Foodie Emojis & Symbols

⠀⠀⠀⠀⠀⢂⠀⢀⠀⠀⠀⠀⠀⠀⢄⠀⣀
⠀⠀⠀⠀⠄⣁⠊⠈⠆⣀⠀⠀⠀⠀⠀⢀⣸⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠠⡂⢀⠘⣸⠃⠆⠀⢀⠀⠁⠙⠉⠈⠙⠙⣿⣥⡀⠀⠒⠀⠄⠀⠀⢀⡀⠔⠛⠀⠀⠠⣀⣀⡀
⠀⠀⠀⠈⢀⡙⣤⡀⠜⠈⠀⠀⠀⢰⠀⠀⠀⠀⠀⢈⣿⡇⠘⢦⡂⡒⢐⠒⠆⠲⡀⡶⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠁⠈⠃⠁⠀⠀⠀⠀⠠⡀⠀⡀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠉⠙⠚⠓⠛⠊⠉⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣻⣄⢀⣠⣿⣿⡟⠀⠀⠀⠒⡀⣀⠀⠀⠀⡇⠀⠀⠀⠄⠀⢀
⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠿⠛⠁⠀⠀⠁⠀⠀⠀⡆⠀⢠⠁⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠌⠀⠘⣷⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠙⠈⢀⣤⠃⠀⠀⢇⣀⠀⣀⣀⣦⠆
⠀⠀⠀⠀⡀⠀⠠⡏⠀⠀⠀⠀⢋⡀⠀⠀⠀⠹⣶⣶⣾⡟⣰⠀⠀⠀⠀⠀⣸⠆⠀⠀⠀⠙⠛⠛⠋⠁
⠀⠀⠀⠀⢁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠕⠚⠁⠀⠀⠐⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀
⠀⠀⠀⠀⢸⠀⢸⠁⠀⠀⠀⠀⡀⠀⣀⣶⠀⠀⡀⣀⢠⡄⢀⠀⠀⠀⠀⣼⠀⠀⣧⡀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠁⢸⠀⠀⠈⠳⠤⡧⡴⠟⠃⠠⠥⠼⡿⠟⠛⠻⣷⡄⠀⠀⣧⠀⠀⠈⠳⢦⣤⣤⡴⠷⠟⠁
⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠈⠀⠀⠀⢸⡇⠀⠀⢸⡀
⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠇⠀⠀⠀⣀⠀⠐⢄⠀⠀⠀⣠⣠⣼⠇⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠄⣤⡼⠋⠀⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⠀⢠⠆⠀⠀⠀⢀⠀⠀⣠⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣤⣶⣤⣤⣤⡄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⡞⠀⠀⠀⠀⡸⠿⠛⠏⣗⢀⡀
⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⡿⠆⠀⠸⣤⣀⠀⠀⠀⠀⢀⣄⣀⣽⡿
⠀⠀⠀⠀⠀⠈⠙⠉⠉⠉⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⠐⠢⠐⠘⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣄⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠐⠘⠀⠀⠛⠢⠀⠀⠈⠁⠀⠀⠀⠉⢀
⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠄⠀⠀⠀⠘⠘⠀⠈
⠀⠀⠀⠀⠄⠀⣀⣀⠀⠄⠂⠁⠀⠀⠀⠀⠐⠠⢀⡀⢀⠤⠂⠀⠀⠀⠀⡄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠀⠀⠀⠀⠀⠧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠤⠀⠠⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠐⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠂⠠⠄⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠊⠠⡔⠂⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠒⠀⠀⠀⠀⠀⠢⡄⠈⠀⠀⠀⠀⠀⠗⢀⠀⠀⠆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠥⠄⠁⠂⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡆⠀⠁⡀⠀⠘
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁
⠰⢆⠠⠄⠠⠔⠀⠀⠀⠀⢠⠀⠀⠀⠘⡀⠀⠀⠀⠀⠁⠄⠀⠀⠀⠤⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠐⠲⠂⠁⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠂⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠂⠀⠐⠒⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠦⠀⠀⠀⠀⡀⠀⠀⠀⠈⠐⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠄⠀⠀⠘
⡄⠒⠠⡀⢀⡀⠀⠀⠀⠀⠠⠀⠀⠁⠀⡀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠁
⠃⠀⠀⠈⠀⠉⠀⢀⠁⠀⠠⠂⠀⢀⠂⠉⠁⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢐⡄⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠇⠀⠑⠠⠄⠀⠤⠘⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠄⡈⠣⡙⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠠⠍⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⣀⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠐⠣⠄⠀⠀⠀⠀⠀⠐⠀⣀⣑⡎⠀⠀⠀⠀⠀⢀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐
⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⠀⠀⠉⠙⠒⠄⠁⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⣂⣄⣠⠴

⠀⠣⠀⠀⠀⠀⡠⠒⠉⠁⠀⠈⠀⠠⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠃⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠂⠁⠀⠁⠀⠁⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠙⢦⣀⠀⣀⣀⡴⠂⠀⠀⠀⠀⢁
⠐⡀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠈⠢⢀⠀⠀⠉⠢⠤⢀⣀⠀⠀⠔⡣⠒⠒⠒⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸
⠄⢀⡠⠊⠁⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸
⠰⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢀⠀⠐⠠⠄⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠠⢄⡀⠀⡠⠂
⠀⠈⠀⠀⢀⡠⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠔⠁⠀⠀⠈⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠠⠁⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢀⣠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠬⠥⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠦⢠⡴⠶⣦⡀⣠⡶⠶⣤⠀⣶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠂⢿⡀⠀⢸⡇⣿⠀⠀⣸⠇⣿⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠈⠛⠛⠋⠀⠈⠛⠛⠋⠀⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⣾⡄⢠⠞⠓⠀⣦⠆⢠⠞⣓⡂⣾⣳⢠⠞⠓⡆⢶⢰⠆⡷⣄⡆⣾⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠋⠘⠉⠙⠈⠓⠚⠀⠋⠓⠈⠓⠚⠁⠉⠑⠈⠓⠚⠁⠙⠚⠀⠃⠘⠃⠛⠚⠁

⠀⢀⣀⣀⡀
⠑⡈⠶⠆⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠖
⠄⢰⠸⠀⢸⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡠⠂⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠚⠁⠀⠀⢄
⠀⠀⡠⠀⠐⢦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠑⠐⠢⠄⣀⠉⠂⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠀⢀⠀⠀⠀⣀
⠒⠈⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡠⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠢⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠀⣀⠠⢔⡡⠒⠀⠀⠁⠒⠢⢄⠀⠀⠈⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠇⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠂⠀⠀⣠⠖⠛⠛⠛⠶⣄⠀⠀⡴⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢰⡆⠐⠀⠀⠀⡅⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⢧⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡄⠘⡀⠈⠂⠄⣀⠀⠀⢀⡠⠔⠁⠀⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣤
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠙⠲⢤⡟⠀⢸⠇
⠀⠀⠀⠀⠀⠀⣠⠟⡧⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⣀⣠⠴⢾⣁⣀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⣀⣀⣤⠖⠛⠛⣆
⠀⠀⠀⢀⣶⡈⠉⢻⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣸⠁⣠⠖⠺⣅⣛⢳⡿⣆⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠉⣉⣀⡀⠀⠀⢿
⠀⠀⣤⣏⣤⠟⠉⠙⢷⣄⠀⠀⠀⠉⠓⠶⠤⣤⢶⠀⠀⠀⢠⣧⣯⡞⡿⠛⠙⢯⣹⠏⠀⢹⡀⠀⠀⠀⠀⠀⠈⠳⣦⠀⢠⠞⠉⠈⠉⢳⡄⠈⠳⢤⡀
⠀⠀⠀⠀⢹⡄⠀⠀⠀⠉⠳⢦⣤⣀⣀⣀⡤⠿⣼⠀⠀⠀⠘⡇⠉⠙⢛⠒⠒⣿⠃⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⣠⠞⠀⢺⡀⠀⠀⠀⢸⡇⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠈⠉⠙⠛⢦⠶⡆⠀⠀⠀⠀⠹⡄⠀⠉⠀⡼⠁⠈⠀⠀⠀⠸⡆⠀⠀⠀⠀⡞⠁⠀⠀⠀⠓⠦⠤⠶⠋⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣤⣤⣤⣤⠴⢿⣸⠇⠀⠀⠀⠀⠀⠙⣆⢀⡾⠁⠀⠀⠘⠃⠀⠀⢻⡀⠀⠀⠘⣇⠀⠀⠀⢀⣠⣤⣤⣤⣀⡀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠈⣿⠁⠀⠀⠀⢀⠀⠀⠀⠈⣧⠀⠀⠀⠈⠛⠒⠛⠉⠀⠀⠀⠀⠈⠉⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⡄⠀⠈⠁⠀⠘⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠈⢳⣄⠀⠀⠄⣀⣤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⣩⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢯⣭⡇⠀⠀⠈⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⢀⣄⣴⠓⢶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠻⡄⠀⠀⠀⠀⣴⠂⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠻⣄⣽⢾⣄⣽⣴⠻⣦⢶⡀
⠀⠀⠀⠀⣀⣀⣀⣀⣀⣾⣼⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⢠⡶⠧⠤⠽⢶⡄⠀⠸⡇⢺⠁⠀⠀⠀⣠⣾⠟⠀⠀⢠⡶⠤⣽⣃⣠⠟⡇⣸⣆⠈⢷⡃
⠀⠀⠀⠼⣧⡤⠤⠤⠤⠤⠴⠶⠶⠶⢶⡾⠇⠀⠀⠀⠀⠀⣸⠶⠶⠶⠶⠾⣇⡀⠀⣿⠘⢡⡟⠙⠻⣿⠁⠀⠀⠀⠘⠓⠒⣦⡉⠻⣼⡇⣿⠙⣆⠈⢳⣀
⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠈⢳⠀⣩⡤⢬⣷⣄⣈⡿⠀⠀⠀⠀⠀⠰⣶⠿⢷⣤⣬⣷⣧⡼⠿⠖⢛⡏
⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢸⠀⢯⡀⠀⢘⡏⠉⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢰⡟⠛⡻⣿⠳⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⢀⡴⠶⣴⣷⣴⣀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢿⡀⠁⠀⠙⣯⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠚⠛⠛⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⣲⣾⠷⠮⡤⠾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣄⡀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠛⠓⠲⠦⣤⣀
⠀⠀⠀⠀⠀⣰⡯⠶⠓⠶⢭⣉⢿⣩⣽⣇⣀⣀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡤⠶⠖⠒⣖⠶⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣾⣀⡀⢠⡄⠀⠈⠙⠶⣄
⠀⠀⠀⢀⡾⠁⠀⠀⠁⢀⠀⠈⠳⣄⢿⣍⢳⣈⠳⣄⠀⠀⠀⠀⢀⡾⢋⡐⠶⠀⣦⠀⠁⠶⠈⠻⣆⠀⠀⠀⠀⠀⠀⢸⡷⣄⡉⠙⠛⠦⣄⣤⠀⠀⠈⠳⣄
⠀⠀⠀⢸⡇⢀⡀⠀⠀⠈⠀⠠⠄⠈⢧⡈⣿⣩⡗⢹⠀⠀⠀⠀⠸⣇⠛⠀⠀⠀⠠⠴⠀⠀⠚⠃⠸⡇⠀⠀⠀⠀⠀⢸⣧⠉⡷⠀⢘⣂⣀⣙⠳⣴⠞⠀⠘⣧
⠀⠀⠀⠀⠙⢦⡀⠀⠃⠀⠀⠀⠀⠘⠂⢷⠀⣻⣿⢸⠃⠀⠀⠀⠀⣿⣉⣛⣛⡛⠛⢛⣻⣟⣛⢛⣿⣇⠀⠀⠀⠀⠀⢸⠷⠚⢁⡾⣫⣤⢲⢯⣳⣬⠷⠞⠋⠉
⠀⠀⠀⠀⠀⠀⠙⠲⣤⡀⠀⠃⠀⢀⠀⠘⣧⣿⣼⡟⠀⠀⠀⠀⠘⣯⣉⣁⣨⣭⣿⣭⣥⣤⣭⣭⣥⡾⠀⠀⠀⠀⠀⢸⣤⡀⠘⣏⣳⡼⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣈⡀⠀⢻⢡⡞⠀⠀⠀⠀⠀⠀⠘⢯⣉⠀⠀⠀⠉⠛⢶⣄⢀⣴⠃⠀⠀⠀⠀⠀⣿⣠⡽⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠲⠶⠖⠛⠉⠋⠁⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠀⠈⠁⠒⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡘
⠀⠠⣀⡀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⣰⠖⠂⠀⠀⠀⠀⠀⠀⠠⢠⠄⠀⠠⠆
⠀⠀⠈⠀⠀⣠⠴⠉⠀⠀⠀⢀⡀⡈⠀⠠⠤⠒⢀⣰⡾⣍⣉⠜⠀⢂⣻⣄⠄⠀⢀⠀⠀⠀⡀⠘⠁⡠⠀⠀⠀⠀⢀⠀⡀⣣⠋
⠄⠀⠀⠀⠀⠈⢖⢒⣛⣥⡽⠁⠤⠖⠛⠓⠂⠀⣀⠀⠀⠀⠠⠀⠀⠀⠉⠁⠩⠭⠤⠔⠂⠉⠀⠀⠰⡁⠀⢀⡀⡄⠄⠈⣽⠏⠓⡲⠖⠚⠀⠀⢀
⠀⠀⠀⠀⠂⠀⠈⠉⠉⠤⠤⠤⠒⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠐⠀⠀⠨⣟⠓⠂⠈⠀⠀⠀⠆⠀⠨
⠀⠀⠀⢣⠀⠀⠀⠀⠀⠔⠈⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠀⠀⠀⠀⠀⠀⡼
⠓⠄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠐⢦⣀⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠐⠀⣠⠞⠁⠠⠄⠀⠀⠁⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣽⡇⠀⠀⠀⠀⠀⢈⠀⠀⠉
⠀⠀⠀⠀⠒⠛⠖⠂⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠸
⠀⠘⡿⡄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠄⠃
⠀⠀⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⡊
⢀⣠⠌⢉⢻⡖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣂⠄⠀⠀⠀⠀⠀⠘⠰⢒
⠀⠀⠀⠈⡟⢶⡤⠄⠒⠊⠁⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⠔⠀⠀⢂⣤⠖⢃⠀⠀⠁⡨⢶⢀⡄
⠀⠁⠀⠀⠘⣟⠛⠁⠠⠀⠀⠀⠐⠊⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣄⡈⠀⠂⠀⠂⠀⠂⢀⠠⣾⠃⠀⡇⠈⠃
⠀⠁⡆⢀⠀⠘⣟⣀⣐⣃⡀⠀⠀⠀⠀⠀⡇⠀⠀⣀⠄⠤⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⡀⠒⠘⢭⣁⡀⢀⣊⠀⠁⠂⠤⣖⡁⠀⣿⡧⠘⠁
⠂⠐⠁⠀⠀⠀⠘⡝⠋⠀⠀⠀⠰⠀⠀⢀⠇⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⣶⡟⠠⢤⠤⣞⡀⠀⢠⡬⠗⢻⠁⠀⣿⡧⠐⠁⠀⠀⢀⣀
⠤⢄⠀⠐⠂⠰⠀⠙⢄⣀⣀⣀⣈⠀⠀⠁⢠⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⢻⡀⢠⣤⡀⢸⣯⠉⣷⡀⢸⡻⠐⠁⡀
⠀⢸⠂⢀⠀⢀⠔⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⠿⣶⢆⠄⢀⡀⠀⠀⠀⠀⠀⠀⡆⠀⡀⠀⠈⠉⠁⠒⠻⠧⠽⠗⠈⠀⡀⠀⠀⠀⡀⠀⢀⠴⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠦⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠐⠂⡣⠤⠞⠃⠀⢀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⠨⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⡀
⠀⠀⡠⢀⠀⠃⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⢀⢤⠴⠇⠋⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆
⠀⠀⠀⠈⠃⠒⠀⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⣀⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣈⠉⠃⠈⠲⠐⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠀⢀⠀⠄⠂⠀⠒⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠊
⠀⠀⠀⢀⠀⢀⣀⡤⠀⠠⠖⠂⠈⢁⠀⠤⠀⠒⠒⠚⠁⠀⠀⡀⠀⠀⠀⠀⠐⠐⠀⠈⠈⠃⠉⠉⠉⠉⠙
⠀⡀⠀⠀⠑⠀⠠⠄⠰⠶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠁⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀
⠀⢩⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠄⠒⠈⡉⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠔⠉⢀⡂⠀⢸⠀⠀⢨⠁⠀⢀⠀⣄⡠⠄⡄⠤⠈⠡
⠀⠀⠣⣀⡁⠐⠒⠈⠅⠀⠀⠠⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠈⠁⢂⠘⠈⠀⠐⢸⠀⠀⠸⠀⠀⢈⣉⠀⠈⠀⡀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠜⠀⠈⠁⠀⢰⠈⠀⠀⠀⠀⠠⠾⠋⠀⠀⠀⠀⠘⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠄⠀⠈⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠈⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢁⠉⠁⢀⠀⢀⠀⠐⠀⠀⡆⠀⣥⠤⠀⠀⠀⠀⠀⢀⢤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⠀⠀⡀⢤⣤⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠈⡍⠍⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠨⠁⠠⠤⠃⠣⠄⠸⠯
⠀⠀⠀⠀⠀⠀⠀⠀⢲⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠸⠄⢀⣀
⠀⠀⢀⡁⡀⣀⡀⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⡁
⠀⢀⠊⠈⠁⠢⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠄⠀⠐⡂⠀⠀⠀⠀⠀⠚⠀⠀⠰⡄⣈⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠐⠇⠊⠀⠀⠀⠠⠀⠄⠀⠒
⠀⠀⠀⣀⠀⠨⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠄
⠀⢰⡄⠀⡶⢢⠀⡄⡄⠀⢸⠀⠀⠀⠀⠀⠀⠾⢁⣈⠷⠆⠀⣀⠁⠀⠀⠀⠀⠀⠰⠒⠠⠒⠃⠀⠐⡀⠀⠀⠀⠀⡄⠀⠀⠀⢀
⠀⠀⠘⠠⠀⠀⠠⠜⠀⠀⠈⠀⠀⠀⡄⠉⡁⠘⠒⣒⡓⣊⠉⠹⡄⠀⠀⠀⠀⠀⠀⢐⠠⠤⣃⡀⠀⠀⠂⠀⠀⠀⠁⡠⠒⠉⠀⠤⠠⠈⠉⠒⣄
⠀⠀⠀⠐⢤⡂⠐⠀⠀⠀⠀⠀⠀⠀⢱⡜⠥⠲⠷⠈⠇⠭⠆⢠⠇⠀⠀⠀⠀⠀⠁⢃⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⡴⠡⠠⠤⠤⠀⠤⠰⠔⠆⢸
⠀⢠⠀⠀⣈⠑⠀⠀⠀⠀⠊⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⣄⠀⠐⠒⠒⠀⢀⡠⠋
⠀⠘⢀⠀⠀⠀⠀⠈⠰⡀⠂⠀⠀⠀⠀⠀⠀⢄⡀⠀⡀⠇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠂⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠉⠙⠛⠛⠋⠁⣀⡤
⠀⠀⠈⠁⠀⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠄⡀
⠀⠀⢠⢴⡧⠖⠚⡛⣷⠀⠀⠀⢀⠌⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢣⠀⢀⠔⣄⠀⢠⣄⣀⡀⠀⠀⣤⢤⡤
⠀⠀⢸⡄⠁⢁⡀⠤⠸⡆⠀⠘⠀⠀⠀⠀⠀⠀⠱⠑⡀⠀⢀⠔⠲⡒⡀⠀⠀⡆⢹⠀⢇⠀⢸⠀⢘⠿⢿⠂⠀⠀⡆⠀⡆
⠀⠀⠀⡧⠠⠀⢒⣂⠁⣳⠀⠰⣄⠀⠀⠀⠀⠀⢀⡴⠁⡠⠃⢄⡄⠈⢶⡀⠀⢁⠸⡆⠀⡕⡅⠀⢀⢳⠁⠀⠀⢀⠇⠀⢇
⠀⠀⠀⢳⡈⠭⢄⡐⠦⠝⠀⠀⠀⠍⠹⠹⠉⠍⡇⠀⣰⢁⣀⡈⠀⠀⣀⢳⠀⠈⢸⠃⠀⠀⡇⠀⠈⢠⠀⠀⢠⡋⠀⠀⠘⢷
⠀⠀⠀⠈⠊⠀⠒⠂⠁⠁⠀⠀⠀⠺⠈⠙⠛⠋⠇⠀⠈⠉⠉⠉⠉⠉⣉⣁⣀⣀⣀⣋⣀⣉⣁⣀⣈⣁⠀⠀⢠⠀⣉⡀⠈⠈
⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠈⠒⢲⣲⡒⠒⠒⢒⣖⡖⠒⠒⠒⠁⠀⢸⡀⣊⣈⣀⢀
⠀⠀⠀⡔⣡⠔⠂⠁⠐⢌⠢⡀⠀⠀⠀⢀⡔⢈⠉⠈⠉⠒⢄⠀⠀⠀⠸⠘⠉⣠⠖⠒⢦⡉⠙⣮⠀⠀⠀⠀⠨⣀⡀⠀⢀⡰
⠀⠀⠈⠘⠔⠒⡄⣀⢀⣀⢡⠡⠀⠀⠐⠑⠁⡎⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⣿⣶⢠⣴⡇⠀⣿⠀⢀⠄⠀⠀⠀⠀⠀⠀⢄⡀
⠀⠀⢀⢸⡀⢀⠇⡣⠿⢝⡜⠠⠀⡤⣦⣤⣤⡄⠐⠒⠒⠒⠒⠚⠢⡄⢰⢀⠀⠈⡷⠒⡏⠁⠀⠿⠀⠸⠼⡆⣷⠲⢷⢸⢈⢼⢃
⠀⠀⠀⠢⠋⠅⣀⣈⡒⢛⠔⢁⣀⡈⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠁⠀⠈⠈⠉⢀⠀⠀⠀⠈⠉⠈⠀⠐⠒⠒⠒⠒⠒⠒⠒⠊⠁
⠀⠀⠀⢸⡸⠁⠐⠀⠀⠀⠠⣟⣒⡨⡆⠀⢀⠔⡒⡒⠒⠈⢕⠌⣇⠀⠀⡏⠀⠤⠀⠐⠃⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠌⠃⠹⠁⠀⣤⠰⠀⠃⠆⠃⣀⠴⡍⠀⠀⢳⠛⠉⣽⣟⡇⠀⠀⢹⠓⣛⡛⣛⠛⡛⢛⢛⠻⣻
⠀⠀⠀⢀⣀⣀⢀⡀⠀⠀⠙⠦⠦⠄⠀⠀⠘⠵⣲⣖⡆⠽⠚⠉⠀⠀⠀⢸⡴⣶⠏⢹⠇⠀⠀⢧⠘⣅⠗⠟⠹⡇⠟⠾⢀⢿
⠀⠀⢰⠧⠤⠄⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠛⠀⠀⠀⠂⠁⠀⠈⠈⠀⠀⠀⠀⠁⠘
⠀⠀⢈⡺⠡⠀⠘⡂⠀⠀⢰⢑⡠⠤⠤⠤⠴⠥⠯⠮⠬⠤⠤⠤⠤⡄⡏⡇⠀⢀⠤⠐⣑⣒⣑⡒⠠⠤⣀⡀⠀⠀⢀⣀⡀
⠀⠀⠘⡔⢄⣀⠰⡱⠀⠀⢸⢸⣈⣉⣉⠉⠉⠉⠋⢹⠉⠉⠉⣉⣉⣁⡇⡇⠀⢨⠢⠉⡇⠆⠀⡂⢉⠢⣤⠛⡂⢠⠇⠀⠘⡆
⠀⠀⠀⠈⠑⣲⠉⠀⠀⠀⢸⢰⠒⠒⡆⡇⠀⠀⡀⢸⠀⠀⢸⢰⠀⠀⡆⡇⠀⢸⡤⣀⡃⠂⠀⠃⡈⠴⠙⢄⡀⠀⢙⠉⠉⡅
⠀⠀⠀⠀⠰⠾⠄⠀⠀⠀⠸⡸⠀⠀⡇⠇⠀⠀⣅⡸⠀⠀⠸⡸⠀⠀⠇⠇⠀⠀⠘⠚⠩⠉⠍⠃⠊⠁⠀⠀⠀⠈⢤⣀⣀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠄⠀⠀⠀⣀⣀⡀⣀⡠⢜⠵⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠠⢄⡢⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠁⠁⠑⠋⠭⠝⠋⠁⠀⠀⠀⢀⠔⡩⠢⠀⠰⠉⠀⠠⢆⠀⠀⠀⠀⠀⠀⠹⣿⣧⠎⠉⠀⠀⠀⠀⠀⠀⡔⢮⣹⠖⢤⡀
⠀⠸⡡⡁⠁⠁⠀⠀⠀⡇⠀⠀⠀⠈⠰⡁⢣⡄⠈⠂⠒⡡⡸⠀⠀⠀⠀⣠⡤⢦⣽⣦⢦⣤⡀⠀⠀⠀⠀⢸⡠⠤⠒⣊⡩⠇
⠀⠀⡱⠕⣂⣀⢀⡠⢮⡀⠀⠀⢄⠘⠂⠘⠒⠃⠀⠀⠁⠚⢁⠄⢠⡤⠼⠿⠿⠿⠿⠿⠿⠿⠷⠤⢤⠀⠀⡗⠐⣋⡉⠥⠔⠃
⠀⠀⠈⠁⠀⠉⠀⠀⠁⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⢀⣄⣠⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣤⠀⣀⡰⢦
⠀⠀⠀⠀⠀⠀⠃⠀⠀⢠⠗⠲⠔⠂⠳⠀⠀⠀⠀⠀⠀⠀⠀⡐⣇⢠⠉⠄⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠖⠀⣔⠉⢂⣸⡭⡤⠖⢈⠅⣠⠋
⠀⢠⣆⣀⣀⡀⢀⣀⣠⣀⡖⠀⠀⠂⢰⠀⠀⠀⠀⠀⠀⠀⠀⠯⠤⠬⠕⠶⠀⠀⠀⠀⠀⠀⠜⢭⡀⢆⣐⠶⠶⠒⠉⠅⡀⢀⣠⠕⢋⣼⠑
⢤⠃⠊⣿⣓⣀⣐⣛⣓⡿⣅⣀⣄⠀⠘⠀⡄⠀⠀⠀⠀⠀⠀⠃⠐⠒⠀⠘⠀⠀⠀⠀⠀⠘⣆⠘⢷⣺⡔⣺⠃⣠⢒⣓⡩⢿⠓⢚⡭⠊⢠
⠀⠈⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠧⠤⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣀⡉⠙⠶⠓⠯⠥⠖⠉⠉⣁⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠒⠒⠛⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⣴⡿⢦⣠⡞⠁⠐⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⢀⡜⢩⡀
⠀⠀⠀⠈⣾⠛⠀⡀⢉⠀⠘⠈⢦⠀⠀⠀⠀⠀⠀⢀⠀⠀⣶⠤⣞⣉⡉⣱⠞⢫⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡟⠝⠓⠈⠋⠢
⠀⠀⠀⢰⣟⡲⠦⠤⠬⠴⠾⠤⣺⣶⠀⠀⠀⠸⡁⠩⣍⡖⣲⠋⠀⠀⢈⢷⣓⡾⠧⣮⠏⡀⠀⠀⠀⠀⠀⢸⣤⣤⣅⣠⣤⣾⡇
⠀⠀⠀⠀⡏⠈⠉⠉⢹⠉⠉⠉⢹⠁⠀⠀⠀⢠⢹⣫⠍⡾⣻⠦⣤⣐⣫⡾⠤⠓⢔⣩⠿⡇⠀⠀⠀⠀⠀⠀⢛⠛⠛⠛⠛⡋
⠀⠀⠀⠀⣇⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⢸⡷⣝⠚⠚⠤⢞⡚⠋⠉⠗⣲⡶⠊⣩⣾⠃⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠄⡇
⠀⠀⠀⠀⠘⣦⣀⠀⢘⠀⢀⣠⠞⠀⠀⠀⠀⠀⠑⣌⠉⠓⠒⠶⢷⡀⢀⡼⠷⠚⢋⡡⠋⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠹⠄
⠀⠀⠀⠀⠀⠈⠫⠭⠭⠭⠭⠏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⠶⢦⣽⣯⠴⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⡀⣸
⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀⣠⠀⢠⣀⣀⡀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋
⠀⠀⣠⠚⢱⠀⠑⣀⣹⣫⣏⣠⣮⢞⣥⡷⠀⠀⠀⠀⠀⠀⠀⣙⡦⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⢰⠃⢁⣌⣵⣷⠛⠁⣤⢸⡍⠁⢺⡀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠀⠁⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠒⠉⠙⠒⢄
⠀⣿⡤⢛⡻⣭⡇⠐⢾⣀⣀⡆⠀⣸⣷⠀⠀⠀⠀⠀⠀⢰⢻⠟⠲⠖⠒⠲⡗⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠀⢈⡀
⠀⣿⢮⣷⣾⣧⣵⣦⣤⣬⣥⣶⣿⡿⣿⠀⠀⠀⠀⠀⠀⢸⠸⡄⠀⠀⠀⢠⠇⡇⠀⠀⠀⠀⢀⣰⠂⠀⠀⠲⠁⠉⠉⠉⠈⠡⠃⠀⠐⣆⡀
⠀⠹⣷⣌⡉⠉⠛⠛⠛⠛⠉⠉⠁⣠⠇⠀⠀⠀⠀⠀⠀⠘⢦⣙⠲⣤⠖⣋⡠⠃⠀⠀⠀⠘⠃⢭⢀⣷⣆⣤⡀⠀⠀⠀⠀⠀⠐⠀⠀⡬
⠀⠀⠈⠳⣍⣙⠒⠂⠀⠀⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣉⣯⡁⠀⠀⠀⠀⠀⠀⠀⠸⣌⣛⣙⣛⣁⣀⣀⣀⣀⣈⣋⣀⡠⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢹⡌⢿⡀⠀⠀⠀⢀⡔⠂⠁⠀⠀⠀⠀⠀⠀⢠⡾⣣⠶⣤⡀⠀⠀⠀⠀⠈⠉
⠀⠀⣀⣠⣄⠁⣤⢀⡀⡄⠀⠀⠂⣤⠤⠄⠐⠀⠀⠀⠀⢸⡀⢸⡧⠈⠣⡄⠀⠠⠉⠶⠀⠀⠀⠂⠀⠀⢀⡰⢿⣜⡱⢶⡌⠀⠀⠀⠀⠀⠀⢀⡴⠶⣤
⠀⠀⠉⠉⠉⠀⠸⠼⠃⠇⠀⠀⠺⠶⠒⠺⠛⠁⠀⠀⠀⠘⡗⠈⠡⠀⣰⠇⠀⠀⠤⠼⠒⠈⠤⠀⠀⠀⠚⢵⢏⣺⡷⠋⠀⠀⠀⠀⠀⠂⠀⢺⣗⣤⠟
⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠖⠛⠁⠀⠀⠀⠀⠀⠀⠤⠒⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⠰⣦⠙⠃⢰⠀⠀⠀⠛⠿⣿⡿⠛⠁⠀⠀⠀⠃⣀⠈⠓⢄⣤⠀⠀⠀⢠⣿⣿⣿⣿⠷
⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⢞⠁⣽⠆⠉⠀⠀⠀⠀⠛⠇⠀⢀⠴⠋⠀⠀⠀⠄⠀⠀⠀⠀⣀⠀⠀⢠⣴⠏⢠⣤⠀⠙⠃⠀⠀⠀⠀⢠⠙⠃
⠀⠀⠀⠀⡀⠻⠀⠀⠀⠀⠀⠧⠀⢠⣠⡤⠀⠁⠀⠀⠠⠄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠃⠀⠙⣁⣠⣤⣤⣤⡀
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠰⠀⢀⠀⠀⠀⠀⠀⠀⣦⠤⡤⠀⠀⠀⠀⠀⠙⠇⢠⣄⠀⠀⠀⠀⠀⠀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⢘⠛⠛⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⡉⠀⠀⠈⠀⣀⠀⠐⢦⡀⠀⠛⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⠀⠐⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⡷
⠀⠀⠀⠀⠀⢾⡧⣴⠄⠀⠀⠧⠀⠁⠀⠈⠀⠀⠛⠀⠀⠀⠁⠀⠊⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⡆⠀⠀⠀⠒⠃⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉
⠀⠀⠀⠀⠀⠘⢷⠜⠃⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠘⠘⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣄
⠀⠀⢀⣴⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⡀⠀⠉⠟⡄⠀⠀⠀⠀⢰⠄⠸⣀⡴⠆⠀⡀⠀⠀⢄⠀⢰⠀⠀⠀⢠⣴⣶⣶⣶⡤⣄⡀
⠀⠀⠀⠀⠀⠀⣃⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⡇⠀⠠⣠⡁⣠⡤⠘⠋⠀⠀⢈⡁⢀⠀⠀⠀⠀⠀⠀⠀⠸⢄⠀⠉⢀⡰⠶⠃
⠀⠀⠆⠀⠀⠀⠏⠀⠀⠀⠀⠀⠈⠀⠀⢸⠁⠀⠀⠀⠀⠈⠁⠈⠈⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⣩⡁⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣶⡗⠀⠀⠰⠟⠆⠀⠀⢀⠀⠀⠀⠀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢤⠄⢨⠀⡀⠚⠁⠀⠀⢀⠀⠀⠈⠁⠀⠠⠀⠀⠀⠀⠈⠀⢀⠟⠀⠀⠀⠂⢀⠐⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣟⣠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠠⠞⠁⠀⠀⠀⠀⠀⠐⢣⠀⠈⠒⠂⠀⠀⠀⠀⠠⢠⡄⢠⣄⢹⡆
⠀⠀⠀⠀⠀⠀⠠⠘⠃⠀⠀⠀⠀⠟⠋⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠯⠜⠃
⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⢠⣴⠶⠿⣷⣶⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣤⣦⠀⠀⢠⣶⡄⠀⠀⠀⢦⠀⠘⢇⠀⠀⠀⠀⠀⢀⣤⣤⣠⡄⠠⠶
⠀⠱⣤⣤⣄⣄⣰⣤⠆⠀⠀⠙⢿⣤⣿⣦⡼⠇⠀⠀⡀⠀⠋⠉⠃⠀⠀⠀⠠⠀⠀⡀⠀⡀⠀⠰⠀⠀⠸⠃⡰⣿⡟⢶⡏⠓⣤⠀⢿⠯⣍⡼⠇
⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠴⠶⠋⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠂⠈⢱⣏⣠⠼⠷⠞⠁⠀⠀⠀⠈⠁

⠀⠀⠀⢀⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠈⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡤⣤⡤⠀⠀⠀⠀⠘⠿⣿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢿⡄⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⣄⠀⠀⠀⠀⠀⠐⠀⡈⠀⠀⠀⠀⠀⠀⠀⠻⠷⠀⠀⠀⠀⠀⠆⣠⠆⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢲⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠺⠀⠀⠠⠀⠀⠀⠈⠻⠶⠶⠶⠟⠁
⠀⠀⠀⠀⣀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠐⠂⠠⠀⠀⢑⠀⠀⠀⠀⠀⠀⣀⣀⡠⠄⠀⠀⠀⢠⣬⡑⠢⣄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣾⣦⠄⠀⠄
⠀⠀⠀⠼⠃⣀⠴⢟⠀⠀⠠⠖⠐⠒⠀⠈⠆⠀⠀⠀⢴⣬⣿⣷⣤⡈⠀⠀⠀⠀⠀⣰⡀⠊⣱⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠰⡶⠒⠶⠐⠿
⠀⠀⠀⠲⠀⠙⢄⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣬⠋⣹⡄⢣⡷⠀⠀⠀⠀⠂⠙⠁⡟⠁⠀⠀⠀⠘⠛⢃⣀⡄⢶⡄⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠐⢠⣤⣤⣀⡀⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠐⠖⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⢱⡄⠀⠀⠀⠀⣀⣤⣴⠾⠟⠂⢀⠀⠀⡤⠈⠀⡀⠺⠆⠀⠀⠀⠀⠘⠛⠛⠂⠀⡄⠀⠀⠀⢈⠛⡀⠀⠰⣺⠉⣧
⠀⠀⠀⢶⣿⠿⠃⠀⠀⠀⠀⠃⠀⠀⠀⠁⠀⠀⠀⣶⠟⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⠦⣿⡶⠀⠀⠀⢄⣠⡀⣀⣸⣀⡲⠐⠀⠀⠀⠀⢀⡀⠀⠀⢑⠊⠁
⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠇⠐⠋⠀⠀⠀⠀⣼⡿⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠺⢀⢈

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⡛⠏⠙⢻⡋⠉⡟⠛⢻⡙⠏⣙⡿⢛⡋⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣿⣿⣷⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡀⣤⠀⠀⠀⠀⠀⡐⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢪⢧⡀⡇⠀⠀⠆⠡⠀⠁⢀⠀⠀⠀⠀⠄⠈⠀⠀⢀⠀⠀⠀⠀⠀⢀⠰⣬⠶⣂⡀⠀⠀⠀⠉⠁⡒⣷⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⢀
⠀⠠⠂⡠⢁⠆⢵⠃⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠅⢀⢀⠀⠀⠀⠐⠀⠀⠀⠨⠑⢆⡃⣩⠶⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨
⢀⡀⢊⠔⠀⢠⠎⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠜⠃⠘⡣⠀⠀⠀⠀⠀⠀⠀⠀⠁
⢸⡤⠁⡤⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠈⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠊⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣰⣿⢻⡟⠄⠀⠀⠀⠀⠀⠀⠀⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠐⠒⠠⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠸⣿⣿⣷⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡄⠀⠀⠀⢰⣦⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠷⠇⠆⠀⠀⠀⢀⠅⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠆⠀⠆⠀⠀⠀⠁⠀⠀⠀⠋⠀⠀⢀⣀⡀
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠄⠀⠀⠀⠀⠴⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠺⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠨⠅⠈⠀⠀⠀⠀⠀⠀⢀⢂⡄⠀⠀⠀⢀⠒⠑⢄
⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⡁⠀⠀⠀⠀⠀⢦⠆⠀⠀⠀⠐⠛⠀⠐⠀⠀⠀⠀⠐
⠀⠀⠈⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠂⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠔⠀⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⢀⠠⠀⠈⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠂⢤
⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠑⠀⠀⠀⠀⠀⠀⠀⠈⠀⠚⠀⠈
⠀⠀⠀⠀⡄⠀⠰⢄⠀⠀⠀⠀⠀⠥⠀⠁⠀⠀⠀⢀⡀⠸⡧⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠈⠒⠂⠀⠀⠀⣀⠄⣬⠇
⠀⠀⠀⠰⠇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠤⠿⣿⣻⣶⡝⢪⢁⢄⠀⠀⠀⠀⠀⠀⠈⠑⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠡
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⡀⠀⠀⠈⠁⠀⠀⠘⠛⣋⣽⢤⣾⣩⣌⠑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠸⡣
⠀⠀⠀⠐⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⡀⠄⠀⠀⠀⠀⠙⠀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠈⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡾⠛⣁⣴⠿
⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⢀⢀⠀⠀⡠⠘⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠾⡫⠋⠁⠐
⠀⠀⠀⠀⠀⠀⠸⣦⣀⣀⣒⡀⠀⠐⠛⠠⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣠⡴⣶⣦⣶⣦⠦⡀
⠀⠀⠀⠀⠀⠀⢀⠏⠉⠾⠉⠻⠝⡏⣩⣗⣜⢩⠗⠀⠀⠀⠀⠀⠀⠀⠙⡛⠉⠸⠛⠈⠙⠏
⠀⠀⠀⠀⠀⡐⠉⠀⠀⠀⠀⠀⠀⢡⠎⠀⠀⠁⠊⠀⠀⠀⠀⠀⢀⡶⠞⠃⣠⣾⠿⠋⣰⡾⠓⠐
⠀⠀⠀⠀⠀⠁⠤⢀⠀⠀⠐⠒⠀⠁⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠨⣤⡶⠟⠋⣀⣴⠾⠋⣠⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠀⠠⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠶⠟⠋⣠⠴⠿⠫⠔⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⣪⣭⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐
⠀⠀⠀⠀⠀⠀⠠⠞⣁⠀⡉⠉⣀⠬⠉⠃⠀⠀⠀⠀⠀⠀⡠⢀⠔⠀⠀⠀⠀⠀⠐⢄⠀⠀⠙⢷⣆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⢁⣀⠀⡆⠀⠀⠀⠀⠀⠀⢘⠠⠩⡀⡀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠘⣿⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⢐⡏⠃⢀⠀⠈⠠⣿⡇⠀⠀⠀⠀⠀⠈⠎⣓⠊⠒⣤⢄⡀⡀⢤⣊⡔⠁⣧⢤⡀⣀⡀⣀⡆
⠀⠀⠀⠀⠀⠀⢸⣬⡋⠅⣸⡿⠗⣀⢴⠈⠂⠤⠄⠒⠀⠀⡁⠌⠓⢒⠉⠁⠄⣀⡤⢋⣁⠀⠀⠉⣁⣙⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢬⡓⣶⢒⠭⠒⠋⠀⡄⠀⠀⢁⠀⠐⢘⠀⡀⠀⠠⠶⠘⠷⠢⠤⠊⠀⠀⠊⡀⢀⡑⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠁⠀⠁⠀⠐⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣌⠀⠀⠀⡀⠀⡠⠀⠀⠀⠄⡀⠄⠒⠀⠉⠀⠉⠉⠀⠂⠀⠢⢄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠊⡀⠒⠰⠉⠘⢀⠉⣂⠈⠄⠀⠀⡈⠑⡄⠀⠀⠀⠰⠀⢠⠄⠀⠀⠐⠀⠀⡜⠛⡂⢎
⠀⠀⠀⠀⠀⠀⢀⡈⠣⠄⠸⢡⣾⡆⠈⠡⠢⠀⡄⠸⠀⠀⠠⠀⠅⣀⡀⠤⠖⡀⠘⠀⠀⠀⠔⠀⠄⢰⠀⡠⠈
⠀⠀⠀⠀⠀⠦⠤⠥⣤⣤⣤⠴⠶⠒⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠁⠄⠘⠃⠂⠀⠈⡀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠓⠚⠁⠀⠀⠒⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠐
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⢀⣠⡰⠊⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠈⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠁⠈⠈
⠀⠀⠀⠀⠀⠀⡀⢀⡠⠠⠄⠀⠀⢀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠠⠄⠄
⠀⡀⠀⠀⠈⠉⠠⠤⠂⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢠
⠀⢁⠀⡀⠀⠀⡀⠀⠀⠐⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠠⠀⠀⠀⠀⠈⠀⢠⡀⠤⠄⠄
⠀⠈⠀⠂⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠅⠀⡀⠀⠀⠀⠀⣠⡆⠀⠀⠀⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠐⠀⠀⠍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⡀⢀⢀⠀⠀⠀⢠⠠⠀⠀⠀⡀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⢀⠠⠀⢄
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠁⠈⠁⠉
⠀⠀⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡁
⠀⠀⠁⠁⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠈⠂⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈
⠀⢀⠈⣠⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⢒⢲⡄⠀⠀⠀⠀⠀⠀⠀⠤⠀⠴
⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⡌⢁⠐⠒⣒⢂⠉⢱⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠔⠀⠠⠠⠁⠐⢀
⠀⠀⠀⠠⠄⠀⠀⠀⡀⠀⠀⠱⠐⠐⠁⠀⠀⠀⠚⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠒⢂⡐⠐⠊⢠
⠀⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⢀⠑⠠⠤⠤⠤⠒⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠐⠀⠀⠉

⠀⠀⠀⡀⠄⢀⠆⡀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⠀⠀⠀⠀⢀⡠⠔⡠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠯
⠀⢀⢢⢨⣰⠁⢐⣤⡆⠀⠀⠘⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠁⠀⢰⠶⠂⠀⠀⡰⠉⠴⡀⢁⠸⠆⠀⠀⠀⠀⣤⠤⠤⠤⠾⠿⢦⡄
⠀⠸⠈⠉⠉⠉⠉⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⢤⠁⠀⢰⡆⠀⠀⠀⠀⠐⠿⣾⢉⡀⠒⢰⠀⠀⠀⠀⠣⠀⠀⢀⡀⠤⠀⡁
⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⣤⠁⠀⢀⡄⠄⠀⠀⠀⠀⠀⠀⠈⠡⠄⠀⠉⡄⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠆⢡⡖⠀⠀⠀⠋⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠠⢣⠀⠀⠀⠁⠀⠀⣀⢀⣀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⢀⠐⠂⠀⠀⠀⠀⠀⠀⢠⠖⠑⠊⢤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢨⠋⠁⠀⠈⠀⠄⠀⠀⠀⠀⠀⣰⠈⢷⠀⢠⣠⠀⠀⠀⠀⡄⠲⡀⢀⡀⠀⡀⠀⠄⢀⠸⠙⠀⠀⠀⠀⠠⠈⡃
⠀⠀⠔⠁⠀⠀⠈⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡏⣘⢦⠀⠀⠀⠈⠢⡑⠄⢠⠀⠀⠀⢂⠀⠁⠂⠀⠀⡀⢀⠀⠀⢁
⠀⠀⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠐⢄⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠈⡿⠔⠀⠀⠀⠀⠀⠐⠀⠄⠂⠀⠠⠔⠁⠀⠀⠸⡀⢀⠀⠀⠏
⠀⠀⠀⠀⠈⠉⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⢀⠶⠁⠈⣀⣀⣀⠀⠉⠀⠀⠀⠈⣲⣷⡀⠘⣶⢧⠖⠀⠀⠀⠀⠀⠀⢈⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⡀
⠠⠀⠤⠘⠉⡽⢏⠉⠐⠀⠀⠀⠀⢹⠀⠁⢸⡙⠳⠀⠀⠀⠀⠀⡠⠉⠉⠀⠁⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⢀⡠⠗⠀⠀⠐⡀
⠀⠀⠀⠀⠉⢰⠉⠀⠀⠀⠀⠀⠀⠀⡆⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⡀⠆⠀⠀⠀⠀⠀⠆⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠑⠚⢻⠟⠉
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢡⢀⠈⡘⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⢀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠲⠖⡄⠀⠀⠀⠀⠀⢠⡴⡆⠴⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠴⡀⠀⠀⠀⠀⢌⠄⡝⠁⠉⠀⠀⠀⠀⢠⡇⠂⠀⠀⠀⠀⠹⡀⠀⠀⠀⡠⠂⠉⠀⠀⠀⢀⠀⠆⠀⠀⡠⠚⠀⠀⠀⡌⠃
⠀⣀⠀⠐⠒⠛⠛⠛⠓⢲⠃⠀⠀⢀⢈⠂⢜⠖⢀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈⠄⠀⠀⠀⠀⠀⠨⠀⡁⠀⠀⢁⠄⠒⠀⠘⠢⣄⠁
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢃⡠⠌⡠⠂⠀⠀⠀⠀⠀⠘⡆⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈


⢀⠉⠃⣶⣴⣶⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢠⣄⣀⡀
⠈⠀⠀⠹⣿⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁
⠀⠀⢰⠀⢸⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⢈⡟⠛⠁⠀⠀⠀⠠⠂⠀⠀⠀⠀⣀
⠀⠀⢾⠀⠀⡇⠀⢸⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⣉⣷
⠀⠀⠘⠀⠀⡇⠀⠸⠀⠀⣠⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠄⠀⠀⠀⢁⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⢀⠀⠀⠀⠀⢀⠐⠤⠀⠠⠌⠁
⠀⠀⠀⠂⠀⠃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠁⠀⠀⠀⠀⠀⠰⠈⠀⠀⠀⠐⠰⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⡄⢥

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣸⠃⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣤⣄⣤
⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⡀⠀⠀⠀⠀⣶⠶⠒⠒⠢⠀⠀⠀⠀⠀⠀⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠀⠠⠀⠀⢀⠀⠂⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⡄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠚⠋⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐
⠀⠀⠀⠀⠐⠂⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠘⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠔⡆
⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠙⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠀⠀⠠
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⣄⣀⣀⣀⣤⣀⣀⣀⣤⣀⣤⣀⣠⣀⣀⣀⣀⣀⣤⣀⣀⣀⣀⣀⣠⣀⣄⣠⣯⣭⣤⣀⣀⣤⣤⣀⣀⣀⣀⣤⣀⣀⣤⣀⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⢠⠀⠀⠀⢀⠀⠀⢀⠀⡠⠄⠄⡀⠀⠀⠀⡀⠀⠀⠀⡀⡤⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠄
⠀⠈⠀⠀⠀⠀⢀⠰⠀⠐⡀⠠⠀⠁⠀⠀⡐⠀⠊⠁⠐⠋⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠐⠀⠲⠄⢠⡂⠐⣶⠂
⠀⠀⢀⣀⠀⠀⠀⠘⠂⠀⠑⢀⠀⠑⠄⠀⠀⢖⠣⡇⠀⠀⠠⠀⠀⠂⠀⠠⠀⠀⢀⠔⠀⠈⠑⠄⠀⠀⠈
⠀⢄⠘⠀⠀⠈⢁⡤⠤⠀⠠⠠⡈⠀⠀⣴⡇⠸⣺⠀⠀⢀⠔⠀⠱⠀⠁⠂⠄⠀⠂⠀⠐⠂⠰⠀⠀⠀⠐⢀
⠀⠈⣀⠘⠀⠐⢁⣀⢠⠠⢠⣵⢪⠂⢀⣉⣀⠀⢿⠀⠀⠘⠄⠠⠼⠦⠀⠀⠀⠀⡀⢀⠈⠒⠀⠠⠀⠁
⠀⢸⠀⢣⠈⠊⣒⡒⣉⣉⡩⠤⠊⠀⡇⠀⠀⡄⠀⠀⠀⠀⣀⡀⠀⠀⣀⣴⣤⣦⡀⠉⠀⠀⠀⠀⠀⡠⢠⠄
⠀⢸⠀⠁⠠⠀⠀⢤⠤⠀⢀⠀⣠⠘⠤⠠⡔⠃⠀⠈⠆⠀⠀⠀⠀⠈⢻⡗⠛⠛⠓⠀⡁⠀⡔⠀⠘⠂⠊
⠀⠀⠑⠒⠁⠠⡀⢈⠐⠀⠀⠐⠀⠀⣀⡤⣄⠀⢀⠀⠀⠀⢀⠤⠀⠁⠁⠀⠒⠂⠈⠀⡀⠇⠀⢀⠄⢢⠐⢀
⠀⠦⠄⠀⠀⠀⠀⠀⠀⠀⢀⠐⡦⠿⠞⢉⠜⢠⡄⠆⢀⡠⠉⠀⠀⠈⢀⠀⠀⠀⠀⠂⠀⠀⠀⠎⠀⠐⠉⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠂⠈⣀⣺⣠⠤⠞⣊⡀⠔⠀⠀⠆⠈⢀⢠⠓⠀⠋⠂⠲⡈⠒⣘⠄
⠀⡀⠐⠈⠓⠄⠀⠀⠀⣀⠀⠀⠀⠉⠀⡁⢠⡀⠀⢰⡿⠁⣄⠀⠋⡄⠀⠦⠀⠀⠀⠀⠀⠁⡁⠀⠀⡐
⠀⠈⠀⡀⢠⠒⠀⠀⠀⠛⠀⠀⠰⠛⠉⠁⠩⠷⠖⠀⣄⠂⠀⢀⡀⠀⠀⠇⠀⠀⠀⠀⠀⡠⢇⠀⠀⠁⠀⠸
⠀⠊⠒⠂⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠊⠀⢀⠀⠀⠀⠀⠀⠀⠀⣒⠀⠠⠤
⠀⠐⠈⠀⠂⠀⠀⠸⠀⠀⠢⠈⠀⠀⠈⠉⠐⠀⠀⢀⡆⠐⠀⠀⢀⠈⠀⠋⣀⠀⢀⣠⠀⠁⠀⠙⠀⠠⠂
⠀⠀⢀⠄⡒⠄⠀⠄⠔⠂⠀⠘⢀⡀⠀⠀⠀⡤⠀⢸⠀⠀⠀⠀⠀⢀⠤⠊⠁⠀⠠⠀⠑⡢⠀⠁⢠⣄⡀⠄
⠀⠈⠀⢀⠀⠨⠀⠐⡀⠰⠀⠀⢸⠁⠀⠠⠀⢀⣠⠌⠀⢀⠈⠀⠄⠃⡀⠀⢀⠀⣀⣀⠴⠰⠀⠀⠀⠉⠁
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠰⢀⠄⠀⠀⢀⠤⠤⢄⠀⠀⠀⠀⠁⠀⠄⠁⠀⠀⡈⠀⡈⠀⢈⠀⠀⠀⠀⠀⠀⠄
⠀⠀⡀⠀⠀⠀⠀⠠⠡⠂⠀⠀⠨⠤⠀⡇⠀⡎⠀⠀⠀⠠⠀⣠⠀⠀⠀⠣⠃⠂⠎⠘⠠⠂⢠⡤⠐⠂⠠⣀⡀
⠀⠈⣤⣖⣲⠄⢠⡀⠂⡀⠀⠀⠂⠀⢀⠉⠉⢀⠀⠀⠐⠀⣀⠀⠀⠘⠀⠀⢀⣠⣄⠀⠀⠀⠰⠀⠀⠀⠀⡰
⠀⢸⡬⠟⠁⢰⠈⠀⢈⠀⠀⡠⣃⢠⢁⠖⠁⣈⠀⠄⠀⠄⠂⠀⠀⠈⢀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠀⠀⠘⣠⠄
⠀⠀⠁⠀⠀⠈⠀⠀⠀⠉⠀⠀⠁⠈⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠂⠀⠛⠤⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠤⣤⡀⣉⡀⠀⠊⢠⠀⠄⠀⠙
⠀⠠⠀⠰⠢⠀⠄⠐⠂⠄⠀⠀⠀⠀⠈⠄⠲⢴⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⣈⠁⡉⡁⠁⠀⠈⠠⡀⢈
⠀⣀⠀⠐⠄⡀⠀⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠉⠁⠠⠀⠀⠀⠀⢸⣄⡉⠻⢷⠇⠄⠀⠀⢰⡆
⠀⠈⠇⠀⠀⠁⠀⠂⠠⠃⡁⠀⠀⠀⠀⠀⠂⠀⢶⣿⠀⠀⠀⠀⠀⠈⠙⢷⣕⡄⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠤⠠⠀⠐⠲⠐⠀⢂⠀⠿⠂⠀⠉⠀⠁⠀⠀⠀⠀⠁⠀⡀
⠀⢠⡀⠀⢀⠀⠀⠀⠠⠀⠀⡄⠀⠀⠀⠈⠐⠒⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡁⠀⠀⠀⠁⠀⠀⠀⢠⡀
⠀⠈⠁⠰⠒⠀⠠⡀⠀⠀⠀⠀⠀⠄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠰⠀⡎⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠈⢿⠀⠄⠀⠀⠀⢀⣤⣤⣤⡄⣠⣤⡄⢴⣶⣶⣶⣄⠀⠀⠂⠀⠀⠂⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠡⡀⠀⠀⣾⢩⣿⣿⣿⢷⣶⠖⣺⣿⡿⣿⡍⡇⠀⠀⠀⠀⠀⠀⢇⠘⠓⡀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣰⡃⢱⣸⣸⣿⣠⣧⣢⣼⣬⣄⠇⠀⠀⠀⠀⠀⠀⣀⠀⠀⣠
⠀⠀⠀⠁⠀⠀⠐⢀⠀⠀⠀⣨⢿⡔⠂⠉⠙⠋⠉⡉⠉⡉⠉⠉⠉⠍⠀⠐⠀⠀⢉⠁⠰⠄⢀⣀⣀⣀⠃
⢰⠀⠀⠀⠀⢀⠀⠀⡀⠈⠸⣄⢈⣆⠠⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⢀⠈⢀⠀⠀⠀⠀⠀⢠⠭⠽⠿⢋⣷
⠈⠀⠐⠠⠀⠈⠀⠠⠁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢁⠔⡠⠄⢀⡀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠘⠀⠀⠈⠀⢁⠀⠀⢁⢤⡀⠀⠀⡄⢰⡓⠒⠂⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠹⠉⠟⠐⠀⢨⠙⠉⠷⠖⠒⠚
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣤⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡐⠀⠠⠀⠀⠀⠀⠉
⠀⠀⠀⠁⠀⢤⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠐⠀⠀⠀⠄⠀⠰⠀⠀⡐⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠁
⠀⠀⠀⠀⣀⠈⠻⢤⣀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠹⠿⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⢠⠀⠀⠀⠀⠀⠀⡀⢀⠄⠠⢀⠀⠀⠀⡠⠀⠀⠀⡀⡄⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠄
⠀⠁⠀⠀⠀⠀⣀⡢⠀⢂⠀⢀⠀⢂⠀⠀⠀⠊⠁⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠐⠄⢠⣂⡉⠦⠂
⠀⠀⢠⡀⠀⠀⠀⠑⠀⠀⠢⢀⠀⠀⠁⠀⢐⣓⡅⠀⠀⡐⡀⠀⠂⠀⠀⠀⠀⡀⠁⠀⠉⠂
⠀⢆⠀⢀⠀⠀⡠⠐⢂⠂⠂⠠⡀⠀⢰⠍⠘⣵⠂⠀⢠⠊⠀⠐⠀⠰⠐⡠⠊⠀⠈⠁⠒⠂⠀⠀⠈⠡
⠀⢀⢄⠈⠀⢈⠀⢀⠤⢀⡦⠦⠏⢀⠤⢄⡀⠻⠀⠀⠈⠂⠠⠛⠑⠀⠀⠀⠀⢀⡀⠁⠁⠀⠂⠁⠂
⠀⢸⠀⠣⠀⠉⠀⠡⠬⠅⠒⠊⠀⡘⠀⠀⡌⠀⢀⠀⠀⠦⠄⠀⣠⣤⢶⣞⣤⠀⢀⠀⠀⠀⠀⡄⠒⠆
⠀⠸⡐⢀⡇⠀⠀⠖⠂⠀⠀⢠⠆⠑⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⡈⠹⠉⠉⠉⡁⠀⢀⠘⠀⠈⠁⠈
⠀⠀⠈⠁⠐⠢⠀⠄⠀⠀⠀⡀⢀⡠⣶⠴⠀⠀⡀⠀⠀⠰⠳⠀⠀⠀⠀⠉⠀⠀⠠⠀⠄⢀⠄⠙⣈⣠
⠀⠓⠀⠀⠀⠀⠀⠀⡄⠀⠄⠐⠂⠉⠠⢊⠐⠃⢃⡲⠖⠀⠀⠀⠀⠤⠀⢀⡀⢈⡀⢀⠀⡀⠀⡀⠀⠈
⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⢠⠀⠴⠔⠒⠂⢉⠴⠀⠀⠀⡀⠀⠀⠂⠅⠀⠀⠐⠈⠠⠈⠀⠃
⠀⢂⠀⠀⠐⡀⠀⠀⢴⡄⠀⠀⣠⠤⠤⠸⢇⣀⠐⠋⡀⠂⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠨
⠀⡠⢐⠂⠚⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠉⠁⡀⠁⠀⠀⠀⠂⠠⠈⠁⠀⠀⠀⠂⠐⠉⢀⠀⠀⠀⠈
⠀⠀⠠⢀⠀⠀⡔⡄⠀⢀⠀⠄⠀⠠⠴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⢄⠀⠲⠆⠈⠁
⠀⠀⢀⣀⠀⠀⢡⠁⡀⠠⠁⡆⠀⠂⠀⠀⢀⠀⢰⠂⡀⠀⠀⠀⠀⢀⠰⠂⠀⠐⢣⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠂⠖⠀⠀⠀⡀⠐⠀⠾⠀⠀⠀⠈⠀⠠⠀⠀⠠⠀⠀⠂⠁⠀⠀⠀⠀⢀⠜⡄⠀⠈⠿⠂⠁
⠀⠀⠂⠒⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠉⠁⠀⠀⠄⠀⠀⠄⠒⠒⠪⠐⠂⠁⠀⠁⠀⠀⠀⠀⡀
⠀⠀⠀⡀⠀⠀⠀⡐⡀⠈⠁⠠⠒⡀⠃⠀⡙⠀⠀⠀⠀⠀⢀⠀⠀⠠⡰⠠⢀⠆⠄⠂⠀⣀⠀⠀⢀
⠀⠐⣀⡀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠒⠃⠀⠂⠠⠀⠀⠉⠀⠤⠀⠀⠀⢀⠀⠀⠀⠀⡉⠀⠀⠀⢩⠃
⠀⢰⢙⠡⠃⠀⠚⠀⠂⠀⠀⡐⠀⠀⡡⠐⠘⠂⠀⢀⡀⠍⠀⠀⠀⠀⠀⡙⠙⠁⠀⠀⠀⠐⠀⠀⠐⢀⡀
⠀⠈⠁⠀⠀⠀⠀⠀⠁⠀⠁⠈⠁⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⡀⠀⠀⠀⠎⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠉⠀⠀⠀⠀⠀⠀⢀⣼⣀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠉⠀⠒⠂⠀⠀⠀⠀⠒⠂⠈⠉⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠓⢺⠤⣄⣀⣀⣀⣀⣀⠀⠀⠠⠐⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⣀⡤⠴⠖⠲⠚⠒⠶⠤⣄⡀⠀⠀⠀⠀⠀⠀⣸⣀⡠⢄
⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠤⠒⠋⠍⢀⡠⠚⣳⢦⡀
⢀⣀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⡀⠀⠀⠁⠀⠉⠀⠉⠙⠳⢄⡀
⠀⢆⣿⡑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣲⠤⢀⣀
⠀⢌⠛⡙⢷⣦⣤⣠⡤⠄⠀⠀⠀⠀⢀⣀⣀⣬⢴⣯⢠⣼⠠⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣾⡷⠤⠒⣟
⠀⢀⣷⡊⠐⠶⠒⠿⣏⣹⣛⣻⠋⢭⣍⣡⣤⣀⣉⢩⣾⠁⠀⠈⠐⢄⠀⣠⠶⣾⡿⠋⣹⣏⣉⣉⡤⣤⡴⣞⣋
⠀⢸⠩⡓⠶⣄⣀⠀⠀⠀⠈⣑⠀⢀⡰⠀⠈⠭⠤⠎⣿⡀⡀⡄⠀⠀⣼⠉⠲⡌⠀⢮⡌⢿⠑⢺⢥⡂⠌⣓⡽
⠀⠈⠳⠄⠀⣄⡈⠛⠀⠤⡄⠀⣄⠉⣀⠀⠀⡀⢠⠞⢱⠙⢤⢣⠆⢸⣿⡇⢸⣌⣵⠪⠷⣘⡆⢘⠶⠼⠷⣧⡂
⠀⠐⡀⠀⠈⠉⠉⠉⠁⠒⠚⠃⠈⠛⠁⠀⠁⠈⠁⡀⠎⠀⠀⠙⢄⣋⠹⣧⠀⢿⠮⣉⡛⢒⠯⡴⣷⠒⠒⠓⠁
⠀⠀⠈⠁⠐⠒⠒⠂⠤⠤⠤⠤⠤⠤⠀⠀⠒⠀⠉⠀⠀⠀⠀⠀⠀⠙⡄⠹⡦⡞⢡⣈⢙⠆⠑⢌⣻⢓⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠴⡐⡴⢳⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠖⠢⡀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⢤⡀
⠀⠀⠀⢀⡴⠒⢋⠉⠓⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠐⠀⠀⠠⢹⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢹⠄
⠀⠀⠀⡎⠤⠠⠂⠲⠅⠀⣧⠀⠀⠀⠀⠐⣿⠽⠯⠿⠽⢿⡇⠀⠀⠀⠀⠀⠐⣏⠴⣠⣄⣰⡿⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣸
⠀⠀⠀⢿⠀⠘⠢⢴⡁⢀⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠒⢸⠀⠀⠀⠀⠀⠀⠀⠸⡆⠡⠈⣼⠁⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⣰⠁
⠀⠀⠀⠈⠓⠧⣤⠤⠴⠋⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢻⡐⣱⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠾⠃
⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⢠⠖⡛⠉⠉⢉⡉⡙⢦⠀⠀⠀⠀⠀⠀⢀⣖⢒⣆⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠚⠓⠲⣄⠀⠀⠀⠀⠀⠀⣴⣞⣿⣿⣿⡶⡄
⠀⠀⠘⣎⡔⠜⠓⢼⠵⢈⠟⠀⠀⠀⠀⠀⢰⡉⠤⡠⠭⣿⠀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣀⣀⣘⡇⠀⠀⠀⠀⠀⢿⣯⢿⢹⢻⣽⠇
⠀⠀⠀⠘⣄⣸⡃⣭⣰⠏⠀⠀⠀⠀⠀⠀⢸⠄⣀⡼⡀⣼⠂⠀⠀⠀⠀⠀⣷⣦⣤⣼⣧⣤⣴⡇⠀⠀⠀⠀⠀⢻⠛⠛⠛⠛⡗
⠀⠀⠀⠀⠘⣏⡵⡴⠃⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡤⠜⠁⠀⠀⠀⠀⠀⠈⠲⣀⣓⠉⢀⢛⡸⠃⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⠿⠿⠂⠀⠀⠀⠀⢠⠋⣿⢁⣾⡇⢳⠀⠀⠀⠀⠀⡶⢷⣾⡶⣄
⠀⠀⢠⢴⠞⠛⠛⠛⠻⢦⣄⠀⠀⠀⠀⠀⠀⢹⣿⣿⠠⠀⠀⠀⠀⠀⠀⠀⡜⠀⡟⠻⣴⡇⠘⡇⠀⠀⠀⠀⡏⢦⢻⣿⣿⣆
⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⢴⡖⠚⣛⣛⡒⢲⡆⠀⠀⠀⠀⠀⣧⠀⣫⡴⢛⡆⠀⡇⠀⠀⠀⠀⡇⠀⠱⡻⣿⣿⣄
⠀⢸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣿⠀⠀⠀⢸⣤⣀⣀⡀⣀⣸⠃⠀⠀⠀⠀⠀⢣⠀⢿⠙⢺⡇⢠⠃⠀⠀⠀⠀⡇⠀⠀⠙⢝⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⡏⠛⠛⠻⠟⢻⠀⠀⠀⠀⠀⠀⠘⣄⣸⣞⢋⣧⡼⠀⠀⠀⠀⠀⠧⠤⣤⣄⣈⣮⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⡏⠉⢳⠏⠉⢷⠀⠀⠀⠀⠀⠀⠰⠀⠀⣀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠉⢱
⠀⠀⠀⢠⣇⡀⣀⢆⣀⣾⠀⠀⠀⠀⢀⡤⠚⠉⠁⠆⠉⠑⢦⡀⠀⠀⠀⠀⣀⢔⠚⠿⠟⢷⢦⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⡾⡛⠁⠀⠀⠀⠀⠙⣿⡀⠀⠀⠀⠀⠀⢸⡀⠀⣸
⠀⠀⠀⢸⡀⠀⠀⠀⠀⡞⠀⠀⠀⠸⣽⡀⠀⠀⠀⠀⠀⠀⢀⣞⡶⠀⠰⡟⠀⠀⠀⠀⠀⠀⠀⢈⣷⠀⠀⠀⠀⠀⠸⡀⠀⡸
⠀⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠙⠻⣖⡒⠒⣲⠾⠛⠁⠀⠀⠀⠙⠒⠒⠒⠒⠒⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠈⡏
⠀⠀⠀⠀⠓⠒⠒⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⣰⠛⠻⡆
⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠉⢻⡏⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⣠⣏⡸⠒⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⣠⠦⠶⠛⢻⠶⣤⡿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠓⠲⢤⣤⠶⠛⠉⠀⢹⡆
⠀⢀⡾⣧⣀⣈⣇⠀⠀⠀⠙⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⡿⢀⣴⣋⣙⣦⣭⣹⡟⢷⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢀⣠⣤⣤⣀⠀⠘⣇
⣴⣯⣤⡟⠁⠈⠙⢷⣄⠀⠀⠀⠈⠉⠛⠲⢶⢺⠀⠀⠀⠀⣾⣼⣶⣫⡟⠉⠉⢳⣤⠏⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⢰⡏⠀⠀⠀⠙⣧⠀⠈⠛⢦⡀
⠀⠀⠘⣇⠀⠀⠀⠀⠉⠻⢶⣤⣤⣤⣤⠤⠚⠾⠅⠀⠀⠀⢹⡀⠈⠉⣉⠛⠋⡿⠃⡀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⣠⠟⠀⢸⡆⠀⠀⠀⠀⡿⠀⠀⠀⠈⣷
⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠉⠉⠙⢲⡴⣷⠀⠀⠀⠀⠀⢳⡀⠀⠉⢀⡼⠁⠈⠁⠀⠀⠀⢷⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠙⠶⠤⠶⠚⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣤⣤⣤⣤⠴⠿⣄⡇⠀⠀⠀⠀⠀⠀⠳⣄⢀⡞⠁⠀⠀⠘⠃⠀⠄⠘⡆⠀⠀⠀⢸⡄⠀⠀⠀⠀⣀⣤⣤⣤⣀⣀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠉⠓⠒⠚⠋⠁⠀⠀⠀⠈⠉⠛⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡀⠀⠘⠃⠀⠐⠂⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠁⠀⡀⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢒⡛⠽⠟⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢻⡄⠀⠈⠛⠶⠶⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⣧⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡋⢳⣤⡏⢻⣆⣠⣯⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡿⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠘⢧⣄⠀⠀⠀⣿⢠⡆⠀⠀⠀⠀⢀⣼⡆⠀⠀⠀⣀⡈⢳⡏⠉⣻⣾⠙⣧⠈⢿⣹⠆
⠀⢀⡶⠒⠒⠒⠒⠚⠛⠛⠛⢛⣛⣛⣻⣆⠀⠀⠀⠀⠀⠀⣟⣉⣉⣉⣉⣹⠂⠀⠀⢿⠘⡇⣠⡤⣤⣴⣿⠟⠁⠀⠀⢸⣏⣉⡙⠳⢴⡃⣿⢰⡿⣧⠀⠻⡄
⠀⠘⠹⡟⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡏⠉⠀⠀⠀⠀⠀⡴⠟⠉⠉⠉⠉⠉⠲⣄⠀⠸⠀⠀⣿⡀⠁⢹⡇⠀⠀⠀⠀⠀⢀⣀⡿⢦⠀⠙⢧⣸⠃⣼⣆⣀⣽⡦
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠆⣰⠛⠛⠻⣿⢦⡼⠃⠀⠀⠀⠀⠀⠈⢿⠙⠛⠓⠒⠚⠛⠚⠛⠉⠁⣼⠃
⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸⣄⣹⣦⡀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠸⡏⠀⠉⢻⡍⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⣠⠶⠛⠶⣿⣶⣦⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢀⡀⠀⢸⡇
⠀⠀⠀⠀⠈⣇⣀⣀⣀⣀⣀⣀⣸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢿⡀⢁⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢛⣿⣿⠷⠮⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠛⠛⠲⠶⢤⣄⡀
⠀⠀⠀⢀⣾⡭⠽⠧⠬⣍⡉⣿⣋⣽⣇⣀⣀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣤⡴⠶⠶⢶⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣴⡀⠀⠀⣤⠀⠈⠙⠳⢦⡀
⠀⠀⣠⠞⠁⡀⠘⠀⡀⠈⠙⢦⡀⣽⡛⢯⡉⠳⣄⠀⠀⠀⠀⠀⢀⡴⠋⠰⢦⠀⣤⠈⠁⣠⠌⠛⢦⡀⠀⠀⠀⠀⠀⠀⢸⣧⣌⠉⠛⠻⢧⣄⣀⡄⠀⠀⠙⢦⡀
⠀⠀⡏⠀⠀⠀⠀⠀⠉⠀⢠⠀⠙⣦⠙⣿⢛⣷⠘⡆⠀⠀⠀⠀⢾⠀⠞⠀⠀⠀⠈⣠⠄⠀⠴⠖⠈⢷⠀⠀⠀⠀⠀⠀⢸⣇⠊⣷⠀⠀⠦⠈⠙⠳⣄⣠⠆⠀⠹
⠀⠀⠹⣄⠉⠀⠠⠄⠀⠀⠀⠀⢠⠌⣧⠉⢻⣽⡆⡇⠀⠀⠀⠀⠈⡿⠶⠶⠶⠶⠶⠷⠶⠶⠶⠶⠶⣾⠇⠀⠀⠀⠀⠀⢸⣏⡴⠏⢠⠖⣛⣉⣽⡳⣬⣻⣦⡤⠶
⠀⠀⠀⠈⠳⢦⣀⠀⠀⠰⠆⠀⠀⠀⠘⡇⢸⢉⣷⠇⠀⠀⠀⠀⢰⡟⠖⠛⠛⠳⢶⠶⠛⠉⠳⠶⠞⣩⡷⠀⠀⠀⠀⠀⢸⡁⠀⠀⣟⢾⣙⣧⣷⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠐⠀⠀⢻⠟⢫⠏⠀⠀⠀⠀⠀⠀⢻⡗⠛⠛⠛⠛⠻⢿⣝⡛⠛⠋⣹⠃⠀⠀⠀⠀⠀⣾⠛⢳⣀⡽⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣤⣸⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⣄⣀⣀⣀⣨⡿⢦⠾⠃⠀⠀⠀⠀⠀⠀⠿⠖⠋⠁
⣶⣶⣶⠶⡶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠶⢤⡐⠓⠒⠓⠒⠓⠒⠒⠒⠢⢤⣶⡄⠀⠀⠀⢀⣤⡴⢲⠖⢢⣄
⠀⠀⠀⢀⣴⠞⠋⢉⠉⠛⢦⡀⠀⠀⠀⠀⠀⠈⠀⠀⠛⠒⠚⠒⠚⠛⠓⠉⠁⠀⠀⠀⠀⠀⢀⡾⣠⣤⣼⣄⣤⣼⢳⠀⠀⠀⠀⠀⢰⠨⠤⠤⢼⡀
⠀⠀⠀⣾⠁⠀⠀⣀⡀⠀⠈⠿⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⡞⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀⠟⠀⠒⡒⠚⣣⡀
⠀⠀⠀⣟⠁⠀⢰⠋⠙⠂⠂⣸⠃⠀⠀⠀⠀⠀⣰⡟⠀⠁⠀⠀⢀⢄⡀⣸⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠉⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠘⢦⣀⡉⡄⣀⣠⡴⠋⠀⠀⢠⣀⡆⠀⣿⡅⠀⣾⠙⡶⠻⠼⠋⢹⣿⡃⣠⡏⢰⡟⡇⣾⣹⡀⠀⠀⠀⠰⠄⠀⠀⠀⢀⣇⣀⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⣀⣤⠞⣿⡀⠀⠘⠳⠔⠛⠚⠁⠀⠀⠀⠈⠁⠉⠉⠛⠉⠀⠉⢉⢽⠇⠀⠀⣠⠶⣦⡀⠀⠀⠘⠛⠋⢥⢈⡭⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡋⠀⠄⠊⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠒⠀⢀⠀⠈⠋⠀⢀⡾⢥⣬⣏⣝⣷⡄⠀⣀⣴⠟⠀⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣐⡡⢀⠁⡆⣿⡄⠀⠀⠀⠀⢀⣀⠤⠔⠒⠀⢐⠒⠤⣀⠀⠀⠄⠀⠀⣿⠄⣺⢲⠓⡇⢁⡟⠀⠉⠉⠉⠉⠉⠉⠁
⠀⠀⣠⠶⠛⠛⠛⠛⠓⢦⠀⠘⠿⢻⣄⢀⠢⢀⡇⠀⢀⡤⠚⠉⠀⠀⠴⠀⠀⠀⠉⣢⡈⠡⠀⠐⠢⡀⠙⠶⣍⣹⢙⣳⠟
⠀⠀⡯⢏⠉⠉⣢⠀⠀⢸⠀⠀⠀⠀⠙⠳⠾⠛⠀⡴⠉⠀⠀⠀⠀⠀⠀⡐⣈⠀⠂⠀⢌⠀⠀⠀⠀⠈⠢⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠈⠓⠚⠛⢶⠖⣾⠋⠀⠀⠀⠀⠀⠀⠀⢀⡞⢠⡦⠀⠀⠀⠀⠀⠀⡀⠁⠀⠁⠐⠐⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⣴⣲⣶⣾⣷⣰⣶⣶⡄
⠀⠀⠀⠀⠀⠀⣼⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠘⠀⠻⠀⠀⠀⠀⠀⠹⡛⠂⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠨⡇⠆
⠀⠀⠀⠀⠀⠀⠳⠛⠾⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⠄⣀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⢀⡠⠤⠤⣄⠤⡤⢤⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠲⠒⢈⡶⠤⢴⡄⢰⠋⠁⠀⠀⠀⠀⠀⠈⡃⠀⠀⠀⠀⠧⠤⠤⠤⠤⠤⠤⠼⠂
⠀⠀⠀⠀⢀⠎⠁⢰⢏⠤⠂⠑⠀⢸⠆⠀⠀⡆⠀⠀⠀⠉⠢⠤⠄⢀⣀⡜⠙⠀⠸⡁⢙⠀⠀⢀⡄⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠘⣄⠐⠬⢀⡀⠠⠊⣠⠞⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⢈⡃⠀⠀⠀⡇⠀⠀⠀⡄⠀⠀⠀⠀⡼⠀⠀⠀⡀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠈⠑⠒⠶⠶⠚⠋⠁⠀⠀⠀⠀⠀⢠⣤⢴⠶⣀⣲⠶⣤⣼⣄⠀⠀⠀⡧⠀⠀⡠⠇⠀⠀⠀⡴⠁⠀⠀⠀⠀⢿⠀⠀⠆⠀⢀⡿⢶⡆
⠀⠀⠀⠀⠀⣤⠤⢤⠤⠤⠤⡄⠀⠀⠀⠀⠀⠀⠈⠓⢧⠤⠭⠥⢴⣎⡓⢋⠁⠀⠀⣤⠤⠚⠀⠀⠀⢀⠜⠁⠀⠀⢲⠀⠀⠸⡄⠀⠂⠀⢠⣧⠟⠁
⠀⠀⠀⠀⠀⢷⠋⠉⠉⠙⢲⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⢩⠀⡀⠀⠀⠤⠀⠀⢀⡀⠞⠁⠀⠀⠀⣴⠀⠀⠀⠀⢇⠀⠥⠀⢸
⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠈⡇⠀⠀⠀⣀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠀⠐⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⠒⠒⠒⠃
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣧⠀⠀⠀⣧⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⡀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⣤⠤⢤⣤⣤⣤
⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⡸⠀⠀⠀⢸⠀⠀⢰⠃⠀⢺⣯⣭⣭⣝⣳⠀⠀⠀⠀⠰⣽⣿⣿⣯⡿⠀⠀⠀⢠⢻⣷⠀⠀⠀⠀⠀⠀⠈⠉⠛⢛⠉⠉
⠀⠀⠀⠀⠀⠈⠲⠶⠦⠤⠞⠁⠀⠀⠀⠈⠈⠉⠉⠀⠀⢠⠇⠀⠀⠀⣇⣠⣤⣄⠀⠀⠘⢼⣿⡿⠀⠀⠀⠀⠘⠾⠟⠀⠀⠀⠀⠀⠀⢠⠴⠚⡚⠒⢄
⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⠀⠀⣀⡀⣹⣇⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣿⣫⠄⠠⢑⡊⡇
⠀⠀⠀⣔⣒⣒⣚⣛⣒⣒⣒⣆⣀⣀⣀⣠⡤⣤⡄⠀⢸⣇⠀⠀⠀⠀⢨⡿⠋⠀⠀⠀⠀⠀⠀⠀⣠⡔⣊⣉⣀⣀⣀⣉⣑⣦⡀⠀⠘⠰⠷⠶⠶⠶⠥⠗
⠀⠀⠀⣇⣭⣄⣬⣡⣤⣄⣤⡟⠉⠁⠓⠛⠉⠉⠁⠀⠀⠛⢷⣦⣤⣴⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢫⣿⣭⣭⣥⣭⣭⣭⣭⣭⠇

⠀⠀⠰⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⢀⡀⠀⠀⠀⠀⠠⢒⠀⠀⠀⠀⠀⠀⢀⣞⠁
⠀⠖⠶⠖⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⡜⠁⠀⠐⢤⡹⠀⠈⡀⠀⠀⠼⠉⠉⠉⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⡀⠀⠀⢠⡄⠀⡠⠀⠀⠀⠀⠀⠉⠡⠀⢁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⡀⠂⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠘⠀⠀⠀⠀⠀⡀⢤⠀⡀⡀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠠⠄⠀⠀⠀⠰
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⣭⡢⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⢀⠀⠀⠈⡀
⠀⠐⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈

⠀⡀⠠⠀⠤⢠⠀⠀⠀⣀⡀⢠⣠⠄⠀⠀⠀⠀⠀⡀
⠈⢀⠰⢒⣶⠀⠀⠀⠀⢘⠓⢀⠿⡅⠀⠀⠀⡀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⠐⠻⠋
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢀⠀⠀⠀⠀⣠⡄⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠐⠀⢀⣀⣀⠀⡀⠀⠀⠀⢀⠁⠈⠀⠀⠀⣼⠁⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠂⠀⢀⠁⡀
⠀⠢⠀⠀⠀⠀⠘⠁⠀⠰⡄⡀⠁⠀⠀⠀⠀⢉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠔⠈⠀⠈⠐⠠

⠀⠀⢀⣀
⠀⠀⠹⡿⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⠆
⠀⢰⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠟⠉⠀⠀⠀⠂⠀⠀⢠⣄
⠀⠸⠀⢸⠀⠁⠀⢀⣀⣀⣀⣀⣀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚
⠀⠀⠂⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠤⠄⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⢠
⠀⠰⠀⠀⠀⠀⠀⠀⢑⣄⠉⢠⠁⠔⠀⠈⢢⠀⠀⢀⠇⠠⠔⠀⠠⠝⠀⠁⠀⠀⠀⠈⠀⠄⠀⠐⠀⠐⢈⠀⠩⣎⡀⢀⠄⠒⣢⢠
⠀⠀⠀⠀⠠⠄⠒⠀⠒⣆⠀⠈⢆⠀⠰⠠⡀⢣⠀⠢⣀⣤⠠⠄⠀⠀⠀⠄⠀⠀⡀⢀⠀⠀⠁⠀⡀⢁⠎⠀⠤⡌⠀⠙⠒⠒⠊⠉
⠀⠀⠀⡦⠄⠀⠀⠀⠨⠐⠀⠀⠀⠑⠠⡐⢈⠐⠀⣀⢸⢞⠵⠀⠀⠀⠠⡡⠤⠀⠇⡀⠀⠁⠀⠀⡰⠁⢎⡀⠀⠀⠀⢀⠀⠀⣀
⠀⢸⡀⠈⢈⠀⠀⣀⠴⠲⢙⠌⠜⡐⠢⡀⠀⠀⣾⠆⠀⣧⣟⠀⢀⣢⡌⠀⠀⠘⠈⠀⠇⠐⡠⢊⠀⠀⢘⠈⠉⠉⠀⠀⠀⠀⠀⢤
⠀⠀⣀⡀⠈⠀⡘⢑⣠⡀⣄⡄⠰⣔⡢⠽⠀⣀⣁⡀⡀⠘⡇⠀⠀⠈⠒⠠⠤⠻⠑⠀⠀⠁⠀⠈⠜⢀⠈⠁⠉⠀⠰⠀⠁⠆
⠀⠀⡇⠘⣆⠈⠐⠂⠀⠊⠐⢒⣉⡠⠔⠁⠸⠇⠀⠈⣡⠂⢀⠀⠀⠀⢀⢈⠁⠀⠀⣀⣠⣤⣤⣌⠀⠙⠀⠀⠑⠀⠀⠀⠀⠄⣀
⠀⠀⡇⡔⠈⡆⠀⠉⠈⢉⠉⠁⠀⠀⠀⠀⢺⡀⠀⠀⠟⠀⠘⢐⡀⠐⠁⠈⠀⠀⠺⠿⣯⠿⠷⠽⢧⠀⠆⠀⠀⠆⠀⢰⣅⡠⠂
⠀⠀⠣⡈⣠⠇⢀⠀⠈⠧⣈⠁⠐⠈⡩⠃⠀⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⠤⠔⠁⢀⣀⠀⠤⠂⠁⠠⠒⠁⠀⢀⣀⠀⡀
⠀⢀⠀⡀⠀⡐⠑⠄⠈⠆⠀⠀⠈⠀⡀⢀⡄⢴⣯⠒⡄⢀⢔⡀⠄⠀⠠⢏⠝⠀⠀⣀⠀⠀⣀⢀⠀⠀⠔⠈⠄⠀⡴⠁⠈⣆⣄⡅
⠀⠓⠒⠀⡐⠀⠀⠀⠀⠀⣀⠀⠨⠌⠰⠖⠘⢁⡠⠊⠔⠗⠐⠠⢤⡶⠂⠀⠀⢄⠀⢠⡄⠀⢀⠀⠀⢁⠀⠀⠀⠐⠠⢀⠔⠁⠀⠁
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠚⠀⠐⠂⠀⠒⠈⠀⣀⣩⣄⠦⠔⠛⣡⡀⠀⠀⠀⢀⠇⠀⢀⠀⠮⠩⠠⠍⢡⠘⠂⡈⢒⣈⠦⠀⡀
⠀⢀⠀⠆⠊⠣⡀⠀⠀⠀⡰⠀⠤⠀⠀⠘⠃⠀⠉⢠⡄⠀⠀⣚⠭⠁⣄⡀⠐⢁⡀⠀⠀⠈⠡⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠁
⠀⠘⠦⠀⠀⠀⡤⠀⠀⠀⠚⡟⠠⠈⢀⡴⠖⠋⠃⠚⣳⣠⡄⠈⡀⠄⠈⠀⠀⠈⠁⠀⣰⠀⠀⠀⠀⠀⠀⠀⢩⡀⠀⠀⠖⡄⡠⡄
⠀⠠⢄⡈⠡⠊⠀⠃⠀⠀⠀⠈⠂⠀⠈⠀⡀⠀⠀⠀⠀⡀⠀⠈⠐⠄⠂⡄⠀⠂⡬⠂⠀⠁⠐⠒⠒⠒⠒⠊⠉⠃⡀⠀⠀⠀⠀⠃
⠀⠐⠀⡀⠀⢁⠀⢊⠔⡠⢄⠐⠀⠠⠄⠀⠀⡠⡴⠄⡈⠀⠀⢠⠀⠀⠀⢀⠋⡀⢄⠀⢠⠆⠀⠀⠀⠀⢀⢀⠀⠸⣰⠀⢨⠙⠈
⠀⠀⠂⠒⠈⠀⠀⠘⡌⠃⠈⠀⢑⠀⡄⠄⠠⡀⠀⠀⠀⠀⡀⢸⠀⠀⠁⠀⠀⠀⠀⠀⠀⢠⠪⠩⠉⢬⡇⠈⠀⠠⡀⠀⠀⠂
⠀⢀⠀⡒⠒⡋⢆⠀⠣⠠⠊⠀⠁⡐⠁⣀⠄⠀⠀⠀⡐⠀⠀⠻⠀⠈⠐⠂⠀⠀⢀⠤⠊⠁⠀⢀⠤⠀⠘⢲⠔⠁⠀⠰⣶⢂⠡⠄
⠀⠈⠀⠀⡄⠀⢈⠀⠀⠊⣉⠢⠀⠈⠁⠃⠃⠀⠢⠀⠀⢀⣀⠄⠀⠀⠀⠃⢀⠄⢃⠀⠀⠠⢀⠀⠀⢀⡠⠃⡆⠀⠀⠄⠋⠉
⠀⠀⠈⠀⠉⢀⠀⠀⠀⡈⠀⢠⠀⢀⠀⠀⠀⠀⢀⣀⣀⠉⢀⠀⠀⠀⠕⠀⢘⠠⠂⠉⠁⠉⠡⠊⠛⠩⠐⠊⠀⣐⠀⠀⠀⠀⢠
⠀⠀⠀⠄⠀⠀⠀⠀⢀⠰⠀⣀⠉⠂⢠⠔⢠⠸⡁⠀⡩⠆⠀⡜⠀⠈⠀⠀⠀⠀⠀⠀⡴⣲⠀⠔⠢⢠⠐⡆⠀⠀⠀⢀⣀⡀⠀⠁
⠀⠠⠴⠀⢁⠈⠀⠀⠀⠑⡃⠀⢀⣀⡀⠙⠉⠀⠥⠤⠧⠀⠠⠀⣀⠈⠂⠒⠃⠀⢀⠀⠈⠁⠀⠂⠁⠀⠘⠀⠀⡚⠃⠀⠀⠀⠑⢲
⠀⠀⡴⡺⠀⡼⠃⢀⣄⡀⢀⠄⠁⠀⢘⠀⠀⡠⠐⠀⣂⣄⠀⠀⠈⠀⢠⠄⠀⠀⠈⠠⠄⠂⣤⣴⣴⠀⠀⠀⠀⠱⡀⠀⠀⠀⡠⠋
⠀⠐⣇⠤⠑⠁⢠⠀⠀⠀⡁⠀⠀⡠⢊⡀⠈⢠⠊⠁⡀⠀⠂⠤⠤⠄⠊⠀⠠⠀⠁⢀⣀⡠⠂⠀⠠⠀⠀⠀⠀⢀⠁⠀⠀⠀⡀⢴
⠀⠀⠈⠐⠒⠂⠚⠀⠀⠀⠈⠀⠀⠀⠈⠀⠘⠁⠀⠀⠈⠀⠀⠀⠀⠀⠐⠂⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠐⠂⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠉⠂⠀⡛⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠈⠒⢤⡀⠘⣜⣷⣦⣭⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⣿⡿⢶⣄⠀⠀⠀⠉⢦⡈⠛⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⣀⣼⣿⡻⢇⢤⡀⠀⠀⠀⠹⣄⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣧⠀⠀⠀⠀⠀⠀⠀⢀⣤⣯⣛⠇⠫⠻⠏⠁⠀⠹⢿⣶⣄⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⣧⡀⠀⠀⠠⡤⣤⣸⡟⠋⠉⠛⢯⠈⠳⣄⡄⡀⣼⣿⣿⡆⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠈⣡⣶⣺⡟⢶⣜⠦⣴⣿⡝⢯⣾⣺⣿⠇⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⣴⡾⠟⣿⣿⠷⢋⣙⣷⠉⠿⠻⡾⠉⠉⠀⠀⢲⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⢀⣨⡍⠀⠜⠁⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⡀⠀⣤⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡳⣄⠀⠈⢛⡞⠁⠀⠀⠀⠀⢠⠾⠋⡀⠄⣠⣾⣿⣬⣾⠿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⠀⠀⢠⡛⢦⣄⡀⠀⠏⠀⠀⠉⠀⣘⣿⡿⠟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣦⡀⢷⣄⠈⠙⠛⠓⠒⠚⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⠀⠀⠀⠀⠠⠤⠤⠆⡒⠚⠛⠁⠤⠤⠤⠄⠀⠠⠤⠤⣄⣀
⠀⠀⠀⠀⠤⢀⠠⣄⠀⠀⢠⢀⣴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠉
⠀⢀⠠⠒⠂⢠⠄⠄⠀⣰⡟⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⡀⣀⡀⠊⢀⡘⠈⠢
⠀⠈⣀⠀⣤⠄⢈⡑⢊⣀⡀⢡⣤⡀⠀⠠⠀⢀⠄⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡀⠀⠐⠤⡞⣀⣌⡉⠉⠑⠀⠀⠀⠀⠐
⠀⠀⢋⢳⡆⠀⠈⠉⠉⠁⠠⠄⡁⢀⠠⢒⢀⠦⣨⠀⠀⠁⠀⠀⠀⠠⠀⡄⠀⠀⢀⡀⠌⡆⠂⠀⠀⠀⠈⠉⠑⢒⢚⡀⠀⡾⡁⠀⣤
⠀⠀⠀⣑⣌⠱⠂⢰⡂⢀⠈⣰⠀⠕⣤⠥⢮⣖⠆⠀⠀⠀⣤⠖⠂⠀⡸⠤⠀⠁⠣⣹⢶⡶⠤⠄⠀⠀⠀⠀⠀⢀⠞⠐⡰⠐⡇⠀⠠⠁
⠀⠀⠀⠈⠙⠷⢾⡤⡤⠄⠰⢩⠿⡛⠛⠋⠉⠀⠀⠀⠀⠀⡎⢀⡴⠡⡇⠚⠹⠤⠄⢤⠼⠁⠀⠀⠤⠀⠀⠀⣠⠎⣠⠖⠁⣸⠃⠀⠰⠂
⠀⠀⠀⠀⠆⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠐⡄⢸⡀⢲⠀⠀⠀⠀⠠⠀⠈⠀⠀⠡⠄⠀⣤⡞⢁⡴⠀⢀⡴⠃⠀⢀⠒
⠀⠀⠀⠀⠀⠤⠖⢴⣞⣁⣄⣚⣂⡠⠀⠀⠀⠀⠀⠀⠀⠂⠈⢺⠙⣏⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠞⠁⠔⣻⣥⠔⠋⠀⣀⠰⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢰⣄⠀⠀⠀⠉⠛⢶⠖⠈⣛⢅⢀⠀⠈⠀⠀⠘⣀⠘⡔⠋⠁⡐⠒⠛⠛⢋⠍⡩⠇⠊⠤⢀⠀⠤⠄⠒⠒⠚⠁⡸
⠀⠀⠀⠀⠀⠈⠃⠀⠀⠒⢠⡀⠹⡤⠤⣴⣎⠀⠀⠀⠀⠀⠻⠉⣇⠀⠘⠤⣤⠤⠒⠁⠀⣀⣴⣊⠀⠀⠀⠀⠤⠀⡀⠠⠊⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⢧⠈⢥⠇⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠦⢤⣤⠖⢞⠁⠀⠉⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠛⢤⡀⠀⠀⣠⠈⣆⢉⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠋⠑⠒⠐⠂⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠀⠘⠌⠦⣼⡄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠳⢆⣀⣄⣀⠞
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠙⠀⠀⠀⠀⠀⠀⠰⠂⠀⠤

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

⠀⠧⠀⠀⠀⡠⠒⠉⠀⠀⠁⠐⢀⠀⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⡈⢡⠀⠰⠁⠀⠀⠀⡀⠀⠀⠀⠡⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢧
⠀⠀⠀⠀⢈⠀⠀⠀⠈⠋⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠈⠓⠦⣤⣤⠴⠋⠀⠀⠄⠀⢀
⠀⢀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⡠⢃⣀⣀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢈⠦⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⢀⠀⠀⠀⢸
⢠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠇⠂⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⢀⡀⠀⢀⠠
⠀⠀⠀⠀⢀⠄⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠄⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈
⠀⠀⠀⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡛⢂⡶⠛⠲⡄⣴⠚⠳⣆⢰⡗⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠙⢧⣀⣰⠇⢷⣄⣠⠟⢸⣄⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⢠⡀⢀⡤⣄⢀⣀⠀⣠⢤⠀⣤⣄⢀⡤⡀⢠⢀⠀⣄⢠⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠂⠞⠳⠸⢤⡤⠸⠣⠀⠧⡶⠆⠿⠇⠻⣤⠟⠸⡼⠀⠏⠾⠸⡦⠇

⠀⢀⣀⣀
⠀⠘⡔⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠄⠀⠀⠀⠇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠠
⠀⡡⠂⠀⠑⠂⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠈⠑⠂⠤⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢀⡠
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⡠⠀⠀⠀⡠⠀⡀⠀⠀⣀⠀⠀⠀⠲⢁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠔⠁⠀⠀⠀⠀⠉⠐⡄
⡄⠀⠀⠀⠀⠀⠀⢸⠀⠀⠄⠀⢀⣠⠴⠶⠦⣄⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⣄⠠⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠈⢳⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢐⠀⠀⠀⠀⠁⠀⠀⠀⡘⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢐⡀⠑⠄⢀⠀⠀⢀⠠⠞⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢸⣯⣓⢦⡀
⠀⠀⠀⢀⡴⢋⠡⠈⠄⡀⠍⠙⣦⠀⠀⠀⠀⠀⣰⣒⣚⣛⣛⣶⡀⠀⠀⠀⠀⠀⢸⡇⢸⡀⠀⠀⠀⠀⠀⣠⢞⣩⠴⣿⣼⣚⣍⣳⣽
⠀⠀⠀⢸⡧⠬⠤⠤⠤⠤⠤⠤⣼⠆⠀⠀⠀⠘⣧⡤⠤⠤⠤⣤⠇⠀⠀⠀⠀⠀⣞⡉⠉⣧⠀⠀⠀⠀⣼⢡⢏⠤⡅⡏⠿⢟⣫⡵⣆
⠀⠀⠀⢸⡗⠛⢒⣒⣛⣒⠒⠓⢺⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⡟⠀⠀⠀⠀⠀⠸⡇⢹⡇⣸⠀⠀⠀⠀⣇⢸⠘⢒⠋⠷⢚⣭⡀⡇⣿
⠀⠀⠀⠀⢿⣙⣯⡉⠉⢉⣽⣋⡟⠀⠀⠀⠀⠀⠈⡇⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⡟⠉⠀⣿⠀⠀⠀⠀⠹⡜⢧⡻⠗⣡⣌⣋⡼⣡⠏
⠀⠀⠀⠀⠀⠉⠉⠙⠶⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⣸⠃⠀⠀⠀⠀⠀⢠⣇⣀⣀⣻⠀⠀⠀⠀⠀⠙⠦⣍⣛⣓⣛⣩⠖⠋
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⣠⣞⢻⡏⣿⢓⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢿⡳⣄
⠀⠀⠀⢸⠷⠾⠮⠷⠧⠾⠶⣿⠀⠀⠀⠀⠀⠀⣤⣤⣯⣯⣤⣄⠀⠀⠀⠀⠀⣠⠖⠋⡀⢀⠐⡈⠓⢦⡀⠀⠀⠀⠀⣰⢋⠀⡁⢈⠙⣿
⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡿⢛⡧⠀⠀⠀⠙⣶⠓⡶⠚⠲⡖⢳⡞⠁⠀⠀⠀⠀⣏⠠⠀⠄⣠⡼⠁
⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣀⣀⣿⣀⣀⣀⣀⣟⣋⣀⠀⠀⠀⠀⢸⡄⢹⠀⢸⠃⣼⠀⠀⠀⢀⣤⠞⣩⠷⠖⠛⠁
⠀⠀⠀⠀⠸⢤⡤⠤⠤⢤⠼⠀⠀⠀⠀⠈⠧⣄⣀⣀⣀⣀⣀⣀⣤⠟⠀⠀⠀⠀⠀⠳⣼⣧⡾⡴⠃⠀⠀⠀⠘⢦⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⣉⣳⣆
⠀⠀⠀⠀⠀⢀⣀⡤⠞⣧⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⣀⣄⣀⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠻⡄⠀⠀⠀⣸⣥⣤⣽⣧⣬⣧
⠀⠀⠀⠀⣰⠯⠤⠤⠤⠬⢷⡀⠀⠀⠀⣰⠋⠀⠀⠏⠀⠀⠟⠁⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⣠⡏⠙⠓⢿⠀⠀⠀⠹⡞⠛⢚⣷⢶⡏
⠀⠀⠀⠀⡷⠶⣤⠴⢤⡴⢶⡇⠀⠀⠀⣟⣶⣒⣲⣒⣲⣒⣒⣖⣒⣶⣻⠀⠀⠀⠀⠀⢀⡞⠉⠙⠦⣄⣸⠁⠀⠀⠀⢻⣚⣩⡴⡾
⠀⠀⠀⠀⢹⡀⢸⠀⢸⠀⣸⠁⠀⠀⠀⣿⠦⠭⡽⠯⢥⡬⠵⠮⡭⠴⣻⠀⠀⢀⣠⢾⡉⠙⢦⡀⠀⢈⡗⠀⠀⠀⠀⠈⣏⣡⢴⠃
⠀⠀⠀⠀⠈⣧⣸⣄⣼⣠⡇⠀⠀⠀⠀⠈⠉⠙⠛⠓⠒⠒⠚⠛⠛⠉⠁⠀⠀⠘⠲⢤⣷⣀⣠⠿⠖⠋⠀⠀⠀⠀⠀⠀⠹⣄⡟
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢴⢶⣤⡀⠀⠀⠀⠀⢀⣤⡀⠀⢀⣤⡀⠀⠀⠀⠀⢠⡤⠤⣤⢀⣾⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡿⢦⣄
⠀⠀⠀⠀⠀⠀⢀⡴⠛⣧⡾⡶⣴⢧⡀⠀⠀⣴⠋⣄⠙⣶⠋⣄⠙⣆⠀⠀⠀⠈⡏⠉⡇⠸⡷⢾⡇⠀⠀⠀⠀⠀⠀⣠⢞⡼⣳⠋⠈⢹⡄
⠀⠀⠀⠀⢀⡴⠋⠀⠀⣿⠶⢿⣹⠋⠀⠀⠰⡇⢀⡼⠀⢸⢀⡞⠀⢸⠀⠀⠀⢀⡇⠸⣧⡞⠁⠈⢳⡆⠀⠀⢀⡴⢞⡵⣫⠟⠁⠀⠀⣸⠃
⠀⠀⠀⣴⠋⠀⠀⢀⡴⠃⣠⠞⠁⠀⠀⠀⠀⢳⡈⠃⣠⢾⡈⠇⣠⠟⠀⠀⠀⡏⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⢿⢚⡿⠞⠁⠀⠀⣠⠞⠁
⠀⠀⠀⠘⢦⣀⡴⠋⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠙⠶⠋⠀⠙⠶⠃⠀⠀⠀⠀⡇⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠈⠻⣄⠀⢀⣠⠞⠁
⠀⠀⠀⠀⠀⠙⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠲⠚⠓⠒⠶⠚⠃⠀⠀⠀⠀⠈⠉⠉

⡿⢿⠿⠿⡿⠻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣻⣛⣿⣿⡿⣿⣿⣿⣿

⠀⠀⠀⠀⠠⠀⠀⠠⢄⠄⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣐⠻⣷⡶⢀⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣀⢆⣂⡠⠧⠄⢀⡀⠀⠀⠀⠀⠈⠐⠨⠻⣭⣑⢲⣤⡀⠀⠀⠀⢰⣿⡒⢂⡀⠀⢀⣴⡿⡀⠀⠀⠀⠀⡄⠐⠀⡀
⠀⠀⢹⡀⢙⢴⣤⣾⣾⣿⣽⡁⠀⠀⠀⠫⡇⣰⠶⡧⢢⣜⣰⠂⠀⠀⠐⣭⣛⡻⢟⠶⠗⠚⣡⠀⠀⠀⢀⡀⡀⠁⠠⠁⡀
⠀⠀⠀⠀⠀⠈⠙⠛⠛⠁⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠉⠍⠋⠀⠠⠀⠀⠀⠀⠀⠚⢦⣄⡔⢌⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠶⠀⠀⠒⠆⠀⠐⠂⡀⠀⠀⠀⠀⢠⣶⣦⣄⡔⠦⢤
⠀⠀⢀⣄⡟⠛⠂⣸⢻⣵⠦⡀⠀⠀⡀⢂⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠈⢻⢿⢿⣷⣞⠨⣧⡄⠀⠀⠈
⠀⠀⠿⣀⠀⠀⠰⣿⢲⢵⣡⡶⠀⠀⠀⠀⡈⠐⠀⠀⠚⠈⢠⠀⠀⠀⠀⠀⠀⠐⠯⠷⠏⠉⠛⢳
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠉⠀⠀⠀⠀⠀⠀⠲⠤⠠⠠⠤⠶⠈
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⡐⠀⢄⠀⠂⠈⠁⣀⠀⠀⠀⠠⡚⠢⠈⠙⠴⠿⠆⠀⠀⠀⠀⢀⠀⢔⠂⠀⠂⠀⠀⠀⢰⡎⣻⣷⢿⣯⣗⣦⣄⡀
⠀⠀⠀⠣⠩⠄⢄⢠⣤⠔⠀⠛⠀⠀⠀⢷⡖⢂⣂⠀⠀⡀⠢⠂⠀⠀⠆⡀⢀⠀⠐⠀⡀⠀⠀⡀⠀⠉⠉⠦⢤⠿⠒⠣⣴⠼⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠉⠀⠁⠀⠀⠀⠈⠑⠦⢄⠀⠘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⡔⠀⠀⠀⢠⢦⠤⠀⠀⠀⠀⡀⠀⣠⠀⠀⠀⠀⠤⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠄⢠⠀⠀⠀⠀⠀⢀⢀⡖⢒⡀
⠀⠱⠔⠀⠀⠀⢉⠝⠀⠀⡠⡐⢎⠋⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⢐⡈⡈⡁⢘⠀⠀⠀⠨⡩⠎⠨⠀⢤
⠀⠀⠀⠀⣉⠄⠀⠀⠀⠀⠐⠂⠀⠀⠀⢸⠀⠀⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠒⢣⠀⡆⣀⠀⠀⠀⠀⠰⠝⢈⡑⠉⣀⡀
⠀⠀⡠⠀⠀⠀⣀⠀⠀⠀⠐⢄⡀⠄⠠⠂⠀⠀⠀⠁⠂⣤⠀⠀⠒⠁⠀⠀⠀⠰⢍⣏⣜⣨⠕⠃⠀⠀⠀⠀⠀⠀⠇⠴⣬⠘⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⢀⣀⡀
⠀⠀⢀⢀⠔⠀⢰⠒⠒⢄⣀⠀⠀⠀⠀⠀⢶⣐⢊⡙⠄⡀⡀⠀⠀⠀⠀⠰⠛⠓⠶⡀⡄⠀⠀⠀⠀⠀⢀⠋⠠⠤⠇⠀⠈
⠀⡁⠜⢐⠒⡠⠀⠙⠪⡦⠄⡀⠀⠀⠀⠀⠀⠁⡀⠉⠐⠘⠘⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⠶⠀⠄⠀⠀⠀⠓⠀⠂⠐⠀⠐⠂
⠀⠀⢬⡃⠀⠑⠒⠂⠀⠊⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠈
⠀⠀⢀⡤⡀⢀⠀⠀⠀⡠⠀⠀⠀⠄⠀⡤⡏⠁⠀⠀⠀⠀⣀⢀⠀⠀⡂⠀⠀⠐⠣⣀⡀⢤⠰⣐⠀⠀⠀⠈⠉⠱⡄⣔⣲
⣰⡓⡆⠌⡌⠩⠈⠦⢴⡁⠀⠀⠇⢀⣞⠷⢁⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠆⠀⠀⠤⠅⠀⠈⠀⠠⠀⠀⠀⠀⠐⠀⠰⡌⠩
⡌⠀⠐⠂⠈⠁⠧⠢⠖⣣⠀⠈⠁⢦⠏⠠⠊⠀⠀⠀⠀⡁⠰⠀⢠⠴⡀⠃⠀⠀⠀⠐⠂⠁⠀⠰⡆⠀⠀⠀⠀⠀⠀⠀⠠
⠈⠑⠒⠲⠆⠀⠀⠐⠈⠊⠀⠘⡔⣣⠆⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠊⠀⠂⠀⠀⠀⠀⠈⢄⡠⠇⠃⠀⠀⠀⠀⠁
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠁⠀⠉
⠀⡠⠀⠃⠀⡠⣢⠰⡀⠀⠄⠀⠀⠀⠀⢀⠀⠒⠒⠒⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠰⠀⠈⠁⠀⠀⠀⣔⠲⢣⡀⠀⢀
⠀⠃⠀⢀⡔⠈⠈⠢⠀⠀⠰⠈⠀⠀⠀⢊⠳⣀⡠⢄⠤⡚⡄⠁⠀⠀⠀⠀⠀⢠⠆⠒⠠⠈⠀⠀⠁⠀⠀⠱⠊⣁⢝⣠⠍⣬⠂
⠀⠢⡈⠆⢄⣉⣄⢠⣀⡀⢁⠆⠀⠀⠀⠈⠁⠐⠼⠠⠐⠁⠁⠀⠀⠀⠀⠀⠀⠰⠄⠄⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⠛⠼⠑⠁⠆
⠀⠀⠀⠈⠁⠀⣀⠀⠉⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠐⢤⣀⣀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠁⠦⠂⠄⠀⠀⠀⢀⡀⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠈⠀⠈⠑⠉⢂⠀⠀⡤⠂⠉⠀⠈⠐⢄⠀⠐⠢⠑⢈⠂⠉⠀⠀⠰⠄⣖⠀⠀⡀⠀⣄⠀⠀⡠⠈⠒⠉⠣⢀⠈⠀⢀
⠀⠀⠑⡀⠄⠀⠁⢀⠌⡀⠀⢃⠀⠀⠀⠀⠀⠼⠀⠀⠈⣇⢉⠇⠀⠀⠀⣀⡀⡺⠐⣉⢠⠀⠀⠀⠐⠁⠈⠁⠀⠀⠀⠐⣰⢯⢄
⠀⠀⡀⠈⠒⠒⠒⠀⠀⡀⠀⠀⠄⢉⢀⡈⠈⠀⠀⠀⠀⠘⡬⠀⠀⠀⠀⠀⠀⠜⠒⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠴⠘⠚⠆
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣀⣀⣐⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣔⣁⣀
⣿⣿⠋⡛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢧⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⢦⠳⣄⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠈⠳⠜⢠⡀⢰⡖⠈⣿⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠞⢁⡄⢀⠀⠀⣴⠚⣹⠂⢿⡇⠀⣰⠀⠀⠀⡀⠹⣞⣿⣄⣩⠒⠊⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⣆⣹⣦⠉⣰⠋⠀⠀⣉⠳⣿⣤⣄⣉⡈⠁⢀⡴⠂⠹⣷⠾⣧⠉⠉⠀⠰⢯⡀⣷
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣯⠀⠈⢷⡈⠓⣠⣞⠁⣦⠙⣦⡙⠆⠀⣄⠠⣄⠉⠴⠆⣰⠞⠀⠀⣀⡀⣿⠙⡎⠳⠇
⠀⠀⠀⠀⠀⠀⠀⠘⠁⠘⢷⠀⠀⠁⠘⣇⠈⢷⡌⠓⠋⠙⠀⣀⠙⢧⡙⣦⠀⠚⠁⣠⡶⠈⣧⠙⡞⠳⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⡘⢧⡘⢷⡀⠙⢂⣀⣴⢋⠙⣿⠾⢷⠌⠁⠀⠰⠻⣤⠆⠙⠦⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢻⣾⠁⠀⠙⠚⣅⢀⡈⣷⠹⣏⣠⡌⠃⠀⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⠀⠀⣠⣜⣧⠙⢾⣧⠘⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢰⡶⣌⢿⡛⠷⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠈⠷⡼⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀⠀⠂⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢘⡲⠀⠙⠉⠛⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠀⠀⠘⣂⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠓⢂⡄⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡜⠀⡄⠀⡷⢶⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣀⠀⠀⠀⠀⠀⢐⡖⠀⠋⢉⠀⢠⡄⠀⠀⠀⠀⠀⠀⠈⠀⠁⣈⠐⠀⢀⣠
⠀⠀⠀⠀⠀⠛⠋⠁⠖⢠⡻⡄⠹⠁⠀⣠⣤⣤⣬⣠⣬⢇⣾⡤⣏⣀⣤⣀⢠⣆⠁⠀⠀⡼⠃⡤⠴⠛⢉
⠀⠀⠀⠀⠀⠘⠂⠀⠈⠀⠐⠳⠠⠀⡀⣈⢳⣿⡾⢫⡇⠉⣻⣿⡀⠘⠀⢇⣸⣿⣿⡿⢰⣣⣄⠄
⠀⠀⠀⠒⠉⠁⠉⠡⠦⠀⢠⡀⠀⣾⠑⠟⢈⣣⡆⣼⡟⠛⠻⣤⡠⠾⠟⠃⠙⡟⠒⢴⢿⣏⣥⣖⣴⢂⢀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠙⣴⣯⣰⢷⡴⡄⠀⠈⢢⣼⠾⠿⣷⣼⠦⣤⣴⣾⣶⣶⣾⣿⠛⠛⣿⣿⣋⣀⣤⢀⡖⠁
⠀⠀⠀⠀⣀⡀⢈⠀⠀⠠⢀⢀⠁⢼⣿⣿⣿⠽⣦⡰⣮⣄⢀⣄⠩⣿⠐⢋⣴⣿⣿⡿⢿⡿⣿⢿⣿⣷⣿⣿⠷⠲⠄
⠀⠀⣴⣾⣿⣿⠂⠀⣤⡀⠀⣈⣳⣂⣸⣿⡇⠀⣙⠀⠀⠰⣿⣿⣿⣃⡴⠿⠛⠉⣿⣧⣿⠁⢻⣦⢿⣿⣿⣶⣶⣙⣆⠂
⠀⠈⣟⣤⣌⠉⣶⡀⠋⢙⡿⠉⠉⢩⣿⣿⣇⠀⢩⠀⠐⠘⢌⠉⠷⢛⣷⣦⣴⣾⠃⠀⠀⠲⣾⠏⣉⣉⣨⢉⠛⡁⢫
⠀⠀⠙⠛⠁⠀⢲⡄⣴⣾⣿⠆⠀⠀⢁⡀⠈⠳⣦⠀⠀⠀⠈⢰⡶⠋⣹⣥⣿⣿⣄⠀⠀⣽⢧⣼⣏⣩⣿⠇⠈⣁⣠⡄
⠀⠀⠀⠄⠀⡀⢼⠗⠰⢾⣁⠊⠀⠀⠀⣋⡙⠆⢠⡀⠠⢤⡈⠁⠀⣠⠋⠉⠀⠉⢻⠿⢿⣿⣤⠍⠙⠉⠉⢈⣠⣛⠛⠀⡀
⠀⠀⠈⠀⠘⣋⣴⣷⠀⣾⡟⣿⢥⣠⠎⣹⣿⠐⢀⢳⣤⣴⡏⢡⠋⠈⠖⢒⣿⣿⠛⠲⠊⣹⣿⣿⣶⣗⣲⣿⣟⣛⡉
⠀⠀⠀⠀⠀⠁⠘⢋⢰⣿⡣⠙⢛⠃⠾⡿⠃⣴⢿⠟⠛⢿⣧⡀⠠⠞⠃⠈⠉⠈⠁⠛⠉⠺⣽⣿⣯⣼⣿⣿⣿⣿⡅⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⠋⣨⡛⠳⢊⡡⠾⢿⡯⣤⡄⠀⠋⠀⠀⠀⠀⣀⢠⣤⣀⣀⣤⣤⣤⣙⣿⣿⣿⣿⠋⡿⠑
⠀⠀⠀⠀⠀⠀⠀⣘⣤⣜⠀⠀⣽⢻⡏⣰⣧⣮⢀⣀⣤⡆⠀⣀⣤⣶⣯⠉⠀⢀⡁⠈⠘⣿⣿⢏⣽⣿⠿⠿⣦⣄⠀⢨
⠀⠀⠀⠀⠀⢀⣸⠿⣿⣧⠀⣰⣿⡓⠻⡿⠋⠀⠀⠈⢉⣵⣶⢿⡯⠙⡟⠓⣶⣿⣿⣦⣤⣿⣷⣾⣷⡦⠂⠈⡟⠿⠷⠾⢅⠠
⠀⠀⠀⠀⠒⣻⠟⡦⠸⢷⣠⠛⣿⡨⠂⠀⠀⠀⢀⡴⠟⣿⡟⠸⣧⣼⣿⣦⣹⣿⣿⣿⣿⣿⣿⠏⠙⣿⢾⣿⣷⣖⢃⣠⡀⡼
⠀⠀⠀⠀⠀⡰⣦⡀⠤⠀⣩⠆⠉⠀⠀⠀⣠⣾⣿⡠⠾⠛⢿⣿⡿⠛⠙⣛⣿⣿⡟⠉⠁⠀⣽⡄⣤⡿⢀⣿⣿⣿⡛⣿⣆⢰
⠀⠀⠀⢀⣴⢂⣅⣰⠤⠛⠁⠀⠀⢀⣤⣾⢿⠯⣭⣄⡈⣈⡀⠓⡇⠀⠉⢉⣿⠡⡤⣴⠆⢼⠋⠀⢨⡷⢿⡃⣼⣿⣿⣤⣿⢈⡄
⠀⠀⠀⠀⠀⠀⠈⠙⠶⢶⡤⠰⢾⠟⠉⣅⡀⠘⠷⠦⣀⠉⢭⣙⣹⠿⠿⢿⣿⣾⣀⣤⣀⣼⡗⠚⢻⣅⡼⢿⣿⣿⣿⣿⣿⣬
⠀⠀⠀⠀⠀⠀⢀⣀⣀⠲⠀⡀⠀⠀⢾⡏⠟⠀⠀⠀⣸⣷⣿⠋⠀⣠⠀⠀⠀⠀⢹⣧⡀⣠⣀⣠⣼⠏⠀⣠⣿⢿⣿⣿⣿⡏
⠀⠀⠀⠀⠶⠒⠓⠈⠵⠆⠈⠆⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠃⢰⣿⡇⠀⠀⠀⢀⣾⣿⢻⣇⣀⣀⡀⠀⢸⠏⢻⣤⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣰⡀⠀⠀⠀⣀⠀⢀⣾⣿⣷⣧⣀⣻⡆⠰⢢⣤⣴⣿⣿⣏⡁⣾⣿⣷⣶⠿⠲⣿⠁⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣶⣿⣿⣥⣾⣿⡿⠿⠿⠋⢿⠉⠑⠲⠶⠿⣻⢋⣽⣿⣿⡟⡙⠦⣹⣷⠎⠉⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⡉⠂⡄⣤⣀⣈⡀⣠⣵⢾⠾⠃⠀⠛⠛⠁⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠓⠋⠐⠻⠚⠫⣽⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠔⠒⠈⠉⠉⠉⠉⠉⠐⠒⠢⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⢀⣤⡶⠾⠛⠛⠉⠉⠉⠙⠛⠛⠷⢶⣤⣄⡀⠀⠀⠈⠲⣄
⠀⠀⢠⢀⡄⣠⣠⡀⠀⠀⠀⠀⢀⡔⠁⠀⠀⣠⣾⣟⠥⠒⠈⠉⠁⠒⢤⡀⡰⠉⠉⠓⣄⠀⠉⠻⢷⣄⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⢀⢄
⠀⠀⢸⣾⣿⣿⢻⡇⠀⠀⠀⢠⠊⠀⠀⢀⣾⢫⠊⠀⠀⠀⠀⠪⠕⠘⠓⢹⣧⠀⠀⠀⢨⠗⠲⣦⡴⠋⠙⣆⠀⠀⠈⠣⡀⠀⠀⠀⠀⢸⠀⠑⡄
⠀⠀⢸⣧⣿⣿⣾⡇⠀⠀⢠⠃⠀⠀⣰⡟⡱⠁⠀⠀⠀⠀⠰⠆⠀⠆⢰⡆⡟⠀⠀⠀⠈⢦⣁⣎⣣⣌⣰⠽⣷⡄⠀⠀⠱⡀⠀⠀⠀⢸⠀⠀⠸⡀
⠀⠀⠘⣿⢿⠿⣿⠃⠀⢀⠃⠀⠀⢰⡟⢠⠃⠀⠀⠀⠀⠀⠀⠀⢰⡲⠀⢀⠃⠀⣀⡀⣀⠀⣃⠤⠈⣧⠶⣀⣠⢿⡄⠀⠀⠱⠀⠀⠀⢸⠀⠀⢀
⠀⠀⠀⠈⢲⡖⠁⠀⠀⡎⠀⠀⢀⡿⠁⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢉⡉⢡⣒⡄⢍⠙⠶⡴⣿⡯⠟⠀⠀⢿⡄⠀⠀⠇⠀⠀⢸⠀⠀⡸
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠇⠀⠀⢸⡇⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢁⡳⠞⢔⡣⠈⠒⢁⠼⢄⣩⠧⠀⢀⡀⠘⣷⠀⠀⢸⠀⠀⢸⢀⠜
⠀⠀⠀⠀⢸⡇⠀⠀⢰⠀⠀⠀⣼⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢣⠃⢞⡆⣀⡰⠽⠃⠀⠀⠀⠀⠀⠀⠘⡄⣿⡀⠀⠈⠀⠀⢸⡏
⠀⠀⠀⠀⢸⡇⠀⠀⠈⠀⠀⠀⢿⢀⠎⠀⠀⠀⠀⠀⠀⡀⠔⠊⠀⢔⡲⠣⠗⠭⡼⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⣿⡇⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⢸⢰⠀⠀⠀⡇⠀⠀⡼⠋⠀⠀⠀⠀⢠⠔⠉⠀⠀⡴⠒⠲⢤⡀⠪⢵⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣿⠀⠀⢸⠀⠀⢈⣿
⠀⠀⠀⠀⢸⢸⠀⠀⠀⢡⠀⠀⠑⣾⣄⣀⡀⢠⠃⢠⣊⠉⢆⠙⢅⠠⠀⠛⡄⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢫⡟⠀⠀⡆⠀⠀⠸⢨
⠀⠀⠀⠀⢸⠸⠀⠀⠀⠀⢇⢰⠒⠛⠀⡇⠈⠁⠀⡆⠀⠐⡎⣰⠫⢿⠒⠛⢁⢴⠦⢕⠢⢤⡀⠀⠀⠀⠀⢀⠞⢠⡿⠀⠀⡸⠀⠀⠀⡆⢸
⠀⠀⠀⠀⢸⠀⡆⠀⠀⠀⠈⢎⠒⠢⣀⣼⡀⠀⠀⣇⠄⢸⠃⡌⠀⠬⡆⠀⢂⢏⠔⣹⡤⡖⠸⡂⠤⠤⠔⠉⣰⡟⠁⠀⡰⠁⠀⠀⠀⡇⢸
⠀⠄⠀⠀⢸⠀⡇⠀⠀⠀⠀⠈⠣⡀⠀⠈⢿⣦⡀⠈⠋⠁⠀⠹⡀⣴⠀⢀⡤⠹⢏⠐⡤⠬⡷⡝⠀⠀⣠⡾⠋⠀⢀⠔⠁⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⢸⠀⢡⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠈⠻⣦⣄⡀⠀⠀⠈⠁⠀⢺⡈⢆⣲⠇⠈⠑⢉⣠⣴⠟⠋⠀⢀⡤⠋⠀⠀⠀⠀⠀⠀⡄⢸
⠀⠂⠀⠀⠈⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠉⠛⠷⢶⣤⣤⣄⣀⣑⣶⣥⣴⠶⠞⠛⠉⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠉
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠐⠒⠒⠒⠒⠒⠂⠉⠉

⠀⠀⠀⠀⠈⠀⢀⠀⠀⢀⠀⠀⠀⢀⡍⠑⢖⠓⢀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠈⠀⠀⠀⠐⠀⠠⠀⠀⠀⠀⠜⠁
⠐⠄⡈⠒⠀⠐⠂⡁⠀⠀⠀⠀⠀⠀⠁⠉⢀⡙⢌⡁⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢄⠆
⠀⠀⠰⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⣀⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠄⠀⠄⠒⠂
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⢀⠄⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⣀⠀⠀⠀⠀⠀⠀⡠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⣠⣤⡖
⠀⢀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⣠⢠⡾⣞⣷⢠⠃⠀⠀⠀⠀⠁⡉⢀⠀⠐⠀⡎⠉⢲⠀⠈⡓
⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠃⠀⠀⡽⠐⠑⠡⠋⢈⠆⠀⠀⠀⠀⠀⠀⠄⠀⠀⡄⠓⠒⠚⠁⢀⠁
⠀⡀⠐⢠⠀⠀⢀⡂⣀⠤⠂⠀⠀⠈⡀⠀⠀⠀⡘⢸⠀⠀⠀⠠⡴⠀⠀⠀⢀⣤⣄⠀⣀⡤⠖⠁⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠆⠀⢀⢠⠟⠁⠂⠀⣁⡀⠀⠀⠀⠀⠀⠀⢀⠑⠂⠀⠁⠀⠑
⠀⠀⡄⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⠔⢬⡀⠤⠂⠉⠀⢀⣀⣀⡀⠀⠀⠀⠙⠀⠻⡄⠀⢀⡄
⢀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡈⠀⠀⠀⠈⠉⠂⠄⠀⠀⠀⢣⡐⠉
⠈⠃⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⢀⡀⠢⠀⢀⠀⠀⠠⠄⠀⡀⠁⡀⠌⠀⠀⠀⠀⠀⠈⠂⡀⠐⠀⠀⠪⢠⠀⠐
⠀⠀⠀⠀⠀⠀⠒⠊⠀⠀⠀⠀⠀⠈⠑⠀⠀⠄⠀⠀⠀⠀⠘⢀⠀⠀⠐⠀⡈⠐⠀⠀⠄⠀⠈⡄⠰⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠄⠀⠀⠐⣤⠀⠀⠆⠀⠀⠈⢢⠈⡇⠀⠀⠀⡅⠀⠀⠘⠀⠀⠀⢀⠀⠀⠀⠀⠀⡁⠀⡅⠀⠀⠀⠨⠃
⠀⠀⠀⠐⠋⠀⠀⠀⠂⠈⠁⠄⠀⠱⡀⠀⠀⠀⡇⠀⠀⠀⢃⠀⠀⡓⠂⠀⠀⠀⠀⠁⠀⠀⠐⠀⢰⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡙⠓⢄⢀⡇⠀⠀⠁⠨⢆⠐⢀⠀⠐⠀⠠⠀⠀⠀⠄⠀⠤⠁⠀⠀⠠
⠀⠀⠀⠰⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠄⠀⠀⠱⠤⡈⠀⠀⠀⠂⢀⣀⠴⠊
⠁⣀⡀⣠⣶⣿⣧⣴⣾⡟⠀⠀⠀⠀⢀⡀⠋⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⡄⠀⢠⠀⠀⠀⠀⠀⠀⠠
⣈⣿⣿⣍⣟⣿⣿⣿⣯⣷⣤⠤⠄⠒⠀⠀⠀⡀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡲
⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣛⠆⠀⠀⠀⠄⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠟⠛⢻⢿⣿⣿⠂⠃⠀⠙⠋⠀⠀⠀⠀⠀⠈⠂⠈⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠘
⠀⠀⠀⠛⡙⠉⠀⠀⠀⠀⠀⠀⠠⠔⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⣀⡤⠄⠀⠠

⠀⢀⡔⠋⠉⠓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⣉⣙⢢⡀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠒⠒⠒⠦⡄
⠀⢸⠀⠀⠐⠠⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⢿⣈⣉⣿⢀⡇⠀⠀⠀⠀⠀⠀⢀⠎⢠⡤⠀⠛⠁⠀⠸
⠀⠈⢧⡀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⡿⠿⠛⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⣯⡔⠋⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡀⠰⠶⠀⠛⠃
⠀⠀⠀⠹⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⡏⠹⠋⠉⣈⣁⡤⠤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡉⠁⠀⠰⡦⢀⡰
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠶⠒⠒⠋


⠀⣀⣠⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠙⡲⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠊⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⣀⠀⢶⢲
⣰⠛⠃⠰⠶⠀⠛⢣⡀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⡅⡽⠀⠀⠀⠀⠀⠀⠀⢰⠉⠈⠀⠈⡈⢱⠀⠀⠀⠀⠀⠀⢀⡞⡡⠒⠒⠚⠀⡸⢸
⢇⠰⠗⠀⠀⠰⠗⢀⠇⠀⠀⠀⠀⠀⠀⢮⠀⠀⠀⠌⡼⠁⠀⠀⠀⠀⠀⠀⠀⢨⡶⡶⠶⠶⣶⢢⠁⠀⠀⠀⠀⠀⠀⠉⠁⢯⡓⣄⢾⡥⠋
⠈⢹⢒⠒⡒⢒⢺⠁⠀⠀⠀⠀⠀⠀⠀⢀⣷⣄⣌⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢱⠿⠷⡁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠘⡆
⠀⠸⠼⠦⠧⠾⠼⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⠼⠾⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠼⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⢀⣤⣤⣀⣀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⣎⣁⡉⠲⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀
⣿⠁⠀⣭⢻⡅⠀⢹⡇⠀⠀⠀⠀⠀⠀⡠⠛⠉⠣⠔⢍⢳⠞⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠤⢤⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣋⣛⣿⣿⣷
⠹⡆⣀⡜⢧⡀⢠⡾⠁⠀⠀⠀⠀⠀⡎⠒⠀⠄⠁⣠⠞⠊⠀⠀⠀⠀⠀⠀⠀⡞⠹⡇⠀⠀⠸⠈⣇⠀⠀⠀⠀⠀⢸⡟⢿⣿⣿⣿⣿⡿⢻
⠀⠚⠋⠶⠦⠙⠮⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠪⡭⠖⠓⠦⠴⠓⠮⢭⠇⠀⠀⠀⠀⠀⠙⠲⠤⢤⡤⠤⠞⠉


⠀⡤⠤⠤⠤⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⡀
⠀⢳⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⡋⠉⠉⢑⡄
⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠴⢖⣋⣉⣀⡙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡤⣤⡾⠁⠀⠀⠀⠀⠀⠀⠀⢈⡱⣾⡛⠓⠒⠻⡄
⠀⢸⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠺⠷⣶⣶⣦⣤⣭⣍⡁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡜⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣗⡯⣒⣒⣺⡇
⠀⢧⣠⣴⣖⣒⣈⠆⠀⠀⠀⠀⠀⠀⠐⠒⠒⠦⠤⠭⢭⣍⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⡱⠿⣗⣓⡾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⢆⣼⠀⠀⠀⢸⡟⣗⣿⣿⣺⣄⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣿⡆⢚⠀⡄⣿⣉⣹⣿⣿⣯⣿⣧⣤⠶⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣀⡘⣿⣿⡧⢾⡶⢧⣶⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣦⠐
⠀⠀⠀⠀⠀⠀⠀⢰⢇⣿⣿⣿⣟⢻⣿⠟⠛⠃⠀⠀⠈⠙⠋⡭⠿⣟⣗⣺⣿⡎⣉⠘⠿⣿⣗⢀
⠀⠀⠀⠀⠀⡀⠀⠚⠛⠿⠥⡈⢈⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⣹⣶⣿⣸⠟⠟⠛⠏⠙⠻⢿⣯
⠀⠀⠀⠀⡄⠀⠀⣀⡄⠀⠀⢸⣘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠄⢿⣛⣵⡃⡄⠠⣰⠀⠀⣰⢻⣿⣿⡆
⠀⠀⠀⡄⣾⣄⡀⣀⣀⣀⣠⣿⣩⣭⣽⣿⣷⠄⠀⠀⢠⣿⣿⣿⣿⣿⣙⠓⠴⠿⠷⠄⣚⣿⣿⣿⡇
⠀⠀⠀⠉⠿⠿⠿⠿⠿⠿⠿⢿⡿⠿⠿⠷⠾⠶⢾⡶⢶⠾⠿⠿⠾⠷⠿⠿⠿⠾⠿⠿⠿⠿⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠛⠉⠉⠉⠉⠉⠋⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣷⡄⠀⠀⠾⠂⠀⠀⠀⠛⠆⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡟⠀⠀⠀⢀⡀⠀⢀⢄⣀⠀⠀⢧⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⢛⣻⣿⡀⠀⠀⠀⠉⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣌⣣⡙⠃⠀⠀⢰⠀⠘⠲⠼⠀⠀⠀⠀⢸⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣈⠙⣧⠀⠀⠈⠙⠦⣀⣀⣀⣀⠴⠀⠀⡟⠀⠀⠀⢹⡃
⠀⠀⠀⠀⠀⠀⠀⠚⠃⣤⣀⠉⣻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⢀⣸⣯⢳
⠀⠀⠀⠀⠀⠀⠀⡴⠯⣀⣨⠟⠃⡏⠙⢦⣄⣀⡈⢀⣓⣃⡤⢾⣅⠀⠀⠀⠁⣽⢛⠿⣀⡴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢉⣀⡂⠇⠀⠀⣼⠋⡏⠉⢫⠀⠱⠸⣏⢦⡀⠀⠘⣌⠷⢂⣩⠟
⠀⠀⠀⠀⠀⠀⠀⣰⠯⢻⢩⢉⡟⣧⢀⣼⠃⠀⠃⠀⠘⡀⣄⢤⡹⣆⡛⣤⠀⢸⠀⡎
⠀⠀⠀⠀⠀⠀⢰⡇⡇⠘⢸⢸⡇⡎⢹⡃⠀⠀⢞⢢⣠⠁⠟⢌⡇⠙⢟⠁⠀⡸⠀⡇
⠀⠀⠀⠀⠀⢠⡏⡇⣧⠀⢸⢸⡇⠃⣨⡧⠀⢠⠈⡇⠁⠀⢀⣘⡵⠁⠈⡇⢠⠃⠀⢹
⠀⠀⠀⠀⠀⣸⡃⡇⢹⣧⢐⣨⡷⠟⢫⡀⠀⣸⣅⡇⢠⠞⠉⣡⣤⣤⡼⠱⡾⠀⠀⡼
⠀⠀⠀⠀⠀⣿⡇⡇⠀⢹⠻⣿⡄⠀⠀⣿⡛⢫⠟⢠⢻⢳⢻⣽⠀⠳⣄⢀⡠⠄⠰⠳⢤⡄⡀
⠀⠀⠀⠀⠀⣿⠁⠇⠈⢸⢀⠀⢷⡄⠀⠘⠷⠋⠀⣾⢸⢸⣹⡇⠀⠀⢠⠋⠐⠒⠀⣀⣠⠤⠈⣶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⣿⠷⢿⣦⣼⣬⣀⣆⣻⣄⠀⠀⠀⣸⣃⣸⣴⣿⣡⣤⣶⠾⡎⠁⠐⠁⠀⠀⠀⣠⠏⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠉⠉⠉⠙⠛⢧⣀⣴⣯⣿⣿⣿⣿⣿⣿⣿⣄⠈⠒⠤⠤⠤⠔⠚⢁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⠃
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠤⠴⠶⢦⣤⣙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⠻⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠙⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⠻⣆⠉⠻⣿⣿⣿⣿⣿⣿⣿⠿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⣤⣤⣤⣤⣤⣤⣼⣿⣀⡀⠀⠀⠈⢷⡀⢿⢀⣩⣿⣿⠋⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠉⠛⢦⡀⠀⠀⢳⣾⣿⣿⣿⣿⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠻⣄⣴⣿⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣿⣿⡿⢫⣉⠁⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠀⠘⠿⣿⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣤⡆⢀⠀⠲⠒⢲⡶⠶⠶⣶⠶⠖⠠⢀⣀⢀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠓⠀⠈⠀⡀⠈⠀⠀⠀⠈⠀⠀⠀⠤⠀⠀⠰⠀⠈⢩⣟⠻⡿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠞⠃⠉⡀⠀⠀⠊⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠅⠀⠐⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠁⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠤⠀⠀⠀⠙⠁⣽⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠛⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢤⣿⣿⢦⡀
⠀⠀⠀⠀⠀⠀⢀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⢸⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⣘⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡄⠐⣻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠘⣟⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⣷⣤⣼⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⢛⠿⢶⣦⣤⣀⣀⣀⣀⣄⣀⣀⣠⣤⣀⡀⠀⢀⣀⣀⣀⣀⣀⣤⣀⣀⣤⣤⣤⣤⣶⣿⣿⣿⠿⣟⣛⡭⣉⣠⢶
⠀⠀⠀⠀⠀⠀⠀⠀⢈⢿⣷⣦⣈⠉⢉⣛⣛⠛⢛⣻⣟⠛⠟⠻⢿⢿⣿⣯⣿⣯⣍⣭⣭⠽⠈⢦⡉⠁⢀⣰⡟⢉⠾⠋⢗⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠰⠚⣉⡙⠿⠿⠍⣉⣿⣿⣿⡟⢻⣿⣿⣦⣤⣤⣴⠿⣷⠾⡯⠟⠛⠿⢿⡴⠋⠳⢍⣻⡿⠻⠷⠁⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣭⡥⣄⡀⠀⠋⠙⠿⠻⠿⠛⢻⠿⢻⡿⡯⠋⠀⠋⠉⠀⠐⠂⠒⠉⠀⠀⣀⣀⣀⣀⣀⣀⣠⣤⣶⣶⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠧⣿⣿⣷⣶⣏⡋⠉⠀⠀⠒⠓⠀⠊⢀⣠⣤⣴⣶⣶⠶⣶⣶⣶⣾⣿⣿⣿⣿⡿⢛⣽⣿⣇⣼⢧⣼⡏⣨⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣌⢙⣧⣄⡙⢟⣷⣄⠀⠀⢀⣠⣾⣿⣯⣤⣶⣿⣭⣼⡿⢃⣾⠏⢀⣾⠿⣿⢹⣟⠉⣸⣿⣏⣾⡯⣴⡏⢀⡀⠘
⠀⠀⠀⠀⠀⠀⠂⠈⠉⡃⠛⢮⠛⠿⢙⣛⢻⣿⣧⣴⣿⣿⣛⠉⢻⢿⣭⣼⣿⣋⣾⡿⠿⠿⠿⢛⣴⣟⣨⡿⣿⣿⠿⡿⡗⠓⢄⣁⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠶⡥⢄⡠⢀⣀⠀⠀⣈⡉⣉⣉⣤⣤⣞⡀⠒⡢⠈⠟⠀⢐⠊⣀⣀⣉⣡⣽⣄⣤⣤⣏⣀⣿⡿⠶⠾⢿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠙⠛⠻⠙⠿⠟⠋⠛⠻⠗⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠁⠉⠹⡟⠀⡀⢠⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⣄⠀⠀⠀⣰⣀⣼⣦⣼⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠶⠤⠤⠤⠤⣤⣤⣤⣄⣤⢀⣀⣠⣤⣄⣴⣶⣴⣤⠤⠴⠾⠿⠿⠒⠶⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠃⢠⠀⠀⠀⢈⡐⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠁⠤⠀⠀⠀⠑⠀⠀⢈⠤⠀⢠⠈⢦
⠀⠀⠀⠀⡠⠔⠁⣀⣀⣀⢀⡀⠀⠀⠀⢀⠁⠀⠈⣠⠀⣀⣀⠀⠀⠀⠀⠐⠂⠀⠀⢱⠁⠘⠀⡈⠳⠦⠤⠀⢀
⠀⠀⠀⢆⣁⡨⢉⠀⠠⠀⠀⠀⠀⢀⠴⠀⠀⠀⠀⠉⢤⢌⡉⣀⠀⡁⣦⠘⠀⠀⠀⠀⠙⠬⡤⠤⡀⠐⠒⠊⠁⡀
⠀⠀⠀⠀⠀⠁⠘⠑⠞⠀⠮⠐⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⠚⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠰⠤⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⠤⣀⠀⡀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠚⢉⠀⠀⠘⠄⢧⠀⠘⢷⣄⠀⠀⠀⠀⠄⠀⠀⠠⠀⠈⢂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠐⠁⠀⠀⠀⠀⠂⠀⠣⠀⠈⣉⡉⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⢄⣀⣀⠀⣀⣀⠀⢀⣙⣎⠙⠦⣠⠊⠀⠀⠀⠀⠁⠀⡀⠂⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢥⡠⣄⢐⣀⠆⡀⢸⡄⠁⠈⣳⡞⢁⣠⠔⠒⠒⠛⡉⠁⠀⠠⢄⡤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠾⠄⠟⠀⠀⠀⠸⣄⣀⡤⠄⢄⡁⢈⡀⢁⡀⣠⠦⠊⠀⠀⠈⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠀⢠⠀⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠛⠒⠛⠀⠙⠋⠀⠀⠀⠀⠀⣠⠘⠀⠀⠐⠐⠄
⠀⠀⠀⠀⠀⠄⠁⠀⠀⢈⠑⠢⡀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠔⠁⠀⡀⠀⠀⢀⠁
⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠰⠀⡆⠀⠀⠒⠦⣄⠀⠀⠀⠀⠀⠀⢀⠀⠆⢠⠤⠔⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠐⠆⣄⠠⠤⠀⢤⣀⡀⠄⡀⡀⠀⠾⣁⡘⠄⢰⡀⠈⠛⠶⠶⠶⠂⣠⠞⠀⣈⠀⠄⠀⠀⡈⡱⠋
⠀⠀⠀⠀⠀⠈⠃⣰⡄⣤⠕⣠⢤⡈⠙⠁⠀⠀⠸⢌⡓⠄⠙⠀⠑⠀⠀⠀⠉⠁⢀⢠⡵⠂⢴⡦⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠑⠲⠦⠥⢼⡉⠙⢂⣍⡠⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠌⠉⠐⠀⢀⠀⠀⠀⠀⡄⡀⠀⠀⢀⠂⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠓⠀⠃
⠀⠀⠀⠀⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⢓⠀⠀⠐⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠱⡀⠀⢀⣀⠀⣴⠂⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⢡⠶⠂⢠⠆⠀⠀⠀⠀⠜⡁⣈⡈⠀⠀⣀⢠⡀⡀⣄⣀⡠⠀⠀⠀⢰⡆⠀⠄⠈⠀⠉⠁⠈⠀⠀⢻⣄⡀⠀⢀
⢀⠀⠀⠀⠀⠂⠀⣄⠀⠀⠀⠡⠆⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠈⠁⠈⠀⠀⢠⡄⡒⠚⠀⠀⠀⠉⠁⠄
⣄⠀⡆⠀⠀⢀⡀⠀⠶⠀⡠⠐⠁⣀⣄⣰⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠸⣾⠡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠁⠸⠛⠓⠲⡀⠀⠀⠀⠉⠈⠈⠀⠀⠀⠀⠀⠀⠀⠛⠀⠄⠀⠀⠛⣠⠄⠠⠆⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⢰⡀⢠⣰⡀⡠⠀⠀⠀⡀⠀⠀⠀⠀⠤⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡘
⠀⠀⠠⠤⣭⣿⣿⢿⣤⡤⠀⠀⠻⡏⠀⠀⠀⣷⡞⠀⠠⠰⣀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⡾⢠⣉⠅⣿⡀⠀⠙
⠀⠀⠀⠰⠤⠞⠸⠦⠤⠀⠀⠀⠀⠀⠀⠀⠊⠁⠀⠐⠀⠠⠁⠰⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠸⠉⠐⠤⠗⠹⠇⠀⠈⠡

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠀⠠⠀⠀⠠⣶⠄⠀⠀⠀⠀⠀⠰⠚⠀⠀⠀⠀⠀⠄⢤⣄⣀⣤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⢠⠀⠀⢀⡀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠆⡈⢁⠀⠀⢀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠜⠢⠀⡂⠀⠀⢆⠀⠒⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⡀⠡⠴⡂⠀⠀⢩⡸
⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠒⠐⠁⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⡄⠀⠀⢀⠀⠖⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠙⠶⠶⠚⡠⠁⠀⠀⠀⠀⠁⠀⡐⢁⠐⠁⠀⠀⡠⠖⢦⠀⠀⠑⠦⠤⠴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⢀⣀⠀⠀⠀⠂⠰⠁⠁⠀⠀⣀⠀⠧⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠄⠇⠀⠀⠀⠀⠀⠀⢑⣰⠉⠀⠀⠀⠀⢔⠀⠀⢀⣠⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡆⠀⠀⠁⠈⠀⠀⠀⠀⣀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠎⠀⠐⣶⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡄⠀⠀⡆⠀⡀⠀⢷⣀⡀⢀⡠⠂⠀⠀⠐⠋⠀⠀⠈⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠦⠤⠒⠀⠀⠀⠄⡂⠇⠀⠀⠉⠉⠉⠀⢄⢠⠷⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⢀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠄⣀⣴⣾⣥⠀⠀⠀⠀⠀⠀⠀⡀⠀⢄⠁⠀⢀⡰⠀⠀⠀⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⠋⠀⠀⠶⠶⠖⠀⠈⠀⠀⠀⠙⠋⠉⠀⠀⠀⠔⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⣠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠐⡀⠀⢀⠀⡀⠀⡠⡀⠠⠀⠀⠀⠀⠀⡀⠀⡠⠀⢀⠐⠀⣀⠁⣀⠄⡀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡀⠀⡀⢀
⠀⠀⠀⡄⠀⠀⠀⠰⠈⠋⠃⢡⠀⠘⠂⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⣅⡄⣇⡷⠠⡀⢣⡜⠇⡘⠀⣴⡠⡀⠀⠀⠀⠀⠀⠀⠆⣤⠀⠀⠛⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠁⡆⢏⡃⠸⣱⢇⠙⠄⠑⠐⡆⠆⣸⠃⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠂⠄⠀⠀⠀⠀⠀⠘⠣⣴⡀⡇⢮⠘⣂⡔⢸⣬⢶⣁⢀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⡀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⠀⠀⠀⠀⠀⠀⠀⠉⠙⠂⠓⠙⠁⠈⠀⠈⠉⣸⠀⠀⠀⢂⡀⠀⠀⠀⠀⠀⠀⣭⣁⠒⠠⡀
⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢿⡇⠀⠀⠀⠀⢠⠀⠠⢀⡀⠀⡠⢀⠀⠂⣠⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠂⠀⠦⢤⢤⣤⢶⣠⡾
⠀⠀⠀⠘⠢⢄⡀⡀⠀⠀⠀⠀⠀⠀⠀⣤⠴⠆⠊⣧⠀⠀⠀⠀⠘⡄⠀⠂⠀⠂⠐⠚⠒⠊⠬⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡈
⠀⠀⠀⡡⠤⣀⠀⠈⠁⠉⠉⠉⠁⠀⠀⠀⠀⢚⡋⣽⠀⠀⠀⠀⠀⠸⠐⠂⠀⠀⠀⠀⠀⠀⠐⠂⠸⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠂⠐⠢⠄⢰
⠀⠀⠀⣧⢤⠀⠗⠁⠀⠉⠀⠀⠶⠤⠶⠋⠀⠀⠀⣉⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠅⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠉⠈⠱⣦⣁⠀⠀⠀⠀⢀⣀⣠⡀⠀⢀⡴⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⡀⠀⠀⡔⢀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⡉⠁⠉⠀⠀⠈⢁⣠⡤⠔⠉⠀⠀⠀⠀⠀⠀⠀⠁⠀⠆⠠⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢰⠀⡆⢀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⡄⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⢀⠈⡐⠛⢢⠠⣤⡉⠡⢈⣀⣂⡂⠀⢀⡀⢠⡒⠲⠦⢤⠄⠒⠒⠀⠀⠀⠀⠀⠀⠀⠈⠓⠖⠢⣤⣠⠔⠁
⠀⠀⠀⠀⠀⠀⣆⠘⠉⠀⠀⠉⠁⠀⠀⠓⠦⠖⢠⠄⢀⡙⡤⠀⢀⠈⠀⠻⡄⠀⢁⠀⣀⡀
⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠉⠀⠘⠁⠈⠁⠈⠁⠈⢣⠀⠀⠀⢀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠳⢇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠀⠀⡀⠁⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠘⠳⠷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠃⠄⠒⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐⠠⠀⢀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌

⠀⠀⠀⡀⠄⢀⠆⡀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⢀⠀⠀⠀⠀⢀⡠⠔⡠⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠯
⠀⢀⢢⢨⣰⠁⢐⣤⡆⠀⠀⠘⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠁⠀⢰⠶⠂⠀⠀⡰⠉⠴⡀⢁⠸⠆⠀⠀⠀⠀⣤⠤⠤⠤⠾⠿⢦⡄
⠀⠸⠈⠉⠉⠉⠉⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⢤⠁⠀⢰⡆⠀⠀⠀⠀⠐⠿⣾⢉⡀⠒⢰⠀⠀⠀⠀⠣⠀⠀⢀⡀⠤⠀⡁
⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⣤⠁⠀⢀⡄⠄⠀⠀⠀⠀⠀⠀⠈⠡⠄⠀⠉⡄⠀⠀⠀⡁⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠆⢡⡖⠀⠀⠀⠋⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠠⢣⠀⠀⠀⠁⠀⠀⣀⢀⣀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⢀⠐⠂⠀⠀⠀⠀⠀⠀⢠⠖⠑⠊⢤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢨⠋⠁⠀⠈⠀⠄⠀⠀⠀⠀⠀⣰⠈⢷⠀⢠⣠⠀⠀⠀⠀⡄⠲⡀⢀⡀⠀⡀⠀⠄⢀⠸⠙⠀⠀⠀⠀⠠⠈⡃
⠀⠀⠔⠁⠀⠀⠈⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡏⣘⢦⠀⠀⠀⠈⠢⡑⠄⢠⠀⠀⠀⢂⠀⠁⠂⠀⠀⡀⢀⠀⠀⢁
⠀⠀⡄⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠐⢄⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠈⡿⠔⠀⠀⠀⠀⠀⠐⠀⠄⠂⠀⠠⠔⠁⠀⠀⠸⡀⢀⠀⠀⠏
⠀⠀⠀⠀⠈⠉⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⣀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⢀⠶⠁⠈⣀⣀⣀⠀⠉⠀⠀⠀⠈⣲⣷⡀⠘⣶⢧⠖⠀⠀⠀⠀⠀⠀⢈⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⡀
⠠⠀⠤⠘⠉⡽⢏⠉⠐⠀⠀⠀⠀⢹⠀⠁⢸⡙⠳⠀⠀⠀⠀⠀⡠⠉⠉⠀⠁⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⢀⡠⠗⠀⠀⠐⡀
⠀⠀⠀⠀⠉⢰⠉⠀⠀⠀⠀⠀⠀⠀⡆⠀⢰⠂⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⡀⠆⠀⠀⠀⠀⠀⠆⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⠑⠚⢻⠟⠉
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢡⢀⠈⡘⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡀⢀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠲⠖⡄⠀⠀⠀⠀⠀⢠⡴⡆⠴⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠴⡀⠀⠀⠀⠀⢌⠄⡝⠁⠉⠀⠀⠀⠀⢠⡇⠂⠀⠀⠀⠀⠹⡀⠀⠀⠀⡠⠂⠉⠀⠀⠀⢀⠀⠆⠀⠀⡠⠚⠀⠀⠀⡌⠃
⠀⣀⠀⠐⠒⠛⠛⠛⠓⢲⠃⠀⠀⢀⢈⠂⢜⠖⢀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⠀⠇⠀⠀⠈⠄⠀⠀⠀⠀⠀⠨⠀⡁⠀⠀⢁⠄⠒⠀⠘⠢⣄⠁
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⢃⡠⠌⡠⠂⠀⠀⠀⠀⠀⠘⡆⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈


⢀⠉⠃⣶⣴⣶⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢠⣄⣀⡀
⠈⠀⠀⠹⣿⠃⠀⠄⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁
⠀⠀⢰⠀⢸⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⢈⡟⠛⠁⠀⠀⠀⠠⠂⠀⠀⠀⠀⣀
⠀⠀⢾⠀⠀⡇⠀⢸⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⣉⣷
⠀⠀⠘⠀⠀⡇⠀⠸⠀⠀⣠⠦⠤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠄⠀⠀⠀⢁⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⢀⠀⠀⠀⠀⢀⠐⠤⠀⠠⠌⠁
⠀⠀⠀⠂⠀⠃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠁⠀⠀⠀⠀⠀⠰⠈⠀⠀⠀⠐⠰⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⡄⢥

⠀⠀⢀⠔⠒⠈⠉⠁⠐⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠋⣛⣶⡄
⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢤⡒⣻⠧⠜⣡⠖⠉⣨⠵⣿
⠀⠰⠤⠀⠀⠤⠄⠀⠀⠀⠀⠠⠧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⣞⠹⠉⠀⠥⠬⠴⠖⢋⣡⠔⠋⠀⠀⠀⡇
⢈⡄⠀⠠⠄⠀⠀⠀⠀⠀⠠⠤⠶⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠄⠀⠔⡇⠀⠀⠀⠀⠀⠀⠀⠀⡌⣰⠖⠀⠶⠶⠖⠛⠉⠀⠀⠀⠀⠀⡴⠁
⠀⠟⠉⠒⠂⠒⠐⠃⠛⠖⠰⠚⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠚
⠀⢞⠉⠉⠀⠒⠒⠒⠒⠒⠒⢲⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⠒⠒⠒⠒⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠐⠒⠒⠉⠁
⠀⠀⠈⠉⠉⠉⠉⠁⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠤⠀⠤⠀⠠⠄⠤⠄⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠓⠤⠀⠀⠀⠀⠀⠀⠤⠄⠋⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⠀⠀⠀⠀⠀⠀⠀⠀⠬⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡒⠒⣍⣱⡞⢉⢹⡉⣧⡀
⠀⠀⠀⠀⠀⡔⠓⠚⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢚⡉⠘⣀⡀⠀⠁⠀⢙⣉⡗
⠀⠀⠀⠀⢀⡗⠒⠦⣄⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠏⠈⠀⠁⣉⣠⠋⢃⣬⡀⠷⡀
⠀⠀⠀⠀⡼⠂⡊⢳⠄⠱⡄⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠶⠒⠒⠳⠲⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠖⠢⡤⠤⡥⠤⢤⡤⣤⢤⠖⠁
⠀⠀⠀⣾⠀⠀⠉⠈⠀⢀⠡⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠞⢈
⠀⢀⣞⠉⣀⣀⠀⠀⣄⠀⣹⡇⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⠀⠸⠀⠀⠀⢂⠋⠀⠉⠁
⠀⡜⠁⠀⢣⣬⡥⠶⠞⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠆⠈⠀⠀⠀⣼
⠀⠓⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠩⠭⠥⠬⠭⠭⠋

⠀⠀⠀⠀⠀⠀⣀⡤⢶⡛⠓⠦⣀
⠀⠀⠀⣠⠴⠋⠁⠐⢏⡽⠂⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢚⡉⣉⡁⠒⠢⣄
⠀⣴⣏⣥⡤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠀⣉⠤⠤⠤⠤⠬⣑⠚⢷⡄
⠀⣧⣀⣀⠤⢄⡀⢀⣠⠤⠤⣀⣠⠴⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠕⠀⠄⠐⠈⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠔⠋⠀⠀⠀⠀⠀⠀⠀⠙⢦⣿
⠀⢏⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠠⠤⢊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠻⠋⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⡏
⠀⠈⠉⠈⠑⠒⠒⠒⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠈⠲⠐⠒⠒⠀⠈⠅⠐⠀⠀⠀⠉⠈⢑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠉⠀⠈⠉⠀⠈
⠀⠀⠀⠀⠀⠀⡴⢀⡖⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣏⡁
⠀⠀⢀⣀⣀⣀⠀⠄⠤⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢩⠈⡋⠉⠀⠑
⠀⠘⡥⣤⡒⠒⠒⠀⠀⠐⠒⢤⣷⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠈⠉⠉⠉⠁⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡎⠀⡇⠀⠃⠀⡀⡀
⠀⠀⢱⡀⠀⠈⠉⠉⠉⠉⠉⢸⡟⠹⡼⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠤⠀⡀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠀⠀⠀⡀⠀⠀⡀
⠀⣠⠀⠱⣦⢀⣀⣀⣀⡀⢶⡇⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠘⠋⠋⠀⠀⢀⠼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠈⠀⠈⠁⠈⠁⠀⢁⡖⠀⢁
⠘⠦⣤⣤⣈⣁⣀⣀⣉⣉⣁⣠⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⠐⠂⢀⠀⣉⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⠀⢠⠘⠀⠖⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣥⣤⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⡟⠉⠉⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿