Jackass Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣤⠀⠀⠀⢀⣄⠀⣀⠀⢀⡀
⠀⠀⠈⠱⡀⡐⠀⠄⠀⠀⠀⠀⠀⢠⡀⢄⠀⠀⠀⠀⠀⠀⣀⠀⠀⢸⠘⡄⠀⣰⢹⡇⠀⠀⠀⢙⡛⢛⡁⠚⠁
⠀⠀⠀⠐⠃⢈⡁⠵⠀⠀⠀⠀⠀⠈⠻⠈⠀⠂⠐⢂⡤⠈⠁⠀⠀⠈⢀⣧⣤⣿⡈⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠍⣿⣿⣟⠅⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡊⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢂⣀⠀⠂⠀⡃⠀⠀⠀⠀⠀⠀⠀⠻⣷⣶⣽⠇⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⡀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣄⠀⢠⡆⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡀⠀⠀⠀⠀⣿⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣴⡟⠀⠈⣿⣾⡏
⠀⠀⢠⣾⣿⣿⣷⣴⣿⣿⣿⣿⣷⡀⠀⠀⢠⣿⣿⡇⠀⠀⢀⣀⣀⠀⠀⠀⣀⣴⣿⣿⡇⠀⠀⣿⣿⣿⣦⣀⣀⣀⣀⣀⣀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠁⠈⠉⠀⣠⣤⣼⣿⣿⡇⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⣀⢼⣿⣿⡿⣿⢿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠿⣿⣿⡟
⠀⠁⣸⡟⡿⠀⣿⠈⣿⠀⠀⠀⠀⠆⢿⣿⠿⣿⣿⠃⠀⠈⣿⡿⠁⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠘⣿⡇⠂
⠀⠀⣿⠀⣇⠀⣿⠀⢹⡀⠀⠀⠀⠀⠈⡏⠀⣿⡇⠀⠀⠀⠿⠧⠀⠀⠀⠀⣸⣿⡀⠀⠀⠀⠀⠀⠀⢸⣿⡁⠀⠀⠀⠀⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡶⢺⡄⠀⠹⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⣾⣄⠠⣌⢻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⢿⣿⣷⢈⠛⠛⠛⠋⠀⠒⠤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣶⣷⣧⣿⣿⣷⣶⣦⡄⠀⠀⠀⠙⢯⠙⠂⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣻⡿⡿⠿⣿⠿⢋⣀⣤⠤⣤⣼⣦⣠⣀⣀⣠⣭⠛⠋⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⡿⣻⣿⡟⡙⠀⠀⠀⠉⠀⠀⠠⠀⠘⠋⠜⠻⠯⠙⣻⣿⠀⠰⠶⠂⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⠿⠋⠀⣿⣿⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣴⠟⣠⣤⠀⠊⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣿⣿⣿⣿⠿⠁⠀⢠⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠋⠻⠏⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⣿⣿⣿⠿⠋⠀⠀⠀⣴⣶⣿⣿⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣿⣿⣷⣦⣌⠛⢿⣦⣀⡀
⠀⠀⠀⠀⠀⣠⣴⣿⣿⠿⠋⠉⠁⠀⠀⢀⢰⣾⡿⣿⡟⣿⣿⣿⣿⣧⣲⠀⢠⣴⣶⣿⡿⠛⠉⠀⠀⠀⠀⠀⠈⠻⣦⣄⡤
⠀⠀⠀⠀⣐⣿⣿⡿⠋⠀⠀⠀⠀⠀⢸⣰⡿⠟⠁⠘⣿⡹⠻⢻⣿⣿⣿⣿⣿⣿⠉
⠀⠀⠀⠘⠿⠛⠋⠁⠀⠀⠀⠀⣀⣰⣾⠿⠀⠀⠀⠀⠀⠁⠀⣸⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣿⠿⠇⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠃⠀⠀⠀⠀⠀⢀⢀⣶⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⡠⢈⣼⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣘⢻⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⢶⣌⢿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠡⠋⠉⠉

⠀⢰⡰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣭⣧⣤⣤⠉⠉⢉⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣷⣀⣤⢍⠀⢀⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠟⠟⠉⠋⠻⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⢸⣿⠃⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠘⠛⠀⠀⠀⢹⠀⢀⣤⣶⢶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠟⠀⠀⠀⠀⠀⠀⠀⢽⡿⢋⡴⣶⠋⠙⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⣇⣀⣠⠀⠀⠀⠀⠀⠈⣠⠏⢰⡟⠀⠘⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠃⠀⠲⠿⡷⣿⣷⠒⠛⠁⣤⡙⠃
⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⠋⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⢠⠀⠀⠀⠀⢀⣠⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⣯⡀⠀⠀⠀⠻⣿⠽⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣦⣽⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⢩⣵⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠋⠀⢲⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠈⠉⠻⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡄⠀⠀⠀⠀⠀⠛⠓
⠀⠀⠀⠀⠀⠲⠶⠒⠶⠶⠛⠓⠛⠛⠒⠶⠀⠴⠶⠖⠂⠦⠶⠦⣦⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣷⣶⣬⡄⡀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣤⣶⣮⣼⣯⢽⣿⣏⣬⣛⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠻⣛⠟⠛⣿⠟⢸⣿⠿⢛⢻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣾⡏⠈⢡⠊⡰⠻⠛⠊⢈⠌⢱⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣿⣦⣤⣤⣤⣤⣄⣤⣀⣀⣀⣸⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣻⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣿⡇⠉⠛⠛⠛⠋⠀⠙⠛⠛⠛⠁⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⠀⢀⡨⣛⣾⣧⡀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣛⡩⡞⣙⠞⡙⢿⣷⣬⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣵⣹⣟⣻⣿⣦⡙⢿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⣿⣿⣿⣿⣿⣿⣿⣿⡶⠟⠢⡀
⠀⠀⠀⠀⠀⢀⡠⠤⠖⠊⡰⠀⠀⠀⠠⣀⠘⢿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠈⢦⡦⣤⣀
⠀⠀⠀⣠⠞⠁⠀⠀⠀⡰⠃⠀⠀⠀⢀⣭⠳⠬⣉⣙⣉⣁⣀⡤⠆⠀⠀⠀⠀⢿⡄⠉⠓⠦⣄
⠀⠀⠞⠁⠀⠀⠀⠀⠈⢥⣀⣠⣤⠀⢨⣯⡀⠀⠀⠀⠈⠀⠀⠀⣄⣀⠀⠀⠀⠈⡷⠀⠀⠀⠀⠙⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⣀⠀⢀⣀⣀⣀⣀⣠⣤⣴⣤⣶⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣄⠀⠀⠀⠀⣀⣴⣾⡿⢟⣿⠟⣻⣿⠒⣿⣿⣿⣾⣿⣿⣿⠻⠟⠻⠛⠿⣿⣿⡿⠟⠿⢿⣿⣶⣦⡀
⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠙⣿⣧⣦⣶⠿⠋⠉⠊⠀⠀⠁⠐⠀⠃⠀⢘⣿⢻⡅⠻⢿⣿⠀⠀⠀⠀⠀⠉⢷⣽⡄⢀⣤⠙⣿⠛⢷⡀
⠀⠀⠀⠀⠈⢟⠉⣅⣠⣤⣠⣄⢌⣹⠋⠀⠊⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠨⢀⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣁⢤⣿⡄⠐⣃
⠀⠀⠀⠀⠀⠀⠐⢾⣿⡋⢻⣁⣿⣿⣦⣄⣀⡀⠀⣴⣢⣴⢤⠄⠀⠀⠂⣿⢸⣽⡀⠀⠀⠀⠀⠀⠀⠀⣄⣴⣤⣳⠀⣸⣿⣿⣿⠁⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⠿⢿⣿⡿⣿⡿⠿⣿⣿⣿⣿⣿⣿⣷⡀⣠⣶⠏⠈⠉⣿⣤⣶⣷⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⣿⣯
⠀⠀⠀⠀⠀⠀⠀⢸⣿⢁⡂⣾⣿⣷⣿⣾⣦⣼⠿⠿⢿⣿⣿⣿⣿⣿⣅⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠛⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣿⣫⣿⣿⣿⣿⡇⠀⠀⠀⠙⣿⣿⣿⣿⣆⢐⠿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⠿⠋⢻⣿⣿⣿⣿⣿⣶⠀⠀⠀⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⣹⣿⣿⡿⠋⠈⣿⣶⣿⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣹⣿⠀⠙⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⢩⣿⡿⠃⠀⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠉⣻⠁⠀⠀⠀⠀⠀⠀⠙⣿⡇⠀⠀⠀⠐⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⠃⠀⣀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢶⠏⠀⠀⠀⠀⠀⠀⠀⣽⡿⠀⠀⠀⠀⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⢻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠸⣿⡿

⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠐⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠄⢀⣠⠈⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠠⠄⢀
⠀⠀⠀⠀⠀⠑⠀⠀⠀⠐⠠⣿⣟⣲⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠐⠒⠂⣌⠀⠀⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⡍⡟⠇⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡁⢙⠉⠀⠀⠀⠀⠀⠀⠐⠀⠒
⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠖⠚⠓⠛⠰⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡰⠔⠛⠚⠃⠦
⠀⠀⠀⠀⠀⠀⠈⠉⠋⠁⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠀⢀⠀⠈⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠉⠀⡀⠀⡇⠐⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣀⣸⣀⣤⣶⣾⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡴⢄⣀⠇⣀⠔⠐⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠋⠹⠩⠛⣻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡲⢠⡄⠷⢂⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣀⡀⠀⠈⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⣀⡖⠁⢀
⠀⠀⠀⢀⣴⣿⣦⠀⠀⠀⠀⢸⠀⢠⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣾⣿⣿⣿⡄⠀⠀⢀⣶⣶⣎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⣠⠀⠀⠀⠀⠀⢦
⠀⠀⠀⠈⠛⠛⣿⠀⠀⢰⣿⣿⣻⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠘⢿⣿⣿⠿⡀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⡀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⡴⡾⢀⣏⡼⢀⣶⠅⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⣁⠁⠀⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⣀⠎⣿⠃⡞⣸⠇⡞⠁⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⢠⡇⠀⠀⡕⢠⠊⠀⠀⠀⠀⠀⢱
⠀⢀⡠⣶⡉⢰⠉⠘⡗⡜⡟⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠁⠈⠀⢣⠠⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠻⠾⣿⡿⢟⠤⠪⠐⠛⠦⣄⣀⣀⣀⣀⣀⣀⠴⠣⠤⣀⣀⣀⣀⡄⠂⠀⠀⠀⠘⠤⡀⠀⢐⡢⠖⠡⠐⠢⢀⣀⠀⠀⠀⣀⣀⣠⠾⠄⠀⡀⠀⡀⢀⠐⠀⠄
⠀⠀⠀⣠⣶⣿⣦⣤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠈⠁⠀⡄⠀⠀⠀⠀⠈⠉⠈⠉
⠀⠀⠀⠈⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠀⠠⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠔⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⡖⠛⠛⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣴⣀⡠⠖⠁⠀⠀⠀⠀⠀⠀⢀⠴⠓⠦⠤⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢀⣎⡷⠀⠀⢀⡤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡘⣆⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⣠⠋⠀⠀⡠⠒⠺⢤⡀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⡠⢲⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠑⠢⢭⡑⢦⠀⠀⠀⠀⠈⣧⠀⠀⠊⣱⣀⣀⠤⠋⠁⠀⠀⠙⢦⡼
⠀⠀⠀⠀⠀⠀⡼⠀⠄⠀⠀⠀⠀⣰⠃⢱⠀⠀⠀⠀⠀⠀⠀⢹⡤⠷⠖⠒⠦⢴⡁⠀⡔⠋⠉⠁⠀⠀⠀⠀⣀⡴⣞⡼
⠀⠀⠀⠀⢀⡎⠀⠀⢰⠀⠀⡠⠊⣡⡆⢸⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠈⠛⠧⣄⣀⠀⠠⠤⢶⡋⠁
⠀⠀⠀⠀⢸⠁⠀⠀⢸⢠⠎⢀⡴⢡⠀⡞⠀⠀⠀⡶⡀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⢸⠀⠀⠀⣧⡏⢰⡞⢀⡞⣰⠃⢀⠴⠋⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠘⡆⠀⢸⣿⠀⢸⡠⢎⡴⢁⡴⠃⠀⠀⢰⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋
⠀⠀⣀⡠⠔⠊⠉⠀⠹⠀⠜⣴⣉⠴⠊⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠈⠉⠛⡖⣶⠒⠒⠛⠉⠁
⢀⣀⠨⠂⠀⡠⢀⡴⠋⠀⠀⠢⣀⠀⠀⠀⣠⣔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⣿
⠀⠑⠒⠇⣬⡹⠉⢀⠶⡀⠀⠀⠀⠉⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⢰⠇
⠀⠀⠀⠈⠁⠹⡟⠁⠉⡝⢀⡤⠴⠤⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⣠⠏
⠀⣠⢤⣰⠗⣀⠲⠦⡐⠀⡏⠀⠈⣀⣸⢿⠀⠀⠀⠀⠀⠀⠀⢀⣀⠔⢁⡴⠃
⢰⢀⡞⠁⠐⠋⡠⠀⠈⢺⢇⡴⠛⠅⣾⡁⣄⣀⣠⠘⡇⠀⠀⣋⣤⠞⠋
⠈⢻⠀⠀⠀⠀⠁⠀⠀⢸⠋⠀⠀⡞⠁⠀⢸⠉⠉⢛⠁⠀⠀⡏
⠀⠸⣆⠠⡀⠀⠀⠀⣠⠋⡠⢀⠜⠀⠀⠀⣼⠀⠀⢸⠀⠀⠀⡇
⠀⠀⠘⠓⠮⢶⠒⠋⠁⣹⠋⠁⠀⠀⠀⠀⡏⠀⠀⡏⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠉⠲⠚⠁⠀⠀⠀⠀⡀⣼⠁⠀⣸⠁⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣍⣀⡞⠇⠀⠀⠀⢸⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣏⠀⠉⡿⠒⠤⠤⠄⣶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠺⢧⣀⣀⣀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠉

⢰⣶⢶⣤⡀
⢸⡇⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⢶⡀
⢸⡇⠀⣤⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠉⢠⡾⠁
⢸⡇⢰⣿⣇⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠁⠀⢠⡿⠁
⠘⣿⠀⣿⣿⣦⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⢁⣤⣶⣿⠃⣠⡟⠁
⠀⢿⡆⠸⣿⣿⣷⡄⠈⠻⣦⡀⠀⢀⣤⣠⡆⢠⣦⢀⣴⠞⠋⠀⣠⣶⣿⣿⠟⠁⣰⡟
⠀⠈⣿⡀⠹⣿⣿⣿⣦⡀⠀⠹⢷⡾⠹⠏⢹⠏⢹⡿⠃⠀⣰⣿⣿⠟⠉⠀⠀⢰⡟
⠀⠀⠘⣷⡀⠈⠻⢿⣿⣷⡄⠀⣀⡁⠀⢀⣠⣤⣤⣄⡀⢸⣿⣿⡏⠀⠀⠀⢠⡟
⠀⠀⠀⠘⢿⣄⠀⠀⠙⠛⣴⡟⣉⠙⢿⡟⠉⣠⣤⡘⣷⠈⠛⠟⠃⠀⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⢿⣌⣛⣁⣾⣅⣀⣿⡿⢃⣿⠀⠰⣦⣀⣴⠾⠋
⠀⠀⠀⠀⠀⠀⣠⣿⣦⣄⠈⠙⠛⠉⠉⠉⠉⠛⣛⡛⠁⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⢰⣿⠀⣤⡘⣷⡶⠶⠶⣦⣠⡾⠛⠉⠙⢶⡀⢀⡾⢻⣷⡄
⠀⠀⠀⠀⠀⠀⣻⣶⠈⠀⠙⠀⠀⠀⠈⠛⠀⠘⠿⠀⣾⢁⣾⢡⡟⢩⣿⣄
⠀⠀⠀⠀⠀⣴⡟⠁⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⣾⡏⢸⡇⣿⢠⡿⠀⠛⠻⣶⣴⣤⣤⡶⠿⣦⡀
⠀⠀⠀⠀⠀⣿⡀⢀⣠⡶⠟⢻⡟⠳⣄⡀⠀⠀⠀⠉⢻⣿⣇⣿⣸⣧⣄⣤⡾⠃⠀⠸⠟⠀⠀⠘⠻⠶⣤⣀
⠀⠀⠀⠀⠀⢸⣿⢛⣉⡀⠀⣾⠃⠀⠈⢛⣿⠏⢀⣠⡾⠛⠋⠉⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⣄
⠀⠀⠀⠀⠀⢈⣿⠟⣿⠛⠛⠛⠛⠾⣿⣿⣥⠶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⣠⠟⠁⡾⠉⠛⠛⠛⠛⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⣠⣞⠁⢀⡾⠁⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⢼⣿⣫⢎⡾⠁⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⠀⠀⠀⠀⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠹⢯⠞⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠘⢷⣄⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⠀⠀⠙⠷⣴⣾⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠛⠈⠻⢦⣀⠀⠀⠀⠈⠉⠙⠛⠛⠛⢻⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⢹⡿⠷⣤⣀⠀⠀⠀⠀⠀⠉⣙⣛⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣼⠇⠀⠀⠉⠻⢦⣄⠀⠀⠀⠉⠻⢿⡟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⣀⠀⠀⠀⠀⠀⣰⡟⠀⣼⠏⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⢤⣤⣙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⣰⠏⠀⠀⠀⣠⡾⠋⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠹⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⣼⠏⠀⠀⢀⣾⡏⠀⠐⣷⣄⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣽⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣋⣤⡾⠋⠀⠀⣠⡾⣿⡇⠀⠀⢿⡍⢷⡀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠉⠀⠀⠀⢀⣴⠏⠀⢹⣇⠀⠀⣘⣷⠀⣿⠀⠀⠈⠛⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡋⠁⠀⠀⠀⠀⢰⡾⠃⠀⠀⠈⢿⣿⣿⣿⣿⢿⣏⠀⠀⠀⠀⠀⠘⣷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣧⡀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠹⣧⠀⠀⠀⣀⣴⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣷⣶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣶⣿⣿⣿⣿⣿⣿⣿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢀⣀⡀⡠⠺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡀⢴⣆⡀⠘⠛⢉⢀⠆
⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠁⠀⠀⠀⠈⠀⠁⠈⠁⠘⠆
⠀⠀⠀⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⠀⠀⠤⠀⠀⠀⠄
⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡸⠀⠀⠀⣀
⠀⠀⠀⢳⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠐⠁⠐⡠⠀⢻
⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡀⠀⠀⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠀⢀⠁⠈⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠈⡇⠀⡆⠀⠀⣀⡴⡷⠋⠀⠀⠀⠀⠃⠂⠴⢂⣸⡀⠀⢠⢢⠂⡠⢶⠁
⠀⠀⡀⠀⠀⢘⡴⠁⠀⠀⠀⠀⠀⠠⢀⡀⠀⠀⢀⣀⡀⠀⠁⡃⠀⡁⠐⠊⢠⠃
⠀⠀⣷⠄⢰⠋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠅⠊⠸⡀⠀⠘
⠀⠀⢻⠀⢸⡄⠷⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⢀⠂⠀⠀⠀⡁⠈
⠀⠀⠀⠂⠀⢳⡀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠁⠀⠀⠀⠀⠘⠄⢀
⠀⠀⠀⠀⠀⠀⡇⡠⠸⡄⠀⠀⠀⠀⠀⠀⠀⠔⠁⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠇⢻⡜⠀⠀⠀⠀⠀⠀⠀⠀⠟⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⢀
⠀⠀⠀⠀⠀⠀⣴⣤⣶⡄⠀⠀⠀⠀⠀⠀⠐⠳⠾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠷⣿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⢀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣶⣌⠻⣿⣿⣦⣽⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢞⣿⡿⢿⣿⣭⠁⢭⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢛⣼⠟⣁⢆⡘⣱⢛⠀⠰⡎⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠋⠁⠉⢳⠆⣿⡟⠠⣿⡉⣅⠐⠃⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢚⣯⡝⠇⠋⠘⢀⣤⠇⣾⣿⣇⣠⡟⣿⣦⠆⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠛⣻⣿⣶⡶⢶⣤⣶⣤⣤⣶⣶⣶⣿⣧⠆⠀⠙⠄⠀⠀⣠⡾⠃⠘⡏⢘⡿⠃⠾⣟⡉⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣇⢰⣿⠏⣟⠁⠡⡁⠀⠈⠉⠨⠹⣛⢿⡯⢉⠀⡀⠀⠀⣤⣷⠛⠁⢠⢂⣠⠏⠀⠀⠀⠘⢷⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣺⣿⠹⣸⡏⡄⠉⠀⠀⠠⠀⠀⠀⠀⠂⢍⡜⠀⠀⠀⠅⠀⠀⠏⠁⠀⣀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢻⣿⣛⡶⠂
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠏⠀⣄⠃⣿⣵⠀⠠⠇⢀⠄⠀⠀⠠⠊⢁⠶⣾⠂⠀⢰⡀⠀⠀⢠⠄⣏⣴⡏
⠀⠀⠀⠀⠀⠀⠀⣿⢿⢸⡟⠀⣏⡖⠛⠃⠀⠏⠀⠀⠀⠀⠀⡰⢦⣤⣤⣤⠀⠀⢸⢧⣤⣄⣀⡘⠙⠆⡇
⠀⠀⠀⠀⠀⠀⢠⣿⢸⡘⣅⡐⡼⢰⣷⣦⡀⠀⠀⠀⠀⠀⠀⠐⠉⠉⠉⣿⠀⠀⣿⣾⣏⠟⠋⠀⠀⣶⠇
⠀⠀⠀⠀⠀⠀⣿⡏⠀⣿⣿⡞⣡⢿⣿⢿⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡇⠀⠹⡿⠂⣀⣂⡼⠁
⠀⠀⠀⠀⣠⣢⣿⠁⠀⢸⡟⠀⡏⠀⠙⠀⢀⠁⠀⠈⠐⠀⠒⠀⠀⠀⠈⠹⡟⡅⠐⠀⣻⢻⠏⢉⡇
⠀⠀⠀⠀⣿⡿⠁⠀⠀⢸⣇⣰⠇⠀⣇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠻⡌⠀⡇⠀⠀⡼
⠀⠀⠀⢰⠏⠀⠀⠀⠀⢸⣿⡟⠀⢀⣟⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣴⣰⢠⣇⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣟⠀⢹⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⠿⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇⠀⠀⣿⢩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣟⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⢸⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠘⣿⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣯⣯
⠀⠀⠀⠀⠄⠤⣶⣤⡤⣠⡿⠿⢦⣴⠤⠀⢿⣍⣁⣀⣀⠀⢀⣀⣀⡀⠀⠀⠀⢿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠚⠓⠀⠃⠴⠦⢿⠅⣭⣷⡺⣭⢀⣍⣹⣧⣍⣾⡛⠛⢋⠉⢳⣤⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠶⠒⠚⠛⠛⠓⠲⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠙⠶⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⡀⠀⠈⠉⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣄⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠹⣦⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⢹⡄⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣾⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⡏⠀⢠⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣦⠀⢻⣇⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⢸⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠀⠈⢿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⠻⣿⣿⠿⠋⠀⢀⣤⣄⠀⠀⠈⠻⣿⣿⡿⠃⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⢳⡄
⠀⠀⠀⠀⣼⠋⠙⢳⡄⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⣀⣠⡼⡆⠀⠈⣧
⠀⠀⠀⢠⡏⠀⠀⣾⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⣀⣤⠶⢛⣩⡴⠞⢷⡀⠀⠘⣇
⠀⠀⢀⡾⠀⠀⢰⠏⠙⠳⢦⣍⣛⠶⢤⣄⡀⠀⠀⠘⣟⡿⢳⡶⣦⢤⡤⢤⡤⣤⠶⡞⢿⣻⡇⠀⢀⣠⡤⠶⣛⣭⠶⠛⠉⠀⠀⠀⠈⢧⠀⠀⠘⣦
⠀⢠⡞⠁⠀⢠⠟⠀⠀⠀⠀⠀⠉⠛⠶⢮⣝⡓⠶⣤⣉⠙⠋⠈⠷⠼⢧⡼⠧⠾⠶⠛⢋⣩⡴⢞⣫⡥⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⣀⣬⢷⡀⠀⠈⣷
⠀⣟⠀⠀⣰⡿⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⣭⣙⡳⢦⣄⣀⠀⠀⣀⣤⠶⢚⣩⡴⠚⣏⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⣛⣭⠴⠚⠻⠶⠚⠋
⠀⠈⠛⠛⠋⠙⠓⠶⣭⣛⠲⢦⣄⡀⠀⠀⠀⠀⠀⢠⡟⠀⣹⠷⠦⣍⣻⠞⣫⡶⠚⠉⠈⢷⠀⠘⣇⠀⠀⢀⣠⡴⠞⣋⡥⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢮⣍⡛⠶⣤⣀⢀⡿⠀⢠⠏⣠⡴⢋⡵⠿⣭⡛⢦⣄⠀⠈⢧⡀⣹⠶⢚⣫⡵⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢬⣝⡳⢤⡿⢞⣡⠞⠋⠀⠀⠀⠙⣳⣍⣳⠶⣛⣭⠴⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠾⣛⠭⠲⣯⣛⡶⠶⠶⢚⣛⣫⣭⣥⠶⢿⣍⡓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢞⡫⠵⠒⢉⠤⢖⣪⡥⠶⠖⠛⠛⠛⠶⠦⢭⣭⣝⣛⠦⢌⡙⠒⠬⣙⡳⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠗⠊⣁⠤⣒⣩⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢮⣝⡒⠤⣈⡑⠲⢭⣷⣀
⠀⠀⠀⠀⣀⣠⣤⠶⠚⢉⣡⡴⠶⠯⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢭⣓⣦⣤⣉⠛⠲⢦⣄⣀⡀
⠀⠀⠀⠀⢻⡁⣨⡷⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢦⣏⠉⣹⠃
⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠜⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠧⣄⣀⣀⠀⠀⣠⠏⢀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⡀⠉⠙⢶⡏⠀⡎⡀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠸⡇⠀⡀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇⢠⣀⢳⡀⢳⡀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷⡜⣧⡞⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢛⡿⠟⠋⠉⠇⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡅⣴⠉⠀⠀⠘⠁⣷⠀⠀⠀⠀⠀⠀⣠⢞⠽⢢⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢍⢱⡅⢀⣠⡼⢿⡇⠀⠀⠀⠀⡞⠁⠀⣠⠞⢁⣀⡤⠴⠶⡶⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣼⠉⠉⠀⠸⣇⠀⠀⠀⠀⠙⠶⠾⣽⣿⠽⠷⠒⠋⠉⠉⠙⠲⡝⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⢀⣀⠀⠀⠀⡏⢸⠀⠀⠐⣿⣦⣀⠀⠀⠀⠀⣀⣤⠴⠖⠒⠒⠲⢤⡀⠀⠀⡿⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠀⠀⣡⣌⢳⡰⣦⡇⣼⠀⢲⠀⠻⢛⣿⣷⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⣦⡞⢡⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠘⢧⠀⠈⠻⢸⡇⣿⡇⠸⣄⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡶⠀⠀⠐⢚⣠⠇⢻⠀⠘⡷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣠⣶⡛⠋⠀⠈⣿⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⡎⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⡿⠟⣧⠀⠀⠘⢧⡀⠀⠀⢸⠀⠀⠀⢸⡇⠀⠀⢀⡴⠋⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠋⠀⠀⠀⠀⠉⢻⣶⣾⡿⠀⣠⣼⣷⣶⡞⠉⠀⠀⠘⣛⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠞⣡⠞⠁⠻⣟⠉⢳⡦⠤⠴⡞⢡⡞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⢀⡇⠀⠀⠀⣸⢡⠞⠀⠀⠀⡇⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⢧⣠⡞⡉⠙⠻⢤⡀⠀⢸⢷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡖⠒⠒⠚⠐⡿⣆⣌⡁⠀⠂⣀⣠⣿⠶⢋⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠲⠀⠄⠸⣥⠞⠫⠝⠲⣾⣩⠾⠥⢀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⠤⠤⠼⠋⠛⠒⠒⠚⠻⣥⣀⣀⣀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢰⡆⠀⡐⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣧⡤⢧⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⣿⣇⢠⣾⣿⣷⣿⣿⣿⣿⣿⣿⣿⡷⢺⡄⠀⠠⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡤⠟⠛⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠉⠓⠒⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠐⠛⠛⢩⠉⠁⢀⣀⣠⣤⣴⣾⠏⡄⠀⠀⣤⢠⢸⣿⡇
⠀⠀⠀⠀⠀⠀⢰⡀⠀⢠⠀⠀⠀⣆⠀⠰⠀⡀⠀⠐⣀⠰⢶⣾⣾⣿⣿⣿⣿⣿⡿⠋⢸⣷⠀⢠⣿⠀⢚⠛⠃
⠀⠀⠀⠀⠀⠀⣸⡇⢰⣼⠧⠊⢙⠯⢆⡄⢘⡓⠊⡉⠄⢛⠸⠛⠋⠉⠀⢁⠈⠥⠦⣀⡈⢉⠒⠼⠿⡆⠋
⠀⠀⠀⠀⠀⠀⣿⠓⢈⠀⠀⠔⠃⢠⠀⠀⢀⡀⠀⠋⠉⠁⠀⠄⠂⢉⡀⣿⠀⠠⠄⠀⠈⠿⠲⠀⠀⢈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡜⠂⢀⠀⠀⠀⢰⡆⣀⠄⠁⣸⣧⡿⠧⠠⠖⠀⠀⠀⠀⠆⠀⠸
⠀⠐⠀⠤⢀⠀⠀⠀⠐⠀⠺⠿⠯⠿⠆⠀⠉⠁⠐⠃⠸⠧⠈⡉⠈⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠐⠂⠈⠰⣶⣦⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠲⢢⢤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⢀⠀⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠘⠛⠀⠀⠀⠀⠒⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣄⠀⠲⠴⠿⠷⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢰⡝⠋⢙⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠲⣆⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢰⡄⠀⠀⠑⣾⠃⣬⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠶⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠎⡀⢰⠄⢸⠿⠛⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⢢⡀⠀⣆⡀⠀⠀⠀⠀⠒⠀⣺⠏⠀⡉⡉⣁⠀⢠⣤⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡌⢠⣡⠜⠀⠀⣠⣤⠄
⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⡶⢀⡹⢷⡀⢻⡇⠀⠀⣀⣤⣤⣄⡉⣤⣼⣿⣡⣿⣰⣾⠁⣤⣄⣀⡀⣷⢾⣤⠀⠀⣠⡿⠈⣁⠤⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠠⣦⠀⠀⠀⠆⠙⢬⣥⠀⠀⠀⢠⠿⣯⣽⣯⣿⢸⡟⠛⢻⣿⣿⠛⠛⡟⢙⡏⢹⣿⣷⣾⣶⢀⡿⠀⠂⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⣀⣤⡄⠀⣠⡄⠈⠃⠁⢠⠉⠉⣁⡴⣠⣷⠀⣿⠟⠁⢹⣷⣤⣴⡟⠿⠆⢀⣵⣤⡵⣿⣿⣟⣿⢋⣼⣷⣿⠞⠋⣀⡀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠘⠛⠒⠀⢷⡌⠠⣽⡇⠘⠉⠠⣾⡿⠇⣿⠟⢠⡉⣿⣶⣶⢻⡟⠉⠀⠀⢾⡉⠙⠿⢿⣿⣾⣿⣭⣿⣍⣆⣴⠄⠀⠀⠀⢀⣀⡐
⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠄⠠⠀⠀⠛⣶⣿⣽⡾⣿⡿⣾⠀⠀⠈⢲⣦⡿⠿⠿⣿⣶⣿⢦⣶⣶⢿⣿⣶⣿⣿⣿⡏⠛⠛⣿⣿⣟⣭⣤⣴⠆⣼⠋
⠀⠀⠀⠀⠈⠁⠀⠈⡉⠀⠀⠰⡄⣠⢆⠡⢈⣿⣿⣿⣿⡞⣧⣀⢠⣾⣁⡀⢀⡀⢉⣻⡇⠘⠋⣠⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⠶⣤⠀⠄
⠀⠀⠀⣤⣴⣿⣿⣶⠈⠠⢉⡀⠠⠛⠛⣦⣜⠛⣿⣿⣋⠀⠛⣿⠀⠙⠉⣹⣾⣷⣶⡿⢃⣠⣾⣿⠛⢿⣿⣗⣾⡟⣼⣏⣛⣿⣿⣿⣿⣧⣤⠲⣏⠠⡄
⠀⠀⣾⡗⠿⠺⠿⣏⠀⠠⣿⣷⣤⣈⣷⣾⠷⣿⣿⣿⡇⠀⢰⡖⠀⠈⠢⡘⢿⢿⣟⣳⣾⡁⠉⠀⣀⣾⠟⠿⠿⠊⢘⣿⣿⣿⠿⡛⠿⠿⣿⡷⢾⡇
⠀⠀⢻⣾⣿⣶⠀⠹⣷⡀⠁⢀⣼⡏⠀⠰⠤⣾⡿⠿⢧⡀⠀⢰⠀⠀⠁⠐⣦⠐⠛⣋⣽⣿⣿⣿⣿⡇⠀⠐⠀⢈⣿⡟⠁⣤⣶⣴⣷⣤⠌⡥⠨⠇
⠀⠀⠈⠙⠛⠁⠤⠐⣿⡴⣶⣾⣿⡿⠃⠠⠀⠀⣄⡀⠀⠙⢶⡄⠀⠀⠀⠀⠀⢶⣾⠟⢀⣿⣭⣿⣿⣦⠀⠀⠀⣨⡿⣦⣼⣏⣀⣽⣿⢦⠈⣇⣀⣴⠇⠀⠀⠂
⠀⠀⠀⢀⠄⠀⠀⢰⣿⢧⡩⠶⡟⠠⠏⡄⠀⠀⠨⠛⠻⣧⠀⠁⠀⢀⣠⡄⠚⠁⠀⠀⡼⢋⡉⠉⠉⠹⣿⣿⣿⣿⣧⣼⠛⠛⠛⠛⢻⠟⣠⡿⠿⠷⢀⡀
⠀⠀⠀⠆⠀⠰⠶⠂⣹⣬⠀⢠⣿⡷⣦⡖⠀⣀⠖⣻⣷⠈⣥⠙⣤⡀⣈⣻⡶⠂⡶⠛⣦⡠⣤⣴⣶⣶⠾⣀⡼⢿⣿⣿⣶⣤⣬⣤⣤⣾⣿⢿⠷⠖⠉⠁
⠀⠀⠀⠀⠀⠀⠲⠟⣿⣿⠀⣾⣿⠠⣿⣿⣿⢋⣰⢻⡿⣄⣠⣶⣻⣿⣿⣿⡁⢸⠀⢀⣯⡀⢰⠿⠟⢧⣀⣍⣡⣚⣿⣿⣿⣿⠛⣶⣿⣿⣿⣿⡶⠂⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠠⡉⢱⣠⣿⣯⡶⣀⣈⡉⠘⢛⡌⠁⣸⢏⡿⠉⡉⠙⢿⣷⠄⠰⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢿⣿⣷⣾⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣟⠁⣼⡉⠛⠞⢉⣴⠿⠿⣿⢧⣤⣤⠐⠚⠁⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⣠⣤⣤⣶⣄⣹⣷⣾⣿⣿⣿⠋⣽⠗⠚⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⣄⣸⠷⠈⠉⣻⡿⣿⠏⣰⣆⣼⡇⠀⠀⣈⣤⠀⠀⠀⣀⣤⣶⣻⠉⠀⠀⢉⠉⠉⢨⣿⣿⣿⠟⣻⣿⣿⣿⣿⡵⣄⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⢀⡀⢞⣿⣿⣿⡂⠀⢀⣿⡷⣽⣶⣿⡿⠋⠁⠚⠛⠻⠟⣠⣴⣿⣿⠻⢿⣿⣄⣀⣴⣿⣦⡀⠀⣿⣿⣏⣼⣿⣍⣁⠄⢸⣿⣿⣷⣄⣼⡇⢘
⠀⠀⠀⠀⠀⠀⣡⣴⣿⠁⢻⣯⡓⢀⣾⣿⡇⢄⡸⠋⠀⠀⠀⠀⢀⣴⣾⣿⡿⣿⡿⢁⣾⣄⠈⢿⣿⣿⣿⣿⣿⣿⣿⣮⣿⣿⣿⣉⣠⣤⣿⣉⣉⡉⠙⢳⢈⡁
⠀⠀⠀⠀⠀⠉⠹⠿⢉⡇⠈⠿⣧⡾⠉⢿⡷⠊⠀⠀⠀⠀⢀⣴⠟⠛⣽⣿⡇⢸⣿⣾⣿⣿⣷⣼⣿⣿⣿⣿⣿⠿⢿⡿⠃⠀⢻⡿⢿⣿⣿⣿⣯⣤⣴⠀⢴⠃
⠀⠀⠀⠀⠀⠠⣄⠲⣎⡀⢤⠄⢀⣵⠆⠁⠀⠀⠀⠀⣠⣶⣿⣏⡤⠿⠟⠻⣿⣿⡿⠟⠉⠙⡛⣿⣿⣿⠋⠁⠀⠀⢨⣿⡄⣤⣿⠃⣸⣿⣿⣿⣏⠻⣿⣿⠈⡇
⠀⠀⠀⠀⠁⣀⡶⢚⡇⢲⣀⡴⠊⠁⠀⠀⠀⠀⣠⣾⣿⣿⣙⣋⠁⠈⠀⠓⠀⠷⣆⠐⠊⠉⠙⣿⠯⣤⣀⣠⣄⣠⡿⠋⠀⢈⣷⣼⣿⠋⣹⣿⣿⣷⣬⣿⡗⢷
⠀⠀⠀⠀⠈⠉⠑⠛⠳⢯⣥⣄⡀⠀⢀⣤⣶⡿⢟⠃⠘⠣⣬⣍⣙⠛⠚⠳⠖⢶⠷⣤⣤⣴⣶⣿⣤⡜⠉⠏⠀⠈⣷⣤⣤⣾⡟⠀⣿⣶⣿⣿⣿⣿⣿⣿⡅⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠟⠋⠈⠙⠁⢀⣼⣷⣦⠀⠈⠉⠉⢳⡆⣹⣟⣶⠶⠛⠉⠉⠙⠛⠛⠳⣶⠟⠰⠾⠟⠁⠀⢨⣷⠞⠛⠻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡤⠍⠃⣠⡄⠀⠀⠺⠿⠧⠋⠀⠀⠀⠀⣾⣿⣿⡟⠁⣀⣠⠆⠀⠀⠀⠀⢀⣿⣷⣄⣠⠷⣤⢴⣿⠟⠀⢀⣾⣿⠛⢿⣿⣿⣿⣿
⠀⠀⠀⠀⠰⡿⠶⠋⠒⠈⠵⠷⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠀⢸⣿⡿⠀⠀⠀⠀⠀⣴⣿⡿⢿⣯⣀⣀⢀⡀⠀⠀⣿⠉⢻⣦⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⠀⠀⠀⠀⠀⢀⡄⠀⢀⣿⣿⣿⣽⣆⡈⢿⡇⠀⣶⣦⣀⣀⣿⣿⣿⠟⠛⣬⣿⣿⣷⣤⣴⣿⢤⣾⠟⠉⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠺⠷⣦⣠⣤⣶⠟⣠⣴⣿⣿⣿⣿⣿⢿⣿⠿⠿⣤⣄⣘⣿⣿⣿⠿⣻⣿⣧⣾⣿⣿⣉⠻⣧⣤⡴⠛⢶⣶⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⡿⠿⢿⡿⠿⠿⠙⠛⠋⠉⠌⢿⡂⠀⠠⢉⣉⣉⣽⠋⢺⣯⣿⣿⠟⠡⠌⢻⣴⠿⠋⠐⠀⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣱⠞⢶⡶⣦⣤⣄⣤⡶⠾⢻⠟⠁⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⠛⠛⠋⠑⠻⠟⠛⠯⣹⣿⠄⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢿⠏⠩⠁⠀⠀⠀⠀⠤⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⢰⢠⠄⡄⠀⠂⠈⣄⡉⠉⠫⠿⠫⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⡠⠄⠰⢏⣟⣯⣒⣂⣀⡀⠘⠃⠤⢠⣤⡤⠘⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟⠒⠊⠉⢠⠤⣞⣠⢟⣎⣞⣿⣶⡶⢄⠂⣠⠀⢀⠀⠀⠌⡀⠹⢎⣳⡽⢂⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠄⢀⣀⠐⠄⠿⠟⣻⡿⡿⡿⢿⣞⢴⣏⠀⢣⢀⡒⣆⢠⢦⠁⢀⠀⢁⡵⠛⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⢠⣾⣽⣿⣷⡁⢪⢼⡟⣙⣗⣯⣿⣄⠛⢀⡀⢾⠘⠢⠌⠻⣃⠂⢉⠟⠒⣚⢁⢀⣠⡤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣭⣾⣼⣿⢾⡿⠿⣷⡽⢃⢋⡟⣉⡤⢻⠧⠈⢳⣄⣠⡀⣥⡄⠁⠀⠀⣁⣠⢿⠁⢐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣮⡹⡾⣿⣾⣏⣯⠸⣿⣣⢁⣸⡟⠡⠆⠀⠲⡀⢸⠛⠾⣛⠚⣷⢀⡀⢦⠘⣧⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⢿⡿⣷⣿⣷⡿⣳⣾⢋⡔⢁⣀⠤⠒⠒⠒⠶⣭⣿⠀⣃⣼⣙⣿⠟⢦⣈⡿⠇⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⣭⢷⣺⢹⠟⣷⣿⡷⣯⣴⣿⠁⠀⠀⠀⠀⠀⠘⣷⣦⣮⡘⠺⣏⡔⡐⣾⣛⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡭⢽⣋⠿⣬⣻⠿⣿⣽⡿⠀⠒⠀⠀⠀⠀⠀⢻⢋⣢⡑⢾⡋⠞⢻⠯⣁⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣵⣿⢿⣿⣿⠾⣾⢽⡼⣿⡏⠁⠀⠁⠀⠀⠀⠀⢀⣿⡘⠷⣻⠮⢯⡟⢛⠒⣅⣐⣋⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⣟⣿⣟⣛⡾⢺⣿⠇⠀⠀⠀⠀⠀⠀⣀⣼⡿⠉⣻⠆⡜⣦⣌⡿⢉⠀⢿⣧⡄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣴⣤⠀⠀⠟⡷⣸⣿⠀⠀⠀⠀⠀⠀⠀⠙⠋⢀⣼⡅⢾⣷⢄⣿⡷⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⠿⣾⡇⢆⣱⢸⣿⠀⠀⠀⠀⠀⡠⠂⠀⠐⠿⢿⣿⣾⣻⡫⠫⡧⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⢹⢟⢻⡄⠀⠀⠀⠈⠀⠀⠀⠀⠘⣷⡿⣿⣧⠧⢘⠴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢿⠸⣄⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢸⣏⣔⣁⣄⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⣉⣻⡟⠦⣄⣀⠀⠀⠀⢀⣷⡀⣀⠔⢹⢹⡤⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣌⢄⡿⣉⣙⣿⣙⡿⢋⣻⣿⠤⠧⢜⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢭⡟⠁⣠⠸⢿⡮⣌⠈⠑⣦⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡼⠁⠄⣮⡀⠁⠳⢄⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠀⠁⠀⠉⠒⠒⠚⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⢠⠀⣀⠀⠀⢠⣀⣀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢂⠠⠴⠶⠶⠬⢌⣀⣙⣛⣀⣡⡤⠤⠶⠤⠌⡑⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣔⠕⣠⢞⣡⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣦⣍⡑⡄⢀⡠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡇⣰⡿⣻⣵⣷⣴⣴⣾⣿⣷⢭⣥⣭⣤⣶⣾⣿⣤⣴⣬⣙⢳⣾⣆⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢰⣿⣤⡿⣛⢫⡥⠭⢛⠴⠒⠲⢩⠵⠚⠒⢝⠉⠭⠻⢟⣻⣷⡌⣿⡄⢸⡔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢐⠆⣾⣿⡯⠉⡁⠀⡀⠀⣨⠀⠀⠀⢸⠀⠀⠀⢰⡀⠀⢀⠀⠈⠻⣿⣜⣷⠘⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢭⢰⣿⣿⣹⣀⣷⣤⣷⣶⣿⣶⣶⣶⣾⣷⣶⣶⣾⣷⣶⣿⣴⣇⣠⢘⣿⣿⡆⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡇⢀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠈⣖⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠇⢸⣿⣿⢛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⡇⢨⣭
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠈⡿⣿⢠⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢳⠻⣿⣿⡇⠬⠤
⠀⠀⠀⠀⠀⠀⠀⠈⢀⣷⡀⣇⣿⡖⢒⣻⣿⡿⠋⠉⠀⠉⠻⣿⣿⠟⠃⠁⠀⠉⢻⣿⣗⡒⢷⣿⣿⡇⣾⡦⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠼⠿⠇⢿⣿⡄⢠⠾⣿⠃⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠈⣿⣿⡀⢸⣿⣿⢠⣛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠸⣿⣷⠏⠀⣿⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢿⠏⣿⣿⣿⡇⠼⣿⠟⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⡀⢻⣿⣷⣷⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣬⢟⣾⠟⢸⣷⣤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⣴⢆⢹⣷⣿⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢛⣿⣿⠟⢰⣷⣌⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠋⠀⢿⣿⣷⣿⣷⣤⣆⣤⢀⡄⢀⡠⣌⣤⣶⣾⣷⣿⣿⡷⢠⣿⡙⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠀⠙⠻⢿⣯⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠿⠻⢋⠰⣦⠙⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⡰⢀⣌⠁⡻⣿⢿⣿⣿⣿⣿⡿⢁⡀⠄⠂⠛⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠰⠁⡌⠓⢤⡡⠄⠋⠔⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣤⡟⠁⠀⢀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠀⠀⠀⣴⣿⠫⠄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣄⡀⠀⠀⠀⠉⠙⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢙⣷⠀⠀⠀⠀⠀⣿⣬⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣾⣯⣀⣀⣄⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢉⣿⠃⠀⠀⠀⠀⢀⣾⠧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⢸⡟⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣶⣶⣖⡒⠛⢻⣿⣿⣷⣼⣷⣶⣶⣶⣶⣤⣴⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣿⣿⣿⣿⣧⡄⠤⡄⠀⠀⠀⢨⣭⣿⣿⡟⠀⠀⠈⠉⢉⣿⣛⡙⠿⠛⢿⣿⣦⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣿⣌⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣴⣿⣿⣯⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣉⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣾⣿⢿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿⡿⣿⣿⣿⣇⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣿⡿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣗⠾⣿⣟⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⡿⣿⣿⣿⣻⣿⣿⣿⣯⣿⣿⣿⣿⣷⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⣿⠋⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣿⡇⣽⠟⠛⠛⢿⣿⡿⠛⠉⠙⢿⣿⡿⠛⠋⠉⠛⢿⣯⡀⢀⠈⣿⣾⣿⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢿⣿⣿⣿⣿⣦⢳⣄⣾⣿⠨⣿⣤⡄⢻⣿⡄⢺⣤⡄⠀⣾⣿⣷⣥⣼⣿⠿⣏⠉⠑⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣾⣯⠉⠉⢻⣿⣷⣿⣿⣿⣧⣷⣿⣷⣿⣿⣿⣦⣭⣤⣾⣿⣿⣿⡿⢿⡁⠀⠘⣦⣀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣼⣿⣂⣤⣿⣯⡉⠉⠀⢻⡟⢻⡿⠟⠋⠉⠉⢻⡟⠋⠉⢹⡏⠀⠀⠀⣿⣤⣾⡟⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣾⣷⣤⡀⣀⣀⣼⣷⣤⣴⣾⣿⣦⣶⣼⣿⣷⡿⠷⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠉⠛⠛⠟⠿⣿⠿⡿⢿⡿⠿⠿⠿⠛⠛⠛⠛⠛⠛⠙⠉⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠂⠀⠀⠒⠀⠤⡀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⡆⠠⠀⣀⣤⣤⣶⣶⣶⣦⣤⣀⡀⠠⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣠⣾⣿⣿⣿⣿⣿⠟⣻⢿⣿⣿⣶⡐⣽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢸⣿⣿⣿⣿⣬⡟⠻⣬⣶⢳⣿⣿⣿⣿⡸⣷
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣰⣀⠀⢸⣿⣿⣿⣿⣿⡷⢠⣼⡿⣻⣿⣿⣿⣿⠇⢨⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠿⠆⡼⣿⣿⣿⣿⣿⣷⣾⣷⣿⣿⣿⣿⣿⡿⠀⠼⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢸⣿⣷⡹⣿⠟⢛⣉⠉⠉⠯⠉⠛⠻⢿⡿⣣⢷⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣩⣏⣅⡀⠉⠀⠈⠁⠀⠀⠙⠛⠂⠒⠉⠀⠈⠙⢉⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣇⡙⢿⣿⠓⠶⣤⣀⣀⠀⠀⠀⢀⣀⣂⣴⠴⢾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠁⠂⣬⣿⣶⣶⣦⣬⣭⣤⣤⣬⣥⣤⣶⣾⣿⡁⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠧⠤⠌⠻⠋⠅⠈⣿⣿⣿⣿⣿⠀⠀⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠘⣄⠀⠻⠁⠛⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠛⠇⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⢀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⡀⢸⠃
⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢿⣿⠇⠀⠀⠀⠀⠀⠘⠛⠋⠛⠛⠃⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠈⠹⠟⠉⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⠁⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠿⠿⡿⠿⠿⠟⠻⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠁⣀⣀⣀⣀⣀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢾⡖⠂⠀⠀⠈⠀⠠⠉⠓⠠⣀⠈⢻⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣖⣽⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣄⠉⠉⠙⠻⣿⣿⣿⣿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠉⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣽⣿⣿⣿⣿⡏⠉⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡸⠉⠙⠻⠿⠇⣠⣤⣶⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡨⠇⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣀⣴⣶⣶⣾⣿⣿⣿⣿⣿⡄⠀⠀⣀⣠⠤⠖⠒⠚⠉⠉⠀⢄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⡿⠛⢿⡿⠿⢿⣿⣿⣷⡿⠿⠟⣳⠀⠈⠉⠀⢠⣆⣂⠀⠀⠀⡔⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⣀⢠⡀⢀⠇⠃⠈⠩⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠛⠋⠀⢠⠞⠅⠸⡇
⠀⠀⠀⠀⢀⣀⡀⠀⠐⠖⢻⡌⢷⣾⡼⣷⢠⠀⠀⠀⠀⢀⡌⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠈
⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠈⠁⠈⠻⠗⠙⠁⠠⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⣾⠄⠀⡘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⡁⠸⣃⡇⠀⢃⣞⠀⠀⠀⠀⠀⠀⡀⠀⠉⢀⠘
⠀⠀⠀⠀⢀⡀⡀⢀⣾⣀⠀⣶⠀⠀⠋⠄⠀⠰⡄⠻⣃⠛⣧⣶⠀⣴⠴⣹⢀⡸⣶⠃
⠀⠀⠀⢀⣾⠏⠀⣿⡿⢁⣾⡏⠀⠀⠀⠀⠀⠀⠁⢨⠋⠉⠁⠀⠾⠉⠋⠃⠀⠈
⠀⠀⢀⣿⠏⠀⣸⣿⠁⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⢸⣿⣦⢠⣿⣿⠀⣿⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⣄⠀⣿⣿⣿⠿⣿⣿⡆⠸⣿⡀⠀⠀⠀⠀⠘⣆⠐⠒⢤⣀⠀⠀⠀⠀⠀⠀⠁
⢻⣇⢻⣿⣿⣦⣿⣿⡇⠀⢹⡇⠀⠀⠀⠀⠀⠙⣷⣶⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣶⠾⠷⢶⣄⡀⠀⠀⣀⡴⠞⡓⠲⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠑⠋⠀⠀⠀⠀⠈⠉⠛⠛⠉⠀⠀⠉⠛⠓⠮⣝⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢀⣠⣤⣤⣿⣦⣄⣀⠀⠀⣠⣾⣥⡤⠶⢦⣤⣄⡀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢀⣤⡾⠟⠋⠁⠀⠀⠉⠉⠙⠛⠛⠉⠉⠀⠀⠀⢀⣾⣿⣿⣷⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣇⣠⣤⣶⣿⣿⣄⠀⣰⣦⣤⣤⣄⣠⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⠟⠉⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⠀⠀⠙⢿⣿⣿⠿⠟⠛⠉⠉⠉⠁⠈⠉⠻⣿⣟⠛⠛⠛⠻⢿⡿⠃⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠙⣦⡀⠘⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠈⢳⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⢻⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡳⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡐⠳⣶⣤⣤⣤⣤⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⢬⣭⠥⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠈⠀⣤⣀⠀⠀⠀⠀⠀⠨⠆⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢀⠀⠀⡀⣈⡉⠻⣄⣰⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡑⠆
⠀⠀⠀⣸⣧⠀⠻⣿⢋⣉⣩⠽⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡙⠮⠀⠀⠀⠀⠀⠀⣄⡀
⠀⠀⠀⣿⣿⡇⣶⣫⢘⣟⢒⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⢩⠟⠁⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⢿⠛⣷⣿⡿⣆⣻⣏⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣄⠄⠀⠀⠀⠠⠀⣀⠀⠠⠈
⠀⠀⠀⢈⣧⡀⠘⡗⠊⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣗⡀⠀⠀⠀⣁⡌⢱⡄⠩⣐
⠀⠀⣠⣿⡗⢿⡳⢿⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠙⠂⠤⢼⣿⣿⡛⣡⠗⡣
⠀⠀⣿⣿⣿⣄⠸⣿⠢⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠴⠖⢀⠀⠉⣉⣨⠅
⠀⠀⣿⣿⣿⣿⣦⣿⣧⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠲⣶⣯⣍⡙⠿⠃⠂⠀⡀
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠉⠛⠋⠉⠉⠀⠀⠀⠁
⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⠆⠀⠀⢀⣀⠀⠀⠀⡀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠁⠀⠀⠀⠈⠉⠀⠀⠈⠀⣈⢰⠦⢶⠋⣱⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣾⣀⠀⢀⠁⣾⢀⡴⢋⢀⠀⠠⠀⠐⣮⠛⢶⣦⣿⡉⢿⠁⢸⣇⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡌⢿⣿⠀⠀⠀⢰⣾⣱⣸⣿⣆⠀⠀⠘⢿⢦⣈⣿⣛⣿⢯⡵⠎⠉⣤⠥⡼⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⣿⣇⠀⢡⣌⣿⡻⣿⣿⠏⠀⠀⠀⢘⣦⣴⡎⠉⢳⠀⣖⡀⠈⠀⠸⠯⣬⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡟⠨⡭⠝⣻⣦⡀⠓⠌⠛⠾⠿⠿⠀⠀⣠⣾⢿⠷⢾⠲⣦⣤⠃⠋⠀⠀⠰⢇⣱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠁⢈⠀⠀⢀⡴⢋⣿⡟⠦⣄⣀⣀⣠⠤⠔⠚⠁⠀⠀⠀⠀⢱⢦⣿⡆⢳⡀⠗⣀⡪⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⢴⣍⣠⡤⣂⡿⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡽⠈⢠⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠚⠉⡏⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠄⣀⡈⠁⠐⢁⡐⠃⠀⠀⠀⣀⣀⣀⠀⣶⠀⠀⠻⠇⠀⠀⢘⣤⣬⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠀⠀⠏⠀⠀⠀⠀⢏⠙⠦⠴⠿⠉⠀⠀⠀⠀⠀⠀⢷⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠆⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠉⠓⠂⠀⢁⡄⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠞⡀⢀⣀⣀⠀⣀⣈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠀⠀⠀⠀⣠⣾⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⡏⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠈⠀⠀⠀⢰⠋⢠⡎⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣦⣨⣄⠘⠁⣊⠳⣄⠀⠀⠀⠀⠀⠀⠹⣦⣤⣀⣀⣀⣀⣀⣤⣾⣧⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⠩⠿⢳⣽⡷⠀⠁⠄⠀⠐⢶⣤⠀⠀⣀⠀⠘⠛⠋⠁⠈⠉⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢻⣥⡀⣖⢘⣧⣉⠁⠘⢷⡄⠀⡀⢹⠀⠘⡿⣿⣷⣶⣄⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢺⠿⠋⢹⠆⠊⢻⡶⠺⠫⣴⠀⣤⡤⠀⠀⠀⠀⠀⠉⠙⠛⠶⠤⢠⣤⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠌⠀⠀⢄⠸⠋⠑⠆⡐⠂⠀⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠈⣱⠂⡤⠠⢣⠀⠲⠀⠈⠘⠆⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⡾⠁⠀⢰⠀⡿⡷⠦⠖⢶⠦⠀⠴⡀⠀⠉⢉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢥⣤⡆⣼⠆⠠⠆⠈⠉⠄⣀⣨⠟⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⣈⡝⠀⣤⠄⠴⠛⢤⠻⣥⡴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡄

⠀⠀⠀⠀⠀⠀⠐⠤⡀⠀⠀⢀⠠⠤⢄⣀⠀⠀⠀⠀⠀⢀⡀⠀⣠⣀⣀⣀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⢹⣂⣴⣷⢖⡟⡛⠾⣙⠲⣖⣶⡿⣛⣾⠿⠦⣼⡿⠤⠙⠋⠁⠀⠀⠈⠀⢐⡴⠒⢂⣀⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⣶⡿⣫⡾⠁⣾⣀⣱⡀⢉⢴⣬⡉⠉⢁⡠⠖⠒⠒⠢⠦⣤⣀⣀⣀⣀⡠⠔⠃⣴⣾⠭⠟⢉⡀
⠀⠀⠀⠀⠀⠀⢀⡛⢿⣉⠈⢦⠟⠉⠛⣧⡄⠀⠀⢱⠞⠁⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠳⠶⠤⢤⡟⢀
⠀⠀⠀⠀⠀⠀⠀⠁⠠⣈⢳⡆⢀⣶⡄⠈⢇⢀⡐⠁⠀⣠⣴⣿⣭⣭⣍⡙⠲⠦⣤⣤⠴⢾⠳⢓⡯⢷⣿⣭⣴⠏⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣷⣿⣿⣻⣦⠔⠋⢀⡴⠚⣉⣥⣶⣿⢣⢒⠈⢦⣤⣤⣤⣦⣵⣾⠭⠴⣬⣿⣿⡿⢰⠁
⠀⠀⠀⠀⠀⠀⠈⠿⣝⡲⣄⣝⣮⣉⣉⣁⣤⠴⣋⡴⠛⠁⠀⠀⢦⠔⢩⡵⡀⠙⠉⠉⠉⢉⣵⣞⣿⣿⣿⣿⠃⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣙⣻⠷⠶⣶⣿⣿⣿⡶⠟⠩⠴⠶⢤⣤⣴⣮⣂⣢⠜⣜⢄⠀⣀⣤⢟⡵⣫⡹⣾⣿⠏⢸⣿
⠀⠀⠀⠀⠀⠀⠀⣱⡟⠓⠆⢶⢦⣤⣄⣀⣀⣠⣴⠯⠖⢚⣽⣟⡿⢯⠭⣟⣾⣷⣟⡹⣴⣿⣛⣹⡿⠟⠁⣠⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⣟⠿⡔⠦⡀⠈⠲⢬⢉⠉⢀⣠⣔⢾⣟⢋⣭⣽⡆⣠⣾⠟⣳⠿⢛⣋⣉⣭⣥⣤⣴⣾⣻⡟⣮⣻
⠀⠀⠀⠀⠀⠀⠀⠦⠀⢵⠀⠀⣶⣴⡞⡉⠙⠛⠳⣤⡉⢿⠔⠈⠋⠙⡿⢡⣾⡷⠚⠋⠛⠙⠒⣶⣾⢟⡗⠟⣻⡿⢹
⠀⠀⠀⠀⠀⠀⠀⠹⠀⠸⡄⠀⡎⢿⣿⣶⣿⣷⡾⣿⣿⣦⢫⠜⢠⢠⠀⣾⠿⡿⡓⣣⢚⡼⠞⣋⣭⢽⢿⠟⡻⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⡇⠀⡟⠆⡛⠛⠾⢾⣞⠽⠫⣿⡟⣰⢣⠃⣰⠏⣿⡿⡇⣰⠟⣠⡞⢻⡶⣶⣮⣔⣁⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⢧⠐⣷⠤⠬⢭⣿⣦⢹⣞⡳⣼⣇⣧⡏⣰⡿⣥⢈⣶⡿⠋⣰⡿⣫⢚⠷⣾⡿⡋⢙⡿⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡘⢦⣜⣿⣅⣚⣟⣛⣻⡵⠜⣛⡉⠥⠬⢬⣩⡟⣛⣋⣠⡶⠋⣈⣠⣍⡛⠰⠴⡞⣫⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠙⠻⡙⠛⣻⠿⠶⣦⣽⣤⡶⠐⠒⠚⣼⣷⣯⣬⣥⡶⣟⠉⢺⣼⣯⣿⠻⢛⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢞⣳⣦⣬⣮⢤⢤⣄⠈⣟⠻⠰⡥⣀⢉⣽⠟⡞⠹⢹⢟⢺⡳⢦⣭⡾⣹⣷⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣷⠀⣶⣿⡄⣺⣶⠋⢀⠜⡠⠋⠨⠃⠜⡡⠁⠎⠼⠀⠛⣧⠀⡧⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠼⠾⢱⣿⢁⣄⣰⣛⡋⢳⡒⣂⣋⢉⣲⣤⣾⡂⠈⠩⡆⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⣮⣿⠁⣵⣬⡙⠮⣝⢀⣀⣉⡉⠍⠚⠉⣻⠽⠇⣨⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢧⣈⣁⣟⠀⠀⢈⡼⢉⠔⣡⠄⡠⠈⣳⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠭⣴⠶⢋⡠⠋⡴⢁⡞⡰⠇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠚⠁⠊⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠄⠀⠀⠀⠀⠀⠀⠀⠖⠒⠈⠀⠒⠛⢃⡀⠀⠀⠀⠀⣠⣴⠶⠔⣇
⠀⠀⠀⢀⡶⠦⣦⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⡀⠀⠠⠄⠤⠀⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⢀⠘⡄⢀
⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣇⣃⣀⣧⣤⠁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠖⠚⠛⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠡⠉⠠⠀⠀⠀⠀⠀⠀⣄⠀⠘⠀⠘⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠘⣃⣤⣠⣤⣄⠀⠐⠲⠎⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀⣤
⠀⠀⠀⢀⠀⠀⠠⠠⠀⠀⠀⠀⠀⣴⢀⠖⠉⢀⠀⠀⢡⠈⠉⠉⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠃⠀⢀⡤⣄⠀⠀⠀⠀⠈⠉⠋⠉
⠀⠀⠈⠈⠀⢀⠀⠀⠀⢀⡀⠀⠀⣸⢛⡁⠶⠈⠀⠰⠆⢤⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠸⣤⠟
⠀⠀⣤⠴⠂⠛⣡⡴⠦⣭⡁⢰⣿⠇⠀⢹⡄⠀⣠⠀⣴⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠠⣾⠏⠀⠀⠘⠿⠟⠻⣄⣀⣀⣈⠇⠀⠀⠀⡄⠀⠀⠀⢰⡞⢁⡴⢲⡄⠀⠀⠀⠺⠖⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⣤⠴⢮⣻⣼⡏
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣈⠃⠀⠀⠈⠁⠑⠀⣀⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⠛⠀⠠⠀⠐⠀⠒
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡂⠄⠨⠀⠠⠅⠸⠀⠀⠓⠃⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⣭⣭⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠵
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠀⠀⠀⠀⢠⠀⠐⠀⠀⠀⣀⣠⡤⠠⠀⠀⠀⠆⠰⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠲⠶⠂⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⣤⠊⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⡚⡒⠀⠀⠀⡀⠉⠵⠆⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠈⠁⣈⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠐⠆⠀⢨⣍⡥⠀⠁⠀⢁⠀⠒⠀⠄⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⢀⠘⠛⠛⠛⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠈⠁
⠀⠀⠀⠀⡤⠤⠀⠈⢙⠉⠀⠋⠀⠀⠤⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠻⠚⠴⢇
⠀⠀⠀⠀⠐⠶⠲⠶⠶⠶⠒⠂⠀⠀⠀⠰⠞⠀⠀⠀⠀⠴⠦⠄⠀⠀⠀⠀⠀⠀⠸⠏⠀⠀⠚⠛⠀⠀⠀⠀⠀⠀⠀⢀
⠃⠓⠢⣤⠀⢰⣶⣀⠀⠉⢉⣴⠒⠀⠀⠀⠀⠀⡀⠂⡔⠀⠀⠀⠀⠀⠀⢀⠀⡔⢄⠀⠀⢤⣀⣀⠀⠀⠀⠀⢠⠾⠿⠋⠀⡤⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠰⠀⠁⠀⠀⠀⠀⠰⠶⠀⠐⠈⠔⠂⠀⠀⠀⢀⡀⠹⠋⠠⠄⠀⠀⠀⠀⢠⡟

⠀⢠⠀⠀⢸⣷⠀⠀⢰⣶⢰⠀⠀⡶⠄⠲⠶⣶⡶⠐⠀⢀⠀⠠⠄⢲⠀⠀⣻⠿⣲⣦⢸⡇⠀⠁⠀⠀⠀⡀⡆
⠀⠀⢰⠄⢸⣿⠀⠀⢸⢀⢺⠀⠀⡇⠀⢀⣿⠋⠁⢦⣴⠏⠀⢀⣠⠟⣾⡰⠙⡀⢩⠏⢸⡗⠀⠀⠀⠀⠀⠁⠇
⠀⠀⠀⠀⢸⡇⢈⠀⠘⠉⢸⠠⠈⢧⣼⡾⠁⣤⡻⠞⠁⣀⠰⠉⠀⠈⠽⠛⠃⣙⠀⠀⠈⠸
⠀⠀⠀⠀⠨⣇⢸⠀⢸⠘⢉⠀⢸⣸⡏⠁⢿⣼⠟⣁⡶⠡⠀⠀⢂⡀⢀⣾⣽⣁⣶⠀⡀
⣶⠀⠒⠀⠀⣟⣾⠈⢹⠈⠈⠀⣾⣿⠑⡜⢿⡟⠀⠀⠃⠀⡀⠙⠚⠗⠸⠻⠛⢿⠟⠰⠙⠻⣦⡄
⣿⠀⡇⠀⢀⣿⠈⡄⢸⠘⢠⣤⣿⡣⣄⢓⣚⣷⣦⡴⣤⣤⣬⡀⣀⣁⠂⠁⢀⠀⠀⠀⠐⠠⣽⣿⠆⠀⠀⠀⠀⠤
⢿⠀⠀⠀⢸⣿⠀⠀⣸⢏⠈⠿⠉⣗⡀⠀⣻⣴⠟⡷⠖⠠⣔⠑⠒⢚⢷⠄⠸⢓⣶⡀⢴⣶⢾⠏⠀⠀⠄⠀⠀⠀⢀
⣿⠀⠀⢠⣾⣿⠀⠀⣸⢬⠀⠁⣾⡑⣳⣪⡿⣫⢆⡥⣠⢴⣯⠞⢩⡅⠀⠀⠘⠈⠙⠡⠀⠙⠂⠀⢰⠀⡀⠀⠀⠐⣾
⢹⡂⠀⠈⢹⣿⠀⠠⢸⠈⠀⠺⢻⣷⡉⠩⠂⣽⣥⠠⣾⡿⠃⠀⠀⠀⠀⠈⠀⣤⡀⢀⣠⣶⠆⡁⢸⠃⠁⠀⠀⠀⣽
⢸⡆⠀⠀⢸⡯⠀⢀⢸⠸⢀⡈⢈⣽⠎⢙⠀⢳⣉⠀⠀⣠⣤⣶⣷⣦⣤⣤⡴⢫⠆⢈⡹⠁⠔⠃⠘⠀⠀⠀⠀⠀⠙
⢸⡇⠀⠀⢀⣿⠀⠍⢸⠷⠐⢠⣿⠡⠴⡟⣄⠐⠿⣷⠀⢟⣤⣤⠌⠓⠀⠀⠉⠑⠚⠈⠀⠀⠀⠀⠀⠠
⠈⣧⠀⠀⢸⣿⠠⠒⢸⡄⡀⠄⠀⠀⢀⢨⠊⢷⣆⣈⡀⠨⢸⣥⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐
⠀⢿⡄⠀⠀⢻⡀⠀⠻⠷⡑⠩⠤⠀⠋⣻⡇⠀⣿⣯⠀⠄⢀⠀⣠⣶⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢸⣿⠀⠀⢸⠇⠀⠠⢤⡟⠠⠀⠒⢊⡝⠑⣳⠛⣁⠀⠀⣄⡑⠛⠋⠉⢙⡇⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞
⠀⣾⠁⠀⠐⣾⠀⠠⠌⢰⠇⡆⢠⣬⠟⡷⣿⣿⣾⠫⠀⠲⣤⠉⠛⣿⠃⡘⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠶⠛⠁
⠀⢸⡄⠀⠀⢿⠐⠀⠀⡟⢀⣿⠪⠁⠘⣿⣦⣈⠀⠚⠁⠂⣸⠀⢠⡏⢰⠇⠀⠘⣇⠀⠀⠀⠀⠰⠄⢰⠖
⠀⠈⣷⠀⠀⢸⠀⣴⢀⠆⢩⡾⣰⠂⠂⢰⢤⣭⠤⢄⡴⠿⠋⣀⠞⣡⡎⠀⢀⢶⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐
⠀⠀⣿⡆⠀⢸⠀⢻⠘⣆⠹⣴⠇⠀⢧⣀⣀⢸⡷⣬⣙⣛⣩⡵⠾⠃⠀⣠⣾⣾⠿⠀⠀⠐⠀⠀⠀⠀⣀⠀⠀⠀⠄
⠀⢠⡏⠀⠀⢸⡄⠈⢸⡉⡆⡜⣀⣤⡤⠋⠉⡸⠃⠈⠛⠋⠁⠀⣀⣤⣾⢿⣿⠷⢠⢀⠀⠀⠀⠀⠀⠀⠈⠸⠀⠀⠠
⣸⣿⠁⠀⠀⡈⠃⠈⠘⢃⡏⠀⢠⠶⠶⢶⣋⣡⣤⡄⠀⠰⢺⢟⣽⣥⠀⣿⠅⠀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⢸⣇⠀⠀⡀⣧⡀⠐⠀⠨⡁⠀⠀⠀⢻⣽⣿⣞⣯⣤⣴⣿⠈⢸⡏⡂⣸⠁⠁⢸⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠼⠋⠀⠀⠀⠙⠻⠆⠀⠀⠙⠖⠀⢲⠕⠟⡿⠻⠿⣿⡿⠏⠀⠘⠀⠁⠾⠸⠀⠈⠸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠃⠀⠀⠀⠀⠀⢀⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢘⠁⠀⠀⠀⠀⢊⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡆⠀⠀⢰⡀⠀⠀⠀⠀⠀⠶⢇⠆⠀⠀⠀⡇⠀⠀⠄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢊⡂⠀⠀⠀⢀⡀⠠⡜⠀⠀⠀⡌⠁⠀⠀⠀⣤⠀⠀⠘⠃⠀⠀⠂⡇⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢈⠀⠀⠈⠧⢤⠀⠀⠀⠀⢀⠂⠀⠀⠠⢻⡆⠀⠀⠂⠀⠀⡀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠉⡌⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢐⠳⠋⠀⠀⠀⠀⣀⠌⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠀⠂⠀⠀⡀⠀⠀⠀⠀⠛⠁⠀⠂⠀⠀⠀⠁⠀⢠⢠⠀⠀⠀⡄⠨⢧
⠀⠀⠀⢀⠀⠀⠀⣸⠀⡄⠀⠀⠀⣮⢀⠀⠀⠀⠘⠀⠀⠀⠑⠂⠀⠀⢠⡐⠂⢠⢸⠀⠀⢀⠀⠀⠈⣸⠀⠀⠀⠁⡀⢹⡇
⠀⠀⠈⠀⠆⠀⠰⠉⠀⢀⠀⠀⠀⣼⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠒⠟⠉⠙⠁⠉⠀⠀⠀⠛⠀⠀⠀⢈⡄⠺⣷⠀⠀⠀⢸⠿⡆
⠀⠀⠀⠠⢭⣶⣶⣂⣀⢾⠀⠀⠀⢨⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢀⣤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠈⠄⢫⣿⣄⠀⠀⠸⡦
⠀⠀⠀⠐⢉⠛⠻⡉⠫⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣏⣿⡇⠀⠀⠀⡃⠀⢀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠃⢸⣶⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⢈⠃⠀⠀⠀⠀⠀⠀⠘⠀⠀⣘⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠅⠀⠀⠀⢇⠀⠀⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠈⡩⡟⢿⠀⠀⠀⠀⠀⠀⠀⠰⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠘⡄⠀⠀⠀⢀⢀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣷⡀⠀⠀⠉⠍⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⡄⢱⠀⠐⠈⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢐⡈⣱⠾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⠍⠁⡈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠝⠛⢄⠀⠀⠀⠀⠀⠀⠀⠠⢤⠦⣰⣇⠀⠒⠀⠀⠜⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡇⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠁⠈⡄⠀⠀⠀⠀⠀⠀⠀⠻⢛⠛⠻⠀⢀⡄⠛⢰⠹⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⡅⠈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡆⠈⠃⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡃⠀⠶⠀⠁⠀⠘⡆⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡠⠌⠁⠀⡁⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠈⠀⠠⡄⠀⠀⠉⠙⣇⠀⠀⠀⠀⠀⠀⠀⣴⡄⢆⠀⠀⠀⠆⠀⠰⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢥⢸⠀⠀⠀⠀⠀⠀⠀⠀⢘⣀⠀⣤⠸⠃⠀⢀⣀⠀⠀⡀⢈⡄⠀⠀⠀⠀⠀⠀⠈⠋⠈⢆⢰⠠⠆⠀⣎⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⡄⠐⠂⠀⠈⠝⣢⡀⢹⣆⢻⡀⠀⠀⠀⠀⠘⢻⡤⠌⠐⢧⡄⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⢃⠌⠀⠀⠠⠀⢀⣀⠉⠙⠶⣽⣦⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠁⡠⠀⠘⣟⣧⡆⡀⠀⠉⠛⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠴⠘⠱⠂⠈⠹⡿⠱⠄⠀⠐⠂⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⣷⣿⣿⣶⣶⣶⣤⣲⣞⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣠⡾⡻⣿⡁⢿⣿⣿⣿⠿⡌⠙⠉⣠⣶⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⣥⣤⣠⣏⣳⣾⣇⠈⠁⠱⢷⣶⠃⠀⢠⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣼⣾⣿⣿⡇⠻⢿⣿⣿⣷⣵⣤⣀⣀⠀⣴⣿⣿⣿⣿⣿⡿⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⡅⠀⠻⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠢⣻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⢿⣿⣿⣦⡀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠶⣄⣠⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⣿⣿⣿⣿⣿⠛⡿⣿⣿⣷⡄⠀⠀⠈⠛⠻⢿⠿⠿⣿⠘⣿⣷⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⠘⠀⠀⢸⣿⣿⣿⣶⣷⣶⣿⡆⣠⣶⣾⣿⠰⣿⣿⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⠉⠁⠀⠛⠈⠉⣴⡿⢻⣿⣿⣿⣿⣿⣿⣿⣳⣷⣿⣿⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⣷⠟⠷⣿⣿⣯⣽⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠟⠉⠀⢸⡟⡿⠿⣿⣿⣿⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡇⠀⢀⠀⢘⡀⢠⣴⠟⠋⠀⠑⠆⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠹⣿⣷⣄⣈⣛⣿⣏⠆⠀⠀⠀⠀⠀⠀⠀⠒⠿⣶⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠀⠐⠂⡀⠰⠀⠀⠀⠀⢰⠁⣴⣿⣿⣯⡙⠿⠿⣻⣤⣙⣲⣦⣄⡀⠀⠀⠀⠀⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠙⠂⠀⠀⢀⠀⠀⠀⠀⠀⡈⠀⢿⣿⣿⣶⣿⣶⣾⣿⣿⣿⣿⣿⡿⢛⣦⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⢷⢽⣿⢇⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠷⠋⠀⠀⠹⠠⠄⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢘⢉⡉⣻⣟⠉⠁⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⣼⢿⡷⠩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⣸⣟⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣐⠛⠿⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⣿⠂⠀⢀⣈⠁⠀⠀⠀⠂⠀⠀⠀⠄⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡷⠶⠿⠟⠁⠳⠶⢶⣀⡤⠀⠀⠛⢷⣦⣭⣼⣷⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣶⣦⣤⣀⡀⠀⠀⠴⢧⠠⣤⠀⢸⣷⣽⣿⣿⣿⣷⡀⢃⠀⠀⠀⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⡀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠻⠿⠷⠢⠀⠀⠠⠿⠶⠼⠿⠿⢿⣿⣿⣿⣷⡀⢷⡄⠀⠀⠀⠀⠀⠈⣥⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣦⣄⣀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣉⡀⠀⠀⠀⢠⣼⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠀⠛⠋⠉⠁

⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠉⠳⣄⠀⣠⠶⠛⠉⠉⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠹⠟⠁⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⣶⠋⠁⠀⠀⠉⠳⠦⠤⠶⠚⠉⠁⠀⠉⠛⢦⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⢀⡴⠞⢁⣴⣿⣿⣿⣿⣿⣷⣀⠀⠀⣀⣤⡀⠀⠀⠀⣠⣤⣀⠈⣧⠀⠀⠀⠀⠙⢦⡀⠀⠀⢸
⣿⠀⠀⠐⢿⡀⠰⣿⣿⣿⣿⡿⠟⠉⠀⠉⠙⣻⠿⠛⠙⠲⠶⠚⠁⠀⠉⠉⠙⠳⢦⣤⡄⠀⠀⣹⡆⠀⢸
⣿⠀⠀⠀⠀⠹⣆⠘⣿⡿⠋⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⢀⡼⠋⠀⠀⢸
⣿⠀⠀⠀⠀⠀⢸⣶⠋⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⢀⡴⠋⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⣼⠁⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡧⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠙⠳⢦⣤⣀⣀⣀⣀⣤⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼

⣿⣿⣿⣷⢻⣎⠻⣮⣿⣆⠳⣌⠛⠷⣶⣶⣽⣿⣿⣿⣾⣿⢃⣴⣿⡿⢟⣫⣾⣧⣾⣿⢟⣠⣿⣵⠏⢀⣾⣿⣿⣿⣿
⣿⣿⣿⣿⡄⢻⣧⡀⠹⣿⣿⣿⣿⣶⣄⡈⠙⣿⡎⢻⣿⣿⣾⣿⣯⡾⣫⣭⣿⣿⣿⣿⣿⣿⠏⣠⣶⣿⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡀⢻⣷⠀⣿⢇⣤⣌⡙⠻⢿⣦⣹⣧⣾⣿⣿⣿⣿⣿⣴⣿⡿⠛⢉⣡⣤⣸⣿⣾⡿⠋⣠⡿⢣⣿⣹⣿
⣿⣿⣿⣿⢿⣷⡀⢻⣷⣿⣸⢳⣎⣙⢦⡀⠙⠿⠛⠋⠉⠉⠉⠙⠛⠿⠋⢀⡔⣋⣥⠸⡇⣿⡟⣠⣾⠟⠁⣼⢣⣿⣿
⣿⣯⢻⡟⣧⡹⣿⣌⣿⣏⣿⢸⣙⡾⣧⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡰⣿⣿⡃⡇⣿⣿⠟⠁⣠⣾⣿⡿⣿⣿
⣿⣿⣎⢿⣌⠻⣿⣿⣿⣿⣾⡘⣛⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⢣⣷⣿⣯⣴⣿⣿⢟⣩⣾⣿⣿
⣿⣷⣿⣾⣿⣦⣌⣻⣿⠿⠟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢟⣿⣿⣯⣶⣿⢟⣱⣿⣿
⣿⠶⢈⣙⣻⣿⣯⡉⠉⠁⠀⠀⠀⠀⢀⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⠀⠀⠀⠀⠀⠈⠉⣉⣽⣿⣿⣿⡿⠛⢻
⣿⣫⣭⣭⣿⣟⣛⣛⡶⡄⠀⠀⠀⠀⡞⠀⢰⡏⠳⡄⠀⠀⠀⢠⠞⣽⠀⠈⡧⠀⠀⠀⠀⠀⢾⣛⣿⣿⣿⣿⣿⣿⣻
⣿⡿⢟⣿⣿⣫⣭⠍⠁⠀⠀⠀⠀⠀⠸⡄⢸⡇⠀⡇⠀⠀⠀⢸⠀⢿⡇⣠⠃⠀⠀⠀⠀⠀⠈⠭⣭⣛⣿⣯⣟⡻⢿
⣿⣴⢟⣿⣿⠟⠁⢀⣀⣀⣀⠀⠀⠀⠀⠈⠚⠓⠊⠀⠀⡤⠀⠈⠑⠚⠛⠁⠀⠀⠀⠀⣀⣀⣀⡀⠈⠻⣿⣿⣷⣭⣻
⣿⣶⣿⣿⢇⡴⢋⣭⠿⠛⠉⣿⡷⢦⣄⡀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠀⠀⢀⣠⡴⣾⣿⠉⠙⠻⣍⠛⢦⣹⣿⡿⣿⣿
⣿⣾⣿⣿⡟⢀⡾⠁⠀⢠⠾⢫⡇⠀⠈⠙⠳⠦⠤⣤⢰⣿⣂⡤⠤⠴⠚⠋⠁⠀⢸⡙⠧⡀⠀⠈⠳⠀⢿⣿⣿⣿⢻
⣿⣿⡇⢹⣧⠸⠁⠀⠀⠀⠀⢚⣇⠀⠀⠀⠀⠀⠀⢀⡏⡇⢯⡀⠀⠀⠀⠀⠀⢠⣼⡃⠀⠀⠀⠀⠀⠀⣼⣿⣿⣧⣾
⣿⣿⣧⠈⢿⡄⢤⠀⠀⣀⡤⢟⣿⠀⠀⠀⠀⠀⢀⡞⣠⣿⡌⢧⠀⠀⠀⠀⠀⢸⣿⠳⢤⡀⠀⠀⡄⢠⡟⠟⢸⣿⣿
⣿⣿⣿⣷⡈⠳⠸⡷⠤⣤⣴⡿⢻⣷⠀⠀⠀⢀⡞⣰⠃⡇⠹⣌⢧⠀⠀⠀⢸⣾⠟⢷⣤⣤⠴⣾⠇⠟⠀⣠⣿⣿⣿
⣿⣿⣿⡿⢿⣷⣶⣿⣷⡿⢯⣤⡀⢿⣴⠀⠀⣼⡼⠁⠀⡇⢀⠘⢮⣧⠀⠈⣾⡟⢀⣤⡽⣿⣾⣷⣶⣶⡾⢿⣿⣿⣿
⣿⣮⠻⣷⡀⢠⣾⣿⣿⣿⣶⣌⢻⡌⣿⡀⠀⣿⣇⠀⡀⠟⠀⠀⣼⡿⠀⢀⣿⢠⡟⣡⣾⣿⣿⣿⣷⡄⢠⣿⢏⣵⣿
⣿⣿⣧⠘⣷⣿⣿⡸⣿⣼⣿⢿⣾⣇⣿⠙⢆⢸⣿⠀⠀⣤⠀⢀⣿⠇⡴⠋⣿⣾⣾⡿⣿⣷⣿⢡⣿⣿⣾⠃⣾⣿⣿
⣿⣿⣿⠀⢸⣿⠹⣿⣿⢿⣿⣸⣿⣿⠇⠀⠈⢿⣿⡆⡦⠀⠄⢸⣿⡾⠀⠀⢻⣿⣿⣅⣿⡿⣿⣿⠫⣿⡇⢠⣿⣿⢻
⣿⢻⣿⣇⠈⣿⣷⡿⣃⠘⣭⣿⣿⣿⠀⠀⠀⠸⣿⡇⠀⠀⠀⣸⣿⠁⠀⠀⠀⣿⣿⣿⣭⠁⡛⣿⣾⡿⠀⣼⣿⠏⣸
⣿⣶⣿⣿⣷⣬⣝⣛⣻⠿⣿⣿⣿⣿⡀⠀⠀⠀⣿⣷⠀⠀⠀⣿⣿⠀⠀⠀⢠⣿⣿⣿⡿⠿⣛⣋⣭⣤⣾⣿⣿⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡶⠾⠟⠛⠛⠛⠻⠶⣦⣄
⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⣤⣴⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⡀⠀⣀⣤⣴⡶⠶⠶⢶⣦⣤⣀
⠀⠀⠀⢸⣿⡛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠿⠋⠉⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣀
⠀⠀⠀⠀⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄
⠀⠀⠀⠀⢻⡏⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀
⠀⠀⠀⠀⠘⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣀⣀⣠⣿⠉⠉⠉⠉⠉⢹⣿⠛⠛⠷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄
⠀⠀⠀⠀⠀⢻⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⡀⠀⠀⣿⡇⠀⠀⠀⠀⢨⣿⠻⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣷⡆
⠀⠀⠀⠀⠀⠘⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣾⣿⣦⣤⣤⣭⣽⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⢹⣇⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⢾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⣹⣿⠿⠛⠉⠉⠀⠀⠉⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢡⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⡿⠛⠁⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⡿⠟⠋⠁⠀⠀⠀⣰⡿⠃
⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠛⠋⠁⠀⠀⠀⠀⠀⣠⣾⠋
⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⢀⣤⡾⠋⠁
⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⢀⣀⣤⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠿⠿⠿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠶⠶⠶⠶⠶⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠄⠀⠀⠀⢀⣤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣴⣿⡿⢿⣼⣴⣶⣎⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡷⠶⠛⣩⡅⠀⠀⠉⠃⠉⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠊⠉⠉⠒⠢⠤⠠⠤⠤⠴⠚⠋⠉⠉⠉⠉⠁⠀⠀⠈⠀⠀⣠⠄⠀⠀⡀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⣄⢀⠀⠈⠀⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡾⠋⠀⠀⠀⠹⣄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡿⠘⡆⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠘⣆⢰⠇
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢠⢠⠀⠀⠀⣰⠻⢿⣤⣀⡀⣀⡀⣀⣸⡧⠀⠀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⢠⣮⡆⠀⡼⠀⠇⠀⣼⠃⠀⠀⠈⠉⠉⠋⠉⠉⢸⠁⠀⡞⢹
⠀⠀⠀⠀⠀⠀⠀⠛⠀⡔⠃⣴⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢰⠃⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⢸⠙⡅⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⢀⡟⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⠀⠰⡈⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⣾⠃⠸⠀⢀
⠀⠀⠀⠀⠀⠀⠲⠄⠘⠆⠀⠰⠠⠱⠘⠆⠠⠀⠀⠀⠀⠀⢀⠈⠀⠃⡀⠀⡰⠛⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠄⠤⠠⡦⢰⢀⡀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠅⠰⠞⠒⠐⠒⠄⠀⠀⠀⠁⠉⠉⠈⠀⠀⠀⠀⠀⢠
⣀⠀⡀⠀⠀⠀⠀⠀⠐⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⢀⣀⣀⣀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⣿⠿⠿⠛⠛⠛⠛⠛⠛⠋⡁⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠉⠙⣿
⣀⣀⣀⣤⣤⣄⣀⢀⠀⠀⣈⡒⢀⠀⠐⠂⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣦⣴
⠉⠈⠉⠉⠉⠉⠉⠭⠤⠤⠬⠄⣀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠙⠛⣛⡛
⠅⠀⠂⠈⠉⠉⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻
⣛⠻⠖⠓⠒⠒⠂⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠛⠛⠉⠩⠯⠭⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠠
⣂⣀⣤⣒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠉⠉⠉⠉⠉⠁
⡀⡐⠐⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠍⢃⡀⠤⢤⣄⣀⣀⣴⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣠⣤⣿⣯⣶⣿⣶⣶⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠟⠋⠉⠉⠉⠉⠉⠉⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣠⣶⣤⣦⣤⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡆⠀⣿⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣿⢿⠂⠀⢀⠀⢰⣿⡛⣷⣶⣤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠀⠸⡿⠀⠀⠾⡗⠿⠻⢶⡆⣄⡀⠀⠀⡄⡅⠀⢹⡟⠀⠀⠐⠚⠻⡿⠭⠻⠏⠙⢺⣿⡅⢱⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⣧⠀⠀⠀⠀⢀⣤⡈⠉⠀⠁⠀⠀⡀⢡⠀⢸⣇⠀⠀⠀⠀⠀⠁⠀⢀⠀⠂⠈⠛⠘⠇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⣧⣹⣿⣿⣈⣀⣤⢾⠣⠀⠀⠀⠀⠀⡓⡀⡇⠈⣿⣦⣀⣀⣀⢀⡀⠀⠐⠾⠿⢦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡘⢿⣿⣿⣿⣏⠙⣶⠀⠀⠀⠀⠀⠀⣒⢨⢿⣀⣻⣿⣿⣿⡇⡽⢁⣀⣴⣶⣿⠻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣮⢻⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢐⣏⠘⣿⣿⣿⣿⣿⣿⣿⣿⠿⣯⣤⡉⠁⠺
⠀⠀⠀⠀⠀⠀⠐⠒⠶⣤⣀⠀⢹⣷⡹⣿⡿⢻⠀⠀⠀⠀⠀⠀⠀⠀⠩⣆⠘⢿⣿⣿⣿⣿⣿⣿⣤⡈⣻⡟⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠆⠀⠙⢷⡽⡇⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡌⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆⡹⣿⣿⣿⣿⣿⣿⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢹⡀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠘⣿⣧⡘⢿⣿⣿⡟⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠻⠿⠇⠀⠀⠀⠀⠀⠻⣿⡄⠀⠈⠹⣿⣷⡌⣿⣿⠀⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣭⡿⢻⡿⠀⠀⠀⠀⠀⣀⠀⣠⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢧⠚⠁⢠⢄⠀⠐⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢢⠉⠀⠀⠀⡠⠔⠒⢂⠎⣸⡖⠁⣴⢦⣄⠈⠙⣿⣿⣤⡀⠀⡌⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠩⣐⣚⡁⠀⡀⠠⠘⠁⠘⡄⠙⠚⠿⣿⠦⣼⠛⠿⠛⠀⣀⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣹⠇⡀⠄⢇⠀⢠⡁⣤⠔⠊⠀⢡⠈⡟⢂⠀⠀⡉⠀⠀⢠⡾⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠾⡻⢃⡀⣴⡆⠱⡀⠀⠸⣉⠦⠒⠋⠺⠁⠺⣦⡐⠸⠀⢀⣩⣴⣿⣛⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠒⠲⠆⠻⢯⣬⣿⣾⣏⢀⣀⠃⠀⡀⡀⠀⢠⡀⠈⠈⢇⠀⠀⠀⠈⠻⠟⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣂⢠⣠⡄⠐⠒⢩⠛⠉⣔⡄⠀⣉⠲⡄⠃⣀⣠⣤⠀⡠⢀⠉⠉⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⡁⡨⢣⡀⢰⠁⠀⠀⡽⠧⠛⠃⠀⡎⢁⡮⠛⠃⠪⢄⣨⠐⣊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠨⠅⠀⡋⠉⠲⠏⠉⠋⠀⣼⡀⡠⠒⠉⠉⠁⠲⡷⢃⢠⡕⡀⣧⠕⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠁⡀⠙⠢⢭⣳⠀⡄⠀⠰⠆⠀⢹⠀⠰⡆⡴⠶⠖⠘⠇⡸⠱⢡⣏⣀⡊⠑⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠂⢐⡡⠚⡇⠀⢠⣤⣴⡄⠀⠀⡀⠄⠠⠀⣤⠀⠀⡟⠀⢀⠸⡃⡐⢍⢣⡊⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢔⣈⣏⣀⣈⣑⣉⣀⣀⣀⣇⣑⣘⣘⣛⣀⣀⣃⣀⣈⣀⣇⠠⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⢸⠄⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⣀⣀⠀⠀⠀⣼⣿⣿⣿⡆⠀⠀⠀⠈⠁⠀⠀⢀⣶⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣦⠀⠘⠻⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠸⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⡇⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠐⠒⠒⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡄⢀⠄⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⡈⠉⢁⠀⠏⢠⣋⣀⣀⣀⣤⣶⠊
⠀⢀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣿⠛⢻⣕⣶⣢⣧⣶⣷⣶⣶⣿⣿⡿⠋⠉⠉⠁⡀
⠀⢨⡉⠓⠒⣲⣌⣀⣔⣄⣁⠀⡄⠀⠀⠀⣠⣬⢤⣍⣛⣃⣬⣽⣷⣿⣿⣻⣩⣙⣻⣟⣿⡿⠁⠀⠀⠈⠉
⠀⠈⣯⣫⣭⡶⠟⢓⣺⡟⣏⠀⠀⠒⠶⠾⠋⠉⠳⣬⣭⣯⡭⢴⣶⣶⣾⣿⣽⡯⢷⡿⠋⠀⠀⢀⠄⡘
⠀⠀⢛⣫⣟⣽⣟⣑⢎⣽⣮⢳⠂⠤⠤⠤⠦⣤⠀⠀⢨⣿⣿⣿⣿⢷⣶⣾⣽⣿⣋⣤⣄⣤⣶⣅⡠⠓
⠀⠀⠀⠉⠉⢙⣻⣖⣻⣯⢺⢆⠀⠀⠀⢀⣀⣌⡇⠀⢸⣿⡟⠁⣤⡀⠨⣙⣫⣽⣷⢮⡉⠍⠛⢦⣄
⠀⢰⣄⣛⣲⣤⣤⣷⠳⣗⡷⡘⣟⡝⣏⣽⣛⢟⠇⠀⠈⠛⠛⠮⣭⣤⣭⡶⣶⣄⠁⠠⠉⣰⠀⢸⡯⠛⠴⢤
⠀⠈⢮⡋⢓⡙⠘⢻⣧⠈⣿⢿⣓⣋⣩⢥⣽⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⣿⢷⣿⣧⡴⠮⣄⣀⣀⣤⣱⡖
⠀⢀⣄⠈⠀⠈⢻⠧⣿⣷⣌⡳⠭⡭⢶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⣿⣛⣻⡵⣋⣝⣪⣉⡉⠙⠛⣃
⠀⠘⢧⣄⠀⢊⣍⣙⣾⣿⣿⣻⣿⣿⣿⣿⣾⣶⠊⠁⠀⠀⠀⠀⠠⢀⣧⣬⣉⣫⣽⣿⣶⣿⠿⠛⠛⠿⠥⠞⠉⣀
⠀⠀⠦⠜⢉⠀⣿⣟⡭⣿⣿⡿⠿⣿⣿⣍⣿⣿⣿⣷⣦⣤⡄⣠⠀⣿⠿⠷⣷⡞⣶⣾⢷⡾⣒⣚⡳⢄⡀⠀⢸⠃
⠀⠀⠉⠙⣶⣿⣻⢏⠞⠛⢙⠯⣁⣲⣬⢭⣿⣻⡿⠛⠛⠋⠀⣿⠂⠙⡟⠷⣿⣟⠿⠿⣿⡿⠭⢍⢻⣤⣥⠄⠁
⠀⠀⠀⣨⠝⠋⠁⠀⠀⠊⠉⠳⠖⢶⣽⣷⣽⣽⡇⠀⠀⠀⠀⣾⣄⠀⣇⣤⣼⡳⣭⣽⠏⠀⠁⠀⣧⣨⣥⠛⠛⠁
⠀⠀⠀⠹⠰⠄⠈⠀⡄⠐⠀⠀⢀⣁⣉⠿⠿⠾⣧⣀⣀⣠⣴⣿⣥⣾⠿⠋⠉⠑⠦⠜⠀⠀⠀⠀⠈⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠀⠀⠀⠈⠉⠙⠓⠋⠉⠀⠀⠀⠉⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡄
⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⣀⣠⠴⠒⢿⠉⠉⠁⠙⡏⠀⠉⠉⡿⠒⠢⣄⣀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⢀⡞⠁⠀⢀⡴⠊⠉⢃⠀⠀⢘⣄⢀⣀⣠⣇⣀⡀⣠⠃⠀⠀⡘⠉⠑⢦⡀⠀⠈⢳⡀
⠀⠀⠀⠀⡞⠀⢀⣴⠃⢡⠀⣀⣼⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣧⡀⠀⡌⠙⣦⡀⠀⢳
⠀⠀⠀⢸⠁⢠⡫⠈⣤⣴⣿⡿⠿⠛⠛⠛⠛⠿⢿⣿⣿⣿⠿⠛⠛⠛⠛⠿⢿⣿⣦⣴⠀⠿⡄⠘⡇
⠀⠀⠀⢸⠀⣿⣱⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣦⣿⠀⡇
⠀⠀⠀⠸⡄⠈⠻⣍⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣩⠟⠁⢠⠇
⠀⠀⠀⠀⢳⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡞
⠀⠀⠀⠀⠀⠱⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣠⠎
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣤⣀⣀⣀⣀⣤⣤⠴⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢀⡠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠉⡀⠊⣠⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢾⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⣠⡗⠀⢀⠆⠀⠀⠀⠁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⢐⣤⠀⢠⣆⣀⣬⡤⢐⣊⠭⣶⣚⠋⠀⠀⠀⠀⠀⠴⣾⡟⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⣈⠛⠖⠄⣼⠟⠁⠛⠋⠉⠉⠉⠉⠛⠙⠃⢀⣀⣀⣄⣀⡌⣆⠀⠀⠀⠠⠤⠠⠄
⠀⠀⠀⠀⠀⠀⠀⡰⠊⢐⠁⠀⠀⡠⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⢹⡷⠤⠤⠼⠀⠠⠄⠀⣈⡁⠢⡀
⠀⠀⠀⠀⠀⠀⡻⠂⠠⠞⠛⠒⣶⣇⣀⣠⣤⣶⣶⡦⠀⠀⠀⠀⠰⣿⣬⢕⣂⠀⠀⠀⠀⠀⠈⠑⢌
⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⡀⠀⢁⣨⣿⣿⣄⣼⠟⠀⠀⠀⠀⠀⠀⠨⣷⣤⡉⠓⠀⠀⠠⢀⡀⠀⠀⠁
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣤⡭⠤⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠁⠀⠉⠳⠑⠂
⠀⠀⠀⡄⠀⠘⡟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢰⡀
⠀⠀⠀⢛⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠴⠄⢀⣰⣴⣶⡈⠀⠀⠀⠀⣠⠃⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠙⠿⣷⢤⣤⣤⣤⣤⡖⠁⠠⠐⢡⡾⣿⣿⣷⠀⠀⠀⠠⠃⠘⠃⢦⡄⠀⠰⡄⠀⠀⡘⠀⠈
⠀⠀⠀⠀⠀⠀⠰⠄⠀⢀⡀⠈⡇⠀⠀⠀⡋⠀⠘⣿⣿⡇⠀⠀⢀⠊⠀⠀⠈⠳⠀⠀⠃⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⢰⣷⠀⢰⠲⠇⢠⠂⣼⢿⠇⠀⢠⠏⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠃⡆⠾⠤⠌⠀⢸⠟⠀⢀⡏⠀⠀⡀⡆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠦⣴⡶⠀⠀⢠⡂⡀⠁⢀⠀⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠐⢋⡴⠯⡇⠈⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠀⠀⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⣾⢁⣤⣶⣿⣯⣶⠟⠉⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣀⣐⣚⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣓⣀⣀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢻⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⡟⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠸⣞⠛⢿⣿⣷⣾⣿⠛⠉⠉⠳⠙⣿⢿⡿⣿⠋⠞⠉⠉⠛⣿⣷⣾⣿⡿⠛⣱⡇⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠉⠛⠛⢿⣿⠛⠛⠀⠀⠀⠀⠀⠈⠘⠃⠀⠀⠀⠀⠀⠀⠛⠛⣿⡿⠛⠛⠉⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣶⣶⣾⣿⣀⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠀⣿⣷⣶⣶⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣹⣿⣿⣿⣿⣷⠟⠀⠀⠀⠀⠀⢄⠀⠀⡠⠀⠀⠀⠀⠀⠲⣄⠈⢿⣿⣿⣏⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠿⣿⣿⣧⡀⢿⣿⣶⣦⣄⠀⠀⠈⢦⣦⣴⡴⠁⠀⠀⣠⣴⣶⣿⡷⢀⣼⣿⣟⠿⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣭⠀⠐⣿⣿⠁⢘⣳⣄⢀⡀⢸⡇⢀⡀⣠⣞⡇⠈⣿⣿⠂⠠⣭⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⣿⣿⡿⡋⠀⠀⠀⠙⠻⢷⣤⣥⡾⠟⠛⠟⠻⠛⠻⢷⣤⣤⡾⠟⠋⠀⠀⠀⠙⢿⣿⣿⣝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣵⠇⠀⠀⠀⠀⣀⡀⠙⢷⣿⣷⣦⣴⣾⣿⡾⠋⢀⣀⠀⠀⠀⠀⠸⣦⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⢸⡇⠀⠀⣞⠏⡹⠳⣄⠉⠙⠿⠿⠋⠉⣠⠞⣏⠹⣳⠀⠀⢸⡇⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠉⢸⣿⣿⣿⣿⣿⣧⡅⢤⠘⢷⣇⢠⡍⣙⢲⢶⡶⡞⣋⢩⡀⣹⡾⠃⣤⢠⣼⣿⣿⣿⣿⣿⡏⠉⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⣿⣿⠏⣿⣿⣿⣿⡇⠀⠀⢸⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⡇⠀⠀⠸⣿⣿⣿⣿⠹⣿⣿⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠰⣿⡟⣿⣿⢰⡆⠀⢸⡇⠹⣿⠿⡿⡿⢿⢿⠿⣿⠏⢸⡇⠀⢰⡆⣿⣿⢻⣿⠇⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⢻⣿⣿⡇⡄⠈⠷⣿⡴⠦⠞⠓⠚⠳⠴⢦⣿⠾⠃⢀⢸⣿⣿⡟⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⣿⣿⣷⣷⣄⠀⢀⠀⠀⡀⠀⠀⠀⢠⠀⠀⠀⣠⣾⣿⣿⣿⠃⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⢿⣏⢻⣷⣿⣀⣆⣿⡄⢀⣿⣸⢠⣴⣾⡟⣹⡿⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠙⢿⣿⣿⣿⣷⣼⣿⣿⣿⡿⠋⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠻⣿⣿⣿⣿⠟⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⢄⣀⠀⠀⠀⠀⣀⡠⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⠀⠀⠀⠀⠈⠑⠦⠔⠊⠁⠀⠀⠀⠀⠀⠙⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠒⠉⠀⠈⠑⠒⠤⢄⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⢻⠻⣿⣿⣿⣿⣭⣁⣈⣻⠉⠉⠉⠉⡏⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢸⠈⠉⠉⢉⣋⣉⣭⣽⣿⣿⣿⠟⢩⠏
⠀⠀⠀⠀⠀⠀⠀⢳⡈⠻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣷⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣶⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠈⠻⣿⣿⣿⠟⠋⠉⠉⠉⠙⢻⡿⠛⠋⠉⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⠟⠁⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢨⠏⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢬⡿⠁⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢠⠃⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠀⡰⠋⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡠⠊⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠉⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢃⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠒⠒⠋⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣯⣍⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⢿⡷⠰⠾⡿⠿⠷⠾⠿⠿⠿⣿⡭⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣛⡻⠿⠿⠿⠻⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡶⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠈⠀⠉⠩⠿⠟⠻⠟⠛⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠘⠒⠃⠉⠠⠟⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⢀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠞⠿⣿⡿⠿⡿⣿⣿⣻⣿⣿⣿
⣿⣿⣿⡋⢐⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡀⠀⠰⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠓⡀⠀⠀⣻⣿⣻⣶⣿⣿⣿⣼⣿⣿⣿
⣿⣿⣿⡿⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⣋⠀⠀⠀⠉⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣷⣦⡀⠰⠀⠀⠲⣂⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⠿⢟⣿⣿⣿⣿⣿⣿
⣿⣿⣷⡷⡟⠛⠉⠁⠴⢘⣺⣿⡏⠀⣹⣿⣅⣀⡀⠀⡀⠀⠀⣴⠾⠶⣦⣿⡟⠃⡀⣢⡀⠀⢀⣀⠀⡠⠀⢑⠀⠀⠀⢶⣤⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣥⡀⠀⣀⣀⣸⣿⣿⣿⣷⣿⣿⣿⣷⣿⣤⣀⣬⣡⣴⣿⣷⣤⣤⣿⣿⣮⣽⣯⣿⣷⣿⣿⣷⣶⣶⣼⣶⣿⣷⣶⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣷⣿⢽⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⡒⠖⣠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡤⢤⣤⡤⢠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠛⠁⠀⠀⠀⠉⠻⣆
⠀⠀⠀⠀⠀⠀⠀⡔⠒⠶⠂⠒⠶⠂⠒⠳⠓⠒⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢁⡿⠁⠀⠀⠀⠀⠀⠀⠀⠹⣯⠉⢑
⠀⠀⠎⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠀⠀⠀⠀⠀⠀⡓⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡖⡎
⠀⠀⠳⡄⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴⠀⠀⠀⠀⠀⠀⠁⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⡇
⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠆⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠀⣤⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇
⠀⠀⠀⠀⠀⠀⠈⠑⠒⠠⢤⠠⠄⠄⢤⠤⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⣷⣵⣦⣤⣤⣤⣤⣤⣶⣵⣯⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠊⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠂⠤⠤⠤⠤⠤⠒⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⣀⣰⣄⣀⣀⣀⣀⣀⣀⣼⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣼⣀
⠀⠀⠀⠀⠀⠀⠀⠣⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠴

⠀⠀⠀⠀⠀⠀⠀⣠⡤⢤⣀⣀⣀
⠀⠀⠀⠠⣶⣧⣗⣼⣖⡖⠈⠷⡝⣿⣶⣄⡀
⠀⠀⡰⠅⢶⠰⠟⠛⡶⠙⣷⢱⣇⣈⣇⡼⣿⠻⡿⣶⣦⣄
⠀⠀⠁⢀⠈⣿⣾⠿⣆⠖⠹⢸⣭⡙⠁⠏⡻⢀⠇⣿⢸⣿⣿⠲⣄
⠀⠀⠐⠒⠵⠃⣉⣴⡟⡠⣴⡿⠀⠀⠀⠀⡇⣿⠸⣳⣫⢿⡿⢶⣿⣷⢦⡀
⠀⠀⠀⠀⠀⠐⠿⠛⠈⠀⠈⣿⠧⠵⣖⡒⠿⢻⠠⣿⣿⣾⣁⣴⡾⣯⢳⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠗⠒⠂⢢⣳⣼⡷⣷⢸⡹⣿⡋⢠⣶⢬⡻⣿⣟⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣞⣛⣻⣠⠿⣕⠉⠛⢤⣽⣾⣿⣮⣦⢞⣽⢽⠛⢖⣿⢧⡀
⠀⠀⠀⠄⠠⠔⠀⠐⠂⠤⠀⠟⠬⣍⠃⢠⣾⣿⣦⣘⣻⣿⣛⣾⣟⠾⢡⣾⠛⣒⣿⡶⣷
⠀⠀⠐⡂⣡⡤⢰⢀⠀⠀⠀⠀⠀⠪⠀⠸⡿⠯⢝⠺⢍⡛⢝⡯⡙⣷⣼⡣⡞⢋⣭⣵⣿⣌⣦
⠀⠀⠁⡁⠟⠱⠉⠉⠀⠀⠠⢀⡀⠀⠀⠀⡇⠀⠀⠙⠂⠉⠢⣷⣈⠋⠳⡷⣷⣽⢁⠴⢬⣆⣧
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⢧⠹⣦⡟⢧⡙⡏⠠⡞⠉⠉⠑⠒⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠙⠙⢿⡃⣄⢐⠀⠀⠀⠀⠀⠘⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⣿⠘⡏⢆⡀⢠⢄⣸⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡟⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠛⠛⠶⢤⣀⠀⠀⢀⣠⡴⠞⠛⠛⠛⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠂⠀⠀⠀⠀⠈⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠈⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⠀⠀⡄⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⢀⣠⡴⠒⠒⠚⡏⠉⠉⠒⠒⠒⠲⠒⠒⠋⠉⠉⢹⠉⠑⠲⢇⣀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⢀⣤⣾⣿⣿⣧⣤⣄⣠⡇⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⢸⣀⣀⣠⣾⣾⣷⣶⣄⡀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⣠⣶⣿⣿⣿⡿⠟⠛⠛⠛⠿⠿⢷⣶⣤⣤⣤⣾⣧⣤⣤⣴⣶⡿⠿⠛⠛⠉⠉⠉⠛⠿⣿⣶⣦⣉⠄⠀⠙⠷⣄
⠀⠀⠀⠀⠘⣇⠀⠠⢴⣾⣿⣿⣿⡿⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⣿⣿⣿⣿⣶⠄⡀⣹⠆
⠀⠀⠀⠀⠀⠸⣆⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠃⠁⢠⡟
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣾⣿⡿⠁⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⠁⠂⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠇⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⢰⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⡸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⢦⣤⣤⣤⣤⣤⣤⠴⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠀⠀⢳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⠤⠀⠀⠀⢻⣞⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡻⣿⣧⣶⣷⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠿⣾⣿⣷⣾⣿⣿⣽⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠪⠉⠑⠙⠙⠒⠤⠤⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣿⡿⡿⢉⣅⣫⣾⣿⣿⢶⣿⣿⡏⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⢉⢆⣴⠏⡐⢆⠀⢀⣄⠀⢀⠌⠉⠉⠉⠋⠉⣹⠟⣟⢋⡩⢇⢻⣸⣿⣿⣿⣿⣿⣿⢿⠷⢻⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠓⣁⣸⣭⢁⡄⢁⢀⣣⢈⠉⠀⠀⡐⠠⠂⡐⠡⣺⠏⢀⣳⣿⣽⡾⣻⡟⣿⣻⣿⣿⣿⣿⣿⣴⣿⠻⣮⡃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠎⣏⣿⢥⡃⠈⠎⠀⢈⡀⠀⠀⠀⠐⢀⡜⣰⠇⡿⠨⠆⣿⣿⣿⣿⠇⠳⣸⣿⣿⣿⣿⣾⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⣾⡘⠸⢣⠴⡘⠀⠀⠀⠀⠀⠈⣠⣾⢠⡇⡀⠸⣿⣿⣿⣏⣿⢸⡿⢿⣿⠛⠉⠻⣿⣿⣧⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣽⣯⡶⢿⣽⣿⣷⣷⣶⣢⡀⠀⠀⣀⢘⢰⣿⣿⣻⠇⢀⠜⣿⣿⣿⣿⡟⢋⡷⠋⠀⠀⠀⠀⠈⠉⠙⢿⣘⣟⡶
⠀⠀⠀⠀⠀⠀⠀⠞⣿⣿⢳⢸⣯⡝⠻⠟⡿⡿⢟⡇⢗⢳⠈⢺⣿⣿⡗⠁⡨⣀⣾⣿⣿⣿⡾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⡴⢸⠀⣿⣾⢿⣿⣿⠗⠀⠀⠁⠈⠁⠀⠈⠀⠉⢻⣿⣿⡥⠛⠙⠋⠓⢛⠋⠙⠁
⠀⠀⠀⠀⠀⠀⠁⠆⠀⢸⣞⣾⣿⠋⠀⠀⠀⠀⠉⠙⠃⠐⠀⠐⠀⠙⣿⠋⠁⠀⠀⣀⡄
⠀⠀⠀⠀⠀⢣⠀⠀⠀⢸⣹⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠈⢹⡿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⡀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢯⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣦⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡟⠀⠈⣿⡇
⠀⠀⠀⠀⠠⣦⠾⠦⣠⠈⣷⢾⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠁⠒⠒⠦⡦⠤⠤⠆⢀⣀⠀⠀⠀⢀⡿⡇⠀⢸⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠊⠓⢞⡻⠿⣥⡘⣟⣧⠐⠈⣿⣛⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠿⡉⠇⠢⠬⠭⠔⠒⠖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⡜⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀⢠⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣬⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠿⠿⠿⠿⠷⠿⠶⠶⣶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡰⠟⠛⠀⠉⠉⠉⠛⠿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⢆⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠿⢷⡀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⡈⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⢀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡆⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⣤⣸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⡴⠟
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠄⡀⠀⠀⠀⠀⠀⠀⠉⡘⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣜⠠⠁
⠀⠀⠀⢀⢦⡄⢊⣥⣤⣬⠒⠀⠀⠀⠀⠀⠀⠀⠀⢁⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠙⡜⢛⡳⡉⣦⠀⠀⠀⠀⠀⠀⠀⠀⢊⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠳
⠀⠀⠀⠀⢀⢠⣥⠂⠘⣱⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠌⠓⢦⣤⡀⢀⣀⠀⣀⡤⢒⡍⠚
⠀⠀⠀⠐⠂⠀⠙⠻⠿⠚⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⡤⠋⠀⠀⠀⠀⠘⠓⠲⠷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣠⣴⡾⠿⠟⠛⠛⠛⠻⠿⣦⣄⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⢠⣾⢟⣠⣴⠶⠚⠊⠉⠙⠛⠒⢦⣽⡆⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠘⣿⣿⣿⣿⣿⣶⣤⣤⣄⡀⠀⢠⡿⠃⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢻⡀⠀⠀⠀⠈⠻⠿⣿⣿⣿⣿⣿⣷⡶⠞⠋⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢹⣿⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⡾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡛⠛⠿⠿⠿⠿⠟⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠙⢿⡛⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠈⠁⠀⠀⠀⠀⠀⠀⣔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣿⣿⣷⠤⠄⠀⠀⠀⠀⠀⠀⠀⣾⠀⡀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠳⣶⠆⠀⠈⢳⡈⠀⠀⠀⠀⠀⠀⠀⠃⢠⡇⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢹⠋⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⣸⡟⡀⠀⠀⠀⠀⠀⠀⠈⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠼⣷⡿⣯⣤⣤⣤⡤⠴⠊⠀⠀⠀⠀⢢⡄⠻⠅⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠢⠤⠤⠶⠶⠖⠓

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠿⠿⠿⠿⠿⠿⡻⠿⢿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⢿⣿⣿⡛⢻⣿⡟⠿⢿⡿⠿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣟⣛⣿⣻⣿⣿⣶⣶⡆⢀⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶⣶⣶⡯⠡⠏⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⠿⢛⣵⣿⣿⣿⡟⠿⡧⠴⠶⠿⠛⠻⠟⠟⠋⠁⠀⠀⠘⠻⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠉⠿⠟⠿⣿⠀⢿⣾⣿⣿⠉⠀⠠⠤⠀⠠⠄⠀⠀⢀⣶⣿⣷⣤⣶⡄⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣴⣟⣿⣶⡘⣦⣌⠛⢃⣀⢀⣠⣀⣄⣀⣀⠀⠀⠀⠈⠻⢿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⢹⣿⡿⠟⠁⣨⣿⠁⠰⠿⢻⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⢀⡏⠀⠀⠀⣠⣶⣿⢠⡇⢸⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⣰⣾⣷⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢸⡇⣿⡗⣾⣿⢟⣀⣈⣠⣾⣿⣛⣟⡃⠿⣿⠃⠀⠀⠀⠀⠹⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠆⠈⢻⣿⡟⠋⠉⠀⠍⠻⠉⠙⠻⢿⣷⣦⣄⡀⠀⠀⠘⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⡁⢰⢃⣼⡟⠀⠐⠲⠦⠄⠀⠀⠀⢊⠄⣩⡙⠟⠃⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⡷⢸⠿⡃⠀⠘⠀⠀⠀⠤⠀⠀⠀⠀⠀⠈⣡⠃⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣷⣷⡖⠛⢀⠀⠀⠀⠄⡀⠀⠀⠀⠄⠀⠀⠀⠒⠀⠀⠀⣤⣤⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢛⣿⠀⢸⣿⡦⡀⠀⠀⡐⢦⣄⡀⠀⠀⢀⣠⣄⠀⠁⠸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣼⣿⠀⢸⣿⡅⣄⠀⠀⠀⠀⠉⠙⠛⠉⣈⣻⡏⠧⠀⢀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡋⠀⢸⣿⣗⡙⣺⣶⠶⠦⣀⡀⢀⣈⡿⢻⣿⣀⠀⠋⡄⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⢿⣿⢿⣿⣿⣿⣿⣿⢇⡠⠟⠋⣿⣿⣿⣾⣿⢏⠠⡈⡇⡔⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⡟⠾⢿⡧⠿⠟⢽⡿⣿⡿⠛⠙⠙⣷⣾⣿⣿⡷⣾⠀⠫⠐⣢⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⣦⠤⣤⠀⣌⠉⢮⡉⠁⠀⠈⠙⠛⠛⠻⠇⢿⡄⢆⣀⣒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠙⠛⠉⡰⠛⠂⠛⠀⠀⠘⠛⢶⠀⠀⠀⠀⠀⢺⡏⠉⠻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣷⣶⣇⣀⣄⣀⠀⠀⠀⠀⢠⡀⣷⣶⣤⣶⣶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠉⠛⠻⠏⠙⡟⠣⠀⠀⠀⠀⠀⠀⠐

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡟⡍⠀⢸⣿⠋⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣉⣸⡇⠁⢀⣾⣿⣄⠿⣿⣏⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⢻⣽⣟⣴⣿⣿⣿⣿⣶⣻⣯⣟⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⣸⣿⡿⠇⠸⠿⠿⣿⣯⣯⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣯⣾⣽⡇⠐⣦⣀⣁⣴⠊⠈⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢰⣾⣄⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⣿⣇⣀⣈⣻⣿⣁⣀⣸⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣦⠀⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣠⣬⣥⣍⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣶⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣈⣹⣯⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⠿⣟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣟⣛⣿⣿⣿⣟⣛⡛⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡁⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⠛⢻⣿⣿⠿⠿⠿⠿⠀⠰⢤⣿⣿⠿⠿⠿⠿⠿⠿⠿⢿⣿⣿⡿⠿⠟⠒⠀⠀⠠⣤⣄⠀⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣶⣶⣶⣶⣶⣦⣤⣼⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣥⣤⣤⣤⣤⣤⣤⣤⣙⣿⣿⣷⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⡿⣿⣶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣟⢟⡛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡾⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣶⣿⣿⣿⣿⣿⣯⣿⠛⠉⠛⠛⠿⠧⣄⣶⡇
⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⣿⣛⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⡟⠿⣿⣿⡟⠁⠀⠙⢿⡻⣿⣿⣿⣿⠁
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣛⣯⣠⣄⣄⣀⣸⣿⠿⠼⠁⠁
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣾⣷
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⣙⣿⣿⣿⣿⣿⠋⠃
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠉⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠈⣇⣤⣴⣿⠁
⠀⠀⠀⢿⣿⣿⠟⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⢿⣿
⠀⠀⠀⣿⣿⠏⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⢸⣿
⠀⠀⠀⣿⠏⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⣷
⠀⠀⢠⣿⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡅⠀⠐⢿⣄
⠀⠀⠸⣿⡀⠀⠀⠀⠀⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠘⠛⠃
⠀⠀⠀⠸⠿⠂⠀⠀⠀⠀⠙⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠶⢦⣄⡀⢀⣠⣴⠶⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⣠⣤⠶⠟⠛⠉⠉⠉⠉⠛⠳⠶⣤⣄⡀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⣴⠟⣁⣠⣤⡶⠟⠋⠁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠉⠛⠳⢦⣤⣀⡈⢳⣄⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠻⣿⣿⣏⣩⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣹⣿⣿⠏⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠻⣿⣿⣿⣿⠿⠟⠛⠛⠻⠿⢿⣿⣿⡿⠛⠉⠉⠉⠉⠉⠛⠿⣿⣿⠟⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠹⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠘⢿⣟⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠙⢷⣌⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠈⠙⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⡀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⠶⠶⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠶⠖⠛⠛⠋⠁




⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠋⠉⠒⠠⡀⠀⣀⠄⠒⠉⠉⠉⠉⠑⠢⡀
⠀⠀⠀⠀⠀⢀⣀⣀⣀⡔⠁⠀⠀⠀⠀⠀⠀⠘⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠤⠒⠒⠢⢄
⠀⠀⠀⠀⠔⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⢀⡀
⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠄⣀⠀⠀⠀⠀⠀⠠⠤⠤⡀⠀⠀⢀⣀⡀⢀⡀⠤⠤⢼⣠⢚⠉⠙⠒⠲
⠀⠀⠀⢱⡀⠀⠀⠀⠢⢄⠞⠁⠀⠀⠀⠀⠈⠲⢄⠀⠀⠀⠀⠀⠈⠠⡀⠀⠀⠘⠁⠀⠀⠀⠀⠈⢂⠀⠀⠀⡸
⡠⠚⠣⠚⠁⠀⠀⠀⠀⠀⠑⠀⠀⠀⣀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⣠⡄⠀⠀⠀⠀⠃⠀⢠⠃
⢣⠀⠀⠀⠀⢰⣉⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⠀⠀⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⢀⠃
⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⠀⢠⠄⠀⠀⡜
⠀⠈⢧⠀⠀⠀⢠⣤⠴⠒⠳⡀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠘⠐⠒⠒⣟⣀⣠⠼
⠀⠀⠈⢇⠀⠀⠈⡀⠀⠀⠘⣌⠂⠄⠤⠀⠀⡰⠻⡑⠀⠀⠀⠠⠀⢨⡇⠀⠀⠀⠀⠀⠀⠠⠞⠉⢱
⠀⠀⠀⠈⢆⠀⠀⣱⠀⡄⠀⠈⠑⠒⠀⠒⠊⠀⠀⠑⠢⠤⠤⠤⠒⠱⣇⠀⠀⠀⠀⠀⠀⢰⠼⠚⠁
⠀⠀⠀⠀⠈⠶⣉⡤⢶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠤⠜⠁⢠⠤⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠄⠠⠔⢦⡀⠀⠀⠀⣀⠔⠳⣄⠀⠀⠀⣠⡀⠀⣀⠜
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣿⣿⣿⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡆⢰⡆⠀⠀⠀⢠⡜⢳⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣄⣀⡀⠀⠀⠀⣷⡄⠀⠀⠀⠀⢸⠇⢸⠀⠀⠀⠀⠀⠒⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠰⢞⡀⡐⡁⠀⠀⠀⣿⣿⣦⡀⠀⠀⢸⠀⠛⠀⢀⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⣿⡇⠙⢿⣷⣤⣬⣀⣀⣴⣿⣄⡀⢀⣀⣤⣶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃⠀⠀⠈⠙⠛⠛⠋⠁⠙⠛⠿⠛⠛⣿⡟⠀⢠⡤⠤⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠙⢷⣶⠾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠿⢧⣀⢘⡇⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠛⣦⣞⠁⢀⣀⣀⡀⢈⡿⢻⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⢉⣀⣠⡾⠷⠤⢤⣄⣾⣻⢧⡀⠀⢠⡇⠀⠸⣧⣼⠟⣭⠿⠛⠛⠙⣿⡇⠀⢿⣀⡀
⠀⠀⣀⣀⡄⠀⠀⠀⠉⠛⣿⡟⠁⠀⣀⣀⠀⠈⠙⣿⠅⠙⣆⣸⠀⠀⠀⢹⣿⣄⢹⣤⡤⠀⠀⡿⡷⠒⠺⣄
⠀⠀⣽⣀⡡⠀⠀⠀⠀⠀⣿⣿⢴⡾⠛⠛⠳⡄⠀⠘⣷⣀⠈⠛⠀⢰⡄⠀⢻⡉⠉⠉⠀⣀⡼⣡⣿⣤⣤⡟⠛⠛⠓
⠀⠀⠀⠀⠁⠀⠀⠀⣠⣾⣿⣿⣿⡀⠀⠀⠀⣻⠀⠀⣿⣿⣦⡀⠀⡾⢷⣀⣈⣿⠶⠶⠟⠋⣼⠁⠈
⠀⠀⠀⢀⣠⡤⠶⠿⠿⠿⣿⣿⣿⡳⢦⡤⠔⠃⠀⣰⣿⣿⡌⢳⡶⠇⠈⠛⠉⠁⢀⢠⣀⣀⣘⣦⡀⠀⠀⠠⠁⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⠿⢿⣿⣀⣀⣀⣠⣴⣿⡛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠜⠳⡘⢦⡀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠊⢁⡴⠃⠀⠀⠟⠛⠛⠋⠉⠀⠉⢿⡄⠀⠀⣠⠖⠋⠉⠓⠦⡆⠀⠙⠦⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⣷⢀⡾⠁⣠⠖⠛⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡞⠃⠐⠆⠀⠀⠀⠀⢹⡾⠁⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠗⠲⡼⠀⠀⠀⠀⠀⢸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣴⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡗⢂⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡃⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⣾⣿⣷⡀⠒⠦⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣯⣴⣿⠛⠟⠛⠁⠒⠀⢀⠋⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠻⠀⠀⠀⠀⠀⠀⣀⡒⣒⠚⠁⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠠⠤⠤⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣦⣀⣀⣠⡄⠀⠀⠀⠨⣥⡄⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢻⣤⠀⠀⠁⠈⠀⠀⠒⣂⣿⡇⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠂⠀⠀⠀⠀⢦⣹⣃⠀⠀⠀⠀⣠⣴⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⡌⠀⠠⠀⠐⢾⣻⡷⠀⠀⠄⠰⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠰⡄⢀⠀⠀⢙⣷⣄⡀⠄⠀⣹⣿⡇⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠛⠙⢄⠀⠶⠻⣿⣿⡆⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡶⠆⠻⢶⣿⣿⣿⠃⢀⣠⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠨⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⣽⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀
⠀⠀⠀⠀⠀⢀⣀⠀⣀⡀⠀⡀⠈⠉⠛⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⣰⠓⠚⡶⠿⢋⡶⣯⣷⣟⣣
⠒⠒⡾⠿⠿⠻⠿⠻⠿⠻⢟⠳⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣶⣿⡿⡿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣿⣿⣯

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠶⠶⠶⠶⠶⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢚⡭⠶⠤⣀⣀⡤⡴⢯⣕⣆⠀⠈⠙⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠸⡀⣠⣖⣿⣿⣽⡗⠫⣭⣿⣿⣷⣦⡄⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⣴⢻⡿⠛⢍⣻⠺⢿⣿⣴⣿⢿⣦⣧⣿⢢⡀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠈⣇⠘⢧⡀⠀⠙⣿⣏⡼⣓⣼⣧⡿⢷⡯⠠⠃⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠳⠤⣍⣹⠟⠷⢿⡋⠩⠭⠭⠗⢮⡇⠐⠦⣤⣀⡘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠊⠛⠒⠒⠒⠋⠀⢀⡴⠶⡎⠱⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⣰⣫⣭⡳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠘⣦⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⣿⡇⢀⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡧⠀⠀⣤⣶⣞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠈⢧⠠⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠀⠀⢀⣤⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠈⠧⢤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠖⠒⠚⠁⠀⠀⠉⠀⠀⣶⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣤⡀⠀⠀⠀⠒⠒⠶⠶⢾⣿⡆⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠐⢦⡀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠙⢾⡿⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠉⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃





⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⢠⣦⣄⣿⡟⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠈⠛⣿⣿⠇⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠛⢉⣽⣿⣿⣷⠄⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠁⠀⣰⣾⣿⡉⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⡎⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠙⠿⣿⣿⣷⣄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡼⠁⠀⠘⣿⣤⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢀⣾⣋⠀⠀⠀⠀⠀⠀⣀⣨⣍⣿⣧⣀⣀⣀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠻⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠻⠿⠿⠿⠿⣷⣆⠀⠀⠀⢣
⠀⠀⠀⠀⠀⣀⡀⢀⣄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣿⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠻⣿⣿⡟⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⢸⣇⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡐⣬⣷⣵⣿⠏⠀⠀⡇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⣙⣿⠛⠛⠛⠷⠷⠟⠛⠛⠂⠀⠀⢠⣶⠾⠶⠷⠿⠿⠿⣿⣷⣄⠀⠀⠁⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣴⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⣄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣠⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⣻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣄⡀⡀⡄⢀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣦⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⠶⠛⠛⠛⠛⠻⠿⡾⠾⠷⠶⠷⠴⠶⠾⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣶⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⣬⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣤⣤⣶⣶⣶⣴⣤⣀⡀⢀⠀⣀⣠⣠⣀⡀⢀⢀⢀⣀⣤⣤⣀⡀⣀⣠⣠⣤⣤⣶⣴⣾⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠟⠛⠋⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢿⣿⣿⡿⡿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠙⢋⣴⣟⢫⢻⠀⡏⣸⠋⣽⣦⣀⡁⠁⠙⠋⢉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠟⠋⠁⠀⠀⣿⣷⢰⡿⣿⣸⢧⠏⣸⠏⢘⣿⡄⠀⠀⠀⠉⠀⠉⠛⢿⣷⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣋⡁⣠⡶⠿⠛⠁⠀⠀⠀⠄⠀⣿⣿⣾⢳⣷⣿⠟⣴⠋⣴⠟⣽⣿⠂⠀⠀⠀⢄⡀⠀⠀⠚⠛⠷⣦⠐⣉⣻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡿⠛⠛⣿⠟⠄⠀⠀⢄⠁⠀⠀⢀⣿⣿⣿⣿⡿⣫⡞⣱⢞⣥⣼⡿⢿⣄⠀⠀⠀⠀⠀⠲⠄⠀⠀⠞⢯⡟⠛⠻⢿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠏⠀⣀⣈⢈⣀⣀⣀⣀⣀⡑⠲⣶⣾⣟⠿⣽⣿⣿⣿⣿⣡⠾⣛⣽⣶⣾⡟⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢸⣦⢀⠘⠿⣿⣿⣿⣿
⣿⣿⣿⣍⢀⣴⡟⠀⠀⠀⡀⠀⠀⠈⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠷⣾⣷⠀⣶⣿⣦⣄⠀⠀⠀⠑⠀⠀⠀⠀⠈⣷⡄⢈⣽⣿⣿
⣿⣿⠏⠊⡍⠋⠉⠀⠠⠂⠀⠀⠀⠀⠀⠀⠋⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡏⠀⣠⡿⠸⣿⣿⣶⣄⡀⠀⠀⠀⠢⠀⠈⠉⠫⡈⠋⢿⣿
⠿⢿⣤⣾⡀⣀⡀⠊⠀⠰⣤⣴⣄⠴⣵⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡿⠉⠀⠀⣿⡇⢰⣿⣯⣙⡿⣿⣦⡀⠀⠀⠈⢂⣀⡀⣸⣦⣼⠿
⠐⠉⠉⠉⠚⠛⠑⠀⠀⠀⢸⠿⠏⠀⠀⠀⢈⢻⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣾⡇⢀⣤⣿⣿⢁⣾⣿⣛⣿⣷⣶⣽⣿⣶⣄⠀⠀⠉⠛⠋⠉⠉⠰
⡀⠄⠀⠀⠀⠀⠀⠀⠀⣠⡾⠆⢀⣠⣶⣾⣿⣇⢿⡿⠿⢿⣿⣿⣿⣷⣿⣿⣟⠀⠀⣿⣿⠟⣾⣿⣿⡿⠛⠁⠀⠈⠉⣿⣼⣷⣤⡀
⠀⠉⠒⠠⠀⠀⣀⣴⣟⣯⣶⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣾⣿⣿⣿⣿⣻⣿⣤⣀⣿⠇⣠⣾⣿⣇⣀⣀⡦⣶⣶⣧⣿⣿⢛⣙⢻⣄⠀⠐⠚⠁
⠀⠀⠀⢀⣴⣾⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣻⢿⣿⣿⣿⣿⢟⣉⣨⣿⡄
⠀⠰⢾⣻⣉⣁⣀⡀⡀⠀⠀⠀⣿⣁⣀⡀⠉⠙⠋⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣷⣿⣿⣿⣿⣿⣧⣼⡿⠋⣙⡇⠀⠐
⠀⢰⠌⣉⣥⣤⣤⠼⣤⠤⠀⢀⠹⢿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢿⣻⣿⡟⢘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣿⠟⣿⣿⣿⣧
⠀⠘⣷⣬⣼⣶⠿⢿⣿⣿⣯⣠⣴⡖⠉⠉⢸⣷⡀⠀⠀⢀⣠⣾⣿⣿⡃⢺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣥⡾⣯⣶⣿⣿⣿⣿⣬⣦⣀
⠀⣨⡿⣽⣿⣁⣀⣀⣾⣟⣃⣼⣿⡇⠀⠀⠀⢿⢷⡀⠰⣟⣿⣿⣿⣿⢃⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣡⣶⣾⣿⣿⣿⣿⡿⣿⣿⣿⠿⠟
⠀⠹⣿⣓⣛⣚⣛⣛⣛⣚⣓⣳⣷⣶⠀⠀⠀⠈⠃⠁⠀⠀⠉⠉⣡⡿⣯⣯⣝⣿⣿⠀⠀⠀⠈⠹⣿⣿⣿⣿⡿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠺⠿⠿⠋⠀⠀⠀⠀⠀⠈⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣶⣄⡀
⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠖⠒⠒⣦⣀⠀⢀⡖⠉⠉⠉⠙⢿⡻⣦⡀
⠀⠀⠀⠀⡴⠋⣠⠴⠒⠒⠒⠒⠶⢤⣄⠀⠀⠀⠀⠀⠀⢀⠇⠈⠉⠉⠀⠀⠀⠀⠀⠀⡹⣆⠻⡟⢾⡛⠙⠛⠓⢦⣀⡀
⠀⠀⠀⡼⣡⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣽⣆⠹⡄⠹⡄⠀⠀⠀⣏⠙⠳⢦⡀
⠀⠀⢸⣷⠷⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⢳⠀⠀⠀⠀⠀⢻⠀⠀⠀⠹⣦
⠀⠀⣿⠃⠀⠀⣿⣾⣿⣿⣿⣦⡀⠀⠀⠀⠀⢀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢻⣇⠸⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠈⠳⣄
⠀⢸⠙⢄⣀⣴⣿⣿⣿⣿⣿⣿⣷⠀⠀⠱⡃⠆⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠶⣶⠏⠀⠘⣿⠀⠀⡄⠀⠀⠀⠀⢰⠀⠀⠀⢀⠀⢹⢷⡀
⠀⡎⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⣸⠁⠠⠀⠀⢀⣎⠀⠀⠀⠀⢳⠘⠀⢻⡀
⠀⣧⠀⠀⠀⣿⣿⣿⣿⣿⡿⢿⣿⠀⠀⠀⠀⠀⡄⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⢰⡏⢠⣧⠤⠤⣤⠞⠉⠉⠳⣤⠤⠀⢸⠀⠃⠈⡇
⠀⢸⡀⠀⠀⠹⣿⣿⣿⣿⣧⣾⢃⣄⣄⡀⢀⡄⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⣼⣡⠟⠁⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢸⠀⠀⠀⡇
⠀⠈⢷⡀⠀⠀⡈⠛⠿⠟⠋⠁⠉⣿⠿⢣⣾⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⢸⠀⢀⢠⡇
⠀⠀⠘⣷⢄⡪⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⡞⠠⠃⡾
⠀⠀⠀⠈⢷⡍⠒⠦⠤⠤⠴⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡠⠊⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠈⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠈⣠⡴⠋⢀⣤⠤⢤⣄⡀⠀⠀⠀⠀⣀⣠⡤⠚⠀⠀⢀⣠⠞
⠀⠁⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠑⠠⠀⠀⠀⠠⢀⠤⠷⠤⠒⠤⣀⣀⣤⠾⠋⢀⡔⠉⠀⡀⠀⠀⠉⠙⠛⠿⠭⠭⠀⠀⠠⣊⡵⠛⠁
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⢤⣤⣀⣀⣀⣀⣠⣤⡴⠶⠛⠉⠀⠀⠀⡞⠀⣠⠿⠶⠦⢤⣔⣂⣀⡠⠤⠴⠶⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣙⠲⢤⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣔⣒⣀⠒⠶⠶⠶⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣺⣽⠟⢉⣩⣤⣤⣤⣤⣤⣬⣿⣒⠂⠀⠀⠀⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠟⠯⠛⠁⠢⢴⡿⠟⠙⣓⡚⢓⠛⡛⠳⠮⢤⣀⣄⡐⠻⡢⣄
⠀⠀⠀⠀⠀⠀⠀⢀⢔⡵⡫⠂⣰⡆⢴⣆⣤⣤⣈⠛⠿⢛⠉⠁⢀⣅⢀⡀⠀⠈⠙⠻⣦⣌⠐⠕⢄
⠀⠀⠀⠀⠀⠀⣠⣿⢿⠏⠠⣺⠟⣡⠀⠸⠟⠉⣤⢶⣳⣬⡛⢿⠿⣶⣦⣬⣉⠒⢦⡀⠈⠻⣷⣄⠲⡡⢀
⠀⠀⠀⠀⠀⣰⣳⠋⠁⢀⡼⢁⠞⡱⠃⡨⢤⣼⡾⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⣙⢾⡀⡈⢿⣷⣔⡹⣷⡀
⠀⠀⠀⠀⢰⢳⡏⢀⢠⡿⢠⢃⠠⠀⠐⣁⡈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢴⣄⢩⣍⡈⠛⠻⠎⢻⢳⡀
⠀⠀⠀⠀⣿⢿⠇⠆⡟⠁⠋⢁⡄⡸⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠞⣆⢻⡟⣦⣶⠀⠈⣏⣧
⠀⠀⠀⠀⣿⡞⢠⠁⠀⠁⠠⣿⢣⠃⣿⡇⣀⡤⡄⠀⠀⠀⠀⡠⣄⣀⣀⣃⡀⠄⠀⠀⢸⡘⡈⠗⢇⡀⣴⢻⢸⣿⡀
⠀⠀⠀⣶⣿⡇⡀⢸⣠⡆⣄⣈⠘⢢⠟⠋⠁⢀⠇⠀⠀⠀⡜⠀⢿⣿⣶⠏⡘⠀⠀⠀⠈⠓⠐⣿⢹⠆⣿⠸⢸⣿⡇
⠀⠀⠀⣿⣿⡇⣷⠈⢿⡇⡇⢻⠞⠁⠀⠀⢀⠎⠀⠀⠀⠀⣇⠀⠀⠀⣠⠜⡤⠊⠙⠀⡘⢠⠰⣿⠈⡄⡿⢀⢹⣿⡇
⠀⠀⠀⢻⢿⠀⢸⣇⠸⣟⢰⣸⡄⠀⠀⠀⢇⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⣜⣠⣄⡸⡰⢃⠃⣦⠁⠘⠄⠁⡈⣸⣻⠃
⠀⠀⠀⠸⣾⡇⠈⢏⡆⢿⣖⠗⣷⡀⠀⠀⠈⠷⢄⠀⠀⠶⠮⣥⣦⠀⠀⠈⠉⣩⡞⠁⢃⣼⣿⠃⠈⠀⢠⢡⠇⡿
⠀⠀⠀⠀⢿⣿⣆⠘⣺⡜⢿⢆⠻⡷⠀⠀⠀⠀⠀⠉⠒⠦⠤⢤⡤⠤⠤⢶⠻⠗⢀⡀⠾⠙⠁⠞⠀⠐⣿⠏⡼⠃
⠀⠀⠀⠀⠈⢻⣎⢆⠱⡹⣎⠻⣧⣿⠀⠀⠀⠀⠀⠀⢀⡠⠤⢶⡲⢤⣴⣋⣤⠴⣪⡵⡣⢦⠄⠀⠀⠠⢊⡾⠁
⠀⠀⠀⠀⠀⠀⠛⢯⣧⡙⢿⢧⡈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡤⣤⣤⠴⠾⣋⠤⠖⢁⠔⡹⢋⡴⡫⠂
⠀⠀⠀⠀⠀⠀⠀⠪⡻⣟⠎⠳⣝⡻⡆⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠷⠾⠋⣀⠤⣚⡵⢊⠕⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡷⣤⡀⠙⢳⠀⠀⠀⠀⢸⠍⢉⣳⣄⣀⣴⣛⡤⢄⣠⣶⠟⢉⣪⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⡻⣶⣧⠀⠀⠀⠈⣗⣒⡲⠞⠒⠒⢒⣉⣉⣥⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢷⡀⠀⠀⢸⣽⡿⠿⠟⠛⠛⠛⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣵⣄⡀⠀⢀⣥⣤⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠋⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠛⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⠀⢀⣀⣤⣴⣶⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⢷⣶⣤⣄⣀⠀⠀⠈⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣰⡿⢃⣠⣴⣾⣟⣛⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣙⣻⣿⣶⣤⣀⠻⣷⡀
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠷⣶⣶⣶⣶⣶⣶⣶⡶⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⡄
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣿⡟
⠀⠀⠀⠀⠀⠀⠹⣿⡄⠉⠙⠛⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠛⠉⠁⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⢀⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣶⣶⣶⣶⣶⡾⠿⠛⠉

⠀⠈⠇⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠐⠀⠀⠀⠸⣿⣿⣿⣿⣏⠐⢀⡁⢀⠀⠀⠀⠄⠠⠘⠛⣛⠘⢸⡟⠀⢹⣷⣷⠘⢡⡆⣶⢤⠀⢀⣴⠗⡀⢤⣿⣷⢡⣶⢿⣿
⠀⠀⠓⠀⠀⢁⠼⣲⢛⣾⡤⣀⠠⡶⠀⢀⡀⢠⣿⣿⣿⣿⢧⣗⣦⡴⢫⣄⠀⠀⠀⠈⢲⡿⣟⣀⠼⣧⡄⣸⣿⣿⡿⢦⡅⣀⣿⢷⣶⣴⣶⣿⡟⣿⣿⣿⣷⣿⣿
⠀⠀⠒⢂⣤⣭⣼⣻⠟⠿⠽⢉⠤⣄⠀⠈⠛⠀⠉⣿⣿⣿⣾⣿⣧⣷⣧⣾⣷⡄⢀⣴⣬⠁⠟⣃⡂⣟⠄⢿⣿⣏⣴⡾⣿⣿⣽⣿⣿⣿⣻⣾⡇⢀⢀⣤⣿⣿⣿
⠀⠀⠈⠀⠻⠹⡛⢯⣖⠀⢀⠀⠤⢾⠄⠐⠃⢀⡜⠉⢿⣿⣿⣾⢿⣿⣿⡿⣿⣿⡾⣿⣿⡀⠚⣀⠀⢹⡏⣿⡿⡏⣄⣠⣷⡯⣷⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⢀⠀⠠⠇⢁⠂⣝⠂⣴⣆⡀⠠⣦⠐⠶⠋⠀⢀⢻⣿⣿⣟⣸⣷⣿⣿⣿⡝⠿⠻⢿⠇⣠⣿⣀⣼⢇⣷⣿⣿⣿⡿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠁⠰⠀⠐⣿⠛⣿⣿⠗⠱⠁⠂⠠⠀⣚⢹⣿⣿⣿⠻⠿⣷⣿⣿⣿⡒⠈⡤⠃⠀⣏⡿⣿⠺⡇⣿⢸⣿⡿⢋⡚⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠙⠋⠻
⠀⠀⠀⣫⡀⠔⠺⡆⠹⡶⠋⢉⡀⠉⡈⠀⠀⣤⢠⣴⡁⠈⠙⠆⠀⠙⠛⢿⠟⠁⠀⠓⠶⠀⢸⣿⣿⢁⠿⣾⣼⣿⣶⣞⣐⢦⣾⣿⠿⣯⡿⣿⣿⠿⣿⣤⠜⠛⠛
⠀⠀⢠⡟⠣⠄⢀⠁⠀⠄⠀⠀⠐⢶⠃⠀⡠⣈⡀⠈⠁⠀⠀⠤⢃⠀⢀⠀⠁⠚⠀⠃⡀⠀⠘⡇⣿⠸⠂⢾⣿⣿⣭⣿⠃⠐⠿⠿⠷⣯⣤⣼⠛⢿⠞⠹⠆⠐⢆
⠀⠀⠸⡇⠀⠱⠂⠀⠄⠀⠀⠀⠀⢠⠄⠀⠀⠈⠙⢡⣤⣤⣄⠥⠈⠁⠀⠀⠀⠀⢠⡄⠀⡀⠀⠀⠈⠀⠀⠈⠙⠘⠉⠀⠀⠉⢠⡟⢰⣼⡍⠀⠰⣄⠠⠆⠀⠀⠈
⠀⠀⠀⠹⠀⢀⠀⢬⡀⠀⠀⠀⠀⠀⠀⠰⠀⣀⠀⠈⠀⠁⠀⠀⠈⠀⠀⠀⠀⠙⢀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠠⣀⠀⠀⠈⢧⡁
⠀⠀⠀⠀⠠⠘⠁⠀⠁⠀⠀⠀⠀⠤⠐⠃⠈⠁⠐⠂⠀⠀⠛⢆⠀⠀⠀⠀⠀⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠀⠀⠶⠀⠀⠆
⠀⠀⠈⠀⠀⠀⠀⠊⢀⣘⢟⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⣀⡀⠐⣀⠀⠀⠀⠀⠢⣀⣠⡈⣤
⠀⡀⠀⠀⠀⠀⠀⠀⠂⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠔⣶⠘⣿⣅⡾⠏⣁⠀⢠⣾⣷⣾⣿⣤⠹⢤⠀⢀⠄⠐⠀⠄
⢠⡇⠀⠶⠀⢀⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠵⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢿⣿⣿⣿⣤⣟⣿⣿⣯⣿⣿⣿⠷⣦⣾⣾⣿⡯⣖
⠀⠃⡀⣿⠀⠉⠀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⢀⠘⣻⣯⣯⣿⣹⣯⠙⣿⡟⢹⢃⣿⣿⣿⣿⣯⣿⡴⠇
⠀⠀⣡⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⣄⢫⣿⢩⣿⡦⣿⡆⣰⠿⣿⣿⣻⣿⣏⣿⠁
⠠⣀⢿⣯⡛⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⡏⣯⡛⣶⡇⠱⡛⠁⠉⣰⣿⣿⣿⣿⡟⠈

⠦⡜⢲⠀⠀⠀⢀⡀⠀⠀⠠⡄⠈⠣⡀⠘⡄⠈⠀⠓⠊⠁⡀⠠⠀⠀⠠⡀⣀⠀⠀⣼⢗⠞⢕⠟⠁⠹⣼⠀⢁⣀⢧
⠀⠁⠀⠐⢂⣀⠀⠀⠀⠰⠆⠀⠀⡀⠈⠢⡘⠀⠀⠀⠖⢨⠅⠖⠈⠁⠠⡄⠰⠶⠸⢈⣇⡸⡘⠀⠀⠁⠀⡄⠀⠁⠠
⠀⠈⢿⣿⣿⣿⠁⠀⠀⠀⠄⠁⠀⠐⠃⠀⠈⠻⠆⠀⠁⠄⠐⠀⠀⠀⠀⠁⠀⠀⠀⠙⠖⠊⠃⠀⠀⣄⡤⢀⡁⠀⡄
⠀⠀⠀⢿⣿⠃⠀⢀⣧⠀⠀⠀⢀⠠⠀⠀⠐⣀⠀⠀⠁⠀⠀⠀⢴⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⣸⢋⡉⢛⣓⣓⠿
⠀⠀⢴⡎⠁⠀⠀⠘⠋⣀⣀⣀⣀⣀⡀⠃⠀⡄⠀⠀⠀⠀⠸⢄⠀⠐⠃⠀⠤⠀⣶⠄⢬⠿⢆⡹⠧⠿⠧⣬⣩⡕⠿
⠎⠀⠀⣔⢕⣚⠶⡀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢀⠴⠚⢡⡆⢰⡇⢠⡀⠀⠀⠀⠐⠛⠀⠀⠀⠛⢋⠈⠛
⠀⠄⠀⢋⢜⠈⡎⡆⠘⣿⣿⣿⣿⣿⡇⠨⠂⠉⣁⡂⠀⠀⢠⠄⠀⢠⡆⢀⠈⢁⠘⠃⠀⠀⠁⠀⠰⠆⠈⠱⠓⣴⡔
⢀⡂⠛⢀⢋⠸⠳⡁⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠀⠀⠀⠰⡇⠈⠁⢺⠇⠙⠀⣤⠀⠀⢀⠀⣠⡀⠀⠀⠀⠁
⠘⢌⣭⠫⡆⣤⠞⠘⠀⠋⠉⠉⠙⠋⣁⠀⠀⢄⡄⠀⠀⠀⠀⠀⠀⠸⠀⡄⠀⣶⠀⠛⠀⣀⠀⠀⠈⣥⠀⠀⢂⠀⠳
⠀⠀⠁⠀⠈⢀⠀⢠⣆⡃⢠⡄⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⡀⣠⢠⠄⠀⠁⠀⠀⠀⡤⠐⠀⠆⠀⠀⠀⠀⠀⠈⠐⠂
⠀⠀⠀⢰⣆⣠⣶⣿⣿⣿⣿⣿⣾⣥⠆⠀⠀⣶⠄⠀⠀⠤⠯⠑⡖⢙⡖⠀⠀⢀⠀⠀⡀⠈⠌⠠
⠀⠀⠔⠀⣹⣿⣿⣿⣷⡿⣿⣿⣿⣿⢀⡁⠀⠘⠀⠀⠐⠑⡎⣹⣉⠍⠅⢠⣦⠀⠀⠀⠀⠀⠀⠰⠂⢱⠄⡀
⠀⠀⠀⠰⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠾⠃⠀⠀⠀⠀⠀⠈⠨⠁⠘⠀⢀⡀⣀⡀⠠⠆⠘⢄⠐⠀⠀⠘⠒⢉⡁⠄⡀
⡀⠀⠀⣀⠀⠈⠛⠿⠿⠿⠿⠿⠛⠀⠀⣤⡀⣤⠶⣆⠀⠀⠂⠀⢀⡮⠳⠔⠛⠺⠀⠀⠀⢀⠀⠀⣀⠀⢨⠰⠈⠁
⠀⠀⠄⠉⠀⠀⠰⠀⠀⠀⡄⠀⡆⠀⠸⡯⣚⣇⣸⢮⢞⣠⣆⠀⢀⢸⢧⢢⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⡀
⠀⠀⢻⣿⣿⡿⠀⢀⡀⠀⢀⠀⠀⠀⠶⠀⠛⡘⠓⠀⠈⠓⠀⠀⠈⢗⢆⡩⡆⢀⡀⠀⠁⠀⠒⠀⡀⠀⠀⠀⢠⡀⠡
⠂⠀⠀⢻⡿⠙⠛⠟⠀⠀⠸⢷⣄⠀⠀⠙⠏⠁⠀⠛⠀⠀⠀⠀⠛⠈⠈⠉⠠⣿⡿⣠⣾⡧⠀⠀⡀⠀⠀⠀⠄⠃⠐
⢰⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⡀⠀⠀⢀⡀⠀⠠⠆⠀⠜⠃⠀⣠⣄⢟⣽⣿⣧⠀⣤⠈⠁⠂⠐⡀
⡿⠧⠠⠠⠸⠂⠀⠀⠀⠀⠀⠀⠀⡌⢡⡀⠀⠀⢈⠁⠠⠁⠜⠂⢤⠀⡄⢿⢿⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⡂⢐⡀⠀⠀⢀⠀⠀⠦⠀⠀⠶⠂⠀⠆⠰⠈⠀⠁⠠⠁⠀⠀⠀⠀⡠⠁⠈⠿⣿⣭⡄⠀⢠⡄
⣁⡽⢼⣠⠀⠛⠃⠰⠀⠄⠀⠀⠒⠀⢈⢃⠚⠀⢠⡀⠄⠀⠠⠁⡠⢁⠠⠀⠀⡠⢉⠀⠀⠈⡃⠀⢀⠀⢀⠀⢠⠀⡳
⡼⢤⠼⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠔⠁⠀⡘⢃⠀⡷⠀⣀⢀⡀⠀⠈⠏⠀⠀⠐⠈⠀⡴⠾⠍⡻⢏⢩⡢⠀⣀⡍⢨
⠀⠁⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⡟⡿⣿⣿⣿⡟⣰⣶⣶⣶⣶⣿⣬⣭⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣽⢦⣶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠙⠻⣿⣿⣟⣣⣍⣡⣽⡇⣿⣹⣩⢹⣿⣿⣿⣟⠿⢧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢣⠹⡄⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠟⠟⠻⠟⠛⠛⠿⠿⠟⣾⠿⠿⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣷⡀⠳⡱⡜⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣾⣿⣿⣿⣶⡟⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⡿⠋⠁⠈⠋⠀⠀⠀⢀⡜⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣾⡿⠋⠀⠀⠀⠀⢀⠀⠀⠀⠱⠶⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠫⣽⢰⠂⠈⠀⠐⠒⠛⠉⠛⠶⡶⠦⠤⢤⠤⠤⣴⠶⠶⢾⠻⠇⠀⠀⠀⠀⠀⠀⠀⢠⡾⢧⣄⡀⠀⣀⠀⠋⠙⡄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠱⠙⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠙⠲⢟⢠⣀⢠⡇
⠀⠀⠀⠀⠀⠀⢀⣿⣿⡗⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠉⠋⠉
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣧⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⠙⠀⠀⠀⠰⢀⣿⣧⣴⠀⡐⠆⣠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠹⣾⡮⡤⠀⠀⠂⣺⣿⢿⣾⣾⣿⣼⣧⡀⠀⡀⠀⠁⠀⠀⠀⠸⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⢸⣇⠀⠘⣯⣧⡀⠀⠀⣿⣟⡂⠀⠀⠉⠉⠀⠂⠀⠁⠀⠀⠀⢀⣿⢸⠇⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⣸⠙⡇⠀⢹⣿⣷⠀⢠⢻⠉⠙⠻⠶⠮⣤⣤⣤⠤⠶⠶⠶⠶⠶⢿⡄⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⣿⢀⡇⠀⣸⡇⠀⠀⣡⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⡀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⢻⣾⡇⢀⡿⠉⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠊⠀⡿
⠀⠀⠀⠀⠀⠀⠈⢻⠁⣼⠇⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠁⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣇⠀⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣆⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣿⡀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢠⠘⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡜⣇⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣾⣶⡇⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠽⣷⣚⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⣬⡷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠈⠉⠓⠲⠶⠖⠚⠋⠁⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⣠⡄⠀⠱⠦⢄⡀⠀⠀⠀⣀⣠⣴⠂⠰⠶⢀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⣠⡔⠈⠀⠁⠀⢠⡀⠀⠀⠀⠙⠁⠀⠀⠀⠳⠈⠀⢢⠑⢦⡀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⣴⣿⣿⣶⣾⣀⣀⣨⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣨⣷⣶⣿⣄⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⣴⣿⣿⣿⠿⠟⠛⠻⠿⠿⢿⣷⣶⣶⣿⣿⣷⣶⣿⣿⡿⠿⠿⠿⢿⣿⣿⣷⠄⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠘⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢹⡿⠃⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢨⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⡀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠉⠉



⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⣰⣾⣷⣤⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⣿⠟⠙⠿⠁⠁⠈⠈⠁⠉⠙⢻⡿⣖⢤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠿⠿⠿⣿⣿⡆⠻⠀⠀⠰⣶⢤⣤⡤⠶⠄⠁⣿⢸⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⣀⠀⢰⣿⣿⠃⠀⠀⡀⠀⠂⠀⠀⠀⠂⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠈⠁⠀⢠⠟⢻⡆⠀⠀⣡⠐⠀⠀⠀⠀⠀⠋⠁⣸⣿⣿⠿⠿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢹⠀⠀⠀⢀⠀⠈⢻⡄⠀⠉⠀⢎⡽⣭⣌⠀⢸⣦⡿⠛⠀⠀⠀⠈⠉⠻⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣇⡈⠸⠀⡆⢸⠁⠀⠀⠙⣶⣾⡓⠸⠀⣉⠻⠀⣾⠉⠀⠀⠀⢰⡆⢫⣀⠀⠀⢻⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠟⠃⢠⡾⠁⢼⡀⠀⠀⠀⠈⢿⣷⣦⣀⣾⣤⣼⠏⠀⠀⠀⠀⢸⡇⠀⠻⣦⡀⠀⢻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠟⠁⢀⣼⣿⡄⠀⠀⠀⠀⠙⠿⣿⣿⡿⠃⠀⠀⠀⠀⠀⣿⣿⣧⡀⠀⠙⠀⠀⠻⣾⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡄⠀⠀⢀⣿⣿⣿⣿⣶⣦⡐⠲⢤⡶⠿⠿⠷⠀⠀⣀⣤⣴⣾⣿⣿⣿⢿⣶⡄⠀⠀⠀⢸⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠟⡟⠂⠀⢠⣾⢿⣿⣿⣿⣮⡉⠁⠀⠀⠀⣠⡀⠀⠀⠀⠈⠻⢛⣿⣿⣿⣿⠀⠙⢿⣆⠒⠀⠀⠙⢿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⠀⠀⠀⠸⠇⠀⣿⣿⣿⠉⠛⠒⠀⠀⠚⣭⡛⠓⠂⠀⠐⠚⣻⣿⣿⣿⠇⠀⠀⠀⠻⣧⡀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⣴⠀⠀⢹⣿⣿⣷⠈⠂⠀⠀⠘⣿⠛⠗⠀⠀⠶⢶⣿⣿⣿⡟⠀⠀⠀⠀⠀⠙⣿⠀⠀⠀⣷⢹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⢰⣯⠀⠀⢨⣿⣿⣿⣶⠆⠐⠲⠶⠾⡿⠦⠀⠀⣀⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠛⠈⣿⣿⣄
⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆⠀⠀⠀⢹⣇⣠⣼⣿⣿⣿⣿⣿⣷⣤⣶⣴⣾⣦⣤⣦⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⣿⠆⡀⠀⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⡀⢠⡀⠀⢽⣿⠋⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢹⡇⣇⠀⠹⣦⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⢄⣙⠀⠘⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⢸⡇⠸⠀⠀⢻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣶⠌⠣⠀⠈⢣⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠛⠿⠿⠿⠿⣿⣿⣦⠀⠘⣿⠀⠀⠀⠈⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⣿⣿⣅⠀⠀⠀⠀⣼⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠈⣻⣿⣧⠀⣿⡇⣤⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠟⢀⡿⣏⣿⡦⠀⠀⢼⣾⣏⠉⠀⠀⠀⠀⠉⠁⠀⠈⠙⠻⠿⣿⣿⣷⣷⠀⠀⠀⢀⣽⣿⣿⣧⣿⠓⣏⠇⢀⣄⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣾⣿⣿⣇⠀⠀⠉⢿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⣿⣄⣤⣴⣾⣿⣿⣿⣿⠏⠀⠙⣦⡈⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠈⣿⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠘⠢⠀⠀⠙⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⡀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⡀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⡴⢂⣤⠘⣽⣿⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⣰⣇⣴⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠮⠶⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⡠⢦⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠙⠛⠛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⢩⣷⠋⠀⠀⠉⠀⠀⢀⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⠁⠀⢀⡀⢤⠰⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠈⠁




⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣁⣀⣀⣀⡀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⢀
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠠⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠒⠦⠾⠴⠒⠒⠂⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠠⠖⢀⣀⠀⠀⠀⠀⠀⠀⠐⠶⠶⣄⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠂⠀⠁⠢⡘⡉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠁⠀⠀⠀⡔⠁⠀⢀⠐⠠⡐⡉⠢⡀⠀⠀⠳⠤⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠨⠤⡢⠄⠀⠀⠀⠉⣦⠤⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⢀⠀⠀⠀⠀⠸⠤⣔⡔⠀⠒⠀⠈⢢⣄⣱⣤⡄⠀⠀⣀⠇⠄
⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⡄⠀⡀⠀⠀⡀⠀⡁⠈⠊⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢁⠤⢺⣧⡀⠀⠒⣠⣀⠀⠀⠀⣀⠋⠀⠛⢡⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠈⠅⠀⠛⠚⠱⠁⡀⠓⠚⠁⠀⡸⠡⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡊⠉⢠⠁⠀⠘⠿⠛⠞⠀⠻⠿⠃⠀⠠⢋⣀⣌⡀
⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠘⠋⠉⠀⠀⠀⠈⢀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡄⠀⠙⢷⣶⡄⡒⠃⠀⠀⠀⠔⠁⡀⢩⠡⣈⠆
⠀⠀⠀⠀⠀⠀⠸⣀⠀⢀⢤⡿⡐⣂⡐⢀⡽⢢⠄⠚⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⣅⠂⢀⢤⡺⡉⢃⡀⠂⡸⣢⡀⠐⠁⣼⠀⠉⠑
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠮⣑⣭⣭⣭⡭⡭⡕⠣⣊⠥⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣔⠮⣳⠯⠭⠭⢭⣭⣭⢝⡻⣆⠐⠸
⠀⠀⠀⠃⣀⠀⠀⢰⡢⡽⢽⣒⣒⣒⣒⣒⣲⣔⢭⡒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣢⡝⢐⡓⣓⣒⢛⣿⣟⡌⢒⡭⣆
⠀⠀⠀⠀⠀⠀⡄⠈⠙⠀⡒⠖⠒⠒⠒⠒⠖⡈⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠉⠀⠘⡶⠶⠒⠲⠶⠞⠂⠀⠛⠉⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⠆⠀⣢⢃⣸⣷⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⢨⠇⠈⠭⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠐⠀⠘⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠀⠙⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠐⠀⠃⠊⠛⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠈⠃⠀⠀⠁

⡠⡀⠀⠀⢪⠑⢆
⠡⠘⢄⠀⠈⡆⠈⢧
⠀⠣⡈⠢⡀⣧⠀⠀⢧
⠀⠀⠑⣄⠈⢻⡐⠀⡘⡆
⠀⠀⠀⠈⠑⢄⢧⠀⠁⢱⡴⠤⢄⣀
⠀⠀⠀⠀⠀⠈⡮⠦⡀⠀⠇⠉⠒⠤⣑⠂⠤⣀
⠀⠀⠀⠀⡨⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢥⣀⠀⠀⠠⣄
⠀⠀⠀⡘⢜⢡⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠲⣦⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⣀
⠀⠀⢠⠇⠘⠉⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⣀⣀⣠⣤⡴⠋⠀⠀⠀⠀⠉⠳⣄⡀
⠀⠀⣼⢀⡀⠠⣤⢤⠀⠀⢀⡜⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⢠⡇⠀⠈⠑⠏⠀⣠⠖⠉⠀⠀⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⣇
⠀⠈⣆⢮⠁⠸⠴⠋⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⢃
⠀⠀⠘⢦⣃⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡿⢸
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆⠀⠀⠀⠀⠀⠀⡼⠁⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡓⢴⡄⠀⢰⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠹⣄⠀⠀⠀⠀⢸⠃⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⣷⠀⠀⡏⠓⠦⣤⣄⣀⣀⣀⣤⡴⠞⠹⡄⠀⢰⠙⣦⠀⠀⠀⠸⡄⠀⠀⡏⠑⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣿⠀⠀⣷⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠙⡄⠘⡆⠈⠛⠦⣄⠀⠉⢳⡄⢧⢀⠀⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠉⠧⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠇⠀⠀⠀⠈⢧⢀⠞⠀⠈⢧⣃⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⢱⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⡎⠀⠀⠀⠀⠀⡼⢸⠀⠀⠀⠀⠉⠛⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⣆⡸⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⡴⠃⠀⠀⠀⠀⢀⠇⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠓⣴⡋⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠉⡇⠀⠀⠀⠀⢀⠛⠤⠖⢫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢏⣀⣠⠞⠀⠈⠉⢹⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠳⠤⠤⠖⠋
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⣶⣶⣶⣶⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣋⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢹⠤⠒⠒⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠲⠦⢤⣤⠿⠤⡤⢤⡀⣿⠔⠒⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠙⠛⠁⠀⣸⠃⡿⠀⠀⠀⢿⡤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠠⣄⠀⠀⢀⣀⣤⠾⠃⢰⡇⠀⠀⠀⡟⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠈⢹⣿⣿⠏⠀⠀⠀⣼⠁⠀⠀⢸⠇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢀⡰⠞⠛⠻⣿⣄⣀⠀⢶⡿⠀⠀⠀⡿⠀⠀⠀⠀⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⠉⠀⠀⠀⠀⠈⠙⠻⣿⣿⣏⢀⣀⣀⣧⢀⠀⠀⣼⡏⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣭⡿⠿⠦⠿⠿⠋⠉⢡⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠀⠀⠀⠀⠀⢀⣠⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⣤⣀⣀⣀⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣋⠉⠀⠀⠀⠀⠀⠀⢁⣀⣀⣈⣙⣻⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣹⠅⠉⠡⣀⡠⠤⠀⠉⠭⢍⣉⠙⠿⠿⢿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠂⠛⠋⠉⠉⢁⣀⣀⡀⢀⣤⣄⡄⢠⣤⢀⣤⣀⣀⣀⡀⠉⠉⠙⠛⠑⢲⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠀⠀⠀⠀⠀⠺⣿⣙⠃⢻⡇⣿⡇⢨⣧⢸⡿⢶⣿⠘⢩⣿⠹⢻⡷⠀⠀⠀⠀⠀⠉⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣡⠀⠀⠀⠀⠀⠀⡿⠦⠀⠚⠓⠈⠛⠛⠋⠘⠛⠘⠛⠀⠺⠿⠀⠾⠅⠀⠀⠀⠀⠀⣰⡀
⠀⠀⠀⠀⠀⠀⢀⡴⠙⠉⢧⡀⠀⣀⣀⣀⣀⣀⣀⠶⠶⠆⠀⢠⠴⠤⠀⡄⠰⠶⠶⣄⣀⣀⣀⣀⣀⠀⠀⣼⠋⠙⢧⣀
⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠘⣿⣿⡏⠉⠀⢸⡏⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⠀⠀⣿⣿⠀⠉⢹⣿⣿⠇⠀⠀⠀⠈⢣
⠀⠀⠀⠀⡸⠃⠀⠀⡀⠀⣠⠤⠿⠿⠀⠀⣾⡇⠀⠀⠀⠀⠀⣾⠀⠀⢸⠇⠀⠀⠀⠀⢻⣿⠀⠀⠾⣿⣤⣤⠀⠀⠀⠀⠀⢧
⠀⠀⠀⡔⢰⡤⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠤⣦⢡⡀
⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠿⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡋⣙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⡟⢲⣾⣾⣶⡄⣶⣶⣶⡆⣶⣶⣶⣶⢶⣦⢰⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡏⠉⠁⢸⣿⣁⣿⢷⣿⡇⣿⣧⠁⢠⣿⠇⠸⣿⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⢸⣿⢿⡇⠀⣿⠶⢿⡇⠀⣼⠇⠀⠀⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣠⡇⢀⣿⣼⣿⣶⣿⣿⣿⣷⣾⣯⣀⡀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⣻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡷⠮⠉⠛⠛⠛⠛⠛⠛⠉⠉⠀⠀⠀⠀⣼⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠤⠭⠭⠍⠁⠀⠀⠀⠀⠀⠀⠁⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⡀⢀⣠⣀⡀⠀⠀⠀⠀⣠⣶⡆⢄⠲⡄⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠘⣴⠀⠿⣿⠏⣆⠀⢀⡀⠙⠛⠁⢸⡇⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⣿⣄⣀⣀⣠⠿⠚⠊⠳⣤⣤⣴⣿⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢹⣿⠿⠛⠁⣴⣰⣆⡄⠈⠻⠿⠿⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣆⠀⠀⠀⡠⠀⠘⠋⠙⠃⠀⠀⣤⡀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⢼⣧⡤⢤⣤⠄⠠⠤⠶⣿⠃⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⣿⣶⠀⠀⠈⠀⠀⢸⣿⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⢏⠻⠶⢶⢶⢶⠞⠋⠌⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠆⠉⠐⠀⠐⠐⠈⠀⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠐⠂⠐⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⢱⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⡠⠓⠉⢉⠤⠐⠀⠀⠀⢉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⡰⠁⡠⠊⣀⠤⠀⡀⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡰⢡⠞⠊⠁⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡔⢁⣠⠚⠀⠁⢀⣤⠂⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠐⠣⠎⠀⠀⠀⠀⠀⠌⠀⠈⠢⡐⠧⡀
⠀⠀⠀⠀⠀⠀⠀⢸⢔⣠⡀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠿⢿⣷⡿⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠑⠠⡀
⠀⠀⠀⠀⠀⠀⡜⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠓⠤⣀
⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠑⠂⠄⣓⠀⢤⡀⢀⣀⡀⠤⠤⠄⠀⠀⠐⠒⠀⠐⠀⠠⠄⣀
⠀⡀⠤⠊⠣⡈⠢⣀⠀⠀⠀⣀⠀⠀⠤⠐⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄
⡎⡠⠠⡀⠀⠉⠢⣀⠑⢢⠊⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⢄
⢃⠉⠉⠀⠀⢀⡔⠀⠙⡁⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠑⡀
⠀⠑⠠⠤⠴⣀⠄⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⢆⠘⡄
⠀⠀⠀⠀⠀⠡⠂⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠈⡄⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠆⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠸⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡒⡄⠀⠀⠀⠀⢀⠦⠤⠀⠀⣀⡀⡀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠹⡁⠈⠲⢀⠀⠀⠀⠰⡀⠀⠀⢠⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⢣⠀⠀⠀⠑⢄⠀⡇⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠘⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⡄⠀⠀⠀⡘⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠠⠂⡇⠀⠀⠰⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⢠⠁⠀⡇⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢸⠈⡄⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢀⠃⠀⠀⠃⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⢸⠀⠁⠀⠀⠑⡀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠘⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠒⠰⠂⠉⠉⠉⠈⠃⠀⠀⠀⠀⡐⠊⠉⠉⠐⠃⢀⠐⠓⠒⠂⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⣀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⡔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣆
⠀⠀⠀⠀⠀⠀⣼⣿⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆
⠀⠀⠀⠀⠀⢰⣿⡟⠀⢾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀
⠀⠀⠀⠀⠀⣾⠋⠀⠀⢈⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⣽⣆⡀⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣦⢺⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⢠⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣯⣿⣧⢿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡃⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⢹⡾⣿⡿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡄⠀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣗⡿⣾⣿⣄⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⣿⡿⣿⣆⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢀⠀⠈⠛⣷⣞⣛⣿⣿⣿⣛⣶⣤⡀⠀⠀⠀⡀⠈⠀⠀⠀⠀⠻⣷⣄⡹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⡉⠉⠀⠀⠈⠀⠉⠀⠈⠉⠉⠉⠉⠙⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⡗⠄⠀⠀⠒⠀⠒⠀⠀⠀⠀⠀⢘⢙⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣧⠐⠂⠀⠀⠀⠀⠀⠀⠀⠃⠂⠂⣳⣿⠿⠛⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠉⠀⠀⠀⠀⠀⠀⢠⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠁⠈⠁⠀⠀⠀⠈⠁⠀⠀⠀⠉⡁⠉⠈⠋⠿⢿⠟⡿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢁⠀⠘







⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆


⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠈⠳⢛⢦⣀⠀⣠⡄⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⣐
⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣻⣟⣋⣈⠙⠀⠁⠤⠀⣤⣶⣰⣦⣴⣞⠶⣯⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⢀⢐⣦⣶⣶
⠀⠀⠀⠉⠁⠺⢿⠿⣟⣿⡿⠿⠿⢿⣿⣿⡿⣿⣿⣿⣿⣿⠿⠿⠟⠁⠞⢶⠤⢒⣴⣄⠀⠹⣿⣿⣶⣯⣿⣿⣿⣿⣿
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣭⣿⣿⣿⣭⣭⣥⣤⣤⣴⣦⣤⣤⣤⣤⣤⣭⣤⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣤⣴⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣄⣀⢦⡰⠢⠞⠢⠚⠤⠚⡤⠢⣠⣄⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡴⠢⠎⠛⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠈⠋⠳⡴⢄⢀
⠀⠀⠀⠀⠀⣀⡰⢦⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠣⣀⡄
⠀⠀⠀⠀⡴⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⡄
⠀⠀⠀⡸⠁⠀⠀⢀⢀⡠⠤⠀⠐⠂⠀⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠰⡀
⢀⠤⠠⣇⠀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣄⡠⠴⠒⠂⠙⠉⠁⠀⠀⠀⠀⠀⠉⠑⠲⣄⠀⢱⡤⠤⡄
⠈⠰⠲⡌⡞⠀⠀⠐⠦⣤⡤⢀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢀⡠⢤⠤⣤⠶⠂⠀⠩⢱⠎⣠⢤⠘
⠀⢸⢠⣼⠃⠀⠀⠐⢿⣞⠛⠒⢻⣷⡤⣀⣠⡎⠀⠀⠀⢊⠀⠀⠀⢀⣆⠤⢞⢋⡿⣷⠚⢻⡄⠀⠀⠀⠈⣞⡁⢸
⡀⡄⣿⡟⠀⠀⠀⠀⠀⠈⠓⠮⣶⣯⠥⠤⠟⡿⠂⠀⠀⠀⠀⠀⠀⠙⣏⠒⠮⢿⡟⠓⠊⠁⠀⠀⠀⠀⠀⢿⢹⢸
⡇⡇⢹⠁⠀⠀⠀⠀⠀⠀⠐⠚⠫⠤⠤⣄⡞⢀⡤⠖⠊⠉⠙⠒⠢⢄⠈⣆⡜⠓⠚⠓⠂⠀⠀⠀⠀⠀⠀⠘⡞
⢣⠈⠃⠀⠀⢳⢄⠀⠀⠀⠀⠀⠀⠀⡠⣿⡮⠕⠒⠉⠉⠉⠉⠉⠁⠒⠳⢽⢧⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢃⠜⢠
⠀⢹⠀⠀⠀⠈⡆⠁⣀⠀⠀⠀⡤⢪⠏⠙⢄⣀⣄⡀⠀⠀⠀⢀⣀⡀⡠⠎⠳⡝⠢⣀⠀⠀⢀⡴⡛⠀⠀⠀⠘⠖⠁
⠀⠀⢦⡀⠀⠀⠰⡄⠈⠲⡤⠊⢀⠎⠀⠀⠀⠀⢶⡁⠀⠀⠀⠸⡄⠈⠁⠀⠀⠹⡀⠈⠳⠖⠁⢀⠇⠀⠀⠀⢰⠇
⠀⠀⠈⢮⡀⠀⠀⠱⡀⠐⠀⢀⡟⠀⠀⠀⠀⠀⠀⠈⠢⠤⠒⠉⠀⠀⠀⠀⠀⠀⢡⠀⠄⠀⢀⡜⠀⠀⠠⢂⡟
⠀⠀⠀⠀⠙⢤⡈⡨⠷⡄⢂⡌⠆⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣠⠾⠣⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⢣⠀⠔⢘⣼⢱⠀⠀⣠⡔⠊⢹⢈⠣⠜⠦⠁⠌⠤⢙⠀⢐⡤⢄⡀⢸⢚⣇⠁⠀⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢃⠀⠢⠘⢸⢠⡏⠠⡘⢄⢸⠀⠀⠀⠀⠀⠀⠀⠸⡠⢋⡂⠀⠙⠪⢈⠁⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠆⠈⡀⠘⠃⢣⠀⡇⠀⡛⠀⠀⠤⠤⠤⠄⠀⣘⠁⠸⡛⠀⡌⠀⢸⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠃⠀⠀⠈⡆⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢳⠂⣰⠀⠀⠸⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⠸⣼⡄⢦⠀⠀⠀⠀⠀⠀⠀⠰⣄⡎⢠⠃⠀⠀⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⢹⡟⠈⢦⢓⡔⣣⢓⡜⢡⠁⢹⣰⠃⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠳⢊⣉⣀⣀⣀⢀⡈⠩⠦⠜⠁⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣑⣀⣠⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣔⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⢋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠛⠛⠳⢦⣄⣀⣤⠶⠛⠛⠛⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⡀
⠀⠀⠀⠀⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⡀
⢀⣠⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⣤⣤⣀
⣿⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣽⣦⣄⣠⣴⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⡤⢿
⢸⡇⠈⠉⠛⠻⣿⡟⠛⠛⠛⠛⣿⠋⠉⠉⠀⠀⠈⣿⠀⠈⠉⠙⠛⠛⣶⠶⠶⠶⠶⠶⢶⣶⠚⠛⢛⣿⠋⣩⡿⠋⠀⠀⣾
⠀⢿⡀⠀⠀⠀⠙⢿⣷⣶⠶⠶⠻⣦⣤⣤⣤⣤⣼⣿⣦⣀⣀⣀⣀⣠⡿⠷⠶⢶⣶⡶⠟⠉⠛⠛⠋⢁⡾⠋⠀⠀⠀⢠⡟
⠀⠘⣷⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠻⢦⣄⠀⣀⡴⠋⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠘⣧⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠟⠋⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠘⣧⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣴⠟⠁
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣴⠞⠁
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⣠⠴⠛⠁
⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠁
⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⣤⣄⣀⣀⣀⣀⣠⣤⣤⡴⠶⠛⠉
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶