Beach ball Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⠒⠛⠛⢛⡿⠛⠛⠛⠛⠒⠶⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀
⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀
⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⢀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢷⡀
⠀⡼⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠘⣧
⢰⠇⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⢹
⣼⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈
⡟⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁
⡇⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⣠⠴⠖⠒⠛⠒⠶⢤⡀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⠎⠁⠀⠀⠀⠀⠀⠀⠀⠉⢦⡀⢀⣀⡤⠖⠉
⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⢳⡀⢀⣀⣀⣠⠤⠖⠚⠉⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⢻⡉⠉⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⣀⠀⠀⢀⣀⡤⠞⠁⠀⠀⠀⠉⠙⠒⠦⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡟
⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢹⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠒⠒⠒⠖⠒⠒⠚⣹⠋
⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⡀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠤⠀⠀⠒⠒⠀⠀⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣔⣩⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣀⠀⠀⠀⢀⠀⠿⢿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠊⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠉⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠈⠐⠠⢄⣀⣀⣀⣴⣾⣤⡀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⢰
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠈⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⢤⣀⡀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠚⠛⠿⠿⠟⠛⠛⠛⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠶⠶⠒⠒⠒⠒⠶⠶⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⢭⠀⢸⠀⣂⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠭⠽⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠁⠚⠲⣅⡀⠘⠀⢹⡀⠀⠀⣠⠖⠈⢁⠤⠀⢀⡀⠀⠫⠥⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠫⠊⠀⡔⠁⢠⠂⢀⠜⢳⡴⠚⣓⠒⡚⠯⠁⠀⠠⠏⠤⠂⠁⠀⠀⠤⡀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠁⠀⡜⠀⢀⡡⠤⠓⠒⡏⠰⢇⣀⠤⠊⡠⠃⠈⣱⠖⠒⠦⢄⡐⠏⣁⣈⡄⠀⢴⠺⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠃⠀⠀⠀⣠⠗⠋⠁⠀⠀⠀⠀⡸⡖⠒⠒⠒⠉⠀⠠⠊⠁⡠⠊⠀⠀⠉⠓⢤⡀⠀⠀⠀⠈⠀⠉⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢰⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⡠⠿⠞⠀⡀⢂⠀⠈⡀⠠⠐⠉⠀⣀⠔⠀⢀⠄⠀⠙⣦⡠⡀⠑⡀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠈⡴⠋⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⢧⡣⣣⠂⢀⡀⡀⠤⠊⠀⢀⠔⠀⠀⢀⠞⠀⠱⣄⠀⠃⠀⢠⢌⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣠⠞⠀⠀⠀⠀⠀⠀⠀⢀⠎⠐⠡⢢⢀⠀⠀⠀⠀⠀⢸⠡⠀⢀⡠⠒⠁⠀⡠⠒⠁⠀⠠⠀⠘⣦⠀⠀⠈⠢⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡿⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠈⠢⠷⠊⠀⢀⠄⠀⠀⠀⠙⢃⠀⠀⠀⠐⠉⠀⢀⠴⠊⠀⢀⠄⠈⢷⠀⢠⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⢠⡇⡟⠀⠀⠀⠀⠀⠀⠀⠀⣸⠔⠀⠀⠀⠀⠀⠀⢄⠠⠅⡄⠀⠀⠸⠆⠀⠀⡠⠔⠊⠁⠀⡠⠖⠁⠀⡠⠘⡇⠄⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠆⠩⡅⡀⠀⠀⠉⠉⠀⠀⡄⣒⣗⠈⠁⠀⢀⡠⠔⠉⠀⢀⠴⠊⠀⠀⣷⠀⢠⡀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠳⠭⠵⠁⠀⢀⠄⠄⠀⠀⢧⣓⣻⡄⠀⠀⠁⠀⢀⠤⠚⠁⠀⠀⣠⠖⠸⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣆⢀⠀⠀⠀⠀⠀⠀⡇⢈⠆⡆⠀⠀⠀⠀⢇⠀⠠⠐⠈⠀⠀⠀⡠⠔⠊⠀⠀⢠⡆⠀⢈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠘⠷⠃⠀⠠⢐⣂⠀⠀⠈⠑⠉⠀⠀⠐⠩⢅⢺⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡠⠔⠁⡏⡄⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠰⣔⣊⠔⠀⠀⡀⠄⠀⠀⠘⠬⠥⠊⡇⠀⠀⠀⠀⠀⢀⡠⠔⠉⠀⢀⢴⠓⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⢈⡡⣹⢈⠀⠀⠀⠀⠀⣃⠀⠀⠤⠐⠈⠁⠀⠀⡠⠒⠁⡜⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⢣⠀⡀⢒⡂⠀⠀⠀⠑⠒⠉⠀⠀⠀⢊⠭⣗⠀⠀⠀⢀⣀⠤⠒⠉⠀⡀⣸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠈⣆⠣⣕⡢⠆⠀⠀⠀⢀⠠⠀⠀⠈⠢⠭⢾⠒⠒⠈⠉⠀⢀⡠⠐⢁⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⡇⢎⡄⡀⠀⠀⠀⡌⠀⣀⠤⠐⠊⠁⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣤⣀⠈⠳⣔⣀⠀⠀⠀⠈⠒⠊⠀⠀⢠⢊⠏⠁⠀⣀⣠⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⢽⣶⣄⣀⣀⣠⣀⣀⣀⣈⣮⡥⠴⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁


⣀⡀⣀⣀⣀⡀⣀⣀⡀⣀⣀⣀⢀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠤⠴⠶⠶⠶⠶⠤⢤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠛⠛⠒⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢳⡄
⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠙⢦⡀
⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠈⢳⡀
⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⣀⣀⠀⠀⡾⠀⠀⠀⠀⠀⢻⡄
⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⠋⠉⠉⠉⠻⢧⡀⠀⠀⠀⠀⠀⢳⡀
⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠈⣇
⠀⣸⠁⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⢹
⠀⣿⡤⠤⠖⠒⠛⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠒⠒⠶⢤⣸
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⢙
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣄⡀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⢸
⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠈⠉⠙⠉⠙⡆⠀⠀⠀⠀⠀⠀⢸
⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⡟
⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣸⠃
⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢠⠏
⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣠⠏
⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⣰⠏
⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢃⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀⣀⣠⡤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣟⡋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⠶⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠛⠋⠉⠉⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠉⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠏⡀⠀⢀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠁⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿
⣿⣿⣿⡟⠀⠀⠀⠀⢀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⠈⣿⣿⣿⣿
⣿⣿⡟⠀⠀⠀⠀⠐⠁⠀⠢⢀⠀⠀⠀⢀⠠⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿
⣿⡿⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠍⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿
⣿⠇⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣿⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⡇⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⡏
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⡇
⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿
⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿
⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⣠⣾⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⡾⠛⠋⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠙⠛⠳⠶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣇⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣶⣶⣶⣦⣤⣤⣤⣍⣻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠉⠳⣄⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠛⠛⠛⣻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⣠⣿⣄⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣶⣶⡖⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⣼⠇⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⢠⣿⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⢸⡇⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⣿⡇⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⡇⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⢸⣇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⠁
⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡏
⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠁
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣷⣄⢀⣀⣀⣀⣠⣤⡴⠶⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠉⠉⠀⠙⢄⠀⠀⠀⠀⠈⠉⠑⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⣠⠔⠉⠈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣊⣀⠀⣀⣀⣀⣀⠀⠀⢀⡤⠒⠉⠉⠉⠙⠒⠾⡁⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⢀⠜⠉⠀⠀⠀⠀⠀⠀⠀⠉⢹⠋⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠐⠒⠒⠤⢄⡈⢧
⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆
⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⣀⠴⠚⠁⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠀⣀⠔⠁⠙⠢⣀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⡇⠀⠀⠀⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⢠⠋⠉⠉⠉⠉⢫⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⡇⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⡇
⠀⠀⠀⠀⡇⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⡇
⠀⠀⠀⠀⢳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢀⠃
⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡞
⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠺⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠀⠒⠒⠒⠒⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣾⣿⣿⣿⠿⠛⠋⠉⠉⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠙⢻⣿⡿⠿⠿⢯⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⢰⠟⠁⠀⠀⠀⢀⣿⣴⣤⣤⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⣤⣶⣿⣤⣀⣀⣠⡴⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⢂
⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡐
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣷⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢷⣄⡀⠀⠀⠀⠀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣷⣌⡁⠒⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⡘⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠃⠀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠈⠁⠢⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⡇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⣶⣧⡀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠆⠉⠙⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠘⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠈⢆⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⢹⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠈⠢⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢿⣿⣿⣿⣿⣿⢋⣀⣀⠠⠄⠂⠉


⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠶⢾⣋⡉⠉⠉⠉⠉⠉⠉⠙⣛⣲⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⠀⠈⠉⠳⢦⣀⣠⡴⠞⠋⠉⠀⠀⠀⠈⠉⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⠉⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⠾⠳⠤⠴⠻⢦⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⣀⣤⠴⠚⠋⠉⠁⣴⠋⠀⠀⠀⠀⠀⠈⢳⡀⠉⠙⠓⠶⢤⣄⡀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠈⠉⠓⢦⣄⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⢀⡟⢀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣀⠸⡆
⠀⠀⠀⠀⠀⠀⣼⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣽⡀
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡤⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⢤⣤⣀⣀⣀⣀⣀⣀⣀⣤⡤⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁


⡿⢿⠿⠿⠿⡻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣻⣟⣛⣿⣿⣿⣿⣿⣿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠀⠐⠀⡲⢂⠈⢉⠉⠉⠉⠁⠐⠀⠀⠠⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠉⠀⠀⠀⠀⡼⡣⢔⠎⢀⠨⢐⡨⠔⢒⠫⠤⠒⡀⠠⠄⡉⠒⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⣀⠄⡐⣸⠁⡊⠔⡨⠔⢊⠅⠂⠨⠐⡢⠄⢐⣀⢠⣭⡵⠶⢖⣠⣈⠁⠢⢄
⠀⠀⠀⠀⠀⠀⠠⠦⢄⣀⠀⣠⣤⣶⡿⠋⢗⡿⣿⣖⡥⢔⡩⠀⠤⢂⣤⡴⠤⠄⠓⠚⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣛⠦⡀
⠀⠀⠀⠀⠀⠔⢀⠔⣒⡿⣿⢮⡩⠐⠒⠉⠀⠈⠉⠃⢾⣽⣿⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⣈⡠⡄
⠀⠀⠀⢀⠎⠠⠂⢥⣓⣋⡝⠁⠀⢠⣠⡀⠄⡀⠀⠀⠈⠙⡅⢪⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠪⢌⠢⡀
⠀⠀⠀⠂⣀⠁⡒⠿⢗⡎⠀⣠⡵⢋⠀⠙⢦⣪⣀⠀⠀⠈⢰⢀⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢍⡂⠤⡑⠄
⠀⠀⡄⡀⢕⡡⡐⣿⣿⠁⢀⢼⡇⠁⢒⣃⣠⣿⠗⠀⢠⢂⠇⢐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢌⡐⢌⠈⢢
⠀⡘⠠⢔⡵⠞⣙⣫⡉⡆⠀⢟⡿⣿⢿⠲⠛⠁⢀⠰⣡⠞⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠢⢈⠲⢅⠆⢣
⠀⣡⠔⠁⠠⠈⠃⢜⠧⡘⢄⡀⠈⠀⠀⠀⠀⣀⡡⠞⠃⠀⠈⠀⠈⠑⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠑⠄⡀⠑⢄⠲⡀⢃
⠸⠁⠀⠀⠁⠀⠀⠀⠈⠐⠀⢉⢟⡶⠒⠏⡉⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⢦⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⢄⠑⢄⠀⢲⡅⠈⠄
⠈⢈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢣⠀⠏⢢⣈⠰⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠑⢄⠑⠄⠡⡈⢗⠀⡇
⡄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠸⠀⠠⢸⠈⣦⡀⠘⠠⠀⠀⠀⠀⠀⠀⠀⡀⠱⡈⠂⠈⢄⢱⡥⠂⡇
⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡆⠀⢰⠀⠀⢸⠀⡇⡹⢄⠀⠑⠀⠀⠀⠀⠢⡀⠘⡄⠐⡄⢂⠈⡤⣃⠀⡄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⠁⡇⠸⠀⡆⢸⠀⡇⡇⠸⢢⡀⠀⠀⠀⠰⡀⢡⠀⠈⠀⠸⠈⡄⢹⠕⠀⡃
⢡⠰⠁⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇⠀⠀⠀⠀⠀⢀⠀⠀⠐⢀⠁⡈⡈⢠⢀⠆⠀⠂⡄⢠⠀⠀⡆⡆⣷⡀⠀⠀⡄⢱⠀⢃⠀⠂⠀⡆⢰⠖⠂⢠⠁
⠨⠀⡀⡔⠀⠀⠀⠀⠀⠀⠠⠀⡇⠀⡀⡠⢠⠀⠃⡘⢠⢃⠆⢠⢀⠃⠌⡜⠀⡌⢠⠁⠈⢰⢰⢠⠀⡇⣷⠀⣂⠘⡄⣆⠈⡀⢰⠀⣠⣹⡍⢀⡆
⠀⢣⠠⠀⠀⡄⠀⠀⠀⠀⠐⠀⢙⡐⢡⢁⠃⡌⡐⢀⠃⡜⢀⠂⠆⡘⢰⠀⠰⠀⡌⠀⢄⠆⡏⠈⠘⠃⠋⡇⠘⡇⢿⢸⡄⣇⢸⡶⣾⡖⠀⡾
⠀⠀⢧⠀⠰⠀⠀⠀⠀⠀⠀⠀⠈⣀⠇⠂⡌⡠⢁⠎⡐⠀⠎⡘⢠⢣⠃⢀⠃⡰⠁⡐⠘⡰⢱⠂⠚⠒⠐⢛⡂⠓⠘⠛⠃⠛⠈⠋⠙⠁⡼⠁
⠀⠀⠀⢣⡡⢀⠀⠀⠀⠀⠀⠀⠀⢯⠆⡜⠐⠁⠈⡠⠁⡌⡰⢁⠂⠆⢀⠆⢰⠁⠰⢠⠰⠁⠋⡸⢱⠃⠏⡜⢳⠘⡘⢇⡗⢺⠒⠃⠀⡞⠁
⠀⠀⠀⠀⠱⡌⢠⠀⢰⠀⠀⠀⠀⠘⡎⡠⢃⠌⠰⠁⠌⡰⠁⠄⡜⢀⠎⢠⠃⠠⢡⢃⠇⡌⡰⢁⠆⡸⢠⢃⠛⠀⡗⡧⣭⠝⠁⢠⠎
⠀⠀⠀⠀⠀⠈⠢⡉⠂⡄⠀⠀⠀⠀⢹⣁⠌⡰⠁⠜⡰⠁⠎⡘⢀⠎⢠⠃⡰⢁⢢⠊⡜⡰⠁⠌⢠⢁⠦⡮⣽⡇⣗⡗⠂⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠁⠀⢁⠀⠀⢫⡴⢁⠎⡰⢁⠎⡔⢀⠊⣠⠃⡔⢡⢃⢂⠌⣐⠁⡬⣠⠣⡬⡽⣱⣻⠆⠇⢉⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⡀⠑⠧⢢⢳⣦⡾⣁⢮⡜⢤⠂⣴⣁⠾⣴⣱⢧⡞⡶⢭⣟⣰⢃⡼⣵⢃⢏⢿⣀⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠀⠘⠓⢦⣄⣀⢹⡜⡡⢟⡰⢏⡾⣵⢫⠼⡴⢯⢏⡞⣡⠏⡘⢃⠌⡰⣡⡣⠗⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠁⠀⠓⠊⠩⠵⢚⠴⢯⡴⣥⣯⣮⣴⣡⣎⣴⡥⢾⠔⡷⠞⠋⠑⠠⠅⣒⡤⢒⠠⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠁⠈⠀⠈⠀⠈⠁⠈⠁⠀⠁⠒⠉⠐⠂⠩⠄⠢⠅⢲⠭⢑⡂⠄⡒⠤⣀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠀⠉⠻⢿⣮⡉⠙⠛⠿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠉⠛⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⢠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⢠⣿⢿⣷⡄
⠀⠀⢠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⢠⣿⠃⠀⢻⣿⡄
⠀⢠⣿⡟⠀⢀⣀⣤⣤⣶⣶⠶⠿⠿⠿⠟⠛⠛⠛⠻⠿⠿⠿⠶⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⣀⣿⣷⣤⣴⡿⠃⠀⠀⠀⢻⣿⡄
⠀⣿⣿⣶⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠿⠷⣾⡟⠉⠀⠈⠻⣷⠀⠀⠀⠀⠀⢿⣷
⢸⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⢠⣿⣶⣤⣀⠀⠀⠸⣿
⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠷⣶⣾⡟⠁⠀⠉⠛⠿⣶⣄⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⠙⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⣿
⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⣿
⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⢰⣿
⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣾⡿
⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⣼⣿⠃
⠀⠀⠘⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⣼⣿⠃
⠀⠀⠀⠘⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⢀⣾⡿⠃
⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⢀⣤⣶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢃⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣴⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣶⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣶⣿⣿⣟⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠲⡒⠋⠉⠉⠙⢲⠖⠢⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠀⠀⠀⣠⣽⠖⠒⠒⠲⣧⣄⠀⠀⠀⠉⠑⠦⣀
⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⣀⡤⠤⠒⠒⢻⠹⣑⠤⣄⣠⠤⣊⠏⡟⠓⠒⠢⠤⣀⡈⠳⣄
⠀⠀⠀⠀⠀⢠⢞⡥⠖⠉⠁⠀⠀⠀⠀⠀⠑⣮⠭⣭⣭⠭⢵⠊⠀⠀⠀⠀⠀⠀⠉⠓⠮⣳⡄
⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣆
⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠾⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠼⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠢⠤⠤⠤⠤⠤⠤⠔⠒⠊⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⣿⡟⠉⠀⠀⠈⠉⠁⠒⣢⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⠿⢿⣿⣿⣿⣿⣿⣿⡇⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠻⣿⠟⠋⠉⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⠉⠉⠉⠛⠿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⠀⠀⠀⢠⣤⣾⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣧
⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⠋⢀⣼⣿⠃⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣉⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡆
⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⡃⣰⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣆⠈⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣟⣹⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠒⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⣫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡓⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋⡡⠖⠋⠉⠉⠛⠛⠻⢿⣿⡿⠟⠛⠉⠉⠐⠠⣈⠓⢄
⠀⠀⠀⠀⠀⠀⢠⠞⠁⠐⠊⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣙⢆
⠀⠀⠀⠀⠀⣴⣣⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡀
⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡄
⠀⠀⠀⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡄
⠀⠀⢠⣿⣿⣿⣿⡿⠋⠒⠒⠦⠤⢄⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡤⠤⠖⠒⠙⢿⣿⣿⣿⣧
⠀⠀⢸⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿
⠀⠀⣿⠘⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠋
⠀⠀⢻⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠸⡄⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⠛⠛⠛⠛⠛⠿⠿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⢧⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠈⢧⠀⢹⣤⣄⣀⡀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⢀⣀⣤⣶⡁⢀⠆
⠀⠀⠀⠀⠈⢧⣸⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣇⠊
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⢀⣀⣠⣾⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠿⣿⡟⠋⠀⠉⠉⠉⠉⠉⠀⠀⠙⣛⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠒⠒⠒⠒⠒⠋⠉
⣶⠖⡶⠶⠶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⣉⠙⠳⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡴⠚⢉⣉⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣾⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⠁⠈⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢸⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⠀⣸⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠳⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⣴⠃⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠙⠇⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠞⠁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠻⣄⡀⠀⠀⠀⠀⠀⠀⡼⠃⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠈⠻⠷⠀⠀⠀⠀⠘⢁⡴⠉⠀⢀⣠⡤⠶⠒⠒⠶⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⣠⠴⠋⠀⣠⣾⣿⣿⡃⠀⠀⠀⠀⠀⢠⠋⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣿⠀⢀⡾⣿⠟⠋⠀⠈⠑⢢⣴⣶⣶⣿⣄⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢄⠀⠀⢰⢃⡄⠀⠀⢹⠀⡞⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡦⣀⣀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⡴⠒⠲⢤⡀⢀⡤⠞⠉⠀⠈⠉⠑⠳⢾⡁⠀⠀⠀⢻⡇⠀⢸⡀⠀⠀⢀⡠⠚⠛⠻⢿⣿⠟⠀⠀⠀⢿⣷
⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠠⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠢⢤⣸⡇⢠⣿⣿⣶⡖⠁⠀⠀⠀⠀⠀⣅⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⣠⢾⠇
⠀⠀⠀⠀⠀⠀⢿⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⢀⣀⣴⣿⣿⣿⡞⣱⠏
⠀⠀⠀⠀⠀⠀⢸⡄⠀⡀⠉⠀⠀⠀⠀⠀⢀⢀⣀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢒⠸⠀⠹⣿⣿⣿⣿⣿⠞⠁
⠀⠀⠀⠀⠀⠀⠈⠓⠞⠳⠤⠴⠛⠢⠖⢶⣶⣄⣀⣤⠀⠀⣴⡄⠀⢀⣀⣀⣀⣀⣤⡤⠛⠿⠶⠶⠶⠿⠿⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠁⠈⠉⠉




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢸⡇⣽⠀⠀⢀⡶⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠘⣆⠀⠀⠀⠀⠀⢸⠛⠋⠀⠀⣼⣥⡟⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠀⠀⠈⣿⠻⡦⠀⠀⠀⠀⠈⢠⠀⠀⠘⠃⠼⠁⠀⣠⣞⣁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡀⣠⠀⠈⠁⠀⠀⠀⣀⠰⣆⡎⠀⢠⡆⠀⠀⠀⠐⠋⡼⠉⠀⠀⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣤⣀⠀⠀⠙⠃⠀⠀⠀⠀⠀⢀⡆⣙⠈⣇⠿⣶⣤⠀⠀⠀⠀⠀⠀⠀⣠⠶⣏⣡⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢾⣗⠈⠙⠂⠀⠀⠀⠀⠀⠀⣦⠤⡌⢻⡰⠚⣄⣃⠮⡤⠀⠀⠀⠀⠀⠀⠀⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⣏⣷⢼⡏⠣⣀⡸⡥⢾⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣶⠦⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣉⢦⡿⢣⡏⢠⣗⣩⠏⠀⠀⠀⠀⠀⠀⠀⠀⠻⠴⠶⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠿⣥⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡻⠍⢻⣖⣩⡏⣡⣛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢍⣹⣽⠼⠶⣽⣧⠜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢎⣀⠶⡉⣈⢶⠛⢆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠀⣴⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣤⠊⢣⡀⠛⠄⢀⢧⠚⡄⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠋⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⣠⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⢰⡎⢈⢶⠃⢑⡤⠚⢇⡠⢾⡇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠛⠀⠚⠃⠀⠀⠀⠀⠀⠀⠀⠐⡼⢇⢀⠷⠁⢈⡤⠊⢃⡠⡇⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠛⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠜⠣⣀⠵⡁⢈⡶⠉⢲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣔⢣⣀⣱⡉⡈⡤⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⣤⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠁⣴⠟⣉⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⢰⡿⣴⠟⢁⣀⠀⢀⣀⡀⠀⣀⡀⢸⣇⡀⠀⠀⠀⠟⢰⡟⠀⢸⡇⣀⣀⠀⣀⣀⠀⣠⡀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣿⢀⣟⣹⠇⣿⢩⡇⣼⠋⠓⣾⠋⣿⠀⠀⠀⠀⣼⠇⢀⡾⢱⡏⣹⠆⣿⢹⡇⣿⢹⡇⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⠏⠈⠿⣥⠾⠿⠾⠷⠿⠦⠴⠿⠀⠷⠾⠀⠀⠀⣿⠛⠋⠁⠸⠷⠿⠾⠃⠸⠷⠷⠾⢷⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠶⠖⠒⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠒⠶⠦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠛⢉⡁⠀⣠⡀⠀⡠⡄⠀⢠⢤⠀⢀⢤⠀⠀⡤⠀⠀⣤⠀⢀⣉⠙⠓⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⡟⠁⠀⣠⠒⡎⢸⢒⡇⣟⣛⡇⣟⣉⡋⢸⣉⣻⢸⣋⣹⠀⣛⣛⠀⣓⡚⢸⠒⣄⣀⠀⢙⠛⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⡷⠚⠋⠉⠉⢣⡌⠉⠧⠋⠈⠳⠃⠀⠘⠎⠀⠘⠞⠀⠈⠶⠀⠘⠴⠁⠩⡼⠉⠁⠉⠙⠛⠀⠀⠈⠙⢶⣄
⠀⠀⠀⠀⠀⣠⢾⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⣍⡳⣄⡀
⠀⠀⠀⣠⣾⠵⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠙⠪⡻⣄
⠀⢀⣼⠟⠁⠀⢸⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠻⣧⡀
⢀⣾⠋⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⢷
⣼⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈
⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸
⢻⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢠
⠈⢷⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⡞
⠀⠀⠻⣆⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⣠⠟
⠀⠀⠀⠈⢷⣄⢘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠘⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠙⠿⣅⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣀⡷⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣀⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠶⠤⣤⣄⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⣀⣀⣤⡤⠴⠶⠚⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⠶⠶⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡽⣫⡴⠛⢉⡤⠀⠒⠀⠐⠊⠛⠓⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣩⠟⠉⠠⠴⠀⠀⠀⡀⠀⠂⠐⠛⠀⠀⠙⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠾⣥⠟⠀⠰⠞⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⣻⠞⠁⠀⠞⠃⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣝⡷⠋⡀⠾⠃⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣆⠰⠃⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⣿⢠⡆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡸⠀⢀⠐⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢣⡚⠀⠀⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣾⣧⠀⡦⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⣻⠀⢀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠆⡤⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣋⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⡀⠒⠀⠀⡔⠀⠀⠀⠀⠠⠀⣨⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠶⠶⠴⠶⠶⠖⠚⠋⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢸⣷⣀⣤⡾⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣶⠲⣶⡄⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣏⠀⠀⠀⠀⣟⣿⣿⣷⠀⠀⢠⣿⡟⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⣿⣿⢠⣿⡟⠀⣰⣾⣿⢷⡀⠀⠀⣼⡿⠉⠻⢷⡄⠀⠀⠾⣿⠛⠛⠀⠀⢸⣿⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣿⣿⣼⠿⣤⡀⠹⣿⠟⠛⠁⠀⠀⠟⠁⢀⣠⣄⡀⠀⠀⠀⠀⢀⣠⣄⠀⢸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢸⣿⣿⠃⠀⢸⣷⡀⠀⣠⣶⣶⠀⠀⠀⣰⣿⡟⣡⣿⡇⠀⠀⢠⣿⠃⠀⠀⢸⣿⣿⡾⢻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢸⣿⡇⠀⠀⢸⣿⡇⣰⣿⣿⠟⠀⠀⠀⣿⡟⢰⣿⣿⠀⠀⠀⣸⡏⠀⠀⠀⣰⣿⡿⠁⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⢀⣾⡿⠀⠀⠀⢸⣿⠇⣿⡿⠁⠀⠀⠀⣴⣿⣷⠏⢹⣿⡆⠀⢀⣽⣿⣄⣠⠞⢹⣿⠇⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣼⠟⠁⠀⠀⠀⣼⠏⠀⢿⣿⣀⢀⣠⠾⠁⠈⠉⠀⠘⠿⣷⡶⢛⡁⠈⠉⠀⠀⢸⡟⠀⠀⣿⡟⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣡⠞⠁⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠀⠀⠀⠀⠈⠁⠀⢸⣿⠇⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣦⣀⠉⠀⢀⣴⢦⣄⠀⣤⡶⣤⠀⠀⣾⣿⣂⣴⣿⠆⣀⣾⣿⢃⣠⡖⠀⢀⡀⠀⠀⠀⠙⣛⣉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢋⣩⠀⣾⣧⢸⣿⣾⡟⢰⣿⡆⠀⠞⠉⣹⣿⠇⠀⢈⣿⣿⠛⠉⠀⢀⣿⡿⠀⣴⡄⢉⡙⠻⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⣡⢸⡏⣿⢈⣿⠻⢷⠿⣿⣷⡀⠀⠀⣿⣿⣠⡴⠛⢻⣿⡆⠀⢠⡿⢿⣧⣴⢿⣿⠀⢻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⣴⣿⢸⡇⣿⡟⣅⢶⣤⣄⠈⠻⢿⣷⡶⠛⠉⢁⣀⡀⠀⠙⠿⠖⠋⠀⠀⠉⠁⠀⢿⣇⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠇⢸⡇⣿⡇⢿⣦⠉⠉⠀⢶⣄⣀⣀⠀⣾⣿⣿⣿⣦⠀⣀⣤⣶⡶⢛⣴⣾⠇⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣿⣻⡇⠈⠻⠇⢠⡖⣯⣿⢿⣍⠀⠿⠛⢿⣯⠟⢰⣿⣿⠟⣠⣿⡟⠁⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠇⠀⠀⠀⢿⣿⣿⣿⣿⣿⡧⠀⠈⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⢻⢿⣿⢿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁


⠀⠀⠀⠀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠂⡲⢂⠌⡉⢉⡉⠉⠀⠀⠐⠀⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⣸⠃⡲⢁⠠⠐⠨⠑⡂⠍⠒⠒⠄⢀⣀⠈⠑⠂⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⢠⣤⡰⢠⣇⣅⡪⠔⡈⠅⠂⡀⠢⠁⡒⠠⣄⣴⡶⠛⠋⣴⠶⣀⣁⣢⣀
⠀⠀⠀⠀⠀⡠⠋⣐⣦⣄⣶⡟⢟⣉⠘⠽⠽⣻⢶⢥⣦⢀⣤⠴⠚⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢑⠄
⠀⠀⠀⢀⠌⢀⠍⣴⡿⢯⠕⠈⠀⠀⠀⠀⠀⠀⠑⢿⠛⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣒⠈⢄
⠀⠀⠀⠊⠠⡃⣼⣞⡶⠁⢀⣤⠗⠓⣄⡄⠀⠀⠀⠠⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠨⢀⠱⡄
⠀⠀⠌⢐⠅⡈⣽⢶⠇⠀⣺⠓⠈⠴⠈⣽⡯⠀⢀⠄⠆⠨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡢⢑⠈⢆
⠀⡈⢠⢕⡵⠚⣚⡛⡆⠈⢜⣷⣶⡿⠿⠛⠁⢠⢊⡞⠤⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢⢌⠂⢕⠄⢣
⢀⡡⠐⠁⠀⠔⠹⡣⡘⢄⠀⠀⠀⠀⠀⢀⡠⠔⠃⠀⠀⠀⠁⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠢⠀⠑⢄⠲⠄⢂
⠘⢁⠀⠈⠀⠀⠀⠀⠐⠀⠩⢳⣖⠚⢩⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⡈⠢⣄⠢⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠑⠌⠢⡀⢱⡕⠸
⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠹⡀⠣⢱⢄⠘⠔⡀⠀⠀⠀⠀⠀⠀⠀⢠⠑⡄⠢⠈⠄⠻⠀⡇
⡆⠈⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢘⢸⠈⠧⡀⠁⠂⠀⠀⠀⠀⡀⠀⡄⠡⡈⠀⠱⠘⣖⠁⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⠸⢨⠀⠇⠀⢨⠀⠀⡟⣆⠀⠁⠀⠀⢀⠐⡄⠈⠄⠑⡈⠀⢩⠕⠀⡇
⠃⠠⠀⠀⠀⠀⠀⠀⠀⠠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⠆⡀⡘⠀⡀⠈⠀⠀⢀⢋⢣⡀⠀⠀⡈⠆⠰⡀⠀⠀⠃⢡⣘⠁⢠
⢀⠀⠂⠀⠀⠀⠀⠀⠀⢘⠀⠃⠀⠀⠀⡀⠰⢠⠁⠄⠄⠀⠠⢀⢁⠃⠠⠀⠃⠘⠸⠘⠈⢈⢱⠀⠄⠡⠈⡄⠡⠀⠀⠘⠰⡖⠀⡀
⠀⠆⢠⠀⢀⠀⠀⠀⠀⠠⠀⠖⠐⠐⠰⢁⢁⠃⡌⡘⠀⢂⠂⠆⡌⢀⠆⠘⠀⠀⠃⠃⠄⡀⡘⣇⠘⠄⠃⢁⠀⠀⠃⢨⡯⠁⠰
⠀⠘⡌⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⠁⢁⢂⠎⡔⠰⠁⠄⡌⡐⡐⠀⡈⢠⠁⠀⡘⡘⠘⢠⢁⢃⠛⡆⢃⢰⠸⠀⣆⣸⡐⠃⠠⠁
⠀⠀⠘⢌⠄⡀⠂⡀⠀⠀⠀⠈⡧⢠⢂⠎⡐⠠⠁⡌⡘⠠⠡⠁⡐⢀⠂⠀⢡⠰⢀⠃⠆⡈⠨⢠⢣⠘⡈⣀⡐⡦⠈⠀⡠⠁
⠀⠀⠀⠈⠢⡁⠄⡀⠀⠀⠀⠀⢱⢁⠌⡐⢠⠃⠌⡐⢡⢁⠃⡐⢀⠆⢠⢀⢣⢃⠆⡌⡐⢠⠃⢃⣚⡄⡗⠦⡭⠉⢀⠜
⠀⠀⠀⠀⠀⠑⢦⠁⠄⡀⠀⡀⠀⢣⡔⠠⠁⠌⡐⢠⢃⠊⡐⢁⠎⡠⠡⢢⢀⠎⠌⠰⢁⠂⣜⡞⢼⡇⡏⡗⠁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠁⢀⢠⢈⢶⢁⠊⡔⡠⢃⠂⠔⢠⠂⡔⡡⠣⢀⠂⠬⣰⢣⠎⡜⣺⢡⢿⠃⢁⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢤⡈⠉⠂⢻⢪⡶⣱⢆⡞⣴⢣⠎⡕⡸⣷⢣⠏⡴⣣⠏⡼⠱⠃⣃⡻⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠨⠛⣒⡢⠷⢌⣡⣋⡔⡳⢣⢏⢝⠝⡡⢋⢞⣱⣁⣎⣴⠔⠋⠁⣀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠉⠊⠉⠛⠙⠋⠟⠛⠋⠉⠋⠕⠊⠄⠂⠔⠢⠜⠃⠌⢈⡒⣬⠐⢂⡐⠠⠀⢠⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⢈⣁⣀⣀⣄⣄⣤⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣖⣂⠔⠬⢯⢥⣤⣤⣤⡴⠶⠶⠶⠶⠖⠚⠛⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠤⠭⠭⠀⡇⢸⠤⠤⠤⠴⠤⠦⠴⠶⠶⠲⠒⠒⠒⠒⠒⠒⠒⠒⠒⠓⠒⠚⠛⠓⠓⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⢀⣄⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠃⠫⠣⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⡛⠷⡠⠀⣇⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡨⢢⠒⠉⠹⠇⠀⠀⡦⠄⡀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠚⠹⡇⠉⠀⠀⠒⠈⠁⢣⠮⡤⠐⠏⢦⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⡖⢱⣄⠂⠍⡇⢀⡑⢶⠦⡆⣚⢅⠁⢸⡔⠠⠄⠗⡍⠐⣶⠶⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠉⣴⢀⣁⢩⡉⠀⢆⠉⠓⠋⠘⠓⣄⠛⢊⡤⠎⢢⡀⠀⣀⣘⠎⠑⣓⣤⡈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⢀⡝⣀⠈⠑⢂⠄⠋⠀⣆⢰⣭⡤⠮⠝⢡⠂⠀⡰⡁⠉⠉⡑⣡⣨⢅⢷⣝⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠮⣖⠲⡑⢄⡘⣃⠀⠉⠁⠠⠹⠒⠲⠊⠀⠫⡡⠂⡲⠄⠾⣩⣄⠀⠪⢠⠎⡆⢀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠶⣾⣄⣡⡟⡸⠀⠀⣭⡅⡰⠃⠋⠈⠀⢘⠀⣹⢶⠀⠈⠀⠈⠀⠀⠚⣈⣠⣼⡶⠟⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⢦⣍⡛⠿⠷⣶⣶⣶⣤⣤⣤⣤⣥⣦⣭⣧⣤⣯⣶⣶⣶⠿⠾⠿⠛⢛⣉⣥⠶⢻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠈⠙⠛⠶⢦⣤⣤⣄⣉⣉⣉⣉⣉⣉⣉⣉⣀⣀⣤⣤⡤⢶⣶⣟⠋⠉⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⣀⣀⣀⣀⡀⠈⣽⡟⣩⣿⠟⣛⣛⠿⠿⠛⠛⠻⣶⡌⢻⣧⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⠿⢛⣋⣛⣛⠻⢿⣿⣤⡿⣧⡾⢛⣟⠻⣻⡿⢿⣷⣼⣷⣼⣿⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⡿⢛⣙⡛⠻⣶⣷⣾⢷⣟⣻⣟⣫⡇⣬⠍⢷⡟⢋⣉⡉⢻⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⠟⠛⠻⣷⡌⡿⢈⡿⡤⠯⣼⠴⡶⣷⣷⣣⡿⠛⠛⢿⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⢸⡇⠳⣾⣿⣾⡛⢿⣯⣽⣿⢁⣿⢡⣾⠿⣶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢿⣘⢿⡛⠿⣦⡙⣿⡾⠛⣩⣤⡾⠏⣼⠇⡶⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣟⡻⣷⡼⣷⣿⢡⣿⠏⣡⣶⣾⣫⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉

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

⠀⢠⣴⣶⣿⡖⠀⠐⣾⣿⣶⣤⠄⠀⠀⠀⠠⠔⠈⠉⠓⠠⠀⠀⣲⣾⠿⠗⠀⢀⣀⣀⣀⡀⠀⠺⠿⣷⣖
⠀⠉⠉⠀⡀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢠⠖⠒⢆⠀⠀⠀⠈⠀⠀⠀⠀⠄⠄⠀⠠⠄⠀⠀⡀⠀⠁
⠀⠀⠀⠀⢣⠀⣀⡀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢀⣬⣡⡄⠀⠀⠀⠀⠀⠈⣤⣤⣤⣤⣤⣤⣤⣤⡤⡇
⠀⠀⠀⣤⣸⣤⣤⣤⣼⣠⡄⠀⠀⠀⠀⠀⠄⡀⠉⠏⠁⡠⠄⠀⠀⠀⠀⠉⠀⠉⡉⠉⠉⠁⠈⠁
⠀⠀⠀⠈⠉⠉⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠈⠀⠘⠈⠉⠉⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠘⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣷⣶⡤⠄⠀⠀⠀⣴⡾⠿⠂⠀⣀⠀⠐⠿⢿⣶⡀
⠀⣠⣴⠀⢀⢠⢰⠒⠃⢀⢰⣤⡀⠀⠀⢀⡰⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⢠⣴⡄⠀⢀
⠀⠉⠁⠀⣰⡄⠀⠀⢖⡊⠀⠉⠁⠀⠀⠸⡿⠀⠀⢁⡀⠀⠀⠀⠀⠀⠀⠀⣥⠀⠀⠀⠀⠀⣤
⠀⠀⠀⢸⢿⣧⣜⢿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢿⠿⢿⣷⠀⠀⠀⠀⠀⠀⣀⢰⡆⡆⣆⢐⢰⡆⣀
⠀⠀⠀⠸⠴⠻⠿⠾⠇⠇⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⣀⣤⣴⣶⡤⠀⠀⠤⣶⣦⣦⣀⡀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢀⡐⠂⢀⠔⡁⠀⠀⠀⠀⠺⠟⠛⠉⠁⣀⣀⠈⠉⠙⠻⠟⠂⠀⠀⢀⢄⣠⣷⠂⠤⡀
⠀⠀⠀⠺⡿⠀⢀⢀⣀⠀⠀⠀⠀⠀⢠⣌⣦⣿⡿⠿⣀⣠⠀⠀⠀⠀⠀⠀⠠⠿⠿⠋⠰⠦⠈
⠀⠀⠀⠀⠀⠛⣹⡿⢻⡂⠀⠀⠀⠀⠈⢉⡉⠉⠀⠠⠋⣻⡈⠃⠀⠀⠀⠀⢀⢀⣈⣉⣉⡉⡉
⠀⠀⠀⠀⠀⢈⣉⢀⣉⡁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠁⠀⠀⠀⠀⠀⠈⠉⠉⣉⠉⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠴⠶⠒⠚⠛⠋⠉⠉⠉⠉⠛⠛⠒⠲⠶⢤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠲⣄⡑⠦⢰⠌⢿⠳⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢤⣀⠹⠖⠬⣍⠒⠄⠉⠀⠀⠈⠂⠙⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢦⣄⠉⠑⠒⠦⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢤⣀⣉⡉⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣤⣄⡀⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⢠⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢡⠶⠖⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⢠⢟⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⣤⡤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⣾⠛⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⣀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⢸⠣⠞⠁⣀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⡟⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠶⠦⢄⣠⠴⠖⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⢸⠇⠈⣠⠶⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⣼⠀⠀⠁⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠓⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⡿⠀⠀⠼⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⠀⣠⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⡇⠀⠀⢀⠴⡶⠶⠶⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠁⣀⣤⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⡇⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⣾⠟⠁⠀⢀⡄
⣷⠀⠀⠀⠞⠙⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣠⡾⠋
⢹⠀⠀⠀⢀⡼⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉⠉⠋⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠘⡇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⠖⠶⡟⠁⣠⡞⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⢿⠀⠀⠀⠴⠛⠶⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⣴⠾⠋⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠈⣇⠀⠀⢠⡴⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⢀⣰⣤⡾⠃⣠⠇⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠘⣆⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠛⠁⢀⣴⠶⢏⣀⡞⠀⢸⠁⢰⠀⣴⢀⡆⠀⠀⡀⢰⠇
⠀⠀⠀⠘⣆⠈⠛⠛⠳⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⢁⣠⠞⠉⣱⠖⢣⡤⢇⣰⣃⣾⣠⡤⠼⣿⠋
⠀⠀⠀⠀⠘⢦⠐⠲⠷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠞⠁⡠⠟⢠⠞⣡⠋⡜⠁⢁⡾⠃
⠀⠀⠀⠀⠀⠈⢳⡴⢤⣍⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠙⢶⡤⣝⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣾⣙⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣭⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⠦⣤⣄⣀⣀⣀⡀⠀⠀⠀⢀⣀⣀⣀⣤⡤⠶⠖⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠚⠉⠁⢀⣴⠞⠁⠀⠀⠀⠉⠉⠛⠲⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣎⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣄⡀⠄⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠙⠻⠶⣦⣤⣤⣾⡷⠶⠶⠚⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠙⠛⠦⣽⣄
⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢇
⠀⠀⠀⠀⠀⠀⢀⠏⠀⢀⣠⣤⣤⣶⠶⣾⡿⠶⠶⣶⣶⣦⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⣸⡴⠟⠋⠉⠁⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢀⣀⣸⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠀⣠⣀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⣴⠾⠛⠛⢻⣿⠋⠙⠛⠻⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠸⡇⢀⣼⠏⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠈⠙⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⡇
⠀⠀⠀⠀⠀⠀⣧⣾⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⡇
⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟
⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣄⠀⠀⣠⣴⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣄⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣙⣿⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣻⣿⣿⣷⣤⣄⠀⠙⣷⡄⠀⠀⠀⠀⣀⡀⢀⢀⣠⣴⣾⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣼⣿⣶⣿⣿⣾⣷⣿⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡿⠟⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠘⠁⠉⠉⠉⠉⠉⠉⠁⠁⠀⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⢦⣴⠟⠉⠉⠉⢿⣀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢦⡾⡃⠀⠀⢡⡂⠀⠀⠀⣨⡍⠉⠁⠈⠙⠻⣟⠻⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠐⠉⣀⠐⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⡀⠀⠀⠁⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡶⠞⠛⠁⠀⡀⠀⠀⠁⠀⠀⠀⠀⣀⠀⠀⠀⠦⠀⠀⠘⠏⠀⠀⠀⠀⠀⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⡭⠉⠀⢀⡄⠀⠀⠀⣠⠄⠀⠃⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠁⠀⠀⠘⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢁⠀⠀⠀⣀⠀⠀⠀⢴⢲⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⠟⠈⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠙⠀⠀⠀⠀⠀⢤⠄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣿⠀⣴⡀⠀⠀⠀⣠⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢸⡟⢦⣄
⠀⠀⠀⠀⠀⠀⣠⡾⠋⣰⡟⠀⠠⡄⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⡀⠀⠀⠀⠺⠑⠀⠀⠀⠀⠀⠀⢠⡄⣾⡅⠀⢻⣆
⠀⠀⠀⠀⠀⠀⣿⡀⠀⢿⡄⠧⠀⠉⠀⠀⢾⣉⡀⠀⠀⠀⣏⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⣾⣿
⠀⠀⠀⠀⠀⠀⡟⠳⣄⠈⠙⢶⣄⡀⠀⢠⡄⠀⢀⡴⡄⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⢀⡾⠃⣿
⠀⠀⠀⠀⠀⠀⣿⠀⠈⠛⢶⣄⡈⠛⠷⣤⣄⠀⠈⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠩⠃⠀⠀⣤⡶⠾⠋⢀⣴⠟⠁⢀⣿
⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠈⠙⠶⢤⣄⡙⠷⠶⠿⠿⣶⣤⣤⣤⣌⣁⣀⡀⣀⢀⡀⡀⠀⣀⣀⣀⣤⠶⠶⠶⠞⢃⣠⡴⠞⠋⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠶⠦⣤⣄⣈⣉⠉⠉⠉⠙⠙⠛⠛⠛⠛⠉⠉⣉⣀⣠⡤⠶⠞⠋⠁⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠉⠙⠛⠲⠶⠶⠦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠴⠶⠞⠋⢁⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⣦⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡴⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⠿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣄
⠀⠀⠀⠀⠀⢀⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠿⣿⣿⣧⡀
⠀⠀⠀⠀⣠⣿⡿⠋⠉⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣦⠀⠛⠉⢿⣿⣄
⠀⠀⠀⣰⣿⡟⠀⠀⠈⠛⠛⠃⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⡿⠀⠀⠀⠀⢻⣿⣆
⠀⠀⣰⣿⡟⠀⠀⠀⠀⠀⠐⠶⢾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢿⡀⠀⠀⠀⠀⠀⠀⢻⣿⣆
⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣰⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢾⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡆
⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿
⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿
⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⣠⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡙⠋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⢻⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣄⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿
⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣴⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁
⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢲⡄⢈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣤⣤⣀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠃
⠀⠀⠀⠘⣿⣷⡀⠀⠀⠀⠀⠀⣤⠈⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠏⠈⡉⠀⠀⠀⠀⠀⢀⣾⣿⠃
⠀⠀⠀⠀⠈⢿⣿⣆⠀⠀⠀⠀⢿⣦⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠛⠆⠀⠀⣰⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⣿⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⣶⣤⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣷⣶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣾⣿⠿⠟⠋⠁

⠢⡀⠀⢸⣵⡴⢡⡤⢚⣭⣞⡵⠃⢒⠭⣓⡂⡿⠿⢷⣿⠿⣿⣿⣿⣿⣴⣶⠴⣻⣧⡶⢃⢽⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣯⡀
⣀⣘⣶⣿⣿⣿⣿⣿⣛⡽⠏⡴⣡⢱⣝⠲⢭⣯⣾⠿⠟⣿⣟⣽⣿⣟⠻⠿⣮⠍⣻⡗⠁⢌⢻⣿⣿⣿⣿⣿⣷⡽⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣭⣽⣟⣿⣣⣾⣿⣿⠺⣯⣶⣶⠟⡉⢉⣿⣿⣿⠷⣤⠤⣺⣿⡇⡀⡵⣹⣿⣿⣿⣿⣿⣿⣿⣦⡹⢿⣿⣿
⢋⣿⣿⣿⣿⣿⣿⣿⣯⣥⠝⢩⣿⣧⣿⣏⠁⢿⣋⣁⣠⣴⢿⣿⣿⣿⣷⡌⢷⣽⣿⡟⢻⣧⠱⡿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣽⡿⣿⣿⣿⢿⣿⡿⣿⠶⣦⠽⠟⣿⢡⡑⠀⠙⣿⡿⠁⣼⠋⠙⢹⣾⣷⣽⠿⠋⢨⣿⣿⣧⢻⠈⠏⠛⣿⣿⡿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⡃⢈⠀⠻⢪⠀⠙⠷⢀⠀⠉⠀⠀⠀⠀⠈⠃⠳⣇⠀⡞⢸⣿⠟⠉⠀⠰⡿⣿⡟⠏⠂⠁⠀⠀⠘⠈⠀⠘⢿⣿⢿⣿
⣿⣿⣿⣿⣿⣶⣄⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠻⠳⣝
⡝⢿⣿⣿⣿⣿⣮⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢒⣬⣾⣷⣿
⡝⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣒⣞⣿⣿⣿
⣿⣏⢿⣿⣿⣿⣿⣿⡝⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⣉⣽⣿⣿⣿
⣿⣿⣖⢹⣿⣿⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⡠⡄⠀⠀⠀⠀⠀⠀⠀⡼⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⣛⣽⣿⣿⣿
⣿⣿⣿⣷⣿⣿⣿⡿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢄⣴⠃⣀⠀⡀⠀⢀⡄⣼⢋⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡹⠟⠑⡉
⢻⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠠⡏⢀⡼⢸⡋⢾⢽⡧⣏⠰⠟⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⢠⠀⡶
⠀⠛⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⣤⣤⣄⠈⣩⣄⠀⢠⣤⣤⡀⣤⣤⣤⣤⣤⡀⢠⣤⠀⠀⠀⠀⠠⣢⡐⠌⠃⡀⡀⢁
⢰⢠⢏⣾⣿⣿⣿⣿⡷⠂⠀⠀⠀⠀⠀⣿⣥⣿⢂⣿⣻⡄⢸⣯⣼⡿⠀⢹⡏⠀⠘⣷⡿⠃⠀⠀⠀⠀⠀⠲⢮⣿⣶⣿⣾⡎⣦
⣈⣜⣚⡻⠷⢾⣿⣿⠟⠀⣠⠈⠀⠀⠀⠿⠁⠀⠾⠏⠙⠷⠸⠏⠹⠷⠀⠸⠇⠀⠀⠸⠇⠀⠀⠀⠈⢤⡀⠈⢿⣿⣶⠶⠟⣛⣺
⠤⣄⠲⢭⡛⠲⠀⠀⠀⢌⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢋⠄⠀⠁⠰⢚⣫⠕⣂
⣝⢦⣙⣢⣀⣀⣀⡀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⣀⣠⢚⡥
⡎⣿⡏⢽⣿⣿⠏⠵⡷⠶⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡐⠛⢿⠳⠻⣿⣿⡷
⡇⢻⡗⣀⠘⣿⣠⡿⠁⢀⠞⢹⡀⠀⠀⠀⠀⠀⢠⡀⢐⣿⣿⢗⡀⠀⠀⠠⠀⠀⠠⣀⡘⠦⡀⠀⠀⣼⡄⠳⡀⠘⣇⡀⣿⠃⢀
⣷⣸⣷⠀⢠⣿⣿⣷⣞⣡⣴⣿⡇⠀⠀⠀⠀⠀⢸⡏⢸⣿⣿⠿⢂⠀⠉⠂⠀⢈⣐⡦⠝⠓⣬⢒⢸⣿⡿⣧⣼⣶⣿⣿⣇⠄⢠
⣝⣿⡙⣿⣿⣿⣿⣿⣿⡭⠾⢿⡇⠀⡀⠀⠀⡀⠀⢣⢟⣫⠴⣊⠡⣍⠂⠀⠀⡲⠾⡭⠔⠁⡄⡎⣿⡿⠛⢷⣿⣿⣿⣿⣷⣶⠿
⣿⣿⣿⣿⠻⠿⠿⣤⡬⢤⣦⣿⡇⠀⠐⡀⢸⠀⠀⠮⠓⠋⢉⡂⠀⢀⠀⠬⣿⣿⣿⢃⡇⡇⢧⢹⢸⣟⠓⠶⠦⡤⠿⡿⢿⣿⣾
⠚⣿⠻⣿⣻⣾⣤⡀⠀⣐⣾⠏⡂⠀⠁⠹⠈⢠⠃⠤⣒⠿⣑⠂⠀⠠⢄⣶⣿⣧⣿⢸⡇⠇⠘⡀⢁⢻⡯⣅⣀⣤⣼⣶⢿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠒⠒⠂⣈⣉⠭⠵⠶⢖⡒⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉⠁⠀⢀⡤⠒⠉⠁⠀⠀⠀⠀⠀⠈⠑⠢⢤⣉⢲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⣀⣤⡶⠾⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠁⠈⠢⣄
⠀⠀⠀⠀⠀⠀⢀⠞⢱⣴⡶⠟⠋⠁⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⡰⠃⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⡜⠁⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡶⠒⠊⠉⠉⠉⠉⠉⠉⠑⢺⣆⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⡸⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⢠⠃⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠸⠒⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⣠⡇
⠀⠀⡇⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠓⠒⠒⠒⠉⠙⣵
⠀⠀⡇⠀⠀⠀⢿⡄⠀⢀⣀⡤⠤⠒⠉⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢰⠀⠀⠀⠘⠏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠘⡄⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⢱⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⢣⡀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡹⠶⠶⠖⠒⠶⠾⠿⠟⠛⠳⢄⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠱⣄⣸⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠈⢯⡀⠉⠒⠤⣀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣎⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠀⠉⠑⠒⠲⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠦⣀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⠤⠽⢷⣄⣀⡀⠠⠤⠴⠒⠊⠉

⠀⠀⣰⣿⣄
⠀⠀⢸⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣰⣦⡀
⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃
⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠻⢟⠛⣻⠔⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡧
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣻⣿⡀⠉⢁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣴⠆
⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠁⢛⡍⠋⠗⢠⣿⣇⠀⠀⠀⠀⠀⠀⠠⢴⣦⣄⠀⠀⠀⠀⠀⢀⡀⠈⢹⣿⡟
⠀⣇⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⣄⠙⠁⠪⠹⠀⢜⣿⡄⠀⠀⠀⠀⠀⠀⡋⠉⢹⣆⠀⠀⠀⣰⣿⢑⣿⣿⣿⣧⡀⢀
⠀⣿⡄⠀⢹⣿⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⡩⢁⢺⣟⠀⠰⠟⢠⢿⣿⣷⣄⡀⠀⣠⡿⠃⠀⠀⣿⡄⢀⣼⡟⡁⠄⠘⢉⠩⠁⠄⣿⡇
⠀⠹⣷⠀⠸⣿⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠱⣾⣿⣿⣞⢀⣤⡀⠁⠈⠉⠛⠛⠛⠻⠗⠂⠀⠀⢻⣿⣿⠟⠁⢀⠂⡁⠦⡐⢈⢸⣿⡇
⠀⠀⢹⣇⠀⣿⠀⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣮⣰⣐⣀⣀⣀⣀⣀⣠⣴⣦⠄⠀⠀⠀⠉⠀⠀⠀⠠⠐⢀⣁⣄⠀⢸⣿⣀⣤⣤⣴⠶⣦⣤⡀
⠀⢀⠀⢻⡄⢿⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⡿⠿⠟⠛⠙⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠠⢘⠠⠁⠾⠟⠛⠉⠁⠀⠀⠈⠋⠊
⠀⢸⣦⡈⢧⢸⡇⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⡁⠄⠐⢈⢠⣡⣤
⠀⠸⣿⣷⣌⣾⣷⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⣠⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⣴⣀⠀⠅⣴⣿⣿⣿⡇
⠀⠀⣿⣿⣿⠿⠛⠛⠉⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠀⢶⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡷⢺⣿⣿⣿⣿⡇
⠀⠀⢹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣠⣤⣹⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⠟⠀⠸⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠠⣤⣤⣄⡀⠀⠀⠀⠀⣸⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡿⠁⠀⠀⠀⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣶⠀⠀⢰⣿⠋⠁⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⢹⣿⣿⡇
⠀⠀⠀⢰⣤⠀⠀⠀⠀⠙⣿⣿⠀⠀⠸⠇⠀⢀⣼⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡄⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣄
⠀⠀⠀⠈⣿⣷⡀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡗⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⡄
⠀⠀⠀⠀⢻⣿⣷⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇
⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⣿⣏⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡄
⠀⠀⠀⠀⠀⠈⠏⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⢰⣿⣿⣦⣄⣀⡀⠀⠀⠀⠠⠩⣭⣭⣝⢛⢻⡆⠀⠀⠀⠠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠋
⠀⠀⠀⠀⢀⣀⠴⠄⠒⠒⠛⠛⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⣿⢿⠿⠿⣿⣟⠿⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣟⣛⣿⣿⣻⣟⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⣷⠀⠀⠈⡟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⣿⣍⡟⠒⠋⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠛⠋⠃⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡗⠀⠀⠀⠀⢀⣼⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣠⡀⠀⠀⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡼⠁⠀⠘⣏⠸⣅⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⢠⣶⣆⣤⣴⡮⠃⠀⠀⠀⢠⣤⡀⠀⠀⠀⣟⣤⣤⠀⠀⠘⠄⣾⡄⠀⠀⠀⠀⠀⣿⡿⢩⡄
⠀⠀⢸⣿⣿⣿⣿⣷⣿⣶⣦⡴⠚⣿⡷⡆⠲⣾⣿⣿⣿⣦⠶⣶⣷⡿⠧⣀⠀⠀⠀⣤⣾⣾⡘⣇⠀⢸⣿⠓
⠀⠀⠈⠉⠉⢹⣿⣿⣿⠷⠀⠁⢼⣿⣿⣷⠀⢻⣿⣿⣿⣿⣀⣾⣿⣧⠷⢿⠀⠀⠀⢿⣿⣿⣷⡙⢀
⠀⠀⠀⠀⠀⠈⣿⣻⡏⠀⠀⠀⠘⣿⣿⠉⠀⣸⣿⣿⣿⣿⠛⠀⠿⠿⠇⠀⠀⠀⠀⠈⢻⣿⣿⠻⢾⡄
⠀⠀⠀⠀⠀⠀⣿⣿⣷⡤⠀⠀⢠⣿⣿⠆⢀⣿⣿⣿⣿⣯⡀⢰⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣷
⠀⠀⠀⢀⣀⡀⢻⡗⣿⡇⠀⠀⠈⢿⣿⠀⠀⣹⣿⣿⣿⣿⡇⠀⣇⠀⢤⡄⠀⠀⠀⠀⢹⣿⣿⣿⡇
⠀⠀⢸⣿⣿⣿⣾⣷⣿⣇⠀⠀⠀⢘⣿⠀⠀⣿⡯⣿⡇⢹⣇⠀⣿⠃⠀⣿⠂⠀⠀⠀⠀⣿⣏⣿⣿⡄
⠀⠀⠘⣿⣿⣿⣿⣿⣿⡄⣀⠀⠀⣾⡏⠄⠂⢹⡇⣿⡅⣾⠇⠀⣿⠀⢸⡟⠀⠀⠀⠀⢠⡿⢹⣿⣿⡏
⠀⠀⠀⠿⠿⢟⣾⣿⣿⣆⣀⣀⠄⣿⣧⡀⠀⣺⣇⣿⣲⣟⢀⣴⣾⣦⣼⡷⣄⡀⠀⠀⣿⡧⣽⣿⣿⠇
⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣶⣾⣿⣿⣹⣟⣛⡉⣿⣂⣸⣷⣆⣠⣄⣴⣿⣶⣿⣿⣿⡳⠀⠀⠀⠀⢀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣟⣒⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣿⣿⣿⣿⣭⠴⠖⣿⣟⣿⣿⣟⡋⠞⢠⠀⡀⢀
⠀⠀⠈⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣠⠔⢊⠝⠉⠉⠉⠻⡍⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣢⣶⣶⣶⣦⣲⣦⡀
⠀⠀⠀⠀⠀⣜⡡⠒⠛⣄⠀⠀⠀⢀⠞⠒⢤⣱⡄⠀⠀⠀⠀⠀⠠⢾⣯⣧⡻⣿⣿⣿⡿⣣⣯⣟⠦
⠀⠀⠀⠀⡜⢰⠁⠀⠀⡼⠉⠉⠉⠳⡀⠀⠀⡇⠸⡀⠀⠀⠀⢠⣿⣾⣿⣿⢟⣾⣾⣿⣮⢿⣿⣿⣿⣷
⠀⠀⠀⠀⡇⡸⠒⠤⢼⠀⠀⠀⠀⠀⢱⠤⠔⢧⠀⡇⠀⠀⠀⢸⣟⣽⣿⡋⣿⣿⣿⣿⣿⡯⣛⣿⡽⣿
⠀⠀⠀⠀⢷⡇⠀⠀⠈⢦⠀⠀⠀⣠⠃⠀⠀⢈⣶⠁⠀⠀⠀⠘⢹⣿⣿⣿⣝⣿⣿⣿⣿⣽⣿⣿⣿⠙
⠀⠀⠀⠀⠘⢷⣄⠀⠀⡰⠉⠉⠉⢱⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀⠩⡻⣿⣿⣟⣶⣶⣶⣎⣿⣿⣿⡫⠁
⠀⠀⠀⠀⠀⠈⠻⢍⡉⠓⢤⣀⡠⠜⠋⣉⠝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⣿⣮⣻⠿⢿⣫⣾⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠛⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⢀⡴⠊⢡⠎⠁⠀⠀⠙⢆⠙⠢⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⣷⣾⣿⣿⣷⡽⣶⣄
⠀⠀⠀⠀⢀⢮⣴⣿⣿⣦⣀⣀⣀⣠⣾⣿⣶⡼⣆⠀⠀⠀⠀⠀⣐⠟⠁⠀⠙⢿⣿⣿⡿⠃⠀⠙⢷⡀
⠀⠀⠀⠀⡎⢸⣿⣿⣿⠟⠁⠀⠈⠙⣿⣿⣿⡇⠸⡄⠀⠀⠀⢰⣿⠀⠀⠀⣠⣿⣿⣿⣧⡀⠀⠀⢸⣿
⠀⠀⠀⠀⡇⡜⠙⠛⢻⠀⠀⠀⠀⠀⡸⠛⠛⢣⠀⡇⠀⠀⠀⢸⣟⣶⣤⣄⣿⣿⣿⣿⣿⣗⣤⣴⣞⣿
⠀⠀⠀⠀⢻⡇⠀⠀⠀⠳⣀⣀⣀⡴⠁⠀⠀⢀⣿⠀⠀⠀⠀⠈⢸⣿⣿⣿⣮⠿⠿⠿⢟⣾⣿⣿⣿⠈
⠀⠀⠀⠀⠈⢻⣦⣀⣀⣼⣿⣿⣿⣿⡀⢀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠹⠿⣿⠏⠀⠀⠀⠀⢿⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠙⠦⣀⡉⠻⣿⠟⠋⣉⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣤⡀⣠⣴⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠋⠉⠉⠉⠉⠉⠉⠙⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⢠⡞⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠉⠀⠀⠀⠘⣇⢡⡄⣤⢠⢀⣦⣰⢄⡄⣤⣰⡄⣤⠲⣆⠀⠀⠀⠀⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⢠⠔⣿⢽⢴⡏⠺⠇⠿⣻⡸⠏⠻⢹⡟⠇⠀⢸⠇⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⡎⠻⣿⣧⠀⠀⠀⠙⠚⠁⠀⠈⠃⠀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠻⠂⠀⠀⠀⠀⣼⣿⠟⢱⣿⣿⢿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⢻⡗⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠃⢸⡟⢿⣿⣿⣿⣿
⣿⣿⣿⣿⠏⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠙⣿⣿⣿
⣿⣿⣿⠋⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠸⣿⣿
⣿⣿⠇⢠⠀⡄⣿⣿⢰⠠⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠖⠔⢄⡀⠀⠠⠄⠀⠀⠠⠀⣀⢺⠀⠀⣀⠄⡐⠀⠀⠀⣿⣷⠀⠠⠀⠹⣿
⣿⠋⠶⠀⠀⠁⣿⣿⠈⠰⡆⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠐⡘⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢀⠌⠸⠁⠀⠀⠀⢹⣿⠀⠀⠀⠀⢹
⣇⠀⠀⠂⠀⢸⣿⡏⠀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢈⠀⠀⠈⠀⠀⠀⡅⠀⠀⠃⠉⠄⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⢸⣿⡇⠆⠂⠀⠐
⠀⠀⠀⠀⠆⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇
⠀⠀⠀⠀⠀⣿⣿⣠⡅⠀⠀⢠⡄⠀⢀⡀⡀⠀⢀⡀⠀⠀⢀⣀⠀⠀⠈⠠⠀⠀⠂⠀⠀⠀⣁⠀⠀⢀⣄⠀⠀⠀⣀⠀⠀⠀⠀⣿⣿⢠⣤⡀
⢠⣶⣤⣷⢠⣿⣿⢿⡇⣤⣤⢸⣷⣦⠈⣿⣦⡄⢸⣿⢋⣀⢈⣿⣠⡄⢤⡀⢀⣀⣶⠀⣠⣄⣿⢡⣤⡸⣿⢀⣀⠀⣽⢃⣤⡀⢰⣿⣿⣾⣿⣇⣤
⣽⣿⣿⠿⣾⣿⣿⣿⣷⣽⣿⣿⣽⣯⣴⢟⣿⣧⡾⣷⣽⣟⣼⣿⣿⣿⣿⣷⢘⣿⣿⣰⣿⣿⣿⣌⣿⣄⣿⣞⣿⣱⣿⣿⣿⣧⣼⣿⣿⣿⣿⣯⣿
⢹⣿⣿⣧⣿⣿⡟⣿⢹⣿⣿⣿⣿⣿⣱⠟⢿⣿⣁⣹⣿⣿⡟⣼⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣯⣿⣿⡿⢹⣿⣿⣿⣱⣟⣿⣿⡌⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣼⣜⣿⣿⣯⣿⣿⣵⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣯⣀⣸⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣽⣿⣷⣿⣼⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⣿⡟⣩⠿⣩⣿⣿⡿⢻⢿⠙⣿⣿⣿⣿⣿⡿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⣿⣿⣿⣿⠃⡟⢰⡏⣰⣿⣿⣿⡇⢻⣿⢸⡿⣽⡿⢿⡏⣼⣯⢡⣽⣿⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⣷⣾⢸⠃⣾⠃⣾⣿⣿⣿⢁⣿⡇⢼⠁⣏⠞⣩⢰⠉⡇⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣷⣿⣷⣿⣿⣿⣿⣿⣿⣷⣾⡷⣿⢃⣿⣾⣤⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣭⣭⠀⠀⢀⡀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠣⡔⠄⠀⠠⣬⣭⣭⠀⠀⣀⡀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⡔⠄⠀⠠
⠀⠀⠀⠀⠈⠩⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠅
⣤⣿⣶⠂⠀⠀⠀⠀⠀⠀⠀⢤⣤⡀⠀⠐⢦⣖⡀⠀⠀⢀⣤⣿⣶⠂⠀⠀⠀⠀⠀⠀⠀⢤⣄⡀⠀⠂⢴⣖⡀
⠘⠁⠉⠀⠀⠀⠀⡴⠚⠀⠀⠀⠉⠁⠀⠀⠀⠈⠀⠀⠀⠀⠘⠁⠉⠀⠀⠀⠀⡔⠊⠀⠀⠀⠈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢠⡀⠀⠰⣶⠆⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⠀⠀⠰⣶⠆⠀⢀⣴⣶
⠀⠀⠀⢀⣠⣠⠄⠀⠀⠀⣴⠗⠁⠀⠀⠦⠀⠀⠀⠙⠉⠀⠀⠀⠀⢀⣠⣠⠀⠀⠀⠀⣶⠗⠁⠀⠀⠶⠀⠀⠀⠙⠉
⠴⠒⡶⠿⠸⠗⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⢀⠔⠒⡶⠿⠹⠗⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⢁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠚⠋⢁⠀⠀⠀⠈
⠀⠀⠀⣶⡿⠆⠀⡔⠀⠀⠀⠀⣰⣹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡿⠖⠀⡔⠂⠀⠀⠀⣀⣿⡿
⠀⠀⠀⠈⠁⠑⢺⡷⠀⠀⠀⠈⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠑⢺⣷⠀⠀⠀⠈⠙⠋⠉
⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠀⣠⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⣭⣭⠀⠀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡔⠀⠀⠠⣬⣭⣭⠀⠀⣀⣀⣀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⡔⠁⠀⠠
⠀⠀⠀⠀⠈⠩⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⠅
⣤⣿⣶⠂⠀⠀⠀⠀⠀⠀⠀⢤⣤⡀⠀⠀⢶⣖⡄⠀⠀⢀⣤⣿⣶⠂⠀⠀⠀⠀⠀⠀⠀⢤⣤⡀⠀⠊⢶⣖⡄
⠘⠁⠉⠀⠀⠀⠀⡌⠊⠀⠀⠀⠈⠁⠀⠀⠀⠀⠂⠀⠀⠀⠘⠁⠉⠀⠀⠀⠀⡬⠊⠀⠀⠀⠈⠁⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢠⡀⠀⠰⣶⠆⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢠⡀⠀⠰⣶⠄⠀⢠⣶⣶
⠀⠀⠀⢀⣠⣠⠄⠀⠀⠀⣶⠟⠀⠀⠀⠶⠀⠀⠀⠉⠉⠀⠀⠀⠀⢀⣠⣠⠀⠀⠀⠀⣾⠟⠀⠀⠀⠶⠀⠀⠀⠉⠉
⠔⠒⡲⠿⠙⠛⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠔⠒⡲⠯⠹⠗⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠐⠚⠋⢁⠀⠀⠀⠈⠁⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⠋⣁⠀⠀⠀⠈⠁
⠀⠀⠀⣶⡿⠆⠀⡜⠀⠀⠀⠀⣰⣹⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡿⠆⠀⡜⠂⠀⠀⠀⣐⣹⡿
⠀⠀⠀⠈⠉⠉⢺⣷⠀⠀⠀⠈⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⢺⣷⠀⠀⠀⠈⠉⠋⠉
⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣠⣄⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⡁⡁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⣤⣤⡤⠤⠤⠤⠤⠤⢤⣤⣤⣤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⣠⡴⠚⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⣦⣄
⠀⠀⠀⣴⠋⠙⠓⠲⠦⠤⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⡤⠤⠴⠖⠚⠋⠙⣦
⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣀⣀⠀⢀⣠⣤⡀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠛⣿⣧⡿⣩⠼⢻⣦⣾⡿⣛⣣⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⡿⠋⢷⣆⣤⡾⠋⢿⣷⣽⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠻⠦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠴⠟
⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠓⠒⠲⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠒⠚⠛⠛⠋⠉⠉⠁

⠀⠀⠀⢀⡠⠤⠤⠤⡀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⢄⡀⠀⠀⠀⠀⣀⣤⣤⣤⣄⡀
⠀⠀⡔⠁⢧⠒⠊⠉⠉⠳⡀⠀⠀⣴⣿⣩⣵⣶⣾⣿⣦⠀⠀⢀⠾⣁⢀⡠⠄⠠⢝⢆⠀⢀⣜⠿⡿⢟⣯⣭⣟⢆
⠀⢸⢇⠀⠈⠢⡤⠄⢦⠤⡇⠀⢈⢿⣿⣷⣝⣛⣿⡟⣟⡃⠀⡎⠀⠈⠉⠀⠀⠀⠈⡞⠀⣼⣿⣿⣿⣿⣿⣿⣿⣾⡆
⠀⠘⡄⠑⢄⡼⠀⠀⡆⢠⠇⠀⠘⣷⣝⡿⢧⣿⣿⢷⣿⠃⠀⠱⣀⠤⠤⢤⣀⣀⡴⡹⠀⠸⡿⣛⣛⡿⢿⣿⡿⡹⠁
⠀⠀⠈⠲⢎⣀⣀⡴⠕⠁⠀⠀⠀⠈⠛⢵⣿⣿⠟⠞⠁⠀⠀⠀⠙⠢⢄⣀⣈⠥⠚⠁⠀⠀⠘⠻⢿⣿⣷⡶⠛⠁
⠀⠀⠀⢀⣀⠀⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⣤⡀
⠀⠀⠰⠛⢁⣀⡀⠛⠻⠂⠀⠀⠀⣠⣤⡾⣿⢿⣦⣄⣤⠀⠀⠀⠀⠀⠀⠀⢈⡛⢦⡀⠀⠀⠀⣠⣾⣿⡿⢦⣍⠓
⠀⢠⡀⠀⣼⣿⣷⠀⠀⣠⡀⠀⠐⢿⣿⠁⠀⠘⣿⣿⠟⠆⠀⠀⠀⠀⠀⣰⠿⠁⠀⠉⠀⠀⣰⣿⣿⠟⢠⣾⣿⠇
⠀⠘⣿⠀⠀⠉⠀⠀⢸⣿⠇⠀⠀⠰⣿⣿⣶⣿⣿⡇⠀⠀⠀⠰⣦⡀⠾⠋⠀⠀⠀⠀⠀⠀⠻⣿⣃⣴⣿⣿⠏
⠀⠀⠀⠀⢰⣾⣶⠄⠀⠀⠀⠀⠀⠈⠻⠟⠉⠙⡿⠟⠁⠀⠀⠀⠈⠙⢦⡄⠀⠀⠀⠀⠀⠀⢷⣌⡛⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣄⠀⠀⠀⠀⢀⡤⠂⠀⠀⠂⣄⠀⠀⠀⢀⢠⣶⣾⣶⣶⠄
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣟⣿⣿⣿⣿⣷⡀⠀⠠⢡⠇⠀⢀⠖⠉⠉⢁⠀⢠⡟⣼⣿⡿⣣⣶⣿⣧
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠂⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⠎⠀⠀⣾⠀⠀⠀⠨⠀⠘⣴⣿⣿⠅⣿⣿⣿⣿
⠀⠀⠀⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣿⣿⣿⣿⠟⠀⠀⠈⢄⠀⠀⠸⣄⠀⢀⠆⠀⠈⢿⣿⣿⣇⠻⣿⣿⠏
⠀⠀⠀⠀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⢁⡂⠀⠈⠋⠀⠀⠀⠀⠀⢉⡛⠛⠓⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⣈⠀⠀⠀⠀⠀⠀⠀⠀⠻⠛
⠀⢻⣦⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢾⠀⠀⠀⠀⠀⠀⠀⠀⣨⡅
⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠⠀⡠⢂⡉⠉⠑⢦⠀⠀⢠⣿⣿⣶⢾⣿⣶⣄
⠀⠀⠀⠩⡑⠀⠠⠐⡈⠩⠴⠀⡀⢻⣦⣤⣤⣶⣿⣿⣿⣤⣄⠀⠀⢸⠀⠠⠐⠂⠀⠀⠁⠀⢻⣷⣿⣟⣿⣽⣿⣿⡇
⠀⠀⠀⠀⠑⠀⠀⠀⠉⢠⡀⠄⠃⠀⠹⣿⣿⣿⣷⡿⠿⠿⠛⠀⠘⣘⡀⠀⠀⠀⠀⢀⠆⠀⠘⣿⢿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠠⠀⠒⠁⠀⠀⠀⠀⠀⠙⠛⠛⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠶⠒⠚⠛⠉⠉⣉⡭⠿⠒⠒⠶⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠋⠁⠀⠀⠀⠀⢀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⢳⡀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⢳⣤⣶⣶⡺⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⣴⡿⠋⠀⢀⡇⡿⠤⠤⠤⠤⠤⢤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⣠⠏⢀⣀⠤⠖⠚⠙⡿⣇⣀⡤⢞⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠒⠲⠤⣄⣀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⢰⡧⠖⠉⠀⠀⠀⠀⠀⡹⠶⠶⠒⠛⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⡀⠀⢹⡄
⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⣧
⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾
⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠘⡇⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⣧⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠸⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠱⡀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠱⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠙⢆⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡽⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠦⠤⢤⣤⣀⣀⣀⣠⣤⠤⠴⠖⠚⠉


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⡾⠓⠲⠦⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢤⡴⠖⠛⠛⠒⠲⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⣠⠏⠀⠉⠛⠛⠉⠀⠀⠀⠀⠠⡀⢀⣀⡀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠐⠀⢀⠀⠀⠤⠀⠀⠀⠀⠤⠤⠀⢀⠈⠳⣄
⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡆⠀⢻⡄⠀⠀⠀⠀⢠⠛⠀⢀⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡄⠀⣷⠀⠀⠀⠀⡎⠠⠇⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⢸⠃⠀⣠⣾⣿⣶⣄⡀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⡿⠇⠀⣹⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⢸⡀⠸⣿⣿⣿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠙⠿⠋⠁⠀⠀⣿⠀⠀⠀⠈⣧⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠘⣇⠀⢹⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⢀⣼⠁
⠀⠀⠀⠀⠀⠹⣆⠀⠛⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠈⢷⡀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⣷⣦⣴⠏⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠈⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⢰⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣄⡀⠀⠈⠀⠀⠀⢀⣀⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠚⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠒⠚⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠶⠤⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⢀⣬⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠈⣆⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⣉⣉⠻⢿⣷⡀
⠀⠀⠀⠀⡌⠀⠀⠉⠉⠛⠻⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠘⣆⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢼⡟⠛⣷⠀⢻⣷
⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣿⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⠾⣿⡀⠀⣿⡇
⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿⣅⢀⣽⠇⣸⣿⡇
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠙⠛⠛⣋⣴⣿⣿⠇
⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⢀⣀⣠⣿⡠⠤⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢿⣿⣿⣿⡿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠚⠋⠉⠉⠒⠒⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠶⠛⠉⠙⠒⠒⠢⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠉⠳⣄
⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⣴⣶⡄⠀⠀⣠⣄⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⢀⡾⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠐⢿⡿⠃⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⡼⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠈⠱⡀⢻⡄
⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠈⢂⠀⠀⠀⠑⠀⢳
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢺⠀⠀⠀⠀⠀⠂⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠘⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⡀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣄⡈⠀⠀⠀⡚⠀⢀⣠⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠿⠿⠿⠿⠿⡿⢯⠻⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣛⣛⣿⣿⣿⣿⣛⣛⣛⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢴⣶⣶⣶⣶⣤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢄⣀⣠⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⡴⠋⠀⠀⠀⠀⠙⢦⠈⠑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⣣⣾⣿⣿⣿⣿⣮⢻⣷⣄⡀
⠀⠀⠀⠀⠀⠀⢠⣋⣠⠖⠋⢣⡀⠀⠀⠀⠀⢀⠜⠑⠲⣄⢹⣄⠀⠀⠀⠀⠀⠀⠀⠠⡾⣛⣽⣦⡻⣿⣿⣿⣿⣿⢟⣵⣯⣛⢷⡄
⠀⠀⠀⠀⠀⢰⠃⣸⠀⠀⠀⠀⡹⠒⠒⠒⠒⢏⠀⠀⠀⠀⡏⠘⡆⠀⠀⠀⠀⠀⢠⣿⢸⣿⣿⣿⡿⣨⣭⣭⣭⣍⢾⣿⣿⣿⣷⣾⡆
⠀⠀⠀⠀⠀⡾⠀⢿⠀⠀⠀⡼⠁⠀⠀⠀⠀⠈⢧⠀⠀⢀⡇⠀⣷⠀⠀⠀⠀⠀⣼⣿⢸⣿⣿⡿⣱⣿⣿⣿⣿⣿⣧⢻⣿⣿⡟⣿⣷
⠀⠀⠀⠀⠀⡇⢠⠋⠉⠉⠛⣇⠀⠀⠀⠀⠀⠀⣸⠛⠉⠉⢱⡀⣿⠀⠀⠀⠀⠀⣿⢯⣶⣶⣶⣆⢿⣿⣿⣿⣿⣿⣿⢣⣶⣶⣶⡹⣿
⠀⠀⠀⠀⠀⢹⣾⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⡰⠃⠀⠀⠀⢀⡷⡇⠀⠀⠀⠀⠀⢨⢸⣿⣿⣿⣿⣎⢻⣿⣿⣿⡿⣣⣿⣿⣿⣿⡇⡁
⠀⠀⠀⠀⠀⠈⢯⢦⡀⠀⠀⠀⡼⠉⠉⠉⠉⢧⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⠀⢣⢻⣿⣿⣿⡿⣱⣶⣶⣶⣦⢻⣿⣿⣿⡿⡙⠁
⠀⠀⠀⠀⠀⠀⠀⠳⣟⠲⠶⠾⣅⠀⠀⠀⠀⣸⠦⠤⠖⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢭⣽⣛⣑⢿⣿⣿⣿⡿⢎⣛⣛⡭⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⢄⣈⡙⢲⡖⣋⣁⡠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢷⣮⠩⣽⡶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢚⡿⠛⠛⠛⠛⢿⡒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⣠⣤⣤⣤⣄⠰⣤⣀
⠀⠀⠀⠀⠀⠀⠀⡴⠋⢀⣠⡎⠀⠀⠀⠀⠀⠀⢱⣄⡈⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠏⣾⣿⣿⣿⣿⣿⣷⠝⠿⣷⣄
⠀⠀⠀⠀⠀⠀⡼⢧⣾⣿⣿⣿⣦⣀⣀⣀⣀⣴⣿⣿⣿⣷⡼⢧⠀⠀⠀⠀⠀⠀⠀⣤⠛⠁⠀⠀⠈⠿⠿⠿⠿⠿⠃⠀⠀⠀⠙⣃⡀
⠀⠀⠀⠀⠀⣸⠁⣼⣿⣿⣿⣿⠏⠉⠀⠀⠉⠻⣿⣿⣿⣿⡇⠀⣇⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⢀⣾⣿⣿⣿⣷⡄⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⡏⠀⡹⠿⠿⣿⡏⠀⠀⠀⠀⠀⠀⢹⣿⠿⠿⣇⠀⣿⠀⠀⠀⠀⠀⣿⡿⣀⣀⣀⠀⣾⣿⣿⣿⣿⣿⣿⡄⣀⣀⣀⢿⣿
⠀⠀⠀⠀⠀⢧⣸⠁⠀⠀⠀⢣⡀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠘⣆⡟⠀⠀⠀⠀⠀⠿⢱⣿⣿⣿⣷⡹⣿⣿⣿⣿⣿⡟⣼⣿⣿⣿⡎⡿
⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⢳⣤⣤⣤⣤⡞⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⠙⠿⠿⠛⠋⣼⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠹⣷⣄⡀⠀⢀⣿⣿⣿⣿⣿⣿⡀⠀⢀⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡏⠀⠀⠀⠀⠀⠸⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣍⡉⠉⠻⢿⣿⣿⡿⠟⠉⢉⣩⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢶⣶⣦⣄⠀⠀⠀⣀⣴⣶⡶⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠢⠤⠼⠥⠤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠒⠛⠛⠉⠁

⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇
⡇
⠓⢲⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⢲⠒
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠖⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶
⠀⠀⠀⠀⠀⠀⢠⣾⣷⠈⣿⣧⣴⣎
⠀⠀⠀⠀⢀⣀⠈⢩⣿⣿⣿⣿⣿⠿⣷
⠀⠀⢀⣾⣿⣿⣿⣷⣽⣿⣿⣯⣠⣤⠶⠾⠇
⠀⢀⣼⠿⠛⢙⣫⣿⣿⣿⣿⣿⣧⣀
⠀⠀⠀⢠⢞⣩⣾⣿⣿⢹⣧⠉⠛⣿⣧
⠀⠀⣠⠶⣻⣿⣿⣿⠃⢸⣿⡆⠀⠙⠁
⠀⠚⠉⠜⠋⢿⣿⠋⠀⠸⠟⠁⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⠀⠀⠀⠀⠀⣠⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⢀
⠀⠀⠀⠀⠀⢸⡇⠀⣴⣶⠀⠀⣀⣴⠏⠀⠀⢠⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣥⣤⣤⠶⠛⠁⠀⣾⣿⡆⠀⠀⠀⢀⣠⣼⣿⣇⡀⠸⣇
⠀⠀⠀⠀⠀⣾⠆⠀⣘⣿⣿⣿⠋⢀⡀⠀⠰⣿⣿⣿⣷⣦⡀⢀⣤⡄⣰⣿⣿⣿⣿⠉⠀⠀⠀⠀⣼⣿⣿⣿⣦⣠⡶⠟⣿⣿⣿⣿⠿⢷⣿
⠀⠀⠀⠀⠀⣿⠀⠀⣿⣿⣿⣿⡆⠈⠻⣦⣤⡿⣿⣿⣿⠻⣷⡾⠃⣰⡿⠹⣿⣿⣿⡄⠀⠀⠀⣠⣿⣿⣿⣿⣿⡟⠀⢀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⠀⢰⡿⣿⣿⣿⡇⠀⠀⠈⠉⣰⣿⣿⡟⠀⠈⠀⢀⡟⠁⠀⢻⣿⣿⣿⣄⠲⠞⠋⢹⣿⣿⡟⠉⠁⠀⣸⣿⣿⣿⣇
⠀⠀⠀⠀⢸⡇⠀⣸⢱⣿⣿⣿⠇⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠁⠀⠀⣸⣿⡿⢿⣿⣦⠀⠀⢻⣿⣿⣿⡄⠀⠀⣿⣿⠙⣿⣿
⠀⠀⠀⠀⣸⠃⠀⠉⠘⣿⣿⣿⠀⠀⠀⠀⠀⢹⣿⠘⣿⡇⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⣹⣿⠁⠀⠘⣿⡏⢻⣷⠀⠀⠸⣿⠀⢸⣿⡇
⠀⠀⠀⢠⡟⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⣼⠇⠀⢸⣷⠀⠀⠀⠀⣴⣿⠏⠀⠀⣰⣿⡟⠀⠀⠀⣿⠃⠀⢿⡇⠀⠀⢹⣷⣾⡿
⠀⠀⠀⣼⠁⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣏⢀⣀⣀⣿⣿⣯⣤⣤⣤⣽⣿⣤⣤⣀⣀⣟⠀⠀⠸⣇⠀⣀⣸⣿⣿⣷⣶⣶⣤
⠀⠀⣸⣇⣠⣤⣤⣴⣶⣿⣿⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⢀⠔⢪⣥⣤⠔⠛⠳⣄⠀⠀⠀⠀⠀⣤⠎⠉⠀⠀⠈⠑⣦⡀⠀⠀⠀⠀⡠⠚⠙⠂⢄⠉⠳⡦⡀
⠀⠀⢠⣃⠴⢿⣿⠿⠤⡀⠀⡇⢱⠀⠀⢀⠎⠸⠀⠀⠀⠀⠀⠀⡄⠘⡄⠀⠀⣎⠝⠉⡲⡄⠀⠑⡀⠈⣸⡄
⠀⠀⢼⡁⠀⠀⠁⠀⠀⠈⣿⣿⡦⡇⠀⢸⠀⠀⠑⡀⠀⠀⠀⠜⠀⠀⡇⠀⢸⡇⠀⠌⠀⢈⠤⠤⠵⠒⠁⡁
⠀⠀⠸⡑⠤⣴⣷⣤⠔⠊⠙⡏⣰⠁⠀⠈⡄⠀⠀⡇⠀⠀⠸⠀⠀⢀⠇⠀⠈⢇⢸⠀⠀⠇⣀⣀⡀⠤⢊⠇
⠀⠀⠀⠑⢄⡿⠻⠻⢄⣀⣤⠗⠁⠀⠀⠀⠈⠢⣜⠀⠀⠀⠀⢑⡤⠋⠀⠀⠀⠈⠺⣄⠀⣄⢀⣀⣀⡴⠊
⠀⠀⠀⠀⠀⠈⠉⠐⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠉⠁
⠀⠀⠀⠀⢀⣠⣄⠲⡆⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⡲⠦⡄⠀⠀⠀⠀⣀⠤⠐⠒⠠⢄⡀
⠀⠀⠀⡔⣉⠤⠔⢳⠺⡶⡯⣑⣄⠀⠀⠀⠀⠀⡤⢪⣱⠴⠋⢿⣿⣦⡇⠀⠀⢠⠚⢧⡀⠀⠀⠀⢠⠟⢢
⠀⠀⢸⠋⠀⠀⢀⠎⠀⡇⠱⡀⠙⡄⠀⠀⢠⢎⣮⠟⠉⠀⠀⠀⠙⢿⠇⠀⠀⠇⠀⠈⣇⠀⠀⢀⡟⠀⠀⡇
⠀⠀⢡⠀⠀⡠⠋⠀⠀⡇⠀⠱⢀⠇⠀⢀⣧⡼⠋⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⡆⠀⢀⡇⠀⠀⠀⣇⠀⠀⡆
⠀⠀⠈⢆⢠⠃⠀⠀⠀⡇⠀⢠⠟⠀⠀⢸⢿⣷⣦⡀⠀⠀⢀⠴⠃⠀⠀⠀⠀⠑⣤⡾⠁⠀⠀⠀⠹⣦⡴⠁
⠀⠀⠀⠀⠙⠢⠤⣀⡴⠥⠖⠁⠀⠀⠀⠘⠄⣙⡿⠿⠖⠊⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠤⠤⠤⠒⠉

⠀⠀⠀⣴⡆⠙⠂⠀⢀⠀⠑⠡⠔⠄⠀⠀⠂⠀⠀⠂⠀⠀⠤⢉⠀⠑⢀⠀⠀⠀⡠⠝⢿⡅⠀⠐⠄⠀⢠⠂
⠀⠘⠇⣠⡀⠸⠗⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠠⠀⣠⡜⠀⠀⠀⠁⠀⠀⡘⠀⢠
⠀⠀⠀⢯⣥⡴⠃⠀⠀⠰⣤⣤⠤⠁⠀⠀⠦⣤⣤⠆⠀⠀⠰⢤⣤⡴⠀⠀⠈⠿⣦⡤⠄⠀⠀⠈⢥⣤⡤⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠔⠒⠒⣒⣲⣶⣦⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠒⠉⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡌⠳⣄
⠀⠀⠀⠀⠀⠀⡠⢾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣿⡿⠟⠁⠀⠈⠑⡄
⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⢀⡞⠀⠀⠀⣠⣤⣤⣤⣶⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⡜⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⢠⠃⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢸⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣶⣄⠀⠀⠀⢠⣿⡇
⠀⠀⢸⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠘⡇
⠀⠀⢸⣀⠀⠀⠀⠘⢿⣿⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠃
⠀⠀⠈⣿⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠰
⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢀⠂
⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠿⠃⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⢀⣠⣿⣶⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣐⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣀⠴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠋⠵⠒⠒

⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡀⠀⣠⣬⡀⡀⢀⠂⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀
⠀⠀⠈⢠⡿⣆⣿⣀⢿⣸⠇⡿⣿⢠⣿⡆⣿⠀⠄⠀⠘⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠈⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠐⠀⠈⠀⠈⠁⠃⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠐⠀⠐⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠤⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠘⠛⠁⠒⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⢀⠀⠀⣢⠄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⢀⡀⠀⣀
⠀⠀⠀⠂⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠁
⠀⠀⠀⠀⠀⡀⠀⠀⠁⠉⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢈⡀
⠀⠀⠀⠐⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢨⡇⠀⠀⠀⡀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠘⡀⠰⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠠⠄⠐⢀⠀⠂⠀⠀⠀⠀⠀⢀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠐⠢⠄⠀⠀⠀⠀⠀⠀⠲⣷⣦⠀⠀⠀⠀⠀⠀⢀⠘⠀⠀⠀⠐⠀⠀⠄⠀⠀⠀⠀⠀⠍
⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢠⠄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⢠⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢠⠂
⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠈⠈⡀⠀⠀⠀⠀⠀⠀⢕⠕⠀⠀⠀⠀⠀⠴⢤
⠀⠀⠀⠀⠳⣀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠴⠂⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣬⠄
⠀⠀⠀⠀⠀⢈⠀⠐⠄⠀⠂⠀⢀⠀⠠⠂⠀⢀⢀⡞⢲⡄⡴⣆⠀⣶⢲⡄⢲⡖⡒⣦⡴⠂⠀⠀⠀⠀⠀⠀⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠈⠀⠀⠀⠀⠀⠘⠟⠛⠼⠛⠻⠆⠿⢿⠁⠸⠇⠀⠸⠇⠈⠀⠀⠀⠀⠒⠂

⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠒⠀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⣠⡤⠀⠀⠀⣤⣀
⠀⠀⠀⠀⠀⣴⣿⣿⣿⠿⠿⢿⣿⣿⣦⡀⠀⠀⡐⠑⠀⠀⠀⠀⠀⠀⠜⠁⡀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⡠⠾⠛⠁⠀⠀⠀⠙⠻⠷
⠀⠀⠀⠀⣸⣿⣿⠏⠀⡴⢦⡀⠙⣿⣿⣷⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⠀⠰⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⢀⣠⣶⣄
⠀⠀⠀⠀⢿⣿⣿⡀⠀⣟⢻⡄⠀⣿⣿⣿⠀⠒⠐⠐⠐⠃⠐⠒⠐⠗⠂⠒⢒⠀⢀⣀⠀⠀⡀⠀⠃⠀⠀⠀⠀⢀⠀⢰⣄⠀⠀⠸⣿⣿⣿⠁⠀⠀⣰⠆
⠀⠀⠀⠀⠘⣿⣿⣷⣄⣉⣉⣠⣼⣿⣿⠏⠀⠐⡀⠀⡐⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠈⢿⠄⠀⠀⠉⠉⠁⠀⠀⠰⡿
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠈⠂⢀⠀⠀⠀⠀⢀⠰⠊⠀⠀⠀⠈⠒⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⢀⠀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⣀⠄⠂⠀⠁⠐⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠐⡂⠁⠐⠂⢀⡀
⠀⠀⠀⠀⠀⠜⢦⠀⠀⠀⠀⠀⠀⡠⠓⡄⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢀⠀⠤⠀⠀⠀⠀⠄⢀⠀⠀⠀⠐⠝⠀⠀⠑⠐⠃⠀⠐⢁⠄
⠀⠀⠀⠀⠈⠀⠀⢧⠀⠀⠀⠀⢰⠁⠀⠘⠀⡀⠀⣿⢠⣤⣤⣤⣤⢤⡄⢸⡌⠢⠀⢠⢀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠰⠀⠒⠀⠀⠀⠀⠀⠒⠠⠆
⠀⠀⠀⠀⠃⠀⠀⣸⠀⠀⠀⠀⢸⠀⠀⢀⠀⠣⡀⣿⠰⠾⠒⠾⠺⠶⠆⢸⠇⡈⠁⢸⠀⠀⠀⠉⠀⠉⠀⠀⠀⢀⡆⠀⢡⠄⠀⣀⡀⠀⣀⣀⠀⠠⡄
⠀⠀⠀⠀⠘⢄⣠⠃⠀⠀⠀⠀⠈⢆⣀⠎⠀⠀⠀⠛⠄⠀⠀⠀⠀⠀⠠⠚⠁⠀⠀⠈⠁⠒⠠⠤⠄⠄⠠⠄⠒⠉⠀⠀⢀⢀⠀⠀⡀⠀⡀⠀⢀⠐
⠀⠀⠀⠀⠀⠈⠓⠄⣀⠀⠀⣀⠠⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⢀⡃⠀⢁⡀⠔⠃

⠀⠀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠈⠐⠠⡀⠀⠀⠀⠀⠠⠂⠁⠀⠀⠈⠐⠠⡀⠀⠀⠀⠀⣠⠒⠈⠀⠀⠈⠑⠢⡀⠀⠀⠀⠀⣀⣰⡖⣿⡪⣿⢰⡦⡀
⠀⠀⠀⠀⠀⠂⠀⠀⣤⡄⢀⣤⡀⠀⠀⠄⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠎⠙⣆⠀⠀⠀⠀⢀⡞⠉⢆⠀⠀⡤⡗⢽⢎⣭⡱⠿⢘⣛⣽⣀
⠀⠀⠀⠀⡄⠀⠀⠀⠙⠁⠈⠛⠁⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠒⠂⠐⠘⠀⠘⠀⠀⢸⡄⠀⠀⠀⢸⠀⠀⠈⡄⢰⣏⣏⠾⢇⣭⡸⠿⢨⣍⠾⣺⠄
⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢰⠀⠀⣸⠁⠀⠀⠀⢹⠀⠀⢀⠃⠘⡧⣯⢿⢎⣭⡱⡿⢨⣭⢻⣺
⠀⠀⠀⠀⠀⢄⠀⠀⠀⠉⠋⠀⠀⠀⠠⠂⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠢⣠⠋⠀⠀⠀⠀⠀⢷⡠⠂⠀⠀⠙⣗⣻⢋⣭⡱⡿⢨⡧⣽⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠤⠀⠀⠠⠤⠊⠁⠀⠀⠀⠀⠀⠚⠇⠿⠘⠿⠘⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠂⠀⠉⠁⠲⣄⠀⠀⠀⠀⢰⡆⠄
⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣸⠇⠀⠈⠑
⠀⠀⠀⠀⣰⣋⠤⠴⠖⠒⠛⠛⠛⠛⠲⣿⠧⣤⣄⣀⡿⠀⠀⠀⢀⡶⠶⢄
⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⣻⠛⠶⢦⣤⣿⠁⠀⠈⢧
⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠁⠀⠀⠀⢠⡟⠀⠀⠀⢸⠟⠣⣄⠀⠈⡆
⠀⠀⡃⠆⠀⠀⠀⠀⠀⣠⡴⠟⠁⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢸⠆⠀⠀⠓⣄⣹⠄
⠀⢈⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⢻⡆
⠀⢸⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠸⡇
⠀⠈⠀⣠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⢰
⠀⠀⠰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡜
⠀⠀⠀⠡⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠉⡄⠄⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⠞⠁⠀⠀⠀⢀⠀⠐⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠟⠁⠀⠀⠀⡠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⠄⣠⡟⠀⠀⠀⠀⠀⢀⣀⣤⠤⠞⠋⠁⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢀⣀⣤⣤⡶⠶⠶⠶⠿⠟⠛⠛⠛⠛⠻⠶⠶⠶⠶⢶⣤⣤⣄⢀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠈⠙⠦⢤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠒⠁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⢻⡀⠀⠀⣀⣀⣬⠦⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠙⠛⠛⠛⠛⠻⢿⠛⠋⠉⠉⠀⠀⠀⠈⠳⠀⠀⠀⠀⠑⢆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣆⣀⣀⣀⣀⣀⡀⠀⠀⠙⠄⠀⠀⠀⠀⠈⠙⠓⠢⠤⠠⣄⡀⠤⠄⠀⠒⠈⠁
⠀⠀⠀⠀⠄⠀⠀⠀⠀⣀⣀⠤⠦⠚⠛⠛⠉⠉⢻⣿⠉⠉⠉⠍⠉⠙⠛⠳⠤⣤⡀
⠀⠀⠀⠠⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡀
⠀⠀⠀⣤⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠻⣿⠟⠛⠳⢦⣄⡀
⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⢿⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠄
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢻⡀⡼
⠀⠀⠀⠀⠳⡀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢈⡃⠁
⠀⠀⠀⠀⠀⢹⡆⢀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⠀⡀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠐⠚⠋
⣄⣤⣤⣤⣤⣀⣤⣄⣀⣤⣤⣤⣤⣤⣄⣠⣤⣤⣤⣤⣤⣤⣄⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣄⣠⣄⣠⣤⣤⣤⣤⣤
⣿⣿⣿⠛⠛⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⠶⠶⠶⠶⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠿⠿⠷⠶⠶⢒⣀⣤⡤⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⣿⣇⠀⠀⠀⣠⣴⣾⣿⣿⣿⣦⣴⡶⠟⣛⣉⣉⣁⣀⣀⣀
⠀⠀⠀⠀⠀⣠⣴⡶⠛⣏⣹⠯⡝⠻⠛⠾⢿⣿⣿⣿⠟⢉⣠⣤⣬⣭⣉⣉⠀⠀⠉⣹⣿⣏⣉⡁⠠⣤⣤⣤⣤⡤⠄
⠀⠀⢀⡴⢟⠵⠫⣨⠟⠍⣈⠤⠖⠊⠉⠉⠚⠛⠻⣿⡀⠉⠉⠙⣿⣯⣉⣉⣭⡉⠉⣉⣭⡭⠵⠶⠶⢾⣷⠴⠒
⠀⢠⠞⢡⢋⢐⢞⠑⡱⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠟⠛⠛⠛⢋⣡⣴⠾⢛⣭⠖⢒⣠⣤⣤⠴⣀⡀
⢠⡏⢀⢎⢈⠯⢄⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣤⣴⣾⣿⣏⣡⣴⠋⣠⣶⣿⣿⡷⠖⣉⠁
⣾⠀⡮⠠⡼⠄⡮⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠟⠉⠉⣹⡿⠟⣡⣾⣯⣥⣤⠶⠚⠉⠉
⣿⠀⡇⠆⡇⠂⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠈⠉⢁⣠⣾⣿⡿⠋⠉⣠⠤⠂
⣿⠀⡇⠃⡇⠃⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠿⠿⠿⠿⠿⠛⠋⠁
⠸⣇⢱⢈⣳⢁⡹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠋⠁⠀⠀⢀⣤⠴⠒
⠀⠙⣦⣂⢨⢧⠠⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣧⣀⠀⢀⣴⣟⣁⣠⡶⠚⠉
⠀⠀⠈⠻⣦⡰⠳⣔⢈⡳⢄⡀⠀⠀⠀⠀⠀⢀⣠⠞⠁⠉⠛⠛⠿⠿⠿⠟⠛⠁
⠀⠀⠀⠀⠈⠙⠾⣬⣕⣦⣖⣉⣒⣠⣤⡤⠶⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡐⠂⠀⠀⠀⠀⡀⠀⠀⠐
⠀⠀⠀⡀⠀⣀⣀⣀⣀⠀⠀⠀⠀⢀⣴⣾⡟⢻⣿⡇
⠀⠀⠀⠀⢾⣿⣟⠉⣿⣿⣷⠀⠀⠸⢿⣿⣷⣾⠿⡁⠣⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠨⠻⠿⣿⠿⠟⠁⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣴⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠉⠉⠙⣦⡀⠀⠀⠀⠀⠀⣠⣤⣤⢤⣤⣤⣀⣴⣿⣁⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⣿⡆⠀⠀⣿⡇⠀⠀⠀⠀⠘⣋⣁⠀⠀⣀⡀⣼⡿⢁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⢰⣿⡇⠀⢀⣿⠃⢀⣴⢿⢦⣾⠋⣥⣠⣾⠋⣹⣿⡕⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢀⣾⣿⠔⢲⣾⡅⠀⣾⡯⢮⢾⣧⢾⣿⣻⡇⡰⣿⡟⣰⣿⠁⣰⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⣸⣿⠃⠉⠁⢸⣿⡴⣿⣡⠃⠀⠁⣾⡓⠉⠋⠁⠛⢡⣿⠃⣰⠃⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠛⠀⣿⡿⠤⠒⠊⣿⣿⣀⡈⠁⢀⡀⢀⡉⢀⣀⣀⢀⡀⢈⡻⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢻⣿⠃⠀⠀⣼⣿⢻⡏⢻⣤⣿⣇⡟⢻⡍⣿⠉⣼⢃⣾⠇⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠿⠀⠀⣴⡿⠃⣾⠶⢻⡿⣿⢹⣷⠟⢠⡟⢀⡙⢛⡿⠀⠀⠀⠀⠀⠆⠀⠈⠀⠀⢄⡀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣠⡤⠾⠋⠀⢸⠇⠀⡾⠡⡟⠿⠹⣦⠸⠇⠸⢧⠾⠃⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⡉⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠁⢥⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⡤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠞⠋⢁⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠙⠓⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠁⣠⠴⠚⠉⠉⠉⠛⠛⠻⠿⢿⣿⣿⣿⣿⣿⠿⠛⠛⠉⠉⠐⠤⢀⡀⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡈⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⡙⢄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣡⣴⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠷⠦⢤⣄⣀⡀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⢀⣀⣠⣤⠴⢿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠈⠉⠙⠓⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⠒⠛⠉⠉⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⢸⢿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡇
⠀⠀⠀⢸⠈⢻⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⠁
⠀⠀⠀⢸⠀⠀⠙⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠋
⠀⠀⠀⢸⡇⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠘⣇⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⢻⡀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠘⣧⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢠
⠀⠀⠀⠀⠀⠘⣆⠀⠀⢹⣤⣀⡀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⣀⣤⡞⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠙⣆⠀⢸⣿⣿⣿⣿⣷⣶⣶⣤⣴⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⣤⣴⣶⣾⣿⣿⣿⣿⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢷⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢤⣤⣄⣀⣀⣀⣀⣤⣤⣤⢶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⡿⠿⠋⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⠦⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⠤⠶⠚⠋⠁

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

⠀⠀⠀⠀⠀⢀⣤⡖⠒⠛⢛⣲⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠔⠒⠛⠛⠓⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⢖⣛⠛⠒⢶⣄⡀
⠀⠀⠀⠀⡴⠋⢠⣿⣿⣿⡅⠀⠀⠈⣟⢦⡀⠀⠀⠀⠀⡰⢫⠁⠀⠀⠀⠀⠀⠀⠀⠏⢢⡀⠀⠀⠀⠀⡴⣭⣄⡀⠀⠈⠑⢄⠀⠙⢟⢦
⠀⠀⠀⣼⡠⠞⠛⢿⡿⠛⠓⠦⣀⢀⣼⡀⢣⠀⠀⠀⣸⠁⠘⡄⠀⠀⠀⠀⠀⠀⢀⡇⠀⢳⠀⠀⠀⡜⡴⠁⠀⡨⠳⡄⠀⠈⢣⠀⠘⡼⢧
⠀⠀⠀⣿⠁⠀⠀⢸⠀⠀⠀⠀⢈⣿⣿⣷⢼⠀⠀⠀⡇⠀⠀⠘⢆⠀⠀⠀⠀⢠⠎⠀⠀⢸⡆⠀⠀⣿⠀⢀⠎⠀⠀⣸⢤⣤⡼⠤⠊⠁⢸
⠀⠀⠀⢿⠳⣄⣠⣼⣤⣀⣀⡤⠚⠻⣿⠃⣸⠀⠀⠀⢳⠀⠀⠀⢸⠀⠀⠀⠀⡏⠀⠀⠀⣸⠁⠀⠀⣿⠀⣸⠀⠀⣰⠁⠀⠀⠀⠀⣀⠴⡿
⠀⠀⠀⠈⢦⡀⢻⣿⣿⣿⠁⠀⠀⠀⣞⡰⠃⠀⠀⠀⠈⢧⡀⢀⡜⠀⠀⠀⠀⠸⡄⠀⣰⠃⠀⠀⠀⠘⢆⢻⠀⠀⡏⠙⠓⠒⠚⠉⢁⡴⠁
⠀⠀⠀⠀⠀⠑⠶⣍⡉⠉⠓⣢⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠙⠯⣄⡀⠀⠀⢀⣀⡬⠛⠁⠀⠀⠀⠀⠀⠀⠙⠦⣀⣹⡖⠤⢤⣴⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⣤⢤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠤⣤⣄⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⣀⡀
⠀⠀⠀⠀⢀⠔⠋⢉⣓⣦⣈⣆⣠⡛⠲⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⣋⣉⣹⢟⣿⣷⣄⢸⠀⠀⠀⠀⢀⣴⣏⠀⠀⠀⠀⠀⠀⣩⣶⡄
⠀⠀⠀⢰⣫⠔⠊⠉⠀⢸⠃⢹⠈⣏⠓⢾⣆⠀⠀⠀⠀⠀⣠⠞⢥⣻⡾⠋⠀⠀⠙⢿⣿⣿⠀⠀⠀⢠⠋⠀⢹⣆⠀⠀⠀⠀⢴⡟⠀⠘⡆
⠀⠀⠀⡟⠁⠀⠀⠀⣠⠏⠀⠸⡄⠘⢆⠀⢹⠀⠀⠀⠀⡴⢡⣽⡾⠋⠀⠀⠀⠀⠀⠀⢻⡟⠀⠀⠀⡟⠀⠀⠀⣿⠀⠀⠀⠀⣿⠀⠀⠀⢸
⠀⠀⠀⣇⠀⠀⠀⡴⠁⠀⠀⠀⡇⠀⠈⡆⢸⠀⠀⠀⢸⣧⣰⠋⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⢧⠀⠀⠀⣿⠀⠀⠀⠀⢿⡄⠀⠀⣸
⠀⠀⠀⠹⡄⠀⡼⠀⠀⠀⠀⢀⡇⠀⠀⣿⠏⠀⠀⠀⣿⣿⣱⣄⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠘⣆⢀⣼⠏⠀⠀⠀⠀⠹⣧⠀⣠⠃
⠀⠀⠀⠀⠙⢦⣇⠀⠀⠀⠀⣸⠀⢀⡴⠋⠀⠀⠀⠀⣇⠙⢿⣿⣷⣤⣀⣀⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣅⡀⠀⠀⠀⠀⠀⣨⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠓⠊⠁⠀⠀⠀⠀⠀⠀⠙⠒⠒⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠒⠛⠉

⠀⠀⠀⠄⣢⣥⠉⠳⢄⠀⠀⠠⠒⠩⡭⣴⠂⡀⠀⠀⠴⠀⠀⠉⠰⠄⠀⠀⢠⡀⠉⠈⠙⠢⠀⠀⠀⠀⡠⣀⡻⢿⣍⡂⠀⠠⢆⠀⠀⢀⡦
⠀⠀⣴⠀⠙⠉⠀⣶⣦⡄⢠⠋⠀⡀⠀⠀⢂⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡇⠀⠉⠀⠠⠐⢁⠀⢀⢨⠞⠁⠀⠀⢹⠁⠀⠁⠈⡆⠀⢸
⠀⠀⠈⡐⣾⣶⠀⢉⡡⠀⠀⢀⡀⠀⠀⡀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡀⠐⠠⠀⢀⠁⠀⠸⣯⣄⠀⠀⠀⠁⠀⠀⢂⡸⠁⠀⠘⣄
⠀⠀⠀⠸⠷⠦⠶⠿⠀⠀⠀⠀⠷⠶⠶⠶⠆⠀⠀⠀⠸⠶⠦⠶⠾⠀⠀⠀⠀⠱⠾⠶⠾⠧⠀⠀⠐⠼⠿⠷⠷⠆⠀⠀⠀⠀⠴⠶⠶⠶⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⣼⣇⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⢹⡏⠁⠀⠀⠺⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⢴⠄⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠗⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣀⡀⠀⠀⠀⠀⢐⣾⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣞⣯⣯⣷⣷⣾⣿⣷⣾⣶⣽⣽⡳⣤⣀⠐⠉⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⣿⠽⢫⢿⢛⣻⣭⣨⣭⣥⣭⣥⣭⣿⡙⡿⡿⣿⣷⣄⠀⠀⠐⠆
⠀⠀⠀⠀⢀⡀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⣲⢾⣿⡷⣾⡟⢩⠿⠏⠿⠿⠛⠿⠿⠸⠿⣧⢿⣷⡬⣿⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠉⠲⣤⣀⣸⡇⣠⠖⠀⠀⣰⢫⣶⡿⣤⣍⢆⣿⣿⡇⣿⣿⡏⣿⣿⡞⣿⣿⣴⣿⣭⢛⣿⣞⣧⠀⠀⠀⠀⠀⠀⠀⠀⠒⡷⠂
⠀⠀⠀⠀⠀⠀⠀⣀⣽⣿⡿⣥⣀⠀⢀⣟⣾⠿⠇⣛⣛⢉⣭⣭⢠⣭⣭⡅⣭⣭⡅⣭⣭⡁⣛⣛⡚⠿⣷⣻⡄⠀⠀⠀⠀⡆⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠉⠁⠀⢸⡇⠀⠀⠀⢸⡧⣿⣿⠹⡿⠿⠸⠿⠿⠸⠿⠿⠇⠿⠿⠇⠿⠿⠇⠿⠿⠇⣿⣿⢾⡇⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⢀⣄⠀⢸⣗⡿⢿⢼⣿⣿⢸⣿⣿⢸⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⣿⡇⣿⢿⣻⡇⠀⠙⢦⣸⣿⣠⠞⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⣯⣻⣿⡖⣾⣯⣬⣭⣭⣈⣍⣛⡁⣛⣩⡁⣭⣭⡅⣽⣷⢶⣿⣟⣼⠃⢀⣠⡼⢿⣿⠿⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣞⢿⣧⢹⣛⡃⠿⠿⠇⣿⣿⡇⣿⣿⠳⠿⠿⢛⣛⡏⣼⡿⣯⠏⠀⠀⠀⠀⠘⣿⠀⠀⠀⠈⠁
⠀⠀⣀⣀⣀⣴⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣏⠿⣿⣹⣿⣇⣶⣶⣆⣶⣶⢸⣿⣟⣿⠿⣫⣿⢿⠋⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠈⠺⣻⣿⣷⣦⣭⣭⣹⣿⣋⣿⡏⣭⣭⣴⣾⣿⣟⠗⠁⠀⠀⠀⢤⡇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠛⠀⠀⠀⠀⠀⠀⠀⠙⠳⢭⣿⣻⣟⢿⣿⡿⣻⢟⣿⣯⠶⠋⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣄⡀⠀⠀⢀⣇⠀⠀⠀⠉⠙⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣼⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⢾⣷⠶⠖⠂
⠀⠀⠀⠀⠀⠀⢈⣽⣿⡦⠀⠛⠀⠀⠀⠀⠀⠴⠾⢿⣿⠛⠛⠉⠁⠠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠁⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⡄⠀⠀⢀⠀⠀⠀⢀⠀⡄⠀⣀⣀⡀
⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⢴⣤⠀⠀⠀⠀⣀⡀⠀⠛⠛⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣿⣿
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢱⣤⣤⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠄⠀⠀⢠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠃
⠀⠀⣀⣈⠀⠀⠀⢶⣲⣲⠆⠀⠀⠁⠚⠒⠀⠀⠀⣀⠀⠀⢀⠀⠀⠀⠀⠀⣀⣀⢀⣀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⢉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠘⠐⠁⠸⠀⠀⠀⠰⣏⣈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢤⡀⠀⠀⠲⠦⠀⢶⠆⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠁⠈⣿⡄
⠀⠀⠘⠛⠀⠀⠀⠀⠀⠁⠀⠀⢻⣿⠀⢀⣿⡇⠀⠀⠀⠀⠃⠀⠀⠀⠰⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⢀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠰⠀⠀⠀⠀⢀⣴⣿⠁⠘⣷⣦⡀
⠀⠀⠀⠀⠀⠀⢐⠟⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⣰⣿⣿⠇⠀⠀⢸⣿⣿⡄
⠀⠀⠀⠀⡆⠐⠙⠀⠀⠁⠀⠀⠀⠀⠀⠑⠊⠉⠀⠀⠀⠀⠐⡅⠀⠀⠀⠁⠀⠿⠿⠿⠀⠀⠀⠸⠿⠿⠟
⠀⠀⠀⠀⠁⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢄⣠⠒⠀⠀⠀⠦⣤⣥⣤⣥⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣓⣒⣒⣚⠃⠀⠀⠂
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⡦
⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠖⠒⠛⠛⠛⠋⠉⠙⠛⠛⠛⠓⠲⠶⠤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠋⢩⠄⢀⢤⣀⡠⢆⣀⣰⢢⣀⡰⢆⣀⡴⣄⣀⠤⠀⡠⡌⠙⠓⠦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⢋⣁⣀⣴⣏⡅⢨⢭⢸⠥⠅⡨⠤⢅⠸⠀⠇⡼⠨⠅⠯⢭⢨⠭⡅⣯⡵⠤⣄⣈⠉⠓⢦⣀
⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⢘⠉⠀⠀⠀⠘⠃⠀⠋⠀⠈⠁⠀⠈⠁⠀⠈⠁⠀⠉⠀⠈⠉⠀⠘⠁⠀⠀⠀⠨⠀⠀⠀⠈⠳⣤⡀
⠀⠀⠀⢠⣾⣭⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠢⣙⣦⡀
⠀⠀⣴⡿⠋⢠⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠙⢷⣄
⢀⣾⠋⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢠⠀⠀⠀⠀⠻⣆
⣼⠁⠀⠀⠀⢸⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⠀⠀⠀⠀⠀⢹
⣿⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢻⡄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⢳⡄⠀⠀⠘⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠀⠀⠀⠀⡼⠃
⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸⠀⠀⣠⠞⠁
⠀⠀⠀⠈⠻⣦⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⣠⠞⠁
⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠶⠤⣤⣄⣀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⣠⣤⠤⠶⠖⠛⠉