Midday Emojis & Symbols

⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⡰⠊⠀⢰⠂⠀⠑⢆⠀⠀⠀⠀⡰⠊⠀⠀⠀⡀⠑⢆⠀⠀⠀⠀⡰⠊⠀⠀⠀⠀⠑⢆⠀⠀⠀⠀⡰⠊⠀⠐⡆⠀⠑⢆
⠀⢸⠀⠀⠀⢸⡅⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢀⡖⠁⠀⠀⡇⠀⠀⢸⠀⠀⠀⢀⣄⠴⠂⠀⡇⠀⠀⢸⠀⠀⠀⢠⣇⠀⠀⠀⡇
⠀⢸⠀⠀⠀⠈⠁⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠈⠁⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠈⠁⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠈⠁⠀⠀⠀⡇
⠀⠀⠱⢄⠀⠀⠀⠀⡠⠎⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⡠⠎⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⡠⠎⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⡠⠎
⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⡰⠊⠀⢰⡂⠀⠑⢆⠀⠀⠀⠀⡰⠊⠀⠀⠀⠀⠑⢆⠀⠀⠀⠀⡰⠊⠀⠀⠀⠀⠑⢆⠀⠀⠀⠀⡰⠊⠀⢐⡆⠀⠑⢆
⠀⢸⠀⠀⠀⢸⡅⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢠⡀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢀⡄⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢨⡇⠀⠀⠀⡇
⠀⢰⠀⠀⠀⠈⠉⠢⠄⠀⡇⠀⠀⢸⠀⠀⠀⠈⢣⡀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠈⠃⠀⠀⠀⡇⠀⠀⢸⠀⠀⢀⠜⠁⠀⠀⠀⡆
⠀⠀⠱⢄⠀⠀⠀⠀⡠⠎⠀⠀⠀⠀⠱⢄⠀⠀⠀⠁⡠⠎⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⡠⠎⠀⠀⠀⠀⠱⢄⠈⠀⠀⠀⡠⠎
⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⡰⠊⠀⢰⠂⠀⠑⢆⠀⠀⠀⠀⡰⠊⠀⠀⠀⠀⠑⢆⠀⠀⠀⠀⡰⠊⠀⠀⠀⠀⠑⢆⠀⠀⠀⠀⡰⠊⢀⠐⡆⠀⠑⢆
⠀⢸⠀⠀⠀⢸⡅⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⢠⡀⠀⠀⠀⡇⠀⠀⢸⠀⠐⠢⣠⡄⠀⠀⠀⡇⠀⠀⢸⠀⠀⠈⢲⡁⠀⠀⠀⡇
⠀⢸⠀⠠⠖⠉⠁⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠈⠁⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠈⠁⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠈⠁⠀⠀⠀⡇
⠀⠀⠱⢄⠀⠀⠀⠀⡠⠎⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⡠⠎⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⡠⠎⠀⠀⠀⠀⠱⢄⠀⠀⠀⠀⡠⠎
⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⢀⠀⡇⡀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠌⣠⣤⣤⣤⡈⠐⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢁⣾⣿⣿⣿⣿⣿⡆⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠻⢿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⠭⠍⠉⠭⠭⠭⠭⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⡀⡇⢠⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠠⠀⡇⡄⢠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢄⡐⢄⣡⣴⣶⣦⣌⠐⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⢄⡐⢈⣤⣶⣶⣦⣅⠂⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣧⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢠⣿⣿⣿⣿⣿⣿⡆⠐
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⣿⣿⣿⣿⣿⣿⡟⠈⠉⠁⠀⠀⠀⠀⠀⠀⠁⠥⠘⣿⣿⣿⣿⣿⣿⠇⠬⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⡿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢡⠈⠻⠿⠿⠿⡋⢄⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⠬⠤⠤⠤⠭⠭⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠐⠀⡆⠃⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣶⣶⠶⣶⠶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠁⠀⠀⠀⣠⣶⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⢀⣴⣿⣿⠿⠛⠉⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣀⣤⣤⣶⣶⣿⣿⡀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣄⡀⠀⠈⠛⠿⣿⣿⣷⣦⣤⣀⣀⡀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠆⠀⠀⠀⠀⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡟

⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣦⣤⣤⠀⢸⣿⠿⣿⣿⠁⢠⣤⣤⠀⢸⡟⠀⣤⣤⡤⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣿⣿⣿⠿⠿⠿⠀⣸⣿⣤⣾⣿⢀⣿⣿⣿⡀⣾⡇⣠⣿⣿⣇⠀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⣿⣿⠀⣤⣤⣤⣶⣿⣿⢿⣿⡿⠙⣿⣿⣿⠋⣿⡏⢻⣿⣿⡟⢹⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⡏⠀⣿⣿⣿⣿⣿⣿⣤⣿⡇⠀⣿⣿⡇⠀⣿⠃⢸⣿⣿⠇⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣷⣤⣤⣤⣼⣿⣿⣿⣿⣿⣧⣤⣤⣤⣤⣴⣿⣧⣤⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⡤⠤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠶⠛⠋⣉⣥⣀⠀⣀⣤⣄⡀⠀⠈⠙⠛⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⢠⡤⢤⣼⠋⢀⣉⣿⣏⣤⣈⣷⣴⠛⢶⡄⠀⠈⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⢀⣀⣿⢀⣤⠿⠛⠋⠉⣽⠀⠾⣦⠉⠙⠛⠾⣷⡞⠳⣄⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⣟⣩⡿⠋⣥⡀⠀⠀⠀⠸⠀⢾⢧⠄⠀⠀⠀⠀⠙⢷⣿⠶⣦⡈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⡾⢛⣿⠋⠀⠀⣿⣷⡄⠀⠀⠀⣰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠙⣦⣸⡇⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢀⣨⣷⡾⠁⠀⠀⠀⢹⣿⣿⡄⠀⣰⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡳⣦⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⣾⠁⣼⠁⠀⠀⠀⠀⠘⣿⣿⣿⣄⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣸⠃⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⣽⣷⡏⢠⣴⡄⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠚⣿⠆⢸⡟⢷⠀⠸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⣸⠁⠹⢾⡇⠀⠀⠀⠀⠙⢿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆⢸⣇⣼⠁⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⢠⡿⢿⠀⢤⠾⠁⠀⠀⠀⠀⠀⠀⠙⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠁⢸⡟⢧⡀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠸⣇⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣸⠇⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⣹⠟⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢿⡛⠉⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠙⠦⣬⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣏⡼⠃⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠋⠻⣆⠀⠀⠀⠀⠀⠀⠀⣼⣧⣤⡀⠀⠀⠀⠀⠀⢀⣤⠞⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄
⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠖⣿⠳⢦⣀⠀⠀⠀⠀⠙⢧⡼⠇⠀⠀⣀⣤⠶⣿⠷⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⢿⡛⠳⣶⣶⠶⠶⣶⣶⠛⢛⡿⠳⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠙⠳⠚⠃⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣤⣄⣠⣤⣄⣀⣀⣀⣠⣤⣤⣄⣀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣿⣿⡇
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⢻⡋⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢛⣋⣉⣉⣉⣉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⢀⣸⡇
⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡠⠖⠉⠉⠉⠳⢤⡀⠀⠀⢀⡴⠞⠉⠉⠉⠲⢄⠀⠀⠀⢀⠴⠚⠉⠉⠙⠶⣄⠀⠀⠀⢠⠴⠋⠉⠉⠑⠦⡀
⡜⠁⠀⠡⣰⠀⠀⠀⢳⠀⠀⡞⠀⢀⡀⠀⢀⠠⠈⢧⠀⢠⠏⠀⢀⠀⠀⠀⠀⠘⡆⠀⢰⠃⠀⣀⠀⠀⠀⠀⠙
⡇⠀⠀⠀⠛⠀⠀⠀⢸⠀⠘⡇⠀⠀⠈⠋⠀⠀⠀⢸⠀⢸⠀⠀⠀⠙⢂⠀⠀⠀⡟⠀⢸⠀⠀⠀⡙⠂
⠙⣆⠀⠀⠀⠀⠀⣠⠎⠀⠀⠳⡀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢳⡀⠀⠀⠀⠀⠀⡰⠃⠀⠈⢦⡀⠐⠀⠀⠀⢀⡞
⠀⠈⠙⠒⠒⠒⠊⠁⠀⠀⠀⠀⠈⠓⠒⠒⠒⠋⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⠋⠀⠀⠀⠀⠀⠉⠒⠒⠒⠚⠉
⠀⣠⠶⠚⠛⠑⠲⢄⠀⠀⠀⠀⡠⠔⠒⠛⠒⠦⣀⠀⠀⠀⢀⡠⠖⠚⠛⠒⠤⡀⠀⠀⠀⢀⠴⠒⠛⠓⠲⢤⡀
⡼⠃⠀⠀⢀⡄⠀⠀⢳⠀⠀⡞⠀⠀⠀⠀⢀⡀⠘⢆⠀⢀⠞⠀⠀⠀⠀⠀⠀⠘⡆⠀⢠⠋⠀⠀⠀⠀⠀⠀⠻
⡇⠀⠀⠀⠚⠀⠀⠀⢸⠀⠰⡇⠀⠀⠀⠒⠉⠀⠀⢺⠀⢸⠂⠀⠀⠀⠒⠒⠂⠀⡷⠀⢸⠀⠀⠀⠐⠦⣀
⠹⣄⠀⠀⠀⠀⠀⢀⠞⠀⠀⢳⡀⠀⠀⠀⠀⠀⢠⠏⠀⠈⢧⠀⠀⠀⠀⠀⠀⣰⠃⠀⠘⢆⠀⠀⠀⠀⠀⠀⡴
⠀⠈⠓⠢⠴⠴⠚⠁⠀⠀⠀⠀⠉⠓⠤⠤⠴⠚⠁⠀⠀⠀⠀⠙⠲⠤⠤⠴⠋⠁⠀⠀⠀⠈⠙⠢⠤⠤⠖⠋
⠀⣀⠴⠒⠒⠒⠦⣄⠀⠀⠀⠀⣀⡤⠒⠒⠲⣤⡀⠀⠀⠀⠀⣠⡴⠒⠒⠢⣄⡀⠀⠀⠀⠀⣠⠴⠒⠒⠦⣄
⡰⠃⠀⠀⠀⠀⠀⠈⢧⠀⠀⡴⠁⠀⠀⠀⠀⠀⠙⣆⠀⢀⡾⠁⠀⠀⠀⠀⠀⠱⡄⠀⢠⠎⠀⠀⠀⠀⠀⠀⢳
⡇⠀⠀⠀⠲⡀⠀⠀⢸⠀⢰⡇⠀⠀⠀⡆⠀⠀⠀⢸⠀⢸⠀⠀⠀⢠⠆⠀⠀⠀⡷⠀⢸⠀⠀⢀⡰⠄
⠱⡄⠀⠀⠀⠑⠀⢀⡞⠀⠀⢧⠀⠀⠀⠇⠀⠀⢠⠎⠀⠈⢦⠀⠀⠋⠀⠀⠀⢠⠇⠀⠘⡄⠀⠁⠀⠀⠀⠀⣴
⠀⠈⠒⠤⠤⠤⠖⠋⠀⠀⠀⠀⠑⠦⢄⣤⠤⠖⠋⠀⠀⠀⠈⠓⠦⢤⣄⠤⠖⠁⠀⠀⠀⠈⠲⠤⣤⣤⠴⠚⠁
⠀⢀⡤⠖⠒⠒⢤⣀⠀⠀⠀⠀⢀⣠⠤⠤⠤⣀⠀⠀⠀⠀⠀⣀⡤⠴⠶⠤⣄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⡰⠃⠀⠀⠀⠀⠀⠈⢦⠀⠀⣰⠋⠀⠀⠀⠀⠀⠱⡄⠀⠀⡼⠁⠀⡀⠀⠀⠀⠱⡄⠀⠀⡴⠋⠀⢀⠀⠈⠙⣆
⡇⠀⠠⠤⠴⠀⠀⠀⢸⠀⢠⡇⠀⠐⠢⡄⠀⠀⠀⢹⠀⢸⠀⠀⠀⠹⠆⠀⠀⠀⣧⠀⢸⠀⠀⠀⢸⡀⠀⠀⠈
⠳⡄⠀⠀⠀⠀⠀⢀⡜⠀⠀⢇⠀⠀⠀⠀⠀⠀⢀⡞⠀⠘⣆⠀⠀⠀⠀⠀⠀⢠⠇⠀⢸⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠙⠲⠤⣤⡤⠔⠋⠀⠀⠀⠈⠳⢄⣀⣀⣀⡤⠊⠀⠀⠀⠈⠳⢦⣀⣀⡠⠖⠋⠀⠀⠀⠱⢤⡀⠀⠀⢀⡤⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⡿⠿⠛⠋⠉⠉⠉⠁⠀⠉⠉⠉⠙⠛⠿⢿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠺⠗⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠛⠁⠀⠀⢾⠇⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠸⡷⠀⠀⠈⠛⢿⣿⣦
⠀⠀⠀⠀⠀⢠⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⡄
⠀⠀⠀⠀⣰⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣆
⠀⠀⠀⢰⣿⡿⠁⠀⠾⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠷⠀⠈⢿⣿⡆
⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡀
⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⣿⣿⡀⠀⢾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡷⠀⠀⣿⣿
⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇
⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠁
⠀⠀⠀⠸⣿⣷⡀⠀⢶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡶⠀⢀⣾⣿⠇
⠀⠀⠀⠀⠹⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠏
⠀⠀⠀⠀⠀⠘⢿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣤⡀⠀⠀⢾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⠀⠀⢀⣤⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢴⡦⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣷⣶⣤⣄⣀⣀⣀⠀⠀⣀⣀⣀⣠⣤⣶⣾⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣖⣒⣂⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⡿⠿⠟⠛⠛⢻⠛⠛⠛⠛⠷⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⣟⠉⠀⠀⠀⠀⢰⡆⢶⡶⣦⠀⠀⠀⠀⠀⠉⡿⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡿⠟⠁⠀⠀⡆⢰⡆⠀⠀⢸⣇⣼⣿⣭⠀⠀⠀⠀⢰⡄⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠋⠀⠀⠀⠀⠀⡇⢸⠇⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⡼⣿⣿⡁⢀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣹⣷⡀
⠀⠀⠀⠀⠀⠌⢰⡟⠀⠀⢸⣾⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣡⡽⠃⠁⠀⠱⣷⡀
⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠘⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠚⠂⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⣿⠁⠀⡴⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⣶⠆⠀⠀⣿⡇
⠀⠀⠀⠀⠀⣿⠉⠀⣭⣭⡽⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣈⣩⠇⠉⠁⣿⡇
⠀⠀⠀⠀⡄⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢠⢸⣧⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣰⣿⠁
⠀⠀⠀⠀⠈⣿⣿⡆⠀⢀⡿⠭⠽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⣻⡀⠰⠆⢠⣿⡟
⠀⠀⠀⠀⠀⠘⣿⣿⡴⠊⠛⠒⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⡉⠳⢠⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠘⣟⢿⣆⠀⠀⠀⠀⠀⠴⠶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠶⠄⠀⠀⠀⠀⠀⣠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠙⢧⡀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⣠⠶⠶⠀⠀⠀⠀⣙⣉⣹⡇⠀⠀⢀⣴⠟⡻⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠠⠆⠉⠀⠀⠀⠀⠀⢿⣋⣹⡆⠀⠀⠀⠀⠉⠑⣆⣠⡶⠋⡁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⣀⣀⣀⠀⠀⠀⢨⠀⠀⠀⣀⣀⣤⡴⠾⠋⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄⠀⠀⠀⠀⠐⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣶⣶⣦⣄⣹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⠇⢀⣠⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⡿⢿⣾⣿⣿⡿⠿⠿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠛⠋⠉⠁⠀⠀⢸⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡎⠻⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⣾⣿⣿⣿⣿⠂⠰⣿⣿⣿⣿⣿⣿⣿⣿⠛⣒⢒⡘⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣴⣦⣤⠼⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢹⣿⣿⣿⣿⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣦⣴⣦⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠸⣿⣿⣿⣟⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⢿⣿⣿⣟⠀⢸⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⡏⠀⠀⠻⠋⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠉⠀⠈⠉⠁⠀⠀⠀⠠⢄⡀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠉⠉⠁⠀⠉⠉⠁⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣴⣶⣶⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣰⡇⢳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⣉⣅⣬⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠉⠀⠀⠀⠈⠉⠙⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⣠⠤⠤⠤⠤⡀⢀⣤⣤⢤⣀⠀⠈⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⡲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⣀⣤⠷⠤⠤⠤⠤⢼⠟⡕⠉⠀⠉⢃⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡳⣋⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡧⢤⡏⠠⣬⣿⣉⣉⣉⣉⠽⣴⡀⠀⠀⣀⢎⡙⢢⣀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠾⠰⢏⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠑⠒⠢⠤⠭⢭⣍⣉⣙⣛⣛⣛⣋⣉⣩⠴⠋⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣅⠀⠀⠈⡧⠤⢤⣤⡀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠂⢄⢀⠀⠀⠉⠉⡉⠥⢀⡀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣍⣉⠈⠈⠉⣉⡩⠟⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡔⢗⣆⣎⣱⣿⣶⠶⣁⢀⡠⠊⢅⣀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣹⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣰⠊⢉⣉⣋⡒⠘⢓⣊⡾⠀⠦⠠⡄⡠⠊⢉⠱⣄⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠚⡦⣀⡇⣷⠋⡉⠉⢳⠀⠀⠀⠀⠀⠀⢸⠀⠈⠲⠦⠬⠭⣭⠭⢭⣭⡭⢥⣬⣌⣍⣉⣭⠭⠴⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣄⣉⣀⣼⡇⣿⣉⡛⢓⣸⣆⣀⣀⠀⠀⠀⢸⠀⠀⠀⠀⣰⠏⣿⣦⡏⣿⣇⠀⠀⣀⣤⢀⡀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠰⣎⣉⣉⣁⣷⣴⣤⣦⣾⣇⣿⣬⣭⣩⣽⣉⣉⣥⠽⠂⠀⢸⠀⠀⢀⡰⠁⡆⢖⣷⢨⢰⣿⣤⡞⠓⣲⣪⢿⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣠⠤⠖⠋⠁⠀⠀⠀⢸⠤⢾⣩⣙⣄⣸⠸⣿⣸⠈⣽⣛⣟⣛⣻⡮⠟⢉⢣⣀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠛⠛⠿⠶⠯⠽⢷⣭⣭⣭⣭⣭⣭⣭⡥⠴⠃⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⡇⠀⣠⠤⢄⣀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⢠⠴⣯⠶⣄⡖⠀⠀⠒⣀⠃⣷⠞⠶⢶⣊⡽⡄⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⣤⢼⣑⣒⣒⠿⡅⠀⠀⢨⢿⠀⣿⡝⠻⢿⣿⡿⠓⠒⠲⢦⡄⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠙⠯⣉⣛⢛⡒⠛⠛⠛⠛⠛⠛⠛⠉⠉⣉⣉⠉⣉⣉⡭⠟⣝⣩⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣧⡀⠀⠀⡀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠢⠘⢃⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠴⢋⣥⡆⡈⠲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⡙⣿⠿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢱⣇⣿⠁⢀⢤⣤⣤⣶⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠜⠹⠿⣟⡓⣲⡦⢶⢬⣭⡝⡥⣆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠈⠛⠟⣛⣛⣛⣖⠶⠾⠿⡇⢸⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠄⠋⢩⣼⣷⠺⠙⠉⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡗⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠦⠿⠃⠄⢤⠀⣂⣴⢔⣂⠂⢤⡄⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡐⣖⣰⠚⢱⣶⣲⡟⣿⢛⠢⡅⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠸⣤⣶⣶⡁⣴⣁⡮⢙⣬⣁⣴⡇⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡤⢀⡉⠙⠳⠶⣷⡶⠟⠃⠈⠉⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠘⠃⠀⣜⣿⣻⣃⣉⡀⣹⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡒⢤⣿⣿⡟⠡⠛⠪⣿⣿⡇⠠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣓⣴⠉⠽⣿⢟⢳⣾⣶⡿⠫⡁⢀⡾⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠈⠓⠠⡅⡌⠠⠟⠇⠈⠉⠁⠈⠀⠐⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣿⣿⠻⠿⠻⠿⡿⢿⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⡇⠈⣧⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣌⠙⢃⠀⡋⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠖⠒⠛⠛⠛⠛⠛⠛⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⢠⡶⠒⠒⠒⠒⠲⢄⢀⢴⡶⢶⣶⣤⡀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢀⣀⡼⠦⠤⣤⣤⣤⣤⣼⡷⢫⠞⠁⠀⠀⠙⡆⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢀⣠⠞⢉⠈⢳⡖⠒⠒⠒⠒⠒⣺⣇⢘⠀⠀⠀⠀⢀⠟⠲⢦⡀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⢻⣄⡈⠉⠓⠛⠷⠶⢶⣶⣮⣥⣹⣾⣦⣄⣤⣴⡯⠶⠂⣸⠗⠒⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠉⠉⠙⠛⠓⠲⠶⠶⠤⢤⣤⣤⣤⣤⣤⡤⠴⠖⠋⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡔⠒⢄⢀⡀⠀⠀⠀⠀⢀⡠⠤⢄⣀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣠⣲⢇⡖⡾⠓⣟⣷⣖⣤⠖⠉⠀⢀⠴⠋⡀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⡴⠒⠓⡬⢆⣅⢙⣛⣛⡫⣽⠁⢈⡍⠉⡃⠀⢀⡟⠓⢶⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠶⠶⣏⠀⠲⠦⠽⠴⣤⣄⣤⣤⣶⣸⡁⢈⡏⢉⣧⣔⣉⣀⡤⠄⣻⣤⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠛⠒⠒⠒⢶⣶⠶⠶⣤⣤⠤⠬⠤⠥⠤⠤⠤⠤⠤⠤⠖⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⣿⢹⣽⣇⣾⠹⣿⣇⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⡞⢸⠀⣧⣿⠘⡇⡧⣿⡀⢠⣶⣉⣠⡴⢛⣇⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⣤⠖⢿⠀⠈⡇⢳⢿⡆⡇⢸⢿⣟⣿⣲⣶⣾⣟⡯⣼⢦⣄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠛⠛⢧⣳⢤⣱⣤⣇⢸⣿⣧⣿⠘⣿⣿⣹⣥⣬⣽⣷⣚⣁⣠⠘⣧⠤⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠉⠙⠓⠚⠛⠿⠯⠥⢭⣭⣭⣥⣤⣤⣤⣬⣭⣭⣥⣤⠤⠟⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢩⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡗⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠞⠁

⣄⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣆⣻⣷⣷⣾⣷⣿⣾⣷
⣿⡿⣡⡶⡠⣂⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣠⡽⡿⣿⣿⣿⣿⣿⣿⣿⢿
⣿⣿⣿⣿⣾⣿⣿⣶⣿⣿⣶⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⡾⣻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠿⡉⠫⡽⣙⠛⢿⣷⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣝⢧⠙⢄⠙⢆⠙⢜⣧⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢁⠋⠁⢹⣿⣿⣿⣿⣿⣿
⣯⣍⢷⡍⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠘⠁⠀⠀⠀⠘⠋⢻
⠙⠛⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠁⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⢀⣁⣤⠤⠤⠤⢤⠈⣠⣿⣀⠘⢱⠙⠀⠀⠀⠀⢼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠙⠀⠀⠀⠀⣀⣀⣀⣀⠀⡔⠛⢛⣟⠀⢸⡇⠀⡀⠀⠀⣬⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⡀⠀⠙⠉⠁⠀⢀⠂⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁⠀⠀⢿⣣⣤⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠠⠀⠒⠒⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠤⠄⠐⣒⠨⣽⠁
⠀⠀⠀⠂⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⢯⣤⣴⣦⠘⣿⣿⣶⠶⠂⠠⠀⠀⡄
⠀⠀⠀⠀⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠥⠀⠀⡀⢀⣀⠄⠃⠀⠀⢀⣠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠠⠀⣀⣀⣀⣀⣀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠙⠀⣠⠖⠋⠉⠀⠀⠀⠉⠛⢦⡀⠀⠠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⣠⠖⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⣀⣀⡀
⠀⣠⠴⠶⠞⠛⠛⠉⠉⠉⠉⠉⠉⠛⠛⠶⠶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢠⠙⠲⠤⢤⣤⡤⠴⠞⢉⠀⠀⠈⠉⠁
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠳⢶⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⡀
⠀⡇⠀⠀⠀⠀⠀⠠⠤⠤⠀⢀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣭⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⣀⣠⡿⢏⠉⠈⠉⠉⢳⠀⠀⠀⠀⠈⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⡠⡇⢀⣰⣿⣿⠁⠀⠘⣶⢶⠆⠀⢸⠳⣄⠀⠀⠀⠀⠀⠉⠛⠲⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⡇⠀⠀⠀⠀⢀⡠⠊⠀⡞⠍⠀⠈⢁⣀⠤⠀⡴⠋⠀⠀⢸⣀⡤⠷⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠶⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⡇⠀⠀⢀⡴⠋⠀⠀⣼⠉⠒⢲⠤⢠⣤⠤⠊⠀⠀⠀⠀⠹⡍⠀⣀⣤⠿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣧⣴⠾⣏⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⣠⠄⠹⡞⠉⠁⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠳⢶⣤⡀⠀⠀⢸⡇
⠀⡟⢳⡄⠈⠓⠶⠦⠤⠤⠤⣬⡙⠂⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠈⠉⠛⠋⠀⠀⠈⠉⠀⠉⠀⠀⠀⠈⠙⠛⠲⢾⡇
⠀⡇⠀⠙⢦⡀⠀⠀⠀⢀⣠⠴⠛⢆⠀⠀⠒⠊⠁⠀⠀⠀⠀⣀⣤⠴⠶⠛⠦⣄⠀⠀⠀⠀⠉⠳⢄⡀⠀⠀⠀⠀⠀⠀⣰⢦⣶⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⡇⠀⠀⠀⠙⢦⣤⠶⠋⠁⣀⡤⠞⠳⡄⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⡆⠀⠀⠈⠳⢦⣀⠀⠀⠀⠀⠉⠲⢤⡀⠀⠀⠀⠸⡎⠀⠛⣷⠀⠀⠀⠀⠀⠀⢸⡇
⠀⡇⠀⠀⠀⠀⠀⠳⣄⡴⠚⠉⠀⠀⠀⠙⢶⣄⠀⡰⠋⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⢉⠿⠛⠦⣄⡀⠀⠀⠉⠓⢤⣀⢸⠇⢀⠀⣼⠁⠀⠀⠀⠀⠀⢸⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠉⠻⣇⠀⠀⠀⠀⠀⠀⠘⢷⢶⣤⡀⣰⣿⣤⡀⠀⠀⠉⠛⠓⠶⠶⠤⢬⡟⠀⠋⣰⠏⠀⠀⠀⠀⠀⠀⢸⡇
⠀⡇⠀⠀⠀⠀⠀⠀⣀⠀⠌⠳⢤⡀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⢀⣤⣷⣌⠙⠛⠋⠈⠳⠶⠦⠤⠤⠤⠤⢤⣤⡀⠀⠀⢰⡏⠳⢤⡀⠀⠀⠀⠀⢸⡇
⠀⡇⠀⠀⠀⠐⠊⠉⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠈⠻⣆⠀⣼⠋⠉⠲⡟⠀⠀⠀⢀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠙⠷⠶⠟⠁⠀⠀⠉⠲⢄⡀⠀⢸⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠈⠻⠿⣄⠀⠀⠱⣄⣰⠎⠙⠉⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠁⠀⢸⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠈⣧⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠁⠀⠀⠀⠀⢸⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠘⣇⠀⠀⣿⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠈⠳⢦⣼⡀⠀⠀⢹⠀⠀⠀⠀⣠⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⠀⠀⠈⠹⢦⣤⡼⢀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠳⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⡀⠀⠀⢀⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠀⠀⠐⠀⠀⠀⢸⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⡤⢠⠤⣤⠄⣤⣼⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠣⢀⣀⠀⠀⠇⠀⠙⢄⠀⠀⠔⠊⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠈⠳⠀⠑⡄⠀⢸⠀⢠⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⡀⠀⡈⠐⢢⣠⠥⠦⠼⠶⠦⢄⣀⠀⢀⠎⡀⢀⠠⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠑⢮⠖⠉⠀⢀⣀⠀⠀⣀⠀⠈⠛⢥⠊⢠⠁⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⢹⠃⠀⠀⠀⢩⣤⠀⠀⣩⡝⠀⠀⠈⢳⡁⣀⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠐⠨⡇⠀⠀⣀⣀⡆⠀⠋⠙⠈⢡⡀⣀⠀⠀⡧⠀⢒⡤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠙⢍⣀⠀⠠⠔⠘⡇⠀⠀⠀⠈⢿⣷⣒⣒⣾⠟⠉⠁⠀⠀⣽⠊⠁⠀⢀⡤⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⢷⠀⠀⠀⠀⠀⢛⢿⣛⠋⠀⠀⠀⠀⢀⠟⠤⢀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠠⠞⠻⢀⠀⡀⠀⠃⠈⡁⠀⢀⠀⠀⠀⠚⠒⠈⠘⠓⢦⠀⠀⢀
⠀⠀⠄⢸⠀⡂⢸⠀⡄⢸⠀⡄⠀⠄⠂⢀⠀⡥⢀⡂⠀⡁⢈⣨⡇⠀⠂⢰⠀⢶⠀⠆⢸⠀⡃⢘⠀⢰
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⡄⠸⢀⠀⠀⠃⠀⡇⠈⠸⠀⠀⠃⢀⡄⠘⠀⠀⠀⠀⠀⠈⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡸⠀⠈⡄⠀⠈⠆⠀⠑⠦⢄⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠓⠊⠀⠀⠀⠈⢂⢀⠆⠀⠀⠀⠀⠱⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣆⠀⠀⠀⡀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠒⢄⠻⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣺⣦⢉⠙⣦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣯⢻⣷⢷⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢸⣾⣷⠋⠀⣀⣀⣀⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠿⣾⣿⡿⣦⣬⣍⣛⣛⣛⠿⢛⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠻⣶⣿⣷⡿⠽⣭⣹⣩⣾⣿⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠶⠶⢻⣏⣗⠮⠵⠶⠂⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⡀⠀⠀⠈⠉⠛⠈⠀⠀⠀⠀⠀⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢹⣼⠀⠀⠀⠀⡁⢀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠈⢉⣀⢁⣻⢌⣚⣛⣵⣷⣤⡛⠢⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡰⢜⣣⣞⠀⢸⠿⠿⢯⡻⠥⠀⣷⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠙⠻⠿⢿⣔⠿⣦⣑⣠⣶⠺⡿⠟⠀⠁⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡃⢰⠀⠠⣙⣛⣿⡿⡉⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠠⣯⠿⣽⡥⣴⠤⣼⣧⣀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡭⠟⣲⣿⣿⣏⡀⠋⠑⣻⣿⡟⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠨⠡⣿⡀⠛⠾⢯⠹⣿⣿⢟⡋⣆⠀⡽⠃⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠈⠙⠸⠄⠆⠔⠚⠃⠀⠈⠁⠀⠀⠂⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⡭⣍⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⡳⢚⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣳⡦⢸⡏⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⡞⢁⠀⢠⠱⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣓⣳⣅⣀⣀⣃⣟⣛⣩⣿⢿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣀⣀⣀⣀⣀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⠙⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣄⠀⢸⠀⣇⡴⠒⠒⠶⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠹⣤⠟⠙⣾⡇⣿⢧⣼⣠⣆⣀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣼⠳⠦⠤⠤⠶⣿⡇⣿⢤⣄⣀⣁⣤⣿⣤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣍⣉⣀⣀⣘⣧⣼⣤⣷⣴⣿⣇⣿⣦⣤⣆⣰⣴⣇⣀⣤⣤⡬⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⣿⠉⣿⠉⠉⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⢀⡤⠤⠤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢞⣹⠦⡄⡴⠒⠒⠒⠲⢄⢸⠀⣿⡶⠯⠤⢤⠖⣋⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠦⠤⠥⠤⣷⡓⠒⠤⠤⠤⢺⣽⠀⣿⣓⣲⣖⣾⣏⡿⢶⣧⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠘⣯⣭⣷⣶⣼⣖⣃⣫⣍⣉⣉⣩⣟⣽⣀⣿⣯⣤⣬⣼⣷⣾⣭⣤⡤⠤⠤⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⠤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠰⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁


⡀⠀⠀⢀⣴⣶⣶⢶⡐⡆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣄⣀
⠀⡳⠘⠸⣿⣯⡤⠾⢿⣤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣟⠛⢿⣷⡄⠁⠘⢰⠂
⠀⠀⠀⠀⠿⣶⣦⡄⠺⣇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⣠⠉⠙⠛⠿⠃⠐⠀⡇
⠀⠀⠙⠂⣄⠀⠹⣆⢀⡜⠓⡦⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣸⠉⠁⠠⠔⠁⠀⠀⠴⠁
⠀⢀⢀⠈⢿⣷⣄⣍⣙⡟⢘⣟⢚⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣀⢰⠞⢷⠤⡔⠏⠠⠀⡀⠁⠀⡀
⠀⠀⠀⠑⠈⠈⢟⠋⣹⡋⣹⣏⠙⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠉⣽⣙⣗⢺⠛⠟⠀⢀⡜⠘⠴⠪⠂
⠀⠀⠀⠀⠀⠈⢡⢁⠘⠋⣽⡅⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⢉⡟⠙⠷⠟⠀⢊⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠡⠲⣍⠀⠀⠄⠐⢤⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆⡀⠀⠀⠘⠛⠟⡡⢂⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡄⠉⠀⠀⠀⢄⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠈⠘⠃⣠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠛⠀⠉⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⡀⠀⠀⠀⡆⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⡇⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢲⣄
⠀⠀⠀⠀⠀⠘⠆⠀⠀⠃⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⡀⠈⣠⣤⣤⣄⡁⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⢿⠃⠀⠀⣿⣷⡀
⠀⠀⠐⢤⡀⠀⢀⣤⣶⣶⣶⣤⡀⠀⢀⠴⠂⠀⠀⠀⠀⠀⠀⣀⣀⠀⣼⣿⣿⣿⣿⣷⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⡀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢻⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⣰⣿⣿⡇
⠀⠒⠒⠂⣀⣿⣿⣿⣿⣿⣿⣿⣿⣇⡀⠒⠒⠂⠀⠀⠀⠀⠀⠀⠊⠁⢀⠈⠙⠛⠉⡀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⠀⠀⠀⢤⠀⠀⠀⡇⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠘⠃⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠺⣄⠀⢻⠑⣄
⠀⠀⠀⠀⠀⠀⠃⠀⣀⣀⡀⠀⠚⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠓⠆⡠⠚⠉⠉⠓⢄⠰⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠺⠁⠀⠘⡇⠈⣇
⠀⠀⠈⠓⠆⢀⡔⠋⠁⠀⠈⠙⢦⡀⠰⠊⠁⠀⠀⠀⠀⠀⠀⠤⠤⠰⡇⠀⠀⠀⠀⢸⠄⠤⠤⠀⠀⠀⠀⠀⠀⢴⡦⠀⢰⣶⡆⢰⠃⠀⢸
⠀⢀⣀⡀⠀⡞⠀⠀⠀⠀⠀⠀⠀⢧⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣠⠄⠳⣄⡀⢀⣠⠞⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡠⠋⠀⢀⡏
⠀⠈⠉⠁⠴⠷⠶⠶⠶⠶⠶⠶⠶⠾⠆⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⢉⡉⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠤⠤⠖⠋⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⢳⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⡀⣄⡀⠙⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⢀⠠⠆⠠⠆⠀⡀⢸⣲⠆
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠶⠦⠒⠚⠀⠠⠸⢨⠍⠀⢁⣤⣤⠀⡌⠘⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠉⠈⠁⣄⣨⠓⠀⠀⠀⠀⠀⠀⠰⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠸⠛⡄⢠⣀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠱⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶


⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣄⠀⠀⠀⡇⠀⠞⠁
⠀⠀⠀⠀⢀⡠⠴⠒⠚⡯⡀⠐⠒⠒⠒⠛⠓⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠞⠉⠉⠑⡄⢠⡤⠤
⠀⠀⢠⠞⠉⠀⠀⣀⠈⠀⠃⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠋⠉⠘⢆⡀⠀⣠⠃
⠀⢰⠃⠀⠀⢀⠜⠁⠀⠀⠀⠀⠁⠀⠀⢀⡠⠤⠴⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⠉⠁⠉⠲⠄
⢀⠇⠀⠀⠀⠋⠀⠀⠀⠀⣀⡤⠤⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠈⠓⠒⠢⡤⠔⠒⠒⠒⠒⢹⣧⠀⠀⢀⡠⠖⠚⠉⠉⠉⣑⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⣿⠀⢰⠋⠀⠀⢀⣠⣶⣿⣿⣿⣧⣷⠒⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⢀⠘⠃⠀⠀⠞⡳⣤⠞⠛⠛⢿⣿⣿⣽⠅⠙⠿⣿⣹⡷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣸⢫⠆
⠀⠀⠀⠀⠀⠀⠀⡖⠛⠛⢉⡟⢛⣝⡦⢀⡈⠙⣛⣉⣑⣶⠶⠟⠹⠤⠶⠖⠒⠒⠲⢤⡤⠤⠤⣤⣀⣀⣤⣿⢻⣸⠆
⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⣸⡕⠿⠭⢤⣒⠯⢍⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣤⣤⠏⠉⠉⠉⢹⡼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢱⣀⣇⠈⠉⠉⠁⠀⠀⠈⠑⠒⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣎⣀⣀⡼⠿⠟⠛⠛⠛⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠒⠚⠉⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠅⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠄⢂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢞⠢⠄⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠂⠀⠂⠀⡔⠠⠠⠺⠂⠀⠢⡈⠂
⠀⣀⡀⡀⠀⠀⡌⠀⠀⡰⠁⠐⠒⠒⠒⠒⠒⠶⠒⠆⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠐⣇⠀⢘⠁⠈⠙⠀⠀⠀⠐⠄⠀⡠⠃⢄⣠⠦⡀
⢡⠀⠀⠀⠀⠀⠰⡀⠐⠀⠀⠀⠀⠀⠀⠀⠰⢤⠀⠀⠀⠀⠀⠉⠐⢺⠀⠀⠤⠀⠀⠀⠘⠕⢀⠀⠒⠠⡀⠀⠀⠀⠀⠀⠀⡀⠶⡄⠀⠈⢢
⠀⢆⠀⠀⠀⠀⠀⠀⠀⢒⠒⠒⠂⠀⠀⠀⢤⡌⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠒⠀⡉⠐⠀⠈⠢⡀⠀⠑⢄
⠀⠈⡄⠀⠀⠀⠀⠀⠀⠈⣄⣀⠀⠀⠀⠀⠀⠀⠹⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠄⢀⣀⠀⠁⠀⢀⡠⡇⠀⠀⠀⠣⡀
⠀⠀⠘⡀⠀⠀⠀⠀⢀⠔⠀⢸⠀⠀⠀⠀⢀⣀⠐⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠠⠤⠐⡆⠉⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠈⢢⠀⠀⠀⠈⢦
⠀⠀⠀⠡⠀⠀⠀⢠⠂⠀⢀⠦⠀⠀⠀⣀⢢⠠⠵⠀⠀⠀⠀⢀⠠⠄⠚⠒⢲⠀⠉⠁⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠑
⠀⠀⠀⠀⢃⠀⠀⠆⠀⢠⠂⠐⠃⠈⢁⡀⠤⠤⢄⣃⣠⡔⠊⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⢀⣈⡦⠠⠤⠀⠀⠒⠚⠒⠀⠉⠉
⠀⠀⠀⠀⠈⠆⠀⠢⠀⠀⠐⠂⠘⡇⠀⠀⠀⠀⠀⠈⠀⠱⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⣀⡀⠀⠠⠤⠄⠚⠒⠀⠉⠉
⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⣧⡀⠤⠄⠐⠂⠂⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣀⡀⠤⠵⠀⠐⠒⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉


⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⠖⡕⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡸⡀⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⢻⡆⣯⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⣋⠀⠘⠃⠛⠆⢚⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢄⡀⠀⠀⠀⠀⠀⠀⣠⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣻⠛⢲⣖⡒⢺⠉⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠈⠉⡑⣀⡅⢀⡈⢀⣀⠀⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡀⠀⠀⠙⠒⠂⠘⠈⠄⠀⠈⠁⢀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠶⠶⣤⡴⠶⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⣤⠤⠏⡗⣒⠦⠤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⡞⠉⠀⢀⠀⠀⠀⣈⣇⠂⡔⢠⣤⢈⣙⡲⡄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢰⠋⠁⠉⠉⠕⠄⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠑⠀⠊⠁⠀⢃⠀⠀⢄⠂⡇⣀⠠⠼⠉⠹⢤⣀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⢀⠼⠀⠀⠀⠀⠀⡌⠐⢠⡄⠳⢤⣀⣀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠺⠋⠁⠀⠀⠀⠀⠀⠈⠙⠶⢒⡩⠚⠉⢻⣧
⠀⠀⠀⠀⣇⠀⠀⠀⠂⣀⣀⠀⢀⡠⠷⠤⠤⠤⠭⠭⣉⡓⡒⠒⠒⠒⠒⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⢀⡼⡹
⠀⠀⠀⠀⠈⠳⢤⡤⠀⢻⣬⢠⢲⠀⠀⠀⠀⠀⠀⠀⢘⣳⡝⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣠⣶⠯⠊⠁
⠀⠀⠀⠀⠀⠀⢠⡷⠒⢣⢃⢃⡨⢇⠀⠀⠀⠀⠀⠀⡟⡍⠉⠉⡙⢲⣀⣠⣄⣱⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⠉
⠀⠀⠀⠀⠀⣰⡿⠁⡠⠃⠞⣏⠀⠀⠁⠀⠀⠀⠠⠘⠁⠃⡖⡀⠀⢺⡏⠄⠀⠌⡏⠣⣀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⣜⢁⡇⢰⠁⡜⠀⠀⠉⠒⠒⠂⠤⠤⠒⠒⠚⠑⠀⠐⠒⠊⡇⡄⠄⢄⡇⠀⠀⠉⠀⠒⠒⠒⠂⠉
⠀⠀⠀⠀⠈⠉⠀⠈⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠸⡿⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⣀⣀⣀⣀⡀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⣀⠀⠀⠀⢀⣤⠶⠛⠋⠉⠉⠉⠛⠳⢦⣄⠀⠀⠀⢀⣠⡴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⣸⡇⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠘⠷⣦⣀⣀⠀⣀⣠⣴⠞⠛⠛⠛⠻⢦⣤⣀⣠⣤⠾⠋⠁⠀⠈⠙⠿⣦⣀⠀⠀⠀⢀⣠⣴⠾⠃
⠀⠀⠀⠀⢠⣄⡀⠉⠙⠛⠋⠉⢀⣠⣤⣴⣤⣤⣀⠈⠉⠉⠀⣠⡴⠞⠛⠻⢶⣄⡈⠙⠛⠛⠛⠋⠉⢀⣠⡄
⠀⠀⠀⠀⠀⠉⠛⠷⢶⣤⡶⠾⠛⠁⠀⣀⡀⠈⠙⠛⠶⠾⠛⠉⢀⣠⣤⣤⣀⠉⠻⢶⣤⣤⣤⡴⠾⠛⠉
⠀⠀⠀⠀⠘⠳⣦⣄⣀⣀⣀⣠⣴⠞⠛⠛⠛⠻⢶⣤⣄⣠⣤⠾⠋⠁⠀⠈⠙⠳⣦⣀⠀⠀⠀⢀⣠⣴⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢊⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡡⣻⣿⣶⣿⣯⣵⣖⡂⢤⣄⣀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠈⠁⠚⠴⡱⣙⡟⠛⢿⣿⣿⣷⣀⠝⠉⢒⠿⢭⣷⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡄⠀⠈⡻⠿⢦⣤⣙⣿⣿⣿⠀⢀⠎⠀⡼⢡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡀⠀⠈⢖⢠⡀⠀⠀⠙⠛⢻⠟⠋⠁⠉⠀⠘⣵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡰⢡⠀⢀⢿⠓⠋⠂⡴⢂⣡⠷⠒⠁⠀⠀⢀⣴⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⢎⠜⡰⡡⢠⡖⢺⠀⠀⢀⣊⡹⠃⠀⠀⠀⢠⠔⡝⢹⠘
⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠑⡀⠒⠄⡀⠀⡠⢣⣪⢊⢴⣿⠞⢷⣮⢔⣠⠾⡟⠁⣠⠄⠚⢡⢎⠌⠀⠈
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠡⢁⠀⠀⠈⠲⢵⠿⢷⣧⢤⣷⣄⣠⣧⣀⣷⡄⠀⡠⠋⠀⣰⢃⠮⢄⣀⡤⢓⠄
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢃⠀⠀⠀⠀⠀⠢⣼⣧⣀⣹⡏⠙⣟⠁⠻⠇⠀⠁⢀⡼⢣⠊⡩⢖⡡⡎⡇
⠀⠀⠀⠀⠀⠀⠀⡀⠂⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⢻⠉⢻⡟⠻⣿⣦⣴⡟⠁⡠⡻⣡⠗⡫⠔⠁⠀⠣⠃
⠀⠀⠀⠀⠀⠀⠀⡇⠈⡀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⣦⣾⡆⢀⣼⡡⠋⣠⢎⡔⣱⠕⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⢩⡗⠄⠀⠀⠀⠀⠀⢸⠛⢙⡿⠋⣀⡴⢛⠝⡔⠁
⠀⠀⠀⠀⠀⠀⢠⠀⠀⣌⠆⠀⠈⢎⠑⠫⣒⣦⣤⠀⠈⠒⢁⣠⢞⡩⢒⢏⡜
⠀⠀⠀⠀⠀⠀⡄⠀⠰⣯⠣⡀⠄⢊⠆⠀⠀⠑⠪⢝⣦⠖⡫⠔⠉⢠⢊⠎
⠀⠀⠀⠀⠀⡠⠁⠀⣾⡫⠤⠒⠪⣑⠢⣀⠀⠀⠀⠸⠕⠊⠀⠀⢠⢣⠊
⡤⠐⠆⠘⠉⠀⠀⢴⠀⠀⠀⠀⠀⠀⠉⠢⢕⠢⢄⠀⠀⠀⠀⡰⢡⠃
⠉⠀⠒⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢍⡢⢄⡴⡱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡞⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⢠⣾⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢿⣶⣤⠀⢀⣴⣾⠿⡿⣿⣦⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢠⣿⠏⠀⠀⠀⠦⠹⣿⡆⠀⣾⠿⠿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⡀⣿⣧⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡄⠀⢻⣿⠀⠀⠀⠀⠠⢁⣿⡏⠀⠛⠛⠛⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⢿⣷⣤⣉⣤⣤⣾⡟⠁⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠉⠛⣛⠛⠛⠁⠀⠀⠙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠟⠁⠀⣼⡿⠀⠀⣿⡇⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠰⣿⠇⠀⠀⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣶⡿⢿⣿⣿⠛⠿⣷⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠿⢿⣿⠋⠀⠀⠙⣿⣿⣦⣄⠈⠙⠛⠿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⢻⣿⡀⠀⠀⣰⣿⠏⠙⣿⣷⠄⠀⠀⢠⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣌⠻⠿⠿⠿⠿⣋⣴⣾⠿⠋⠀⠀⣰⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠉⠻⣿⣦⠀⠀⠀⣀⣠⣴⡿⠟⠻⢿⣶⣶⣶⣾⠿⠛⠁⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠿⠿⠿⢿⣿⣶⣶⣿⣿⣶⣶⣾⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⢠⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⢾⣦⠀⠀⣠⣤⣤⣿⡏⠀⠀⠉⠉⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠋⠀⠀⠀⠀⣴⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠸⣿⣷⣤⣬⣭⣭⣭⣥⣴⣶⣶⣶⣿⣷⣤⣤⣤⣤⣤⣶⣾⡿⠛⠁⠀⠀⠀⣠⣾⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠈⠉⠉⠉⠉⠉⠉⠉⣉⣁⣀⣈⣉⣭⣭⣭⣽⣿⣿⣿⣶⣶⣾⣿⡿⠿⠿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣶⣶⣾⡿⠿⠿⠿⠿⠟⠛⠛⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠘⣿⡇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠻⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⠀⠀⠀⠀⠀⣠⡄⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣶⣶⣶⣶⣦⣤⣈⠛⠻⢿⣦⡀⠀⠀⣿⡇⢀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣁⣠⣤⣤⣤⣄⣀⣉⠉⠛⠻⢿⣶⣄⠙⢿⣆⣠⣿⣶⣿⣿⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣾⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠿⠿⣶⣤⣉⢻⣷⣾⣿⠿⠛⠉⠉⠙⠛⠿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀⣹⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣤⡀
⠀⠀⢀⣤⡶⠾⣿⣿⣶⣄⠀⠀⢀⣠⣶⡿⠟⢛⣽⣿⠋⠉⠉⢹⣿⡿⠟⠉⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡄
⠀⠀⠻⣷⣶⣾⠿⠛⠉⠉⢀⣴⠿⠋⠁⠀⣴⣿⠋⠀⠀⠀⠀⢾⣿⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠁⣀⣀⣠⣾⣟⠁⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⢼⣿⠇⠀⠀⣜⢳⣾⣿⣦⡀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣭⣭⣽⠿⠗⠀⠀⠀⠀⣠⣤⡙⣿⡄⠀⠀⠀⠈⠛⠀⠀⣠⣌⢿⣿⡻⣿⣿⣦⡀⠀⠀⠀⠻⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠏⠀⠀⠀⠀⠀⣰⡟⢉⣿⠀⠘⢿⣆⠀⠀⠀⠀⠀⠀⢿⣿⣧⠙⢷⣌⠻⣿⣿⣦⡀⠀⠀⠈⠙⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⢰⣿⡏⠀⢀⡀⠀⠀⠀⠻⣿⡿⠃⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠈⢿⣿⣧⡀⠻⣧⡙⠿⢻⣿⡄⠀⠀⠀⠀⢸⣿⡏
⠀⠀⠀⢀⣠⣴⣶⣾⣿⠟⠀⣿⣿⠁⠘⠛⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣷⣶⣤⡈⢻⣿⡷⠀⠈⠀⠀⢸⣿⡇⠀⠀⠀⠀⣾⣿⠁
⠀⢀⣾⡟⢁⣠⣿⡿⠃⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⠀⠀⠲⠿⢷⣦⠈⠉⢻⣷⠀⢻⣇⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⣸⣿⠇
⠀⠈⠿⣿⠿⠟⠋⠀⠀⠀⢸⣿⡇⢀⣀⡀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣼⣿⠀⠈⣿⡄⠀⠀⠀⢸⣿⣧⠀⠀⣠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠹⣿⡷⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣥⠀⠀⢹⣇⠀⠀⠀⢸⣿⣿⣀⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠈⣿⣧⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠰⣿⣿⣦⠀⠀⠀⠀⠀⠙⣭⣤⣀⣈⣿⡄⠀⠀⢘⣿⣿⡿⠛⠁
⠀⠀⠀⣀⣤⢶⣿⣿⠃⠀⠀⢹⣿⡄⠀⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣷⠀⠀⠀⣿⣿
⠀⠀⣼⣿⣡⣾⡿⠃⠀⠀⠀⠀⢿⣷⡀⣰⣿⠃⠀⣀⣤⣶⡿⠿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠎⣿⣧⠀⠀⠸⣿⡄
⠀⠀⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⣴⡿⠟⠋⠁⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣦⣤⣾⣿⣷⡀⠀⠹⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠉⣀⠀⠀⠻⠶⣦⣤⣀⡀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⠟⠉⠻⣷⡀⠀⠙⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣀⠀⠀⠈⠙⠿⠷⠀⠙⠃⠀⠀⠀⠀⣀⣤⣶⣿⠟⠁⠀⠀⠀⠹⣷⡀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⣦⣤⣄⣀⣀⣀⣀⣤⣤⣶⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠻⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⢀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠠⠂⠒⠂⣀⠀⠀⠀⠆⠀⠀⠀⠀⡄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⡀⠄⠁⠂⠀⡄⠁⠀⠐⠠⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠳⠢
⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⡄⠓⠀⡸⠤⡄⠀⠀⠀⠀⠀⢱⠁⠀⠀⠀⠁⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠙⠂⠄⠀⠀⠀⠀⠔⠉
⠀⠀⠀⠀⠣⢄⡀⠀⠀⣁⠁⢀⠀⢈⢀⣘⠈⡀⠤⠤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⠀⠤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠯⠀⠀⠀⠀⠀⢀⡀⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠄⠥⠤⠤⠠⠂⠃⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⢄⡠⠋⠘⡀⠀⢷⢄⣉⡧⠶⠰⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠁⠈
⠀⠀⠀⠀⢤⡀⠀⢄⣄⡠⠐⣠⡌⠀⠀⠈⠀⢑⣶⣷⠊⠐⠒⠶⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠒⠒⠂
⠀⠀⠀⠀⠘⠀⠉⠉⠉⠁⠀⠸⡍⠉⠙⠋⠉⠉⣱⠏⠁⠀⠀⠁⣀⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠁⢄⣀⣀⢀⡄⠀⠀⠀⠢⠂
⠀⠀⠀⠈⠑⠂⠐⠒⠒⠀⠀⠀⠈⠁⠀⠁⠉⠉⠁⠀⠀⠐⡀⠔⠁⠀⠀⠀⠒⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠐⠂⠀⠸⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠐⠀⠀⢈⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠀⠀⠋⠀⠀⠀⠀⢸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠤⠤⠤⠂
⠀⠀⢀⠀⠠⠴⠤⠄⠀⠷⠐⡄⠀⡄⠨⢁⡞⠀⠂⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠦⠤⠔
⠀⠀⢈⠀⠀⠀⠀⢴⣲⠤⠇⠡⠄⡥⢀⡾⠀⡈⠀⠀⠀⡜⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠸⠂
⠀⠀⠀⠀⠀⣰⠢⠀⠤⠤⠒⠁⠀⢁⡞⠀⡀⠀⠀⠁⡴⠀⠀⠀⠀⠀⠀⠀⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂
⠣⠀⡀⢀⣀⠨⠀⠀⠀⠀⢀⡄⠀⠻⢀⡈⢀⠀⠀⣰⠃⣀⠀⠀⠠⠔⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢇⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠠⠀⠀⢠⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠁⠰⠊⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⢠⣿⣦⣍⡛⠿⣿⣿⣷⣶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠏⣰⣿⣿⣿⣿⣿⣦⣌⠻⢿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠙⢿⣿⣿⡿⠟⠋⠁⠀⣤⣀⣴⣄⣠⡄
⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⠏⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣷⡄⠙⠋⠀⠀⠀⢠⣴⠟⠋⠉⠉⠙⢷⣤
⠀⠀⣠⣾⣿⣿⣿⣿⣿⡟⢠⣿⣿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡏⠀⠀⠀⠀⠀⠈⣷⣤
⠀⠀⠉⠁⠀⠀⠉⠉⠙⠁⠛⠁⠀⠀⠀⢠⣶⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⡀⠀⠀⠀⠀⣰⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠷⣶⡶⢾⡏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣦⡈⠻⠿⡿⢟⣥⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣦⡀⠀⢸⣿⣿⣿⣷⣄⠀⠀⠀⢀⣴⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣦⡀⠹⣿⣿⣿⣿⣷⣠⣾⣿⣿⡿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠻⣿⣿⣄⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣿⣿⣁⣀⣀⣈⣻⣿⣷⣄⣀⣈⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣉⣁⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⢿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁



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

⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⢀⣴⣶⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠻⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣿⣿⣿⣿⣧⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠂⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⠿⠃⠀⠀⠀⠉⠛⠻⠿⠛⠛⠁
⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣤⣀⡀⠀⠀⠀⠀⣀⣠⣴
⠀⠀⠀⠀⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠁⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡏⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⡠⠐⠀⠀⠀⠐⠠⢀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠀⠀⠀⠐⠠⢀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠀⠀⠀⠐⠠⡀
⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠠⠋⠀⠀⢀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⡠⠁⠀⠀⢀⢠⠀⠀⠀⠈⠢
⠀⠀⠀⡁⠀⠀⠐⢀⠀⠀⡀⡂⢴⡂⠅⠀⠀⠀⠁⠀⠀⠀⡀⠒⠂⠀⠀⠀⠀⠁⠀⠀⠀⠁⠀⠀⡐⠁⡆⠀⠀⠀⠀⠀⡁
⠀⠀⠀⡃⠀⠐⠀⢀⠀⡠⠋⣀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠄⠢⠀⠠⠂⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⢁⠀⠐⢄⠀⠀⠀⠀⡃
⠀⠀⠀⠐⡀⠀⠀⠠⠋⠀⢀⡸⠀⡠⠁⠀⠀⠀⠱⡀⠀⠀⠐⠀⠐⠀⠀⠀⡰⠁⠀⠀⠀⠡⡀⠀⠀⠑⠂⠀⠈⠀⠀⡐
⠀⠀⠀⠀⠈⠂⠄⢁⣀⣠⠁⠤⠊⠀⠀⠀⠀⠀⠀⠈⠢⠄⢀⣀⣀⠀⠄⠊⠀⠀⠀⠀⠀⠀⠈⠢⠀⢀⣀⣀⠀⠄⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢄⠀⠀⠄⠐⠐⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢵⠆⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠈⠂⠀⠀⣀⣠
⠀⠀⠀⠀⠀⠀⢠⠆⠀⠌⠀⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⢠⠏⠀⠄⣀⠤⠀⠀⠀⠀⠀⠀⠀⡝
⠀⠀⠀⠀⢠⠏⠀⠀⠸⡠⣤⠄⣠⡀⠘⡀⠀⠘⡄
⠀⢀⡤⠐⠀⡀⠀⠀⠀⠱⡅⠰⠀⠀⠀⠀⠈⠈⢁
⡔⠁⠀⠀⠀⢡⠀⠀⠀⠐⠐⢠⣆⠀⠀⣀⠀⠀⠀⠑⢤⠐⠒⣄
⡆⠀⠀⠀⠀⠀⢧⠀⠀⠠⠀⠁⡜⠀⠈⣠⠇⠀⠀⠀⠈⡆⢡⠸
⢀⠀⠀⠀⢀⠠⠘⠞⠁⠀⠀⠀⢇⠀⢰⠁⠀⠙⠒⠤⠴⠃⠀⢹⡀
⠈⣄⡴⠺⣟⠀⠂⠀⡠⠀⠀⠀⢬⠠⣸⠀⠀⠂⠀⠀⠀⡠⠔⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊
⠀⠋⠀⠀⠀⠉⠉⠁⠈⠑⢄⢢⡘⣄⡏⠀⠀⠀⠐⠔⠁⠀⠈⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡙⠛⠁⢀⠀⠠⠁⠈⢂⠀⠀⠀⠀⠀⠀⠈⠲⡀⠀⠀⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠠⠚⠐⠁⠀⠐⠀⠑⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠰⠈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀⠠⠊⠀⠀⠀⠄⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⢀⠀⠜⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠐⠂⠀⠈⠳⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠄⠤⠤⠔⠂⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠈⠢⡀⠁⡀⠀⠀⠀⠀⢀⠄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⡘⠢⣀⠑⢆⡀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠙⠳⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⢀⣠⠖⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣿⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣻⣛⣛⣿⣫⣛⣻⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣭⣭⣽⣿⣯⣽⣯⣭⣭⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⡀⠂⠀⠀⠒⠆⠀⢠⠀⠀⠀⡦⠗⡀⢫⠘⠀⢀⣤⣡⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡚
⠀⠀⢠⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣭⠀⠃⣁⠀⠀⠉⠉⢿⣦⠀⠀⡀⠀⠀⠀⠾⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠖⠁
⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠑⠀⠐⢀⣀⣤⣴⣶⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⣤⣤⣶⠾⠿⠿⠛⠋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁
⠀⠀⠀⠀⠑⢀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠊⠁⠀⠀⠈⠑⠢⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠘⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⣄⡀⠀⢀⣴⣿⠆⠠
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠛⠻⠓⣜⠉⠀⠀⠀⡂
⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⣀⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡆⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠙⣦
⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⣛⡡⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡋
⠀⠀⠀⠀⠀⠉⠀⠂⠐⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⠤⠤⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⣠⣴⣿⣤⡀
⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠡⠀⠢⠀⠀⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁⠀⠀⠙⠛⠛⠋⠁
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⢁⠘⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⡀⠀⠀⠀⣀⡀⢱
⠀⠀⠀⠀⠐⠘⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢰⠘⢅⡼⠀⠀⢸⡁⣹⠂⠀⠸⣅⡵⢸⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠰⡄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠈⠛⠷⠷⠿⠾⠿⠟⠛⠛⠛⢀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⡆⠀⠀⠀⢪⡉⠙⠳⣄⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⡴⠢⠤⣄⣤⣠⣄⣄⣰⠤⠦⢣
⠀⠀⠀⠀⠀⠀⠀⠳⣠⡞⢱⠆⠀⠀⠈⢳⡾⠏⢹⠀⠀⠀⠀⠀⠉⠉⠀⠂⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⢀⡀⠀⠈⠀⢀⣀⣠⠀⠀⠀⠻⢦⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠀⢼⣦⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿
⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣿⣿⠿⠇
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠇⠀⠀⢰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡿⠃⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠛⠋⠀⠅⣀⠤⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⣤⠆⠀⠀⠄
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⢸⡄⠀⠀⠀⢀⣀⡀⠀⠀⠙⢦⡀⠀⠄⠀⣀⣀⡠⠖⠛⠉⠀⠀⠀⠒
⠀⠀⠀⠀⠈⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠷⠖⠚⠋⠉⠉⠁⠀⠀⠀⠈⢻⣤⣤⠞⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⠀⠀⠈⠉⠉⠀⠐⠒⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠄⠰⠄⠈⡄⠁⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠐⠁⢈⣠⠤⠤⠄⣤⣤⠒⠜⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠀⠀⠀⢀⠀⠂⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢠⠠⠤⠐⠒⠛⠁⠀⠀⠀⠀⠈⠠⠈⠁⠁⠂⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⢀⠄⠂⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢡⠀⠄⠊
⠀⠀⠀⠀⠀⠀⢀⠀⠀⣠⠗⠀⠀⠀⢀⠴⠋⠉⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠒⠃⠐⠀⠀⢀
⠀⠀⢀⡄⠀⠀⠀⠅⠀⢰⠶⠓⠊⠉⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⢀⠠⠐⠁⠀⠈⠀⠀⠡⠀⠀⠀⠀⠈⠀⠀⠀⢤
⠰⣔⠊⠀⣀⡀⠀⢠⠀⠀⠏⠢⡀⠈⠀⢠⣤⠀⠀⡀⢣⡀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⢠⠎⠰⡌⠉⠀⠀⠘⠐⠂⠱⣀⠈⠐⠀⠀⠄⠄⣁⠀⠔⠩⠄⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠊
⠀⠀⠀⠈⠀⠀⠀⠀⠄⠀⠀⠘⠅⠐⡀⣿⠄⡴⠛⡂⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠌⡐⢎⡃⠀⠀⠀⠀⠀⠀⡂⠠⠀⡀⠀⠀⠀⢀⠀⠀⠀⠉
⠀⠀⠀⠀⣠⠴⠒⠖⠚⠓⠒⠤⣀⠀⠀⠀⣆⡑⢨⡹⠄⠀⠀⠂⠀⠀⡅
⠀⢀⠔⠋⠀⠀⠀⢀⣀⠀⠀⠀⠈⠛⣆⡉⡍⠙⡷⠀⠈⠏⢀⠀⠈⠀⣰⠀⢸⠕⢀⡼
⢀⠉⠀⠀⠀⠈⠉⠀⠀⠸⠕⢂⡀⢀⠈⢧⣰⠀⡦⠈⠆⢘⢀⠀⠀⠀⠀⠶⠦⣄⠠⠄
⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢛⡀⠀⠰⡆⠃⠑⢈⠃⠌⠀⠀⠀⠀⠀⢀⠀⠉
⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠁⠀⠀⡇⠀⠀⡰⣆⠀⠀⠀⢀⡀⣀⠔
⢘⡀⠀⠀⢄⠀⠀⠀⠀⠀⠈⣀⠄⠀⠀⢰⣁⠤⠾⠇⠒⠂⠈⠉⠀⡀⠠⠄
⠀⠻⡀⠀⠀⠁⠀⠀⢀⠀⠰⠁⠀⠀⣠⠋⠀⠄⠀⠀⠂⠀⠁⠈
⠀⠀⠉⠢⣄⡀⠀⠀⠀⠂⠀⣡⡤⠚⠁
⣤⣤⣤⣤⣤⣬⣵⣶⣶⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠑⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⢀⡀⣀⣰⡏⠀⠀⠀⠀⢰⣿⠿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠘⣯⣿⡶⢶⠄⣴⢛⣷⣼⢯⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣠⠟⠉⠀⠀⣀⣁⣸⣿⡿⢿⣟⣦⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠶⣦⣀⠀⠀⠀⣸⣿⣿⣷⣿⣿⣏⣛⣁⣙⣋⣻⣊⣹⣿⣃⠀⢠⣶⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠻⡝⠉⢶⣿⠿⣷⠀⢰⣿⣿⣟⣫⣯⣿⣿⢹⣡⣽⡍⠉⠻⣽⣏⣿⠀⠹⠟⠛⢿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣀⡿⠂⠻⠄⠀⠘⠀⠸⣷⣯⣿⣧⣜⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠉⠀⠀⠀⠄⣀⣹⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡿⠀⠀⠀⠀⠀⠀⠀⠋⢹⣿⣷⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠘⣿⣿⣽⣏⣿⣾⡿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠒⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠂⠐⢘⣿⣿⣆⠀⠀⠀⠀⠀⡟⠷⠾⠡⡟⢸⡇⠸⠀⠀⠀⠀⠀⠀⠄⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣾⣿⣿⢿⣿⣿⣦⡀⠀⠀⠸⣿⡦⣶⡶⠗⠈⠀⠔⠀⠠⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠙⠿⠿⣷⣤⡄⠀⡈⢶⣽⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡟⣁⣤⣾⡄⠀⠀⠀⠚⠉⠁⢸⠫⠅⣀⣀⣀⡀⣀⡀⠀⠀⠀⠀⠰⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡿⠛⠁⠀⠀⠀⠀⠀⠤⢿⠶⢶⣿⡉⣉⠛⠙⣷⣿⢟⡶⡀⣀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⡏⠛⠻⢧⣌⠿⠋⠀⢀⣀⠤⠄⠐⠒⠀⠀⠀⠀⠐⠟⢀⣉⣳⣿⡄⣡⣬⠙⠟⣷⣄⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣷⣤⣀⣤⣿⣤⠀⠺⠀⠀⠰⠂⠦⠐⠤⡀⠓⡒⠀⠂⣠⠟⠋⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⡿⠏⠙⠁⠀⠀⠀⠀⠀⠈⠒⠒⠂⠁⠀⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠏⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⣀⣀⠀⠀⣇⣠⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡈⠍⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⡄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⣀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠘⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⠶⣿⣆⣠⡾⣟⣿⣿⣿⣶⣶⣶⣶⣶⣤⣤⣤⣾⣷⣄⣀⣀⡀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻⣴⣿⣯⣥⣿⣶⠿⠿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢰⣶⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠻⢿⣿⣫⠤⠿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠉⠙⠛⠻⠋
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢐⡿⣁⢙⡺⣿⠖
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣄⢀⠀⠀⠀⣀⠴⣮⣵⣿⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠛⠛⠻⠟⠷⠶⠜⠉⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠟⠻⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣴⣦⣶⣶⣆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠢⠐⢘⡐⠠⢂
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠂⣴⣿⣿⣿⣷⣄⢐⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠒⢚⣛⣛⣛⣛⣛⣛⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠄⠃⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠘⠰⢠⠂
⠀⠀⠀⠀⠀⠀⠐⠢⢁⣴⣾⣿⣷⣦⡉⠔⠀⠀⠀⠀⠀⠀⠀⠀⠂⢌⣴⣿⣿⣿⣦⡈⠔
⠀⠀⠀⠀⠀⠀⠤⠍⣼⣿⣿⣿⣿⣿⡇⠩⠤⠀⠀⠀⠀⠀⠀⠤⠄⢸⣿⣿⣿⣿⣿⣷⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⠈⢿⣿⣿⣿⡿⠃⠌⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠈⠉⠁⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠆⠀⢩⠡⠐⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⣄⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⢒⠒⢢⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣄
⠀⠀⡶⣪⣭⣭⣭⡲⡆⠀⠀⠀⠀⠀⠀⠀⣿⠀⡟⡇⢸⡇⠀⠀⠀⠀⠀⠀⠄⢸⠃⠀⠀⠇⡠⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠈⣿
⠐⢾⣸⣿⣿⣿⣿⣿⣸⡖⠀⠀⠀⠀⠀⠀⣿⠀⡇⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⣠⣿
⠀⠿⡸⣿⣿⣿⣿⡿⣸⠷⠀⠀⠀⠀⠀⠀⡇⠀⡇⡇⢸⡇⠀⠀⠀⠀⠀⡠⠐⣎⠀⠉⠀⢰⡖⢤⠀⠀⠀⠀⢀⠠⠟⠁⠀⠈⠻⠄⡀
⠀⠀⠟⢮⣽⣿⣭⠞⠇⠀⠀⠀⠀⠀⠀⠀⡏⢸⣁⡱⢸⡇⠀⠀⠀⠀⠀⠀⢀⣿⣦⣤⣴⣿⡇⠀⡇⠀⠀⠀⡇⣠⣷⣤⣀⣤⣶⣆⢨
⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠒⠚⠁⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠓⠀⠃⠀⠀⠀⠃⠘⠛⠛⠉⠛⠛⠋⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⡀⡐⡞⣎⢤⡲⣤⡀⠀⠀⠀⠀⠀⡴⠊⠉⠀⠈⠉⠲⡄⠀⠀⠀⠀⠀⠀⠀⣀⣞⣗⡀
⢀⣾⣹⡇⣿⢹⣏⠿⠜⠿⠀⠀⠀⠀⡞⠀⠀⠁⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⡀
⠘⠛⠉⠁⠉⢠⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⠀⣠⠀⣠⠀⣠⠀⡇⠀⠀⠀⠀⠀⢨⢠⠴⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡇
⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢙⡇
⠀⠀⠒⠒⠖⠒⠳⠒⠒⠒⠀⠀⠀⠀⠀⠀⠙⠛⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡬⣀⠨⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢀⡤⢴⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣬⣤⡅⣤⣬⡄⠀⠀⠀⠀⠀⢀⣠⣤⣭⣬⣭⣥⣤⡀⠀⠀⠀⠀⠀⢰⣤⣥⣦⣬⡆⣼⠇
⢸⣿⣿⡟⠙⠋⢻⣿⠉⠉⢣⠀⠀⠀⠀⠀⠸⣿⣿⣸⡿⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⢿⢿⣿⠟⠀⠀⠀⠀⠀⠀⢸⣇⣀⠼⢿⡇
⢸⣿⣿⣧⣤⣤⣼⣿⣿⣿⣿⣷⡆⠀⠀⠀⠀⢻⣿⣇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⢢⣼⡇
⠾⢿⣛⡿⠿⠿⠿⠿⠿⣟⣻⠻⠇⠀⠀⠀⠀⠀⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠉⠀⠉⢃⣀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⢀⡠⣤⠤⢀⣀⣀⠀⠀⠀⠀⢀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀
⠀⠀⠀⣠⣖⡽⣾⣿⡿⣟⠔⠋⠀⠀⠀⢠⣿⣿⡿⣿⣿⣦⠀⠀⠀⠀⠀⠀⢀⣤⣀⢰⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣜⠿⠿
⠀⡜⠇⠀⠉⠉⠉⠛⠋⠁⠀⠀⠀⠀⢠⣿⣿⢿⡇⡿⣻⣿⣧⠀⠀⠀⠀⠀⠺⣿⣿⠆⡙⢛⣋⠀⠀⠀⠀⠀⠀⢠⣟⣻⡄⠈⠙⠻
⠉⠫⣤⡀⢠⡀⢀⡄⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡀⣾⣿⡿⠃⠀⠀⠀⠀⠀⢰⣬⣉⠶⡏⠻⠏⠀⠀⠀⠀⠀⠀⣤⣘⢻⣀⣤
⠀⠀⠁⠀⠋⠉⠉⠉⠩⠛⢄⠀⠀⠀⠀⠀⠈⠉⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁⢲⠖⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠐⠒⠒⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠒⠒⠚⠒⠓⠒⠂⠀⠀⠀⠀⠀⠐⠒⠒⠚⠒⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠐⠁⠀⠀⠀⠀⠐⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠠⠀⠢⢀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠈⢣⡠⢀⠀⠀⠀⠀⠀⠰⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⡀⠈⠂⠄
⠀⠀⠀⣤⠀⠀⠀⠴⠊⠁⠠⠒⢂⠀⠀⠀⣀⠅⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠊
⠀⠀⠀⠈⠉⠀⠀⠐⠀⠀⠀⠀⠁⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⠀⠀⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠂⠂⡁
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠈⠀⠂⠀⠓⣆⣋⡙⢛⣲⣤⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠸⠂⠚⠛⠚⠒⣛⠠⠤⠖⠶⠛⡟⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠐⠐⠒⠒⠊⠀⠀⠀⠠⠋⠀⠀⠀⠤⠀⠞⠀⠀⠀⠀⠀⠈⠉⠩⠀⠀⠀⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠄⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⢀⡴⢁⣡⡶⠂
⠀⠀⠀⠀⢀⢀⠀⣈⢀⠀⠀⠰⠀⡈⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠃⡊⠛⠉
⠀⠀⠂⠈⠉⢉⣤⣈⡄⢀⢀⠈⡔⠀⠂⠀⢀⠌⠀⠀⠀⡀⠀⠀⠀⠐⠆⠁⠀⠀⠀⠰⠀⠀⠈⠉
⠀⠀⠀⠀⡠⠤⠭⠤⠔⠀⢀⡼⠁⠀⠀⠀⡸⠀⠀⠀⠀⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠁⠠⠀⠀⠀⢀⣀⣀⠠⣀⣸⣀⣀⣀⢀⡴⠁⠄⠀⠀⠂⠀⠊⠀⠀⠀⠠⠀⠀⠀⠀⠘⠦⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⣀⣀⡀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠠⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠾⠄⡽⢋⠟⢉⣠⡄⠺⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⡟⣷⢂⡏⡼⠁⣿⣵⢟⡍⠁⠀⡜⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠬⠶⡽⢡⠏⠉⠀⠀⠀⣼⠇⡜⡿⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢻⡆⠰⠃⠀⠀⠀⠀⠀⠘⣿⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠦⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⣵⡟⡼⠁⠀⠀⠀⠀⠀⠀⠀⠈⡧⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟

⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⣈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⡴⠉⠀⠀⠀⠀⠀⠀⢁⠤⠔⠚⠓⠃⠤⣄
⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⡠⠔⠡⢂⠄⠀⢀⣾⡁⠀⠀⠀⠀⠀⢀⡔⠑⣧⠀⠀⣀⡙⠂⠈⢳⡀
⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢀⡤⠊⠀⠀⠋⢸⠦⢴⠾⣥⡨⠀⣀⠤⠊⠀⡌⠀⠀⠈⠀⠀⠉⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠱⣀⡐⠉⠀⠉⠀⠀⠀⠀⣇⠠⡀⠀⠀⠀⠀⣀⠀⠀⠀⡇
⠀⠠⡀⠀⢀⠴⠊⠉⠀⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠉⢙⡆⠀⠀⠀⠀⠀⠀⠘⢦⡈⠙⠛⠛⠉⠀⠀⣀⠞⠁
⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⢀⠤⠐⠈⠀⠀⠠⠿⠯⢦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠒⡖⠋⠁
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⡠⠄⢤⣄⣠⠃⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⣀⣀⡜⠀⠀⢠⠛⠉⠉⠀⠀⠐⠒⠚⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⡜⠀⠀⢠⡶⠶⠶⠶⠦⠤⣤⠤⠞⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣀⡁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢒⡟⠀⠀⢠⡿⠓⠚⠀⠐⠒⠒⢓⠆⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣤⡼⠉⢉⣓⠲⣤⣀⠴⠒⠋⠁⢀⠞⠀⠀⣠⡿⣄⠀⠀⠀⢀⣀⡠⠋⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠳⢶⢖⠛⠛⠛⠛⢲⠏⠀⠀⣰⠿⠤⠿⠶⠶⠶⠾⡄⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣣⠀⠀⢀⡎⠀⠀⣰⡏⠀⣀⠀⡀⣀⠀⠊⠀⣴⠏
⠀⠀⢀⡀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣀⣀⡔⡲⢤⣄⣀⠒⠧⢂⢀⡞⠀⠀⢰⣯⣬⣭⣭⠇⠤⢆⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⢸⠁⠉⠉⠉⠛⠛⠛⠛⠳⠮⠛⠀⠀⢠⣟⠀⣀⣀⡀⠀⡠⠎⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢀⠴⠋⢙⠖⠒⣶⠦⠤⠤⠤⣀⣀⣀⠀⠀⣼⡦⠤⠬⠭⠍⢭⠁⢰⡏⠐⢦
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠁⠀⢀⠔⠁⠀⢀⠎⠀⣴⠟⠀⠐⠂⢀⠎⢠⡿⡄⠀⢹⡆⠀⠤⠀⠀⠈⡆⠈⣷⠐⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⡲⠁⠰⡦⢝⡟⠀⣼⠏⠀⠀⠀⢀⠊⢠⡟⠀⢥⠀⠀⣿⠀⠀⠁⠀⠀⠸⡀⠘⣗⠂
⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠹⣷⡶⠀⠀⠀⡜⠀⡼⠋⠀⠀⠀⠀⣣⣤⣽⠀⠀⢸⡄⠀⢹⡆⠀⣀⠀⠀⠀⢣⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠚⠁⠀⠀⠀⠰⠀⠉⠉⠁⠂⠀⠀⢷⠀⠈⢱⠀⠀⡀⢈⠀⠠⢆⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠉⢓⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣀⠀⠀⣧⡄⠀⠀⠀⠀⢀⡀⠉⠙⠛⠲⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠛⠛⠶⠶⠶⠤⠄⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠵⠦
⠀⠀⠀⠀⠀⠀⢠⢆⣄⠸⣿⣧⣀⠀⣠⣮⣂⣤⣾⠟
⠀⠀⠀⢀⣠⣤⣬⣿⣿⣷⣿⣿⣿⣾⣿⣿⣿⣿⣷⡶⠶⠖
⠀⠀⠈⠉⢉⣉⣉⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⡀
⠀⠀⠀⣊⣉⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⣄⡀⠀⠉⠉
⢀⣴⠿⠿⠟⠟⢛⣩⣽⡿⢟⡿⠻⣿⣿⣿⠿⣿⣾⣯⡕⠄
⠀⠀⠀⠀⠀⣰⣿⠟⠉⠀⣸⡇⠀⠙⢽⣿⣷⣌⠙⠋⠁
⠀⠀⠀⠀⠀⠋⠀⠀⠀⢠⣿⠀⠀⠀⠀⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⣴⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢠⣾⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠉⠀⠀⠀⠀⠀⠀⣿⡇⠀⣰⣿⣿⣿⡿⠿⠋⢉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠻⠟⠋⠉⠀⢀⣶⣿⣿⡷⠀⠀⣴⣶⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⣄⡀⠀⠀⠀⠿⣹⣿⣇⣀⣠⡿⠟⢀⣼⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠐⢾⣿⣿⣶⣄⡀⠀⣿⣿⣿⣿⣷⣤⣀⣾⣿⡏⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠈⠙⢿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣿⣿⣷⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣆⠀⠀⠀⠀⠈⣻⣿⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⡛⠛⠃
⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⡀⠈⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠇⠀⠀⠁⠀⠀⠀⠀⡄⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠛⠛⠁⠀⠀⠀⠀⠀⠠⣤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡄⠈⠉
⠀⠀⠀⠀⠀⠀⠀⢰⣟⣿⣿⣃⠈⠲⡄⠀⠀⠀⠀⠀⠠⠀⠁
⠀⠁⠀⠀⠀⠀⢀⠀⠈⠻⢿⣿⡅⠀⠈
⠄⠀⠀⠀⠀⠀⠈⢱⠶⠲⠜⠛⠃⠠⣀⠀⠀⠀⠀⣄⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣀⠀⠀⠈⠉⠀⠀⠀⠀⠐⠆⠀⠀⠈
⠀⠀⠐⠂⠀⢠⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡾⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠶⠶⠶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⡿⠛⠛⠉⣀⣠⣤⣄⣄⣈⠉⠙⠛⠿⢷⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠻⣿⣆⣴⠾⣶⠜⠛⠙⠛⠛⢿⣿⣷⣶⣶⣤⣄⡙⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⣄⣠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⠋⠙⣿⣟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣿⣧⣼⠛⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⣿⣿⣷⣀⣠⣬⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿⣷⣾⣠⣿⠿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣿⠻⠟⠛⠛⠋⠉⠉⠉⠙⠛⠱⠄⠈⠉⠀⠸⠿⣧⠀⠹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⡀⢀⣀⣀⣾⠇⢀⣹⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⣾⣿⣷⠶⠿⠿⠿⠿⠿⠿⠿⢿⣿⠿⣿⣿⣿⠁⣤⠘⢻⣿⣿⠟⣷
⠀⠀⠀⠀⠀⠀⢠⡄⢀⣿⣿⣇⣤⡌⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢶⠀⢻⣿⣦⠈
⠀⠀⠀⠀⠀⠀⣿⠇⢸⣿⠏⠘⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠻⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠹⣧⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠀⠠⠄⠀⠀⠀⣀⡀⠀⣀⢀⣀⠀⠀⠤⠤⠤⠤⠶⠆⠴⠶⠄⠀⢻⠀⠹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⠀⠶⠶⠀⠀⠉⠛⠁⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡆⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⣣⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⢿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆⢸⣿⠀⢠⣤⣶⠖⠀⢷⣄⠀⠠⠆⠀⣴⠆⠠⠤⠐⠀⠀⠀⠠⢘⣿⣦⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠋⢻⡇⠸⣿⠟⠁⠈⠁⠀⣀⡘⢿⣆⢀⣤⠈⠋⣀⣤⣴⣶⣶⣶⠄⠀⣿⣿⣿⠀⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠙⢃⡼⠿⣧⣾⣿⣿⣿⠿⠿⣿⣿⣷⡄⠻⣿⣽⣿⣷⣿⣿⣿
⠀⠀⠀⣤⣤⣤⡄⠰⡿⣿⡆⢸⣿⣶⣤⡾⢶⡤⣾⠿⠀⢸⣿⣿⣿⣄⣀⠀⣴⣿⣿⣿⡷⠀⠘⣿⣿⣿⣿⣿⣿⣦⠄
⠀⠀⠈⠛⠉⠀⠀⠀⠀⠈⢀⡀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⢀⡈⢩⠍⠉⠀⠀⠀⣿⡟⠻⠿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣿⣿⣿⣶⣾⣿⣶⠀⠀⣀⠀⢸⣟⠉⢙⠋⢻⣀⣠⣄⣿⡇⠀⢿⠳⣶⣄⠈⢿⣿⣿⣧⣄
⠀⠀⠀⠀⠀⠀⢀⣀⣠⡿⢃⣸⠟⢹⣉⣹⣿⣿⣿⣇⠀⠀⠀⠀⠉⠉⠀⠀⠈⠉⠀⠀⠀⠀⠀⠘⠀⠈⢿⡿⠀⠈⠙⢿⣿⡀
⠀⠀⠀⠀⠀⠀⢸⣿⡟⢀⣾⡟⢰⣾⢉⣉⣉⣠⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠘⠋⠰⡿⠟⠀⣼⣿⠿⢿⣿⣿⡟⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⠃⢰⣀⣀⣀⣠⡆⠀⠀⠀⠀⠑⠆
⠀⠀⠀⠀⠀⢠⣶⠄⠀⠠⣀⣰⠟⣿⡄⠘⠛⠛⠁⠀⣰⣧⠀⠀⢤⠞⢲⡄⠀⠀⠈⠉⠁⠙⣷⡞⠛⠟⠉⠉⠃
⠀⠀⠀⠀⠀⣼⢃⣰⣿⢃⡈⠻⠊⢻⣷⣶⣿⣿⡖⣿⣿⣿⣧⣀⣀⠀⣺⣿⣤⣤⣴⣶⣶⣿⣿⣿⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⣴⡇⢸⡟⠀⠿⠁⠀⠀⠀⣥⣻⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠾⠿⢀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠙
⠀⠀⠀⠀⣿⠀⠀⢀⡾⠀⠰⠇⣰⡄⣿⣧⣿⣿⣟⣿⣿⣿⣿⠿⠿⠿⠿⠟⠻⠟⣻⣿⣿⣤⣿⡟⠀⠀⠀⣼⠀⠀⠀⠀⢀⣿⡇⠀⢸⡇
⠀⠀⠀⠀⢉⣹⠃⠘⣷⣌⠀⠈⣻⣿⡿⠛⠻⡿⠟⠛⠻⠟⠛⠿⠛⠛⠻⠓⠀⠻⠋⠛⠃⠀⠀⠀⠀⠠⠖⠀⠀⠀⢀⣰⡿⠋⠀⠀⢸⡇⢠⣾
⠀⠀⠀⠀⠘⢿⣷⣶⣞⣛⡷⣾⣿⠋⠀⠀⠀⠀⠀⣴⣶⣄⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⢠⣤⡿⠇⣾⣿⣿
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣾⣿⢰⣄⣀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠤⠄⠊⠉⢁⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⣹⡄⠈⠛⠷⠂⠲⠂⠀⣀⢀⣀⡀⠀⠀⠀⠀⠤⠤⠤⠖⠂⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⡀⢸⡇⣨⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆⢀⡀⣿⡇⢠⡴⠶⠂⠲⠖⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠒⠒⠀⠈⠉⠉⠁⠀⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣿⡗⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⣤⣤⣤⣄⠴⠶⠿⠿⠃⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠻⠋⠙
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣤⣿⣿⡄⠀⠀⠚⠛⠛⠓⠂⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠰⠞⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⣤⠀⠀⠀⠚⠃⠀⢸⣿⠟⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⡾⠿⠿⠿⣧⡄⠀⣤⠀⢠⣶⠀⠀⠀⠘⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠈⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠋
⠀⠀⢀⠀⠐⠒⠐⢠⢀⢀⠰⠀⠀⠼⠄⠆⠀⠀⠀⢀⠂⠂⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⠑⠈⠀⠀⠁⠀⡀⠀⠀⢀⡧⠂⠀⠈⠃⠉⡂
⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⣀⡓⠆⠾⠷⠾⠠⠄⠤⠐⠒⠉⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡁⠀⣤⣄⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁⠘⠿⠳⠀⢀
⠀⠀⠀⠈⠙⣛⣛⡋⠉⣛⡁⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠒⠒⠂⠠
⠀⢀⠄⠀⠀⣀⠀⠀⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⠀⡇⠀⢰
⠀⠘⠀⠀⠁⣀⡀⠀⠀⠁⢈⡁⠀⠀⠀⠀⠀⠀⣖⣒⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠠⠥⠀⠼⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠐⠀⠀⠀⠀⠀⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡅⢀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠃⠀⡠⠀⠀⠀⢄⠀⠈
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⣀⠀⠀⠀⣀⡎⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⣠⡄⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⡟⠛⠋⠉⠙⠉⠀⠀⠀⣿⡶⣂⡴⠛⠀⢈⢁⡏
⠀⠀⠀⠀⠂⠄⠀⠒⠒⠶⠤⠀⠀⠀⠀⠀⡁⡁⠀⠀⣀⣁⠀⠀⠀⠀⠀⣇⡘⠋⢐⣁⠀⠀⠀⠀⡏⠳⢯⣆⣠⣐⡶⠋
⠀⠀⠀⠀⠐⠀⠉⢀⠀⠰⠀⠔⢀⠀⠀⠀⡅⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈⡩⠀⢨⡇⠀⠀⠀⠀⠀⠂⠐⠒⠂⠀⠀⠤
⠀⠀⠀⠐⠆⠀⠀⠇⠹⣅⠀⢠⡼⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢤⡆⠀⢀⡁⠀⠀⠀⠀⠀⣄⠀⣀⠀⠄⠀⠄⠀⢠
⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠃⠀⠠⡇⠀⢐⢨⠀⠀⠀⠀⠀⠀⠀⢲⡆⠀⠒
⠀⢀⠵⠾⠤⢀⠀⢐⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢼⡇⢀⡆
⠀⣦⠀⠑⠀⠎⠀⠀⠀⠀⠸⣄⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠁
⠀⠈⠀⢀⢀⣀⡁⢀⣀⢀⣀⡀⠁⠀⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣄⢠⡾⣿⠀⠀⢀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠹⣟⠀⠙⣧⣠⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⢰⡏⠀⠀⢻⡄⠀⠘⣿⠀⢻⣤⣤⣤⣤⣤⣴⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡍⠉⠛⢾⣇⣠⡴⠾⠓⠛⠲⠿⣤⡼⠿⢤⡀⠀⠀⠈⣿⢀
⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⣈⣷⡀⠀⣠⡟⠉⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢿⡍⠉⠛⠛⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠶⠶⣿
⠀⠀⠀⠀⠀⠀⠀⣤⡶⠿⣤⣀⡀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⠶⢾⡇⠀⠀⠶⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠉⠙⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⠚⣿⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣿⠞⠋⠻⣄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠛⠛⣿⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⢀⣠⣤⠿⣳⣦⣄⣀⣀⣀⣤⣾⠀⠀⢸⡇⠀⠀⠛⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⠶⢻⡟⠁⠀⣰⡟⠀⢨⡏⠉⠉⢻⣾⠀⠀⢸⡇⠀⣀⣉⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⢸⡇⠀⢠⡟⣷⠀⠀⣷⠀⠀⢸⣿⠀⠀⢸⡇⠀⠉⣉⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢀⣾⠁⢸⡇⣰⠟⢷⣄⣿⢹⠀⠀⢸⡇⠀⠀⣉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠁⠀⠈⣿⠏⠀⠀⠈⢉⣿⠀⠀⠸⣇⠀⣤⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣼⠁⠀⠀⠀⢸⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣀⣠⡾⠁⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣅⣀⣀⣀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠄⠠⠤⠀⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠒⠂⠀⢦⡒⡦⠒⠒⡶⠒⠒⠒⠒⠒⠒⠒⠒⠂⠂⠐⠖⠒⠒⠲⠒⠐⠒⠖⠒⠒⠖⠂⠒⠐⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠉⠀⡠⡀⠀⠀⢐⠢⠈⠑⡄⠉⠀⠀⡞⡆⠀⡤⠦⣄⢀⣀⡤⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠊⠀⠙⠲⠂⠁⠀⠀⠀⢹⠀⠀⢸⡇⠈⠁⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⢤⡀⠀⠀⠀⠀⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠙⣆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⠁⢀⠀⠀⠀⢸⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡀⠸⠀⢀⡰⠃⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢦⠀⢀⣠⠠⠤⠖⠊⠉⠙⠒⠒⠒⠙⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢸
⠀⡅⠀⠀⠀⠀⡔⠂⠒⠒⣎⠑⠢⡄⠀⠀⠀⠀⠀⠀⠀⠙⠒⣤⡠⠒⠊⠉⡇⠀⠀⣿⠢⠤⠒⠀⠐⠤⠤⢄⣠⠄⠒⠁⢢⡀⠀⠀⢀⣀⣀⣀⡠⠔⠋⠈⠓⢦⣸
⠀⠇⠒⠒⠂⡜⠀⣰⣧⢴⠟⢳⣦⠉⠁⠢⡤⠴⠦⠤⠤⠤⢄⣀⣀⣀⣀⣠⡇⠀⠀⣯⠤⠤⠄⠠⠤⠀⢀⣀⣀⣀⣀⣀⣀⢓⣒⣒⠁⠀⣈⣁⣀⣀⣀⣀⣀⣀⣹
⠀⡆⠀⠀⠀⢆⢰⠈⠪⡺⢃⠿⣹⢶⠂⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⠀⠀⠨⡏⠣⣀⢜⠕⠈⣠⣆⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡆⠀⠀⠀⠀⠙⠲⣬⣍⣉⣉⠥⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⠀⣀⠀⡐⡆⠀⡿⠀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⣈⣡⣤⣷⣾⣿⣷⡶⠾⠷⠒⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡇⣀⢧⣱⣇⡸⢐⡏⠀⣼⣡⡧⠒⡶⠀⣀⣤⣶⣾⣿⣿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⡟⠀⣟⢽⠟⡗⢺⡷⢺⢻⡏⣲⣟⢲⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠩⠅⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡠⢊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢀
⠀⠀⠀⠀⠀⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⢢
⠀⠀⠀⠀⠀⠀⢀⣠⠤⠀⡀⠀⠀⢀⠊⢡⣀⡠⠀⠀⠀⠀⠢⢁
⠀⠀⠀⠀⡀⢠⠊⢴⣞⣦⠄⠆⣸⠁⢠⠄⠈⠂⠀⢃⢦⠀⠀⠂⡄
⠀⠀⠀⠀⡆⠁⢦⡟⡀⡤⢊⠒⠄⢡⢐⡇⠀⢀⡆⡀⠅⠀⠑⡆⠇
⠀⠀⠀⢀⠣⠀⠀⠄⣀⣆⠘⠤⢂⠀⠀⠉⠀⠬⠧⠊⢀⡀⠔⠃⠂
⠀⠀⢀⠀⠀⠀⠉⠒⠬⠉⠀⠂⠀⠒⠂⠀⠀⠀⠐⠋⠁
⠀⠀⢸
⠀⠀⠸⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⡔⣦⡀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠠⡌⠀⣀⠠⠚⠙⠣⠀⠀⠀⠀⠠
⠀⠀⠀⢀⠀⠈⡟⠉⠀⠀⠈⡆⠐⢨⠀⠄⠀⠀⢤⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⠇
⠀⠀⠀⠛⠀⠀⠙⠀⠲⠦⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠀⠀⠀⢠⠈⠀⠀⠀⠀⠀⢆⠀⢀⣀
⠀⠀⢠⠀⠀⠀⠉⠙⠓⠢⠀⢀⣀⣀⠀⠀⠒⠒⠚⠉⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢄⠀⠈⠀⠀⠁⠋⠉⠁⢫⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠈⣉⠀⠀⡀⠀⣀⡀⠀⠀⠀⠰⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢠⠀⠀⠀⠐⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠁⠀⠀⠀⠀⢩⠃⡀⠀⠀⠀⠀⠂⣀⣀⡦⠀⠄⡀⠀⢀⠀⠄⢼⠢⠚⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣁⢶⣀⠷⠋⠁⠈⡀⠀⠀⠀⠀⠈⠀⠁⠀⠑⠀⠉⠇⢉⠁⠊⠉
⠀⠀⠀⠀⠠⠂⠀⡘⠀⠀⡀⡠⠀⠀⠀⠀⠂⠀⠀⠁⠀⠢⡄⠂⠀⠀⠀⠀⠢⠤⣀⣈⣉⣁⣠⠤⠖⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠂⠀⠀⠀⠉⠑⠚⠁⠀⠘⠐⠀⠒⠀⠁⠀⠀⠀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠈⠒⠲⠤⠤⠀⡀⠀⡀⠀⠠⠶⠒⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠄⠀⠀⠀⠁⠠⠺⠂⡐
⠀⢀⠄⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⣰⠄⢠⠄⣦⣰⠦⠐⠴
⡔⢣⢔⡇⠀⠀⠀⠀⠀⠀⠀⠀⡦⢀⣠⡀⠀⠀⠀⠀⠀⠀⠧⡀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⠢⠬⠴⠊⠁⠀⣀
⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠂⠐⠀⠒⠒⠚⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣧⡀⠀⣰⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣾⣷⣶⣾⣿⣿⣿⣿⣿⣧⢰⣿⣿⣿⣿⣿⣿⣶⣶⣷⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⢿⠿⠿⢿⣿⣿⣿⣿⣿⣿⠟⠙⢿⣿⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠘⠋⠉⠉⠉⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠹⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠉⠉⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠋⢈⣵⣆⣠⣄⣠⡆⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠞⠛⠋⢿⣿⠋⠀⢀⣴⠏⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⠠⠾⠁⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⢀⡔⠀⢀⡄⠀⠀⠀⠀⠀⢀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⣿⣿⣿⣿⡇⣠⠄⠀⠀⢠⡟⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣿⣿⣷⡏⠀⠀⢀⡞⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠂⠀⠀⠀⠁⠀⠀⠙⡟⠀⠀⢀⡞⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠁⢀⣠⢾⠋⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠐⠛⠋⠁⠀⠠⠆⠀⠀⠀⢀⣠⡴⠞⠋⠁⣀⣤⠖⠋⠀⣼⡆⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⠀⢀⣤⠄⠀⠀⠀⢀⣤⡶⠛⠁⠀⣠⡴⠚⠉⠀⠀⠀⠀⢽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠴⠟⠁⠀⠀⢀⡴⠟⠁⠀⣀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣷⠒⠲⠶⠄⠀⠀⣀⣀⣴⠏⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠉⠉⣿⠖⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉


⣿⣿⡟⠻⠟⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿