Hedonistic Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠿⠛⠋⠉⠉⠉⠉⠉⠛⠻⢿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠋⠈⣯⠀⢀⣾⣿⡆⠀⠀⠀⠀⣴⣦⡄⠀⠛⣿⢻⣿⣿⣿⣄⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠈⠀⣾⣿⣿⠇⠀⠀⠀⣸⣿⣿⡇⠀⠀⠙⠀⢻⣿⣿⣿⡄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⠀⠀⠀⢿⣿⠟⠀⠀⠀⢰⣿⣿⡿⠁⠀⠀⣠⣶⡄⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⡇⠀⢀⣾⣿⣿⡇⢸⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆⠀⠀⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣴⣿⣿⣿⣿⡇⣸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡀⠀⠸⣿⣷⣄⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠁⠻⢇⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⡀⠀⠘⣿⣿⣷⣤⣀⣠⣴⣾⣿⣿⣿⠟⠁⠀⠀⢀⣾⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣷⣄⠀⠈⠻⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⣠⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣄⡀⠀⠉⠉⠉⠁⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⠿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣷⣶⣦⣶⣶⣶⣾⣿⣿⣿⣿⠿⠋⠁⠀⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⠿⠿⣿⣿⣿⣿⣿⣿⡿⡿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⡇⠀⠲⠀⠀⠖⠀⠀⠀⠀⠀⢰⠃⠀⠶⠀⠐⠆⠀⠀⠀⠀⠀⢸⠁⠐⠆⠀⠰⠂⠀⣳
⠀⠀⠀⠀⠀⢣⡀⠢⠤⠤⠖⠃⡼⠀⠀⠀⠘⣇⠀⠀⠐⠒⠀⢀⡞⠀⠀⠀⠘⣆⠀⠊⠉⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠙⠦⢤⡤⠴⠚⠁⠀⠀⠀⠀⠈⠳⢤⣤⣤⠴⠋⠀⠀⠀⠀⠀⠈⠳⠤⣤⡤⠶⠋

⠀⠀⠀⠀⠀⠀⢀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠄⢤⡀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⠄
⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⡜⠁⣤⠀⢠⡄
⠀⠀⠀⠀⠀⣇⠀⠀⣁⣀⡃⠀⢠⡇⠀⠀⠀⡇⠀⠘⠀⠐⠂⠀⣿⠀⠀⠀⠀⡇⠀⣠⣤⣀⣀⠀⢠
⠀⠀⠀⠀⠀⠹⣄⠈⠛⠛⠃⣠⠞⠀⠀⠀⠀⠻⣄⠈⠉⠉⢁⣰⠏⠀⠀⠀⠀⠱⣄⠙⠛⠛⠋⣠⠏
⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠛⠁⠀⠀⠀⠀⠀⠀⠈⠙⠓⠛⠋⠁⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠋⠁

⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠒⢦⡀⠀⠀⠀⠀⣠⠖⠋⠉⠙⠳⢄⠀⠀⠀⠀⠀⢠⠔⠋⠉⠁
⠀⠀⠀⠀⢀⡇⠀⠤⠄⠠⠤⠀⢻⡀⠀⠀⢰⠃⠀⠶⢀⠰⠆⠈⣇⠀⠀⠀⢠⠃⠐⠀⠀⠐
⠀⠀⠀⠀⠈⣇⠀⠠⠒⠒⠀⠀⣸⠃⠀⠀⢸⡄⠀⢸⣿⣧⠀⠀⡟⠀⠀⠀⠸⡄⠠⣀⣀⣀⡴⠃⡖
⠀⠀⠀⠀⠀⠘⠦⣀⣀⣀⣀⡴⠋⠀⠀⠀⠀⠙⠀⠀⠉⠁⣀⠜⠁⠀⠀⠀⠀⠙⢦⣀⣀⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⢀⡤⠖⠛⠉⠉⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠉⠛⠲⢄⡀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠉⠛⠲⢤⡀
⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹
⡟⠀⢠⠞⠳⠄⠠⠞⠳⠄⠀⢻⠀⠀⠀⠀⡏⠀⠀⢾⠆⠀⠀⢾⡇⠀⠀⢷⠀⠀⠀⠀⡏⠀⠀⢾⡷⠀⠀⢼⡷⠀⠀⢻⠀⠀⠀⠀⡟⠀⠀⠺⠗⠀⠀⠺⠗
⣧⠀⠀⢠⡀⠀⠀⢀⡄⠀⠀⣼⠀⠀⠀⠀⣇⠀⠀⢀⡀⠀⠀⢀⡄⠀⠀⡾⠀⠀⠀⠀⣇⠀⠀⠀⣀⣤⣤⣀⠀⠀⠀⣼⠀⠀⠀⠀⣧⠀⠀⢤⠤⠤⠤⠤⡄
⠘⣆⠀⠀⠉⠓⠛⠉⠀⠀⣰⠃⠀⠀⠀⠀⠙⣆⠀⠀⠙⠓⠚⠉⠀⢀⡴⠃⠀⠀⠀⠀⠘⣆⠀⠘⠁⠀⠀⠈⠃⠀⡰⠃⠀⠀⠀⠀⠘⣆⠀⠘⠦⣄⣠⠴⠃⠀⣰
⠀⠈⠓⠦⣤⣀⣀⣤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⣀⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⣀⣤⠴⠋⠁⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⣀⣤⠴⠚⠁


⠀⢀⡤⠖⠛⠉⠉⠛⠲⢤⡀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠉⠛⠲⢄⡀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠉⠛⠲⢄⡀
⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⢠⠏⠀⠰⣄⠀⠀⣰⠆⠀⠱⡄⠀⠀⠀⠀⢠⠏⢀⡀⠀⠀⠀⠀⢀⡀⠱
⡟⠀⠀⢾⡷⠀⠀⢾⡷⠀⠀⢻⠀⠀⠀⠀⡏⠀⠰⣤⡴⠀⠐⢦⡴⠂⠀⢷⠀⠀⠀⠀⡏⠀⣀⣙⣋⣀⣀⣛⣋⣀⠀⢻⠀⠀⠀⠀⡏⠀⠀⣉⠶⠀⠀⠶⣉
⣧⠀⠀⢠⣤⣤⣤⣤⡄⠀⠀⣼⠀⠀⠀⠀⣇⠀⠀⠀⣠⡤⢤⣀⠀⠀⠀⡾⠀⠀⠀⠀⣇⠀⣏⠉⠉⠉⠉⠉⠉⣹⠀⣼⠀⠀⠀⠀⣧⠀⠀⠀⣀⣤⢤⣀
⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠙⣆⠀⠚⠁⠀⠀⠈⠃⢀⡴⠁⠀⠀⠀⠀⠘⣆⠈⠳⣤⣀⣀⣤⠞⠁⡰⠃⠀⠀⠀⠀⠘⣆⠀⠘⠁⠀⠀⠈⠃⠀⡰
⠀⠈⠓⠦⣄⣀⣀⣠⠴⠚⠁⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⣀⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣈⣁⣤⠴⠊⠁⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⣀⣠⠴⠚⠁


⠀⢀⡤⠖⠋⠉⠉⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠛⠲⣄⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠙⠲⢤⡀
⢠⠏⠀⠐⠛⠀⠀⠛⠂⠀⠹⡄⠀⠀⠀⠀⣰⠏⢀⠀⠀⠀⠀⠀⢀⠈⠳⡄⠀⠀⠀⠀⢠⠏⢀⡀⢀⡀⢀⡀⢀⡀⠱⡄⠀⠀⠀⠀⢠⠏⠀⡀⠀⠀⠀⠀⠀⠀⠹
⡟⠀⠀⠺⠗⠀⠀⢺⡗⠀⠀⢻⠀⠀⠀⠀⡏⠀⢀⣹⠶⠀⠠⢾⣉⠀⠀⢳⠀⠀⠀⠀⡏⠀⢀⡵⢏⡀⢀⡽⢯⡀⠀⢻⠀⠀⠀⠀⡟⠀⠀⣉⡷⠄⠀⠰⡷
⣧⠀⠀⠀⣀⣤⢤⣈⠁⠀⠀⣼⠀⠀⠀⠀⣇⠀⠀⢀⡀⠀⠀⢀⡌⠀⠀⡾⠀⠀⠀⠀⣇⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⣼⠀⠀⠀⠀⣧⠀⠀⢡⡀⠀⠀⢀⡄
⠘⢆⠀⠘⠁⠀⠀⠈⠃⠀⡰⠃⠀⠀⠀⠀⠹⣆⠀⠀⠙⠛⠛⠉⠀⢀⡴⠃⠀⠀⠀⠀⠘⣆⠀⠉⠉⠉⠉⠉⠉⠀⡰⠃⠀⠀⠀⠀⠘⣆⠀⠀⠙⠛⠛⠉⠀⠀⡴
⠀⠈⠓⠦⣤⣀⣀⣤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠈⠓⠦⣄⣀⣀⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⣀⣤⠴⠊⠁⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⣀⣤⠴⠊⠁


⠀⢀⡤⠖⠛⠉⠉⠛⠲⢤⡀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠉⠉⠙⠳⢤⡀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠛⠲⢄⡀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠉⠛⠲⢤⡀
⢠⠏⠀⠠⠴⠂⠀⠦⠄⠀⠹⡄⠀⠀⠀⠀⣰⠋⠀⠠⠖⠀⠐⠲⠄⠀⠱⡄⠀⠀⠀⠀⢠⠏⠀⠰⢤⡀⢀⡤⠄⠀⠱⡄⠀⠀⠀⠀⢠⠏⠀⠠⣄⠀⠀⣠⠄⠀⠹
⡟⠀⠰⣄⣠⠄⠠⣄⣠⠆⠀⢻⠀⠀⠀⠀⡏⠀⠀⣠⠞⠉⠙⠳⡀⠀⠀⢳⠀⠀⠀⠀⡏⠀⠀⣴⣆⠀⠀⣰⣦⠀⠀⢻⠀⠀⠀⠀⡟⠀⠀⢾⡿⠀⠀⢿⡷
⣧⠀⠀⢨⡀⠀⠀⢀⡄⠀⠀⣼⠀⠀⠀⠀⣇⠀⠀⣯⣠⡤⢤⣀⡇⠀⠀⡾⠀⠀⠀⠀⣇⠀⠀⠈⣁⣤⣤⣈⠁⠀⠀⣼⠀⠀⠀⠀⣇⠀⠀⢠⣤⣤⣤⣤⣄
⠘⣆⠀⠀⠉⠓⠛⠉⠀⠀⣰⠃⠀⠀⠀⠀⠘⢆⠀⠈⠳⠤⠤⠟⠁⢀⡼⠁⠀⠀⠀⠀⠘⣆⠀⠘⠁⠀⠀⠈⠃⠀⡰⠃⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠈⠓⠦⣤⣀⣀⣤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠙⠶⢤⣤⣤⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⣀⣤⠴⠋⠁⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣀⣀⣤⠴⠚⠁

⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠠⠄⠀⠄⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⢀⣂⠀⠀⡂⠀⠀⠀⠡⠄⠀⠠⠀⠀⠀⠀⢀⡀⠀⣀
⠀⠀⠠⣥⣀⣤⠀⠀⠀⠀⢀⠀⠀⡠⣀⠀⠀⠀⢤⣠⣠⡄⠀⠀⠀⠹⡼⠟⠛⠛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⣤⡌
⠀⠀⠁⠂⠀⠆⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠐⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⡔⢐⡒⡶⣒⠒⡆⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠠⠀⠄⠄
⠀⠘⠋⠉⠈⠉⠛⠁⠀⠀⠠⠤⠤⡄⠀⠀⠀⠀⠀⢈⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠦⠤⢶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠤
⠀⠀⠀⢁⠀⠁⠀⠀⣰⡆⠐⠀⠀⠆⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⢀⡄⠀⣠⠀⠀⠀⠀⠈⡄⡄⡌
⠀⠀⠀⢤⣠⠀⠀⠀⠙⠇⠂⡀⠀⡐⠰⠋⠀⠀⠀⠤⠄⠀⠄⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠈⠀⠄⠀⠤⠀⠀⢠⡉⠠⠤⠈⡠
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⡄⠀⠤⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠤⠀⠀⠁⠀⠀⠀⠠⠀⠤⠀⠀⠀⠀⢶⣶⠐⣶⠆⠀⠀⠀⢴⠆⠀⠶
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠠⠶⠶⢁⠀⠀⠀⡀⠠⠒⠄⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠸⠅⠀⠀⡵⠀⠀⠀⠬⠄⠀⠠⠅⠀⠀⢘⠄⠀⠀⠀⢘
⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⢰⡀⠠⣆⠀⠀⠀⠿⣿⠟⢿⣿⠷⠀⠀⠀⠤⠀⠠⠄⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠀⠠⡄⠀⡄
⠀⠀⠀⠂⠦⠐⠀⠀⠀⠀⠈⠠⠄⠁⠀⠀⠀⠀⠀⠀⠆⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠐⠦⠤⠖
⠀⢠
⠀⠰⢄⠀⠀⢀⢀⡀⠂⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡀⠀⠀⠀⠀⣤⣶⣶⣶⣄⠀⠀⠀⡐⠀⠀⠐⡀
⠀⠀⣬⣀⢀⣰⣆⠁⠀⠀⠀⠀⠀⡀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠶⢈⠀⠀⠀⠀⢀⡌⠉⢀⡀⠀⠀⠀⠘⡀⠀⠚
⠀⠀⠻⠍⡈⠭⠃⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢶⣶⣿⣶⡶⠀⠀⠘⢜⠎⠉⣒⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠁
⣿⣿⣿⣿⣻⣻⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣟⣻⣿⣛⣛⣿⣻⣛⣿

⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⡴⠒⠀⣠⠄⠀⠀⠀⠀⢀⣤⠶⠒⠒⠢⠤⡀
⠀⠀⠀⡞⠀⣴⡄⢴⣦⠐⡄⠀⠀⠀⠀⣠⠤⠤⠤⢄⡀⠀⠀⠈⣯⠤⠜⠁⢩⠠⠐⣏⠀⠀⢠⡟⠁⣴⡆⠀⢰⡆⠈⠢⡀
⠀⠀⠀⢣⠀⠉⠰⠀⠀⡠⠃⠀⠀⡰⠋⢠⡄⠀⣤⠀⠈⠆⠀⠀⢃⠠⠂⠀⠀⣰⠀⡿⠀⠀⡿⠀⠀⣘⣃⣀⣘⣃⡀⠀⢻
⠀⠀⠀⠀⠉⢀⣀⡼⠉⠀⠀⠀⠠⠀⡀⠈⠁⠀⠉⢀⠀⠸⠀⠀⠈⠳⠄⢲⠾⠅⠚⠁⠀⠀⢧⠀⢸⠀⠀⠀⠀⢠⠏⠀⣼
⠀⠀⢰⠽⣆⣉⣉⣡⣤⣦⠀⠀⠀⢆⠙⠦⠀⠀⠠⠋⠀⠂⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠈⠳⣄⠑⠤⠤⠴⣋⡠⠾⠃
⠀⠀⠘⠴⠒⠛⠀⠉⠱⠞⠀⠀⠀⠀⠑⠦⠤⠤⠴⠊⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠉⠳⣦⠀⠀⠉⠙⠛⠉⠁
⠀⠀⠀⣀⠴⠒⠒⠒⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⠀⠀⠀⠀⠀⡾⣿⣿⣿⣿⠟⣿⣿⣷⣾⣧
⠀⠀⡴⠁⣀⣀⠀⣀⣀⣀⢳⡀⠀⠀⠀⠀⠀⠀⠘⠀⣧⠀⠀⠀⠀⡇⢠⡉⠉⠁⠀⠉⢛⠛⢁⣿
⠀⢰⠁⠀⠀⠉⠀⠀⠈⠉⠀⡇⠀⠀⠀⢠⡀⠀⠀⠔⠁⢹⠀⠀⠀⠳⡀⠙⠦⠀⣠⠴⠋⣀⡾⠃
⠀⠸⣇⠀⠀⠀⢀⣀⡴⠀⣠⠁⠀⠀⡄⠀⠉⠀⠀⡠⠒⠁⢰⠀⠀⠀⠈⠀⠠⠤⠤⠴⠚⠉
⠀⠀⠙⠲⢤⣀⣉⣡⣤⠞⠁⠀⠀⠠⠓⠤⠄⠀⠈⠀⡀⠔⠋⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢄
⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⢧⣀⠀⠀⠀⠀⠀⠀⡀⠴⠃⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⡔⠀⠀⣾⠆⠀⢰⠀⠀⠣
⠀⠀⠀⢀⡴⠋⡁⠀⢀⠈⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⣤⣠⠴⠖⠛⠓⠲⢮⣸⠇⠀⠀⡇⠀⠀⠙⠀⠀⠙
⠀⠀⠀⡞⠀⠘⠗⠀⠻⠇⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠞⠁⠀⠀⠀⢀⡤⠄⠹⣦⠀⠀⣇⠈⢧⡀⠀⠀⠀⣰⠃
⠀⠀⠀⡇⠀⡴⢄⢀⡤⢄⣠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠒⠛⠷⠀⠿⠀⠀⠀⣿⠀⠀⠘⢄⡀⠙⠒⠒⠋⠁⢀⠄
⠀⠀⠀⠻⣄⠁⠀⠉⠀⠀⣁⠜⠀⠀⣀⣤⠤⢄⣀⠀⠀⠀⡇⠀⠀⡀⠀⠀⠀⣰⠃⣰⠏⠀⠀⠀⠀⠉⠙⠒⠒⠒⠊⠁
⠀⠀⠀⠀⠀⠉⠑⠒⠚⠋⠁⠀⣰⠟⠁⣄⠀⠀⣤⠁⠢⡀⠈⠢⠀⠈⠐⠒⠚⡡⠞⠋⠀⠀⣠⠖⠉⠉⠉⠓⢦⡀
⠀⠀⢀⠄⠒⠀⠀⠢⡀⠀⠀⢰⡏⠀⠈⠿⠀⠀⠿⠀⠀⠹⣄⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢰⠃⠀⠿⠀⠸⠀⠀⠑
⠀⠀⠀⠀⠋⠀⠃⠀⠀⠀⠀⢸⡀⠀⡖⠒⠛⠛⠛⣻⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣠⠔⡂⡂⢲⢢⠀⠆
⠀⠀⠀⡑⠀⠀⢈⠀⠀⠀⠀⠈⢷⣀⠳⣀⣀⣀⡴⠃⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠁⠒⠂⠒⠚⢊⡔
⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠓⠦⠬⠴⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠶⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⡄⠀⠀⠀⠀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⢀⣀⠀⠀⠈⠓⠀⠀⠰⠚⠉⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⠞⠛⠷⠶⣦⣄⣀⠙⠢⡀⠀⠀⢀⠤⠐⠒⠒⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⣶⣦⡀⠀⠀⠉⠛⠷⣦⡙⣄⠞⠁⢀⣀⣀⣀⣀⣀⡙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠈⠙⣯⣶⣿⣿⡉⠉⠉⠉⠉⠉⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⣙⣛⣉⣀⣀⡀⠀⠀⠀⠀⢀⡿⣶⣿⣿⠃⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠉⠉⠙⠓⠢⠤⠎⠐⡄⢉⣀⣀⣤⣤⣀⣀⣀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣤⠴⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⣀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠒⠒⠒



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

⠀⠀⠀⠀⠀⠀⠸⠇⢀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢰⠅⠁⠁⣠⠂⠀⠀⡄⢠⢀⠀⠀⠃⡀⡀⢏⠀⢀⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠀⠠⠀⠀⠰
⠀⠀⠲⠖⠀⠀⠀⠄⠀⠉⠃⠀⠀⠀⠀⠀⠜⠀⠀⠂⠀⠀⠎⠀⠈⠎⠒⠊⠀⠀⡄⠀⠴⠋⠀⠀⢐⠈⠟⠠⠀⠀⠱⠀⠀⠀⠀⠀⠀⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠂⡀⠁⠀⠀⠀⢀⣀⢸⠀⠀⠀⠄⠴⢡⠀⠀⠂⠀⠀⢣⠀⠀⠀⣀⡆⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡐
⠀⠀⠀⠀⠂⠀⠀⠀⠋⠙⠈⠀⠀⠀⠘⠀⠂⠀⠀⠀⠃⠐⠃⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⢀⠔⢒⠢⠄⠀⠀⣀⠀⠠⡤⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⡀
⡼⠗⠁⡀⠈⠀⠀⠉⠀⠀⢈⠀⠀⡉⠐⠂⠹⠀⠀⡀⢈⡀⠸⠀⠠⠐⠀⠂⡇⠀⠀⠀⣀⠤⠆⠀⠀⢓⣘⡋⠀⠀⠀⠖⡰⢈⠀⠀⠀⠒⠘

⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠒⠢⣄⠀⠀⠀⢀⡤⠒⠒⠒⢤⠀⠀⠀⠀⣠⠔⠒⠒⠲⢄⠀⠀⠀⠀⡠⠒⠒⠒⢦⡀⠀⠀⠀⢠⠔⠒⠒⠲⢄
⠀⠀⠀⠀⠀⠀⢰⠁⠐⠆⠰⠀⠈⡆⠀⠀⡎⠀⠲⠀⠆⠀⢡⠀⠀⢰⠁⠐⠂⠰⠂⠈⡆⠀⠀⡜⠀⠒⠀⠒⠀⠱⠀⠀⢠⠃⠐⠀⠐⢑⠈⡇
⠀⠀⠀⠀⠀⠀⠸⡄⠢⢄⡠⠆⣠⠃⠀⠀⢣⠠⠖⠂⠲⢄⡜⠀⠀⠘⣄⠲⢄⡠⠖⢠⠃⠀⠀⢱⡀⠀⢀⠠⠂⡴⠀⠀⠈⢆⠹⣉⢉⡽⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠒⠚⠁⠀⠀⠀⠀⠙⠒⠢⠒⠋⠀⠀⠀⠀⠈⠑⠒⠒⠚⠁⠀⠀⠀⠀⠙⠒⠄⠒⠊⠀⠀⠀⠀⠈⠑⠂⠐⠒⠁


⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠤⢄⠀⠀⠀⠀⠀⢀⠤⠤⠤⡀⠀⠀⠀⠀⠀⡠⠤⠤⢄⠀⠀⠀⠀⠀⢀⠠⠤⠤⣀⠀⠀⠀⠀⠀⡀⠤⠤⢄⡀
⠀⠀⠀⠀⠀⠀⢠⠪⡖⡦⢴⢢⠑⡀⠀⠀⡔⠁⠂⠀⠒⠈⢆⠀⠀⢀⠎⠰⡂⢈⡂⠑⡄⠀⠀⠰⠁⢤⠀⡤⠈⢣⠀⠀⢀⠎⢰⡂⢀⣲⠙⡄
⠀⠀⠀⠀⠀⠀⢸⡀⢩⡄⢨⠅⢀⠇⠀⠀⠇⠀⠉⢠⡍⡔⠞⡢⠀⠸⡀⠀⣁⣈⡀⠀⡇⠀⠀⢃⠀⠈⣀⠉⠷⢠⠀⠀⠘⡀⢈⠅⠂⢍⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠑⠤⣁⣁⠤⠊⠀⠀⠀⠈⠢⢄⣈⡡⠜⠚⠁⠀⠀⠑⠤⣀⣀⠤⠊⠀⠀⠀⠈⠢⢄⣀⡨⠔⠃⠀⠀⠀⠙⠮⣒⣐⠮⠊


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⢈⠙⢦⠀⠀⠀⢠⠊⢍⠀⡨⠑⡄⠀⠀⠀⡔⠩⠄⠀⠍⢢⠀⠀⠀⢠⠞⠉⠀⠈⠑⢄⠿⠀⠀⡴⠊⡁⢀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⢸⠀⣈⠉⠈⡁⠀⡇⠀⠀⡇⠀⠒⣀⠂⠀⢸⠀⠀⢸⠀⠀⣃⣘⠁⠀⡇⠀⠀⠆⢀⠐⠀⠑⡁⢈⠀⠀⠰⠀⠀⣉⢈⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠈⢦⡈⠻⠟⢀⠜⠁⠀⠀⠑⣄⠊⠀⠑⣠⠂⠀⠀⠀⠣⡐⠇⠘⢂⡴⠁⠀⠀⠘⢄⠑⠒⠊⣡⠎⠀⠀⠀⠣⡀⠚⠙⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁


⠀⠀⠀⠀⠀⠀⠀⣠⠖⠂⠐⠢⡀⠀⠀⠀⢀⠤⠒⠀⠒⢤⠀⠀⠀⠀⣠⠔⠂⠐⠢⣄⠀⠀⠀⠀⡠⠒⠀⠒⠠⡀⠀⠀⠀⢀⠔⠂⠁⠒⢄
⠀⠀⠀⠀⠀⠀⢸⢇⣒⡲⢆⢒⡻⡄⠀⠀⡎⠀⠰⠀⠆⠀⢣⠀⠀⢰⠁⠀⠆⠰⠀⠈⡆⠀⠀⡜⠀⠭⠀⠬⠀⠱⠀⠀⢠⠁⠀⠦⠰⠆⠈⡇
⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⣀⠄⣰⠃⠀⠀⢣⠀⠒⠖⠢⢀⡌⠀⠀⠘⡄⠫⡉⢉⠝⢠⠃⠀⠀⢱⡀⠢⣄⠴⠀⡰⠀⠀⠈⢆⠀⠠⠔⠂⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠐⠊⠁⠀⠀⠀⠀⠙⠒⠀⠒⠉⠀⠀⠀⠀⠈⠑⠀⠀⠚⠁⠀⠀⠀⠀⠉⠒⠠⠐⠊⠀⠀⠀⠀⠀⠑⠒⠒⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠒⠂⠀⠀⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠛⠦⠤⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠄⠀⠑⠄⠀⠀⠈⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠘⠉⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠐⠁⠀⠄⠀⠀⠊⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠐⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠰⢷⠀⠀⠀⠀⠀⠀⠙⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢠⡂⠀⠡⠂⠀⠄⠀⠀⠀⠀⠠⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⡁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠔⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠰⠀⠀⠀⠀⠀⠀⠀⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠰⡁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠒
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⢀⡀⠀⠄⠞⠂⡑⢄⠀⠀⠀⠀⠔⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡈⠊⠈⡀⢀⠀⠀⠀⠀⠘⢄⠁⠀⠀⠀⠈⠢⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⢴⡀⠀⠀⠀⠀⠀⠀⠀⠄⠰⡄⠀⠄⠈⠕⠀⠀⠀⠀⠀⣬⡤⠴⠓⠀⡐⠀⠀⠠⠑⠀⠀⠠⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠢⡑⢄⠂⠀⠀⢈⠢⡀⠢⡑⣌⠢⣀⠘⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⣦⠀⠊⠁⢈⣣⡚⠀⠀⢂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⢀⠁⠁⢀⠀⠋⠜⠂⠈⠑⠶⠈⢢⡄⠀⡀⠤⣖⡱⠐⠀⠀⢀⠀⠰⡣⠀⠀⠨⠓⠁⠀⢀⢘⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⢌⠢⢃⠂⢄⠈⠀⠀⠒⠲⠦⣤⣤⠖⠋⠁⠰⠂⠁⠘⠛⠛⠃⠁⠀⠀⠁⠘⠁⡤⣌⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢡⣌⠓⡀⠄⠐⣊⣤⠗⠋⡙⠦⢰⢤⠂⡿⠀⢀⣀⣀⣀⣀⣀⣀⡀⠀⢀⡆⠋⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣁⠀⠜⢋⡡⠶⡛⠁⠀⠀⣚⣅⢀⡉⡆⠰⡏⠀⠀⠀⠉⠉⠉⠉⠙⢻⠀⢸⠀⠁⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢁⠡⠂⠀⠀⠀⠢⡙⢯⠀⠈⠁⠀⠀⠀⢠⣘⣇⠀⠀⣠⣤⡀⠀⠀⠀⠌⠀⢸⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠢⣑⠄⠀⠀⠀⠰⡏⠀⠀⣹⣿⠁⠀⢙⣷⣤⣤⣤⣤⡞⢠⠍⠀⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠒⠊⠁⠈⠑⠒⠛

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

⠀⠀⠀⠀⢀⣀⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⠀⢀⣀
⠀⠀⠀⠀⠈⠉⠁⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⡆⠀⠀⠀⠀⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠦⠀⠄⠂⠀⠀⠀⠁⠀⠔⠃⠀⠀⠀⠀⠀⡤⠂⠤⡄
⠀⠀⠀⢀⣯⣤⣶⣶⣄⣄⠀⠀⠀⠈⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢈⢠⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠆⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⣼⣿⣿⡆⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⠠⠀⠀⠀⠀⠀⠀⢈⡀⠀⠀⠀⠀⠘⠛⠟⠁⠀⠸⡆⠀⢀⡤⢀⣀⣀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠊⣉⠥⠐⠛⠁⠀⠈⠈⠩⠉⠀⠂⠀⢼⣆⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⡀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣠⠁⠀⠁
⠀⠀⠀⡀⠀⠀⠀⠀⠈⠀⢸⣿⠀⠀⣠⠶⠦
⠀⢀⠈⡠⠂⠀⠀⠀⠀⠀⢸⣿⠀⠀⣴⠀⠀⠀⠄⠀⠀⡀⢀⣶⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠘⠁⠔⠀⠀⠀⠀⠀⣸⠏⠀⠀⢼⣒⠲⠞⢒⣠⣈⡀⣸⡏⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠘⠓⠀⠀⡆⡂
⠀⠀⠀⠰⠖⠀⠒⠀⠀⠞⠁⠀⠀⠀⠀⠉⠛⠛⠛⠻⠿⠶⠞⠁⠀⠀⠚⠓⠚⠓⠀⠐⠐⠛⠓⠛⠂⠀⠀⠀⠀⠀⠄⠀⢀⢯⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⢡⠋⠔⠁⠀⠀⠠⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⡀⣠⢀⡀⢀⣠⣤⣤⣶⣶⡆⢾⠁
⠀⠀⠠⢀⠀⠀⠀⠀⠀⠄⠀⠠⢁⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⡟⠋⡽⠋⠹⠈⠈⢣⡼⠁⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⣀⡀⠂⠀⠀⠤⣤⣤⣤⢃⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠊⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡤⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠙⠒⠶⠀⠀⠀⠀⠀⠀⠀⠉⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⡶⠦⠄⠀⠀⠀⡀⠠⠂⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡟⢸
⠀⠀⠀⠀⠀⢀⠴⠶⢾⠲⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠐⠀⠄⠈⠆
⠀⠀⠀⠀⠠⠀⠀⠀⠘⠄⠐⠓⠀⠂⠐⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠤⠤⠖⠛⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⡅
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠊⠀⠀⠀⠀⠠⠤⡄⣤⣤⣤⣠⣀⣤⣠⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⣸⣈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣐⡄
⠀⠀⠀⢠⣦⡄⠀⠀⠀⠀⠀⠋⠄⠀⠀⠀⠐⠒⠀⠀⠱⠀⢀⠀⠸⣹⣿⢳⡆⠀⣾⣹⣿⡿⢿⠀⠀⠀⣀⡀⢀⣀⠀⠀⠀⣤⣦⣤⣦
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⢰⣀⣶⠀⠀⠀⢀⣀⣸⣀⣀⠀⠘⠤⠄⢻⠀⠀⠀⠀⠿⠯⠥⠥⠼⠃⠀⠀⢻⡯⣝⠛⠀⠀⠀⠷⣿⠿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠰⢀⠀⠀⠀⠀⠀⣿⣦⠀⠀⠀⠀⠀⣤⣤⣤⠀⠀⠀⠀⢠⡶⢶⠀⠀⠀⣀⣤⣤⡄⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠄⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠉⣿⣿⣿⣶⡆⠀⠠⣿⢟⣷⡿⠃⠀⠠⠒⠶⠶⠖⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠻⠿⠿⠀⠀⠀⠀⠿⠦⠤⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠙⠟⠁
⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⣿⣿⣿⡿⠀⠀⠀⠰⠶⣾⣶⣶⠀⠀⠰⠶⣾⣂⣀⠀⠀⠀⡀⢸⣦⠀⠀⠀⢀⣶⣿⡏⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃
⠀⠀⢺⡿⢷⡦⠀⠀⠀⠰⠴⠿⠿⠿⠀⠀⠀⠀⢹⠉⠁⠀⠀⠀⢙⣍⣙⠃⠀⠀⠠⠤⠤⠤⠿⠧⠀⣰⣷⣾⣧⣤⡀⠀⢾⣦⡎⠱⠿⠆
⠀⠀⠈⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠋
⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⢾⡥⠙⠀⠀⠀⠀⣴⣶⣶⡄⠀⠀⢰⣦⣀⣠⣞⠀⠀⢠⣀⣂⡄⠀⠀⠀⠀⣠⢀⣀⣀⠀⠀⠀⣬⠀⢀⡃⠀⠀⠀⠀⠶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠀⠀⠀⠈⠁⠈⠀⠁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⠋⠛⠛⠋⠀⠀⠀⠀⠙⠈⠁

⠀⠀⠀⢠⠞⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠓⠀⠀⠀⠀⢀⡄⢀⣀⣀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⢀⣶⣠⡄⠀⠀⠀⡶⢶⠶⢤⡀
⠀⠀⠤⠀⠀⠙⠠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢰⠄⠀⠀⠀⠘⠛⠛⠉⠛⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠛⠟⠀⠀⠀⢀⣷⣾⡶⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁




⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠒⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠐⠀⠂⠀⠀⠀⠀⠀⠂⠀⠘⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢀⣤⣴⣦⣤⡄⠀⠀⢐⠒⠒⠂⣀⡀⠀⠀⠀⢀⣰⣾⣾⡆⠀⠀⠀⠠⢤⠤⠀⠀⠀⠀⠀⣠⣾⣧⣠⠂
⠀⠘⠿⠿⠿⠿⠇⠀⠀⠘⠀⠀⠣⠀⠀⠀⠀⠻⡿⠛⠻⣻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣆⠀⠀⠀⠀⠄⣦⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣾⣾
⠀⠀⢸⣿⣤⣄⠀⠀⠀⠀⠸⠿⠿⠿⠄⠀⠀⠀⠀⠚⠁⠟⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⢰⣾⣶⣾⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢠⣾⣿⣄⠀⠀⠀⠀⠠⢨⡂⠀⠀⠀⠀⢸⡇⣶⣿⣿⠀⠀⠀⠀⠀⣠⡺⠟⠁
⠀⠀⢹⣿⣾⡿⠀⠀⠀⠀⢠⢏⠷⡄⠀⠀⠀⠈⣇⣻⣿⡟⠀⠀⠀⣠⣦⠟⠁⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢠⣤⡄⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⡏⡇⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⣀⣤⣶⡦
⠀⠀⣾⣿⣿⣿⡄⠀⠀⠈⠉⠉⠉⠈⠁⠀⠀⠀⠀⡇⢥⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⠉⠉⠁

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

⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⣀⡀
⠀⠠⠄⠫⠀⠀⠀⠀⠤⠸⠁⠀⠀⠀⠠⠀⠇⠂⠀⠀⢀⠔⠫⠐⠀⠀⠀⡠⠈⠅⠀⠀⠀⠠⠄⠢
⠀⠀⠈⠀⠁⡄⠀⠀⠀⢥⡌⠠⠀⠀⠀⠈⠀⢁⠄⠀⠀⠈⠁⠉⡐⠀⠀⠀⠉⠉⢁⠀⠀⠀⠈⣤⠁⡄
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠖⠂⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⠠⠖⠀⠀⠀⠀⣀⡴⢀
⠀⠘⠵⠉⠦⠀⠀⠀⠉⠌⠠⠀⠀⠀⢾⣦⢥⣶⡆⠀⠐⠡⠌⠤⠀⠀⠀⠊⠀⠡⠀⠀⠀⠐⢡⠉⡄
⠀⠀⠀⠛⠠⠃⠀⠀⠀⠘⠃⠜⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠒⠀⠊⠀⠀⠀⠈⠉⠔⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀
⠀⢀⠄⠭⠀⠀⠀⠀⠤⠨⠅⠀⠀⠀⠠⠀⠍⠀⠀⠀⢀⠄⠩⠁⠀⠀⠀⡠⠀⠅⠀⠀⠀⢀⠄⠯
⠀⠀⠘⠀⠋⡀⠀⠀⠀⢤⡤⢠⠀⠀⠀⠀⡄⠁⠄⠀⠀⢠⡀⠋⡠⠀⠀⠀⣃⠘⢀⠀⠀⠀⠐⠀⠂⡀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈

⠀⢀⡤⠖⠋⠉⠉⠓⠲⣄⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠉⠉⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠋⠉⠉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⣠⠖⠚⠉⠉⠙⠲⢤⡀
⢠⠏⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⢀⡞⠁⠀⡀⠀⠀⠀⡀⠀⠹
⡏⠀⠰⠋⠳⠀⠰⠋⠳⠀⠈⡇⠀⠀⠀⣸⠀⠀⠸⠷⠀⠀⠸⠷⠀⠀⢹⠀⠀⠀⠀⡇⠀⠀⠾⠇⠀⠀⠿⠆⠀⠈⡇⠀⠀⠀⢸⠁⠀⠘⠟⠀⠀⠘⠛
⢧⠀⠀⢤⡀⠀⠀⣠⠄⠀⢀⡇⠀⠀⠀⢸⡀⠀⠠⣄⠀⠀⣀⡄⠀⠀⡼⠀⠀⠀⠀⣇⠀⠀⢀⡤⠤⠤⣄⠀⠀⢠⡇⠀⠀⠀⢸⡀⠀⢰⡖⠒⠒⠒⣶
⠘⢦⡀⠀⠉⠉⠉⠁⠀⣠⠞⠀⠀⠀⠀⠀⠳⣀⠀⠈⠉⠉⠁⠀⢀⡼⠁⠀⠀⠀⠀⠘⢦⡀⠉⠀⠀⠀⠈⠀⣠⠞⠀⠀⠀⠀⠀⠳⣄⠀⠓⠦⠤⠖⠁⢀⡴
⠀⠀⠙⠲⠦⠤⠤⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⠤⠤⠴⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⠤⠤⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠤⠤⠴⠖⠋

⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⣠⠞⠉⠁⠀⠀⠉⠙⢦⡀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠀⠀⠈⠉⠲⣄⠀⠀⠀⠀⠀⠀⣠⠞⠉⠁⠀⠀⠉⠑⢦⡀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠀⠀⠈⠉⠳⣄
⣰⠃⠀⢀⡀⠀⠀⣀⡀⠀⢹⡄⠀⠀⠀⢠⠏⠀⡀⠀⡀⠀⡀⠀⡀⠘⣆⠀⠀⠀⠀⡼⠁⠀⣘⣦⠀⢠⣞⡀⠀⢳⡀⠀⠀⠀⢠⡏⠀⢤⡀⠀⠀⢀⣠⠄⠘
⡇⠀⠀⠛⠃⠀⠀⠛⠃⠀⠀⡇⠀⠀⠀⢸⠀⠀⠓⠚⠁⠀⠓⠚⠁⠀⢸⠀⠀⠀⠀⡇⢠⡤⠤⠤⠤⠤⠤⠤⣄⠀⡇⠀⠀⠀⢸⠀⠀⠴⠛⠁⠀⠙⠲⠄
⢳⡀⠀⠒⠒⠒⠒⠒⠂⠀⢰⠇⠀⠀⠀⠸⡄⠀⢀⡴⠒⠒⠶⡄⠀⢀⡞⠀⠀⠀⠀⢧⠀⢧⡀⠀⠀⠀⠀⣰⠇⢰⠃⠀⠀⠀⠸⡆⠀⢀⡴⠒⠒⠲⣄⠀⢀
⠈⠳⣄⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠈⠳⣄⠙⠒⠶⠖⠚⢁⡴⠋⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠈⠉⠒⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠒⠉⠁

⠀⠀⢀⣀⠤⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⣀⡀
⢀⡴⠋⢀⠴⠀⠠⢤⡈⠳⣄⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠙⢦
⡼⠀⠀⣴⡄⠀⠀⣴⡄⠀⠸⡆⠀⠀⠀⢰⠃⠀⠲⣤⡀⠀⣠⠴⠂⠈⢧⠀⠀⠀⠀⡞⠀⠐⣦⡖⠀⠰⣤⠖⠀⠹⡄⠀⠀⠀⢰⠇⠀⠰⢤⡀⠀⢀⣤
⡇⠀⠀⠈⠁⠀⠀⠸⠀⠀⠀⡇⠀⠀⠀⢸⠀⠀⠚⠉⠀⠀⠈⠙⠂⠀⢸⠀⠀⠀⠀⡇⠀⠘⠁⠙⠀⠘⠉⠓⠀⠀⡇⠀⠀⠀⢸⠀⠀⠐⠋⠁⠀⠀⠉
⠹⡄⠀⠴⠋⠉⠉⠳⠄⠀⣸⠃⠀⠀⠀⠘⣆⠀⠈⠳⠤⠤⠖⠃⠀⢠⠏⠀⠀⠀⠀⢳⡀⠀⠒⠒⠒⠒⠒⠂⠀⡸⠁⠀⠀⠀⠘⣇⠀⠈⠳⠤⠤⠖⠋⠀⢠
⠀⠙⢦⣀⡀⠀⠀⣀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⢀⣠⠴⠋⠀⠀⠀⠀⠀⠀⠙⢦⣀⡀⠀⠀⣀⡠⠞⠁⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⢀⣀⠴⠋
⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⠀⠀⣠⠴⠖⠒⠒⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠛⠛⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠒⠒⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠒⠒⠲⠦⣄
⢠⠞⠁⢠⡤⠀⠠⢤⠀⠙⢦⠀⠀⠀⠀⢀⡜⠁⠀⡤⠆⠀⠦⡄⠈⠳⡄⠀⠀⠀⠀⢠⠞⠁⢠⣀⠀⢀⣤⠀⠙⢦⠀⠀⠀⠀⠀⡴⠋⠀⣀⠀⠀⢀⡀⠈⠳
⡞⠀⢠⣀⣠⠀⢠⣀⣠⠀⠈⡇⠀⠀⠀⢸⠁⠀⢀⡴⠚⠛⠲⡄⠀⠀⢳⠀⠀⠀⠀⡏⠀⠀⣤⡄⠀⠀⣤⡄⠀⠘⡇⠀⠀⠀⢸⠃⠀⢰⣾⠁⠀⢹⣶
⣇⠀⠀⣉⠁⠀⠀⢉⡁⠀⢀⡇⠀⠀⠀⢸⡀⠀⢸⢀⣠⣤⡀⣿⠀⠀⡼⠀⠀⠀⠀⡇⠀⠀⠉⣁⣠⣀⡉⠁⠀⢀⡇⠀⠀⠀⢸⡀⠀⢀⣀⣀⣀⣀⣀
⠘⣆⠀⠈⠙⠒⠚⠋⠀⢀⡼⠁⠀⠀⠀⠈⢧⡀⠈⠻⠤⠤⠞⠁⠀⡴⠃⠀⠀⠀⠀⠹⣄⠀⠚⠁⠀⠀⠙⠀⢀⡞⠁⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠈⠓⠦⣄⣀⣀⡤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣤⣤⡤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⣄⣀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣀⣀⣠⠴⠚⠁

⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠒⣦⡀⠀⠀⠀⠀⠀⠀⣠⢔⠒⠒⠦⡀⠀⠀⠀⠀⠀⠀⢀⠴⠒⠒⠢⣄⠀⠀⠀⠀⠀⠀⢀⡴⠒⠒⠲⡄
⠀⠀⠀⠀⠀⠀⢰⠀⠤⠋⠣⠄⢴⠀⠀⠀⠀⠀⢰⠃⣬⣶⣶⣅⢹⡀⠀⠀⠀⠀⠠⡏⠻⠃⠈⠛⠘⡆⠀⠀⠀⠀⠀⡎⠐⠂⠈⢠⡿⡆
⠀⠀⠀⠀⠀⠀⠸⣄⠠⠖⠦⢀⡞⠀⠀⠀⠀⠀⠘⣆⠻⠿⠿⢟⡼⠀⠀⠀⠀⠀⠀⢧⡀⠉⠉⠁⣰⠃⠀⠀⠀⠀⠀⢳⡀⠀⠐⠻⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠊⠁


⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠲⢤⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠲⢤⡀⠀⠀⠀⠀⠀⠀⢀⡤⢶⠶⠦⡄⠀⠀⠀⠀⠀⠀⠀⡠⠶⠒⠦⡤
⠀⠀⠀⠀⠀⠀⢰⠓⠿⠃⠻⠗⢳⠀⠀⠀⠀⠀⢰⠃⢤⡀⢀⡤⢹⡀⠀⠀⠀⠀⢀⡯⠀⡀⢀⣷⠸⡆⠀⠀⠀⠀⠀⡞⠀⠆⠀⠆⠐⡇
⠀⠀⠀⠀⠀⠀⠸⡄⠳⠤⠴⢃⡜⠀⠀⠀⠀⠀⠘⣆⠢⠤⠤⠄⡼⠁⠀⠀⠀⠀⠀⣃⠸⠶⠿⠁⣰⠃⠀⠀⠀⠀⠀⢣⡀⠀⠄⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠒⠋⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠒⠊⠁⠀⠀⠀⠀⠀⠀⠈⠑⠒⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠙⠒⠶⠚⠁


⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠤⡤⢦⠄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠦⣤⡀
⠀⠀⠀⠀⠀⠀⢰⠋⠺⠀⠺⠊⢣⠀⠀⠀⠀⠀⢠⠇⠀⠀⠡⠀⢼⠀⠀⠀⠀⠀⢀⡎⠐⠂⠀⠂⠹⡄⠀⠀⠀⠀⠀⡜⠁⠤⠢⠠⠘⡆
⠀⠀⠀⠀⠀⠀⢸⡀⠧⣤⡴⠃⡼⠀⠀⠀⠀⠀⠸⡆⠀⠐⠀⠀⣸⠁⠀⠀⠀⠀⠈⣇⠈⠓⠺⡿⢠⠇⠀⠀⠀⠀⠀⢧⠠⣾⣿⣷⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠙⠲⠦⠶⠊⠁⠀⠀⠀⠀⠀⠀⠈⠳⠤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠈⠓⠦⠴⠖⠁⠀⠀⠀⠀⠀⠀⠀⠑⠮⠬⠗⠋


⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠨⣦⠀⠀⠀⠀⠀⢠⡎⠀⠀⠨⠀⢷⠀⠀⠀⠀⠀⠀⡖⡀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⡜⠁⠂⠀⢂⡙⡆
⠀⠀⠀⠀⠀⠀⢸⡀⠈⠀⠈⠀⡸⠀⠀⠀⠀⠀⠸⡄⠈⠀⠀⠁⣸⠃⠀⠀⠀⠀⠈⣇⢰⣀⣀⡴⢠⠇⠀⠀⠀⠀⠀⣇⠄⡀⠀⠻⢇⡇
⠀⠀⠀⠀⠀⠀⠀⠑⠦⠤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠙⠦⠤⠤⠖⠁⠀⠀⠀⠀⠀⠀⠈⠲⠬⠥⠔⠋⠀⠀⠀⠀⠀⠀⠈⠀⠤⠤⠵⠊

⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛
⣿⠀⠀⠀⠀⢀⡠⠤⠤⢄⡀⠀⠀⠀⠀⠀⣀⢤⡤⣀⠀⠀⠀⠀⠀⠀⣠⢤⠤⣀⠀⠀⠀⠀⠀⠀⣠⠤⠤⣄
⣿⠀⠀⠀⠀⡎⠠⠆⠰⠄⢱⠀⠀⠀⠀⡎⠠⠦⠰⠆⢱⠀⠀⠀⠀⡎⠐⠆⠰⠂⢱⠀⠀⠀⠀⡎⠰⠆⠰⠆⢱
⣿⠀⠀⠀⠀⢇⠠⠤⠤⠄⣸⠀⠀⠀⠀⡇⠠⣤⣤⠄⢸⠀⠀⠀⠀⡇⠨⣟⣻⠇⣸⠀⠀⠀⠀⡇⠀⣿⣿⠀⡸
⣿⠀⠀⠀⠀⠈⠓⠒⠒⠚⠁⠀⠀⠀⠀⠈⠒⠶⠶⠒⠁⠀⠀⠀⠀⠈⠒⠛⠋⠒⠁⠀⠀⠀⠀⠈⠒⠒⠒⠚⠁
⣿⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⣿⠀⠀⠀⠀⡜⠡⡄⢠⠌⢳⠀⠀⠀⠀⡔⢩⡄⢤⠉⢢⠀⠀⠀⠀⡔⢡⡄⢠⡌⢢⠀⠀⠀⠀⡜⠡⠄⢠⠌⢣
⣿⠀⠀⠀⠀⡇⢀⣤⣤⡀⢸⠀⠀⠀⠀⡇⠰⢶⣶⡄⢸⠀⠀⠀⠀⡇⠀⣰⣆⠀⢸⠀⠀⠀⠀⡇⢐⣶⣶⡄⢸
⣿⠀⠀⠀⠀⠘⠢⠤⠤⠔⠃⠀⠀⠀⠀⠙⠤⠬⠭⠥⠊⠀⠀⠀⠀⠙⠦⠥⠬⠴⠃⠀⠀⠀⠀⠘⠦⠬⠭⠴⠃
⣿
⣿⠀⠀⠀⠀⡰⢋⡉⢉⡙⢦⠀⠀⠀⠀⡰⢊⡉⢉⡑⢄⠀⠀⠀⠀⡰⢊⡉⢉⡑⢆⠀⠀⠀⠀⡴⢪⡍⢩⡑⢆
⣿⠀⠀⠀⠀⡇⣀⢁⡈⣀⢸⠀⠀⠀⠀⡇⢀⣥⣬⡀⢸⠀⠀⠀⠀⡇⣀⡁⢈⣀⢸⠀⠀⠀⠀⡇⣴⠶⠶⣦⢸
⣿⠀⠀⠀⠀⠑⢌⣉⣉⡡⠎⠀⠀⠀⠀⠳⣜⣋⣉⣣⠎⠀⠀⠀⠀⠱⢌⣉⣉⡡⠎⠀⠀⠀⠀⠱⢍⣛⣋⡡⠎
⣿
⣿⠀⠀⠀⠀⣠⠒⡒⢒⠒⢄⠀⠀⠀⠀⢠⠔⡒⢒⠢⡄⠀⠀⠀⠀⢠⠖⡒⢒⠲⡄⠀⠀⠀⠀⣠⠖⠒⠒⠲⡄
⣿⠀⠀⠀⠀⡇⢈⡁⣈⠁⢸⠀⠀⠀⠀⡇⢈⣁⣈⡅⢸⠀⠀⠀⠀⡇⢈⣥⣩⡁⢸⠀⠀⠀⠀⡇⠘⠃⢘⡁⢸
⣿⠀⠀⠀⠀⠣⣈⠛⠙⣃⠜⠀⠀⠀⠀⢣⡰⠛⠛⢆⡜⠀⠀⠀⠀⢣⡘⠚⠛⢃⡜⠀⠀⠀⠀⠣⡀⠀⠈⢁⠜
⣿⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⣿⠀⠀⠀⠀⢀⠤⠶⠶⠤⡀⠀⠀⠀⠀⢀⡤⠤⠤⢄⡀⠀⠀⠀⠀⢀⠤⠤⠤⠤⡀⠀⠀⠀⠀⢀⠤⠤⠤⠤⡀
⣿⠀⠀⠀⠀⡇⠀⠃⠘⠃⢸⠀⠀⠀⠀⡎⠰⠆⠰⠆⢱⠀⠀⠀⠀⡏⢐⠃⠘⡂⢹⠀⠀⠀⠀⡇⠐⠆⠰⠂⢹
⣿⠀⠀⠀⠀⢇⠘⠛⠲⠆⡸⠀⠀⠀⠀⢇⠰⠶⠶⠆⡸⠀⠀⠀⠀⢇⠸⠿⠿⠇⡸⠀⠀⠀⠀⢇⠒⠛⠓⠂⡸
⣿⠀⠀⠀⠀⠀⠉⠚⠓⠉⠀⠀⠀⠀⠀⠈⠑⠒⠒⠊⠁⠀⠀⠀⠀⠀⠙⠒⠒⠉⠀⠀⠀⠀⠀⠀⠉⠓⠒⠋
⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠐⠚⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⣤⢠⡄⢀⠊⠀⠐⠦⡀⡆⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣈⠉⠙⠓⠶⠦⣤⣄⣀
⠀⠀⠀⠀⠤⠀⠀⠛⡀⢠⠇⠀⠀⠂⠂⠼⠇⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⠀⠀⠀⠁⠀⠈⠉⠙⠓⠲⠶⢤⣄⣀⡉⠉⠛⠒⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠱⢤⠀⠀⠀⠀⠀⠀⠀⠀⢹⠳⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠶⠤⠤
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⡠⠁⠀⠐⠂⠀⠀⠀⠀⠒⠀⠀⠀⠀⠱⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⡠⢤
⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢸⡤⣤⢀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⡈⠛⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠋⠔⠁⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠢
⠈⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃
⠀⠐⠀⢹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡂⠀⠀⠀⠀⠠⠀⡀⠀⠀⠓⠐⠁⠀⠀⠀⠀⠀⠒⡌⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⣴⠟⢻⣧⢀⣼⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠙⠷⠾⣿⡾⠃⢠⡞⢻⡗⣴⠟⠷⣰⠟⣿⠇⣺⠟⢃⡾⢠⡞⢻⡆⣸⠟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠈⠟⠁⠀⠘⠛⠛⠓⠙⠓⠒⠛⠛⠛⠒⠛⠓⠘⠓⠚⠛⠛⠑⠋⠘⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠄⠄⠠⠄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡤⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠁⠠⡂⠀⠀⣀⠊⠀⠈⠛⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢠⠁⠀⠁⠀⠀⠇⠓⠠⠄⠠
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⢠⡤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠦⠀⠀⠰⠀⠀⠀⠒⠀⢤⡄
⠀⠀⠀⠀⠀⣀⣉⡂⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠟⠀⠀⠉⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠀⠈⠇
⠀⠀⠀⠘⠿⠟⠛⠃⠐⠿⡷⠆⠀⠀⠁⠀⠀⡀⠀⠀⠀⢀⠀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃
⠀⠀⣴⣶⣄⡀⠀⠀⢀⣠⣶⣦⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠀⢀
⠀⠀⠈⠛⠿⠋⠀⠀⠈⠿⠟⠁⠠⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠸⣿⠟⠃⣠⣈
⠀⠀⠐⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠘⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠲⢠⡶⠀⡰⠠⡀⠀⠀⠠⠼⠁⠀⠀⠀⠀⠆⠀⠀⠀⠀⠻⠿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⡀⢸⠀⠀⠀⠀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠉⠀⠐⠚⠁⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢠⠃⠀⠠⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⣀⡤⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠒⠦⢤⡀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠶⠦⠤⣀
⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⣠⠊⢁⠀⠀⠀⠀⠀⡀⠙⢆
⠀⡼⠀⠀⣀⠀⠀⠀⠀⢀⠀⠀⠹⡀⠀⡎⠀⠐⣦⣀⣀⣀⣀⣴⡂⠀⢹⡀⢰⠃⠀⢀⡑⠄⠀⠠⢞⣁⠀⠈⣇
⠀⡇⢠⠀⠛⠀⠀⠀⠀⠛⠃⢠⠀⡇⢸⡇⠀⠈⠋⠀⠀⠀⠀⠙⠁⠀⢈⡇⢾⠀⠀⠙⠃⠀⠀⠀⠈⠋⠀⠀⢸
⠀⢧⠘⣆⠀⠀⠀⠀⠀⠀⢠⠏⢰⠃⠀⢧⠀⠀⠀⠤⠤⠤⠤⠄⠀⠀⣸⠁⠸⡄⠀⠀⢀⣀⣀⣀⣀⠀⠀⢀⡏
⠀⠈⢣⡈⣷⡤⣄⣀⡤⠔⢋⡰⠋⠀⠀⠈⠣⣀⠀⠀⠀⠀⠀⠀⣀⠜⠁⠀⠀⠙⢄⡀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠈⠛⠦⠤⠤⠴⠒⠋⠀⠀⠀⠀⠀⠀⠈⠙⠒⠶⠶⠒⠋⠁⠀⠀⠀⠀⠀⠀⠉⠒⠶⠤⠶⠒⠋
⠀⠀⠀⢀⡤⠴⠒⠒⠲⠤⣄⠀⠀⠀⠀⠀⠀⢀⡠⠤⠶⠲⠦⢄⡀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⣄⡀
⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⢀⠔⠉⠳⠤⢤⡤⠴⠚⠉⠢⡀⠀⠀⢠⠞⠉⠀⠀⠀⠀⠀⠈⠳⣄
⠀⡞⠀⠀⣉⠉⠀⠀⠉⣉⡁⠀⠸⡄⢀⡎⠀⠀⣀⠀⠀⠀⠀⣀⠀⠀⢱⡀⢰⠃⠀⠐⠒⠀⠀⠀⠒⡂⠀⠘⡆
⠀⡇⠀⠀⠉⠀⠀⠀⠀⠉⠁⠀⠀⡇⢸⡅⠀⠈⠋⠀⠀⠀⠀⠙⠁⠀⢈⡇⣾⠀⠀⠙⠃⠀⠀⠀⠘⠛⠀⠀⢹
⠀⢣⠀⠀⠀⣤⣤⣤⣤⡀⠀⠀⣰⠃⢾⣇⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⣸⡷⢸⡀⠀⠀⢀⣀⣤⣄⡀⠀⠀⠀⡞
⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⠀⠈⠣⡀⠀⠉⠙⠋⠉⠀⢀⠔⠁⠀⠀⠳⣄⠀⠉⠀⠀⠀⠉⠀⣠⠞
⠀⠀⠀⠀⠉⠓⠒⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠈⠑⠲⠦⠴⠖⠊⠁⠀⠀⠀⠀⠀⠈⠑⠢⠤⠤⠤⠴⠚⠁
⠀⠀⠀⣠⠔⠚⠋⠉⠓⠲⢤⡀⠀⠀⠀⠀⠀⢀⡤⠴⠒⠒⠦⢤⡀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠶⠦⢤⣀
⠀⢠⠞⢀⣠⠀⠀⠀⠐⠲⠄⠙⣆⠀⠀⢀⡖⠁⢀⠀⠀⠀⠤⢤⡈⠳⡀⠀⠀⣠⠞⠁⡀⠀⠀⢀⣀⣨⠑⢄
⠀⡏⠀⠉⣤⠀⠀⠀⠀⣤⡄⠀⠘⡆⠀⡏⠀⠚⣁⠀⠀⠀⠀⣀⡀⠀⢹⡀⢰⠃⠐⢋⡁⠀⠀⠀⢀⡀⠀⠈⣇
⠀⡇⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⡇⢸⡇⢰⠈⠋⠀⠀⠀⠀⠙⠁⣴⢈⡇⣾⠀⠀⠙⠃⠀⠀⠀⠈⠋⠀⠀⢸
⠀⢳⡀⠀⠙⠦⣀⣀⣀⡤⠀⠀⡼⠁⠀⢧⠘⢦⠀⠀⠀⠀⠀⠀⣰⠃⣸⠁⠸⡀⠀⠀⠤⠤⣄⣀⠀⠀⠀⢀⡏
⠀⠀⠙⢦⣀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠈⠣⣀⠙⠲⠤⠤⠴⠚⣁⠜⠁⠀⠀⠙⢄⠀⠀⠀⠀⠈⠁⠀⣠⠞
⠀⠀⠀⠀⠈⠉⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠲⠶⠒⠋⠁⠀⠀⠀⠀⠀⠀⠙⠒⠦⠤⠴⠒⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠒⠂⠀⠉⠉⠉⠉⠉⠁⠀⠐⠂⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣆⠀⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣶⠄⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⣴⡆⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⢠⠒⠒⢄⠸⠀⠀⠀⡀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠇⠀⠀⠀⠀⠀⣀⠤⡀⠀⠀⠸⢀⠔⠒⢢
⠀⠀⠀⠈⠢⣀⠀⠈⠣⣀⠘⡄⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⠃⠀⠀⠀⢀⠔⠀⠀⡜⢀⡠⠋⠀⠀⡠⠊
⡈⠁⠉⠒⠤⢀⠑⠤⡀⠀⠑⠌⡒⢄⠀⠑⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⢀⠆⠀⠀⡠⠔⠁⢀⠔⡈⠔⠁⠀⡠⠔⢁⠠⠐⠊⠁⠉
⠈⠀⠀⠀⡀⠀⠈⠁⠚⠶⠀⠀⠈⠉⠀⠀⠀⠈⢢⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⡠⠔⠁⢀⠔⠁⠀⢠⠊⠀⠀⠀⠈⠉⠀⠀⠰⠞⠂⠉⠀⠀⡀⠄⠐⠊
⡎⠀⠀⠀⠐⠋⠶⠦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠈⠙⠭⠀⣀⣁⣈⡁⠠⠄⠊⠁⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⠎⠓⠀⠈⠉⠈
⠈⠁⠀⠒⠂⠠⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠤⠀⠒⠂⠀⠉
⠀⠀⠀⢌⠉⠉⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⢉⡀
⠀⠀⠀⠀⠀⠉⠁⠀⠒⠠⢄⡀⠀⠀⠀⠀⢀⡠⠃⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠣⣀⠀⠀⠀⠀⠀⣀⠤⠐⠂⠀⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣭⣭⣤⣤⣤⣤⣤⣬⣭⣴⣶⣤⣤⣤⣤⣤⣴⣦⣬⣥⣤⣤⣤⣤⣤⣤⣭⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣉⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢠⠖⠋⠉⠙⠲⣄⠀⠀⠀⠀⢀⠔⠋⠉⠉⠓⢤⠀⠀⠀⠀⠀⣠⠖⠋⠉⠙⠲⣄⠀⠀⠀⠀⠀⡴⠚⠉⠉⠑⠢
⡇⠐⡃⠀⠀⣃⠈⡆⠀⠀⠀⡞⠀⢓⣀⣤⣛⠀⡇⠀⠀⠀⠀⡇⠐⣃⠀⢐⡂⠘⡆⠀⠀⠀⢸⠁⠨⠗⠀⠫⢀
⠳⣄⠉⠉⠉⢁⡴⠁⠀⠀⠀⠘⢄⡉⠀⠀⠈⡠⠃⠀⠀⠀⠀⠣⣀⠈⠉⠉⢀⡼⠁⠀⠀⠀⠈⢦⣻⠶⠒⠊⣁
⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣤⣄⠻⡧⠀⠀⠀⠀⣀⣀
⣠⠊⠉⠀⠉⠑⢦⠀⠀⠀⠀⢠⣞⣉⡁⣈⣙⣦⡀⠀⠀⠀⠀⡰⠋⠉⠀⠉⠑⢎⠓⠀⠀⠀⢀⣔⣉⣁⣈⣉⣳
⡇⢠⣍⣀⡬⣥⠌⡇⠀⠀⠀⢎⠙⠿⢃⢙⠿⠁⡇⠀⠀⠀⠀⡇⠐⠒⠀⠐⠂⠈⡇⠀⠀⠀⢸⢿⣿⣿⠻⣿⣿
⠑⢄⣓⠦⠔⣋⠜⠁⠀⠀⠀⠘⠦⣀⡈⠁⣀⡴⠃⠀⠀⠀⠀⠑⢄⣘⠒⢀⣀⠜⠀⠀⠀⠀⠀⠣⣍⣀⠖⢋⡠
⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⣉⣩⠷
⢠⠞⠉⠉⠉⠒⢄⠀⠀⠀⠀⢀⠔⡫⠉⠉⠗⢦⡀⠀⠀⠀⠀⣠⠞⠉⠉⠉⠒⢄⠀⠀⠀⠀⠀⡴⠊⠉⠉⠙⠢
⡇⠈⠓⠀⠚⠋⠈⡆⠀⠀⠀⣞⠀⠶⠀⠰⠚⠀⡇⠀⠀⠀⠀⡇⠀⠒⠀⠐⡂⠈⡆⠀⠀⠀⢸⠀⢐⠃⠀⠚
⠱⣄⡀⠋⠉⢀⡴⠁⠀⠀⠀⠘⢄⡀⠪⠝⢀⡠⠃⠀⠀⠀⠀⠳⣄⠐⠉⠁⢛⡼⠁⠀⠀⠀⠈⠢⣀⠑⠒⠀⣠
⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢠⣄
⢀⠔⠚⠛⠓⠢⣄⠀⠀⠀⠀⢀⡴⠚⠛⠓⠲⢄⠀⠀⠀⠀⠸⣸⠖⠚⠛⠓⠺⣼⠀⠀⠀⠀⠀⡠⠖⢟⡛⠒⢤
⡏⢰⣖⡆⢔⣗⠌⡆⠀⠀⠀⡜⠀⠒⠀⠀⠒⠈⡇⠀⠀⠀⠀⡇⠐⠶⠀⠴⢂⡘⡄⠀⠀⠀⢰⠁⠲⠆⠹⣿⣦
⠣⡀⠩⢶⠶⠀⡰⠃⠀⠀⠀⠸⣄⠀⠀⠻⠻⣧⠇⠀⠀⠀⠀⠣⡘⢍⣉⣉⠏⡰⠁⠀⠀⠀⠈⢆⡀⠤⣀⠤⢂
⠀⠈⠁⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠈⠁⠚⠓⠉⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠊⠁

⠀⠀⠀⢰⣶⢲⣶⣦⣶⣶⢲⡖⣶⣴⣖⣴⣶⣴⣶⡶⣶⡆⠀⣶⣶⣶⡀⣴⣆⣶⣲⣶⣴⠀⠰⠶⠖⢶⡆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠠⠤⢀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠤⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⢤⠀⠠⢄⠱⡀⠀⠀⠀⠀⢠⠋⡭⡀⢀⢤⠑⡄⠀⠀⠀⠀⢀⠊⡠⠀⠀⡤⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠉⣀⡀⠁⠀⡇⠀⠀⠀⠀⢂⠀⠉⢀⡀⠁⠀⡁⠀⠀⠀⠀⠀⠀⠀⣠⣠⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠛⠃⢀⠔⠀⠀⠀⠀⠀⠈⠦⡀⠘⠃⢀⡴⠁⠀⠀⠀⠀⠀⠢⡈⠚⠙⠚⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠂⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠐⢰⠒⢒⡐⠒⡆⠀⠀⠀⠀⠀⠠⠁⠐⠂⠀⠆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠄⠀⠀⠀⠀⢀⠀⢉⠁⠈⠉⠀⠀⠀⠀⠀⠀⠠⠀⢀⠤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⣀⣀⡀⠔⠁


⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠉⠉⠐⢄⠀⠀⠀⠀⠀⠀⡄⠂⠉⠉⠑⢀⠀⠀⠀⠀⠀⠀⡠⢂⠉⠉⢁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠻⠀⠸⠣⠀⠆⠀⠀⠀⠀⠈⠐⠤⠂⠐⠤⠂⠁⠀⠀⠀⠀⠰⠀⠸⠆⠀⠿⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⣠⠐⢢⡀⢀⠃⠀⠀⠀⠀⠠⡀⠀⢔⡢⠀⢀⠄⠀⠀⠀⠀⠘⡀⠰⢶⣦⠶⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠤⠠⠐⠁⠀⠀⠀⠀⠀⠀⠁⠂⠠⠄⠐⠈⠀⠀⠀⠀⠀⠀⠈⠂⠀⠄⠄⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢈⣀⠀⣀⣈⢠⠀⠀⠀⠀⠀⢀⠀⡁⠀⠀⢌⠀⡀⠀⠀⠀⠀⠀⡐⣉⠀⠀⢈⡑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠦⠴⠼⠤⠼⠼⠤⠇⠀⠀⠀⠀⠀⠐⠒⠂⠐⠒⠂⠀⠀⠀⠀⠀⠰⡘⠤⠅⠐⠥⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠠⠂⠰⠄⢀⠂⠀⠀⠀⠀⠀⠡⡀⢤⡠⠄⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠐⠉

⠀⠀⠀⠀⠀⠀⢐⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⡐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠶⠶⠶⠶⢤⣄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⣀⣠⣄⣀⣀⡀⠈⠙⣦⠡⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⡇
⠀⠀⠀⠀⠀⠀⠐⠀⢀⠄⡀⠀⢂⣠⣠⣤⣐⣲⣤⣤⣤⣤⣀⣀⣘⣷⣿⢉⣀⠀⠈⠩⠙⣳⣶⠋⠄⢂⣠⣤⠒⣠⣐⡠⠠⠀⠄⣒⣄⣂⢠⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢐⠪⣢⠶⠶⠶⠿⠛⣫⣩⠟⠛⣲⣶⡿⠟⠉⠉⠭⠿⠿⠍⠩⠭⠭⠿⠿⠿⠿⣿⡿⠟⠓⣲⡮⠽⠟⢛⣛⣛⣛⠛⠫⢉⢳⡄
⠀⠀⠀⠀⠀⠀⢈⠰⣿⡀⡀⢀⡠⠞⠁⠀⠀⢸⡏⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢸⡏⠀⠀⢎⠀⠀⠀⡀⠈⡆⣯⠀⡗⠀⡄
⠀⠀⠀⠀⠀⠀⠠⠁⣿⠀⡴⠁⠀⠀⠀⠇⠀⠘⢣⠀⠀⠀⢈⡄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠘⡇⠀⢀⠀⠙⢆⡒⠋⠀⢷⡇⢰⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠰⡅⢻⠜⠁⠀⠀⠀⠀⠛⠛⠛⡟⠀⠀⠀⢀⠈⠁⠁⡰⠖⠀⢀⠀⠀⠀⠀⠀⠟⠉⠉⢺⡇⠀⠀⠀⠀⠀⠙⢄⣀⡜⣇⠀⣧⠀⡇
⠀⠀⠀⠀⠀⠀⠐⠠⢺⠀⡀⠂⠁⠂⠘⡀⠀⡠⠇⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠘⢄⠀⡠⠛⠑⠀⠀⠀⠀⠠⡐⠦⠀⠇⢻⠀⣿⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠂⣿⠀⠁⠀⠀⠀⠀⢸⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠐⡝⠀⠀⠀⢸⠀⣿⠀⡄
⠀⠀⠀⠀⠀⠀⢠⡀⣿⠀⠀⠁⣤⠆⠀⣼⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠒⠚⠈⠀⠀⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠸⠁⣿⠀⠀⠈⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⡀⠀⠀⣿⠠⠁
⠀⠀⠀⠀⠀⠀⢸⠀⣿⠀⠄⠠⠤⠄⡀⢨⠀⠀⠀⠀⠄⡀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢨⡀⠙⠊⠀⠂⠄⡀⡇⠀⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠸⠀⣿⠀⠁⠀⠀⠂⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡇⠀⠀⠀⠁⠅⣁⣀⠌⠙⢺⠃⠃⡆⠀⡟⠀⡇
⠀⠀⠀⠀⠀⠀⢸⠀⢸⣄⠀⠀⠀⠠⡀⢸⠀⠀⢠⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠆⠀⠀⠀⠰⠇⠀⠀⠓⠠⠀⠈⠁⠒⢿⠆⢀⠀⡇⢸⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠸⠁⣯⠀⠣⡀⠀⣠⠶⢸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡀⠠⠀⠀⠀⡀⠀⠀⡀⠀⢡⠀⠀⠀⠀⢀⢸⠀⡇⠈⡇⠀⠁
⠀⠀⠀⠀⠀⠀⢸⡀⣿⢀⣰⠈⢦⡀⠀⠸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⣠⡄⢣⡘⠆⠄⠈⡇⠀⠀⡇⢀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⡇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠻⠶⠶⠶⣶⡿⠶⠶⣤⢤⣼⠷⠤⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡏⠀⠀⠀⡠⠂⢐⡦⠀⣠⣿⡶⠇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠰⠻⠁⠦⠄⠐⠒⠂⠉⠀⠘⠆⠠⠁⠀⠈⠉⠉⠉⠩⠉⠙⠛⠛⠛⠛⠙⠉⠝⠓⠲⠶⠟⠛⠓⠿⠤⣤⣤⣤⡼⠋⠂⠈⠗⠀⡇
⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠤⠀⠀⠠⠬⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⢀⠂⠀⠀⠀⠈⠠⠀⠀⠠⠈⣀⠀⢀⡈⠂⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⡀⠱⠀⠀⠠⠄⠀⠀⠀⠔⣁⠀⠀⢀⡑⠀⠀⠀⠄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⡙⠀⠀⢃⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠃⠀⠘⡀⠀⠀⠀⠰⣏⣷⣶⠶⣿⠀⠀⠀⠠⠀⠀⠀⢀⠀⠀⠀⠐⠀⢘⣁⣀⡙⠀⡀
⠀⠀⠂⢙⠙⠉⡋⠀⠀⠀⠀⠌⠒⠠⢐⠊⠨⠀⠀⠀⠌⡋⠩⢙⠡⠂⠀⠀⠰⠍⠁⠀⠀⠠⠒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⠙⠛⠁⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⡠⠀⠀⠀⠀⣀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⡀⠀⠀⢀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⢸⠉⣭⡹⢏⣍⢙⡇⠀⠀⠀⠒⠀⠐⠀⠀⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⡄⠀⠀⠀⠁⠐⠀⠂⠀⠈⠂
⠀⠘⡉⠍⠀⠈⠉⠉⠁⠀⠀⡀⠒⠒⠶⠄⡐⠀⠀⠀⠀⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠢⣤⣤⠴⢀⠂
⠀⠀⠈⠀⠀⠀⠊⠀⠀⠀⠀⠈⠐⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠁⠀⠀⠀⠀⣷⠶⠶⢾⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡈⠄⠐⠀⠀⠀⣬⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠠⠀⠒⡀⢐⠂⠁⠀⢠⡤⠀⡤⠀⠠⠄⠠⣄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡀⠀⢀⠀⠀⠀⠀⠈⢂⡀⡀⣐
⠀⢀⠀⠀⠁⠈⠀⠀⠀⠸⣇⢠⠀⠀⠀⢠⢀⡿⠀⠀⠀⠀⣀⠀⣀⠀⠀⠀⠀⠀⢁⠤⡈⠀⠀⠀⠀⡀⠈⠁⠀⠉⡄⠀⠀⠀⡀⠎⠁⠁⠑⡆⡀
⠀⠀⠠⠈⠛⠋⠠⠂⠀⠀⠈⠠⠉⠀⠈⠡⠊⠀⠀⠀⠀⡈⠉⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⡠⠌⠀⠀⠀⠙⢄⠈⠉⠀⠋

⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠐⠚⠠⡄⠀⠀⠀⠂⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⡀⠠⠀⠀⠀⠀⠈⠀⠀⠀⠂
⠀⠈⠀⠶⠀⠀⠆⠀⠀⠀⠀⠀⠠⠀⠠⠀⠈⠀⠀⠄⠀⠀⠒⠀⠀⢀⠀⠀⠀⠀⠒⠀⠒⡀⠀⠀⠀⠐⠿⠟⠘⠿⠗⠀⠀⠀⠀⠿⠀⠀⠻⠂⠁
⠀⠀⠄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠂⠒⠀⠐⠀⠀⠀⡀⠠⠤⠄⠀⠌⠀⠀⠠⠀⠶⠒⠾⢁⠀⠀⠀⠂⠀⠒⠓⠖⠢⠀⠀⠀⢀⠐⠀⠀⠂⠠⠁
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡁⠀⠀⠀⠀⠀⠁
⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠰⣊⠁⠀⠨⣑⠀⠀⠀⠰⣩⠀⠀⢨⣱⠀⠀⠀⠂⠄⠐⠀⠠⡔⠂
⠀⠀⠁⣀⠀⢀⡀⠀⠀⠀⠀⠀⡤⠀⢠⡄⠀⠀⠀⢶⣷⣶⡶⣶⣶⣷⠀⠀⠈⢀⡈⠉⢁⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠁⢐⠀⠀⣀⠈
⠀⠠⠀⡉⣀⡀⣁⠀⠀⠀⠀⠀⠛⢀⠘⠃⢀⠀⠀⠀⠉⠉⢀⠈⠉⢠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀⠘⢁⣀⠙⠀⠀⠀⠀⠀⣌⣁⣀⣡⠀⠄
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠁⠀⠀⠀⠀⠠⠈⠀⠂⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠁⠀⠊⠀⠀⠀⠀⠀⠉⠉⠁⠊
⠀⠐⡀⠀⢀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀
⠀⠈⠃⡤⠀⠀⠤⠢⡤⠁⠀⠀⠀⠀⠀⢀⢀⠶⠄⠀⠀⠀⠀⠀⠁⢀⠀⠀⡀⠀⡠⠂⣄⠁⠀⠀⠀⡰⠿⢿⣿⠿⠷⡀⠀⢀⡰⡁⠀⠀⢈⠆⡘
⠀⠈⢴⣄⣀⣀⣼⡇⠀⠀⠀⠀⠀⠀⠀⡄⢠⡶⠀⠀⠐⠂⠀⠀⠂⠀⠀⠀⠀⠀⠄⠛⠠⠀⠀⠀⠀⠀⢤⠀⡁⠠⠄⠀⠀⠀⡀⠉⡀⢀⠈⠀⡁
⠀⠀⠚⠦⠄⠠⠖⠁⠀⠀⠀⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠠⠀⠀⠀⠱⣶⣿⣿⣷⡶⠃⠀⠀⠱⣙⠂⠀⢛⠔
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⡠⠔⠊⠉⠉⠉⠁⢒⣤⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢀⣀⠀⢠⣎⣀⠀⠀⠀⠀⢀⠔⠉⠀⢛⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⡄⠀⢝⠂⠀⠀⠈⠙⢲⡀⢠⠀⠀⠀⠀⢸⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢟⡉⠉⠋⠀⠀⠀⠀⠀⠀⢱⣇⣀⡀⠀⠀⠀⡇⠀⠀⠆⠀⠀⠀⠀⠀⢀⠀⡀⡰⣖⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣠⠀⠀⠀⠀⠆⡄⠀⠀⠀⠀⠀⣸⠋⠑⢄⠀⡇⢀⠀⡾⠀⠀⠀⠀⠀⠀⠠⣀⡳⠜⠀⡏⢀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠈⢀⡀⠀⠀⠀⣰⠃⠀⠀⠈⠷⠋⡠⠈⠴⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣴⢁⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢀⢤⠠⠒⣓⡄⢠⢀⠤⢡⠒⠢⢴⠃⠀⡠⠀⢀⡠⠊⡱⠷⢆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠈⠖⢥⠀⠀⢠⠃⠀⠀⠀⠑⡏⣀⠴⢋⠔⠙⠦⠤⠊⢀⡀⠀⠀⠀⢀⠔⢲⡤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢽⡖⠨⡷⠔⠂⠄⠀⠀⡾⠀⠀⠀⢀⣠⢼⡥⢚⡁⠄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠸⡠⠎⢳⣀⣠⠗⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠃⠠⡀⠔⠀⠐⢦⣀⣇⠀⡠⠞⠉⠀⢀⡟⡉⢁⡀⠀⠀⠒⠀⠀⠀⠢⡀
⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢀⡿⠀⠄⠉⠋⠀⠑⠀⡇⠀⣏⠀⠀⠀⠀⣼⠁⡀⠄⠩⡒⠀⠒⠆⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣠⠒
⠀⢀⡗⡁⠀⠀⠀⣀⣂⣀⣃⣤⣼⢥⣿⣿⣱⠁⣠⣨⣁⡖⡀⣉⣞⣀⣑⣤⡠⠾⠷⠏⠘⠚⣢⠈⠂⠀⢄⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣳⡜⢻⡄
⠀⡌⠁⠁⢠⠀⣀⡤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⠙⡖⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠉⠀⠉⠂
⠀⡃⠀⠘⢰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠇
⠀⠿⠲⢶⠃⠀⠀⣠⠔⠒⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡏
⡴⠛⠈⠚⠲⡀⢸⠁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠄⠀⠀⣠⣇⣀
⡇⠀⠀⠀⠀⡇⠀⠀⢠⠁⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠀⡆⡴⠁⠀⠀⠈⡷⠀⠀⠀⠀⠀⢈⠀⠀⠃
⠘⠠⠄⣀⠴⣧⠃⠀⠘⢀⡀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠠⠀⡠⠀⢁⢧⠀⠀⠀⡰⠃⠰⠄⠉⢹⡂⠘⠆⠁⢀
⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠙⡤⠤⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⠄⠀⠀⠀⠀⠀⠈⡏⠍⠉⣉⢱⠀⡔⠀⠀⠠⠂⠀⠄
⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⣀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠈⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠈⠉⠈⠛⠁⠉⠋⢹⠙⠋⠈⠙⠉⠉⠁⠀⠀⢸⣿⣿⣿⣷⣾⣷⣴⣿⣶⣴⣶⣦⣾⣷⣦⣾⣷⣿⣿⣿
⠀⠀⠀⠀⢠⣦⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠙⢿⣧⣿⢿⣦⣄⣬⡴⠶⢦⣄⣀⠀⠀⠀⠀⢸⣿⣿⣿⣦⡉⠉⢠⣈⠉⠻⠟⣋⣉⣛⠿⢿⣿⣿⣿⣿
⠀⠀⢀⣀⣞⣀⣉⣛⣾⣭⣵⣞⣛⣛⣾⣯⡀⠀⠀⠀⢸⣿⣿⣿⠿⢱⠿⡶⣬⠑⠒⠋⣡⢶⣬⡉⠚⢿⣿⣿⣿
⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⢸⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠁⠀⠉⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⢀⡰⡄⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⡠⠤⠖⠉⠀⠠⠜⢤⡘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠸⣅⠈⠁⢠⠀⠈⠁⣰⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠘⣄⠀⠠⠄⠀⣠⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠋⠀⢗⠂⠐⡿⠀⠙⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠀⠀⠄⣡⣌⠀⠀⠀⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⡴⣹⡠⠊⠉⠉⠙⠉⠉⠉⠑⠄⠏⢆⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠗⠂⢄⠀⢀⡼⠥⠛⠂⠄⡀⠀⠀⠀⠀⢀⠠⠒⠚⠬⢧⡀⠀⠠⠐⠺⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠑⢢⡠⠒⠁⠀⠀⠀⠀⠀⠀⠁⠉⠉⠈⠀⠀⠀⠀⠀⠀⠀⠒⢄⡔⠈⠙⢆
⠀⠀⠀⠀⠀⠀⠀⢰⡑⡐⣠⢠⠁⠈⠒⠒⠒⠒⠒⠒⠒⠂⢤⠄⠒⠒⠂⠒⠒⠒⠒⠒⠁⠈⡄⣄⢂⢪⡆
⠀⠀⠀⠀⠀⠀⠀⠈⢧⣇⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠖⠂⠁⠢⢄⠀⠀⠀⠀⠘⠁⣼⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣇⣀⣀⣀⣀⣈⣐⣤⣀⣀⠤⠔⠁



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

⠀⠀⠀⠀⡠⠒⠂⠐⠢⢄⠀⠀⠀⣀⠔⠒⠀⠒⠤⡀⠀⠀⢀⠤⠒⠀⠒⠢⣄⠀⠀⠀⣠⠔⠂⠐⠒⢄⡀⠀⠀⢀⠤⠒⠀⠒⠢⡀
⠀⠀⠀⠎⠀⠀⠙⠃⢀⠀⢃⠀⠰⠁⠐⠂⠀⠐⠂⠐⡀⠀⠎⠀⠀⠒⠂⠀⠈⠆⠀⠰⠁⠀⠀⠆⠆⠀⠱⠀⢀⠊⠀⠀⠤⡄⠀⠈⠆
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡸⠀⢠⠀⠀⠀⠀⠀⠀⢀⠃⠈⡀⠀⠀⠠⠀⠀⠀⡀⠀⢃⠀⢦⣀⣀⣠⡟⢀⠃⠰⡀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠘⢄⡀⠀⠀⣀⠔⠁⠀⠈⠢⣀⠀⠀⢀⡠⠊⠀⠀⠑⢄⡀⠀⠀⣀⠔⠁⠀⠈⠢⣀⠁⠀⢉⡠⠊⠀⠀⠑⢄⡀⠀⠀⣀⠜
⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⣀⠤⠒⠂⠤⡀⠀⠀⠀⢀⡠⠀⠒⠠⢄⠀⠀⠀⠀⣠⠄⠒⠂⠤⡀⠀⠀⠀⢀⠤⠐⠒⠠⣀⠀⠀⠀⠀⡠⠄⠒⠢⢄⡀
⠀⠀⠀⡜⠁⠀⠄⠠⠀⠈⠆⠀⢠⠃⠀⣄⠀⣀⠀⠱⠀⠀⠌⠀⠀⠴⠆⠀⠈⡆⠀⢰⠁⠀⠠⠦⠀⠀⠣⠀⢀⠎⠀⠀⠀⡀⠀⠘⡄
⠀⠀⠀⡅⠸⣦⣤⣤⣼⠂⠸⠀⢀⠀⠀⠀⠀⠀⠀⠀⠇⠐⠀⢾⣿⣿⣿⣿⠇⡀⠀⠇⠰⡤⢀⣠⠄⡴⠀⠃⢸⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠑⢄⠈⠐⠈⠁⡠⠃⠀⠈⢦⡀⠀⠀⠀⢀⠜⠀⠀⠱⣀⠉⠙⠋⢁⡰⠁⠀⠈⢄⡀⠀⠀⠀⣠⠎⠀⠀⠣⡀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁
⠀⠀⠀⠀⡠⠐⠒⠒⠢⢄⠀⠀⠀⢀⠔⠒⠒⠒⢤⡀⠀⠀⢀⡠⠒⠒⠒⠢⡀⠀⠀⠀⣀⠔⠒⠒⠒⢄⠀⠀⠀⢀⡤⠒⠒⠒⠠⡀
⠀⠀⠀⡎⠀⠀⠀⠀⠀⠈⢂⠀⠰⠁⠀⠀⣤⠀⠀⠑⡀⠀⠎⠀⠀⣠⡀⠀⠈⠆⠀⠰⠁⠀⢀⣀⠀⠀⠱⠀⢀⠊⠀⠀⣀⡀⠀⠈⡆
⠀⠀⠀⡄⠀⠀⠘⠂⠀⠀⡸⠀⢠⠀⣰⡾⠿⢷⡄⢀⠇⠈⡀⢠⡄⠀⠀⢠⡄⡀⠀⢃⠀⠀⠈⠉⠀⠀⢀⠃⠰⡀⠀⠀⢠⡄⠀⠀⡄
⠀⠀⠀⠘⢄⡀⠀⠀⢀⠴⠁⠀⠈⠢⣀⠀⠀⢀⡠⠊⠀⠀⠑⢄⡀⠀⠀⣀⠔⠁⠀⠈⠢⣀⠀⠀⢀⡠⠊⠀⠀⠑⢄⡀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⣀⠤⠐⠀⠤⡀⠀⠀⠀⢀⡠⠄⠒⠠⢄⠀⠀⠀⠀⡠⠤⠐⠢⠤⡀⠀⠀⠀⢀⠠⠄⠂⠤⣀⠀⠀⠀⠀⡠⠄⠐⠠⢄⡀
⠀⠀⠀⡜⠀⠀⣠⡄⠀⠈⢆⠀⢠⠋⠀⠀⠀⠀⠀⠱⠀⠀⠎⠀⠀⠤⠀⠀⠈⡄⠀⠰⠁⡄⠀⠶⠆⢈⡳⠀⢀⠎⠀⠀⠲⠆⠀⠘⡄
⠀⠀⠀⡄⠰⣀⡀⣀⣠⡆⠸⠀⢀⠀⠀⠀⠛⠀⠀⠀⠇⠀⠀⣴⣶⣿⣿⣿⡆⡀⠀⢃⠀⣿⣿⣿⣿⣶⢀⠇⢨⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠑⢄⠉⠁⠘⠉⡠⠃⠀⠈⢦⡀⠀⠀⠀⣀⠜⠀⠀⠱⣈⠋⠉⠙⢋⡰⠁⠀⠈⢄⡀⠀⠙⠛⣡⠎⠀⠀⠣⣀⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠉⠐⠀⠁⠀⠀⠀⠀⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠈⠉⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠠⡀⠀⠄⠀⠀⠀⣼⡏⢤⡧⢸⣷⠀⠀⠀⢀⠄⡀⠀⠀⠀⠀⠀⠉⠷⠛⠇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠈⡀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢈⠋⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀
⠀⠀⠒⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠐⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠞⠁⠚⠑⠈⠲⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠙⠿⠟

⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡴⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠘⠋⠋⠀⠀⠀⠞⠉⠩⠌⠀⠀⠀⠀⠀⣠⣴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠱⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⣤⠴⣤⡁⠂⢄⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠁⠀⡤⢾⣦⡰⡟⠻⡉⠉⠙⢦⢌⠢⡈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡕⠁⠈⠁⠈⠛⠒⣻⢏⠎⣂⢰⠀⠀⣼⠀⠑⡈⢂⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠒⡄⠀⠀⠀⠀⠎⢀⠇⠯⡀⠘⠔⠁⠀⠀⠀⠈⡄⢂⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡔⠀⠀⠀⠀⠀⠉⠀⠖⠺⠀⠀⠀⠀⠀⠸⣮⠿⡀⡀⢠
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠆⢀⠀⠀⢄⠀⠀⢀⣀⣀⠌⠀⠀⠀⠀⠀⠀⠀⠀⢐⠵⠾⡇⠁
⠀⠀⠀⠀⡀⠨⠰⠉⠉⠉⣷⠨⠀⡀⠈⠓⢄⣇⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⡄⡀⢀
⠀⠀⠀⠎⠇⠀⠀⠀⠀⠀⠀⠀⠀⡉⡄⠀⠀⠀⠙⠶⠒⠂⠀⢀⠀⠀⠀⠀⠀⠑⠂⢲⢁⠁⠈
⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⡀⢀⠀⠁⠀⠀⠀⠀⠠⡀⠀⠀⠀⡄⠵⠤⠤⠤⠤⠤⡧⠾⠴⠓⠲⢟⣚⡛⢍⠉⠙⠛⠛⢋⠆
⠀⠀⢰⠀⠘⠠⡷⠀⠀⠀⠰⡧⠈⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡏⠈⢻⡆⠂⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠘⣄⡀⠀⠀⠀⠀⠀⠄⠁⠰⢢⢀⠀⠀⠀⠀⠰⠀⠀⡠⢄⠙⠒⠚⠁⠃⠀⠀⠀⠀⡔
⠀⠀⡄⠀⡠⠐⠒⠒⠒⠒⠒⠒⠠⠀⠀⡷⢤⡁⡐⠂⠀⠒⠀⠒⣘⡜⡠⠀⠡⠄⠀⠬⠅⠀⠀⠈⢆⠀⠀⠠⠀⠀⠀⠀⠀⡠⠂
⣆⠀⠀⠀⠃⠤⠤⠤⠤⠤⠤⠤⠄⡆⠀⠂⢀⠧⠀⢀⡀⠀⠀⡀⠠⠖⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⢀⠦⠀⡖⠐⠀⠂⠈⠀⠠
⡇⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠰⠠⠀⣠⠑⠶⣷⣴⡀⠀⠀⠀⠀⠀⡔
⠣⣘⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢈⡠⠂⠐⠒⠓⠒⠒⠓⠒⠀⢀⠀⠀⠀⠀⠀⢀⡤⠊⠈⠁⠐⠃⠀⡀
⣀⣈⣄⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣄⣌⣀⣀⣁⣀⣀⣀⣀⣀⣈⣀⣎⣶⣶⣶⣦⣬⣤⣦⣤⣖⣒⣒⣚⣉⣉⣉⣉⣉⣉⣉⣉
⣿⣿⣋⢛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⠀⠀⠀⡠⠀⠀⠐⠄⠀⠀⠀⠀⠂⠀⠀⠂
⠀⡤⢊⠄⠀⠀⠀⡀⠠⠀⠀⠀⡡
⠀⠄⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⢀⠰⡄⠀⡆⠄
⠀⠠⠀⠀⠀⠀⠀⠈⠘⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠤⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠒⠒⠒⠒⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀

⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢰⣿⣿⣿⣿⣿⡇⡄⠀⢀⣶⣿⣿⣿⣿⣿
⠀⠀⢹⣿⣿⣿⣿⣿⣷⠁⠀⠀⢿⣿⣿⣿⣿⣿⡾
⠀⠀⠀⠙⠿⠿⠿⠛⠁⠀⠀⠀⠈⠛⠿⠿⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡾⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠿⠟⠃⠢⡤⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⡀
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⡯⣽⣛⣛⣛⣛⣛⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⢆⣀⣀
⣿⣿⣿⣿⣿⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢤⠂
⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⣿⣿⣿⡿⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⡆⠀⠀⠀⠀⠀⠀⢀⠀⠒⠀⠀⠀⠀⠀⠀⠀⡄⠘⠁
⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⢇⠀⡇⠀⠃⠘⠢⡁⢸⠀⠀⡇⠀⢣⢰⠀⠀⠂⣿⠀⢸⢰⡀⠀⠁⠀⠀⠀⠀⠀⢀
⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠈⠀⠈⠀⠁⠈⠁⠀⠉⠀⠁⠀⠀⠈⠀⠈⠀⠁⠀⠀⠀⠀⠀⢀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⠀⢀⡀⠀⡀⠀⠀⠀⡀⢉⠀⡁⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣨⠀⢈⡆⠀⣧⠸⡀⠀⠇⢸⠀⡇⢈⠑⡄⠀⠀⢀⣠⡀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⠀⠀⠀⢿⣿
⠀⠀⠀⠀⢰⣬⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⢸⣿
⠀⢠⡀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿

⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⠈⣙⢿⣾⣿⣿⣿⣶
⣿⣟⣴⡏⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢒⣿⣿⣿⣿⣿⣿⢿
⣿⣿⣿⡷⣿⡿⢶⣿⣷⣿⣿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠿⠀⠁⡀⠰⣿⣍⢛⢿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢱⡿⢿⣿⣿⣿⣿⣿⣿
⣿⣯⠀⠀⠀⠈⠆⠙⠿⠿⠤⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⡠⠿⠛⠛⢻⡿⣿
⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⠀⠀⠀⠀⠀⠀⠀⡄⢠⣄⠀⡴⢠⡄⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⠃⠀⠀⠒⠂⠚⠉⠁⠂⢀⣿⣿⡆⠀⡏⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠠⠤⠶⠒⢂⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⢸⣆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⣀⣠⠤⠤⠤⠆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠚⠻⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠈⢀⠀⡠⠤⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣀⣀⠈⣭⣿⣥⣤⠀⣀
⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠈⠍⠉⠛⠂⠙⠉⠉⠀⠠⠡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠀⠀⢤⣤⣰⣾⠃

⠀⠀⣀⡀⠀⢀⣄⡀⠀⠀⠀⣀⣀⠀⢀⣤⡀⠀⠀⠀⢀⣀⠀⢀⣠⡀⠀⠀⠀⢀⣀⠀⠀⣀⣀⠀⠀⠀⠀⣀⡀⠀⣀⣄
⠀⠸⢿⠿⠀⠻⠿⠃⠀⠀⠀⠿⡿⠀⠸⠿⠏⠀⠀⠀⠻⠿⠃⠘⠿⠏⠀⠀⠀⠻⣿⠇⠀⠿⠿⠀⠀⠀⠸⣿⠗⠀⠻⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠒⠈⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠂⡈⠄⠀⠀⠀⠀⠀⠀⠀⣀

⠀⢠⣶⣦⠀⣴⣿⡆⠀⠀⠀⣴⣦⠀⢰⣶⣦⠀⠀⠀⣴⣶⡄⢠⣾⣦⠀⠀⠀⣴⣶⡄⠀⣾⣷⠀⠀⠀⢠⣶⣄⠀⣴⣶⡄
⠀⠀⠙⠉⠀⠈⠉⠀⠀⠀⠀⠙⠋⠀⠈⠉⠁⠀⠀⠀⠙⠋⠀⠀⠉⠁⠀⠀⠀⠈⠋⠁⠀⠉⠉⠀⠀⠀⠈⠛⠃⠀⣉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⣀
⠀⢰⣿⣷⠀⢾⣿⠇⠀⠀⠀⣾⣷⠀⢸⣿⡷⠀⠀⠀⢿⡿⠂⠸⠿⠗⠀⠀⠀⢴⣿⡆⠠⣿⣿⠀⠀⠀⠸⣿⠗⠀⠿⡿⠃
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈
⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠺⠆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠲⠶⠆⠀⠀⠀⠀⠀⠀⢠⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⢀⣠⣀⠀⣠⣤⡀⠀⠀⠀⣠⣄⠀⢠⣤⣄⠀⠀⠀⢀⣀⠀⢀⣤⣄⠀⠀⠀⢠⣤⡀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠘⠿⠟⠀⠙⠿⠃⠀⠀⠀⠻⠟⠀⠘⠛⠋⠀⠀⠀⠿⠿⠃⠘⠿⠟⠀⠀⠀⠹⠿⠃⠀⠛⠛⠀⠀⠀⢸⣿⡗⠀⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠖

⠀⢀⣤⣄⠀⣠⣦⡄⠀⠀⠀⣾⣶⠀⢰⣿⡆⠀⠀⠀⣠⣄⠀⢀⣤⣄⠀⠀⠀⣠⣤⡀⠀⣤⣤⠀⠀⠀⢀⣤⡄⠀⣤⣦⡀
⠀⠘⠻⠛⠀⠙⠛⠁⠀⠀⠀⠉⠁⠀⠀⠉⠀⠀⠀⠀⠻⠿⠃⠈⠻⠛⠀⠀⠀⠙⠿⠃⠀⠛⠛⠀⠀⠀⠘⠿⠋⠀⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠠⠀⠀⠀⠀⠄⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠁⠀⠁⠀⠀⡁⠀⠀⢀⠀⠀⠈⠀⢈⠀⠀⠀⠠⣤⣤⣤⡄⠀⠀⠀⠀⢠⣤⣤⡄
⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠂⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠐⠉⠀⠉⠀⠀⠀⠀⠀⠀⠉⠉⠐

⠀⠀⠀⠀⠄⠂⠐⠠⡀⠀⠀⠀⡠⠀⠀⠂⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⡀⠀⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⢀⠀⠂⠐⠠
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠐⠀⠀⠀⠀⠀⠿⠿⠓⠿⠿⠂⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠜⠻⠿⠃⠂⠀⠀⠀⠠⢀⠀⡀⠀⠀⠀⠀⠐⢁⡀⢀⠐⠁⠀⠀⠈⠀⡀⢀⡀⠂⠀⠀⠀⠀⢀⠀⡀⠐⠀⠀⠀⠐⠄⡀⢀⠠

⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠢⠤⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠂⠀⢀⠀⠀⠂⠀⠀⠐⠀⠄⠀⠀⠐⠀⠀⠀⠀⠶⠂⠶⠈⠀⠀⠀⠈⠀⠂⠀⠀⠁
⠀⠀⠀⠀⠘⠿⠿⠃⠀⠀⠀⠀⠄⠀⠶⠀⠀⠀⠀⠀⠢⠙⠛⠛⠡⠁⠀⠀⠀⠔⠁⠀⠁⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠰⠂⠀⠀⠦⡀⠀⠀⣀⠆
⠀⠀⠀⠀⣰⣀⣀⣆⠀⠀⠀⠀⠁⠀⠄⠀⠁⠀⠀⠀⠈⠀⠀⠀⠈⠄⠀⠀⠠⠁⡀⢀⡀⠡⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⢀⠀⠃
⠀⠀⠀⠠⡙⠋⠙⠋⠄⠀⠀⠀⠀⢴⣶⠦⠀⠀⠀⠀⢂⠀⠁⠀⢀⠂⠀⠀⠐⡰⣶⣶⡦⠐⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢄
⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠈⢀⠀⡀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠠⠀⠀⠀⠀⠂⠀⠀⠀⠄⣀⣤⣄⠐⠀⠀⠀⠐⠀⠀⡀
⠀⠀⠀⢀⠀⠀⠀⠄⡀⠀⠀⠀⡀⠀⠠⠀⠀⠀⠀⠀⢄⠀⠠⠀⠀⠄⠀⠀⠠⠠⣤⣤⡤⠠⠀⠀⠀⠄⡿⠛⢿⢀⠀⠀⠀⢀⠀⠀⠀⠁
⠀⠀⠀⠀⠑⠀⠀⠂⠀⠀⠀⠀⠈⠂⠀⠂⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠁⠂⠀⠂⠀⠀⠀⠀⠈⠀⠉⠀⠁⠀⠀⠀⠀⠁⠂⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠂⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡄⠁⠀⠀⠑⡄⠀⠀⢀⠀⠀⠈⠀⢀⠀⠀⠀⠀⣀⡀⣁⠀⠀⠀⠀⠀⢈⢀⣀⡀
⠀⠀⠀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⡠⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠁⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠈

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠤⡤⠒⠒⠒⠒⠂⠐⡖⠐⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠁⠀⡇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⠖⠂⢩⠶⠿⠙⠉⠀⠀⠘⠟⠛⠙⠉⠀⠒⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡘⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠂⢂⡀⡄⠈⠀⠤⠤⢤⡤⠤⠤⣤⢤⡀⡆⠈⠀⣉⠁⠐⠂⠳⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢁⡄⠀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠑⠈⠀⠰⢀⠀⠉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢀⣀⠀⠀⠀⠀⠀⠀⢠⠖⠀⡠⠀⠀⠀⠃⠈⠀⠉⠈⠀⠘⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠊⠀⠁⠀⠀⢀⠠⠓⠖⠁⡀⠉⠀⠀⠀⠀⠀⢀⡀⠤⢀⡤⠶⡶⢿⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠠⠊⠀⠀⠀⠀⢀⠄⠈⠀⣠⠞⠁⠀⠂⠀⠀⠀⠙⢦⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠃⠀⠀⠀⠀⡰⠁⠀⠀⡜⠁⠀⠀⠌⠀⠀⠀⠈⠀⠀⢣⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠠⠂⠀⡀⠀⠁⠀⠀⠀⠀⢀⠀⠀⠀⠑⠂⠀⠘⠀⠀⠀⠰⠄⢀⣀⡀⣀⠀⠀⠀⡇⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠰⢷⡴⠻⡿⠿⠦⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⠐⠦⠤⠀⣀⣀⠁⠀⠀⠈⠁⠐⠃⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⢳⠼⣦⡀⣿⠉⢹⣿⠗⠀⠢⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠏⠘⣡⠆⠀⠀⠉⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢀⣈⠙⠉⠘⣿⣷⣼⡋⠈⠋⢀⠀⠀⠀⠀⠀⢇⠀⠀⠀⡤⠀⠀⠀⠀⠀⢀⠇⠀⡾⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠰⠀⠙⠶⠶⠶⠛⠿⠿⠷⠦⢀⠀⠁⡀⠀⠀⣤⠀⠑⠀⠞⡈⠀⠀⠀⡀⠀⢘⡄⣪⠃⡜⠁⢙⠃⢆⠅
⠀⠀⠀⠀⠀⠀⠀⠰⠀⠂⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢠⣌⣉⡀⢈⠀⠀⠈⠀⠀⠀⠀⠑⡄⢋⠜⢁⡞⠁⡠⢞⡴⠁
⠀⠀⠀⠀⠀⠀⢀⠂⠐⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⠀⠁⠀⠀⠀⠀⠐⠶⣀⠀⢞⣐⡭⠞⢟⣤⠞⠁⠘
⠀⠀⠀⠀⠀⠀⠈⠀⠃⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢀⠂⠀⠀⠀⠀⡀⠠⢼⢝⠳⢯⡐⠦⣞⣪⠦
⠀⠀⠀⠀⠀⠀⠐⢀⡃⠐⠀⢲⡎⠉⠉⣶⡎⠉⠙⣦⣀⣤⣤⣤⣤⣤⠧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡬⠑⠂⠈⠓⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠙⠒⠊⠉⠙⠒⠺⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠀⠀⠀⠀⠀⠁


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

⠀⠀⠀⡠⠒⠀⠐⢦⡀⠀⠀⢀⠔⠂⠀⠒⢄⠀⠀⠀⢠⠔⠂⠐⠢⡄⠀⠀⠀⡠⠒⠀⠐⠢⡀⠀⠀⢀⡴⠒⠀⠒⢤
⠀⠀⢸⠀⠒⠀⠐⠂⢡⠀⠀⡎⠐⠂⠀⠒⠀⡇⠀⠀⠃⠒⠀⠀⠒⠘⠀⠀⢸⠀⠒⠀⠐⠂⢱⠀⠀⡌⠐⠋⠀⠑⠀⡇
⠀⠀⠘⢄⠢⠤⠔⣠⠂⠀⠀⠱⡀⠒⠐⠢⡠⠁⠀⠀⢣⡠⠤⠔⢃⠜⠀⠀⠘⢄⠫⢉⠩⢃⠎⠀⠀⠐⣄⠊⠉⠑⡠⠃
⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠈⠉⠈⠉⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠉⠀⠉⠁⠀⠀⠀⠀⠀⠉⠀⠉
⠀⠀⠀⢀⠤⠤⠤⡀⠀⠀⠀⠀⣀⠤⠤⢄⡀⠀⠀⠀⠀⡠⠤⠤⢄⠀⠀⠀⠀⢀⡠⠤⠤⣀⠀⠀⠀⠀⢀⠤⠤⠤⡀
⠀⠀⢰⠁⡄⠀⢠⠌⢆⠀⠀⡜⠑⡄⠀⡴⡘⡄⠀⠀⡎⢠⠀⠀⠄⠱⠀⠀⢠⠃⣄⠀⢀⡌⢣⠀⠀⠰⢡⡤⠀⢤⠌⡆
⠀⠀⠸⡀⠠⠤⠄⠀⡌⠀⠀⢃⠀⠤⠤⠄⢋⠇⠀⠀⡆⠀⠀⢀⡄⢰⠀⠀⠸⡀⢠⠒⣠⠀⡘⠀⠀⢡⠠⡤⠤⢤⢄⡆
⠀⠀⠀⠙⠢⠤⠔⠊⠀⠀⠀⠀⠑⠢⠤⠐⠁⠀⠀⠀⠈⠒⠬⠥⠒⠁⠀⠀⠀⠈⠂⠤⠔⠊⠀⠀⠀⠀⠑⠪⠭⠕⠊
⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⢀⠞⡁⠀⢈⠑⡄⠀⠀⠠⢊⡁⠀⢈⠢⡀⠀⠀⡔⢉⡀⢀⡉⢢⠀⠀⢀⠔⠁⠀⠈⡑⠄⠀⠀⢠⠪⡁⠀⣈⠵⡀
⠀⠀⢸⠀⠁⣀⠈⠁⡐⠀⠀⡇⠈⢁⠀⠉⠀⡇⠀⠠⣳⢀⣀⣀⡀⣞⠄⠀⢸⠀⠋⠀⠈⠃⢸⠀⠀⢆⠀⡩⠤⣉⠀⡅
⠀⠀⠈⠢⣀⣉⣀⠔⠁⠀⠀⠘⠮⣉⣉⡩⠜⠀⠀⠀⠑⢌⣒⣐⡡⠊⠀⠀⠀⠳⢍⣉⣉⠵⠃⠀⠀⠈⠢⣣⣤⣮⠔⠁

⠀⠀⠀⡠⠒⠀⠒⢤⡀⠀⠀⢀⠔⠒⠐⠒⢄⠀⠀⠀⢠⠔⠂⠐⠢⡄⠀⠀⠀⡠⠒⠂⠒⠢⡀⠀⠀⠀⡤⠒⠀⠒⢄
⠀⠀⢸⠐⠖⠀⠐⠂⢁⠀⠀⣎⣄⠃⠀⢃⣄⡆⠀⠀⠃⠘⢀⢀⣁⠸⠀⠀⢰⠀⠒⠀⠐⠂⢱⠀⠀⡌⠐⠏⠀⠱⠀⡇
⠀⠀⠘⣄⠀⠄⠄⣠⠆⠀⠀⠹⡉⠐⠒⠈⡹⠃⠀⠀⢣⡀⠘⠙⢊⡜⠀⠀⠘⢄⠑⢶⠖⢁⠎⠀⠀⠰⣌⠫⠭⠝⣠⠃
⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠈⠁⠂⠉⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⠀⠀⠀⠈⠁⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⡶⠿⠿⠿⠿⠿⠿⠿⠿⢶⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠛⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠙⠻⣦⡀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⢀⣠⣴⠶⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠺⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⢀⣾⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠋⠉⠉⠙⠻⢶⡀⠀⠀⣤⣾⠿⠛⠛⠛⠻⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷
⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⣾⠟⠁⠀⠀⠀⠀⠀⠀⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧
⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡄⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⣀⠀⠀⣀⣠⣶⡿⠁⠀⠙⢦⣄⡀⠀⠀⣀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⠀⢹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⢸⡿⠀⠀⠀⡄⠀⠈⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏
⠀⠀⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢷⣶⣶⠾⠃⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿
⠀⠀⠈⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⡟⠁
⠀⠀⠀⠀⠻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟
⠀⠀⠀⠀⠀⠘⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⡀⠀⢀⣀⣤⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣷⣶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣄⠄⠠⠠⠀⠀⠠⠄⠄⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢾⡆⣾⣿⣴⣿⢀⡀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠀⠀⢀⡀⣿⣦⣿⣷⢸⡷⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣷⡹⠟⣼⣫⠟⠁⠀⠀⠈⠻⣿⣯⣽⣿⠟⠀⠀⠀⠈⢿⣝⣧⠻⢏⣿⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⢀⣠⣤⣤⣤⣭⣭⣤⣤⣤⣄⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⠀⠀⠀⣠⣜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣣⣄⠀⠀⠀⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣿⣷⣾⣿⣿⠗⠁⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠸⣿⣿⣶⣾⣿⣿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠟⠃⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠻⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣶⣦⣌⣛⠿⢿⣿⣿⡿⠿⣛⣡⣴⣶⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⣥⣚⠿⢿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣮⢻⣿⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣝⡻⠿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠒⠉⠙⠛⠿⠿⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠈⠠

⠀⠀⠀⠀⣄⠀⢀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠤⠀⠀⠀⠀⠀⢀⠔⡒⠒⠢⣀⠀⠀⠀⠀⠀⣠⠶⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⣤⡿⠓⠿⡶⠂⠀⠀⢲⣾⡶⠋⠀⠁⠅⡶⠛⠁⠀⢰⢇⡀⠇⠸⠂⣈⡆⠀⢠⣴⣯⠤⠒⣰⠖⠂⢗⣄⡀⠀⢀⣰⡿⣿⢛⠛⡶⢄
⠀⠀⠀⣴⢯⣠⣸⠷⠄⠀⠀⠀⠣⣝⠒⠰⠒⢉⠔⠀⠀⠀⠸⡄⢻⡶⠤⡾⢁⠇⠀⠀⠈⢦⡙⠛⠤⠄⠒⡡⠊⠀⠀⠀⠀⠐⠠⠤⠊⢴⠈⠁
⠀⠀⠀⠀⠘⠁⠘⠃⠀⠀⠀⠀⠀⠈⠙⠛⠛⠁⠀⠀⠀⠀⠀⠈⠲⠥⡥⠖⠃⠀⠀⠀⠀⠀⠉⠳⠶⠶⠊⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⡀
⠀⠀⢰⣦⡀⠱⢇⢀⣼⠇⠀⠀⣴⠋⣤⢠⡌⠳⡄⠀⣀⣀⡤⠒⠙⠓⠒⠒⠒⢦⡄⠀⠀⠀⢀⡴⠒⠒⠢⣄⠀⠀⠀⠄⢤⣼⠉⠀⠘⢲⠔
⠀⠀⠀⠹⡝⠃⠘⠋⡟⠀⠀⢸⡇⢳⣄⣀⣰⡇⣿⠀⠀⢉⠑⠶⢶⣀⣄⣰⡤⠖⠛⠋⠀⠀⡏⠘⠃⠐⠃⠘⡆⠀⠀⠀⠀⢸⣛⠣⠛⡯
⠀⠀⠀⠀⠻⠶⠶⠶⠃⠀⠀⠀⠳⣈⠋⠀⢇⡰⠃⠀⠀⠀⠳⣤⡀⠀⠀⠀⣀⠴⠁⠀⠀⠀⢣⡰⠋⠉⠳⡰⠁⠀⠀⠀⣤⠚⡉⠲⠶⠋⠢⣩⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠉⠓⠛⠋⠁⠀⠀⠀⠀⠀⠀⠉⠛⠚⠋⠀⠀⠀⠀⠀⠈⠒
⠀⠀⠀⠀⠀⢠⠶⣆⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄
⠀⠀⠀⠲⣶⠛⠀⠈⣩⠟⠀⠀⢀⣞⣁⠀⠈⠙⢲⠀⠀⠀⢀⡔⠛⡆⢘⠓⢦⠀⠀⠀⠀⢀⣀⣴⠓⠢⠒⠒⣄⡀⠀⠀⠀⠀⠀⡏⠉⠁⣿
⠀⠀⠀⠀⢸⣇⡴⢦⣼⡄⠀⠀⠘⠮⠍⠡⠙⣻⣫⠃⠀⠀⢸⠐⣮⠁⣈⡠⣸⠀⠀⢤⣖⠉⠀⢹⡄⠀⠀⢀⡏⠀⣤⡄⠀⠀⣠⣧⠀⢰⡟
⠀⠀⠀⠀⠘⠉⠀⠀⠈⠁⠀⠀⠀⠐⠦⣤⠴⠁⠀⠀⠀⠀⠈⠣⣌⣷⣤⡅⠁⠀⠀⠀⠉⠉⠁⠉⠙⢦⡠⠊⠈⠉⠁⠀⠀⠀⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⣠⠔⠚⠉⠉⠉⠒⢄⠀⠀⠀⢀⡠⠐⠂⠀⠐⠒⠤⡀⠀⠀⠀⠀⣠⠔⠒⠒⠒⠦⡀⠀⠀⠀⠀⣠⠖⠉⠉⠉⠓⠦⡀
⡐⠁⠀⠀⠀⠀⢀⡀⠀⢣⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢀⠞⠁⠀⠀⠀⠀⣀⠈⢦⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠘⢦
⡇⠀⠙⠀⠀⠀⠈⢁⠀⢸⠀⡇⠀⠀⠀⠆⠐⠇⠀⣠⠀⢰⠀⠸⠀⠘⠃⠀⠀⠈⠉⠀⠈⡇⠀⡇⠠⡄⢀⡀⢠⡄⢹⠀⢸
⢣⠈⠢⣀⠀⠀⣀⠞⠀⡜⠀⢣⠐⢇⠠⣀⣄⣠⠤⠜⠀⡄⠀⢸⡀⢲⣖⣖⣺⣹⣭⡟⢀⡇⠀⢣⠀⠳⣈⠁⠀⣠⠞⠀⡸
⠀⠳⢄⡀⠉⠉⢀⡠⠞⠀⠀⠀⠳⢄⠀⠀⠀⠀⠀⣀⠜⠀⠀⠀⠑⢄⡉⠛⠚⠒⢁⣠⠎⠀⠀⠀⠳⢄⣈⠉⢉⣁⡠⠞⠁
⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⢀⡤⠒⠒⠛⠒⠢⣄⠀⠀⠀⠀⢀⡤⠖⠒⠒⠶⢄⡀⠀⠀⠀⠀⣀⠤⠒⠒⠒⠦⣀⠀⠀⠀⠀⢀⡠⠖⠒⠚⠒⢦⡀
⢠⠋⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠱⡄⠀⢀⠞⠁⠀⠀⢀⠀⠀⠈⢣⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠙⣆
⡇⡀⠀⠈⠁⠈⠁⠀⠠⠈⡆⢸⠁⠀⠶⠀⠀⠘⠓⠀⠀⣷⠀⡘⠀⠀⠀⠁⠀⠀⡤⡀⠀⡇⠀⡇⠀⣠⡀⠀⠀⢀⣀⠀⢸
⢇⢣⠀⠀⠀⠀⠀⠀⣰⢡⠁⢸⡀⢤⣔⣒⣒⣒⢦⠟⢀⡏⠀⢱⠀⢀⢔⣚⠉⠉⠉⠂⠀⡇⠀⢇⠀⠈⢡⠔⢤⠈⠁⠀⡜
⠈⠢⣙⠢⠤⠤⠤⣚⠵⠃⠀⠀⠳⣄⠙⠢⠤⠒⠁⣠⠞⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠈⠢⣀⠀⠀⠀⢀⡠⠞
⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⢀⡤⠒⠚⠓⠒⠦⣄⠀⠀⠀⠀⢀⡠⠖⠚⠛⠒⢤⡀⠀⠀⠀⢀⡤⠒⠚⠛⠒⠦⡀⠀⠀⠀⠀⢀⡤⠖⠚⠛⠒⠦⣄
⢠⠋⠀⠀⠀⠀⢀⠀⠈⢳⡀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠙⡄⠀⢠⠋⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠱
⡇⠀⠨⠛⠀⠐⠻⠀⠀⠀⡇⠀⡇⠀⡤⠢⠈⠀⠔⠄⠀⣷⠀⣾⠀⠀⠁⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⠐⠀⢀⣀
⢧⠀⠐⠒⠒⠒⢶⡲⠂⢀⠇⠀⣇⠀⠀⠀⢰⡦⠀⠀⢀⡏⠀⠸⡀⠀⠀⠀⣀⡀⠀⠀⡸⠀⠀⢇⠀⠒⡖⢾⠉⠉⠉
⠈⠳⢄⡀⠀⠀⠀⣀⡴⠋⠀⠀⠈⢦⡀⠀⠀⠀⢀⡠⠞⠀⠀⠀⠑⢄⡀⠋⠀⠈⣠⠔⠁⠀⠀⠈⠳⣄⡙⠋⠀⠀⣀⡤⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣉⣸⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡓⢀⡐⠈⠏⠀⠀⠀⠀⠀⡀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠋⡰⠁⠀⠀⠀⢀⠘⢝⣂⢴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣷⣶⠂⠍⠀⣵⣀⠀⠀⠀⠈⠿⠁⠀⠂⢙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⠚⢀⣼⣿⣿⣿⣦⣄⣠⠂⠣⡈⡴⠑⢄⡠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⡇⣠⣿⣿⣿⣿⣿⣿⣿⠀⡀⢄⠔⠥⠂⠰⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠉⠑⠢⡀⣴⣿⡿⠁⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⡿⢠⠀⠀⠂⠀⠀⠹⠤⣺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠺⠟⣿⡀⠘⡟⡿⠁⢀⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁⣐⠀⠈⠶⢤⠢⡀⠀⠆⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⠀⢸⠇⠤⡉⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠉⠓⢁⣀⣘⡆⠀⠘⢀⠜⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠙⠀⠀⠉⠚⠠⠟⠀⠀⠟⠛⠉⠘⣿⣿⣿⣿⣿⡷⠀⠀⠀⠎⠉⢹⣿⡖⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⢂⠀⠁⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛⠉⢁⠀⠀⠆⠀⢠⣤⠀⠀⡻⢃⠆⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢀⠔⠁⠄⠁⠀⠀⠀⠈⠀⠀⢢⠀⡇⠀⣠⠀⠀⢀⠠⡀⠈⡄⠀⢦⠀⠀⠐⠶⠔⠁⠸⠀⠀⠀⣸⠋
⠀⠀⠀⠀⠀⠀⢊⠠⠀⠀⠂⢠⠀⠀⠀⠀⠀⢈⢢⠁⠞⠁⠀⢀⠌⠀⢳⡀⠀⠀⠀⠇⠀⡌⢀⠐⠀⢀⡄⠀⢠⣃⣠
⠀⠀⣀⣤⣤⣤⠃⠀⢠⣼⣀⠇⠀⠀⠀⢀⠀⣮⡜⠀⠀⠀⠀⡌⠀⠀⠀⠱⡄⢀⡀⣀⠐⠀⣰⠀⠀⢀⢙⣈⢉⣴⠟
⠀⠘⠻⠿⠿⣧⣤⣶⣿⣿⣿⠀⠒⣻⣿⠁⢀⣿⡇⠀⠀⠀⣼⣿⣷⣦⡀⠀⣈⠃⡈⠀⡤⠊⠑⢄⣀⣤⣾⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⢠⣿⣷⠀⢾⣿⡇⠀⠀⢰⣿⣿⣿⣟⡁⠀⠀⠀⠀⠂⠋⡆⢠⠞⠛⢿⣿⣿⡿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠈⠻⢷⣾⠛⠇⠀⢀⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠘⠴⠃⠘⠀⣠⠂⠈⡁⠀⠣⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠢⣄⠒⣾⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠐⠁⢀⠀⠈⠲⢤⠀⠡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠥⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢘⡁⠰⠃⡡⠄⠀⠀⠀⠀⠑⣄⡈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⣱⠀⠤⠄⠁⠀⠀⠀⠀⠀⠏⠠⠃

⠀⠀⣠⠔⠚⠉⠉⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠉⠉⠓⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠋⠉⠉⠓⠦⡀
⠀⡜⠁⠀⠀⠄⠀⠤⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠄⠀⠀⠀⠀⠀⠈⢦
⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠁⠀⠈⠈⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠰⠂⠀⠀⠲⠀⠀⠘
⢸⡀⠀⣆⠀⠀⠀⠀⠀⡟⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢆⠀⠁⠉⠉⠈⡿⠀⢰⠇⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⢳⡀⠈⠲⠤⠤⠴⠊⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠈⠓⠤⠤⠤⠚⠁⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠈⠉⠀⠀⠀⢠⠞
⠀⠀⠙⠲⢤⣤⣠⣤⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣤⣠⣤⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢤⣤⣀⣤⡤⠞⠉


⠀⠀⠀⢀⣠⣤⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢠⢤⣤⣀
⠀⣠⠚⠁⠀⠀⠀⠀⠈⠒⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠙⢦⡀
⣸⠁⠀⠀⡀⠀⠀⣠⠀⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠦⠀⠀⠰⠂⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⢘⠆⠀⠰⣂⠀⠀⢹
⡇⠀⠀⠐⠋⠀⠀⠙⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠘⠀⠀⠀⠈⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢉⠡⠤⠄⡁
⢻⡀⠀⠀⠀⠀⠂⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠒⠒⠤⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⡐⠁⠀⠀⠀⠈⢂⠀⣸
⠀⠳⣄⡀⠀⠀⠀⠀⢀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣉⠉⠉⠉⠉⠉⣁⡴⠃
⠀⠀⠈⠙⠓⠒⠒⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠒⠛⠉


⠀⠀⠀⢀⣠⠤⠤⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⢤⣀
⠀⢀⠞⠉⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⠑⢆
⢀⡏⠀⠀⠠⠀⠀⠀⠉⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠐⠀⠀⠀⠀⠐⠄⠀⢧⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠔⠀⠀⠀⠀⠀⠀⠈⡇
⢸⡀⠀⠀⠻⠀⠀⠀⠙⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠘⠟⠀⠀⠀⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠶⠜⠀⠀⠶⠆⠀⠀⣿
⠈⢧⠀⠀⠀⠠⠤⠠⢐⡂⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠐⠦⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠤⡀⠀⠀⢠⠇
⠀⠈⠳⣄⡑⠠⠤⠀⢊⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣀⠀⠀⠀⠀⣀⡴⠃
⣤⣤⣤⣤⣽⣿⣿⣿⣯⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣿⣿⣿⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣿⣿⣿⣿⣥⣤⣤⣤
⣿⣿⣤⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠰⡀⠀⠀⠁⠈⠁⠈⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣀⣄⣠⣶⣶⣷⣶⣶⣦⡀⠀⠀⠙⠒⠀⠂⠁⠤⣀⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣴⡿⠃⡀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠋⠀⠀⢿⠆⣤⢸⣿⣿⡿⣿⣿⣿⡟⠀⠀⠀⠀⣠⣰⣿⣤⡄⠀⠀⠀⠀⠘⣿⣿⣷⣶⡀
⢠⡶⠂⠀⠀⠀⠀⠀⠻⠃⡠⠀⢀⢀⣤⣤⣀⠀⢠⣿⣿⣵⣶⣾⣿⣿⣿⡀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣤⣣⠀⠀⠀⠉⠙⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡁⠉⠛⠛⠻⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢻⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢛⠉⠉⢰⣶⣶⣴⣶⣤⠀⣉⠋⠀⠀⠀⠀⠀⣤⡀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⣀⣴⣿⣿⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟⠛⢿⣿⣿⣿⡦⡤⢤⣀⡀⠀⠀⠀⢀⣸⣿⣶⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅
⠀⠀⠀⠀⠀⠒⠒⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠏⠉⠉⠉⠉⠉⠁⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠉⠉⠻⣿⣿⣇⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠈⠛⠿⣷⣦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣿⣸⠿⠋⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢂⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠁⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠴⢶⣦⣤⣄⡀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⠘⣧⣀⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠈⡙⠁⠀⢠⠀⣈⢙⠛⠿⣦⣄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⡀⠼⠞⠒⠐⠠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣚⡁⠀⠀⠠⠌⠐⢄⠈⠙⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠂⣀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣼⠀⠨⠀⠀⠉⠃⢤⡀⠈⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠋⠂⠀⠀⢆⡄⠀⢀⣈⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣋⣅⡼⠃⢠⠐⠃⠀⠀⢀⣿⡖⠁⠐⢠
⠀⠀⠀⠀⠀⠀⠀⠀⡁⣀⠗⡐⠀⠀⠀⠀⠘⠙⢢⢀⣄⠈⡄⠶⡀⠀⢀⠚⠁⠀⡀⠐⠀⠀⢀⣀⣤⡠⠛⢂⡀⠀⠚⠁⠀⠰⡖⠠⠦⠀⠀⣠⠜⢋⡿⠂
⠀⠀⠀⠀⠀⠀⢀⠆⠭⠀⠈⠀⠀⠠⠔⠀⠀⢁⣤⠾⠯⢤⡨⠀⠉⣵⡆⠀⠀⠘⠿⠂⣶⠠⠛⠁⠉⠀⠀⠀⢀⠀⠀⠀⠀⠀⠿⠃⠰⠀⡈⣥⠞⠋⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠘⠐⠀⠀⠀⠠⠎⠀⠀⠀⣰⢫⠁⠀⠀⠀⢹⠀⠀⠀⠈⢂⡀⠀⠐⠀⣀⠀⠀⠀⠀⠐⢀⠤⠀⡄⡀⡤⠀⠈⠠⢉⡀⠆⣀⠘⠠⠀⢠⡀⢠⠼⣍
⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⢀⠀⠠⣲⠶⡯⠀⠠⡄⣦⣄⣚⠤⠀⠀⠀⠀⠁⢠⠀⠀⠀⢡⠀⠀⢀⣀⢈⠱⠚⠁⠀⠀⢀⠀⠀⠰⠃⠀⠉⢎⣀⡊⣉⠁⠁
⠀⠀⢀⠄⠒⠒⣀⠉⠋⠀⠀⠔⠈⠁⣀⠄⡤⠄⠀⠈⠋⠤⢧⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⢠⠇⠸⠡⠀⠒⣃⠀⠃⠉⠀⠪⢀⠈⡀⠀⠀⢴⠶⠁⠀⠀⠆
⠀⣀⠛⠛⠋⠱⠚⠄⠀⠀⡠⠞⢹⠶⠋⠀⢀⣶⡆⠀⣴⣶⠇⠕⠀⠀⠀⠀⠀⠀⠀⠘⠌⠃⠈⠁⠉⠩⡑⠀⢀⠀⠀⠀⠈⠐⠀⠀⠀⠃
⢀⠀⣐⡀⠀⠀⠀⢰⡔⡀⠑⠠⢀⠦⡀⠀⠈⠉⠄⠀⢁⠘⠉⠐⠂⠀⠴⠤⣤⠦⠴⠂⠀⠀⠀⠀⠀⠀⠈⠂⢠⡑⢄⡀⠀⡹⠄⠀⠁⡠⠀⠀⠀⠀⢀⠌
⡔⠀⠀⡥⣀⣌⠉⠆⠀⠀⠀⠀⠀⠉⠈⠐⠠⡄⠀⠆⠁⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠠⣷⣶⣞⠒⣶⣯⣽⣖⣉⣭⡵⡆
⢐⠀⠐⠀⠀⠐⠂⠁⠀⠀⠀⠂⠀⢠⠀⠘⢟⠲⡦⢤⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠤⠤⠤⠀⠀⠀⠀⠉⠉⠁⠀⠻⣿⣯⢉⣫⣶⠶⡇
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠁⣠⠀⠈⠀⠐⠷⠔⠲⠤⣄⡀⠀⠀⡀⠀⠀⠀⠀⡠⠄⠉⠀⠀⣀⣠⣰⡞⠛⢂⠀⠀⠀⠀⠀⠀⠀⠿⡅⠂⠰⠚⠁
⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⣬⠡⠙⠙⢿⢙⠀⡀⠀⠀⠀⠀⠀⠀⠈⢳⣦⣤⡬⡷⡀⠠⡊⠀⠈⠿⣤⡤⠉⠀⣀⢠⡄⠀⠡⡀⠀⡀⠀⠀⠠⠈
⠀⠀⠀⠈⠀⡀⠀⠀⠀⠓⠬⣅⣀⣉⡭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢉⡚⠛⢋⡙⠠⡌⢣⠀⠀⠀⠀⠀⢀⡠⠅⢲⡤⠀⣄⠠⠄⠑
⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠀⠀⠙⠧⠘⠃⡀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢉⡀⠀⠁⢤⡄⢳⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣀⣄⣤⣄⣌⢠⠀⠩⠄⢰⠅⠈⢹⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣷⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣿⡿⣿⣿⣿⡋⠀⠀⠀⠀⠙⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠿⣿⣷⠄⠀⠙⠿⠇⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣀⣀⣀⡀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⠿⠿⠟⠛⠛⠛⠛⠛⠻⠿⠿⣿⣿⣿⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣄⣀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⣠⣿
⠀⠀⠀⠀⠀⢠⣾⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣀⠀⠀⠀⢀⣠⣾⣿⣷⣶⣶⣾⣿⠟
⠀⠀⠀⠀⣴⣿⠟⠁⠀⠀⠀⠠⣾⣿⣿⣿⣿⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⡿⠟⠋⠀⠈⠉⠉⠁
⠀⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠈⠉⠻⢿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠹⣿⣧⠀⠀⠀⢠⣶⣿⣿⣷⣦
⠀⢀⣾⡿⠁⠀⠀⠀⠀⣀⣴⣾⡿⠿⠿⠿⢿⣶⣄⡀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠘⣿⣧⠀⢠⣿⡟⠁⠀⠈⣿
⠀⣼⣿⠃⠀⠀⠀⠀⣴⣿⠟⢁⣠⣤⣄⡀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠈⣽⣿⠟⢉⣠⣤⣄⡀⠀⠉⢻⣿⣆⠀⠀⠀⠀⠹⣿⣇⠀⢿⣿⣤⣀⣴⣿
⢰⣿⡏⠀⠀⠀⠀⣸⣿⠃⢠⣿⡿⠛⢿⣿⠀⠀⠀⢹⣿⡀⠀⠀⠀⣸⣿⠇⠀⣿⡿⠛⢿⣿⠀⠀⠀⢹⣿⡆⠀⠀⠀⠀⢿⣿⡀⠀⠙⠛⠛⠛⠉
⣼⣿⠀⠀⠀⠀⠀⣿⣿⠀⠀⢿⣿⣶⣿⡟⠀⠀⠀⢸⣿⡇⠀⠀⠀⣿⣿⠀⠀⢿⣿⣶⣿⡟⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠸⣿⡇⠀⠀⢀⣤⣤⣄
⣿⣿⠀⠀⠀⠸⣿⣿⣿⣦⡀⠀⠈⠉⠁⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠸⣿⣇⠀⠀⠈⠉⠁⠀⠀⠀⣀⣼⣿⣿⡿⠆⠀⠀⠀⣿⣧⠀⢰⣿⡟⠛⣿
⣿⣿⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣤⡀⠀⠀⣀⣤⣾⡿⠁⠀⠀⠀⠀⠀⠙⣿⣷⣄⡀⠀⠀⢀⣴⣾⡿⠟⠉⠁⠀⠀⠀⠀⠀⣿⣿⠀⠈⢿⣷⣶⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠈⠉
⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠈⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿
⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃
⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⣶⣶⣶⣶⣶⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇
⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠻⠿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃
⠀⠀⠀⠀⠘⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡷⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⠀⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣆⡀
⠀⠀⠀⢀⡶⣄⡀⠀⣀⣴⣾⣿⡿⠛⠀⠀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠘⠿⣿⣿⣦⣄⠀⠀⣀⡴⡆
⠀⠀⢙⣺⣷⣿⢿⣿⣿⣟⣉⣁⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣉⣙⣿⣿⣿⢿⣷⣷⡊
⠀⠀⠀⠀⠈⠁⢾⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠆⠉
⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢛⣿⣿⣿⣿⣿⣟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠟⠁⠙⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠁⠀⠀⠀⠀⠻⠿⠿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣽⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠶⠶⠖⠛⠛⠛⠛⠛⠛⠛⠛⠲⠶⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠲⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠖⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⠛⠛⠛⠛⠶⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠛⠛⠛⠛⠛⠶⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠆⠀⠀⠀⠀⠀⠀⠰⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⠄⠀⠀⠀⠀⠀⠀⠀⠀⢿
⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿
⣿
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⢹⡇
⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⢀⣾⠃⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠶⣦⡀⠀⠀⢀⣼⠋⠀⠀⠀⢀⡾⠃⠀⠀⣠⡴⠟⠋⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠀⠀⠈⣷⠀⣠⡞⠁⠀⠀⠀⢠⡾⠁⢀⣤⠞⠋⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⣴⠏⠀⠀⠀⠀⣰⠟⢀⡴⠛⠁⠀⠀⠀⠀⣠⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⢰⡿⠃⠀⠀⠀⢀⣼⣫⡾⠋⠀⠀⠀⠀⢀⣤⠞⠋⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠟⠁⠀⠀⠀⣠⣿⠟⠉⠀⠀⠀⠀⣠⡴⣋⣥⠶⠛⠉⠉⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠟⠁⠀⠀⠀⢀⣤⣾⡿⠞⠋⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠛⠉⠀⠀⠀⠀⢀⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠀⠀⠀⠀⣀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣭⡴⠶⠶⠶⣄⠀⠀⠀⠀⣀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣾⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠋⠉⠁⠀⠀⠀⠀⣀⡼⠂⣀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡴⠶⢞⣛⣭⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣭⡥⠶⠶⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣀⣀⣀⣀⣤⠶⠟⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠁⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⡀⠐
⠀⠀⠀⠀⡌⠀⠀⢀⠀⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐
⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠠⡀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢄⠛⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠄⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠔⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⢀⡀⣠⠅⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⡃⠁⠀⠈⢆⠰⣄⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠌⠂⠀⠀⢆⡈⠀⡀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⣀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠃⠁⠄⢄⢂⠄⠘⠠⠬⣃⡑⣀⣀⠿⢉⣤⢤⠤⢤⠀⢸⡟⠝⠛⠛⡏⠀⠈⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠦⣞⡦⠔⣂⠴⠚⠩⡦⠀⠀⣀⣤⣀⠀⠀⡾⠉⠈⢄⣠⡄⠀⢢⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠸⠀⢠⠔⠂⠀⠐⠉⢄⠀⠀⠀⠀⠀⠃⣧⣀⣼⠀⣰⣿⡤⠖⢊⠁⠐⣰⡧⠀⡀
⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠈⠀⠀⠀⠘⣿⠠⠓⣀⡥⠖⠋⣿⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠲⣦⣅⣀⡀⢰⡇⠀⠀⠀⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠒⠀⠀⠀⠀⠈⠀⠁⠰⠁⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠤

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠛⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠛⡈⢻⡟⠻⠿⢿⠿⠿⣿⠿⠿⠿⠿⠿⠿⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉


⣀⣀⣀⣀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢳⣤⠀⠀⢠⣤⣴⡆⠀⣿⣿⡆⢴⣶⣶⡆
⣿⣿⣿⣿⣿⣿⣿⣶⣶⣾⣶⣶⣶⣶⣶⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⡤⢼⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣵⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣎⢸⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⣿⣿⣿⣿⠀⠀⠀⠽⣿⣿⣾⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⠀⠀⡀⠀⠀⢰⣆⠀⠢⡄⠀⠀⠀⠀⣉⣠⠀⠀⠏⠉⠻⠇⠀⠀⠀⠲⣏⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡽⣿⣿⣿⠀⠈⠉⠉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⢹⣿⣿
⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⣿⠿⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣷⠀⢰⠀⠀⠀⠀⠀⡀⢨⢼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢶⡟⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡆⠀⠀⣄⠀⠀⠀⠀⣳⣿⢿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⣠⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣿⡄⠀⠀⢀⣽⠻⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠙⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢹⡇⠀⠀⢸⣿⡏⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢸⣧⠀⠀⠀⠀⠀⢹⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⢾⣿⡆⣀⡼⢠⣴⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⣿⠁⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠸⣿⣿⣿⡄⠀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣿⣿⣿⡇⢀⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⣿⣷⠈⢹⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢹⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢸⣶⣾⣿⣿⣷⣦⡇⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣼⣿⣿⣼⣿⣷⠀⠀⠀⠀⠀⠀⣾⣷⣭⣿⣿⣭⣾⣷⠀⠀⠀⠀⠀⠀⣾⣿⣧⣽⣿⣥⣽⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⢿⣿⠛⠛⠛⠛⣿⡿⠀⠀⠀⠀⠀⠀⢿⣿⣿⠛⠛⠻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣶⣶⡿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣶⡿⠟⠁⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣶⣾⠿⠋


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⣴⣿⠿⣿⣿⠿⣿⣦⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢰⣿⣿⣶⣿⣿⣶⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⣷⣿⣿⣷⣾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣟⣿⣛⣿⣿⠏⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣧⣻⣿⡿⠀⠀⠀⠀⠀⠀⠹⣿⠏⣛⣛⣯⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠛⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⢻⣿⣿⢻⣿⣧⠀⠀⠀⠀⠀⠀⣾⣿⠛⣿⣿⠛⣿⣷⠀⠀⠀⠀⠀⠀⣴⣿⡟⣿⣿⡟⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⣿⣿⣿⡿⠿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣧⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣼⣿⣿⠟⠀⠀⠀⠀⠀⠀⠘⢿⣧⣤⣶⣤⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⣹⣿⣿⣹⣿⣷⠀⠀⠀⠀⠀⢀⣿⡍⠉⢉⡉⠉⢩⣿⡀⠀⠀⠀⠀⠀⣾⣿⣍⣽⣿⣏⣽⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⡿⣿⣿⡿⠀⠀⠀⠀⠀⠘⣿⣿⣶⣿⣿⣾⣿⣿⠃⠀⠀⠀⠀⠀⢿⣿⣿⠿⢿⢿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠙⢿⣷⣿⣿⣾⡿⠃⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡟⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠚⠛⠛⢀⠀⠘⠛⠛⠛⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⠀⠲⠶⠖⠈⡇⠀⠳⠶⠃⢸⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡄⠀⠀⠀⠘⠁⠀⠀⠀⠀⣸⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣄⠀⠈⠓⠒⠋⠀⢀⣴⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡦⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⣥⣀⣀⣀⣬⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠸⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢿⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢸⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡄⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⡿⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠳⣇⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⠁⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠋⢷⡀⠀⠀⠈⠓⠦⣖⣒⠒⠶⣤⠶⠋⠀⠀⢀⡴⠛⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢀⣀⣀⣀⠀⠙⠳⢤⣀⣠⡶⠤⠭⠇⠀⠀⠀⢀⣠⡴⠋⠀⠀⢀⣀⡈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠉⠙⠓⠶⢤⣈⡉⠓⠲⠶⠶⠶⠒⢛⣉⣥⠴⠖⠚⠋⠉⠉⠉⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⣤⣤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠓⠒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠓⠶⠶⠒⠒⠚⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⣀⠀⠀⢀⢀⣀⢀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿