠁⠀⠀⠏⠀⠀⠂⠀⣀⣉⠀⠀⠀⠀⠀⠀⠉⠂⠀⢀⠙⠀⠠⠤
⠀⡀⠜⠷⣤⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠀⠀⠒⢒⣂⣀⣀
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠈⢀⣀⡀⠀⠀⠀⠈⠋⠉
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠀⠉⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⠛⠀⠀⠀⠀⠀⢐⡦⠄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣞⣃⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻⣁⣀⣀⣀⣀⣈⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⠗⠶⢦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠋⢕⡢⢄⠉⠛⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⡉⠒⢑⣤⠀⠈⠻⢶⡄
⠀⠀⣶⠀⢲⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢾⣿⣿⣶⣄⠀⠙⣦⡀
⠀⢸⣿⠀⢸⣿⡀⠀⠀⠠⡀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⣌⣻⡄
⠀⣿⡗⠀⢸⡿⡇⠀⠀⠀⠈⠢⢄⠙⢆⠀⠀⡀⠀⠀⠀⠀⠀⠈⠙⠛⠛⢻⣿⠋⠑⢦
⢸⡿⢇⠀⣾⠃⡇⠀⠀⠀⠀⠀⠈⠑⢌⢳⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠈⡇
⢸⡇⠘⠀⣿⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠢⣟⢤⣄⣠⣄⣀⠀⠀⠀⠀⠀⣿⣿⣄⣀⡠⢓⠰⣶
⣼⡇⠈⢸⣷⣠⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢿⡆⠹⣯⠖⠻⠿⣦⢄⡀⢠⣿⠿⠉⠉⢡⠟⡄⢸⢧
⣿⡇⠀⢾⣿⡏⠀⠀⠀⠀⠀⠀⠀⣴⡡⠞⢲⣿⣆⠘⢿⡦⣄⡀⠉⠉⣻⣿⡇⠀⢀⣿⠀⢷⠀⣸⡀
⣿⡇⠀⠀⠘⡽⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⢸⡸⣿⠀⠈⠻⣮⠙⠦⣠⣿⡿⠛⠷⣮⣴⠀⠺⡀⣿⡅
⣿⣧⠀⠀⠀⣷⠀⠀⠀⠀⠀⢰⡳⠁⠀⠀⣿⣿⢿⡇⠀⠀⠘⠷⡀⢾⢿⣧⡀⡐⠈⣿⠲⣦⡇⣸⡇
⢹⣿⡀⠀⢰⢳⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⡿⣿⠈⢿⡄⠀⠀⠀⡇⢸⡎⣯⠛⢅⣨⡏⠀⣹⠛⣷⣇⡀
⠈⣿⣿⣷⣮⣦⣠⣤⠀⢀⣮⠃⠀⠀⠀⠀⢻⡹⣧⡌⠑⠶⠶⠚⣰⠟⣰⠋⢳⠀⠹⣄⣼⠏⡘⡾⠀⣙⠳⢤⣄⣤⠔⠛⠶⠂
⠀⠈⠻⣿⠋⠈⠉⠈⢳⣦⣥⣤⣤⣶⣤⣤⣤⣵⣝⠻⢶⣶⡶⢟⣫⡞⠁⠀⢸⡄⠀⠘⠏⡰⣡⠇⣼⠛⠉⠉⠈⠉⠓⠒
⠀⠀⠀⠙⠻⢶⣤⣤⣾⡿⠀⠀⠀⠀⣠⡤⣸⣿⣿⣿⣷⣶⣿⣿⣿⣧⠀⠀⠈⣧⣀⠀⢘⣿⢋⣾⠏
⠀⠀⠀⠀⠀⠀⢀⣽⠿⠿⣿⡿⠟⣿⣗⣛⠿⣿⣽⣿⡄⠈⠛⢿⣮⡻⣧⣄⡀⢘⣿⣷⣾⡧⣿⠃
⠀⠀⠀⠀⠀⢀⡾⠁⠀⠊⢁⣴⠶⣿⠊⠙⢿⡶⢭⣽⣿⣄⠀⠈⢻⣷⣹⣿⣿⣿⣷⣿⣿⢿⠁
⠀⠀⠀⠀⢠⠞⠁⠀⣠⠶⠋⠀⣠⠇⠀⠀⠀⠈⠁⠊⠛⢻⣷⣄⣀⣿⣿⣿⣿⡿⠿⠟⠛⠛⡄
⠀⠀⠀⣴⠋⠀⠀⠀⠋⠀⠀⠀⠋⢀⣤⣀⣠⣶⣶⣾⣿⣿⣿⠿⣿⣿⢟⣽⠋⣠⡔⠂⢉⣴⣿⡆
⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣰⡽⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣫⣿⡩⠔⠚⠁⠠⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣩⣤⠖⠊⠀⢀⣽⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣟⡋⠁⠤⠂⠀⠈⣹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡦⣀⡀⠴⠊⠛⣻⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣯⡠⠔⠊⠙⢙⣷⣦⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣀⣠⣴⡏⠙⢿⣿⣭⡋⠋⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣿⣿⣿⣿⠹⠀⠀⢻⠋⠳⣄⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⣿⡟⣿⣿⠁⠀⠀⢸⡶⠾⠃⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠏⠀⠸⡇⠘⡿⣤⣤⣤⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣴⣾⠿⠛⠃⠈⠉⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣛⣛⣛⣻⣏⣌⣛⣟⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣭⣿⣭⣽⣿⣭⣭⣽

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⢸⣇⠀⠀⢠⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⣿⣀⣴⠟⠁⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡾⡄⠀⢰⠏⢧⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⢀⡞⠀⠹⣤⠏⠀⠘⣇⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⣼⠀⠀⠀⠈⠀⠀⠀⢹⡀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡘⢦⡀⠀⠀⠀⠀⣠⢟⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣟⣛⠻⠶⣦⣤⣀⣀⠀⠉⠛⠻⠿⣷⣶⣶⠿⠿⠛⠉⠀⢀⣀⣤⣴⠶⠟⢛⣛⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠲⠦⣭⣉⡀⠀⠈⠉⠛⠻⠶⣶⣤⣄⣀⠀⢀⣀⣤⣴⠶⠟⠛⠉⠁⠀⠀⣈⣩⡤⠶⢺⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠰⠦⣬⣉⡛⠲⠦⣬⣙⣓⣶⣤⣽⠿⠟⣛⣩⡥⠶⢚⣋⣡⠤⠶⢚⣋⣩⠤⠖⣀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⢶⣬⣭⣿⡶⠶⠟⠛⠉⠀⠐⠚⣋⠉⠀⠀⢈⣉⡅⠀⠀⣛⣩⣥⣶⠾⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢾⣿⣋⣩⠤⠖⢚⣋⣥⠴⠖⠛⠉⠁⠀⢐⣛⣩⣥⣶⡾⠻⠿⣭⣙⣿⡷⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢡⠖⠲⣌⢻⡆⠀⣈⣩⡥⠴⢒⣋⣤⣴⠶⣾⣿⣙⡛⠶⢤⣍⣉⠀⢠⣿⢡⠶⠲⣎⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠹⣤⣠⠟⣸⣇⣈⣭⣴⠶⠟⠛⠉⠁⠀⠀⠀⠈⠉⠛⠻⠶⣶⣭⣁⣘⣷⡸⢦⣠⠞⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⣶⠾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⢶⣶⠾⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠋⠀⠀⠉⠉⢳⣀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠛⠀⣀⣠⠞⠋⠙⢲⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣤⣤⣤⣤⣤⣤⡼⠃⠀⠀⠀⠀⠀⠀⠀⣰⠋⡽⠟⠁⠀⠀⠀⠀⢸⠇⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢿⡀⠙⠒⡶⠒⠒⠒⠒⠒⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢫⡉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠉⣛⠉⠐⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣚⡋⠙⠓⠿⣄⠈⢧⣀⡤⠴⠒⠒⣒⣦⣤⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠲⢤⣘⣆⢸⣧⡶⠒⠾⠯⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⣹⠾⢤⣍⠉⠳⢦⠤⢽⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡼⠁⠀⠀⠈⠙⠲⣌⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠑⡾⠁⠀⡤⠚⠉⣩⣷⡀⠉⠀⣠⠖⠋⣩⣷⡄⠀⠀⢠⠖⠉⢉⡭⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣅⣰⠃⠀⡼⠁⠀⠘⣇⠈⠀⢀⣰⠃⠀⠀⢧⡀⠁⠀⣠⠏⠀⠀⠸⣄⡀⠀⣀⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⡿⠐⠋⠁⠀⠀⠀⠈⠉⠛⠉⠁⠀⢀⠀⠀⠉⠛⠛⠁⢀⣀⣀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠓⠒⡇⠀⠠⠞⠋⣉⣳⡄⠀⠀⢠⠞⠉⢉⠭⣦⠀⠀⢀⡞⠉⢀⡼⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⡇⠀⠀⠀⠀⢇⡈⠁⠀⣠⠏⠀⠀⠹⣄⡀⠀⣠⠞⠀⠀⠘⢦⣀⣀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠦⠤⠴⣇⣀⣀⣀⣀⣀⣉⡛⠋⠁⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠒⠒⠒⠒⠒⠒⠒⠒⣚⣛⣋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢿⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⠶⠶⠶⠦⠤⠴⢶⣟⣉⠉⠉⠉⠉⠉⠉⠉⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠃⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠂⢢⠀⢰⠀⣒⠀⣦⠀⠀⠐⠀⠀⢆⠐⠂⢰⡂⡔⠐⢠⡄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠂⠀⠀⠈⠈⠀⠀⠂⠈⠂⠐⠀⠀⠂⠀⠀⠀⠀⠀⠊⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡄⠀⠀⠀⠀⢀⣴⣿⡏⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡏⠀⠀⠀⠀⢠⣿⣿⣿⠀⢸⣿⣿⣿⣿⠀⠀⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠃⠀⠀⠀⠀⢸⣿⣿⣿⡀⠸⣿⣿⣿⣿⠀⣰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⢹⡇⠀⠀⣄⠀⢸⣿⣿⣿⡇⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⢸⡇⠀⢀⣿⣇⠈⣿⣿⡇⣷⠀⢻⣿⣿⣿⡿⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⣸⠇⠀⣼⣿⣿⠀⢿⣿⢡⡟⠀⢸⣿⣿⡏⠀⢸⡿⢀⣴⣾⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠏⠀⣰⣿⣿⠏⠀⣾⠏⣼⠃⠀⢸⣿⣿⠀⣰⠟⢠⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣾⣿⣿⡟⠀⢰⡟⣸⡏⠀⠀⢸⣿⡟⢰⡏⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠀⣰⡟⢀⣿⠀⠀⠀⣼⣿⠃⣿⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣿⡿⠿⢿⣿⡟⠉⠀⢸⣏⠀⠀⣰⡿⠃⠀⢿⡀⠀⣼⠋⢿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢳⡟⠁⠀⠀⠈⠉⠀⠀⢸⣿⣤⡾⠋⠀⢀⠀⠈⠛⠛⠁⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣟⣼⠁⠀⠀⠀⠀⠀⠀⢀⣾⠟⠋⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⣸⣿⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣿⡈⢧⣀⣀⣿⠈⠀⠀⠀⣠⠀⠀⠀⡾⠁⠀⠀⠀⠀⢰⣆⢻⡆⠀⠀⠀⣰⣿⠿⠿⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢷⡀
⠀⠀⠀⠀⠀⠀⣼⡿⢻⡏⠉⠛⠻⠃⠀⠙⠋⢹⣧⠀⠀⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠘⠃⠀⢀⣴⣿⠃⠀⠀⠀⠠⠶⠶⠖⠒⠒⠒⠂⠀⣀⣸⣇
⠀⠀⠀⠀⠀⢰⡟⠀⡀⣿⠀⠀⠀⠀⠀⠒⠂⠀⠙⢧⡀⠀⢿⡈⣙⣦⡀⠀⠀⠀⠀⣼⣷⡟⢀⣠⣴⣿⠟⠛⠋⠉⣉⣉⣤⣤⣤⠤⠤⠤⠤⠀⠀⠈⢩⡿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠐⠊⠹⣥⣤⣤⣆⣠⣤⣿⣷⣬⣿⣿⣿⣇⠀⠀⣠⡾⢿⣿⣴⣟⠙⠻⢿⣟⠳⢶⣶⣶⣶⣶⣶⣶⣶⣶⣤⠤⠄⠀⠀⣼⠇
⠀⠀⠀⠀⠀⢸⡇⠸⢆⣿⡆⠀⣀⣤⡭⠿⠿⠟⣛⣛⣻⣯⡭⠭⠉⠉⠛⣧⣰⣿⠀⠘⠋⠀⡀⠀⠀⠀⠀⠉⠐⠀⠉⠙⠳⢾⣿⣛⠛⠛⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⢀⣿⣾⣿⣿⠛⠛⠉⠀⠀⠒⠊⠉⠟⠛⠛⠉⠉⠀⠀⠀⠀⠘⣿⡟⢿⣦⣄⡲⣬⡓⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⣨⡽⠿⠶⢦⡀
⠀⠀⠀⠀⢀⡾⠁⠀⠀⠉⢷⣄⠀⠀⣀⣠⣷⠄⠖⠀⠀⢀⣀⡤⠴⠂⢀⡀⣿⣟⠲⠌⠛⠿⣿⡿⠷⣦⣀⠀⠀⠉⠲⡶⣠⡞⡉⠀⠀⠲⣆⢻⡄
⠀⠀⠀⠀⣸⢃⡄⡄⢠⡈⡆⢻⡄⠈⠉⠀⠀⠀⠀⣀⣩⣥⣶⣶⣿⠿⣋⣼⠟⠛⠻⢦⣷⠀⣀⠉⠓⠦⣍⠓⠂⠀⠸⣿⢋⡔⠀⣴⡆⠀⠙⣸⡇
⠀⠀⠀⠀⢻⡌⣧⢓⠀⠇⢹⠸⣇⠀⠀⠀⠀⣂⣭⠵⢒⣫⣽⠶⠟⠛⠉⠁⠀⠀⠀⠀⢹⡀⢣⡿⢶⣄⡲⢤⡀⠀⢰⡏⡾⢁⠀⡼⠃⠀⢠⡿
⠀⠀⠀⠀⠘⣧⢳⡘⠦⠄⡎⢸⡏⠀⠤⠖⣋⣭⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠀⠀⠈⠙⠷⣮⣀⣸⡏⣧⠺⡤⢞⡥⣠⡿⠁
⠀⠀⠀⠀⠀⠙⣧⡓⠄⠈⢀⣾⣥⡴⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣌⣁⣀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠂⠁⠀⠉⢐⡤
⠀⠀⠀⠀⠀⠁⠀⣠⠤⠤⠤⡀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠂⢀⡠⠋⠁
⠀⠀⠀⠀⠀⠀⣞⠁⠀⠂⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂⠠⠀⠘⠀⠀⢀⡷⠋⠀⠉⠀⠀⠀⠉⠐⢤
⠀⠀⠀⠀⡀⠄⠘⠤⣑⣰⡤⠚⠀⡀⠀⠀⢀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣤⠠⠃⠀⠀⠀⠀⠀⣄⢀⠠⠄⠐⠁
⠀⠀⠀⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠢⠀⠓⠂⠊⠓⠀⠠⠔⠳⢤⠤⠄⠒⠂⢰⣼⣆⣊⡠⠢⠔⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠡⠐⠀⠁⠀⡠⣎⣩⠅⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⡠⠓⠉⠀⠀⢸⠦⢐⣳⠀⠀⠀⠠⠤⠄⡰⡩⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡰⠤⠊⠀⠀⠀⠀⠀⠈⠹⡇⠀⣄⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠐⠦⠤⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠐⢭⠄⠚⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇⡀⠴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠒⠂⠀⠠⣀⡠⠰⠀⠂⢄⣠⠄⠠⢜⣶⡒⠈⢁⢀⡠⠄⡀⠀⢀⡠⠀⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠂⠾⡠⠀⠀⠀⠀⠀⠈⠱⡂⠀⠀⠈⠫⠀⠀⠀⣹⣁⠠⢘⣷⠀⠀⡀⠁⠛⠉⠀⠀⠘⡅⠀⠈⠐⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢹⡇⠈⠀⢠⡔⠡⢅⡤
⠀⠀⠀⠀⠀⠀⢀⡖⠉⠁⠒⠈⠉⠀⠀⠀⠀⠀⢀⠉⠁⠀⠀⠀⠀⠀⣀⣀⠤⡤⠄⠀⠤⠀⠚⠕⠂⠀⠘⠒⠄⠘⠁⠀⢀⡀
⠀⡀⠠⠖⠀⠐⠈⠁⠀⠀⠀⠀⢰⠀⠀⠀⠀⠈⠀⠀⢀⡠⠖⠚⡫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠁⠈⠑⢢⡀
⠼⠤⠐⠀⠀⠤⠐⠂⠀⠀⠀⠒⠀⠀⠀⠀⠀⠐⠀⠀⠉⠛⠀⠂⠀⠐⠀⠠⠤⠄⠀⠠⠄⠀⠀⠀⠀⠤⠤⠉⠁⠄⠀⠤⠄⠀⠄⠐⠀⠹⠤
⠀⠈⠈⣀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠂⠀⠂⠀⠀⠀⠀⠂⠒⠒⠒⠀⠀⠀⠂⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠤⠀⠀⠀⠀⠒⠂⠀⠌
⠀⠀⠠⠄⠀⠀⠀⠀⠂⠀⠐⠂⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⡀⠀⠀⠀⠂⠒⠂⠐⠀⠀⠀⠀⢀⠀⠀⠤⠀⠀⠀⠐

⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢾⣿⣼⣿⣻⣟⣩⣿⣾⣀⢴⡿⣿⠯⢀⣩⡐⢺⠦⣿⠙⣽⣾⢻⣟⣹⡯⣿⢻⠤⠦⢀⣶⣂⠤⣤⣤⣄⠀⠃⣶⣴⡄
⠀⠀⠀⠀⠉⠉⠁⠉⠉⠁⠉⠉⠀⠀⣩⣿⣿⡿⠻⠙⢷⣄⡙⠀⣇⣼⡞⣯⣿⣷⣿⣨⣧⡏⠈⠁⠝⡘⣯⡿⢹⠋⢰⢞⢼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⡟⢋⣠⣤⣦⣿⣿⣿⣀⠈⠭⠵⠯⠌⠸⠟⠟⠇⢤⡤⠙⣿⣿⠇⠀⣴⣗⠼⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣫⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⣧⠀⢸⡧⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣯⣿⣻⣿⣿⢟⣻⣿⣿⣷⣯⣷⣶⡀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣼⡇
⠀⠀⠀⠀⢀⡀⣴⢿⣿⣿⣿⣿⣿⣿⡛⠩⡽⠎⠈⠓⠊⠁⠉⠙⢼⡽⠃⢘⣿⡯⣵⠉⢻⣿⣷⣄⡀⠀⠀⠀⠀⠉⠛⣻⡷⠇
⠀⠀⢰⡾⣏⡿⢋⣿⣿⡟⣿⣿⣿⠁⠂⠀⠀⢀⣀⠀⠀⠀⠀⢠⡶⠁⠀⠈⠉⠁⠀⠀⠈⠴⠬⠻⣧⡀⠀⠀⠘⠳⠾⠙⠇
⠀⢠⢤⣷⡽⣤⣿⣿⣿⣴⣿⡿⠉⠀⠀⠀⣀⠜⢿⣦⠙⢷⣤⣸⣿⠳⠤⠀⠀⠀⣀⡔⠀⣀⣤⠴⠒⣬⣶
⠀⢹⡄⢿⣷⣿⣿⣿⣿⡿⣿⡇⠀⠀⠘⠋⣁⡈⠀⠙⠃⠘⠻⠿⠌⠳⣄⠈⠶⠬⠄⡁⠈⠙⢁⣴⢋⠀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠈⣿⣷⠙⣿⣻⣿⣿⣿⣿⣷⣤⠶⣶⣾⣿⣿⣿⣿⣿⣶⣶⣤⣤⣴⣽⣿⣦⣤⣤⣬⣷⣤⣥⣈⣙⣳⢦⡆⠀⠀⠀⣿⣿⠋
⠀⢀⣿⣿⠀⠛⢿⣿⠻⣿⣿⣾⣧⢀⣿⣿⣿⣿⣿⡿⣻⣾⣿⣿⣿⣿⠿⣻⣯⣥⣼⡿⣿⣦⢈⠉⢭⡿⠎⠀⠀⠀⠀⠈⠉
⠀⠈⣽⣿⣧⢀⣠⠙⣷⡌⠛⠚⢿⣿⣿⡇⣾⣿⣿⠷⠾⣫⣾⣿⣿⣿⣿⠿⠋⢉⣿⣿⠇⠀⠀⠀⠄
⠀⠀⠸⣻⣿⣦⡈⢁⣙⠻⣦⣀⠈⠉⢻⡇⢸⣿⣯⡿⠟⣵⣿⡿⢃⣴⣶⣶⠏⢉⠛⠉
⠀⠀⠀⠹⣿⠿⠿⢦⣝⣄⠀⠉⠳⣀⣠⣇⢸⣿⠏⢀⣠⣷⣻⠿⠋⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠸⠟⠙⠋⢂⠰⡶⠾⣿⡧⢿⡇⠀⣰⣶⣦⣤⡤⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠵⣮⠓⠉⠁⢾⡇⠀⠀⠀⠤⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣀⣒⣒⣖⣢⡤⣶⣶⣶⣦⣴⣶⣶⣶⣶⣶⣖⣒⣖⣒⣒⡒⠲⠶⢖⡒⠒⠶⢶⠒⣶⣖⣲⣶⣶⣦⣔⠶⢶⠶⠶⣶⣶⡶⠶⣶⣖⣶⣒⣲⣶⣶⣶⠶⠶
⠒⢒⣚⣛⣉⣛⣯⣭⣭⣽⣷⣶⣶⣿⣷⣿⣿⣺⡷⠶⣿⣿⣿⡟⢻⣏⣘⣛⣛⡉⣭⠿⡿⣿⣿⣿⣿⣿⣶⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣯⠭⠿⠿⣿
⣩⠭⠭⢭⡭⠯⠭⠩⣭⠷⣿⣿⣿⣿⠿⠿⣷⣶⣿⣿⣿⣿⣿⣟⣛⡯⠭⠛⠻⣭⠿⠻⠿⠿⣿⣿⡉⠉⠻⠿⠯⠁⡆⠶⠟⠿⠿⠒⠈⠁⠠⠤⠈⠉⠉
⠖⠒⠷⠒⠐⠋⠈⠩⠭⢭⣄⣀⠉⠙⠀⣦⣼⣿⣛⣋⠉⠉⠙⢂⣀⡀⠈⠋⠛⣀⣀⣀⠀⠀⠀⠈⠉⠤⠦⠀⠀⠀⠀⠙⠃
⠿⠆⠀⠀⠀⠀⠀⣀⠀⠀⠠⠴⠶⢶⣄⡀⠀⠀⠀⠀⠠⠴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠣⠔⡤⢤⢤⡦⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⢀⠀⠁
⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣿⣶⣶⣦⣀⣀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠂⠀⠀⠀⠀⠀⢀
⣿⣿⡿⠿⢿⣯⣀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⠀⠀⠀⢀⣶⣽⣿
⠀⡀⠀⠀⠸⠿⡿⠗⠀⠀⠀⠁⢤⠀⠀⣠⣤⡴⠀⣈⠉⠛⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⢶⣤⣄⡀⡤⠀⡀⠀⠈⠛⠃⢀⣴⣤⣄⣀⣀⠀⠿⠟⠋
⠘⠻⠷⠂⡀⠺⠇⠀⠀⠰⠾⣷⣦⣤⠀⠻⠟⠁⠀⠀⠀⠀⢠⠀⠀⠴⠀⢀⡀⠀⠀⠀⠀⠀⠀⠠⢼⣧⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠆⠠⣦⡄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣙⣛⣒⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⢠⠀⣤⣴⢦⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⡠⢇⢀⣤⣀⣄⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⣰⠶⣿⣿⣿⣫⣥⣤⣄⣀⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠈⠉⠀⠀⠀⠉⠀⠋⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠿⣿⡿⠶⢷⣭⣀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠘⣡⣾⠸⡈⢳⡄⠉⠛⡌⠺⠀⠀⠀⠀⣠⣾⣶⢒⠶⠄⠀⣐⣆⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⣡⣠⢹⣿⡀⠓⢾⡿⣦⠀⠀⠀⠀⠀⠐⣷⣞⣿⣧⡄⠹⢤⣴⢛⣿⣟⢛⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠛⠈⣿⠁⠀⠈⣿⠈⠘⠂⠀⠀⠀⢸⠓⠀⢠⣿⣽⡇⠸⠏⢻⡁⠍⢳⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢦⡈⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠳⢤⣀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠦⣄⡀⠀⠀⠀⠉⠲⣄⡀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⣀⠀⠀⠀⠙⠢⣀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⢀⣀⣠⡀⠀⠀⠀⠀⣀⡇⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⣀⡄⠀⠈⠳⣤⣄⠸⣧
⠀⠀⠀⠀⠀⠐⠒⠛⠛⠓⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢀⣀⠄⠀⠀⠀⢀⡀⠀⠀⠀⠙⣶⣦⠄⠀⠈⢻⣦⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣤⡤⣤⠤⡤⠤⠤⠖⠛⠉⠄⣀⡀⠐⠙⠁⠀⠀⠈⠁⠠⠈⠻⣯⣦⡀⠀⠻⡄
⠀⠀⠀⠀⠒⠒⠒⠂⠈⠉⠉⠉⠉⠉⠁⠀⣀⣀⣀⣀⣀⣀⡀⠀⢀⡠⣤⣤⠴⠾⠋⢹⠀⠀⠀⠀⠀⢀⡤⠤⠐⠘⣿⣷⡀⠀⠁
⠀⠀⠀⠀⠀⠀⣀⠀⢀⣠⣤⠴⢚⣛⣩⣭⣭⣥⣤⣬⣬⣍⣀⣀⣁⣀⣀⣀⣠⠴⠞⠃⠀⠀⡀⠠⠚⠉⠀⠀⠀⠀⠸⣿⣷
⠀⠀⠠⠄⠤⠤⠤⠔⠒⠂⠐⠋⠉⠉⢁⣀⡠⠌⠀⠠⠤⠚⠉⢉⡉⠉⠊⠀⠁⠀⢀⣔⠚⣏⣴⣠⡤⠖⠀⠀⠀⠀⠀⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣉⠥⠀⠀⢀⣀⠀⠄⠀⠐⠋⠀⠀⠀⠀⣀⢴⣧⡶⢞⣼⣃⣀⡏⠁⠂⠀⠀⠀⡀⣸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠀⠠⠖⠊⠉⠀⠀⠈⠀⠀⠀⠀⠠⠂⠉⠁⠋⠚⠃⠀⠉⠀⠉⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢳⣄⠀⠀⠀⠀⠀⠀⢀⡤⢚⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⣿⣾⣾⣿⣿⣿⣶⣤⣤⣾⣍⣴⠋⣀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡱
⠀⠀⢀⣠⣤⣶⡾⢿⣿⢿⣿⠿⠿⣿⡿⡿⢿⢿⡟⣻⣿⡿⣿⢿⢿⡿⣿⣿⣷⣤⣄⣀⣀⠀⠀⠀⣰⠋⣰⠁
⠰⢾⠋⠩⣽⣿⠃⠀⠉⢷⣶⣶⠶⠾⠿⠷⠚⠳⢶⣷⡌⠀⠁⠉⠚⠁⠉⠁⠋⠙⠛⠛⢛⣿⣾⣾⣿⣿⠃
⠲⢦⣧⡶⠈⠁⠀⢀⡄⣾⣸⣄⣀⠄⠒⠒⠒⣈⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠟⠋⠋⠉⠉⠙⣿⠿⢇
⠀⠀⠈⠉⠛⠲⢦⣼⣿⣟⣻⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣤⣶⣶⣶⣾⠿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠈⢣⡈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣟⠿⡿⠛⠛⠛⠛⠋⠉⠉⠉⠙⠯⣉⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢬⣦⣄

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣉⠈⠙⠛⠣⠤⠌⠈⠁⢤⣶⠲⠀⠀⠀⠀⠙⠻⠿⣿⣛⣿⣿⣿⣿⣿⣿⡿⠿
⣿⣿⣿⡿⡿⠋⠉⠙⠛⠛⠛⠛⠛⠃⠀⠀⠠⣤⣄⣀⠀⠀⠀⠐⠖⡀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⠉⠀⠀⠀⠸⠿⠿⠿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⣿⣿⣿
⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣠⠀⠀⠀⠀⠉⠉⢩⣭⠔⢲⣶⣶⣶⠶⠶⠶⣶⡶⣒⣲⣶⣿⣿⣿⣿⣿⣿
⣿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⣻⣷⣤⣤⣤⠤⠤⠤⠐⠒⠒⣊⣀⠀⠀⣠⡀⣾⣯⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿
⣥⣴⣶⣾⣷⣶⣶⣾⣿⣿⣿⣿⢿⣋⣉⣀⣐⠶⠒⠚⠛⠉⢻⡇⠀⠀⣿⡇⣿⣿⣿⣿⣿⣿⣿⣭⣥⠶⢿⣯⣿
⠿⠿⠿⢛⡛⢛⣛⣟⣽⣷⡾⠝⠛⠛⠉⠉⠀⠀⠀⠀⢀⣀⣿⡇⡆⡍⣿⣇⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣾⣿⣿
⣶⣶⠾⠟⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⣿⣿⣀⣀⣤⣴⣿⡏⣿⡇⠃⣦⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣿⣻⣿⣿⣿
⣿⡿⠗⠒⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⡟⣿⣿⣿⣿⣿⣿⣗⣺⣿⣿⣿⣿⣿⣍⣽⣿⣿⣿⣿⡿⣿⣿⣿⣿
⠁⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡿⣿⣯⣿⣟⣹⣻⣤⣾⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⣰⣷⣿⣯⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⢿⢿⣲⣄⣿⣿⣿⣿⣿⠿⠛⠙⠉⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣯⣴⣶⣶⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠈⠉⠁⠉⢉⣻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⣿⣿⣿⣿⣿⡈⠠⢤⣄⡀⣠⣶⠟⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠿⠁⢰⣿⠟⠉⡟⠿⣿⣄⣤⣽⣿⣿⣿⣿⣝⠋⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⣼⡏⠀⠀⡇⠸⢿⡟⢉⣿⣿⣿⣿⣿⡛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡀⠈⠀⠀⠠⡇⠀⢸⠃⣼⠟⡜⣿⠇⠙⢷
⠀⠀⢤⣤⡀⠀⡀⡀⢀⡠⢀⣠⢘⠀⠀⠀⠩⡢⠀⣀⢸⣄⣀⣤⣀⡀⡜⠀⠈
⠀⠀⠛⠚⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠂⠈⠈⠙⠉⠉⡼⠉⠉⠉⢉⠞⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠓⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠋⢱⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠑⠀⠠⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠈⢦⠁⢈⣀⠀⠄⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠈⠁⠈⠀⠀⠀⠂⢨⠀⢁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣬⠐⠀⠐⠀⠠⣢⢠⢁⠀⠀⠢⢠⡾⠀⠉⠠⠿⠇⠄⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠾⢮⡁⠁⠈⠉⠹⣘⠉⣀⡄⠀⠀⠆⠐⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃
⠀⠀⠀⢀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠐⠁⠐⠋⠓⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⣠⡇⢀⠶⣾⣤⣤⡿⡦⠀⡀⣾⣷⣴
⠀⠀⠀⠀⢀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⠉⠉⠀⠀⠁⠘⠚⠀⠀⠀⠀⠙⠀⠈⠁⠈⠋
⠀⠀⠀⠀⠀⠀⣀

⠀⠀⠀⠂
⠀⠀⠀⠂
⣀⣀⣀⣐⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣐⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿