Snowmen Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠊⠉⠉⠉⠉⠉⠉⠉⠉⠐⠒⠒⠢⢤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠂⠠⠤⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠲⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⠒⠈⠉⠙⣄⠀⠀⠀⠀⠈⠉⠀⠒⠒⠀⠀⠠⠤⠤⠤⠤⠤⠄⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠘⠂⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⣦⣤⣀⡀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠒⠒⠒⠂⠒⠒⠒⠒⠈⠀⠀⠈⠑⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠈⠉⠛⠂⠤⠤⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⣠⠒⠒⢄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠐⠒⠂⠀⠉⠉⢻⡅
⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠐⣁⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⡴⠂⠀⠲⡄⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠒⠂⢁⠀⠀⠀⡀⠀⠀⠀⢦⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡠⠤⠐⠂⠈⠉⠀⠀⠀⠉⠢⡀⠀⠀⠁⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠉⠲⠄⣄⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⡔⠒⢠⠈⠉⠐⠒⠒⠊⠁⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠁⠶⠈⣀⢀⡀⠀⠀⠀⠀⠀⣀⣄⠀⠇⢀⠅⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠇⠀⠄⠠⠉⢙⡂⠀⢀⣈⠅⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⢀⠴⠚⢙⣤⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠦⣀
⠀⠀⠀⠀⠀⠀⢠⠃⢀⡴⠁⢀⡽⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠺⣅⠈⠱⡀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⣈⢀⠎⠀⢀⠎⠀⠀⡜⠉⠁⡛⠂⠀⠦⠴⡄⠀⠚⠛⠉⠉⠀⠀⠀⠈⣦⠀⠘⢆⠀⠹⠄
⠀⠀⠀⠀⣠⠞⠉⠮⡀⠀⡎⠀⠀⢰⠁⠀⠰⡇⠀⠀⣾⠀⢣⣀⣀⠀⢤⡤⠀⠒⠊⠉⠈⡆⠀⠈⡄⡰⠳⣄
⠀⠀⠀⡴⠁⠀⠀⠀⠈⠚⠧⣀⢀⡈⠀⠀⠀⠀⠀⠀⢿⠀⠈⣍⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠴⠋⠀⠀⠈⢦
⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⣬⡀⢀⡀⣘⡀⠀⢩⡄⠀⠀⠀⢤⠄⠒⠒⠉⠁⣧⠀⠀⠀⠀⠀⠈⢧
⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⢌⠉⠉⠉⠁⠈⢉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠀⠈⣧
⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠈⡆⠀⠀⠀⠀⢹⡄⢀⣤⠄⠀⠒⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘
⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠚⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠠⠴⠒⠀⠉⠈⢱
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠀⠙⡄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣨⡄
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠷⠶⠶⠦⠄⠂⠈⠋⠁⠀⠀⢡
⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡆
⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣴⠤⠶⠔⠞⠛⠛⠉⣉⢏⠴⠄⠀⠀⠀⣠
⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⠾⠶⠈⠓⠋⠁⠉⠈⠀⠀⠀⠀⢠⡏
⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏
⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠖⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠈⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠸⠀⣀⠢⠀⠀⠀⠀⠀⠐⠂⠠⠄⠀⠀⡄⠤⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡈⠀⠀⠀⠀⠈⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠛⠀⡠⢘⣁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⢀⠔⠉⠈⠁⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⣀⠀⠀⠌⠈⡵⠂⠰⡀⠀⠀⠀⠀⠀⠄⠠⢲
⠀⢌⠀⠀⠀⠀⠀⠓⠉⡇⠀⠂⠀⠀⠈⠂⢀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠄⠀⠀⠠⡀⠀⠀⠀⠀⠀⢀⠂
⠀⠘⢄⠀⠀⠀⠀⠀⣪⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⡀⠀⠀⠀⠀⠈⠙⠦⠲⠴⠂⠁
⠀⠀⠀⠑⢦⣀⠔⠈⠀⠠⡀⠀⠈⠆⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠡⠀⠀⠀⠀⠀⠀⠈⠒⠂
⠀⠀⠀⠀⠀⠱⠀⠀⠀⠀⠀⠐⢤⡄⠀⠘⠀⠀⠒⡆⠀⠀⢉⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⢀⠔⠁⠀⠁⠒⠀⠀⠀⠤⠄⠐⠂⠀⠀⠀⢀⠙⢇⠒⠠⢤⠶⠷⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠑⡀⢠⠂⠀⠀⠀⠀⠀⠀⠀⠀⣶⠄⠀⠂⠀⠀⠀⠈⡄⠈⢆⠀⠆⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢰⠒⡂⠒⢈⠁⠀⠈⡀⢃⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠉⠐⠂⠀⠀⡀
⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠀⠣⣀⣀⣀⣀⣀⡀⢀⠤⠔⠒⠒⠒⠒⠒⠢⠶⠅⢀⠀⠀⠀⠠⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠉⠁⠀⠀⠀⠀⠈⠉⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠒⠋⠉⠉⠀⠀⠀⠀⠀⠀⠈⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⡀⢡⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⢣⠈⠀⠀⢁⣀⣀⠤⠤⠔⠒⠒⠒⠒⠚⠋⠉⠛⠛⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡈⠂⣀⡤⠔⠒⠉⠁⠀⠀⠀⠀⠀⠀⡀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠓⠉⠀⠀⠀⣀⡠⠤⠤⠒⠒⠉⠉⠉⠉⠀⢀⠀⠀⠘⡅⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣠⠴⠚⠉⠁⠀⢛⠀⠀⠀⠀⠀⠀⠀⠀⣉⠀⠀⠀⠘⡤⠖⠉
⠀⠀⠀⠀⠀⢠⡇⠀⠠⠖⡏⠀⠀⠀⠀⠀⠀⠻⠇⠀⠀⠐⠀⠀⠀⠜⠷⠂⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠳⢤⣀⣀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢴⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⢦⣉⠉⠑⠒⠒⠒⠒⠒⠋⢁⣤⠞⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠈⢙⡖⡲⡶⠒⠒⠒⠋⠁⠀⢳⡀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⡀⢀⡎⢰⠏⡇⠀⠀⠀⠀⠀⠀⠀⢣⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⡇⡼⠀⢼⡀⢸⡀⠀⠀⠀⠀⠀⠀⠘⡆⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⣀⡴⠁⣏⡀⣸⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⡷⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠊⠉⠉⠲⡄⠀⠀⠀⣀⡞⠉⠈⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣤⣀⣀⣠⠞⠉⠉⠉⠙⠧⢤⣤⣤⠤⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⠿⠩⠗⠓⡈⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣤⣤⣤⣤⣤⣴⣾⣿⣿⣷⣶⣾⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣾⣿⣿⣿⣿⡿⠟⠛⠉⠉⠙⢿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⠟⠛⠉⠁⢀⣤⡀⠀⢰⣦⠀⠙⣆⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠈⠛⠃⠀⠈⠉⠀⢀⣉⡭⠔⠊⠁
⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⢠⠀⡀⠀⠀⠀⢒⠩⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡖
⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⠀⠀⢀⡴⢧⠀⠀⠀⠀⠈⠁⠚⠀⠃⠉⢀⡴⠋⣧⡀⠀⠀⠀⢀⣠⡴⠚⠉⠁
⠀⠀⠐⢤⣤⣬⣷⣀⠀⠀⠀⠀⢰⠋⠲⢄⠑⠠⠠⠀⢀⣀⣀⡤⠴⠚⢉⡠⠚⣡⣷⣠⠴⠖⠋⠉⠉⠓⠦⠄
⠀⠀⠀⠀⠀⠠⠴⠋⠛⠲⢦⣀⡸⡆⢀⠀⢀⠀⡀⠀⠀⠩⣀⠤⢰⣞⠉⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠗⢶⠀⠀⠀⠁⠀⠀⠀⡆⠀⠈⢋⣀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠘⡋⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⣤⠀⠀⠀⠀⡇⠀⠀⠘⠿⠀⠀⣠⣏⡀
⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠷⡄⠘⠛⠱⢷⣶⡰⠀⠀⠀⠀⢀⡀⠀⠁⠈⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⠦⣤⣤⣄⣀⣀⣤⣤⠤⠶⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢀⣤⠤⣄⠀⣠⠶⠋⠉⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣀⣤⣀⠀⣠⠶⢦⣄⡶⠋⠑⢦⡞⢁⠈⢱⣾⣥⡤⠬⠿⠷⠒⠺⡆⢀⡇
⣠⠖⠒⠒⢤⣀⡰⠋⠉⠳⣾⠁⢀⣉⣿⣁⣤⡤⠼⠗⠒⠒⠚⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣎⡀
⣇⠀⠀⢀⣠⠼⠧⠤⠒⠒⠛⠊⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢹⡆
⠈⠳⢄⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⢿⡀
⠀⠀⡞⠉⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢀⡿
⠀⠀⠷⣤⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠶⡀
⠀⠀⢰⠋⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⡶⠁⠀⠀⣠⣄⣠⡄
⠀⠀⠈⢳⡶⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣬⡏⠲⡄⠀⢸⠃⠀⠀⠀⠈⠁⠒⢠⡄
⠀⠀⠀⣏⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡤⣴⠒⠒⠛⢻⣍⠁⠀⠀⠀⣹⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⣄
⠀⠀⠀⠈⣳⠞⢿⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠤⠤⠒⣶⠚⡏⠉⣯⡀⠀⣠⡟⢦⣀⣠⠟⠈⠙⠒⠒⠚⠁⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⣾⠁⠀⠸⡧⣤⡤⠖⠚⣿⣏⠉⣁⡜⠳⢄⡠⠞⢻⡀⢿⠛⠀⠙⠛⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⢷⡀⠀⣀⡴⠋⠙⠒⠛⠀⠈⠉⠉⠀⠀⠀⠀⠀⠘⡇⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠷⠄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠘⡇⠀⠀⠀⠀⠀⠀⡛⠉⠛⠓⠶⣤⣌⠀⠀⠀⠀⠈⠁⠦⣀⠀⠀⠀⠀⠀⢠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⠀⢠⣆⠀⠀⠀⠙⢦⡀⠀⠀⢀⠈⠙⠲⣤⣈⠑⠦⣄⠀⠉⠲⣄⠀⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣸⣀⠘⣿⣷⣦⡀⠀⠀⠛⠚⠿⠀⠀⠉⢑⠒⢬⠑⠦⣄⡙⠶⣄⡈⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠁⠉⠳⡌⢿⣿⣿⣿⣤⣤⡤⠀⠀⠀⠀⠈⠛⢦⡈⠓⢬⡉⠲⢬⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⣿⣿⣿⣿⣷⠀⠀⠀⣴⡂⠀⠀⠁⠀⠀⠉⢢⡀⠉⠓⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⣸⠀⡆⠘⠻⠿⠿⠿⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠱⠤⠀⢀⣉⣷⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⠶⣤⡴⣾⠃⠘⡇⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠹⡀⣿⡄⠀⢰⠀⠀⣀⠉⢲⣦⣤⣤⣤⣤⣬⠷⠄⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠈⠉⠹⡇⠀⠰⢷⡀⠈⠱⣿⠟⠛⠛⢿⡿⠋⠀⠀⠀⠀⠀⣠⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⢣⠀⣤⡀⠉⠒⢤⠈⠁⠒⠂⠉⠀⢀⡀⠀⡀⡤⠒⠁⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠈⠟⠀⠙⠀⠀⠀⠈⠁⠒⠲⡆⠚⢏⠉⠈⠁⠀⠀⠀⠰⠀⠀⠀⠄⠀⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⢳⠀⠀⠀⠀⠘⠀⠀⠀⢠⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡏⠀⠁⠂⠤⠀⣀⡀⠀⠀⠀⠀⠀⣿⢸⠀⣀⠠⠄⠚⠦⣀⠀⢻⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⢐⡟⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢠⣤⠄⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⢢⣄⡀⠀⠀⢀⣤⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠀⠀⠀⠀⣼⠁⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠢⡄⠀⠀⠀⣀⣨⠀⠀⣼⠃⠀⠀⠀⠀⢀⣠⠞⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠋⠙⠛⢿⣄⠀⠀⠀⠀⠀⠈⠐⠠⠀⠉⠁⠀⢠⡟⠀⠀⠀⠀⠀⠀⠣⣄⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⢀⡤⣤⡀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢻⡃⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⡀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠉⠢⠀⠘⣷⡀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠸⣇⠀⠀⠀⠀⠀⢀⣀⣴⣶⣾⠟⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠙⢦⡀⢀⡠⠾⡟⠙⠳⠐⣌⣳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣁⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢟⠳⣌⠀⢰⡌⠒⠉⣩⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠃⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣶⣶⡶⠛⢷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⠟⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠶⣶⣶⣶⠶⠶⠾⠷⠶⠾⠟⠛⠋⠉⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣄⣀⡀⠀⣀⣀⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠉⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣉⣟⣋⣙⣉⣙⣋⣀⣉⣙⣏⣋⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣬⣿⣥⣯⣤⣬⣭⣤⣿⣿⣯⣭⣥⣬⣽⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣠⣦⣄⠀⠀⠀⠀⠀⣠⣶⣤⡀⠀⠀⠀⠀⢨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⢿⣿⡿⢀⣠⢴⡄⠀⠻⣿⡿⠃⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠾⠿⠤⠼⠇⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⢀⣤⣾⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣷⣤⡀⠀⠀⠀⠀⠀⢺⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣠⣿⠃⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣤⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢻⣧⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠻⣧⡀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⢀⣴⡿⠋⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣄⠀⢀⣴⠟⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠉⠉⢿⣦⠀⠀⣠⣿⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠁⠻⣷⣾⠋⣰⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡾⠋⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠿⢿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣴⣾⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡇⠀⠙⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⣄⣀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⣀⣤⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⣦⣤⣤⣤⣤⣤⣤⣤⣴⡶⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡇⠀⠀⠀⠐⠀⡠⠒
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠉⢰⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠠⠋⠉⠉⠉⠚⢓⠛⠃⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠋⢣⡀⠀⠀⣀⠀⠀⠀⠀⠐⠼⣝⠛⠃⠦⠶⠦⠅⠀⡀⢬⡴⣞⡤⠂⠀⠀⠄⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠈⠫⡒⠊⠊⠀⠀⠀⠀⢄⣀⠸⠀⠀⠀⠀⠀⠄⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⣠⠆⠀⢀
⠀⠀⠔⠄⠀⠀⠀⠈⡄⠀⠈⠀⠀⠀⠀⠈⠙⠓⠶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠙⠠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⣀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⠜⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⢀⣇⠀⠁⠀⠀⠒⠒⠐⠋⡂⠀⠀⠀⣰⠖⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⢢⠂⠀⠀⠉⠐⠒⠠⡤⠤⠥⠴⠋⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⣴⡆⠀⠀⠈⢆⠀⠈⠀⠻⠙⡀⠀⠐⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢟⡶⠀⠀⠀⠀⠀⠙⢄⣈⠣
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠄⠀⠠⣰⡅⠀⠀⠀⠀⠀⢀⣀⣉⢻⣏⡀⠀⠀⠀⠀⠀⠀⣠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⣀⣘⣢⣤⡴⠧⠬⣤⠄⠀⠀⠀⠀⠀⠙⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠐⠀⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠒⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠐⡍⠠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠠
⠀⠀⠀⠁⠄⢠⠐⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠤⢀⣀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠙⡷⠚⠁⠀⠲⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⠡⠄⠀⠋⠀⡀
⠀⠀⠀⠀⠈⠪⣀⠀⠀⢀⡶⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⣷⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠉⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠉⠂⠁⠀⠀⠀⠀⠀⠀⠀⡀⠈⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠈⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⢀⠈⡀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠒⠀⠀⠀⠀⠀⠀⠀⠘⣒⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡆⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠤⠀⠰⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠄⠒⠒⠐⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⣀⠠⠀⠒⠂⠀⠒⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡊⠁⠀⠀⠀⠀⣀⠀⡀⠴⠀⠀⠒⡷⠀⠀⠀⠀⠀⠀⠀⢐⠒⠂⠀⠤⠄⠤⠤⠠⡤⠠⠤⠔⠖⢶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠵⠐⠒⣈⡉⠤⠄⠒⠂⠈⠀⠉⠁⠢⢄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⢐⠖⠋⠉⠀⠀⠀⢀⣀⠀⠀⠀⣠⡄⠀⠀⠀⠉⠢⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣀⠄⠀⠀⠀⠘⠛⠀⢠⠤⢌⣁⣀⠀⠀⠀⠀⠙⡄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⣠⠖⠊⠉⠓⠢⡀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠉⠁⠒⠒⢒⣦⣤⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⣶
⠀⠀⡾⠁⠀⠀⠀⠀⠀⠙⣄⡠⠤⡄⠀⠀⡇⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠳⠄⠀⠐⠒⠒⠂⠈⠉⠀⠸⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢀⠃
⠀⠐⡇⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡜⠀⠀⢃⠀⠀⠀⠀⠀⠑⠤⡀⠀⠀⠀⠀⠀⠀⣀⠴⠂⠀⠀⠀⢰⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎
⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠉⠁⠐⠂⠈⠉⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠙⠒⢤⡤⣦⣴⡶⠊⠁
⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⡠⠖⠛⣄⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⡴
⠀⠀⠀⠀⠀⠈⠳⣤⠔⠉⠀⠀⠀⠈⠣⡄⠀⠀⢸⠉⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠈⠑⠦⣘⠀⠀⠀⡏⠁⠂⠀⠂⢶⠀⠐⠒⠈⠉⠀⣀⠀⠤⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢀⠔⠉⠉⠂⠄⣄⡀⠀⠀⠀⢈⡀⠀⣀⣀⡍⠀⠀⠀⠀⠈⡉⠲⡤⢄⣀⡀⠀⠀⢠⣴⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠉⠉⠀⠀⡄⠀⠀⠀⢀⠀⢥⠀⠙⣄⠀⠉⠙⡰⠋⠉⠉⠙⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣶⠀⠀⠀⡇⠈⠁⠀⠀⠀⠀⡄⠀⠈⢆⠀⢸⠁⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢥⡤⢤⠄⠤⠴⠖⠃⠀⠀⠈⡆⠸⡀⠀⠀⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡄⠀⠀⠒⠂⠢⠄⠐⠁⠓⠁⠀⠀⠀⢱⠄⠵⢄⡀⠀⣀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠈⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠙⠀⠒⠂⠤⡄⠀⡆
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠉⠁⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⣄⣀⣀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⡇⠀⡏⠉⠐⠀⠤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣤⠤⠤⠤⠤⠤⢤⣀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠢⠤⠀⠀⠀⠀⠀⣇⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠟⠛⠋⠉⠉⠉⠀⠀⠀⠀⠈⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣷⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠋⠀⠀⠀⢀⣀⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠿⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⣴⣶⣿⣿⡿⠿⠛⠋⠉⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⢶⡄⠀⠀⠀⠀⡴⠛⠂⡀⠀⠘⢍
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣇⣀⣠⡇⠀⠀⠀⠀⣷⣄⣴⠿⡄⠀⠈⢆
⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣧⣬⠁⠀⠀⠀⠀⠸⣿⣿⣿⡇⠀⠀⠈⡄
⠀⠀⣠⣾⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠃⠀⠠⠀⣀⢠⡇⠉⠉⣉⣠⣜⣄⣤⣤⡶⠃
⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⢧⣰⡿⣿⣷⣿⣿⣿⠿⠛⠉⠀⢸
⠀⠈⠙⠛⠛⠛⠛⠉⠉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⠾⠻⠛⠉⠀⠀⠀⠀⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⢺⣅⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣶⣤⣄⣀⣀⣀⣀⣀⣠⡤⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢷⣄⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⣠⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⣄⠹⢷⣄⡀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠿⠛⠛⠋⠀⠀⠀⠀⠀⢀⣤⡾⠋⡟⠒⢄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⢣⡀⠀⠀⠀⠙⠻⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⡾⠟⠋⢀⡴⠁⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠙⢦⣀⠀⠀⠀⠀⠀⠈⠉⠙⢛⠛⠒⠛⠒⣶⠛⠛⠛⠉⠉⠁⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠉⠛⠶⣤⣄⣀⠀⠀⠀⠈⠀⠀⠀⠀⡿⠀⠀⣀⣀⣤⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⡇⠀⠀⠀⠀⣿⠛⠛⣿⣯⡅⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠁⠂⢠⣀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⠀⠀⣿⣿⡿⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⢄⠀⡇⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡇⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⢸⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⡇⢀⣼⣇⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⣠⡎
⠀⠀⠀⠀⠀⠸⠀⠀⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⠀⠀⠀⠀⢹⡄⠀⢹⠈⠿⡿⠇⠀⠀⠙⠦⣤⣄⣤⣤⠶⠟⢹⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠛⠷⠶⢦⣤⣤⡴⠶⠛⠀⡇⠀⠀⠀⠀⠸⡇⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢻⡀⠀⠱⣀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠈⣧⡠⣶⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⣀⣀⣤⣤⢾⡷⠛⠋⠙⠁⠀⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠸⣭⣭⣭⣵⡶⠾⠇⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠶⠶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠶⠶⠚⠛⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣟⣩⣿⣹⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢠⡿⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣠⡿⠁⠈⢷⡀⠀⠺⠃⠀⠀⠀⠀⠀⠀⠸⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⠟⠁⠀⢀⡄⠱⡄⢀⠔⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⠟⠀⠀⢸⡇⠈⡇⠀⠀⡗⠀⠀⠀⠂⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣛⠛⠉⠀⠀⠀⢸⡇⠀⣿⠀⢰⠇⡄⠠⡀⠦⡀⡀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣀⠤⠀⢄⢀⠀⠀⠈⠏⠀⠀⠀⠸⡀⠓⠀⠧⠀⠇⠙⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⡼⠁⠀⠀⣸⡇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣸⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢠⠀⢸⠃⠄⠀⡀⠀⠉⠀⠀⢠⠀⠀⠈⠋⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠓⠃⢸⡇⢶⠀⠇⡄⣨⠰⣇⣸⠂⣶⢰⡄⡇⣰⢀⡄⠸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⡴⠙⠃⠾⠈⠸⠇⠙⠂⡹⠻⠎⠛⠘⠸⠇⠉⠉⠧⠀⡽
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣙⣉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠒⠀⠀⣴⠀⠀⠀⠀⠀⣻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡷
⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠐⣹⣏⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⣺⡃⠀⠀⣼⣿⠄⠀⠀⠀⠀⠀⠀⠓⠀⢀⣼⣄
⠀⠀⠀⠀⠀⠠⠟⠁⠀⠀⠀⠜⣹⣏⠢⡀⠀⠀⢀⣿⣧⠀⠀⢀⢼⢤⠀⠀⣼⣿⡄⠀⠀⠀⣤⠀⠀⠀⢀⣤⣿⣷⣤⡀
⠀⠀⠀⠀⠀⣠⢤⠤⠀⠀⢀⠴⣻⣟⢧⡀⠀⢀⣾⣿⣿⡆⠀⠠⢺⡣⠄⠈⣹⣿⡍⠀⠀⢰⡿⡆⠀⠀⣀⣴⣿⣿⣤⠄
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠔⣻⣟⢦⡈⠀⣼⣿⣿⣿⣿⡄⠒⢹⡑⠆⠼⢿⣿⠛⠂⠀⣾⣩⣿⠀⢀⣠⣼⣿⣷⠤⠤
⠀⠀⠀⠄⠀⠀⢠⠀⠀⠀⢀⠼⠋⡟⢦⠉⣸⣿⣿⣿⣿⣿⣷⡐⢩⠙⠀⢠⣿⣿⣧⡀⣸⣿⡣⣿⣇⠉⢉⣽⣿⣿⡷⠒⠂
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠠⠇⠀⠀⠉⠉⠉⢹⠉⠉⠉⠀⠸⠀⠀⠛⠉⡏⠉⠁⠛⠛⠛⠛⠛⠀⠛⠉⢹⠉⠛⠓

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠱⠎⡁⠀⠀⠀⠀⠀⠠⣶⣿⣿⣿⣿⣷⣶⠂⠀⠀⠀⠀⠀⠄⠀⡈⠴⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠁⠙⠻⢦⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⠰⠀⡀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠶⠀⠀⠰⠄⢀⠈⠀⠀⠂⠀⠈⢀⠀⠰⠀⠀⠰⠆⠀⠁⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⢰⣷⡀⠀⠘⠀⠀⠀⠃⠀⠁⠘⠀⠀⢰⣷⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠆⠀⠀⠈⠁⠄⠀⠀⢾⣿⡇⠀⠀⠐⠄⢀⢁⠀⠔⠀⠀⠀⣿⣿⡆⠀⠈⠀⠉⠀⠀⠀⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠆⠄⠰⠐⠀⠆⠀⠆⠀⠀⠰⠰⠀⠀⠆⠂⠀⠆⠀⠂⠀⠀⠆⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⡀⠀⠀⡀⢄⠠⢤⠉⠆⠀⠀⠀⡀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠎⢁⠴⢀⠄⣀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠼⢀⡵⢘⡆⣹⠀⡅⠐⠁⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⠘⠀⠇⢰⡁⢞⠱⣅⠘⠄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⡀⠈⠀⠁⠀⠀⢀⠆⠀⠀⢀⠀⠀⡆⢴⣶⠀⡆⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠈⠀⢈⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡉⠀⠀⢀⠁⠁⢀⡀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⣀⠀⠃⠁⠀⠀⠈⢉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠋⠀⠀⠀⠀⠁⠀⠀⠈⠂⠀⠀⠀⠀⠀⠈⠀⠀⠀⠉⠀⢄⠀⠉⠛⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⠰⠘⠀⠀⠀⠀⠘⠃⢰⣶⠀⠛⠀⠐⠀⠀⠈⠐⠠⠄⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠆⠄⠄⠂⠁



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

⠀⠀⢀⡀⠤⠠⠄⠀⣀⠀⢀⠀⣆⢠⠀⠀⠀⠀⠀⠀⠀⣠⠶⣄⡠⢄⠀⢰⣶⡆⣠⣄⠀⠀⠀⠀⢠⢤⣠⡤⡴
⠀⠀⠰⣴⣴⣼⣧⢙⣾⠘⢢⣶⣟⣩⠏⠀⠀⠀⠈⠙⠫⠁⠐⢲⡀⠈⠣⣤⣭⡄⠛⠛⢀⡀⡔⠒⠋⠀⢀⠀⣇
⠀⠀⠐⠷⠶⠮⡻⢿⣿⣟⠲⢿⣿⣷⣾⠏⣰⠟⣡⣶⣶⣄⡀⡀⠉⠢⠀⠀⡟⢁⡏⠈⠉⢿⡁⠀⠀⡸⠃⠀⡈⠂
⠀⠀⠀⠀⠐⠛⠈⣛⣓⠟⣴⠀⣿⣿⡟⣰⢃⣾⡿⢋⡥⠶⠛⠪⣀⠃⡅⠀⠵⠚⢀⠂⠀⢰⠁⠜⠋⠁⢀⣸⡅
⠀⠀⠀⠀⣷⠉⣤⠊⠙⣇⠸⣇⢻⣿⣧⠿⡞⠛⢵⣫⣴⣾⣿⣿⣿⡇⠀⢸⠆⢄⡦⠀⢀⠼⠂⣠⠤⢔⣅⣴⣤⣤⣆
⠐⠿⠿⠶⠙⡃⢻⡆⢸⣿⣧⣘⠷⡽⢡⠁⠑⠄⡀⠙⣛⣩⣭⣉⡉⠳⠰⠛⠀⠸⠁⢠⠃⠀⠉⠲⠶⣿⣿⢿⡟⠓
⠀⠀⠠⠾⠿⣋⣐⢅⢨⠛⢿⣿⣷⡇⠒⠓⡀⠀⢣⠀⢱⣶⣶⣬⣍⡓⠸⣿⡷⠥⣴⣮⣤⣀⠀⠒⢤⠈⠛⠲⠛⠊⠓
⠀⠀⣤⠀⠚⢛⣩⣴⠜⠻⢦⣌⣙⠃⠱⡀⢘⢀⡇⣀⢀⠙⠻⠿⠟⠡⣾⣿⠀⣸⣿⡿⠋⠁⢀⣂⣤⡀⣀⠀⡆
⠀⠀⠀⠈⠀⠐⠈⠅⢐⡷⣦⣌⣉⣹⠤⠓⠈⠀⠀⠀⠀⠀⠈⡂⣰⠀⠘⢿⡀⢿⡿⢀⣶⣿⣿⣿⣿⡍⠀⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣄⣈⠑⠜⢷⣯⣥⣀⡀⠀⠉⢿⣠⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠚⣖⡛⠿⡖⠀⠀⠀⠀⢀⠀⠀⠀⡛⠛⠛⠛⢋⣵⡞⣧⠉⠻⣿⣷⣄⢸⠟⠴⠟⠃
⠀⠀⠐⠀⠀⠀⠀⢀⠋⠀⠀⣸⣶⣭⣛⢧⠀⠀⠐⠶⡀⠬⠛⡀⠐⣦⣶⣾⣿⠏⢰⣿⡇⠀⢹⣿⣿⡇⢿⣦⠙⠿⣶
⠀⠀⠀⠠⠒⠂⠀⠎⠀⠀⠀⢻⣿⣿⣿⣿⣆⠀⠀⠀⠈⠻⣿⣥⣔⣺⡿⠋⢀⣴⣿⣿⡇⠀⡸⠛⠉⠃⠈⠙⠃
⠀⡊⠈⣓⣀⠀⡀⠀⠀⠀⢰⣼⣄⣉⠛⠻⣿⡐⠀⠀⠀⠀⠘⢷⣶⣚⣻⣶⡈⠉⠉⠉⠁
⠀⠀⠀⢇⣀⡽⠀⠀⠀⠀⣽⣷⣯⣉⠙⠲⢤⣇⠈⠄⠀⠀⠀⠀⠻⣿⢟⠿⢅⡒
⠀⠀⠀⠤⠤⠆⢀⠄⢄⠀⢿⣿⣿⣿⣿⣷⣦⣉⡀⠈⢂⠀⠀⠀⠀⠙⠞⠐⠤⠉
⢀⣠⠔⠁⢀⡔⠁⢀⠼⣷⡾⠛⢷⡛⠛⠿⢿⣿⣧⠀⠀⠀⠀⢀⠀⠀⢂
⢀⡄⣀⣀⠁⣀⢤⣯⡀⢿⣠⡾⠟⠛⣟⠲⠦⣬⡙⠆⠀⠰⠀⠎⠀⠀⠰
⠘⣉⣁⣸⣿⣷⣾⡙⠛⢲⡿⡙⠲⣶⠎⣷⣶⣤⣉⠻⠀⠀⠃
⠀⠠⠬⠿⢛⠟⣫⠗⣶⣟⢀⣿⣤⠋⠀⢙⠛⠿⣿⣿⣇
⠀⠀⠀⠀⠀⠘⢱⡿⣿⢫⢻⣏⠳⠀⢀⣼⡟⠶⣤⣉⠻⡄
⠀⠀⠀⠀⠀⠀⣋⣼⣿⡀⣿⠑⠂⠀⢉⣡⣸⣷⣶⣍⣻⠇
⠀⠀⠀⠀⠀⠘⢩⣿⠿⡟⠀⠀⠀⠰⠟⠋⠆⢿⣿⠛⠋
⠀⠀⠀⠀⠀⠈⡱⢹⠀⠁⠀⠀⠀⢀⣶⣿⠹⣶⡍⠓
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠉⣿⡆⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⠤⢖⠒⠒⠂⢒⠐⢒⡶⠆⠠⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠂⠉⠀⢀⠀⠀⠈⠉⠀⠒⠻⣑⠭⠀⢀⣀⠀⡀⠀⠉⡒⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⢁⠀⠀⠀⠀⠀⠀⠂⠀⠀⣴⠂⠀⠀⣰⠆⠀⠀⠉⠲⣄⠀⠀⢸⡗⠁⠉⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⢀⠆⢀⠁⠀⣛⣛⣬⣬⣭⣭⣭⣥⣼⣒⡀⠤⢈⡃⠀⠜⠀⠀⠀⠀⠀⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⢀⠀⠀⢠⡴⢓⣨⣴⠾⠋⠉⠉⠀⠀⠀⠀⠀⠉⡉⠛⠛⠻⣶⣮⣔⡠⡀⠀⠀⠰⠀⠘⠉⠙⢦
⠀⠀⠀⠀⠀⠀⡠⡁⠀⠀⠀⣠⠞⢃⢜⣥⣾⡟⠉⠀⠀⠀⠀⠀⠀⠘⠛⠂⠀⠀⠀⠀⠀⠀⠀⢛⣿⣿⣦⣕⠄⡀⢀⡀⠄
⠀⠀⠀⠀⢀⠌⠀⠉⠩⡍⠀⢀⢜⣵⣿⣿⡟⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣷⣔⢾⠟⠀⠱⢆
⠀⠀⠀⠀⠎⠀⠀⠀⠀⠘⡤⣢⣾⣿⣿⡿⣤⣾⡿⠃⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠹⣿⣿⣿⣧⡹⠿⡀
⠀⠀⠀⡜⠀⠀⠀⠀⠀⡰⣱⣿⣿⣿⣿⣵⣿⡍⠀⠀⠀⠻⠁⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢳⡀⠀⢿⣿⣿⣿⣷⡐⡀⢡
⠀⠀⢐⠀⠀⠀⠀⠀⠠⢱⣿⣿⣿⡿⣿⣿⣿⣷⣦⣶⡀⢀⣹⡆⠀⠀⢀⣤⠶⠚⠛⠉⢹⠿⠷⢶⣮⣇⡀⢸⣿⣿⣿⣿⣿⡘⠻
⠀⠀⡎⠀⠀⠠⡆⠀⢣⣿⣿⣿⣿⣧⡹⣿⣿⣿⣿⣿⣷⣿⣿⣧⣴⣾⡥⠄⠀⠀⠀⢠⣠⡤⠤⠈⢻⡟⢿⣿⣿⣿⣿⣿⣿⣧⢹
⠀⢠⠀⠀⠀⠉⠀⣤⢸⣿⣿⣿⣿⣷⣗⢹⣿⣿⣿⣿⣿⣿⡟⠛⢿⠃⢀⡤⢤⣷⡀⠙⠇⠀⠀⠀⢈⣉⡉⠻⠿⢿⣿⣿⣿⣿⡈
⠀⠸⠃⠀⣦⠀⢀⠇⣿⣿⣿⣿⣿⣿⣿⡿⣧⣿⣿⣿⣿⣿⣷⡀⠘⠛⠉⠀⠀⠙⣿⡄⠀⠀⡆⠀⠊⠐⠀⠄⠀⠈⠙⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⡌⠁⣿⣿⣿⣿⠿⠿⠫⠟⠐⠈⢺⣿⣿⡏⠻⢿⣿⡇⠢⠄⣀⡴⣁⠤⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡇
⠀⠸⠀⡀⠀⠘⠁⢠⢻⣿⣿⣿⣢⡐⠀⠀⣠⣶⣿⣿⣿⠃⠀⠀⠈⠀⠀⡬⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⣤⠀⠀⠀⠀⢘⣿⠃
⠀⠀⡆⢇⠀⠀⠀⠀⠸⣿⣿⡟⡼⠁⠀⠰⠿⡿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⢤⣤⠖⠛⠛⠉⠙⠁⠀⠀⠀⠀⠀⣿⣰
⠀⠀⢐⠀⢷⡀⠀⢀⣠⣿⣿⠋⠄⠂⠀⠀⠀⣀⢸⣿⣿⣷⡄⠀⠀⢀⢰⣿⣿⣿⡋⠻⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷
⠀⠀⠈⠆⠀⢙⣴⣿⣿⣿⠟⠀⠀⠀⠉⠀⠀⠀⡀⢻⣇⢍⠟⣷⠀⡈⡀⠐⠤⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⣴⣾⡿⢟⠁⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠈⣾⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⣴⣿⡟⣡⠏⠐⠀⠳⠀⠀⠀⠀⢀⠀⢀⣋⣠⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⣾⡟⠟⠀⡉⠀⠁⠀⠀⠀⠀⠀⠰⠀⣠⣾⣿⣿⣿⣧⣴⣿⠃⠐⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⣿⣦⠀⡆⠙⠀⠀⠀⠀⢠⡴⠂⠀⠀⠙⣿⣿⣽⣿⣿⣿⣶⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢸⡇⢺⠀⠀⠀⠀⠀⠀⠀⠌⠐⠊⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣯⣿⣿⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠄⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠂⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠐⠛⠷⠶⣦⣄⡀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠌⠛⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠤⠐⠀⠀⠀⠉⠛⢷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣖⠙⠀⠀⠲⠅⣀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠓⠀⠀⠠⣀⠀⠀⡀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢒⣉⠿⠀⡔⠂⠀⠀⣹⣦⠊⠀⠄
⠀⠀⠀⠀⠀⠀⢀⡀⠘⠈⠀⠀⠀⠀⠉⠢⢠⡄⢠⠺⣄⡀⠐⠋⢀⡀⠀⠀⢀⣀⣠⠐⠛⠀⠀⠘⠁⠀⠰⡂⠶⠀⢀⡤⢛⡽⠂
⠀⠀⠀⠀⠀⢀⠃⠃⠀⠀⠀⠐⠀⠈⣡⡶⠚⠓⢦⠂⠈⠻⠅⠀⠀⠛⠁⠷⠊⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⢋⡀⠂⠌⣞⠉⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⣰⠛⠀⢀⡀⠀⢇⠀⠀⠀⠠⠀⠈⠀⠢⠀⠀⠀⠈⠤⣁⠠⠀⠂⠀⠀⠀⡄⠁⠤⠀⢁⠴⠆⠔⠛
⠀⠀⠀⠀⠠⠘⠻⠆⠀⠠⠄⠊⣉⢉⣀⠀⠺⢏⣳⠋⠀⠀⠀⠀⠈⠐⠀⠀⢁⠀⠆⡁⠤⠀⠠⠐⠀⡔⠀⠂⠀⠀⣀⡰⠂⠀⡀
⠀⡐⠷⠒⠲⠖⠄⠀⠀⠴⢲⠴⠋⠀⣠⡆⢀⣤⡮⡡⠀⠀⠀⠀⠀⠀⠘⠰⠁⠀⠐⠚⠀⠁⠀⠀⠀⠐⠈⠈⠀⠂⠈
⠀⠀⢂⠀⢀⡀⢦⢂⠀⠂⠀⣂⡀⠀⠉⠀⠀⠁⠊⠀⠀⠀⠤⠤⠤⠖⠂⠀⠀⠀⠀⠀⠙⠂⢤⠠⡀⢀⡳⠀⠈⠠⢀⡀⠀⠀⡌
⠈⠀⠰⠠⠤⠐⡀⠀⠀⠀⠀⠀⠀⣀⡆⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣷⣶⠁⣾⣷⣿⣮⡵⠟⡆
⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢲⡂⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⠉⠈⣀⣤⡀⠀⠀⠀⠀⠘⢻⣷⠒⠚⣻⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢘⢒⡲⠶⠶⠇⠀⠀⠀⠉⠀⠉⠑⣇⣀⣀⢠⠀⠀⠔⠈⢶⣀⡀⠒⠁⠙⣀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠐⠬⢆⣀⣒⠉⠁⠁⠀⠀⠀⠀⠀⠀⠈⣛⠛⠗⡓⢠⡑⡀⠀⠈⠁⠀⣈⢁⠥⣀⢈⡁⢄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠙⠆⠃⡀⠀⠀⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢨⠄⢈⡐⠆⡸⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠲⠦⠐⠀⠀⠸⠇⠀⠴

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠿⡷⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡲⣷⢳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣽⢏⡟⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣿⠸⡗⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡙⠺⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣴⣧⠗⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⡁⣔
⠀⠀⠀⠀⠀⠀⠀⠀⢦⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠿⣿⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡙⠺⠿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⣼⡤⣀⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢺⡿⢿⡿⠞⠿⢦⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡱⢝⠫⠖⣀⢚⣛⡀
⠀⠀⠀⠀⠀⠀⡈⠦⠤⠌⣀⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣿⡇⣉⣤⣾⣶⡶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢘⡓⣻⡇⢌⠉⠻⣭⡄
⠀⠀⠀⠀⠀⣀⠛⠲⠀⠤⠁⠐⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣶⣿⣷⡟⣿⣟⡻⣷⡷⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠉⢉⣵⡖⢹⣄⠻⠆⠖
⠀⠀⠀⠀⢠⠈⠁⠈⠘⠃⠁⠈⢁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣽⣿⣷⣿⣿⣿⣿⠃⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⣋⣋⢉⣁⣠⠠⠀⢡⠚⠋
⠀⠀⠀⢀⡀⠙⠓⠶⠒⡄⠙⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡁⣻⣿⣿⣿⣿⣿⡿⣆⢀⡀⠀⠀⠀⠀⠀⠀⠈⠋⢶⢁⣉⠁⠐⠒⠳⠿⠓⢚⡁
⠀⠀⠀⢨⠇⠠⠄⠰⠶⠰⠆⠀⠀⠞⠀⡀⠀⠀⠀⠀⠀⠀⢤⣤⡤⣭⣿⠋⠵⣿⢩⣯⢹⣟⡟⢋⢠⠀⠀⠀⠀⠀⠀⣫⠖⣩⢿⣷⠞⣽⣄⠑⠎⠞⣁⢀⣀⡀
⠀⠀⠠⠀⠀⢠⢀⠀⠀⠀⠀⠐⠴⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⢛⣷⣿⣶⣿⣸⣿⣶⣿⣻⡿⠉⠀⠀⠀⠀⠀⠰⠭⢙⠃⣘⡋⣀⡅⠉⢴⠒⣈⡄⠉
⠀⠀⢤⡀⠀⠀⠈⠁⠒⠀⠐⡀⠀⠄⠄⠂⡠⠀⠀⠀⠀⠘⢦⣢⡼⢟⣭⠟⢩⣿⡎⣿⣷⣿⣿⣤⣆⣤⡖⠀⠀⣈⣰⣠⡆⣀⡘⠉⠹⠗⠂⠀⠜⠣⣿
⠀⠰⢌⠀⠃⠒⠂⠰⠂⠀⠂⠉⠀⡀⠀⠀⠀⠓⠀⠀⠀⣀⣄⣈⣴⣿⣿⢿⣺⣿⣿⣉⣹⣿⠦⣟⡿⣍⠀⠀⠠⣌⣛⣻⡍⢩⣥⡀⣶⡇⢒⡶⣦⡀⣰⢶⣆⠠⠄
⠀⠀⠀⠀⠀⠉⠉⠐⠐⠒⠘⠁⠛⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠻⣹⣿⣏⣤⣿⣿⠻⣿⣷⣲⣦⢼⡿⠒⠋⠀⠀⠀⠉⠋⠀⠃⠺⠞⠟⠃⠂⠀⠈⠘⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠈⠙⠷⠜⠛⠛⠋

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣀⣀⣀⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⣴⣾⢃⠀⠀⠀⠀⠀⢀⢸⠀⢠
⠀⠀⠀⠀⠀⠀⣳⣄⠀⠀⠀⠀⣇⢸⡁⠀⠀⣻⣿⡟⣡⣴⣼⣧⠀⠸⠈⣤⢸
⢀⠀⠐⠃⠀⠀⢻⣿⠀⠀⠀⣎⢿⢼⣧⠰⠀⣿⣽⣿⣿⣿⣿⡟⡀⠒⢀⢿⠀⠀⠀⠀⠀⠀⠀⢰⣷⡄⠀⡀⠁
⣸⣿⠀⠂⠀⠀⡏⣗⠀⠀⢸⣿⣿⣾⠛⠘⠀⠁⢹⣿⣿⣿⣿⡏⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⣿⡿⠇⠘⣳⣶
⣿⣿⣄⠀⠀⠀⠁⠃⠀⠀⠀⢹⡿⠋⠀⠀⠀⢀⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡿⠃⠀⠀⣽⡟
⢸⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⠿⠟⠋⠁
⠸⠟⠿⣿⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣀⣴⣶⣤⣤⣈⣿⣿⣇⣠⣄⠀⣶⣶⣄⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⢠⡄⢠⣄⣹⠀⠀⣹⣿⣏⠛⢿⣿⣿⡿⣿⣿⡇⣸⣿⣟⣹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣼⣷⠀⠈⠁⣤⣼⣿⡤⣔⣸⣿⣿⣿⣿⠿⣿⣶⣦⡾⠱⠟⢾⠉⢍⣀⣦⠴⠞⢓⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣾⣿⣿⣋⣀⠀⠀⠼⢿⣷⣔⡙⠛⣩⣿⡏⠀⠈⠻⣿⣦⣄⡀⠀⠓⢌⠛⢇⡠⢂⣼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣽⡿⢟⣿⢿⣦⣴⡄⠉⠛⡇⠘⢿⣿⠁⠀⠀⠀⠘⣿⢿⡟⠛⠶⠀⡄⠀⣡⣾⠯⣁⠀⣄⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣒⣄⠉⢠⣶⢾⠟⣿⣿⣧⡊⠀⠉⠀⠈⠛⠀⠀⠀⠀⠀⠁⠘⠀⠀⠀⠀⣽⢷⣿⣿⣶⣍⡀⠈⢡⣾⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⢉⣿⠀⠙⢀⣿⣄⣝⣽⡏⢫⠘⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⢄⠻⠻⢿⡄⢹⣿⣿⣿⣬⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣆⡀⣬⠀⠒⣿⡟⣿⣀⣴⠏⠁⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠼⣧⣰⣾⣧⠈⣹⣿⣿⣍⠁
⠀⠀⠀⠀⠀⠀⣠⡜⠉⠉⠻⠁⠈⣙⣿⣷⠁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢾⣿⣼⣿⡷⠸⠅⣀
⠀⠀⠀⠀⠀⠀⣩⠀⢠⡴⣤⣄⠀⠠⢻⣁⣀⣈⣇⡀⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠏⠀⠹⡿⣿⠃⠐⠀⠈⣈⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠫⢿⣄⣄⣽⣿⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⣼⡤⢄⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢫⡇⠈⠻⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⢿⠁⠃⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⡀⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⢿⣿⣷⡆⠀⢰⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠀⠀⠀⠀⠀⠀⠻⠃⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⡨⢿⠙⣿⡿⠈⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⣿⠾⠲⣆⠄⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣴⣤⣾⣤⣴⣶⣶⣿⠿⠆⠸⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢿⢀⣤⡿⢶⣿⡅⠀⢠⣶⠄⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡅⠹⠛⠷⣯⡝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢱⠾⡿⠁⠀⢶⣻⣄⠛⠋⠶⠄⠀⠀⠀⠀⠀⠀⠒⠃⢾⡉⠹⢿⠀⠀⠤⣫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⠛⠃⡄⠀⣶⣏⡃⠙⠀⠀⠀⠀⠀⠀⣠⡀⠀⢠⡀⠀⠉⣷⠊⠛⠿⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠇⠉⠀⠀⠀⠀⠀⠀⢲⣿⠛⢿⣿⡏⠀⣴⣿⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠁⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⣀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⣀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠛⠋⠙⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣤⣶⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⠿⢋⡀⠅⣨⣿⣿⡿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⢠⣿⣤⣼⣮⠁⠀⠀⠈⣻⠃
⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⣤⣶⣾⣿⣿⣿⣿⣶⣶⣤⣴⠃
⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀
⢿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠙⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿
⠰⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡎⠀⢀⣴⣶⣦⠀⡇⠀⡠⠊⠉⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿
⠀⠀⠀⠀⠀⠒⢏⠀⠀⠀⠀⢅⠀⠸⡟⠋⠉⠉⠁⠒⠿⣿⣷⡀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⠛
⡇⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠑⠲⠀⠀⠀⠀⠀⠀⠀⠈⠻⠃⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠇⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠱⣄⠀⠀⠀⠀⠀⢀⠦⠤⠊⠁⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⡈
⠠⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠉⠒⠀⠒⠐⠁⠀⠀⠀⠀⠀⠀⢀⡤⠊⠉⠀⠀⠀⠀⠀⡇
⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣶⣤⣀⡀⠀⠀⠀⣀⣠⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠈⠐⠤⡀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠐⠉

⠀⠀⠀⠀⠀⠀⠠⣀⡤⣢⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⢤⡄⠀⠀⠀⠀⢠⠤⣤⠎⢷
⠀⠀⠀⠀⠀⢀⡿⠀⠁⠘⣓⠀⠀⠀⢀⣠⠴⠚⠉⠁⣀⠔⠊⣇⠀⠀⠀⠀⣸⠧⠀⠀⢉⢩⠗⠀⠀⢠⣀⢠⡄
⠀⠀⠀⠀⠀⠑⠓⡆⣠⣌⠇⠀⢠⠞⠋⢀⡠⠤⠒⠉⠀⠀⠀⣿⣀⣀⠀⠈⠓⢲⡂⣠⣈⢻⠀⠀⠠⣮⠁⠈⢵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⡉⠀⠀⠀⣀⠠⠐⠈⠀⡌⠀⣨⠇⠀⠀⠈⠒⠁⠈⠉⠀⠀⠀⠱⠷⠸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠴⢢⡀⠀⢙⣦⠀⠀⢀⣀⠤⠒⣉⠤⠊⠉⡑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠭⢀⣐⡃⢠⡏⠀⢈⡉⠡⠄⠒⣉⠀⠀⠀⠈⠳⠀⠙⣆⠀⢠⡞⠳⡴⠚⠉⠙⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢹⠃⠀⠀⠀⣀⠀⡩⠄⠤⣀⠓⠀⠀⠀⢹⠀⢸⡇⠀⠁⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠘⢄⠣⢄⣀⠼⠀⠀⠀⠀⣸⢠⡞⠁⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⢢⡆⢴⡄⠀⠀⠀⢠⠷⣄⠀⠀⠀⠈⢷⣶⠖⠂⠀⢀⣀⣰⡧⠞⠑⢄⡈⠒⠤⡔⠋⠀⡖⠂⠡⣄
⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⢿⠀⠀⣠⡼⢤⠀⠉⠖⠠⢤⠤⠀⡤⢎⠉⣁⠈⢆⡇⠀⠀⠀⠈⢉⡟⠁⠀⠐⠢⣠⠜⠅
⠀⠀⠀⠀⠀⠀⠀⠹⠃⠛⠃⣠⠎⠁⠀⠀⠑⠢⣄⡀⠘⠀⠀⠠⠀⢡⠀⠀⠀⠱⣄⠀⠀⢀⡞⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⡀⠀⠈⠉⠁⠂⠀⠓⠈⠫⡀⣀⠠⠘⠓⣤⠏⠀⢰⡰⠶⡞⢼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⢠⠋⠉⠒⠈⠉⢑⠄⠀⠀⠀⠙⡀⠀⢀⠠⠘⡆⢀⠴⠓⠀⠀⢈⣩⠕
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣽⢆⡀⠀⠀⡆⢠⠂⠀⠀⠀⠉⠲⡀⠀⠀⠀⡋⠁⠀⣀⢴⡇⠈⠘⢻⢅⣰⣠⢋
⠀⠀⠀⠀⠀⠀⢐⠔⠉⢂⠄⣿⠀⠈⠑⠒⠧⣸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⣉⡁⠀⢸⡇⠀⠀⠈⠊
⠀⠀⠀⠀⠀⠀⠁⢢⠰⠼⠀⢻⠀⠀⠀⠀⠀⠀⠉⠒⠤⠄⠤⠊⠀⠀⠀⠀⠐⣿⡟⠀⠸⠷⠒⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠐⡲⠻⠉⠿⢆⡂⠀⠙⣦⠔⠊⠉⠉⠉⠒⠠⡀⠀⠀⠀⣀⡤⣎⠀⠀⠀⢀⣠⠖⡋⣀⢤⣦
⠀⠀⠀⠀⠀⠀⠰⠟⠀⠀⠀⢺⡄⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠘⣶⠒⠋⠁⠀⠈⠓⠒⠛⠉⠀⠀⢘⠛⠀⠁⠿⣖
⠀⠀⠀⠀⠀⠀⠀⠉⠻⣠⠟⠑⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⣀⠟⠀⠀⢰⠐⠉⢦⠀⠀⠀⠀⠀⢛⢗⣤⡀⡿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠒⠚⠛⠉⠁⠀⠀⠀⠁⢂⠤⠵⠀⠀⠀⠀⠀⠀⠀⠙⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠐⠀⠀⠀⠂
⠀⠀⢀⠨⠄⢠⠀⠀⠀⠆⠀⠀⠀⠄⠉⠀⠀⠀⠐⠀⠐⡂⠀⠢⡀⠀⠁⡀⠂⠀⠠⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠄⠀⠂⠀⠀⠀⠂⠀⠀⠰⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠈⠀⠀⠀⠀⡀
⠀⠈⠠⠀⢀⠘⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠄⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠕⠀⠠
⠀⠀⠐⠀⠀⠄⠁⠈⠀⠁⠀⠀⠀⠀⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡁⡚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⢐⣤⣰⢄⣤⢐⣂⣤⣤⣄⠤⣀⣠⣄⣀⢀⡄⣀⣠⣴⣤⣦⠖⣰⣶⣦⡤⣂⡴⣶⢦⢀⠂⣤⣬⣤⣆⣀⠤⣀⢀⡀
⠀⠹⠟⡵⢫⣴⡿⠛⠻⠯⠠⠾⠛⠿⡟⡿⢋⣾⠾⠟⠛⠉⠋⠚⠉⠍⠙⠾⠾⢿⠛⠟⠣⠾⠍⠯⠷⠿⡟⠾⣿⠼⠛⠒⠂
⠀⠈⠐⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠈⠀⠀⠀⢠⠀⠀⠀⠃⡀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠘⠀⠐⠀⠀⠀⢠⠀⠸⠆⠀⠀⠀⠀⠀⠀⠀⠨⠂⠀⠃⠀⠰⠆
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡸⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢀⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⡄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠋⠀⠀⢀⣾⠃⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠄⢀⣿⡇⣴⢏⣴⣦⡄⣴⢀⡤⣦⡶⢀⢤⣄⣤⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⢀⠤⠐⠒⣾⠏⢠⢏⡟⢱⣟⣼⡣⣋⣼⡿⠰⣡⡞⣿⢡⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠛⠳⠐⢁⣤⡄⣰⠏⠀⠘⠈⠁⠈⢹⡟⠀⠉⣸⠏⠀⠁⢀⢜⡿⠁⢀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠉⠀⠀⠀⢀⣰⣾⡿⠞⣱⡇⠀⠀⠀⣴⡇⣈⠀⠀⠀⢁⣾⠃⠀⠥⠋⠈⠻⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡠⠖⠉⣾⡟⣀⣼⣟⣴⡦⣄⣸⡟⣠⡛⢀⣤⣤⣾⠋⣤⣶⣤⡄⣤⡄⢀⣤⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⣀⡠⠤⣾⡿⠉⢰⢟⣿⠿⢲⢻⡟⣸⡟⣰⡿⠋⣾⠃⣾⠟⣵⠟⣸⡟⢁⣾⠇⣿⠟⣡⠴⠒⠂⠒⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⠀⠀⣰⡿⠁⠀⡟⠈⠧⠔⠁⠾⠈⠻⠊⠻⠔⠁⠿⠚⠗⠂⠿⠊⠻⠄⣿⠏⣸⡟⠋⠀⠀⠀⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⣰⡟⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣾⠏⡔⣽⢣⣀⣠⣴⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠰⣤⣀⣤⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⣰⠏⠀⠛⠁⠀⠙⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡼⠋


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⣠⡶⠚⠛⠛⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠛⠉⠙⢷⡏⠀⠀⠀⠀⠀⠘⠷⠶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠄⠀⠀⢀⣤⠶⠞⠛⠛⠛⠛⠶⢦⣴⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣀⠀⢀⡴⠋⠁⠀⠀⠀⠀⡀⠐⠂⠀⠀⠉⠛⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣹⠟⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⢀⠐⠂⠈⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣀⠘⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠁⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡠⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠂⠄⠃⠀⠀⣀⣀⣠⣤⣤⡤⠴⠶⠶⠶⠶⠶⠶⠦⣤⣤⣄⣀⡈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⣀⣠⣤⠶⠞⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢁⣠⡴⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠶⠶⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠛⠛⠲⠶⢦⣤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⢀⣠⡤⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⢀⣀⣀⣀⡀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠉⠉⠒⠢⢄⠀⠀⠀⠰⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⠀⢀⠇⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⣀⡀⠤⠐⠊⠁⠀⠀⠀⢀⠎⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠈⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣦⡀⠀⠀⠀⠀⠉⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉⠀⠀⣠⠞⠛⣧
⠀⠀⠀⠀⢿⠛⣧⠀⠀⠀⠀⠀⠀⠀⢷⠈⠙⠲⣤⣀⡀⠀⠀⠀⠈⠑⠒⠀⠤⠤⠤⠤⠄⠐⠒⠈⠁⠀⣀⣤⠶⠛⠁⠀⠀⣽⠀⠀⠀⠀⠀⠀⣼⢳⡆
⢀⣀⣀⣀⣼⡇⠹⣇⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠉⠙⠛⠲⠶⠶⣤⣤⣤⣤⣤⣤⣤⣤⡴⠶⠶⠛⠛⢉⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⣸⠃⢾⣥⣄⣀
⢻⡍⠉⠁⠀⠀⠀⠻⢦⣀⠀⠀⢾⡁⠀⢀⠠⠄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠀⠀⠀⠀⠀⠀⢻⡄⢀⣠⠶⠋⠀⠀⣀⣀⣩
⠈⠛⠛⠛⠒⠓⠶⢦⣀⠈⠛⢦⣼⠿⣦⡈⠐⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣀⡴⠿⣾⠋⢁⣴⠞⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⣾⠃⠀⠈⠙⠳⢦⣤⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣀⣠⡴⢶⠛⠉⠀⠀⠹⣶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠶⠶⠶⠶⠦⠴⠦⣶⠶⠶⠶⠖⠛⠛⠉⠉⠀⠀⠀⢣⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠃⠀⠀⠂⠘⠀⠀⡀⠀⢧⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⡔⠘⠀⠀⠀⠀⢀⣀⠀⡀⠸⡆⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠑⠀⣆⠀⠀⠠⠀⡠⠒⠐⢀⠆⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢨⡀⠀⠀⠄⠀⡠⠔⠉⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠠⠐⠂⠄⡀⠀⠸⢤⡤⠐⠂⠉⠀⠀⠀⠀⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠤⠤⠤⠤⠤⠚⠀⠀⠀⠀⣀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⠦⣤⣤⣤⣤⣤⣤⣤⡤⠶⠶⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠀⢀⡤⠖⠁⠀⠀⣹⡆⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⢀⣽⡗⣰⠟⠀⠀⠀⢀⣨⣭⣄⠻⢦⣄⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠇⣴⡿⠁⣼⠏⠠⡄⠀⠀⢾⣏⠀⠀⣷⡄⠀⠀⠀⠀⢸⣿⠄
⠀⠀⠀⠀⠀⠀⣞⠀⡠⠋⣸⣿⠃⣼⡏⣠⠾⠃⠀⢠⣶⡙⡛⠋⣻⣇⠠⣤⡀⢴⣯⢉⣶⡄
⠀⠀⠀⠀⠀⢀⣈⡅⠀⢠⣿⡟⢰⣿⢉⣴⠶⢠⣾⢺⣿⠃⢸⡇⣿⡇⠀⣼⡇⣾⡏⢸⡿⠀⢳⡄
⠀⠀⠀⢀⣼⠋⣿⣀⡄⣾⣿⠁⣿⡇⣾⡏⠀⣾⡏⢸⣿⢀⣿⠃⣿⡇⣰⠟⠁⠿⠇⢸⡇⣠⠟⠁
⠀⠀⠀⢸⡏⠀⠈⠛⣹⣿⠇⠀⣿⣧⠹⠷⠄⠻⠃⣿⡇⠉⠁⢸⣿⠇⣠⠔⠂⠀⢀⡿⠉⠁
⠀⠀⠀⠈⠻⠄⣀⣴⠿⠃⠀⣠⡭⠁⠀⠀⣰⡿⠁⣿⡗⠀⠀⣬⡯⠀⢿⣦⣄⠠⠊
⠀⠀⠀⠀⠀⠀⠀⣴⣿⠀⣼⡟⠀⠀⠀⢠⣿⠇⢤⠉⠀⣀⢠⣿⠇⣀⣀⣤⡄⣤⡄⣴⣦⣾⠟
⠀⠀⠀⠀⠀⠀⢠⣿⡇⢰⣿⠁⣰⠖⡀⢸⣿⢀⣾⡆⣾⠋⢸⣿⢰⡿⢸⣿⠁⣿⠃⣿⡏⢿⡆
⠀⠀⠀⠀⢰⡎⢠⣿⡇⣼⡿⢸⡟⠀⠀⣾⡏⢸⣿⠸⣿⠀⢸⣿⢸⡇⢸⣟⢸⣿⢀⣿⡇⠀⢻⡄
⠀⠀⠀⠀⢀⣩⣽⣿⠀⣿⡇⠸⣧⣀⠀⢹⣷⠘⠿⠄⠻⠷⢺⣿⡈⠛⠈⠉⢀⣉⢹⡿⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠠⠞⠉⢧⠸⣿⠀⠈⣵⠂⠀⠀⢀⡴⠀⠀⠀⠘⢛⡥⠀⠀⠀⠘⢿⣾⣇⣀⡀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠙⠳⠸⣇⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣤⣀⡸⣦⡀⠀⠀⠀⠈⠛⠷⠶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠒⠒⠒⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣚⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢉⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢐⣡⣿⣿⣷⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢴⣴⣷⡆⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⠠⣑⣦⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠖⠒⠒⠻⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣇⣀⣀⣨⣷⣿⣾⣿⣿⣿⣿⠀⠀⢡⣏⠀⠘⠩⠀⠀⠲⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢩⡭⡥⠼⠿⣿⣿⣿⡟⠉⠀⠀⠀⢼⣂⠀⢐⠚⠺⣖⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⣀⣸⣿⠃⠀⠀⠀⠀⠀⠈⠋⠀⠀⠂⠀⠀⠂⠄⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡍⠨⢭⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠩⠬⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸




⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣉⣝⣋⣍⣹⣝⣹⣟⣏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠋⠉⠉⠉⠙⠛⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⢘⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⣀⠤⠈⠀⠀⠑⡀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⢀⡔
⠀⠀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢿⣀⣀⣀⠀⠄⠈⠁⣠⠤⠀⢠⡞
⠀⠀⡴⠁⠀⠀⠀⠀⠀⠘⠀⠀⣀⠀⠁⢐⣄⢘⣿⣿⣇⣀⠄⢀⡀⠀⢀⣰⠎⠀⢄
⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠠⣜⠃⠀⢐⠉⠉⠉⠛⠻⢿⣿⣀⣈⣀⣠⣿⡿⠎⠀⢸⠀⠀⠀⠀⠀⠀⣀⡀⢀
⢀⡀⠒⠀⠀⠀⠀⠀⠒⠀⠌⠀⠀⠀⠠⢕⡄⠀⠀⠐⠀⠈⠉⠙⠛⠉⠅⠀⠁⠠⠊⠄⡀⠀⠀⠤⠟⠛⠁⠀⡄
⠀⠳⡀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣰⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⣀⠘⠐⢿⡦⠀⠈⠢⡀⠀⠀⠀⠀⠃⢰
⠀⠀⠀⠐⠂⠈⠁⠀⠀⠀⢠⡀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢧⡔⠀⠀⠈⡄⠀⠓⣻⡀⠀⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⠊⡴⠁⠀⠀⡯⠀⠀⠀⠠⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠂⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠢⠖⠉⠙⢦
⠀⠀⠀⠀⠀⢀⣀⡀⠀⣀⣤⠤⠤⠶⠾⠦⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢉⡒⠃⠒⢤⠀⠀⠈⠑⣦
⠀⠀⠀⢀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠇⠀⠀⠀⠸⡃⢠⡀
⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⡀⢀⣀⡴⠂⠀⣿
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡍⠁⢀⠀⠀⠙⢦⣀
⠀⠀⠀⢡⠔⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣠⠵⢦⡀⠀⠈⠳⣤⡀
⠀⠀⠀⢦⠀⠀⢀⡤⢊⠀⠀⠀⠹⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠙⢦⣄⠀⠀⠙
⠀⠀⠀⠀⠙⠛⠁⠀⠸⡀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠓⠦⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣻⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢄⡀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠙⣆⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠘⣆⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⢦⡄⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠦⡤⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠈⠛⠲⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠘⠫⣀⠀⠀⠀⠀⠀⠀⠉⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣄⠀⠀⠀⠀⠀⠀⠉⠳⢤⡀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⣀⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣤⣄⣀⣀⣀⣀⣠⣤⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠤⠀⠂⠈⠉⠀⠀⠀⠀⠈⠉⠀⠒⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡠⢊⠀⡀⠁⠀⠀⠀⠀⠀⢲⣺⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⡠⠋⠔⣴⣾⣶⣦⠂⠀⠀⠀⠈⠹⠛⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠉⠲⠄
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡀⣁⢃⠀⠰⡀⠌⠀⡡⢀⡿⣿⣿⣿⠀⠠⠐
⠀⠀⠀⠀⠀⠀⠊⠁⠄⠈⣀⣁⠀⠄⠀⢋⢀⠈⡠⠂⠹⣿⣻⡟⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⢀⡐⣆⣠⠄⠀⣾⣿⣿⣷⠄⠀⠈⡄⠂⠀⠀⠘⢻⡽⠃⠀⠿⠗
⠀⠀⠀⠈⣽⠿⡟⠖⠀⣿⣿⣿⡿⡄⢁⠀⢱⠂
⠀⠀⠀⠀⠀⠈⢁⣀⠀⢽⡧⣿⢀⠺⠈⢠⠃⠀⠘⢈⠀⠀⢄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠃⠀⠈⠟⠋⠈⠀⢣⠀⠀⣰⣤⣦⣄⢠⠀⠐⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⢲⠃⠈⡀⣿⣟⣿⢿⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢳⡟⠀⠻⢶⣤⣬⣤⣼⣤⣷⡿⣯⡟⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⢾⡀⠀⠀⠀⢀⡠⠄⠀⠀⠛⠻⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠐⠦⠴⠂⠀⢻⣧⢀⠴⠊⠁⠀⠀⠀⠀⠀⠀⣻⣧⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠈⠀⠀⠀⠀⠘⣿⣿⡀⢀⡠⠔⠘⠛⠛⠛⠻⣿⣿⡀⢐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠈⠃⠀⠀⠀⢿⣿⣿⠏⠀⠀⠘⠃⠛⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⣤⠈⣿⣿⠀⠀⠀⠰⠁⠀⠆⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠁⠀⣾⣿⣧⣀⠀⠀⠁⣀⠁⠀⣀⣾⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣷⣶⠶⠴⠖⣛⣋⣩⣥⣤⣤⣴⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⣰⠏⠛⢿⣿⣿⣿⣿⣿⣿⡿⣟⣿⣿⣿⠿⢻⣌⢻⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠉⠉⠉⠀⣠⣾⣿⡿⠋⠁⠀⢘⣿⡄⠹⣿⣿⣷⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⣴⣿⣿⣆⠀⠀⠀⠀⠀⣠⡾⣻⣿⠟⣠⠖⠒⢦⣼⣿⢿⣦⡈⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⣰⣿⠋⠀⠹⣿⣦⣄⠀⢀⡴⣫⣾⡿⠃⠀⠹⣄⣃⣼⣿⠏⠀⠙⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠠
⠀⠀⣰⡿⠁⠀⠀⠀⠈⠻⣿⠷⣫⣴⣿⣿⣥⣤⣴⣶⣿⣿⠟⠁⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠗
⠀⢠⣿⠃⠀⠀⠀⠀⠀⢾⣥⣾⣿⣿⠻⠿⠿⠿⠟⠛⣹⢋⡛⢦⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠁⠀⠀⠀⠀⠀⠀⠻⣬⣅⠞⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣻⣅⡿⠆
⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⣀⣦⡄⠀⠈⣉⠿⣿⠛⡶
⠀⠘⣿⣇⠀⠀⠀⠀⠀⡔⣰⡐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠹⠉⠀⠀⠉⠀⠻⠃
⠀⠀⠹⣿⣦⡀⠀⠀⠀⠢⢉⠱⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠔
⠀⠀⠀⠙⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠋⠀⠀⣠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠀⠀⠀⠀⠒⠂⠁
⠀⠀⠀⠀⠀⠙⢿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⡿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣷⣶⣶⣶⣶⣾⣿⡿⠿⠟⠋⠁⠀⠀⠉⠀⠀⠂⠀⠀⠐⠒⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠐⠂⠐⠀⠂⠂⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠰⣍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⡀⠀⣄⡠⠀⢤⢖⠀⢄⠀⠀⢰⣷⣀⣰⣸⡍⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠂⠀⠀⠀⠉⠚⢩⡅⠀⣤⠀⠑⠈⢛⠀⠀⠀⠁⠀⠀⠀⠀⠀⠡⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⡴⠋⠉⠒⠛⠛⠃⠀⠀⢨⡿⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢻⣄⠈⢂⠀⡀⠀⠀⢀⠔⠀⠀⠀⠀⠀⢁⠀⠒⠂⠐⠂⠒⠒⠢⡈⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⢉⡷⠲⢀⠿⡿⢀⣶⣐⡖⠲⢄⡤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⢱⠸⡇
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢈⢠⡾⠆⣀⣀⠀⡇⠀⠀⣣⣠⡝⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠂⠀⠀⣘⡇⠀⠓⠈⠉⠉⠙⡀⠀⠀⠀⠂⢀⠀⣀⠀⠉⠢⡀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠁⡀⢀⡀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠉⠰⡮⠀⠀⠀⠀⠀⠉⠑⠀⢱⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠈⠁⠋⠁⠀⠀⡌⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⢿⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠠⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⢳⡀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠈⠀⠀⣠⠎⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠶⠦⠤⠐⠒⠚⠉⠉⠀⠻⣄⡀⠀⠀⠠⡄⠀⣠⣤⠞⠋⠀⠄⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⢳⠠⠉⠀⠀⠀⠁⢠⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠤⠴⠒⢦⠀⣧⠰⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡄⠀⠸⡆⢿⣆⠀⠘⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⣀⣀⣹⡀⢻⣆⣀⠀⠈⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠆⠀⠀⠀⠉⠉⠀⠀⠬⠣⢀⡿⠙⢧⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠎⠉⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠆⠒⠈⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡃⠀⠀⠓⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠐⠃⠉⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⡄⠀⠀⠀⠀⠀⠈⠀⠐⠘⠂⠀⠀⠀⠀⠆⠀⠘⠓⠀⠐⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢎
⠁⠀⠀⠀⠀⠈⠓⠋⠉⠀⠉⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠶⠋⠁⠈⠀⠉⠁⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⢤⡤⢀⠀⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢀⣀⣤⡤⠄⠒⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠙⣷⣿⣂⣀⣀⠹⡆⠋⠀⠁⠀⠉⠁⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢹⡄⠀⠀⠀⠀⠀⠂⠈⠁⠘⠉⠓⠐⠂⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠉⠁⠀⠐⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢀⠀⠀⠀⠀⠀⡀

⡀
⠃

⠀⠀⣀
⠀⠀⠉⠁⠠⠄⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠆⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠃
⠀⠀⠀⠀⠀⠀⠈⠋⠀⠲⠀⢴⠆⠀⡄⠀⣴⠄⠠⠤⠀⠺⠇⠀⠉⠀⠀⠀⠙⠀⠤⠀⣀⡀⢀⡀⢠⣤⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣶⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣦⢤⣠⠗⠂⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣮⣉⣩⣉⣭⣤⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣤⣶⣤⣾⡿⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⢠⣄⢉⣁⡈⣉⣤⢒⡹⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⢛⡛⢋⣭⡥⠂⠀⠀⠀⠀⠀⠀⠀⠈⢉⡋⠳⠛⠚⣁⣠⣤⠂⠀⠀⠀⣠⠄⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠋⠁⠀⠀⠀⠀⠠⠀⠄⢀⣄
⠀⠀⠀⠀⠘⠋⠙⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⢻⠶⠒⠒⣋⠩⠄⡀
⠀⠀⠌⠀⠀⠀⠀⠀⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣶⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⣤⣀⣈⣀⣠⠴⢟⡁
⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠰⣿⣿⣷⣿⣿⣿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠁⠄⠨⠄⠐⠈⠁
⠀⠘⠂⠀⠀⠀⠀⠀⠀⡹⠁⠀⠀⠀⠀⠀⠀⣀⠉⠀⠙⠁⡈⢁⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠈⠙⠢⠤⠤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣾⢷⣾⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤

⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⣾⣤⡆
⠀⠀⠀⠈⢳⣤⣽⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢩⠿⣶⠿⡏⠁
⠀⠀⠈⠛⢛⡿⣤⢾⣛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠋⠀⠿⠀⠉⠁⠀⠀⠀⠀⠀⠀⡀⢀⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢽⣿⣳⣿⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⡇⣀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠉⠏⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠴⠼⣟⢉⣷⠴⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⣤⢐⠋⠈⠗⠂⡄⠠⢀⠀⠀⠀⠀⠀⠠⠟⠉⡏⠙⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠀⠀⠀⠈⠃⠒⠊⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠏⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠧⠘⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠈⠑⠂⠤⠀⣀⣀⣀⠀⠤⠒⠉⠀⠀⠀⠀⠡
⠀⠀⠀⠀⢦⣼⣦⡴⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢠⣀⣴⢀⡄
⠀⠀⠀⠉⡽⢷⡾⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠐⢲⣿⣭⣿⡒⠂
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠈⠀⠋⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⢰⠀⡀
⠀⠀⠀⠈⠢⡄⠀⠀⠀⠀⠀⠀⠀⢐⠄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠠⡃⠀⠀⠀⠀⠀⠀⡸⠊
⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠄⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠊⠢⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣀⡠⠊⠖⠒⠒⠒⠒⢒⠒⠒⠒⠒⠂⠀⠀⠀⠀⠈⠉⠉⠉⠃⣤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠁⡜⢰⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⡀⠀⠢⠀⢀⠠⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠈⠁⠐⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⣀⣴⠊⠁⢀⣀⠀⠀⠀⠈⠙⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠉⠀⣀⣉⡐⠂⣄
⢀⠞⠁⠀⠀⠀⠀⠀⠀⠉⠐⠠⠤⠀⠈⠶⠒⠈⠀⠀⠀⠀⠀⠈⠁⠐⠠⠄⣀⣠⠔⠊⣁⠠⠔⠈⠁⠀⠀⠀⠀⠀⠙⠲⢤⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠱⡀⠀⠀⠀⠀⠀⠠⠁⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠘⢃⠀⠀⠀⢄⠀⠀⠀⢠⠂
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠐⢍⠀⠀⠈⠀⠀⠀⠀⠈⠰⡂
⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⠀⠀⠀⠀⢤⠀⠁⠀⠀⠀⠄⠀⠀⠀⢤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠉⠀⠂⠀⠠⠸⠀⠀⠀⠀⠘⠂⠀⠰⡀⠈⠀⠉⠢⠄⠀⠈⠁⠐⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠀⠀⠀⣠⠂⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⢙⠀⡄⠀⠀⠀⠙⢠⠄
⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠛⠃⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡅⠀⠀⠀⠀⠀⢁⡐⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⢀⡀⠀⠈⡄⢀⠄⠀⣀⠔⠀⠉⠀⠀⠀⡇⠀⠀⠀⠈⠓⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⡀⠀⠀⠀⠀⠉⠢⠀⠱⡈⠈⠁⢀⣀⡀⠄⠁⠀⡠⠁⠀⠀⠠⡄⠀⠈⢁⡀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⢀⠈⠓⠤⣄⣀⣀⡠⠤⡺⠀⠄⠒⠉⢀⠁⡀⠈⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠁⠀⠀⠀⠈⠱⢠⠊⠀⠀⠉⠒⠀⠠⠤⠤⠗⠊⡁⠢⠤⡤⠒⠉⠀⠀⠀⠀⠉⠶⣤⡄
⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠆⢈⠢⣄⠋⠐⠁⠃⡄⠠⠁⠀⠰⡄⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡈⠀⠀⠀⠈⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡐⡠⢉⠀⠒⠂⠁⠀⠀⠀⠀⠈⠑⠠⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⠒⠔⠒⠒⠂⠬⠗⠂⠼⠇⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠉⠀⠑⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠌⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⠂⡔⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡘⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣼⠀⢳⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⣿⡀⠘⢆⠙⢕⡠⢀⡁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡛⢿⢿⣿⣷⣦⣌⣷⣄⠈⠁⠨⣵⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⠀⠄⠉⠛⠿⢭⣙⠳⢦⣤⣤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢿⣿⡷⠶⣴⣿⣶⣤⣈⠙⠲⠤⣉⣛⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣀⠀⠉⠛⠒⠲⠻⠿⣿⣿⣿⡶⠂⠄⠉⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⠶⠶⢶⣤⣤⣄⣢⣬⣉⠛⠛⠓⠚⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠿⣷⣶⣤⣤⣤⣄⣉⠙⠛⠛⠛⠛⠛⠋⠋⣙⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠶⠦⠭⠭⠍⢩⣉⣭⣭⣥⣤⣴⣶⣾⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⣹⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢰⣽⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣆⡀⠀⡀⠀⠀⡀⠀⠀⢀⣼⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⢶⣤⣤⣴⣴⣦⣾⣷⠾⠿⠛⠁



⣿⡏⢹⣟⠿⣿⢛⢟⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡦
⠀⠀⠀⠀⠀⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣛⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷⡄
⠀⠀⠀⠀⢰⣿⣧⠀⠀⠀⠀⠀⠀⠀⠺⠿⡿⢟⣃⡀⠀⠀⠀⠀⠀⠀⢀⠆⠀⢁⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣟⠂
⠀⠀⠀⢀⣿⣷⣿⣇⠀⠀⠀⠀⠀⠸⠿⠿⢿⠿⣟⣗⠀⠀⠀⠀⠀⠀⠀⠦⠉⠀⠄⠀⠀⠀⠀⠀⢘⣿⣿⣿⡀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣦⡀
⠀⠀⠀⣼⣿⣿⣿⣿⡆⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⡿⣇⠀⠀⠀⠀⡌⠀⠂⠠⠀⠈⠀⠀⠀⠀⠐⣻⣿⣿⣿⡷⠄⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣏⠙
⠀⠀⢰⡿⠿⣿⣿⣿⣿⠀⠀⠀⢰⡾⣭⣽⣽⣷⠾⣿⠿⠇⠀⠀⠠⠀⠀⠀⠀⠀⠐⠡⠀⠀⠀⠠⢿⢿⣿⠿⡷⠀⠀⠀⠀⠠⠶⠿⠿⣾⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠘⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠰⠷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠙⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠶⠚⠛⠋⠉⠉⠉⠉⠉⠉⠛⠛⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠁⠀⠀⠀⢀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⡠⢇⡀⠀⠀⠀⢠⡄⠠⠀⠀⠒⠀⠀⠀⠀⠀⠀⠈⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠐⠣⡜⠐⡇⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣈⣧⣤⣤⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⡈⠀⠀⢘⠃⠀⠀⢀⣀⡤⠤⠶⠒⠚⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠉⠈⣀⡥⠴⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡧⠖⠋⠁⠀⠀⠀⠀⠀⣀⣀⣤⠤⠴⠒⠒⠚⠋⠉⠉⠉⠉⠉⠉⠉⠻⡉⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⢀⣠⠤⠖⠚⠋⣭⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⢻⡀⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⡀⠀⠀⠀⠀⣷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠴⠋⣧⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠀⠀⠀⠰⠊⠉⠁⠐⠢⠘⠛⠃⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⡀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠋⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠞⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠳⣄⠉⠉⠙⠓⠖⠒⠖⠒⠒⠚⠛⠉⢀⣠⠞⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠈⠙⠒⢦⠤⣤⣤⣤⡤⠤⠤⠶⠒⠋⠉⢳⡀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⢠⠏⢰⠇⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⢰⠀⢠⠏⠀⡿⠀⢿⠀⠄⠨⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⢸⠀⡞⠀⢀⣧⠀⠚⡆⠀⣀⡀⠀⠀⠀⠀⠀⠀⢹⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣀⠀⠀⢀⡞⢰⠏⠀⠄⣟⠉⠉⠁⠀⠀⠃⠀⠀⠀⠀⠀⠀⢸⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⠋⠉⠀⠘⠓⠓⠒⠛⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡖⠋⠉⠉⠓⢄⠀⠀⠀⠀⠀⠀⣰⠊⠉⠉⠉⠳⣦
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠈⣷⠶⠶⠶⠒⠺⣇⠀⠀⠀⠀⠀⢈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠒⠒⠛⠁⠀⠀⠀⠀⠀⠈⠙⠛⠓⠚⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠁⠀⠀⠀⠈⠉⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⣷⣲⣶⣶⣶⣶⣶⣶⣶⣖⣺⣯⣵⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠉⠉⠉⠉⠉⠉⠉⠁⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠏
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⣍⣽⣭⣹⣟⣽⣭⣭⣹⣿⣝⣭⣯⣯⣍⣹⣿⣯⣽⣿⣯⣽⣿⣯⣽⣿⣿⣽⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⢀⣀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢄⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⡤⢀⡄⠠⡔⠒⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠓⠒⠒⠒⠂⠸⢄⢸⣄⠀⣸⣤⡡⠴⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⣃⠀⠀⠀⠀⢀⣀⣮⣀⡉⠛⠁⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠈⠉⠉⠉⠁⠁⣀⡬⠶⠈⠁⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⢐⢲⣾⣿⣿⣥⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠂⠀⠀⠘⣄⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠐⣄⠐⠃⣠⠀⠀⠀⠄⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢹⠀⠉⠐⠛⡄⠠⠟⢲⣂⠀⠤⢄⠉⠉⣠⠔⠊⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠶⠦⣄⠀⠚⠇⠀⠘⣧⣀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⣠⠴⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠈⣧⠀⠀⣀⡴⣇⢈⡗⢂⠔⠠⠄⢤⠐⠢⠀⠊⠁⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⣷⢀⠾⠉⠀⠙⠢⠁⡾⠁⠀⠀⠈⠀⢠⡀⠴⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⢠⠁⠀⠨⠀⠀⡀⠄⢧⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢦⣀⠄⠀⠀⠀⠀⡼⠀⢸⠆⠈⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⣧⡀⣞⠀⠀⠀⠀⡀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣿⠁⡿⠀⠐⠰⠚⠀⠀⢹⡄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⢹⣠⡇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠠⣨⠄⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⡼⢹⠇⠀⠀⠀⠀⠠⠚⢘⡇⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏⠀⠀⠉⠉⡀⠚⠃⠸⢀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠸⠀⡷⠀⠀⡀⠠⢤⡀⠐⣧⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⣿⡀⠀⣣⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⢻⠀⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠐⠎⠡⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠶⣤⡴⠞⠁⠀⠀⠀⠰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠰⢦⣤⣀⣀⣤⠴⠂⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⣀⠈⢉⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⢹⡀⢸⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠸⡇⡘⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⢱⡇⠀⠀⠀⠀⠀⠀⠀⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⡄⠀⠀⠀⠀⠀⠀⠀⢈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠻⣦⡀⠀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠶⠶⠞⠛⠉⠀⠀⠀⠀⠈⠙⠓⠶⠶⠞⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠯⢯⣿⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠒⠐⠀⢾⣯⠿⠽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣶⣶⡀⠀⠀⠀⣀⠔⠲⡀⠀⢰⣿⣷⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢀⡶⠶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠙⠋⠀⣀⠴⠊⠁⠀⠀⣣⠀⠀⠉⠁⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠶⣆
⠀⠀⣀⣀⣸⣇⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⠀⠾⠀⠒⠒⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⢀⣿⣀⣀⡀
⠀⢸⣏⠉⠛⢿⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠤⣀⠀⠀⠀⠀⢀⡠⠂⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣸⠟⠋⢉⣿
⠀⣀⣉⣿⣦⠄⠀⠀⢿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⡀⠀⠀⠀⠉⠁⠈⠉⠁⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⠇⠀⠀⢤⣾⣏⣁⡀
⣾⡋⢉⣀⣠⣤⣴⣶⣄⡈⠛⢷⣤⡀⠀⠀⠀⢀⣴⠾⠋⠉⠉⠒⠤⠄⣀⣀⣀⣀⡀⠠⠔⠊⠁⠉⠛⢶⣄⡀⠀⠀⠀⠀⣠⣴⠟⠋⣀⣴⢶⣤⣤⣀⣈⠉⣻
⠈⠛⠛⠉⠉⠀⠀⠀⠉⠻⢶⣄⡈⠛⠷⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣠⡴⠟⠉⣀⣴⠞⠋⠁⠀⠀⠈⠉⠉⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⣀⣴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠉⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⣦⣤⣄⣀⣀⣀⣀⣀⣤⣤⡶⠾⠛⠉
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣇⣀⣀⣀⣄⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⠋⡄
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢀⣭⠂⠀⠀⡀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⣴⡌⠀⢀⣾⡷⢧⡀
⠀⠀⠀⠀⠀⣺⣁⠀⠀⠀⠀⢀⣋⠉⠀⠀⢠⡀⠀⠀⠜⠉⡀⠀⠀⢠⡒⡄⠙⠁⠀⣹⣿⡶⠉⠛
⠀⠀⠀⠀⣠⡾⠉⠀⠀⠀⠠⠛⠃⠀⣀⠀⣪⢡⡄⣀⠶⠈⠃⢰⠀⣠⡗⣧⡀⠁⠈⡿⢋⣠⠴⠛⡇⠠⡆
⠀⠀⠔⣰⣿⠗⣂⠀⣧⡀⢰⠿⠀⢠⣼⠀⣿⢼⡁⠋⢀⣴⡷⣴⣏⣁⣀⣀⣬⠷⠆⠴⢻⠄⢀⠤⠁⣰⢡⡄
⠀⠰⡐⣿⡉⡖⢀⡈⠀⠕⠆⠀⠻⠆⠉⠰⠁⠈⣧⠀⠘⠈⠰⣯⣤⣠⣄⣤⣤⣾⡷⠈⢼⠏⢩⠀⠀⡍⠀⢭
⠀⠀⠃⣿⣷⣭⠦⠦⢖⠌⠀⠀⢠⠀⠀⠀⠀⠀⢸⣦⠀⠀⠀⠻⣞⣛⣚⣛⣋⣹⠇⠀⠀⠐⠀⠀⣰⠦⠀⠰⢧⡀
⠀⠀⠀⠀⠙⠉⠀⠀⠀⠀⠀⢴⣿⣷⡖⢂⠀⠀⢸⠁⠐⠀⠂⠀⠈⠙⠀⠀⠊⠁⠀⠀⠀⠀⠀⠚⠿⠿⢿⠿⠿⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠋⠓⠈⢧⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠄⠀⠘⠘⠀⢰⠁⠘⠀⠘⠉⠃⠀⠀⠀⠘⠋⠀⠘

⠆⠀⠀⠀⠀⠀⠀⠂⠄⠀⡀⠀⠀⠀⢿⣦⣤⡴⢿⠃⠀⠀⢀⠀⢄⠀⠀⠲⠀⠀⠀⠀⠀⠀⠐⠂⠁⠀⡀⠀⠀⠘⣷⣤⣤⡴⡿⠀⠀⠀⢀⠀⣄
⠀⢰⡟⠋⠁⠰⠀⠀⣀⣥⣝⠂⡤⠀⠈⠙⠙⠛⠁⠀⠀⢰⡀⢠⣦⠟⢠⠀⠀⢴⡟⠉⠈⠢⠀⠀⣀⣬⣛⢀⡆⡀⠈⠉⠙⠋⠀⠀⠀⣴⠀⣰⡴⠛⡀
⠀⠘⡃⠀⠀⠀⠃⢠⠞⢡⠈⠏⡀⠀⠀⠀⠐⠂⣠⡄⠠⢮⣭⢿⠿⣄⠁⠀⠀⠸⠀⠀⠀⠐⠀⡠⠏⣄⠉⢋⠀⠀⠀⠀⠘⢀⣤⡀⠠⣯⡭⣿⢯⡈⠃
⠀⠀⡈⠐⢦⣁⠀⠃⡄⠀⠀⠀⠀⠆⠀⡄⠀⠊⢉⡡⠐⠛⠣⠿⠰⠋⠀⠀⠀⠀⡁⠐⢦⡇⠀⠃⡀⠀⠁⠀⠠⠀⠀⠄⠐⠉⣉⡅⠒⠛⠲⠟⠸⠉
⠀⠈⠛⠀⠀⠁⢀⡀⠀⠂⡀⠀⠀⠼⠃⠀⠀⡴⠛⠁⣰⣾⠿⠲⠀⣀⠀⣤⠀⠘⠋⠀⠀⠀⣀⡄⠀⠂⠀⠀⠀⠜⠁⠀⠀⠜⠛⠀⣴⡾⠿⠦⠀⡀⢀
⡶⠒⠀⠀⠀⠀⠺⠣⠀⠀⠀⠂⠁⢀⠀⠀⣀⢠⠀⠀⠹⡛⠛⠛⢃⣼⣿⣿⠖⠂⠀⠀⠀⠀⠻⠃⠀⠀⠐⠀⠀⣀⠀⠠⡀⠀⠀⠀⠿⡛⠛⠛⢀⣽⣿
⠛⠀⠀⠀⢀⠀⠀⢀⡀⠀⣀⠀⠀⠙⠁⠠⠈⡐⢄⠀⠀⠻⠃⠀⡀⡀⠿⠉⠓⠀⠀⠀⢀⠀⠀⢀⠀⢀⡀⠀⠀⠛⠀⠠⠡⡂⣌⠀⠀⠿⠀⢀⢀⡀⠟
⠀⠰⠄⢈⡘⠀⠤⠊⠀⠈⠚⠃⠀⠀⠀⠀⠀⠃⠀⠀⣀⣀⠀⠠⢿⣿⠂⠀⠀⠠⠤⣀⢈⡈⠄⠂⠀⠈⠻⠂⠀⠀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠸⣿⣷
⠠⠄⠀⡂⠄⣈⠒⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢰⣦⣤⣤⡁⠀⠀⠈⠀⠀⠀⠠⠄⠐⠠⠈⡏⠒⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⣰⣤⣤⣬
⠀⠀⠐⠁⠀⠐⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⠀⡄⠀⡴⠁⠀⡌⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⢀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⡞⠀⢢⡄
⣱⣄⡠⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⢀⣠⣥⡄⠸⣿⣷⣤⡄⠁⠀⠀⠀⠀⢊⣴⣀⡄⠀⡀⠀⠀⠀⣴⡀⠀⠀⠀⢀⣠⣡⡄⢸⣾⣶⣤
⢀⠀⠀⠀⢻⣦⠀⠀⠘⣿⣴⡾⠿⠟⠋⠀⠀⠀⠈⠉⠁⠀⣠⣶⣶⣦⡀⠀⢀⠀⠀⠀⣿⣆⠀⠀⢹⣿⣶⡾⠿⠟⠁⠀⠀⠀⠉⠉⠁⠀⣴⣶⣶⣦
⠸⣄⢠⢀⣼⡟⠀⠀⠀⠿⠋⠀⣀⠀⠀⢀⣀⣴⣾⠃⠀⣀⠹⠟⠛⣽⡗⠀⠸⡀⢠⣀⣿⠏⠀⠀⠸⠟⠁⠀⣀⠀⠀⣀⣀⣴⡿⠀⢀⡈⠹⠛⠩⣿⡇
⠀⠈⠛⠛⠁⠀⠠⠀⠠⠀⠀⠀⠛⠀⡞⠉⠀⠀⠙⠄⠀⠁⠀⠀⠀⠚⠁⠀⠀⠉⠛⠋⠁⠀⠀⠘⠀⠀⠀⠈⠋⢀⡎⠉⠀⠈⠳⠀⠈⠃⠀⠀⠐⠋
⠆⠀⢀⢀⠀⠀⠀⠊⠀⡀⡀⠀⠀⠀⢿⣦⣤⡴⢿⠃⠀⠀⢀⠀⢤⢀⠀⠻⠂⠀⠀⣀⠀⠀⠐⠀⠀⢀⡀⠀⠀⠘⣿⣤⣤⡴⡿⠀⠀⠀⣀⠀⢄⡀
⠀⢰⡞⠉⠉⠑⠀⠀⣀⡥⣍⢀⡔⢀⠀⠉⠉⠉⠀⠀⠀⢰⣀⣠⣦⠛⣡⠀⠀⢰⡞⠉⠀⠲⠀⠀⣠⡤⣏⢠⡆⡀⠈⠉⠉⠉⠀⠀⠀⣦⣀⣰⣶⠋⡀
⠀⠘⡁⠀⠀⠀⠁⡠⠚⠡⠀⢋⡀⠀⠀⠀⠘⢃⣠⡄⠠⢮⡤⣿⠻⣄⠁⠀⠀⢘⠀⠀⠀⡀⠀⡄⠏⠤⠈⢃⠀⠀⠂⠀⠘⢀⣤⡀⠰⣧⡤⣿⢣⣈⠁
⠀⠀⣀⠀⢦⡥⠀⠃⡄⠀⠀⠄⠀⠆⠀⠀⠐⠉⣁⡥⠐⠋⠒⠟⠰⠋⠀⠀⠀⢀⡁⠐⢦⡅⠀⠃⡀⠀⠁⠀⠐⢀⠀⠄⠐⠉⣈⠄⠐⠛⠒⠟⠐⠁
⠀⠈⠛⠀⠀⠀⢀⡄⠀⠂⡀⠀⠀⠼⠃⠀⠀⠼⠋⠁⣰⣿⠟⠓⠀⣀⡀⣶⠀⠘⠋⠀⠀⠀⣀⡄⠀⠂⠀⠀⠀⠞⠁⠀⠀⠎⠉⠀⣴⡿⠛⢂⠀⣄⢀
⡗⠋⠀⠀⠀⠀⠹⠓⠀⠀⠀⠃⠁⣀⠀⠀⣄⠠⠀⠀⠹⣏⠙⠙⢁⣼⣿⣿⡓⠃⠀⠀⠀⠀⠛⠃⠀⠀⠈⠂⠀⣀⠀⠠⡀⠀⠀⠀⠻⡋⠛⠙⢠⣽⣿
⠙⠂⠀⠀⢀⠀⠀⠀⡀⠀⣀⠀⠀⠉⠁⠠⠈⡐⢌⠀⠀⠻⠃⠀⡀⡀⠿⠉⠓⠀⠀⠀⢀⢀⠀⢀⠀⢀⠀⠀⠀⠉⠀⠠⠀⡂⠌⠀⠀⠛⠁⢀⢀⡄⠟
⠀⠐⠠⢈⡐⡀⠤⠁⠀⠈⠚⠃⠀⠀⢀⠀⠀⠁⠀⠀⣄⡀⠀⠀⢿⠿⠁⠀⠀⠐⠠⣠⣐⡀⠄⠀⠀⠈⠚⠂⠀⠀⡀⠀⠀⠀⠀⠀⣄⡀⠀⠰⢿⢟
⠀⠄⠀⡐⠆⠊⠑⠒⠠⠀⠀⠀⠀⠀⠘⠀⠀⢰⢦⣴⡤⡀⠀⠀⠀⠀⠀⠀⠠⠀⠐⡰⠀⡏⠓⠂⠀⠀⠀⠀⠀⠀⠋⠀⠀⢰⢦⣴⡤⡀
⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠆⠀⡴⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⢀⠀⠀⠠⠀⠀⠀⠀⠀⢀⡄⠠⠀⠀⡖⠀⢠⡄
⡵⣄⡤⠀⣀⠀⠀⠀⣰⡆⠀⠀⠀⣀⣠⣤⡄⠸⣿⣿⣤⠄⠀⠀⠀⠀⠀⢪⣵⣤⠄⠀⡀⠀⠀⠀⣼⡀⠀⠀⠀⣀⣤⣤⠄⠸⣿⣷⣤
⢠⠀⠀⠀⢻⣧⠀⠀⠘⣿⣶⡾⠟⠛⠁⠀⠀⠀⠀⠉⠁⠀⣴⣾⣿⣶⡄⠀⢀⠀⠀⠀⣿⣆⠀⠀⢹⣿⣶⠿⠟⠛⠁⠀⠀⠀⠈⠉⠀⢀⣴⣾⣷⣦⡀
⠘⣆⢰⢀⣼⠟⠀⠀⠀⠟⠉⠀⣀⠀⠀⢀⡠⢴⣿⠃⠀⣀⠙⠛⠁⢿⡇⠀⠸⡀⡠⣀⣿⠏⠀⠀⠘⠟⠁⠀⣀⠀⠀⣀⠤⣴⣿⠀⢀⡌⠛⠋⠙⣿⠇
⠀⠈⠙⠛⠁⠀⠀⠀⠠⠀⠀⠀⠉⠀⠞⠉⠀⠀⠙⠂⠀⠉⠀⠀⠀⠋⠀⠀⠀⠈⠙⠋⠀⠀⠀⠐⠀⠀⠀⠈⠉⠠⠎⠁⠀⠀⠱⠀⠈⠁⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⠀⡀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠈⠁⠁⠀⠀⠀⠁⠁⠀⠈⠈⠀⠁⠀⠀⠀⠁

⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠒⠀⠀⠠⠇⠈⠀⠀⠄⠈⠀⠀⠀⠀⠙⠃⠀⠀⠀⣀⣾⡿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠈⠀⠣⠀⡀⠰⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠀⠀⠀⢠⠆⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠁⢀⡾⠁⠀⠀⠀⠀⠀⠀⠑⠀⡇⠀⢀⠋⠆⠋⠀⠀⠀⠀⠀⠀⠐⠀⣀⣀⠀⠀⠀⠀⣾⣿⣆⠐⠀⠀⠀⠀⠀⢠
⡀⠀⠀⠀⠀⢀⡾⠁⠀⢀⠀⠀⠀⠀⠀⠀⠠⢀⠀⠸⢀⠄⠀⠀⠀⠀⠀⠀⠜⢠⣶⣟⣽⠃⠀⠀⠀⠙⣿⣿⣇⠀⠀⠂⣠⠔⠁
⣗⠀⠂⠀⣤⣿⣤⠾⠗⠋⠀⣀⡂⠀⠂⠀⠀⡈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣰⢟⣽⡟⠃⠀⠀⠆⠀⠀⠈⠙⠇⠀⢀⠀⠡⣠⣴⣿⡆⠐⠂⠀⢐
⣿⠄⢠⣶⠛⠋⠀⠀⠀⢀⣾⣿⣿⣦⠀⠀⡀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⡿⠛⠉⠀⠀⠀⢀⡰⠈⠀⠀⠀⠇⠀⠀⠀⠀⠘⣿⣿⣷⠀⠀⠀⣼
⠁⠀⠋⠀⡠⠐⣂⣐⠠⡈⠻⣿⡿⠏⠀⠈⠁⡀⠀⠀⡆⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⠃⠁⠀⠀⠀⢠⠀⠀⠀⢠⣾⣿⣿⡇
⡂⠀⠀⠈⡔⠁⣠⠀⡁⠌⠀⠀⠀⣴⣦⡀⠀⠃⠀⠈⠔⠁⠀⠀⠳⠀⠁⠀⠀⠀⠐⢂⠉⠨⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⠻⣿⡿⠁⢀
⡅⠀⠀⠀⠆⠀⠉⠁⢠⠂⠀⢀⣾⣿⣿⣷⡄⠀⠀⠀⠀⠋⠀⢁⣀⠀⠈⠃⠀⢀⠀⠀⠀⠀⣀⠠⠀⠀⢄⠠⠐⠀⠀⠣⠄⠊⠀⠀⡀⠀⠀⠀⡁
⠄⠀⠀⠀⠁⠁⠤⠁⠀⠀⢰⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠈⡉⠀⠁⠀⠠⠀⠁⠐⠐⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠀⠀⡃⠀⠡⠁⠀⠀⡅
⠃⠠⠄⠀⠀⠀⡀⠀⢀⠀⢸⡏⠉⢹⣏⣉⢹⣧⠀⠀⠀⠐⠂⠀⡀⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⡀⠀⠃⠀⠀⠆
⡀⠡⠈⠀⣰⣦⠀⠀⠁⠀⢸⡏⠉⢹⡏⢉⢸⡿⠀⠈⠀⠀⣀⠀⠐⠀⢀⠀⠐⣶⡀⠀⠀⠀⠀⠀⠀⢀⠀⠈⢿⣿⣿⣷⣄⠰⠄⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠉⠉⠄⠀⠀⠸⣷⣿⡇⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⠈⠉⡁⢀⣶⣆
⠀⢰⡎⠘⠛⠟⠃⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠘⠂⠀⠸⣧⣿⡿⠁⠀⠀⠀⠀⠀⠀⡁⠁⠀⠀⠀⠀⠀⠘⣿⣿⡆⠀⠀⠀⠉
⣤⡿⠁⠀⠀⢀⠀⠀⢀⠀⠀⢰⠀⠀⠀⠀⣤⡀⣤⣄⢀⣤⠀⠀⠀⠀⠀⢹⡟⠀⠀⠀⠀⠸⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟
⡿⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠹⢿⣾⣿⣾⣿⣧⣀⠀⠀⠀⠻⠃⢀⠀⠀⠀⢀⠤⠀⠀⣀⠀⠤⠀⠀⠀⠀⠀⢀⠀⢀⣆⠀⢀⣴⠞
⠁⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢊⢙⠁⢀⡀⠀⠀⠈⠉⠉⠉⠙⠛⠀⠠⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠂⠀⠀⠀⠁⠀⠄⠀⠀⠀⣾⢿⡀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡼⠀⠁⠀⠚⠈⠁⠀⠀⠘⠃⠀⠀⢀⠀⠀⠠⠀⠀⠀⠑⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⣿⣧⠀⠀⣸
⠀⠀⠈⠀⢀⣴⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣂⠀⠀⠀⠧⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⠤⠄⠀⠤⠤⠀⠀⠀⠀⠀⢠⣿⣿⢻⣿⡆⠀⠋
⠀⠀⠀⠔⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⣀⠀⠀⠀⡀⠀⡀⠀⠀⠀⢀⠀⡀⠀⠀⠀⣀⠀⠄⠀⠄⠀⠀⠀⣾⣹⣿⣿⡟⣿⡀
⣶⣦⠀⠋⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀⠂⠀⠀⠀⢀⣿⣿⣿⡄⠀⠀⠀⠈⣤⣤⣤⡤⣤⣤⡄⠠⠀⠈⠁⠀⠀⠂⡀⠀⣠⠈⠛⠿⠿⠿⠿⠟⣡⣴
⠟⠋⠀⠀⠀⠀⠄⠀⠀⠀⢀⢿⣋⡁⠀⢀⠘⠁⣾⣿⣿⣿⣿⠀⠀⠀⠀⢻⣿⣿⡇⢸⣿⡧⢀⠔⠀⠂⡀⠀⠰⠀⠀⠀⠈⠁⠢⠆⠀⠀⠾⣿⡿
⠀⠀⠀⠀⢠⠀⠀⠀⠉⡄⠀⣸⣿⣦⡀⠆⠀⠰⠿⠿⣿⡿⠿⠧⠀⠀⠀⢸⣿⣿⡇⢸⣿⡇⠨⠄⠑⡀⠡⠠⠆⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠁⠈⠀⠀⠀⠀⠠⠀⠀⠀⣸⣿⣿⣿⣷⡄⠀⠐⠀⠀⠉⢡⡄⠀⠀⠀⠀⠀⠙⠛⠓⠚⠛⠁⠀⠀⠀⠄⠰⠀⠀⠀⠀⠀⠂⠚⠃⢠⠀⠀⠈
⠀⠒⠂⠉⠀⠀⠀⠀⠀⠀⠛⠿⠿⠟⠛⠉⠀⠀⠀⠀⠀⣿⣇⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠆⠘⠀⠀⠀⠀⠀⠁⢐⡀⣘⠀⢀
⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠘⣿⣿⣡⣶⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⡀⡃⠈⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠆
⣀⢀⡀⣠⠂⠀⠈⠀⠀⠁⢁⠀⠀⠀⠐⠀⣀⠁⢠⡁⠀⠀⠈⠻⣿⡇⠀⠀⠀⠀⢀⣶⣠⣿⣷⣿⠁⠀⠀⠀⠀⡀⢤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⡿⢿⡿⠿⡿⡻⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣻⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠂⠄⠀⠀⢀⠀⣿⢀⢀⠀⠀⣀⣤⣶⣿⠿⠛⠁⠀⠀⠸⣿⡀⠀⠀⠀⠀⠄⠀⠀⣠⠿⡔⠠⢤⣶⣔
⠀⠐⠂⠀⠀⠠⠀⡀⢱⠇⠉⣠⣴⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⢻⣧⠀⠅⠀⠀⠀⣀⣴⠋⠀⠈⢷⠀⢹⠀⡀
⠐⠀⠀⠀⠁⢀⣼⠛⡄⠀⣾⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⣇⠀⠁⠀⡠⢚⡁⠀⠀⠐⠀⠑⠪⠀⠠
⢀⠀⠀⠀⢰⡿⠃⠀⠘⠦⡘⢿⣿⣆⠀⠀⠀⠀⠀⢀⠀⠀⣐⣶⣶⣿⣿⣀⠂⠈⠉⠽⠧⣶⡆⣶⣚⠁⠑⠂
⠀⠀⠀⠠⠾⡶⠀⠀⠀⣤⠤⠂⠘⣿⡆⠀⠀⣀⣴⣼⣗⣴⣿⣿⡿⠿⠿⣛⣛⣛⣻⣿⣶⣤⡀⢝⠙⠁⠄⠀⠈
⠀⠄⠘⣷⣙⣁⣶⠀⡔⠫⠂⠀⠀⢸⣿⣠⣼⣿⡿⠿⣛⣩⣥⢶⣾⣛⣿⠽⠿⠿⠟⠛⢻⣿⣷⠘⠏⠀⡀⠂
⠐⠀⠀⠁⠀⣴⣝⡀⣯⠢⢀⣠⣴⣾⡿⢟⣫⣵⢶⣻⡯⠷⠛⠋⠉⠀⠀⣀⣀⣤⠤⠤⣾⣿⡏⠀⠀⠆⠱
⠘⠀⠀⠀⠀⢈⣿⠀⠃⣴⣿⠟⣫⣵⢾⣿⡿⠞⠉⠁⢀⣀⡤⠴⠒⠛⠉⢁⣀⣠⣤⣴⣿⡏⠀⠠⠼⠀⡤⠑
⠀⠀⠀⠛⠉⠁⠸⠀⠀⣿⣏⣼⢫⡿⠋⠁⢀⣠⠴⣚⡩⠅⠀⠀⠀⠀⠈⡉⠁⠀⠀⠀⠹⣿⡄⣀⠗⠀⣈⠳⠐
⠀⠀⠀⠀⠀⡢⠠⡀⣀⠈⠻⣿⣿⣷⣤⣞⣫⡴⠋⠁⣾⣿⠄⠀⠀⠀⢾⣿⠆⠀⠀⠀⠀⣿⡇⢐⣀⠠⣄⠋
⠀⠀⠠⣠⡼⠀⡐⣤⠏⢶⣂⠄⠙⠻⣿⡏⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠁⢀⡤⠀⠀⠀⣿⠇⣿⢿⡇⣡⣤⡀
⠈⠀⠀⢰⡿⣼⡅⠁⠀⠀⠋⢲⠀⠀⣿⡇⠀⠀⠀⠀⣴⣄⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⣼⡟⠀⣿⣿⡿⣋⣽⣿
⠀⠀⠐⡿⠁⠀⠭⡉⠁⣴⣿⠈⠀⠀⢸⣿⡤⣄⡀⠀⠀⠙⢿⣶⣶⣶⡾⢟⣁⡤⠤⠔⣿⣷⡶⠟⢻⣾⠟⡡⠈
⠀⠀⠈⣱⣇⠀⠈⠓⠂⣉⣋⣡⣶⣶⣿⣟⠙⢾⠉⠉⡷⠒⣶⠒⠒⠂⠘⡁⠀⣀⡤⠞⠛⠷⢭⣳⢜⣿⡆⠑
⠀⠀⠂⣾⣣⠀⣠⣾⢿⣻⠿⠟⠋⠉⠁⠈⢳⠞⠀⣸⠃⢀⡿⠤⠤⠴⠒⠋⠉⠁⠀⠀⠀⠀⠀⠙⢿⣿⠠⠄
⠀⠉⠃⠀⢃⣼⣿⣟⠉⠀⠀⠀⠄⠀⣠⠖⢁⡠⠶⠿⠴⠾⠦⠤⠤⢤⣤⣴⠶⠶⠶⠶⠚⠛⠛⠛⠉⢻⣷⠈⠄
⠀⠈⠀⣴⣿⡟⠉⠹⣧⡀⠀⠀⣠⠞⢁⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠆⠀⠀⠀⠀⠀⠀⡀⠀⠀⢻⣧
⠀⠂⠀⢿⣯⡀⠀⠀⠈⢻⣶⣾⣥⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠠⠐⡌⠻⣿⣦⣤⣴⡿⠋⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⣿⡇
⠐⡀⠀⣸⠃⠀⢍⠉⠁⠐⡀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠰⣾⠋⠀⠀⠀⠉⠒⣆⠙⡀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⡆⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⡆⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣧⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⡀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣄⣈⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⠟⠛⢉⠉⠉⢉⠻⠇⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠋⠀⠀⠘⠛⠀⣀⠘⣃⣠⡔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠰⢂⡀⠙⠛⠡⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢻⡤⣤⣀⣤⣤⠀⣅⣁⣤⣦⠀⠀⠀⠀⠀⠀⠀⣠⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠛⠓⠦⢤⣀⠀⠀⠀⣸⣿⡿⠿⠿⠿⠿⢷⣿⣾⣿⣦⠀⣀⣤⠶⠒⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣐⠉⠀⠀⠀⠀⠀⠀⠀⢉⣻⣿⢻⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡉⠻⠒⠀⠀⠀⠀⠀⠀⠈⠁⢹⣧⢻⣧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠘⠒⠊⠀⠀⠀⠀⠀⠀⠀⠶⠈⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⠄⣀⣠⡀⢀⠀⠀⠀⠀⠛⠀⠈⡟⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠭⠛⠋⠉⠉⠉⠉⠈⠋⠙⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠠⣴⣶⣿⠶⣾⣮⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢘⣒⡈⠠⣺⣿⣿⣿⡶⣬⣄⣂⣀⡀⠀⠀⠀⠀⠀⢀⣀⡠⠄⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠚⠶⠞⠉⠐⠋


⣶⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣭⣷⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠂⠘⠻⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⡚⠉⠁⡂⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡠⠦⠖⠀⠙⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠸⠁⡀⠀⠉⠑⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠁⠀⠀⠀⠀⠀⠀⠁⠐⠠⡀⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡠⣤⣴⡖⠒⠒⣤⣄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡠⠤⠀⢀⠤⠀⠀⠀⠀⠀⢸⣀⠀⠀⠈⠋⠁⠀⢠⠻⠿⠳⡀⠀⢸⠀⠀⠀⠀⠀⠀⢤⡀⠀⠠⢄
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠳⣆⠀⠀⢦⡀⠣⡈⠂⠀⠀⠱⠀⠎⠀⠀⠀⢀⣠⠈⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠑⢄⡀⠀⢠⡮⢦⡄⠀⠀⠀⢠⠊⠱⢄⡀⣉⠀⠀⠀⠂⣐⣠⡀⠀⠀⠀⠀⢰⡶⢕⡀⠀⣀⠤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠁⠙⠶⣄⢀⣼⠒⢰⣁⣠⠔⣂⣀⣠⠀⠈⠂⠉⠢⡀⣠⠶⠁⠈⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢛⠀⠦⣈⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠙⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠊⠈⠀⡏⠀⠀⢰⡁⡠⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠦⠤⠄⢅⠇⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢋⣆⢀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠁⡱⠀⠀⠀⢀⠀⡀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢒⣛⠓⠐⡄⠀⠀⠀⠸⠤⠂⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠉⠉⠉⠓⠢⠤⠤⠤⠴⠖⠊⠁



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠒⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⣄⣀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣀⢈⣉⣉⡁⠀⠀⠀⠘⢆⣀⢀⠀⢀⡎⠃⢧⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠉⠉⠀⠀⠀⠈⠉⠒⠒⠒⠢⠤⠭⠭⢍⣀⢰⡘⡄⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠒⠚⠛⠒⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⢡⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢄⡀⠀⠀⠀⠀⠀⢀⠏⡆⢓⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠲⡒⠁⡔⠉⠉⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⣖⠚⠥⠤⠤⣄⠀⠺⠇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢧⡀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠉⠒⠤⠤⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠳⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡅⠀⠀⠉⠒⠢⠤⢄⣀⡀⠤⠤⠒⢋⣠⠔⢁⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⠈⠓⠒⠂⠤⠤⠤⠤⠤⠐⠒⠒⣊⣁⠤⠠⠾⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠉⠑⠒⠒⠒⠶⠖⠶⢲⡖⠊⠁⠀⠱⡀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠺⠇⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠱⡄⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠈⢧⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠀⠀⠸⡀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡠⠤⠒⠒⠒⠃⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠰⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⢄⣀⣀⣀⣀⣀⣀⣀⠠⠔⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣓⣒⡒
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣦⣶⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠐⠂⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢘⣴⣤⣷⣔⣶⡄⣠⣆⣠⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⡎⠀⠀⠀⠀⠆⠠⡾⠿⠟⠻⢿⣿⣿⣿⡿⠃⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢿⡿⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣀⠀⢀⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠃⣀⡀⠛⠛⢀⡀⠀⠀⠀⠀⠜⠀⠌⠛⠛⠛⠙⠥⢾⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⡟⢀⠂⠙⠛⠄⠐⠀⣀⠀⣀⢀⣴⣞⣀⠘⠁⠀⠠⠂⢠⡆⢴⣿⣆⠀⠀⠀⠀⠀⠒⠉⠑⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⠃⢴⢆⣈⠹⢻⡈⠂⢡⣀⡛⢈⣅⢻⣿⠀⠀⠀⠀⠀⣾⡸⣤⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣦⡔⢢⡀⠀⠁⣀⠛⣿⣿⣿⣿⠏⣸⠂⠀⠀⠘⢆⣛⣿⣿⣽⡿⠓⠁⠀⠀⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⡷⢦⡎⠉⠛⠙⠳⢿⣾⢿⣿⠏⠘⠟⠀⠀⠀⢰⣾⢿⣿⣿⣿⣆⣀⢠⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢸⣷⡮⣤⣹⣶⣾⣷⠘⢛⡿⢻⣦⣄⠀⠀⠀⠘⠗⣿⠛⣹⢿⣿⣿⣯⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⠙⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⠙⠋⠀⠂⠸⠂⠸⣮⡿⣼⡿⠋⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠮⣉⣿⡝⠛⣋⣾⡟⢽⣿⣿⠀⣀⠀⠀⢸⠄⢤⡛⠿⢟⢄⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡛⢿⣯⣿⣿⡒⢪⠘⣧⠹⠷⠀⠉⠶⡆⢀⣤⣾⠿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣥⣬⣭⣭⣥⣤⣮⣴⣼⣶⣿⣯⠾⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢿⣿⣿⣿⣿⣿⠟⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉



⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠿⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣮⣒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⣠⣌⠳⠆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠾⢷⡿⢿⣿⣷⣤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡴⠋⢁⡾⢿⣿⣾⣥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣅⢙⢴⣿⡿⠞⣩⠗⣷⡾⠁⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⠛⢟⡿⠟⣨⣽⣍⡉⣛⣤⣶⣖⣡⠃⢀⣠⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠟⢖⠉⣀⣰⣿⣿⣤⣩⣵⣦⣤⣻⡿⣿⠿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢤⡴⢂⣠⣼⣷⣿⣿⣾⣿⣿⠄⠼⢯⣹⡻⢿⠷⡾⡛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⠻⣿⡿⠟⢫⡿⢿⡽⠿⠷⣶⣦⣄⣸⡃⡀⢉⣭⣬⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠷⠀⠰⡌⠉⣠⣤⠿⢓⠾⣿⣒⠒⠊⢿⣭⡈⠛⠻⠿⠥⠷⢀⣠⡄
⠀⠀⠀⡰⣰⣶⣤⠀⠻⠴⢿⡦⣰⣿⠺⢋⣠⣶⢽⣦⠈⠻⣿⡀⠀⡜⢻⠿⣶⣼⣶⠟⠋⠉⠁
⠀⠀⠀⢻⠿⣱⠃⣀⣀⠀⢈⣿⠟⢁⣀⣽⣷⣟⣹⣿⣀⠀⠸⢿⣷⣬⣭⣄⠈⠛⠤⣀⠀⢀⣴⣄⣿
⠀⠀⠀⠏⢠⢳⣎⢿⣿⡗⠋⢁⣴⣦⢿⣿⣧⣤⣠⣿⣿⣶⡦⢰⣬⡟⠺⡁⠿⠛⠶⣦⣭⣽⣿⠛⡿⠤
⠀⠀⠀⣇⢺⣀⢿⡜⠟⠛⣘⣟⣩⣬⣿⣿⣿⡟⠉⠀⠀⢹⡇⣿⣿⣇⣞⣥⣦⣄⠀⡏⡞⣻⠇⢠⠛⠁
⠀⢀⣴⣿⠀⢳⣾⣴⣾⠛⢻⣾⣿⡏⠀⠸⣻⣇⡼⠛⠻⡖⠤⠤⣽⣿⣿⠁⠀⢻⣦⠧⢛⣫⣮⢏⣀
⠀⠀⠺⠟⠣⣼⣻⠟⠋⡀⢰⣿⣿⣄⢀⢰⡇⢽⣇⠠⢸⣆⡀⠐⢿⣿⠙⡀⢃⠛⣿⣯⡽⠛⠳⣦⢤⠐
⠀⠀⠀⣰⢲⠙⢟⠻⢿⣥⠏⣩⣏⠈⠑⠚⠁⣸⣱⣤⡴⠷⣠⡖⢾⣿⣷⣦⣅⢖⠁⠙⢂⠧⠄
⠀⠀⠀⡧⢈⢤⣼⣶⣤⢰⢬⣉⠛⠳⢦⣴⣶⣿⣿⣿⣿⣴⠅⣴⠾⠿⠟⠛⠉⠀⠀⠀⣸⣷⠄⢠
⠀⠀⢠⢻⡇⠸⡻⠏⠁⢸⣸⣿⢠⣀⠀⡀⠀⠉⢡⠰⢰⠀⠀⠀⢀⢠⣄⣠⡄⣤⢢⢀⡿⢡⠄⠊
⠀⠀⢸⠋⢳⣰⠑⠦⢤⣀⡈⠉⠃⠸⠀⠇⠯⡇⠸⠀⠸⠽⠼⠸⠏⠞⠒⠛⠋⢉⡀⢼⢀⡞
⠀⠀⠸⣆⡿⠁⠀⠀⠀⠀⠈⠉⠙⠒⠤⣀⢤⣀⣀⣀⣀⣀⡀⠤⠴⠤⠐⠊⠉⠀⠀⠀⠉
⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣶⣶⣶⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⡿⠛⠉⠉⠉⠉⠉⠙⠻⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⣿⠋⠀⠸⣿⠆⠀⠀⢾⡿⠀⠈⢻⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢀⣀⣤⣤⡴⣄⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⢸⡇⠀⠈⠉⠛⠛⠷⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⡟⠀⠀⠀⠀⢧⠀⠀⠐⠦⠤⣤⡤⠤⠖⠂⠀⢠⠇⠀⠀⠀⠘⡇⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠿⣧⡀⠀⠀⢰⡾⡷⢶⣦⣤⣤⣤⣤⣤⣶⣶⠶⠿⣶⠀⠀⠀⣠⡿⠷⠶⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⢸⣯⣭⣭⣭⣇⣀⣀⣀⣀⣮⣭⣭⣭⣿⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠋⣿⣰⣽⡇⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⣷⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⣿⢹⣼⡇⠀⢠⡶⣦⠀⠀⠀⠀⠀⠈⠁⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⣿⣾⣿⡇⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢿⣻⣻⡇⠀⢰⣏⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠉⠉⠀⠀⠀⣉⡁⠀⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠸⣧⡿⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠷⠦⣄⣀⠀⠀⠀⠀⠀⢀⣀⡤⠾⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡋⡛⣙⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠁⢀⡤⠞⡖⠒⠒⣁⡤⠴⠒⠒⠒⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠂⠀⣸⠁⠀⠀⡏⠀⢀⠃⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠖⠁⢠⡧⠈⢑⡄⠈⠉⠀⠀⠀⢄⠈⠱⠀⠀⡔⠈⠳⡄⢀⡼
⠀⠀⠀⠀⠀⠀⢀⣠⠶⠛⠉⡿⠀⠀⣼⣀⡴⠋⠀⣄⠀⠀⣧⢀⡀⢤⠀⣤⠀⠈⠂⠤⡿⠋
⠀⠀⠀⠀⠀⢠⠎⢀⠤⢤⡀⡇⢀⣴⡟⢉⠄⣴⠀⣿⢈⡇⣿⢀⡇⢾⣠⡏⢠⠎⠉⡼⠉⢦⠀⣀⡤⠶⠶⠦⣄
⠀⠀⠀⠀⠀⠘⡀⠸⠀⠠⢃⡿⠋⢰⡇⠸⡄⠿⠄⡏⠚⠃⣿⠉⠁⠀⢸⣇⡸⢶⣊⠜⣀⣼⣴⣇⠀⡴⠲⡄⠀⡇
⠀⠀⠀⠀⠀⠀⣈⠀⠀⢠⢿⡇⠀⠘⡇⠀⠰⣄⠀⡇⠀⠀⠿⣠⣔⡈⣹⠀⠀⠀⢀⡞⡱⠃⢠⣈⡇⢇⡈⠀⡠⠃
⠀⠀⠀⠀⣴⠋⠁⢉⡆⠋⣼⠁⠀⠀⠳⣀⡠⠋⠀⡡⠔⠈⠸⣇⢀⣠⠋⠙⢦⡀⢸⠋⠀⠀⠀⣀⠤⠤⡀⠉
⠀⠀⠀⠀⢧⡀⠀⠉⢀⡴⠃⠀⡴⢳⠀⠀⠀⡴⠋⠀⠀⠀⠀⠈⠉⠁⣠⠊⠀⢷⠘⣄⠀⡠⠊⡄⠀⠀⡨⢷⠤⣄
⠀⠀⠀⠀⣀⠉⣛⡋⠉⠀⠀⣸⠵⠋⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠟⠀⠈⢳⠗⠚⠁⠀⠀⠓⣋⡀⠈⣷
⠀⠀⠀⢎⠀⠀⠀⢙⣦⠒⠉⣿⠀⠀⢀⡟⢰⡔⡄⢀⠞⠁⠀⢱⡄⠀⠈⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠌⠁⠿⢀⡟
⠀⠀⠀⠀⠁⢀⠔⠁⡈⡇⠀⣿⠀⠀⣼⠁⠀⡰⠃⣾⠀⠴⣠⠞⠀⡇⠀⠀⠀⢀⡀⣄⢠⠳⠶⠀⠀⠀⠈⠓⠚⠉
⠀⠀⠀⠀⢠⡏⠀⠿⠭⠓⠀⣿⠀⢠⣇⣤⠞⠁⢠⡧⠖⡋⠁⡠⠠⡇⣴⠙⡇⢸⡇⣿⠠⢭⠆⣠⠔⠂⠀⠒⣄
⠀⠀⠀⠀⠘⣇⠀⠀⠀⣠⠀⣿⡤⢾⡏⠀⡴⠐⣤⡇⠀⡇⠀⣇⡠⢧⠙⠒⠛⠀⠉⣿⠀⢀⠞⠁⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠈⠛⠒⢚⠵⠋⣿⠀⢸⡇⠀⠣⠴⠃⠓⣂⣭⠥⠶⠶⠶⠶⠖⠦⠤⢴⠷⣴⠯⠤⠤⠴⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣀⣿⠀⢸⡇⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⣠⠏⠗⠀⣷⠀⠀⠀⠀⠙⠦⢤⣀⣀⣤⠤⢔⣚⡥⢤⡾⠥⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢤⠀⡠⠞⠋⢀⡴⠋⡴⠂⠀⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⡸⠁⠧⠴⠚⠁⠀⠀⠣⠤⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠋⠁

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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠤⠤⠤⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠺⣀⠤⠤⠐⠒⠒⢄⠀⠀⠀⠀⠶⡴⡄⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⠤⠄⠀⠀⠠⠄⣀⣀⡈⠒⠠⠤⠤⠞⢀⢸⡀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠠⣤⡤⢀⡀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠒⠾⣇⢇⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠈⠑⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⡟⡘⢄⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⠤⠤⡤⠒⣡⠓⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡤⠿⠅⣀⣀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⡇⠀⢇⠀⠀⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠉⠒⠤⠤⠤⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠉⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⢋⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣄⠀⠀⠉⠒⠒⠤⠤⠤⠐⠒⣊⡡⠔⠋⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠧⣀⣉⡉⠀⠀⠀⠒⠂⢀⣉⡩⠤⡄⠒⠚⠣⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⣀⡀⠀⠉⠉⠉⠉⠙⡇⠀⠀⠀⠱⡀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠑⡄⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠈⢆⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠈⢆⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠘⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣀⣀⠤⠤⠤⠇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠰⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠤⠤⠤⠤⠄⠒⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠉⠀⠀⢀⠤⠀⢁⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠔⢋⡆
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⣂⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⢀⠎⠀⠀⠀⠈⠉⢉⡉⠉⡀
⠀⠀⠀⠀⠐⠨⡳⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⢝⣙⡛⠛⠢⠤⢖⣒⣂⣀⣀⣂⣋⡤⢷⢃⠜⠀⠀⠀⠠⠀⠀⠀⠘⠊
⠀⠀⠀⠀⠀⠀⠈⠋⠢⠄⢊⠘⠀⠀⠀⠀⠄⡀⠀⠨⣅⢀⠂⠀⠀⠀⢀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⢀⣄⠀⠀⠀⠀⠀⢂⢀⠀⠀⠀⠆⠀⠀⠉⠑⢲⠤⣄⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠘⡏⠠⡂⠄
⠀⠀⠈⠈⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠉⠛⠁⠀⡀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠔⡄⠂⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢦⣄⠀⠀⠀⠀⠀⢰⠹⢆⠀⠁⠀⠁⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⡠⡢⠊⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⢀⠀⠀⠀⢤⣀⡀⠀⠀⠀⠉⠉⠁⢋⠀⡇⠀⠀⠀⣀⡾⠋
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠑⠵⠊⠀⠀⠈⠉⠒⠒⠢⣤⠤⠬⠤⠖⠉⠂⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠠⠀⣔⠀⠀⠀⠈⢦⠀⠀⠈⠀⠻⠛⠀⠀⠀⠠⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠃⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⡇⠀⠀⠀⠀⡄⡤⡀⠀⠀⠀⠀⠀⠸⡄⠀⠱⡤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠓⠛⠁⠀⠀⠀⠀⠀⠀⠈⠢⠤⠘⠁⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢥⠀⠀⠀⠀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠢⡀⠀⠸⢜⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠈⢈⢧⢂⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠁⠃⠀⠀⠈⠇⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠐⠠⣄⣠⡀⠀⢀⠀⠀⠀⠐⡀⠀⠐⠀⢀⣠⠖⠁⠀⠀⠀⠐⠀⢀⠄⡠⢠⠀⡀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠤⢲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣷⡆⠐⣦⣭⣿⣷⣦⣀⠀⢀⡤⠚⢁⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⡇⠀⣠⣿⣿⣿⣿⣿⣶⡋⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⠇⠀⢹⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡄⠀⠸⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⡀⠀⣀⠀⠀⠀⢀⡿⠿⠿⠿⠿⠛⠛⠓⠒⠲⠒⠾⠿⠿⠿⠿⠿⢿⣗
⠀⠀⠀⠀⠀⣇⠈⣾⠀⢣⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠰⡍⠙⡧⠘⠃⢸⡠⠤⡀⢹⠉⠉⠉⠉⠁⠀⣉⡉⠉⠉⠉⠉⠉⠉⠉⠁⢲⠃
⠀⠀⠀⠀⠈⠱⠀⠐⠉⠉⡠⠒⠃⠘⡆⠀⠀⠀⠔⣋⣉⠁⠀⢙⣛⢦⡀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠑⢤⣔⣺⠃⠀⠀⠀⣧⠀⠀⠀⠘⠀⠈⠂⡔⠁⠀⠃⠀⠀⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀⠀⠀⢸⠀⠀⠀⠠⠠⣿⠸⢰⡶⢀⠆⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣶⣾⡇⠀⠣⡀⠁⠈⠀⠈⠁⠂⢠⡄⠀⢠⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠈⣷⣶⣤⣤⣶⣾⡟⠀⠀⣼⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠐⢿⣿⣿⣿⠿⠋⠀⠀⢀⡇⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢀⡘⢿⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣀⣀⡀⠀⠀⠀⣀⣀⡠⠏⠀⠀⡏⠈⠉⠉⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡍⠉⠉⢹⣿⠀⠀⠀⠀⠀⠑⢇⠀⣠⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣿⣧⡀⣠⣾⣿⣶⢶⣤⣄⡀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠉⠻⣿⣿⡿⠃⠻⣿⣿⡿⠋⠉⠀⠈⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⠤⠴⠖⠋⠁⠀⠀⠀⠀⠙⠓⠦⠤⠤⠴⠃

⠀⠀⠀⠀⠴⢠⣼⣿⠿⢛⣽⣿⣿⠟⣿⣿⡿⣿⣿⡟⠛⠉⠉⠉⠉⠉⠉⠀⢈⣿⣿⣿⣶⣿⣷⣿⣿⣿⣿⣿⣿⡛⣿⣿⣷⣤⣁⠛⠿⠤
⠀⠀⠀⠀⣦⣴⡶⠒⠀⣸⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢻⣿⣿⣼⣿⣯⣿⣿⣿⣿⣌⣛⠻⠟⣶⣶⣤
⠀⠀⠀⠀⣀⣠⡴⠋⣽⣿⣿⣿⣟⣻⣿⣿⣿⢻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣸⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣮⡛⠳⢶⣶⠖
⠀⠀⠀⠈⠉⣁⠀⢺⣿⣏⠻⣿⡙⢿⣿⣻⣿⣿⣿⣿⣇⣀⣀⣀⣀⣀⣠⣤⣿⣿⣿⡿⣿⣿⣿⣏⣿⡿⢻⣿⣿⣿⣛⣿⣿⣿⣷⡦⣬⡤
⠀⠀⠀⠰⠟⢣⣶⡚⠿⣿⡆⠈⠓⠈⢻⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣟⡿⠁⠀⣴⣯⡽⢿⣿⣯⣿⣿⣿⡿⣷⣗⡀
⠀⠀⠀⠀⢠⢠⣞⠻⢦⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣤⣀⣀⡀⠀⠀⠀⣀⣀⣿⣿⣿⣿⡟⠀⠀⠈⠋⢁⣴⣿⣿⣶⣿⣯⣿⣷⡌⠋⡈
⠀⠀⠀⠀⢸⣿⣿⣷⣦⣤⣄⣀⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠀⠀⠀⠀⠀⠘⣉⣩⣾⢻⣿⣆⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⣹⣾⡿⢉⣾⣿⣿⣿⣷⣦⣤⣀⡀⠀⠀⠀⠀⣀⠀⠉⠉⢁⡀⠀⠀⠀⢀⣀⣀⣤⣤⣲⣿⣿⣿⣽⣿⣿⣿⣿⢳⡄⠙⠻⠛
⠀⠀⠀⠀⣠⠄⣩⢴⣽⣿⠿⢡⣿⢿⣿⣿⣿⡇⠁⠀⠀⠀⠉⢀⡀⠀⠘⠃⠀⠀⠈⢸⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠱⣶⣠⣀
⠀⠀⠀⠀⣤⣾⡿⠟⠋⢡⡖⣿⣿⣿⣿⣿⣿⣧⢃⠀⠀⠖⡀⠻⠿⠦⠄⠰⠆⠀⠰⣸⣿⣿⣿⣽⣿⣿⣿⣭⣿⣿⣿⢿⣿⣿⣷⡈⠻⡶
⠀⠀⠀⠀⠉⢁⣴⣿⡾⢂⣺⣿⣿⣾⣿⣿⣷⣾⣧⣠⡀⠠⠇⡃⢲⢰⡎⠃⠀⢀⣵⣿⣟⣹⣿⣿⣿⢻⣿⣏⣿⣿⣿⣆⢭⣛⡛⠿⠦
⠀⠀⠀⠀⠚⠋⠛⢋⣴⣿⣿⣯⣿⣿⣽⣿⢿⣿⣿⣿⢻⣶⣤⣥⣍⣀⣤⣴⣾⣿⣿⣿⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⣉⣉⠛⠗
⠀⠀⠀⠀⣠⢴⣎⣻⣿⣿⣿⠿⣿⣿⣿⣿⣾⣿⠟⠙⠿⢿⣿⣿⣿⣿⣿⣿⠿⠛⢿⣿⢻⣿⣿⣿⠿⣿⣿⣿⢦⣿⣧⡈⣉⣡⡌⠛⠷⡄
⠀⠀⠀⠀⣺⣯⣿⠟⣋⣼⣿⣿⣿⣻⣿⣿⠋⠁⠀⠀⠀⠀⠈⣿⣽⣿⠁⠀⠀⠀⠀⠉⢿⣿⣷⢿⣿⣿⡯⣭⣽⣿⣿⣿⣦⣭⣈⣛⣢
⠀⠀⠀⠰⠊⢉⣀⣾⡿⣻⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡆⠀⠀⠀⠀⠀⠀⣿⣷⣾⣿⣿⠇⢁⠀⠸⣿⣿⣿⣝⠷⠷⣟
⠀⠀⠀⠈⣱⡾⠛⣩⣾⣿⣿⣿⣼⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣡⣀⣸⣄⣀⣈⣿⢿⣿⣇⣠⣍⣀
⠀⠀⠀⢀⣥⣴⣾⡟⠉⠓⣩⣾⣿⣿⣿⠏⠳⠤⣀⡀⠀⠀⠀⠈⣿⣿⣿⡄⠀⢀⡠⠴⠋⢻⡭⠭⡇⠀⠀⢸⠁⠀⠀⣿⠆⠛⢿⣿⣻⡆
⠀⠀⠀⢠⣴⣶⢶⡶⠂⣶⣿⣼⣿⣿⣿⠀⠀⠀⠀⠉⠁⠀⠀⠀⢿⣽⡿⠃⠀⠀⠀⠀⠀⠀⣿⡀⡇⠀⠀⢸⠀⠀⠀⣿⣗⡾⢶⣬⣉⠃
⠀⠀⠀⠰⠟⠋⣀⡴⣿⣭⣉⡉⠛⠻⢿⡀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⡇⠀⠀⢸⠀⠀⠀⣿⣿⣿⣬⡙⠻⠿
⠀⠀⠀⠀⠶⣼⣿⣻⣿⠿⠿⠿⢿⣶⣼⠳⣄⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⣠⠾⣿⣶⡇⠀⠀⢸⠀⠀⠀⣿⣿⣿⡾⣿⣢⣄
⠀⠀⠀⠀⠀⠈⠉⠀⠀⣀⡀⢀⣼⣿⠁⠀⠀⠙⠲⠤⣄⣀⡀⠀⠀⠀⢀⣀⣠⠤⠖⠋⠁⠀⠹⣟⠃⠀⠀⠸⠦⠐⠐⠉⠉⠛⠛⠻⠶
⠀⠀⠀⠀⢴⠶⠖⠓⢂⣀⣠⣽⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣭⡀⠀⠀⠀⠤⢀⣀
⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣶⣶⣤⣤⣄⣉⣉⠐⠒⠒
⠀⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⠀⠀⠀⠉⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⣿⣿⣿⣿⣶⡶⣯⣽⣿⣿⣿⣿⣿⣿⡧
⠀⠀⠀⠀⠀⠀⠼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⢿⠿⠿⡿⡿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⡛⢋⢻⣛⡚⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⠉⠉⠁⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⣷⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠗⣌⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢦⡘⢷⡱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣳⣿⣿⣄⠹⣆⠻⣮⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⢏⣴⣿⡿⣇⠈⢦⡘⢷⣌⡪⡙⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⣻⠟⣡⡞⣽⡿⣡⡏⢧⣀⠙⣦⣙⢍⠪⣷⣍⠛⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡡⣚⡵⡾⢋⣾⢟⣵⠏⣧⠀⠹⣷⢌⠻⣗⢷⣤⡉⠛⠦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⣡⢞⣵⡿⣫⣾⠏⣰⣏⠱⣄⠈⠳⡙⠮⣓⢬⡙⠶⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠷⣫⣯⢞⡽⢃⣴⠋⡟⢷⣌⠳⣦⣈⠢⣈⠑⠻⢶⣤⡉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢠⣾⠟⣡⠎⣰⡿⢃⡞⡷⣄⠹⣷⣌⡻⣗⠮⣓⢤⡀⠈⠉⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⣡⠞⣡⣾⠏⣴⡟⣰⡗⢌⢷⣄⡙⢿⡾⢷⣮⣙⠻⠷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣠⣾⠵⣫⠟⣡⢾⢞⡴⢹⡇⠀⠙⢿⣿⡲⢌⣓⢭⣙⠻⠶⣦⣬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢁⡤⣚⡥⢚⡕⣡⠊⠀⢸⠃⠀⠀⠀⠈⠛⠷⣬⡉⠛⠻⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠟⠋⢁⡴⣫⠞⠁⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠦⢤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣫⠞⠁⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠾⠗⠊⠁⠀⠀⠀⠀⠀⠀⠸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⣷⣠⠶⣆⠀⢀⡤⡄⠀⠀⣠⠀⠀⡀⠀⢀⡄⣠⠤⡄⢀⡶⠀⠀⣀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠘⠃⢸⡇⠀⣏⢀⣽⠀⠀⣿⢠⠋⢹⡦⢼⡗⠁⣠⡿⢹⡇⠀⣰⡏⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠧⠊⠉⠁⢿⣀⠐⣿⠏⣐⣻⠃⢸⠁⠸⡵⠃⠀⠑⣈⣸⣇⠤⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⢙⡆⠀⠀⠀⠀⠀⣠⡄⠀⠀⣿⠀⠉⠁⠀⠸⠀⠀⠀⡴⠚⠉⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣟⡠⠔⠋⠀⠀⠀⠀⠀⣼⢁⠇⠀⠀⠉⠀⢀⡴⠀⠀⠀⠀⢸⡅⠀⢀⡰⠃
⠀⠀⠀⠀⠀⠀⣠⢼⡇⠀⠀⠀⣴⠛⠳⡄⣸⠗⠁⢀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠉⠉⠉⠀⢀⡤⢤⡀⠀⣤
⠀⠀⠀⠀⠀⢰⡇⠸⣇⠞⣷⠀⢸⡗⠒⡏⣿⠀⠀⣌⠀⢠⠞⢻⡏⠀⣰⠋⢹⠄⢀⡾⠁⠀⣤⢸⣇⠘⣁⡤⠋
⠀⠀⠀⠀⠀⠀⠉⠀⠟⠀⡿⠀⣼⣄⡰⠁⢿⣀⢴⡇⠀⣿⣤⢾⠀⠀⣿⠄⣿⠀⡸⣇⣀⣼⢃⠔⠻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠔⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⠀⠘⠦⠔⠁⠀⠈⠉⠀⢀⡼⠁⢿⣄⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠤⠤⣤⣄⣀⡀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠉⠛⠻⢶⣤⣼⣕⠒⠉⠉⣳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢤⣀⣀⣀⣠⠤⠴⠒⠉⡜⢉⡉⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠼⠁




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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣾⡿⠉⠈⠢⠤⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠒⢤⡀⢸⡁⠛⠀⢀⠀⠀⢀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠐⠉⠋⠀⠀⠀⠀⠀⠊⠂⠉⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣤⣶⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⢀⠀⠀⠀⠉⠀⠐⠄⠚⠒⠔⠰⣶⣶⣶⣶⣶⣾⣷⣦⡀⠀⠀⡆⣀⣸⣿⣿⣛⣏⣻⣿⣿⠆
⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠻⣿⣿⣿⣿⣿⣿⣿⠟⠂⠐⢿⠛⠻⢿⣷⣬⣦⡟⣿⠃
⠀⠀⠓⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠿⢋⣠⠆⠀⠀⠀⢡⠀⠀⠈⠙⠛⠻⠿⣾⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⢁⠂⢘⣃⠀⠀⢘⠀⠀⠀⠀⠤⣦⣷⡀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠈⠉⠀⠀⠈⡩⠂⠈⢢⡈⠀⢿⢷⣶⣶⣤⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠤⠤⠤⠀⠒⠁⠀⠀⠀⠀⠑⣠⣿⣿⣿⣿⡿⠣⠀⢰⣤⡎⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠉⠉⢛⠟⡟⠁⠀⠀⠀⠙⢧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠘⡂⠀⠀⠀⠀⡀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠂⠀⠀⠀⢀⡀⠅⠊⠉⠀⠰⠗⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠋⠉⠉⠁⠀⠀⠀⠀⠈⠉⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠁⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠐⡀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠠⠊⠱⡁⠂⠀⠀⠀⠀⢀⣀⣀⡠⠤⠤⠤⠶⠦⠚⠒⠲⠶⠦⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠢⠀⠀⣁⡤⠤⠒⠊⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⠴⠚⠉⠀⠀⠀⠀⣀⣀⡤⠤⠤⠖⠒⠒⠚⠉⠉⠉⠻⡒⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⢀⣠⠤⠒⠊⠩⠥⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⢱⡀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⡼⠁⠀⢀⣤⠚⠉⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⢰⣖⠄⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⣇⠀⠀⠁⠸⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡓⠦⠤⣀⣀⣀⡀⣀⣀⣀⡠⠤⠖⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠁⠈⠳⢤⣀⣀⡉⠉⡁⢀⣀⣀⠤⠲⡅⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⡼⢩⣏⡏⠉⠉⠁⠀⠀⠀⠘⡄⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⢠⠀⡼⠀⡾⠰⡇⠠⠈⠀⠀⠀⠀⠀⢹⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⢸⢠⡇⠀⣧⣀⣱⠀⠀⠀⠀⠀⠀⠀⠀⡆⢠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡤⠤⠋⢸⣠⣀⣱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠟⠉⠈⠙⠢⡀⠀⠀⢀⣀⠎⠁⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣄⣀⣀⡤⠏⠉⠉⠉⠙⠦⣤⣀⣠⠤⠟

⠀⠀⠀⣠⡄⠀⠀⣀⡀⠀⠀⣀⣠⢄⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠘⡻⡧⠤⠞⠟⠋⠀⡌⠈⣿⡿⣦⢬⡆⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⠿⢿⣶⣄⣀⣀⠀⠀⠀⠠⠀⠀⠀⠀⠄⡀
⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠂⡈⠨⠁⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⡉⡉⣱⠀⠉⠉⠁⡑⠦⠀⡀⠄⠁
⠀⠀⠀⠀⡠⠀⠠⠄⠀⠀⠀⠄⠁⠀⡁⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⢜⡾⠀⠀⠀⠀⠎⠀⠀⠑
⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠈⠁⠀⢰⠁⠄⣸⠀⠀⠈⠑⠢⢄⣆⠀⠀⢀⠀⠀⠀⠉⠁⢀⡀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠐⣆⠀⠀⡰⠃⠀⠀⠀⠀⡇⠀⢠⣇⠀⡆⠀⠂⢀⠀⡏⢉⢉⣀⠀⣀⣀⠀⡀⠈⠁⠀⠀⠀⠲⢴⣤⣿⣶⣤⠶
⠀⣀⠎⠀⢀⠀⠀⠀⢠⡄⠀⠀⠀⠃⠀⠀⡏⠆⠉⡆⠇⢣⠐⠇⠸⠸⠹⠰⠇⠃⠈⣤⠀⠀⠀⠀⠀⠀⠀⠈⠛⢛
⠀⠀⠀⠀⠊⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⢀⠀⢈⠒⠦⣄⣐⠀⠀⡀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠨⣤⡦⠄
⠀⠀⠔⠁⠀⡠⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⢸⠄⢼⢀⢀⠄⡏⢩⠍⡇⠀⡀⡀⠀⠀⡔⠀⠀⠀⠀⠀⠶⠀⠀⡮⠏⣑⠚⣦
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢸⠀⠸⠘⠀⠇⠃⠃⠀⠀⣕⠋⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡗⠂⠶⢠⡏
⠀⢀⠀⠐⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢸⠀⠀⠀⠎
⠀⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠊⠉⠀⠶⠀⠀⠀⠘⢀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⢰
⠀⠀⢱⠀⠀⠴⠀⠀⠀⠀⠭⠄⠀⠀⠀⠀⠀⠀⢠⠀⣄⠀⠀⠀⠀⠀⠀⣢⣤⠖⠛⠃⠰⠀⡠⠔⠐⠂⠉⠀⠀⠀⡄
⠀⠂⠈⢸⠀⠂⠀⠀⠀⣾⠭⢭⣷⣶⠀⠀⠠⣻⢿⣿⡗⢶⣄⠤⠀⠚⡋⠉⠀⠂⠀⠀⡐⠀⠣⠤⠤⠀⣀⣀⣀⣠⠃
⠀⠀⠀⠀⠱⡄⠀⠀⠀⠦⠀⠀⠀⠻⠀⠀⠀⠀⠈⠰⠉⠀⠀⠀⠀⠐⠒⠂⣤⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠿

⠀⣀⠀⠀⠀⢀⡀⢰⠅⢨⠶⠲⡀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠄⠀⠀⠀⠀⠈⠲⡄⠀⠀⢈⠀⡰⠦⣄⢇⠂⡇⡀⣀
⠀⠀⠀⢀⠞⠁⠀⢀⢆⠸⠆⠁⠐⠀⠀⠀⠀⠀⠀⠨⠷⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠂⠐⠠⠊⠄⠀⠈⢿⣉⣧⠧⠮
⠻⠜⢢⣼⠀⠀⠀⠀⠘⢂⠑⢤⢤⠖⠀⡀⠀⠠⠠⣦⣤⡀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠔⢀⠀⠀⢀⠀⠀⢸⠋⢣
⠀⠠⠌⣿⣧⡀⠘⢀⠀⠀⣡⢄⡸⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⢀⠀⢐⠇⠀⠀⣀⠀⠀⠈⠃⠀⠁⠀⡂⠎⣈⡘
⣬⡶⠚⣉⠓⢿⠂⠠⠉⢊⡁⠀⠀⡀⠀⠀⠀⠀⠰⠰⠀⠀⠀⠀⣀⣴⠀⢀⠀⠀⠀⠀⣈⠀⠀⠰⣊⢅⣢⠔⠁
⠯⠤⠊⠀⢃⡸⠀⠀⠾⢣⣟⢃⠀⠀⠀⠀⠐⡆⠀⢀⣄⠀⠀⠀⢀⠀⠐⠨⠀⠀⢴⡀⠀⠀⠀⠀⠘⠉
⠀⠀⠀⠀⣠⢣⡀⠀⠋⣖⡪⠂⠀⠂⠀⠀⣷⡇⠀⢸⠇⠀⠀⠀⢀⠐⠀⠁⠀⠀⠀⠈⠢⠤⣀⣀⣠⠵⠖
⠷⢄⣀⠔⠁⠀⠀⠉⢲⠇⠀⠀⠀⠀⡄⢀⣿⠀⠀⣾⠁⢀⡖⣦⢸⠄⡆⠘⡇⣰⠀⡖⠀⣴⠀⣀⠀⣀⠀⠢⣀
⠀⢀⢂⠀⠐⠀⠀⠀⠾⠀⣀⢤⠀⡀⢀⡞⢻⡀⡰⡇⠀⢾⡖⢁⠄⢸⡇⠘⠑⡏⢸⡇⣠⡇⠀⠀⠀⠀⠀⣀⠀⠉⠓
⢄⠁⠈⠂⠄⠀⠐⠀⢠⠞⠁⠀⠀⢸⡏⡎⢠⡄⠀⠉⢠⠀⠑⠒⠦⣶⣭⣀⣠⠟⡴⠚⣹⠉⠙⠆⣀⠀⢀⠇⠈⢉⠕
⡎⢀⠀⡁⠀⠀⠀⠀⡿⠀⡸⠀⢀⡼⢹⡥⣀⠃⣾⠀⣴⠀⣏⠃⢰⠇⠀⡦⢐⠞⢻⢞⡟⠉⣶⢸⣌⠃⠦⠔⡄⠈⠁
⠔⠁⠇⠀⠐⠂⠀⠐⣷⠈⠁⠀⠉⠀⡾⢀⠞⠀⡇⠰⡇⠀⡹⣆⢹⠀⣼⠁⣸⠀⠏⠸⣇⡠⣇⡠⠿⣆⠀⡔⢁
⠀⢀⠜⠂⠐⠒⠂⠠⢘⠦⠀⠀⠀⠀⠀⠸⠀⠀⣀⣀⠀⠘⠠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠉⢩⠇
⠀⠂⡠⣄⡀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠂⠀⠘⢿⣽⣇⡀⠀⠐⠂⠀⡀⠊⠒⡆⠀⠄⠀⠀⠸⠍⠀⠨⠇⠰⠥⠤⠔
⣀⠞⠀⢡⠈⠆⠀⠀⠀⠀⠈⠱⡄⠀⠀⠄⠀⢀⡟⢻⠻⡟⣆⠀⠀⠀⠈⠥⠒⠂⠀⠠⠀⠀⠐⠀⠉⠁⠒⢄
⡵⠂⠤⠼⠀⡥⠒⠂⠀⠀⠒⠀⡀⠀⠀⠀⠀⣼⠷⣶⢖⢛⣍⡇⠀⠀⠀⠀⠠⠄⠀⠀⢀⠁⠤⠀⣀⠀⠄⠀⢡
⣡⠤⠤⣀⢘⠀⠀⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⡟⠛⡛⠋⠉⢡⡀⢂⠀⠀⠀⡀⢠⣤⣄⠸⡀⠀⢘⡰⠃⠀⠀⡸⣠⣾
⠧⠶⠖⣄⠸⣆⠀⠀⠀⠀⠀⠡⠂⠀⢀⢄⠀⠇⠀⠀⠐⠁⠊⠀⡘⠀⠰⣴⡗⢿⣿⠯⠳⣷⣄⡈⠘⣀⣀⣼⣿⣯⣿
⠤⠒⡲⢞⡓⠼⠛⠛⠯⠤⠞⠀⠀⢀⣑⣤⣬⣼⣦⣤⣀⣈⣤⣾⠧⢄⣰⠻⡟⠙⠛⠿⢿⡿⠿⣿⣿⣿⣷⣿⣟⠻⡁
⢀⠞⠀⠸⡄⠀⠀⠀⠀⠀⠀⠰⣄⠀⠼⠤⠧⢋⣍⠉⠉⠉⣏⠁⠀⠀⠉⢲⣄⠀⢠⢔⠏⠀⠀⣤⡠⡀⠉⢻⣿⣿⣾
⢸⠀⠀⠀⠹⠤⣀⠀⠰⣿⣿⠀⢈⡗⠀⣰⡗⠋⠀⠀⠀⢀⠇⣆⠀⠠⢀⣵⠋⠀⢧⣸⢀⣀⣤⠑⠔⢁⠀⠀⠙⣿⣉
⢿⠀⠀⠀⠀⠀⠀⠉⠲⠎⠶⠒⠹⠀⡜⠓⡦⠤⠤⠭⠭⠼⠀⠘⠒⠉⠁⠈⡆⠀⠀⢸⠀⠀⠀⠀⡀⠈⠑⠤⠤⠻⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠐⣷⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⣠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠡⢠
⠀⠀⠈⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠑⠈
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠂⠀⠠⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⢈⠃⠀⠀⠉⠉⠀⠀⠿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁⠀⠀⠀⠀⠃⠀⠀⠀⠔⠈⠀⠀⠀⠀⠨⠤⠀⠀⠀⠀⡀⠀⠮⠌⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠛⠛⠛
⠀⠀⢲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢤⠈⣌⡁⣧⡀⣇⣀⠱⡀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⡡⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡄⠄⢀⠀⠀⠄⠀⢀⢠⡀⠠⡄⠀⠀⡄⠀⠀⡠⠀⠀⠀⣰⣿⠀⠀⠫⣶⠙
⠀⠀⠔⡃⠀⠀⠀⠀⠀⢀⠀⠐⠤⠀⠇⠳⠘⠒⠄⠂⠐⠅⠀⠳⠀⠇⠘⠐⠃⠐⠐⠒⠀⠀⠊⠟⠫⠀⠀⠀⣿
⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⠀⣀⠀⢠⠀⠠⠄⠐⠂⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠸⠿⠇⠀⠀⠀⠀⠈⣠⡄⠀⢀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⡆⢀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠂⠀⠀⠀⠀⠐
⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠐⠀⠀⠂⠀⠁⠀⠀⠀⠈⠈⠄⠀⠘⠀⠀⠀⠈⠀⠀⠀⠁⠀⠠⠄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣯⣭⣭⣬⣭⣯⣽⣽⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠈⠈⠐⠃⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠲⠀⠀⠀⠸⠂⠀⠀⠀⠀⠀⢤⡀⠀⢀⠔
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠸⠠⠀⠀⢠⡄⠀⢀⠀⠀⠀⠀⠀⠀⠈⠐⡒⠀⠀⠀⠀⠀⠀⢄⠠⡜⢣⡜⣤⠀⢠⡄⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠀⠐⠆⠰⠀⠀⠀⠀⠀⠀⠰⠄⠄⣤⠢⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣄⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠁⠌⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠈⠃⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠉⠀⠀⠀⡄⠀⠀⣀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠁⠒⠀⡠⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢠⠛⡄
⠀⠀⠀⠀⢀⠔⣁⠀⠀⠀⠀⠀⠒⡀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⢠⠀⠈⠀⠀⠀⠀⠀⠀⢀⠀⠁⠀⠈⠢
⠀⠀⠀⠠⡁⠐⠉⠀⡀⠀⠀⠀⠈⢀⠄⠀⠀⠀⡇⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⣀⡀⢀⡀⢤
⠀⠀⠀⢀⠐⢀⣤⠐⠀⡀⠀⠀⠀⠉⠀⠀⠀⠀⠁⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⡀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠠⡃⠀⠂⠀⠁⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄
⠀⠀⠀⢈⠶⠀⣄⠈⠫⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀⡀⠀⠀⠀⠀⠀⢀⠠⠈
⠀⠀⠀⠁⠀⠈⡅⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠣⣸⣎⠐
⠀⠀⠑⠰⠀⢀⣀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⡀
⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢠⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠊⢀⠀⠀⠀⠀⠀⠠⢄⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠴⠀⠀⠀⠆⠀⠀⠀⠀⢐⣀⣠⡊⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠈⠙⠉⠀⠁⠘
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠄⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠈⠒⠄⠄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⣶⣿⡀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠘⠠⠄⢀⣀⠀⠀⠈⠁⠀⠀⠀⠉⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠄⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠁⠁⠠⣀⠁⠀⠀⣀⣦⡀⠀⠀⠀⠀⠘⠤⠃⠀⡄⢀
⠀⠀⠀⠈⡄⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⢀⠆⠀⠀⠈⠀⠀⡆⠀⠀⠀⠀⠀⠔⠁⡃⠘⠂⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠻⠩⠦⢀⣀
⠀⠀⠀⠀⠘⠉⠉⠁⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠐⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠉⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⠀⡀⠀⠈⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡀⠗⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠤⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⠁⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠐⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⣀⣀⠃
⠀⠀⠀⠀⠀⠢⣤⠀⠀⢀⡀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢇⡀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡊⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⡤⢶⣴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢠⠀⠈⣠⠖⣡⢞⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⡌⠐⠤⡈⠛⠓⠚⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡤⠔⠂⠀⠀⠀⠀⠀⣀⣀⣠⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠶⠶⠾⡁⠠⠴⠾⠿⠋⣉⡤⠤⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⢀⡀⠠⠀⠀⠀⠀⠀⠵⠒⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡟⢁⣴⣿⡿⠃⣀⣤⣄⠀⠀⠐⠚⣛⣻⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠆⠀⠤⠤⠄⠀⠀⠀⠀⠤⠤⢶⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠒⡂⠀⠀⠀⠤⠄⠠⢤⣶⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠳⡁⣈⢍⠋⠙⣉⢏⣿⣛⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣅⠀⢁⣜⠈⢱⣽⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡄⣨⠶⣁⠈⣡⣼⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣅⠄⣨⠖⢡⣾⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡤⠒⢤⡀⢸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣂⢴⡊⣹⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⠙⣶⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣜⣹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡏

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⠛⡛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⡉⠉⠉⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠁⠀⠀⠀⠈⠁⠙⠀⠒⠢⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠂⡤⠤⠤⠤⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⡀⢰⠁⠀⠀⠀⠀⢀⠎⠀⠀⠉⠁⠐⡲⠂⠰⠀⠠⡄⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠉⠁⠐⠒⠀⠤⠼⠄⣀⣀⡀⠀⢰⠀⠀⠀⠀⠀⠀⠎⠁⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠸⠏⠉⠉⠁⠒⠒⠒⠘⠂⠤⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠈⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠐⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠉⠁⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⠑⠒⠂⠤⠤⠤⠄⠴⠒⠋⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡤⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⡀⣀⡀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⣀⠀⠀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠍⡉⠈⠀⠀⠀⣯⠀⠁⢉⣁⡉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⡜⠀⡇⠀⠀⠀⠀⠛⠀⢰⠁⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⢠⠁⠀⢇⠀⠀⠀⢀⡖⠀⠀⠑⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠢⢄⠀⠈⣉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠎⠉⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⣯⠂⠀⠀⠀⢀⠀⢀⠀⠀⠄⠀⠀⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢀⠀⠰⠀⢀
⠀⠀⠀⢐⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠂⠀⠀⠀⣦⣼⣤⡄⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣔⠀⠤⠀⢀⢁⠋⠀⠌⠊
⠀⠀⢀⠀⠀⠀⢀⠀⢀⠀⠀⡀⠀⠀⠀⠃⠀⠀⠐⠀⠀⠰⠐⢶⠄⣇⠀⠀⠀⠄⢨⡑⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠁⢀⠀⠀⠈⣀⠄⢀⠀⢂
⠀⠀⠀⠁⠀⠀⠁⠀⠀⠐⠀⠀⢆⣄⠁⠀⠂⠀⠀⠀⠀⠀⡀⢈⡁⠀⠀⠐⠁⠀⠀⢁⠠⠀⠀⠀⠀⡗⠦⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⡀⡀⠀⠁⠀⠀⠁⠈⠐⠛⠤⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣠⠊⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢰
⠀⠀⢀⠀⡀⠀⠀⠀⠠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠀⠀⠱⡄⠀⠀⠸⣉⡇⠀⠀⠀⠀⠱⠀⠀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠘⠀⠁⠠⠀⠐⠀⠌⠁⠁⠀⠀⡠⡆⡀⠀⠀⠈⠇⠀⠀⠀⠃⠀⠠⠀⠀⠀⠀⠀⠀⠁⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢬⠓⣥⣧⡕⢫⠀⠀⠀⢀⠀⠀⢠⠖⠁⠑⢆⠀⠀⠊⠉⠀⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢃⠺⣧⣤⡟⢐⠛⠀⠀⠉⠀⠀⢇⠀⠀⠀⢨⠀⠀⠀⠀⠀⢀⠼⠀⠀⠀⣀⠀⠀⠠⠇⠀⠀⣀⠀⠈⠠⠀⠀⠠⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠄⡇⠌⠳⠀⠀⡀⠀⠀⠀⠈⠳⠀⠔⠋⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠘⠁⡄⣆⣆⢣⡈⠃⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠠⠤⡄⠭⢰⡏⣛⣗⠬⠀⡦⠄⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠊⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⡟⡛⡱⠍⠀⠀⠀⢀
⠀⠀⠀⠔⢻⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⡾⠁⠀⠀⠀⠀⠐⠂⠀⠀⠘⠃⠈⢠⡅⠁⠈⠳⠀⠀⠜⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⢀⠀⠀⡀⠀⠀⢄⠀⠁⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⣀⠀⠰⠀⢐⠀⠀⠀⠀⠀⠀⡈⢇⣀⠀⠀⠀⠀⠀⣦⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄
⠀⠀⠀⢀⡨⣩⠕⢭⠭⡀⠀⠀⠈⠁⠀⠀⠈⠓⢂⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠆⠰⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠈⢐⣙⡦⣚⣒⠉⠀⠀⢀⣠⣥⣀⠀⠀⠀⠈⠁⠀⠀⠀⠸⠖⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠉⠀⠰⠀⠈⠀⠀⠀⠈⣿⠜⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡞⠀⠀⢈⡟⠒⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠈⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠶⣦⣿⣿⠿⠿⣿⡿⠋⠁⠀⠀⢀⣀⡀⠀⠀⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠛⠋⠀⠀⠋⠀⠀⠀⣠⠴⣋⡀⠀⢁⡹⣦⢁⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠚⠱⣦⣌⡇⠀⣈⣽⣽⡿⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢀⡤⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠉⠉⠀⠀⠿⠿⠛⠁⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣴⣶⣿⡾⠗⠂
⠀⠀⠀⣲⢯⣷⣄⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⠟⠋
⠀⠀⠀⠈⠙⢿⣿⣿⣷⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⠙⠿⠿⠟⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠁
⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⣀⠀⠀⠀⠀⢀⣀⣴⣾⡗⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⠛⠿⣿⣿⣿⣿⢿⣿⣿⣿⡏⠀⠀⠱⣄⣀⣠⣤⣶⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠈⢹⣿⢸⣿⠀⠈⠉⡀⠀⠀⠘⡏⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣧⣤⣤⣤⣴⡶⠾⠿⠿⠿⠁⠀⠀⠀⠀⠀⣼⣿⣾⣿⠀⠀⠘⠿⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠉⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⣠⡀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠆⠀⠀⠻⠇⢀⡼⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠛⢦⣄⡀⠀⠀⠀⢙⡛⣛⠒⠀⠀⢀⣠⠶⠋⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠈⠙⠛⠲⠶⠶⠶⠶⠶⠚⠛⠉⠁⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⣤⣄⣀⣀⣀⣀⣠⣤⣤⠴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠱⡄⠀⠀⢄⡀
⠀⠀⠀⠀⠀⠀⢀⡠⠤⠀⠐⠒⠲⠂⠤⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⢇⡇⠀⡀⠴⠀⠀⠈⡉⠀⠐⠤⣀
⠀⠀⠀⢀⠔⠊⠈⠇⠀⠀⠀⠀⢠⠁⠀⠀⠀⠑⠄⡀⠀⠀⠀⢀⠔⠁⠀⠈⠨⠉⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠑⡄
⠀⠀⠔⠁⠀⠀⡈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠐⡀⠀⢀⠆⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠈⢂⠀⠀⠀⠀⠘
⠀⡔⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⢤⡀⡌⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢡
⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡊⠀⠀⠀⠀⠀⡀⢔⡧⠃⡄⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠌
⠀⡷⡀⠀⠀⠰⡁⠀⠀⢀⣀⢰⠅⣄⡐⠲⠬⡒⠛⢄⡆⠀⢠⠀⠀⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⢸
⠀⠉⠺⠀⠐⢶⠙⠛⢧⡀⠉⠫⡁⠀⠑⢄⠀⠈⠢⣤⠀⠀⠈⡄⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠱⣄⠀⠑⢄⠀⠈⠢⡀⠈⠲⢄⠀⠑⠢⡀⡄⠀⠀⠀⢌⠢⢄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⡨⠀⠀⠀⢀⠖
⠀⠀⠀⠀⠘⠗⢄⠀⠑⢀⡀⠈⠢⡀⠀⠑⢄⠀⢘⠃⠀⠀⠀⠈⡓⠢⢈⡑⠒⠧⠀⠀⣀⡀⠀⣸⠀⠀⢀⡤⠃
⠀⠀⠀⠀⠀⠈⢂⠑⢄⠀⠈⠢⡀⠈⠢⡀⠀⠑⡞⠀⠀⠀⠀⠀⠇⠀⠀⠀⠉⠐⠒⠠⠄⠤⠌⠭⠩⡬⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠣⡀⠙⢤⡀⠈⠢⡀⠈⠑⢄⠇⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠙⠢⡀⠈⠢⡀⠸⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢕⢄⡀⠈⠢⡀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠉⠠⡀⠈⢲⠁⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⢄⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠁⠀⠀⠀⠀⠀⢰⣒⣲⣶⣒⣒⣖⣲⣖

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠒⠒⠒⠂⠀⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⠀⠉⠐⠒⠂⠀⢴⢶⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠿⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠒⢛⠀⠈⠑⢦⣄⣀⠀⣤⠶⢿⣿⣧⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡘⢦⡘⢧⡀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠇⢀⣽⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡦⣌⡐⠈⠲⢦⣤⣤⣠⣤⣴⡫⠥⠒⣩⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠏⠀⠀⠈⠉⠁⠀⠒⠒⠒⠒⠒⠀⠉⠉⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢠⣾⡆⠀⢀⣴⣤⠀⢀⣶⡄⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠘⣿⠟⠁⠈⠉⠁⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣗⠀⠀⢰⠇⢷⡀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠠⠔⠉⠐⠒⠚⡆⠘⡇⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠒⠛⠒⣤⣀⡀⠀⠀⠀⠀⣳⣶⠗⠚⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡁⢯⠀⠰⢆⠀⢸⡈⠉⠘⡟⠉⠻⠀⢰⡀⠀⠀⣰⠷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠙⢆⡡⠀⠋⡀⠀⡗⢲⠒⣇⠀⠀⠀⠉⠻⠛⠈⠀⠀⠀⠉⠛⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⢀⠔⠈⠳⠀⠈⠷⠀⠀⡇⠀⡇⠀⡄⢻⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⡄
⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⣦⡀⠀⠀⢸⡁⠀⡇⠀⠇⢿⣤⣤⣀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠁⠹⣄⣀⣼⡇⠠⡇⠀⠷⣤⣀⣉⡉⠙⠻⠋⠁⠀⠀⠀⡰
⠀⠎⠀⠀⠀⠀⠀⠠⠆⠀⢠⡶⠋⠁⠀⠀⠀⠀⢰⡄⠀⠈⠉⠉⠀⠘⠀⢀⣀⣀⣤⠁
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠁⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞
⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⡴⠞⠋⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣠⣴⠋
⠀⠀⠙⠶⣤⣄⣀⣀⣤⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⣠⠾⠿⠻⡇⣸⠇
⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠖⠛⠁⠀⠀⠀⠃⣿
⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠞⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠦⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⢤⡀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿
⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⣀⡠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⠾
⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⣠⡴⠶⠛⠛⠛⠓⠲⢤⡀⠀⠀⠀⣠⡴⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⣀⣀⠀⠀⠀⠀⠈⠀⣠⡼⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠶⡄⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⢀⡴⠶⠖⠲⢦⣶⠋⢧⡀⣀⣤⡀
⠀⠀⠀⠀⠀⣼⠋⠉⢹⣧⠀⠀⠻⢤⠀⣴⠒⠒⢦⣰⡏⠉⣩⡉⠻⡇⠀⠘⠃⠀⡿⢦⠀⠉⢁⣠⡇
⠀⠀⠀⠀⠀⢹⡄⠀⠀⠛⠀⠀⠀⠸⡆⡇⠀⡄⠈⢿⡇⠀⠈⠀⣠⢿⠀⠀⣶⠚⠁⣼⠀⡾⠉
⠀⠀⠀⠀⠀⠀⢷⠀⠀⢀⣠⠀⠀⠘⣷⠇⢀⡤⡄⠘⣇⣀⣸⣏⡁⠘⠶⢖⣋⣀⡀⢙⡶⣇⠀⠀⣀⡀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠸⡆⠀⠈⣟⣇⠀⣀⣸⠓⠚⢁⣹⣾⠭⠿⡟⠉⢉⠙⢦⣾⠁⠁⠙⣿⣄⠈⠳⠚⠉⣹⠏⠀⠀⣉⡇⠀⠀⠀⢀⡶⠛⠳⣆
⠀⠀⠀⠀⢀⣀⡀⠳⣤⠤⣏⣈⠉⡟⠛⢳⡄⠸⣥⡀⠀⡴⣇⠀⢸⣷⠈⡇⠀⠒⠀⠹⡜⣧⠀⣴⠚⣽⠗⠦⠄⠉⢳⠀⣀⣀⣸⠁⠀⠀⢻
⣠⡤⠤⣴⡋⠉⢻⣄⣰⠋⠉⡉⠳⣷⠀⠀⣇⣀⣨⡇⠀⣧⣿⠀⠈⢁⣼⣇⣀⡟⣧⣀⣿⢿⣠⡏⠀⠹⣄⣀⣀⣠⠞⣸⠋⠉⠻⡆⠀⠀⣸⠟⠙⢳⡀
⢿⠀⠀⠸⠗⠀⠀⠘⣏⠀⠐⣿⡆⢸⡀⠀⠉⠈⣧⣤⡤⠼⠛⠛⠋⠉⣠⣭⡉⠀⠈⠉⣠⣤⡀⠀⠀⠀⠀⠉⣉⣁⣀⣹⣄⣀⡀⠡⠠⠤⠥⣀⣠⣾⣥⣤⣤
⠘⣧⠀⠀⢀⡀⠀⠀⢿⣆⡀⠈⢀⡾⠳⠖⠛⠋⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠙⢦⢤⡞⠁⠀⢻⠀⠀⠀⠀⣿⠉⠉⠉⠁⠀⡀⡃⠀⠀⠀⠀⠀⡠⠊⠀⠀⢸
⠀⠸⡆⠀⠸⣿⣀⣀⣨⡇⠉⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠶⠶⠾⠲⠶⠶⠃⠂⠳⠖⠒⠺⠷⠶⣶⠀⣿⡀⠂⠀⡠⠈⠀⡃⠀⠀⠀⠀⠋⠀⠀⢀⠔⢸
⠀⠀⠻⣤⡤⠏⠉⠉⠁⡴⢶⣴⠛⣇⡴⢶⡄⠀⠀⠀⠀⢸⡇⢀⠀⠄⠄⠀⠠⠀⡀⠀⠄⠀⠠⠴⠂⢻⡄⢻⠁⠀⠌⠀⠀⠈⠐⠀⠀⠀⠀⡀⠀⠐⠁⠀⣸
⠀⠀⠀⠀⠀⠀⢸⠛⠻⣇⠈⡟⢠⡿⠁⣼⣥⡀⠀⠀⠀⢸⣗⠒⠒⠒⠒⠒⡒⠀⣇⠀⢋⡉⠉⠉⠉⢽⠆⢸⡆⠁⠀⠐⠁⠀⢠⠀⠀⠀⠀⠂⠀⠀⡠⠊⢸
⠀⠀⠀⠀⠀⠀⣾⢧⡀⠙⣄⡏⢸⣃⣞⣡⣾⣥⣤⡤⢤⡄⣿⠀⠀⠀⠀⠀⡳⠀⠀⢠⣸⠦⠀⠀⠀⢸⠀⢸⡇⡠⠀⠀⠀⠂⠰⠄⠀⠀⠀⠀⡠⠊⠀⠀⢸
⠀⠀⠀⢠⣤⡤⠼⠷⠾⠓⠛⠉⠉⠈⠉⠉⠀⠀⠀⠀⢸⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⣸⠀⢸⡇⠀⠀⠀⠀⢀⠀⠂⠀⠀⠐⠊⠀⢀⠄⠀⢸
⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣼⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠈⣧⠀⠀⢀⠄⠀⠀⠀⠀⠀⠨⢇⠔⠁⠀⢀⢼
⠀⠀⠀⠈⣗⠒⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣿⠀⠀⣿⠀⠔⠁⠀⠀⠀⢒⠀⠀⠐⠁⠀⢀⠄⠀⢸
⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⠈⠀⢸⠀⠀⠀⠀⠐⠀⠀⡠⢺
⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢿⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠀⠠⠊⠀⢸
⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠓⠛⠛⠛⠛⠛⠛⠛⠛⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢹⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠄⣘⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠙⡇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⢀⢤⡀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠲⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠃⠀⠠⠁⡀⠃⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⡔⠁⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⢿⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⢀⡐⠾⢀⠄⡠⠂⠀⠀⡀⠀⠀⠁⠋⢃⠄⠀⠀⠀⢘⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⡁⠈⠁⠐⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⣠⣾⣿⣏⣶⠀⠀⠀⡎⠠⠀⠀⢆⣀⣷⣤⠑⠀⠀⡏⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠒⠘⢺⡀⠀⠀⡜⠀⠀⠀⠀⠔⣆⢶⣿⣿⣿⣿⣿⡆⠀⢸⣀⣀⣸⣠⡿⣿⣿⣿⣜⡇⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠈⠁⠸⡇⠀⠀⣗⠀⠀⠀⢰⣨⣻⣿⣿⣿⣿⣿⣿⡇⠀⠀⢛⠉⠉⠉⠉⠉⢻⣿⠟⠀⠀⡇⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠒⠒⡗⠇⠠⣷⣤⣄⣄⣴⣷⣿⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⡄⠀⠀⠀⠀⣾⡏⠀⠀⢠⠃⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢲⡖⠘⠛⠀⠀⠈⠙⣥⣤⣤⣴⣾⣿⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⢸⣧⣒⢲⡦⠤⣶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣿⣿⠉⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⡏⠀⠀⠀⣼⣯⣭⣥⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡃⠀⠀⠀⠀⠀⠀⠀⢶⣒⣒⣚⣻⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣾⠁⠀⠀⠀⠀⠀⢈⠟⠛⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠈⠧⠠⢽⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢰⠇⠀⠀⠀⠀⠀⠀⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠹⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⠀⠀⠀⠀⠀⠑⠤⠤⠐



⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣟⠉⢹⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣿⣿⣿⣗⠀⢸⣿⣿⣿⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣿⣿⣿⣷⠀⢘⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣷⡂⢰⣿⣿⣿⣿⡇⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡼⠛⠋⠉⠉⣁⣀⣀⣤⣬⣷⣾⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣶⣶⣿⠾⠟⠛⠛⠛⠋⠉⠉⠉⠻⡟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠏⠀⠀⣤⡀⣴⣦⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠀⠀⠀⢈⣀⠈⠋⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠯⣉⣉⠈⠉⠀⠉⠙⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⠏⢙⠒⠚⠁⠀⢀⣀⡀⣀⡶⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⡤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠉⠑⢄⠤⠞⢿⣼⣿⠟⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⣷⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠨⣦⣀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠀⢀⣴⡇⠀⠀⠀⠀⠀⠀⠀⢘⠹⣄⣀⣀⣤⣰⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣤⣄⣰⢟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠉⠛⠒⠲⣤⠤⢤⣤⠤⠤⠖⢚⣻⣽⠀⠀⠀⠀⠀⠀⠀⢀⢞⡴⠋⠀⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠈⠉⠈⠳⡦⣄⣀⠠⡤⢀⡤⠊⠁⠀⠉⠓⠒⠞⠲⠶⠶⠒⠖⢻⣻⠉⠀⠀⠈⠢⡀⠀⠀⠀⡴⡡⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠗⠂⢈⠟⠀⠀⠀⠀⠀⢀⣶⣦⠀⠀⠀⠀⠸⠸⠁⠀⠀⠀⢪⣉⣉⣉⣙⣋⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠘⠻⠋⠀⠀⠀⠀⢀⢀⠴⡄⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢐⡂⠀⢳⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠈⠀⡠⠸⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠺⡿⠇⠀⠀⠀⠀⠀⢸⡃⢀⣀⡀⠀⠀⢀⠔⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡌⠉⠉⡁⡅⠀⠀⠁⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣧⢤⢰⣿⠷⡄⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠄⠀⠉⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉⠐⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠤⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠄⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣼⣇⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠙⠟⣿⣿⣿⣟⢀⣄⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡬⣿⢿⡷⢶⣿⡿⢿⣼⢟⣻⡇⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢀⣀⠉⠾⣅⢹⣿⣷⣾⣿⣫⣧⣶⣦⣤⣄
⠀⠀⠀⠀⠀⠀⣠⣴⣤⡀⠀⠀⢀⣤⠆⣸⡯⠶⠋⢿⢾⣿⣿⣷⣿⡿⣿⣿⢶⡿
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣆⠀⠀⣿⣀⣿⠗⠚⡧⣸⣼⣿⣿⣿⡛⣿⠓⢈⠘⠁
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣷⣤⣶⣿⣿⠟⢐⣟⢻⠟⣹⣿⣿⣿⣿⣶⢶⣾⣤⣶⡧⣤⠄
⠀⠀⠀⠀⠀⠀⠼⢹⣿⣿⣿⣿⣿⠟⢁⡴⢢⣥⣴⡇⡋⣹⣿⣿⣿⣿⠿⠚⢭⠉⠉⠛
⠀⣴⣾⣿⣦⡀⡀⠀⠈⣿⣿⣿⣿⠀⢜⢻⢮⣌⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠻⠛⠁
⠀⢿⣿⣿⣿⡟⢻⣄⣶⢾⣿⣿⣿⣗⣺⢭⣛⠹⠏⢟⣿⣿⣿⣿⡏⢰⠁⣸⠉⣠⣶⣶⣄⢀⣤⣄⣀
⠀⠀⠉⢻⣿⣿⣾⣿⡇⣾⣿⣿⣿⡟⠄⢸⣭⣷⣿⣿⣿⣿⣿⣿⣿⣿⣯⠟⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠘⣿⣿⣿⡟⠀⣿⣿⣿⣿⣧⡴⢻⢛⡿⢾⣿⣿⠀⣾⠀⢸⣿⣿⢟⡂⠛⠛⠛⠛⢉⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⣿⣿⣿⡇⠀⣾⣿⣿⣿⣿⣷⣾⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡕⠞⠁⡔⠛⠛⣻⣿⡇⠀⣹⣿⣿⣿⡏
⠀⠀⠀⠰⣿⣿⣿⠃⢠⣿⣿⣿⣿⣿⡟⢣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣁⣀⡇⠀⢀⠐⠿⠞⢛⠉⠀⠀⣿⣿⣿⣿⠃
⠀⠀⠀⠀⢹⣿⣿⠀⢸⣿⣿⣿⡿⠟⢿⢻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣦⣼⣿⣧⣴⢿⡆⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⣿⣿⣿⠄⠀⣿⠋⣿⡇⣎⡽⡿⠛⣹⠋⠉⣿⡟⢻⠛⠿⢿⣿⣿⠉⠀⡜⠉⠈⠘⡆⠀⢸⣿⡟⣿⣧
⠀⠀⠀⠀⣿⢹⣿⠀⣴⣿⠀⣼⡟⠃⢀⠀⠀⢻⠠⠀⡧⠄⠈⣎⠀⠀⢻⠉⠀⠀⡇⠀⠀⠀⠃⠀⠸⣿⠇⣿⣿⠆
⠀⠀⠀⠀⠛⢻⣿⣦⠈⠿⠄⠈⠿⠄⠀⠀⠀⠺⠀⠀⡇⠀⠀⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠶⠟⠠⣴⡿⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢰⠖⠲⠶⡭⣄⠡⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠖⠒⠒⠦⠤⣀⡜⠙⠦⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⡀⢾⠇⢀⣀⠀⣶⡆⠀⠀⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠠⠀⠀⠀⠺⠂⠀⠠⠀⠅⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠑⠤⢀⣀⠠⠔⠁⠀⡰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠒⠠⠄⡀⢀⠀⠤⠄⡖⢺⠩⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢁⢜⠦⢄⣀⠀⡀⢀⠀⢠⣀⣆⠴⠾⡉⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢠⢂⠎⠁⢢⢉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠑⡄⠈⢢
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠃⡜⠄⢀⣹⠒⠈⠠⢤⡄⠀⠀⠀⠀⠀⠀⢰⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢰⠀⠈⠒⠐⠊⠀⠀⠘⠒⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⡀⠀⠀⠀⠀⠀⠀⢰⠉⣷⠀⠀⠀⠀⠀⠀⢰⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⣉⣀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠧⠜⠀⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⣀⠤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⣖⠒⠁⠑⢀⡰⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⡠⠤⣡⠀⠀⠀⠀⠀⢀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠙⠀⠀⠀⠀⠀⠈⣧⠀⠆⠠⠠⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢶⡴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣡⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣦⠀⠀⠀⢀⣄⣀⣄⣀⣀⣠⠞⠁⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⢀⡀⣤⠀⣷⣼⡟⣸⡇⣸⡇⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣦⠀⣸⢃⠟⣀⡀⠀⣸⣷⣿⢸⡿⠙⢷⠟⠛⢿⠇⠀⠀⢀⡴⠁⢀⡰⠂⠤⠤⠴⠒⠋⠁⠒⠁
⠀⠀⠀⢀⣤⠶⠟⠋⡇⠀⣿⠋⢸⡟⣿⠆⣿⠏⠧⢾⡇⠀⢠⠀⢀⡿⠀⠀⠖⣺⠂⠈⠀⠀⠀⠀⠀⠀⠀⠀⠾⠂
⠀⢠⠶⠋⠀⠀⠀⢸⠔⠈⣿⠀⣿⣇⣿⠼⡿⠀⠀⠸⠀⠀⠀⠉⠋⠁⠀⠀⠈⠁
⡰⠃⠀⠀⠀⠀⢰⡿⠀⠀⢻⣴⠋⠛⠁⠀⡇⠀⠀⢀⡀⠀⠀⠀⠀⣀⡀⣶⣄⠀⠀⠀⠀⠀⣤⣀⠀⠀⢰⡆⣼⣿⡄⢀⣴⣶⣶
⢇⡀⠀⠀⠀⣄⣼⠃⢰⣷⠀⠀⣰⡆⢠⣶⣦⡀⠀⢸⡿⠀⠀⠈⢙⡿⠛⢸⣿⠛⢦⠀⠀⠀⣿⣿⠀⠀⢸⢀⣿⣿⠀⣸⣿⡟⢹
⠀⠀⠀⠀⠀⠛⠁⠀⢸⣿⣀⣀⣿⡇⣿⡟⠈⣿⡀⢸⡇⠀⠀⠀⢸⣿⠀⢸⡇⠀⠈⣧⠀⠀⣿⣿⡄⠀⠸⠾⣿⣿⠀⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠉⠉⣿⠁⣿⡇⢀⣿⡇⢸⣧⠀⠀⠀⢸⣿⠀⢸⣇⠀⢀⣿⠀⣰⣿⣿⣿⠛⠂⠀⣿⡇⣀⠈⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⣿⡄⢻⣷⣾⣿⡇⢾⣿⣶⣶⡄⣾⣿⡀⠸⣿⣤⡾⠃⠀⣸⡟⠀⢿⡀⠀⢰⣿⡇⠻⣧⣸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠻⠇⠀⠙⠻⠟⠀⠈⠙⠁⠀⠀⠈⠛⠃⠀⠈⠁⠀⠀⠸⣿⣇⠀⠈⠳⠀⠈⠛⠇⠀⠈⠛⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢢⣦⡄⠀⠀⠀⠀⠀⠠⠀⠒⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠊⠡⠜⠀⠀⠀⠀⢀⠀⠄⠥⡂⠐⠀⠀⠪⡄⠃⠰⢤⡄⢙⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠈⠉⣹⠀⠀⠈⠢⠄⠠⠌⠀⠀⠀⠀⠠⢀⣀
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣶⣾⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠛⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠾⠈⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠈⠂⠀⠀⠀⠂⠀⠀⠀⢀⡯⢦
⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢣⡀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢅⠉⠁
⢀⢀⣤⣬⣤⣴⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡐⠀⠃⡄⡏⠂⠄⠀⠀⠀⠀⠀⠀⠀⠠⢀⣃⠈⡓⢲⡀⠠
⠀⠈⠀⠈⢹⡏⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠐⢤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠄⠀⠐⠂⠁
⠀⠠⠀⠀⠀⡀⠂⠀⠀⣞⢶⡀⢀⡶⡦⠀⠀⠢⢀⢀⠀⠀⠀⠀⠀⠀⢠⣁⡄⠢⠀⠀⠐⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⢫⡉⠙⡞⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⢀⠀⠩⠃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠄⣐⠀⠓⠀⡆⢀⡀⠀⠀⠀⠀⠀⠀⠀⠠⢄⣰⣬⣦⣴⡉⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠘⣭⡌⠁⠀⠀⠀⠀⢀⡀⡀⠀⠀⠈⠀⠀⠸⠿⠘
⠀⠀⠀⡠⠤⠀⠀⠀⠀⠀⡀⠀⢈⠔⠀⠀⠀⠀⠠⠁⠀⠺⠀⠀⠀⠄⡀⠀⡀⠈⠀⠀⠀⢀⠤⠴⢳
⠀⠀⠘⣍⠉⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹⡀⠖⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠅⣄⠀⠀⠃
⠠⣀⣂⠼⢄⢰⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠼⠖⣶⣲⣆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠠⣈⠆⡼⣄⡰⠀⡀
⠀⠀⠨⢜⡈⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠈⠀⠀⠀⠀⠀⡀⠤⠀⠀⠀⡂⠀⣻⠅⠵⠯
⠀⠑⠄⠀⢀⠠⠀⠀⠀⠀⡀⠆⡀⠄⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⢀⣘⣛⢦⢴⣯⣽⡆⠱⢄⣀⣀⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠈⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⢅⠀⠸⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠜⢢⢤⢶⣧⠄⠂⠀⠀⠀⠀⠀⠀⠀⠠⢄⣲⣜⡆⣴⡀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠿⣽⠙
⠀⠀⠀⢀⡤⢦⠀⠀⠀⠀⠂⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡀⠀⠠⠂
⠀⠀⠐⠊⠡⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠶⠾⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⡀⠀⢢⡀
⢀⠀⣄⢹⢀⣠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⡈⠃⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣄⣙⡀⣠⠂⢀