Confection Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠙⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⡪⢋⠻⣿⢄⡒⢤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠶⠾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢢⢤⡀⠀⠀⠀⠀⡎⢠⠋⢠⠃⠀⠀⢡⠘⢆⠃⠀⠀⠀⠀⠀⠀⡸⣤⣰⣀⣀⣠⡼⢇
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢤⣆⣊⠜⣣⠄⠀⠀⡼⠺⡤⠜⠠⠤⠥⠐⠂⠒⢳⡀⠀⠀⠀⠀⢠⠁⠀⠀⠰⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⢠⠊⢤⠀⠀⠉⢳⠉⠀⠀⠀⠘⡃⠒⠰⠖⠒⠒⠒⠒⠐⠈⢁⠃⠀⠀⠀⠐⠯⠿⠶⡶⠶⠶⢶⠟⠋⡏
⠀⠀⠀⠀⠀⠀⠨⠀⠀⡀⠐⠆⡐⠀⠀⠀⠀⠀⠇⠀⢠⡄⠀⠀⠀⠠⠦⠀⡜⠀⠀⠀⠀⠀⠘⢄⠈⠁⠀⠀⠈⠀⡰
⠀⠀⠀⠀⢀⡔⡸⡦⣄⣀⠠⠔⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠉⠉⠀⠀⡴⢀⠢⡀
⠀⠀⠀⠀⠀⠙⠺⢼⣏⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠈⠑⠒⠒⠒⠒⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⡜⠁⠂⠀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠙⣿⡿⠿⠀⠀⡸⠁⠠⠆⠀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣤⣀⡠⠏⢢⣀⠠⡀⠀⠀⠀⠀⠀⢀⠜⠂⠀⠒⢅⠀⠀⠀⠀⠢⣀⢄⣈⣡⣴⡾
⠀⠀⠀⠀⠀⠀⠐⢸⠒⠂⡙⠢⡀⠀⠀⠀⠀⠀⠸⣀⣄⠵⠘⠉⠀⠀⣸⡄⠀⠀⠀⠠⢁⠀⠲⠀⣀⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢏⡉⠉⣉⣃⠀⠀⠀⠀⠀⢸⠁⠀⢀⡠⠔⠊⠁⠀⠈⡆⠀⠀⢸⡍⢧⠶⣠⡄⡠⠃⠀⠀⠀⡠⢔⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡤⠤⠤⢈⡆⠀⠀⠀⠀⠀⢗⠉⠀⠀⠀⣄⠤⠒⠀⢡⠀⠀⣸⠻⡀⢶⡹⠋⠀⠀⠀⠀⠾⠄⣠⣏⣨⡋⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣀⠲⠇⠀⠀⠀⠀⠀⠘⠤⠐⠊⠁⠀⣀⠠⠔⠊⠀⢀⡿⣎⣱⠎⠀⠀⠀⠀⠀⢸⠤⠐⣆⡸⠷⢛⣄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⠤⡀⠀⠈⠢⠔⠊⠁⠀⠀⠀⠀⠀⢸⢛⡽⠃⠀⠀⠀⠀⠀⠀⠘⣤⠋⡬⠓⠶⠻⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⡀⢮⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠠⠤⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠂⡀⣪⡸⠋⠶⠲⠤⠤⣄⣀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⣠⡤⢦⡄⠀⠀⠀⠀⠈⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⠙⠁⠀⠀⠀⠀⠀⠀⣀⣤⢆⠔⠒⠲⡠⣄
⠀⠀⠀⠀⠀⠀⣿⣇⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⣿⠀⠀⢀⡀⠀⠀⠀⠀⡴⠍⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠂⠀⠻⣷⡀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠈⠑⠢⢤⣀⣾⡇⠀⠀⠏⢈⡷⠀⠀⢸⠃⠀⠈⢡⠄⠛⢄⠉⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⣼⡟⠀⠀⣴⣳⢀⡴⠀⣠⡶⠀⢸⣿⠓⠒⠒⠒⠋⠀⠀⠀⢰⢄⠀⠀⢣⡀⠀⢀⠇⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⢀⣿⠃⢠⡄⢈⢇⣾⠁⢰⡿⠁⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢮⡀⠀⠀⠉⠈⠁⠀⠀⢠⠏
⠀⠀⠀⠸⢤⣀⡀⠀⣀⣼⡿⠸⣿⣀⣼⣿⡌⢸⡏⠀⢼⡇⢀⠜⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣠⡀⣀⣀⡠⠞⠉
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠉⠉⠀⠉⠀⠀⠁⠀⠀⠁⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠤⠤⠶⠖⠒⠒⠒⠚⠛⠛⠛⠒⠒⠲⠶⠦⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄
⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⢀⣠⠴⢖⠚⢻⡟⢿⡓⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠘⣷
⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢧⣸⠇⠀⠀⣀⡿⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⢸⡇
⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⠤⠶⠶⠖⠛⠛⠉⢀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⡴⠟
⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠀⣼⠉⠁⠉⢹⡇
⠀⠀⠀⢸⣿⠆⢠⠶⠤⣄⣄⠀⢀⠀⡔⠚⠛⡆⠀⠀⠀⢰⠉⡆⢸⠀⠀⠀⢆⢀⡴⣿⠀⠀⠀⣾
⠀⠀⠀⠀⢿⣆⡾⢠⠀⠈⠫⡁⢀⠤⡿⠀⠀⣧⠀⠀⠀⣸⠀⠙⠞⠀⠀⠀⠘⠦⠾⠃⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠈⠁⠀⢧⠀⠀⠈⠓⠚⠁⠀⠀⠘⢦⣠⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⣠⡤⠶⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠒⠒⠶⠖⠒⠒⠒⠚⠋⠉

⠀⠀⠀⠀⠀⣠⡤⠤⠤⢤⣤⣤⠤⠤⠤⣄⠀⠀⠀⠀⠀⠀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣰⢀⡒⣎⠜⣁⠦⣤
⠀⠀⠀⠀⠀⣿⡂⠀⠀⢸⣿⣇⣀⡀⠀⣿⠀⠀⠀⠀⠀⢠⡿⠿⠿⠚⣿⣶⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⡿⠿⠿⢿⣿⡾⢷⣦⣌⣔⠁⡸
⠀⠀⠀⠀⠀⣿⡿⠿⠿⢿⣿⡿⠿⠛⠛⣿⡀⠀⠀⠀⠀⠀⣇⣀⣀⣀⣿⣿⣀⣀⣀⣀⡶⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⢸⣿⡇⠀⠀⠉⢹⡇⣘⠋
⠀⠀⠀⠀⠠⣿⣀⣀⣀⣸⣿⣇⣀⣀⣀⣿⠂⠆⠀⠀⠀⢠⡿⠿⠿⠛⣿⣷⡿⠿⠿⠿⡇⠀⠀⠀⠀⠀⠐⣶⣿⠿⠿⠿⢿⡿⠛⠿⠿⢿⢿⡇⢉
⠀⠀⠀⠀⠈⠿⣿⣿⠿⣿⡏⢛⠛⠛⠛⠿⡡⢘⠂⠀⠀⠸⣇⣀⣀⣀⣿⣿⣀⣀⣀⣀⡿⠀⠀⠀⠀⠀⠐⣯⡵⠀⢀⡠⠸⡄⠀⠀⠀⠀⢠⠀⡶
⠀⠀⠀⠀⢠⣾⣿⣿⠿⠛⠀⠀⠀⠀⠠⠄⠳⡇⠀⠀⠀⢀⡿⠛⠛⠛⣿⣿⠿⠿⠿⠿⡇⠀⠀⠀⠀⠀⠀⠛⠛⠉⠉⠘⠓⠀⠀⠀⠀⠀⣟⣰⠁
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠸⣇⣀⣀⣀⣿⣿⣀⣀⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠛⠛⣿⣾⠟⠛⠛⢻⡄⠀⠀⠀⠀⠀⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣤⣄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠸⣇⣀⣀⣀⣿⣷⣀⣀⣀⣸⡇⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢠⣾⠋⠁⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⢰⡟⠛⠋⠙⣿⣿⠛⠛⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠤⠀⢀⣴⣿⣅⡀⣸⠏
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢒⡒⠛⠙⠀⠀⠀⠀⠀⠸⠧⠤⠤⠤⠿⠿⠤⠤⠤⠼⢇⣤⡴⠓⢄⠀⠀⠀⠁⠀⠀⢀⣼⣿⡟⠙⠻⣿⡏
⠀⠀⠀⠀⠀⣇⡀⠀⢀⡀⣀⣐⠤⢩⡿⣴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⣿⠟⠁⣠⠼⠃⠀⠀⠢⠀⢴⣋⣾⡟⠀⣠⣰⠏⠘
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⡶⣾⣿⠏⠙⢾⣻⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⢤⣱⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣿⡇⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⠞⠁

⠀⠀⠀⠀⠂⠀⠀⠉⠉⠀⢠⡀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠉⠉⠀⢠⡄⠀⠀⠉⠉
⠐⠄⠄⠀⠀⠀⠀⠀⠀⡤⠔⢇⠀⠀⠘⠀⠀⠀⠀⠀⠐⠄⠄⠀⠀⠀⠀⠀⠀⡤⠔⣇⠀⠀⠘
⠀⠀⠀⠀⣄⠐⠂⠀⠀⠓⠲⠂⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠐⠂⠀⠀⠓⠲⠎⠀⢀
⠒⠀⠀⠀⠈⠙⠂⠀⠀⢀⠄⠀⠀⠄⠈⠉⠁⠀⠀⠀⠒⠀⠀⠀⠈⠙⠂⠀⠀⢀⠄⠀⠀⠄⠈⠉⠁
⠀⠀⠀⠘⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠖⠋⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠖⠋⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠘⠄⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠈⠄⠀⣀⠆
⠂⠀⢐⠘⠙⢢⠄⠀⠀⠈⠀⣀⠀⠀⠀⠀⡀⠰⠙⢢⠆⠀⢘⠘⠉⢢⠀⠀⠀⠈⠀⣀⠀⠀⠀⠀⡀⠰⠙
⠀⠀⠈⠓⠒⠉⠀⢠⡄⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠙⠒⠉⠀⢠⡄⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣤⣴⠆⠀⠉⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⠆⠀⠉⠀⠀⠀⢠
⠀⠀⠀⠀⠢⠀⠀⠉⠉⠀⢠⡀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⠉⠉⠀⢠⡀⠀⠀⠉⠉
⠐⠄⢄⠀⠀⠀⠀⠀⠀⡬⠔⣃⠀⠀⠘⠀⠀⠀⠀⠀⠐⠄⠄⠀⠀⠀⠀⠀⠈⡭⠔⣂⠀⠀⠘
⠀⠀⠀⠀⣄⠐⠂⠀⠀⠓⠲⠆⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣄⠐⠂⠀⠀⠓⠲⠊⠀⢀⠀⠄
⠒⠀⠀⠀⠈⠙⠂⠀⠀⢀⠄⠀⠀⠀⠈⠉⠁⠀⠀⠀⠒⠀⠀⠀⠈⠙⠂⠀⠀⢀⠄⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠖⠊⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠖⠋⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠈⠄⠀⢀⠆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⡀⠀⠀⠈⠄⠀⢀⠆
⠀⠀⢈⠘⠙⢢⠀⠀⠀⠈⠀⣀⠀⠀⠀⠀⡀⠰⠙⢀⠄⠀⢐⠘⠉⢢⠀⠀⠀⠈⠀⣀⠀⠀⠀⠀⡀⠰⠙
⠀⠀⠈⠑⠒⠉⠀⢠⡄⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠙⠒⠉⠀⢠⡄⠀⠀⣿⡄
⠀⠀⠀⠀⠀⡀⢠⣤⣴⠆⠀⠉⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⣤⣴⠆⠀⠉⠀⠀⠀⢠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡄⠀⠀⠀⠀⠀⢀⠔⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠜⠄⠆⠢⠂⠄⠴⢣⠄⠄⡐⡡
⠀⠀⠀⠀⠀⠀⠀⠱⣌⡢⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠯⣌⠙⣷⣄⠄⠀⠀⠀⠀⠀⠀⠀⢠⡄⠐⢲⣴⠄⠒⢢⠀⠀⠀⠀⣀⡀⢀⡠⠤⢤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡀⠠⠒⢊⡂⡀⠀⠀⠀⠀⢸⣷⠶⢾⣿⡶⠶⢾⡀⠀⠀⠀⠈⠁⠈⠃⠒⠐⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣶⡚⢻⣯⠆⠀⠀⠀⣾⣧⣄⣸⣿⣤⣤⣼⡇⢂
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⣀⣀⣀⠉⠀⠐⠁⠀⠀⠀⣉⣿⣿⡿⠃⠉⠉⢉⢇⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢤⡄
⠀⠀⠀⠀⣤⣐⡒⢚⠳⠶⠞⠳⠛⠓⠶⠿⠦⠦⡄⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣆⣈⠂⢀⣠⣵⡆
⠀⠀⠀⠀⠈⠛⠩⣙⣛⠛⠚⠳⠖⠒⠒⠛⠺⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⣲⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠈⠠⠤
⠀⠀⠀⠀⠀⠀⡀⣠⡄⠂⢠⠰⠐⠀⣀⣤⣶⡿⠃⠀⠀⠀⠠⠀⠀⠀⠀⠐⢄⡉⡃⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣄⠀⠀⢀⣐⣀⣴
⠀⠀⠀⠀⠀⠛⠛⠶⢷⣼⣶⣶⣾⣿⡽⠟⠋⠀⠀⠀⠀⠀⠘⠂⠀⠐⠲⠂⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡄⠀⠈⠉⢠⣈⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⣌⢄⡒⠂⠒⡀⢀⠀⠀⠀⠀⠠⠀⠐⢀⡉⠀⠂⡤⣔⡾⠟⠀⠀⠀⠀⠀⠀⠁⠉⠉
⠀⠀⠀⠀⠀⡀⠀⠀⣌⢀⡜⠊⢛⠀⡳⢄⠀⢉⣮⣤⠶⠂⠀⠺⠯⣎⣤⢡⡄⢶⡤⠚⠁⠀⠀⠀⠀⠀⢤⣀⢀⠀⠀⠀⡀
⠀⠰⣦⠉⠀⠙⢌⠚⣀⠀⠀⠄⢈⣢⣤⡶⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠉⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠁⠀⠀⠲⡐⡖⠂⠄
⠀⠀⠈⠿⠂⠢⠂⠱⣍⣤⠼⠟⠛⠉⠀⠀⠀⢀⣄⠤⠀⠐⠂⠀⠀⢠⡄⣀⣒⠦⠀⠀⠀⠀⢀⡀⠀⠉⡔⠀⠈⢄⢐⡜⣏⠉⠂⡀⢤⣰⡂
⠀⠀⠀⠀⠐⠷⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠘⠂⠀⠀⢴⣤⠀⠀⠈⠀⠀⠀⠀⠀⠈⠙⠘⠞⠢⣤⠔⠂⠙⠈⠃⠼⠷⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⢀⣴⠦⠳⡤⠷⠀⠀⠀⠀⠀⠀⠀⢀⣤⣷⡾⣤⡀⠀⠀⠀⠀⠀⠀⠀⣘⠡⢲⢎⢳⢢⢱
⠀⠀⠀⠀⠀⡠⢸⡁⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⡎⡀⠀⠀⢇⢱⠀⠀⠀⠀⠀⠀⠀⠰⡰⢞⣮⡛⢎⡜
⠀⠀⠀⠀⠀⠑⢤⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣓⣓⣒⣒⣚⣒⠆⠀⠀⠀⠀⠀⠀⠘⠕⠋⠭⠜⠢⠇



⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠠⠤⣀
⠀⠀⠀⠀⠀⣠⣣⣜⣒⣢⣄⡀⠀⠀⠀⠀⠀⠀⠀⡠⠼⠌⠡⠧⢄⠀⠀⠀⠀⠀⠀⠀⢰⣁⣠⠔⢄⠈⢧
⠀⠀⠀⠀⠀⣷⣦⣴⣳⣦⣴⣟⠀⠀⠀⠀⠀⠀⠀⠑⡆⠀⠀⢰⠊⠀⠀⠀⠀⠀⠀⠀⠸⡀⠘⠢⠊⢉⡏
⠀⠀⠀⠀⠀⠋⠛⠋⠀⠛⠋⠃⠀⠀⠀⠀⠀⠀⠀⠮⣀⠖⠢⣀⠵⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠒⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣀⡤⡖⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠒
⠀⠀⠀⠀⠀⠀⠠⡓⢝⢮⣲⠃⠀⠀⠀⠀⠀⠀⠀⢸⠭⠝⠫⠭⡇⠀⠀⠀⠀⠀⠀⠀⢰⠉⠉⠉⠉⣓⢢
⠀⠀⠀⠀⠀⡠⢖⡝⠢⠓⠃⠀⠀⠀⠀⠀⠀⠀⢰⠭⠕⠭⠭⠪⠭⡆⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⢀⡵⠃
⠀⠀⠀⠀⠘⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠒⠒⠒⠒⠃⠀⠀⠀⠀⠀⠀⠰⠭⠥⠬⠭⠔

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⢄⣀⠀⢠⠚⠱⠦⠰⡖⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⡠⠒⣄⡀⠀⣠⠛⠐⠁⡠⠠⡈⠚⠓⣄⢂⣰⠀⡀⣨⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠉⢰⡀⢠⠶⡖⢚⠓⢚⢛⠛⡓⣦⣸⠈⠚⡕
⠀⢱⠦⡑⠚⠫⠭⣱⢄⠀⠑⠒⢁⠤⢔⠬⡎⡁⠨⣀⠸⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠤⢬⡋⡀⠘⡌⡆⢰⡄⠀⡃⢸⣇⡀⠈⢣
⣠⠊⠀⠀⠀⢀⡴⠋⠏⠂⠀⠀⠘⢄⠜⢀⣿⠪⡆⢀⡆⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⣁⠀⣤⡀⡷⡂⠀⡇⡇⢸⣷⢀⣇⡿⠹⣱⠋⠁
⢧⣀⣠⠞⠳⡀⠉⢲⡴⣈⢁⣈⢂⠄⢒⠞⠘⢦⣥⡼⠀⠀⠀⠀⣀⠤⠤⢖⠒⠖⣲⠶⠤⢤⣀⠀⠈⠋⡿⢸⠔⠉⠁⠈⠚⠛⠃⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠑⠒⠊⠙⠻⠤⠤⠼⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠏⣈⠐⠀⠤⠟⠟⠓⠶⣐⠲⢬⡇⠀⠀⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠉⠙⠒⠒⠖⠒⠒⢚⠋⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢠⠀⠀⠀⡇⠀⠀⢸⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠄⣤⠤⣀
⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⢇⡀⢸⠀⠀⠀⡇⠀⠀⢸⣀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢎⠀⠀⠈⢰⠒⢢⠑⡄
⠀⠀⠀⠀⠀⡎⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠙⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⡠⠂⡄⠐⡌⠙⠉⢠⠸
⠀⠀⠀⠀⠀⣧⡀⠘⢦⡀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠈⠀⠀⠈⠈⠁⠔⠢⡌⠓⠇
⠀⠀⠀⠀⠀⢣⠈⠢⣀⠈⠓⠤⠤⠀⠤⠴⢛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠊⠁⠀⠉⠑⢒⡢⠤⣀⣀⠀⠀⠀⠀⠘⢇⢑⠀⠄⡹⠀⠓⠊⣠⠔
⠀⠀⠀⠀⠀⠈⠳⣄⠀⠉⠑⠂⠤⠤⢤⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⣁⠀⠀⠀⠀⠠⠞⠉⠀⠀⠀⠀⢉⠱⠆⠀⠀⠀⠙⠢⠄⠴⣠⠶⠒⢩⣑⣲
⠀⠀⠀⠀⠀⠀⠀⡼⠙⢲⠤⠤⠴⠒⠉⠀⠀⠀⠀⠀⠀⢀⠔⠲⡬⡄⠀⠀⠀⠀⡉⠂⠀⠀⠤⣀⠀⢀⠤⠊⠁⠀⢸⠀⠀⠀⠀⠀⠀⠠⠌⠒⢤⠃⢣
⠀⠀⠀⠀⠀⠀⢠⠃⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠓⠒⠒⠠⠝⣶⡤⡀⠀⠀⠀⠀⠀⠀⡠⠊⡅⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢣
⠀⠀⠀⠀⠀⢠⠏⢠⠃⠀⠀⠀⠀⠀⠀⢀⠴⣚⠁⠀⠀⠀⠀⠀⣀⠔⠡⠊⠙⠒⠲⢤⣖⠙⠦⡀⠀⣷⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⢧
⠀⠀⠀⠀⢠⠏⢀⠇⠀⠀⠀⠀⠀⠀⠀⢘⠓⢤⡑⠢⣄⣀⣠⡢⠴⠥⣀⣀⣀⣀⠐⠁⠔⠃⠀⣇⠔⠉⠀⠀⠀⠀⢀⡠⠴⠒⠒⠶⣶⣄⠀⠀⠀⠀⠀⠑⠒
⠀⠀⠀⠀⠫⣀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣀⠈⠇⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢉⠀⢀⡸⠤⠃⠀⠀⠀⠀⢠⠞⠉⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠁⠚⠈⠀⠈⠓⠊⠁⠉⠛⠒⠉⠀⠀⠀⠀⠀⠀⢰⡏⡀⠀⢀⡴⠛⢉⠵⣖⢒⠠⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠬⢦⠏⠀⡔⠓⢁⡇⠀⠈⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣸⡧⠀⠳⢤⠀⠀⠀⠀⠀⠀⠀⠹⣄⡀⢘⡄⢀⠼⠖⠉⡌⢆⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠒⠚⢍⡑⢄⠀⠈⣦⡤⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣏⡙⠷⣌⣀⣠⡷⠚⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⠋⠍⡑⢄⠀⠀⠀⠹⡘⡄⣠⠛⠷⠤⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠈⢦⠘⢆
⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⠔⢈⡉⠒⢄⠠⡀⠀⠀⠑⠀⡆⣀⣠⠴⠗⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠳⡀
⠀⠀⠀⠐⡀⠀⢫⠑⠒⠚⠒⠀⠈⠆⠀⢱⢰⣀⡠⠴⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠙⢆
⠀⠀⠀⠀⡟⠑⠂⡹⠒⢲⠐⠥⢀⠤⠤⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠜⠁
⠀⠀⠀⠘⣇⠀⣾⠝⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡞⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣿⠀⡇⢀⠀⠀⠀⠉⠛⠛⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡖⠛⠉⠉⠉⠉⠙⠀⠀⠏⠀⢀⡤⠔⠀⣀⣀⣀⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠉⡡⠴⠊⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢷⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣤⠴⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢤⡀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠈⠳⣄⠀⠀⠀⠀⠈⠛⠦⣄⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠈⠙⠳⢦⣾⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⣛⡙⠁⠀⠀⠀⠀⠀⠙⠶⣤⣀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⣠⠞⠁⠠⠒⠉⠁⠠⠖⠂⠀⠀⠀⠀⠀⠀⠀⠉⠙⢛⣿⠟⠁
⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢶⡶⠤⠶⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠶⢤⡀⠀⠘⠀⡆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠁⡄⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠘⠚⢁⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡾⠁


⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣻⣿⣻⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⠀⠁⠀⠁⠈⠛⠉⢰⠢⡀⠀⠀⠀⠐⢀⣠⣠⠐⠂⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⣠⠤⡀⠀⠀⠀⠁⠠⠀⢀⠄⣠
⠀⠀⠀⠀⠀⠀⠘⠧⢀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⠝⠂⠀⠀⠈⠀⢻⠿⣆⠀⠀⣀⣤⡾⢿⣁⢰⠀⠀⠀⢡⢀⡹⠳⣂⢀⣀⣤⠟⢿⡦⡇
⠀⠀⠀⠀⣀⡀⠀⠀⠀⠉⠘⠀⠒⠒⠐⠓⠛⠋⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠙⠛⠋⠉⠀⠀⠈⠀⠀⠀⠀⠀⠙⠁⠀⠙⠛⠛⠁⠀⠀⠉⠃
⠀⠀⡔⠉⠁⠀⠸⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣠⠀⠀⠀⢀⡆⣠⢄⡠
⠀⢠⠈⢃⠀⠀⠀⡦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠀⢤⣄⠔⠀⠀⠁⠀⠁⠀⠉⠉⠈⠁⠈⠁⠀⣦⡄⠉⣻⠀⠀⢾⠋⢡⣤⡿⠀⠀⠀⠀⡆⡈⠤⠆
⠀⠀⢶⣬⣠⣠⣶⣿⠃⠀⠀⢀⡤⠖⠲⣦⡄⠀⠙⠛⠋⠉⠷⠶⠶⠶⠒⠶⠶⠶⠶⠶⠶⠶⠶⠶⠏⠙⠚⠿⠀⠀⠈⠤⣰⡼⠁⠀⠀⠀⠀⢰⡀⡴
⠀⠀⠀⠉⢻⣿⠋⠁⠀⠀⠀⣾⣤⣴⣾⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢘⠿⣦⡀⠀⠀⠀⠀⡜⢿⣷⣆
⠀⠀⠀⠀⢨⠿⠀⠀⠀⠀⠈⠀⠁⠙⢿⣿⣿⣿⠀⠀⠀⢠⣤⣀⠀⠀⣄⣀⡀⣤⠀⣀⣠⠀⠀⡀⠀⠀⠀⠀⠀⣌⠑⠏⠀⢹⣟⡆⠀⢠⠀⠀⠀⠁⠠⣧
⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠄⠄⠽⠿⠿⠃⠀⠀⠀⢸⣺⣍⣷⣌⠏⠉⠀⠀⠀⠈⠉⣷⣮⡁⠀⡇⠀⠀⠀⢅⣀⣦⣀⣀⣽⡇⠀⠸⣠⣤⣤⣤⣴⡿
⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠸⠿⠋⠉⠙⠶⠤⠤⠤⠴⠶⠾⠃⠉⠛⢾⠇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡆⠀⠀⠠⠤⠤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠒⠀⠀⠀⠐⠺⢛⠑
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢶⠂
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡆⢀⣀⣀⣀⣀⣿⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣈⡇⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⣀⢧⣸
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠓⠀⠒⠒⠒⠒⠋⠀⠀⠀⠀⠉⠀⠈⠉⠉⠈⠀⠉⠉⠈⠉⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠉⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⢰⣦⡀⠀⠀⢀⠈⠛
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⠚⠛⠒⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡏⠀⠀⠀⠀⠀⠂⠀⠀⡀
⠀⠀⢦⣀⣀⡠⠢⣀⠀⢀⡠⠶⣄⣀⣠⠇⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡆⠀⠀⠀⢐⠐⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠠⣶⣾⣷⣬⣭⣵⣶⣷⣶⠮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠈⠙⠛⠿⠿⠟⠛⠋⠁⠀⠀⠀⢀⠤⠒⣒⡙⠹⢢⢀⠜⠨⢤⠂⠑⡄⠀⠀⠘⠿⠶⣤⣤⣀⣀⣀⣠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡄⣼⣿⣿⣶⣤⠁⣠⣤⣴⡖⣖⠓⢦⠀⠀⠀⠀⠈⠀⠉⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⠹⢿⣟⣿⡼⠀⢻⣿⣿⣿⠏⣰⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣠⡆⢨⣡⠄⡗⣠⠈⢩⡁⣰⠆⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠃⠉⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠶⠄
⠀⠀⠀⠀⠀⠀⠘⠋⠂⡄⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠒⢀⣌⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⣃⠲⠈
⠀⠀⠀⠀⠀⠈⠒⠠⠒⢁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣀⣀⣴⣤⣴⣿⠆⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣷⣤⣤⣴⠟⠓⠲⠶⢿⣿⠿⠟⠛⠁⡸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠟⠛⠋⠁⠀⠀⠀⠀⢠⠀⠀⠠⠀⠀⢀⠉⠀⠀⠐⠃⠀⠂⠀⠐⠀⠀⠀⠀⠄⡣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⣠⣴⣶⣲⣶⣦⡄⠀⠀⠀⠀⠀⠀⢠⣴⣾⣿⣷⣶⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣤⣀
⠀⠀⠀⣤⠼⢻⡿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣘⢿⣿⣻⣵⣿⠿⣣⡄⠀⠀⠀⠀⢠⢏⣤⣉⢿⣿⣿⣷⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⡯⢝⣒⢾⣽⣿⣿⠟⠋⠀⠀⠀⠀⠀⣿⣷⣾⣿⣿⣶⣿⣿⠃⠀⠀⠀⠀⠿⣌⣙⠛⢸⣿⣿⠿⠃⠀⠀⠀⠀⣽⣿⣛⣛⣻⣭⣾⠃
⠀⠀⠀⠈⠒⠬⠽⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠺⠛⠁⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠋⠁


⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⣶⣴⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⣴⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡞⠙⣿⡄
⠀⠀⠀⠀⣿⣿⣿⣛⣻⣿⡿⡃⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⢀⠴⠿⣿⣦⡻⣷⡀⠀⠀⠀⠀⠀⢠⠋⢻⣿⡀⢿⣷
⠀⠀⠀⠀⣮⣛⣻⣛⣻⣽⣾⠇⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⣿⣿⣮⡻⣇⢻⡇⠀⠀⠀⠀⠀⠘⠀⢸⣿⣧⣼⡿⠂
⠀⠀⠀⠀⠙⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠻⢮⣟⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠻⠿⠷⠿⠘⠁⠀⠀⠀⠀⠀⠓⠤⢀⡿⠟⠁


⠀⠀⠀⠀⠀⢸⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄
⠀⠀⠀⠀⠀⢠⣿⣿⣇⣿⠀⠀⠀⠀⠀⠀⠀⠠⣖⠒⠿⠶⠇⢒⡄⠀⠀⠀⠀⠀⠀⠀⣤⡸⣷⣆⢠⠀⠀⠀⠀⠀⠀⢴⣾⣯⣿⣿⡿⣦
⠀⠀⠀⠀⠀⠘⣿⣿⡏⣿⠀⠀⠀⠀⠀⠀⠀⢰⣾⣭⣭⣭⣭⣴⣶⠀⠀⠀⠀⠀⢠⣿⡎⣿⡎⣿⡞⡇⠀⠀⠀⠀⠀⣶⣝⠿⣽⢟⣫⣵
⠀⠀⠀⠀⠀⢸⣿⣿⡷⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣧⠻⢇⣿⣧⣽⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢠⣿⣿⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠈⠻⠿⠛⠉
⠀⠀⠀⠀⠀⠈⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣠⣄⡀⠀⠀⠀⠀⠀⠀⢰⣶⣶⣶⣶⣶⣶
⠀⠀⠀⠀⠀⠀⣀⣠⣜⢾⣝⢾⣿⡄⠀⠀⠀⢀⣤⡞⠙⢷⡹⣦⣄⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⣠⣤⣶⣯⣿⣾⣧⣿⡷⠛⠁⠀⠀⠀⣼⣿⣄⢃⣸⣿⣼⣿⡆⠀⠀⠀⠀⠸⣷⣿⣿⢻⣿⣿⡟⠀⠀⠀⠀⠀⢸⣿⣟⣿⣿⣿⣿
⠀⠀⠀⠻⢿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⠧⠟⠁⠀⠀⠀⠀⠀⠹⣿⠏⣾⣿⡿⠃⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

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

⠀⠀⠀⠀⠀⠸⡓⠒⠦⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠈⠉⠑⠒⠤⡤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⢉⠑⠂⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢀⠔⠁⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠲⠤⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⡠⠋⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠉⠑⠒⢤⠤⠤⣄⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠾⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⣈⠭⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠉⠉⠐⠒⠤⢤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⢀⣀⠤⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠒⠢⠤⡤⢂⣀⠀⢀⣔⡁⠤⠒⡺⠋⠀⠀⠀⠀⠀⠀⠀⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠠⢄⣄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡏⠁⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠤⠤⣀⡀⠀⠀⠀⡇⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠘⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠋⢱⠀⣀⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠈⠲⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠚⢓⠆⠀⠀⠀⠉⠁⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠑⠒⢦
⠀⠀⠀⠀⢠⡤⠤⠤⠔⠋⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⡀
⠀⠀⠀⡞⠉⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠋⠉⠉⠈⠉⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠬⠙⠛
⠀⠀⠀⠈⠓⠒⢤⠀⠄⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣀⡤⠴⠒⠉⠉
⠀⠀⠀⠀⠀⠀⡠⢳⢓⠒⢟⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⢀⠎⠀⠀⠈⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡚
⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⠒⠒⠒⠚⠋⠙⢣⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠋
⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⢧⠀⠀⠀⢀⠴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠗⠢⠤⢀⠠⠤⠒⠋
⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠳⠶⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⢸
⡇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⢣⠀⠀⠀⠀⢀⠇
⠳⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⣀⠀⡸
⠀⠈⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⡇
⠀⠀⠀⠀⠈⠉⠑⠒⠒⠒⠒⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠸⠀⠰⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠠⢀⠀⠀⠈⡀⠈⡀⠈⡀⠈⡀⠀⠀⠜⠡⠄⢀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠏⣿⡇⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⡓⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠂⢰⢈⠀⠀⠀⠀⠀⠀⠈⠀⠘⡀⠈⠀⠘⡀⠘⠀⠠⠓⠐⠀⠘⠀⠀⢀⠀⠐⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠲⠀⠐⠀⡠⠀⠈⠀⠂⠀⠀⠨⠀⠄⠀⠀⠀⠤⠄⠂⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢄⠀⠁
⠀⠀⠀⠀⠀⢠⡑⠀⠀⣀⠀⢀⠀⠀⡔⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠁⠀⢀⠄⣰⡒⠄⠀⡀⢀
⠀⠀⠀⠀⠀⠠⡄⠀⠉⠉⠀⢀⠈⠃⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢈⢸⣱⠖⡠⠀⠀⠘
⠀⠀⢀⠀⠀⠀⠙⠁⢀⣀⣠⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠠⠊⠴⠁⠀⠠⠀⠁⠂⡈⠑⠉⠉⠀⡀
⠀⠤⠀⡁⢀⠠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⡀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⡀
⠈⠂⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠑⠀⠀⠀⠀⢀⠀⠠
⠀⠀⠀⠀⠡⠀⡀⠀⠀⢀⡀⠀⠀⠀⢀⢀⠀⠀⠀⢀⠃⠀⠈⠀⠀⠀⠀⣐⠃⢀⡀⠀⠈⠀⠀⠀⡐⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠂
⡠⠂⠀⠀⠀⠀⠀⠀⠀⠂⡠⠀⢀⠀⠀⡀⠀⠀⠀⠁⠀⡐⠁⠀⠄⠀⠀⡄⠁⡄⠀⠀⠀⠀⣰⠀⠃⠀⠀⠁⠀⠢⢄⠀⠀⠀⠀⠊⡀
⠃⠀⠀⠀⢀⠂⠸⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⠈⢈⠔⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢸⠉⠀⠀⡠
⠈⠀⠀⠀⠈⠀⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡔⣫⠭⡐⢄⠀⢨⠀⠀⠈
⠀⠀⠀⠀⠁⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⢀⠀⠀⢸⠀⡏⠦⠆⠀⠀⠈⠀⠀⠀⠄
⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣷⠀⠀⠀⠀⢠⣯⣿⡃⠁⠀⠄⠀⠈⠧⣉⡒⠒⠁⠀⢘
⠀⠑⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠻⠟⠋⠐⠄⠀⠀⠉⠛⠿⠀⠑⠈⠁⠀⠀⡀⠀⢩⡀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠀⠀⠀⠈⠐⠀⠀⠀⠈⠀⠀⢀⠀⠀⠄⢠⡀⠀⠀⠀⠀⢀⠀⠐⠀⡀⠀⠀⠈⢄⠁⠀⠀⠂⠀⡢
⠀⠀⠀⠀⡀⠀⠘⠀⠀⠀⠆⠐⠀⠀⠀⠀⠀⠀⠆⠀⢠⠉⠀⡠⠀⠂⠀⠂⠀⡀⢀⠘⠀⠀⠀⠡⠈⠄⠡⠈⠄⠡⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠐⠂⠀⢄⠀⡀⠀⠀⢀⠀⠸⠀⠀⠀⠀⠀⠂⠀⠈⠂⠰⠀⠄⠒⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠀⠀⠀⠀⠄⠂⡐⠀⠀⠀⡀⠀⢀⠀⢠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆⠀⠀⠁⠌⠀⠐⠅⠠⠃⠀⠀⠀⢺⠀⠘⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢸⠀⠄⠀⠀⠄⠀⠄⠀⠀⢀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠈⠢⠀⠀⠀⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣐⣠⣀⣀⣀⣈⣁⣀⣀⣂⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⣋⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠊⠀⢄⠀⢪⠀⠀⠀⠀⠀⠒⠢⠀⣠⠀⠁⢀⠀⠀⠀⠀⠀⠊⠔⠀⠀⠀⡠⠈⠀⠀⠀⠀⠀⠀⢀⠼⡄⡄⢄⢠⢁⠀⠀⠀⠀⠀⡀⢊⠀⢄
⠀⠑⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⡀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡡⠈⠀⡄⠠⠀⡄⠀⠀⠀⠂⠀⠀⠀⠈⠀⢀⠂⠀⠀⠀⠀⠀⢆⠑
⠎⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⡌⠀⠀⠀⠈⠉⠁⠁⠉⠈⠈⠈⠀⠀⠀⠀⠀⠈⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠄⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⡀⠂
⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠤⠈⠀⠀⠁⢀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠙⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠤⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠊
⠄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠈
⠐⠂⠀⠀⠀⠀⠀⠰⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠐⠀⠸⣁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠙⠀⠂⠘⠀⢄⠐⠆⠀⠀⡀⠀⠂⠀⠀⠀⠀⠀⠠⠀⡂⠄
⠀⠀⠀⠀⡃⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠂⡐⢀⠁⠀⠐⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠂⠂⡠⠈⡁⢀⢀⠀⣠⢀⠐⠀⠀⠀⠀⠀⠈⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠤⠌⠀⠼⠅⠤⠅⠤⠍⠤⠎⠠⠌⠤⠬⠡⠁⠀⠀⠒⠈⠀⠀⠈⠐⠂⠀⠀⠀⡀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂⠀⠀⠀⢐⠀⠐⠀⠀⠀⠀⡂⢐⠀⡚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢤⠀⠅⠀⠀⠀⠠⠀⠠⠀⠂⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠠
⢀⠀⠠⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠂⡀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠂⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡐⠐⠄⠐⠠⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠀⠀⠐⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠐⠀⠀⠀⠐⠀⠄
⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢊⠠⠄⣀⡤⠀⠠⣄⡀⠤⢉⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠀⠠⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐
⠂⠤⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢈⠀⠠
⠊⠀⢄⠐⠀⠀⠀⠀⠀⠀⠁⠁⠐⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⢐⠀⡀⠀⠀⠀⠀⠀⠀⠠⠎⠀⢄
⠀⠑⠀⡠⠘⠀⠀⠀⠀⡔⠀⠈⢀⡠⠂⢀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠘⠀⠀⠀⡠⠀⠀⠀⠀⠐⠄⠀⠄⠀⠆⠦⠀⠀⠀⠀⠀⠀⡣⠀⠑

⠀⠀⢀⠂⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡎⠀⠀⠀⡰⠁⠀⠀⠰⢤⡀⠀⠸
⠀⠀⢀⠐⠄⠀⠤⡰⣄⣀⣀⡸⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡉⠀⠲⢦⠄⠀⠀⠀⠀⠀⠀⠁⠀⠠
⠀⠀⠈⠉⠠⡈⠀⠐⠂⠒⢦⣔⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⣼⠆⠀⢀⠄
⠀⠀⠀⢨⠓⠠⠄⠀⠀⠀⠀⠄⠀⠁⠘⠂⠀⠀⠀⠐⠒⢲⠊⣄⣀⣀⠌⠎⠀⠀⠑⠀⠐⡘⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠂⠠⠀⠈⠀⠀⢀⡄⠀⠀⠈⢙⠆⠀⠀⠈⠓⠼⠄⠂⠀⠀⠀⠀⠄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⠀⠰⣤⣀⣠⡞⠀⠀⠀⢀⠎⠀⢠⣤⢤⣤⡀⠀⠀⠀⠀⢠⡄⡠
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠈⠙⠳⢦⣤⣠⡟⠀⠀⠞⡕⠙⢹⠿⡀⠀⠀⢰
⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠛⠤⠄⠄⠀⠐⠋⠀⠀⡀⠙⠒⠒
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢦⢀⣔⣤⢾⢆⠀⠀⠀⠀⢀⡀⠀⢠⣾⣡⣀
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣤⣠⡴⢻⡿⢊⣭⢾⣧⣄⠀⠀⠸⣿⣦⣀⠉⠲⣬⡙⠲⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⠀⠀⠀⠘⢧⣾⡿⠴⠿⠛⠿⢷⢶⠏⡀⠀⠀⠈⠳⠍⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣄⠀⠀⢀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⢎⠀⢀⡠⠂
⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠢⢀⡆⠀⠀⠀⠄⠀⠉⠃⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠊⠀⠀⠀⠘⣄⠀⠈⠀⠃⠀⠀⠀⠘⣧⠀⠀⠀⣀⣀⡲⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠠
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡄⠠⠀⠀⢜⠳⣄⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⠸⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠃⠀⠀⠈⠀⠀⠐⠁⠀⠀⠳⢾⠞⠁⠀⠀⠀⠢⠀⠀⠘⠥⠒⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⡂⣩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠇⠙⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⢀⢈⠂
⠀⠀⠀⠀⠀⠈⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠚⠁⠀⠀⠉⠀⡺⢤⡄⠀⡀⣠⠞⠁⠈⠳⣄⠀⠀⠀⠀⡎⠉⠱⠤⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡀⠀⠀⠑⠎⠁⠀⠀⠀⠀⠀⠀⠊⣀⡷⠈⠓⣸⠁⠀⢀⡀⠀⠈⢣⠀⠀⢀⠇⠀⠁⠀⡀⠀⠈⠳⣤⡀⢀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡬⠀⣀⣀⣀⣘⡬⠖⠨⠿⠀⢄⠀⣴⢤⡀⡤⠂⡀⠈⠀⠀⣈⣇⠀⠔⠁⠈⠢⠀⢸⡃⢰⢫⡆⠀⠀⠈⠉⢀⡴⠤⢷⠟⠉⢀⡘⣆
⠀⠀⠀⢀⠀⢰⠀⢠⠖⠋⠁⠀⠀⠉⠳⣌⠄⣐⠉⡁⠡⠼⣆⠙⢦⠀⢀⡰⠧⠀⠈⣍⢢⣄⡀⠀⣀⣄⡋⠙⢣⠚⡇⠀⠀⢠⠖⠉⠁⢀⠀⠀⠀⢸⡉⠉
⠀⠀⠀⠀⠀⠀⢠⡏⠀⢀⠀⡀⠀⠀⠀⢸⡄⠈⠣⠀⠀⠀⣽⠀⠈⢧⡀⠀⣄⡠⠀⠘⠆⠀⠀⠀⠀⠀⠀⠀⢸⠇⢧⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠀⠀⠀⢸⡧⠤⠖⢲⡶⠞⠁⠀⠀⠀⠉⠉⠛⢻⡶⠦⢤⣤⠄⠀⠀⠀⠔⠢⣼⠂⠸⣆⠛⣷⠀⠋⠀⠀⠀⠀⠀⠀⡟⠁
⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠐⠂⠀⠀⢸⡀⠀⠀⠀⠀⢡⠀⠂⠀⠀⠂⠀⣀⠂⠀⠀⠀⠈⠑⢦⣀⣠⣄⣀⣿⡀⠀⠘⢧⣉⣧⣀⠀⢰⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠈⠙⣆⠀⠂⠀⠚
⠀⠀⠀⠀⠀⠀⢠⠈⠀⠙⠲⣄⣀⠀⠀⠀⠘⠦⣄⡁⢀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠁⠀⠀⠀⠀⠀⠸⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡰⠦
⠀⠀⠀⠀⠀⠀⣀⠀⠤⠀⠀⠸⡉⠉⠛⠛⠛⠛⡏⠁⢨⣤⣤⠀⠀⠀⠰⠶⠶⠄⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠉⠳⡄⠂⠀⠀⠀⢀⠀⠀⡏
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡬⠠⣾⣉⢉⣷⣥⠤⢤⡄⠀⠄⠐⠒⠒⠂⣤⠖⠚⠓⢦⡀⠀⣜⠀⠀⠀⠀⠀⠀⣹⣤⡀⠀⢀⠀⠁⢾⠁
⠀⠀⠀⠀⠐⠤⠀⠐⠒⡞⢈⠉⠹⣴⠋⠀⠀⢸⣷⣤⣌⡷⠀⠠⢘⠀⢀⡞⠁⠀⠀⠀⠀⠙⢾⠁⠀⠀⠀⠀⠘⠄⠣⣁⡏⠐⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠸⠂⡀⠁⣿⠐⠀⠀⠚⡇⠀⠀⡇⠀⠢⣸⣠⠟⠠⠤⠄⠀⠀⠠⠤⠘⢧⣀⣶⠀⣀⠀⣴⡄⠀⢹⡀⠀⠀⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡇⠀⠀⣿⠀⠀⠀⢀⡇⠀⠀⢷⡀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠁⠀⠀⠀⠀⠐⣧⡤⢶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢈⣠⢀⣿⠀⡤⠖⠉⠀⠀⠀⠀⠉⠓⢾⡁⠀⠀⠒⣀⣄⣠⣀⠂⠀⠀⠸⡄⠀⢠⠞⠉⠙⢦⡂⢃⣳⠺⢋⡒⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠂⠉⠈⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢳⡄⠠⠤⠉⠉⠉⠉⠤⠀⠐⠈⣟⢳⠏⠄⠀⠠⠄⠳⡀⠐⠢⢄⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⢸⡇⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡤⠄⢲⣇⡏⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢰⠟⢖⠒⠦⠤⠤⠾⢄⠀⠀⢀⠽⡧⠤⠀⠀⠀⠀⠄⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠃⠈⠀⠃⢂⠀⠀⠀⣀⡴⠃⡃⠄⣀⠐⠀⠄⠀⢡⠀⠅⠀⠀⠉⠓⠶⠤⠶⠶⠚⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠚⠉⠁⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠒⠐⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠓⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠴⡀⠦⣤⣀⡴⠟⠁⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠚⠀⠀⠐⣤⢀⣿⠁⠀⠨⣴⣴⣿⣻⣧⣼⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠞⢶⡀⠀⠴⣠⣬⡵⣾⣿⡆⠀⠀⠛⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⢤⠀⠀⠈⢿⣸⠂⠉⢉⢉⣉⡛⢿⣦⡆⢠⣾⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠱⣟⡷⠈⣵⠶⢦⣐⡺⢴⡼⠊⣿⣿⠿⣿⣿⣾⢿⣷⠦⠄⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠙⠲⣠⠞⣋⣷⣂⠀⣤⣶⡄⠈⢳⣖⣸⠿⢋⢴⣿⡀⠀⠰⢿⣏⣀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣾⠃⠀⢠⡟⠉⠉⠈⠿⠀⣼⣛⡓⣶⢨⡟⢡⣾⣧⡘⣿⣿⠷⢦⡐⢻⣅⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⢡⡄⢰⣫⡶⣶⡀⠀⣻⠀⡆⢠⣤⣾⣿⣇⢒⡳⢨⣿⡜⡏⠀⣠⣾⠋⣰⡆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣿⣿⡆⣡⣈⣧⣅⣉⠳⣤⣥⣾⡗⠩⢍⠿⣿⣿⣭⣶⢟⣼⢃⡏⠘⠿⢋⡴⢫⣾⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠹⣽⠣⢙⣭⣬⣻⠛⠟⢨⣿⡿⢿⣏⠀⠀⢀⣽⡿⠃⣿⡟⠉⣛⣽⣿⡿⣷⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⢦⣀⣼⣿⣡⣰⣴⣿⣧⢙⣋⣉⢀⣀⣭⠉⣀⢀⢏⣯⣾⡿⣻⣡⣶⡿⠟⣋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⡆⣬⡙⠛⠮⠼⠿⡿⣉⣉⣉⢉⡉⠙⣛⣛⣾⣿⣿⣿⠿⠿⠛⢋⣁⣤⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢹⣇⠈⠉⣰⠲⠶⣦⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⢻⡀⠀⢡⠀⠀⠁⠀⠉⠟⡉⢿⣿⣿⡿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠘⣧⢁⢸⣇⠀⠠⢠⣷⣤⢰⢾⣿⣿⣷⣿⣿⢟⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣿⠀⠘⣿⠆⣽⢸⣿⣶⠰⢾⣽⣿⢿⣿⣿⣻⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠂⣿⢆⠚⣺⣿⣿⡉⣿⣿⣿⣸⣿⡟⡿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⣷⢸⠻⡀⣿⣿⣿⣦⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⡅⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⠷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣾⣿⣭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⢿⣿⣿⣿⣿⡗⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⢀⠀⠀⠐⢆⠐⠀⢀⡍⠀⠀⢁⠔⠀⠀⠀⠘⠯⣽⠆⠀⠀⠀⢀⠀⢴⡦⠄⠀⠠⠆⠀⠀⠀⡀⠐⠻⢶
⠀⠀⠌⠙⢙⣿⣭⠇⠀⣿⡿⠿⢧⣠⡆⠀⠀⢄⠀⢀⢀⣸⡦⠀⡀⠸⠷⣶⣿⠿⢠⡿⠀⠀⠀⢰⡿⠉⠈⠉⢰
⠀⠀⠢⠄⣭⡵⢖⡃⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⠀⠘⣿⣷⠇⠀⠁⠀⠀⠛⠃⠀⠈⠛⠀⠤⠂⢸⡿⠷⡆⠀⢾
⠀⠀⠀⠀⠚⠋⠁⠀⢀⠈⠁⠀⠀⠀⣀⣴⣀⣀⡀⠀⠉⠉⠀⠀⠈⢀⡀⢤⡤⡄⠀⠲⠲⠶⠂⠸⣧⣤⣄⠀⠤
⠀⠀⠀⠀⣤⣥⣀⠂⠤⠂⠀⠀⠀⠞⠻⠮⠭⣯⣄⠀⠀⠀⠀⠀⠀⠒⠂⠘⠊⠙⠙⠛⠛⢋⡁⢀⣀⣀
⠀⠀⠀⠀⠸⣾⡽⣿⣏⣷⢦⡀⠀⠈⣁⣀⡒⠠⢿⠀⠀⠔⠋⠀⠑⢛⣿⡇⠀⠀⠀⠀⠠⠬⡥⠍⠉⢩⣥⢾⠃
⠀⠀⠀⠀⠀⠙⠛⠓⠻⠮⡾⠁⠀⠉⠒⠢⢈⣑⣶⠀⠀⠀⠀⠀⠀⢻⡿⠀⠀⠀⠐⢶⣤⠒⠄⠐⠒⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣾⣿⠿⣛⣿⣿⣛⠿⣿⣿⣿⣷⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⠿⡿⠿⣿⣟⣛⣫⣾⠟⠿⣿⣿⣷⣴⣶⣮⡝⣿⣛⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⣫⣵⣾⣿⣿⣯⡉⠀⠀⠀⠀⠀⠀⠉⠉⠛⢿⣿⣿⣿⣿⣿⣦⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢟⣫⢶⣿⣿⣿⣿⣿⣿⠃⠀⠀⣠⣴⠀⠀⠀⠈⠉⢉⣿⣧⣿⣿⣿⣿⢸⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢟⡵⠋⠀⠸⣿⣿⣿⠉⠽⠋⠠⠖⢋⣁⣀⠀⠀⠀⠀⠀⣾⣽⣿⣿⣿⣿⣿⣮⡛⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⣱⠋⠀⠀⠀⠀⠉⠙⠋⠀⠀⠀⢠⣾⣿⣿⣋⣿⣆⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡹⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣟⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⢻⣿⣿⣿⣿⣿⣿⣿⣿⡝⣿⣿⡄
⠀⠀⠀⠀⠀⠀⣼⣿⡟⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⣿⡿⠋⠀⠀⣠⣴⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡼⣿⣿⣀
⠀⠀⠀⠀⠀⢰⣿⡿⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⠉⠀⠀⢠⣿⣿⣿⣿⢿⣻⣿⣿⣿⣟⣻⠿⣿⣷⣆
⠀⠀⠀⠀⠀⣾⣿⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⣿⡄
⠀⠀⠀⠀⠀⣿⣿⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⢿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿
⠀⠀⠀⠀⠸⣿⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⢤⣄⣀⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⡏
⠀⠀⠀⠀⠀⣿⣿⡞⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢇⣿⣿⠁
⠀⠀⠀⠀⠀⠸⣿⣷⢻⡀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣴⣿⡿⠃
⠀⠀⠀⠀⠀⠀⢻⣿⣯⢧⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⣿⣿⣿⣿⣿⢳⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠈⢿⣿⣎⢧⡀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠀⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⡿⣳⣿⣿⣿⣿⣿⡿⣳⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⡳⣄⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣵⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣮⡳⣄⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣫⣾⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣮⣓⢦⣀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣵⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣮⣝⡲⢤⣝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣛⣵⣾⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣶⣾⣭⣭⣽⣿⣿⣿⣭⣭⣷⣶⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠻⠿⠿⠿⠿⠟⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠋⠉⠉⠉⠛⠒⠶⠤⣄⣀⡀⠀⠀⠀⡤⠾⠃⠻⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠊⢉⡿⠷⠞⠁⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣠⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠴⠖⠉⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡤⠽⡒⠊⢉⠽⠁
⠀⠀⠀⠀⣼⠋⠙⠓⠶⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡰⠖⠒⠫⠁⠂⡀⠌⢁⣀⠀⠒⢀⠠⢀⡀
⠀⠀⠀⢠⡇⠤⡀⠀⠀⠀⠀⠈⠉⠓⠲⠤⣄⣤⠤⠤⠤⠼⠀⠀⠀⠀⢀⠤⣪⣴⠾⠚⠥⢰⣀⡠⠦⢁⣀⠁⠃⢨⠀⠤⢃⠀⢠⠐⠙⡄
⠀⠀⠀⠀⠉⠙⠒⠦⢤⣀⡀⠀⠀⠀⠀⠀⠈⢉⡇⠀⠀⠀⠀⠀⠀⣠⠵⣚⣿⠍⠂⣀⠤⠀⡀⣈⠙⠂⢠⠤⠔⣃⠠⢄⠀⠋⠀⠀⠀⢘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠦⠤⣄⣀⠀⠉⠊⠙⣄⡀⠀⠆⡽⠺⠋⢠⣀⠀⠀⠀⠑⠂⣁⠠⣚⠢⠤⣀⠤⠋⠀⠀⠀⠀⡠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⢤⡤⠜⠀⠣⠳⣄⠀⠀⠀⠉⠉⠀⠠⠎⣀⠀⢀⠭⠒⠠⠀⠀⠀⡀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠀⠀⠀⠀⠓⠘⢦⣀⡀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢀⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠔⠒⢦⡀⠀⠀⠀⠀⠈⠉⠛⡶⠦⢤⣀⡀⠰⡟⢋⠠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠚⠙⠲⠤⠤⠤⠵⠀⠀⠀⠉⠙⠋⠁




⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠈⠐⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⡀⠀⠄⢀⣀⣀⢀⡈⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠋⠉⢀⡠⠄⠠⡀⠀⠀⠀⠈⠃⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⢀⠴⠉⠀⠀⠀⠈⢢⠀⠀⢠⠃⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠴⣁⠈⠂⠊⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⡆⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠈⠣⡀⠀⠀⡠⠂⠐⠒⠀⠐⠁⠀⠀⠀⠃⠀⠀⠤⡀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠘⡄⠀⠀⠀⠈⠁⠉⠀⠀⠀⠀⣀⠤⠤⣀⠀⣀⢀⠀⠀⠀⡇⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⢀⡤⠒⠀⠣⡀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠉⠀⠀⠑⡀⠀⠈⢆⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⣎⢄⡀⠀⠀⠣⠠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⣀⣰⠀⢀⡠⠜⠒⠒⠈⠁
⠀⠀⠀⠀⢀⠔⠁⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠉⠁⠀⠀⠀⡃⠈⡆⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⢰⠂⠐⠒⠚⠢⠔⠊⠁⢱⠀⠀⡎⠀⠈⢆⠀⠀⠀⡠⠠⠔⠁⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⢃⠀⠀⠀⠑⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠴⠁
⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠘⣄⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠠⠄⠒⠀⠉⠙⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠂⠒⠂⠐⠒⠒⠒⠒⠒⠂⠒⠒⠒⠀⠒⠒⠀⠒⠂⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔
⠀⠀⠀⠀⠀⠀⠀⠐⢄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠠⠤⠄⠠⠄⠀⠒⠒⠒⠀⠉



⣿⣿⠛⠛⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠀⠀⢠⡤⠭⠀⠀⠀⠀⠀⠀⠀⠭⠄⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠆⠒⠀⠀⠀⠁⠀⠀⠀⠈⢉⠆⠀⢀⠀⠀⣠⠀⠀⠀⠀⠀⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠠⠊⣿⣿⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡌⠀⠃⠀⠀⠀⠀⠱⠒⠉⠙⠲⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⢀⠀⣀⡀⡀⢀⠁⢀⡀⢀⡀⢀⠄⠀⠀⠀⠆⠀⠀⠀⠀⠀⠤⢈⠈⣠⢍⣀⢡⡀⣬⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠒⠀⠀⠼⠄⢀⡁⡇⠀⢸⠀⠄⠀⠀⠀⡆⣂⢠⣠⡇⠀⣀⠀⠀⠀⠒⢰⠀⡈⠸⢄⢘⡇⠤
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠈⣀⡀⠉⠠⠁⠊⠁⠀⠀⠉⠀⠀⠀⠀⠀⠈⢠⡄⠈⠉⠈⠁⠈⠁⠀⠄⠁
⠙⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠐⠛⡛⠈⠄⠂⠀⠀⠐⠒⠀⠀⠀⠀⡈⠁⠀⠀⠀⠀⠀⢰⠰⠈⠉⠀⠀⠀⠀⠠⠀⢀⠀⠸⠂
⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠶⢆⠀⠀⠀⠄⠀⠠⠤⠀⠀⠀⢀⡠⠄⠠⠀⠀⠀⡠⠐⠀⢀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⣠⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⢨⣦⣉⣁⠠⡍⠁⠄⠀⠈⠉⠀⡀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠂⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⣀⠠⠐⠊⠉⠀⠀⠍⠹⢻⡇⠴⠿⠖⠀⠀⠐⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢿⠀⠀⠀⠐⠶⣶⣀⠀⢀⠀⠀⠄⠀⠀⢀⠈⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠆⠀⠀⠀⠀⠀⠌⠀⠀⠀⠠⠆⠒⢦⠀⠄⠀⠀⢒⠀⠠⢀⢄⡏
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠲⠤⠀⠀⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⢴⠀⣀⢩⠓⠠⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠐

⠀⣠⣤⣄⣤⣤⣤⣄⣤⡀⣠⡄⠀⣤⣤⡄⢀⣤⡀⢠⣄⡠⠠⢄⠄⠀⠀⠀⠀⠀⡀⡀⠀⠀⠠⡀⢠⠄⠀⠠⠄
⢰⣿⡛⠛⠉⣿⡏⠁⣿⠁⣿⡇⢸⣿⠉⠁⢸⣿⣷⣿⠛⠀⠁⠊⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠀⠄
⠀⢻⣷⡀⠀⣿⡇⠀⣿⡇⣿⡇⣼⣿⠀⠀⢸⣿⣿⡃⠀⢂⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⡀⡄⠀⠀⠀⠀⠠⡀
⣠⡄⢻⣷⠀⣿⡇⠀⣿⡇⣿⡇⢸⣿⠀⠀⢸⣿⡿⣿⡆⡀⠂⠀⠀⡇⠀⠀⠀⠀⠀⠂⠀⢠⠀⡀⠀⠀⠦⠐⢄
⠹⣷⣾⠟⠀⢻⡗⠀⢻⣷⣿⠇⠈⢿⣷⣿⠇⣿⡇⠈⢧⣀⠀⠀⠀⠃⠀⠀⠀⠁⢀⠀⠈⠀⠊⠀⠈⡀⠀⠀⢀⠣
⠀⠀⠀⠀⠀⣴⣷⡆⠀⡈⠁⢀⢄⣤⡌⠁⣄⣬⣄⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⣤⡄⠀⣄⠤⣤⢠⡀
⠀⠀⢶⣷⠀⣻⣿⡏⠀⣿⠿⠈⡤⠃⠀⠀⠸⠰⠞⠎⠁⠀⠄⡀⠀⠀⠀⠀⠀⡀⠈⠘⠄⠃⠀⠀⠸⠸⠞⠎⠁
⠀⠀⠀⣿⣧⣻⣿⣇⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢀⠀⠀⢀⡄⡀
⠀⠀⠀⠈⠻⣿⣿⣿⢿⡇⣀⣄⢀⣀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⢸⡄⢰⣇⣀⣄⢀⣠⣀⣤
⠀⠀⠀⠀⠀⢸⣿⡣⢀⡠⠤⠤⠬⢄⡀⢤⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠃⠀⠀⠀⠀⠈⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠸⢿⠊⠀⠀⠀⠀⠀⠀⠀⠑⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⠀⠀⠰⡩⢉
⠀⠀⠀⠀⠀⠀⢘⠰⠒⠦⢴⣦⡦⢼⣗⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠠⠤
⠀⠀⠀⠀⠀⠀⠈⢮⡀⠰⠴⠛⠦⠆⢀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠈⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⢐⡂⠉⠑⡒⠒⠒⠚⢉⢀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡒⠀⠀⡀⢀⠀⠀⢉⢀⠦
⠀⠀⠀⠀⠀⢀⡌⠀⠉⠂⠁⠈⠀⠘⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠈⠂⠁⠈⠀⠘⠈

⠀⠁⠀⢸⠀⠀⢀⠇⠀⠈⠉⠉⠉⠀⠘⡄⠀⠀⡰⠉⠣⠤⠧⠤⠊⠱⠀⠀⠀⠸⠀⠑⠛⠒⠚⠁⢱⠀⠀⢸
⠀⠃⠀⢸⠀⠀⢸⠀⠐⠒⠠⡄⠊⠂⠀⡇⠀⠀⠇⠀⠤⢀⠀⢤⠀⠀⡇⠀⠀⡇⠀⠀⢀⠀⠠⠀⠀⡆⠀⢸⢀⠘
⠀⠀⠀⣎⡀⠀⠸⡀⠀⣀⠊⠁⠁⠀⢀⠇⠀⠀⠀⠁⠀⠚⠓⠀⠈⣀⡀⠀⠀⢇⣀⠀⠈⠁⠀⠀⡰⠀⠀⠘⡄
⠀⠀⢠⠃⠙⠤⠤⠥⠜⠉⠆⠀⠀⠀⢨⠓⣄⢀⡇⡠⠓⡄⠀⠀⠰⠁⠑⠤⠤⠞⠁⢱⠀⠀⠀⡔⠙⣄⢀⣸⠔⠱⡀
⠀⡔⠁⠀⣀⠀⠀⠀⣀⠀⠈⡆⠀⠀⠇⠀⡈⠈⠉⡀⠀⢡⠀⠀⠃⠀⣤⠀⠀⢠⠀⠀⡇⠀⢰⠁⢀⡀⠀⢀⡀⠀⠇
⠀⡇⠰⠀⠀⠀⠶⠠⠀⠀⠀⠘⠀⠸⡀⠄⢁⣰⣀⠁⠀⠸⠀⠀⡄⠂⠀⢤⡣⠀⠀⢀⠃⠀⢸⠀⠈⠁⠒⠈⠁⠂⡀
⣀⣣⣠⠊⠳⡀⠀⠀⠀⡴⢢⣎⣀⣀⡗⢢⠀⠀⠀⠀⠀⡆⠀⠀⠇⠀⠀⠀⠀⠀⠀⡜⠣⣀⣠⣠⠒⢄⠀⠀⠀⠰⠓
⡀⠀⠀⣄⠀⠃⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠎⠙⠤⠴⠤⠎⠙⡄⠀⠀⠸⠀⣀⡀⠀⠀⠀⠈⠆⠀⠀⡇
⠁⠀⠧⠀⠀⢰⠀⠀⢰⠀⠌⠁⣰⠀⠁⠀⡀⠀⠀⢸⠀⢠⠄⠀⠀⡄⠀⢃⠀⠀⠾⠐⠀⠤⠓⠄⠀⠂⡄⠀⠀⡇⠠
⣀⠀⠀⠀⢀⠗⢄⠀⠈⣆⠔⢆⠀⠀⠀⠀⣇⡀⠀⢨⠘⠀⠀⠛⠖⠀⠀⢸⠀⠀⠘⠆⠀⠀⠀⠀⠀⢰⣁⡀⠀⡅
⠈⡆⠀⠀⡌⠀⠈⠉⠉⠉⠀⠀⡆⠀⠀⢀⠋⠈⠦⠼⠤⠄⠀⢀⠀⠀⠀⢸⠛⢄⢸⡀⡴⠑⡄⠀⠀⢸⠃⠘⠒⠓⠒
⠀⢰⠀⠠⠀⠀⠛⢀⡄⠘⠀⠀⡇⠀⠰⠁⠀⣀⡀⠀⠀⡠⡀⠀⢣⠀⠀⡇⠀⠀⡀⠀⢀⡀⢸⠀⠀⡆⠀⠤⠀⠀⠰
⠀⡘⠀⠀⡇⠈⠀⠈⠁⠀⠁⢰⡁⠀⡇⠀⣀⠀⠀⠼⠄⠀⠀⠀⢘⠀⠀⡄⠀⠈⠁⣰⠈⠡⠀⠆⠀⢣⠀⠀⠐⠓
⠎⠑⠤⠤⠕⠉⢆⠀⠀⠀⢰⠁⠑⠀⠚⠊⠀⢣⠀⠀⠀⠠⠒⣄⣘⢀⡔⠳⡀⠀⠀⠀⡤⢄⢸⠀⠀⣸⢤
⠀⣀⠀⠀⡄⠀⠈⡄⠀⠀⡇⠀⣠⠀⠀⠤⠄⠈⠀⠀⢀⠃⠀⡀⠀⠀⡀⠀⢣⠀⠀⠈⠀⠀⠉⠉⠉⠁⠀⢃
⠀⠠⠼⠤⠀⠀⢀⠄⠀⠀⢇⠀⠀⠒⠓⠂⠐⢠⠀⠀⢸⠀⠌⠁⣰⡀⠉⠄⢸⠀⠀⡇⠀⠚⠀⣤⠀⠃⠠⢸⠀⠀⢘
⡆⠀⠀⠀⢀⠖⢾⡄⠀⡰⠻⡄⠀⠀⠀⢀⠀⢱⠀⠀⠀⡇⠀⠀⠀⢀⠤⡀⠇⠀⢀⢇⠀⠀⠈⠀⡙⠉⠦⠸⠤⠤⠋
⠈⢆⠀⠀⡌⠀⠀⠉⠈⠀⠀⢱⠀⠀⢠⠁⠑⠼⠄⠤⠊⠘⡄⠀⠀⡎⠀⠉⠉⠐⠋⠀⢇⠀⠀⡜⠁
⠀⠈⠀⠀⡇⠀⠒⢠⡄⠒⠀⠀⠂⠀⡎⠀⢠⠀⠀⢠⡄⠀⢱⠀⢸⠀⠘⢀⡄⠰⠀⠀⢸⠀⢰⠀⠀⠐⢒⣠⣆⡐⠊
⠀⢰⠀⠀⡱⠀⠀⠀⡀⠀⠀⠜⠀⢀⡇⠀⠀⠀⡧⠀⠐⠀⢸⠀⠈⡆⠀⠉⠁⠀⠈⠀⡜⠀⠘⡄⠀⠀⠀⠈⢁⡀
⣦⣴⣭⣷⣥⣤⣤⣼⣭⣦⣤⣼⣴⣧⣷⣤⣤⣤⣤⣤⣤⣤⣦⣤⣤⣧⣤⣤⣤⣤⣶⣤⣧⣤⣴⣷⣦⣤⣤⣤⣧⣽⣦
⣿⣿⣤⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠉⠛⠿⢿⠿⠿⠿⠟⠁
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⢀⣤⣶⣶⣤⣾⣿⡷⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣾⣿⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣴⣶⣶⣿⣿⣷⣶⣦⣤⡀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⣴⣶⣾⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⣀⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⡍
⠀⠀⠀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⣿⣿⡿⠿⣿⡇
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠙⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⡀
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢠⣤⣶⣶⣷⣿⣿⣶⣄
⠀⠀⠀⠈⠿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠐⢿⣿⣿⣿⣿⣿⣿⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⣾⡿⠉⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⣿⣿⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⣾⡿⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠈⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⣠⡞⠁⣠⢾⣿⣿⠿⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣄
⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⢀⣴⠏⢠⡾⠁⢸⣿⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠑⣄⠘⢿⣦⡀
⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⡁⢠⡟⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠻⣷⡄
⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠻⣷⡟⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠙⣿⣆
⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⠏⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠈⢿⣦
⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣧⠈⣿
⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⠀⠀⠀⠀⠀⢀⣠⣴⠾⠟⠋⣀⣾
⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠻⣷⡄⠀⠀⠈⣉⣁⣠⣤⣶⣾⡿⠛
⠘⠿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠙⢿⣿⡿⠿⠿⠟⠛⠋⠉
⠀⠀⠈⠙⠿⢷⣶⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⠿⠿⠿⠿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠹⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⠆⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠾⠟⠋⢁⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣷⣶⣤⣤⣀⣀⣀⣀⣀⠀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣿⡿⠟⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣙⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣋⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠛⡟⢟⣙⠛⣻⢛⣻⢿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠘⠐⡃⢀⡬⠑⣦⠀⠀⠀⠀⠀⠐⠐⣀
⠀⠀⠀⢦⣀⣀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠨⠅⠀⠇⡡⠀⠀⡀⠀⠠⠤⠖⠁⠈
⠀⠀⠀⠀⠉⠛⠛⠿⠧⠀⠀⠄⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⡀⠀⠠⣀⠾⠂⠡⣮⡭⠝⢃⡐⠷⠦⠀⣀⡁⠀⠀⠀⢀⠀⠠⠄
⠀⠀⠀⠨⠵⢦⣄⣠⠤⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠓⢠⣀⠀⠐⠛⠻⠁⠴⠦⠬⠍⠉⠴⠖⠂⠁⠠⠀⠀⠄⠀⠢⠦
⠀⠀⠀⠀⠈⠀⠀⠒⠀⠀⠀⠀⠀⠀⠁⠀⠃⠀⠀⠀⠈⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠿⠀⠘
⠀⠀⠀⠀⠰⠠⠀⠲⣐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⢀⡀⠀⢂⠀⠀⠀⠐⠦⠤⠄⠀⠀⠀⠀⠀⠁⢀⡤⠀⠀⠀⠠⠐
⠀⠀⢀⠄⠀⠄⠀⠀⠀⠀⠠⠤⣀⠀⠀⠀⠀⠸⠈⣁⠀⠀⠄⠇⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠆⠀⠀⠄⡀⢀
⠀⠀⠀⠠⣄⠀⠑⠀⠀⠀⠢⡅⠠⠐⢀⢄⠀⠀⠑⠖⢂⣈⣀⠴⠁⢴⣿⣿⣿⢿⣾⣶⣄⠀⠀⠀⠈⠉⠓⠂⠀⠄⠀⠤⠀⠜
⠀⠀⢠⠀⣈⠉⠓⠦⡀⠀⠀⠈⠂⠀⠀⠀⠠⠒⠢⠀⠀⠀⠀⠀⠀⠈⡙⣿⣿⣶⣿⣏⣿⠆
⠀⠀⠸⠀⠀⠀⠀⢀⡐⠄⠀⠀⠀⠀⠀⠑⠤⣄⡉⠉⠡⠦⢄⠀⠀⠀⠈⠁⠀⠠⠬⠙⠉⡀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠉⠒⠦⣀⠀⠈⠑⢄⠀⠀⠀⠀⠀⡠⠈⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠑⠀⠈⠳⡤⠀⠈⠉⠒⠠⠀⠀⠀⠀⠐⠃⢀⠀⠀⠀⠀⠀⡈⠀⠰⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⡇⡘⢀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠖⠁⢀⠀⠀⢰⠀⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠀⠁⠀⠀⠀⠀⠀⠙⠛⠋⠉⠙⠛⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⣠⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠐⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐⠂⠊⠉⡍⠉⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⣀⠀⠀⠀⣤⠀⠀⠀⣄⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⡀⠀⠀⠀⠄⠀⠀⠀⢸
⠀⠘⠿⠃⠉⠈⠁⠀⠀⠀⠿⠂⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡤⡄⠀⣀⠀⠀⢸
⠀⠈⠢⠀⠀⠀⠀⠀⠁⠀⠰⠄⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠉⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠁⠀⠤⠀⠰⡦⠀⠀⠀⠻⠀⠀⣶⠀⠺⠃⠀⠀⣴⠀⠘⠟⠀⠀⠀⠘⠋⠀⠀⡀⢀⣀⠀⠀⠀⠠⠄⠈⠃⢸
⠀⠀⠀⠀⢠⡄⠀⠀⠀⢀⠠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡀⠈⠋⠀⠀⠀⠀⠀⠈⠀⢸
⠀⠀⠠⠄⠘⠃⠀⠁⠀⠀⠀⠀⠂⣄⠀⠀⠀⠘⠃⢀⠀⠀⠀⠀⠗⢀⠀⠀⠀⠀⠀⠀⢴⣶⠀⠀⠉⣀⡀⢴⡆⠀⢸
⠀⠁⠀⠀⠀⠀⢀⠐⠆⠀⠁⠀⠀⠉⠀⡤⠀⠺⠆⠀⠀⢠⠀⠰⠷⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⡁⠲⣬⡀⠀⡂⠀⡔⠊⢉⠒⢄⡈⢙⡴⠊⣉⠉⢢⠀⣾⠉⡄⠀⢸⡇⢡⡠⠤⠀⠰⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠈⢳⠈⠀⠀⠁⠸⠀⠰⠉⢱⠘⡇⠀⢠⠎⠀⠇⠀⡆⢸⠀⡇⠀⠸⡇⢸⠃⠆⠀⢴⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠐⢆⠀⠇⠀⠀⠀⢠⠀⠁⠀⠸⢀⡇⠀⠋⠀⠀⢸⠀⡇⠸⠀⢃⠀⡸⠃⢸⠀⢀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣈⠓⠚⠀⣦⠀⠘⣄⠈⠒⢁⠜⢃⠈⠀⠀⠀⡌⢠⠀⠀⢆⠀⢉⣠⡄⢸⠀⠸⡀⠨⠖⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠁⠀⠀⠈⠑⠂⠁⠀⠈⠛⠀⠀⠀⠙⠃⠀⠀⠀⠁⠈⠀⠑⠃⠀⠀⠉⠢⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠤⠄⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠒⠈⣉⠤⢐⠀⠀⠀⠀⠒⠀⠤⠀⣀⠈⣉⡒⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠠⡤⠖⠉⠠⢊⡔⠁⠀⠀⠀⠀⡀⢀⣄⠀⠀⠀⠀⠑⠢⡉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⡺⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠐⠀⠈⠡⠈⠦⣱⠀⠠⠀⠀⠆⠑⢄⠀⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⠔⠁⠀⡔⢹⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠠⠠⡑⢄⡀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢞⠐⠁⠀⠀⠘⠖⠁⠀⠀⢆⡄⣠⢖⠀⠀⣀⠀⠀⠀⠀⠀⠤⢀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠙⡄⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⠂⢴⡪⠍⠛⠀⠀⠀⠀⠀⠀⠐⡡⠊⠀⡘⡘⠀⠀⡠⢪⠂⠈⠡⢕⠀⠀⠀⠀⢀⢊⠀⠀⠀⢠⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠌⡄⢀⠀⠀⠀⢠⢣⠀⠀⠀⠀⠀⠀⠀⠀⣠⡥⠅⠠⠈⠶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆⠊⠀⠀⠀⠈⢆⠀⢁
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡏⡄⠀⠀⠀⠑⠃⠀⠀⠀⠀⠀⡠⠊⡠⠄⠒⠒⠒⠒⠱⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⢂⠈⠃
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠠⠄⠀⠀⠀⠀⢀⠠⡀⠀⠀⠊⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡑⡀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⠀⠁⡤⢐⠆⠀⠀⠀⠠⢋⠔⠀⠰⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢁⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈
⠀⠀⠀⠀⠀⠀⡆⠀⠧⠔⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⡄⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⠀⠈⠀⠀⢀⠠⢐⠂⠀⣤⠀⠃
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠰⠀⠀⠀⠀⠳⠈⠀⢀⣀⢏⡄⠀⢠
⠀⠀⠀⠀⠀⠀⢰⠀⠣⡀⡲⡀⠀⠀⠆⡀⠈⠖⠀⠀⠣⢌⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢁⠂⠀⠄⡀⠀⠀⠀⠠⠉⠌⠀⢁⠀⣼
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⡑⠨⠀⠀⠀⠀⠀⠀⠀⠀⢦⠈⠢⠙⢂⡄⢀⣀⣀⠀⠠⠔⢋⡠⠂⠰⡁⠊⠀⠀⠀⠀⠓⠈⠀⠀⠘⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⡜⡘⠀⠀⠀⠠⢞⠉⠉⠉⠉⠐⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⢃⠀⠀⠄⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠱⠀⠀⠐⠄⠀⠶⠀⠀⠀⠀⠀⠀⠀⢀⠔⠆⠀⠀⠔⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡈⢆⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⡠⢀⠆⠀⠀⠀⠀⠀⠀⠂⠀⠀⠦⠘⠀⠀⡌⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠱⢄⡀⠀⠀⠀⠀⢀⡀⠀⠈⠐⠊⠉⠀⠺⠤⠋⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠀⣀⣴⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠑⡄⠀⠀⠐⣄⡀⠀⠀⠀⠀⠠⠐⢄⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⡠⠂⣉⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡐⠂⣀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠢⠕⠀⠀⠄⠂⠀⠀⠀⢀⣠⡡⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄⣉⠐⠀⠠⠤⠤⠤⠤⠤⠀⠀⠀⠠⠐⢈⠩⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠀⠲⠦⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢄⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀
⠀⠀⠀⠀⠀⠀⢠⡄⠀⠰⣀⡸⠀⠀⠀⠀⠀⠀⠀⢎⡀⡱⠀⢀⣄
⠀⠀⠀⠀⠀⠀⡃⠈⡄⠀⠖⠲⠀⠀⢀⠴⡄⠀⠀⢠⠀⠄⠀⡌⠀⡂
⠀⠀⠀⠀⠀⠀⡭⢭⠀⠀⠀⢸⠀⠀⠨⣀⠸⠀⠀⠐⠀⠀⠀⢨⢭⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⢰⠀⢦⠀⠀⠸⠀⠀⠀⠐⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠄⠒⠊⠉⠑⢄
⠀⠀⠀⠀⠀⢀⡄⠠⠒⠒⠀⢸⠉⠉⢹⠀⢘⠉⠉⠙⠀⠒⠂⢆⠀⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠐⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠰⠉⠀⠀⠀⠀⠀⠉⠉⠀⠀⢸⠀⠸⠀⠀⠈⠉⠁⠀⢐⠀⡇⠈⠢⡀⠀⠀⢀⣤⣤⣒⡀⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠷⢀⠀⠐⠚⠀⠀⠀⠀⠀⠀⢸⠀⣨⠀⠀⠀⠀⠀⠀⠘⠒⠃⢀⠴⡁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠒⠂⠀⠐⠒⠒⠂⡞⠅
⠀⠀⠀⡂⠀⠁⠒⠀⠤⠤⠀⣀⣀⣀⣈⣉⣁⣀⣀⣀⡀⠠⠤⠄⠐⠊⠁⠀⡇⠀⠀⠰⠆⠀⠀⠀⠤⠤⠄⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣣⡆
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠐⠒⡏⠄
⠀⠀⠀⣉⠑⠠⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⢈⠀⠀⠀⢐⠒⠂⠀⠠⠤⠤⠤⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡆
⠀⠀⠀⠈⠉⠒⠠⠤⢀⣈⠉⠈⠉⠀⠀⠀⠀⠀⠀⠉⠈⢉⣀⠠⠤⠒⠈⠨⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠉⠈⠉⠁⡏
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠠⠤⠄⠄⠀⢀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠆
⠀⠀⠀⠈⠒⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠐⠒⠒⠂⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠐⠂⠒⠒⠒⠒⠒⠒⠂⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢠⣄⠤⢀⡤⠠⢄⡠⠤⣄⣀⡀
⠀⠀⠀⠀⠀⢀⠔⠉⡠⠔⢒⡠⠶⠺⣦⠴⠦⣴⠳⠶⢄⠀⠩⡢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⢠⠊⡠⠊⠀⠠⠊⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠑⣄⠈⠢⡱⡀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠤⡀
⠀⠀⠀⢠⠃⡔⠁⠀⢀⠃⠀⠀⠀⢰⠀⠀⠀⠀⢸⠀⠀⠀⠈⠆⠀⠑⡘⠄⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄
⠀⠀⢀⠆⡜⠀⠀⠀⡘⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠘⠀⠀⠐⡈⠆⠀⠀⠰⡁⠑⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠒⢁⠇
⠀⠀⠎⡜⠀⠀⠀⢠⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠃⠀⠀⠐⡈⠄⠀⠀⠋⢲⡐⠢⠤⠬⣉⣉⠈⠉⠀⠁⣉⣀⣀⡉⣁⠠⠀⢐⡴⠙⠆
⠀⠈⡶⠀⠀⠀⠀⠆⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠘⡀⠀⠀⠰⡆⠀⠀⠁⠦⠌⣁⠐⠂⠀⠄⠀⠠⠨⠤⠀⠀⠠⠀⠀⠒⣈⣁⣰⠋
⠀⢰⠁⠀⠀⠀⠸⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠃⠀⠀⠀⢁⠀⠀⠀⠈⠒⠤⡉⢈⡁⠀⠐⠒⠀⠀⠀⠈⠉⢉⣀⣁⠤⠒⠁
⠀⠈⠒⠀⠄⠀⠇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠰⠂⠀⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠒⠂⠉⠂⠤⢀⣀⠠⠔⠊⠁⠒⠒⠒⠒⠁

⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⣀
⠀⠀⠀⠀⠀⢀⣏⣀⣀⣀⣀⣀⣀⢸⡄⠀⠀⣴⠀⠀⡎⠉⠢⡔⠉⠀⢱⠀⢰⠊⠙⢤⠀⠠⠂⠀⠀⠀⠀⠀⡀⢬⡉⠙⢦⠠⠀⠀⣀
⠀⠀⠀⠀⣌⠒⠉⠉⠉⠉⠉⠛⠛⠁⠐⢄⠀⠈⠀⡀⡆⠀⢸⠀⠀⠀⡇⠀⡘⠒⢤⠁⠀⠁⠀⠀⠀⠀⠀⢘⢴⠆⢸⠀⠀⢯⡀⠀⠓
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡋⠉⢃⠀⡇⠀⠀⢰⠆⠉⢨⠇⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⢸⡄
⠀⠀⠀⢠⠇⠀⠀⠸⠟⠀⠀⠸⠟⠀⠀⠸⡇⠀⠑⡀⢘⠀⠁⠀⢀⡇⢀⣎⣁⠀⠠⠃⠀⠑⢤⣄⣀⣀⡀⣀⣀⡤⠒⠀⠀⢨⡱⠀⢠
⠀⠀⠀⢸⠀⠀⠀⠀⠐⠀⠀⠆⠀⠀⠀⠀⡇⠘⢏⢷⢸⡆⠀⠀⡼⢠⢋⡨⠼⠃⠀⢌⢉⠆⠀⠡⢈⠀⠉⠀⠉⠀⠀⠀⠠⣘⡢⠀⠡
⠀⠀⠀⢸⠀⢀⠔⣳⠤⡤⣄⣐⣹⡄⢄⠀⡇⠀⢈⠿⠤⠧⠤⠴⠧⠿⢁⠀⠣⠅⠰⠆⠀⢀⢀⡤⡀⠀⠉⠉⠈⠉⡄⠀⠀⢻⢲
⠀⠀⠀⠸⡠⣈⠉⠑⠚⠓⠓⠮⠔⠁⣁⢄⠇⠀⠠⠉⠩⠍⠭⠍⠍⠉⢱⠀⠀⡠⠊⠉⣠⡀⢀⣄⠈⠫⢁⡅⠀⠊⠇⢮⠄⠀⠈⢛⣦⡀
⠀⠀⠀⠀⠈⠑⠋⠉⠀⠖⠒⡂⠈⠁⣀⣁⢀⡀⢸⠀⠀⠀⠠⠀⠀⠀⠸⠀⠎⠀⠀⠀⠉⠁⠈⠉⠀⠀⠀⢱⠀⢠⠆⢀⠀⠀⠀⠈⠸⣇
⠀⠀⠀⠀⠀⠀⠟⢃⠀⠀⢶⡀⠇⠘⡘⠂⢃⠏⠀⠢⢀⣀⣀⣀⣠⠤⠂⢀⠣⡐⠉⠂⠀⣀⣀⡀⠀⣀⠀⡘⠀⡀⡀⠏⢀⠀⠀⠀⠰⡇
⠀⠀⠀⠀⠤⡀⠘⢆⢦⠀⠀⠤⠤⢄⡈⠲⠃⠰⠅⠀⣈⣑⣚⣀⣁⣀⣀⣉⣀⣈⣉⣉⣀⣀⣀⠀⢅⠀⠉⠀⢢⠐⢔⢄⡒⠤⡀⢠⠀⡇
⠀⠀⠀⢰⡄⠈⣠⠤⠤⠤⠤⠤⠤⠤⠬⠶⡄⢀⣾⠛⢻⡿⠙⡟⢻⣿⢹⡏⢻⠛⣿⡟⢻⣿⣿⣷⡄⠀⠶⠈⠁⠰⠮⠬⢀⡽⠃⢸⠘⠛⠁
⠀⠀⠀⢸⠑⠊⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⣿⠀⠘⡇⠀⠃⠈⠙⢸⠀⠘⠀⣿⣧⣴⣶⠌⣿⠇⠀⠀⠀⣀⡀⠀⠄⠈⠡⢀⡁⢀
⠀⠀⠀⢸⠀⠀⢀⠀⠀⢀⡀⠀⠀⢀⠀⠀⡇⠀⢿⣤⣄⣁⣦⣴⣤⣤⣾⣰⣦⣄⣿⣿⣯⣵⡾⠏⠀⠎⠊⢹⠃⠀⠀⠀⠀⠀⠀⠹⠀⠊⡄
⠀⠀⠀⢸⠀⠀⢸⠀⠀⠿⠿⠀⠀⠻⠇⠀⡇⠀⠀⠈⠉⠉⡉⠉⡁⢠⠤⣄⠀⢀⡈⠉⢁⠠⡄⠀⠀⢷⡄⠸⠀⠀⠶⠀⢴⠆⠀⠀⢀⢴⠃
⠀⠀⠀⠸⡀⠀⢸⠀⠀⠀⠀⠒⠒⠀⠀⠀⡇⢀⠠⢀⣂⠥⠒⠐⠲⢍⣂⠢⢀⠘⠃⣀⠏⠄⠈⠢⢄⠀⢹⡆⢄⠀⠀⠤⠀⠀⢀⠆⡼⠁
⠀⠀⠀⠀⠘⠢⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠘⢺⠉⠀⣀⠀⠀⢀⣀⠈⠹⠚⠃⡞⠁⠀⠀⠀⠀⡀⠑⠀⠫⠬⠗⠄⠀⢀⠔⠯⠦⠃
⠀⠀⠀⠀⠀⢀⡈⠁⠉⣁⠀⠀⢀⠀⠩⠩⠤⡀⢸⠀⠈⠋⠀⠀⠈⠋⠀⠀⠀⢠⠋⠀⠀⠻⠃⠘⠟⠀⢄⠀⠀⠀⢠⠀⢀⠀⠀⣤⠒⡄
⠀⠀⠀⠀⢔⠕⠈⠀⠈⠐⠕⠄⢠⣀⣀⣀⢀⠄⠸⠤⠤⠀⠀⠀⠀⠠⢤⠼⠀⢸⡀⠀⠀⠀⠂⠀⠀⠀⣠⠀⠠⠊⠠⠀⠀⠈⠦⠙⠒⠁
⠀⠀⠀⢰⠈⠀⣶⡄⣴⡆⠈⢸⢀⡤⠤⠖⠐⠂⠀⠀⠀⠀⠀⠂⠒⠒⠒⠤⣄⠀⠉⠒⠢⠤⠄⠀⠀⠊⡁⣀⣀⡤⠤⠴⠖⠦⠩⣙⢳⢄
⠀⠀⠀⠈⡐⡀⠀⠄⠄⠀⡀⡘⠸⠀⠀⠚⠃⡔⠈⠉⠀⠈⠈⠐⡆⠛⠃⠀⠈⠀⣴⢚⣋⣉⣉⡓⣶⠀⡏⠁⠀⠀⠀⢀⠀⠀⠀⡅⠈⠀⡆
⠀⠀⠀⠀⢈⠂⠅⡀⡢⠍⠊⠀⠈⢠⠄⠠⡄⠇⠀⣶⠄⢰⣦⠀⠇⢸⡣⡢⠀⠁⡇⠈⠉⠉⠉⠉⠀⠀⡇⠀⠛⠃⠀⠻⠃⠀⠀⡇⠀⠀⡇
⠀⠀⠀⠀⠨⠃⢰⠁⢳⠀⡠⡀⢀⠈⠡⠌⠀⡇⠀⠠⠤⠤⠀⠀⡅⠁⠑⠷⢀⠀⡃⠰⠿⠀⠺⠇⠀⠀⡇⠀⠀⠀⠀⠂⠀⠀⠀⡧⢠⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠈⠀⠈⡁⠉⠑⠀⠡⠤⠤⠤⠤⠤⠤⠂⡔⠉⠁⡹⠀⠣⣀⡀⠒⠂⣀⠔⠀⠋⠫⠗⠒⠢⠤⣄⣀⣀⠃⣰⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠀⠒⠒⠒⠀⠀⠀⠐⠒⠒⠂⠀⠤⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠁⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠀⠀⠁⠒⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⡀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠢
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⢀⡀⠤⠄⠐⠒⠀⠤⠄⣀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⠑⡄
⠀⠀⠀⡇⠀⠀⠀⠁⠀⠀⠀⠈⠊⠀⠀⠈⠀⢀⡖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠤⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠢⠤⠤⣀⣀⣀⣀⡀⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⢤⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠚⠀⠀⡀
⠀⠀⠀⠸⡀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⡎⠀⢆⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠔⠀⠀⠀⣀⠤⣠⣴⠊
⠀⠀⠀⠀⠸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠺⡿
⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠉⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⢀⡤⠖⠀⠀⠂⠀⡀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠈⠑⠤⠄⠠⠚⠁⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⠤⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠒⠒⠒⠒⠒⠒⠂⠈⠉



⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡋⣙⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠔⠒⠋⠉⠉⠉⠐⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣏⠀⠉⠒⠠⠀⠀⠀⢀⣠⡤⠖⠊⠁⠀⠀⢀⣀⠼⣃⣰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠓⠨⣍⣒⠤⢀⠀⠀⢰⠁⠀⠀⣀⠀⠀⢀⣩⠤⡶⡺⠁⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⢀⠢⠈⡏⠂⢀⣀⠚⠖⣋⣡⢤⢤⠞⠁⣈⠀⠀⠀⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⣷⣦⣀⠀⠀⡇⢸⠋⠁⠀⣤⢋⣠⠴⠿⠞⠛⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢹⡍⠻⡷⠦⣄⣸⣤⡤⠚⠉⠁⠀⠀⠀⣀⣁⣤⠿⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⢤⠀⠹⣄⡿⠢⡈⠰⠧⠄⣀⢀⢀⣀⣠⣤⡤⠴⠒⢒⠖⢩⡽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡃⢀⠀⠙⢇⠀⠙⢶⠒⠛⠉⠟⠋⠀⢸⡟⣀⡔⢀⠊⠐⣀⣈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠢⠴⠯⡿⠉⣹⠂⣌⠢⡘⢸⠀⠠⠀⠀⣠⢤⠮⠚⠛⠒⠛⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢱⣟⡆⠀⡐⠀⠀⠑⢆⡜⡇⠉⠈⠉⠉⠉⠀⠠⢤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠠⠀⠁⠈⠷⠁⠀⠀⠀⠐⠀⠒⠿⠟⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣀⢀⣴⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣟⣁⣀⣀⣈⣻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⣀⡀⢁⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣭⣭⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠋⣠⣤⡌⠛⣨⡝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣟⠉⠸⠷⠿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡈⠀⠗⠘⢛⠟⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⢿⣿⢿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣇⣄⣰⣀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢻⣿⡟⢻⣿⡟⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢐⢐⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠸⠘⠇⢨⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣿⡇⢸⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢠⠀⠄⡀



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⢀⠀⢀⡀⣀⣀⠀⢀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⣿⣀⣿⣸⢿⡃⣿⣹⣿⣼⠀⣽⠿⣿⣿⡀⠰⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡄⠀⡖⠒⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠔⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⡇⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⢈⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⡇⠀⣇⣀⠀⠀⢈⠀⠀⠀⢸⠀⠀⠀⢰⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠇⠀⢧⣤⡄⠀⢠⣤⡄⠀⠸⣤⣤⠀⠈⢦⣠⠞


⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⢠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⢁⡤⠤⣈⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⢂⡡⠤⡈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠙⢢⡈⠳⠤⠤⠴⠦⠤⠤⠔⢉⠔⠊⠁⠀⠀⠰⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⡄⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⢀⠃⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠐⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⡞⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠸⣿⠇⠀⠀⠀⠀⠀⠀⠐⢿⠇⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠀⢶⡶⠀⡀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠈⠳⡊⢑⡞⠁⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠉⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⣀⣀⠴⠀⣀⡀⠠⠂

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⢿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠁⣼⠏⠀⠙⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠋⠀⣠⣴⠾⠋⠀⠀⠀⢀⣿⠛⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠛⠉⣀⣤⡶⠟⠋⠁⠀⠀⠀⠀⢀⣼⠏⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⢁⣠⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⣹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⣠⡶⠟⠉⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁⠀⠀⠀⢀⣴⡿⠉⠻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠋⠀⠀⠀⠀⠀⢀⣠⣶⠟⠋⠁⠀⠀⠀⠀⢀⣤⡶⠟⠉⠀⠀⠀⣸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⢀⣠⡶⠟⠉⠀⠀⠀⠀⠀⢀⣤⡾⠛⠁⠀⠀⠀⠀⢀⣴⠟⠉⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⣠⡾⠛⠁⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣷⡀⠀⣰⡿⠁⠀⠀⢀⣀⣀⡀⠀⣴⠟⠀⠀⠀⠀⠀⣀⣴⡾⠛⠁⠀⠀⣀⣤⣾⣧⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡅⠈⢻⣶⣿⣤⣴⠶⠟⠛⢻⡏⠻⢿⣯⣀⣀⣤⣴⠾⠛⢻⣿⠛⠷⢶⣶⡟⠋⠁⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⢻⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⢻⡟⠉⠁⠀⠀⠀⢸⡏⠀⠀⠀⣿⠁⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠈⢿⡄⠀⠀⠀⠀⢸⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⡿⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠈⢿⡄⠀⠀⠀⠘⣷⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⣸⡇⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠘⣷⡀⠀⠀⠀⣿⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⢀⣿⠁⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⢹⣧⠀⠀⠀⣿⠀⠀⠸⣿⠀⠀⠀⠀⠀⣼⡇⠀⢸⡏⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⡀⢿⡆⠀⠀⣿⡄⠀⠀⣿⠀⠀⠀⠀⠀⣿⠀⠀⣿⠁⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢶⣦⣾⣧⣤⣤⣿⣄⣀⣀⣀⣴⣿⣤⣴⣿⣶⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⢉⡀⢀⡀⠀⢉⠀⠉⠀⠀⠀⠁⠀⠂⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢰⠄⠀⢀⡀⠀⠘⣀⢀⠀⣀⣠⡀⠀⠀⠀⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣍⠀⠀⠀⠀⠀⠉⣤⠀⣀⠀⠀⠄⡄⠉⠀⠉⠉⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⣀⠀⠀⡀⠀⢠⡄⠀⠀⠁⡀⠀⣰⠣⠀⠀⠀⠤⠀⠀⡠⠔⠁⠔⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠆⠉⠀⠀⠀⣀⠔⠀⣀⠾⠭⠄⠁⠁⠉⠈⠠⠄⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠓⠀⠀⠠⠀⠀⠂⠁⠀⠀⠚⢅⡀⠁⠠⡀⢀⠄⠀⢀⡀⠀⠐⠂⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠒⠂⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠀⠒⠒⠚⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⡠⢤⡇⢰⠒⠒⠒⠒⠒⠒⠒⠠⠤⣀
⠀⠀⠀⠀⠀⠀⣀⠗⠤⢻⡟⣛⣁⣀⣀⣀⣀⣀⣀⣀⠠⠜⣆⡀
⠀⠀⠀⠀⠀⣎⡘⠤⠤⠄⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠤⠤⠞⣈⡆
⠀⠀⠀⠀⠀⠗⠺⠭⠴⢒⣒⣀⣐⠶⠶⠶⣖⣀⣐⣒⠲⠬⠵⠚⠇
⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡧⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡇
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠈⢉⡅⠐⠒⠒⠒⠒⢂⣈⠉⠉⠀⢠⠀⠀⣀⠔⠒⠢⣄
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⡞⠹⣆⠀⠀⠀⢀⡾⠹⣆⢀⡠⠜⠒⠚⣓⡦⠤⠤⡬⠶⠶⠮⠾⣛⣁⡉⠙⠒⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⣾⣿⣿⡆⠀⢀⠜⢁⢤⡴⠮⠛⠁⠀⠀⣀⣈⣦⣤⣒⣒⠒⠢⠬⣉⣒⣠⣈⠫⠑⣄
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢿⡏⣹⠃⠀⣮⢞⠕⠉⠀⣀⡤⠖⠛⠉⠉⠀⠀⠀⠀⠉⠉⠓⠲⢤⡀⠀⠈⠉⠣⣨
⠀⠀⠀⠀⠀⠀⠀⠛⠐⠒⠂⠤⠤⠤⠭⠥⠤⡴⠱⠁⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⢀⡾⠁⠀⠀⠀⠐⢤⣀⡀⠀⠀⠀⠀⣀⣠⠔⠀⠀⠀⠀⠈⢧⡀⡌⡇
⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠊⡾⠁⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠁⠉⠉⠀⠀⠀⠀⠀⠈⣷⢱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢅⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠂⠤⠤⠤⠤⠤⠤⠤⠙⢧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠲⠶⠦⠤⠤⠤⠤⠤⠤⠤⠤⠶⠖⠒⠚⠋⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠶⠒⠚⠛⠛⠉⠉⠉⠉⠙⠛⠛⠒⠲⠶⠶⠦⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠉⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠦⣄⡀
⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠰⡒⠢⣀⠀⠀⠀⠈⠓⠒⠒⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀
⠀⠀⠀⣠⠖⣹⠃⠀⠀⠀⠀⠀⠈⠲⠼⢀⣠⠴⠒⠦⢄⡀⠀⠀⢀⡔⠒⠒⠶⠖⠋⠉⠳⣄⠀⠠⡶⣤⡀⠀⠀⠀⠉⠳⣄
⠀⢀⡼⠃⣼⠁⠀⣀⠴⢢⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠉⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠑⢄⠙⢷⠀⠀⠀⠀⠈⢷⡀
⠀⣾⠁⠀⢹⡀⡞⣡⢔⠃⠀⠀⠀⢠⡇⠀⠀⠀⢀⣠⣤⠴⠶⠶⠶⠦⣤⣄⣀⠀⢉⡓⢦⡀⠳⣄⠀⠀⠙⠚⠀⠀⠀⠀⠀⢸⣇
⣸⠇⠀⢀⡞⠀⠉⠑⠋⠀⠀⠀⠀⢸⠀⣠⡴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⣌⠳⡙⡆⠈⠳⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿
⣿⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠁⢀⡄⠀⠀⠀⠀⠀⢀⡤⡀⢀⡞⠈
⣿⠀⣤⠀⠈⠑⠲⣄⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡴⠋⢀⠤⡀⠀⠀⠀⡞⢠⠇⣏⠀⡀
⢹⡆⢸⡄⠀⠀⣠⠏⠀⠀⠀⣀⠀⢀⠀⠈⠓⠦⢤⣀⣀⡀⠀⠀⠀⠀⣀⣀⣤⠴⠞⠋⠁⠀⣴⠃⡜⠀⠀⠀⠈⠓⠁⣀⡼⡸⢠
⠀⢻⡄⢷⡀⣼⠁⠀⢠⠖⠊⠁⠀⢠⡇⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠳⠊⠀⠀⠀⠀⢀⡴⠊⠁⡰⠁⣾
⠀⠀⠻⣄⠳⡼⣄⢀⡼⠀⠀⠀⠀⠸⡆⠀⠀⠀⢀⡤⠖⣫⠇⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⡴⠁⣼⠃
⠀⠀⠀⠙⢦⡙⠪⠉⠁⠀⠀⠀⠀⠀⠉⠳⡄⠀⠻⠖⠋⠀⠀⠀⠀⠀⠙⠒⠒⠚⠃⠀⢀⣀⣀⣀⣀⠀⠀⢠⡇⣠⡾⣡⠞⠁
⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠘⢆⣀⣀⣀⠀⠀⠀⢀⡤⡀⠀⠀⢀⡴⠒⠋⠀⠀⠀⠈⠙⢛⣩⠞⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣀⡀⠀⠀⠀⠀⠈⠉⠉⠉⠓⠚⠉⠀⠹⡄⢠⡏⠀⠀⠀⠀⠀⠀⠀⣀⣭⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠈⠋⣀⣀⣀⣠⡤⠶⠚⠋⠉

⠀⠀⠀⠀⠀⠀⣄⠀⠠⣶⠀⠀⠀⣠⣤⣤⣶⡶⢦⣀⡴⠟⢂⣥⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠘⢷⡀⡿⠀⠀⣸⣯⣼⠛⣫⣷⣾⣿⣷⣾⣿⠛⡹⢉⣿⡄⠠⢦
⠀⠀⠀⠀⠀⠀⠀⣼⣿⡟⢦⡀⠉⣼⣯⣭⣿⣿⠍⠁⠟⣧⣝⢿⣌⠟⣿⠇⠀⠀⠾⠆
⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠟⢳⣄⣿⣉⡟⣱⣟⡀⠀⣅⣘⣿⡆⣷⠰⣟⡄⢀⡄⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠾⠏⢻⣷⢋⣹⣿⣟⠻⠞⢻⣿⣷⣧⡌⣿⣯⣩⠼⠁
⠀⠀⠀⠀⠀⠀⠀⠸⣿⠁⠀⠀⠘⣿⣿⡜⠿⣿⣷⠠⠈⠽⣿⣿⣇⣽⠋⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⡀⢠⡘⣿⣿⣿⣿⣿⠦⣖⡴⢿⢿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣟⡟⠁⠛⣿⣯⣿⣿⢿⣿⣿⣿⣶⣿⣆⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠈⢻⣿⠇⣸⣿⣿⠻⠽⠻⢿⣟⠹⢾⣻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠛⠀⠦⠘⢿⣦⣹⣿⡏⠀⠀⠀⠈⠛⣶⣛⣻⡟⢉⣷⠀⠀⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠙⣿⣿⡿⣄⠀⢀⣤⣴⢿⣼⣿⠃⣾⣯⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣯⣥⣞⣱⣏⣴⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⣽⢿⣿⣿⡛⢻⣿⣿⣦⡈⣻⣿⣿⣷⣾⣿⠿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⣾⠃⢻⣷⣾⠋⢿⣟⠛⢿⢿⣿⣿⣿⣿⣾⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⡇⠀⠀⣻⣧⡀⠘⣿⣧⠀⢸⣿⡿⠋⠙⠿⢿⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣦⣥⣼⣿⣿⣦⣼⢿⡷⣿⠛⠀⡀⠀⠀⠀⠙⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⣬⢉⣰⡿⠈⣯⠁⠀⢹⣿⠀⠨⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠈⣹⡇⠀⢿⣤⣄⠘⣿⠀⢐⡛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⣶⣿⡇⠀⢸⡏⢡⣤⣿⠀⢹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣦⣤⣾⠁⠀⠀⣿⢶⣾⣿⣄⢢⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⡉⣿⠀⠀⠀⣿⣿⣿⠶⣿⡏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⡈⣳⣿⡀⠀⠀⢮⣿⣿⠀⣹⣿⣄⠀⠐⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⡛⢻⣿⣿⣧⠀⠀⢺⣿⣿⣃⢸⣏⣛⣷⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⣿⣇⣾⣿⣿⣿⠀⠀⠈⣿⣿⣿⣀⣼⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢠⣴⠶⠾⠛⠟⠻⣿⣿⣿⣿⢿⣴⠶⠶⠞⣿⣿⣿⣿⢏⠤⠠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠁⠛⠛⠛⠃⢈⢋⢀⡀⠀⠛⠛⣿⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠹⠀⠛⠂⠀⠸⠈⠐⠀⠀⠀⠉⠉⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⡀⡀⠤⠀⠀⠀⠐⠀⠠⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠁⠀⠀⠀⠀⠀⠃⡄⠀⠀⠀⠀⠀⠑⠂⡀⠀⠀⠀⠀⠀⢀⠡⡀
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⡀⠀⠈⠁⠸⠛⠂⠈⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⡠⠤⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢤⠀⣀⡜⠁⠀⠀⠀⠀⠀⠙⣂⠀⠆
⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠐⡇⠑⠀⠀⠀⠐⠋⠀⠘⠃⡆⠀⠐⠄⠀⠀⠀⠠⢀⠒
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠘⠇⠀⠀⠤⠄⠀⠀⠀⠤⠀⠅⠂⠀⠀⠀⠀⠀⠀⠂⠈⢀
⠀⠀⠀⠀⠀⠈⠉⠉⡄⠈⠁⠉⠁⠀⠀⠀⡖⠥⠀⠀⠀⠀⠀⠀⠉⠁⠐⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠁
⠀⠀⠈⠒⠰⠄⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠶⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠃
⠀⠀⠀⣀⠄⠀⠀⠀⠂⠐⠌⡁⢀⠀⠀⠀⠀⠩⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢠⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠒⠈⢠⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⡡⢄⠀⠀⠐⠀⢀⠀⠁⠀⠀⢀⣁⠠⠠⠄⠤⠤⠤⠈
⠀⠀⠈⠠⢄⠀⠀⠁⠠⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⣀⡀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠐⠀⠀⠈⠈⠐⠀⠀⠁⠀⠐⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⢀⠀⡀⣾⣿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠦⠀⠀⠀⡀⠄⠀⠠⠀⠀⠀⠀⣀⠍⠅⠀⡅⠈⠉⢁⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠂

⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠀⠀⠀⢠⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠋⣉⣩⣭⣉⣤⣦⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⣉⣉⣭⣍⣥⣴
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣥⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣯⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣈⣩⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢠⣈⣉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠐⠀⠐⠆⠀⠀⠀⢐⠁⠀⠈⣡⠕⠀⠀⠀⠸⢏⣙⡆⠀⠀⠀⠀⠀⢠⡆⠤⠀⠀⢤⠀⠀⠀⢀⡠⠜⠿⢦
⠀⠀⣈⠙⠓⣾⣛⣷⠀⢰⣿⡿⢿⣂⣸⡄⠀⠀⡀⠀⠀⠀⣸⣄⠀⠀⠠⣷⣦⣽⣷⢆⣰⡆⠀⠀⠀⣾⡟⠒⠚⠈⢰
⠀⠀⠦⡀⢘⣫⡭⠶⠀⠈⣿⠂⠂⠈⠉⠀⠀⠀⠰⢸⢸⣿⢯⡇⠀⠃⠀⠀⠹⠿⠀⠀⠻⠆⢄⡤⠀⢸⡷⣦⡄⠀⣼
⠀⠀⠁⠀⠬⠷⠚⠉⠀⠀⠛⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⠙⠊⠁⠀⠐⠀⠀⢀⣀⡀⠀⢠⣤⣤⡤⠀⢸⣄⣈⡁⠀⣈
⠀⠀⠀⠀⢀⢀⠀⠤⢀⡢⠀⠀⠀⢠⣾⣛⣛⡿⠞⠀⠀⠀⠀⠀⠀⠀⠤⡅⠈⠧⠺⠖⠶⠶⠶⠖⠀⠈⠉⠉⠉
⠀⠀⠀⠀⢸⣿⣟⡶⣶⢤⣌⡀⠀⠀⠐⠀⠤⢍⣙⣷⠀⠀⠠⠔⠀⠀⣤⣶⣢⠀⠀⠀⠀⠀⢀⣚⣁⠚⠻⢶⢂⣰⠄
⠀⠀⠀⠀⠀⠷⣿⣿⣻⣏⣫⡟⠀⠀⠯⣉⡓⠢⢤⣙⠀⠀⠁⠀⠀⠀⡠⣾⡏⠀⠀⠀⣄⡀⣉⣉⠉⢀⢠⠼⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠀⠀⠀⠀⠈⠑⠺⠗⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠈⠙⠂⠐
⣶⣶⡶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠠⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⣀⠀⠀⠀⣠⣉⠦⡉⠁⠢⡀⠀⠀⠀⠀⠀⠀⠶⢲⣨⠀⣠⠷⠀⠀⠀⠰⠁⠈⢡⠀⠀⠀⠀⠀⡰⠭⠤⠀⢠
⠀⠀⢀⣀⡄⢂⣁⡘⠀⠀⠁⠀⠄⢠⠀⠀⠀⠀⠀⠀⠰⢻⣞⠟⣅⠀⠀⠀⠀⡤⠁⡲⣤⡀⠀⠀⠀⠼⠀⢄⠤⠔⠂
⠀⠀⠘⠤⠀⠀⠐⠦⠶⠒⠂⠀⠊⡀⠀⠰⠀⠀⢀⢟⡖⠓⡿⠽⠙⡄⠀⠁⠀⠀⢠⠁⢈⡁⠀⠘⠀⠠⢀⠘⠀⠇
⠀⢔⠉⠑⠂⠀⠀⠐⠐⠒⠀⠉⢀⡀⠔⠁⠠⠄⠀⢎⠵⠀⠁⠐⡽⠁⠀⠀⠀⠂⠠⢠⠄⠃⠀⠀⠀⡊⠡⠀⠀⢔⠠
⠀⠋⠁⠀⠀⠒⠒⠒⠀⠀⢠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⠀⠄⠀⠀⣀⠀⠀⠀⠀⠘⠀⠀⠀⢀⠀⡈⠁⠀⠈
⠀⠀⠀⠀⢀⢄⠀⢀⡤⢀⠀⠀⠀⠀⠀⡤⠀⠒⢀⣐⢄⠀⠀⠀⢸⠀⠁⡆⠁⠀⠀⠉⠀⢐⠑⠃⢀⠄⠀⠀⠀⡀⠉
⠀⠉⠀⡐⣡⠯⡉⠍⣎⡦⢥⠀⠀⡐⠀⠀⠊⠀⠀⠐⢠⠄⠀⠙⠠⢄⡄⠘⠢⠀⠀⠀⢀⠹⠅⣠⠌⠰⠀⠀⠀⠁
⠀⠀⠀⡧⣅⣮⠀⠀⡸⣧⠈⠀⠈⠀⠊⠀⠀⠀⠀⠈⡘⠄⠀⠀⠀⠀⢄⢀⡴⠐⠂⢀⠀⠉⠂⠈⡠⠠⢄⡩⠠⠢⡀
⠀⠀⠀⠐⢜⠤⢮⢉⡱⢛⠇⠀⠐⢤⡁⢄⠀⠀⠀⠀⠈⠌⠢⠈⠁⠀⠀⠀⠦⡤⢍⡢⠀⠀⠀⡐⠔⠁⠄⠐⢄⠁⢺
⠀⠰⠀⠀⠀⠁⠀⠉⠉⠐⠀⠀⠀⠀⠈⢧⡡⢀⣀⠠⢂⣡⠞⠀⠀⢀⠀⠀⠐⠃⠀⠀⠀⠀⠀⢙⠠⠘⢄⣀⠐⠀⣇
⠀⠘⠀⠀⠀⠀⢀⣀⠠⢤⠤⢀⠀⠠⠄⠀⠱⣄⣠⠴⠋⢀⢀⠐⠋⣦⠄⠂⠀⠀⠀⠀⠀⠰⠀⠀⠢⠂⠂⢄⡐⡠⠋
⠀⠀⠀⢀⠠⠒⠄⠑⡆⠈⠃⢈⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠘⡔⠚⠳⡄⢤⠀⢤⡥⠤⣤⢤⡤⢄⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡐⠫⣆⠀⠃⠀⠀⠠⡠⠊⠀⠀⠀⢀⢰⠌⡉⢁⠢⡀⠀⠈⠀⠀⠃⠚⠒⠒⠓⠀⠒⠂⠓⠈⠀⠀⠀⢰⠆⠀⠈
⠀⠀⡀⠀⠈⠀⢀⠰⠑⠊⠀⠀⠂⠀⣀⠓⠃⠀⠃⠀⠓⠐⢀⡄⠀⠀⢀⠔⠂⠀⠀⠂⢄⠀⠀⠐⠀⠀⡠⠂⠠
⠀⠀⠊⠀⠈⠁⠀⠀⢀⢀⠀⠀⡀⠀⠑⢖⠐⠂⠒⠒⠒⡰⠁⠀⠀⢀⠃⠠⠊⡀⠄⡁⠀⠂⠰⠀⠀⡠⠀⠀⠀⢑
⠀⠀⠀⠀⡐⠂⠀⠪⠀⠀⠘⡁⢀⠀⠀⠀⠀⠉⠉⠉⢉⡀⠀⠀⠀⠀⡀⢀⠀⠒⠀⡀⠀⡄⠀⠀⠀⢄⡀⠀⠀⡀⠆
⠀⡀⠀⢰⡀⠀⠀⠀⠑⠀⢀⠌⠀⢀⠄⣢⡆⢀⡠⡀⠀⠀⠀⠀⠀⠀⢑⣄⠑⠒⠊⡀⠔⠀⠶⠀⠀⢸⣽⠎⣟⠁
⠀⠀⠀⡌⠀⠑⠠⠀⡠⠋⠀⠀⠰⠅⠮⡀⠎⠌⠙⠐⠀⠤⠀⠉⢀⢔⠕⠁⠀⡀⠀⢀⠀⡄⠀⠀⠀⠐⢛⡘⢩⠀⣀
⠀⠀⠀⡕⠀⠀⠔⠀⠀⠆⠀⠀⠘⠢⡐⡐⡈⠌⢦⡅⠀⠀⠀⡀⡁⠀⠀⠀⣅⡨⡀⠣⠝⢢⡀⠀⠀⠀⢗⠶⡇⠀⠉
⠀⠀⠀⠑⠂⠀⠀⠀⡀⠀⠀⠀⠠⡑⠄⣜⡈⡼⢌⠔⠀⠀⠬⠊⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⢠⠀⠀⠀⠸⠭⢁⡀
⠀⠀⠐⠂⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠁⠀⠂⠂⠁⠀⠀⠀⠀⠀⠒⠂⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠁⠀⠀⠀⣶⣶⣆⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀⠀⠈⠻⣿⠿⠛⢁⣠⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣷⣤⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⣴⣾⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠾⣿⣿⣿⠁⠀⠀⠈⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣯⣿⠿⣿⣿⣿⣿⣿⣤⣴⣿⣿⠃⠀⠀⠀⠀⠘⣿⣿⣦⣤⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣤⣤⣾⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⣀⡀⠀⠀⠀⣀⡈⠙⠻⠿⣿⣿⣿⣿⠋⠀⢠⣶⡄⠀⠀⠀⠀⢠⣶⡄⠀⢙⣿⣿⣿⣿⠿⠟⠋⢁⣀⠀⠀⠀⢀⣀
⠀⠀⠀⠈⠙⠛⠀⠀⠈⠙⠋⠀⠀⠀⠀⠈⠩⣿⡷⠀⠘⠿⠃⠀⠀⠀⠀⠘⠿⠃⠀⢾⣿⠍⠁⠀⠀⠀⠀⠙⠋⠁⠀⠀⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣶⣶⣦⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠿⠿⠿⠿⣿⣿⣿⡿⠿⠿⠿⠟⠋



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣰⣾⣿⣿⣿⣿⣦⣤⣶⣦⣤⣀⣠⣶⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿⣷⣄⣀⣤⣴⣶⣤⣤⣾⣿⣿⣿⣿⣦⣀⣀⣀⣀⣀⣀⣀⡀
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠉⠙⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠟⠛⠻⣿⣿⣿⣿⣿⣿⠟⠛⠻⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⠟⠛⠿⠛⠛⢿⣿⣿⣿⣿⣿⠟⠛⠛⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⡸⠻⠿⠿⠿⠿⠿⠟⢇
⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⣿⣷⣶⣤⣄⡀
⠀⠀⠀⠀⢀⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⠿⠛⠛⠛⠻⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⢸⠂⠉⠒⠢⠤⠤⠤⠤⠒⠉⡙⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠋⢁⡤⠤⢤⡀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣦⣤⣶⣶⣶⣦⣤⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⢸⠀⣦⢰⡄⡄⢠⠀⢰⡠⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣄⠻⢤⣤⣤⠟⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⠀⣿⣼⠀⡇⣶⠀⣾⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⢸⣄⠁⠸⠁⠁⢯⡀⠎⠓⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣶⣶⣶⣿⣿⣿⣶⣶⣶⣿⣿⣿⡿⠁
⠀⠀⠀⠀⢸⠈⠑⠒⠤⠤⠤⠤⠔⠒⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠒⠒⠉



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠿⠔⠶⠶⠶⠤⢤⣀⠉⠙⠲⣄
⠀⠀⠀⠀⣠⠴⠛⠛⠛⠒⠒⠛⠛⣋⣋⣳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⣀⣾⠦⣄
⠀⠀⠀⡔⠛⠃⠁⠉⠉⠉⠉⠉⠉⠉⠉⠁⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣞⣹⣄⣀⣀⣀⣀⣀⣀⣀⠀⣴⣿⠛⠛⠀⠀⠸⡆
⠀⠀⠀⠸⣄⣀⣠⣤⣤⣤⣤⣤⡤⠤⠤⠤⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠥⠤⠤⠶⠶⠶⠶⠶⠦⠤⠤⢤⣤⣉⡉⠋⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦⠀⣶⣤⡀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⢠⣶⣶⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠆⣿⠛⠁⠀⡇
⠀⠀⠀⠀⠀⠀⢇⠀⠀⠘⠛⠛⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⢸⠀⠟⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⢀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⢸⢹⣹⢳⠀⡾⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⣀⣀⠀⠀⠀⠀⠛⠉⠛⠈⠛⠟⠃⣠⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⢿⣿⣿⡿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣷⣌⣡⣾⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣛⠿⣿⣿⠿⣛⣛⠿⣿⣿⠿⣛⣃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣮⣵⣿⣿⣿⣿⣦⣵⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣝⡛⢿⡿⣛⣫⣝⣛⢿⡿⢛⣫⣝⣛⢿⡿⢛⣋⣥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣧⣾⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣭⣝⠻⢟⣭⣭⣭⣍⡻⢟⣩⣭⣭⣍⡻⠟⣫⣭⣭⣭⡻⠟⣫⣭⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⣤⣤⣬⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣥⣤⣤
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠈⠉⠉⠉⠉⠉⠉⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠄⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠉⣀⡶⠀⠀⠀⠀⠀⠀⠀⢀⠀⠬⠉⠉⠁⢀⣀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠠⠴⠄⠀⠀⠀⠀⠀⠀⠠⠈⣀⣀⣀⣉⡑⠚⣉⡀⠡⠀⠀⠀⠓⠦⠧⠤⢀⠢⣴⠤
⠀⠀⠐⠂⢄⣀⢀⣤⠶⠂
⠀⠀⠀⠀⠐⠈⠻⢤⣢⣥⡤⠀⠉⠀⠀⠀⠀⠒⠀⠈⣄⠀⠀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⢂
⠀⠀⠀⠀⠀⠁⠠⠄⠀⠐⠆⠴⠦⠀⠀⠀⠈⢆⡰⠶⠊⠀⠀⠀⠠⠤⠀⠀⠀⡠⠀⠀⠀⠈⢦⣀⣤⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠜⠴⠎⠂⠀⠀⠀⢡⣠⠀⠀⡀
⠀⠀⠀⠀⠀⡀⢀⠄⠒⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣡⣤⡶⠏
⠀⠀⡆⠖⣀⠛⠃⠀⠀⢵⡦⡄⠳⠃⠀⠀⠠⠄⢂⠂⠠⣒⠍⠁⠀⠀⠀⠀⠀⡤⢀⠀⢀⠤⠀⠀⠀⠈⠁
⠀⠀⠉⠉⠙⠦⠐⠚⠘⠃⠒⠁⠀⠀⠀⠀⠠⠆⣤⠶⠖⠥⠒⠖⠢⠀⠀⠀⠀⢣⡀⠀⠈⠑⠒⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⣀⣠⠴⠤⠔⠚⠁⠀⠀⠀⠀⠁⠉⠉⠉⠀⠙
⠀⠀⠄⠒⠊⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⣤⡄⠀⠀⠀⣀⠀⠀⠀⠠
⠀⠀⢠⡐⠀⠈⠆⠀⠀⠀⠀⡠⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣼⠆⠀⠀⠀⠅⠀⠀⢀⣀⡀⢀
⠀⠀⠀⡆⠀⠀⢀⡄⠀⠀⠀⣀⣀⡀⢁⠤⠀⠀⠀⣠⠁⠀⠀⠀⠀⠂⢀⣠⢀⠏⠀⠀⠀⠀⠉⠀⠈⠈⠀⠀⠉
⠀⠀⠀⢹⠂⠈⠀⠀⠀⠀⠀⢃⠁⠉⢁⠤⠬⢥⠊⠗⠀⠀⠀⠀⠀⠉⠙⠒⠃
⠀⠀⠀⠈⢧⠀⣀⠤⠃⠀⠀⠈⠄⠠⠤⠤⠰⠒⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢠⠤⠐⠐⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡠⠄⠠⠀⠒⠀⠘⠄⠀⣀⣌⣣⡤⠦⠞⠂
⢀⠀⠀⠤⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠈⠳⣀⣀⣤⠽⡴⠶⠛⠛⣏⠉⠁⢀⠹⣄⣀⡤⠥
⡀⠤⠤⠀⠀⠣⠀⠀⠀⠈⠀⢁⠉⠑⠀⠀⠀⠀⠀⢈⣷⠚⠛⠉⢉⠀⠀⠀⣀⡀⠠⠴⠞⠂⠊⡉⠁⣀⠄⠤⠄
⠐⠀⠒⠊⠀⠀⠀⠀⠀⠐⡖⠂⢦⣶⠄⠂⠁⠀⠀⠀⢧⣀⠤⠶⠒⢃⠉⣩⣀⡀⠤⠀⠚⠃⠋⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣀⠀⠰⠀⠀⠀⠀⠀⠀⠈⠫⠀⠒⠒⠉⠁
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⡀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠄⠐⡀
⠀⠀⠀⠀⠀⢀⡆⠀⢀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠛⠃⠀⠀⠀⠀⠀⠀⢸⡔⠀⠀⠀⠀⠀⡠⠔⠀⢰
⠀⠀⠀⠀⠀⠸⠃⠀⠈⠖⠀⢺⠀⠀⠀⠁⠀⡰⠂⠀⣀⠀⠸⣆⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠈⠀⠀⣀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡂⠀⢸⡇⠀⡄⠀⠘⠁⠀⠀⠉⠀⠀⠈⡇⠀⠀⠀⠀⣷⠞⠁⠀⠀⡀⢠⠔⠉
⠀⠀⠀⠀⠀⢸⡆⠀⠀⠄⠀⠈⠁⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣿⠀⠀⠀⠀⢁⠁⢀⡠⠄⢰
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠲⠂⠀⠘⢦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡴⠀⠀⠀⢹⡶⠃⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⡄⠀⠀⠀⠀⠀⠈⠉⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠸⣤⠴⠀⠀⠈⣿⣴⠂⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠜⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡤⠔⠒⠂⠐⠚⠁⠀⠒⠠⠔⠉
⠀⠀⠀⠀⠀⠀⣔⠅⠂⠀⠈⣂⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⡀⠉⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠉⠀⠐
⠀⠀⠀⠀⠀⠀⠘⠂⠒⠂⠐⠃⠀⠀⠀⠈⠛⠓⠐⠂⠐⠀⠀⠒⠒

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠔⠒⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠔⠒⢲⣞⠁⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢦⣤⠞⠉⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠀⠀⢀⣈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⠁⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⢹⣦⠀⢠⣶⡾⠟⢋⠩⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀⠀⣤⣴⣶⠿⠟⡋⣃⡈⠐⢂⠁⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠄⢀⣀⣤⣶⡿⠷⠜⠋⠡⠀⠈⠀⠀⠘⢷⡄⠈⢂⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⣾⠿⢛⠉⠁⠒⠙⣶⡄⠀⠀⠀⠀⠀⠀⠈⢻⣄⠈⢆⣀⣠⣤⡶⠟⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠁⠈⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⣀⣠⣼⣿⣦⠸⢛⣩⢥⡲⣯⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⣻⣆⢀⡶⠿⣛⠫⢭⣤⠶⣾⣿⡿⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⢀⣤⣶⡾⠿⣛⣭⣿⡶⠿⣞⣗⣥⠬⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡐⢨⣿⣷⣾⣿⣏⡦⠽⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⠾⠟⠛⠉⠁




⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤
⠀⠀⢠⡾⠁⠉⠀⠀⣀⡀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠴⠂⠀⠘⠁⠀⠀⠚⠉⢀⡀⡀⠀⠀⠐⠉⠀⠀⠀⠀⠀⣠⡀
⠀⠀⡌⠀⠀⣴⠄⠀⠈⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⡀⠘⠁⠀⡤⠀⠀⠀⠀⣨⠏⠀⢀⣆⠀⠚⠁⠀⠀⠀⣤
⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢗⠈⠀⣀⠤⠐⢀⣀⠿⠒⠈⠀⠀⠀⠘⣇
⠀⠀⣇⠀⠀⠀⠀⠺⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠐⠛⠂⠀⠀⠶
⠀⠀⠙⠀⠀⠴⡄⠀⠀⠀⣠⠀⣤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⠀⠀⠀⠀⠀⠀⠈⠂⣀⣀⠀⠐⢶⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⣠⡶⢛⣷⠀⣾⠿⠿⠶⣦⣾⠷⠋⠤⢀⣀⣞⡆⠀⠀⠀⠈⠛⠀⠤⠴⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢡⣿⠃⣠⠶⡀⡶⢲⣰⣿⣸⢧⡟⣿⢈⣜⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⠙⣰⡿⢤⠿⣟⡾⠻⠟⣧⣈⡯⠭⡅⠻⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⣠⠜⠉⠛⠫⣤⣬⣴⡶⠞⠋⠙⠲⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠴⠀⠐⠛⠃⣀
⠀⠀⠀⠴⣀⠀⠤⠀⠀⠈⠉⠀⠀⣤⡄⠀⠀⠀⠀⠀⣠⠖⠒⣀⠃⠈⠙⠂⠀⠀⠀⠀⠀⢰⣧⠶⠒⠉⠁⠉⠂⠀⠀⠒
⠀⠀⢰⡄⠉⠃⠀⠀⣀⠘⠋⢀⡀⠀⠀⣀⠀⠀⡰⠀⡅⠀⠈⠉⢤⠀⠰⠖⠀⠦⠀⠀⠀⠘⢃⠰⡷⠤⠤⠤⠤⢖⠀⠀⠢
⠀⠀⣼⣿⣦⣈⣉⡈⢙⣁⠀⠋⠉⢀⣰⠁⠀⢘⡇⠀⠲⠀⠀⠀⡀⢠⡀⠀⠀⠀⠀⠀⠀⢸⡿⠋⠀⠀⠲⠀⠀⠀⠈⠘
⠀⠀⠻⣿⣉⣩⡉⠹⠟⠛⠉⠉⣽⣧⣡⡆⠀⠘⠂⠀⠀⠀⠀⠀⠀⠐⠁⠀⠐⠀⠀⠀⠀⢈⠁⠀⠛⠀⠀⠀⠀⠉⠀⠀⠐
⠀⠀⠰⠿⠿⠗⠒⠶⠶⠶⣾⠛⠛⠉⠉⣠⠀⠀⠀⠀⢠⠀⠀⠀⠀⠤⠀⠐⠀⢠⠠⠀⠀⢸⡔⠂⠀⠀⠀⠲⠆⠀⠀⣄
⠀⠀⠘⣿⠗⢲⡶⠶⢶⡾⢯⠶⠶⠞⠛⢃⠀⠀⠀⠀⠀⠀⢀⡤⠤⠄⠀⠀⠀⢀⠀⠀⠀⠈⢧⠀⠛⠀⢠⠀⠀⠀⠃
⠀⠀⣾⡟⣲⠶⣥⣤⣤⡤⠬⠴⠖⣒⠉⠍⡄⠀⠀⠀⠈⡁⠀⠀⠠⣤⡄⠀⠀⠘⠁⡤⠀⠀⠈⠲⠄⢀⠀⠀⠤⢀⠤
⠀⠀⠐⠳⠿⠧⠤⠛⢂⣀⣠⣤⣤⠭⠗⠊⠀⠀⠀⠀⢀⠈⢤⡀⠀⠀⠀⠠⡄⠀⠈⠁⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⣠⣾⡛⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠶⠶⢶⣦⡄
⠀⠀⠀⠀⢠⣿⠀⠙⣄⠀⠈⠙⠷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠁⠀⠀⠀⣰⠋⠈⣿⡀
⠀⠀⠀⠀⢸⣿⠀⠀⠈⢧⡀⠀⠀⠈⠻⣦⡀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⡰⠋⠁⠀⠀⠀⠀⢀⡞⠁⠀⠀⢹⡇
⠀⠀⠀⠀⠸⣷⠀⠀⠀⠈⢷⡀⠀⢀⡤⠾⠛⠋⠉⠉⠉⠁⠀⠀⠉⠉⠉⠉⠛⠓⠶⣤⡀⠀⣠⠏⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠃⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢹⡆⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠻⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠇
⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡏
⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢠⡶⠛⠛⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⢦⣤⡀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣠⡴⠚⠛⠳⣦
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢰⡏⠀⠀⠀⠀⠈⠓⠀⠀⠀⠙⣿⠃⠀⠀⢰⠏⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢸
⠉⠙⠛⠓⠶⢦⣿⣀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠰⣄⠀⠀⣠⠿⣄⠀⠀⣀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢀⣀⣿⠤⠶⢶⡾⠓⠒⠒⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⢹⡏⠑⠂⡠⠐⠀⠀⠀⠀⠀⠀⠈⡏⠉⠁⠀⠈⠉⢙⡇⠀⠀⠄⠒⠒⠀⠀⠀⠀⠀⠉⢸⡏⠀⠀⣸⠃⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠔⠊⠉⠉⠉⢺⠁⠀⠀⢄⠀⠀⠀⠀⢰⠀⠀⢠⡿⠁⠀⠀⣿⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⣀⡼⢿⣏⡀⠀⠈⠁⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣳⣿⣅⡀⠀⠀⣿⠀⠀⠀⢰⠏
⠀⠀⠀⢀⡴⠚⠁⠀⠀⠉⠻⠶⣤⣄⣀⡀⠀⠀⠀⠀⠈⠙⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠀⠈⠙⠷⣄⣿⠀⠀⠀⣿
⠀⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⡛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⢹⣦⡀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⢀⡟⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢄⡀⠀⡆⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⣠⠟⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠉⣻⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⠋⠁⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⠎⢠⠄⠀⠀⡾⠀⡀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⢀⣼⠧⠤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⠾⠤⠴⠚⠳⣼⣀⣾⣀⣠⡴⠿⣀⣀⣀⣀⣀⣐⣒⣚⣩⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠖⠂⠉⠀⠀⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠀⢸⠃⠀⠁⠀⠀⠀⢀⠔⠵⠒⢒⠀⠙⣆
⠀⠀⠀⠀⠀⠀⣀⡠⠴⠒⠒⠛⠋⠉⠁⠀⠀⠀⠀⡈⡀⠀⠐⣅⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠔⠒⠉⠉⣀⡟⠀⡾⠐⠊⢀⡴⣶⡦⢼⣏⣰⣿⣾⡇⠀⢹⡄
⠀⢀⡀⠤⠒⠉⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡑⠠⠀⠀⠠⠋⠀⠀⠀⣀⠄⠀⣀⣥⢀⡴⣿⣛⡶⢛⣽⠃⢠⠇⠀⢰⣿⠈⠳⡼⢀⣟⠭⠶⠛⠀⢀⣾⡇
⠀⠀⠙⣄⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠈⠀⠀⢠⠚⠀⠀⢀⠞⠁⢠⡞⢠⡏⡂⢹⠛⠮⡽⠊⡛⠀⠸⠀⠀⢸⣄⣁⣒⠒⠋⠀⠀⢀⣀⣤⠞⡻⠁
⠀⠀⠀⠀⠑⠘⠤⢄⡀⣠⠀⠀⡀⠀⢀⡀⠀⡠⠀⡀⠃⠁⠀⠀⢀⡎⠀⣰⡻⢧⡸⠗⣢⣛⣿⣟⢙⠖⠁⢀⠃⠀⠀⠈⠺⠭⢉⠙⠛⠉⠊⠉⣁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠉⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡞⠀⣶⢺⠗⣶⢘⠙⠙⣻⠯⠁⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡿⣯⣩⠥⠜⠛⠚⠁⢀⡠⠔⠋
⠀⠀⠀⠀⢀⣠⠴⠚⠋⠉⠉⠁⠀⢩⠛⠒⠦⣀⠀⠀⠀⠀⢀⠇⠀⡰⠛⠉⠀⢀⣠⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⣄⣠⠂⠀⠀⠀⣄
⠀⠀⢀⠴⠋⠁⠀⠀⠀⠀⠀⡆⠀⡏⠀⠀⠠⡈⢣⠀⡔⠈⣸⠀⢀⡥⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠐⠈⢳⣺⠁⠀⠀⠣⠆⢀⠀⠒
⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⡁⡤⠀⣧⣀⡀⠁⠀⠀⠀⠑⠒⢯⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠀⠻⣞⠇⠀⠀⠀⠈⠋⢀⠀⠀⠀⣁⠀⠀⠁
⢸⣁⠤⠤⢤⡀⠀⠀⠀⠀⠃⣀⠴⢋⡟⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠘⢖⢪⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣀⠤⠔⠓⠉
⢸⠁⠀⠀⠀⢘⣦⣤⠤⠖⠉⠀⠀⢸⡀⢀⠔⠁⠀⠀⠀⠀⠀⠀⢀⡠⠔⠲⣖⢺⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡁⠀⠆⠒
⢸⡀⣀⢀⠀⠚⠛⠒⠢⠤⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡤⠀⠘⢶⢻⠀⠀⠀⠈⠋⠀⠀⠀⠀⡅⠀⠀⠚⠊⠁
⠀⠳⣅⡀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⢀⡤⠒⠑⢎⡅⠀⠀⠈⠉⠀⠀⠀⠀⡈⠀⠒⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡤⠒⢲⢦⡄⣤⡤⠶⠤⠤⣀
⠀⠀⠀⠉⠑⠒⠒⠉⠁⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⣽⣿⡻⠋⠀⢀⡡⣾⠔⠉⠀⠀⠀⣠⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⣿⠋⠀⠀⠀⣼⠟⠁⠀⠀⠀⠀⡼⣛⣡⠽⠛⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠠⠤⠤⠤⠤⣀⡀⠀⠀⠀⢰⡃⠀⠀⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣼⠗⠉
⠀⠂⠀⠀⠀⡀⠔⠊⠩⣭⣭⣭⣍⣑⠲⣄⠀⠀⡠⠒⠉⣀⣠⡴⠶⠤⢲⣦⣀⣀⡈⠑⠢⡀⠈⢧⡊⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴
⠀⠀⣠⠔⠋⠀⠴⢤⣤⣄⣀⠀⠉⠛⣢⡞⠀⡜⠁⠀⢺⡏⣤⣄⣜⣦⡌⢀⣤⣡⠟⡶⠀⠱⠀⠈⠍⡒⠦⢄⣀⣀⣀⡀⠀⢀⣀⣀⣀⣀⡤⠤⠖⠒⠉⣹
⢠⡞⠁⠰⠶⠶⣤⣤⣀⠈⢙⣣⠶⠋⠁⠀⠀⠀⠀⢄⠀⠀⠴⢧⣠⣤⣀⣬⡭⠗⢩⠐⠀⠀⠀⠀⢢⢀⠀⠢⠀⠀⡉⠉⢉⡉⠉⣉⠀⠀⡄⠀⠠⠆⣸⠇
⡏⣭⣬⣭⣭⣓⠢⡈⢉⡴⠛⠁⠀⠀⠀⠀⠀⢢⠀⠈⠈⠐⠀⡂⠐⠐⠀⢂⠐⠬⠂⠁⣠⠆⠀⠀⠈⢦⣨⠐⠐⠄⠄⣀⢀⡀⡄⣀⣠⠀⠤⠆⠒⣸⠏
⠑⠮⠈⠉⠉⣛⣁⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣠⣀⠀⠀⠀⠀⠀⠀⣀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠉⠙⠒⠶⠦⠤⠤⣤⣤⡦⠤⠤⠴⠚⠋⠁

⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡀⠀⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⣀⣀⢀⣀⣀⡀
⠀⠀⠀⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⢄⣀⠌⠉⠠⣃⠀⠀⠀⠀⠀⠸⠉⢶⠃⡇⠀⠀⠀⠀⠀⠐⡧⠶⠤⠴⠯⠭⠍⠠⠤⠬⠟
⠀⠀⠀⠀⠀⢏⠀⠉⠂⣾⢡⠀⠀⠀⠐⠂⠄⠀⣹⠀⠚⠀⣨⠃⠀⠀⠀⠀⠀⠑⢠⠞⠀⠀⢀⠀⡄⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣶
⠀⠀⠀⠀⠀⡰⠁⢀⠀⣿⠀⡀⠀⡁⠀⡀⢀⡄⢸⣄⡈⠀⠝⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⡌⠀⠀⣀⡀⠀⠀⠠⠤⡀⠀⡇⠉
⠀⠀⠀⠀⠀⢈⡆⡀⢀⡽⢆⡀⠀⠀⣀⣀⣠⡤⠞⠀⠉⠓⠲⠚⠀⣀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⢰⠃⠀⡀⠣⢟⡀⠴⢐⠐⠁⠀⡇
⠀⠀⠀⠀⠀⠸⣨⠔⠋⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⢄⢣⠈⡇⠀⠀⠀⠀⡜⠀⠀⠚⠀⠥⠝⠰⣉⠇⣴⠂⣷
⠀⠀⠀⠰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡒⠤⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠈⠒⠃⠙⠲⡄⠀⢠⡇⠀⢎⣨⠂⢜⠂⡶⠀⠘⠔⠁⢻
⠀⠀⠀⠀⠁⠀⠀⠀⣠⠀⠀⠀⠐⢮⡁⠀⢯⠀⠀⠀⠀⠀⠀⠀⢰⠒⠠⡀⢠⠀⠀⠀⠀⣰⠃⠀⠈⠓⠒⠶⠶⠶⠶⠶⠶⠶⠒⠒⠲⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠀⠀⠀⠀⠀⢔⠒⠁⠀⣰⠃⠀⠓⠶⠖⠋⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣤⠤⠤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠤⠖⠁⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣄⡨⠆⠀⠀⠀⠀⠀⠸⠧
⠀⠀⢐⡆⠀⠀⠉⢀⠴⠂⠉⠀⡤⠉⠙⠦⡀⠀⠀⢀⢒⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠘⠓⠁⠀⢀⣀⠀⣀⡀⠀⠁⠔⠒⢢
⠀⠀⠈⢠⢢⠄⡔⠁⠘⣀⡤⠤⣄⡀⠀⠄⠙⢦⠀⠈⠁⠀⠀⠀⠀⠀⠀⡠⠔⠢⡄⠀⢀⠔⠊⠁⠀⠀⠀⠈⠓⣎⠀⠀⡞⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠆⠀⡞⠀⠀⡼⠁⠀⠀⣄⠙⢦⠀⡤⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠀⠈⢦⠏⡀⡜⠀⡐⡐⠀⡀⢀⢘⡇⠀⠈⠓⡆⠀⠀⣹⡗
⠀⠀⢰⠀⢸⡃⠀⠐⡇⠀⠄⠀⢸⠂⠘⡇⠀⠀⢸⡄⠀⠀⢴⡞⠀⠀⠀⣏⠅⠀⠐⢿⡔⡜⠀⡔⡰⠀⡰⢡⢃⣼⣁⠀⠰⡞⠁⠀⠈⠓⠃
⠀⠀⢸⠀⠈⣇⠀⠄⠈⠲⠤⠴⠋⠀⢰⠇⠘⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⢈⡆⢈⠈⡴⠻⢤⣜⣜⣀⣔⣴⠷⠋⠀⠙⠣⣀⡟
⠀⠀⠀⢧⠠⡌⠦⣀⠀⠀⠀⠐⢀⡰⠋⠠⠀⢀⡟⠀⠀⠀⠀⣠⠀⠀⠀⢯⡐⣡⠞⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠈⠳⣄⠀⠈⠙⠒⠒⠛⠉⢀⡀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢔⠖⠀⠀⠀⠀⠕⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⣤⣤⣤⡭⠴⠛⠁⠀⠀⠀⠀⣀⣠⠎⠉⠐⠉⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣍⡉⠙⢳⡄
⠀⠀⠀⡰⠤⠆⠀⠀⢴⡄⢰⢸⠀⠀⠀⠀⠀⠈⠃⠀⠈⢆⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⢠⡞⠡⣠⡞⠉⠉⡇⠈⣿
⠀⠀⠘⠢⡤⠷⠀⠀⠀⠀⢸⢸⡆⢀⠀⠀⠀⠀⢀⣀⠀⠀⠖⠲⠶⠞⢣⡀⠀⠀⠀⠀⠀⠠⠗⠀⠀⠀⣰⠋⣄⣰⠋⠀⢠⡞⠁⣸⡟
⠀⠀⠀⠀⠁⠀⠀⠀⢀⡀⢸⠸⡇⠘⠇⠀⠀⠀⠬⠄⠀⡐⠀⢀⢀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⢀⣼⠁⣧⡜⠁⠀⠀⠈⠙⠛⠋⠀⠀⡀
⠀⠀⠀⠀⢠⢄⠀⠀⠈⠃⢸⡆⡇⠀⠀⠀⠀⠀⠀⢠⠞⠃⠐⣒⢋⣀⠀⢀⡆⢳⡀⠀⠀⠀⠀⢠⢾⠘⣦⠋⠀⠀⠀⠀⣠⡂⠀⠀⠀⠘⠃
⠀⠀⠠⠒⠇⢸⠀⠀⢀⠀⠈⡇⣧⠀⠀⠀⠀⠀⢠⠃⣈⠣⠐⠊⢀⠂⢂⢠⠀⣸⠃⠀⠀⠀⡰⢧⢀⡿⠃⠀⠀⠀⠀⢀⡽⣓⢦⡀
⠀⠀⠀⠁⠀⠞⠀⠏⢏⠇⠀⡇⢿⠀⠀⠀⠀⠀⠘⠦⣌⣃⡈⠀⠚⢀⣑⣨⡴⠋⠀⠀⠀⠀⠳⠼⠟⠁⠀⠀⠀⠀⠀⢾⡘⠀⡇⢱⠀⢀
⠀⠀⠀⠀⡄⠀⠀⠀⠉⠀⠀⢧⠜⠀⠀⠀⠰⡷⠂⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⣤⡤⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠘⠫⠭⠴⠃⣠⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⡙⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠁⠀⠈⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⢰⠀⠀⠀⠀⠀⠀⡀⠉⣆⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢃⡀⠠⢀⠀⠀⠀⠀⠈⢀⠈⠁⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠆⠈⠙⠲⣄⡀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠈⠛⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣀⣰⠏⠀⠐⠀⠀⠀⠀⠀⠙⢢⡀⠎⠠⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡚⠃⢈⡿⠷⠀⣀⠀⠀⠀⠀⠀⠀⢀⡜⢉⡛⢦⡀⠂⢄⠀⡤⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⢿⡀⠀⠙⢦⡙⠢⡀⠀⠀⣠⠎⠠⠊⠀⠀⠈⠓⢤⣑⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣀⣀⠀⡙⢦⡀⠀⠉⠒⢄⣀⡴⠃⠀⠀⣀⠀⠀⠀⠀⠄⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠉⠈⠋⢻⠀⡉⠢⣄⠀⠀⠻⠶⢄⠀⠀⠉⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢁⠔⠉⢂⡀⠈⠉⢹⣠⠞⠳⣤⡁⠀⠀⠑⠂⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠈⠄⠠⠀⡵⢢⡀⠈⠡⣴⡾⢧⡈⠓⠦⣄⡀⠘⡿⢏
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠘⠞⣡⠏⡉⣄⡀⠈⠀⡸⠀⢀⣄⣀⣉⡙⠁⡟⠛
⠀⠀⠀⠀⠀⠀⠀⣴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⠛⠆⢘⠸⡟⠙⠋⠈⢁⡜⠱⠦⣷
⠀⠀⠀⠀⠀⠀⣬⡁⠠⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⡁⢅⠆⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⠀⠀⠀⠀⠀⣵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⢀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⢄
⠀⠀⠀⠀⢀⡠⠔⠂⠉⠁⠄⠀⠀⡀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⢠⠃⠀⠂⠐⠈⠠⠀⠈⠀⠀⡀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊
⠀⠀⠀⢠⠀⠂⠀⠐⠀⠂⠀⠈⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠊⢥⡿⠳
⠀⠀⠀⠀⢣⠀⠁⠀⠀⠈⠀⡰⠐⢆⠀⢩⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠩⠀⢘⣄⢀⠀⡰⢅
⠀⠀⠀⠀⠈⡄⠁⢸⠉⠑⠒⠁⠀⠈⠂⠔⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⡀⠀⠀⠉⠈⠁⠠⠱⡀
⠀⠀⠀⠀⠀⠸⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢀⣤⡦⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⢱
⠀⠀⠀⠀⠀⠀⠘⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢀⢤⡞⡻⠁⣿⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⡡⠊⡜⠀⠀⢇⠁⠚⠤⡔⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⢰⠁⢐⠁⠀⠀⠀⠳⡄⠀⠀⠻⡝⢧⡇⣐⢲⣄⣀⡤⡀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⣀⣀⡀⡤⠒⢺⡅⠀⢠⠀⠐⡆⠀⠀⠀⠀⢸⠀⠀⠀⣟⠻⠀⢏⠁⠈⢢⣠⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢰⡀⡜⠑⠤⠌⢦⡀⠘⣦⣀⢀⡀⠜⠀⠔⠊⠇⠓⢖⠈⠙⢍⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠕⠒⢘⡛⠊⠍⣢⡠⠊⠢⡠⠚⠳⣠⠞⠒⠤⠒⢆⡤⠲⢖⡚⡳⣆⣞⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡹⠁⢙⠒⠶⠀⢵⠀⠀⢆⠀⠀⡆⠀⠀⠇⠀⣘⡠⠚⡉⠁⠄⠀⠀⠀⠠⠉⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠘⡀⠘⡀⠀⡆⠀⢸⠀⠀⡇⠀⢸⠀⡠⠋⠀⢂⠀⠀⡤⠤⠊⠢⢄⡀⠁⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢱⣀⡵⠤⣰⠀⠘⡂⠀⠀⠀⡌⢠⠁⡀⠀⠀⢪⠝⠉⠈⠉⠈⢰⠇⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⡔⠉⠈⠹⠆⠀⠺⡁⠈⠛⠀⠀⠈⡇⠀⠇⠀⠀⠀⠇⢰⣀⡀⢀⡁⠀⡑⠲⠄⠒⠒⠅⠀⠀⡘⠑⢲⠃
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠈⠑⡌⠁⠘⣄⡠⠤⡀⠀⡤⠤⠰⠋⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⣀⠠⠊⠑⠠⠄⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠄⣀⠀⠀⠈⠉⠀⠀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠴⠒⣲⠞⠋⠉⠉⠉⠉⠛⠲⣖⡲⠦⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄⡀⠈⠉⠛⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠯⠤⠶⠖⠒⠋⠁⢀⣀⣠⣄⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠲⠶⠾⠷⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⠀⠀⠀⠀⠀⡴⠒⠛⠉⢁⣀⣨⠇⠀⠀⢰⡏⢹⡆⠀⠀⠀⠀⠀⠀⣠⠴⠲⡄⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⠒⠛⠉⠁⠀⠀⠀⠀⢸⠃⢸⡇⠀⠀⠀⣀⡴⠋⠁⣠⠞⠁⠀⠀⠀⠀⠀⢸⣧⡀
⠀⠀⠀⠀⠀⠀⡴⢋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠃⠀⠀⠐⣇⣠⠴⠋⠁⠀⠀⢠⠖⢦⡀⠀⠈⡇⠹⡄
⠀⠀⠀⠀⠀⡼⠁⢸⠃⠀⠀⠀⠀⣀⣀⣤⡤⠤⠤⣄⠀⠀⠀⠀⠀⠀⠀⠘⠲⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢳⡀⠀⣧⠀⠹⡄
⠀⠀⠀⠀⣼⠁⠀⡾⠀⠀⠀⠀⠸⣅⣀⣀⣠⣤⡤⠼⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢳⡀⠘⢦⡀⢹⡄
⠀⠀⠀⢰⠇⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠛⠉⠉⠙⠒⠋⠉⠉⠛⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠼⠁⠀⠀⠙⢦⣷
⠀⠀⠀⣾⡴⠋⠀⢰⠋⠳⡄⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠖⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣶⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⡟⠁⠀⠀⠈⢳⡀⠙⣆⠀⠀⠀⠀⠀⡼⢡⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡽⠀⠀⠀⠀⠀⠀⣠⠞⠛⡆⠀⠀⠀⢻
⠀⠀⢸⠁⠀⠀⠀⠀⠀⠳⡄⠘⡆⠀⠀⠀⠀⢷⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢀⡴⠋⢀⣠⠞⠁⠀⠀⠀⣸
⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠙⠚⠁⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢿⣠⡴⠋⠀⠀⠀⠀⠀⡴⡇
⠀⠀⠀⡿⡄⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⡇
⠀⠀⠀⣧⠙⣆⠀⠀⠀⠀⢀⡞⠁⣹⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢀⡟⠀⠀⠀⠀⠀⢀⡴⢦⡀⡼⠀⢠⡇
⠀⠀⠀⢹⠀⠘⣆⠀⠀⢠⠟⠀⡼⠁⠀⠀⠀⠹⣜⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⠉⠀⠀⠀⠀⠀⠀⡾⠀⣸⠃⢷⠀⢸
⠀⠀⠀⠸⡇⠀⢸⠀⠀⣏⢀⡜⠁⠀⠀⠀⠀⠀⠈⠉⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢀⣀⠀⠀⠀⠀⠀⣼⠁⢠⠇⠀⠸⡄⡟
⠀⠀⠀⠀⢻⡀⢸⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⢤⣀⣀⣤⢤⣄⣀⣤⠴⢻⠇⠀⠐⣏⠈⠳⢤⡀⠀⠀⢧⣤⠏⠀⠀⠀⢿⠁
⠀⠀⠀⠀⠈⢧⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠋⠁⠀⠀⠀⠉⠓⠒⠋⠀⠀⠀⠈⠓⢦⡀⠙⢦⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠈⢿⡀⠀⣠⠤⠤⠤⠤⠴⢦⡄⠀⠀⠀⠀⢀⡴⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⣦⠀⠀⠀⠀⠙⠶⠞⠁⠀⠀⣀⡤⢶⠏
⠀⠀⠀⠀⠀⠀⠈⢧⠀⠧⣤⣤⠤⠤⠤⠴⠃⠀⠀⢀⡴⠋⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣰⠚⠁⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠃⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣶⠶⠤⢤⣄⣀⠀⠈⠉⠀⠀⠀⢠⡞⠛⠦⣄⡀⠀⠀⠀⠣⠤⠇⠀⠀⠀⠀⠀⠀⠀⣏⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣄⡀⠈⠉⠲⢤⡀⠀⠀⠀⠙⠲⢤⣀⠉⠓⣆⠀⠀⢀⣀⣀⣀⣀⠀⠀⢀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣀⣉⠳⢤⡀⠀⠀⠀⠈⠙⠒⠃⣠⠔⠋⠀⢀⣈⡭⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠓⠶⠤⣤⣤⡤⠾⠷⠒⠚⠋⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠄⠀⢠⠠⠄⠀⠠⠀⢠⠀⠤⠠⠀⠀⠀⠀⡀⠄⠠⠠⠠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⢸⠠⢠⠀⠀⡀⠀⠠⠀⢀⠀⠐⠀⠠⠀⠀⠀⠚⠚⠉⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠐⠀⠩⣌⣁⡀⠀⠉⠑⡠⠀⡅⠤⠉⢈⡡⢐⡄⡀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠅⠐⠒⡁⠠⠀⠸⠂⢓⢎⡤⠀⠶⠈⠰⢩⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠨⠀⠈⠆⠄⢀⠀⠉⠏⠻⡤⢒⠀⡛⠆⢋⠬⡃
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠉⠀⠒⠐⠀⠀⠘⠀⡏⠒⠂⠄⠁⠀⢋⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠤⠤⠀⢨⡁⣤⠀⠐⠁⠀⢀⠀⠀⠀⠀⠀⠢⡀⠀⠀⢨⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠂⠐⠓⢢⠶⠥⢍⡀⠁⠶⠌⡳⠀⠂⠀⢰⠀⠁⢈⡇⠀⢇
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠛⢀⠆⠁⡀⠀⢈⠀⢇⢰⡄⠀⠀⠂⡀⠀⠀⣼⢣⡝⢁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⢀⣂⠙⠀⡀⠑⡀⢊⠘⠁⡛⠚⠄⠂⠀⠀⠇⣀⠐⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠄⠨⠉⠘⠀⠈⡏⠁⠈⠀⠐⣨⠀⠉⠘⠀⠡⠀⠀⠙⠘⠀⢰⠛
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⢠⠄⠀⠀⠈⠀⠀⠀⠀⠐⠈⠀⠈⠂⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢴⡄⠀⢠⠑⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⡀⠀⠀⠀⠈⠀⠀⠀⠄⠡⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⠀⠀⠍⠢⣈⠀⠀⠀⠀⠀⣄⠤⠀⠁⠠⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠒⢁⠀⠄⠀⢀⡀⠀⠌⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠈⠀⠀⠐⠈⠁⠉⠀⠀⠐⠂⠐⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⠤⠶⠶⠒⠒⠶⢶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠻⣷⡄⠈⠉⠓⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡉⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠉⢻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠙⢿⣦⠀⠀⠀⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⢻⣏⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣯⡀⠀⠀⠀⠀⠻⣷⣄⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠈⣿⡄⠀⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠹⣷⡄⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⢹⣷⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⣿⡄⠀⠀⣀⣠⣤⠿⠷⠶⠶⠒⠲⠾⠿⠦⢤⣤⣀⣀⡀⣿⡇⠀⠀⠀⠀⠀⣿⡇⠀⣀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣀⣠⣤⠽⠟⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠒⠶⠦⠤⠤⠿⠷⠚⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⢠⣶⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⡄⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡂⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⡀⠀⠀⠀⢀⡄⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡶⢿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣄⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠶⠖⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠓⠓⠚⠚⠓⠛⠛⠛⠒⠛⠛⠉⠉⠁





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣯⢭⣟⣛⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠈⣿⣄⡟⢸⠉⠙⡇⠀⢸⡷⠾⣧⢼⠉⠙⡆⣟⣹⠦⣯⠁⠀⢸⣉⣽⢸⠋⠉⣧⣿⣙⡆⣾⢸⣷⣸⡇⣿⣩⡇
⠀⠀⠀⠘⠇⠙⠃⠘⠷⠾⠃⠀⠸⠃⠀⠟⠘⠶⠾⠃⠟⠳⠀⠷⠄⠀⠸⠶⠟⠈⠳⠶⠃⠿⠻⠀⠻⠸⠃⠛⠀⠦⠼⠁
⠀⠀⠀⠀⡀⠀⠀⣀⠀⣠⣄⠀⣀⣀⠀⣀⡀⠀⢀⣀⠀⠀⣀⣀⡀⠀⣀⠀⢀⡀⠀⡀⢀⠀⢀⡀⣀⡀⣀⡀⠀⢀⣀
⠀⠀⠀⠀⢿⣶⣴⡏⢸⡁⠈⣷⣿⣩⠇⡏⢉⡇⠸⣏⠁⠀⣿⣤⡟⢸⣿⣆⢸⡿⣦⡏⢸⢷⣼⢻⡷⠀⣯⣽⠇⠻⣍
⠀⠀⠀⠀⠘⠋⠛⠀⠈⠓⠚⠁⠛⠛⠂⠛⠋⠀⠛⠛⠀⠀⠛⠒⠃⠛⠀⠙⠈⠃⠘⠁⠘⠀⠛⠈⠓⠂⠛⠓⠈⠛⠋
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢀⣀⢀⡀⢠⠀⢔⠀⠶⠎⠢⠯⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀
⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠈⢡⢤⢀⣀⣀⣢⡄⠤⠖⠽⠂⠀⠈⠀⠀⠐⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠓⢄⠀⠀⢈⡤⠤⠴⠲⠛⠑⠈⠂⢉⠉⠈⠤⣄⣠⡤⢤⡄⠀⡄⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠁⠀⢠⠠⢄⠁⠀⠀⠀⣠⠀⡒⣤⣷⠆⠸⠰⠚⠚⠀⠈⠉⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠤⠀⠤
⠲⠶⠤⠤⣤⣥⣀⣀⡀⠀⣤⠬⣤⣤⣤⣤⣄⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⢀⣀⣀⣤⡤⠴⠶
⠀⠀⠀⠀⠀⣾⣿⡟⣹⢻⡇⠀⠀⠀⢸⣿⡏⠻⡛⢛⣽⢛⣿⣿⣿⢛⣻⡟⢿⡟⡻⣿⣿⣿⠀⠀⠀⢸⣿⠿⢿⣿⡅
⠀⠀⠀⠀⢀⣿⣿⣧⣤⣿⡇⠀⠀⠀⢸⣿⣷⡷⠷⠶⠽⠮⢿⣿⣿⣐⣼⣰⣎⣇⣧⣿⣿⣿⠀⠀⠀⢸⣿⣀⠳⠟⠃
⠤⠤⡀⠀⣀⠀⡀⠉⠉⢹⡇⠀⠀⢠⡄⠐⠢⠐⠲⠄⠠⠤⢼⠛⢛⠛⣋⣉⠉⢉⣉⢉⠀⠀⠀⠀⠀⢸⣅⣀⣀⠠⢤⠦⠆⠂
⡀⠀⠀⠀⠀⠁⠈⠉⠈⢻⠁⣐⠒⠀⡅⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠁⠀⠀⠀⠀⠀⠃
⠁⠈⠄⠀⠀⠀⠀⠀⠀⣸⠀⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⡃
⠀⢀⠀⠀⠀⣀⣀⣠⣤⡿⠴⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣦⣼⣄⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠛⠛⣧⣤⣤⣤⣤⠤
⣛⣿⢿⢿⢿⣿⡁⠀⠀⠀⠀⣿⣿⡧⢺⣠⣿⣯⠙⢫⢉⡏⠿⣛⣻⣿⠋⠉⠙⠛⠛⣿⣈⠇⢿⠸⣿⣿⠀⠀⠀⣿⣻⣿⣿⡆
⣿⣿⣼⣈⣤⣻⡇⠀⠀⠀⠀⠸⠿⠛⠛⢻⠟⠛⠛⠿⠾⠷⠶⠧⠿⠿⠀⠀⠀⠀⠀⡿⠿⠿⠿⠟⠛⠛⠀⠀⠀⣧⣩⣾⣿⡇
⠿⠿⠿⠿⠛⠛⡇⠀⠂⠀⠀⠀⠢⠄⠒⣾⠀⠀⠈⠑⠈⠒⠂⠠⠤⠤⠀⠀⠀⠀⢸⡇⠤⠤⠤⠀⠀⠀⠀⠀⠀⣏⣉⣀⠀⠠⠄
⠀⠰⠀⠈⠘⠈⣿⠐⠀⠀⠠⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⣼⠀⠀⠀⠀⠀⠀⠠⢶⠄⠀⡏⠀⠀⠀⠦⣀
⠀⠠⢥⠀⠀⠀⢻⠀⠀⠀⠐⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⡧
⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠊⣸⠀⠀⢀⣤⣄⠀⠀⠰⢤⠤⠀⡇⢀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠄⣀⣀⡀⠀⠀⡀⢀⣀⠀⠤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⡇⠆⠀⠀⠀⠀⠀⠀⠀⠀⣞⠀⠀⠀⠀⠀⠀⣤⣤⣀⣀⣀⣀⣀⣀⣠⣤⡆⠀⠀⠀⠀⢨⠅⠊⠀⠀⠀⠀⠀⠀⠀⠀⡨⠁
⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡘
⠀⠀⠀⠀⠀⠿⠶⠶⢶⣶⠶⠶⠶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠶⠶⠶⠟⠛⠛⠁





⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⢀⣤⡶⣶⣦⡀
⠀⠀⠀⢠⣾⣟⣿⣶⡀⠀⠀⢠⣾⣿⣿⣿⣦⠀⠀⣾⣿⣧⣿⣿⡇⠀⠀⠀⣾⣿⣷⣿⣿⣿⠀⠀⢀⣴⡶⣶⣤⠀⠀⠀⢀⣴⣿⢻⣷⣦
⠀⠀⠀⢸⣿⣿⢻⣿⠇⠀⠀⠸⣿⣿⢻⣿⡿⠀⠀⠹⣿⣯⣽⣿⠇⠀⠀⠀⠹⣿⣿⣹⣿⠟⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⢸⣿⣿⠿⣿⣿⠂
⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠙⠻⠓⠛⠛⠀⠀⠀⠀⠙⠛⠒⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠘⠳⣤⣤⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢦⣤⡴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⡀⠀⣠⡶
⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣛⣉⣀⣀⣀⣀⣀⣀⣀
⠀⢼⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢼⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠻⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣴⣶⣶⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠺⡷⠿⠟⢤⣀⢀⠀⠀⠀⠀⠀⠀⠀⠉⣻⣿⡇⡀⠀⠀⠀⠲⣦⣄
⠀⠀⠀⠀⣿⡆⠀⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢀⡞⠀⠀⡄⠈⣿⣯⣦⠀⠀⠀⢾⣶⣤⣴⡿⠋⠈⠻⢦⣤⣤⣤⡿⠟
⠀⠀⠀⠀⢿⡟⠀⠃⡘⠱⢃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢀⣾⠀⠀⠀⢿⠀⢸⡿⡌⡆⠀⠀⠀⠉⠉⠀⠀⢠⣴⣦⣄⠀⠀⠀⠀⠒⠂⢶⡄
⠀⠀⠀⠀⠘⣿⣄⡀⠠⠀⠀⠐⠃⡀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠇⠀⠀⠀⢸⠀⢸⡇⣇⠁⠀⠀⠀⢰⣁⡀⢀⣠⣿⡿⠃⠀⠀⠀⠀⢀⣼⣿⠃
⠀⠀⠀⠀⠀⠘⢿⣿⢠⠠⢊⡄⠀⠀⡰⠁⠀⠀⠀⠀⠠⡇⢽⠀⠀⠀⠀⠈⠀⢸⣧⣿⠀⠀⠀⠀⠀⠉⠛⠛⠉⠁⠀⠀⠀⠸⣧⣶⣾⠿⠃
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⡄⠀⠖⡀⠀⠊⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡀⠈⡏⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣆⠈⠱⠎⡀⢡⠆⠀⠀⠀⢄⢠⡆⠀⠀⠀⠀⡟⢰⡟⣿⠃⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣐⣶⠧⠐⢲⣄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣦⣈⢳⡄⠈⠀⠀⠀⢸⡌⣿⣦⠀⠀⢸⣷⣾⣿⡟⠀⠀⠀⠀⠀⢀⡂⠈⣽⠟⢻⣿⡿⠦⢴⣾⣏⢀⡄⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣷⣦⣈⡒⠀⠀⠸⣧⣹⣿⣧⡄⣸⣿⣿⡿⠁⠀⠀⣠⣤⡀⠈⣙⣿⠇⠴⣾⣿⣦⣶⣦⣿⣿⠄⣰⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠙⢿⣿⣿⣧⣿⣿⠟⠀⠀⣤⣀⡀⣼⣿⣿⣍⣥⣴⣾⣟⣿⠩⢿⣿⣯⣷⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⣄⠓⠒⠒⠒⢢⡐⠶⠒⠒⢲⡌⠉⠛⠋⠁⠀⠀⠀⠀⠈⠙⠻⢿⣶⣻⣶⣶⣽⣿⡿⠿⠿⠿⠛⠛⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⢀⠄⠀⡘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠬⣿⠠⣤⠤⠤⢼⡅⢠⡤⡤⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠠⠠⣀⠀⠀⠀⠀⠁⠀⡀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢸⣿⠀⠀⠀⠀⢺⡷⠀⠀⠂⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠓⠀⠀⠀⠀⠀⠠⠂⠀⠐⠁⠀⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣼⣏⣤⣄⠠⣄⣸⣇⣤⣀⡀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢡⣿⠈⠉⠁⠠⣽⡆⠉⠉⠴⣿⣇⠀⠀⠀⠀⠀⠐⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⢀⣀⡈⢿⣆⣤⣀⣄⣿⣧⣤⣤⡄⢬⠞⣦⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣛⡎⠀⠘⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠁⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⣀⡀⠀⢐⣛⣛⣛⣐⣰⡿
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣰⠇⠠⣄⡽⠁⠀⠀⣠⣄⡀⠀⢈⡛⠛⠛⠛⠓⠈⠹⠗⠂⣀⣄⣠⣶⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣞⣉⣿⣿⣿⣿⣶⣶⣶⣿⣿⡇⠠⣄⡀⣍⡁⠛⠷⠦⡹⣿⣛⠛⠛⠶⠶⢶⣤⣤⡤⣼⡿⣿⣧⡀⢀⣤⣴⣶
⠀⠀⢀⣿⣦⡀⣄⢀⣀⣿⣦⣾⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠐⠮⡛⠶⢿⣛⠲⣤⣀⣀⠉⠁⠐⠒⠐⢛⡋⠁⠀⠀⠀⣠⣴⣿⣿⣿⣿⠛
⠀⢀⠊⠁⠊⠛⠚⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠉⠢⡀⠙⠳⣴⠛⠛⠛⠛⠶⣶⣤⣄⡀⠀⠀⠀⣿⣿⣾⣿⣿⣿⣿⣷⣆
⠀⠠⡼⠋⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠑⠀⡈⠻⠦⣠⣴⣶⣶⣿⣽⣿⣿⣦⣸⣿⣿⣿⣿⣿⣿⠿⠿⠋
⠀⠂⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢴⡿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉
⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⡀⠠⠤⠀⠀⠀⠠⠤⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠊⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢄
⠀⠀⠀⠀⠀⠀⠐⠀⠀⣀⠀⠈⠀⢀⡠⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠉⠘⠢⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⢀⣀⡤⠇⠀⠐⠀⠀⠐⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠐⠧⣄⣀
⢀⡴⠚⠉⠀⠀⠀⠂⣀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠘⠑⠐⠀⠀⠀⠀⠀⠠⠀⠀⠈⠙⠲⣄
⣿⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⡇⠀⠂⠀⠀⠀⢀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⣀⣀⡀⠀⠠⠂⠁⠀⠀⠀⠀⠀⣼
⠈⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⢀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋
⠀⠀⠀⠀⠉⠉⠛⠓⠶⠶⢤⣤⣤⣤⣀⣁⣂⣒⣀⣀⣒⣒⣀⣐⣒⣈⣉⣀⣀⣀⣀⣠⣤⣤⣤⠶⠶⠖⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠃⠀⠁⠀⠹⡄⠐⠙⠲⢤⣄⠒⢎⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠜⣦⡀⠠⣠⠘⣻⣾⣾⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⡁⢀⣀⡠⠜⢀⣟⠘⢋⡁⠠⠐⠋⠀⢼⣿⠁⠀⠀⢸⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠣⠴⠶⠩⠚⠾⡤⠔⠚⠉⣩⡴⠛⠈⠳⡀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⡀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢀⡗⠠⡾⠁⠀⠀⠀⠀⢰⣶⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠉⠀⠀⠂⢤⣄⣀⣄⣠⠟⠁⢀⡇⠀⠀⠀⠀⠀⣿⠁⣯⡩⠛⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣡⠾⠁⠀⢀⣠⡴⠚⠏⢀⢸⣁⢀⣾⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠣⣄⣠⣤⢤⣄⣄⠤⠴⠤⠤⠀⠊⢉⣠⠴⠒⠛⠛⠉⠁⠀⠀⣔⣸⣿⡵⡿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠈⠛⢦⣃⠀⠀⠀⠠⠀⣠⡴⠞⠉⠀⠀⠀⣀⣀⣶⣶⡿⣿⣿⠟⡟⠿⠟⡭⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠈⠓⠶⠶⠶⢿⣿⣷⢶⢤⢴⣶⠿⣿⠛⠻⠋⡀⠋⢠⣯⣤⣼⣵⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⠲⣦⣀⡀⠀⡀⠀⠀⠀⠀⠀⠉⠀⠒⠈⢎⡴⠀⡔⣉⣴⣶⣸⣿⣾⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⢣⠹⡏⠙⣿⠆⢺⠷⢾⠷⠿⡿⠿⡿⡿⣿⠿⢻⠛⢻⡋⣽⣿⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠘⡆⢿⠀⢿⠀⠸⡇⢸⡆⢠⡏⠀⡗⠀⡏⠀⣾⢀⣿⣧⣿⣿⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠱⡸⣇⢸⣧⠈⣷⢈⡧⡘⣷⠀⣇⢰⡇⣰⡿⣴⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠰⣿⣿⢾⣧⠁⣿⣮⣧⣻⣿⢰⡷⣼⣷⣿⣷⣾⣿⣿⣟⣿⣿⣿⣧⣤⣤⣄⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⣠⡤⠀⠀⢀
⠀⠀⠀⠀⢀⣶⡠⢤⡀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠈⠉⠢⡀⠀⡿⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⣼⡏⠀⣾⠇⠀⠀⠀⠀⣾⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⢃⡀⠀⢠⠴⠒⠲⣦⣴⠊⠁⠀⠠⣀⠈⡆
⠀⠀⠀⠀⣿⠓⠚⣏⢠⠞⢳⡧⢠⣿⢶⡅⢀⡾⢁⠆⡞⣶⠇⢰⡇⢰⡿⠀⠀⠀⠸⣸⡇⣰⠋⠀⠀⠀⠈⡿⠀⠀⠀⠀⠸⡞⡇
⠀⠀⠀⠀⡿⠀⢀⣿⢿⡠⢸⣇⣼⠇⢸⣇⢸⠁⡠⠊⢸⡏⣠⣾⡧⣾⠇⠀⠀⠀⠀⠣⣸⠡⣀⠀⠀⠀⠀⣿⠠⠀⢀⡤⢀⡿⠃⠀⠀⡸⡓⠂⣰⠧
⠀⠀⠀⠰⢤⣤⠾⠃⠀⠀⠈⣡⠏⠀⠈⠁⠀⠉⠀⠀⠈⠉⠁⠈⣰⠏⠀⠀⠀⠀⠀⠀⠉⠀⣈⠳⠶⢬⠀⣿⡔⢋⣩⠕⠋⠀⣴⠥⢠⠞⠁⠀⢳⡀⢨⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠚⠉⠁⠀⠀⠀⠀⠈⡌⠠⡉⣥⠁⡄⢩⠉⣭⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠐⠀⣰⣿⠟⠁⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠸⡄⢃⡘⠀⠇⠜⢀⢧⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⠉⠁⢠⡟⠁⠀⠀⢠⠟⠁⠀⠀⠀⣠⠾⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠳⠄⣁⣀⣀⡈⠨⠘
⠀⠀⠀⠀⠀⠀⠀⢀⡴⢂⠁⠀⠀⠁⠒⣄⠀⠀⠀⠌⡀⠀⠀⠀⠊⠀⠀⠀⠀⠃⢤⣀⣀⠀⠐⠃⠀⠄⢂⡄
⠀⠀⠀⠀⠀⠀⢀⠎⢠⢀⡤⠄⠀⠀⠀⠈⢧⠀⠈⠀⠠⣀⣀⣀⣀⣠⡤⠀⢘⡉⠉⠀⡐⠒⣒⠒⠈⠩⠭⠊⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⢦⠠⣤⠇
⠀⠀⠀⠀⡴⠊⡝⢀⠀⢸⠀⣀⠈⣶⡄⠈⣾⣇⠀⠀⠀⠀⠀⠨⠄⠐⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠒⠊⠉⠁⠀⠀⠠⠈⢃
⠀⠀⠀⣼⠁⠀⣇⠀⠀⣾⣧⠈⢛⡟⢸⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⢌⡙⠛⠳⢶⠽⢭⣤⣭⣁⣀⣀⣀⣤
⠀⠀⠰⡇⠀⠀⠻⡄⠤⢏⣿⠀⠀⡰⠃⠰⢣⡏⠀⠀⠀⠀⠀⠀⣴⣿⣟⠩⣶⠲⣦⠤⡄⠀⠀⠀⠀⠀⠀⠀⠈⠐⠶⣤⣤⣶⣡⣄⡈⠁⠈⠁⢍⠩⢉⣛
⠀⠀⠀⢣⠀⠀⠁⢈⠙⠛⣁⠴⠊⠀⡀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠠⢿⣿⣷⠬⢗⠲⠶⠶⠞⠀⠀⣠⡀⠀⠀⠀⠀⠀⢉⡀⠒⠀⠈⠛⠶⠼⠷⠶⠶⣶⠇
⠀⠀⠀⠈⠃⠀⢄⣀⡈⣉⣠⠴⠖⣋⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠙⠓⠒⠒⣶⣤⣦⠟⠋⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠭⠶⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠈⠁⠤⠔⠊⠀⠀⠀⠀⠀⠠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠤⠐⠒⠒⠂⠠⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠙⢿⡄⠈⢣⠀⡀
⠀⠀⠀⠀⠀⠀⣀⡤⢶⣬⣍⡉⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠆⠀⢈⠑⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠻⣷⡄⠀⠀⠀⠄⠘⣇⠀⣸⠀⠈⢢
⠀⠀⠀⠀⠀⠘⠇⠀⠀⠰⢀⠠⠀⠁⠂⢀⠀⠀⣀⣀⣤⡴⠶⠿⠛⣓⣼⡇⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠈⠷⠘⡆⠀⢈⠁⠁⠁⠛⢘⠔⠊
⠀⠀⠀⠀⠀⠀⡞⠀⠄⠀⢀⡀⢁⠀⢠⠠⠇⣈⣉⣤⠴⠶⠶⠛⢛⣉⢹⠀⠀⠀⠀⠀⠀⡄⢠⡀⢀⡶⠂⠀⠰⢷⠈⠨⠂
⠀⠀⠀⠀⠀⢸⡇⠁⠀⢃⠀⠀⠈⠀⠀⠂⢀⣀⣠⡤⠤⠀⡠⠾⠛⠁⢀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉
⠀⠀⠀⠀⠀⢸⢠⡀⠀⠀⠀⡆⠀⠃⠀⠀⠈⣿⠀⠀⠀⠀⢀⣴⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠤⡄⠤⣤⠄⠀⠰⢶⠐⣴⠶⡆⠶⢶⡒⠤⢄
⠀⠀⠀⠀⠀⠸⠈⠁⠆⢂⠀⡀⠃⡤⠀⠀⠀⠟⠀⠀⢀⣀⣘⡭⠶⢂⠇⠀⢀⣤⠄⠒⠒⠻⣯⠘⠀⢙⡆⠚⠀⢈⡇⠉⠀⣨⡇⠁⠠⠿⠀⠶⠃⢀⡠
⠀⠀⠀⠀⠀⠀⠀⠑⠠⠀⠀⠃⠆⡤⠀⡇⠐⠿⢖⣿⠙⣿⡃⠤⠒⠁⠀⠐⠁⠀⣀⣁⣀⣀⠛⠀⣀⣈⣁⣀⠀⠈⠡⠤⠤⠒⣀⣐⣠⠴⠿⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡼⠤⠤⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠒⠒⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠐⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠁⠀⠀⠀⠀⠊⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠴⠀⠀⠰⣯⡿⠃⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠆⠢⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠖⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢁⡀⠤⠘⠱⠕⠂⢄⠀⡄⠀⠀⠀⠀⠀⠀⢀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠠⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠙⢁⠀⣀⠐⠀⠀⢀⠀⡌⠀⠀⠃⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠁⠌⠠⠄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⢀
⠀⠀⠀⠀⢀⡀⢀⡀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠐⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⢯⣉⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣯⣽⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠰⣧⡤⢤⡤⣤⡷⠀⠀⠀⠀⠀⠀⠀⢠⠟⠲⠤⠬⡇⠀⠀⠀⠀⠀⠀⣠⠼⠁⠀⠀⠈⠦⣄⠀⠀⠀⠀⠀⠀⡟⠲⠊⠙⠊⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⢦⣙⡞⠀⠀⠀⠀⠀⠀⠀⠀⢸⠒⠒⠒⠒⢻⠀⠀⠀⠀⠀⠀⣇⢀⣀⠀⢀⣀⠀⣸⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡦⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣟⠛⠛⢛⡏⠀⠀⠀⠀⠀⠀⠈⢻⡀⡍⢩⠄⡏⠁⠀⠀⠀⠀⠀⠀⠈⠒⠶⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⠤⠼⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢭⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣇⡖⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⠒⠢⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠾⣄⣠⢧⡀⠀⠀⠀⠀⠀⠀⡴⠉⠉⠉⠱⡖⠁⠀⠀⠀⠀⠀⠀⢀⡤⠧⠾⢤
⠀⠀⠀⠀⠀⢠⠴⠋⠀⠀⠀⠀⠀⠀⠓⢤⡀⠀⠀⠀⡞⠛⠒⠛⠛⠛⠋⣻⠀⠀⠀⠀⠀⠰⣧⣠⢄⣤⣤⡷⠀⠀⠀⠀⠀⠀⠀⣸⠖⠦⠔⠺⡇
⠀⠀⠀⠀⠀⠘⠲⣍⣙⣚⣉⣙⣒⣋⡹⠚⠁⠀⠀⠀⡿⠿⠿⠿⠿⠝⠛⢿⠀⠀⠀⠀⠀⠀⠘⢦⣶⣤⡞⠀⠀⠀⠀⠀⠀⠐⢾⣛⣒⠒⠒⣓⣛⡶
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠈⠉⠁⠉⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠙⠙⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⡎⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡗⢯⣉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠷⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡖⠒⠲⢄⠀⠀⠀⠀⠀⠀⢀⡔⣩⠥⠬⣝⢦⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⣿⣿⣽⣯⣿⣿
⠀⠀⠀⠀⠀⠀⢠⠎⣡⠤⣍⠓⣄⠀⢳⠀⠀⠀⠀⠀⢸⢸⠁⡏⠵⣸⢀⡇⠀⠀⠀⠀⠀⢸⡁⢀⡀⢀⡀⢀⣧⠀⠀⠀⠀⠀⠀⣿⣿⣼⣧⣿⣿
⠀⠀⠀⠀⠀⠀⢸⢸⡁⣄⠈⡇⢸⡆⣸⠀⠀⠀⠀⠀⠈⢮⡳⢬⣯⡵⠾⠃⠀⠀⠀⠀⠀⣿⠙⣯⢹⡏⢹⡇⣹⠂⠀⠀⠀⠀⠀⣿⣿⣯⣍⣉⣽⡇
⠀⠀⠀⠀⠀⠀⠈⢦⡳⣌⣙⣁⡼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⠁⠀⠀⠀⠀⠀⠀⠀⠸⡆⢿⢸⡇⣼⢠⡏⠀⠀⠀⠀⠀⠐⡏⠉⠉⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠚⠓⠛⠛⠀⠀⠀⠀⠀⠀⠈⠷⠶⠶⠶⠶⠾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠲⢄
⠀⠀⠀⠀⠀⠀⠀⣰⠉⠀⠀⠠⡄⢱⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡼⢮⡹⣆⠀⠀⠀⠀⠀⠀⠀⢧⢠⡤⣸⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠖⠒⠦⣄⡀
⠀⠀⠀⠀⠀⠀⢰⠁⠸⠁⠀⢀⠁⠀⢳⠀⠀⠀⠀⠀⠀⣰⢻⡄⢳⠀⡟⠋⠀⠀⠀⠀⠀⢰⡋⠚⠁⠀⠙⢋⣷⠀⠀⠀⠀⢰⢏⠀⢧⠀⠀⡼⠁⡹⡆
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠈⠃⢀⡏⠀⠀⠀⠀⠰⣎⠳⣀⢣⣨⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⡷⠀⠀⠰⡏⠀⠀⠀⠀⠀⠸⣄⢹⡚⠓⠚⢑⡟⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⣤⡖⠛⠋⠀⠀⠀⠀⠀⠀⠘⠲⠼⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢀⡴⠲⣄⠙⡆⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⠉⠁

⠀⠀⣀⣠⠤⠤⠔⢒⣒⣂⣌⣉⠉⠭⠭⠭⠭⠭⠉⣉⣁⣐⣒⡒⠂⠤⠤⣄⣀
⡴⢊⡥⠖⠚⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠲⢬⡙⢦
⡗⠮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⢺
⡗⠒⠤⢌⣉⠓⠒⠒⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⠒⠒⠚⣉⣩⠤⠒⢺
⡇⠀⠀⠀⠀⠉⠉⠐⠒⠒⠒⠤⠤⠤⠤⠤⠤⠤⠤⠤⠒⠒⠒⠂⠉⠉⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⢀⡤⠒⠒⢤⡠⠞⠁⠀⠈⠳⢄⡤⠒⠒⠤⡀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⢠⠖⠒⠲⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠖⠒⠲⡄⠀⠀⢸
⡇⢀⣀⡆⠀⠀⡴⠤⡤⠀⢠⠖⢲⠀⢀⡔⠂⢄⡀⢀⢀⣀⣀⠤⠤⢤⠀⢽⣀⡀⢸
⣷⠋⠀⠀⡠⠤⡽⠀⣧⣤⡬⠆⠸⠤⣄⣉⠙⠒⡫⠒⡿⢻⡄⣾⠭⢥⠀⠀⠀⠉⣾
⡿⣄⠀⠘⠓⠒⢶⢠⣉⣉⣉⡇⢸⠉⠙⠯⠭⠲⣷⢰⡇⢸⡇⣿⠀⢸⠀⠀⠀⣠⢿
⡇⠸⣄⠀⠀⠀⠈⢀⠂⠀⠚⡃⢸⠀⢀⣀⡤⠞⣥⢰⣇⣡⣬⣽⠂⡆⠀⠀⢠⠇⢸
⡇⠀⡇⠀⠀⠀⠶⣈⡉⠭⠭⠥⠜⠀⠸⣄⣀⡜⢨⣛⣣⣤⣤⣼⣁⡇⠀⠀⢸⠀⢸
⡇⠀⠙⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⠋⠀⢸
⡇⠀⠀⠀⠀⠑⠒⠲⣄⣠⡄⠀⠀⢀⠤⠄⠤⡀⠀⠀⢀⣄⣠⠖⠒⠊⠀⠀⠀⠀⢸
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠓⠉⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣷⢻⡼⠂⠀⠀⠀⠀⠀⡤⢤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡀⠀⠀⠀⢸
⡯⠽⠚⠁⠀⠀⠀⠀⢸⡹⣉⠖⡄⠀⡠⢢⠤⡀⠀⠀⠀⠀⠀⡜⣖⢱⢼⠀⣾⡹⣿
⣯⠿⣱⠄⣜⡽⣗⡆⠀⣙⣖⣉⠀⠸⣙⢭⢗⡇⢀⢎⠽⣑⡆⠈⢢⠕⠊⠈⠣⣓⣿
⣏⣀⠔⠈⠢⣓⡯⠇⢰⢳⠚⡬⡄⠀⣈⢖⣉⡀⠘⢮⣑⠥⠃⡴⡥⢫⣱⠀⣴⣲⣾
⣗⣶⢢⡀⡰⣲⡶⡄⠈⢳⡽⠒⠁⢰⡳⣊⡦⡇⠀⣔⣲⠲⡄⠑⢍⡪⠜⠐⢏⠧⣿⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⡟⢴⣫⠔⢅⠧⣏⡥⢠⢯⠽⣙⡀⠀⠙⡎⠚⠁⠘⣜⠦⣋⠇⣠⣊⣖⡢⠤⠐⠛⣛⣉⣉⠩⠭⠭⠭⠤⠤⠤⠤⠤⠤⠭⠭⠤⠍⣉⣉⡒⠒⠢⠤⣀⡀
⡯⣭⢄⠀⢠⢭⡥⡀⠘⢮⣺⠴⠃⢠⢯⠜⣍⡆⠀⡨⢭⢤⡀⠣⡟⢁⠔⠒⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⢤⠉
⡿⡩⢞⠡⣃⢏⡗⡣⢀⣖⣳⠲⠀⠈⠳⡭⠕⠃⠰⡹⢍⠗⡇⢸⡏⠛⠦⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠾⠋
⣗⣚⡉⠀⢈⣒⣋⠁⠸⢜⢴⣩⠇⢀⣞⡱⡒⡄⠀⢘⣒⣉⠀⢯⡻⣄⡀⠀⠀⠈⠉⠉⠙⠛⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠚⠛⠉⠉⠉⠁⠀⠀⢀⠴
⢧⡙⠚⠦⣮⡞⡧⠇⠀⡴⣣⢤⠀⠘⢮⣓⡣⠇⢰⢳⡚⡮⠇⢀⡹⣋⣙⠦⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁
⠀⠈⠑⠢⠤⣈⡉⠛⠚⠿⠤⠶⢦⡀⣴⣷⡤⣄⠤⠷⠬⠶⠓⠚⢉⣡⠤⠔⠊⠉⠒⠦⢄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠐⠒⠲⠶⠒⠀⠀⠀⠒⠶⠖⠒⠂⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠰⠯⣉⣉⠉⠉⠙⠛⠛⠉⠉⢉⣉⡉⠵⠂
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⣚⠭⠭⣍⡉⢙⣓⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⡫⠤⠤⠞⣁⠀⢀⡀⠩⡉⠀⠀⢹⡙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⡼⢁⠀⠀⠀⠿⠀⠀⠁⠀⠉⢀⡄⠀⢉⠓⢌⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠞⠉⠀⠀⠙⠀⠀⢀⠀⠀⠈⠁⠀⠈⠀⠀⠞⠀⢸⠇⢳
⠀⠀⠀⠀⠀⠀⠀⠀⡼⢸⠀⠠⠔⠒⢀⡇⠀⣨⠗⠚⠓⠒⢦⡀⠉⠓⠀⢀⠈⢧⡈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠎⠀⠀⣀⠀⠈⠀⢰⠁⠀⠀⠀⠀⠀⢱⠀⠠⢤⠈⠁⠀⢱⣽
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢠⡀⠈⠁⢀⠀⢸⡀⠀⠀⠀⠀⠀⣸⠀⣠⠂⠀⡆⠀⣸⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢧⣷⠀⠁⠀⡆⠀⠁⠀⠳⢄⣀⣀⣀⡴⠃⠀⠀⡴⠂⠑⠀⡇⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⢤⡀⠸⠃⠀⠀⢢⠀⢠⠎⠉⣅⡀⠀⠇⠀⠀⠰⠄⠀⣹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠹⡆⠀⠲⠄⠀⠀⡁⠀⠀⡀⠀⠀⢠⠂⠀⣀⣠⢞⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿⡢⠤⣄⡀⠀⠙⠄⠀⠙⠆⠀⠀⢀⣠⣤⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠤⣍⣲⣖⣚⣉⣓⣦⣤⡼⠗⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⢔⡬⠑⢠⡾⠿⣶⣀⣿⠀⠀⢠⡾⠿⣦⣰⣿⠿⣶⣰⡷⣼⣦⠀⣸⣇⢔⠤⢕⠀⠀⠀⣾⡟⣷⡄⣴⡿⠿⣦⢠⣾⠿⣷⡄⣿⣠⣾⠇
⠀⠸⢘⠀⠀⣸⡿⠆⣸⣿⣿⠀⠀⣿⡷⠆⣹⣿⣿⣤⣿⢻⣟⢻⣿⣷⣿⢹⢸⠦⢌⠆⠀⠀⣿⠷⢿⣧⣿⡷⠀⣿⣿⣿⠆⣸⡿⣿⣿⣁
⠀⠀⠪⠲⠬⠙⠿⠶⠟⠁⠿⠿⠛⠙⠷⠶⠟⠘⠿⠻⠷⠘⡿⠸⡇⠹⠇⠀⠢⠑⠫⠂⠀⠀⠿⣷⡾⠋⠹⠷⠾⠋⠘⠿⠶⠟⠁⠿⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠙⢦⣀⣀⣀⣀⡴⠋⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠉⠓⢤⡀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⢠⠏⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠱⡄⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣦⢟⡾⢯⡝⠛⠛⠛⠛⠛⠛⢻⡽⢿⡻⣴⣾⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏⠸⠋⠉⠳⣀⣀⣀⣀⠜⠉⠙⠇⢹⢸⢸⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡹⣄⣠⠤⣺⠷⢿⡿⠾⣗⠤⣄⣠⢎⣾⠏⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡉⠙⠉⠉⠁⢰⣿⣛⣒⣚⣛⣛⣛⣋⡥⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣄⡀⠀⠀⠙⠉⠀⠈⢉⣩⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠉⡀⠉⠉⠛⠓⠚⠛⠉⠉⢀⠉⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⢀⣠⠤⠶⠗⠒⠒⠒⠒⠒⠒⠒⠒⠺⠶⠤⣄⡀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢤⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠒⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠒⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⣀⡼⢤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⢧⣀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡉⠉⠉⢹⠋⠙⡏⠉⠉⢉⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣸⠀⠀⣇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠳⠶⠞⣹⠀⠀⣯⠳⠶⠞⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⡰⢻⠀⠀⡟⢦⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠈⠓⠋⠀⢸⠀⠀⡇⠀⠙⠚⠁⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠓⠲⣄⡤⠤⣼⡀⢀⣧⠤⢤⣠⠖⠚⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠁⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⡿⠲⠆⢤⡀⢀⣀⡀⠀⠀⠀⠀⢀⠀⣀⣠⢴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠿⣿⢿⡿⠿⠶⢯⣄⠀⠀⠀⠀⠀⠁⠢⠌⠀⠂⢶⣾⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⡄⠀⠀⠀⠊⠹⣿⣿⣦⣄⣀⣀⠀⠀⠀⠈⠀⠀⠁⠀⠉⠈⡀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣄⣠⠀⡁⠉⠛⢻⣛⣿⣿⣿⣿⠛⠉⠋⢈⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣟⣿⣿⣿⠿⠿⢿⣟⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⢾⣿⣿⢻⡆
⠀⠀⠀⠀⠀⢘⣄⡀⠀⠀⠀⠀⠛⠿⣿⣤⣍⣉⡙⠛⠛⠛⠓⠚⠛⣛⣛⣿⡿⠃⠰⣿⣶⣿⣿⢧⡨⠝⣄
⠀⠀⠀⠀⠀⣸⠧⠭⠕⠂⠀⠤⢀⠀⡀⠈⠉⠉⠉⣿⣿⣻⣿⣟⠉⠉⠉⠁⠀⠀⠀⠘⢿⣿⣿⣦⠑⢄⠈⠳⢤⡀
⠀⠀⠀⠀⠀⢻⣕⠒⠤⠤⢤⢀⣁⣀⣀⣀⣤⣀⣌⣹⣿⣟⣟⠛⠧⠀⠀⠄⠄⠀⠒⠀⠀⠿⢿⣿⣷⡌⠳⣄⠀⠐⠰⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠶⠤⠤⠤⠤⠤⠤⠤⠴⠞⠛⠻⣿⡛⠲⠲⠦⠶⠤⠀⠀⠠⠀⠤⠬⢽⣿⡇⠀⠨⡙⠢⣄⡈⠀⢯⣼⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⠒⠲⠆⠤⠤⠤⠤⠤⠦⠒⠋⠁⠀⠀⠀⠈⠙⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠖⠒⠈⠉⠁⢀⣈⣢⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢰⡶⠿⠋⣉⣭⠶⠛⣋⣴⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡏⠀⠈⠉⠛⢛⠟⠛⠭⢠⡄
⠀⠀⠀⠀⠀⢀⣀⠤⠴⠒⣢⣀⠀⠀⣾⠀⠀⠀⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⡟⠓⠒⠦⢤⣄⡀
⠀⠀⢀⠴⠊⠉⠀⢔⣮⡅⠻⢮⣿⣿⣿⡶⢤⣤⣇⠀⠀⠀⠀⠀⡇⠀⠀⠀⣌⣬⣵⢦⠄⠀⠉⠑⠦⡀
⠀⠀⠀⠀⠀⣶⣾⣿⣭⠵⠶⠛⠋⣉⣉⣿⠿⠿⢿⣯⣯⣷⣒⣶⣧⣄⣀⣀⣿⠛⠉⠁
⠀⠀⠈⠢⢄⡀⠀⠈⠐⠀⠀⢴⣿⠿⠖⠒⠛⣩⣽⣛⡥⠴⠟⠛⠙⠛⠓⠒⠋⠀⠀⠀⠀⠀⣀⡠⠖⠁
⠀⠀⠀⠀⠀⠈⠉⠓⠲⠦⠤⣤⣀⣀⣀⣀⣀⠈⠁⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⡤⠤⠖⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠖⢿⣂⠀⠀⡐⠀⠀⠀⠀⠀⠀⠉⠐⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⣀⣤⠤⠀⠀⠀⠠⠄⣀⠀⠀⠀⠀⠀⠀⠈⠐⠠⡀⠀⠀⣁⠢⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂⠈⠐⠠⠄⡀⠀⠀⠈⢢⡀⠀⠀⠀⡀⠀⠀⠀⠑⠂⠠⠐⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⠀⠀⠌⠁⠂⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢃⠋⠁⠂⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠁⠀⠀⠀⠀⠀⠀⠑⢢⡀
⠀⠀⠀⠀⠀⠀⠀⢄⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢈⡇
⠀⠀⠀⢎⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠂⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⠉⢸⠟
⠀⠀⠀⡄⠑⠄⡀⠀⠀⠈⠉⠒⠂⠤⢤⢤⣠⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⠄⠄⠀⠐⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠂⠀⠀⣀⠤⠒⠉
⠀⠀⠀⠈⠢⢄⠀⠁⠒⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠤⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠀⢀⣀⠔⠚⠉
⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⠀⠉⠒⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠀⣀⠤⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠤⣀⠀⠈⠁⠐⠠⠄⣀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⢀⣀⣠⠤⠄⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠤⢄⣀⡀⠀⠀⠀⠀⣀⣀⣠⡤⠤⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠙⠋⠟⠛⠂

⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⣀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡆⠁⠀⣿⠤⡀⡆⠀⠀⠀⠀⢀⣧⢄⠀⡇⣶⡄⢸⡤⠄
⠀⠀⠀⠀⠀⠀⢸⠶⠶⢾⡶⠶⠶⡷⠖⠷⡇⠀⠀⠀⠀⢸⡷⠶⠶⣷⠷⠶⢮⠶⠶⠶
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⠇⠷⠈⡟⠁⠀⡇⠀⠀⠀⠀⢸⡇⠉⠀⡿⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠋⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⢸⡟⠛⠉⡞⡛⠛⢳⣛⠛⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠘⢸⡇⣚⣀⣇⣁⣂⢸⢋⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⡟⣭⠁⣙⠉⠉⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣴⣿⣶⣶⣤⡶⠒⠃⠀⠀⠀⠀⣯⠭⠤⡭⠭⠤⣥⡤⠤⢼
⠀⢰⡀⠂⢀⣀⣤⣶⣾⣿⣿⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡇⡠⠀⢳⠀⠀⢸⠀⠀⣠⣔⠂⠁⢀⣀⣀
⠀⠖⠛⠋⠉⠀⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢸⡗⠒⠒⡖⠒⠒⣾⠒⠒⢺⠀⠀⠈⠙⠳⠾⠯⠙⠉
⠀⠀⠀⠀⠀⠀⠹⣿⣭⣁⣀⣀⣀⣀⣀⣀⠄⠀⠀⠀⠀⠘⡇⢀⣀⡃⠀⠀⣻⣀⣀⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠐⣿⣷⡤⠤⠽⣶⣶⠒⠛
⠀⠀⢀⣀⠀⣶⣦⣿⣿⣿⣿⣦⡀⡀⠀⠀⠀⢀⣠⡄⠀⠶⡀⣀⣹⠶⣶⡔⠀⠀⠀⠀⠘⣷⣰⣤⣤⠬⣃⠶⣶⠛⠣
⠀⠐⢿⣿⣿⣿⣿⣦⣭⣟⣛⠉⢛⡳⢐⣻⣅⡈⠻⣤⡒⠂⠈⢳⠄⣤⡜⠋⠪⣟⢀⣀⣀⠛⠋⠉⠈
⠀⠀⠀⠈⠛⢿⣯⡉⠽⠿⣿⣿⡵⠖⠉⠀⠛⠂⠀⠙⣿⣾⣝⠃⣀⣙⣆⣴⣶⣶⣿⣿⡅
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⠀⠁⠀⠐⡆⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⢤⡀⠐⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠳⢭⠆⠀⠀⠀⠀⠀⠲⠃⠀⠀⠀⡀⠀⠀⠘⠓⠚⠳⡵⠛⠀⠀⣀⠀⡀⠀⠂⢄⣀
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠀⠀⠀⢇⡗
⠀⠀⠀⠀⠠⠊⠀⠀⢄⡄⠀⠀⠀⠀⠀⠲⠖⠋⠀⠀⠀⠀⠀⠉⠀⠀⡠⣲⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠈⠀⠀⡑⠄
⠀⠀⠀⡰⢡⠃⠰⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⠀⠀⠀⠀⠘⢢⣶⠇⠀⠀⠀⣬⡇⠈⡄
⠀⠀⠀⢀⠀⠀⠀⠀⠎⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠉⠀⠀⠰
⠀⢠⡡⠖⠁⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣾⣷⣖⣴⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣠⠄⠃
⠀⢐⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠿⠛⠛⠛⠛⠛⠛⢶⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠸
⠀⠨⠀⠀⠀⠀⣾⠟⣶⠿⠿⠀⠀⠀⠀⠀⠀⠈⠓⠢⠤⠤⠄⠀⠄⠐⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣧⡇⠀⠀⠀⢀⣾⠃⠄
⠀⢀⡆⠲⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢗⣾
⠀⠈⢤⣤⣈⢻⣷⣤⡀⢠⠀⠠⡄⠀⠀⠀⣤⠀⠀⠀⠀⠀⢠⣒⣆⡰⠀⠀⠀⠀⣦⠇⠀⠀⠀⠀⠀⡀⢀⣤⣾⠟⢉⣵⣾⡟
⠀⠀⢘⠙⢿⣧⡹⠿⠋⠓⠮⠉⠀⠀⠀⠮⠎⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣨⡿⣿⠿⠁⢀⣾⣿⣿⠃
⠀⠀⠀⢂⠀⠀⠻⣶⣦⡄⠀⠺⠷⠥⠐⠴⢿⣯⣠⣤⣤⢤⣤⣤⣤⣤⣤⣤⡴⢶⡶⡶⠿⣿⡷⠮⠝⢉⣀⣤⣤⣾⣿⡿⠃
⠀⠀⠀⠀⠑⢄⠀⠀⠙⠻⢶⣶⣦⣤⣤⣤⡀⠉⠻⠿⣿⠿⠟⠋⣉⣉⣉⣍⣥⣶⣶⡀⣀⣀⣤⣴⣾⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠁⠉⠙⠻⢿⣶⣄⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢀⣀⡀⠀⠀⠈⠛⠹⠛⢉⣀⣡⣥⣬⣤⣾⣿⣯⣿⣿⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠂⠐⠂⠀⠒⠴⠿⠷⠟⠛⠓⠚⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⣰⢿⣿⣦⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢮⣄⣁⣀⣀⣵⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡥⠊⡡⠃⢨⠙⡝⠢⡈⢢⠀⠀⠀⠀⠀⠀⠀⢠⠁⡀⠀⠁⠉⠈⠀⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡝⢱⠤⡄⠀⠀⠀⠀⢇⢸⠀⢠⠃⠀⢸⠀⢸⠀⠑⣜⠀⠀⠀⠀⠀⠀⠀⡸⠙⠓⠞⠦⠶⠒⢒⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠂⠒⢷⣵⡡⣊⡩⠆⠀⠀⢠⠊⠙⠖⠊⠁⠒⠲⠒⠋⠉⢉⣉⣧⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠃⠀⠀⣸⡄
⠀⠀⠀⠀⠀⠀⠀⢠⠋⢰⡄⠀⠀⠀⢹⠀⠀⠀⠀⠀⢸⠉⠀⠲⠖⠒⠒⠒⠒⠂⠩⠅⠀⡆⠀⠀⠀⠀⠀⢳⠘⠛⢿⠗⠛⠛⢻⡛⠛⢹⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠲⠂⡸⠀⠀⠀⠀⠀⠈⡆⠀⢠⣤⠀⠀⠀⠀⠠⣦⠀⢰⠁⠀⠀⠀⠀⠀⠀⢧⠀⠈⠁⠀⠀⠈⠁⢀⠇
⠀⠀⠀⠀⠀⢀⡠⢚⢦⣀⠀⡀⣀⠔⠁⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠒⠒⠊⠁⠀⠀⣤⠒⢦⡀
⠀⠀⠀⠀⠀⠈⠲⢵⣡⢿⡋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠑⠤⠤⠤⠀⠠⠤⠤⠔⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⣜⠀⠈⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⠒⢤⣴⣿⣷⠀⠀⠀⡼⠀⢡⡀⠀⡀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⣀⣀⢸⠿⠛⠉⠀⠀⢰⡃⠀⠈⢡⠄⠙⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠤⢴⠓⡌⣥⠤⠒⢦⠀⠀⠀⠀⠀⠀⡰⠊⠁⠀⠀⠉⠢⠀⠀⠀⠀⠈⠚⠯⠷⢒⣒⠦⠝⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠰⡉⠉⣉⠉⢲⡀⠀⠀⠀⠀⠀⠀⠸⣈⡦⠼⠒⠉⠀⠀⢀⡨⢆⠀⠀⠀⠀⢸⣀⡀⠙⠃⠠⡄⠀⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣉⣀⣀⡈⣣⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⣀⠠⠀⠉⠀⠀⠀⣁⠀⠀⠀⢸⡅⢳⡼⢇⣰⢀⡠⠁⠀⠀⠀⢀⠤⡖⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠤⠤⢄⣙⡄⠂⠀⠀⠀⠀⠀⢖⠊⠉⠀⠀⢠⣀⣠⠄⠚⠙⡀⠀⠀⣾⠶⣉⡱⣈⠟⠈⠀⠀⠀⠀⣰⠅⣀⣸⡋⢉⠓⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠤⠠⢬⡇⠀⠀⠀⠀⠀⠀⠸⣄⡀⠤⠒⠊⠁⠀⢀⣀⠤⠃⠀⢀⣧⡔⢫⣤⠋⠀⠀⠀⠀⠀⢠⣁⡀⢼⠁⢹⣩⠵⡋⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠀⠀⢀⣀⣀⠀⠀⠀⠘⢄⡀⣠⠤⠐⠊⠁⠀⠀⠀⠀⣸⣧⢻⡝⠁⠀⠀⠀⠀⠀⠀⠘⡁⡠⢚⠳⢇⣨⢶⠉⡹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠁⢈⡱⡄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢅⡈⠁⠄⠙⢀⠗⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠶⠈⡳⢸⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠈⢠⢈⣧⠞⠉⠙⠚⠛⠷⠶⢶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣴⠶⡆⠀⠀⠀⠀⠀⠀⠑⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠉⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⢆⠝⠋⠙⢖⠢⣀
⠀⠀⠀⠀⠀⠀⠀⣿⡇⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⠮⠅⠀⠀⠀⠀⠀⠀⠡⠉⣷⡀
⠀⠀⠀⠀⠂⠀⠀⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣄⡀⠀⣾⡟⠀⠀⠴⠋⢹⣆⠀⠀⢠⡇⠀⠀⠚⢂⡠⠶⢄⠘⠂⠀⠘⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣆⠀⠀⠀⣰⣿⠃⠀⠀⣠⡄⠀⣀⠀⠀⣀⡄⠉⢻⣿⠧⠤⠤⠤⠤⠞⠁⠀⠀⢸⡁⠀⠀⠀⡈⠀⠀⠀⢱⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀⢀⣿⡏⠀⠀⠘⢿⡇⣴⠏⠀⣼⡏⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠦⠀⠀⠈⠦⢤⠤⠊⠀⠀⠀⣿
⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⣿⣧⢸⣿⠁⢰⣶⠀⡌⣸⡿⠀⢸⣿⠁⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢶⡀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠃
⠀⠀⠀⠀⠙⠦⣤⣄⣀⣤⣴⣿⠇⠸⣿⣤⠼⢿⡶⠁⢻⡇⠠⠸⣇⠀⠔⢹⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⠋⠷⣄⣤⡤⠤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠞⠛⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠲⠶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠀⠀⠀⠀⠀⠀⠀⢶⡀⠀⠀⠀⠀⢲⡄⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠀⠀⠀⠀⠀⠀⠙⠷⣄
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠠⠞⠀⠀⠀⠀⢀⣠⣤⠶⠶⠶⠶⢦⣤⣀⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠈⠷⠀⠀⠀⠀⠀⠀⠀⢻⡄⢀⣤⠶⠶⠶⢦⣄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠈⢻⡀
⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠛⢿⣄⣀⡀⠀⠀⠈⣳⣄⣴⠟⠀⠀⢠⡀⠀⠀⠀⠈⠙⠂⠀⠀⠈⣷
⠀⠀⠀⠀⢸⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠉⠉⠛⠛⠋⠉⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⣿⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢿⠀⠀⠻⣤⣀⣀⡴⠞⠳⡆⠀⠀⠀⠀⠐⢦⡀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡄⠀⠀⠀⠀⠀⠀⠶⢦⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⢸⡇⠀⠀⠈⠉⠉⠀⠀⠀⣿⠀⠀⣠⢦⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁
⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣸⠇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⠞⢁⡟
⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠻⠶⠋⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⣿⠀⠀⢀⣴⠋⠉⠈⠉⠉⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⢻⣄⣀⡾⠁⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⣀⣀⣀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠳⠶⠶⠦⢤⣤⣤⣤⣤⠴⠶⠶⠛⠉⠁

⠀⠀⠀⠀⠀⠀⢀⡠⠄⠒⡒⠒⢄
⠀⠀⠀⢠⠒⡉⢀⠠⠈⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔
⠀⠀⠀⡃⠀⠀⠠⠀⠈⠀⠄⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⣰⢦
⠀⠀⠀⠰⠀⠂⠀⠀⠐⠀⠄⢠⠀⢰⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠉⢇⠀⠉⢀⣇
⠀⠀⠀⠀⢣⠀⢰⠉⠂⠚⠀⠀⠃⠔⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠉⠉⠁⠈⠣⡀
⠀⠀⠀⠀⠀⢆⡸⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⣀⡴⡆⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⢔⠞⠝⠀⠣⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⢠⠊⠠⠃⡌⠀⠀⠣⡈⠁⠒⢽⢄⡠⡀⣀⡀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⣀⣤⠁⠀⠃⠀⡇⠀⠀⠀⠘⡄⠀⠀⠣⢕⠁⡇⠓⢖⠊⡦⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠈⠩⠀⡸⠆⣀⢃⠀⠐⣄⠀⠀⢀⣄⣀⠴⣗⢤⠭⠑⢆⢀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠬⠉⡾⠥⢓⣄⡠⠢⣉⠔⠫⣉⠜⢅⠔⢀⣀⢴⡤⠵⢤⣠⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠂⢹⠒⠆⠨⠇⠀⢠⠀⠀⡄⠀⠰⠀⢠⡡⠔⠈⠉⠀⠀⠀⠉⠁⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⡆⠘⡀⠸⠀⠈⡀⠀⠄⠀⡄⢀⠊⠀⢀⠀⢠⠦⣔⡑⠤⡀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⡀⢀⣘⠀⢀⡀⢸⡤⠓⠠⣇⠀⠃⠀⠀⠀⠇⡆⠠⠀⡀⠱⡋⠀⠀⠀⡈⠃⠀⢀⡀⢐
⠀⠀⠀⠀⠀⠀⡎⠀⠀⠙⠀⠈⠂⠀⠁⠀⠀⢸⡀⠐⠀⠀⡐⠀⣧⠲⠠⢄⠀⠈⠙⠉⠁⠀⠀⡠⠁⢈⠇
⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⢀⠇⣀⠀⣀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠓⠊⠑⠤⠊⠉⠈⢀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠠⠤⠄⠒⠀⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿