Biologist Emojis & Symbols

⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠃⠀⡆⠀⡀⠒⢋⡤⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠰⠬⠀⡈⠃⠈⠀⠄⠀⠀⣈⣦⣎⣀⠀⠃⠜⠃⠂⠀⠀⡀⠼⡑⢀⢥
⠀⠀⠀⠷⠶⠀⠀⠀⠀⠀⠠⠀⡂⠀⠀⠀⠁⠀⠘⠀⠐⢨⡃⡙⠀⠁⢂⡐⠀⠀⠉⠀⠀⢉⠀⠀⠈⠀⠀⠀⠀⠄⠄⠀⠑⠄⠅⢠⡷⠆⠡⠄⡼
⠀⠀⠐⠂⡲⠀⠀⠀⠤⡄⠀⠀⠉⠀⠐⠀⠈⠁⠀⠀⠀⠠⣄⠨⣀⠀⠀⢀⢠⢠⠀⢠⡄⠘⠁⠀⠄⠀⠠⠄⠠⣀⢠⠃⠉⡄⢠⠀⠉⠑⠒⠊⠀⠀⠁
⠀⠀⠀⠀⠄⠀⠀⠀⠑⣂⠄⡠⡀⠀⠀⠘⢀⡀⠀⠀⠀⠀⡁⠐⠀⢀⡀⠀⠀⠀⠀⠀⠁⠀⠋⠀⠈⠀⠀⠀⠀⢀⢀⠃⠘⡄⡀⠁⣀⣄⡀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠄⠐⠠⢊⣴⢀⠀⠐⠤⠀⠐⠀⠀⠀⠐⠀⠀⠐⠉⣉⣀⠠⠤⠊⠀⠀⠀⠂⠀⠀⠀⠋⠉⣦⠀⠀⠁⠈⠀⠘⢀⡀⠙⢷⡄⠸⡉⡱
⠀⠀⠀⣸⠀⠆⠰⠀⣤⠀⠀⢩⡬⠀⠀⠀⡴⠶⡀⢠⣤⡄⣠⡀⠀⣄⣤⠀⡄⠊⡀⠠⠀⠀⢠⠀⠀⣐⣒⣒⣳⣖⣲⡀⠀⡘⠒⠀⠂⡀⠈⠁⠀⠈⠄
⠀⠀⠀⠉⡓⠰⠂⠔⠛⠀⠀⠀⠀⠈⠀⠤⢉⠈⠀⠰⣄⠟⣩⠁⢀⡀⢀⠐⡄⢰⡆⠍⠆⠈⠀⠁⠀⠅⠦⠶⠴⠦⠀⠨⠀⠈⢁⠈⠈⢉⠁⠠⠖⠂
⠀⠀⣁⡀⠚⠃⠚⠧⠀⠀⡀⠤⠀⠀⠀⡫⠚⠀⢴⣀⠈⠉⠁⠐⢦⠁⠡⡄⠀⡸⠀⡀⠀⢁⠀⢀⠐⠀⠀⠀⠀⣠⣄⣶⡀⠀⠀⠀⡊⠒⠈⠦⠤⠀⠂
⠀⡜⠉⠙⡄⠸⠀⠂⠀⠀⠰⠀⠀⢀⠀⠙⠇⠀⠣⡠⠃⠈⠠⠄⠚⠈⠃⢀⣈⠀⠀⠀⠀⠀⢀⠘⡀⠀⢼⡧⠼⠛⢃⡍⠀⠂⠈⡓⠥⢿⠀⠔⠀⠀⠆
⠀⢧⠒⢀⠇⠀⠀⠀⢀⡄⠀⠀⠀⠐⠛⠀⠰⡦⠀⠀⠀⠀⢠⡄⠀⠁⠀⢨⢬⠀⠸⠕⠀⢠⣄⠀⢀⣤⡄⢀⡤⠒⠁⠤⠄⠀⠐⠝⠁⠐⡷⠀⠈⡀⢀
⠀⠀⢉⡁⠀⠀⠀⠳⡄⠀⠀⠀⠊⠉⠉⠁⠀⠐⣠⠀⢠⠀⠀⡕⠀⠐⡀⠐⠀⠀⠈⠰⠂⢈⣃⡀⠈⠒⢀⠈⠀⠀⠒⠀⠂⠐⣿⡆⣒⠐⠀⠊⠙⠛⠈
⠀⠀⣜⣗⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄⠀⠀⠈⠋⠠⠀⢀⡠⢄⢨⠃⠀⢰⠁⠀⢸⠀⢴⠱⠨⠈⡄⠠⠀⠉⠀⢻⠂⠈⠁⠀⠀⠐⢃⠂
⠀⠀⠛⠉⠀⣀⠀⠀⢀⠀⠀⠀⢀⣀⡀⠀⢀⠆⠈⠀⠁⠀⢀⢠⣤⣄⣀⠄⠀⠀⠀⠀⢀⠑⠐⠣⠀⠁⣊⡐⡁⠊⠀⣰⠀⠀⠸⠀⠀⠀⡐⢀
⢀⣐⢒⠔⠆⡀⠀⠘⠈⠀⠀⠛⢹⠂⠁⠰⣃⡐⠀⠁⠀⠐⠉⠼⠞⠛⡙⠆⠀⠁⢀⣀⠀⠐⠀⠀⠂⣤⡀⠈⠄⠐⠲⠣⠀⠀⠂⣀⠀⠀⠈⠁
⠀⠀⠘⢡⢀⠉⠀⠀⠐⠀⠀⠀⠘⠀⢠⣀⣌⣀⠀⠀⠀⢀⣀⡀⠀⠁⠀⠁⠀⠂⠈⠷⠂⢀⢰⠄⡘⠗⡧⠘⠤⣃⣐⡠⠄⡈⠨⠤⡅⢅⠀⠀⡀⡀⠐
⠀⠉⡱⠀⠌⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠀⠀⠃⠀⠸⠛⠆⠀⠠⠀⡀⠀⠀⢀⣇⠀⡀⠀⠀⡐⠀⠄⠤⡀⠠⠀⡖⢤⠀⡈⢁⠅⡀⠀⠀⠙⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠂⠉⠉⠉⢉⡽⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⣀⣀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⢀⡴⠋⢀⣀⡠⣤⡤⠤⣤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⣄⠀⠀⠀⠀⠈⠉⠳⢄⡀⠰⠃⠀⠀⠀⠀⢠⢋⡤⠚⠉⠁⠀⠀⠀⢀⡠⠤⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀⠀⠀⠀⠀⠀⠙⠿⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⢀⠴⠊⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠤⠤⠤⢽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠉⠉⠁⠀⠈⠉⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠤⠵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠶⠤⣀⣠⣄⠀⠀⠀⠀⠀⠀⣀⡤⠤⠶⠐⠒⠒⠒⠀⠲⠦⢤⣀⠀⠀⠀⠀⠀⠀⠘⠻⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠁⠀⠀⠀⠀⡠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠺⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢙⠆⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⣈⢁⣠⠤⣄⠀⠀⠀⠀⠀⡸⠃⠀⡤⠤⠚⠙⢦⠀⠀⠀⠀⠀⢠⠎⠘⠂⢤⡀⠀⠸⡄⠀⠀⠀⠙⢏⡉⠑⢦⣇
⡀⡄⠀⠀⠈⠀⠀⠀⢔⡢⠀⠀⠛⠁⡠⠖⠉⠀⠀⠀⠀⣴⠁⣠⠊⠀⣀⣄⣤⣈⠇⠀⠀⠀⠀⣏⣠⣠⣄⡀⠙⢆⠀⡁⠀⠀⠀⠀⠀⠙⢄⠀⠉
⠙⠃⠀⠀⣎⢹⠆⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⡆⣼⡵⢊⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣈⡙⠦⣥⢹⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⣤⠁⠀⠆⠀⠀⠀⠀⠘⢇⣀⣀⠞⠑⢦⡀⢰⠃⠀⢰⡁⢠⣶⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⣶⡄⢈⠆⠀⠈⣆⠀⡠⠊⢳⡤⠀⠼
⠀⠀⢀⠖⠉⠈⠉⠐⢢⠀⠀⠀⠀⠀⠀⢨⠀⢤⣀⡿⠚⠀⠀⠀⠉⠉⠉⡵⠊⠉⠑⣤⠤⣤⠖⠉⠉⢲⡉⠉⠁⠀⠀⠀⠀⢹⣠⠖⢸⡇
⠀⠀⡠⢿⣏⣿⠛⣻⢧⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢱⠦⡴⠖⠃⠀⠈⠓⠦⡴⡞⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇
⠀⠀⣟⠢⠤⣿⡔⠁⠀⡇⠀⠀⠀⠀⠀⠈⡀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⢈⡻⣆⠀⠀⠀⠀⠀⢠⣷⡁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣸
⠀⠀⣯⣉⣈⣿⡍⢻⠀⣇⠀⠀⠀⠀⠀⠀⢧⡀⢀⣸⡄⠀⠀⠀⢀⡴⠊⠁⡤⠊⢑⠖⠒⠶⠊⠓⠄⠀⠉⠒⢄⠀⠀⠀⠀⠟⠢⠴⠋
⠀⠀⢹⡦⠿⠤⠴⠦⢧⠈⠻⡦⣀⡀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⡎⠀⣀⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⣄⡀⠀⢈⡇⠀⠀⡜
⠀⣰⠃⠀⠀⠀⠀⠀⠀⢣⠀⠇⠀⠉⠓⠲⠶⠤⠤⠤⠤⢷⡀⠈⠓⠋⠘⠤⠞⢭⣷⡔⠉⠒⣋⣩⡟⠃⠈⠉⠁⠀⠀⡼⠁
⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢇⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⢀⠾⡀
⠣⣀⣀⣀⣀⣀⣀⣀⣀⣀⠜⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢒⣤⢉⡒⠤⣀⣀⣀⣀⣀⣀⣀⡤⠔⣊⣤⠒⠁⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠳⠦⠠⠤⠄⠤⠤⠠⠴⠖⠒⠒⠊⠉⠁⠙⡀⠁⠀⠀⠈⠙⢌⡃⠸⠁⠀⣸⠅⢻⡀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠓⠦⣀⠀⠈⢻⠇⢀⠞⠁⠀⡈⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠈⠑⢄⠀⣆⠇⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠱⡿⠀⠀⠀⢀⠜⠓⢤⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⢀⡄⠀⠀⠀⠀⠀⠰⠀⠀⠀⣏⠀⠀⠀⠙⡄⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠒⠛⠉⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠙⠲⢶⡛⢽⣆⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣀⡵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢳⠒⠒⠶⠶⠶⠒⠲⡏⠈⠙⠉⠁⢹⠏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠋⡆⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢸⠀⠇⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣀⠀⡰⠀⢠⣀⣀⣠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠈⢳⢠⠋⠀⠀⠀⢱⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠤⠴⠃⣠⣾⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⢑⣤⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⢀⣴⣿⡿⠻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⣠⣴⡿⠟⢛⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⠋⠀⣠⣾⠟⠉⡶⡾⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⣼⣿⣷⣾⣿⠿⠢⠞⠁⣿⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⢀⡼⢋⣙⡿⠃⠀⠀⠀⠈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⢻⣷⣄⠀⠈⠁⠀⠀⠀⠀⠀⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⢻⣆⠀⠀⢜⣋⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⣶⣯⡻⣇⣶⣾⣷⡀⠀⠀⠀⠀⣀⠴⠟⣫⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠑⢺⣇⣀⣿⢷⡲⣶⣶⣶⣶⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⠈⣷⡌⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢹⡿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡿⠀⠀⢳⡹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣿⣧⣤⣤⣼⣷⣼⣧⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣾⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣿⣿⢿⣟⣻⣶⠄⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠠⣶⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⣾⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣷⡙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣀⣀⣀⣀⣤⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⡿⠇⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣯⣿⣽⣟⣿⣻⣿⣿⣟⣯⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠉

⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠂⠀⠀⢀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠠⠄⠀⠀⠗⠀⠀⠀⠐⠀⠄⠀⠀⠀⠀⠀⠀⠑⠀⠂⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠸⠄⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠐⢀⢁⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⠀⠠
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡠⢄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠄⠀⠁⠸⠀⠀⠀⠲⠟⠀⡠⠐⠂⡖⠀⠶⠀⠀⡄⡄⡠⠰⠶⠖⠀⠠⡆⠀⠀⡀⠀⢀⠠
⠀⠀⠠⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠓⠁⠤⠐⠧⠀⠡⠀⠼⠠⠃⠁⠴⠈⠥⠀⠀⡇⠀⠀⠉⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠄⠀⠠⠤⠄⢤⣤⢠⣤⡤⣤⠀⣤⣠⣀⣠⣤⣤⣴⡄⠀⠆⠀⡠⠀⡀⠀⡄⠀⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⡁⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠁⠀⠄⠀⠤⠤⠔⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⢀⠀⠀⠀⠀⠀⠁
⣶⣶⣶⢶⠶⠶⣶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶

⠸⠿⠿⠀⠀⢰⣶⠄⢠⡖⣿⣮⣍⠘⣾⡟⠁⠀⠹⠇⠀⠀⠈⠛⠛⠉⠀⠙⠛⠋⠁⠈⠓⠚⠉⠀⠙⠓⠋⠀⠙⠒⠒
⠀⣤⣤⢰⣶⣦⢠⡀⣸⣇⣽⣥⣬⣅⣉⣡⡄⠀⠀⠀⠀⠰⠋⠈⣧⡞⠁⢱⡞⠁⠙⣶⠋⠈⣷⠋⠀⢱⡾⠁⠸⡾⠁⠈⣧⠀⠀⠀⠀⠀⠀⠀⠺
⢀⡈⢡⡌⠛⠁⠀⢠⣾⣿⣿⣷⣿⣿⣶⣿⡿⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⢸⣷⠀⠀⣿⡆⠀⣹⡆⠀⢸⢷⠀⢀⢿⡀⠀⡿⣇⠀⡀⢀⣶⣄⣀⣖
⠻⠟⠀⢸⣿⠆⠀⢸⣍⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠐⠀⢀⡀⠈⢀⡁⠈⠀⠨⡄⠉⣈⠁⠈⠀⠁⠀⠁⠈⠀⠁⠈⠀⠈⠀⠁⠈⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣤⣠⣄⣠⠀⠀⠀⠀⠀⠠⠀⠈⠁⡀⠈⠁⠐⢄⣢⣶⣶⣷⡴⣴⠃⠀⠀⠀⠀⠀⠀⠀⠘⠉⢉⠀⠀⠋⠻⠿⠋
⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣿⣞⣿⡄⠀⠀⠁⠠⠶⢄⠀⡀⠁⠐⠢⣴⣿⡟⠟⡛⡻⣷⣾⣷⣖⡠⠄⢰⣿⣿⡆⠀⣶⢠⡄⠰⡟⡇⠠⠐
⠷⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣹⣟⣿⣟⡇⠀⠀⠀⢀⣠⡄⠀⢁⡀⢠⣸⣿⣿⣿⣄⣽⣿⡏⠉⣿⣿⡀⠀⠀⠛⠛⠁⠀⠛⠀⠀⠛⠻⠛⠿
⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠠⠄⠠⠖⠛⠋⠙⠦⠀⢨⠝⠀⢺⣯⣽⣿⣁⢹⣿⣯⣿⠿⣿⠉⠉⠀⡀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠘⢻
⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⣿⠀⠣⣤⣠⣴⠞⠀⠀⡀⠈⢁⠼⢿⣿⣹⣿⣿⣿⣿⡶⠙⠂⠀⠀⠀⠀⢀⣀⣀⡀⠀⢯⣉⡀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠷⠶⣼⡁⠀⠊⠉⠁⠉⠓⠀⠀⠧⠀⠀⠠⠎⠙⠛⠿⠿⠛⡅⠑⠀⠀⠀⠁⠊⠉⠋⣉⣉⣅⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇⠀⠀⠈⣷⠀⢳⣤⣤⣶⠚⠀⡀⠀⠁⠀⠐⠂⠀⠀⢁⣀⡀⠉⠀⠀⣀⣠⣠⣤⣴⣿⣿⡿⠿⠃⢴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦⣄⣰⠃⠀⡉⠀⠀⠀⢉⠀⠀⠀⠻⠋⢢⠀⠈⠀⣿⣿⡿⠀⠀⠠⠼⠯⠽⠟⠋⠉⠀⠀⠀⢴⣌⣍⢱⣴⣤
⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠙⣧⠀⣙⣶⠶⠛⠁⠀⠀⠀⠈⠀⠀⠀⠀⣠⠀⢉⠀⠀⠀⠀⠀⠰⠶⡶⠶⠠⠴⠒⠀⢀⡜⠛⣌⠻⠟
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠟⠀⡁⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⣀⣀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⡀⡉⢠⣶
⠈⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⡆⣰⣶⣆⣤⡌⠁⢀⠀⢠⣦⣦⣤⡄⣋⡀⠈⠿⠿⠀⢰⣶⣿⣶⣦⡀⠀⠀⠀⡀⢚⠐⢢⠀⠀⠀⠀⠀⠀⠙
⠀⢀⣀⣀⠀⠠⣄⡰⢫⣷⡆⠀⠀⠀⠈⠛⢣⣭⠁⠸⣿⡆⠰⣿⣿⡏⢷⣿⠃⢠⡤⠀⠀⢿⣿⣿⣿⣿⡇⠀⠀⠀⠑⠀⠀⠀⠀⠀⢀⡀⡀⢀
⠀⣀⠀⠉⠀⠒⢠⣿⠠⢓⡇⠀⠀⠀⢠⣶⣦⠉⠀⢀⣻⣿⢄⣁⠉⠀⠀⠉⢀⢀⠀⠘⠂⠈⠹⠿⠿⠉⠀⠀⠀⠀⠀⢀⠀⠀⠀⡌⠉⡁⠑⡄
⠀⣻⡄⠀⠀⠄⡾⣩⣜⣿⡀⠀⠂⢠⣾⠛⣋⠠⣶⢸⡿⢻⣿⡿⡿⡀⠀⠐⣻⠽⢲⠀⠀⠛⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠲
⠁⠘⠁⠀⠀⠘⣇⢿⡽⠇⠒⠐⠀⢴⠅⢸⡟⠀⣿⣿⡀⠈⠓⠉⠳⠈⠀⠀⠈⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠠⠀⠀⠀⢠⡆⢺
⠢⠀⠀⢀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢀⣀⡈⠁⠀⢹⣿⣷⠀⣠⣄⣤⣶⠖⠀⠈⠀⠀⠀⠛⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⡇
⠀⡄⠀⠛⠻⠷⠀⠀⠀⠀⢀⣶⣻⣿⣿⣼⣶⡠⠀⢿⣿⣷⡿⠷⠛⠁⠀⠀⣠⠀⠁⠀⠐⠀⠐⠀⠀⠀⠀⣾⣷⠀⠀⠐⣠⣤⣤⣬⣀⠂⡀
⠐⡇⠘⠻⠂⣤⠈⠓⠀⠀⣿⣷⣟⠉⠿⣿⣿⡧⠄⠈⣽⣟⣿⣿⡟⣷⠀⠀⠈⠀⠐⠀⢠⡄⢠⣶⣦⠀⢀⡀⠁⡀⢠⣿⠟⣿⣿⣟⣻⣷⡄⣀
⠠⡇⢰⡶⠀⠻⠀⢸⡄⠀⠘⢿⣿⣻⣿⣷⡾⢀⠀⢠⣿⣿⣿⣿⡷⠻⠿⡷⠀⠈⠀⣀⠀⠀⠀⣹⡁⠀⢙⡋⠀⠄⢾⣿⣿⣿⣿⣿⣿⣿⡇⠠
⠈⣁⣀⣀⡀⢀⣀⣈⡃⠀⠀⠀⠈⠉⠛⠍⠀⠀⣀⠀⣉⣙⠛⠿⢿⣿⡆⢰⣿⣿⣤⠉⣻⠷⠸⣿⡿⠀⢿⡿⠀⢀⠸⣿⣏⣿⣿⣿⣫⣿⠃
⣴⣿⢾⣧⣜⣫⢖⡇⡍⠣⢴⡂⠀⠠⠀⠀⣤⡀⠙⠃⠀⡉⠉⠀⠀⠀⠀⠀⠙⠋⠀⠈⠁⠀⢠⣾⠄⠀⠿⠀⠿⠇⠐⢈⠛⠿⠿⠿⠋⡁⠂⣀⣤
⡠⣿⣬⣖⡣⠂⠟⠆⠡⣻⡦⣧⠃⢠⣠⣼⡟⠀⠶⢀⡾⠃⠐⠛⠙⢳⣤⠓⠋⠛⢦⡴⠛⠛⢲⣥⠖⠛⠛⢦⡶⠛⠛⠀⠈⠀⠀⠈⠀⠀⠀⣯⠿
⢠⣧⣄⠀⠠⠶⠶⠆⠀⠀⠀⣠⣠⣿⣿⣿⡇⠀⣤⠀⣤⡖⠀⠀⠀⢠⣏⡀⠀⢀⣼⡁⠀⠀⢨⣇⠀⠀⢀⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤
⠀⡟⢨⠰⠂⠀⣠⠶⠾⠟⠉⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡤⠞⠀⠀⠀⠀⠀⠀⠈⡇⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡌
⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⠀⠶⠀⡀⡀⠠⠛⠘⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠆⠀⣠⠄⠀⠈⢀⡀⠀⠀⠀⠀⠠⡀⠀⣧⠀⠀⠀⠀⠀⢠⣡⡄⠉⠉⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠐⢣⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⢿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠠⠀⠄⠀⠀⠀⠄⠂⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠆⠀⣠⠀⠀⠀⠀⢀⠀⠀⢠⡆⠀⠀⠐⠃⠀⡠⠀⢐⢀⠄⠀⠀⠀⠀⠀⠀⠀⣤⡇⡀
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠞⠂⠀⢠⠀⠀⠀⠀⣄⠻⣏⢀⠔⠁⠀⢀⠈⠀⠀⠀⠀⠀⠐⠁⠀⠠⠒⠀⠀⢀⣴⡇⡘⣟⠃
⠀⠀⠌⠀⠀⠀⠒⠨⠉⠀⠀⠀⠀⠞⠁⠀⠀⡠⠚⢋⠀⠀⢀⠄⠀⠈⠀⠀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠦⠚⣣⣓⡉⢑
⠀⢰⠂⠀⢰⡆⠀⠀⠀⢀⢈⠀⠀⠀⠠⠀⠀⠇⡰⠋⠠⡄⠈⠀⡀⠀⢀⢞⠑⢂⠀⢀⡀⠀⠁⠀⠀⠁⠀⠐⠛⣿⡾⡀⠎
⠀⢸⠂⠀⠀⠀⠀⠀⠶⠀⠀⠀⠁⠀⠀⣀⠀⣆⠁⠀⣶⠰⣄⠘⠁⠀⡈⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⢮⠂⢀⣀⠈⠉⠁⠀⠠⠤⠀⣇⡀⢸⠂⡱⠧⠂⣾⡇⢠⠿⠀⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⢀⠀⠀⠒⠀⠀⠸⠆⠃⡄
⠀⠚⠀⢸⠛⢀⠀⠀⠀⣁⠀⠀⠈⠀⠈⢇⠁⠂⡜⠱⠹⣺⠃⢀⠄⣄⡜⠂⠀⢸⠃⢀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠘⠰
⠀⣴⡦⠛⣶⢤⡀⠀⠀⠐⠤⠀⠀⠀⢀⠈⠣⡾⠀⡄⠆⠁⠀⠈⠡⢻⢻⠵⠀⠀⠀⠈⡀⣀⠀⠉⠒⢒⣁⣸⡤⠆
⠀⠀⠁⠀⠸⡛⠁⠀⠀⡀⢡⠒⢲⠂⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠟⠀⢀⡞⠉⠀⢘⡇
⢤⡀⠀⣠⠇⠁⠀⠂⠉⣩⠖⠈⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠄⠀⣰⠀⠀⠀⠀⣀⣸⣇⣀⡤⠞⠀⡸⡖
⢨⣜⡜⠃⡠⠀⠀⠠⠈⠀⢀⠀⢀⠀⠀⠀⠐⠠⠀⠀⠀⠊⠀⠀⠀⠉⠁⠂⢤⠃⠀⠀⠀⡞⠉⠉⣯⠀⠀⠀⠀⠀⠿
⠘⠯⣥⠋⠁⠀⠀⠀⠉⠀⡀⠀⠀⡀⠀⠀⠀⠀⠤⣀⡠⠒⠀⠀⠀⠀⠀⠀⡘⠀⠀⢀⣠⣷⡤⠞⠃⠀⣀⣲⢀⣀
⠀⠀⠁⠀⠀⠀⠂⠀⠠⠁⡀⠈⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⡀⠒⠀⠂⠄⠉⠀⠀⠀⡏⠀⢈⡇⠀⠀⣀⡿⠟⠙⠋⢷⣄
⠀⠀⣶⠀⢠⠀⠁⠄⠐⠀⠀⠀⠀⠀⠀⠀⣀⣈⡁⠁⠀⠀⠐⠄⠀⠈⠀⠁⠀⢀⡤⣷⠒⠉⠀⣄⠀⠀⢸⢂⠀⠀⣠⠁
⠀⠀⠏⠀⠀⢣⡀⠀⠀⠮⠂⠐⠊⠋⠉⠁⠀⠀⠀⠀⢀⣀⣴⣶⡾⠿⠖⠀⠀⣸⠴⠋⠀⠀⠒⠿⠀⠀⠀⠙⠧⢈⠉⠁
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉
⣿⣿⣿⣿⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣛⣿⣟⣻⣟⣛⣛⣿

⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡀
⠀⠀⠀⠀⡄⠀⢠⡀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠒⡀⢀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠈⠠⡀
⠀⠴⡀⠀⠀⠀⠈⠉⠀⠁⠀⢀⠴⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣄⠀⠀⠀⠀⠀⠀⣴⠩⢷⣄⠻⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡤
⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⡋⢸⠊⠀⠀⠀⠀⠀⠀⠈⠻⣦⣿⣷⣤⣈⠁⣀⠀⠀⠀⠀⠀⠀⢈⠀⠀⣙⠫⢄⡀
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠄⠀⠀⠀⠀⠀⡟⢨⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣷⠟⠀⠀⠀⠀⠀⠀⠀⠉⠟⡙⠑⠶⡄
⠀⢠⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⣸⠃⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠁
⠀⠀⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠀⠀⠀⠀⠀⠻⠖⠋⡀⠁⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⢖⣦⡀⠀⠀⠀⠈⠉
⠀⠀⠉⠀⢠⠂⠀⢰⠇⠀⠆⠰⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣦⣤⣄⣀⣃⣀⡒⠀⠀⠀⠀⠀⣾⡇⢠⢺⣿⡀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣿⣿⣿⣿⣿⣛⢋⡆⠁⠀⠀⠀⣿⠃⠨⣭⠁⡆⠀⠀⠀⢀⡐⠀⣩⣿⣇
⠀⠀⠐⠧⣆⡖⢂⣀⡀⣠⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⠑⢸⡟⡼⠀⠀⠀⡰⠂⠥⢐⢣⣿⡇
⠀⠀⠀⠀⠈⠁⠉⠉⠉⠉⠉⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠙⠛⢿⣿⣿⠿⠉⠁⠀⠀⠀⠀⠙⠏⠉⠈⠁⠀⠀⠸⣗⠔⣁⣼⡼⠋
⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠉
⠀⠀⠀⣀⡀⠀⠙⠙⠙⠛⠿⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⢀⠀⢠⡀⣆⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠤⣀⠄
⠀⠀⠀⡏⢻⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠑⠂⠁⠀⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⢀⠞⢠⡖⡌⢻⠡⠤⡴⢰⡀
⠀⠀⠀⠇⢸⡄⢀⡖⢦⠀⠀⠀⠀⠀⠀⠀⠀⢡⠦⢤⡀⡀⠀⠀⠀⠠⢤⣠⠍⢀⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⡽⢧⣼⣛⣾⣯⣽⣾⢹⡲⠿⡄
⠀⡴⠲⢶⣤⣷⣎⣰⠃⠀⠀⠀⠀⠀⠀⠀⢽⡸⡄⣸⠃⠀⠀⠀⠀⠀⠀⠉⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢹⠭⡿⠻⡿⣛⢻⡟⡙⡶⠆⣾⣧
⠀⠻⢤⣬⠿⡟⢫⣼⣉⠓⢦⡀⠀⠀⠀⢸⠉⡇⣳⡏⠀⠀⠀⠀⠀⠀⠐⠒⣖⠂⠀⠀⠀⠶⠀⠀⠈⠀⠁⠁⠀⠀⠈⢃⡥⢡⡿⢿⣿⠟⠱⣦⠙⡯⠁
⠀⠀⠀⠀⠀⠻⣄⣳⢉⣷⣤⡿⠀⠀⠀⠈⣠⣛⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣩⠦⠀⢠⠀⠀⡀⠂⢀⠀⠀⠀⠀⠀⠀⠀⠮⣆⠀⢄⠱⠂⢐⣁⠞⠃
⠀⠀⠀⠀⠀⠀⠈⠁⠛⢧⣽⠀⠀⠀⠀⠀⠁⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⢀⡀⡰⠤⠀⢄⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡠⠈⠁⠤⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢄⠁⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⢰⡆⠙⠀⠰⠀⠀⠀⠀⢤⡤⠀⠀⠀⠀⠀⠀⠘⠒⣀⠐⠄⢀⠄⠀⠐⢦⡤⢘⠢⣀⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⢳⠀⣄⠄⡸⠀⠄
⠀⠀⠀⠛⠃⠀⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⡀⠀⠀⠀⠸⠀⠰⡀⠀⠀⠁⠀⠂⠀⢼⢠⣼⣅⡌⢀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡘⠃⡉⠊
⠀⠀⠀⣨⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠄⠀⠀⡃⢈⡛⠂⠀⡖⠃⣨⠁⠈⢣⠈⠁⠀⠀⠀⠀⠀⢈⠴⠾⡂⢖⣿⡇⠐⠢⣀
⠀⠠⡐⡉⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣀⠙⠀⠀⠀⠀⠈⢄⠠⢀⠡⣀⠄⠀⡁⠀⠀⢀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠏⠉⠏⠀⠀⢈⠁⠈
⠀⠀⠀⠛⠑⠃⡂⠀⠃⠀⠀⠀⡀⠢⠙⠃⠀⠀⠀⠀⠀⠀⠀⠡⠄⠳⡀⠀⠀⠈⢲⠃⠰⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠘⠙⠁⢖⠐⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⢟⠀⡀⠀⠐⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠾⠿⠿⠿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠋⠀⠀⠀⠀⠀⠀⠉⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⣤⣤⣤⣀⣀⣠⣤⣤⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠻⢶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣀⣤⣴⡶⠟⠋⠁⠀⠀⠀⠀⠈⠙⠻⢷⣦⣤⣀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⠀⠀⠀⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠁⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⢀⣀⣤⣴⡾⠿⠋⠙⠻⢷⣦⣤⣀⡀⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠷⠿⠿⠟⢛⣋⣉⣁⣀⣀⣀⣀⣀⣀⣀⣉⣙⡛⠛⠿⠿⠿⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⣠⡾⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣦⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⠀⢿⣆⡀⠀⠀⣠⡿⠿⠿⠿⠿⢿⣆⡀⠀⠀⣠⣿⠃⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠙⠻⠿⠟⠛⠁⠀⠀⠀⠀⠀⠙⠻⠿⠿⠛⠁⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠸⢷⣶⣶⣶⠗⠀⠀⠀⠀⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⢻⣟⠻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⢿⣦⣿⠿⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣤⣀⣀⣀⣀⣀⣀⣠⣴⣶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⢿⣇⠀⠈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠉⠛⠛⠛⠛⠛⠛⠉⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⣀⣀⣈⣿⣆⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠘⣿⡏⠛⠛⠛⢿⡆⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⢿⣟⠛⠛⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠛⠛⢻⣿⢶⣦⣄⠀⠀⠀⠀⠹⣷⡀⠀⠀⠘⣿⡄⠘⣿
⠀⠀⠀⠀⠀⠀⢀⣼⠟⠉⠀⢸⣿⠀⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠀⣸⡏⠀⠈⠻⣷⡄⠀⠀⠀⠘⢿⣦⣤⣴⢿⣷⣸⣿
⠀⠀⠀⠀⠀⢀⣿⠏⠀⠀⠀⠈⣿⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⣿⡇⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠙⠿⣷⣤⣿⣿⡏
⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠻⠷⣶⣤⣄⡀⠈⢿⣷⠶⠶⠶⠾⣶⣿⠃⠀⣠⣤⣴⡾⠿⠃⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⠁
⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠇⠀⠈⢻⣦⠀⠀⣰⡿⠁⠀⠘⣿⡉⠀⠀⠀⠀⢀⣤⣤⣤⣤⣿⣤⡀⠀⢀⣀⣀⣀⣀⣨⣿
⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⢀⣶⠀⣼⣟⠀⠀⠀⠀⠻⣧⣴⡟⠁⠀⠀⠀⢸⣧⠀⣴⡆⠀⢸⣿⠉⠉⠉⠉⣿⡇⠀⢹⡇⠀⠀⠀⢨⣧
⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⢀⣾⠏⠀⠈⠛⢷⣦⡀⠀⠀⢹⣿⠀⠀⢀⣤⣾⠟⠁⠀⠘⣿⡄⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠉⠻⣷⣄⣸⣯⣠⣶⠟⠋⠀⠀⠀⠀⠀⢸⣷⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣿⠀⠀⠀⠀⣿⡇⠀⢸⡇⠀⠀⠀⢸⣿
⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢠⣤⣤⣤⣾⣧⣼⣿⠀⠀⠀⠀⣿⣧⣤⣾⡇⠀⠀⠀⢸⣿⣤⣤⣤⣤⣤⣤⡀
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⢿⣷⣶⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⢹⣿⠀⠀⠀⠀⣿⡏⠉⢻⡇⠀⠀⠀⢸⣿⠉⠉⠉⠉⠉⣿⡇
⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⢰⣿⢸⣿⠀⠀⠀⠀⠶⣶⠆⢸⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣿⡇⠀⢼⡇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⢸⡿⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⣿⡀⠀⠀⢀⣿⠇⠀⢸⣇⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⣾⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠙⠿⣶⣶⠿⠋⠀⠀⠈⠻⢷⣶⣶⠟⠁⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⢀⣿⠁⢸⣿⠀⠀⠀⠀⠶⠾⠆⢸⣿⠀⠀⠀⠀⠀⢸⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣿⡇
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡟⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⡇
⢤⣤⣴⣟⣤⣤⣶⣶⣶⣶⣾⣷⣶⣾⣿⣶⣶⣶⣶⣶⣶⣶⣾⣿⣶⣶⣶⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣟⣧⣤
⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣃⣀⣀⣀⣀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⣀⠴⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠂⠀⠀⠤⠚⠁⠀⠉⠐⠉⠀⠀⠀⠀⠐⠂⢙⠉⢥⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⡀⠤⠞⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠉⠑⢆⣀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠈⠀⠀⢰⠀⠀⠉⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠈⠀⢀⠁⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⢀⡀⣀⣀⣀⡀⠀⠀⢀⠜⠉⠣⠄⠠⠒⠉⠓⠦⣀⣀⠤⠆⠁⠠⠄⣈⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠖⣡⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⣼⠑⠆
⠀⠀⠀⠀⠀⠀⠸⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⢰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠸
⠀⠀⠀⠀⠀⡐⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⢃
⠀⠀⠀⠀⠀⢇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡘⠁
⠀⠀⠀⠀⠀⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠛
⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡋⠁⠲⠶⠀⠀⣀⣉⣤⡉⠀⠰⠶⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠊⠉⡙⠋⠀⠒⠒⢠⡄⠀⠀⠄⣤⠐⠒⠒⠂⠛⡍⠐⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠸⠁⠲⣄⠀⠀⢀⡇⠀⠀⠀⣿⠀⠀⠀⣠⠔⢺⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⢀⠃⠀⠀⠈⠓⡄⢨⡇⠀⠀⠀⣿⠀⣠⠊⠁⠀⠀⠲⡀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⢠⠉⠀⠀⠀⡠⠎⠀⢸⡇⠀⠀⠀⣽⠀⠈⢢⠀⠀⠀⠀⢡⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⡆⠀⠀⠀⠀⠙⢄⠀⠀⡇⠀⠀⠀⠸⠀⠀⡰⠃⠀⠀⠀⠀⠦⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠳⣀⠇⠀⠀⠀⢀⢀⠎⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⡘⠃⠀⠀⠀⠀⠀⢀⠴⠖⣨⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⣶⢀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠈⠓⠐⠋⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠈⣥
⠀⠀⣀⡤⠊⠀⠈⠑⠢⢄⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣀⠤⠒⠁⠀⠣⢄⡀
⡤⠚⠁⠀⠀⠀⠀⠀⠀⠈⠙⡇⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠐⣶⡟⠁⠀⠀⠀⠀⠀⠀⠉⠓
⠉⢰⠆⢀⡀⠀⠀⠀⠀⣀⡴⢄⠀⠀⣠⡞⠋⠉⠉⢛⢻⣶⡦⠤⢤⡤⠤⠴⠦⠤⠀⠀⠀⠀⠀⢸⠀⢀⡿⠀⡄⠀⠀⠀⠀⢀⠀⠰⡆
⠀⠈⠶⣟⠁⣰⠆⢀⣤⡀⣷⢀⣇⢠⡏⠀⠀⠀⠀⠀⠈⢹⡇⠀⠐⠇⠀⠀⡆⠀⠀⠀⠀⢀⠀⠀⠀⢨⡏⠀⠇⣀⡀⠠⣄⠈⣷⠶⠃
⠀⠀⠀⠈⠒⠉⠒⠂⠈⢻⡉⠃⢧⡘⣧⡀⠀⡀⠀⠀⠀⣼⡇⠀⠐⡆⠀⠀⡇⠀⠀⠀⡰⠺⣷⣦⠀⣼⠛⡀⢸⠁⠐⠀⠛⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⣠⢸⣦⣬⣷⣶⣤⣤⣤⡾⢁⡦⠀⢠⡇⠀⠀⡇⠀⠀⠘⢤⡀⢘⣿⢠⡏⣭⡏⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢻⣌⣤⣤⣤⢱⣿⠀⠠⢄⠨⣟⠀⢸⡇⠀⠀⡇⠈⠀⠀⠀⣹⣏⣹⣿⣀⡤⡄⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡈⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⣿⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢁⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⣿⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⢀⠃⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠈⠱⠆⠠⠄⠴⠋⠀⠀⠀⠀⣿⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠈⠲⠄⠀⠠⠴⠋⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠃⠀⠸⡇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠤⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠐⡇⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠆⠺⢿⣭⣭⣤⣤⣬⣽⡋⢸⡏⠘⢯⣭⣭⣭⣭⣽⡟⠿⠃⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠛⠃⠀⠀⠀⠀⠈⠉⠁⣼⠣⠘⠃⠀⠀⠀⠀⠀⠰⠟⢀⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢭⠴⠆⢀⣀⡀⠰⢦⡁⠞⠓⢨⠴⠆⣀⣀⣀⡀⠰⠮⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠄⠆⠀⠀⠈⠀⣠⠀⠐⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠒⠀⠀⠁⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⣠⠀⠀⠀⠈⠀⠀⠀⠀⡀⠀⣄⡀
⣠⣶⠀⠀⠀⠛⠁⢀⠴⠀⠀⢸⠃⠀⠀⢴⢤⠏⣆⠀⠀⠘⢁⠀⠀⠀⠀⠄⠈⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁
⣿⠇⠀⠀⠀⠀⠀⠈⠚⡀⠀⠈⠀⠀⡠⠐⠈⡆⠀⠀⠀⢴⣿⠀⣠
⠛⠀⠀⠀⠀⠀⠈⢀⣄⠷⢀⡴⠀⠀⠀⠀⠀⠘⠀⠀⣰⣿⠇⠀⡴⠀⢀⠄⡀⠀⠀⠀⠀⠈⢠
⡄⠀⠀⠀⠀⠐⢾⢦⡁⠀⠀⠋⠂⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠀⠀⢀⡈⠀⠀⠠⠆⠀⠈
⡹⠀⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⠁⡀⢀⠀⠀⠀⠀⠀⠰⠂
⠡⠆⠭⠛⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠀⠈⠆⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢠
⢱⣸⡶⡄⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠠⠀⠰
⠂⠞⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠠⠄⠀⢀⠀⠀⠀⠉
⠀⡄⣠⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⡀⠀⠀⠀⠀⠘⠆⠀⠄⠘⢦⡀⠄⠑⠄⠀⡄⠀⡀⠀⠀⠀⢠⣦⡤⠀⠐
⢃⢠⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢐⡇⠀⠠⡀⠀⠀⠀⠀⠣⠀⢠⠟⢦⣀⠀⢀⡇⠂⠁⠀⠡⠀⢨⠍⠀⠉⠱
⠈⠀⡀⢰⠀⠀⣀⠠⠔⠀⠀⠀⠄⠈⠁⠀⡑⣾⣮⠠⠂⠀⠀⠑⢌⠈⠁⠈⠢⡼⠀⠀⠀⠀⢘⠀⠘⢦⠀⢀⠄
⠀⠀⠈⡿⠒⠒⠤⡀⠀⠠⢦⡀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠈⠂⠀⠈⠀⠀⠀⠁⠀⢀⣀⠈⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠀⢀⠀⢣⡀⠀⠀⢹⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⣚⠀⠤⠀⠀⠀⠘⠄⠀⠉
⢀⠇⠀⠀⠉⠓⠢⡾⠴⠤⡄⠀⠀⠀⠗⠀⠀⠀⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠢⣸⢺⠋
⠈⠁⠀⠀⡀⠀⠀⣧⡀⠀⡴⠀⠀⠀⠈⡆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸⠁
⢀⡤⢤⢸⣶⡆⠀⠀⠉⣹⠛⠲⡄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠘⠁⠀⠀⢉⠃⠂⠀⠀⠻⢄⡀⡿⠀⠀⠀⢠⠈⠀⠀⠀⠄⠀⠀⠁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁
⠴⠄⠀⣠⡼⠀⠀⠠⠀⡀⠀⠈⣟⢳⡀⠀⠀⢠⣤⣤⣤⡀⠀⠀⠀⠐⠂⠠⠤⠤⢤⣀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⡈⠙⠦⠄⠀⠀⠀⠉⢉⠉⠉⠁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⡁⢒⠀⠀⠈⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⣀⣤⣤⠶⠶⠚⠛⠋⠉⣉⠉⠁⠐⠒⠤⠄⠀⠀⠀⠀⢀⡠⠤⠀⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠈⠁⣢⠔⠊⠉⠀⠀⠀⠈⠉⠐⠂⠤⣀⠀⠉⠐⠢⢄⡀⠉⠑⠲⢎⡁⠀⠀⠀⠀⠀⠀⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢀⡀⠄⣤⠴⠉⡿⣿⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⡀⠀⠈⠓⠦⡀⠀⠈⠓⢶⡴⠦⣀⠀⠀⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠎⠁⢀⠜⠁⠀⠀⡇⠙⣦⡀⠈⠁⠒⠤⠄⡀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢄⡀⠀⠉⠒⠤⣀⠈⠑⠤⢃⡀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢠⠀⢠⠊⠀⠀⠀⡠⠀⠀⠈⢻⣦⣀⠀⠀⠀⠉⠑⠂⠤⢀⣀⠀⠀⠀⠀⠀⠁⠒⠂⠤⠄⠀⣉⣐⡶⢿⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢾⢠⠃⠀⠀⢀⠔⠁⠀⢀⡴⠃⠈⠑⠞⡡⠒⠀⣀⠀⠀⠀⠀⠉⠉⠐⠲⠖⠒⠲⢶⣶⠶⠊⢉⣁⡠⠞⡧⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣀⠞⠁⠀⣀⠔⠃⠀⢀⠴⠊⠀⠀⠀⠀⠀⢀⣉⡐⠠⣤⣉⣉⡀⠐⠒⠒⠀⠈⠉⣉⣉⠀⠬⠽⠿⠉⠶⠾⣇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠺⠧⣤⣄⣋⣁⠠⠤⠚⠋⠐⠒⠂⠀⠠⠤⢴⠋⢉⡉⠶⢈⡉⠉⠧⠚⠛⠛⠛⠛⠉⠉⠉⠀⠤⠤⠤⢤⠤⠴⡏⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢠⡅⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢨⣵⠟⣋⢥⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⡈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢺⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢀⠃⠀⠀⢠⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠆⠀⠀⠈⡄
⠀⠀⠀⣀⡴⠋⠀⠀⢀⠆⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠘⡄⠀⠀⠘⢆⡀
⡔⠂⠈⠁⠀⠀⢀⡴⠃⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠁⠒⠂
⠈⠁⠒⠶⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⠦⠀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠀⠀⠀⠰⠁⢌⣱⠋⠉⠒⠠⣤⡹⠹⠷⠀⠀⣀⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⢤⣀⣠⢣⠋⠀⠡⠤⣀⠀⠀⠀⠁⠛⠲⢦⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣴⣤⢄⠆⠀⠀⠀⠀⠀⠉⠑⠢⣄⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⢴⣡⠁⡌⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠉⠐⠢⠼⢦⡉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⡐⢃⠆⠐⢠⠞⢳⡆⠀⢠⡂⣀⠰⢦⡞⠳⣄⠀⠀⢤⡹⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠤⢤⢃⣼⠞⠋⠁⠀⠸⠁⠀⡈⠻⣤⡴⢚⡇⠀⠈⠑⠺⣦⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⢀⣤⡦⣀⣹⣤⡈⠀⠀⠀⠀⠀⠈⡅⠀⠀⠘⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣤⣤⠷⣤⣄⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⡀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⣄⡀⠿⢁⣀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⢀⡡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠘⣟⢻⠛⠛⠀⠉⠚⠃⠤⠄⣀⣈⠀⠀⠀⣍⣀⣀⣤⡴⠞⠏⠙⠓⠀⣶⠐⠛⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠓⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠊⠉⠛⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣀⡀⠉⠓⠢⢤⣀⠀⠀⠀⠀⠀⠀⢀⡘⡌⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⣀⣘⠀⢀⣿⠀⢀⠤⠤⣹⡶⢦⣀⠀⠀⢦⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠉⠉⠙⢷⣴⡏⠀⠀⠒⠐⢸⡏⠉⡏⠉⠛⡎⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠠⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⢸⡇⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣞⠂⡾⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⢦⣤⣤⣴⡞⣿⠀⠀⢀⡖⠀⣼⠃⠀⡇⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢠⠉⢙⠃⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠛⠛⠛⠛⠋⠈⠃⠀⠙⠛⠈⠂⠀⣧⠀⠀⡇⠀⠀⠀⠀⠘⠓⠓⠛⠛⠋⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⡇⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠢⣀⣀⣀⣀⡠⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠘⢤⣀⣀⣀⣀⠴⠁⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠃⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠤⠄⠀⠀⢤⠄⠠⠀⠀⠀⠠⠤⠄⠶⠀⠀⣏⠀⠀⢠⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢤⡔⠒⣒⣒⣒⣲⡶⠶⠒⣷⠒⡾⠛⣛⣛⣛⡛⠲⣶⡤⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣇⠰⠾⠯⠭⠭⠭⠥⠴⠖⢠⡟⠀⠶⠿⠯⠭⠍⠙⠛⠳⠄⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣕⢂⣄⠀⠀⠀⢀⣄⠒⡩⠶⡑⢂⡀⠀⠀⠀⠀⢠⣀⡺⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠠⡶⡆⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢀⠄⠀⠀⠀⠈⠀⠐⠂⠀⣯⡅⠐⠒⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠇⠈⠁⠣⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⡄⠀⠆⠢⠁⠀⠀⠀⠀⠀⠀⠐⠀⡄⠀⠀⡄⠀⢀⠠⠀⠀⠉⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠠⠀⠀⠀⠀⠈⠃⠀⠆⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⣲⢏⣀⡀⠈⡎⠁⠆⠀⠀⠀⠠⠺⠀⠇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠈⡀⢀⠐⡁⠀⠀⠈⠀⢀⠀⢀⣀⣀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠑⠒⠁⠀⠀⠀⠀⠀⠐⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡡⠈⠀⡀⠀⠀⠀⠘⠀⠀⠀⠀⡇⠀⠀⠐⠀⠀⠀⠀⠀⠀⠂⠀⠀⣀⠀⠈⠀⠀⠀⠀⠈⠀⢀
⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠐⠠⠀⠀⠀⠁⠀⢐⣚⣚⣚⣓⣛⣛⣓⠀⠀⠈⠀⠀⠀⣀⠀⠀⠉⠄⠀⠠⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠔⠀⠁⠀⠀⠀⢈⡡⠞⢀⡈⠤⠀⠈⢠⠡⠬⠀⠠⠀⠀⢈⠀⠒⢁⠀⠀⠂⠀⠀⠾⠂⠀⠀⠀⠀⠑⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⠀⠄⠈⣶⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠛⠿⡀⠾⢦
⠀⠀⠀⢀⠐⠀⡄⠀⠀⠀⠀⢲⠆⣠⣀⠀⢀⣤⡀⠀⢀⣤⣄⠀⠀⣄⠀⠀⠀⢀⣤⣄⠀⠀⣀⣤⣄⠀⠠⣄⠀⢀⡄⠀⠀⠻⣀⣃⡰⠂
⠀⠀⠀⠀⠩⢒⡇⠀⠂⠀⠀⠀⠀⣿⣸⠇⠀⣿⠀⢠⡟⠁⠹⣇⠀⣿⠀⠀⢠⡟⠀⢹⡇⢰⡏⠀⢉⡁⠀⠹⣆⣾⠁⠀⠀⡀⠀⠉⠀⠠⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠙⡧⠀⣿⠀⠸⣧⡀⣠⡟⠀⣿⠀⡀⠸⣇⠀⣸⡇⠸⣇⠀⣹⡟⠁⠀⣹⠇⠀⠀⠠⠜⠠⢌⠀⠠⠤
⠀⠀⠀⠀⠀⡀⠀⡀⠠⠄⢀⠀⠀⠛⠋⠁⠈⠉⠁⠀⠉⠛⠉⠀⠀⠉⠉⠉⠀⠙⠛⠉⠀⠀⠙⠛⠋⠀⠀⠀⠉⠀⠀⠰⠀⠀⢄⠀⡀⠰⡀
⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠠⠊⠈⡆⠀⢀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠁⠉⣄⠠⠌⠀⠁
⠀⠀⠀⠀⠀⠀⡠⢄⡠⢄⠀⠀⠔⡅⠊⠀⡐⠠⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠀⠀⡀⠀⡀⠀⠀⠀⢀⠀⠀⠂⠤⠐⠀⠀⠀⠂⠐⢀
⠀⠀⠀⠀⠀⠁⠀⠀⠠⠂⠐⢀⠀⠀⡠⡌⠀⠐⠂⠄⠀⠀⠀⠀⠘⠀⠀⠂⠠⠀⠀⠀⠣⣄⠀⠀⠀⠀⠰⠂⠀⠀⠀⢀⡈⠀⠉⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠃⠠⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐⠀⠄⠀⠀⠀⠆⠀⠈⠀⠀⠀⠀⠀⠲⠀⠀⠈⠀⠐⠀⠘⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠤⢦⠀⡂⠠⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢤⠀⠀⠀⢠⡦⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⡀⢀⢀⡀⠀⠀⠀⠀⠀⡄⢀⡄⠀⡀⠀⡀⢀⠆⠀⠀⠀⠀⠡⠂⢀⡀⠀⠀⠀⠈⠦⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠣⡈⢀⠀⢁⡠⠇⡀⠘⠁⡘⠄⣠⠃⢀⠀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡄⠀⠐⠀⠀⣀⠂⠠⡈⠀⠀⠄⠀⠀⠹⠠⢄⣈⣈⠶⠃⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠤⠔⠳⠀⠀⠀⠘⠋⠁⠈⠑⠂⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠃⠀⠀⠴⢉⡺⠄⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⣷⣤⣄⠀⠛⠋⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡆⠈⣷⣠⠶⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣇⠀⠈⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣠⣤⣤⣲⠥⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢠⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢠⣤⣤⣾⣿⡿⠃⠀⠀⠀⠀⠁⣼⢠⣄⡀⠀⣀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀⣀⣀⣴⣯⡘⣿⣿⠛⠛⢿⣧⡀⠀⠀⠀⣶⠀⣿⣼⣿⠋⠈⢽⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣟⡋⢽⠟⠩⠀⠸⢿⣿⣿⡀⠀⠀⠉⠁⠀⣀⠀⢿⣰⡿⣿⢿⡄⢰⣿⣿⣷⣶⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠠⠚⠢⠀⠀⠈⣿⣿⣧⠀⢰⣦⠀⠈⢿⠃⠸⢻⡇⢀⠛⢱⣿⡉⠉⠉⢉⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠜⢧⡀⠀⠀⠀⠠⠀⠀⢙⣿⣿⣇⣿⠋⠀⢀⣏⠁⢀⣿⡄⢈⡡⠟⣻⣿⢾⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣶⠐⠀⠁⠀⠀⢀⠀⠀⢠⣀⣼⣿⣿⣿⡇⠀⠉⣹⡗⠈⠙⠁⠁⠀⢰⣿⣿⡾⠉⠉⠛⣉⠉⣷⣾⢷⣄
⠀⠀⠀⠀⢀⣀⡤⠾⠶⠶⠶⠶⠠⢮⠀⡀⠀⣹⣶⡈⣿⣿⡇⠀⠀⢿⠁⠀⠀⠀⠀⠀⢸⠟⠉⠀⠀⠀⠌⠀⣤⡿⠈⠀⠙⢧
⠀⠀⠀⠀⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⢀⠻⣿⣿⣿⣷⡄⠀⣼⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢀⠁⣠⠞⠫
⠀⠀⠀⠀⠙⣶⠶⠖⠦⠒⠤⠀⠀⠀⢠⣄⡀⠙⣶⣻⣿⣿⣿⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛
⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣌⣻⣿⣿⣿⣇⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡉⠻⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⢠⣀⡐⠆⠀⠂⠀⠀⠀⠀⠀⠀⠀⠁⠰⣿⣿⣿⣿⣧⡄⡀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠈⠉⠛⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣐⠁⠀⠀⠀⠀⠀⡀⢃⣰⣂⣤⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣈⣿⣿⣿⣿⣿⣦⠀⠂⠚⠿⢿⣿⣿⣧⣿⡉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⣿⣿⣶⣶⣿⣴⣦⣴⠞⠛⠉⠉⠉⠀⠉⠉⢿⣿⣿⣷⣶⣤⣀⠀⠉⢹⠋⠉⢻⣦
⠀⠀⠀⠀⠀⠀⠀⣿⡈⢉⠙⠛⠛⠛⠛⠋⠉⠀⠀⠀⠅⠀⠂⠀⠀⠀⢀⣀⣉⠿⣿⣿⣿⣆⠀⣽⡇⠀⠀⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠘⣷⣌⣀⡀⠀⠈⠀⠖⠀⠃⠀⠀⠀⠀⢀⡠⣤⡶⢋⡽⠟⡶⣿⠋⣽⢏⣀⢸⣧⠀⠀⢿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠻⠷⢷⣦⣄⣤⡤⠤⠀⠀⠀⢠⡁⣰⡿⠋⠀⣤⣼⣿⣷⠿⠛⣋⠀⣿⡆⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⠟⠙⠀⠀⢤⡟⠙⠇⠀⣠⡾⠏⠀⣿⢻⡄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢱⠉⠀⠀⠀⢀⡾⠀⠀⢀⡐⠋⠀⠀⢰⡇⠀⢣⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⠞⠀⠀⠀⣼⠃⠀⠀⠀⢻⠀⠀⠈⡇⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠁⠀⠀⠀⣸⠇⠀⠀⠀⠀⢸⡄⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⡿⠛⠻⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⣤⣤⣤⣤⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄
⠀⠀⠄⠀⠀⠀⠀⢠⡄⢤⠀⠀⠀⠀⠑⠀⠀⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠌⠌⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡜⠕⠀⠀⡄
⠀⠀⠀⠀⠂⠠⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⢈⠀⠀⠀⠈⠀⢀⠁⠀⣤⣤⠀⠀⠁⠀⠀⠀⢮⠈⡀⠂⠀⠁⡄
⠀⠀⠀⠀⠈⠀⠂⠀⠂⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠃⠀⠀⠁⠀⠈⠁⢰⡕⢃⡀⠀⠀⠄⢀⠀⠆⢈⡁⠀⢁⡴⠁⠀⡀
⠀⠀⠀⠀⠀⠀⢈⡠⠄⠀⠀⠈⠠⠄⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡄⠀⠀⠀⠀⠀⠄⠁⠀⠈⠡⡀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠁⠀⠀⠀⠀⠉⠁⢂⡀⠀⠀⠀⠀⠀⢀⠁⠀⢀⢌⡤⡁⠌⣡⠀⠀⠀⠀⢀⢑⣲⣉⢀⡀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀
⠀⠀⠄⠠⠀⠀⠀⠀⠙⠉⠀⠀⠁⠀⠀⠃⠀⠀⠀⠜⠀⡀⢀⠀⠀⠀⠀⠀⠈⠉⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢰⡀⠠⠀⠌⣍⠀⠀⠀⢀
⠀⠀⠀⠠⠄⠀⠀⠀⠐⠀⣀⠀⡀⠀⠠⠀⠀⠀⠀⠀⠠⠂⠄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⠀⢀⠈⢠⠀⢠⠀⠁⠈⠉⠀⠀⠀⠀⠀⠀⢄⠈
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠛⠇⠀⠀⠰⠃⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⡀⣀⠀⠀⠁⠀⠀⠀⠀⠄⠾⢀⠁⠀⠈⠀⣸⡁⠀⠰⢪⠐⠀⠀⡁⠀⠀⠀⠆
⠀⠀⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠀⠴⣁⡚⠆⠔⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠂⠀⢀⠠⠁⠄⠋⠀⠀⠀⠀⠀⠁⠀⠀⠈⠂⠀⠪
⠀⠀⡦⠤⠀⠀⢤⣴⡄⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣒⣓⣒⣚⣓⣒⣚⣲⠀⠀⠀⡀⠀⠚⠉⠀⠛⠧⠀⠀⠀⠀⠤⢀⠘⢀⠀⠄⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⣤⠉⡶⠙⠉⠁⠀⠀⢃⠐⠂⣤⠈⠁⢨⠁⠆⠀⠀⠉⠯⠉⠍⠩⠭⠡⠈⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐⠀⢀⡐⠀⠂⢢⠀⢢
⠀⠀⠀⠀⠀⠀⠈⠲⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⡁⢩⠀⡀⠠⠂⠂
⠀⠰⠋⡈⠱⡀⠀⠀⠀⢀⠀⠀⠀⢰⡟⣶⠀⠸⡿⠂⢀⡾⠛⢷⡀⢰⡇⠀⠀⠀⣴⠛⢳⡄⠀⣴⠛⠻⠆⠀⠻⣆⢀⡾⠁⠀⠀⠈⠀⠐⠃⠀⠀⠀⣎⠀⢱
⠀⡇⠀⣀⠀⡇⠰⠈⢻⠄⠓⠀⠀⢸⡷⣯⡀⠀⣿⠀⢸⡇⠀⢸⡇⠘⣇⠀⠀⢸⡏⠀⠈⣿⢸⡇⠀⠰⣦⠄⠀⠹⣾⠃⠀⠀⠀⢀⠐⢀⠀⠀⠀⠀⠈⠉⠁
⠀⠐⠀⢠⠘⠀⠀⠀⢸⠀⠀⠀⠀⢸⣧⡼⠃⢤⣿⠄⠘⢷⣤⠾⠃⠀⣷⣤⣤⠈⢿⣤⡾⠃⠀⢷⣤⣴⠟⠀⠀⢸⠇⠀⠀⢀⠀⠀⠀⠀⠀⠔⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣮⠀⠒
⠀⠀⠂⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢀⢲⡊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣘⠓⠀⠀⠀⠀⠀⠀⠒⠀⢀⠀⢀⣴⣶⢰⣦⠀⠀⠀⠁⠀⡽
⠀⠀⢀⠀⠀⣀⠀⠀⠈⠄⠀⠠⡄⠀⠠⣝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣐⠂⠀⠀⠢⠼⠀⠀⠀⠀⠀⠤⠀⢐⣫⠤⢬⡛⠋⣈⠁⠀⠃⠀⠀⡠⠃
⠀⠔⠻⠂⠀⠀⠀⠀⠾⠆⠀⠀⠀⠀⠘⠯⠀⠀⠀⠈⢠⠈⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⢢⠀⠀⠀⠀⢀⣠⠴⠊⢀⣀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⠃⠀⠐⠀⠀⠀⠀⠀⠀⢀⠈⠑⠀⠀⠐⢚⠤⢃⠀⠀⠐⠋⠀⠀⠀⠉⠁⠀⠀⢐⣀⠀⠐
⠀⠠⢘⢣⡈⡠⠰⡄⠀⠀⢀⡈⠃⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⡀⠄⠄⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⠀⢀⠀⠀⠀⢐⡉⠀⠁⡀⣀⠄⡀
⠀⠀⠀⠈⠃⣀⡀⠉⠀⠀⠀⢠⠀⣀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠴⢀⢐⠀⠊⠀⠀⠀⠀⠀⠐⠀⠆⠀⠀⡐⠂⠂
⠀⠀⠐⢦⠈⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠢⠀⡀⠀⠠⠵⡀⠀⠀⡀⢠⠀⠨⠀⡀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠋⠈⠁⡀⢀⡀
⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⡀⡀⠀⠀⠀⠀⢋⠴⠃⠀⠀⣇⠀⡁⠀⠀⠈⠉⠉⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠀⠦⠀⠤⠀⠀⠐⠂⠀⠤⢀⡲⠀⢂⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠘⡀⠀⠀⠀⠀⡀⠋⣶⠀⠀⠀⡈⠉⠀⠀⠀⠈⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠄⠐⢀⠀⢠⠋⠐⡀⠀⠀⠀⠀⠓⠐⠠
⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠁⠀⠀⠀⢦⣤⠀⠀⢀⠀⠐⡵⠄⠀⠀⠀⠀⠀⠀⠀⣀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠤⠂
⠀⠀⠀⠃⡀⠀⠈⠁⡴⠀⠀⠠⠀⠀⠀⠈⠉⠀⠠⢌⡐⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠤⠀⠀⡄⠀⢀⠀⠀⠀⠀⡀⠀⠀⠀⠠⠀⠀⠀⠀⠐⠀⠀⠂⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⡀⠀⢸⢖⠣⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⡸⠀⠠⠄⠘⠀⠈⠀⠀⠀⠀⠳⠈⢁⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⠀⠁⢀⡀⠀⡀⠠⡇⢀⡀⢠⡀⣀⠀⠉⠄⢔⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠀⠀⢠⡜⠁⠁⠉⠚⠛⠋⠉⠀⠀⠙⢦⡀⠀⠀⢐⠒
⠀⠀⠀⠀⠀⡀⠈⠠⠌⢁⡀⠢⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠄⠀⠀⠠⠤⠔⠂
⠀⠀⠀⠀⠀⠀⢀⠤⠂⢀⠀⢸⡇⠀⢠⠞⠁⠀⠀⠀⠉⠑⠀⠀⢸⣇⠀⠐⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣷⣀⡔⠒⠖⢤⡀⠀⡴⢈⣝⠰⣾⠃⠀⢀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⡟⠅⠀⢀⣽⡦⢁⣉⠘⢳⣦⠀⢼⠃⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢁⠂⡼⠀⢃⠀⠀⠘⡻⢞⠄⠘⡄⠀⠁⠠⡼⠀⠀⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⡞⢀⢑⠆⠈⠒⠫⠄⠀⠺⠓⣰⠎⡯⠀⢄⠀⠀⠀⠀⠀⣀⡠⠀⢀⡀
⠀⠐⡀⠀⠀⠀⠀⠀⠀⠔⠀⠁⠈⢲⡀⠀⠒⠤⣄⣀⡴⠞⢠⠞⠁⠀⠀⠀⠀⢀⡔⠉⢠⠀⠉⠉⠠⣆
⠀⡆⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣤⠀⠈⠀⠁⣠⠞⠂⠀⠀⠀⠀⠀⣸⠀⠀⢾⡁⠀⠀⠀⡯
⠀⠘⡄⢳⣠⠎⠁⠀⠀⠀⠀⠀⠀⣀⡠⠚⢢⠙⠒⠛⠛⠁⠀⢰⡟⣀⠀⠀⡼⠋⠀⠀⠀⢱⣀⠀⡀⠁
⢀⡄⠀⡀⠙⠀⢰⠀⠀⠀⣠⠔⠉⠀⠀⠀⠀⠀⠱⠆⠚⠐⠀⠴⠁⢻⡀⠼⠁⠀⠀⢀⠆⠈⠁
⡤⠀⠀⠐⡆⠀⠈⡄⠀⠀⣿⠀⠀⠀⠀⠘⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠀⠀⠀⡸
⠑⠀⡸⠀⠛⠀⠀⡇⠀⠀⡿⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢀⣿⠈⠧⣀⣀⠇
⠀⠀⠈⠢⡀⠀⠀⢰⠀⢸⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠏⡀⠀⢨⠉
⠀⠀⠀⠀⣦⠀⠀⠐⣇⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠠⠀⡆⠀⠀⠀⢻⡀⠁⠀⡄
⠀⠀⠀⠀⣿⠀⠀⠀⢸⡏⠀⢸⡀⠀⠀⠀⠀⠂⠀⠀⠄⠇⠀⠀⠀⢸⡇⠀⢨⠇
⠀⠀⠀⠀⢸⢀⡀⠤⠜⢯⠄⢸⡇⠀⠀⠀⠀⠀⠀⠄⠀⡇⠀⠀⠀⠸⣇⢀⡟
⠀⠀⠀⠀⠈⠻⡄⠀⠀⠸⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⡀⠤⣿⠊
⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⣠⠟⣿⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⠏⢀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠠⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⣀⢠⡔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⢛⡏⠀⢲⠀⠁⠉⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠃⠀⠸⡄⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠷⡄⠀⡸⠀⠀⠀⠀⠉⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡦⠀⠀⠀⠀⡀⢰⠁⠀⣣⠔⠀⠀⠀⠐⠒⠛⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⠒⠒⠂⢤⡀⢹⠇⠈⡗⢂⢁⠒⠉⠁⠻⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⡀⠀⠈⠉⠉⠢⢠⠟⠀⠀⠀⠀⠘⠁
⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣙⠲⣤⣤⣀⡀⣉⠀⠤⠀⠀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⠿⠿⢿⠿⢿⠿⠻⠿⡿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣛⣟⣛⣿⣿⣿⠿⠿⠿⠿⡻⠿⣿

⠀⠀⠀⡆⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠲⠀⡖⠂⠰⠒⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⢲
⠀⠀⠈⡏⠉⡍⢁⠀⠀⢤⠀⠀⠀⠀⠀⣶⠾⠰⠆⡇⠶⠰⠰⢲⡆⠀⠀⠀⠀⠀⠈⡏⢉⠍⢅⠀⠀⠀⠀⠀⠀⠀⠘⠙⠀⡠⠀⠸⣀
⠀⠀⠀⡇⠸⣶⡶⠂⠀⠀⡀⠀⠀⠀⠀⣿⠘⠀⠀⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠠⡇⠸⣶⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⣤⣀⣀⣀⡇
⠀⠀⢠⣧⣤⣤⣤⡄⢾⡿⡧⠀⠀⠀⠀⠿⠚⠛⠒⠛⠓⠚⠛⠺⠇⠀⠀⠀⠀⠀⢠⣧⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠠⠙⠿⣿⡿⠟⠁


⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⢰⠏⠁⠉⣷⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡏⠈⡇⡉⠈⡇⠀⠀⠀⠀⠀⠀⢀⡔⠉⣠⡄⠉⢢⡀
⠀⠀⠀⠀⠀⣸⣦⣄⣤⠟⠀⠀⠀⠀⠀⣏⠀⠀⢠⠦⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣷⣶⡇⣆⣀⡇⠀⠀⠀⠀⠀⠀⢼⠐⠳⠌⠁⠻⠇⡇
⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠐⠁⠀⠈⠀⠒⠁⠀⠀⠀⠀⠀⠀⣿⣿⡇⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⣄⠺⠆⠸⠗⣠⠃
⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠋


⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⣠⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠁⠀⠀⠀⠀⠀⠀⠀⢠⣾⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡁⣦⣤⢛⠁
⠀⠀⠀⢠⣾⢿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣛⡋⢙⡇⠀⠀⠀⠀⠀⠀⠀⠐⠢⠬⢿⣿⠧⠄⠆
⠀⠀⠠⡜⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣭⣽⣿⣿⣥⣄⠀⠀⠀⠀⠀⠀⠀⠰⠀⢡⡉



⠀⠀⠀⢀⣔⠉⠟⠟⣑⡄⠀⠀⠀⠀⠀⠀⡀⠀⡭⠀⣀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠈⠉⠀⠀⠀⡅⠁⠀⠀⠀⠀⠀⠀⠁⠉⣄⠀⠈⠦⣐⣂⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⢀⣁⣀⣀⡀⢠⣤⣴⡀⠀⠀⠀⠀⠀⠀⠚⠀⠈⣄⢀⠨⠄⡀⠀⠀⠀⠀⠀⠀⢠⣷⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⣿⠂
⠀⠀⠈⠻⠿⠛⠀⠾⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠤⠾⠿⠷⠤

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠋⠩⠍⣉⡙⠛⠛⠿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀⠀⠀⢉⣿⠋⠉⠀⠀⠀⠀⠀⠀⠃⠦⣀⠀⠀⠑⠢⢄⡀⠉⠙⠫⣀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⣠⣤⣶⡤⠚⠉⠻⡇⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⡀⠀⠈⠒⠤⣀⠀⠉⠲⢶⣦⣄⡀⠀⠀⠹⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⣾⣿⣿⠋⠀⠀⠠⠂⠙⣦⡀⠀⠈⠑⠢⠄⣀⠀⠀⠀⠀⠀⠈⠑⠂⢤⠀⠀⠉⠒⠤⠀⡈⠻⣧⠀⠀⠀⢻⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢰⣿⡿⠁⠀⠀⢀⠆⠀⠀⢨⠿⢦⢄⡀⠀⠀⠈⠁⠒⠠⠄⣀⡀⠀⠀⠀⠈⠁⠒⠒⢀⣤⠼⠛⣻⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡿⠁⠀⢀⡴⠃⠀⢀⠔⠁⠀⠀⠉⠒⠭⣐⠒⠠⠤⠄⠀⣀⣀⣉⠉⠩⠭⠽⠿⠯⢁⣤⡴⣊⣩⠃⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⢀⡴⠊⠀⡠⠖⠁⠀⣠⡴⣁⣀⡀⠀⠀⠀⣠⠶⠦⣀⠲⠶⢦⡄⣤⣤⣤⣤⡤⠤⢦⠄⠀⠈⠉⠀⠉⣛⡆⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⢻⣿⡖⠒⠈⠁⠀⠀⠀⠀⠀⠀⠉⠉⢇⠰⢆⣬⡴⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⢹⣿⣿⠀⠀⠀⢸⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠈⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⠁⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣷⠀⠀⠀⢿⣿⣿⣿⣿
⣿⣿⣿⣿⡿⠃⠀⠀⣰⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠤⠤⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣧⠀⠀⠘⢿⣿⣿⣿
⡿⠛⠛⠉⠀⠀⢀⣴⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣧⡀⠀⠀⠙⠻⠿
⣿⣦⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⣠⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠎⢌⣱⠎⠁⠒⠤⣄⡛⠿⠆⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⡄⣠⠈⡜⠀⠙⠤⣀⠀⠀⠀⠈⠓⠶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢻⢧⠆⡐⠀⠀⠀⠀⠀⠉⠑⠢⢄⡀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢐⠧⡌⠄⠀⡀⠀⠀⠀⠠⢤⠀⠀⢀⠀⠉⠲⠓⠄⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠎⡘⣈⡠⠞⠉⡇⠀⢀⣅⠤⠚⣷⠉⠑⢄⠀⡘⠄⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠒⠚⢴⠛⠉⠀⠀⠐⠁⠀⠄⠙⡶⠎⠽⠃⠀⠀⠉⠹⡦⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠒⠛⡶⠚⠲⠀⠀⠀⠀⠀⠀⡂⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠒⠒⣭⠶⠶⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣤⡤⠤⠳⠤⡤⢀⡀⠀⠳⠂⠉⠰⠞⠀⠀⠀⣠⣤⠮⡤⠀⣀⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠳⣆⡀⠀⠀⠀⠀⠈⠉⠒⠚⠀⠀⠀⠓⢒⠛⠛⠥⡆⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠈⠑⠲⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠃⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠐⠁⢰⡆⠀⢈⣉⠳⡦⣄⠀⠀⠀⡜⠎⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋⠛⠻⣤⣹⠃⠀⠣⠤⠜⡗⠈⡟⠓⠶⡜⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢰⠃⡴⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠦⣤⣤⣴⢻⡇⠀⠀⣔⠀⢰⡇⠀⡟⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⢈⠃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢰⠉⠙⠉⠉⠉⠘⡀⠀⠉⠀⡇⠀⣷⠀⠀⡇⠀⠀⠀⠀⠛⠉⠉⠉⠉⠈⡆⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢸⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⡁⠀⣿⠀⠀⡇⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠓⠤⠤⠤⠤⠊⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠑⠤⠤⠤⠤⠚⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣿⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡟⠀⠀⠐⠒⠒⠒⠒⠒⠒⠒⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣀⣀⣤⣀⣀⣀⣄⣀⣧⣀⣠⣤⣤⣤⣤⣤⣀⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢩⣴⣶⣒⣒⣒⣛⣭⠀⣿⠀⣥⣴⣶⣶⠶⣶⣾⡋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢄⠀⠀⠀⠀⠀⠀⠀⠜⣅⠢⡀⠀⠀⠀⠀⠀⠀⡡⣺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠇⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣻⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠟⠋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⣰⣿⣿⣿⣿⡿⠋⠀⠀⠀⠈⠹⠿⠿⠿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠀⠀⠀⠐
⠀⠀⠀⣰⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣶⣶⡿⠿⠟
⠀⠀⢠⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠿⢿⣛⣫⣭⣷⠶⠛⠁
⠀⠀⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠚⠛⠛⠛⠋⠉⠁
⠀⢰⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢠⣤⣤⡄⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⡤⠟⠉⠉⠁⠓⠶⠶⠦⠤⠴⠶⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠀⠂
⠀⢸⣿⣿⣿⣿⡿⠋⠁⠀⠈⠉⠻⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿
⠀⠈⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠂⢠⠆
⠀⠀⠹⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠙⣿⣿⣷⣄⡀⠀⠀⣀⣴⣿⣿⡇⠀⠈⠋⠉⠉⠉⠉⠉⠉⠋⠙⠁
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠢⠤
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶
⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠃⠀⠀⢀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢠⣄
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⡄⠀⠀⡎⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠉⠀⠀⠈⠀⠀⢰⠀⠀⠀⠀⠰⠆⢀⣄⠀⡀
⠀⠀⠀⠈⠁⢲⠀⠀⠀⠀⠀⠀⢀⡅⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢓⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⡀⠀⠀⠀⣀⡀⠈⠉
⠀⠀⠀⠀⣶⢈⠀⠀⠀⣀⠀⠀⠀⡡⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⡣⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣂⠀⠀⠀⠙⠁⠀⢂
⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡁⠀⠀⠀⠀⠠⠀⠔
⠀⠀⠀⠀⠺⠒⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⢴⡄⠀⠀⠀⢄⠀⠐⡃⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⢠⡁
⠀⠀⠀⠀⠒⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠈⢂⠈⣡⢊⠐⠁⠀⠀⠀⠀⠀⠀⠀⠉⢀⠄⠀⠀⠀⠀⠸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠊⠉⠀⠀⠀⠀⠀⠀⢐⠀⡀⠀⠀⠀⠀⢣⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢻⢾⠢⡒⠀⠀⠀⠀⣀
⠀⠀⠀⠀⡄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠈⡏⠀⠐⠀⠀⠄⠀⠀⢀⡔⡉⢙⠒⠃⠈⠀⠀⠀⠘⠿⠧
⠀⡀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣀⠀⠀⠀⠀⡀
⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⢃⡀
⠀⠀⠀⢤⡀⠂⠀⠀⠂⠁⢄⣳⣤⠀⠀⠀⢀⣼⣥⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠉⠅⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠁⠀⠀⠠⠂⠀⠀⠟⠀⠀⠀⠀⠺⠓⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢬⠶⠘⠀⠀⠀⠙
⠀⠂
⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠖⠒⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡇⢸⠀⠀⠀⠀⠀⣠⠊⠁⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⠀⡴⠋⠀⢸⢸⠀⢉⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⡇⡇⢸⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⣸⠁⠀⠀⢸⠘⢚⡥⠖⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢹⢸⠀⡇⡇⢸⠀⠀⠀⢀⢇⡀⠀⠀⣿⡀⢠⡀⠀⢣⠀⠀⠀⢹⠀⠀⢹⢀⣀⠀⠸⠚⠉⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡟⢹⡇⡇⢸⢸⠀⡇⡇⢸⠀⠀⠀⢸⢸⠁⠀⢠⡧⡵⣌⡏⢶⢬⣇⠀⢸⠈⡇⠀⠀⡏⠉⡇⠀⠀⠀⢀⡰⠋
⠀⠀⠀⠀⠀⠀⣀⣧⣸⣇⣇⣸⣸⣀⣇⣇⣸⣀⠀⠀⢸⢸⠀⠀⡾⠰⠀⠈⠉⠀⠆⢹⠀⢸⠀⡇⠀⣠⠕⠸⢵⡒⠒⠚⠉⠀⠀⠀⢀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡘⡆⢸⡇⠀⠀⠠⠄⠀⠀⢸⡆⢸⢀⡇⠀⠛⠚⠒⠚⠃⠀⢀⣀⠀⠀⠀⢸⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠤⢤⣄⠀⠀⠀⠀⠀⠳⡙⣾⠙⢤⡀⠻⠟⢀⡴⢋⡹⣼⡞⠀⠀⠀⠀⠀⠀⠀⢀⡷⠾⢤⡀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡄⠸⠬⢷⠀⠀⠀⠀⠀⠈⠳⠞⢦⡏⠑⠊⢹⡤⠚⠓⠙⠀⠀⠀⠀⠀⠀⢠⢴⡏⠀⠀⠀⠹⡽
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⡇⢐⣒⣒⡂⢸⠀⠀⠀⠀⠀⣀⣠⡴⢻⠁⠀⠀⣈⣟⠦⣀⣀⡀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⢀⡞⠉⠀⠈⠙⡇⠈⠭⠭⠅⢸⠀⠀⡰⠋⠉⠁⢼⠀⡏⠀⠀⠈⠀⢸⠀⣹⠈⠉⠓⣄⠀⠀⠀⣤⠤⠤⠤⠤⠤⠤⣤⡤⢤⡄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠀⠷⠶⢶⠶⠖⠚⠀⠀⡇⠀⠀⢀⡜⠁⡗⠒⠒⠒⠒⢻⠈⢣⡀⠀⠀⢸⠀⠀⠀⡷⠒⠒⠒⠒⠒⠒⠛⠓⠲⡇
⠀⠀⠀⠀⢠⠜⠃⠀⣄⢸⢀⡄⠀⠸⢤⠀⠀⠀⢸⠁⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⡏⠀⡘⠀⠀⠀⠘⡃⠀⠀⡇⠀⠀⠠⡏⠉⡆⠀⠀⠀⡇
⠀⠀⠀⠀⢏⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⡇⠀⠀⡼⠀⠀⠀⠀⢸⡀⢹⠀⠀⠀⢠⠃⣰⠃⠀⡆⠀⠀⡇⠀⠀⡇⠀⣀⣀⣉⣉⣓⣀⡀⠀⡇
⠀⠀⠀⠀⠈⠳⠤⠤⠤⠤⠤⠤⠤⠤⠚⠁⠀⠀⡇⠀⠀⠀⠀⠀⢧⠈⡇⠀⠀⡼⢠⠏⠀⠀⡗⠀⠀⢻⠀⠀⡇⠀⠭⠭⠭⠭⠭⠉⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢹⠀⠀⠘⡆⢻⠀⢰⠇⡞⠀⠀⢰⡇⠀⠀⢸⠀⠀⠳⠶⠶⠶⠶⠶⠶⠶⠶⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⢀⡀⣸⡀⣀⣀⣸⣸⣆⣜⣼⢀⣀⣀⣸⡀⣀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⢸⡇⠉⠈⠁⠉⠉⠈⠁⠉⠁⠁⠉⠁⠉⠉⠉⠉⢹⡏⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣏⡀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢤⣘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⠯⠥⢜⣦⣠⠎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠣⣿⡹⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠉⢹⣿⣶⠟⠁⠀⠀⢀⡧⣙⣯⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠉⠙⠚⠻⠋⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠸⠤⠤⠤⠴⠋⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠈⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⢂⢰⣾⣿⣿⣶⠂
⠀⠀⠀⠀⠰⡀⠀⠀⠈⢿⡀⠈⠰⢿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠓⢄⠀⠀⠀⠃⠀⠁⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠑⣀⠀⠀⠀⣀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠂⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡔⠋⠉⠉⠉⠁
⠀⠀⢠⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄
⠀⠀⠈⢇⠀⠀⠀⠀⠈⠑⠒⠶⣦⡀⠀⠀⠀⠀⠀⢠⣤⠐⣦⣤⡀
⠀⠀⠀⠸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢀⠀⠀⠀⠀⠐⠀⢀⡀⢹⠗⠢⡄
⠀⠀⠀⠀⠈⠳⣀⠀⠀⠀⠀⠀⠀⠀⢀⣌⠷⣄⣀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠁⡘⡄⠀⠁⠀⠀⡆⣴⡝⠁⠀⠈⠛⠷⠀⠀⠀⠀⠀⣴⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⢿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡚⣛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⢄⠀⣆⢠⠀⠀⠀⠀⠁⠞⠋
⠀⠀⠀⠀⠀⠀⢶⣦⣴⣶⣶⣶⣄⡀⠀⠀⠀⢸⣶⠇⠀⠀⠀⠀⢰⣴⣫⣥⣠⡤⠀⠄
⠀⠀⠀⠀⠀⣀⠀⢿⣰⣿⣿⣿⣿⣷⣧⠀⠀⠀⠉⠀⠀⡀⠀⠀⠛⠻⠟⠉⡀
⠀⠀⠀⠀⠀⠈⠃⠘⢯⣿⣿⣿⣿⠿⣿⠆⠀⠀⠀⠀⠀⠝⠲⣦⠄⠀⠀⠀⠐⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠛⠙⠑⠈⠛⠃⠀⠀⠀⠈⠀⠀⠠⠛⣷⠀⠀⠀⠀⢠⣶⢶⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡀⠀⠀⠀⢾⣿⣿⣿⣿⣷⣵⡀
⠀⠀⠀⠀⠀⠀⠉⠴⢦⣀⠀⠀⠀⠀⣀⣀⠄⠀⠀⠀⠀⠀⠀⡀⠩⠀⠠⠀⠄⠈⠃⢉⣿⠿⡿⣻⣇
⠀⠀⠀⠀⠀⠈⠀⠀⠬⣿⡏⠻⣤⠀⠙⣿⣦⣄⠀⠀⠀⣠⠾⠛⢠⠳⠀⣀⠰⠂⠀⢀⣁⢘⡃⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠊⠀⠉⠀⠀⠉⠈⢿⣎⠠⠀⠀⠁⢀⢈⠀⠀⠉⠳⠀⠀⠠⠀⠈⠉⠲⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠁⠀⠈⣿⠂⠀⠐⠚⠉⠛⢻⡆⠀⣀⣤⡄⠸⣤⡴⡤⣠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠨⠛⣦⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣍⣬⣯⣠⣍⣽⣍⣽⣫⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠑⠠⠑⢀⠀⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠠⠀⢐⠀⠂⠀⡠⠀⠁⠀⠁⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠠⠤⠄⠀⠰⢁⠠⠀⠀⠂⠀⢀⠀⠜⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠠⠠⠂⠈⠁⠀⡇⠨⠭⠍⠀⠀⠂⠀⠀⠀⠂⠈⠀⠁⢄⠀⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠊⢁⠁⡀⠀⢀⡈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠄⠄⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢈⠤⠤⠄⢘⠃⠀⠘⡃
⠀⠀⠀⠀⠀⠐⠁⠀⠉⠀⠈⠂⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⢀⠄⠂⠀⢸
⠀⠀⠀⠀⠀⠀⡀⠀⣀⠀⠀⠀⠀⠤⠠⠤⠀⠠⠄⠤⠄⠀⠀⠀⠀⢀⠘⠀⠀⠀⠀⢠⠀⢠
⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠁⠀⠊⠀⠒⠀⠘⠀⠒⠂⠀⠀⠀⡆⠙⠑⢄⠀⠀⠀⠀⠅⠄
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠐⠁⠀⠀⠁⢀⡀⠀⢠⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠠⢀⠄⠀⡀⡠⠠⡀⠀⢈⡁⡀⣉⡄⡄⡄⠀⠀⠀⠄⠃⠣⠜⡠⠠⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠈⠈⡀⠁⡀⠀⠀⠀⠁⠀⠁⠄⠀⢠⡀⠄⠀⠀⠑⠤⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠅⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡀⠀⠒⠒⠁⣇⠈⠀⠀⠀⠀⠀⡀⠀⠑⠂⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠉⠉⠁⠀⠀⠁

⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣛⡛⠛⠛⠛⣛⡛⢻
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠾⠿⠟⠟⠇⠸⠁⢸
⣿⢰⡦⣧⣶⣤⣤⡄⢰⢠⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠽⠗⠷⠂⠀⠀⢸
⣿⢀⣤⡀⡁⣈⠈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠘⠷⠛⠛⠿⠻⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⢰⡯⣤⡦⣆⣥⣇⣄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠉⠈⠁⠁⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⢠⢤⢀⢀⡀⣀⣀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠈⠈⠉⠉⠉⠟⠁⠉⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠰⠼⠳⠶⠲⠶⠲⠰⠶⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⢰⠦⣦⣠⡤⡄⣤⢠⣠⡀⣤⢠⢰⣄⡤⢠⢀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠐⠠⡀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠠⠄⠀⢀⠄⠂⠈⣉⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠉⠀⠀⠀⠀⠠⡁⠀⠀⠀⠀⠀⠀⠄⢀⡀⠀⡈⠁⠀⠀⠀⠀⠀⠀⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⡀⠒⠂⢀⠀⠐⠀⠀⢤⡀⠀⠀⠀⠀⠀⠠⡤⠀⠀⠀⠐⣀⠀⡈⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠨⢀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡄⠀⠀⠆⠀⡀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠸⠀⠀⡀⠦⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠒⢄⠀⠸⠂⠊
⠀⠀⣰⡶⠶⠶⠶⠶⠶⠶⠶⢶⣆⠀⠀⢰⠀⠎⠀⠀⠀⠑⠤⣀⠀⠀⠀⠀⠀⢀⡠⠚⠀⠀⠀⠀⡱
⠀⠀⡿⠐⠄⠀⠀⠀⠀⠀⡠⠀⢿⡀⠀⢸⠀⠑⠀⡆⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⢀⠀⠀⡜⠁
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠸⡇⠀⢸⠀⠀⣄⠈⠒⠂⢇⠀⠀⣠⡀⠀⠀⣀⡀⠼⠀⠥⠤⡤⠄⠠
⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡰⣣⠀⠀⠀⢅⠒⠤⣀⠀⠀⠀⠠⠭⠋⠀⠀⣀⠄⠒⡡⠀⡀⠀⠀⣐⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⡴⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠼⠮⠷⠤⠤⠤⠤⠥⠽⠤⠬⠴⠤⠥⠤⠤⠤⠭⠤⠭⠭⠤⠤⠧⠾⠥⠭⠬⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠬⠥⠥⠤
⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇

⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢀⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣇⠀⣨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢒⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡄⠻⠇⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⡷⣧⣶⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠛⠙⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠘⠒⠐⠂⠐⠀⠒⠂⠂⠐⠒⠒⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠚⠛⠛⠛⠛⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⠏⠉⢀⣀⡤⢤⠶⠤⢤⣄⡀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⣠⠖⣋⠥⠚⠈⠁⠁⠈⠘⠛⠶⣄⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⢠⠞⡥⠋⡠⠐⠈⠁⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⢰⣇⠋⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣾⡌⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢹⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⣸⠁⠀⢲⢧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⡴⠃⠀⢄⠿⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠑⢦⣀⠀⠀⠀⠀⠀⠀⣂⣠⠔⠋⠀⡠⣪⠛⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠉⠉⠛⠛⠉⠉⠁⠀⠀⢄⡮⠞⠉⣤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⣠⠞⣳⠲⠤⣤⣀⣀⣀⣀⣤⠤⠔⢚⠉⢁⡸⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡪⠂⠀⢀⡠⢺⢀⠖⠉⠑⠲⠤⢦⣼⣄⣥⣰⡤⠦⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠊⠀⢀⡴⠋⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⡴⢋⣠⠞⠁
⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣀⡔⢃⡤⠊⠁
⠀⠀⠀⢀⡴⠋⠀⠀⣠⠞⢁⡴⠋
⠀⢀⡴⣉⠀⠀⣠⠞⢁⡴⠋
⠀⢸⠀⠀⠙⡎⣡⠞⠁
⠀⠀⠓⢧⣠⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⠿⢻⣗⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠇⠀⠀⠉⠀⢛⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⢸⠁⢿⡣⢰⣶⣶⡿⠁⠀⠀⣶⣖⣶⣀⣀⣀⣀⣷⣆⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣡⡟⠹⠿⣷⣄⢨⡄⠀⣀⠚⠉⣽⠇⠀⠀⠀⣇⠄⠉⠀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⢀⡠⣰⠃⠀⠁⣈⡽⠖⠒⠢⠽⢳⣀⠛⣠⡞⠁⠀⠀⠀⠀⣇⡩⠆⠀⠀⠀⠀⡇
⠀⠀⢀⡤⠚⢹⠇⢇⠴⡎⠉⠁⠀⠀⡣⠀⠀⣯⡧⠽⡟⢳⣄⠀⠀⠀⠀⣃⡕⠂⠀⠀⠀⠀⣧
⠀⢠⠏⠀⠀⠈⣻⠛⠀⡇⠀⠀⠀⠀⡆⠀⢘⣗⠛⠇⢀⡼⠈⠑⣤⠀⠀⠹⡞⠇⠀⠀⠀⠀⡇
⢰⡃⠀⢀⣀⣾⣇⣀⡼⠁⠐⠀⠀⠀⢁⠀⢸⣄⠒⠀⢨⡆⠀⣼⢿⠀⠀⠘⢿⠃⠀⠀⠀⠀⡇⠀⠀⣀⡀
⠀⠉⠉⠙⠛⠚⠉⢹⡇⠀⠄⢁⠀⠀⠈⡀⠈⠀⡝⣆⠈⠧⣤⣀⣺⠀⠀⡰⢄⡆⠀⠀⠀⠀⣇⡴⠋⠉⠉⠑⡆
⠀⠀⠀⠀⠀⠀⡤⢼⡇⠀⠈⢂⠂⠀⠀⢀⢸⠁⡏⠈⢦⡇⣸⠉⠛⡆⠀⡁⢎⡁⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡇⢸⠃⠀⠀⠀⠑⠢⠀⠀⢸⠀⡇⠀⠱⡔⠋⠀⠀⢱⡀⡣⡊⡁⠀⡠⠊⣠⡔⠲⣤⣠⣀⣴⠃
⠀⠀⠀⠀⠀⠀⠧⡿⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠹⡄⣼⢇⠀⠀⠀⡼⠃⡅⡜⣃⣈⣓⡉⠀⡇⣸⠁⢸⠀⠸⡀
⠀⠚⠒⠒⠒⠒⠒⠓⠒⠒⠒⠒⠒⠒⢲⠋⠀⠀⠀⠹⡗⠒⠚⠒⠚⣧⣤⣧⣉⣿⠀⠰⣷⣶⣷⠗⠒⢺⠒⠒⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠒⠒⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠒⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠓⠲⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠀⠀⠀⠉⢲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⡈⠙⠲⢤⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠉⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⢀⣀⣀⣀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⣰⠋⡀⠀⠀⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢿⠀⠢⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠠⠉⡒⠤⣄⣀⣰⠙⢟⠢⡀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠈⢀⡼⠃⠀⠈⢧⠙⢆⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠤⢤⣀⡴⠋⠀⠀⠀⠀⠈⡆⠈⡆⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠒⡒⠒⠒⠒⠒⠒⡄⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣒⣲⣒⣶⣒⣖⣲⠇⠀⠀⠀⠀⡸⠀⢸⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⣀⣀⣀⣠⠎⠀⠀⠀⠀⣠⠃⢀⠇⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠴⠶⠒⠒⢺⠁⠀⠀⠀⠀⡗⠒⢒⡲⠖⠁⡠⠋⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣤⣤⣀⣀⠀⠀⢸⠀⠀⠀⠀⠀⢻⢉⣁⣠⠴⠊⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣉⠭⠟⠁⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠷⠶⣶⣶⣶⡶⠶⠶⠶⠶⠿⠽⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠁⠀⠀⠀⠈⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⣀⠴⠒⢢⡀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠚⡓⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣎⣁⣀⣀⡀⠙⢄⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣰⢋⣩⣽⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⡀⠀⠀⠉⠓⠮⡑⢤⣀⣀⡀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡐⠋⠴⢚⣷⡀⠀⠀⠀⠀⠀⠀⠘⢿⣈⣛⣰⡀⠀⢴⡄⢸⠖⠋⠀⢹⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠹⣝⣿⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠛⠉⠲⠤⠴⠋⠀⣤⣠⠞⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠃⠀⠘⡟⣆⠀⠀⠀⠀⠀⠀⠀⡷⡀⠰⠤⠴⠀⠀⢀⡴⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⡿⣼⡄⠀⠀⠀⠀⠀⠰⢇⣈⣓⣶⠴⠶⠒⠋⠀⡧⣄⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣻⣙⣛⡩⣷⠈⠁⠀⠀⠀⠀⣠⠖⣻⠟⢱⠟⠳⣄⣠⠴⠚⣳⠈⢻⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠀⠀⣿⠀⣴⢲⣄⣠⠞⠁⠾⣅⡀⢸⣄⣴⡿⡅⠀⣰⠃⠀⢸⡉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⣠⡏⠉⣿⠁⠀⠀⢠⠞⠁⢸⠈⢹⠀⠱⡾⠃⢀⣀⣈⡇⠀⠈⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢻⠀⣧⣴⣛⠉⠙⠒⠾⢧⡀⢸⠀⡟⢀⡼⠁⠀⠻⡄⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢀⣟⡭⠤⠀⠀⠀⠀⠀⠉⢿⡀⣧⠞⠀⠀⣠⠔⠃⠀⣀⠔⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⣈⡯⠾⣉⣁⣀⣀⣀⣀⠀⠀⠙⢧⡀⢠⠞⠁⠀⠀⡴⠁⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠒⠛⢉⡝⠀⠀⠈⠳⡄⡏⠀⠘⢦⣀⡠⠏⣹⠓⢤⡀⠀⡾⠁⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⢹⣄⡰⠃⠀⠀⠉⢺⡁⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠖⠒⠒⠒⠲⢄⣿⠀⠀⢀⡞⡼⠃⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⣸⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠈⠓⠦⣀⠀⠀⠀⠀⠀⠀⣠⠏⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⢄⣀⣀⠴⠁⠀⠀⠳

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠿⢿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠟⠛⠿⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠉⠀⠀⣠⠴⠚⠛⠳⡤⠶⠒⠲⣄⠀⠀⠀⠀⠀⠀⢀⡴⠒⠒⠒⠒⠚⠋⠀⠀⠀⠀⠀⠉⠻⢿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⢿⣤⣀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄
⠀⠀⠀⠀⠀⣠⣾⣿⠯⠖⠚⠳⡄⠀⠀⠀⠀⢩⡟⠁⢀⣤⣤⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠛⢷⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⢀⣠⡿⠒⠒⢶⡀⠈⠻⠶⠟⠉⠉⠁⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⢰⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⡄
⠀⠀⢠⣿⠟⠀⠀⠀⠀⠀⠸⠟⠁⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠘⠑⠓⠀⠀⠀⠀⠀⠘⠷⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄
⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢸⡇⠀⠀⠀⢶⣶⣤⣀⠀⠀⠀⢀⣀⡀⠀⠀⢻⣷
⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⠀⠀⢀⣤⣾⠿⠿⠿⠟⠀⠀⠀⠀⠘⠿⠿⠿⠿⣶⣄⠘⣧⣀⡀⠀⣀⣿⠈⠙⢷⣄⣰⡟⠙⣇⠀⠀⠘⣿⣇
⢰⣿⠇⠀⠀⠀⣠⣤⣤⡀⢺⡟⠃⠀⠀⠀⠀⠀⠀⠈⠁⣠⠴⠒⠒⠲⢤⡀⠀⢀⠤⠒⠒⠒⢦⣀⠉⠁⠈⠙⠛⠛⠛⠁⠀⠀⠀⠉⠉⠀⠀⠻⢶⣶⠾⢿⣿
⢸⣿⠀⠀⠀⠿⠯⢤⡈⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠙⡴⠁⠀⠀⠀⠀⠀⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣾⣿⣤⣀⣀⣀⣀⠀⣿⢀⣀⠀⠀⢀⣴⡿⠛⠛⠻⣾⡇⠀⣀⣀⢀⣀⣀⣀⣇⡀⣀⣀⣀⣀⡀⠀⢹⠀⣴⠞⠉⠉⠉⠓⠦⣤⣤⠤⠤⣄⡀⠀⠀⠀⠀⠀⣿
⣿⡿⠈⠉⠉⠉⢻⡇⠉⠉⠉⠉⠙⣾⣿⠀⠀⠀⠀⢘⣿⠁⢹⡿⠀⠀⠀⠈⡇⠀⠀⢼⡿⠀⠀⠁⡿⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠹⣿⣀⠀⠀⠠⣂⢽⣦⡀⠀⠀⠀⢀⣴⢻⣄⠀⠀⠀⠀⢀⣼⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢶⡄⠀⣿
⣿⣿⠀⠀⠀⠀⣿⠠⣶⡧⠀⠀⠀⠀⠉⠛⠿⢿⣶⡕⠊⠈⢿⣶⠤⠶⣻⠋⠀⢻⣳⠶⠴⠶⣻⠏⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⠀⠀⢀⣧⠀⣿
⢸⣿⡄⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⣦⣀⠀⠙⣷⡋⠁⠀⠀⠀⠉⠛⠒⠋⠁⠀⠀⠈⠻⣦⣤⣤⣤⡀⠀⠀⠀⠀⠚⠋⠀⠀⠀⣸⠇⢠⣿
⠈⣿⣇⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠈⠛⢷⣄⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⢻⡄⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣼⣿
⠀⢹⣿⡄⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⢀⡽⠷⠶⠿⠷⠴⠶⠶⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⣾⠋⠀⠀⢠⣿⡏
⠀⠀⢻⣿⡄⠀⠀⠀⠀⣿⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⢀⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⣿⠀⠀⢠⣿⡟
⠀⠀⠀⢻⣷⡄⠀⠀⠀⢻⡄⠀⠀⣼⠃⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠗⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⢰⡟⠀⢠⣿⡟
⠀⠀⠀⠀⠻⣿⣆⠀⠀⠘⣷⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⣤⣤⣴⡿⠁⣰⣿⠟
⠀⠀⠀⠀⠀⠘⢿⣷⡄⠀⠈⠻⣶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⣀⣴⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⣠⠶⠒⠚⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠈⠉⠓⣦⢀⣠⣾⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣷⣾⡋⠀⠀⠙⠲⠤⠤⠤⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣾⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣤⣤⣶⣶⣶⣿⣿⡿⠟⠛⠉
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣭⣿⣿⣿⣿⣿⣿⣿⣿⣭⣭⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣍⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⡀⣀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴
⠀⠃⠦⠉⠀⠰⠟⠛⠋⠁⠀⠀⠀⠀⠄⣀⠂⠀⠰⠊⠀⢀⢀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢈⠀⠁⠰⠰⠀⠁⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠰⠀⠤⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠞⠁⠀⠞⠀⠀⠀⠓⡀⠀⠀⠀⠀⠐⢺⡆⠀⠀⠀⠀⠚⠻⠀⠀⢰⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠈⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠄⠂⠀⠁⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⢠⠀⠀⠀⡀⡀⠀⢠⠆⠀⠀⠘⠀⠀⠄⢀⡀⢄⠀⠀⠀⠀⠀⠀⣴⣃
⠀⠀⣠⠀⠀⠀⢀⣀⠈⠋⠀⠀⡄⠀⠀⠀⢬⡻⣄⠔⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⢶⡇⡘⣏
⠀⠀⠃⠀⣀⠈⠐⠀⠀⢀⠀⠉⠀⠀⠀⡐⢉⠥⠂⠠⠆⠀⠀⠀⣠⣀⠀⠀⠀⠀⠆⠀⢠⠀⢈⣩⣵⣵⠇
⠀⣸⠀⠀⠛⠀⠀⣀⠐⠈⠀⠄⠀⠀⢀⡁⠊⢀⡛⡀⠠⠆⠀⠘⠑⠀⠀⠀⡦⠀⠀⠀⠈⠀⠀⠀⠹⡏
⠀⣼⠀⠀⠀⠐⠀⠁⢀⡀⢀⠀⠐⠂⢣⡞⠄⣼⠃⢹⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⠀⠀⢠⡄⠄⡀
⠀⠦⠀⡿⠇⠀⠀⠀⡀⠀⠌⠁⠀⢇⠁⢀⡾⡟⢎⡎⠀⠀⣀⡰⠄⠊⡷⠀⠀⠀⠈⠀⠂⠀⠀⠀⠰⢠⠁
⠀⣴⡔⢳⣦⣀⠀⠀⠐⠤⠀⠀⢀⠈⠣⡾⠈⠠⠌⠀⠀⠁⠻⢯⠆⠀⠁⠈⢀⣀⠈⠓⠒⣂⣸⡧⠄
⠀⠀⠀⠀⢋⠁⠀⢀⡀⠤⢒⡖⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠏⠀⢰⠋⠁⠀⡇
⠲⣄⢠⡞⠀⠀⠀⢀⠖⠋⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠀⠀⢠⠆⠀⠀⣀⣤⣼⡤⠴⠊⠀⠼⣆
⢰⡿⣆⡔⠀⠀⠀⠠⠀⠂⠀⠀⠀⠀⠀⠐⠀⠀⢈⡀⠀⠀⠀⠀⠁⡆⠀⠀⠀⣇⠀⣸⠇⠀⢀⠀⠀⠛
⠀⠙⡏⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠉⡒⠁⠀⠀⠀⡄⡀⠖⠀⠀⣰⠚⢻⡍⠁⠀⢰⣶⠧⠶⣄
⠀⢀⡄⠀⡀⠐⢀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠠⠂⠀⠨⠄⠀⠀⢑⠈⠀⢀⣻⠤⠞⠁⡀⠈⠉⡇⠀⠀⢉⠃
⠀⠘⠏⠀⠱⡀⠀⠀⠖⠀⠀⠒⠚⠉⠉⠉⠁⠀⣀⣀⣴⣶⡶⠆⠀⢀⣯⠟⠀⠀⠢⢏⠀⠀⠑⠧⡐⠛
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⢀⠗⡄⣠⡄⠀⠀⣴⠚⣀⠖⢁⠄⠀⠀⡦⣔⡼⢲⡆⠠⡦⡖⣦⡦⡆⣶⠤⡄
⠀⡖⢰⡤⡆⣦⢔⡤⡖⠀⣴⠀⣔⡄⡤⢰⣴⢦⡆⢀⣄⣠⠞⠓⠾⢱⢺⠘⣄⣟⡽⠴⠎⠑⢄⠚⣀⠞⢉⠴⠃⡤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣤⠀⠀⠀⣸⣷⣿⢙⡁⠀⠀⠀⠀⢇⢡⡖⢋⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⡠⠖⠁⢹⡜⡿⠋⠒⠒⠠⠤⠼⡆⠰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⢣⡴⡎⣴⢚⡇⢸⡇⡃⠺⣷⣄⠀⡴⠚⠓⠦⣄⡤⡄⢰⡄⣤⢠⠤⣢⢴⢴⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣄⡰⠃⠀⠀⠀⠀⠹⠃⠏⣧⣼⡇⣇⠎⠉⠻⠟⠉⠀⠀⠴⣡⢶⠃⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠄⠀⠀⠀⠀⠀⢀⡴⠉⢻⡁⢻⡀⠀⣀⣤⡀⡀⣠⣠⣀⡄⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⣀⣀⣀⠤⠤⠒⠊⠁⠀⠀⠈⡇⡏⠣⡀⡾⣄⠤⠤⣤⢤⡦⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣵⠀⠈⠑⠠⠤⠀⠀⣀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣉⣍⣉⣩⣭⣍⣉⣉⣉⣩⣽⠃⠸⡉⡉⠉⣉⣩⣍⣉⣩⣭⡍⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠡⣴⣶⠋⣉⣹⡯⢞⡧⠀⢮⠄⠀⠙⣍⣉⡑⠻⢶⡍⢉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢒⣿⠟⢫⠟⢩⣿⣱⣣⡀⢻⣁⠀⠠⣽⣦⣶⣦⠀⠁⠐⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡿⣻⣿⢦⣼⣅⡀⠀⠀⠉⠀⠉⠀⠀⡴⡴⣲⢶⢴⢴⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠁⠈⣥⡿⢻⣼⣇⠙⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⢠⣄⣠⡀⠂⣴⢄⣺⡫⢛⠀⠂⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢤⡀⠒⢀⣿⡟⠛⠏⣅⠨⠤⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⠂⠡⠃⠘⠾⠀⠃⣀⢌⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⣄⠓⠄
⠀⠀⠀⠀⠀⠆⠄⠠⠀⡄⡌⠀⠂⠀⢀⡨⠁⠧⠀⠠⠀⠀⠀⠀⢀⠀⠀⠠⡀⠀⣠⣘⠻⠀⠀⠠
⠀⠀⠀⠀⠀⢷⢈⠂⠠⠈⠀⠀⣤⠐⠌⠱⠆⠀⠀⠀⠀⢄⠀⠀⠈⡠⠈⠃⡅⢷⢠⠈⡄⢁⠢⠂
⠀⠀⠀⠀⠀⡉⠴⢆⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢰⣄⠈⢷⣄⠀⠘⣅⢎⠛⣿⡠⠖⣖⠂⠜⠁
⠀⠀⠀⠀⢠⠀⠄⡐⢦⠀⠀⠀⠂⠀⡀⠀⠀⠀⠀⠀⠁⠰⡌⠢⣚⠀⡈⠺⢷⡞⠁⠠⠀⠠⠂
⠀⠀⠀⠀⠘⠀⠀⠀⠂⠬⠀⠀⠀⠀⠈⢶⡤⢀⡀⠀⠀⢀⡈⠠⠉⢤⡈⠀⡄⠛⣐⣈⣘⣐⣆⠴⠚⠁
⠀⠀⠀⠂⠀⠉⠀⠀⠀⠚⠀⠀⠄⠀⠀⠀⠱⠏⠲⠂⠀⠀⠘⠄⠘⡄⠀⠨⢠⣌⠀⣈
⠀⠀⠀⠀⠀⢈⠀⠂⡤⠀⡀⠀⠀⠢⠄⠀⢀⠀⠀⠄⠢⢄⠀⢀⠀⠔⢰⠀⠉⠍⠀⡈⠀⢛⠉⠟⠒⠂
⠀⠀⠀⡀⢀⡄⠐⢀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠐⠤⡈⣀⠏⠀⡀⠀⠀⠒⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⢂⡐⠙⠀⢁⠀⡀⠠⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠂⠁⡋⠀⠄⠄⢀⠀⠠⢠
⠀⠀⠄⠀⢀⠈⠡⠀⢀⡜⢁⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠄⠈⠈⠀⠀⡀⠀⠀⠀⢀⡀⠤⠆⠐
⠀⠀⠠⠀⠠⠐⡂⠐⢀⡰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⠃
⠀⠀⠀⠘⠀⠀⠁⠈⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠆
⠀⠀⠀⠀⠀⡀⠁⠃⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡠⠀⠀⠀⠠⠈⠁
⠀⠀⠀⠀⢀⠀⠰⠂⠀⠰⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢀⠁⠀⡆⠀⠀⠄⠁
⠀⠀⠀⠐⠠⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠠⠐⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⢀⠀⠀⠀⡀⠄⠐⠀⢈
⠀⠀⠀⠠⠀⠀⠀⢸⠀⢇⢀⡀⠠⠔⠒⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡈⠀⠹⣄⠀⠀⠂⠀⡄⠀⠀⠀⠀⠀⠈⠀⠃⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠠⢈⠀⠀⠀⠡⠀⠀⠀⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠁⠘⠀⠀⡀⠑⢀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⣿⡛⣛⢻⣾⣗⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠿⠛⠋⠛⠛⢿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠇⠀⠀⠀⠀⠀⠈⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⢖⡶⣄⣠⢾⠝⢼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠈⠁⠇⠘⠤⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣆⠀⢨⣀⡄⢀⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⢄⠀⠀⠒⣿⣿⠏⠀⠠⠀⠠⠂⠿⣿⢷⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⡈⠁⣱⠠⢉⡄⢀⠀⠀⠀⠐⠀⠐⠈⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡴⠖⠂⡆⠂⠀⠀⠐⠉⢠⡁⠀⢸⡇⠈⢿⣿⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠸⠙⢄
⠀⠀⠀⠀⠀⠀⠀⢀⠁⠁⠀⠀⠀⠀⠀⠡⣀⡴⢖⡠⠖⠲⢶⠦⠈⠆⠀⡘⢻⡿⢀⡴⠋⠀⠀⠀⣀⠀⣤⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⠀⣦⣠⣴⣾⣯⣥⣤⣄⡀⠀⠀⠀⠀⠀⠀⠈⠒⠈⠱⡏⠀⠐⠒⠤⠀⣿⣾⠃⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠤⠼⠿⠛⠉⠉⠉⠉⠉⠉⣷⣄⠀⢀⡀⢀⣄⡎⢧⠀⠁⢀⠀⠀⡀⠘⢻⡇⠀⠀⠀⠀⢀⣀⡀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⢟⣧⣵⠸⡆⠐⡇⠠⠄⡀⠀⠸⠃⠀⠈⠉⠑⢏⠡⡀⠀⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⡩⠍⠉⠡⠞⠛⢻⣄⡇⠀⠑⠀⠀⠈⢰⣶⡶⢤⣀⠀⠀⢸⠇⡵⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠱⡀⠀⠀⠀⠀⣾⣧⣤⠠⠀⠀⠀⠀⣾⣿⠃⠀⠈⠛⠲⣾⢠⣧⣾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠑⠀⠀⠀⠜⠛⠛⠁⠀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠁⠀⠈⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣧⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡶⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⡀⠀⠀⢸⣿⡿⠛⣿⡀⢻⡷⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠀⠘⣧⠀⠀⠸⠟⠁⢀⣻⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣇⠀⣿⠀⢠⡄⠀⣠⡘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⣄⠀⠀⢸⣿⣿⣿⠇⢀⡛⣤⣽⣷⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⣿⣿⣿⠆⣿⠛⠉⠉⠿⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣾⡿⠀⢹⣿⣿⡄⠀⣠⠞⠁⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⣿⢿⣿⢳⠛⣬⣹⣷⣾⠛⣿⣶⣿⠇⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⡾⢷⣾⣟⣿⠉⣀⣤⠘⠋⠙⠁⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⡟⠳⣾⣭⡉⣿⠠⠉⠁⠀⢀⣤⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡀⠹⣿⣿⠿⠦⠶⠌⠃⣈⣡⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣧⣠⣿⣁⣤⣠⠀⣴⠂⣠⣿⣿⣿⣿⣿⣶⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡿⠁⠉⠉⠛⠶⠿⠿⠿⠿⠛⠋⠉⠁
⠀⢲⡶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣄⡀⠀⠀⠀⢰⡆⢀⣼⠃
⠀⣄⠀⠀⢾⣷⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⡀⠀⢸⣧⣸⡿⠃⠀⠀⠀⢠⠄
⠀⠈⣿⡇⢾⣿⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣧⠈⣻⡏⣀⣤⠞⢁⣴⡟
⠀⠀⠛⠃⣀⠻⠂⠀⠘⠃⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⠟⠉⢀⡤⣉⠎⠁
⠀⠀⠀⠈⠁⠀⠀⠀⠀⢄⠈⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣆⠙⢿⣿⡿⢦⣐⣴⣿⡾⠁
⠀⠀⠀⠀⠀⠀⠲⠾⢧⡼⢃⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⠈⣿⡆⠈⠿⣿⡿⠟⠋⠉⠀⠀⠀⣠⡤
⠀⠀⠀⠀⠀⠀⠈⢀⣀⠀⠺⠀⠀⢠⡄⠀⠀⠀⠀⠀⢸⣿⣿⣧⡸⣧⠀⣿⠀⠀⢀⣄⠠⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀⠀⢠⡾⠁⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣸⣾⠃⣰⡆⠛⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡆⠈⠁⠀⠀⠀⣄⡀⠀⢸⣿⣿⠛⢿⣿⣟⠸⠿⣄⣤⣶⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢰⣿⣍⠻⣷⣌⣿⡏⠀⠈⠹⠉⢀⣶⢟⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣾⣿⣅⣴⠀⠀⢸⡆⠹⣿⣿⠀⠶⠀⠀⣠⣟⣵⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣾⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣦⣀⠀⣤⡄⢹⣿⡀⢸⡆⠀⣼⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠸⣿⡎⠉⠛⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⣿⢋⠉⠉⠉⠀⠘⢿⣮⣿⣧⠀⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⠀⣶⣤⣬⡀⠀⠁⢨⣿⣦⣿⠇⠀⠀⢀⣤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⢀⡎⣀⣠⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⠙⢿⣿⣿⣦⣄⠀⠙⣿⠇⢀⡄⠀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣀⣿⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣾⠀⣿⠛⢿⣿⣿⠸⠀⣿⢠⡌⢡⣾⠋⠀⠀⠀⠀⠀⢠⣄⠀⠀⣀⠀⠀⢻⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠆⠁⠀⠀⠻⠇⠸⡆⠈⣿⣷⠟⠁⠀⠀⠀⠀⠀⠀⠀⠛⣷⣆⠁⠀⢰⡄⠀⢀⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣄⠀⢀⡆⠀⠀⣴⡆⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠙⣄⠀⣧⣼⡶⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⣸⡇⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⣷⣿⣏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠙⢻⡏⠀⠀⠀⠘⣿⣧⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⡄⢸⠿⣿⣤⣴⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⠀⢰⡄⠀⣼⡆⢻⣿⠃⠀⠀⠀⠀⠀⠀⠀⣴⠆⠀⣿⢧⣈⣴⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠙⢷⣎⣡⠀⣿⡇⠸⣿⠂⠀⠀⠀⣠⡄⠀⠘⠋⠀⠀⣘⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⣀⠀⠰⣌⡹⠁⠈⠁⢠⣯⠀⠀⠀⠈⠉⡀⠔⢀⣤⠀⢀⠋⢀⣤⣤⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣶⣍⣳⣷⠀⠀⢀⡏⠀⠀⠀⠀⢀⣤⣤⠸⣿⣆⣨⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡋⠻⣿⣿⣿⣿⡇⠀⡇⠀⡀⠀⣸⡿⢿⣿⠀⠹⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠈⠙⢿⣿⡁⠐⡇⠘⢃⡼⠋⣀⣰⣿⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⠀⠀⠙⢿⣿⡇⠰⠟⠁⢰⣿⠛⠛⠆⢀⣠⣤⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡀⠀⠆⠀⢹⠁⠀⣼⡇⢰⣿⡇⠰⢼⡟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡀⠀⠀⠀⣇⢰⣿⡇⠸⣿⡿⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⡀⠀⠀⣿⠀⢹⡇⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣶⠀⣿⠀⠈⠁⠀⣱⣶⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠘⢿⣿⣟⠛⢰⣿⠀⢠⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢻⣿⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇⣹⣿⡄⢹⣶⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣟⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠴⠖⠒⠛⣋⠉⠉⠉⠉⠙⠛⠒⠲⠦⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⡿⢧⣀⠀⠀⠀⢿⠹⡇⠀⠀⠀⠀⠀⠀⣀⠤⢄⣀⠈⠉⠓⠲⢤⣀
⠀⠀⠀⠀⠀⠀⣠⡖⠏⡑⢯⣀⡞⢉⣷⡄⢀⠞⢿⣾⡀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠑⡄⠀⠀⠀⠈⠙⠳⣤⣀
⠀⠀⠀⠀⢀⣼⠯⡂⠁⠀⠀⠙⢦⡞⠀⠿⠈⢢⢻⡇⢱⠀⠀⠠⡞⠒⢣⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠈⣛⢿⣦⣄
⠀⠀⠀⢠⠟⡂⠅⠀⠀⠀⠀⠀⠈⢛⡀⠁⣠⣚⣚⡏⠉⠀⠀⠀⢇⠀⣠⣇⣶⣴⣷⣿⠁⠀⠀⠀⠀⠀⠀⠨⣿⣿⣿⣿⣦⡀
⠀⠀⢀⡿⢑⠂⠀⠀⠀⠀⠀⣄⢲⢹⠃⡔⠋⠀⠀⡇⠀⠀⠀⠀⣀⣧⠉⣻⢿⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⡿⣿⣻⡽⣿⣦
⠀⠀⢸⠯⠐⠀⠀⠀⠀⡞⡧⠛⠄⠁⠀⡇⠀⠀⠀⠃⠀⣠⣴⠟⣽⣼⢊⡴⣩⠛⠢⣀⠀⠀⠀⠀⠀⣠⡾⢿⣛⠽⠗⠋⠉⠁⠨⡲⢕
⠀⠀⢸⠭⠀⠀⠀⠀⣀⣧⠀⠀⠀⠀⠀⡇⠀⠀⠰⠖⣩⣿⣿⢠⡿⠀⣫⢖⡁⠜⢴⣚⣦⣠⢴⣲⠿⠗⠋⠉⠀⠀⠀⠀⠀⠀⠀⠨⡑
⠀⠀⢸⡅⠀⠀⠀⢸⠦⠽⢧⠀⠀⠀⠀⢣⢀⣠⣴⣿⣿⣿⡇⢸⡵⠊⣀⡼⠀⠀⠚⢿⣿⡏⠉⠀⠀⠀⠀⠀⢀⣴⣿⢿⣶⣄
⠀⠀⢈⡧⠖⣒⣶⣬⣯⣉⣚⣷⠀⠀⠀⠘⢿⣿⠿⠟⣿⣿⣧⢊⡤⠊⠁⠀⠀⠀⠀⠀⢻⣷⠒⠒⢶⠒⠒⡞⡿⡈⠁⡀⠙⢮⠇
⠀⠀⡞⢸⣿⣿⡿⣿⢿⣿⣄⣽⣇⣀⣀⣀⠀⠀⠀⠀⣸⣿⠱⠋⠀⠀⠀⠀⢠⣆⠀⠀⣸⣸⠀⠀⠀⠀⠀⣇⣱⠣⡀⢉⣰⠞⢦⡀
⠀⠀⢣⡼⠟⢁⡀⠉⣸⡇⢣⠀⠀⠠⠞⠛⠳⣤⠞⣶⣿⡇⠀⠀⠀⠀⠀⢰⠁⣸⠀⡠⣿⣿⠀⠀⠀⠀⣷⠀⠈⣳⠋⢋⣡⣰⣴⣽⣄
⠀⣴⣿⣟⢳⣌⢀⣠⣿⢃⢸⠀⠀⠀⠀⠀⡾⠓⠚⠉⠉⣇⣀⣀⣤⠔⠒⠉⠉⢀⣠⡿⣟⣽⢶⣒⠒⠒⢿⠀⡴⠃⣠⡎⠳⣄⣀⣀⣀
⣼⣿⣿⡟⠛⢻⣿⣿⣻⠏⠛⠇⠐⡄⠀⠀⢹⠀⠀⢦⣤⡟⠀⣢⢰⠀⣠⣾⢿⡻⠕⠊⣿⣟⣩⡖⠒⢲⣾⠟⢀⣼⣻⠁⠀⣾⣿⡛⠛
⣿⣿⠏⠉⣿⠾⣿⣿⣿⠀⠀⠀⠀⢳⡀⠀⠈⡆⠀⠀⠛⠛⣿⣿⣿⣦⣷⣾⡇⠀⠀⠀⢿⣿⡝⡇⠀⢸⠁⣠⣾⣏⡇⠀⣸⣿⡦⡝⢦
⠸⣿⠀⢸⣿⣷⡼⣿⣿⡆⠀⠀⢀⣿⣿⣋⣥⣷⠖⣶⣶⣿⣿⣿⡿⠿⠛⠓⢻⠀⠀⣠⣿⣿⣷⡁⠀⣸⠾⠛⠋⡽⠀⢠⣿⣗⠭⠂
⠀⢿⠀⠘⣿⣿⣧⣦⣿⣧⣀⡤⠾⠛⠋⠉⠀⡟⠀⣿⠟⠋⠉⠀⠀⠀⠀⠀⢸⣀⣰⡿⠿⠛⠋⣇⠀⠙⢦⣄⠰⣇⠀⣼⣿⡪⠕⠀⢸
⠀⠘⣷⡶⠿⠿⢷⡿⣿⣉⣹⣀⣠⣤⣴⣶⣿⢟⣶⣷⠤⣄⣀⣀⣀⣀⣀⣀⡸⠏⠀⠑⢄⡀⠀⠈⠙⠛⢿⡿⠀⢳⣝⣿⡳⢮⣀⠀⣿
⠀⢠⣿⣁⣀⣀⣸⣄⣀⣀⣈⣉⣿⣿⣯⣽⣾⣿⣸⣿⣀⣀⣀⣀⣀⣀⣀⣿⣇⣀⣀⣀⣀⣙⣦⣀⣀⣀⣀⣀⣀⣘⣿⣿⣿⣷⣭⣻⣿
⣿⣿⠟⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠑⠒⠄⢀⠐⢂⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠨⢤⡠⠀⠀⠀⠀⠀⠀⠘⠂⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠚⠓⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢪⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠘⠛⠛⠶⠄⠀⠀⠀⠀⠀⠀⠱⠢⠀⠀⠀⠀⠀⠀⠀⠀⢉⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣤⠀⠀⠄⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠋⠀⡠⠴⢦⡀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠥⣤⠀⠠⠤⣦⢸⣆⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⣰⠀⢸⣿⠀⠀⠐⠂
⠀⠀⠘⡢⠤⠤⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠒⠂⠐⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠴⠋⢸⠀⠀⣎
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠦⠤⢤⠔⠚⠁⠀⠀⠀⠀⢠⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⡄
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣤⠤⠖⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠔⠀⡲⠊
⠀⠀⠀⣗⣀⣸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠊⠈⠳⣄
⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠡⢄⠀⠑⠲⡤⠤⣤⠤⢠⠔⠖⠚⢙⣫⠀⠀⠀⠀⠀⠈⠳⣄
⠀⡞⠁⠱⣄⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠁⠀⢀⠊⠀⠀⠀⣡⠀⠀⡖⠁⠀⠀⢞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀
⢀⠡⠤⣄⠚⢀⠀⠀⠀⠃⠄⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠑⠢⡀⠀⠙⣠⠎⢀⣠⠄⠶⠚⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⢇⡀⢀⣈⠆⢸⡟⠃⠀⡀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢄⠿⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠈⢧
⢨⡉⠉⠙⡄⢸⡇⠀⡘⠉⢧⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠠⠆⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠈⢧
⠰⡉⠙⡏⠀⢸⡁⠎⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠸
⠀⠈⠉⡇⠀⢸⡇⠀⠀⠀⣰⠃⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠰⢄⣠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠇⠀⢸⠁⠀⢀⡴⠃⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠁⠀⢀⣀⣀⡀⢇⡘⠦⡀⠀⠀⠀⢀⣀⣤⠔⠋⠀⠀⠀⠀⠀⡸
⠀⠀⠀⢧⣀⡼⠀⠘⠋⠑⠦⣀⠀⠀⢀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠠⠄⢀⣀⣀⣀⣀⠈⢽⠀⠀⠙⢏⠉⠀⠀⠀⣂⠀⠀⠀⠀⢀⠜⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠘⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠈⠄⠀⠀⠀⠨⡄⠀⣠⠔⠁⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⣀⠀⠀⠠⠋⠀⠀⠀⠀⠀⢰⠀⠀⣀⠠⠖⠈⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡆⣤⣤⣤⣤⠖⢀⠄⠀⠀⢠⠏⠐⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢰⠀⠀⠀⢀⡠⠂⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠛⠉⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠧⠤⠤⠤⢤⠤⠄⠀⠀⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠢⠤⠤⢤⡤⠤⠤⠤⠤⠤⢤⡤⠄⠀⣀⣀⣀⣀⣀⣀⣀⡤⠤⠤⠄⠒⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀⣀⡀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣌⠀⠀⠀⠀⠀⠀⠸⠆⠀⢀⠀⠀⠀⠀⠀⢈⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠶⠤⣤⣤⠀⠀⠶⠖⠛⠋⠙⠥⠄⠤⠄⠖⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠁⠀⠀⠀⠀⠀⠀⣀⠤⠚⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣢⣤⣤⣤⣤⣤⣚⣋⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠋⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣿⣷⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣴⣾⡇⠀⠀⠀⠀⠀⠀⢀⠸⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦
⠀⠀⢠⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⢸⠃⠀⠀⠀⠠⠀⠀⢀⠀⠀⢀⣴⣿⣟⡁
⠀⠀⠤⣾⣿⡯⠅⠀⠀⠀⠀⠀⠀⠠⠄⠁⠀⠀⠀⠨⡗⠀⠀⠀⠀⢄⠒⠀⠀⠀⣠⣿⣿⣿⣵⠦
⠀⠀⠚⣿⣿⡛⠁⠀⠀⠀⠀⠀⠀⠐⠢⠀⠊⠀⠀⠉⢿⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⢿⣿⠷⣒⣉⠥⠄
⠀⠀⣰⣿⣟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⠀⠀⠀⠀⠀⠀⠀⠀⠐⢲⣭⣿⡻⣿⣖⣒⠁
⠀⠀⠀⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⣈⣻⣿⡽⠶⠖⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠓⠀⠀⠀⠀⠀⢸⠀⠀⠙⠳⠂⠀⠀⠀⠤⠬⠜⣯⠭⠄
⠀⠀⠀⠀⠀⡀⠀⠀⢠⠀⠀⠀⠀⢠⡀⠀⠀⠀⢀⠀⠀⠀⠀⠘⠀⢀⡀⠀⠀⢀⠀⠀⣀⡀⠀⠒⠒⠂
⠀⠀⠀⠀⢰⣿⠀⠀⢸⡆⠀⠀⠀⢈⠑⠀⠀⠀⢸⠀⠀⠀⣇⠀⠀⠀⢹⠀⠀⢸⠀⠈⢻⡋⠀⠀⠀⡄
⠀⡀⠀⠀⠻⣿⠀⠀⢸⠀⠀⡀⠀⠀⠀⢐⠃⠀⢸⡄⠀⠀⣿⠀⠀⠀⢸⠀⠀⠈⠀⠀⠀⡁⠀⠀⠀⡇
⠀⠀⠃⠀⠀⠛⠀⠀⠸⠀⠰⠗⠀⠀⠀⠀⠀⠀⠉⠓⠀⠀⠿⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠁

⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⣤⣀⡀⡀⣠⢄⢠⡤⣠⢄⢀⣤⢀⣀⢠⡀⡀⣤⢀⠀⡀⡤⠀⡠⡀⡀⡠⡀
⠀⠀⠀⡤⠞⠉⠁⠀⠀⠈⠙⠲⣄⠀⠋⠁⠋⠃⠳⠼⠀⠇⠳⠼⠁⠽⠂⠏⠸⠙⠇⠓⠸⠉⠇⠯⠄⠯⠇⠇⠭⠃
⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⢶⣤⡀
⠀⣸⠀⠀⠀⢠⣀⡀⣤⣄⠀⠀⠀⠸⡆⠀⡦⢔⠴⣴⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⡄⣤⡤⣤⡤⠤⠙⡢⣬⣿⡇
⠀⢹⠀⠀⠀⠈⠉⠉⠉⠈⠀⠀⠀⢰⢇⣀⣀⣀⣀⣀⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⢠⣺⣼⣽⠏⠁
⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⡈⢁⠁⠉⠉⠀⠛⠘⠀⠀⢀⣀⣀⣧⢞⡻⠆⠀⡴⠚⠓⠒⠢⣤⣞⣽⣿
⠀⠀⠀⠙⢦⣀⡀⠀⠀⣀⣠⠴⠫⣄⢬⠉⡇⠀⠀⠀⠀⠀⠀⠀⠺⠗⠺⡟⡏⠀⢀⡼⢏⣉⣉⠉⠒⠮⠽⣿⣧⣤⡀
⠀⠀⠀⠀⠀⠀⠉⠉⠉⢏⢈⡆⠀⠀⠘⡄⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣇⣤⣯⣄⠀⠈⠉⠙⠛⠚⠛⠛⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⣈⠒⠢⣄⡀⡗⠚⡠⠴⣶⣤⡀⠀⠀⠀⠀⠀⡇⢿⡟⠀⠙⣧⣞⣉⠓⢦⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠼⠈⢩⣞⣋⣉⣡⡽⠉⠛⠲⢦⣄⠀⠃⡾⡇⢠⠜⠟⠿⠉⠀⢨⡟⠉⠉⠀⠉⣲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⡁⡏⠈⣀⢀⡄⠀⠀⠀⠙⡷⡆⠁⡇⠸⡄⠀⠀⢀⣠⠞⡉⡖⢒⣖⢊⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣿⠙⢎⠁⠘⠢⢄⠀⠀⠀⢱⡉⢀⡇⠀⠈⠙⠛⡉⣀⠀⠋⠘⠙⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠳⠛⢢⠀⣧⠀⠀⠘⡇⢈⡇⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠉⠉⠉⠁⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠲⠐⠸⠆⠦⠚⢆⡰⣃⡤⠋⠀⠀⠀⡇⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣦⣄⢤⣄⢄⢤⣩⡛⠉⠁⠀⠀⠀⠀⠀⡇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⠀⠀⠉⠈⠀⠀⠀⠀⠀⣀⣄⣀⡇⢀⣇⣀⡀⠀⠀⠀⣀⠀⠀⢀
⠤⠤⠤⠤⠖⠒⠒⠒⠓⠒⠒⠒⠒⠒⠲⠤⠤⠤⠤⠤⠤⠔⠋⠉⠁⠀⠀⡇⢸⡇⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠘⢇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⢀⣄⣄⣀⣀⣀⣻⡗⢄⣠⣄⡤⡪⠑⡆⢰⠓⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠈⠁⠉⢁⡈⠉⣉⠉⣽⡣⠾⣧⣿⠋⠀⢀⠀⢸⠀⠀⠀⠹⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣈⡭⠖⠀⠧⠝⠘⠞⢠⢤⠠⡲⠘⢛⣴⡶⠫⡄⢨⠭⢶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣖⠒⣲⠀⠀⠮⠗⠠⣖⡄⠀⠥⠀⣴⣾⢟⢺⡄⣤⢷⣏⠀⣸⡏⢻⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⢠⡒⣲⠄⠆⠆⠸⠹⢀⣘⠊⠈⡁⢸⣻⠒⣿⡯⠄⠀⠀⠘⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠉⠁⠈⠉⠁⠘⠋⠟⠓

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣷⣶⣤⡀⠀⣀⣠⣤⣴⣶⣿⣿⣿⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⢠⣾⣿⠟⠉⠁⠀⠀⠈⠙⠻⣿⣦⡘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠂
⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⢛⣉⣅
⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⢤⣍⣙⠛⠿⠛⣋⣩⣤⡶⠶⠿⣿⣿⡧
⠀⠀⠀⠀⠀⠈⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⢠⣶⣦⣬⣉⢋⣩⣥⣴⣶⣶⣶⣶⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣤⣄⣀⣀⣠⣴⣾⡿⠏⣰⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠟⢛⣉⣴⣾⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⡿⠿⠿⠿⠿⠿⠿⠿⣿⣿⢸⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢰⣶⣾⣿⣿⣿⣿⣷⣶⣶⣦⢠⣴⣶⣶⣶⣿⣿⣿⣶⣶⣶⣶⣦⣼⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⢶⡀⣰
⠀⠀⠀⠀⠀⠀⢮⣸⣥⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠘⠛⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠶⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡴⠇
⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⣴⠀⠀⠀⠀⠀⠀⠀⢰⡦⠀⢀⡀⠀⠺⠇⠀⡀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠈⢿⡽⠋⠙⠷⡄⠀⠀⢵⡄⢰⠛⠇⠀⠀⠀⠀⠀⠀⠀⠒⠛⠋
⠀⠀⠀⠀⠀⠀⠀⢷⣴⠏⠁⠀⠀⠀⠀⠀⠀⠠⣿⣢⠀⠀⢀⡀⠹⣗⠀⠈⢣⣼⠀⠀⠀⠀⠀⠀⠀⠠⠴⠦⡤⠶⠓⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤⠠⡶⠋⠁⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⢀⢠⣦⣤⡤⣴⣴⣦⣦⡈⠃⠀⠀⠀⠀⠀⠀⠀⠰⠌⠉⠏
⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡷⠟⠋⠀⠀⠀⠉⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡉⢦⣤⣦⠄⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠊⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠢⠴⠣⠂⠀⠂⠉⠃⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡵⢆⢀⡔⠊⠀⠀⠀⡠⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠌⢁⠀⠀⠀⢀⠃⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠠⣂⣠⣀⡁⡠⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠈⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⡀⡀⠠⣀⡀⠀⢀⡀⢠⢤⠶⢠⠊⡇⠈⠃⠁⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠡⠄⠠⠥⠥⠴⠥⠤⠍⠈⠀⠄⠐⠂⠈
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢠⠚⠀⡀⠀⢀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣦⣎⣥⣶⣶⣮⣿⣶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⢫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠻⣿⠋⠀⢈⣿⡿⠿⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠚⠉⢁⡀⠀⠀⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠈⠀⣼⣿⣿⣿⡔⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⠊⠀⠈⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢈⠁⠀⠠⠈⠀⣠⣤⣦⣀⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣶⣾⣧⠄⠀⠀⠡⠼⣿⣿⣿⣿⣷⣬⣿⣿
⠀⠀⠀⠀⠀⠂⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢈⣽⣿⡍⢀⠀⠀⠀⠠⠄⠀⠙⢿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⣠⣀⣻⢤⣀⡐⣻⣿⠋⠀⠀⠐⠈⠐⠀⢀⡀⠀⠙⠻⣿⣿⣿
⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢉⡽⢟⡩⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣹⠀⠀⠀⠈⠻⣿
⠀⠲⣴⣤⠀⢄⠀⣀⡀⠀⠀⠀⠀⠀⠀⠄⣀⣠⣤⣿⠿⠿⣾⠶⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠉⠒⠶⠦⢔⢀⣂⣀⠄⠈⢁⡈⠉⠩⠻⠃⠀⡠⠒⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢊⡥⢔⡈⠀⠀⠠⡉⠀⡠⠚
⠀⠀⠀⠀⠀⠀⢀⣤⣶⣻⠷⠚⠋⣰⠻⢅⠎⠀⡤⠄⣦
⠀⠀⠀⣀⣠⣾⡿⠟⠋⠁⠀⠀⢰⣟⣿⡇⠀⠀⠑⣖⠌⡆
⣷⣶⣬⡏⠉⠁⠀⠀⠀⠀⠀⠀⣿⣤⠟⠀⠀⠀⠀⠙⠲⢿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾
⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿
⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿

⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⢀⠀⠀⠀⡠⠋⠊⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⡠⠋
⡰⠋⠀⠀⠠⠔⣒⠒⠐⠄⠀⠀⠀⠀⠀⠀⠰⠀⢀⢾⣷⠶⠋⠀⠀⠀⡰⠋⠀⠀⢠⠔⣒⠒⠀⢄⠀⠀⠀⠀⠀⠀⠈⠀⢀⢾⣿⠶⠋
⠀⠀⠀⠀⠁⠠⣴⠄⠀⠀⠑⢄⠀⠀⠀⠀⠠⡠⢄⡀⠀⠀⠀⣀⠴⠊⠀⠀⠀⠐⠁⠀⣴⠄⠀⠀⠁⠀⠀⠀⠀⠀⠘⡠⢄⡀⠀⠀⠀⣀⠴
⠀⠀⠀⠀⡄⠀⠹⡄⠀⢀⠀⠈⠆⠀⠀⠀⠀⠈⠈⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠹⡄⠀⢀⠀⠈⠆⠀⠀⠀⠀⠈⠈⠀⠀⠀⠉
⠀⠀⠀⠀⠐⡄⠀⠹⣷⣾⡇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠙⢷⣾⡇⠀⠈
⡀⠀⠀⠀⠀⠈⠳⣄⣀⠐⢾⡰⣼⠀⠀⢀⠤⠒⠒⠉⠉⠉⠁⠀⠐⠤⡀⠀⠀⠀⠀⠀⠲⣄⣀⠐⢾⡴⡱⠀⠀⢀⠠⠂⠒⠉⠉⠉⠉⠀⠐
⠈⠢⠀⠀⠀⠀⠀⠀⠉⠛⠓⠋⠀⠀⠀⠁⠀⠀⢀⡀⠂⠄⠄⠤⢀⠀⠈⠲⡄⠀⠀⠀⠀⠀⠉⠛⠓⠋⠀⠀⢠⠃⠀⡀⢀⡀⠂⠤⠄⠤⢀
⠦⡀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣯⠉⠁⠀⠀⠀⠀⠘⠢⣀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⣯⠁⠁
⠲⡘⡂⠐⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠈⠲⣌⢆⠀⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠈⠳⣄⡀
⣿⠟⠛⢀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠉⠓⠶⠶⣶⣿⠟⠟⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠉⠓⠷⠶
⢀⣀⢌⣳⠋⠀⠀⠀⢀⠀⠠⠤⣤⣀⡀⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⢀⣀⢐⣳⠋⠀⠀⠀⢀⠀⠤⠤⢤⣀⡀⠀⠀⠀⢀
⠭⠞⠋⠁⠀⢀⠔⠊⠀⠀⠀⣀⡀⠍⠻⣦⠀⠀⠀⠉⠐⠢⠤⠬⠬⠬⠭⠖⠋⠁⠀⢀⠄⠊⠀⠀⠀⣀⡀⠍⠻⣦⠀⠀⠀⠈⠐⠢⠤⠬⠤
⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⣹⠏⠂⢈⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⢹⠇⠆⠈⡻
⠀⠀⠀⢠⠁⠀⢀⠀⠀⠀⡠⠋⠋⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⢀⠀⠀⠀⡠⠫⠊⠀⢰⠏
⠀⠀⠀⠀⠄⢀⢾⣿⠶⠋⠀⠀⢀⡰⠃⠀⠀⡠⠒⠀⠀⠒⢄⡀⠀⠀⠀⠀⠀⢰⠀⢀⢾⣷⠶⠋⠀⠀⠀⡰⠋⠀⠀⡠⠒⠀⠀⠒⠄⡀
⠀⠀⠀⠰⡴⢄⡀⠀⠀⢀⣀⠴⠊⠀⠀⠀⢰⠁⠀⣴⠀⠀⠀⠙⢄⠀⠀⠀⠀⠀⡰⢌⡀⠁⠀⢀⣀⠴⠊⠀⠀⠀⠀⠁⠀⣴⠆⠀⠀⠐⢄
⠀⠀⠀⠀⠈⠁⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠈⡄⠀⠸⡄⠀⢠⠀⠈⢂⠀⠀⠀⠀⠈⠁⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠹⡄⠀⢀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠀⠙⣿⣶⡇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠹⣷⣾⡆
⠀⠀⢀⠄⠐⠚⠉⠁⠀⠉⠁⠒⠤⡀⠀⠀⠀⠀⠈⠳⣄⣀⢐⣿⡴⡧⠀⠀⢀⠤⠒⠚⠉⠁⠀⠁⠀⠀⠤⡀⠀⠀⠀⠀⠈⠳⣄⣀⢈⣮⡴
⠀⢠⠃⠀⠀⢀⡂⠒⠠⠄⠄⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠉⠙⠓⠉⠀⠀⢀⠃⠀⠀⢀⡐⠒⠢⠄⠤⠀⠀⠈⠒⡀⠀⠀⠀⠀⠀⠉⠙⠓⠉
⠀⡆⠀⠀⠐⣿⠁⠁⠀⠀⠀⠀⠙⠦⣀⠈⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣯⠈⠁⠀⠀⠀⠀⠙⠦⣀⠈⠦
⠀⠠⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠈⠰⣌⢆⠀⣣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠳⣌⢦⠀⣃
⠀⠀⠱⡀⠀⠀⠀⠀⠉⠓⠳⠶⢶⣿⠟⠛⢀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠉⠛⠳⠶⢶⣿⠟⠓⢀⣸
⣤⡀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⢀⡀⢔⡣⠃⠀⠀⠀⣀⠤⠀⠤⣄⣤⡀⠀⠈⠂⢄⠀⠀⠀⠀⠀⠀⠀⢀⢀⢰⡳⠋⠀⠀⠀⣀⠤⠀⠤
⡀⢛⡧⠀⠀⠀⠈⠒⠲⠤⠬⠬⠭⠽⠞⠋⠀⠀⢀⠔⠊⠀⠀⠀⣀⡀⠌⢛⣦⠀⠀⠀⠈⠐⠲⠤⠤⠬⠬⠽⠚⠋⠀⠀⢀⠔⠊⠀⠀⠀⣀
⠃⢈⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⣹⣇⠂⢈⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⣸
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⢀⣠⣤⣤⣤
⠀⠀⠀⡏⡴⠋⠉
⠀⠀⠀⢻⡸⡄
⠀⠀⠀⠀⢣⣳⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣦⣄⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠹⡅⢸⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢹⠹⡄
⠀⠀⠀⠀⠀⡟⢿⡘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢀⡞⠀⠉⠓⠦⣄
⠀⠀⠀⠀⠀⢱⡘⣧⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⢠⠏⠀⠀⠀⠀⠀⢸⣆⢰⣆
⠀⠀⠀⠀⠀⠀⢧⢉⣁⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠁⠀⠀⠉⠛⣿⣿⣿⣿⣧⠀⠀⢸⠀⠀⠀⠀⠀⣀⣾⣿⢸⣿⣤
⠀⠀⠀⢀⣤⣶⣾⣿⣟⡁⢷⠀⠀⠀⠀⠀⠀⠀⢸⠉⠙⠟⠛⣫⠛⠷⠶⠚⢻⣿⣿⡿⠀⠀⠈⢳⣦⠰⠖⠛⢡⣿⣟⣸⣿⣿⡇
⠀⠀⢀⣼⣿⣿⣿⣿⣿⣧⣬⣇⠀⠀⠀⠀⠀⠀⢸⣀⡘⠛⡸⠁⣇⠸⠗⠀⣼⡙⡿⠁⠀⠀⠀⠸⣿⣧⠀⢠⣾⣿⣿⣿⣿⣿⠇
⠀⠀⠈⠿⣿⣿⣿⣿⣿⠛⠡⠼⡀⠀⠀⠀⠀⠀⠀⠉⢩⠉⢥⡄⠉⠉⠉⠛⣯⠜⠁⠀⠀⠀⠀⠀⣿⣿⣶⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣆⠃⠀⢣⠀⠀⠀⠀⠀⠀⠀⠈⡆⠤⣶⠴⠂⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣦⣤⡼⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⣉⣁⣤⠞⠁⣧⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠘⣿⠿⠛⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣹⠀⠀⠀⢹⡍⠂⢄⡀⠀⠀⠀⢰⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢀⡤⠦⠤⡄⠀⠀⠀⠀⠀⠀⢀⠀⠁⡼⠀⠀⠁⠀⠙⢦⠀⠙⣄⠀⠀⢸⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⢰⠓⠒⠚⠀⠀⢳⣄⣀⡀⠶⣒⣨⡇⢀⣜⠀⡟⠺⢄⣀⣸
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⢸⠀⠀⠀⢠⠇⠀⠀⠘⠂⢰⡄⣿⣿⣿⣿⣿⡟⡔⠁⠀⢹⠃⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡄⠀⢀⠎⠀⢀⡀⠀⣠⠏⠀⣿⣿⣿⣿⡟⠀⢹⡀⠀⡞⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣇⠀⡞⠀⠀⢸⡇⡰⠁⠀⠀⣿⣿⣿⡟⠀⠀⣠⠃⣸⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢻⡼⠁⠀⠀⣸⠃⠸⡀⠀⠀⣿⣿⡿⠀⢀⡜⠁⢠⡏⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠸⡇⠀⠀⢠⡏⠀⠀⠱⡀⠀⣿⣿⠁⣰⠋⠀⠀⡾⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣷⠀⢀⡞⠀⠀⠀⠀⠱⣘⣿⢇⡼⠁⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⣿⠀⠸⡄⠀⠀⠀⠀⠀⢹⣿⠞⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⡿⠀⠀⣧⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⢰⠇⠀⣠⣿⠀⠀⠀⠀⠀⢸⡃⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠈⢀⡼⠃⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢀⡴⠋⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠴⠚⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢷⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠞⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⠄⢠⣧⠎⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⢤⣀⠀⠠⢄⣀
⠀⠀⠀⢠⣄⣤⡾⣆⣾⣟⣉⠳⡖⠉⢁⡄⠀⢾⣠⣄⠀⠰⠤⣄⣉⢳⠉⢱⣮⡙⣮⣷⠀⠀⠀⢀⣀⣀⡴⠖⠲⢦
⠀⠀⠀⠀⠉⠛⠿⠛⠛⠻⣷⣶⣶⠎⣿⣧⣼⣶⡉⢉⠉⠀⠀⢺⣿⣼⡷⠘⢻⢳⣿⢧⠀⠀⣴⠋⠀⠋⢷⠀⡁⢸⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⣋⡁⠙⢻⣿⣷⠍⣐⡎⡝⢀⠉⣾⢏⠙⢿⣌⡀⢸⠃⠀⠀⢄⣸⠀⠀⣺⠃⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢶⣿⠋⠽⠿⠿⢉⡙⢯⣿⡿⠿⠏⢙⣻⡇⣹⡇⢂⣾⡀⣇⣿⠀⠀⠀⠀⣿⠀⠀⣿⢀⡟
⠀⠀⠀⠀⠀⢀⣠⠤⣿⡗⠀⡞⠃⢀⣤⣷⣿⣿⣿⣶⣴⣦⠴⣶⠟⠿⠞⠛⠿⡋⠀⣗⣾⣿⠀⠀⠀⠀⣿⠀⢠⡇⢸⠇
⠀⠀⠀⠀⠀⣿⣯⣍⣈⣀⣽⣿⣾⣿⡟⣻⣿⣿⣿⣿⣷⣦⣶⣿⣶⣤⡤⠚⠻⠿⣶⠿⠃⣿⠀⠀⠀⠈⣿⠀⢸⡇⣿
⠀⠀⠀⠀⢀⣙⣋⡀⠀⣀⣯⣽⡁⢈⣻⣉⣋⠀⠙⠿⠦⠽⣿⡟⢓⣨⣶⣞⠕⢀⡴⠖⠶⣿⠀⠀⠀⠀⣿⠀⢸⡇⢿
⠀⠀⠀⠀⢸⡯⢥⡏⠀⢿⠶⢾⠁⠘⣷⠶⡏⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⡿⠀⠀⠀⠘⡇⠀⠀⠀⢿⠀⢸⡇⢸
⠀⠀⠀⠀⢸⡇⠀⡇⠀⢸⡆⢸⠀⠀⡏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⢸⡇⠀⠀⠠⢠⡇⠀⠀⠀⢸⡆⠈⠃⢸⡀
⠀⠀⠀⠀⢸⡇⠀⣇⠀⢸⡅⢸⡆⠀⡇⠀⡇⠀⠀⠀⠀⣀⣠⣴⣾⡿⠛⡏⠸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⢸⡇⠀⣿⠀⢸⡇⠘⡇⠀⡗⠀⣷⢠⣤⣶⣿⠿⠛⠋⠁⠀⠀⡇⢰⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⣼⠀⠀⢸⡀⣸⠀⠀⣷⢠⡇⠀⢹⠀⢹⡟⠁⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⣠⡴⠶⠶⠶⠒⠛
⠀⠀⠀⢀⣿⣀⣀⣈⣇⣿⣀⣀⣸⣸⣇⣀⣸⣇⣸⡇⠀⣀⣀⠀⣀⣀⠀⡇⢸⡇⠀⠀⠀⠀⠈⠳⠄⠀⠀⠀⠀⠀⠈⠜⣻⡇⠀⢿
⠀⠀⣸⣟⣋⣉⣉⣭⣭⣽⣭⣭⣽⣭⣽⣯⣭⣭⣽⣧⠀⢿⣿⠀⣿⡏⠀⡇⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⢸⡇
⠀⠀⠈⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⡏⠀⣤⣤⠀⠀⢠⣤⣄⠀⠀⣠⣤⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⡇⠀⣿⣹⠀⠀⢸⣧⣿⠀⠀⣿⣼⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠉⠀⠀⢸⠀⠀⠀⣀⣀⠀⠀⢸⡇⠀⠀⠀⠈⠛⠦⣤⣀⣀⣀⣀⡀⠀⠀⠀⠀⢸⠇⠀⣸⠁
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣯⢽⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠛⠛⠲⣞⣀⣠⡟
⠀⠀⠀⣿⣞⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣄⣀⣠⣧⣾⣄⣀⣨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠯⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣠⢴⡋⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣤⣤⣤⣤⣤⣭⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣠⠖⠒⢦⡈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠸⡄⠀⠀⢠⠀⠀⠐⠒⠀⣇⠀⠀⢀⡇⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣈⢸⣁⡇⢠⣄⠀⠀⠀⠇⠀⠀⠀⠁⠀⠀⠈⠇⠀⠀⠀⡠⠈⠓⠒⠋⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉⠀⠰⠏⠀⠀⠀⣀⣠⡤⠤⠤⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠖⠉⠁⣀⣀⣠⣄⣀⣀⠈⠉⠲⢤⣀
⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⡄⠀⠀⠐⠋⢀⡠⠖⢋⣩⢇⣠⠤⠞⠈⠉⠲⢄⡀⠛⠇⠀⠀⢠⠤⠤⢤⡀
⠀⠀⠀⠀⠀⠀⢸⢡⡞⡆⡇⠀⠀⠀⣠⢋⡖⠉⠉⠀⠸⠀⠀⠀⠀⢀⣀⣀⠙⣄⠀⠀⠀⢸⢸⢹⡎⡇
⠀⠀⠀⠀⠀⠀⢸⢸⡇⡇⡇⠀⠀⣰⠗⠋⠀⠀⢰⣊⣁⣀⣀⣀⠀⠳⢤⣬⠷⠈⣆⠀⠀⢸⢸⢸⡇⡇
⠀⠀⠀⠀⠀⠀⢸⢸⡇⡇⡇⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⡄⠀⠀⢠⢤⣸⠀⠀⢸⢸⢸⡧⡇
⠀⠀⠀⠀⠀⠀⢸⢼⡇⡇⣇⠀⠸⡇⠀⠀⢠⠞⠉⠉⠉⠙⠒⠚⠉⠀⠀⠀⢸⠆⢹⠇⠀⣸⢸⢸⡇⡆
⠀⠀⠀⠀⠀⠀⡞⢸⠃⢳⢸⡄⠀⢧⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⡼⠀⢠⡇⡞⠘⡇⢳
⠀⠀⠀⠀⠀⠀⠱⣌⣓⡋⠘⠀⠀⠈⢧⠀⠀⠑⠦⡄⠀⠀⠀⠀⠀⠀⠀⢀⡏⡴⠁⠀⠀⠣⣍⣛⡁⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠀⠀⠈⢳⠀⠀⠀⠀⢀⡸⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣄⡀⠉⠓⠦⠤⠬⠧⠤⠴⠚⠉⢀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣤⣀⣀⣤⡤⠴⠚⠉



⣿⣿⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⡀
⠀⠀⠀⠀⣠⡾⠋⣁⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⡀⠀⠀⢀⢀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠉⠛⢦⡀
⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠂⢀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⢀⡄⠄⠀⠈⢿⡄
⠀⠀⠀⣿⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⠀⠁⠀⠀⠰⠀⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⠀⠂⠀⠀⢸⡇
⠀⠀⠀⣿⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⠀⢰⠀⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⠀⢸⡇
⠀⠀⠀⣿⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢸⡇
⠀⠀⠀⣿⠀⢸⠀⢀⠔⠊⠉⠉⠉⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⣿⠀⢸⢠⠏⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠘⣶⠀⠀⠀⡇⢸⡇
⠀⠀⠀⣿⠀⢠⢸⡀⠀⠈⠚⠘⠓⠀⠀⢸⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠘⠁⠡⢄⣻⠛⠀⠀⠀⡇⢸⡇
⠀⠀⠀⣿⠀⢸⠀⢣⡀⠀⠀⠀⠀⠀⣠⠦⣈⠍⠉⠀⠉⠁⠀⣀⡤⣶⡺⠂⢀⣂⣁⣐⢢⣼⣾⠁⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⣿⠀⢸⠀⠀⠉⠒⠆⠠⠖⢚⠁⠀⠂⠀⠀⠀⠀⠀⠀⠉⠈⢹⠀⣰⠋⠐⠶⠤⢥⠬⠿⠷⠂⠀⠀⠀⡇⢸⡇
⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠤⠘⠀⣀⣰⠐⣀⡠⣄⠀⠀⠀⠀⠀⣿⠉⢛⣤⣒⠢⡄⢀⣀⡀⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢠⠿⡤⠴⠊⠉⠙⠳⣄⡀⢹⠀⠊⠙⠁⠀⡿⠀⢀⡀⠕⠀⠀⠀⠇⢸⡇
⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣼⠶⠂⠘⢀⠀⠀⠘⡅⢸⠀⠓⠀⠐⠋⠐⠐⠺⠐⠂⠀⠀⠀⡇⢸⡇
⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠑⠂⠀⠑⠀⠀⡇⢈⠀⠀⠀⠈⠉⠉⠉⠀⠁⠈⠙⠁⠀⡆⢸⡇
⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠁⠉⠉⡤⠂⠐⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⣀⣀⡀⢸⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⢸⡇
⠀⠀⠀⣿⠀⠰⠒⠒⠂⠀⠉⠁⠀⠀⠈⠀⠐⠒⠒⠒⠒⠈⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⢀⠀⠀⢠⡄⠀⡀⠠⠤⠁⠨⠦⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉⠈⠉⠉⠹⠧⠾⣿⠃⠀⠄⢇⠀⠈⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⣀⠐⡒⠊⡈⡈⢀⠁⢀⠀⣂⣤⣞⠉⣀⠊⢹⡶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠉⠀⠁⡄⢠⠠⠈⠀⠄⣐⠋⠃⢸⡧⢿⡇⠈⠁⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇
⠀⠀⠀⣿⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠁⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⡇
⠀⠀⠀⣿⠀⠀⠠⠀⡆⠠⢀⠠⠀⢄⠚⢀⠀⠀⢀⢄⣀⠤⡀⢤⠠⠄⡐⠑⡄⠠⢄⠠⠠⢀⠠⡀⡐⢆⢠⣀⠀⢸⡇
⠀⠀⠀⢿⡀⢀⠐⠈⢀⢸⢐⠀⠉⡸⠀⡬⠘⠂⠬⠦⠁⠀⠃⠈⢨⢀⠠⠨⣄⢈⠸⠀⠳⠮⠶⡍⡆⡠⠦⢉⠀⣸⡇
⠀⠀⠀⠈⢷⣄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠙⠳⢦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠢⣀⠠⠤⠤⠤⠖⣉⡀⠀⠀⠸⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⡁⠀⠀⠱⡀⠀⠀⠀⠀⠀⠈⠓⢄⠀⢲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠁⠀⢢⡴⠂⠤⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢷⣄⠀⢸⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⠆
⠀⠀⠀⠀⠀⠀⠀⡴⠊⠀⠀⠀⡇⠈⠉⠁⠈⡆⠑⠢⢤⠠⠤⣄⣀⣀⣠⠤⠄⢤⠤⠃
⠀⠀⠀⠀⠀⠀⢎⡀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢸⡀⠀⠀⠀⡄⠀⠀⠀⢀⣘⠤⢼⣤
⠀⠀⠀⠀⠀⠀⠘⣇⡄⠀⣰⢀⢰⠀⣀⡀⠀⠀⣇⣤⡖⠒⠈⠙⢲⢺⡁⠀⡄⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠴⠁⠉⠀⠲⡤⡎⠓⠜⠁⠈⢧⡀⠈⣀⢏⠀⠙⠦⠤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠈⠉⠀⠀⠙⢁⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣕⡒⢶⢤⠤⡤⠴⡒⡍⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠈⠙⠣⣤⡓⠐⣇⢧⠀⢸⡄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠈⠑⡤⠛⠚⠓⠁⠚⢻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠈⠳⢄⡀⠀⠀⠀⠀⠀⢰⣀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡏⠒⠲⠤⠤⠰⡾⠋⠀⠀⠑⣤
⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠤⡀⠀⠀⠀⠀⢸⠀⠀⠀⠂⡇⠀⠀⠀⠀⠀⢇⠀⠀⠀⢸⢲
⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⢸⠀⠀⠀⠀⢀⠆⠀⠀⠀⠁⠃⠀⠀⠀⠀⠀⠈⢷⠤⠴⢚⣋⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⠀⠀⠀⠀⠸⢄⣀⡀⣀⣀⣰⣀⡠⠤⢤⠒⠊⠉⠀⠀⡖⠒⢲⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠘⡀⠀⠀⠀⠀⡠⠚⠫⡀⠀⠄⣬⣀⢀⣼⠀⠀⠀⠀⠀⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⢀⠀⠀⡠⠊⠘⢠⣀⡈⢒⡺⠄⣀⠠⠾⣦⡀⠀⠀⢀⠇⠀⠸⢀⠀⠀⠠⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠈⡆⠀⡅⠀⠀⠀⢇⠈⢉⡷⠀⠈⠂⠐⠁⠙⡄⠐⠁⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠰⡀⢣⠀⠀⠀⠀⠉⠉⠀⡇⠀⠀⠀⢀⡰⠁⢡⠀⠀⠀⠀⠀⡘⠀⠃
⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠐⠁⠈⠢⢄⡀⠀⠀⢀⡠⠋⠁⠒⠈⠁⠀⠀⠀⠑⠤⠤⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣐⣒⠚⠂⠀⠂⠤⠀⠀⠉⠈⠁⠐⣢⡀⠀⢀⣀⢀⡔⢒⠞⠑⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣀⡼⠄⠀⠀⠀⠀⡜⠁⠠⠀⢀⡀⠀⠀⠸⠓⡨⠀⠭⠘⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⡠⢞⠓⠊⠀⠀⠀⠀⠀⣸⡵⠟⠁⢑⠢⠄⠑⠂⠜⣁⣀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠄⠀⠀⠀⠀⠇
⠀⠀⠀⠀⣠⡔⠴⠛⠁⠀⠀⠀⠀⢀⣀⢀⢨⠀⠠⠴⠀⠂⢡⡯⠖⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡄⠀⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠥⠤⠚⠪⡢⣀⣄⡄⠀⠚⠔⠀⠂⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢀⣀⣴⡂⠖⠓⠒⠁⠀⠀⠀⠀⠈⠀⠀⢐⡂⠀⢀⠀⠀⠀⠄⠀⠀⠃⠀⣀⠒⠀⠀⠀⠀⠲⠦⠤⣤⣤⠤⢀⠸
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠒⠏⠀⠀⣆⣆⢀⠂⠁⠀⠉
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣀⠜⠃⠀⠀⢀⠀⠀⠀⠸⠀⠡⠄⠀⡀⣧⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢠⡤⠀⠀⠀⢀⣀⣀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠈⠂⠛⠉⣣⢤⠨⢀⠀⠀⢠⡆⠂⠀⠀⠐⡄⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠊⠉⠐⠀⠀⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⢹⡀⠀⠈⠀⢠⡄⠀⠀⠀⠀⠈⠵⠦⡀⠀⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⣇⣀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠠⠀⠄⠀⠈⠀⢀⠀⠀⠀⢌⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠌⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠃⡅⠀⠀⠀⠀⠒⠁⠀⠀⠘⠄⠇
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⠃⠈⠁⠙⡁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢨⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⠬⠀⠀⠀⠄⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣀⡀⠀⣀⠤⠅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⢀⠀⡀⠸⠴⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⠠⠤

⠀⠀⠀⠀⡄
⠀⢀⠀⠆⠃⡀⠀⠀⠀⠀⣌⠃⠀⠀⠀⡴⣾⣰⣀⠀⠀⠀⠀⢀⠀⠀⢰⡄⡁⢠⣤⠀⠀⠀⠀⢀⣠⣤⠀⠀⠀⠀⠐⠋
⠀⠀⢱⠀⠀⢀⠄⠀⠀⢈⡀⣆⠀⠀⠀⡈⠹⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠠⠗⠀⣀⣄⠀⠀⠀⢸⣯⣿⡇⠀⠀⠘⠁
⠀⠀⠀⠂⠀⠘⠀⠀⠀⢈⠁⠫⠆⠀⠀⢱⡀⠃⠀⡀⠀⠀⠀⣷⠀⠀⠀⠀⠰⣷⠋⠁⠀⠀⢠⣿⠙⠁⣿⠆⣰
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⢠⠙⢀⠀⠀⠀⢷⡀⡰⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⣀⡀⠀⠀⠉⢦⡀⠈⡤⠈⢠⠃
⠀⠀⠀⠀⣤⠆⠀⠀⠐⢛⡚⠀⢻⠅⠀⠀⠸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠀⠀⠀⠀⠀⢡⢘⠃⠀⠃
⠀⠀⠉⡐⡟⠁⠀⠀⠀⠀⠈⣑⣁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠂⠀⠀⠀⠰⣾⢿⡏⠓⠀⠀⠀⠘⡏
⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠀⠀⠀⠀⠀⣿⣴⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⢰⣿⣿⠄⠀⢿⡟⠀⠀⠀⠀⠈
⠀⠀⡾⣿⣿⡆⠀⠀⠀⠛⢃⠀⠀⠀⣠⣀⠈⠀⠀⠀⠁⠀⠀⠀⣀⠽⠛⣧⠀⠀⠀⠀⠉⠉⠀⠀⠸⡇⠀⠀⠀⠀⠐⠂
⠀⠀⠀⢸⠿⠅⠀⠀⢀⡈⠀⠀⠀⠀⠉⠠⠀⠀⠀⠘⠀⠂⠀⠈⠁⠀⠀⠉⠘⠁⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠐⢂⠀⠉
⠀⠀⣴⣶⡶⠀⠀⠀⠈⠁⡀⠀⠀⠀⢈⠢⠄⠀⠀⢰⢧⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠂⢀
⠀⠀⠸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⢠⣶⣤⠀⠀⠀⢰⠄⡀⠀⠀⠀⠀⣀⢄⡄⠀⣶⠂⠀⠀⠀⢠⡔⣶⠆⠀⠀⡠⣾⣦
⠀⠀⠀⠀⠀⠀⠀⣿⣾⣷⡀⠀⠀⣤⣈⡃⠐⠛⢘⣣⡌⠀⠀⠙⣦⡀⣿⣿⡍⡤⡟⠀⠀⣜⠦⣹⣿
⠀⠀⠀⠀⠀⠀⠀⢿⢘⠻⣷⣄⣤⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⠛⠂⠉⠞⠁⢤⣤⣹⣶⣧⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠛⣰⣾⣥⣾⣤⣀⣀⠀⠀⠀⠀⠀⠠⣤⠤⠄⠀⣀⠠⢦⠐⢺⣶⣽⣿⡟⠏⡼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠟⢩⣄⠙⢿⣿⣏⣶⣄⠀⠀⠀⠁⠀⠀⠘⢦⣄⣶⣿⡻⠿⠟⡊⠙
⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⢀⣰⠂⠉⠉⠉⣉⣉⠁⠀⠠⢤⠤⢤⠄⠀⠀⣀⣀⠘⠻⠿⠛⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠐⢧⣴⡔⠁⠀⣴⣶⠀⢻⣦⠽⣦⡀⠀⠀⡀⢀⣴⠿⢹⡟⢐⣿⣦⠀⠀⠀⠀⡐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⣽⣆⠀⢿⣮⡑⢪⣆⢠⣴⡑⢈⣰⣿⠀⢸⡿⣿⣇⠀⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⣿⣿⠿⠟⠀⠰⣇⠄⣀⠹⣿⡗⠀⣤⣸⡆⠀⣸⠗⣿⣿⡀⠀⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢷⣦⡀⢾⣉⡀⠠⢘⡀⠀⠙⣶⡟⠀⠉⠀⢼⣦⠋⠀⠀⣿⢠⣿⡿⠀⠀⣀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠛⠃⠈⠛⢧⡤⣘⠁⢀⡼⠃⠀⠀⣀⠀⠀⠛⢆⠀⠸⠿⠚⠋⠀⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠀⠐⣿⣷⣦⠀⠀⠀⠀⠀⣀⣁⠀⠀⠀⠸⣿⣧⣄⣀⠀⠁⣰⣦⣄⡀⠀⠀⢀⣤⣺⣿
⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣷⣀⣠⣶⣿⣿⡟⠃⠀⠀⠀⠲⠶⢤⡙⣷⠀⢸⣋⢿⣿⣦⣤⣿⣿⣟⡿⠂
⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠆⠀⠀⠀⢈⣀⡀⡀⠀⠁⠀⠀⣹⣲⣿⣿⢿⢿⣿⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠻⡿⠟⠙⠃⣿⣿⣿⠇⠀⣶⣦⣄⠀⠀⠀⠀⠀⢀⡀⠀⠸⢿⣿⠇⠀⠀⠻⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣄⡈⠋⠁⣀⠀⢸⡾⣿⣷⣤⣄⣲⣿⣛⠏⠀⣶⣀⡀⠶⠠⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠾⠛⠋⠀⣼⣿⣧⠈⠙⠻⠋⠿⠩⢿⡿⠇⣀⣼⣿⢿⡇
⠀⠀⠀⠀⠀⠀⠀⢤⡾⠉⠈⣀⠀⠀⠀⢿⣿⣿⣧⠀⠀⠀⠀⠀⠀⣀⣰⡿⢟⡗⣿⠁⢘⠃⠀⠐⢻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠃⠀⠀⢰⣍⣻⣿⣷⣦⠀⠀⢠⣾⢟⡹⣾⣻⣯⡏⠠⠎⠈⠀⢐⣄⣻⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⠋⠀⠀⠀⣰⣾⣿⡿⣿⣿⡿⠀⠀⢿⣫⣾⡷⠟⠿⣛⣧⠀⠀⠀⠀⠈⠹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣶⣶⣾⣿⣿⣿⡙⠳⠄⠀⢀⠀⠤⣤⣤⣤⠄⢈⣉⣿⣿⣯⣳⡶⢦⡤⣀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠿⣿⡿⣿⣿⡆⢠⣾⣭⠽⠾⠉⠉⠀⡴⠟⠻⢌⣛⣍⣭⣿⣶⣾⣟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠀⠿⠛⠁⠀⠀⠀⠀⠀⠉⠛⠿⠿⠋⠀⠉⠉⠁⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⣄⣄⣤⣄⣤⠀⣼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡋⠀⠀⣀⡀⠀⢀⣀⡀⡀⠀⠀⠀⠀⣧⣿⣿⣿⡟⠀⢚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣗⣠⠞⣻⣿⢿⣿⢠⠶⠴⠋⠀⠀⠀⠀⠘⣿⡿⢿⠥⡷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠛⠁⠀⠀⠀⠳⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠄⠸⡇⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠚⢀⠀⠀⠀⠠⣵⠠⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢣⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣄⣀⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢿⡄⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠐⣾⣿⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⢰⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣼⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⠀⢸
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣤⡿⡇⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⣽⡆⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⢀⣋⣀⣀⣀⠈⠉⠙⠒⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⢀⡴⠛⠉⠉⠉⠉⢉⣭⣙⣿⣿⣿⣿⣿⠁⡛⠳⣦⡀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⡰⠁⠀⣰⠋⡀⠀⠀⠀⠀⠀⠈⢉⣿⣿⣿⣿⣿⣿⡗⠀⢐⠈⢳⡄⠀⢳⡀
⠀⠀⠀⠀⠀⢰⠃⠀⣸⠃⢂⠐⠊⢐⢀⠀⠀⢀⣾⣿⣿⣿⣿⡟⣛⣸⣿⡀⢀⣆⠹⡆⠀⢳
⠀⠀⠀⠀⠀⡾⠀⢰⣿⠀⠀⣠⣶⣶⣶⣦⣄⢸⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣦⣿⠀⠘⡇
⠀⠀⠀⠀⠀⠇⠀⢸⣿⡇⠀⠻⢿⣿⡿⣿⣿⣾⣿⣿⣿⠟⠩⠀⠀⠀⠈⠈⡉⢿⣿⣿⡇⢀⢷⡤
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣾⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⡀⠠⠀⠀⠀⠀⢀⠀⣾⣿⣿⡇⠈⠻⠃
⠀⠀⠀⠠⢾⡷⠀⠸⣿⣿⣿⡿⢛⠛⡉⠉⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣼⣿⣿⣿⠁⠀⡞
⠀⠀⠀⠀⠀⣇⠀⠀⢻⣿⣿⣿⣴⡙⠁⠣⠛⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⣹⣿⣿⣿⠏⠀⣸⠁
⠀⠀⠀⠀⠀⠸⡄⠀⠀⠻⣿⣿⣿⡿⠞⠔⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⠋⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠙⢿⣿⠁⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠈⠛⠿⣿⣿⠻⡟⠻⠛⣟⢻⣛⡽⠿⠋⠁⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣀⡀⠀⠀⠈⠉⠉⠉⠉⢉⠉⠁⠀⣀⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠲⠶⠂⠰⢿⡒⠒⠋⠁

⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢀⡀
⠀⠂⠀⠉⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢀⠀⠐⠋⠋
⠀⠂⠀⠀⠀⢣⢀⢸⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠤⡉⡰⢀
⠀⠀⠀⠈⠀⠀⠸⠊⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠂⠤⢀⠞⢠
⠀⠀⠀⠀⢤⠂⠀⠆⠨⠉⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⢂⡀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠀⠰⠃⢀
⠀⠀⢀⠀⣦⠁⠃⡌⠐⠋⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠄⠠⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠃
⠀⠠⠄⠀⠀⠀⠀⠤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⡂⠀⠐⢊⠤
⠀⠀⢳⠂⠀⠀⠀⠀⣀⠀⠀⠀⠠⠤⠐⠀⠀⠈⠁⢰⠠⠀⠉⠀⠀⠀⠀⠀⡀⠐⠑⠂⠀⠀⠀⡀⠃
⠀⠀⢸⡀⠀⠀⠀⣸⡃⠀⠀⠀⠐⠒⠈⡀⠀⠀⢀⣀⡓⠘⢀⡄⠀⠂⠾⠃⠀⠀⠀⠀⠀⠀⠐⢌⠍
⠀⠀⢸⠀⠀⠠⡐⢕⣀⠀⠀⠐⠛⠆⠂⠀⡀⠀⠀⠀⠠⠄⠋⠀⢦⡀⣤⣄⡀⠈⠀⠀⢀⠈⠀⠤⠂
⠀⠀⡞⠀⠀⢤⣈⣩⠢⠂⠀⠢⣀⠀⢀⠀⠁⠀⠀⠀⠀⠈⠉⠱⡆⢢⠀⡀⠀⠀⠀⠀⠀⠁⠲⠘⠋
⠀⠀⠀⠀⠀⠢⣭⣠⠶⠖⠂⠀⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠠⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⢀⠀⢀⠀⡀⢀⣀⣀⢀⡀⢀⡀⡀⡀⠀⡀⢀⢀⡀⡀⠀⠀⠀⠀⣀⠀⠀⡀⢀⣀⢀⣀⣀⣀⣀⣀⣀⡀⢀⡀
⠀⠀⠀⡏⠉⠉⡉⣉⠉⣉⠉⠉⠉⣉⡉⡉⡉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠳⠦⠉⢩⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⡇⠀⢀⡁⠈⠀⠉⠀⠉⠈⠈⠁⡈⠁⠉⠈⠀⠀⠀⠀⠀⠀⠀⠠⠤⣤⣄⠠⠃⡆⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠀⠈⠀⠀⠀⠀⠉⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡆⠇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠴⠎⢤⠘⢆⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢀⢈⠠⡁⠀⠀⠀⠀⡰⢀⣀⡙⠒⠤⠤⠴⠒⠋⠅⠤
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠐⠄⠀⠴⠋⠀⠀⢱⠔⠐⢂⠐⠂⢄⡄
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢸⠃⠀⠈⠃⠈
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠀⠀⠠⢀⠀⠀⠀⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢀⡈⡐⠀⠀⣜⠀⣒⠂⢁⠠
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣰⣤⠅⠐⠈
⠀⠀⠀⡇⠀⠀⠀⠐⠀⠀⠀⠀⠄⢈⠀⠀⡀⠐⠀⠀⡅⠁⢄⡀⢁⠈⠀⠂⡠
⠀⠀⠀⡇⠀⠈⠀⠀⠈⠀⠀⠁⠢⠀⠄⠀⡀⠈⠂⠀⡆⠦⠄⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⡇⠀⠀⠀⠀⠀⡀⢤⠐⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡀⠐⠀⠀⠃
⠀⠀⠀⡇⠀⠠⠄⠁⠐⠀⠄⠐⢂⠔⠀⢈⡀⠍⢀⢄⠀⢀⠀⠠⠀⠐⠀⠠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠐⠁⠔⠀⠀⢀⡀⠤⠤⠐⠀⡄⠀⠐⠈⠀⠐⠁⡀⡑⠀⠀⠀⠀⡖
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠁⠉⠁⠁⠉⠀⠀⠀⠀⠘⠀⠀⠁⠐⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⡟⡀⠀⠀⠠⠀⠄⠀⠄⠀⠀⠀⠀⠤⠀⠐⣦⠂⠂⠀⠄⠀⠤⠀⠒⠰⠇⢠⡀⠀⠤⠀⠄⠀⠠⠀⠄⠀⠤⡦
⠀⠀⠀⣧⠄⠄⠡⠄⠐⠀⠄⠀⢀⠂⠄⠐⠐⢒⣞⠈⢚⣱⡦⠀⠄⠠⠄⠤⠠⠀⠀⣀⣀⠀⠠⢤⠤⠀⠧⠀⡁⢠⣤
⠀⠀⠀⡧⠈⠄⠀⠀⠁⠀⠠⠑⠠⠀⠀⠀⢠⠠⠎⢁⡉⣀⠀⠠⣄⠀⠠⠤⠀⠀⠀⠉⠉⠐⠂⠄⠐⠀⠄⠀⠀⠀⠶
⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠐⠂⠁⠁⠀⢆⠀⠐⠀⠻⠈⠉⠠⠈⠀⡀⠂⠁⠀⢂⡘⠚⠠⠀⠀⠄
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠒⠁⠀⡀⠀⠀⠐⠄⠖⠈⠁⢈⠷⠔⢠⠈⠀⠓⠈⣆⠀⣊⠀⣄⢁⡇⠀⠀⠀⠐
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡐⠄⠀⠇⠀⠇⠀⢇⡀⠀⠠⠈⠀⠈⠀⠈⠉⠁⠀⠀⠁
⠀⠀⠀⡇⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠂⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠈
⠀⠀⠀⠧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄

⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢀⣸⢿⣝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⢀⠀⠀⠀⠀⠀⠀⠀⣦⣄⠀⠀⠀⣴⡶⠞⠋
⠀⠀⠐⠘⢣⣶⠏⠀⠀⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠂⡄⠀⠄⠀⠀⢹⣹⣾⡆⣴⠋
⠀⠀⠨⠜⢀⠈⠓⠀⠀⠀⠀⠀⣀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠙⠿⢿⡿⠶⠶⠶⠤
⠀⠀⠀⠌⠻⠳⠆⠀⠀⠀⣤⠆⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠀⠀⠀⠈⢀⣱⣤⡄⠠⠀⠓
⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⣠⠁⢸⠄⠀⠀⠀⠀⠀⠀⠡⠒
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⠋⠛⠐⠀⠀⠰⠇⠀⠀⠀⠀⠒⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⢠⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠶⠀⣶
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣄⠘⣦⣼⡄⠀⠒⠐⠠⣖⡀⠀⠀⠀⠀⠀⠉⠵⡔⠃⢀
⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⢿⣿⠿⠁⠀⠀⠀⠙⠿⣤⠀⠀⠀⣤⠆⠀⢸⡶⠘⠃
⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠀⠀⠀⠀⢸⣽⠿⢃⣿⠟⠈⣷⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠄⠱⠆⠠⢦⡀
⠀⠀⠀⠀⠀⠀⠃⠄⠀⠀⠀⠀⠀⠀⠘⡇⠀⠙⢷⠂⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⠖⠠⠶⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⡠⠀⠀⠸⠄⡰⣷⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⢀⢳⡀⠀⠀⠸⠇⠀⠀⢀⣠⠋⠀⠀⠀⢠⣦⠀⠂⠌⠁
⠀⠀⠀⠀⡠⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⡐⠃⠀⠁⠀⡀⠀⡆⠀⠀⡞⠁⠀⠀⠀⠈⠀⠀⠀⠀⢠⢀⣰⣦
⠀⠀⠀⢠⠀⠀⠀⠀⢰⠃⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠡⢦⣴⡄
⠀⠀⠀⡼⠑⠁⠀⠀⠀⠀⡇⢀⠀⠀⠀⣄⠀⠀⠀⣸⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⡀⠀⠁⠏⣡⠄
⠀⠀⠀⡃⠀⠀⠀⡀⢰⡆⡁⠘⠀⠀⠇⠈⠀⠀⠀⡇⠀⠀⣼⠀⠀⠀⣀⡀⠀⠀⠀⠀⠰⣬⡃⠀⠀⠠⢄⡴⠇
⠀⠀⠀⡂⠀⠀⠀⢰⣾⣿⢁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡏⠀⠀⠀⢿⣿⡧⣀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠁⠀⠀⠀⠀⢿⣿⡎⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢠⠁⠀⠀⠀⠀⢛⡹⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠁⠀⠀⠀⢄⡀⠀⠀⠀⠀⢰⠈⠀⠀⠀⠀⢀⠀⠑⠊⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢀⣤⠤⣾⠁⠁⠀⠀⠀⢸⠄⡀⠈⠀⠀⠈⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡹⢼⡿⣿⣖⠀⠀⠀⢸⠁⡄⠀⠀⠀⠀⢾⡱⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡞⢣⠈⣤⡄⡟⣡⠀⠀⢸⡆⠀⠀⠀⠀⠁⠈⠉⢉⠀⢰⡆⠐⡁
⠀⠀⠀⠀⠘⠆⠀⠉⠀⠀⠀⠀⢄⡈⢳⠶⠛⢉⠀⠀⠀⣿⠀⠀⠀⢀⣠⣀⠀⠀⢸⠈⠋⠈⠉⠛⠢
⠀⠀⠀⠐⠂⠠⠀⠀⠀⠀⠀⠀⠘⠉⠚⢖⠷⢠⠄⠀⠀⡏⠀⠀⣪⣿⣿⠁⢈⠶⡏⡆⠀⠀⠀⢀⡀
⠀⠀⠁⠀⠀⠀⡀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠳⠗⠀⠀⠀⠁⠀⠈⣴⣟⠃⠀⠁⠀⠀⠁⠀⠀⠀⠘⠛⠁
⠀⠀⠀⠀⠒⠀⢄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢹⠃⠀⠀⠀⠀⠀⠀⢠⡅⠤⠀⡄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣤⣤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣷⣒⣿⣭⣭⣭⣭⣭⣭⣭⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁⠰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠁⠄⣀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⣀⢄⠀⠀⠈⢀⠠⠐⠈⠀⠀⠈⠀⠉⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠁⠈⡗⠉⠉⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⢠⠄⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠢⠧⣀⣀⠜⠲⣤⠖⠛⠓⢦⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⢇⠀⠀⠀⢨⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠤⢵⣊⠈⢉⠛⠑⠒⢤⡀⠀⠀⡀⡠⠄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠁⠰⠀⠀⠀⠀⠇⠐⠐⠁
⠀⠀⠀⠀⠀⢤⢠⠀⠀⠀⠀⠀⢀⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⢀⠠⠀⠠⠔⠁
⠀⠀⠀⠀⢀⠚⠘⠀⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⡄⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⠀⠀⠀⢀⠗⡀⠀⠀⠈⠃⠀⠒⢦⡔⠒⣶⣶⣾⣿⠿⠿⣿⡇⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠋⢸⡔⠁⠀⠑⠀⠀⠀⢀⠀⠀⠈⢿⣿⣿⡟⠉⠉⠀⠀⠜⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⢰⠀⠄⠀⠀⠐⠀⠀⠀⠢⡀⠀⠸⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠔⠓⠒⠀⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⢀⣀⡀⠀⠀⠈⠂⡤⠀⣀⣀⡀⠀⠀⠀⠐⠈⠀⠀⠀⡀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠖⠤⢱⠄⠁⠀⠀⠀⠀⠀⠂⠈⠩⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⣆⠀⠈⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠂⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠠⠉⡀⠀⠀⠀⠀⡀⠀⠀⠀⡆⠀⢂⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠉⠀⠈⠢⡀⠀⠤⠂⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣷⣤⡀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠉⠂⠀⠀⠀⢀⣀⣀⣤⣄⣀⣀⣬⣤
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⢠⡴⠿⠟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠉⠉⠉⠙⢿
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⣈⠁
⣶⣶⠶⠶⠶⢶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣴⣦⣶⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⢶⡾⠟⠀⠀⢸⣟⡛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣦⣀⠀⠀⠀⢸⣧⠀⠀⠀⣾⣿⣯⡀⠀⠀⠀⠀⢰⡿⠛⠷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠿⠷⠀⠀⠈⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠘⠿⣶⠄⠀⢀⣴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣦⡀⠀⠀⠛⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠻⣶⡾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣟⠃⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠀⠀⢀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠀⢀⣀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⣤⡀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢃⠠⠃⡈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⣿⡿
⠀⠀⠀⠀⠀⠀⠈⠻⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠂⠄⠁⢡⠈⠀⡀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠺⠃⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠤⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠘⡆⢀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢾⣿⠃
⠀⠀⠀⠶⣦⣄⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠀⠀⠈⠀⠠⠃⠀⢤⡂⡀⢱⠈⢡⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣼⣿⡶⠟
⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠘⣄⠈⠢⠀⠀⠰⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⣤⠀⠀⣀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠉⠀⡄⠀⠀⠐⢂⠈⠁⠀⠀⠀⠀⠀⠀⢠⡶⠷⢶⣄
⠀⠐⣿⣀⣠⡿⠀⠀⢀⠀⡇⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠺⠇⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⣾⢠⡿
⠀⠀⠈⠛⠋⠁⠀⠀⠀⠉⢅⠸⡀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠉⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢰⠤⠁⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⡆
⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⠛⠻⠇
⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⡡⡀
⠀⠀⣿⠸⣿⠙⡷⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠻⢶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠁
⠀⠀⠀⠀⢀⣴⠶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠸⣿⡀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣥⡶⣦
⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡈⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡄⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡛⠻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢀⣤⠀⠀⣀⡀⠀⣀⡀⠀⠀⠀⡀⠀⠀⠀⠀⣴⡿⠻⣶⡀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⣴⡾⠃⠀⠀⠙⠛⣿⠛⠃⠀⠀⠀⣿⡀⠀⠀⠀⠹⣧⣤⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠋⠻⡄⠀⣠⠴⠂⢲⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠟⠁⠀⠀⠀⠀⣿⠟⠁⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡁⠀⠀⠀⠀⠴⣾⠁⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⡴⡿⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⠀⠀⠹⡆⠀⠀⠀⢀⡀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⣼⢃⡴⠚⠙⠲⣤⡀⣾⡟⠀⠀⠀⠀⠀⠹⣆⠀⠚⠉⡉⠈⠁⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠀⠀⠀⠀⠈⠙⢯⡿⢦⡀⠀⠀⠀⠀⠙⢧⡀⡿⠙⡟⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣏⣿⡄⠀⠀⠀⢀⣀⣭⡇⢀⡇⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠶⠦⢤⣽⣷⣿⠤⠖⠚⠉⠉⠀⠙⠛⠓⠞⠷⢤⣤⣤⣤⣄⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠴⠶⠶⠶⢦⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠛⠛⠛⠛⠲⠶⠦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠷⢦⣤⣤⣤⣤⣤⣤⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣄⣀⠀⠀⠄⢀⡀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠛⠻⠶⢾⣷⣤⣬⣵⣤⣤⣵⡶⠶⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⡀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠃⣙⢦⡀⠀⣠⡟⠀⠀⠶⠖⣻⣿⠟⠓⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠘⠁⣿⠂⢙⡾⠋⠀⠀⣠⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⣿⡶⠟⠁⣠⡴⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⣾⠀⠀⠸⣧⠶⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⣿⣄⣤⠶⡿⢲⣤⣿⡄⠀⠀⠀⠀⠀⠀⠀⠰⣎⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⣽⣷⣭⡙⢲⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣠⠀⣈⡝⢿⡀⠙⢿⡈⣿⡄⠀⠀⠀⠀⠀⠀⠀⢰⡿⣇⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣄⣠⣶⣶⠾⠷⠿⠿⣷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⡯⠀⣿⠷⢼⡇⢰⠜⠃⡇⢻⡀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣷⣄⢹⣦⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠠⣾⣥⣤⣤⣤⡴⠛⣻⣶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⢳⠀⠸⡇⠈⡇⢸⠀⢸⡿⣾⡁⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⠙⢷⣜⣧⡀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⡇⠀⢷⠀⣿⢸⠇⢸⣇⣿⢷⡀⠀⠀⠀⠀⠀⠀⠀⣟⠳⠦⣄⡈⠻⣷⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢿⠀⠸⡇⢸⡿⠀⠈⣿⢹⣆⣿⣤⢴⣶⡤⠶⣶⣆⢹⣷⠤⢀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⠛⠋⠛⠉⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢠⣤⢿⡀⠀⠸⡇⠀⣿⣸⣧⣤⠶⠛⠉⠉⠀⠀⢰⣿⠀⠀⣿⡽⠦⠿⠄⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠛⠶⠖⠲⣾⠉
⠀⠀⠀⠀⠀⠀⠀⠈⣇⠈⠃⠀⠀⢿⡤⠼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⣀⢹⡗⣶⠶⢆⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣒⣚⠛⠛⠛⠛⠛⣦
⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠈⣧⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣉⡚⣣⡇⠀⢠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠈⠙⠓⠶⠶⠞⠁
⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠸⣿⡃⠀⣀⣀⣀⣀⣀⣀⣀⡀⢸⣿⡟⠉⠉⠁⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⣿⡏⠙⣿⠉⢻⣏⣉⣠⡤⠶⠚⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⣀⠀⠀⠀⠀⢀⣀⣤⠾⠃⠀⢿⣆⣠⣿⠀⠘⣏⠉⠀⠀⠀⠀⣿⣤⠤⠤⠴⠶⠶⠶⠖⠚⠛⠛⠛
⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⢸⡇⠁⣿⠀⠀⣿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⣿
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠙⠓⠶⠶⠂⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠸⣧⣤⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⣤⠤⣤⠼⠟
⠀⠀⠀⠀⠀⠀⢸⡇⠈⠉⠉⠉⠉⠉⠛⢛⣻⣿⣿⣿⠿⠧⠤⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠒⠒⠂⣉⡿⠋⠀⣮⠈⠛⠓⠶⠶⢠⡿
⠀⠀⠀⠀⠀⠀⣾⡀⠀⠀⠀⠀⠤⠚⠁⠀⠀⠀⣿⠀⠀⠀⠀⢀⡾⠁
⢀⣀⣀⣤⣤⣤⣿⣦⣀⣀⠀⠀⠀⠀⠀⢀⣀⣠⣿⣀⣤⠴⠶⢿⡷⠻⠛⠒⠒⢠⡄
⠻⣤⣀⣀⣈⠹⣦⣹⣯⣭⡿⠿⠛⠛⠋⠉⠁⠀⠀⠉⠉⠐⠶⠾⠶⠧⠶⠶⠾⠋⠁

⠀⠀⠀⠀⠖⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠐⠀⠂⡀⠂⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⡄⠄⠀⡼⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⡀⠀⠸⠄⠀⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢣⡀⠈
⠀⠀⠀⠠⠀⠐⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠚⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠹
⠀⢀⠀⠀⠀⠁⠁⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⠒⠀⠀⠈⢀
⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠆⢱⠀⠀⠀⣀⡴⡄⠠⠀⣀⠤⣀⠀⢀⠀⠀⠀⡀⠀⢀⡀⡀⡀⠀⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠄⠀⠘⠀⠀⠀⠃⠈⠀⡘⠀⠀⠀⠀⠉⣤⢺⠁⠀⣸⠁⢨⠥⠀⣠⠃⡇⢸⠈⠩⡍⠀⠀⢹⠀⠀⠀⡆⠀⠞
⠀⠐⠒⠂⠈⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠘⠉⠐⠃⠐⠚⠀⠋⠐⠁⠁⠚⠁⠒⠃⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠂⠀⠈⠙⠋⠀⠿⠧⠽⠟⠟⠿⠉⠿⠯⠤⠤⠷⠾⠾⠿⠀⠈⠁⠀⢖⠀⢆⠀⠲⠀⠠⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠆⠀⠀⠀⡀
⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠴⠆⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠀⠀⡠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡇⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⢄⡀⠀⠀⠀⠀⠀⠀⠐⠀⠐⠀⠀⠊⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠆⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⡀⢀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡰⣠⠔⠠⠉⣀⣸⣷⣶⣶⣶⣶⠀⠀⢨⡄⠐⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡉⢟⠉⠐⡀⢠⣾⡿⠟⠋⠙⠛⠿⠋⠀⠀⢿⣿⣟⠂⠀⠈⠲⢄
⠀⠀⠀⠀⠀⠀⠠⢊⡈⠀⣒⠀⢀⣼⠟⠁⠀⠀⠀⠀⠀⠄⡰⢀⠠⠿⣿⣧⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠰⠣⠉⠉⠀⠁⠂⠸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠋⠀⠀⠀⠀⠀⠈⠧⡀
⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣷⢴⡡⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⢀⣸⣿⣿⣿⣿⣿⡤⢹⡀
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⠈⠉⠉⠀⠀⠀⡅
⠀⠀⢠⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⢸⡀⠀⠀⢰⣿⡏⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠈⡧⡀⠀⠸⣿⡧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⢣⢹⣦⣄⣠⣄⡘⠒⠛⠒⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣦⣄⣈⣉⡸⠁
⠀⠀⠀⠈⡎⢿⣿⠿⠟⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣰⣿⣿⣿⣿⣿⣿⡇⢠⠃
⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⣄⣀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢠⠃
⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣾⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠉⠆⣠⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠄⠂⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⡐⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣉⣉⣉⡙⣁⠀⢈⠨⠀⡁⠀⠑⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠄⠀⠀⠐⠂⠈⠀⠀⠈⠒⠴⠐⠁

⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⣀⣀⡀⡀⡠⡀⣀⢀⢀⢀⡀⣀⡀⡀⡀⣀⢀⢀⢀⠀⣀⡀⣀⣀
⠀⠀⢀⠴⠋⠁⠀⠀⠈⠙⠢⡀⠛⠁⠋⠋⠃⠋⠃⠘⠘⠑⠙⠘⠀⠋⠃⠃⠘⠙⠘⠁⠊⠓⠓⠙
⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠒⣷⡆
⠀⢸⠀⠀⠀⠢⢆⠶⠶⠀⠀⠀⡧⠀⠓⠋⠓⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠲⠒⠖⠒⠒⡸⣰⣿⠿
⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠖⠒⠶⠒⢲⡖⠆⠀⠀⠀⢠⣀⢤⡀⠀⢀⠤⠤⣄⡀⡨⣾⡿⠋
⠀⠀⠘⢦⣀⠀⠀⠀⠀⢀⡴⣏⣙⠚⡆⠀⠀⠀⠀⠀⠀⣴⡿⢿⢷⠋⠁⣰⡗⠒⠒⠦⢝⣻⣿⣇⡀
⠀⠀⠀⠀⠈⠉⠛⠛⡏⢹⠄⠀⠀⡇⢡⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⣠⣾⡁⠈⠉⠓⠒⠲⠒⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠮⣉⠒⠤⣀⣳⢚⡤⣖⣦⣄⠀⠀⠀⠀⢸⠸⣿⠁⠙⣦⣎⡙⠢⡀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠃⣡⡿⣭⠤⠴⠋⠉⠛⠶⣄⣸⠰⠋⢠⠋⠛⠏⠀⢀⣿⠀⠀⠀⣉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣴⣇⠤⠤⡖⠀⠀⠀⠹⡿⠀⠀⠈⢦⣀⣀⠤⠊⢬⢍⣭⣯⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠈⠣⣤⢌⠑⢄⠀⠀⢱⠀⡇⠀⠀⠀⠀⠤⠤⠤⠤⠄⠤⠠⠤⡤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢠⣤⢤⢄⢄⠤⠁⡸⢀⠜⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⣠⣒⠛⠂⠁⠀⠀⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠉⠈⠉⠉⠀⠀⠀⢀⣀⠄⣸⠀⣧⣀⣀⠀⠀⣀⡀⠀⣀⡀
⠠⠤⠖⠒⠒⠚⠉⠉⠑⠒⠉⠉⠒⠒⠤⠤⠤⠖⠒⠋⠉⠀⠀⢸⠀⡇⠀⠈⠉⠉⠁⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣠⠜⠀⣱⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠖⠲⠓⠖⠲⠶⠶⠶⣿⢉⡖⣶⡮⠊⠹⢠⡇⠉⠛⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⢠⡀⢴⣲⠠⡲⣈⡉⡉⡛⠿⢀⣤⣚⠀⣣⣤⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⡤⠬⢍⠁⢠⡲⠀⡤⡀⠑⡅⢈⣤⡞⢽⣀⣸⣰⠁⢸⡟⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⣤⢒⡄⠔⠆⠰⠰⢀⡛⠉⠈⢼⡷⢾⣿⠇⠈⠀⠟⠉⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣀⣉⣁⣈⣉⣁⣙⣙⣋⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣷⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡿⣿⡿⠟⠉⢿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠛⠟⠛⠁⠻⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠋⠁⣀⡀⠀⠀⠀⠀⠙⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠋⠀⢀⡀⠀⠀⣐⠈⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⠀⠀⣰⡆⠀⠀⢀⣌⠀⢨⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠃⠀⠘⠛⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠁⠀⠀⠈⠋⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⠀⠀⠀⠀⢀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣆⡀⠀⠀⠀⠀⠀⠀⣴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⠗⠀⠀⢾⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣦⠀⠀⢠⣶⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣇⠀⠀⠀⢀⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⣿⣇⠀⠀⠈⣿⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣆⠀⣾⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠹⠿⣷⣄⣾⠿⠂⠈⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠤⣤⢰⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠿⠀⣼⡆⣹⡟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⢠⡀⠀⣀
⠀⢠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠁⢘⣿⣿⣿⣿⣿⣿⣿⡟⠿⢶⣿⠃⠀⣿
⣠⣿⣿⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣇
⠋⠉⠉⠀⠘⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠟⠃⠀⠀⠻⠇

⠀⣠⣤⣤⡀
⠀⠹⠿⠟⠃⠀⠀⣀⠀⠀⢰⠄⣤⣠⣤⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠋⠋⠂
⠀⠀⠀⠀⠀⠀⢸⢿⡇⠀⡀⠴⠻⣿⣟⢻⡆⠀⠀⠀⠈⡀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢠⣾⢲⡿⠳⡾⠿⠁⠀⠀⠀⠁⠀⠀⠀⠀⢱⡞⠂⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠉⠀⠈⢀⡢⠴⠂⠀⢀⣀⡀⠀⢀⠀⠀⠀⠸⠇⠀⠀⢀⡋⣀⠀⠀⠍
⠀⠀⠀⠃⠀⠀⠀⠀⠢⢠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠚⠃⣀⠙⡀⠀⠀⠀⠀⠀⠀⠁⠐⠛⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⡀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠐⢜⡏⡍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠢⠈⠁⢥⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⣾⣶⠟⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠐⠸⠃⢾⡘⠌⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠗⠺⠤⢢
⠀⠀⠀⠐⠆⠀⠀⠀⢠⡈⢉⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠠⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠄⠉⠀⠀⠀⠀⠋⠈⠀⠀⠀⠄⠀⠀⠀⠀⠀⠺⠀⣄⠀⠀⠀⢢⡇⠈⠓⠀⠀⠠⠖⠀⠀⠀⢀⠀⠀⠀⠀⠒⡀
⠀⠀⠀⠘⢲⠀⠐⠀⠀⠀⠀⠀⠀⡀⠃⠀⠀⠀⠀⠘⠓⠀⠌⠀⠀⠀⠐⠈⠀⠀⠀⠒⠒⠀⠀⠀⠀⠈⠁⠀⠀⠐⠏⣤⡀
⠀⠀⠁⠒

⠀⠀⠀⠀⢸⡁⡇⢸⠤⢼⠀⡎⠉⢱⠀⠹⠁⡜⠁⠑⠀⠪⢌⠀⢣⠞⠀⢷⣐⠇⠈⡏⠀⡧⠤⡇⢸⠠⠀⠢⢌⠀⡇⠸⠌⡀
⣀⠀⣀⠀⠘⠀⠀⠘⠀⠘⠀⠙⠒⠊⠀⠘⠀⠈⠒⠊⠀⠑⠚⠀⠘⠀⠀⠃⠘⠁⠀⠁⠀⠃⠀⠃⠘⠒⠀⠑⠊⠀⠃⠘⠒⠁
⠈⠉⠈⠒⠒⣄⣀
⠉⠉⠑⠒⢤⡀⠈⠦⣤
⠀⠀⠀⠀⠀⠈⠢⡀⠘⢢
⠀⠀⠀⠀⠀⠀⠀⠹⡄⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠺⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠰⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠁⠈⢹⡶⠋⠉⠛⣆
⠀⠀⠀⠀⠀⠀⠀⣰⠃⢠⠞⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠺⣧⣀⣤⠼⠧⣄⡀⣠⣿⣤⣀
⠀⠀⠀⠀⠀⣠⠜⠁⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⢀⡞⠁⠀⠀⠀⠀⠙⣏⠀⠀⠘⡇
⣀⣀⠤⠴⠚⠁⢀⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⠶⢾⠁⠀⠀⠀⠀⠀⠀⢸⣤⣠⡼⠃
⢀⣄⣀⠤⠤⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠸⣇⠀⠀⠀⠀⠀⢀⡾⠀⠈⢳⡄
⠉⠀⠁⠀⠀⠀⠀⠰⡉⠠⠄⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⡾⠋⠓⠦⣤⠤⠶⠻⣦⣀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣂⠈⡻⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⣠⣿⠀⠀⠀⡿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢡⠂⢄⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⢹⡏⠛⠒⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⡌⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠑⣴⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢁⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠶⣃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠔⣡⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣆⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣠⣤⠶⠶⠶⠶⠶⠶⠶⠶⠞⢛⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡀⠈⠛⠷⢦⣤⣀⠀⠀⣼⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⣸⣇⠀⠀⠀⠀⠀⠙⢳⣄⣿⣴⣏⡴⠞⠛⠋⠉⠁⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢀⣼⠙⢧⡀⠀⠀⠙⠳⢦⣹⣿⡿⠋⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡴⠁⠀⠀⠀⠙⢶⣤⣀⣀⣀⠹⣿⠁⠀⠉⠛⠶⠶⠶⠶⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠈⠉⠉⠁⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠛⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡷⠶⠶⠶⠶⠶⠶⠶⢶⣶⣦⣤⣤⣤⣤⣴⣶⠶⠶⠾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢉⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣄⠀⠀⣀⠀⠀⠀⠘⠀⠘⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠬⣁⣒⣉⡦⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠤⠄⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡤⠤⢤⡀⠀⠀⣀⡀⣤⡀⣀⣀⣠⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡧⠤⢷⣀⠉⠁⠀⠠⠄⠀⠀⠀⡎⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡇⠀⢠⢈⡗⢶⠛⠉⠒⠲⣤⣰⠃⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢣⠤⠤⠊⠀⠸⡄⠀⠒⢀⠏⢹⠁⢀⡤⠾⣇⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠑⢄⡙⠶⠚⠉⠑⠒⠉⠀⠈⢛⣡⠔⠉⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⡴⢇⡀⠀⠀⠀⠀⠨⠓⢲⡤⡤⢴⠖⠲⠏⡉⠁⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢒⡏⠦⢈⠓⠢⣀⠔⢩⠀⡄⠉⠀⠏⡔⠁⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠛⠁⠲⡌⠀⠀⠀⠀⢸⢀⠃⠀⠀⡐⢁⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡸⠢⠄⢀⠠⠆⡎⠀⠀⠀⠇⠈⡀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⠔⠁⠀⠀⠀⢰⠘⠀⠀⠀⠀⢠⠔⠉⠂⠀⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⡂⠀⠀⡠⠔⠣⢄⠀⠀⢀⠌⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠂⢤⡕⡀⠀⢀⠗⠐⠁⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢠⠃⠀⠀⢸⠓⠛⠡⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⠇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠸⠀⠘⠂⠀⠀⠀⠀⠆⠒⠉⠘⠄⠀⡎⠀⠀⠀⢑⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠑⠢⠤⢀⢀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⢸⢤⣀⡀⠀⠈⠀⠀⠀⠘⡄⠀⡠⠂⠀⠣⡀⠀⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢰⠀⠀⠄⠀⠠⠍⠒⠒⠂⠀⢻⠀⠀⠈⠉⠒⠒⠂⠤⣴⠁⠌⠀⠀⠀⠀⠈⡀⠰⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠤⠄⠠⠄⠀⠸⠀⠀⠀⠀⢸⠀⠀⠀⠀⠑⠤⠤⠤⠤⠤⠐⠊⠁⠀⢣⠀⠀⠀⠀⡸⠁⠎⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠒⠊⠁⡈⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⡀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣄⠚⠈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⣀⡀⠄
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠉⡁⢀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⢀⠀⠀⠑⠒⠁⢀⠖⡄
⠀⠀⠀⠀⠀⠐⠂⠀⡀⠈⠀⠀⠀⠄⠀⠈⡀⠐⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⡡⠂⠈⠁
⠀⠀⠀⠀⡒⠊⡀⢀⢐⡘⢠⡀⠀⠀⠀⠀⠀⢑⠀⠀⢠⠀⠀⠀⠀⠀⠄⠒⠁⡐
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠂⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⡀⠀⡀⣶⣤⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⠀⠀⠀⡀⠀⠈⠐⠂⠀⠀⠀⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠉⠛⡚⠉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠄⠠⠤⠤⠤⠤⠄⢀⠤⠤⠭
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠎⠰⢀⠘⡀⠈⢀⠀⢈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡄⢁⠀⠐⠃⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢨⠐⠂⠁⠈
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⡠⣀⣀⣀⣤⣀⣀⣤⠀⠀⠀⡁⠀⠀⠀⢀⣤⡤⡀⡀⠐⠂⡀⡀⡀⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⣈⣴⡅⢠⣟⣧⣿⣷⡶⡢⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣥⢩⡿⣯⣿⣿⣳⣯⣧⣾⠿⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠍⠛⣽⢛⡿⣾⣟⡏⣧⡼⣗⠷⠆⠰⡀⠰⢄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠵⠘⡋⣎⠻⣷⡝⣃⢈⠀⠀⠀⠈⠊⠂⠈⠀⠨⠄⡀⠄⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⠀⠐⠁⠁⠀⠐⠀⠀⠤⠵⠁⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠈⠑⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠠⢠⠀⠂⠀⢀⠰⠧
⠀⠀⠀⠀⠀⠀⠀⠐⡸⣀⡰⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⡴⠶⠶⢦⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⠒⠒⠒⠒⠛⠈⠛⠛⠛⠛⠀⠛⠒⠒⠒⠒⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠀⢀⣤⠴⠦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⢰⡏⠀⠀⠀⣬⢻⡄⠠⣤⣤⣤⣤⣤⣤⣤⠄⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⣇⠻⣦⡾⠁⣸⠇⠠⡤⠤⠤⠤⠤⠤⣤⠄⢀⣿⠴⠶⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⠶⢤⡴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠐⠒⠶⢦⣄⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠈⠷⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣴⠞⠛⠛⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⣀⣀⣀⣀⢸⡇⠐⠶⠶⠶⠶⠶⠶⠶⠞⢧⣀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⢧⡀⠀⠀⢀⡼⠁⠐⠶⠶⠶⠶⠶⠶⠶⠆⠀⣿⠁⠒⠒⠛⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠙⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡟⠁⠀⠀⠈⢳⡄⢀⣀⣀⣀⣀⣀⣀⣀⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇⠛⠛⠛⠛⢸⠇⢀⣤⣤⣤⣤⣤⣤⣤⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠙⠦⣤⣤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣽⠧⣶⡄⣶⣠⣶⢄⣶⢰⠆⡖⠂⡗⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠉⠀⠉⠀⠉⠈⠉⠈⠀⠉⠁⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡇
⠀⠀⠀⠀⠀⠀⣠⠈
⠀⠀⠀⠀⠠⡄⣿⠘⠃⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢠⢰⣀⠀⣀
⠀⠀⠀⠀⠰⠀⠘⠀⠂⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⡏⣸⢋⡄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡜⠛⡖⠠⢀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠶⣼⡿⠟⠁⣠⠉⠆⠀⠀⠀⠀⡇⠀⡀⠀⢀⢀⣷⣙⣤⠔⠙⠀⢹⡿⢋
⠀⠀⠀⠀⠀⠀⠀⢀⣁⠀⠀⠀⠀⣴⡻⠏⠓⠼⡟⠉⠤⠈⢃⣀⠀⠀⢠⣿⠀⠀⠀⠀⠀⢀⡆⣸⠃⠀⠀⢀⣧⣉⣁⡀⢮⣧⣞⡈⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠸⣤⠠⡀⠛⠁⠁⠀⠲⣷⠇⠘⠓⠤⣼⠀⠀⡆⠀⠀⠀⠀⠀⠀⠛⠡⠃⠀⠀⠈⠻⠏⠄⠀⠀⣾⢋⣉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠼⠋⣹⣶⠀⣀⣁⣤⡀⠃⢸⠀⠁⠐⠦⣸⠀⠘⠀⠀⠀⣠⠒⡆⠀⠀⠀⠀⠀⢤⠄⠀⢀⡸⠃⡼⢿⣸⣏⣀⡀
⠀⠀⢀⠀⠀⡀⢠⡴⠀⣸⡏⠀⠀⢹⣿⣿⣭⠀⠈⢠⢀⠀⠀⠀⠀⠀⠀⠀⠖⠀⢀⡇⢼⣵⣄⣶⡆⢼⣳⠀⠊⠀⣼⠁⣤⣭⣿⣿⣥
⠀⠀⠠⠟⠻⣇⠈⠀⢁⢶⡐⣶⠆⣰⣿⠏⠐⠀⢠⡇⠈⢧⡀⠄⠀⠀⠀⠸⠆⠀⣻⣷⣾⣿⣿⣿⣦⡀⠼⠙⠇⡞⠁⣠⡍⢙⣿⣿⡿
⠀⠀⠀⠀⠀⠙⣠⣶⠏⡸⠃⢈⡿⢿⠟⠂⠐⠦⢸⠀⠀⠀⢷⠀⣤⡄⠀⠈⣀⠈⢁⣿⣿⣿⣏⣿⣿⣿⡄⠀⣴⣳⡴⠛⠀⠀⣼⠄⠊
⠀⡃⠰⠀⠀⠀⣿⣇⠀⠋⠀⠀⠘⣚⣀⠈⣄⣴⣿⣀⠀⣶⣶⠖⠛⢳⣧⢀⡈⣰⣿⣿⣿⣿⡎⢡⣟⠏⢷⣼⣯⣏⠀⢈⠁⣀⣴⣾⡇
⠀⠀⣶⡗⣤⣈⣀⣿⠊⣱⣤⠐⢛⡟⠻⢿⣿⣾⣿⠀⠁⠀⢸⣷⠼⢸⣿⡀⠉⢹⡷⡉⠿⠋⢻⡿⠂⢀⡼⣫⣿⢯⣾⣿⣿⣿⣯⣤⣷
⠀⠀⠉⠏⡎⠈⣽⡿⠱⣿⡏⢠⣿⠇⠀⠀⠸⡄⢻⠀⠀⠀⠀⡥⠖⡩⠹⠟⠀⠠⠀⠀⠀⠀⠘⠁⠀⢊⡾⠿⣿⣿⣿⣿⣿⣿⣷⣾⣃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢿⡦⢀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡤⢸⠀⠴⣾⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠙⣿⠀⢸⠀⠀⡼⠋⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠆⠀⣿⡀⢸⠀⢠⠃⣸⣾⣿⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡷⣞⠁⠀⠀⠀⠀⠀⠙⠻⣿⡿⠂⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⡀⠀⠀⠠⣿⣦⠾⢃⣤⠜⠃⠀⠀⠀⠀⠀⠀⠠⠈⠁⣿⣧⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠴⠂⠀⠂⢸⡄⢻⠻⠗⠒⠻⠻⣗⣶⣤⢆⡀⠀⠀⠀⠈⠀⠁⠠⣄⠀⠀⠀⠀⠀⡈
⠀⠰⡓⠀⠀⠀⠀⢠⠔⠋⠀⠀⠀⠀⠀⠀⠉⠉⠁⢀⣤⣒⣆⣸⣧⠉⠃⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⠞
⠀⠀⠈⠢⡀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠘⢁⡟⣷⡿⢦⠀⠀⢀⡠⠤⢄⡀⢠⣀⡔⠀⠀⠈⡇
⠀⠀⠀⠀⠈⠎⠀⠀⠀⠀⣶⠀⠀⡀⠀⠀⢀⠀⢥⣉⡤⠭⡀⢸⣧⠅⠠⠔⠀⢱⡉⠀⠈⢆⣹⡆⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠈⠠⡀⠇⠀⣼⠒⠁⠠⣄⡜⢀⣀⠀⢹⠁⠀⠈⠘⣀⠤⠀⠀⠀⠀⢂⠀⠀⠀⠙⢿⡤⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠸⡴⠞⠁⠀⠀⢈⠜⠁⠀⢀⠝⠉⠑⠀⢄⡨⢌⠀⠀⢁⠀⠀⠀⢦⡀⠀⠀⠀⠉⢨
⠀⠀⠀⠀⠀⠀⠀⠰⣄⢀⡀⢀⣠⠏⠀⠀⣠⠏⠀⠀⢠⢤⢄⣀⡈⣦⠀⠀⢣⡀⠀⠀⠙⢶⣤⠤⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⢟⠃⢀⣀⢴⡟⠀⢀⠠⠃⠠⠊⠓⠀⠚⠳⢄⣀⣙⠦⠤⠠⠜⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣁⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣛⣙⣛⣟⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠚⠛⠛⠛⠛⠛⠛⠛⠛⠳⠶⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠛⠉⠁⠀⠀⣄⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠁⠀⠐⢷⣄⠀⠀⠙⢧⡀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠙⠓⠛⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣠⠞⠋⠉⠙⠳⣦⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⢀⣴⠶⠶⠶⠞⠃⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢀⣤⣤⡼⠃⠀⣠⡤⢦⡀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⣇⠀⣠⡞⠛⠉⠀⠀⢻⣄⣤⠀⠹⣆
⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠶⠶⠖⠀⠀⢸⡇⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠹⣆
⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣀⣤⠶⠖⠒⠲⠶⣤⣄⣀⣀⣀⡤⠀⠹⡆
⠀⠀⠀⠀⢀⡿⠀⠀⢀⡾⠛⠳⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⡀⠀⠀⢸⡇⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⢻⡀
⠀⠀⠀⠀⣼⠇⠀⠀⢺⣅⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠉⠁⠀⠀⢸⡇⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⣿⠀⠶⣤⣄⠉⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠈⢷⡀⠘⢧⣄⡀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢸⡷⠶⠶⠦⠀⠀⢸⡇⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⠷⣤⣀⠉⠉⠉⠉⠉⠉⠙⠛⢦⣄⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⢸⣇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠻⢦⣤⣤⠶⠛⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⢸⡟⠉⠉⠉⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠘⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠉⠛⠶⢦⣤⣀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳⡄⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢀⡄⠙⢦⣄⡀⠀⠀⠀⠀⣀⡴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠈⢷⡀⠀⠀⢿⠀⠀⠈⠙⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⠀⠈⠻⢦⣀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣄⡀⠀⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠶⢦⣤⣤⣤⣤⣤⣤⣤⣤⡴⠶⠖⠛⠋⠁

⠀⠀⠀⢰⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠚⣽⡛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢓
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⠄⡀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠂⢄⠰⡇
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠛⠐⠢⠈⠣⣀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠠⠈⠀⠀⠀⠀⡖⢀⠀⡈⠑⠒⠂⠒⠒⠉⠁⠄⠶
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⢁⠀⠀⠞⠈⠀⠀⢠⡄⠂⠀⢀⠚⠢⢀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠀⠀⡏⠀⠀⠈⠃⠈
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠐⠀⠂⢀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠰
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠁⠠⠀⠀⠀⠀⠀⠄⠀⠊⢀⠀⠂
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠀⠀⠘⡀⠐⠂⣀⠒
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠰⠳⠋⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠁⠀⠀⠀⠀⠈⡀⠀⠰⠀⠈⠐⠀⠠⠀⠀⠀⠀⡀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠂⠀⠄⠀⠉⠀⢀⠘⠒⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣀⠰⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⢸⠀⠀⠤⠀⠠⠐⠀⠠⠈⠘⡠⠒⠀⠉⡀⠁⢀⠠⡀⠀⠠⠀⠀⠀⠐⠀⠀⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠠⠀⠈⠀⢀⠀⠄⠠⠀⠂⢠⠀⠀⠒⠈⠀⠒⠂⠀⢀⠣⠀⠀⠀⠀⠰⠀⠀⠀⠀⠠
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠓⠂⠉⠒⠈⠁⠀⠀⠀⠆⠈⠐⠂⠠⠀⠠⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⢀⠀⠀⠀⠀⠀⠠⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠄⠀⡈⠀⠀⠀⠀⣄
⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⣀⠀⠀⡀⢀⢀⠠⢀⢀⣀⣠⠜⠄⡤⣄⡀⠀⠀⠉⠐⠀⠀⠀⠐⠘⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠁
⠀⠀⠀⢸⠁⠄⠁⠉⠡⠀⠀⠈⠀⠀⠂⠈⠀⠀⠀⠐⠒⠄⠠⠒⠚⠃⠀⠁⠈⠑⠉⠀⠁⠀⠠⠤⠦⠀⠈⠉⠉⠈⠀⠡⠈⠂⠉⠛
⠀⠀⠀⢸⠂⠀⠂⠀⠂⠒⠀⠀⠁⠈⠂⠀⠀⠉⠁⠈⠉⠐⠢⠐⠖⠀⡝⠂⠭⠉⠋⡁⠀⢈⢀⠐⠒⡈⠉⢉⡄⠈⠒⠀⠐⠀⠀⢋
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠠⠄⡀⠀⠀⠀⠈⠀⠀⠀⠀⠈⣀⠀⢀⠀⠁⠀⣀⠀⡂⠀⡠⠁⠀⢀⠀⠄⢄⢈⠀⠀⠀⠘
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⢀⡠⠃⠀⢰⠀⠀⠈⠀⠱⡀⠈⡄⠀⢄⠀⡔
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠢⠀⠨⠀⠈⠄⠈⢓⣀⠀⠐⠀⠀⠀⠀⠀⠈⠁⠁
⠀⠀⠀⢸⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⢸
⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⢀⠀⠀⠀⣀⡀
⠀⠀⠀⢘⡁⢈⠀⢀⠒⠀⠀⠄⠀⠀⠀⠀⣠⣾⣽⣿⣷⣤⣀⠀⢻⡏⠀⣄⢿⠆⠈⢐⣘⣓⡀⠐⠀⢸⣟⠛⣦
⠀⠀⠀⠈⠀⠜⠀⣤⢢⢤⠐⠀⠃⠈⠀⠀⣿⣿⣿⣿⣿⣷⣿⣷⣤⡀⠠⢤⣷⠀⠡⣉⠧⠹⠟⡀⠀⠀⢻⣶⡿
⠀⠀⠀⠀⠀⠀⢠⣟⡞⢖⠣⢯⡃⠀⠀⡀⠈⠻⣿⣽⣯⣴⣺⣭⣿⣿⣷⠀⠀⠀⢀⢻⣀⠀⡴⢹⣯
⠀⠀⠀⠀⠀⠀⠒⠻⢿⣿⣾⢧⡄⢠⠀⢷⣤⣶⠠⢍⣉⠛⠻⣷⣿⣿⡿⠁⠀⠀⢹⠛⠉⣘⢒⢺⣿
⠀⠀⠀⠀⠀⠀⠨⠑⢿⣤⡼⣧⢂⠁⠀⠈⠳⠥⣄⣀⡐⡱⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⡴⠏⢈⢉⣿⠀⠀⠀⣀⣀
⠀⠀⠀⡀⠐⢆⠀⠙⠂⠉⠀⠈⠁⠀⢀⣀⣠⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡶⢾⣿⣧⣹⡄⠀⢀⡿⣿
⠀⠀⠀⠨⠙⣦⡱⢄⠀⣤⡀⠀⠀⠀⣾⠋⣉⠙⡘⣿⠀⠀⠀⠠⢰⠀⡜⠀⠀⠀⠀⠈⢈⢺⣿⣿⢿⣇⠀⢸⣿⡟
⠀⠀⠀⠉⠲⢶⡻⣦⣲⡈⠉⡀⠀⠀⠹⣾⡿⠏⢛⣋⡀⠀⠀⠀⠘⡇⠃⠀⠀⠀⠀⠀⠈⢌⢿⣿⣿⣿⠁⠀⠉
⠀⠀⠀⢀⣠⠤⣬⣷⣽⢛⢷⣶⢯⣖⠀⢠⡶⢿⠘⣿⣿⠆⠀⠀⢀⠘⢶⠀⠀⠀⠀⠀⠀⠀⠑⠝⠛⠡
⠀⠀⠀⠘⠃⡎⣴⠛⠿⢞⣬⠻⣿⣟⣥⠀⢿⣄⣶⠻⠿⠃⠀⠈⠀⠀⢈⠀⣧⡄
⠀⠀⠀⠀⣀⠈⢋⡎⡙⣤⣿⣧⢿⣿⣿⠂⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠘⠐⠛⡁⠀⠀⠀⠀⣡⣶⣶⣶⡅
⠀⠀⠀⢾⡟⣧⠈⠟⡻⡏⠡⠏⠀⠈⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣼⠄⠐⠀⠀⠀⠀⠀⢿⣟⣿⣿⣯
⠀⠀⠀⢸⣇⡿⠀⣏⠋⠋⠀⢀⠴⠄⠒⢂⡁⠠⠀⠀⠀⠀⠀⠀⠀⠀⣨⣅⠀⠀⠀⠀⠀⠈⠀⠿⠾⢿⣿
⠀⠀⠀⠸⠿⠃⠀⠃⠀⠀⠀⡏⠀⠀⠉⣈⠄⠀⠀⠀⠀⠀⠀⠀⣀⠚⠁⠙⢒⢂⠀⠀⠀⠀⠀⢈⢄⡀⣉⠘
⠀⠀⠀⠀⢀⠖⠛⠓⣄⠀⠀⡇⠀⠀⠀⠈⠘⢂⠁⢀⠀⠀⠖⠊⠀⠀⡀⠀⢀⡆⠀⠀⢀⣀⡀⠀⠈⡠⠄
⠀⠀⠀⠀⡎⠀⠐⠂⠀⢑⡀⠈⢀⠀⢀⡀⠘⢅⠃⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣰⣿⣯⠏
⠀⠀⠀⠀⡧⠀⠀⠂⠀⢤⠃⣜⠛⠛⠋⠉⢗⡄⠈⠛⠳⡄⠀⠀⠀⠂⠀⠀⠀⢀⠀⠈⠁⢀⠀⡴⣀⢀⡀
⠀⠀⠀⠀⡀⡇⠀⠰⢄⠎⠀⠯⢦⣿⣿⢶⠆⠀⠀⠀⠀⠈⠀⠀⠀⠖⠉⠳⣄⡈⠛⣲⡾⠗⢂⣞⣛⣋⠁
⠀⠀⠀⠀⡇⠀⠆⠐⣸⠀⣠⣄⣠⣄⠀⠀⠀⠀⣤⣤⢴⢦⡴⢾⠇⣤⣤⡀⠈⠉⠉⢁⡴⠛⠁⠘⢻⠿⠇⣀⡄
⠀⠀⠀⢠⡇⠠⠀⢠⠇⠐⣷⡟⠳⠿⡞⣧⠀⣞⠻⣧⢏⣻⣶⡾⣆⣧⣨⡇⠀⢀⠞⢁⡠⠞⢃⡘⠃⠀⣰⣿⣷
⠀⠀⠀⠀⠑⠾⠖⠁⠀⠈⠫⣿⡛⣶⠟⣯⠀⢿⡴⠏⠾⣾⣏⢳⣽⠎⠉⠀⢠⠋⡀⢸⠀⠀⠈⠥⠄⠀⣿⣿⡿
⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠈⢉⠿⡿⠀⠀⠀⠀⠛⠃⠉⠉⠉⠀⠀⠀⠀⠘⠂⡁⢾⠀⣀⠀⠀⠀⠀⠙⠟⠃
⠀⠀⠀⢀⣴⡜⠻⣿⣀⠀⠀⣤⡀⢶⢶⡟⢻⣀⠀⠀⠄⡀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠲⠌
⠀⠀⠀⢸⣟⡠⢠⡜⠛⠁⠀⠉⢱⡞⢿⣹⣿⣿⠃⠀⠁⠉⡳⠦⢬⣦⣤⡴⠀⠀⢠⠀⠀⠰⠂⡠
⠀⠀⠀⠀⠘⠶⠿⢃⣰⡿⣂⠀⠈⠻⠟⠻⠶⠛⠀⠀⠀⠄⠠⠶⠲⠺⠛⢙⡀⠸⠛⠒⠦⠀⠺⠖⠂
⠀⠀⠀⠀⠀⠀⠸⠟⠃⠙⠛⠀⠀⠀⠀⠀⠀⠐⠤⠎⠁⠀⠀⠀⠀⠀⡖⠁⠀⠀⠀⢠⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⢀⣤⣦⢴⡀⠠⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⡄⠀⢻⣿⣿⣷⠀⠙⠿⢓⣴⣿⠀⠄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠇⢀⡀⠘⣽⢁⠘⢷⣀⣤⣤⣄⣀
⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⡿⣻⣾⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⢀⣀⣀⣄⣀
⠀⠀⠀⠘⠻⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠈⢨⣤⠰⠟⣿⣿⣍⡍⢿⡩⠹⣿⡻⠿⠆⠀⠀⢀⡙⢿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⢦⠀⠈⠻⢿⣿⣿⣷⡄⠀⠀⠀⡼⠀⠀⢀⡰⠙⠛⠷⣶⣽⡶⠤⠒⠀⠀⠀⠀⠈⠹⣶⡙⢿⣿⣿⣿⡄⠠⣶⣤⣤
⠀⠀⠀⠀⠀⠃⡀⠀⠐⡙⢻⣿⣿⡆⠀⠀⡇⠀⠀⡰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢎⡻⣿⣿⡇⠀⡘⠻⣯⣼⠁⡦⡄
⠀⠀⠀⠀⠀⣄⣈⠓⠀⠉⠙⣛⣿⣷⠀⠀⠃⠀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⠃⣰⠃⠀⠙⠙⢿⣿⣤⡆
⠀⠀⠀⠀⠀⢹⣿⣷⣦⡀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠉⠀⠄⠀⠀⠈⢹⣧⢾
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⣤⡀⠀⠀⠹⣆⠀⠀⠀⠀⢀⣀⣤⣤⣤⣠⣇⠐⠁⠀⠀⠀⣠⡄⢀⡄⠀⢀⣀⠀⠈⡶⠁⠀⠀⠀⠀⠘⡻
⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣄⠀⠀⠏⠀⠀⠀⠘⠿⢿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠻⣷⣿⣧⣴⣿⣿⣷⡀⠇⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣷⡀⢀⠀⠀⠀⢠⣀⠀⠈⠉⠻⣿⣿⣷⡛⣝⠆⠀⠀⠈⠀⠹⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⢀⡀⠀⠀⠸⣧⡑⣄⡀⠈⠀⠉⠻⣷⣹⣸⡆⠀⠀⠀⠀⠘⠛⠛⠋⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠿⠋⠈⠓⠆⡠⠀⣀⣠⡛⢧⡿⠀⠀⠀⠀⠀⠀⠃⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⢀⣠⡤⢄⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⢨⣽⢾⡇⠀⠀⠀⠀⠀⡶⡤⠖⠂⠌⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠰⠿⠿⠿⠾⠿⠶⣿⣿⣷⣤⣁⡆⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⡀⠀⣦⣀⢀⢄⡀⠀⠒
⠀⠀⠀⠀⠀⠠⢄⡀⡀⠀⠀⢀⣀⡉⡽⠛⠿⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⢆⣶⣴⣤⣾⡿⠛⠋
⠀⠀⠀⠀⢀⣀⣤⣴⣶⣶⣶⣉⡉⠀⠀⠀⠀⠀⠀⢠⣇⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⡀⠀⢰⠴⣿⣿⣟⡿⠟⠏⠁
⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠈⡄⠀⡀⠀⠀⠀⠀⢻⣆⠀⠁⢰⣎⣸⣿⠿⣉⣀⣀
⠐⢿⡿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀⠀⣰⡆⠘⣿⡿⠂⣠⠀⢴⣟⣿⣷⣴⠏⢁⠟⠟⠓⢂⣤⣬⣀⡀
⠀⠈⣿⣿⡅⢀⡀⠀⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣦⡉⠻⠃⢹⡄⠀⠛⠓⢈⠋⢀⣿⣷⠞⠁⠀⠀⠀⢸⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠈⠻⢟⡄⠀⠀⠀⠀⠒⠋⠀⠀⣙⣛⣻⢿⣿⣷⡀⠤⣌⢳⣆⠀⣤⠀⣠⠞⣁⢹⣆⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠈⠙⠛⠿⠛⠿⠛⠻⠛⠛⠛⠛⠛⠋⠁⠀⠀⠲⣤⣌⣻⣾⣠⣿⡃⠘⠀⠀⠙⠀⠰⠂⠐⢿⡟⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢉⡛⣿⡹⢾⣷⠀⠀⠀⠀⠀⠀⢠⡴⣾⣿⣟⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣽⡧⣬⣿⣿⣶⣶⣶⣤⣀⡀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠈⢰⡆⠘⣆⠉⠻⣿⣿⣿⣿⣿⣧⡀⢀⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⢿⣿⣿⣿⡄⠀⠀⠀⢀⡀⣧⠀⠈⡄⠀⡇⠉⠻⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⡿⠿⢿⡿⢿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⣤⣀⣩⣻⣿⣄⠀⢰⡿⠁⢸⣶⣦⠀⡄⠙⡀⠀⠋⠙⣿⣿⡿⠉⠀⠁⠈⠙⠛⢁⠀⠀⠚⠀⡌⢉⠉⠓
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠈⠘⠣⡄⠀⢠⣼⣟⠛⠳⣄⠀⠑⠀⠀⠀⠈⢻⡇⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣷⣖⣺⣿⣿⣾⡯⢿⣦⠀⠈⠀⠀⢻⣿⣿⣦⣈⢻⣿⣾⣷⣶⣾⣶⣄
⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⠉⠀⡀⢁⠀⠀⠀⠀⠈⠛⡀⢸⡏⠈⠉⠁⠈⢿⣿⣿⡟⢻⣿⣿⡀
⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⢰⣼⠃⠀⠀⠀⠀⠈⠻⢿⣧⠀⠻⣿⠇
⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠘⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠈⠉⠉⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⡤⠶⠶⠖⠒⠒⠀⠀⠀⠀⠀⠀⠒⠦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠚⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠑⠢⢍⣛⠲⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣈⠑⠦⣌⣉⠒⠤⡉⠛⠷⢶⣤⡀⠀⠀⠀⠀⠀⣀⣠⣤⠴⠶⠚⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢌⣑⠢⢭⣑⠢⢍⡙⠒⠤⣀⠀⠀⠈⠙⢷⣄⠐⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠓⠮⣍⣒⠦⢍⣓⠢⠄⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⣠⣭⣷⣦⣌⣁⠐⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣀⣠⣤⣶⣾⣿⣯⣭⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠷⣦⣤⣄⣠⣤⣴⣟⣁⣤⣤⠶⠾⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡿⢻⣿⢿⣿⠻⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⢛⣛⣛⣻⣿⣿⡿⠿⠿⠛⠛⠛⠛⠛⠛⠛⣿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⡜⠘⣯⠉⣿⠶⠶⠶⠶⠶⠶⠿⠛⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠖⠻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠁⠀⠘⢧⣿⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣤⣤⣤⠤⠶⠖⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⡴⢶⡟⣀⣠⣤⣴⣦⣬⣿⣿⣿⣿⣿⣿⣏⣉⣉⣉⣁⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⢀⣤⡶⠟⠛⠉⠁⠀⠀⣼⣿⠏⠉⠀⠀⠀⠀⠂⠠⠤⠤⠤⠤⢤⣭⣉⣉⣉⣉⣉⣉⣛⣛⣛⠛⠛⠛⠷⠶⠶⠶⠶⠶⠶⠶⢶⡾⠿
⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠒⠒⠒⠒⠒⠒⠒⠤⠬⠭⠭⠭⠭⠭⠍⠉⠁⠀⠀⠀⢠⡟⠳⢤⣀
⣼⠃⠀⠀⠀⠉⠑⠢⠄⠀⠀⢿⡇⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣒⡒⠒⠒⠢⠤⠤⠤⠤⢬⣭⣉⣉⣉⣉⣉⠉⠀⠀⠀⠀⠀⢸⠀⠀⠀⠈⠛⠶⣤⣀
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⡀⠄⢀⣀⣀⣀⣀⣈⣉⣉⣉⠉⠉⠉⠉⠉⠉⣛⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢀⣀⣀⣤⣽⡷
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⠶⣦⣤⣭⣭⣭⣭⣽⣿⣿⣿⣿⣷⣶⣶⣶⣶⡦⠄⠤⠄⠀⠀⠀⠉⠁⣀⣀⠀⠀⠙⣟⠛⠋⠉⠉⡟
⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⢤⣀⠀⠀⠀⠀⠉⠉⠉⠉⣉⣉⣩⣭⡿⠿⠟⠛⠛⠛⠛⠛⠒⠶⠶⠾⠿⠛⠀⠀⠀⢸⠃
⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⣤⠞⠛⠉⠁⢀⡀⠤⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⣀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠉⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠄⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠤⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⣀⣀⠤⠀⠄⠀⠀⠀⠀⠀⠀⠐⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⢦⣄⡀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⡤⠴⠶⠶⠒⣛⣉⣉⣤⡤⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣤⣈⡳⣭⣑⠒⠀⠀⠀⠀⠒⠚⢉⣉⣉⣩⣭⣤⡶⠶⠖⠛⠛⠛⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠿⣟⣻⡛⠛⠛⠛⢛⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠛⣃⣽⣶⣈⣿⡟⢀⣤⣶⣟⣿⣿⣿⠟⢋⠉⠹⠛⠛⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠈⠻⠁⢀⣘⣿⣿⣿⣿⣿⣿⣿⡟⠟⠒⠛⠁⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⡟⢃⣤⣴⣤⣀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠉⠁⠙⠛⠛⠛⡃⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⢆⠈⢉⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⣟⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣆⠀⢀⡀⠀⠀⠀⠀⠀⠘⠛⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡏⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣯⣿⣿⣿⡇⠀⠀⠀⠀⣠⣾⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⣰⣿⣾⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣹⠿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⡆⠀⠀⠀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⣼⣿⣴⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⢀⣼⣿⣿⣿⠟⠁⣿⣿⣿⣿⣿⣤⣤⣾⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⠀⣿⣿⣿⣿⡇⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⡏⠹⠇⠀⠀⠀⠀⣿⣿⢹⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣮⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣴⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠙⢧⣄⠀⠀⠀⠀⠀⠀⣠⠞⠉⠙⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠛⠻⣶⣶⠟⠛⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⣻⣿⠀⠀⠈⠙⠋

⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣤⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢧⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢿⣿⡿⠿⠛⢿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠀⠀⠀⣸⣿⣿⡏⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⡀⢀⣴⣶⣆⣀⡘⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡟⢏⣻⠟⢻⡿⡟⠈⡟⠙⢾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠖⠸⡶⠬⠓⠒⠊⠀⠀⠈⣡⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡤⠥⠤⠤⠤⠀⠀⠀⣀⡡⠂
⠀⠀⠀⠀⠀⠀⠀⣴⡶⢆⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠁⠀⠀⠀⠀⢀⡞⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢼⡇⢼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⣶⠶⠶⠋⠀⣧⣀
⠀⠀⠀⠀⠀⠀⠠⠤⢀⡘⠷⠆⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⢷⡝⣆
⠀⠀⠀⠀⠀⠀⣈⠒⣨⡗⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿⡿⠃⠀⠀⠀⢈⠃⠙⢦⡀
⠀⠀⠀⠀⠀⣰⣾⣿⠍⠁⠀⠏⠉⣢⡀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡾⠀⣿⡧⠀⡀⢀⣺⠃⠀⠀⠄⠙⠲⠴⠦⣄
⠀⠀⠀⠀⢰⣿⡿⠿⠚⠛⠛⠛⣖⣿⡇⠀⠀⠀⠀⠀⡰⠋⠈⣿⡿⠃⢸⡇⠀⠀⡽⠃⠚⠖⠚⠋⠀⠀⠔⠀⠈⠳⢤
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⡿⣻⣿⡯⠁⠀⠀⠀⢀⡞⠁⠀⠀⢌⠀⠀⠈⡇⢀⠜⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠈⠳⣤⡀
⠀⠀⠀⠀⠀⠈⢻⣽⣿⣯⣽⡿⠉⢳⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣷⠈⠉⠁⠀⠀⠈⠇⠀⣠⠏⠀⠀⠐⣆⠀⠀⠈⠀⢀⡏⠀⠀⢀⠀⣰⠀⢀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠘⠯⢉⠀⠀⠀⢀⣿⠀⠀⠀⠀⣼⠁⠀⠀⠈⠀⡟⢠⢳⡄⢿⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣧⣿⡇⠀⠀⠀⣻⠀⠀⢰⠤⠤⠧⠤⠸⠇⢠⡙⣿⣿⠷⠦⣄⡀⠀⠀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⠀⠀⠀⢀⡀⠀⠀⢠⣶⣿⠟⢹⡇⠀⠀⠀⢹⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠇⠈⡟⠀⠀⠈⠙⣶⠤⠀⢀⡀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣴⣶⣄⣡⣤⣾⣴⡿⠛⠁⠀⢸⣧⠀⠀⠀⢸⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⣸⠁⠀⠀⠀⠀⢹⣾⠶⢤⣀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⠿⠟⠛⠉⠀⠀⠀⠀⠸⣇⠠⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢀⡾⠁⠉⠁⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⢠⡟⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⢠⡟⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣠⠏⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠉⢠⠄⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠨⠴⠾⠛⢉⠀⠀⠀⠀⠀⠀⠾⠶⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠈⠀⣀⣠⠤⠤⢶
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠛⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿