Mice Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣾⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⢀⣿⡟⠁⠀⠀⠈⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⠿⠟⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠻⠿⣿⣶⣦⣄⡘⣿⡅⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⣀⣴⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣬⣝⡛⠿⣿⣷⣄⠀⠀⠀⣼⡿⠁
⠀⠀⢀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠛⠉⠛⠿⣦⡀⠙⠻⣷⣦⡞⠋
⠀⣰⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠙⠻⣦⣄
⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠻⣷⡄
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣤⣦⡀⠀⠈⠻⣦⡀
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠉⠀⠀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠈⠳⡄⠀⢀
⢻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣴⣶⣿⣶⠁
⠈⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⢷⣄⡘⠇⢀⣿⣿
⢠⡏⠙⢿⣶⣄⡀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣃⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠷⣤⣤⣤⣀⣀⣀⣀⣀⣽⣿⣿⠿⠟⠁
⣼⠀⠀⠀⠉⠛⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣯⠉⠉⠛⠛⠛⠿⠿⢿⣷⣶⣶⣤⣤⣤⣴⣶⣿⣿⣷⡄⠉⠙⠛⠛⠛⠛⠛⠋⠋
⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠻⣿⣿⣿⠛
⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛
⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣿⣶⣶⣦⣄⡀
⠀⠀⠈⠻⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠈⠛⢿⣆
⠀⠀⠀⠀⠀⠙⠻⠿⢿⣶⣶⣶⣶⣶⣶⣶⣿⡿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠚⠛⠛⠛⠛⠛⠓⠲⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⣀⠠⠤⠤⠤⠤⣀⣀⠀⠀⠀⠈⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⠀⢀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠁⢀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠛⠛⠛⠛⠛⠛⠓⠲⠦⣤⣀⡀
⣤⣄⣀⢀⣀⣠⡴⠞⠉⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⡀
⠈⠻⠯⣭⣭⡥⠶⠚⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⠶⠚⠛⠉⠉⠙⠛⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠋⠉⠉⠉⠛⠲⢦⣀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⢀⣾⢛⣧⠀⠀⠀⠀⠀⠀⢠⣾⢻⣦⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠈⠿⣿⠏⠀⠀⠀⠀⠀⠀⠈⠿⡿⠏⠀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠛⠛⠉⠉⠻⣛⠒⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠖⣛⠛⠉⠉⠛⠛⠲⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⢋⣫⣭⣿⣿⣦⠰⣿⣿⣿⡇⣤⣿⣿⣭⣟⡉⠛⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⣴⠋⠁⠈⠲⢄⡉⠀⠙⠿⠋⠀⢉⡡⠖⠁⠈⠙⣦⠀⠀⠙⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠊⠁⠀⠀⠀⠀⠀⠘⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⣷⣶⣶⣾⣿⠿⢆⣽⣦⣀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⢀⣠⡔⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠖⠂⢴⡮⠓
⠀⠀⠀⠀⡀⠻⢿⣦⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⡟⠿⠟⠿⠻⠿⠿⠿⠟⠛⠉⠁⠀⠠⠔⠁
⠀⠀⠀⠀⠀⠐⠾⠟⠀⠀⠀⣠⠞⢿⣿⠋⡀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠠⣔⣊⠤⠀⣤⡔⢁⠄
⠀⠀⠀⠀⢀⡀⠄⠠⠤⠒⠊⠁⠈⠻⢟⠷⢶⠖⠃⠉⠉⢲⣶⣶⣾⣦⡹⣿⡃⠀⠊⠀⠀⠀⠸⠀⡀
⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⡇⢠⣾⣶⣴⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠁
⠀⠀⠳⠤⣀⣘⡙⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣆⡀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠁⠀⠒⠐⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⣏⠴⠄⢀⣰⢤⠄⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⢠⠞⠃⢀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⢠⣿⢟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⡀⠇⣿⡀⠀⠀⠀⠀⠀⠀⣰⡏⠁⠀⢰⡟⢁⣿⣅⣤⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠙⡇⠀⠘⢿⣿⣾⡿⠋⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⠀⠀⠘⣿⣿⣿⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀⠀⠀⠈⠉⣹⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠈⠀⢾⣿⣷⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⢀⣤⣤⣄⡠⣤⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⢀⣼⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⢀⣤⣈⣿⠏⠁⠀⠈⣿
⠀⠠⠖⠒⠛⠛⠛⠓⠲⠶⠶⠤⠤⠤⣤⣤⣤⠴⠶⠛⠉⠷⣞⠉⠉⠙⠳⠖⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠈⣿⣿⡟⠳⣶⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣿⣿⣶⣼⣿⣷⣤⣍⣁⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⠶⠞⠋⠉⠀⠀⠀⠀⠙⣿⣯⠉⠛⠛⠿⠿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⣀⣀⡀⠀⠀⠀⠀⢠⣾⠛⠉⠁⠀⠀⢉⣀⣠⢾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⢶⣄⠀⢀⣿⣿⠀⠀⠀⠀⠐⣿⣹⣿⠀⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣾⣿⡁⢠⡀⠀⡀⠀⠈⠛⠛⢀⣰⣆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣿⣷⣤⣷⣦⣺⣄⣶⣤⣭⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⡀⢨⡅⠂⣴⡶⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣄⠉⠉⠉⠙⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡁⠀⠀⠸⣿⡥⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣖⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡟⠀⣠⡄⠀⠀⠀⠀⠂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢂⡼⠖⢾⣿⡂⠀⣀⣤⣿⡧⢸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠁⠈⠀⠀⠀⠙⠻⣿⣿⡿⣿⣷⣿⣿⣷⣤⣀⣀⣀⣠⡤⠴⠋⠁
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠚⠉⢹⣿⠟⠋⠉⠁⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⡛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢂⠰⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣷⣶⣠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⢟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀⠀⠀⠀⠈⠖⢀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠰⠛⠛⠖⠛⠛⠻⢿⣿⣿⡟⣿⡟⠿⣿⣿⣿⣧⡀⠀⠀⠀⠀⡔⢮⣋⡬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣷⢀⣦⡀⢻⢻⣿⣇⠀⠀⢀⣄⣿⣶⡬
⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠐⠰⠬⣿⣿⣿⡿⠋⠠⣽⣷⣶⣾⣿⡇⠀⠠⣭⢵⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢹⡝⠄⢠⣾⣿⣿⣿⣿⠃⠀⢀⣿⣿⣿⣿⡗
⠀⠀⠀⠀⠀⢀⠀⠰⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣿⡧⢨⣿⣿⣿⣿⣿⣾⣾⣿⣿⣿⣿⡟⠖
⠀⠀⠀⠀⠀⠈⠄⢡⢀⠐⠀⠀⠀⠀⠀⠈⠀⠀⣼⣏⣩⣿⡽⠿⠿⢿⣿⣿⣿⣿⣿⡿⠻⠿⡺⡄⠀⡳
⠀⠀⠀⢀⠀⠂⡀⠘⣮⠈⠄⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠛⠻⠿⠷⠾⢦⡀⠀⡙⠃⠐⠉
⠀⠀⠀⠘⠉⠉⠲⣜⢻⣷⣿⠀⠀⢜⣰⣆⡄⡀⠀⠀⢰⠀⠀⠀⠀⠙⠓⠾⢆⡀⠀⣹⣿⣦⡄
⠀⠀⠀⠐⢁⠉⠹⣼⣿⢿⣿⣿⣥⠈⣿⣿⡧⣱⡥⣇⡤⠤⡤⠴⠦⠤⠤⠤⠖⠓⠛⠁⠈⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠠⠿⣿⡿⢿⡟⢓⣳⣿⣿⢧⠴⢿⠿⠑⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠈⠙⠢⣄⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠁⠀⠀⠈⠉⠲⢄
⠀⠀⣰⠃⠀⢀⠔⠉⠁⠀⠈⠑⢢⡈⢣⡀⠀⠀⠀⣠⠊⢠⠔⠉⠁⠀⠉⠑⢄⠀⠀⠳⡀
⠀⢀⡇⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠱⠀⢱⠀⠀⢰⠁⠰⠁⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⢧
⠀⠈⡆⠀⠸⡀⠀⠀⠀⠀⢀⣀⡠⠴⠓⠚⠓⠒⠛⠤⣇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡼
⠀⠀⠹⣄⠴⠓⠦⣀⣀⣴⣿⡟⢹⡄⠀⣠⣶⠢⡄⠀⠈⠱⡄⠀⠀⠀⠀⣀⠔⠁⠀⡰⠃
⠀⠀⠀⠸⡀⠀⢀⠏⠀⠈⠣⠤⠞⠀⠀⢿⡟⢀⡼⠀⠀⠀⠸⡖⠒⠒⠉⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠈⠉⢧⠀⠀⢀⡀⣀⠀⢰⠉⠑⠉⠉⠀⠀⠀⠀⢀⣏⣓⣒⣋⣉⠁
⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠙⠁⠀⠀⠑⠊⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠈⠉⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣄⡀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⢖⠒⠋⠉⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⣄⠀⠀⡇⠀⠀⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠈⡷⡼⠁⠀⢰⠃⠀⠀⠀⠀⠘⡄⠀⠀⢀⠏⢮⠣⡀⠀⠀⠀⠀⠀⠀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣠⠜⡟⠁⠀⣠⠛⠒⠒⢲⠖⠒⢲⠇⠀⢀⠎⠀⠀⠑⢬⡒⠤⢤⣤⠤⣔⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠁⠀⠀⠀⠳⠤⠒⠳⠤⠴⠋⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⡀⢀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣠⣿⣿⣷⣧⣾⣼⣶⣤⣶⣠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⠀⣀⣼⣿⣿⡿⠿⠟⠻⠿⣿⣿⣿⣿⣿⣃⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠛⣯⠉⠉⠀⣀⣀⠀⢰⠀⣀⠈⠉⢉⡿⠋⠁⠀⠈⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣷⣼⡿⠟⠀⠀⡀⠘⢿⣿⣷⣿⣇⠄⠀⠀⠀⠀⣤⠥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢀⠀⢀⠀⣸⣿⣟⣁⡀⠀⠀⠀⠔⢀⣻⣿⣿⡏⠀⣠⣶⣆⣼⣵⠃⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣦⣀⢾⣿⣿⣿⠟⠉⢳⠀⠀⠀⢰⣏⠟⢿⣿⡿⣿⣿⣿⣿⣿⣿⠿⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢁⡘⡟⢿⣏⣶⣿⣷⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⡟⣿⣿⣿⣿⣗⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠀⠈⢿⣿⣿⣿⣿⡁⢀⠀⣸⣿⣿⣿⣿⣿⠿⠉⣽⣿⣿⡟⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠗⠀⠀⠀⠉⠉⠉⣻⢃⣤⣴⣾⣯⠏⢹⠿⠅⡲⠄⢺⣿⣟⡂⣤⡾⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢠⣌⡄⠀⢈⣴⣿⣧⣀⣩⠎⠁⢩⣿⣿⣱⣿⣿⣭⣷⠄⣘⠩⠉⠩⡍⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠢⠀⠀⢿⣿⡀⢸⣿⣿⠋⠸⣿⡶⠿⡿⢿⣿⡍⢿⣿⣿⡟⣲⣿⠗⠒⢒⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠘⢿⣷⡄⠹⣿⡄⠐⣿⣧⣠⣤⣿⣿⠓⣸⣿⡟⣠⣿⣟⡀⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⡤⠶⣿⣿⣧⣽⣷⣤⣈⣻⣿⣿⡍⣥⣼⣿⣷⣿⣿⣿⢦⣬⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠨⣣⢿⣿⣿⣿⣿⣿⣿⣮⡹⣿⣷⣿⣿⣿⣿⣿⣿⣡⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠁⣾⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⠋⠉⠛⠿⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣗⣿⡏⠀⠀⠀⠀⠀⠀⠉⠛⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⣿⣿⣾⢹⠏⠉⠉⠉⠋⢻⡉⣾⣿⣿⠦⢻⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠘⣿⣿⣧⡏⠀⠀⠀⠀⠀⠀⢧⣼⣿⡟⠻⠆⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠆⠀⢉⣿⣯⠀⠀⠀⠀⠀⠀⠀⢈⣽⣏⠃⠀⠸⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢆⡄⣀⠉⣧⠀⠀⠀⠀⠀⠀⡞⢉⣀⣤⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣇⣾⣇⣾⠿⠋⠀⠀⠀⠀⠀⠀⠻⠿⣧⣼⣧⡸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣀⠀⣴⠒⢒⠢⠀⠈⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⠀⠀⠀⠀⠈⠑⢿⣄⠀⠀⠀⠀⠀⠀⣌⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢀⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠀⠀⣠⠤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⢠⠀⠀⠀⠀⠀⠀⡐⠉
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠈⡀⠀⠀⠀⠀⠀⠀⢀⡏⠀⢸⠀⠀⠀⠀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⢀⡏⠀⡠⠂⠀⠁⠒⠤⢤⡀⠀⠀⠻⣄⣀⡈⢇⠀⠐⡇⠘⠒⣦
⠀⠀⠀⠀⠀⠀⠘⡇⠀⢣⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠼⠇⠀⠙⠦⣀⠄⠘⠋
⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠑⠒⠢⠤⠤⣀⣀⣀⣀⣀⡠⠤⠔⣚⡭⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠶⠦⠤⠤⠤⠤⠴⠒⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⠉⠉⠛⠒⠦⣄⡀
⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠶⠖⠒⠲⠶⠤⢤⣀
⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄
⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⣀⣠⠷⠒⠚⠉⠉⠉⠉⠉⠛⠒⠦⣤⠏⠀⠀⠀⠀⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠈⠳⣀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⡞⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢂⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠐⠣⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠲⢤⣄⣀⣀⣀⣀⣀⣤⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢠⠞⠉⠙⠲⠀⠀⠀⠀⠀⠀⢠⣿⣿⡆⠀⣠⡤⢄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠄⢼⡁⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠁⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠑⠶⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⡸⠤⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢊⣠⠔⠋⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠤⢤⣄⣀⣀⣀⣀⣀⣀⣴⠿⠕⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⡠⠊⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢀⣠⠔⠋⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠈⠢⡀⠀⠀⠀⢀⠴⠊⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠉⠁⠀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⢌⡺⠀⢠⠊⠀⠀⠀⠀⠀⢀⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡧⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠈⠛⠊⠀⠀⠘⠖⠤⠠⠖⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠀⠉⠲⠤⢤⣄⠀⠀⠀⡀⡈⠑⠒⠤⣤⣀⣀⣀⣀⣀⣤⠠⠤⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠚⠛⠋⠉⠛⠛⠶⣤⡀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⡛⠉⡽⠉⡉⠛⠿⣷⣄⠀⣀⣴⣲⣆
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠉⠀⠀⣾⡂⡀⠀⠈⠉⠉⠉⠈⠛⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠙⠿⠗⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⣤⠠⣺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⢀⣤⠿⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣄⣀⡀⢀⣀⣀⡤⠖⠁⠀⠀⠀⠀⠀⠐⣲⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢰⠃⣰⠃
⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠸⡴⢧⡀
⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢧⠀⠙⠶⣄
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠈⢣⣄⡀⣿
⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠛⠶⣄⠀⢹⡟⠁
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣋⠀⠀⠀⢿⣤⡾⠁
⠀⠀⠀⠀⠀⣰⠃⠀⡴⠶⠶⠶⠶⠶⠶⠶⠯⠥⠤⢤⣽⠇⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⢿⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢛⣉⣭⡬⢭⣿⡆
⠀⠀⠀⠀⠀⠈⢷⣀⠈⠓⠦⣤⣀⣀⣀⣀⣀⣀⣠⡤⠶⠛⣉⡴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⣈⠉⠉⢉⣉⣁⣤⠴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁

⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⣄
⡎⠀⠀⠈⠲⡀⠀⠀⠀⠀⠀⡔⠁⠈⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠱⡄
⢧⠀⠀⠀⣄⡇⣀⠀⠀⠀⣘⠀⠀⠀⠀⠈⣣⡤⠒⡐⠒⠢⣄⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠈⠳⠤⠴⢯⡀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠈⠵⢀⣀⠁⠀⠀⠈⠳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⡙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⡷⠦⣄⡀⠀⠀⠀⠀⠀⣀⡠⢴⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠉⠙⢳⠒⠛⠙⠿⡤⠞⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⡜⠀⠀⠀⠀⠒⠚⠁⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢦⡀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠾⢇⠀⠉⠒⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⣡⠤⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠦⣄⡉⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤
⠀⠀⠀⠀⠀⠀⠀⢰⡁⢰⡋⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⠉⢒⠄⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣈⢳⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠒⢈⡠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⢀⣀⠀⡰⠁⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⣁⠴
⠀⠀⠀⠀⠀⠀⠸⣈⠒⠃⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢄⣀⠀⢁⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⡇
⠀⠀⠀⢰⠋⠉⠉⠒⢤⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣅⡴⠚⠋⠉⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠸⡀
⠀⠀⠀⠸⡄⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠱⡄
⠀⠀⠀⠀⠙⢆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠹⡀
⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠆⡇
⠀⠀⠀⠀⠀⠀⠀⣀⣈⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠙⠓⠲⢬⣉⠒⠦⣄⣀⠀⠀⠀⢀⣠⠜⢠⠃
⡠⠒⠒⠒⠂⠉⢉⣀⣀⡤⠤⠖⠦⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣠⣞⣁⡠⠤⠤⠤⠤⡀⠉⠒⠦⣄⣈⣁⣉⣁⣠⠴⠃
⠱⢦⣠⣀⡞⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠙⠛⠋⠉⠛⠧⣤⣄⣀⣤⣤⣤⠤⠤⠤⣄⠀⢀⢀⣸

⠀⠀⠀⠀⠀⠀⣠⣤⠶⠶⠿⠿⠿⠶⠶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠿⠟⠛⠛⠳⠶⢦⣄⡀
⠀⠀⠀⢀⣴⣿⣿⣷⣿⣿⣶⣶⣤⣀⠀⠀⠈⠛⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠋⠁⠀⢀⣤⣴⣶⣶⣶⣾⣿⣿⣷⣄
⠀⠀⣴⡿⠋⠉⠀⠀⠀⠈⠉⠙⠻⢿⣷⣤⡀⠀⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⣠⣾⣿⠟⠉⠀⠀⠀⠀⠀⠉⠛⢿⣧⡀
⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀⠻⣧⠀⠀⠀⠀⠀⠀⢀⣴⠆⠀⣀⣴⠞⠀⢠⡟⠁⠀⠀⢠⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷
⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣆⠀⠀⠀⠹⣧⠀⠀⢀⣠⣶⣿⡷⣾⣿⣿⡷⠖⢠⡟⠀⠀⠀⢀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣧⡀⠀⢀⣿⣦⠾⠛⠛⠩⠴⠾⠛⠻⠷⢦⣴⣿⡇⠀⠀⢀⣼⣿⣿⣿⣤
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠻⡎⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠞⠋⢹⢿⡿⠋
⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁
⠀⠀⠀⠀⠈⠻⢶⣄⡀⠀⠀⠀⠀⣠⣾⠇⠀⠀⠀⠚⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠈⠓⠀⠀⠀⠈⣿⣄⡀⠀⠀⠀⣀⣠⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠲⠶⠿⢿⣿⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⢿⡿⠿⠿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠦⡄⠀⠀⠀⣿⣧⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣭⣿⡀⠀⠀⠀⢀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⢶⣿⣶⣤⣀⣀⠀⠀⣿⣿⣿⣿⡟⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠇⠀⠀⢀⣠⣴⣿⡶⠶⠒⠚⠁
⠀⠀⠀⠈⠉⠉⠉⠉⠙⠛⠛⠛⢿⡿⠶⠶⢬⣭⣙⣛⡛⠿⠟⠋⠀⠀⠀⢀⣠⣤⣤⣀⠀⠀⠀⠀⠙⠿⠿⠿⠖⢚⣋⣉⣥⡤⠾⣿⠿⠛⠛⠛⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢻⡟⠛⠛⠛⠋⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⢧⡀⢀⡽⠃⠀⠀⠀⠀⠀⠀⠈⠉⠭⠵⠶⠖⠶⢾⡿⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⠀⠀⠀⢻⡏⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⢀⣾⣧⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⣀⡀⠀⠀⠀⠈⠙⠛⠛⠷⠼⠟⠛⠋⠀⠀⠀⠀⠀⣀⣤⡶⠟⠉⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣶⡾⠛⠋⠁⠀⠀⠀⠀⠀⢀⡾⢋⣭⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⣾⢱⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡄⠀⠀⠀⠀⠀⠀⢿⡘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠀⢻⡄⠀⠀⠀⠀⠀⠈⢷⡘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠈⣷⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⢠⣽⡄⠀⠀⠀⠀⠀⠀⣾⡤⠀⠀⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⣿⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣠⣴⣶⡿⠀⠀⠀⠀⠀⠀⠀⠻⣷⣦⣄⣼⠟⣿⡀⠀⠀⠀⠀⢀⣼⢃⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⣸⣷⣤⡴⠶⠟⢋⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣤⣤⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠿⠿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⣿⣍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣦⣠⡾⠟⠻⠿⠿⠶⠶⠿⠿⠿⢿⣅⣠⣆⣾⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢁⡾⡄⠀⢀⡤⠒⢲⠾⠛⠋⠉⠉⠉⠉⠛⠻⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠞⠛⠻⠙⠀⣶⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠐⣿⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⣤⡀⠀⠀⠐⠒⢺⡷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠉⠀⠀⠀⢀⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⣼⣀⠀⠀⠀⣠⣼⣿⣿⣿⣟⠂⠀⠀⠀⠲⣦⠀⠀⠀⠀⠀⢀⣟⠀⠀⠀⣼⡲⢄
⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⢷⣌⠁⠉⠁⠀⠀⠀⠀⣿⣆⢀⣀⣠⣾⣿⡛⠀⢐⣦⠃⠉⠲⡝⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⣑⡀⣀⠤⠤⠶⠚⠛⠉⠙⠻⣟⣋⣉⠐⠒⠋⠀⠀⠀⠀⢸⣽
⠀⠀⠀⠀⣾⣧⣴⣶⣿⣿⣿⣷⣄⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠒⠊⠉⠉⠉⠉⠙⠒⠒⠶⠶⠤⢤⡤⠶⠾⠛⠁
⠀⠀⠸⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿⢦⡀
⠀⠀⠀⠀⠀⠐⠛⠋⠉⠁⠙⠛⠉⠀⣀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠋⠉⠉⠛⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠛⠉⠉⠛⠲⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⡠⠖⠊⠉⠐⠢⢄⠀⠀⠀⠙⣦⠀⠀⣀⣀⣀⣀⣀⡀⠀⣰⠏⠀⠀⠀⡠⠒⠉⠉⠉⠲⢄⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠘⠛⠉⠉⠉⠀⠀⠉⠉⠙⠣⡀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡧⠐⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠈⠢⠀⠀⠀⠀⠀⠀⠑⢦⡀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣶⠀⡇⠀⠀⠀⠀⠀⠀⠈⠣⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⡀⠜⠁⠀⠀⠀⠀⠀⢀⣀⣀⣱⡀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡿⠁⠀⢀⣤⠞⠁
⠀⠀⠀⠀⣀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣄⣀⣀⣤⣤⠤⢶⡀⠀⠈⠢⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠽⠿⠧⠴⠶⠚⠋
⠀⣠⠞⠋⠁⠀⠀⠈⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠨⡉⠒⠲⡒⠒⢂⠏⣽⠃
⣼⡥⠖⠚⠛⠛⠲⢤⡀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠘⢦⡀⠑⠒⢁⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⣀⠀⠀⢀⣀⠤⠈⠻⠾⣉⢸⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠈⣄⠔⡹⠋⠉⠲⣒⡄⣨⣟⠶⠚⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠳⢄⠀⠀⠘⡾⠁⠀⢠⣑⠶⡝⢹⢖⣂⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⢀⠧⡀⠀⠀⠀⢠⠜⠀⠉⠀⠀⠀⢣⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⡎⠀⠑⢄⣀⡴⠃⠀⠀⠀⠀⠀⠀⠸⡄⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢳⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠳⢤⣀⣤⣤⣀⣸⡆⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⡔⠁⠀⠀⠀⠉⠻⣄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠛⠉⠉⠉⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠈⠑⠦⡈⢣⡀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧⠂⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠈⠢⣅⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠘⢆⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣬⠷⢦⣀⣀⠀⠀⠀⠑⠤⣈⠑⠦⢄⡀⢀⣠⡤⠖⠉⠀⠀⠀⣀⣤⣖⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⣠⠔⠂⠀⠀⠀⠀⠀⠀⠀⠀⣽⠙⠓⠒⣖⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⢉⣉⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⡇⠀⠀⠀⢀⣀⣠⡤⠴⠒⠋⠁⠀⠀⠀⠘⠲⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢳⠀⠀⠀⢀⣴⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠶⠾⣷⢾⠧⠤⠴⡾⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡉⣆⠀⠀⠀⠈⠛⠿⠃⠀⠀⢹⣾⢆⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢯⣉⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠋⠑⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⠶⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠷⣦⣈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣰⣟⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⢹⣧⡀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠙⠂⠀⠀⠀⡼⠛⢳⣄⣤⠶⠃⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⢤⣠⠞⠀⢰⠏⠉⠀⠀⠀⠀⠀⢸⡿
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠠⣿⣄⣤⡜⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⢀⠞⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠈⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣾⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢰⡇⢸⣿
⢿⡀⠳⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⡀⠀⠀⢸⠇⠀⠀⠀⠀⢀⡼⠃⣸⡟
⠈⠻⢦⣄⣀⣈⣉⠉⠉⠛⠛⠓⠒⠒⠒⠶⠤⠤⠤⠤⠤⠼⠿⢤⡀⠀⠀⠀⠹⡆⣠⠟⠀⣠⡤⢤⡔⠛⣠⠾⠋
⠀⠀⠀⠀⠉⠉⠉⠙⠛⠳⠶⢶⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣿⣀⣤⠒⢲⣿⠷⠶⠶⠿⡀⠀⠉⠛⠷⠖⠒⠖⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠈⠉⠛⢄⠀⠙⠲⠶⠦⢄⠈⠓⠲⠦⠬⠷⠶⠾⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠒⠛⠉⠉⠛⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠛⠋⠉⠙⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⢀⡤⠶⠒⠲⠦⣄⡀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⣠⡴⠖⠒⠒⠦⣄⡀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⡴⠋⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠹⣦⠴⠖⠒⠛⠛⠛⠛⠲⠦⣼⡁⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠈⠓⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣠⣟⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠻⣏⠉⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⣀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠘⢷⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠻⠟⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠻⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣷⣦⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⣀⣀⣀⣀⣀⣠⣤⢤⡄⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣽⢿⣿⠿⠿⠗⠚⠉
⠀⢀⣠⠶⠚⠋⠉⠉⠛⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⢻⠀⠀⠀⠈⣛⠶⠤⣤⣤⡤⠴⣶⢚⡿⠁
⣰⣏⣡⡤⠴⠶⠤⣄⡀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠘⢧⡀⠈⠳⣄⡴⢃⡾⠁
⠛⠉⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠙⢲⣤⣤⡴⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠲⡄⠀⣠⣴⡾⢯⣍⣉⠙⠳⣼⣟⣛⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⢠⡀⠀⠀⠀⢹⡞⣱⠋⠀⢠⣛⠿⣿⣴⣿⢟⣋⠉⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠙⢦⡀⠀⠀⢻⠏⠀⠀⢰⣬⣛⡟⠹⣿⣭⡅⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢠⡿⣄⠀⠀⠀⠀⡶⠛⠀⠀⠀⠀⠀⠘⣧⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⢀⡾⠀⠘⢧⣄⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠈⣿⠞⠛⠛⠓⠦⣽⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡤⠴⠶⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀⣼⠁⠀⠀⠀⠠⣤⡀⠙⢦⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⡀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡀⠀⠀⠀⠀⠀⠉⠳⣌⢳⡀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠁⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠈⠻⣷⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠙⢦⡀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠽⠷⣤⣤⣀⠀⠀⠈⠙⠦⣄⡙⠳⠦⣤⣄⣤⣤⡶⠞⠉⠀⠀⠀⢀⣠⣴⣛⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⣠⠴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠉⠙⠓⢲⡞⠉⠁⠀⠀⠀⠈⠉⠉⠉⠉⢉⣍⣉⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢰⡇⠀⠀⠀⠀⠀⣀⣀⣤⠤⠶⠛⠁⠀⠀⠀⠀⠙⠦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠾⠷⠶⠖⠒⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠶⠤⢤⣤⣄⣀⣼⣤⠴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⠚⠛⠛⠛⠛⠛⠓⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠉⢀⣀⣤⡤⠶⠶⠶⢤⣤⣄⡀⠀⠀⠉⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢀⣠⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⡀⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠁⣠⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⢀⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠽⠷⠶⠶⠶⠾⠶⠤⣤⣄⣀
⣠⣀⠀⠀⠀⢀⣠⡴⠛⢁⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠖⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⡀
⠙⠿⣿⣛⣛⣉⣥⠴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣀⣤⡤⠴⠶⠤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠴⠶⢤⣤⣀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡷⠛⣉⣤⣶⣶⣶⣶⣦⣬⡙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣡⣤⣶⣶⣶⣶⣦⣬⡙⢦⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⢰⣿⣿⣿⠿⠛⠋⠉⠉⠉⠉⠙⠛⠿⠌⣧⠀⠀⠀⠀⠀⠀⠀⣸⠃⠼⠟⠛⠉⠉⠉⠉⠉⠛⠻⢿⣿⣿⣷⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣏⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢈⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⣿⣏⣿⠀⠀⠀⠀⠀⠀⠀⣾⣋⣿⡆⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠛⠿⠋⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠀⠀⠀⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⣻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣏⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⠋⠉⠉⠉⠙⣿⣛⣓⣦⣤⡀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣚⣻⣟⠉⠉⠉⠉⠙⠳⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⢉⣹⣿⣽⣿⣶⠀⣿⣿⣿⡿⢠⣾⣿⣿⣿⣏⠉⠛⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⣰⠋⠀⠀⠙⠷⣬⣀⠈⠻⠟⢁⣈⣵⠞⠋⠀⠈⠻⣄⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⢹⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣦⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠁⠀⣀⣸⡟⠛⢿⣿⣿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣀⣠⣿⠟⠁⠀⠀⢀⣀⣭⣽⣿⣿⣿⣿⠿⠿⠟⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠁⠀⠀⠀⠀⠈⠋⠉⠈⠉⠉⠁⠀⢀⣠⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⣀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣠⠴⠖⠛⠋⠉⠛⠓⠂⠼⣀⠃⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠎⠈⠢⡀⠚⠋⠀⠀⠀⠀⠀⠀⢀⡤⣄⠀⠀⠑⢾⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠐⠒⠁⠀⠀⢰⠋⠳⡄⠀⠀⠸⠀⠘⠂⠀⠀⠀⠙⠓⢶⠤⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⡹⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣝⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠒⠂⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠦⣄⠀⠀⠀⢹⡅⠒⠒⠠⠤⠤⠄⠀⠀⡀⠠⠤⠄⢶⠀⠁⢸⡃⠀⣀⡴⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡉⢠⠉⠙⠲⠤⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢀⡨⠛⠉⠉⠁⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣀⡀⠀⠀⠀⠀⠈⠑⠒⠀⠤⠤⠤⠀⠐⠒⡇⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣄⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢲⡄⠀⠀⠀⠀⠀⠀⠀⠀⠖⠤⠤⡤⡀⡤⡄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠋⠛⠳⠳⠓⠞⠒⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡦⠤⠀⣀⣀⠀⢀⣀⣀⣀⣀⡀⠤⠤⢲⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢠⡞⠉⠀⠀⠀⠀⠉⢳⡀⠀⢸⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠛⠺⠧⠤⣾⠀⠀⠀⠀⠀⠀⠀⠀⢿⠒⠚⠉⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠤⠤⠤⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠸⠶⠶⠶⠶⠚

⠀⡀
⠀⡁⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣶⡦⢤⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢲⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣣⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⢾⣭⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠚⠛⠛⠍⠉⠉⠛⠛⠋⠛⣻⣍⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢷⡤⠔⢉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠁⢀⣿⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠯⠤⠤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢓⡶⠀⠀⠀⠹⣆⡴⠚⠛⠛⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⣄⣀⣀⠴⢲
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⣠⡴⠾⡅⠀⢹⢁⣴⠂⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⡿⠶⠤⣤⣁⡤⠛
⠀⠀⠀⠀⠀⣀⡠⠖⠉⠀⠀⠀⢎⣐⡷⢃⠀⠀⢸⡷⢤⣤⡴⠃⠀⠀⠀⠀⠀⠀⢀⡿⠁
⡴⠚⠓⣦⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⡖⠚⠉
⢷⣀⣠⣟⡀⣀⣠⣤⣤⣀⣀⣀⣀⡤⠒⠑⣂⡴⠳⣤⣄⣀⣀⣤⠗⠚⠋⠉⠁
⠀⠈⠀⠀⢉⡟⢠⠃⡼⠀⠀⠀⠉⣩⠋⡽⠉⠀⣠⠃⣼
⠀⠀⠀⠀⠈⠉⠛⠒⠁⠀⠀⢀⠜⢁⡜⠀⢀⡴⠃⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠊⠀⢠⣏⣀⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢠⠰⣄⡀⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣀⣿⠾⠺⡷⢿⢹⡏⣿⣧⣠⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣤⠀⠀⠀⠃⣿⣿⣿⣶⣿⡄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣆⡘⢿⡿⢫⢟⠿⠃⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢶⣌⣿⡆⣤⣾⣅⣀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣤⣤⣀⣀⣀⣠⣶⣿⣾⡿⠉⠻⣿⣿⣛⠉⠉
⠀⠀⠀⠀⢀⣠⣤⣶⣶⣤⣤⣤⣶⣶⣾⣿⠟⠛⠉⠉⠙⠻⠿⠋⠉⠉⠀⠀⠏⠀⠀⠀⠲⠿⠿⣿⣶⣤⡀
⠀⠀⢠⣾⣿⣿⠟⠉⠙⢿⣿⡿⠟⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣆⠀⠀⠀⠀⠩⣄⠀⣽
⢀⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣿⣿⣿⣿⣶⣾⠟⠓⠿⠛⠛
⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣦⠀⠀⠀⣿⣿⠿⠋⠻⣿⡟⠋⠁
⠈⢹⣿⣿⣿⣦⡀⠀⠀⠀⠀⣤⣦⠀⠀⠀⠀⢀⠀⣿⣿⣿⣷⣧⣼⣿⡏⠀⠀⠀⠿⠃
⠀⠀⢹⣿⣿⣿⣿⣷⣤⣤⣄⣻⣿⣧⡀⠘⣦⣼⣿⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⢸⣿⣿⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⢸⣿⣿⠏⠀⣿⣝⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⡿
⠀⠀⢸⣿⡏⠀⢀⣿⣿⡟⠈⠛⠛⠛⠋⠉⠉⠉⢿⣿⣿⣿⠃
⠀⢠⣿⡿⠀⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡏
⠀⢸⣿⠇⠀⠀⠹⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷
⠀⣸⣿⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⣿⡇⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⣸⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀
⠘⠛⠓⠀⠀⠀⠀⠀⠀⠀⠻⠿⠦⠀⠀⠀⠀⠀⠀⠛⢿⣿⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⣿⡀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣤⣶⣶⣶⣿⡿⠿⠿⢿⣿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣰⢻⡇⠀⠀⢀⣤⠞⠋⠉⠙⡿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠛⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⣧⣾⡿⠶⣶⠏⡎⠀⢠⣖⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠟⠋⠉⠀⠀⠀⠈⠀⠃⠀⣼⣿⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⣤⣬⣝⣛⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣾⣿⠂⠀⠀⠀⠀⠀⠀⠀⣤⣿⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠉⠁⠀⠀⢀⠀⠀⠀⣠⣴⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠈⠀⣰⣶⣶⣾⣿⣿⣶⣄⠀⠀⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣤⠀⠀⠀⠀⣀⣤⣿⣿⡿⠿⣿⡿⢿⣷⡍⠀⠀⠀⠀⠀⠀⠈⢿⣶⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇⠀⠀⠀⠀⠀⣿⣌⡙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠋⠉⠀⠉⠻⣿⣄⡀⠙⠀⠙⠈⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⣱⣾⣿⡿⠧⠀⠀⠰⣤⣼⠃⠈⠙⠶⣌⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠷⢶⣶⣶⣾⣿⣿⡿⠿⠟⠀⢀⣠⣶⠟⠁⠀⠀⠀⠀⠘⣦⢹
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⡛⣈⣁⡀⢀⡠⠴⠶⠶⠟⠛⠉⠛⠋⠀⠀⠀⠩⢿⣋⣉⣀⣠⡄⠊⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⢌
⠀⠀⠀⠀⠀⠀⣼⣿⡀⣀⣤⣤⣶⣿⣿⣿⣷⣶⣄⠀⠀⠉⠉⠀⠸⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣼
⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣯⡾⠁
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠠⠔⠚⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠷⠶⠶⣶⣶⣶⣶⣶⣾⠿⠟⠋⠁
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠈⠉⠉⠉⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠛⠉⠉⠉⠁⠀⠙⠛⠋⠁⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠐⠒⠲⠶⠶⠖⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⣆⡴⠉⢱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠉⠀⢠⣾⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢡⡆⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⠀⠀⠀⠀⠀⠀⠁⢀⠎⠀⠀⠀⠀⣀⣀⣀⠀⠀⡖⠐⠷⠀⠀⠁⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠠⠤⠄⣀⡀⠀⠈⠃⠤⢄⡰⠎⢉⣉⣹⠃⠀⣡⠄⠀⠀⠀⠀⠀⠀⠀⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⡴⠶⠞⠁⠀⠀⠀⠈⠛⡀⣀⣀⣀⠀⠠⠤⠄⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⠀⠀⠀⠚⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⡅⠀⠀⠀⠀⢀⡤⢢⢀⡠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠸⠀⡇⠀⡠⠤⢄⡜⠀⠸⠋⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠙⠁⣤⠁⠈⢣⠀⠈⠁⠀⠁⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢀⣀⣠⣤⣄⣀⣠⠞⠁⠀⠀⢰⠀⠀⠀⠀⠀⠀⢀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠉⠉⠉⠉⠒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⢠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣠⠆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠤⠤⠤⠤⠤⠒⠉⠀⠀⠀⠀⠀⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⣠⡶⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠀⠀⠀⠀⠀⣤⠴⠊⠁
⠀⠀⠀⠀⠀⣜⠁⠀⠀⠀⠀⢠⠎⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⡴⠁⠀⠀⠀⠠⡴⠃⠰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⣀⢀⡤⠟⠁⠀⠀⠀⠀⢀⠃⢀⠃
⠧⣀⣀⣀⠴⡾⠛⢆⠀⠘⢦⡜
⠀⠈⠣⠰⠞⠀⠀⠈⠳⠶⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⣠⡇⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⠚⠉⠛⠢⠤⠄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠈⠁⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⣄⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⢀⡤⠃⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠊⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⣛
⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠒⠒⠢⣄⠀⢀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡤⠄⠋
⠀⠀⠀⠀⠀⠛⠒⠒⠒⠒⢺⠛⠉⠀⠀⠀⠀⠀⠀⠈⢑⠞⠛⠒⠒⠘⠳⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠎
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣾⣷⣶⣶⣶⣶⣶⣴⣶⣶⣶⣶⣶⣦⣤⣶⣶⣾⣿⣿⣿⣿⣿⣷⣶⣶⣶⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⡏⠁⠙⠉⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣷⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣶⡶⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠙⣶⣿⣶⣶⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⡿⠋⠀⠙⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢻⣿⣿⠟⠛⠶⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣶⣶⣿⣿⣯⣄⡀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢹⡿⠛⠋⠉⠉⠉⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠙⢻⡟⠀⠀⠀⠀⡀⠘⠛⢛⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣠⣼⠁⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡠⢶⣿⠞⠋⠙⢿⠛⠿⣿⣿⣿⣿⣿⣿⣿⡿⣅⠀⣿⠀⠀⠀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⢀⡴⠋⣰⢋⡏⠀⠀⢀⡼⠋⠀⠈⠙⠛⠿⣿⣿⡏⠀⢙⣟⣿⠀⠀⠀⠲⣤⣾⠁
⠀⠀⠀⠀⢀⡞⠀⠀⣿⡘⠓⠚⠛⠉⠀⢠⡴⣦⠀⣀⡀⠀⢀⡇⣰⣾⠛⢿⣄⡀⠀⠀⠀⢩⣶⣤⣄
⠀⠀⠀⠀⡞⠀⠀⣾⠉⠀⠀⠀⠀⠀⠀⠻⠴⠏⢸⣡⡟⠀⡾⠀⠀⠀⠀⣰⡿⠻⢤⣄⣀⣬⠿⣿⡿
⠀⠀⠀⢸⠇⠀⠀⠙⣆⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠉⣠⠞⠁⠀⠀⠀⠀⠉
⠀⠀⠀⢸⠀⠀⠀⢠⣿⣷⣤⣴⠋⠛⢶⡶⣤⣴⣶⡞⠁
⠀⠀⠀⢸⡄⠀⠀⣼⣿⠇⠀⠀⠀⠀⠺⣤⣀⣀⡤⠇
⠀⠀⠀⠈⡇⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⣇
⠀⠀⠀⠀⢻⡴⢾⣿⣧⠀⠀⠀⠀⠀⠀⣼⠙⠻⠛⠻⠒⠛⠛⠉⠉⠉⠓⢦
⠀⠀⢀⡖⠋⠁⠈⠉⠹⠛⠓⠒⠲⠶⠿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠰⠤⠤⠷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠶⠶⠶⠦⠤⠶⠶⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠈⠉⠛⠲⠶⢤⣤⣤⣤⣤⡤⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡚⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣤⣼⣿⠸⣷⡀⠀⣰⣾⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣹⣿⣀⣻⣿⣦⣿⣿⣿⣿⣿⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣆⣿⣿⣿⣿⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠑⠄⠀⢈⣙⣍⣿⣿⣿⡅⠈⣿⣿⡟⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡻⢿⡐⠒⣿⢛⣿⣿⣿⣿⣷⣾⣌⢻⣄⠘⠛⠠⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣟⣦⡌⣻⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⠿⠦⠌⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠉⡁⠘⡻⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢠⣾⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⡆⢼⣿⣶⡆⠀⠉⠻⣿⣿⣶⢒⣶⣶⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣌⠁⠀⠀⠀⠠⠺⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠹⢿⠇⢀⣀⠉⠉⡉⠙⠿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⡀⠽⠗⠀⠀⠉⡉⢣⠉⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠴⠛⡳⠢⡾⢋⢿⠀⠀⠀⠀⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠠⠀⠠⠠⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⡆⠀⠀⠐⠇⠀⣾⠀⠀⠀⠀⠀⢠⣿⣿⡀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⠀⠀⢀⡄⠁⠀⠀⠀⠀⠀⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠀⠀⠀⠠⠙⠻⣿⣿⡇⠀⠀⠀⠀⠀⠈⠻⣿⣿⠀⠀⠀⠀⠈⠐⠂
⠀⠀⠀⠁⠀⠀⠀⠀⢠⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠟⠦⣄⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡈⠉⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⠀⢀⢀⣀⡀⠀⠀⢘⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠈⢉⠋⠀⡘⠉⢁⠀⢀⠉⡀⢀⠀⠀⡼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⡄⠀⠀⠘⣧⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⣀⠀⠀⢰⡅⠀⢸⡄⠀⠀⠀⢹⣤⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢀⣴
⠀⠀⠘⣦⡀⢹⣆⠀⠈⣧⡀⠀⣷⡀⠀⢀⣾⡇⠂⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠈⠻⣾⣿⣧⣤⣻⡿⠤⡸⢷⣶⣾⣿⣷⣌⠀⢀⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡯⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣽⣤⣬⣝⡺⣟⣿⣿⣻⣷⣾⣽⣆⠀⠀⠀⠀⠀⠀⠀⣠⣿⠇⠀⠀⠀⢀⣶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡎⠁⠀⠀⠀⠀⢠⣶⣾⠃⠀⠀⣀⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣈⠙⣿⣿⣿⣀⣠⣬⣿⣿⣿⣿⡷⠶⠒⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⣤⣈⣻⣿⣿⣿⣿⣿⠙⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠿⣿⣿⣷⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡅⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⣷⣰⣦⣤⣴⣶⣿⣿⣶⠛⠶⣯⡛⡿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⡄⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠻⣿⣿⣿⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠠⠁⠒⣰⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠙⠛⠉⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢠⣀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠠⠉⢼⣿⣿⣿⣿⣿⣿⡿⢹⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠛⠋⠀⠈⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡮⡸⣿⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⣾⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣶⣤⣄⡀⠀⢢⣦
⠀⠀⠀⠀⢠⡞⠉⠀⣀⠀⠉⠙⠻⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣠
⠀⠀⠀⠀⢸⡆⠀⠀⢙⡇⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇
⠀⠀⠀⠀⠀⠙⠳⠶⠛⠁⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠟⠛⠁⠈⠿⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⠿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⠀⢹⣿⡟⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⠀⠀⠸⢻⠇⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢈⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠁⠈⠻⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⣿⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣀⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣤⣀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⣿⣿⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠻⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⠿⢿⣷⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⠟⠻⠛⠁⠀⠀⠀⠸⠿⠿⠛⠋⠉⠉⠉⠁⠀⠀⠀⠙⠻⠏⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠛⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣶⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠠⠄⠤⠄⠀⠀⠠⠀⠀⠄⠄⠂⠄⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠉⠉⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⢀⡤⠒⠉⠉⠙⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄
⠀⠀⠀⠀⠀⡏⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⢀⣀⣠⣤⠤⢤⣤⣀⣀⡀⠀⠀⠉⠓⠒⠲⠶⠦⢤⣄
⠀⠀⠀⠀⠀⢳⣀⡤⠴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⢤⣀⠀⠀⠀⠀⠀⠈⠙⣆
⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠘⣇
⠀⠀⠀⡇⢠⣀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⢲⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⣿
⠀⣀⣴⣁⠤⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠒⠓⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢀⡟
⠈⠿⣟⠙⠛⠒⠀⠠⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣀⣤⠟⠁
⠀⠀⠈⠱⣦⡤⣀⣀⡀⣀⣀⣀⡠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⣼⠉⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⣠⣆⣀⣀⡤⠤⠽⠦⠀⠀⠀⠀⠀⠀⠀⠀⣤⠴⠒⠉
⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠒⠒⠒⠒⠛⠉⠉⠉⠉⠉⠙⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠚⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠡⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡴⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠑⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣅⣀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠉⠀⢀⡇⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⠇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠛⠢⠄⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠉⠀⠀⠀⡄⠀⠀⠀⠀⣼⣿⣿⡿⠃⠀⢀⣠⣴⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⣀⠀⠀⡀⠀⠀⠀⠄⠚⢿⠟⡉⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⢰⠀⠀⠀⠠⠁⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⡀⠀⠀⢶⣖⠐⢺⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⣥⠀⠀⠀⠉⠉⣡⠛⢿⠿⠿⠿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⣴⣟⠁⠆⠀⠀⠀⠸⣿⣀⢘⡆⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣠⣾⣿⣿⣿⣦⡈⠁⡄⠀⠀⠉⢋⣼⣷⣾⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⡠⠦⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣭⡶⠆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣧⣝⢿⣿⣿⣿⡿⠟⠻⠿⣷⣦⣤⣈⢻⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠙⢷⣦⣀⠀⠀⠉⠛⠿⣷⣿⡿⢿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠙⢿⣷⣄⠀⠀⠀⠈⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣼⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⡸⠟⠋⠁⠐⠠⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠁⠈⠻⢿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠈⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⡁⡀⠀⠈⠙⠻⠿⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣀⣠⠄⠀⠀⠈⣁⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠨⠀⠈⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢀⠠⣾⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠌⠓⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠈⠉⣿⡗⠺⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⣿⡇⠀⢛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⢸⣿⡇⠀⠈⠣⢌⣗⡒⣲⠒⣒⡖⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠆⠘⡆
⠀⠀⣀⢀⡀⠀⠀⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⡩⠖⠚
⠀⡆⠀⠀⠈⠖⠐⠀⠀⣿⡇⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⡔⢧⣀⣠
⠀⡇⠀⠀⠀⠀⠀⠀⠈⠃⠚⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⡀⠀⠀⠀⠀⢀⠤⠐⠒⠒⠐⠛⠛⠒⠒⠂⠀⠠⠤⣀
⠀⠀⠀⠁⠀⠀⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠐⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠁⢈⣿⡄⠀⠀⠀⢠⣾⠋⠁⠀⠀⠈⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⢠⣸⣿⣇⣀⣤⣴⡿⣷⣇⡠⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡟⠋⠉⡡⢾⡇⣿⣯⠄⠀⠀⠀⠀⠀⢸⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⠛⠋⠀⠀⠀⠀⣻⠁⣿⣿⣏⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠈⠀⠀⠂⠀⠀⠀⠑⣱⣿⡿⠋⠀⠀⠀⣀⣼⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣡⡿⢿⣿⠿⠛⠉⠀⠁⠛⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠁⠀⠀⢠⡶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠉⠶⣋⠀⠂⠀⠀⠈⠙⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠘⠀⠀⠀⠀⠘⠿⠿⠗⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⢉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣰⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢈⡺⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡗⠠⡄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠹⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡞⠁⠀⠀⠀⠒⠒⣧⣈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣤⣤⣤⣴⣶⣤⣩⣍⣤⣴⣶⡶⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢆⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠉⠉⠀⠊⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠀⠀⢀⣱⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠠⣴⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⣦⡀⢀⠠⠀⠀⣠⠂⠀⡠⠀⡀⢠⢌⣿⠋⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⢀⠀⠛⢧⣇⢀⣠⣴⠃⠀⠀⠄⠄⢁⣼⠿⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡄⠄⣽⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⢀⣠⣰⣿⡞⠋⠁⠀⢀⣠⣴⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⢀⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠛⠷⣿⣿⡃⡀⣠⡴⠋⠉⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡀⠀⢿⣿⣿⣟⠛⠱⠀⠀⠀⠀⢃⠀⠀⢀⠀⠀⠀⠂⠀⠀⠀⠁⠀⢈⣵⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣼⣾⣿⣵⣷⣌⡆⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⠀⠂⠀⢀⣌⠄⢀⣠⣿⡿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⣟⠋⠙⢛⣛⣳⣶⣶⢟⡛⠛⠿⠾⢶⠆⢀⣀⣤⣼⣴⣾⡿⢛⣩⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠿⠷⠿⠶⠷⠶⠶⠾⣿⣛⣛⣛⣫⣭⣶⠾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠋⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⣀⣤⣴⠶⢶⣾⣿⣿⣿⡿⠷⠶⠶⣤⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠞⠋⠁⠀⠀⠀⠈⢻⣿⠋⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣿⡿⠿⢛⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣎⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢠⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣇⠀⠀⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⢠⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⠀⠘⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣉⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠙⣿⡿⠿⠿⠷⣄⠀⠀⠀⠀⠀⠹⣿⣿⣅⣤⣤⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠋⠉⠀⠉⠙⠻⣆
⠀⠀⠀⠀⠀⠀⢠⣷⠶⠶⣼⠋⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⢋⣉⣤⣤⣤⣤⣌⡉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠛⠙⢳⣄
⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠘⣧⠀⠀⡠⡶⠶⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠛⡟⢠⡶⠛⠛⣦⠀⠀⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢹⡄⠀⠀⢱⡄⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⣰⣴⠏⠀⠀⠀⣿⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⡇⠀⠀⠀⢳⣄⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⣴⣿⠃⠀⠀⠀⠀⣿⠀⠀⣾⢹⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣷⣀⣀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡾⣹⠃⠀⠀⠀⠀⣸⠁⠀⢠⡏⢸⡇⢀⠔
⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠋⠉⠉⠙⠛⠶⣤⡉⠻⢦⣤⣀⡀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠉⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⢠⠏⢠⡾⣱⠎
⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠈⠉⠙⠛⠛⠛⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⡾⢡⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠶⢄⣀⣀⣀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠿⡇⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⠀⠀⠀⠀⢀⣴⠞⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠐⠚⣩⡴⠞⣀⣄⣤⠾⠋⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⣦⣤⣄⣀⣀⣠⣤⣾⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⢤⣤⢤⣴⣾⣿⡉⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣄⣀⡀⠀⣀⣠⣾⡿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⠟⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠈⣷⡀
⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣼⣿⣿⡿⠻⢿⣿⣿⣿⣿⣿⣿⡏⠱⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⢻⣿⣿⣿⣿⣿⡆⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿
⠀⠀⠀⢀⣴⠟⠋⠉⠉⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⣷⠀⠀⢸⣿⣿⣿⣿⣿⣧⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢰⡿
⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⠶⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠻⠿⣿⣿⣿⣿⡏⠀⢀⣾⠃
⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠉⠛⣿⠃⠀⠀⢀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣄⣴⠿⠁
⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⠀⢸⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⣀⠤⠦⢤⡤⢌⣿⡋⠁
⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⡠⠎⡡⠊⠀⠀⠀⠀⠙⣧
⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠹⣿⣿⣿⠿⣽⠏⠀⠀⠀⠀⢠⠞⡠⠊⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⡟⠀⠀⠀⠀⢠⠋⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⣀⠃⠀⠀⠀⢠⢣⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⠶⠛⠋⠀⠀⠀⢀⣮⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⢠⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣤⣀⣀⣀⣀⣀⣀⣤⣴⠾⠛⢧⡀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠛⠛⠛⠉⠁⠀⠀⠀⠀⠙⠷⣤⣤⣞⣁⣀⣀⣀⣀⣤⣤⣴⠾⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣶⣿⣿⡿⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⠿⢿⣿⣿⣿⣷⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⣼⣯⣾⠟⣿⣿⣷⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣧⣼⠟⢿⣦⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⡿⣿⣿⡀⠀⣋⣽⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠋⠃⠈⢹⣿⡿⢟⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣨⣿⣿⡟⠁⡀⠀⠀⠘⣿⡆⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢏⣰⣿⣿⠟⡥⢊⡀⠀⠀⢻⡿⡧⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣠⣾⣿⣿⣿⠇⢠⠂⠺⠀⠀⢀⡀⠠⠀⠛⣿⠁⡀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢊⣼⣿⣿⣿⠙⠁⠂⠘⣶⢂⣀⢀⣨⣾⣤⣦⡀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⢊⣴⣿⣿⢋⣿⣏⣰⠦⠘⣛⢿⣿⠿⡟⣳⣿⣿⠿⠋
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠈⠁⠀⡠⣷⣿⣿⣿⣣⡾⢿⣋⣙⣧⣿⣷⣾⣿⣷⣼⠟⠛⠁
⠀⠀⢀⠄⡪⠋⠁⠀⠀⠀⠀⠀⣰⣿⠿⣿⣿⠿⠿⠻⠊⠁⠀⢿⣾⣻⣼⣿⡟⠁
⠀⣴⠡⠊⠀⠀⠀⠀⠀⠀⠀⢀⢻⣿⡽⠃⠏⠀⠀⠀⠀⠠⠀⠈⣹⠻⣿⠏⠙⠳⣤⡀
⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⣼⣿⣅⠈⠀⠀⣀⠠⠀⢀⣴⠟⠉⢰⡟⠀⠀⠀⠀⠙⠳⢤⣄⣀
⣿⠀⠀⠀⠀⠀⠀⠀⣀⠤⣺⣿⣾⣿⣿⣦⣾⢿⣯⣴⠞⣙⣁⣴⣳⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠻⣷⣔⡠⣤⣤⣶⣯⣶⡾⠟⠛⠙⠛⢿⣧⣴⣾⣿⣼⣿⣿⣿⣿⣿⣅⣀⣀⣀⣀⣀⡀
⠀⠀⠉⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠻⠶⢤⢠⣴⠲⣾⠿⠃

⠀⠀⠀⠀⠀⠀⠀⣠⢴⣦⣄⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⢠⠴⠢⢄
⠀⠀⠀⠀⠀⠀⠐⣷⣯⠿⣛⣯⣭⣝⣫⡖⢾⣿⠀⠀⠀⠀⡎⠀⢠⠈⠋⠉⠉⠑⠲⢅⢈⠇
⠀⠀⠀⠀⠀⠀⠀⡽⣵⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠑⡌⠁⠀⠀⠀⠀⠀⠀⣀⢻⡀
⠀⠀⠀⠀⠀⠀⢰⡧⡿⢿⣿⡻⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡇⠀⠀⠿⠂⠄⣠⡄⢝⠀⡇
⠀⠀⠀⠀⠀⠀⠈⣟⣇⢬⣏⡁⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⣹⡥⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠈⣻⣷⣶⣶⣾⣿⣿⣿⣅⠀⠀⠀⠀⠀⠀⣠⢷⠤⣀⣀⣂⣀⠢⣵⠁
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣹⣿⣿⣿⣿⣿⣷⣿⣷⡀⠀⠀⠀⡜⠁⠀⠇⠀⠀⠀⠀⠀⢃⢧
⠀⠀⠀⠀⠀⠀⡴⣻⢧⣿⣿⣿⣿⣿⣿⣯⣿⣿⣇⠀⠀⢸⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⡎⢣⡀⠀⣀
⠀⠀⣾⠿⣽⣶⠷⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢸⡀⠀⣈⡀⠀⠀⠀⠀⠀⠀⡙⠢⡷⢋⠍⢱⡄
⠀⠀⣿⡀⢸⣿⣿⣿⣯⣻⢿⣿⣿⣿⣟⡵⠞⢿⣷⠀⠀⡜⠠⠀⢄⠑⡄⠀⠀⠀⢀⡰⠁⠀⠁⡀⠀⢸⠃
⠀⠀⠘⢷⣼⣿⣿⡿⠟⠉⠙⠛⢻⣿⣾⠁⠀⣼⡏⠀⠀⠸⡠⠀⠀⠂⢨⡝⠒⠊⠉⠓⢤⣀⠀⢃⡰⠋
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠙⢾⣶⡾⠋⠀⠀⠀⠀⠑⠤⣐⡡⠞⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠰⢿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠆⠀⠈⠉⠉⠙⠛⢻⠀⠀⠀⢀⣴⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⢲⣷⣆⡀⠀⠀⢹⣷⠁⠀⠠⠁⠸⢿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣲⣾⣿⣿⡟⠓⢢⣼⡟⢠⣴⠟⠀⠀⠠⣈⠛⠻⢿⡿⠃⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⡇⠂⠀⡘⠁⢘⠿⣤⣤⣄⣀⡀⠀⢀⣿⣇⠀⠀⣔⣄⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣿⣿⣿⡗⠟⠻⠶⢇⣀⣠⣿⣧⣼⣿⠭⠻⣿⣏⣀⣾⣿⣿⣶⣤⣶⣄⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⣤⣄⣶⡿⣿⢀⣼⣿⠉⠒⠒⠛⠻⠋⠛⣽⢿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⢿⣯⣟⢹⣅⡀⠀⠀⠑⠤⣤⢇⣤⠍⢉⠛⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣧⡄⠰⣄⣤⣾⣯⣏⣢⣄⣭⣭⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣶⡀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣾⣿⣿⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⢻⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣀⣸⣿⣿⣿⣷⣴⣾⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⡄⠀⢀⡴⣶⡆⠀⣠⣤⣶⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣴⣏⡀⣹⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⠃⠈⢉⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣧⣀⠀⢸⣿⣿⣿⣿⣿⡿⣅⣀⠈⠙⠻⢿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡟⡟⠀⠈⠙⡿⣾⣿⣿⣿⡟⠀⠘⡏⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⣿⣿⢸⣧⣀⡀⢸⡇⣿⣿⣿⠏⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⢸⠀⠈⠉⢻⡇⣿⡿⠃⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣀⡀⠘⡇⢿⡁⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⠙⠓⢿⡌⠉⠀⠈⠀⠈⠑⢶⣋⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⢋⡞⠁⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⣙⣦⡀⠀⠀⠀⠀⠀⠈⠳⣄⣤⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣼⣡⣤⣤⡬⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⣇⠈⠉⢻⢦⣤⣀⡀⠀⠀⣀⣻⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣷⠀⡳⠀⠀⣷⠈⠉⢙⡛⠛⠉⣡⢶⠀⡿⠀⠀⠸⠀⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣉⣿⣯⡴⠃⠀⢀⡿⠀⣰⠏⢻⠄⢠⡏⠈⣰⠇⠀⠀⠀⢠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠉⠀⠈⢳⢤⡴⠋⠀⠀⢿⣀⡜⠀⢀⣙⡵⢷⡀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡶⠒⠲⣟⠋⠁⣀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠙⢦⣤⣀⣀⣴⠃⠀⠀⠙⠛⢻⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣠⣿⣿⡀⠀⠀⠀⠀⠀⢠⡞⠿⠛⠫⠗⣶⠟⠉⠉⠉⠉⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢀⠴⣏⡙⠛⡫⠿⣄⠀⠀⠀⢀⡏⠉⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⣠⠞⠁⠀⣀⣀⣀⠀⠀⠈⠳⣄⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃
⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⣼⠃⠀⠚⠉⠉⠉⠉⠉⠉⠒⠀⠈⡇⠈⠛⠶⠦⠤⣤⣤⣤⣤⣤⣤⣤⣤⠤⠼⠁
⠀⠀⠀⠢⣤⡤⠾⠋⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠶⠶⠶⠶⠶⠞⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠛⠛⠳⣦⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⢸⠇⣀⣀⡔⠀⡴⠋⠀⠀⠈⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠸⡇⢀⠀⠀⠠⠘⢋⡉⠉⠉⠛⠧⠀⠀⠀⠀⠀⢹
⠀⠀⠀⣀⠀⠀⠀⠀⢳⣄⠑⠒⣡⢐⠋⠁⠀⠘⠷⡄⡘⠦⠤⠞⢀⡟
⠀⢀⣰⠀⣥⠂⡆⠀⠀⠉⠛⠋⢹⡅⠶⡀⠸⣘⣆⢼⠛⠶⠴⠖⠋
⠀⢣⠘⠆⠁⢸⣀⢀⡀⠀⠀⠀⢸⠈⠉⠀⠀⢈⡀⣸
⠀⠀⢁⠀⠈⠉⡡⠤⠼⠀⠀⠀⢸⡄⠀⠀⠀⠀⠰⡏
⠀⠀⠀⠙⡆⡞⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢸⠃⡇⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⢠⣇
⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⢀⡞⠈⣇⠀⠀⠀⢸⡟⣆⣀⡀
⠀⠀⠀⣈⠀⠓⠒⠒⢒⡒⢒⡞⠀⠀⠸⡄⠀⠀⢸⠁⠸⣦⣉⣉⡛⠓⠒⠒⢒⠒⣶
⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⡞⠀⠀⠀⠀⢷⠀⠀⢸⡇⡀⠘⣆⠀⠀⠉⠉⠉⡿⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠘⡆⠀⢸⠃⠂⠀⠘⣆⠀⠀⠀⢀⡇⡸
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⣷⠀⢸⡇⠀⠀⠀⠈⢧⡀⢀⠼⠰⢇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⢀⠀⣸⠶⢾⣇⠀⠀⠀⠀⠀⢳⣁⠀⠀⠀⠇⡈
⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⡠⠖⠈⠁⠉⠈⣿⣶⣿⣿⡇⠀⠀⠀⠀⠀⢻⡝⠓⠒⠈
⠀⠀⠀⠀⠀⠀⣸⠁⢠⠊⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠈⠢⡀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⢀⡇⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⢸⡇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠘⣇⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⠛⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡍⢿⠛⠒⠒⠒⠚⢻⢻⠉⠀⠀⠱⡄⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⣄⡀
⡠⠒⡉⠉⠉⠉⠓⠒⠲⠤⠤⢤⡽⠜⣆⠀⠀⠀⢠⠏⢾⣤⣤⣤⣤⡽⠶⠾⠗⠒⠒⠒⠦⣀⠀⠀⣀⠴⢉⠴⠋⠉⠑⠢⢵
⠓⠶⣅⣠⡆⣰⠶⠤⢤⣀⣀⣀⣀⣀⡼⠀⠀⠀⠘⠲⠶⠤⠤⠤⡤⣤⣤⣤⢤⡀⠙⡆⢑⣏⣉⣉⣡⠜⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⡀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢀⠇
⠀⠀⠀⠀⠈⠉⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⡶⠶⠾⠶⠦⠤⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠒⠛⠛⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠌⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠳⢦⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠢⣀⠀⠀⠀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡉⠛⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣄⣀⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⣠⠇⠈⢧⡀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡴⠋⠀⠀⣸⣃⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠤⠤⢴⣋⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣌⣷⡄



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠉⠉⠉⠛⠳⢦⡀⠀⢀⣀⣀⣀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⢀⠠⠀⠀⠀⠀⠀⠄⠀⠙⠿⣋⠉⠖⣀⠉⠙⠻⣷⣀⣀⣴⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡄⠀⠈⠀⠰⣿⣠⡀⠀⠀⠉⠁⠀⠉⢹⠃
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠙⠛⠃⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠄⠀⠀⠀⠄⠐⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⢰⡆⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣀⣀⣤⠴⠋⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⠗⠲⠤⠤⠴⠒⠊⠁⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⢸⢠⡏
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠸⡏⠻⢦⣀
⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠀⠀⠀⠹⣄⠀⢹⡆
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡷⢦⣄⡀⠘⣿⠾⠃
⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠈⣷⣀⡿
⠀⠀⠀⠀⠀⣼⠃⢀⣤⣤⣤⣤⣤⣤⣤⣶⣊⣉⣍⣿⡆⠀⠀⠈⠉
⠀⠀⠀⠀⠀⣏⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⣋⣉⣭⣿⣦
⠀⠀⠀⠀⠀⠹⣆⡈⠛⠦⣤⣀⣀⠀⠀⠀⣀⣀⣤⠴⠞⣋⣥⠶⠛⠉⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⣉⠉⠉⠉⢉⣉⣡⡤⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢠⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⣿⣷⣶⣦⣤⣿⣿⣿⣿⣪⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠁⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣷⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⢛⣙⠻⠟⢷⣆
⠀⠀⠀⠀⠀⠠⣤⣶⡁⠀⠀⠀⠀⠀⠀⠂⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠙⠉⠏⢙⡿⠛⠁
⠀⠀⠀⠀⠀⡤⡙⠿⢷⣦⠀⠀⡀⠀⠀⢀⣿⣿⣿⣿⣿⡿⣿⠿⢿⢿⠻⠟⠻⠿⠿⡿⢿⠿⠋⠁⠉⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠁⡀⠰⣾⠿⠄⠀⠀⠀⢀⡼⢿⣿⣿⠏⡁⠁⠁⠀⠈⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⢀⣠⠴⣊⣀⠀⣠⣤⡴⢟⡤
⠀⠀⠀⠀⢀⠪⠀⠁⠀⠀⢀⣀⡤⠔⠋⠘⠾⣟⢿⣦⣉⣤⣴⠄⡲⠶⢤⣤⣤⣤⣴⣆⠙⣶⣶⡦⠍⠩⠿⠀⠀⠈⢉⡴⡩⠄
⠀⠀⠀⠀⣠⠴⠒⠉⠁⠉⠈⠀⠀⠀⠀⠀⠀⠈⠃⠩⠭⠇⠀⠀⠀⠉⠀⠺⠟⠟⠿⠟⠷⣼⠳⠒⠀⠀⠀⠀⠀⠀⠀⠉⠈⠂
⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⡀⠀⠀⢡⠉
⠀⠀⢸⡇⢼⣿⣿⣿⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡐
⠀⠀⠘⢧⣀⢂⠙⠟⠛⠠⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠚⠉⠉⠁⠀⠀⠀⠂
⠀⠀⠀⠀⠈⠉⠉⠙⠂⠨⢧⢅⣌⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡷⡀⢻⣟⣡⡀⠀⠀⣄⠀⠁⣀⠀⡀⡠⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⣘⠓⠏⠁⠙⠓⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⣤⡶⣦⣾⡿⢟⣻⣿⠿⣛⣿⣿⡿⠟⣫⣴⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡞⣼⣿⠏⣴⣿⡏⢰⣿⡿⠃⣴⣿⣿⠋⣠⣾⣿⡿⠛⢛⣿⣿⣿⣿⣶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⢠⣿⡿⢠⣿⣿⠀⣾⣿⡇⠀⣿⣿⠇⢰⣿⣿⠏⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠇⠘⠿⠃⠀⠛⠁⠀⠉⠉⠀⠀⠉⠁⠀⠈⠛⠛⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣦⠀⠀⠀⢴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠿⠿⠿⠛⠃⠀⠀⠀⠘⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢿⣦⣤⣤⣤⣴⣶⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠻⠟⠁⠀⠀⠀⠉⠉⠉⢉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⣿⣿⣏⠉⠛⠿⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠰⠿⣶⣴⣶⣶⣶⣶⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀⠉⠛⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠛⠛⠋⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⢉⣉⣽⣿⣿⡛⠛⠻⠿⣿⣿⣿⣷⣿⣇
⠀⠀⠀⠀⠀⠀⠘⢷⣶⣶⣶⣶⣦⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⡉⠛⢿⣿⠁
⠀⠀⠀⠀⠀⠀⣀⠘⠿⠿⠛⠛⠋⠀⠀⠀⡆⠈⢉⣉⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣉⣿⣿⣿⠛⠛⠿⣿⣿⣿⣷⣾⣿⠆
⠀⠀⠀⠀⠀⠈⠛⣶⣶⣶⣶⣶⡄⣀⠀⣠⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣄⠈⠉⠻⣿⣇
⠀⠀⠀⠀⠀⠀⡀⠻⠟⠛⠛⠛⠁⠈⠛⠋⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣹⣿⣿⠛⠛⠿⢿⣿⣿⣿⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠘⠛⣶⣶⣶⣶⣶⡦⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣀⠉⠛⢿⣿⣆
⠀⠀⠀⠀⠀⣀⡀⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣿⣿⣿⠛⠻⢿⣿⣿⣿⣷⣾⡿⠁
⠀⠀⠀⠀⠀⠉⢻⣶⣶⣶⣶⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀⠈⠉⠻⢿⣷⡄
⠀⠀⠀⠀⠀⣀⠈⠛⠉⠉⠉⠉⠁⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣹⣿⣿⡟⠻⠿⢿⣿⣿⣷⣶⣾⠇
⠀⠀⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⠇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡀⠉⠛⢿⣿⡦
⠀⠀⠀⠀⠠⡤⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢹⣿⣿⡿⠛⠻⢿⣿⣿⣿⣷⣾⣿
⠀⠀⠀⠀⠀⢠⣶⠄⣶⣶⢀⣶⡆⢠⣶⡆⢀⣾⣷⠀⢰⣾⣷⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀⠉⠙⠻⣿⣿⠆
⠀⠀⠀⠀⠀⢸⣿⡀⣿⣿⢸⣿⡇⢸⣿⣷⢸⣿⣿⠀⢸⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⡇
⠀⠀⠀⠀⠀⠸⣿⡄⣿⣿⠈⣿⡇⢸⣿⣿⠸⣿⣿⠀⢸⣿⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⢻⣧⢸⣿⠀⣿⣷⠘⣿⣿⠀⣿⣿⡄⠘⣿⣿⣧⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣽⣷⡘⢿⣦⡙⢿⣧⡈⢿⣿⣦⡙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣿⣿⣾⣭⡿⢷⣮⣽⣿⣶⣮⣽⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣷⣾⣶⣤⣬⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠋⠁⠀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⢸⣿⡿⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⣼⣿⠇⠀⣾⣿⣿⡟⠉⠷⣶⣾⣿⣿⡿⠃⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣿⠀⢸⣿⣿⣟⣷⠀⠀⠈⢻⣿⣿⠇⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⣿⣿⡀⢸⣿⣿⣿⣿⣄⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠹⣿⣧⣘⣻⣿⣿⣿⣿⣷⣤⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣶⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣿⣿⣷⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣴⡾⠟⠁
⢀⣤⣤⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄
⠻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣯⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿

⢀⠀⠀⠀⣤⠀⡄⢀⣀⢀⢀⠀⢠⠀⡀⢀⡀⠀⣄⠀⠀⡀⠀⠀⡀⢀⡀⢀⠀⠀⠀⠀⢱⠄⢀⠀⢠⡄⠀⠀⠀⢀⢶⠀⠦⠀⢢⠀⢉⠀⣆
⠀⠀⠘⠀⠈⠀⠃⠈⠀⠀⠀⠀⠛⠈⠁⠘⠃⠀⠙⠃⠀⠁⠀⠀⠁⠀⠁⠈⠀⠀⠀⠐⠃⠀⠣⠀⠀⠀⠀⠄⠀⠠⠋⠠⠂⠐⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡑⢄
⠀⠀⠀⠀⢠⠖⠉⠉⠑⢢⣀⣀⣀⣠⠊⠉⠁⠙⢢⢀⣀⠤⠄⠒⠒⠂⠀⠐⠒⠂⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⢆
⠀⠀⠀⠀⡇⠀⠀⢀⡔⠋⠁⠀⠀⠈⠑⢦⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⣄⠀⠀⠀⠀⠀⠀⠀⢱⠈⡆
⠀⠀⠀⠀⠱⣄⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⢱⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄⠀⠀⠀⠀⠀⡸⠀⡇
⠀⠀⠀⠀⠀⠈⠉⠇⠀⢰⡀⠀⠀⢴⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⢀⡠⠞⢁⠜
⠀⠀⠀⠀⠀⠀⠀⠸⡀⠈⠁⠀⠀⠉⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠏⢁⡠⠖⠁
⠀⠀⠀⠀⠀⢀⣀⠀⢱⡀⠀⠀⠀⢀⣠⠇⢠⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢈⡉⠽⣆⣴⣄⠴⡁⢀⠇⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢍⣈⠶⠤⠋⠀⢠⣎⣀⣀⣀⣀⣀⣀⣀⣀⡠⠤⠼⠀⠀⢀⣀⠠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣀⣀⡠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⣀⣀⣀⠤⠔⠃




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠋⠉⠉⠉⠛⠒⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⣁⡤⠖⠛⠉⠉⠉⠛⠲⢦⣄⠀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⢋⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠙⣄
⠀⠀⠀⠀⠀⢀⡠⠞⣁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣷⣶⣦⣤⣀
⠿⣶⣤⣴⣚⣩⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠛⠋⠉⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠋⠉⠉⠙⠛⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠚⠋⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠋⠙⠛⠲⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⢉⡼⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠯⣌⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢠⠏⠀⠀⠈⠙⠻⠿⠿⠿⠛⠁⠀⠀⠘⣆⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠉⠉⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⣀⡤⠤⠤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠉⣹⠆⠀⠀⠀⠀⢠⡟⠀⠀⠀⣀⡀⠀⠀⠀⠘⡇⠀⠀⣰⠟⠁⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⢀⡴⠋⠀⠀⠀⠀⠀⣼⠃⢀⡴⠛⠉⠉⠳⣄⠀⠀⣧⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⣾⠁⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠃⠀⠀⠀⠀⠙⣆⠀⢟⣀⣻⣀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠸⡄⠋⣩⣥⣭⡉⠛⣦⣄⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⣿⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣜⣧⠀⠀⠀⠀⠀⠀⢇⣼⠁⠀⠈⠛⠖⠃⠈⢳⣤⠾⢋⣀⡀
⠀⠀⠀⠀⢰⡏⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣤⡼⠗⠃⠀⣿⠀⠀⣴⠄⠀⠤⠗⣘⣇⣠⣿⣩⣷
⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠙⠳⠀⠀⢀⡴⠚⠉⠉⠉⣿⣿⣿⣿
⠀⠀⠀⠀⢸⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠤⠘⠇⠀⢠⣶⠂⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⠀⠹⠿⠟⠙⣆
⠀⠀⠀⠀⠘⣧⠘⡇⠀⠀⠀⠀⠀⠀⠀⣠⠴⠛⣹⠆⢀⣀⠀⠀⣀⣤⡼⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢻⡄⢇⠀⠀⠀⠀⢀⡤⠞⠁⣠⠞⢁⡞⠋⣠⡶⠛⠉⠀⠀⠈⠓⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠈⢷⡘⡄⠀⠀⣰⠏⢠⠶⠋⠁⢀⡞⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡗⠶⠦⠤⣤⡤⠴⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠈⢻⣌⢆⣸⠃⢠⣃⡆⢀⣾⣼⢁⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣿⠀⠀⠻⢶⡼⠃⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠙⠛⡛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⣼⠆⠀⠀⢀⡞⢹⣠⣦⡽⠉
⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣀⠙⢳⣤⣀⡀⠀⠀⠹⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣻⢛⣡⣬⡉⠉⠉⠉⠉⠙⠛⠓⠀⠀⠙⠳⠦⣤⣤⡴⠶⢶⣿⣥⡤⠴⠶⠶⣤⣄
⠀⠀⠀⠀⠀⠀⠹⣾⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⣀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣀⣀⣀⣤⣤⡤⠴⠖⠒⠒⠛⠉⠙⠛⠒⠶⢤⣤⣀⠀⠈⢳⣄⣼⠶⠾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠻⣿⣿⣿⣿⡟⠀⣦⣿⣦⡔⢾⣿⣽⣏⠉⢲⣄⣤⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠈⠻⣿⣿⡇⠀⣙⠃⢠⠶⣿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⠀⣀⠀⣤⡄⠸⠀⠀⠀⠀⠀⠀⠈⠿⠃⠀⠀⡶⢶⣶⣾⣿⡿⣿⡿⠿⠿⠝⠛⠛⠛⠛⠛⠛⠓⠀⠀⠀⠀⠠⠃
⠀⠀⢶⣿⣷⣾⣾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢴⡶⣿⢿⣾⣿⡷⠍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⢀⣻⣿⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢂⣁⣼⣷⣌⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡀
⠀⠀⠈⢻⡿⠛⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣦⣦⣄⣸⣿⣿⣿⣿⣿⣿⣷⣶⣄⠀⠀⠀⠊⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠁⠀⠒⠎⠣
⠀⠀⠐⠖⠳⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⣀⣀⣠⣄⣀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⣴⠿⠋⠉⠉⢀⣈⣿⠞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣦⣤⡄⣠⣴⣾⣿⣿⣿⣿⣷⣤⡀
⠀⠀⢿⣦⣀⣀⠀⠀⠀⠀⢀⣸⣿⣿⠿⠿⠿⠛⠿⠋⠉⠙⠿⠿⢛⣿⣁⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣀⣀⣀⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⡛⠋⠉⠉⠉⠉⠛⢷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠛⠛⠀⠀⠀⠀⠀⠤⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡏⣿⣿⣤⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⠀⠛⠛⠛⣿⣿⡿⠿⠛⠋⠉⠁⠀⠙⠋⠀⠀⢣⠀⠀⠠⠴⠷⢄⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠛⠀⢣⣀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠒⠒⠛⠛⠉⠫⠁
⣶⣶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⢠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡇⠠
⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠈⢣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠶
⠀⠀⢠⣾⡇⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢂
⠀⢠⣿⣾⠃⠀⠀⠀⠀⡆⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⣗⠀⠘⡀
⢠⠏⣼⡿⠀⠀⠀⠀⢰⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠰⡀⠀⠀⠀⠀⠀⡠⠈⠙⣷⣄⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⢦⡀
⡟⢸⣿⠇⠀⠀⠀⢠⡇⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⢃⠀⠀⠀⢀⠜⠀⠀⠀⠘⢿⣦⠀⠀⠀⠀⠀⣿⠀⠀⢸⣏⣧
⠀⢸⣿⠀⠀⠀⠀⣴⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠈⠀⠀⡴⠁⠀⠠⡀⠀⠀⠈⠻⣷⠀⠀⠀⠀⣿⡀⠀⢸⣿⢿⡄
⠀⣼⣿⠀⠀⠀⢠⡏⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢳⠊⠀⠀⠀⠀⠁⠀⠀⠀⠀⠹⣷⣤⠄⠀⢸⡇⠀⢰⣿⣾⣿
⠀⣿⡏⠀⠀⠀⢸⠇⢸⡿⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⡻⠃⢧⠀⠀⠀⠀⠀⠀⠀⠀⢄⣷⠛⣿⡄⢀⢸⡇⠀⢸⢿⡇⢻⡄
⠀⣿⡇⠀⠀⠀⣿⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠘⣇⢸⡇⠀⠀⠀⠀⠘⣀⡴⠋⠙⡀⠸⣷⣠⢸⡇⠀⢠⣾⣇⢸⡇
⠀⣿⡇⠀⢀⠀⣿⠀⣿⠁⠀⠀⠀⠀⠀⠀⠠⠀⣀⠾⠀⢠⠞⠀⠀⢻⡀⣿⠀⠀⠀⢀⡴⠏⠀⠀⠀⠀⠀⢻⣿⢸⡇⠀⢸⢹⣧⢸⣿
⢰⣿⠃⠀⡈⢰⡿⢨⣿⠀⢀⠀⠀⠀⠀⠀⢠⠞⠁⠀⣷⠏⠀⠀⠀⠘⣧⢸⡇⠀⣤⠟⠁⠀⣰⠀⠰⠀⠀⠘⣿⣿⡇⠀⢸⠀⣿⢸⣿
⢸⣿⠁⠀⠁⢸⡇⣸⡟⠀⠀⠀⠀⠀⠘⣰⠋⠀⠀⣰⢿⢠⠀⠀⠀⠀⢻⠀⣷⠘⠁⠐⠀⢀⡇⡆⠀⠸⠀⢠⠹⣿⡇⠀⢸⠀⣿⣿⣿
⢸⣿⠀⠐⠀⣿⠀⣿⡏⠀⠳⠀⠀⢀⡾⠃⠀⠀⡸⠃⠈⡄⢀⡀⠀⠀⠘⣷⢻⡆⠀⠀⠀⣸⠀⠣⠀⠠⠀⠘⡀⢻⣇⠀⢸⠀⢹⣿⣿
⢸⣿⠀⠀⠀⣿⠀⣿⡇⢀⡀⠄⢠⡟⠁⠘⠀⣴⠁⠀⠀⢿⠈⢷⡀⠀⣾⠏⠀⣧⠀⠀⠀⣿⠀⠀⠆⠈⡖⠀⢁⠸⣿⠀⣸⠀⠘⣿⣿
⢸⡏⢴⠀⠀⣿⠀⣿⡇⢈⠁⢀⡿⠀⢀⡀⡾⠁⠀⠀⠀⢸⡆⢈⠇⣼⡏⣶⡀⠸⣆⠀⢸⡿⢠⡶⢤⡀⣿⠀⣿⠀⢻⡇⣿⠀⠀⣿⣿
⢸⡇⠀⠀⠀⣿⠀⣿⡇⠘⠀⣿⠀⠀⠀⣼⢿⡀⠀⠀⠀⠈⢷⡀⣸⢿⣀⣸⡇⠀⢻⡄⢸⣿⠏⠀⠀⢹⣼⠇⣿⠀⢸⣿⡅⢀⠀⣿⣟
⢸⡇⢀⠀⠀⣿⠀⣿⡇⢠⣾⣯⠀⠀⣸⠏⠈⢿⣄⡀⣤⣴⣮⣿⣽⣯⣿⣿⣿⣶⣎⣿⠊⣽⠀⠀⠀⢀⠋⠂⣿⡄⢸⣿⡃⠀⠠⢿⣿
⣼⡇⢘⠃⠀⣿⡇⢸⣷⠸⠃⣿⠀⣸⡏⠀⢴⣆⠾⣿⡿⣿⣿⣿⣿⣽⣿⡿⣏⠛⢏⡡⠊⢹⠀⠀⠀⠟⠀⢸⣟⠀⢸⣿⠁⠀⠸⢸⣿
⣿⡇⢸⠀⠀⣿⡇⣼⣿⡀⡄⡏⣼⠏⠁⢀⣀⣽⡋⠛⠙⢷⣿⣿⣿⣿⣿⣷⣿⠛⠉⢠⠄⣨⣦⣈⢠⡖⠀⣼⣇⠀⠈⢿⡁⡀⢀⣠⡿
⣿⡇⠸⢿⡆⣿⡷⣽⣿⣇⠀⣿⠟⠀⣴⡿⢿⣿⡿⠃⠀⢀⢠⣿⡿⣿⠿⣿⠻⠃⠀⠀⠈⢼⣿⣿⣤⠀⠀⣿⢸⠀⠁⢸⡇⠡⢸⣿⢼
⣿⡇⢠⣾⠀⢹⣷⢸⣿⣿⣀⡟⠀⣠⣿⠒⣾⣯⣍⠀⠰⣿⠃⡤⣠⣯⡞⠁⠈⠿⠄⠐⠀⣾⣟⠋⢹⡏⢠⣿⢸⣼⠁⢼⣿⣡⡿⢃⣿
⣿⡇⠸⣿⣿⢻⣿⠈⣿⣿⡿⠉⠀⣿⣇⣴⣿⣭⣉⣥⣄⣴⣾⡿⢻⣿⡟⣼⣷⣤⣤⣤⡴⢺⡟⢠⠶⣷⣾⡟⡞⢣⣆⠸⣿⡟⢃⣾⢿
⣿⡇⢸⣮⣹⣾⣿⡄⣿⣿⢻⣿⠸⣿⣇⣈⣴⣹⣧⣿⣯⣽⣿⣶⣮⣷⣼⣿⣿⡿⣟⠢⣤⣾⣿⣿⡗⢻⣿⣧⠁⣸⣿⠀⣿⣧⣿⣿⢠
⣿⣧⠸⢷⣿⣾⣿⠀⢻⡟⣾⣿⠁⣿⣁⣿⣿⣿⣿⣿⣿⣿⣟⣛⠘⣻⡟⣉⣸⣷⣾⣿⣿⣿⣿⣿⡟⣻⣿⣿⢀⣿⣿⣄⣿⣿⣿⢿⡇
⣿⣿⢸⣿⣯⣿⣿⡇⣿⣰⣿⣿⣷⠟⣯⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣻⣧⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢻⣿⠃⣸⡷⢋⡀⣿⣿⣿⣾⣧
⣿⣿⣼⣿⡾⢻⣿⣿⠇⢉⣾⢿⣿⣷⠛⢿⣾⡹⡏⠋⠛⠿⠉⠉⠛⢿⣯⢿⡏⠙⠟⠻⠋⠽⠟⠋⡸⠈⣿⢁⡟⢡⣾⠃⣿⣿⣷⣿⣟
⣿⣿⡷⣿⣿⢿⣿⣿⠀⠸⣻⣿⣿⣿⡆⢀⣿⣿⣶⣶⣾⣾⠳⠶⢇⣰⣿⣆⠐⣾⣀⣤⢰⡶⣤⡶⣷⡄⠸⢈⣴⣿⣿⡄⢿⣿⣿⣿⣿
⣿⣿⣧⣿⡿⣿⣿⣿⣷⣠⣿⣶⣿⣿⣿⣿⣿⣿⢛⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⢟⣧⣿⢓⣴⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿
⣿⣿⡇⢿⣿⣿⣿⣿⣿⠿⢻⣿⣿⣾⣿⣿⣯⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣮⣫⣵⡾⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿
⣿⣿⡇⢻⣾⣻⣿⣿⣿⣮⣭⣥⣟⣩⣥⣭⣭⣽⣿⣿⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⠁⣿⣿⣿⣿⣿⡄⢸⣿⣿⣿⣿
⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣷⣶⣦⣶⣿⣿⢿⣿⣯⣿⣿⣷⣿⣿⣿⣿⣿⡟⣰⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿
⣿⣿⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢡⣿⣿⣿⢿⣿⣿⠇⢸⣿⣿⣿⣿
⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣾⣿⣿⡏⣼⣿⣿⠂⣼⣿⣿⣿⣿
⣿⣿⣿⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢸⣿⣿⣿⠃⣿⣿⣿⡄⢹⣿⣿⣿⣿
⣿⣿⣿⣿⡎⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢁⣿⣿⣿⣿⠀⣿⣿⣿⠀⢸⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⠀⠀⡄
⠀⠀⠀⠀⢀⠀⢠⡄⡆⢸⣆⠀⣰⣠⣤⣜⣤⡞⢣⣴⣧⣤⣠
⠀⠀⠀⠀⠈⢸⡈⢿⣇⠀⢹⣾⣿⣿⣿⣿⣥⣾⣿⣯⣽⣿⣗⣋⠅
⠀⠀⠀⠀⢻⣌⣶⣀⡙⣷⣼⣿⡿⠿⡿⢽⠿⣿⣿⡿⠃⠋⠁
⢀⣤⣶⣦⣤⡭⣿⣟⢫⣼⣻⡧⠔⣂⡥⠤⠀⠄
⣷⣭⡿⠿⣝⢌⣉⢻⣿⣺⣿⣿⣿⣿⣟⣷⣦⣤⣴⣶⣤⣀
⠀⠙⠛⠛⢿⣿⣿⡟⡟⢍⠹⠟⢻⢯⣹⢿⣿⣿⡛⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠈⠻⣦⣶⣼⣿⣀⡀⠀⠉⠝⢾⣿⡿⠿⠞⢹⣿⣿⣿⣷⣦⣀⡀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⢿⣿⣾⣦⣤⣿⣿⡟⠀⠉⣶⠙⠉⢿⣿⠛⠫⣙⣿⣿⣯⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠟⠁⠀⠙⢿⣿⣿⣿⣿⠑⠀⠔⠁⣳⣼⡟⠀⠀⢠⣰⣿⣿⣿⠃⠘⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⠀⢬⣿⣯⡑⣾⣖⢼⣿⣿⣿⣯⣄⢼⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡟⠢⠀⢀⡠⣷⡜⣻⣷⣿⣿⣟⣿⣿⣿⣿⠞⡊⣿⣿⡟⠀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢾⣷⣩⣟⡗⣩⣯⣼⣿⣿⣿⣿⣿⣿⣿⡇⢱⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⣟⣼⠙⡿⠿⠿⠿⠿⠿⠟⢻⣯⠘⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡅⢿⠖⡇⠀⠀⠀⠀⠀⠀⠀⠹⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠹⡀⢸⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣘⡁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠐⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢣⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⣸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣤⣐⡃⠄⢠⣟⠴⠀⠀⠀⠀⠀⣀⡘⡡⢴⠷⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠨⠋⠀⠀⠀⣐⡿⣏⢔⣶⠦⣐⠀⡆⠳⠛⠹⠗⠒⠘⠒⠂

⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠤⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠛⠛⠲⣤⡀
⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⢀⣀⣀⡈⠑⢦⡀⠀⠀⣠⣶⣁⣠⣴⣚⠀⠀⠀⡴⢫⢆⠤⠤⠤⡀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠉⠀⠀⠈⢻⡆⠙⢦⡾⠛⠉⠉⠀⠉⠙⠓⠦⣼⠁⣿⡗⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⣰⡇⠀⣠⣶⣦⠀⠀⠀⠀⠀⢰⣶⣦⡀⠘⣷⣄⡀⠀⣀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣤⡀⠠⠤⢤⣶⡿⠀⠰⣿⡿⠇⠀⣀⠤⠤⢄⠈⠿⣿⠇⠀⢻⡋⠉⢉⣡⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠤⣬⠇⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠈⣿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⢶⣾⣤⣄⣀⣀⠀⠀⠀⠘⢤⡤⠃⠀⠀⠠⠤⠤⠶⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠤⠬⣿⡶⠒⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⢀⣀⡀⣰⡿⠓⠂⠤⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡀⠤⠚⠻⣯⣁⡀⠀⠀⠠⠴⠋⠙⠦⡄⠀⣀⣠⣽⠟⠛⠢⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋⠉⠁⠀⠀⠒⠒⠒⠂⠀⠈⠉⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⣰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⢻⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⣿⡄⠀⠀⠀⠀⠘⡌⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠿⣧⠀⠀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⠀⠀⡼⠈⣿⡀⠀⠀⠀⠀⠘⣆⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⢷⡄⠀⠈⣷⠀⠀⠀⠀⠀⠀⢠⡏⠁⠀⡼⠁⠀⢸⣧⠀⠀⠀⠀⠀⠈⢧⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠈⢿⣴⣾⠟⠀⠀⠀⠀⠀⠀⠀⠿⣤⣤⠇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢳⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠈⣇⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡏⠀⠀⠀⠀⠀⠀⠀⣰⢃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣟⠉⠛⠓⠒⠒⠒⠚⣉⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢫⠄⡀⠀⢀⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⣤⡀⠀⣀⢨⡻⣿⠿⠿⠿⠟⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣿⣼⣤⡶⠟⠋⠉⠉⠉⠉⠉⠉⠉⠛⠛⠻⠿⣶⣼⣦⡿⠟

⠐⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠉⢂
⠂⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠂⠀⠀⠈⠀⣄⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣀⠀⠀⠀⠀⢀
⠐⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠄⡀⠀⠀⠰
⠀⠈⠀⠀⠀⠀⠀⠀⠁⠒⠁⠀⠀⠀⠀⠀⠀⠈⠒⠈⠀⠀⠀⢀
⠀⠀⠀⡀⠄⠀⠀⠚⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠠⢀
⠀⠀⠀⢄⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠒⠀⠀⢀⣀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠇⠀⠀⠀⠂⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠄⠀⡀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤
⣿⣯⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣤⡅⠉⠑⠀⠁⠈⠳⠂⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈⠳⠆⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⠉⠀⠠⠀⠀⠠⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠉⠀⡀⠀⠰⠄⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠃⣤⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠯⢑⣢⣄⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡉⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⠰⣦⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠒⠐⠂⠤⠄⡀⣀⠀⠀⠀⠀⠁⢰⡄⢀⠀⠀⠀⠀⠀⠈⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡥⠀⡠⠀⠒⢀⣀⣒⠂⠀⠠⢈⡁⠀⠀⠀⢿⡁⡤⠶⣀⠄⠀⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⡄⣱⣶⠉⠀⠀⠀⠀⠈⠁⠂⠀⠁⠀⠒⠀⠓⠒⠊⣠⠖⠀⠀⠈⠉⢓⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠃⣀⣔⡒⠀⠀⠐⠂⠤⠁⠐⠀⠤⠀⠀⠀⠙⠓⠁⠐⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠙⠳⢆⡙⠏⠉⠀⠉⠐⣤⠀⠀⠀⠀⠉⠀⠐⠒⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⠀⠀⠀⠀⠀⠸⣿⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⣤⠔⠚⠉⠀⠀⠨⠀⢀⣀⣀⣀⡀
⠀⠀⠀⣠⣾⡋⠀⠀⣴⣿⣧⣠⠡⠄⠆⠂⠈⠀⠈⠛⠿⠿⠿⠿⠷
⠀⠀⠠⠿⠟⠛⠂⠈⠉⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢀⠀⢀⠀⡀⠀⢀
⣗⡢⠤⡤⣤⠤⠔⠊⡡⠔⠁⡠⠀⠀⠀⠀⠈
⠦⢬⣑⠒⠒⠒⠊⠉⣀⡤⠊⢀⡄⠀⡔
⠓⠲⢬⣉⠑⠒⠊⠉⢀⣀⠔⠁⢀⠈⢀
⠋⠙⠒⢬⣉⡉⠉⠉⠉⣀⡠⠒⠁⡠
⡔⠉⠛⠲⣬⣉⣉⣉⣉⣁⣀⣤⡊
⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠇⠀⠀⣀⣤⣤⣤⣀⣀⣀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣰⣶⣿⣿⣿⣿⣿⣿⣿⣿⡻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠛⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠉⢻⣿⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠀⡿⠁⡤⠀⠀⡍⢻⣿⠀⠀⠀⠀⣿⣧⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⡟⠠⢀⣇⠀⠀⠉⠀⠸⡆⠹⣷⠲⠶⠴⠿⣧⣤⣀⡀⠈⣻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⣿⠁⠀⢘⣧⠀⡇⠂⠀⢠⣼⠀⢻⠀⠀⠀⠀⠀⠈⠉⠙⠓⠻⠷⣦⣄⡀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠁⣄⣿⡄⠹⠀⣀⠾⣾⠁⢸⠇⠀⠀⠀⠅⠀⠀⠄⠀⠀⠀⠀⠉⠛⠻⠶⣤⣄⡔⡡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠠⠀⠐⠾⠳⣦⡀⠀⠀⠇⠀⠸⠧⠀⠁⠂⠀⢡⣤⡄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⡿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠐⢂⡈⠅⠀⢹⡷⠀⠈⠳⠄⠀⠀⠀⠀⠀⠸⢿⣿⠟⠀⠀⠀⠀⠀⡀⠀⢤⣤⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⣿⠈⠍⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢡⠗⡆⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⣹⣿⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠈⠀⠀⠀⠠⠀⠀⠰⠂⠠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⣀⣤⡶⢾⣿⠛⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠁⠀⠀⠐⠆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⢀⣠⣦⡶⠛⠋⢠⠀⢸⡇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⡀⠀⢐⠀⠄⠀⠁⢀⠀⠀⡀⣀⣴⡴⠶⢲⣿⣿⣿⣿⡇⠠⠀⠺⠀⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣣⠀⠡⠂⠀⠀⣰⣷⣾⣿⣏⠁⠀⠀⡀⢸⣿⣿⣿⣿⣇⠆⠀⠀⠎⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣲⠠⠀⠘⢿⣿⣿⠿⢿⣆⠀⢠⠁⠀⢻⡉⠙⠋⠈⠙⠲⢤⣀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⣿⣛⣹⠂⠀⠀⠀⢉⣛⠳⠶⣬⠷⣌⠁⠄⠀⠙⠦⠬⠤⢬⣁⣀⣬⣽⡷⠶⠾⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠰⠯⣍⡤⠚⠷⠀⡟⢦⣨⢗⣶⣦⣷⣬⣷⠀⣤⠀⣤⡓⠲⡞⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣠⣤⣤⣴⠶⠾⣾⠟⠛⠛⠛⠋⠉⠉⢹⢡⡼⢻⡇⣸⠟⠛⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠼⠃⠀⠒⠶⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠢⡠⠖⠋⠁⠀⠂⠀⠘⠀⠀⠀⠢⠈⠙⢦⣀⠤⠲⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⢴⣶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣶⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡞⠁⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢹⡇⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡀⠸⠿⠤⠤⠿⢇⣀⡀⠀⠀⠀⠀⠈⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⢠⣶⠊⠁⢀⣔⣠⣤⣤⣥⣀⣀⠉⠳⢄⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⡜⠁⠀⠀⠈⠻⠿⣿⣿⣿⠿⠛⠀⠀⠈⣧⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⢣⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⡍⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣙⠦⣄⠀⠀⠀⠴⠧⠀⠀⢀⣠⢴⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠁⠀⠩⠉⠃⢄⠐⠯⠭⠑⠋⠁⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠲⠂⠀⠀⠰⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠈⠑⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠂⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠈⠉⠲⡄⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⢤⡇⠀⠀⠀⠀⠀⠀⢤⣿⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⡇⣀⣀⡀
⠀⠀⠀⠀⠀⣰⠋⠀⣤⡄⠀⡈⣇⠀⠀⠀⠀⠀⠀⠀⢹⠄⠀⠀⠀⣾⠏⠀⠀⠀⠀⠟⠀⠀⣰⣋⠀⢀⠉⢣⡀
⠀⠀⠀⠀⢀⡧⣾⡷⠛⠃⠻⠟⠙⢦⡀⠀⠘⠂⠀⣠⠟⠀⢠⡄⠀⢻⡄⠀⠀⠀⠀⠀⣀⠜⠙⠛⠁⠻⢃⣬⣷
⠀⠀⠀⠀⠀⣷⠀⠀⣾⣿⣧⡀⠀⠀⠉⡛⠛⠛⠉⠁⠀⠀⠀⠁⠀⠀⠙⠦⠤⠴⠞⠋⠀⠀⠀⣴⣶⣶⠈⠁⡇
⠀⠀⠀⠀⠀⠈⠣⡀⠘⠿⠿⠏⠀⠀⢀⣷⠞⠉⠉⠉⠉⠛⠉⠉⠉⠉⠉⠙⠓⠶⣄⡀⠀⠀⠸⠿⠿⠏⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠦⠤⠤⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣄⣀⠤⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣯⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⢹⣿⡟⠉⢻⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣤⣿⣷⣾⢿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣾⣿⣾⣶⣶⣽⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣻⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠛⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣿⠃⠉⠉⠉⠉⠉⠉⢻⣿⣻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣟⣾⡏⠀⠀⠀⠀⠀⠀⡀⠘⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢃⠀⠙⡟⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣄⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⢀⣾⣿⣿⣿⣦⣶⣿⣿⣿⡿⠿⠛⣻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣏⠺⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⢟⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠃⠀⠀⠙⠿⠿⠃⠀⠀⠀⠀⠀⠈⢭⣸⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢖⣛⣉⡉⠛⠲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠶⠦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠁⠀⠀⠙⢦⡀⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⣀⣀⣀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⡟⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⣴⠞⠉⠉⠉⠛⢦⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡟⡾⠀⠀⠀⠀⠐⣆⠀⠀⢸⡄⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠻⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠈⢷⡀⢸⡇⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⢠⡟⢀⣠⡴⠖⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠙⢦⡀⠈⣧⣸⠁⠀⢠⣧⡤⠶⠖⠒⠒⠲⠶⠤⣄⡀⢀⡟⠀⠀⠀⣾⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠹⣦⣿⡏⠀⣐⣋⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢧⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⣿⢏⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠷⣄⠀⠀⢸⣿⣷⡶⠟⠓⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⢀⡾⠁⢀⣴⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠑⠀⠘⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⣠⠏⠀⠀⣾⣿⣿⣿⠿⣿⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣷⡄⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡏⠀⠀⠀⢻⣟⣿⣿⣾⡟⠀⠀⠀⠀⠀⢸⣏⣉⣿⣿⣿⣿⡇⠀⠀⠀⠙⣆⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠉⠛⠋⠉⠀⢀⣀⠀⠀⠀⠈⢿⣿⣿⣿⣽⡿⠁⠀⠀⠀⠀⠸⡄⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠦⠤⠀⢀⠠⠀⠺⣿⣭⣿⡷⠆⠄⡀⠈⠉⢉⡡⠤⠤⠄⠀⠀⠀⠀⡷⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⠭⠂⠉⡟⠁⠀⠀⢰⠀⣩⠁⠀⡀⠀⠀⠑⢦⠁⠦⠬⣙⡓⠂⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡉⠓⠛⠁⠀⠀⠀⠈⠇⠀⠀⠀⠈⠑⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠶⠶⠶⠶⠦⠤⠶⠶⠶⠶⠒⠛⠋⠉

⠀⢀⢀⡀⣀⠀⢀⠀⢀⡀⣀⢀⡀⠀⢀⣀⣀⣀
⠀⠺⠾⠀⠟⠒⠼⠀⠾⠘⠇⠾⠀⠘⠿⠸⠇⠗⠸⠦⠤
⠀⡄⡄⢠⠀⢀⠖⢠⢦⠀⡄⢠⢄⠀⠀⡤⡀⠀⠀⠴⡄⡰⡄⢰⠄⠀⣴⣶⣾⠦⠄⠤⢀
⠀⡇⡿⣼⠀⢸⠀⢸⠈⠀⡇⢸⢸⠀⠀⣇⠇⠀⢸⠀⡇⡇⠀⢸⢸⠀⠻⣿⣧⠈⠁
⠀⠇⠇⠙⠀⠘⠄⠘⠼⠀⠇⠸⠜⠀⠀⠯⠆⢠⠈⠤⠃⠣⠆⠸⠊⠀⠀⠙⣧⣐⣶⡶⠄⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⣠⣴⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⡔⠢⡀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣿⣿⣿⣿⣿⣧⡴⠾⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣩⠭⢶⡏⠋⢳⣸⡠⠽⣄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠈⢧⢠⠜⢳⣞⣿⣷⣧⢤⠼⣆⠀⠀⡾⠶⢦⠀⠀⠙⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⣀⣀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⣠⠆⣉⠁⠓⠛⠂⠠⠌⠦⠤⢂⠈⠀⢀⠀⡴⠋⠀⠀⠘⢦⣀⣤⠄⠖⠉⠀⠀⢠⠖⢪⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠞⠉⠀⠀⠀⠀⠀⠀⠀⠚⠉⠀⠀⠖⠛⠷⠖⠒⠒⠒⢎⠋⠁⠀⠀⠀⢀⡤⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠈⠙⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⢀⠀⡆⡀⠀⠰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣶⣶⣶⡞⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠛⠛⠋⡉⢀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠰⠘⠃⠆⠀⠀⠀⠃⠀⠀⠀⠀⠘⠁⠄⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⠛⠻⢶⣄⠀⠀⠀⣀⣀⣀⣠⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠀⢀⣤⣤⣀⠹⣷⠶⠛⠋⠉⠉⠉⠉⠉⠉⠉⠛⠛⠷⢶⣤⣠⡿⠋⣀⣀⠀⠉⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢰⡟⠁⢈⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢠⣾⠛⠙⢻⣆⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠘⢷⣤⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⣼⠏⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⣌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣁⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠿⢇⡤⠴⢶⣶⡶⢤⣀⢰⣿⡆⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⢰⡏⠀⠀⢙⡿⠃⠀⠈⢷⠉⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⢠⣼⠛⢬⡳⢄⠀⠀⢀⣻⣦⣄⠀⠀⠈⢧⣀⠙⠛⠙⠒⠋⢀⡼⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⣸⣉⡛⠦⣌⡲⣕⠾⣛⠉⠀⠙⠛⠶⣦⣤⣬⣙⣓⣒⣒⡛⣉⣀⣀⣤⡴⠿⣯⡀⠀⠀⣀⡤⠔⣆⣀
⠀⠀⠀⠀⣠⡶⠟⠛⠋⣿⣄⠀⠙⠺⢷⣮⣓⠦⣀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠋⠉⠉⠉⠀⢀⣀⡬⢟⣚⣭⠵⠖⠛⠉⣽
⠀⠀⠀⢸⡏⠀⠀⠀⠀⢿⡄⠉⠲⢤⡀⠉⠛⢯⣝⠿⣦⢄⡀⠀⠀⠀⠀⣀⡠⠤⢒⣊⡭⠽⠒⠋⠉⠁⠀⣠⣤⣤⣤⣿⣀
⠀⠀⠀⢻⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠑⠢⣄⠈⠙⠮⣕⣍⡒⣔⣚⡭⠶⠚⠋⠉⠀⠀⢀⣀⡤⠔⠒⠋⠹⣯⠀⠀⠈⠻⣧⡀
⠀⠀⠀⠸⣧⡀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠉⡆⠀⡏⠉⠉⠉⢸⠀⠀⣀⡠⠴⠒⠋⠉⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⢸⣧
⠀⣠⣶⣦⣝⡻⠶⡶⠟⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡗⠤⠤⠔⣺⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⢸⡟
⣸⡏⠀⠀⠉⢻⣦⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢸⠉⠉⠉⠉⣻⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣠⣴⠿⠷⢶⣦
⣿⢀⣸⡧⢴⡄⠹⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢸⠀⠀⠀⠀⡝⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢹⡏⠀⣴⡄⠀⠹
⣿⠻⠇⣥⣬⠃⠀⣷⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⠇⠛⠰⡿
⢿⡆⢸⣿⣿⣧⠀⣿⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡧⠀⠀⠀⠀⡇⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢸⢀⣾⣿⣧⠀⢠
⠸⣧⠸⣿⣿⣿⠀⢿⣄⠀⠙⠢⣄⠀⠀⠀⠀⠀⡞⠀⡇⠀⠀⠀⢀⠇⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⣼⣼⣿⣿⡿⠀⣸
⠀⢻⡆⠙⠛⠃⠀⠀⠈⢛⣦⣄⠀⠉⠢⢄⡀⠀⡇⠀⡇⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠊⣉⣠⠤⠟⠸⣿⠿⠃⣰⡟
⠀⠈⢻⣆⠀⠀⢀⣠⡶⠟⠁⠈⠙⠦⣄⡀⠉⠲⠇⢠⣇⣀⣀⣀⣸⠀⢸⠀⣀⣠⠤⠒⠚⣉⣀⣤⣶⣞⣋⡉⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠙⠻⠾⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⡀⢸⠢⠭⠭⠥⢾⠀⠘⢉⣁⣤⠴⠒⠋⠉⠀⠀⠉⠉⠉⠻⢶⣤⣤⣤⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣄⣀⠀⣀⡶⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠀⠀⠀⠀⠈⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠈⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⣠⡴⠶⢦⣄⡀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⢀⣤⡴⠶⣤⣀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⢠⡾⠁⠀⠀⠀⠈⢻⡄⠀⠀⢸⡇⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⣿⠀⠀⠀⣴⠏⠁⠀⠀⠀⠙⣧⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⠟⠛⠉⠉⠉⠉⠉⠉⠉⠙⠛⠿⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠻⣦⡀⠀⠀⠀⣠⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣧⡀⠀⠀⠀⣠⡾⠃⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠈⠛⠷⣶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⡶⠟⠋⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢶⣤⡄⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠀⠀⠀⣤⣤⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣿⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⣠⣤⠶⢦⣤⡀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣼⣧⡤⢤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣀⣻⣆⣀⣀⣉⣉⠉⠀⠀⠀⠀⠐⣿⡀⠀⠀⣸⡗⠀⠀⠀⠀⠀⢉⣉⣁⣀⣀⣾⣃⣀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠞⠛⠋⠉⠉⢿⡍⠉⠉⠉⠀⠀⠀⠀⣠⠀⠈⠛⢿⠟⠋⠀⢠⡀⠀⠀⠀⠈⠉⠉⠉⣽⠏⠉⠉⠛⠛⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠘⠷⠶⠶⠿⠷⠶⠶⠛⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⢶⣤⣄⣀⣀⣀⣀⣀⣀⣤⣴⠶⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁





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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⠀⢸⣶⠏⣟⣹⡲⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⡄⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢟⠿⣟⣽⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣠⣴⠖⠂⠀⣤⢴⣾⣾⣟⣿⣷⡾⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠛⢿⣿⣿⣿⣿⣿⣷⣄⣀⣤⠾⢋⡴⠃⢀⣠⣤⣿⣿⣿⣿⣿⣿⠟⣱⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣌⣙⠛⠻⠿⠿⠛⠉⠀⠀⠘⠛⢋⣩⣾⣿⣿⣿⣿⠿⠛⢁⣴⣣⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣽⠟⢛⣒⡶⠶⠶⣄⠙⣻⠟⠛⠿⣍⠻⣝⠛⠓⠛⠛⣩⣽⡯⣴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣶⡿⢿⡷⠀⠈⠛⠉⠰⡦⡀⠈⠁⠈⣷⣤⣤⣤⣤⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣠⠀⠀⠀⠀⠀⠀⠚⠓⠛⠢⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⣼⠃⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⣼⡇⠀⠀⠀⢻⣄⠀⠀⠠⣄⡀⠰⠛⠂⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣿⠃⠀⠀⠀⠈⠻⢷⡀⢢⣕⠮⣷⡘⣆⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀⠀⠀⠀⠘⣇⠀⠉⢻⡄⢷⡙⠀⣠⢳⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⡀⠀⣹⣆⣤⡸⡿⣄⣽⠶⠥⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠁⠙⠀⠙⠓





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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣸⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣨⣧⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⣾⠋⠉⠉⠉⠉⢹⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡏⠉⠉⠉⠉⠉⣷⠀⠀⠀⠀⠀⠀⣻
⣿⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣿⡿⠿⠿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠿⠿⢿⣿⡿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣽
⣿⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠸⠿⠟⢻⣷⡄⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠰⣶⣦⣼⡿⠃⠀⠀⢸⡇⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣻
⣿⣿⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣹
⣿⣿⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣾⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣠⣴⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡀⠀⠈⠈⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣾⣶⣾⠘⢯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣶⣶⣿⣿⣿⣿⠿⡟⣿⣿⣿⣿⡿⢋⡙⢿⡏⢈⣸⣟⡁⠀⠠⣽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⡿⠹⠇⠠⠍⠻⢻⣿⣿⣧⠁⠀⠀⢹⣷⣿⣾⣿⣿⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⢀⢀⡄
⠀⠀⠀⠀⠀⢀⣀⣀⣠⣷⣿⣿⣿⣿⣿⣿⣿⣻⢹⠃⠀⣀⣄⣀⠀⠈⣿⣿⣿⣼⣦⢡⢛⢿⠿⠛⠻⢿⣿⣿⣿⣿⣷⣦⣤⣀⣠⣿⣽⣟⣿⣿⣧⣤
⠀⠀⢴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣠⣠⣴⣿⣿⣿⣷⣼⣿⣿⣿⣿⣷⣷⣾⣴⣤⣴⣤⣴⣾⣿⣠⡟⢹⡿⣻⣿⡯⢊⣭⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠉⠀⠉⠉⠉⠙⠛⠛⠛⠛⠛⠻⠛⠋⠉⠉⠙⠋⠉⠉⠉⠉⠉⠙⢿⣿⠿⡿⠿⠭⠭⣟⣯⣥⠬⣥⣭⣽⣍⣭⣿⠾⠟⠙⠛⠁⠁


⡀
⣷⣦⣤⠀⠀⠀⠀⠀⠘⠿⠂⠀⠀⢀⢰⣆⠀⠀⠀⠀⠀⠀⠀⣠
⣿⣿⣿⣶⣤⣴⣷⣦⣤⣶⣄⢀⣀⣿⣿⣿⣄⣼⣿⣧⣀⡘⢠⣿⣧⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣠⣤⣤⣤⣶⣤⣤⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⣠⠶⢋⣉⣉⡉⠙⠲⣄⠀⠀⠀⠀⠀⠀⣠⠴⠚⠛⠛⠲⢦⣀
⠀⠀⠀⠀⢰⠏⣰⠋⠀⠀⠈⢣⠀⠈⢦⡴⠏⠳⢶⠞⢁⡴⠚⠋⠙⠢⡄⠙⢧
⠀⠀⠀⠀⢺⠀⢿⠀⠀⠀⠀⠀⣀⡀⠌⠛⠀⠀⠘⢀⡏⠀⠀⠀⠀⠀⠈⠀⠸⡇
⠀⠀⠀⠀⠈⢧⡘⠆⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠉⢠⡞⢩⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⠀⢀⡠⠂⢀⡞
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠼⠃⣼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠤⠖⠉
⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢀
⠀⠀⢠⣟⡀⠀⠀⠀⠀⠀⣤⠤⠀⠀⠀⠀⠀⠀⠀⣠⡼⠋⠀⠈⢦
⠀⠀⡾⠀⡿⠀⠀⠀⢀⡔⠹⠀⠀⠀⠀⢀⣠⡴⠞⠉⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠉⠓⠒⠒⠒⠈⠁⣀⡔⠒⢲⡟⠉⠉⠁⠀⣠⠀⠀⢀⡀⠀⠀⠀⠙⢷⣄
⠀⠀⢀⣀⡀⠀⣀⡴⠞⢉⡴⡒⠲⠇⠀⠀⠀⢠⡇⠀⠀⡼⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀
⠀⢰⠟⢫⢂⠈⡃⡤⠤⣞⣩⣔⣀⠰⠈⠉⠛⠋⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⠒⠳⡼⠀⠹⠇⠀⠀⠳⠃⠀⢠⠈⠑⠲⠶⠖⠋⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⢨⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣦⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠉⠉⢉⣉⣉⣉⣉⣉⣉⣉⣙⣛⣛⣒⠲⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠉⠉⠉⠉⠉⣈⢳⣄⠀⠀⠀⠀⠈⠷⢦⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠲⣌⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠶⠶⠞⠛⠉⠉⠀⠈⠙⠶⢤⡀⠀⠀⠈⣑⠦⠀⠀⠀⢀⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡞⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡥⠾⠛⠁⣀⡤⠶⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠴⠶⠖⠚⠛⠛⠋⠉⠉⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡅⠀⢀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⣞⣫⡭⠥⠖⠒⠒⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢋⡿⣿⣿⣿⣿⣿⣿⣃⣠⣶⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⣤⣤⣉⠛⢷⣦⡀⠀⠀⠘⢡⡿⠽⣿⠟⢉⣉⣉⢻⣿⣿⣿⣿⣿⡇⠀⣟⣡⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢉⡟⠿⣿⡹⣷⡀⠀⠀⢈⣥⡀⢎⠐⠿⠟⢳⣿⣿⣿⣿⣿⣿⠀⠀⢫⢿⠟⢩⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣹⣿⣿⣿⣿⣿⣿⣻⠑⢦⠙⠖⠀⠉⠉⢩⠏⠉⡟⠁
⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⣠⣿⣿⣿⣿⣿⣷⡉⠙⠀⠀⠪⠀⠀⠀⠀⠈
⠀⠀⣠⠞⠋⠉⠉⠉⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠸⠁⠀⠀⠀⣀⣀⣼⠇⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⡟⠁
⠀⢈⣠⣶⢻⣿⡏⠉⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⠁⠸⣿⣄⣀⣀⣤⣄
⠀⣾⠃⠹⣼⡿⠃⠀⠀⠀⠀⠀⢀⣴⣿⡿⠟⢻⣿⣿⣿⡿⣿⣿⣶⣤⣤⡉⡟⠻⡟⢟⠇
⠀⣿⡄⠀⠻⠁⠀⠀⠀⠀⠀⣠⣾⣿⠋⣧⠀⠀⢿⣿⣿⡇⢻⣿⣿⣿⡎⡇⠃⠀⠃
⠀⠈⠻⣶⣤⣄⣀⣤⣤⣤⣾⡿⢿⠁⠀⠏⠀⠀⢈⣿⣿⠀⠀⢻⣿⡿⠁
⠀⠀⠀⠀⠙⢯⣏⣉⠏⠉⠉⣧⢾⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠀⠀⣻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣤⣤⡛⠛⠒⠒⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⣇⠙⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⡀⣀⣀⠀⣀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠜⢿⠣⡀⠲⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⠄⡈⠄⠀⡄⠀⠉⠸⣟⣥⠕⠋⠀⢃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠀⠌⠀⠄⠘⢎⢣⡀⠀⠀⠀⠀⠀⠀⢀⣠⣄⣾⣶⣴⣼⡇⠀⡘⢀⠀⠉⠐⠋⠀⠀⠀⠋⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠉⠙⢆⠀⠀⠀⠀⠠⠸⣿⣽⢻⣽⣿⣿⣦⠖⠀⠀⠀⠀⠀⠀⠄⢠⠆⡌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠓⠀⠀⠈⠀⠀⠠⠀⠠⠀⠀⠒⠀⠀⠱⠺⡿⠿⠛⠁⠀⠘⢦⣤⣤⣤⣤⣦⡤⣠⡎⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠻⢶⣤⡀⠀⠀⠀⠈⣿⣭⣿⣿⣵⣿⠃
⠀⠀⠀⠀⣷⠀⠀⣤⡂⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣷⣦⣄⠀⠀⠀⠀⠠⠍⠛⠳⠶⣶⠾⠋⠙⠋⠛⠋⠛⠃⠤⠶⣤⣼⣦⣠
⠀⠀⠀⠀⢸⣇⠀⠀⠈⠂⠐⠊⢀⣴⣶⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠂⡽⠀⠀⠀⠉⠛⢿
⠀⠀⠀⠀⠀⠻⣷⣄⣀⠀⠀⢀⣾⣿⣿⡍⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣤⣀⠀⠀⠀⢀⠀⠀⡀⠘⠲⣤⣀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢷⣿⣿⣿⣿⣧⠀⣿⣿⣩⣿⣿⣿⣿⣿⣿⣿⡿⢥⣿⣿⣿⣿⣿⣿⣦⡤⠊⠀⠀⠉⠁⠀⠹⣿⣿⣦⡄
⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⢹⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣷⣿⣿⣿⣿⡟⣡⣶⠁⠀⠀⠀⠀⠀⠉⠁⠈⠿⡆
⠀⠀⠀⠂⠀⠀⠘⣇⠀⠀⠀⠘⣿⣿⣿⢸⣿⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠟⠋⠁⠉⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⣄⠀⠀⢿⣻⠀⠀⣀⣸⣿⣿⣹⣿⣇⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣩⠿⣋⣡⣤⣶⣦⣤⣀⡀⠀⠄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠰⣷⠘⣿⣆⠸⣿⣿⣿⣿⣿⣿⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣧⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⢈⡀
⠀⠀⠀⠀⠀⢈⣷⡎⣿⡶⡀⠉⠉⠉⠛⠻⠟⠲⠿⠟⠉⠉⠙⠿⣿⠿⠛⠋⠋⠛⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠠⠙⠁
⠀⠀⠀⠀⠀⠘⢿⣷⡸⣷⣰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⠟⢀⣀⣮⣤⢞⠁
⠀⠀⢀⣀⣠⣤⣾⣿⣷⡹⣿⣿⠀⣀⡀⣀⣄⣤⣀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⡶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠉⠙⠛⠉⠙
⠀⠀⠀⠾⠿⠿⠿⢿⣿⣵⣿⣿⣾⣿⣷⡿⠿⠿⢿⡿⣦⠀⣠⣶⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣤⠴⠖⠂⠛⢿⣷⣻⡿⣿⡿⠤⠶⢄⣼⠗⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢻⣵⡷⣌⠉⠻⣿⣾⡏⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡿⣻⣿⣿⣿⣿⣿⡟
⠀⠀⣠⣴⠶⠒⢈⣿⠃⢰⢿⡈⢿⣄⠻⡆⠘⢿⣷⣿⣿⣿⣿⣿⣿⣿⢛⡟⢻⡿⡻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⢠⣶⣶⣦⡄
⠀⠀⠁⠀⢀⣴⣾⣿⡀⠸⣷⣏⡀⣧⡄⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣽⣿⣴⣿⣿⣷⣮⢿⣿⡿⡿⠋⢀⣈⣙⣁⣹⣿⡿⠿⠤⣟⣁
⠀⠀⠀⣠⡾⢻⣯⣽⣷⡀⢺⣯⡥⠈⣛⡄⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⠾⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠙
⠀⠀⣸⣿⣷⠉⣿⣿⣿⣿⡶⣌⣀⠘⠿⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣿⣿⣧
⠀⠀⠿⠿⠟⠻⣿⣻⣿⣿⣦⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣼⣿⣿⣿⣦⠀⠀⠘⣷⣤
⠀⠀⠀⠀⠀⣹⣋⠛⠉⠉⠁⠀⠀⠈⠉⠉⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⢫⣄⣼⣿⣿⣿⣇⣠⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⡿⡿⠿⠛⠛⠛⠛⠁⠁⠉⠀⠀⠀⠀⠀⠉⠉⠻⣿⢯⠁
⠀⠀⠀⠀⠀⠠⢤⣤⣀⣀⡀⣀⣤⣴⠾⠟⢛⣿⣶⣶⡄⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡉⠉⠉⠉⠁⠀⢀⣴⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢀⣸⣣⣴⣂⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠈⠋⠁⠀⠀⠀⠀⠐⠊⠉⠛⠛⠿⡿⠋⠀⠀⠀⠀⠄⠀⠈⠉⠙⠛⠻⠿⠛⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡿⠛⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠐⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣤⠀⢀
⠀⠀⠀⠀⠀⠐⢀⠀⠀⠢⠀⠀⠁⠀⠀⠀⠀⢀⣀⢠⡀⠀⣀⣤⢿⣿⣤⣤⣤⡠⢀⣤⠀⡀⢐⡂⢀⡀⠀⠀⠒⣦⣬⢀⣿⡆⢈
⠀⠀⠀⠀⠀⠀⡀⠐⢄⠠⠀⠀⢠⠀⠀⠀⠀⠀⠈⠠⠓⢼⡿⠀⠈⠈⠁⡌⠻⣧⠸⠻⠿⣿⠛⡉⣻⣇⢀⢀⠀⠀⢀⠀⠈⠑⢒⡤⣀
⠀⠀⠀⠀⠀⢀⠈⢣⡀⠠⠀⠈⠀⠀⠀⠃⠀⠀⠤⠀⣁⠿⠁⣀⠀⠐⢦⣷⣶⡿⠀⠲⣤⣔⠢⠍⠓⠋⣹⠃⠀⣨⣷⢾⣓⡦⠘⢏⠙⣶⣀
⠀⠀⠀⠀⠀⠀⢑⠾⠁⠀⠀⠀⠀⢠⣴⣦⡠⠀⠀⠀⢀⡀⠋⠀⠀⣠⡿⣹⡟⠁⠀⢈⢀⠈⢣⣖⡀⠈⡀⠛⠉⠉⢻⠿⡿⢿⠉⠚⡙⣿⣿⣦
⠀⠀⠀⠀⢀⡀⠁⠀⠀⠀⠀⠀⠆⢿⣿⣿⣿⡀⠀⠀⠀⠂⠳⠐⠿⣯⠞⠃⠀⠀⠀⠀⣁⠐⣇⠈⣵⣠⠀⠁⠈⠀⠞⠀⠠⢌⠦⠀⠓⠹⣯⡘⣧
⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠈⠋⠉⠁⠀⠈⠁⢀⠀⠀⠀⠀⠀⡄⠀⠀⣄⣱⣆⡄⢐⡍⠀⠂⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠂⠀⠸⠟⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠄⠰⣦⠛⠙⢥⠆⠀⠀⠀⠀⠀⠀⠐⠛⠂⠀⢀⠀⠀⠈⠁⠀⠀⡺⣿⣷⠒⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠐⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⣄⠀⠈⠁⠀⠁⠀⠀⢀⡀⠀⠀⠀⠀⢶⡀⠀⠀⠀⠀⠀⠈⠿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠉⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⢦⠀⠄⠀⠀⠀⠀⠀⠁⣐⣿⣇
⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠻⢴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⠄⠸⠟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠉⠀⠀⠀⠀⠀⠶⠳⣾⡩⠤⠀⠀⠀⠰⠶⠶⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠈⠑⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠒⠒⠀⠉⠻⠶⣤⣄⣀⠀⠈⠀⠀⠀⠀⠀⣀⡀⡀⢀⠀⠀⠉⠀⠀⡄⠲⠂⢀⣴⠛⠁
⠀⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⠀⠀⠀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⣄⣀⠁⠄⠤⢀⡀⠀⢀⣀⡀⠦⠐⠈⠀⢀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠀⠉⠛⠿⠠⢯⣭⡅⣤⣀⣀⣠⠤⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⡀
⡔⠉⠉⠉⠒⢄⠀⠀⠀⠀⠀⠀⣠⠊⠉⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠙⢦
⣇⠀⠀⠀⢀⢸⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠘⣄⣀⠤⠤⠤⢤⣀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠈⢧
⠘⢆⡀⣀⣸⡏⠈⠓⠒⠒⠒⠚⠒⠒⠠⠤⠀⠔⣫⠁⠀⠂⠀⠀⠈⠳⣤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠉⠉⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠱⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⡠⠈⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠙⠦⣤⣀⣀⠀⠀⢀⣀⣠⠴⠚⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠈⠉⢹⠉⠉⠉⠻⠶⠖⢃⠀⠀⠠⡀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⢀⡏⠀⠀⠀⠀⠒⠒⠁⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠲⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢦⡀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢼⡇⠀⠙⠲⠶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⢉⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣀⠈⠑⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⢁⡴⠊⠁⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠑⠒⠤⣈⠑⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠯⢤⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡈⠳⢄⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⡠⠔⠊⣠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡳⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⢁⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⢁
⠀⠀⠀⠀⠀⠀⠀⡠⢤⠀⡘⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⢁⡠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠑⢄⣉⣁⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⣇⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢠⠏
⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣤⣀⣀⡀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢸⡀
⠀⠀⠀⠀⡏⠀⠈⠉⠓⢤⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⣠⠖⠋⠉⠉⠑⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢇
⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡈⢧
⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢧
⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠶⢤⣍⣙⠒⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢰⠃
⠀⣀⣀⣀⣀⠤⠤⠖⠒⠛⠉⠉⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠉⠙⠲⢤⣉⠛⠒⠒⠂⠒⠒⠒⠉⣠⠏
⢚⠁⢀⠀⢀⡤⠤⠴⠖⠒⠛⠉⠉⠈⠙⠒⠲⠤⠤⣤⣤⣄⣀⣀⣤⣤⣤⠴⠂⠀⠀⠀⠠⠶⠿⠒⠒⠚⠋⠉⠉⠁⠑⡄⠀⠈⠉⠓⠒⠶⠴⠶⠒⠋⠁
⠈⠛⠼⠦⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠒⠒⠒⠒⠒⠚⠛⠛⢶⠀⢰⣀⡤⠃