Patrick star running Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠆⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢇⣀⣀⡀⠀⢀⠀⠀⣀⣀⡀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢉⠉⠻⠛⢻⠟⠻⠋⠙⠁⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⠢⢀⠠⠂⠡⠄⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⢈⣉⣀⣀⣀⣈⠉⠀⠀⠀⠘⡄⠀⠀⣀⣠⠤⠔⠒⠒⠒⠒⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢀⠀⠈⠉⠁⠤⠐⠀⠀⠀⠀⠀⠠⠀⢳⠖⠋⠁⣀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠶⠒⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⣀⣠⠤⠤⠐⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠃
⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⢠⠼⠀⠀⡀⠸
⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⢀⡀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⡼⠁⠀⢸⠓⠀⠀⢀⠇
⠀⠀⠘⢦⣀⠀⠀⠀⠀⠀⠀⣀⣠⠖⠉⠙⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠓⠦⠴⠋
⠀⠀⠀⠀⠉⠛⠒⠒⢲⠖⠋⠉⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠉⠓⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠂⠅⠂⠄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠤⠄⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣇⠈⡏⠉⠉⠒⠠⡀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠐⠂⠠⠤⠤⠀⠊⠀⠀⠀⣈⢿⠃⠀⠀⠀⢰⢏⡸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠘⠓⠶⡤⠤⣤⣤⠤⠴⠶⠚⠋⠁⡎⠀⠀⠀⣠⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣤⠤⠤⠤⠶⣎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣀⠤⠀⠈⠳⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣲⣤⣶⣶⢦⣴⣶⣄⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⣔⢿⣿⣿⣿⠇⠁⠉⢻⣿⡀⠀⠀⠀⠀⠀⠐
⠈⠁⣤⣄⣉⣁⣀⠂⠀⠠⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣿⠁⠀⠉⠛⠁⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠂
⠀⠀⢘⠛⠛⠛⠛⠻⠿⠶⢦⣤⣈⠀⠀⠀⠀⠀⠀⢠⠄⢙⣲⡆⠀⠀⠘⠿⠀⡀⣀⣿⡄⣀⣤⣴⣒⠚⠿⢿⣿⣿⣶
⠀⣀⣂⣀⣤⣤⣤⣤⣤⣤⣤⣤⣭⣥⣀⣀⠀⠒⢄⢸⡎⡙⠛⠶⢤⣤⣷⡤⢤⡀⠈⠙⠉⣅⠀⠀⠉⣿⣷⣦⠘⠉⣻
⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣭⣴⠶⠶⠤⠤⠤⣀⠈⢉⠙⡉⠹⢁⢀⣀⠠⢄⠈⡁⠀⠀⠀⡽⠀⠀⠀⣼⣿⣿⡄⠀⣼
⠀⠀⣸⣿⡿⠿⠛⠋⠉⠁⠀⡀⠀⠀⢶⡿⠟⢉⣴⣿⡆⠀⠀⠀⠒⠀⣸⠿⣿⠇⠀⠀⠰⡀⠀⠀⢀⣿⣿⣟⠋⠰⣿
⠀⠴⠏⠁⠀⠀⠀⣀⣴⣾⡟⠁⠀⠀⢨⣤⣶⣿⣿⣿⣧⠀⠀⠀⠈⢔⠀⡦⠋⠀⠀⠀⠀⣁⠔⠂⢸⠉⠛⠙⠲⠖⢿
⠀⠀⢀⣀⣤⣶⠿⠟⠛⣩⠄⠀⠦⠀⠸⡟⠛⣻⡿⠛⠻⠀⠀⠀⠀⠂⣤⠤⠤⠴⠒⠀⠨⠀⠀⣠⣾⠀⠀⠀⠀⠀⠈
⠀⠀⠛⠉⠁⠀⠀⠀⢀⠟⠞⠉⠻⣿⣶⡇⠊⡀⠀⠤⠀⠑⢚⠉⠀⠀⠐⠛⠁⠀⠀⢀⣀⣴⡾⠋⠁⠀⠀⢄⠈⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠼⡤⢄⠲⠀⠟⠁⠐⠀⠀⠀⠀⠀⠀⡀⣤⣤⣤⣦⣷⠶⠾⠛⠛⠛⠋⠀⠀⠀⠀⠀⠈⠣⠘⠆
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠑⠈⡁⠙⢊⡀⠀⠀⣀⠀⠀⢠⠚⠤⡨⢉⠏⠨⠁⠀⠀⠲⠦⡀⠀⠀⠀⠠⠂⠈⣠⠂⠀⠈
⠀⠀⠄⠀⠀⠀⠀⠁⠈⠉⠉⠀⣾⣿⡇⠀⢠⠟⠀⠔⠁⠀⠀⠀⠸⣤⢦⣀⠀⠀⠀⠀⢡⠀⠀⠀⠀⢉⠐⣃⠀⠒⣄
⠀⠀⠀⠀⠀⠀⠀⡄⠀⣄⠀⠀⠛⡠⠁⢠⠂⠀⠈⠀⢀⣈⠚⠄⠀⡸⢀⣽⣷⡆⢀⣾⣿⡆⠀⢀⠀⠈⠠⠁⠀⠀⠘
⠀⠀⠀⠀⠀⠆⠒⢡⡀⡈⠐⠂⠊⢀⠄⠁⠀⠆⠀⠀⠋⠀⠈⡦⠄⠀⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠴⠈
⠀⠀⠀⠀⣀⠀⡀⣀⠇⠈⡰⠒⠒⣁⠀⠘⠁⠀⠀⠀⠰⠀⢠⡇⠀⠁
⠀⠀⠐⠁⠀⠀⠀⠀⠀⠛⢁⣢⠀⠀⠀⢰⣍⡷⠀⠀⠀⠀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⢤⠄⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠄
⠀⠐⠀⠀⡀⠀⠀⠀⢢⠀⠀⠀⢀⡀⠀⠀⠀⢀⡤⢘⡉⠀⢀⣠⠆⡠
⠀⠀⠘⠈⠀⠀⠀⠀⠀⠄⠉⠂⠠⣤⣄⣀⡴⠋⠀⠀⠹⣻⡿⠋
⠀⠀⠀⡀⠀⠀⠀⠀⠁⠂⠄⠐⠊⢛⣿⡾⢆⠀⠀⡠⠟⠁⡀⠀⠄
⠀⠀⠈⠁⢰⠀⠀⠀⠀⠀⠢⣀⡀⣼⠿⠷⠙⠓⠀⠒⠂⠀⠀⠐⠁
⠀⠀⠸⠀⠀⠔

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠒⢶⡟⠀⠁⠠⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠖⠁⠈⣁⣤⣤⣼⣤⣤⣈⣀⣀⠀⠀⠈⠑⢦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣼⣆⡀⠀⣽⣶⣿⠿⠿⠿⠿⡿⠻⠿⠿⠿⢿⣿⣷⣶⣦⣤⣈⣀⠀⠙⠠⢤
⠀⠀⠀⠀⠀⠀⢠⣝⣿⣿⣿⢻⡆⠀⠀⠀⠀⣸⠇⠀⢠⡄⠀⠀⠀⠉⠉⠙⠛⠿⢿⣿⣶⣶⣞
⠀⠀⠀⠀⠀⠀⠘⠛⠿⠛⠃⢸⡇⠁⠀⠀⠀⡿⠀⠀⡏⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⡀⠉⣿⠏⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣈⣷⠀⠀⠀⠀⢣⠀⠐⠋⠀⠄⠘⠓⢠⡄⠀⣤⡖⢈⠃⢸⡇⠲⠇
⠀⠀⠀⠀⠀⠀⠀⡔⠊⣉⡄⠀⠈⠑⠄⠀⠀⢸⠀⢠⣾⣦⠈⠀⠀⠀⠐⠀⠀⠁⠈⠀⡾⠑⠠⠘
⠀⠀⠀⠀⠀⠀⠸⠁⠀⣿⡇⠀⠀⠀⢀⠀⠄⣿⠀⣿⣿⣿⣷⣦⡄⣀⠀⠙⣆⠀⠀⣾⠁⠑⢤
⠀⠀⠀⠀⠀⠀⠠⠀⠀⠸⠥⠤⠔⣾⠁⠀⠀⠘⡆⡛⠛⢻⠛⠓⠔⠻⣥⣍⠈⠀⠀⡿⠀⠀⡜⠠
⠀⠀⠀⠀⠀⠀⠀⠁⠀⡉⢄⠀⠀⢸⡧⡄⠀⠀⡇⢃⠀⡆⢀⠠⠀⠰⠦⡀⠀⠀⣸⠛⠳⠚⣁⠆
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠋⠐⠁⠀⠈⢷⣀⣀⣀⢹⡈⢒⣡⣤⡴⠶⣤⠶⠚⠉⢉⡏⠀⠀⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢡⡄⢸⠀⠀⠀⠀⠀⢧⣤⣉⠉⠟⠉⠀⢀⣀⣴⣥⡶⠖⢛⣯⠟⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠈⠯⣙⠿⣿⣶⡿⠟⢛⡻⠅⠲⣄⡤⠞⠲⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⠧⢴⠂⣀⠇⠀⠀⠀⠀⠀⠑⠢⣝⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠯⠈⠂⡁⠀⠀⠀⠀⠀⠀⠈⠑⢌⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣧⡍⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢬⣷⣦⣴⣶⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡅⠀⠀⠀⠀⠀⠙⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢠⡾⠂⠀⠀⠀⠀⠀⢈⡧⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⡴⠋⠑⠢⢤⠃⠀⠀⠈⢢⡀
⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⠇⠀⢀⣀⠈⠣⣴⠲⡄⠀⠱⡀
⢸⠁⠀⠉⠲⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢇⠀⢨⡉⢳⠀⢻⠢⠜⠀⠀⢇
⠈⢧⠀⠀⠀⠀⠈⠒⢄⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠳⣄⠉⠉⢀⠎⠙⠦⣤⣠⠞⢢⡀
⠀⠈⢧⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣰⣎⠙⠚⠉⠀⠀⠀⠀⠀⠀⢀⡑⡄
⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⢸⠀⠀⠀⠀⠉⢱⠈⠑⠒⠢⠤⠤⠠⠤⠔⢞⠉⠀⠈⠢⡀⠀⠀⢀⠤⠐⠂⠉⠉⠀⠀⠈⠁⠒⢄
⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠙⢶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⢱⠆⠲⠦⢤⣠⠤⠤⢤⣀⢘⡶⠊⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄
⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⠀⠙⢀⣀⡤⠞⠋⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⣀⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡏⠀⠀⠀⠀⠈⠑⠢⡀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠈⠓⠤⡠⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢔⡵⠋⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣍⠒⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣉⡴⠃⠀⣀⠴⣪⠕⠉⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠉⠒⠬⣉⠒⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠄⢒⡩⢴⡈⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠉⠑⠒⠠⠍⣐⣒⠒⠀⠀⠀⣐⡂⠨⠥⠒⠂⠉⠀⠀⠀⢹⡀⠀⠀⠀⠀⢯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⡴⠒⠤⠤⠚⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⢀⡴⠒⢦⡀⠀⠀⠀⠀⠈⠙⠐⠋⡁⢹⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢾⣀⠀⢰⡃⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣑⠢⠤⠤⠚⠁⠀⠀⢀⡴⠂⠀⣀⠤⠐⠂⠓⢆⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠉⠉⠲⣀⡠⠔⠒⠒⠒⠒⢤⠈⣣⠀⠀⠀⠀⢀⡴⠋⢀⠴⠊⠁⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⢀⡴⠉⠀⠀⠀⠀⠀⠀⣶⠖⠁⣀⡀⠤⠚⢧⠀⠰⢧⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⠀⠀⠀⠀⠀⢠⠛⠉⠉⠁⠀⠀⠀⠈⠦⡀⠤⠓⢄⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠄⣀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⣀⣀⡤⠖⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠑⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢄⠀⠀⠀⠀⢧⠀⢠⡄⠀⠀⠈⢣⡀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢈⢀⡀⠀⠠⠿⣶⣆⠀⠀⠀⠀⠀⠳⡀⢂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠰⠀⠀⢤⣴⣶⠀⠀⠱⡀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠆⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣤⠀⠐⡷⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡀⠀⠄⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⡐⠉⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠠⢀⠀⠀⠀⠈⢆
⠀⡰⠋⢁⠀⠀⠈⢫⠉⠉⠉⠉⠉⠉⠉⠙⠋⠉⠉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠐⣇⠀⡄⠙⡄⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠣⠪⠳⠤⢴⠀⠀⠀⠀⠱⡦⠐⢆⡀⠀⡠⠤⠲⠃⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⡱⠀⠈⠋⠍⠀⠐⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠙⡄
⠀⠀⠀⠀⣠⢷⡀⢀⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⡄
⠀⠀⠀⢰⠁⠘⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠑⡀⠀⠀⠀⠀⠀⡖⣄⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⣀⡀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠱⡀⠈⠳⠀⠀⠐⠀⠀⠀⢰⠁⡸⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⢠⠊⠀⠀⠴⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⢃⠀⢠⠏⡰⠃⠀⠀⠐⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠆⢀⠄⠀⠀⠀⢸⠖⢡⠚⠀⣠⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠈⠑⠈⠛⠂⠀⠐⠊⠁⠊⠐⠐⠀⠀⡠⠋⠀⠀⠉⠉⠀⠀⠀⠉⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⣀⠀⠐⠄⠀⠀⠀⠀⠀⠀⣀⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⠒⠒⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠶⠒⠛⠛⠛⠲⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⠿⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠛⢧⡀⠀⠀⠀⠀⢻⡆⠀⠀⠀⣀⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⠏⠀⠀⢀⡀⣠⠗⠛⠉⠳⣄⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢻⠀⢀⠀⠀⢀⡟⠀⠀⢸⡿⡷⠃⢀⣀⠀⠀⢸⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⢸⡇⡜⢦⡴⠋⢳⣄⠀⠀⢀⡇⠀⠻⠿⠁⢀⡟⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⣀⣤⠞⠋⠁⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸⣇⡇⠀⠙⢦⡀⠈⠛⠛⠉⢳⣄⠀⢀⣠⠞⠀⠀⣸⠃⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢘⡿⠀⠀⠀⠀⠉⠳⠦⣄⣀⠀⠈⠙⠋⢁⡀⠀⠀⡿⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠉⠉⠀⢠⡇⣠⠶⠋⠁⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⢄⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠳⣌⠢⣀⠀⠰⣐⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⡫⢺⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣨⡧⠀⠈⠳⢬⡑⠢⢌⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠒⣉⠤⠊⠀⣼⠃
⠀⠀⠀⠀⠀⠀⢀⣿⠷⢤⣀⠀⠀⠠⡀⢉⠓⠢⢌⣉⡙⠒⠒⠒⠒⠒⠒⠒⠒⠛⣉⡩⠤⠒⠉⠁⡀⠀⠀⣟
⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠈⠳⣄⠀⠉⠁⡅⠀⠀⠀⡮⣉⠉⠉⡹⠋⠊⠉⠉⠉⠀⠀⠀⠀⠀⠀⠣⢀⡀⠈⢳⣄
⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠘⣧⠀⠀⠺⣦⡀⠠⠔⠀⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠂⠀⣰⡏
⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⣴⠻⠆⢀⣠⠼⠿⠶⢤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣤⡀⠀⠀⠀⠀⢆⠀⣠⡾⠋⠻⣄
⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⢠⡏⠓⠶⠊⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠙⣦⣀⣀⣤⠴⠟⠉⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠈⠻⣤⡀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⣀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣄⣀⣀⣾⣷⢰⠐⢰⣰⡆⣞⡱⠀⠂⣆⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠛⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⢰⣦⡀⠀⠈⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⡰⠋⠻⣶⡾⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⡇⠀⣶⠘⣧⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⢀⣀⣧⠀⠛⣰⠛⢡⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠶⠶⠶⢦⣤⠖⠛⠉⠉⠋⠁⠀⠉⠀⠈⠙⠲⠋⠓⠋⣹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⣠⢾⡋⣹⣷⢦⣤⣤⣤⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠙⠁⠘⠛⠙⡿⡿⢳⡶⠦⣤⡀
⠀⠀⠀⠀⠀⠀⣠⡤⠶⠒⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠙⢳⡗⢦⡀⠀⣀⡇⣇⠀⠀⠀⠀⠉⢳⡀
⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⣀⠀⣠⢤⣿⣾⠉⣷⣏⣷⠤⣄⠀⠀⠀⢹⡄
⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⢙⣇⣿⣤⠿⠛⠋⠉⠉⣁⣠⠟⠀⠀⠀⠀⣧
⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠈⠉⢉⡁⠀⠀⠀⠀⠀⠊⠉⠀⠀⠀⠀⠀⢠⡟
⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣇⠀⠀⠀⠀⠀⠀⠀⣠⠴⢦⡀
⢠⡞⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⡴⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠈⠻⣄⠀⠀⠀⢀⣠⡏⠀⠀⠹
⣿⠀⠀⡀⠀⢠⡀⠻⡄⠀⠀⠀⣸⠃⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠘⣇⠀⠀⢸⣅⢹⡄⠀⡀
⣼⠀⢸⠇⠀⠀⣷⠀⢻⡀⢀⣴⣏⠀⠘⣧⡀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢀⣀⣻⠀⠀⣨⠟⠶⣧⣰⠗
⣿⠀⢸⡀⠀⠀⠿⠀⢸⣷⠟⠁⢹⡄⠀⠈⡻⣮⡓⠚⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠰⣶⠄⣴⠃⠀⠀⠀⢀⡴⠋⠉⠙⠛⠛⠁⠀⠀⢀⣠⡾
⢹⡄⠈⠃⠀⠀⠀⠀⣼⠁⠀⠀⠀⠙⣦⠀⠳⣄⠙⠓⠶⠤⠤⠤⠤⠀⠀⠞⣁⣀⣀⣤⣤⠶⢿⡁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠁
⠘⣧⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢸⡗⠄⠈⠂⠀⠀⢀⣠⡤⠶⠤⣄⠀⠀⠀⣠⠟⠀⠀⠈⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣰⠇
⠀⠘⣧⡀⠀⠀⠀⠀⡇⠀⣠⠞⠛⣆⠈⣧⠀⠀⠀⢠⠞⠉⠀⢀⡀⠀⣙⣠⣤⠾⠋⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⢀⣠⠟⠀⢠⠏
⠀⠀⠈⠻⣄⠀⠀⠀⢻⡴⠃⠀⠀⣿⢀⣏⠀⠀⠀⠀⠀⢀⡴⠋⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠈⠉⠁⠀⣰⠏
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢀⣿⡏⠻⣦⣄⣀⡀⣀⣈⣡⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣤⣤⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠈⢧⣀⣠⡶⣀⠞⢹⡇⠀⢸⠋⣛⠛⠛⢋⣹⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢸⡇⠀⠈⠉⣽⣁⣀⣸⠍⠀⣹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⢻⠆⠀⢀⣉⣩⡥⠀⠀⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⡙⢦⠀⢸⠁⠹⣤⣤⠶⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠛⢻⠟⠉⠀⠀⠀⠷⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠤⠖⠒⠒⠒⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠇⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠤⠤⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⢰⣦⠃
⠀⠀⠀⠀⠀⢀⠐⠁⠀⠀⠀⠀⠀⠀⠈⠁⠒⠤⣄⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⡴⠊⠁⠀⠀⠙⣆⠀⠀⠀⠸⠛
⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠂⠄⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⣠⣶⡄⠀⠏⠉⠉⠑⠂
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⣿⣶⠂⠰⠀⠀⠀⠙⠛⠁⣰⣶⣦
⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡄⠀⢧⣀⠀⣀⡠⠊⠘⠛⠋
⠀⠀⡇⠀⠀⠀⣀⠤⠂⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣄⠀⠈⠈⠉⢇
⠀⠀⠈⠒⠒⠉⠀⠀⠀⠀⠀⢀⠔⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠙⠒⠲⠀⠀⠀⠀⠀⢀⡠⠐⠀⠀⠀⠀⠀⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠈⠻⣿⣿⣿⣿⣿⣿⠷⠢⠄⠀⡇⠀⠀⠀⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠉⠻⣿⣿⠏⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⢠⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠴⠼⠿⠦⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⣼⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠀⠋
⠀⠀⡠⠀⠢⢄⣰⡏⢿⡾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠔⠁
⠀⡜⠀⠀⡀⠀⣿⠃⠣⢿⡽⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢀⠤⠂
⠰⠀⠀⠀⣠⡞⣿⠹⣦⡀⠻⣾⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠔⠁
⡆⠀⠀⢰⡟⢀⣿⡀⠀⢹⡜⣜⣷⣝⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏
⠇⠀⠀⣿⠀⠘⠙⠇⠀⠈⡆⠹⡖⣝⢷⣝⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠰⠀⠀⡟⠰⡈⠙⣆⣠⡾⠃⣴⣞⡍⣷⣍⠳⣮⣛⠶⣤⣀⠀⠀⠀⠀⢆⡐⢃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⢣⡀⣿⠀⢹⡧⢨⡵⠶⠿⠷⠿⠾⠿⢋⠟⣠⠝⠻⠾⣭⣛⠶⢦⣤⣈⠙⠉⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡿
⠀⠀⠁⢹⣏⠛⣡⣼⣿⣿⣶⣶⣿⢷⣶⣿⠛⠿⣀⣀⡠⢤⡉⠛⠳⠶⣭⣽⣛⣲⣶⣶⣖⣒⣻⣿⡿⠟⣽⠃
⠀⠀⠀⠀⠙⠳⣬⣋⠚⠿⠿⠛⠖⣚⣩⢛⡤⢌⠃⣩⠴⠊⠁⠀⠀⠴⣆⠈⠉⡟⢙⣽⣿⣭⠭⣶⡸⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠛⠛⠉⠙⢦⣕⡫⠸⣅⠀⠀⠀⠀⢸⡇⣘⠷⠾⢡⠝⣛⣛⣛⡛⠳⢇⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣬⣍⣉⡓⠚⢫⡴⢞⣣⡴⠖⠛⠉⠉⠉⠉⠛⣮⡊⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢻⣧⡿⡁⠀⠀⠀⠀⠀⠀⠀⠀⢜⣣⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢮⣍⡇⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⢀⡠⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⢀⠀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣦⣶⠶⠾⠿⠛⠛⢻⣿⡿⠿⠿⠛⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠿⠿⠿⠛⠛⡇⠀⠀⠀⢀⢀⡤⠤⠀⡀⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠀⠀⠇⠀⠀⡚⠉⠀⠀⠀⠈⠃⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⡇⠀⡘⠀⣠⡐⢠⣄⠀⢺⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⡇⠀⡇⠀⠻⠃⠈⠿⠀⠸⠳⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⡇⠀⠀⠤⠄⠀⠁⠀⠄⠁⠀⢇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠖⢀⣠⡤⠄⠀⠂⠀⠒⠲⢤⡐⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣰⠟⠁⠀⠁⠀⠁⠀⠀⠀⠠⡙⠶⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠑⠤⣤⣀⠀⣀⣀⣠⣀⡤⠜⠓⠀⢳⡀⠀⠀⠀⠀⠀⢀⠀⢀⠄⠄⣠⠀⡀
⡴⣀⣀⠀⠀⡨⠒⢄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢁⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠹⠒⢄⠀⡰⠉⡹⢄⡎⠀⠀⠈⠢⡀⠀⠠⠞
⠀⠀⠀⠁⣾⠀⠀⠀⡏⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⡐⠀⠄⠀⠙⢄⠀⠁⠼⢄⠀⠀⠀⠀⠸⡔
⠀⠀⠀⠎⠘⠆⠀⠀⠁⠀⠀⠔⠀⠀⠀⠀⠒⠂⠤⢄⠀⠀⠁⠂⠀⠀⠀⠀⠠⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢢⠀⠀⠨⢆⠀⠀⠀⡜⠇
⠀⠀⠸⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⠄⠀⠀⠀⢰⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠁⠀⢀⠀⠀⠱⠀⠸⣀⠌

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠆⠀⢀⣤⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠘⠋⠀⠀⠀⡀
⡠⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠑⡄⠊⠉⠁⠀⠀⠀⠀⡇
⡇⠀⠀⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣰⡆⠘⠀⢠⡄⠀⢰⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠳
⢣⠀⠀⠀⠀⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠀⠀⠸⠃⠀⡌⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣠⠔⠉
⠸⡆⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⣰⠣⠄⠀⠐⠃⢀⣀⡀⠜⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡠⠞⠁⠀⠀⠀⠀⢠
⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠈⠲⣤⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡽⡟⠁⠀⢸⡀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⡌
⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠈⣛⠐⠒⠒⠂⠒⠒⠋⠉⣰⠁⠀⠀⣠⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⡏⢀⡀⢀⣤⠄⠄⠀⡴⠁⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠘⢆⠀⠀⠀⡰⠁⠀⠀⠀⣰⠗⠋⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠈⠳⣄⡜⠁⠀⠀⠀⠾⠽⢀⠀⠠⠤⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃
⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁
⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢱
⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⢸⢙⠢⣀⠀⠀⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢔⣇
⠀⠀⠀⠀⢸⡀⠑⠦⣑⠂⠄⣀⠓⠤⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠔⢊⡡⠖⠉⡇
⠀⠀⠀⠀⠈⣇⠘⡀⢀⡉⠒⠠⠬⡍⣐⣓⡒⠒⠒⠒⠒⠒⠒⣛⣋⣉⣥⠴⠖⠊⠁⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠘⣆⠈⢉⡏⠀⠀⠀⢀⣀⠀⠀⠈⡟⠉⠉⠉⠉⠀⠁⠀⠀⢀⠖⠒⠤⠠⢎⡏
⠀⠀⠀⠀⠀⠀⢈⠦⡈⠑⠠⢤⣤⡼⠈⠢⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⡼⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠰⣅⠀⠀⠀⠀⠈⠙⠒⠦⡤⢤⣀⣀⣀⡀⠀⠀⠀⠀⡎⠉⠁⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠙⡗⠢⠤⠤⠤⢤⠴⠃⠀⠀⠀⠨⣁⠀⠀⠀⠀⢧⠀⠀⣀⣀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠈⠙⣏⠉⠉⠉⠉⠈⣽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢠⣀⡀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣏⠀⠤⡤⠤⠤⠬⢉⣉⠒⠤⢄⡀
⠀⠀⠀⠀⣀⣠⡤⠤⠔⠚⣉⡙⣦⣄⡁⠒⠠⡤⣀⡈⠉⠐⢬⡑⣦⡀
⠀⢀⡴⠚⠉⠀⠀⠀⢄⣻⡬⠷⡤⠿⣽⠛⠲⠦⢌⣉⣁⣀⣀⣹⣿⠉⠀⠂⠤⣀
⠀⣎⡀⠀⠀⣀⣀⡀⣈⣀⣛⠂⠙⠷⡬⠻⠶⠤⠀⠀⠀⣀⡼⠋⠀⠀⠉⠉⠑⠲⢤⣉⠉⡷⠖⠠⡄
⠀⠈⠉⠉⠉⠉⠀⠀⠀⠉⠉⠉⠛⠛⠒⠢⠤⠤⠔⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠠⠤⢤⣀⡐⠂⠠⣤⣄⣀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠛⠙⠒⠲⠦⢤⣀⠀⠀⠀⠀⠀⠈⠑⠲⢾⣅⠀⠉⠀⠒⢤⠞⠁⠀⠀⠈⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠈⠀⠀⠀⠀⠀⠸⠛⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣄⣀⣠⡴⠚⠃⠴⠤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠛⠛⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⠉⠉⠒⠢⣄⡀⡌⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣀⠀⠀⠀⠘⠛⠁⠀⢀⠀⢀⡤⠛⠀⠤⡀⠀⠀⠀⠀⠀⠀⢀⡋⠀⠀⠀⠠⢨⠈⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⡐⠊⠀⠀⠉⠢⡀⢀⣤⡈⠂⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆⠀⠀⠇⠀⠀⠀⣶⣄⠐⡄⠻⠇⢸⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠐⢆⠀⠀⠙⠛⠀⣡⠀⠠⠘⢣⠀⠀⣰⠃⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⣠⡀⠑⠤⢀⡀⠄⠁⠀⠀⣀⠔⢀⡴⠃⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⣿⣶⣤⣤⣤⣤⣤⣶⣿⣧⣠⠞⠁⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠒⠓⠀⠉⠉⠉⠉⠉⠉⠉⠛⠛⠲⠤⣄⡀⠀⢨⡇⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢿⡀⠀⠀⠀⠙⢿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣶⣦⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠦⣌⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⣀⣀⢀⣀⠹⠟⠋⠁⠸⡀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢯⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠲⣄⠀⠀⠀⠈⠀⠪⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀⠀⠙⡶⠉⠑⠾⡀⠀⠉⠢⡐⠄⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠐⡇⠀⠀⠀⠡⠀⠀⠀⠈⠀⠄⡒⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡄⠀⠀⢀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠉⠀⢸⠀⠀⠴⠂⣤⠇⠀⠀⠀⠀⠀⠀⠁⠐⠈⠅⠐⠒⠀⢤⠤⠄⠀⠀⠀⠀⠠⡤⢀⡒⣬⠗⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⢸⣇⠀⠘⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠛⠓⠒⠒⠛⠂⠀⠒⠒⠐⢫⠁⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⢻⡁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⣢⠀⠀⠀⠀⠀⢠⠂⠐⠁⠀⠀⠈⠲⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣄⠀⠀⣀⣀⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣁⣀⡀⡀⢀⣀⠼⠀⠀⠀⠀⠀⢀⣠⡤⠉⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⠉⠀⠀⠀⠉⠛⠦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⠀⢳⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠒⠒⠛⠿⣄⠀⠀⠀⢀⡔⠉⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠰⣏⡀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠚⠓⢄⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡀⠠⣀⢠⡀⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠑⠈⠱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⢐⡭⠄⡷⢑⠄⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠠⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⡒⠈⠤⠚⠂⠢⡀⡄⠈⡤⡌⢂⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣤⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢎⡱⣍⠀⠠⡀⡈⠃⠀⠄⠜⣠⠅⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠿⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠘⠛⠀⠱⣌⠰⣤⣤⣥⠀⣶⣭⡀⠰⠆⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢝⠠⣬⡢⡈⠻⣿⠿⠿⠛⠇⠘⠿⠘
⠀⠀⠀⠀⠀⠀⠶⠖⠀⠶⠆⠶⠆⠰⠆⠶⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⣠⠑⠈⢄⠡⡾⢂⠁⢒⣚⣥⢶⣾⣥⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡀⠀⠀⠈⠁⠀⠛⠠⠘⠐⣚⣻⣷⣿⣿⣿⣟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⠀⠀⠀⢀⣀⠻⢿⣿⣿⠟⠋⣉⡀⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣧⢼⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠙⢆⡨⠏⠉⠀⢸⡏⠑⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠁⠀⠻⠟⠁


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣦⣴⣶⣶⣿⣿⣿⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⠟⣉⠛⢉⡉⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣄⡛⣠⣌⣵⣿⣿⠀⠀⣦⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣤⣾⠁
⠀⠀⠀⠀⠀⣘⣶⣧⡀⠀⢿⣿⣿⣿⣿⡿⢿⢻⣿⣿⠡⠴⠛⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⡽⠋
⠀⠀⠀⠀⠀⠘⠋⠉⠉⠳⠎⢻⣿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠿⠿⠛⣛⣻⣿⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⠟⠻⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⣿⣿⣿⡿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠋⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃⢸⡏⠁⠀⠈⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣄⡀⠀⠶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⡀⠀⢰⣧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣀⠀⣀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠒⠒⠀⠤⠒⠉⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⠉⠀⠈⠁⠀⠀⠀⠀⠈⠉⠁⠉⠉⠀⠀⠀⠙⠂⠐⠂⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⢸⠀⠀⠀⠀⣀⠤⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠃⠀⠣⡀⠀⠸⠁⠀⠀⠘⠂⠀⠀⢀⡀⠀⠀⢰⣶⠀⢀⣀⠀⠀⢀⣤⠀⠀⠀⣿⡆⠀⣠⣄⠀⡇⠀⠙⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠙⠀⠐⢄⣀⣀⡴⠀⠀⠀⢻⡿⠄⠒⠚⠛⠂⠾⣿⠁⠀⠈⡿⠗⠒⠈⠉⠉⠚⠻⣇⠀⠘⠀⠚⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⡠⠆⠲⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠱⣤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⠀⠀⡰
⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠎⠀⠀⢀⠇⠘⠀⠀⣰⠊⠉⠂⠀⢰⠁⠀⠀⡀⠀⡀⠀⠀⠀⠀⢠⠁⠀⠀⡠⠤⠤⡀⠀⠀⠀⠀⠀⢱⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⢄⣀⡠⠎⠀⠀⢃⠀⠹⠄⠠⠃⠀⠀⠀⠠⡎⣴⣶⣌⢣⠀⠀⠀⢸⠀⠀⡜⣵⣾⣷⡜⠀⠀⠀⠀⠀⢸⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣰⠀⢐⣏⠿⠿⢛⡜⠀⠀⠀⠈⡄⠀⠱⡙⠿⢛⡱⠀⡀⠀⠀⠀⡜⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣆⠀⡔⠋⠑⠀⠀⢀⠀⠀⠀⢀⠴⣂⠉⠴⠉⠙⡀⠒⠉⠀⠀⠀⠀⣠⠞⠢⡀⠈⢉⡩⠔⠊⠁⠀⢱⡞⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠑⠤⠚⠀⠀⠈⢣⠀⠀⡎⠀⠁⠘⣀⡀⢠⠇⣀⡀⢀⡀⠰⠊⠁⠀⠀⠙⠉⠁⠀⠀⠀⠀⣀⠜⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⢀⠤⠤⡀⢸⠀⠀⠘⠄⠀⠋⡍⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⡀⠀⠤⠄⢶⡉⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣀⠃⠀⠀⢸⠈⠀⠀⠀⠀⠀⠀⠃⠀⠀⠙⠢⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠳⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡅⠢⠤⠔⠁⢠⠀⢀⠊⠑⢆⠀⠸⠀⠀⠀⠀⠀⠀⠈⣿⠀⠐⠶⠂⠲⠀⠉⢹⠉⠁⠀⣠⠖⠢⡀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⡄⢳⡘⣄⣀⡼⠀⠀⢶⠀⠀⠀⠀⠀⠀⠿⠀⠀⠇⠀⠠⣀⣀⡸⠀⠀⠀⢧⣀⣀⠆⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀⠨⡄⢀⠆⠀⠱⠀⣀⠴⢄⠀⠈⢣⣀⠄⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⣡⠀⠀⠀⠀⢀⢀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⡀⠀⠰⡇⠀⡃⠀⠀⢱⠀⠀⠣⣀⠀⠀⠈⠛⠁⠀⠈⠑⡄⠀⣉⠀⠀⢀⠎⠁⠀⢱⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣁⠔⠃⠘⡀⠀⢠⠀⢣⡀⠀⠸⠂⠀⠀⣈⠓⠦⠄⣀⣀⣀⣀⠤⠾⠒⣁⠀⠀⣇⠀⠀⢠⠌⠀⠃⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⡇⠀⢸⠀⠀⠉⠀⠁⠀⠀⠀⠀⠉⠑⠒⠀⠀⠠⠀⠐⠒⠉⠀⠀⠀⠈⠒⠂⡁⠀⠀⠇⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠁⣀⡀⠀⠀⣧⣀⣠⣀⣀⠠⠔⠂⠤⢄⠀⢤⠤⠀⠀⢴⡦⠤⠤⣤⠐⠒⢒⠶⠀⠀⠒⠁⠉⠐⢻⣀⣀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⠁⣜⠁⠠⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⠞⠀⡰⠲⡏⠀⠑⠖⠁⠀⠀⠀⣀⣀⢀⣀⣯⠁⢨⡤⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢠⡟⢉⣀⣀⡀⠐⡗⠀⢀⣀⣒⣒⡒⠒⠒⣒⣒⣒⣺⠁⠀⢹⡀⠀⢀⡀⢀⡉⠉⠉⢭⠉⢙⢣⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⡈⡇⠘⠠⠀⠇⠀⠀⠀⠲⠤⠀⠤⠋⠀⠘⠤⠀⠘⢧⡀⠀⡠⠃⠀⠘⠁⠘⠁⠀⠃⠉⠀⠸⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠃⢇⣀⣀⣀⣀⠀⢰⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡙⢊⡀⠀⠀⠀⠀⢀⠠⠄⠤⠤⠤⠆⢸⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢾⠀⠀⠀⠈⠁⠀⠀⠈⢘⠃⠀⠀⠀⠀⠈⡍⠉⠈⠁⠀⠀⢸⠁⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠁⠀⠺⢄⠀⠀⠀⠀⠀⠀⠀⠈⠑⠒⠀⡄⢶⠊⠁⠀⠀⠀⠀⠀⠈⠁⠖⢲⠒⠂⠉⠀⠀⠀⢀⡔⠊⠁⠀⠳⡀
⠀⠀⠀⠀⠀⣴⠀⣈⡁⠀⠀⠀⠀⠈⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠀⠀⠀⢠⡒⠒⠊⣀⠀⠀⠀⠀⠡⢄⡀
⠀⠀⠀⠀⠀⠀⣉⠴⢃⣄⡀⢠⡎⠱⣄⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⢠⡆⠀⠀⠀⠀⠀⠀⠀⢠⣆⣄⠀⠀⠀⠀⠙⠈⠁⢸⠃⢀⡀⢠⡶⢤⡬⠂
⠀⠀⠀⠀⠀⠘⣄⣠⠏⢰⠁⠸⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠠⡇⠀⠀⠀⠀⠀⠀⠀⢐⡇⢺⠀⠀⠀⠀⠀⠀⠀⣌⠀⢸⠘⠀⠉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠃⠀⠀⠀⠀⠀⠀⠀⣨⠁⢹⠀⠀⠀⠀⠀⠀⠀⠙⠴⠊⠀⠑⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡸⠒⠢⡀⠀⠀⡴⠈⢇⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠔⠁⠀⠀⢡⠀⣈⠁⠀⠀⠑⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠈⠉⠀⠀⠀⠀⠀⡜⠀⠻⡄⢀⠀⠀⠀⣈⡉⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡁⠘⠚⠁⠀⠀⠉⠚⠀⠀⠀⠈⠙⡁⠀⠀⠓⠋⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢄⣀⢀⡀⠞⠀⠀⠀⠀⠀⠀⠀⠙⠤⣀⣀⡠⠞

⠀⠀⠀⠀⢴⡖⢰⢲⣤⠖⣆⣴⣠⢠⠖⡀⣶⠂⣶⡆⡴⢲⣠⣶⡄⠀⣶⡦⡄⠀⣰⡆⣴⠒⢤⡴⠀⢀⣦⠀⣆⣤⣴⢢⡄⠰⣠⣆⡦⣆⣤⣤⢲⡆⣴⡆
⠀⠀⠀⠀⠐⠛⠘⠉⠈⠓⠋⠉⠙⠈⠓⠃⠛⠀⠓⠋⠙⠚⠙⠛⠃⠀⠓⠋⠛⠒⠋⠙⠙⠂⠉⠙⠀⠘⠉⠃⠁⠋⠙⠚⠁⠀⠋⠙⠀⠃⠉⠉⠘⠁⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠂⠀⠲⠀⠐⠂⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣴⣦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡿⢋⡙⠟⣁⡈⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣇⡘⠛⣠⣙⣵⣿⣿⠃⠀⢶⣴⣆⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢀⣠⣿⠁
⠀⠀⠀⠀⠀⢶⣴⡇⠀⠈⣿⣿⣿⣿⣿⣾⡿⡿⢿⣿⣿⡇⣠⠾⠛⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⡿⠛
⠀⠀⠀⠀⠈⠿⠟⠛⠳⢦⡜⢿⣿⣿⣿⣿⣷⣿⣾⣿⣿⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣿⣿⣿⣿⠿⠟⢛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣭⣴⣶⣶⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣿⠏⠉⠘⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠹⣿⡿⠟⠛⠻⡿⠟⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠘⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⡀⠀⠻⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣤⡄⠀⢸⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢀⠀⡄⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠱⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⢀⠨⠄⠻⢃⢄⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢂⡉⠠⠚⠀⠂⠀⠤⠀⠔⡄⠐⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⣤⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜⣈⠢⣀⠀⡄⠄⠉⠀⠀⠄⣰⠄⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠛⠛⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⠁⠈⠲⡈⢶⣦⣤⣄⣾⣶⡄⠀⡂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠊⢅⢶⡞⢄⢙⠿⡛⠛⢉⡃⠈⢛⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠂⠘⠓⠐⠃⠐⠃⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢤⡆⠁⢢⡄⠺⠣⢀⣉⡭⢶⣻⣯⣶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢂⠌⠀⠀⠀⠀⠈⣀⣀⣀⣩⣽⣿⣿⠿⣿⡯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣴⠜⠛⣿⣿⠏⠁⣴⣄⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠘⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠃⠛⠴⠂⠀⠀⠘⠇⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⠒⠲⠶⠖⠚⠛⠛⠒⠶⠆⠀⠚⠛⠛⠲⠶⠤⠄⠰⠖⠲⠶⠦⠤⠤⠶⠶⠶⠤⠤⠀⠤⢤⡀
⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⡤⠖⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠠⡀⢹⡀
⠀⠀⠀⢀⣤⠞⠁⣀⡀⢸⡀⠀⠀⢈⠀⠀⢀⡼⠀⣤⡀⠀⢸⡇⠀⣰⠆⠀⠀⠀⠰⣆⠀⢀⣿⠀⠀⣤⠀⠸⠤⠔⠁⣸
⠀⠀⠀⡸⠁⠀⠌⠀⠁⠀⠳⡀⠀⠀⠁⣀⠁⠀⢀⡼⠛⠉⠉⠉⠉⠉⠳⢄⠀⣀⠔⠋⠉⠈⠉⠁⠺⢏⠀⠀⠀⠀⠀⡟
⠀⣰⠎⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠐⠁⢠⠋⠀⠀⠀⠀⠀⠀⣀⠀⠈⢳⠁⠀⠀⠀⡀⠀⠀⠀⠀⠱⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⢲
⠀⢿⡀⠀⠀⠀⠑⠜⠀⠀⠀⢰⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠈⣡⣶⣭⠆⠘⠀⠰⢩⣴⣍⠳⠀⠀⠀⠀⡆⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢀⡴⠋
⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠢⡙⠻⠋⠃⡸⠀⠰⣜⣻⣋⡴⠀⠀⠀⢀⡁⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⢀⡤⢠⡿⠒⣻⣄
⠀⠀⠀⣿⠀⠀⠀⠀⠐⠀⠀⠀⡃⠀⠀⠀⠀⠰⠉⠃⠉⠳⢦⡀⠀⠉⣀⠔⠙⢦⡀⠀⠉⢁⡠⠤⠂⠀⠈⢑⡄⠀⠀⣇⠀⠀⠀⠀⠀⢰⡏⠠⣀⣽⠋⠉⢉
⠀⠀⠀⠹⣦⠀⢀⡀⣠⠂⠀⠀⠁⠀⠀⠀⠀⠈⠀⠠⡤⠀⠀⠟⠒⠉⠀⠀⠀⠀⠘⠋⠉⠀⠀⠀⣀⣠⠴⠊⠀⠀⠀⣼⠀⠀⠀⠀⠀⠈⢧⡀⠀⠑⠖⣠⠎
⠀⠀⠀⠀⠈⢣⠀⠉⠁⡰⠋⠑⡬⡀⠀⠀⠀⠀⠀⠀⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⢋⣉⠉⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⢀⡟⢠⠖⠚⠁
⠀⠀⠀⠀⠀⢸⠀⠀⠀⢳⠀⠀⠇⢱⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠒⠒⠒⣶⣶⠒⠊⢹⡏⠉⠁⠀⢀⡀⣀⠀⢸⠁⠀⠀⠀⠀⠀⢀⡾⢠⠏
⠀⠀⠀⠀⠀⠈⠳⡄⠀⠘⠦⠊⠀⢸⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣤⣤⣤⣿⣿⡤⠤⠴⠃⠀⠀⢰⠁⠀⢈⠀⠈⡀⠀⠀⠀⠀⢀⡼⢁⡟
⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⣀⢄⠘⡄⠀⠀⠀⠀⠀⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠈⠒⠒⠁⠀⣼⠶⠒⢢⣀⣠⠞⢠⡟
⠀⠀⠀⠀⠀⠀⠀⢈⡷⠲⣤⡁⠌⠀⢱⠀⠰⠛⠀⠀⠘⢦⣀⡀⠉⠉⠉⠉⠻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠂⣦⠀⢠⠃⠀⢘⣉⣭⡥⠴⠋
⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠸⠁⠀⠀⢸⠀⢀⠊⠈⡱⠀⠢⣈⣉⣛⣛⣛⠛⠛⠉⣁⠀⠀⠀⠀⠀⠀⠑⠘⠁⠀⢸⣤⣤⣬⠜⠁
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣧⣀⠀⣀⣀⣈⣒⣈⣀⡀⠀⣈⣀⣉⣁⣈⠉⠉⠉⢁⣀⣀⣀⣀⠀⣀⣀⣀⣀⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠉⢶⠲⡖⠁⠀⠀⠀⠉⠉⠀⠁⠉⠙⠛⠭⣀⡀⡠⠝⠻⣉⣩⠋⠣⢄⡨⠟⠉⠀⠀⠀⠈⢹
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡏⢽⣤⣶⠒⠶⠀⢀⠀⠀⠀⡀⠀⢀⣈⣀⣒⣶⠃⠘⣖⣒⣀⣀⠐⣒⣒⣒⣒⡒⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⣧⠀⠀⠉⠀⠀⠀⠘⠛⠛⠛⠛⠀⠘⠛⠛⠛⠳⡀⣠⠟⠋⠉⠉⠀⠙⠋⠙⠉⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠙⢶⣤⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠸⣇⠈⣏⠉⠉⠉⠉⠉⠉⣻⠉⠉⠉⠉⠉⠉⠻⣍⣉⣉⣉⣉⡭⠃
⠀⠀⠀⠀⠀⠀⠀⠸⡇⡄⢰⠆⠘⠀⠈⠙⢶⠶⡶⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⡏⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠤⠇⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⣠⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⣿⣦⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠛⠿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠈⠄⣠⣶⣿⣿⡿⠿⠿⣿⡿⠛⠻⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠿⠷⠛⠛⠛⠛⠉⠉⠉⠛⠛⠛⠉⠉⠒⠦⠤⣠⣴⣒⠓
⠈⠢⣴⣿⣿⣿⣿⡟⠀⢰⣦⣤⠀⠰⣦⣄⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⢸⠁⡠⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⢤⡀⠀⢀⢷
⠀⢰⣿⣿⣿⣿⣿⡇⠀⠈⣿⣿⣧⣀⣹⣿⣧⣘⣿⠄⢰⠀⣄⣥⣄⣀⣴⠋⠀⣸⡿⠀⠑⠋⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠹⠤⣤⠝⢀⠁
⠀⣿⣿⣿⣿⣿⣿⣿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣾⠁⠀⠁⢈⠁⠀⣴⣿⠁⠀⠛⠀⠀⣠⡄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢀
⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠋⠀⠲⠄⠀⠀⢰⣿⡏⠀⠀⠀⠀⢰⣿⡤⠀⠀⠀⢠⣿⣤⠀⠀⠀⠀⠀⠀⠔⣠⡄⠛
⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⢀⣼⣿⡇⠀⠀⠄⡀⠸⣿⠇⠀⠀⠀⢸⣿⡏⠀⠀⠀⠀⠀⠀⠀⠿⠃⣠
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⣀⣀⣠⣬⣿⣿⣿⣿⣿⣿⣶⣤⣴⣾⣿⣿⣿⠁⠐⠀⠀⠉⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⡘⠀⣠⣴⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⢐⣤⣀⠀⠀⠌⢠⣶⡌⣼⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠛⢉⣡⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⢹⣇⠀⠀⢰⣶⠀⠀⣀⣿⠇⠀⠀⠀⠸⠟⣼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⠓⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠋⣀⠀⠀⠄⣀⣀⣿⣿⣿
⣿⣿⣿⣿⣿⢟⣩⣽⣶⣭⣛⢿⡋⠉⠛⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣖⣲⠆⠀⠀⠙⠻⠿⠿⠿⠛⠁⠸⡥⠇⠘⡀⢿⣿⣿⣿⣿
⣿⣿⣿⠿⣷⣿⠿⡿⠟⣈⠛⢢⠷⣄⡀⠈⠃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⢾⣿⣶⣤⣤⣤⣴⣶⣿⡆⠀⠀⠀⢀⡁⠜⢿⣿⣿⣿
⣿⣿⣧⡔⢂⣄⠀⠀⠄⠈⡀⣂⣥⣘⣇⣴⣿⣦⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣧⣤⣄⣠⣿⣿⣿⣿⣿⣿⣿⣿⣅⠀⠀⠀⠉⣠⣴⣿⣿⣿⣿
⣿⣿⣿⣶⣿⣷⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⡟⣿⣿⣿⠿⣟⢦⡀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠙⣮⣧⠀⢸⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠙⠀⠉⠁⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠤⠒⠒⠒⠒⠉⠉⠉⠉⠀⠀⢹⠙⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢃⠀⠀⠀⠀⡤⠒⠚⠉⠛⠋⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠃⠀⠀⠀⠈⠳⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⡌⡌⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠄⠀⠀⠐⠀⠐⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⡽⠀⠄⢀⡠⠞⠁⠀⢠⡄⠁⠀⠉⠓⠒⠆⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢘⠁⠀⠀⠀⠀⡴⠀⠀⠀⣀⡀⠀⠀⣄⠀⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠐⢰⠀⠀⠀⠀⠀⢹⠀⢳⠄⠒⢲⠲⡿⣋⠈⠉⠉⠉⢍⠛⢫⠇⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⢠⡞⠁⠘⠢⣀⠀⠑⠈⠉⣆⠀⠀⠀⠀⢈⡔⠀⠀⠀⡜⠀⠀⠀⠀⠉⡀⢠⠏
⠀⠀⠀⠀⢠⠔⠉⠉⠓⢤⡀⠀⠀⠀⣳⣄⡀⠀⠀⠁⠒⠤⠊⠀⠑⠒⠒⠒⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⡔⠁⠀⠀⠀⠉⠐⠈⠲⡄⠀⢻⠈⠙⠓⠦⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏
⠀⢀⣠⣇⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠸⠀⠀⠀⣠⡤⢤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠸
⠀⣯⠤⢼⠀⠀⠰⠨⡀⣀⡴⠁⠀⡖⠒⠀⠀⡀⠦⠐⠀⢡⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠐⣧⠄⢺⠀⠀⢀⠀⠈⠩⠇⠀⠀⢡⠀⡄⠀⠀⠈⠀⠀⠘⢳⠀⠀⠈⠉⠀⠀⣀⡤⠒⠉⠉⠆⠀⠀⠀⢰⠃
⠀⠙⢾⠉⠀⢰⠀⠀⠀⠘⡀⠀⠀⢰⠐⠼⣠⡤⢶⠀⠀⠀⠻⢤⡀⠀⠀⠀⢸⢁⡀⠀⠀⢀⡆⠀⠀⠀⣿
⠀⠀⣀⠀⠀⠄⠳⣄⡀⢀⡅⠀⠀⠻⢦⠞⠁⠀⠈⠓⠲⣄⠐⢄⠈⠀⠀⣀⠼⢋⡼⠆⣠⠎⠀⢀⠀⢠⡏
⠀⠀⢻⠀⠀⠀⠀⠀⠉⢩⣍⠢⠔⣃⠈⡗⠒⠲⢶⡒⡳⠆⣷⣤⡙⠫⠛⣁⠔⠉⠑⠚⠉⠉⠋⠉⠉⢻
⠀⠀⠈⠓⢤⡀⠀⠀⠀⢰⠀⠙⠊⠉⠉⡗⣒⣀⠀⠈⢠⠈⢱⡈⡙⠢⠊⠁⠀⠀⠀⠀⠀⠀⠀⠠⠀⢺
⠀⠀⠀⠀⠀⠉⠲⣄⡴⠋⠀⠀⠀⠀⠀⡇⠉⠉⠁⠙⠛⢆⢠⠛⠒⠀⠰⠶⠦⠄⠀⠉⠀⠘⠛⠛⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⢻⠖⠶⠶⠶⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⣠⡤⠴⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢠⠀⠀⢰⠃⠀⠀⠀⡜⠉⠉⠉⢉⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠃⡼⠥⠎⠀⠀⠀⠀⢱⠎⣱⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡠⣆⠀⠀⠀⠀⠀⠀⠊⢰⡉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡉⠠⣄⠀⠀⠀⠀⠐⣮⠷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣾⣷⣾⣿⡇⠀⢀⣀⣀⣸⣦⣼⣶⡀
⠀⠀⠀⠐⢀⣀⣂⣑⣼⣥⣄⠀⠀⠀⠀⠀⢿⣿⣾⡿⠛⠹⠟⠁⠠⣿⣻⣿⣿⣿⣿⣿
⠀⠀⠸⣿⣯⡽⠾⠾⠾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣰⣟⣁⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⠉⠉⠉⠙⠛⠛⠶⠶⠦⣤⣤⣄⣀⣀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠐⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡿⠛⠓⠲⣄⢀⣤⠶⠚⠛⠛⠲⣤⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⣴⣲⠀⠘⡏⠀⠀⣀⣀⠀⠀⠈⣧⠀⠈⠛⠛⠛⠲⠶⠶⠶⢤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠈⠉⠀⣠⡇⠀⠀⠛⠞⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⢠⠀⠈⠛⠶⠶⠚⠁⠙⠦⣤⣀⣀⣠⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⢸⠛⢶⣄⣀⣀⣤⣤⣀⠀⠀⠈⠁⣀⣀⠀⢠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⣠⡴⠶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⠀⠀⠈⠀⠀⠈⠉⠉⠀⠀⠉⠳⠦⠶⠚⠉⠉⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠁
⠀⠀⣿⣀⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁
⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠞⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⢻⡟⠛⠷⣦⡀
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡴⠶⠛⠉⠁⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠛⢶⣤⠾⠃
⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠘⣧⣄⣀⣀⣤⡴⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣤⣀⣀⣀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢋⣼⡏
⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⣾⠏
⠀⠀⠀⠀⠀⠀⢾⣿⠿⣶⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁
⠀⠀⠀⠀⠀⠀⠘⢿⣷⣄⣹⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣴⣶⣶⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⣠⣤⣤⣶⣶⣾⠿⠿⠛⠛⠋⠉⠁⠀⠀⣰⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣴⣶⣶⡶⠿⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⢀⣀⣤⣤⣤⣶⣶⣶⠾⠿⠟⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠹⣿⣿⣍⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⢶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣭⣤⣴⣶⠶⠆⠀⠀⠀⠀⠀⢀⣼⣿⠋
⠀⠈⠙⠿⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠶⠶⠿⢿⣿⠗⠀⠀⠀⠀⠀⠘⠿⣿⣏⡉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁
⠀⠀⠀⠀⠈⠙⠻⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠂⠀⠀⠀⠀⠀⢀⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣷⣦⣄⠀⠀⠀⠀⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣶⡄⠀⠀⠀⠀⢲⣄⣀⣤⣤⣤⣤⣶⣶⡾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⣠⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⢸⣟⠋⠉⠉⠉⠁⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⠀⠀⠀⠀⠻⣿⣟⣛⣿
⠀⠀⠀⠀⠀⠀⠀⣀⣤⡄⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠙⠿⠿⠟
⠀⠀⣠⣴⣶⠾⢟⣿⣿⠁⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀
⠀⠀⢹⣿⣶⣶⣿⠟⠁⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄
⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠛⠉⠙⠛⠿⣿⣶⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠿⢿⣿⣶⣶⣤⣤⣀⣀⠀⠀⠘⢿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠿⣿⣷⣶⣾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⢀⣴⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢇⣠⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠇⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣠⡴⢶⡄
⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⣾⣥⡴⠞⠃
⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠈⠉⠉⠙⠛⠒⠶⠶⢦⣴⣏⣀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢉⣀⠉⢳⡴⠋⠁⠀⠀⠈⠳⡄⠀⢸⣤⣤⣤⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠘⠚⠁⢀⡇⠀⠰⣿⠆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠲⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⡀⠈⠳⠤⠤⠴⠋⠳⣄⣀⠀⢀⣠⠼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠀⠀⠀⠀⣿⠲⣄⡀⢀⣀⣀⡀⠀⠉⠉⢉⣀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼
⣠⠶⠶⣤⡄⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠙⠲⠤⠞⠉⠉⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠋⠁
⢿⣤⡴⠟⠁⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⢠⡦⣤⣄⡀
⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠛⠉⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠈⠳⣤⣈⡿
⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠈⠉
⠀⠸⣦⣀⣀⣠⡤⠶⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣤⣤⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠖⠋⠉⠁⠀⠀⠈⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢹⠀⠀⠀⠀⠀⠀⢀⣀⡾⠛⠁⠀⣀⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⢸⡇⠀⠀⠀⣠⠊⠁⠀⢑⠤⠤⣄⠙⠂⠀⡰⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⡇⢀⠀⢠⡇⠀⠾⢷⠁⣤⠀⢸⠀⠀⡼⠁⠀⠀⠀⠀⠀⣀⡤⢤
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣇⡎⠻⡁⠓⠤⠤⢾⠈⠋⢀⠞⠀⣼⠁⠀⠀⢀⣠⠔⠋⠁⢀⡞
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿⠃⠀⠈⠓⠦⣄⣀⠑⠒⣉⠀⢠⡇⠀⣠⠴⠋⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⢸⡷⠊⠁⠀⠀⠀⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⢸⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⣏
⠀⠀⠀⠀⠀⠀⣧⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽
⠀⠀⠀⠀⠀⠀⢹⡐⢌⠢⡀⠠⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠪⣻
⠀⠀⠀⠀⢀⣶⣚⠃⠀⠉⠂⢅⡂⠠⠄⠀⠀⠀⠀⡀⠤⠔⣒⠩⠐⠁⢀⡏
⠀⠀⠀⢀⡞⠁⠈⠑⢆⠈⠀⠀⠀⠉⠅⡀⢒⠒⠒⠀⠉⠁⠀⠀⠀⠀⠀⠑⣄
⠀⠀⠀⢸⠀⠀⠀⠀⢈⣧⠀⢙⣦⣐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠁⡰⢯
⠀⠀⠀⠈⢧⠀⠀⠀⡞⠢⠔⠉⠀⠀⠉⠉⠛⠛⠛⠛⠉⠑⢄⣀⣠⠵⠊⠁⠀⢳⡀
⠀⠀⠀⠀⠈⠳⢤⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⡀⠀⠀⢹⡀⠀⠀⠀⢀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠛⠉⠁⠀⠉⠘⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⣸⠃⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⢰⠇⠀⠀⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠀⠀⠀⢀⡟⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⣰⠃⠀⡴⠷⠀⠀⠠⣶⠄⠙⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⣀⣠⣤⠏⢀⢄⠀⠀⢄⠀⠀⠀⠠⡀⠈⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣥⡤⠶⠖⠛⠋⠉⠁⠀⠀⡆⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢿⣉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⡸⡀⠀⠐⢂⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠤⠞⠁⠈⠒⠒⠁⠀⣠⠂⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⢱⣦⣀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠸⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⠀⠀⠀⢰⡋
⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⣦⠀⠀⠀⠙⢿⣿⣿⡟⠙⢋⢉⠿⠿⠛⠁⠀⠀⠀⠘⣧
⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⢦⣄⣀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣀⡴⠚⠁⠀⠀⠀⠉⠛⠲⢦⣄⣀⠀⠀⠀⢷
⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⣦⣼⡇
⠀⡟⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡴⠚⠁⠀⠀⠀⢀⣀⣠⣤⠴⠶⠶⠒⠛⠛⠛⠛⠉⠉⠉⠉⠁
⢸⠇⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⢀⣀⣤⠶⠖⠛⠉⠉
⣸⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⢁⣠⡴⠚⠉⠁
⣿⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⢀⡴⢋⣤⠖⠋⠁
⡇⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⢀⠔⣡⠖⠋
⡇⠀⠀⠀⡎⠀⠀⠀⠀⢀⡔⣡⠞⠁
⣇⠀⠀⢸⠀⠀⠀⠀⣠⢫⠞⠁
⢿⠀⠀⡇⠀⠀⠀⡴⣵⠋
⢸⡀⢠⠃⠀⠀⣸⡿⠁
⠈⡇⢸⠀⠀⢰⡿⠁
⠀⢹⣸⠀⢀⡿⠁
⠀⠈⣿⡀⣸⠃
⠀⠀⠸⣇⡟
⠀⠀⠀⠹⠃
⣿⣿⣿⠿⡿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣧⣤⣤⣤⣄⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣚⣘⡼⡼⡽⠁⠀⠀⠀⠀⠀⠀⠀⠱⡽⠜⢬⣘⣒⣃⡃⢧⢯⠎⠀⠀⠀⠀⠀⠀⠀⠈⢮⠧⡃⣃⣓⣚⣘⠜⡼⡵⠁⠀⠀⠀⠀⠀⠀⠀⠹⡽⡜⢜⣘
⣖⡭⡼⢴⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠻⢬⣕⣶⣪⣥⠇⣾⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⢧⢭⣲⣖⡯⡼⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠴⠬⣑
⠒⠻⢽⣋⣴⠀⠀⠀⠀⠀⠀⠀⠀⠸⣏⣳⠭⠓⠒⠒⠭⣞⣩⠄⠀⠀⠀⠀⠀⠀⠀⠀⢬⣙⡮⠟⠒⠒⠻⢵⣋⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣌⣳⠽⠓
⠀⠀⠀⠀⠀⠀⠀⠀⡴⡳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡳⡄
⠀⠀⠀⠀⠀⠀⣀⢞⣞⣝⢞⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡰⡳⣫⡳⡳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢞⢞⣝⣜⢆⡀
⠀⠀⣤⢖⣲⡮⣵⣪⢎⣌⢮⣲⡭⢶⣒⢦⡄⠀⠀⠀⢠⡴⣒⣖⢭⣞⡵⣡⡱⣝⣮⢥⣖⡲⣤⠀⠀⠀⠀⣤⢖⣲⡼⢵⣫⢎⣌⢮⣳⡭⢶⣒⢤⡄
⠀⠀⠙⢜⢧⢫⡹⡖⡭⠮⡕⡺⣩⣣⢟⠜⠁⠀⠀⠀⠈⠣⡻⡜⣍⢷⢪⠵⢭⢲⢏⡝⡼⡣⠋⠀⠀⠀⠀⠙⢜⢧⢫⡹⡒⡭⠮⡕⡾⣩⢣⢟⠜⠁
⠀⠀⠀⠀⢳⢱⢱⢙⣙⣘⣑⡱⢱⢱⠃⠀⠀⠀⠀⠀⠀⠀⠘⣎⡎⣎⣏⣓⣓⣋⡎⡎⡞⠀⠀⠀⠀⠀⠀⠀⠀⢳⢱⠱⣙⣘⣚⣸⠱⢱⢱⠃
⠀⠀⠀⠀⢸⣼⠻⢬⣓⣓⣫⠴⢻⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡇⠦⣝⣚⣚⡥⠆⡟⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠳⢬⣚⣒⣫⠼⢻⢼
⠀⠀⠀⠀⢸⣘⡻⠕⠒⠒⠒⠭⣛⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣛⠯⠒⠒⠒⠪⢟⣃⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣘⡻⠕⠒⠒⠚⠿⣛⣹
⠳⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡰⡛⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⠞⠳⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡰
⡱⡽⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⡝⣍⢯⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢯⢋⡙⡽⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡕
⣜⢎⣺⠽⣶⡒⢦⡀⠀⠀⠀⣠⠖⣲⡞⠽⣊⢜⣤⡳⣑⡮⢳⣖⠲⣄⠀⠀⠀⢀⡴⢒⣶⢯⢔⡣⣣⣜⢜⡪⠽⣶⡒⢦⡀⠀⠀⠀⣠⠖⣲⡾⢵⣊⢞
⢮⡓⡶⡹⡢⣫⠎⠀⠀⠀⠀⠈⢮⡣⡺⡱⡖⣫⠶⣝⢲⢎⢗⢜⡕⠁⠀⠀⠀⠀⠱⣝⢔⢏⢶⣚⡵⢮⡓⡶⡹⡢⣫⠎⠀⠀⠀⠀⠈⢮⡣⡺⡱⡖⣫
⣚⣘⢼⠼⡼⠁⠀⠀⠀⠀⠀⠀⠀⠹⣼⡜⢸⣘⣒⣃⡃⣧⢣⠏⠀⠀⠀⠀⠀⠀⠀⠈⢧⢧⡃⣃⢓⣚⣸⠘⣼⡽⠁⠀⠀⠀⠀⠀⠀⠀⠹⡽⢜⢜⣚
⣒⡫⠼⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠻⢬⣗⣒⣺⠥⠇⣼⠄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠧⢽⣒⣒⡯⠼⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠼⢬⣗
⠒⠪⠽⣋⡤⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⣳⠭⠒⠒⠒⠭⣞⣩⠄⠀⠀⠀⠀⠀⠀⠀⠀⢬⣙⡮⠕⠒⠒⠪⢵⣋⡿⠀⠀⠀⠀⠀⠀⠀⠀⠰⣌⣳⠭⠒
⠀⠀⠀⠀⠀⠀⠀⢀⡜⡓⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢛⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡛⡄
⠀⠀⠀⠀⠀⠀⣠⢞⢞⣝⢎⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⡳⣫⡳⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢎⢞⣝⢞⢦⡀
⠀⠀⣴⢒⡚⠮⢵⣫⢎⢮⢮⣳⠭⠿⣒⢲⡄⠀⠀⠀⢠⠖⣒⠿⠭⣞⡵⡥⡵⣝⡮⠽⢓⡒⢦⠀⠀⠀⠀⡴⢒⡺⠯⢵⣫⢮⢌⢮⣳⠭⠿⣒⠲⡄
⠀⠀⠙⢞⢧⣫⡱⡒⡥⠦⡕⡲⣩⣣⢟⠞⠁⠀⠀⠀⠈⠳⡻⣜⣍⢖⢪⠴⢬⢒⢎⣝⡼⡳⠋⠀⠀⠀⠀⠙⢜⢧⣫⡱⡒⡥⠦⡕⡲⡩⣣⢞⠞⠁
⠀⠀⠀⠀⢳⢱⠹⢙⣘⣚⣐⠹⠱⢱⠃⠀⠀⠀⠀⠀⠀⠀⠘⣎⡎⣎⣃⣓⣓⣏⡏⡎⡞⠀⠀⠀⠀⠀⠀⠀⠀⢳⢱⠹⣑⣘⣚⣘⢱⢱⢱⠃
⠀⠀⠀⠀⢸⣼⠻⢬⣓⢕⣺⠴⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡇⠦⢕⡲⣒⠥⠆⡗⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠲⢬⣓⢗⣫⠼⢻⣼
⠀⠀⠀⠀⢸⣘⡿⠗⠚⠛⠒⠯⣟⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣻⠿⠒⠛⠓⠻⢟⣃⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣜⡯⠟⠚⠛⠒⠯⣛⣸
⡳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⡳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴
⡹⡝⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡝⣭⢫⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢫⣫⡝⡝⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⡽
⣜⢮⡲⠭⢵⣒⢦⡄⠀⠀⠀⣤⠖⣲⠭⢵⣪⢞⢤⡳⣕⠮⠭⣖⠲⣄⠀⠀⠀⢀⡴⢒⡮⠭⢖⡵⣣⢜⢮⡲⠭⢵⡒⢦⡄⠀⠀⠀⣠⢖⣲⠭⢵⣪⢞
⢮⡕⡦⡹⣣⣫⠊⠀⠀⠀⠀⠈⢪⡣⡻⡱⣖⣩⠶⣝⢲⢎⢗⢜⡕⠁⠀⠀⠀⠀⠑⣝⢜⢏⢶⣚⡵⢮⣕⡶⡹⣢⣫⠊⠀⠀⠀⠀⠈⢪⣣⡻⡱⡖⣭
⣿⠿⠿⡿⠿⢛⠿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣛⣛⣛⣿⣿⣛⣿⣿⣻⣿⣿⣿⣿

⠀⠀⠀⠀⢀⡞⡭⠷⡀⠀⠀⠀⠀⠀⠀⡠⠤⡀
⠀⠀⠀⠀⠘⢭⡗⢡⠃⠀⠀⠀⠀⠀⡰⠱⠆⠈⠉⠉⠢⠤⠤⣀⣀
⠀⠀⠀⠀⠀⠀⠈⠎⡄⠀⠀⠀⠀⠎⢂⠔⠚⠓⠫⡤⠀⢀⠀⠈⠀⠉⠓⠒⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠘⡼⡀⠀⢀⠜⢀⡃⠀⢠⣶⣆⡜⠊⢉⠙⠣⡤⠀⢰⣶⠄⢀⠭⢽⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣣⠀⢸⠀⢪⠉⠳⡈⠛⢻⠀⠸⣿⡷⠀⢱⠀⠀⢀⠴⢡⣶⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠓⡇⠀⠶⡓⠤⣈⠒⠙⢄⠀⡠⠤⣠⠃⠀⡠⠃⢀⠀⠁⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣠⠃⠀⠀⢼⣑⣦⠤⢤⠤⠭⢷⠆⢈⠆⡸⡀⠀⠈⡠⠊⠀⠀⠀⠀⢀⡤⣴⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠠⡆⠀⣜⢉⡬⢿⠯⢤⡴⠁⡀⠀⡞⠀⠛⣠⣊⠀⠀⢀⣀⠠⠤⣊⢸⡼⢽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⡑⠬⠝⣒⢒⡒⠁⠀⠘⠋⡰⢁⡔⠊⠁⣶⡯⠭⠒⠂⠉⠁⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣤⣈⣫⢶⣤⣅⣀⡀⠀⠂⠀⡇⠓⢉⡲⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣍⣋⡙⢿⠉⣾⣯⣭⣍⣑⢺⣓⣊⣭⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠯⡍⢉⠟⠓⠳⠬⢬⣛⣛⢹⣝⣋⣡⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢖⡕⠛⠓⠁⠀⠀⠀⠀⠀⠀⠈⠻⣍⡥⢟⡢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣭⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⡶⠖⠶⠶⢶⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⡋⠉⠀⢻⣿⡇⠀⠀⠀⣼⣿⣿⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢿⣿⡿⠶⠷⠿⣿⣇⠀⣠⣾⣿⠿⠋⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠚⢄⡐⠺⢂⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣾⠃⠀⠀⠀⠀⠀⠹⣿⠿⠛⠁⠀⣀⣴⣾⣿⣧⠀⠀⠀⠀⠀⠀⣤⢱⡌⠑⣶⠏⠰⡇⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠀⠀⠀⠀⢀⣰⣿⣶⣶⡿⣿⣿⣿⡿⢿⣟⣀⡀⠀⠀⠀⠀⠀⠈⡠⠛⣀⠛⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⢿⣿⣦⡀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣶⣤⣴⣶⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⠁⠈⠼⠅⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡜⡾⢛⣿⠇⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠻⠃⠀⠀⠀⠈⢩⡿⠋⠉⠉⠉⠉⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀
⠀⠀⠀⢶⣾⠛⠛⠛⠛⠛⠛⠛⠛⠛⢿⣿⡟⠋⠉⠀⠉⢉⠀⠀⠀⠀⠈⢙⠃⠀⠈⠙⣿⣿⠟⠛⠛⠛⠛⠛⠛⢛⣻⡿⠆
⠀⠀⠀⠀⠉⠻⢶⣄⡀⠀⠀⠀⠀⠀⠸⣿⣷⠀⠀⡴⢻⣭⡙⡆⠀⢰⠞⣭⡟⢦⠀⠀⣿⣿⠀⠀⠀⠀⢀⣠⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⣀⠀⠀⠀⣿⣿⠀⠤⠒⡛⠛⠛⠃⠀⠈⠛⠛⠛⠒⠦⠄⣿⣿⡀⠀⣠⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⣄⣻⣿⡆⠀⠀⠑⢦⣀⠀⠀⠀⠀⢀⣤⠓⠀⠀⣿⣿⡷⠟⠁
⠀⠀⠀⠰⣀⠨⢄⠘⠀⠀⠀⠀⠀⠀⠉⣿⣿⣷⣶⣤⣤⣤⣉⣛⣛⣛⣛⣋⣀⣠⣤⣤⣿⠋⠀⠀⠀⠀⢀
⠀⠀⠠⠰⢌⡶⣎⠰⠘⠁⠀⠀⠀⠀⠀⣿⣯⡛⠛⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟⣛⣛⣿⡆⠀⠀⠀⠀⠰⠆
⠀⠀⠀⢠⠈⢰⡌⠠⠀⠀⠀⠀⠀⠀⢰⣿⣍⡛⠻⢶⣤⣤⣤⣤⣤⣤⣤⡶⠾⠛⢋⣩⣿⣧⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣶⣤⣄⣼⠟⠛⠛⠻⣷⣄⣠⣴⣿⡿⠟⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⠀⠀⠀⣿⣄⡀⠙⠛⣿⠟⠁⠀⠀⠀⠀⠈⢿⣿⡿⠋⢀⣴⣿⡇⠀⠀⣴⣿⣦⡀
⠀⠀⠀⠀⠀⠀⣴⡿⠻⢿⣿⡀⠀⢰⡟⠿⢿⣷⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣶⣿⠿⠛⣿⡀⠀⣿⠟⠛⣿⡆
⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠸⣷⣠⣿⣤⣀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣯⣠⣤⣾⣇⣼⠃⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣦⣌⡉⠀⠈⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⡟⠀⠉⣉⣤⠶⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⣿⣿⣶⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⣶⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠙⠋⠉⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠉⠓⠒⠒⠋⠉⠉⠓⠦⠤⠖⠋⠉⠉⠲⠤⠤⠶⠶⢄
⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠃⠀⢠⡆⠀⠀⠀⢰⠄⠀⠘⠃⠀⢠⠆⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⣀⠤⠾⠤⣀⣀⠑⠳⠶⣷⠒⣴⠁⠙⡖⢒⣓⣒⡓⢋⡹⠷⠶⠦⣄⡀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⡎⠀⠀⣠⠤⠀⠀⣱⠀⠀⠀⠀⣯⠀⢸⠀⠀⠀⠀⠠⡏⠀⠀⢴⠤⠀⠈⡆⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠑⠤⠀⠀⠢⣀⠐⠁⠀⠀⠀⠀⠸⠀⠂⠀⠀⠀⠀⠀⠙⠂⣠⠎⠀⠠⠚⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⡀⠀⠀⠀⠀⠀⠀⠁⠒⠤⣀⣀⣀⡀⠀⠀⢀⣀⣀⣀⠤⠖⠋⠀⠀⠀⠀⠀⢠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠁⠩⠉⠀⠈⡇⡀⠀⠀⠀⠀⠀⠂⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠓⠺⠛⠉⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡋⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠘⢧⣀⣀⣀⣤⣀⣀⣀⣤⠤⠤⣄⡀⠀⢀⣀⣀⠀⠀⠀⠀⣀⣀⠀⠀⢀⠇⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠶⡇⠀⠀⠀⠀⠉⠀⠉⠓⠦⣠⠿⣉⡽⢄⡬⠟⠛⠛⠉⠉⠉⠉⠛⡯⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣿⠒⣒⣒⣒⡒⢒⣒⣒⣒⡒⡾⠀⢹⣀⣶⣶⣶⠶⢶⣖⣒⣒⢲⡇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢹⠀⠉⠉⠉⠀⠈⠉⠉⠛⠁⠣⣀⠞⠉⠉⠉⠉⠀⠈⠉⠉⠉⢸⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠒⢒⠒⠶⢤⠤⠤⢤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⡤⠟⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠸⣸⠀⠀⠈⠉⢻⠛⡏⠁⠀⠀⠀⠀⠈⡛⢹⠋⠉⠀⠀⣆⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡘⠢⡣⡅⠀⠀⠀⠀⣆⣰⠀⠀⠀⠀⠀⢰⣀⡆⠀⠀⠀⢸⠕⠞⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠋⠀⠀⠀⠀⠀⡏⠈⡆⠀⠀⠀⠀⡆⠀⡇⠀⠀⠀⠘⠚⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣠⣇⡀⡇⠀⠀⠀⠀⣧⣀⣧⣠⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⢿⣿⡿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⠙⠉⠁⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⣠⣤⣀⣀⣀⣤⠴⠶⢦⣄⣀⣀⣤⡤⠶⠦⣤⣀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⣀⣠⣀⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠉⠁⠀⠈⠙⠲⠶⠚⠉⠀⠈⠙⠲⠖⠚⠛⠳⡄
⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇
⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⢉⣭⠑⡄⠀⠂⠀⡔⢋⡉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⣀⢤⣤⡀⠀⠀⠀⠀⠣⣈⣛⡠⠃⡠⠤⡀⢇⠘⠛⣠⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢈⡧⠀⠞⠀⢀⡄⠹⠀⠀⠀⠀⠀⠀⠀⠀⢀⡅⠀⢨⠀⠉⠉⠀⠀⠀⠀⠀⠊⠈⠉⠱⡄⢸⡁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠈⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⢀⠌⠁⠰⠃⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⡀⠀⠀⠀⠀⠀⠑⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠁⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⠤⠤⡤⢤⠤⠤⢰⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⠠⠃⠐⠦⠤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠘⢲⠤⠤⠶⠲⠦⠤⠴⢶⣚⠛⠲⢤⣄⣠⡴⠶⢤⣄⣀⣀⣠⠤⠤⣄⣀⣠⠏⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⢻⡆⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠊⡳⢴⡟⠶⠒⠉⠀⠀⠀⠀⠀⠀⠀⣼⢺⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡎⡏⢉⣭⣭⣭⠉⠉⣭⣭⣭⣭⢹⠃⠀⢯⣹⣿⣿⣿⠛⣻⣿⣭⣭⠙⡇⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣧⠀⠉⠉⠉⠀⠀⠉⠉⠉⠁⠙⢦⡴⠋⠀⠀⠈⠀⠀⠈⠉⠉⠉⢸⢁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠉⢙⣟⠓⠲⢶⠶⠤⠤⠤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠞⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢻⣿⠀⠀⠈⠉⢻⡏⢿⠉⠀⠀⠀⠀⠀⢹⠋⣹⠛⠉⠀⠀⣇⠂⡀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡙⢾⢻⡗⠀⠀⠀⠀⣇⢘⡆⠀⠀⠀⠀⠀⣯⣠⡇⠀⠀⠀⢼⡑⡶⠁⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠛⠁⠀⠀⠀⠀⡏⠁⢷⠀⠀⠀⠀⢠⡇⢸⡇⠀⠀⠀⠘⠾⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⣇⠀⢸⠀⠀⠀⠀⢠⡇⣸⣧⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠻⠿⠛⠀⠀⠀⠀⠀⠉⠛⠉⠙⠛⠛⠋⠁

⡀⠀⠀⠻⣷⣘⣛⣛⠟⠃⠀⠀⠀⠈⠹⠛⠇⠀⠀⠀⠀⠀⡀⢸⣿⣟⣃⣀⠀⠀⠙⣿⣿⢟⡀⠀⠀⠐⠙⣿⡄⠀⠀⢀⡀
⣽⣶⡄⠀⠀⠉⠙⠁⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢀⣠⣤⣽⣿⣿⣷⠈⢹⣷⠀⠀⡈⠈⢙⣻⣿⡿⠃⠀⢟⣽⡾⠿⢉⣻
⡃⠀⠀⠀⢀⣾⣷⠀⠀⠀⠀⠀⠀⢘⣛⠋⠁⢀⣴⠟⠋⠉⠉⠉⠉⣀⣠⣾⣿⠂⢈⡀⠀⠈⠉⠁⣀⡀⢀⣾⠛⠁⠀⢬⣿
⢿⣦⣤⣴⡗⣦⡐⠶⣤⣀⣀⣠⣴⠿⠁⠀⠀⠈⠉⠀⠰⠿⠿⣿⣛⡛⣿⡿⠋⢀⣼⣿⣦⠀⠀⠀⢻⣇⠀⢿⣟⢀⠀⠊⠹
⠀⡨⣿⣿⣧⡻⠿⢂⣤⡬⠉⠀⠀⣀⣠⣤⣴⠶⢾⣛⣻⣿⣿⡿⠋⠀⠀⠀⠰⣿⣿⠛⠛⠀⠀⠀⣾⣿⣦⡀⠙⠻⠶⠿⠄
⢸⢿⠆⣴⣶⣶⡾⠛⣁⣤⣶⣾⣿⣿⣿⣷⣾⡿⠿⠿⣿⣿⣿⣿⣟⣂⡀⠀⠀⠈⠹⣷⣶⠶⠆⠀⠈⠀⠿⣿⣷⣶⣶
⠀⠀⠀⢸⣿⣿⢁⣾⣻⣷⡿⠟⠛⠉⠉⠀⠀⠀⠀⠀⢰⣶⣿⣿⣿⣿⣿⣿⡷⠖⠀⢤⣽⣷⠄⠀⠀⠀⠘⠋⢁⣤⣶⠆
⣄⢠⣬⣿⠋⠁⠈⠁⠉⠁⢀⣤⣤⣤⣤⣶⣶⣶⣶⠾⢿⣿⠿⠋⠉⠉⣿⡿⠖⠀⠐⠾⣿⣷⣾⣇⣴⡆⠀⠀⣾⣿⣧⣶⣦
⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣾⣟⡉⠀⣤⣶⡶⠿⠛⠛⠉⠙⠃⠀⠀⠘⠟⠻⡿⣾
⣨⡿⠀⠀⠀⠀⣄⣀⢀⣀⣈⠉⠉⠉⠛⠛⠛⠛⠛⣿⣿⣿⣿⣿⣿⡅⠠⣶⣾⣿⣷⣦⣄
⠉⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣄⣈⣿⣿⣿⣿⡯⠁⠀⢀⣽⣿⣿⢉⢻⣿⡇⠀⠀⠀⠀⠀⠀⣀⠁⢈⣿⡷
⠀⠀⠀⠀⠀⠀⣶⡄⠉⠙⠛⠻⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⡷⠶⠄⠈⢻⣵⡿⠛⠛⠃⡀⠀⢠⣦⣴⣶⣿⡿⣿⣿⡖
⣆⣤⡀⣤⣤⠾⠃⠻⣿⠟⠁⠐⣻⣷⣶⣠⣤⣿⠿⠉⠉⢉⣛⠛⠛⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠟⠋⡙⠛⢉⣁⣰⣬⣻
⠛⢻⣷⠈⠉⣿⣠⣬⣿⡀⠰⠞⠛⠋⠙⠟⠉⢻⣷⣶⡾⢿⠿⢷⣾⣿⣄⣀⠀⠀⠁⠀⠶⣤⣤⣤⣦⠀⢿⣷⣾⡿⠛⠉⠉
⠀⠈⠉⠀⠀⠟⠉⠀⠈⠉⢀⣠⣴⣶⣶⣶⣶⡿⢟⣤⣶⣶⠷⢶⣦⡙⢻⣿⡆⠀⣴⣶⣄⡈⠉⠀⠀⢤⣾⡿⠏
⠀⠀⠀⠀⠀⠀⢀⡀⠤⠶⠋⠉⠀⠈⠉⠙⠿⢣⡿⠋⣠⣶⣦⡈⠙⢿⡌⣿⣤⡇⢿⣿⠛⢿⣶⢾⣷⣄⠻⠿⠆
⠀⢠⣍⠻⣿⣮⠹⣿⡄⢤⣿⣶⠀⠀⣀⣤⡶⣾⡗⢨⣿⣿⣿⣿⠀⢻⡷⢸⣿⣗⣼⠟⣹⣶⡖⠸⣿⠿⠟
⣶⣾⡟⣃⣿⣿⠀⣿⣷⡀⠋⠉⠀⢰⣿⡏⠀⠘⣧⣤⡙⠛⢛⣀⣰⣾⢃⣿⣿⣿⣥⣈⡙⡿⣛⣀⣄⠀⠀⠀⠀⠀⠀⢶⡒
⣈⣬⣉⣉⣿⣿⡦⠈⠛⣻⣷⣶⣶⡎⣿⣇⠀⠀⠈⢛⠿⠶⠿⢟⣋⣵⣾⣿⠿⠀⠈⠉⠁⢰⣿⣿⣿⡇⠀⠀⠀⠀⠀⢾⣷
⠿⣿⠟⠹⠋⠁⠀⠀⠊⠉⠉⣉⣉⣥⣽⣿⣷⠀⠀⠈⢷⣾⠷⢿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠘⣿⡿⣿⡷⠄⠀⠀⠀⠀⠈⠛
⠀⢁⣠⣤⣤⡤⠤⠀⠀⠀⠈⠙⢻⣷⣄⠀⢈⠀⠄⠀⢀⣤⠾⠛⠉⢀⣠⡄⠀⠀⢀⡤⣶⣦⣄⡀⠋
⣴⡿⠿⠛⠓⠀⠀⠀⠻⣿⡛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀⢼⣿⣿⣀⡀⠈⠛⢿⣽⣿⢷⠀⠀⠀⠀⠀⡀⠀⠀⢀
⠇⠀⠀⣶⠤⣬⣿⣌⡛⠻⠿⠀⠀⠀⣶⣷⣆⠀⠀⠀⠀⠀⠈⠛⣷⣦⠈⠛⠻⢿⣷⡄⢀⠀⠉⠉⠀⠐⣶⣄⠀⠀⠀⠀⢿
⣿⣿⣿⣿⣛⣿⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣟⣛⣟⣻⣿⣛⣻

⠀⠀⠀⡔⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⠩⠭⠁⠉⠁⠉⠩⠍⢉⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠂
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⣈⠡⠄⠀⠀⠒⠀⠒⠀⠀⠀⠄⣀⠉⠐⠂⢄⡀
⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⡡⠂⡩⠤⠐⣂⡈⠉⠀⠀⢈⣉⠐⠂⠠⢄⡉⠒⠤⡀⠈⠒⢄
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠄⠀⠪⡔⡡⠔⣁⠄⢂⠩⠄⠀⠀⠀⠀⠀⠠⠌⡁⠒⠠⡈⠑⠤⡈⠑⢄⠀⠁⢄
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠄⠆⠀⠀⠀⠸⠠⣎⠤⢊⠥⠒⣂⠉⠠⠤⠈⢉⠐⠢⢄⡁⠢⢄⠑⢤⡈⠲⣄⠑⢄⠀⠑⢄
⠀⠀⠀⠇⠀⠀⠀⡠⠆⠀⠀⠀⠀⠀⠀⠀⠈⠒⠃⠶⡉⠤⠀⠀⠀⠀⠠⢈⠑⠢⡈⠲⣄⠑⢄⠀⢆⠀⠢⡀⠑⡄⠈⢢
⠀⠀⠀⠆⠀⠀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠢⡈⠳⡈⠣⡀⠱⡀⠑⠀⠈⢆⠈⢆⠀⠱⡀
⠀⠀⠀⡆⠀⠀⠈⠂⠀⠀⠂⠤⠠⠤⠂⠀⠀⣐⡁⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⢆⠈⢆⠈⢄⠘⠄⠈⢄⠀⢂⠈⢂⠀⠱⡀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠈⠁⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⠀⠀⠈⠂⠀⢂⠈⠆⠈⠄⠈⠆⠀⢆⠀⢂⠀⠡
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠀⡆⠀⠀⠀⠀⠀⠀⠀⠈⡀⠈⡀⠈⠀⠘⠀⠈⠀⠈⡀⠀⡄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⢀⠠⠄⠰⠁⠆⠰⠳⠃⡃⡀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢃⠀⢃⠀⢃⠀⢁⠀⢡⠀⢰⠀⠈⡀⠀⠀⠀⠀⢀
⠀⠀⠀⣅⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐⡬⠄⡠⠄⠐⠓⣷⣉⢩⣉⣉⠉⠢⢄⠀⠀⠀⠀⠀⠘⠀⠸⠀⠘⠀⠈⡀⠈⡀⠈⡄⠀⡄⠀⢁⠀⠀⡐⠈⠉
⠀⠀⠀⡄⠀⠈⠄⡀⠀⠀⠀⠀⢀⡠⠇⠒⢈⢒⠊⠉⠑⠀⠐⢀⣀⠙⠆⢈⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⡇⠀⠇⠀⠃⠀⢁⠀⢀⠀⠸⠖⠐⠁
⠀⠀⠀⡅⠀⠀⠀⠸⠤⢀⠀⠀⠎⡠⠛⡴⠂⠈⠑⠂⠤⡔⠈⢰⣴⡿⣓⠁⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠃⠀⠀⠀⢠⠀⠘⠀⠈⠀⠈
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠁⢢⠶⡀⠀⠁⠀⠀⠀⠸⣿⡿⠀⠈⠛⠁⠀⠈⣦⠀⠀⠀⢀⢠⡃⠀⡇⠀⠀⠀⢰
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡆⠀⡱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠆⠀⠁⡄⠀⡜⠀⢀⠀⠀⢃⣤⣂⣤⣼⠀⢴⡀⢀⡀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠊⢈⠈⠂⡤⠓⢄⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⢀⡠⠀⠔⠀⢀⡸⣤⠾⢿⣽⡿⢭⣭⠿⣫⡭⢿⣴⠿⣗⢲⣦⡀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⡐⢆⣀⡔⠁⠀⠀⠁⠒⠒⠒⠒⠒⠂⠀⢤⡈⠁⣠⠘⠀⠀⢈⠀⠉⠒⠚⠋⠶⠞⠳⠶⠼⠷⠦⠛⠈⠛⠋⠁⠰
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠐⠐⠂⠀⠐⠁
⠀⠀⠀⠇⠀⠀⠀⠀⠀⠐⠡⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⡠⢒⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⢐⠄
⠀⠀⠀⣦⣠⣤⣴⠠⡤⠔⡤⠤⡆⠀⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠂⠀⡧⠤⠦⡤⣆⢡⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡬⣠⢤
⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠇⠀⠀⢸⠀⠀⠀⠀⠀⠀⢰⠀⡃⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖
⠀⠀⠀⡁⠀⡐⠒⠒⡖⠐⠀⠉⠉⠀⠀⠀⠀⠀⡀⠀⢠⠀⠀⠀⠈⡰⠉⠁⠀⠐⠒⠘⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⡁⠀⡁⠀⠀⡇⠀⠀⠀⠀⢹⠀⠄⠀⠠⠇⠀⡄⠀⠄⠄⠸⠃⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐
⠀⠀⠀⡃⠀⠐⠄⢀⢰⡀⠀⠀⠤⢬⠀⠀⠀⠀⠸⠴⠀⠀⠀⠀⠀⠤⠄⠀⠀⢠⠁⠀⠴⠓⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠊
⠀⠀⠀⠢⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣂⣀⣀⡀⣈⣀⣂⣀⡀⣀⣊⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣀⣒⣂⣀⣀⣀⣀⣒⣀⣉⣀⣀⣀⣀⣀⣀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠔⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⠎⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠌⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡷⠚⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⠴⠞⠋⠁⡠⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀
⠀⠀⠀⣀⣠⣤⡴⠶⠶⠖⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⢀⡴⠒⠛⠓⠶⣄⠀⠀⢀⣈⡉⠓⠎⠉⠉⠛⠛⠛⠓⠲⠶⠶⠦⣤⣤⣀⣀
⢀⡴⢛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣏⣀⣠⣤⣤⣤⣼⣧⣞⣉⡉⠉⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣄
⣾⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡏⢳⣼⣿⠇⠀⣸⡏⢹⣍⣿⡟⠳⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳
⣿⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠶⢦⠈⢳⣄⣀⣀⣤⡶⠋⠳⣄⣉⣉⣠⡞⠁
⠘⢧⣀⠀⠑⠦⣄⡀⠀⠀⠁⠀⠀⠀⠀⠉⠀⣯⠀⠀⠀⠀⠉⠙⠋⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠
⠀⠀⠙⠳⢦⣄⣀⠉⠑⠲⠤⣄⡀⠀⠀⠀⠀⠈⠳⢦⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⣉⣵⠟
⠀⠀⠀⠀⠀⠈⠙⠛⠶⣦⣤⣀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⣻⡿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠉⣀⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣜⣆⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⣠⣴⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⢀⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⠇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣇⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢡⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢁⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣞⠋⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢎⢻⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠙⠳⣤⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⢻⡄
⠀⠀⠀⠀⠀⠀⢀⡿⠁⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠈⢷⣄⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢿⡀
⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠸⣇⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡈⢦⡀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢧⣄⠘⢦⣀⡀⠀⢀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣝⣦⣀⠀⢀⣠⡾⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠉⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⢠⡀⢀⠏⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡆⠐⠘⠷⣞⠀⠀⠀⠀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠔⠉⠀⠀⢨⠄⠄⣙⠳⣤⣡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⢸⡀⠀⡠⠊⠉⠉⠺⣉⣶⠀⠁⠀⠀⠀⠀⠙⠷⠦⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠄⢠⠊⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢳⣾⠁⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠉⠄⢤⠀⠀⠀⠀⠀⠀⠘⠄⢰⠀⠈⠑⠧⠐⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠻⣆⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡇⠀⠀⠀⠀⢠⠟⢷⡀⠉⠙⠆⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠈⠹⠟⠋⠉⠉⠓⢦⡀⠀⢀⠤⡀⠉⠹⠀⠀⠀⢀⡴⠃⠀⠀⠙⢦⡤⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠷⣀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠉⠉⠁⢀⠇⠀⠠⠀⣀⠴⠋⠀⠀⠐⢄⠠⠦⣹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠈⠉⠛⠥⣀⣀⣠⠔⠃⡇⠀⠀⠀⢀⣠⠎⠀⡠⠷⠊⠁⠀⠀⠀⠀⠀⠀⢱⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠹⣀⠀⠨⠀⢀⡰⠓⠒⠒⠚⠙⡇⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠁⠀⠊⠉⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⢀⣀⣀⣀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⢀⠀⣀⣀⣀⣠⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠉⠉⠹⣄
⠀⠀⠀⣀⣀⣸⡀⠂⣹⠀⠀⠀⠹⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⢔⠃⠀⠀⡄⠀⡽⠀⢹⡄⠀⢁⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠪⢉⣉⠀⠇⠀⠃⠀⢠⡇⠶⣸⣀⣬⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢀⡴⠋⠀⢧⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠐⠀⠀⠀⠐⠒⠊⠁⠛⠛⠉⠁⠀⣷⠀⣠⠆⠀⠀⣀⣠⠴⠛⣏⠁⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠞⠉⠉⢿⠉⠁⠀⠀⠀⠙⣦⣀⣀⣀⣤⠿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠘⢧⡁⠀⠀⠀⢹⡄⠀⠀⠀⠀⢀⣠⡴⠿⣍⣀⡀⠀⣀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⣀⣀⣀⣀⣀⣈⣳⡀⠀⠀⠀⠻⣤⡴⠶⠛⠉⠁⠀⠀⠀⠀⠀⠀⢈⣆⠐⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠙⢯⡉⠉⠁⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠋⢹⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠉⡏⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠘⣴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⣀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡹⠋⢉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⢁⡴⠋⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣾⣶⣮⣥⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠠⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡇⠀⠀⠀⠀⠈⠉⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⡇⠀⠀⠀⠀⠀⠠⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡇⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠹⢂⣈⠭⢄⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠄⠔⠀⡠⢂⠔⠁⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⢀⠜⡰⠁⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢡⠀⠀⠀⠀⠀⢀⢀⠎⠀⠀⠀⢀⣠⣤⣤⣌⣀⣤⣤⡀⠀⠀⠀⠊⠀⠂⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢆⢀⣠⡤⠦⣤⣤⡴⠞⠛⠉⡛⠛⠉⠙⠉⣀⠦⠆⠈⠁⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⢴⡁⠈⠉⢁⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡄⠀⠀⠈⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⡏⠈⠐⠢⡀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⡰⠦⠀⠀⠀⠊⠢⠀⠀⠘⡄⠀⠀⠀⠀⢠⡞
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠂⠈⢄⠀⠈⠀⠀⢐⠒⠠⢄⠀⠀⠁⠀⢀⠀⠀⡠⠀⠀⢠⠃⠀⠀⠀⠀⢠⠀⠀⣰⠋
⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠁⠀⠑⠢⢀⠀⠀⠀⠀⣨⠄⠀⠀⠀⠀⠀⠁⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⣧⠜⠁
⠀⠀⠀⠀⠀⢿⣀⡀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠉⡉⠁⠀⠀⠤⠤⠤⠤⠆⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⢀⣀⣀⠀⠌⠉⠦⠀⣀⡀⣠⡄⠀⠈⠄⠀⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⢠⠋⠁⠀⠀⠀⢀⡤⠂⢈⠀⠀⠀⠀⢀⠈⠂⠀⠱⣦⣤⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⢸⠀⠀⠀⠄⡀⠈⢀⡐⠄⠀⠀⠀⠀⠈⠁⠀⠄⠀⠘⢿⣿⠇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸
⠀⠀⠆⠀⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠈⢦⡀⠀⠀⠀⠌⠀⠀⠀⠀⠠⠄⠀⠀⠀⠘⠆⠀⠠⠀⠀⠢⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠈⠳⣄⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠉⠒⢒⣁⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇
⠀⠀⠀⠀⠀⠀⡌⠑⠂⢠⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⡠⠂⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠛⢂⠉⠂⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠐⠂⠉⠁⠀⠀⠀⠉⠐⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠙⠢⢀⠀⠀⠀⠀⢀⡀⠠⠀⠐⠀⠈⢀⣀⠤⠔⠒⠈⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠒⠈⠁⢀⣀⡤⠤⠒⢂⠉⠁⢄⠀⠀⣀⡐
⠀⠀⠀⠀⠀⠀⢀⣴⣦⣤⣶⣶⠀⢀⠄⠀⠙⠲⠒⠒⠉⠁⠀⠀⣠⣾⡿⠇⠀⡠⠀⠉
⠀⠀⠀⠀⠀⠀⠘⠟⠋⠈⠉⠋⠀⠀⠡⢄⡀⠀⡠⠀⠀⠀⠀⢸⣿⠀⠘⣶⣦⠴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠄⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⢀⣀⣀⣀⡀⠀⢀⣀⡀⢀⣀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⡀⣀⣀⣀⣀⣀⣀
⠀⢀⠀⠀⠙⠃⢤⣀⠈⢢⠀⢳⢸⠀⣼⢆⠀⠀⠀⠀⠀⠀⢧⠀⠁⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⢒⡆⠀⠀⠀⠀⢄⣿
⠀⢸⠷⠖⣤⣄⣀⠈⠓⠄⣱⡄⠀⢀⡿⠈⠡⠀⠀⠀⠀⠀⢠⣤⣄⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣀⠰⠐⠊⠉⠀⠀⠀⠀⢎⠀⠀⠀⠀⠀⠀⣿
⠀⢀⠀⠀⠀⢀⡉⢻⢁⣐⡎⠃⠤⠋⠀⠀⢀⡵⡌⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⣀⣤⣴⣶⣿⣿⣍⠉⠁⠀⠀⠀⠐⠄⣿
⠀⠸⠛⠛⠋⡉⠉⣧⡄⠈⠁⠀⠀⠀⠀⠀⠭⢄⡙⡈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⡰⠁⠀⠀⠀⢘⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣿
⠀⢰⣤⣤⣴⡟⠛⣈⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠛⠛⡄⠀⠀⠀⠀⠀⠀⠲⠄⢀⠸⠀⠀⠾⠿⠿⠿⠿⠿⢸⠀⠀⠀⠀⠀⠀⢀⣀⡢⠲⣤⡀⢀⠔⣿
⠀⠸⠋⠉⢀⣠⣼⢋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣳⣤⢸⠰⠀⠀⠀⠀⠀⠀⠘⠉⠉⠀⠀⠀⠀⠀⠀⠀⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠢⣏⠀⡀⣿
⠀⠀⠀⣠⣾⠿⠒⢻⠇⣀⠀⠀⠀⠀⠀⠀⠀⣏⠉⠙⠻⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠝⠀⡢⣿
⠀⢸⣯⠟⠁⠀⣠⣾⡟⠋⢣⡾⠻⣤⣶⠶⢦⡘⢧⡀⠀⠁⢀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡢⠔⣿
⠀⢨⠉⠀⠀⠒⠳⠿⠀⢀⣿⣏⠀⠘⣿⣇⠀⠙⢶⣷⡀⠀⡀⠈⠁⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⢀⠐⠂⠀⠠⠈⢁⣒⠂⠀⠈⠉⠀⢙⡛⠂⠀⠨⠭⠟⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠑⡁⣿
⠀⠈⣀⠀⠃⠀⠰⠆⠀⢠⠀⠁⣠⠜⠃⠀⠸⠭⠀⠶⠀⢀⡤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠻⣶⣤⣀⣀⡀⠀⠀⢀⣀⡀⠀⠐⡞⠁⠀⠢⡢⣿
⠀⠀⠉⣠⡄⠁⣀⠐⠲⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠂⢄⠒⠉⠍⢁⠒⠂⠄⠄⡌⣀⣁⠘⠀⠉⠽⠛⣛⠋⠛⠛⠉⠙⠶⣄⣠⡠⡀⠐⢔⣿
⠀⠰⠆⠈⠠⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⢀⡠⠄⠀⠈⠈⠉⠑⢒⠶⠆⢠⣍⡈⣈⠒⠲⠠⠭⣉⣀⣀⡡⣿
⠀⢠⠀⠒⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡀⠀⠀⠖⠁⠒⠃⠀⠀⠀⢴⣌⣄⠐⠊⣁⡀⠤⠔⠛⠛⠓⠒⢀⡀⣭⣉⣉
⠀⠈⢀⡀⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠠⠀⠭⣓⠺⠍⠠⠤⠤⠄⠀⠀⠈⠉⠛⠛⡙⡌⠁⠙
⠀⠰⠀⠀⡄⠈⢁⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠀⠀⠀⡠⠈⠀⠀⠀⠈⡂⠂⠒⠒⠒⠀⠀⠀⠀⠀⠀⠰⠛⠟⠒⢿
⠀⠀⠐⠀⠀⠤⠀⠀⡅⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡜⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⢠⡐⠀⠤⢄⣁⠉⡀⠄⠀⠤⠤⠶⣤⠄⢤⣄⣴
⠀⢀⣀⠘⠂⡀⢶⠂⠀⠤⠉⢉⡈⠙⢠⡤⢄⡀⡀⠾⠂⠐⢚⣋⡙⣁⢈⢄⠀⡄⠀⠈⠁⠱⠄⠀⠠⠀⠈⠛⠖⠢⠣⠌⠉⠀⠀⠀⠀⠠⡀⢠⠀⠀⢙
⠀⠀⠀⣠⠈⠋⡀⠐⠂⡀⠴⠀⢀⣀⢨⢥⠴⠒⠒⠈⠹⠸⢰⢠⣡⢃⢮⡜⡱⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⢿
⠀⠀⠀⣀⠠⠀⣋⡈⠤⣔⠲⣍⡣⠜⠚⠧⠁⠁⠁⠀⠀⠀⠀⠘⡇⠀⠀⣻⡔⣣⠜⣢⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠾
⠀⢈⡁⠰⣶⠇⠘⢛⣾⠀⠀⡿⣷⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⢸⡶⢶⣤⠋⡊⠔⣊⠴⢚⣳⡘⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴
⠀⢘⠙⠛⢻⡄⠀⢨⣿⡀⠀⢩⢿⡀⠀⣷⠀⠀⢀⠴⠓⢂⡆⠀⠀⠀⠈⢠⣶⡯⢖⡈⠭⠞⠃
⠀⢘⡉⠙⠛⡇⠀⢸⢾⡇⠀⢸⢸⡇⠀⣿⠀⠀⠈⢳⣤⣬⡅⠀⠀⠀⠐⠿⠏⡥⠁⠐⠒⡋
⠀⢘⣉⣉⣉⡇⠀⢸⣹⡇⠀⣨⢼⣇⣀⣟⣧⠀⠀⠈⠁⠂⢀⢀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠠⠤
⠀⢘⣉⣁⢨⡇⠀⠼⢚⠓⠊⣩⡴⠒⠒⣬⠀⠀⠀⠀⠀⠀⣇⡀⡴⠀⠀⠀⠈⠡⣄⠀⠀⠀⢀⡙⠓⠖⠒⣆⠀⡀
⠀⢘⣉⣡⣤⠀⠒⢺⣯⡄⢠⡊⠕⠢⠖⠉⠀⢀⠄⠀⠀⠀⠉⠙⠀⠀⠀⠀⠠⢅⠂⢅⣀⠒⠤⣄⣈⠙⠛⠳⠆⠁
⠀⠈⠉⠁⠉⠁⠀⠉⠁⠈⠉⠁⠉⠁⠉⠉⠉⠛⠤⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠁⠈⠉⠁⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⡆⠀⠀⢰⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣷⠀⠀⢸⣿⣿⠁⢹⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⢸⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣀⡠⠒⠒⠒⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠸⣿⣿⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣀⠀⠀⡠⠔⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊⠉⠋⠉⢹⣿⣿⣿⣿⣿⡏⣿⣿⣿⣷⠀⣿⣿⠀⢻⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⠀⠀⢠⣿⡛⣷⠀⠹⣿⣿⣿⣿⣇⢿⣿⣿⣿⣇⢻⣿⠀⢹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⢠⠞⠀⡀⠀⠀⠀⠀⠀⢀⣾⣏⠙⠻⣿⣿⣷⣄⠀⠺⣿⣿⣗⡆⢹⣿⣿⣿⣿⠘⣿⡟⣿⣿⢸⣿⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡄⠈⠉⠛⣶⡀⢀⠀⠈⢯⣉⣰⣦⡈⠻⣿⣿⣦⣀⡘⢷⣾⣄⡀⠻⣿⣿⣿⡧⠻⠇⠻⠿⠘⠛⣛⣷⣶⢀⣾⠓⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠈⠀⠀⠀⠀⠈⣿⠿⠇⠀⡄⢉⠛⠿⣿⡿⠿⠛⠛⠉⠓⠠⠙⠻⣟⠦⢉⣉⡤⢤⣤⣶⡿⢷⣦⣾⡏⢹⣿⢸⣿⢸⡿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠘⠀⠀⠀⠀⢀⡠⡋⣁⣠⠤⢤⣤⣄⠐⢀⣀⡒⣻⢿⣿⣻⣦⣼⢿⡶⠶⢾⣩⣙⣩⠹⣿⣧⡀⣼⡟⢁⣸⡇⣸⡇⣾⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠈⠛⣿⣏⣉⠓⢶⠄⠀⠛⠛⠛⠍⠋⠙⡠⠌⠉⣰⣿⠷⠿⠾⣿⣿⠋⠉⣼⡿⠉⣰⠿⠿⢿⡿⢱⡿⣡⣾⠛⠉⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡘⠆⡀⠀⠀⠀⠛⣿⠛⠦⣀⣀⠠⣤⣀⣤⣐⡀⠀⢰⡄⢿⣿⡀⠀⠰⣿⠏⠀⢸⣿⠃⠸⠋⠀⢰⡟⢠⣿⣴⣿⣷⠾⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣀⠀⠈⠀⠒⢠⡼⠻⡏⠠⡀⠸⣿⣿⠿⠀⣾⣿⣿⣿⡇⠈⣿⡇⠀⠸⠿⠂⠀⠛⠛⠀⡀⠀⠀⡀⠁⢸⣦⠿⢤⠴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠰⠄⠈⠀⠀⠀⠀⠀⠂⠀⢀⡀⢀⠀⠿⠃⡀⠀⠁⠀⠁⡀⠀⠀⠀⠀⢤⢠⠀⠈⡇⠀⠈⠁⠀⠀⠀⠀⣈⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠴⣶⣶⠀⠀⠀⠀⠀⠀⠀⠸⠃⠈⣠⡀⢀⠿⡄⠀⠀⠀⢀⣀⠀⠀⠀⢸⠀⠀⠀⡟⠀⠘⡇⠀⠀⠀⢀⠃⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢁⠀⠀⠀⢿⣤⣤⣳⣴⣤⠂⢿⡿⠛⠉⠓⣤⣀⣀⡀⢁⣀⡀⣀⠘⠁⠀⠀⠃⠀⠀⠃⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢏⠁⠀⠀⠀⠀⠀⠉⡉⠉⢠⠋⢠⣌⠁⣤⠀⢀⡼⠉⠃⠈⠉⠀⠘⢫⡶⠚⠉⠉⠉⠉⠳⣀⠴⠋⠉⠑⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⢀⠀⠀⠀⠀⠐⣦⣀⣈⠘⣾⠿⡆⢹⡾⠁⠀⣘⠃⠀⠙⡀⢸⡇⢠⠘⡇⠀⣠⠤⣄⣀⡸⠁⠀⠀⠀⠀⠀⠀⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⠀⠈⠂⠀⡀⠀⠀⠉⠋⠁⠀⠀⠀⠘⢦⡁⠀⠀⠞⠀⠿⠀⠘⡸⢏⣿⢀⡇⠐⢱⢾⠋⣿⠇⠀⠀⣠⠞⢶⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠻⠄⠠⣤⡀⢀⠇⢀⣦⠀⠀⠛⢦⠊⠀⠀⣴⠃⢀⣵⣾⠃⣰⣧⣀⠉⠖⣫⣾⠂⠀⠀⠘⠶⠛⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⡄⠀⠀⠀⠀⠀⠀⠠⣿⠓⢋⣠⣠⠀⠀⠈⣿⠘⠦⠤⠚⠀⠈⠈⠀⠉⠙⠁⠀⠉⠙⠉⠀⠀⠳⢀⣀⣀⡀⠀⢀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣄⡀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⠀⠀⢀⡾⠃⠀⠀⠀⠴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢾⣥⣷⡀⠀⠀⠀⠀⠀⠀⢻⡟⠉⠉⠙⠁⠀⠀⠀⠀⠀⠀⠀⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⡀⠀⢀⣼⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢧⣿⣿⠿⠁⢀⣀⣀⣀⡀⠀⠀⠀⠀⠤⠴⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣠⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣄⣀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⢠⡞⠋⠉⠛⠛⠛⠋⠉⠈⠉⢿⣟⠛⠛⠋⢉⡿⠃⠀⠀⠉⠙⠛⠓⠒⠒⠚⠛⠛⠉⠁⠀⠀⢀⣠⣭⣭⣉⠉⠉⠉⠙⣧
⠀⠀⠀⢸⡄⠀⠀⣤⠶⠶⠶⣦⡀⠀⠀⠙⠛⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠉⢳⡄⠀⢀⡟
⠀⠀⠀⠘⣧⠀⠸⣇⠀⠀⠀⣨⡇⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⣿⠀⣾⠃
⠀⠀⠀⠀⣹⠀⠀⠈⠛⠛⠛⠉⠀⠰⣆⠀⠀⠀⣿⠀⠀⢠⡗⠀⠀⠀⠀⢰⡆⠀⠀⢸⡇⠀⠀⣰⠇⠈⠻⢶⣤⣤⠾⠃⠸⣇
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⡦⠶⠾⠛⠶⠶⣾⡁⠀⠀⠀⠀⠀⣻⡴⠶⠟⠳⠶⠶⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⣠⡶⠛⣿
⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⣰⠏⠀⠀⠀⢀⣴⠶⠶⢶⣄⠀⠈⢿⣼⠃⠀⠀⣠⡴⠶⠶⢦⡀⠀⠀⠈⢷⡀⠀⢰⡏⠀⢰⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⢠⡟⢠⣶⣷⣦⠘⣧⠀⢸⣿⠀⠀⢸⡏⣰⣶⣶⡄⢻⡄⠀⠀⢸⡇⠀⠘⣧⠀⣾
⠀⠀⠀⠀⠀⣾⣤⣀⠀⠀⠀⣿⠀⠀⠀⠈⣧⡘⢿⣿⠟⣠⡟⣠⣼⣿⣤⡀⠸⣇⠻⣿⡿⠃⣼⠃⠀⠀⣸⠇⠀⠀⠈⢻⡇
⠀⠀⠀⠀⢰⡏⠀⠉⢳⣄⠀⠘⣧⡀⠀⠀⠈⠛⠶⠶⠞⠋⣰⠏⠀⠀⠈⣿⠀⠙⠳⠶⠶⠟⠁⠀⠀⣠⠟⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠈⣧⠀⠀⠀⣿⠀⣀⣌⠳⣦⣀⡀⠀⠀⠀⣀⣠⣿⠀⠀⠀⢀⣿⣦⣀⠀⠀⠀⠀⣀⣠⡾⠋⢠⣄⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⢹⡆⢀⣴⠏⣼⠿⣤⡀⠀⠉⠙⠛⠛⠛⠉⠁⠀⠀⠀⠀⠾⠃⠀⠉⠛⠛⠛⠛⠉⠁⠀⢀⡼⠻⣇⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢻⡋⠁⠀⠀⠀⠈⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⣰⣏
⠀⠀⠀⠀⣴⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠙⠛⠳⣶⣶⠖⠚⠛⣿⠉⠁⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⢰⡏⠙⣦⡀
⠀⠀⠀⣸⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣀⣀⣿⣿⣀⣀⣀⣿⠀⠀⠀⠀⠀⣰⠟⠉⠈⠉⢳⡄⠸⣇⠀⠈⣷
⠀⠀⠀⣿⡀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣌⣉⢉⣉⣁⣌⣉⡉⢉⣁⡴⠟⠁⠀⠀⢿⡀⠀⠀⠀⢠⡇⠀⣿⠀⠀⢸⡇
⠀⠀⠀⠈⣿⢙⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠈⠛⠶⠶⠾⠋⠀⠀⣿⡟⢻⡏⠁
⠀⠀⠀⠀⡇⢸⡟⣧⡀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⢀⣠⣤⣤⣤⣄⣀⠀⠀⠀⣀⣀⠀⠀⢀⣀⣀⡀⢀⣼⠃⣿⠸⡇
⠀⠀⠀⢰⡇⢸⡇⠈⣿⠛⠛⠛⠶⠶⠚⠋⠉⠙⢿⣍⡉⠉⣻⣿⣅⢀⣴⠿⣄⠉⠛⣻⡿⠟⠋⠛⠛⠉⠉⠉⠉⣿⠁⠀⣿⠀⡇
⠀⠀⠀⢸⡇⢸⡇⠀⢸⣆⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣾⣋⣀⣿⠛⣷⣀⣙⣷⣛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⡟⠀⠀⣿⠀⣷
⠀⠀⠀⣸⠇⠘⣧⡀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣹⠇⠀⢸⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢹⡇⠀⣰⡟⠀⣿⡀
⠀⠀⢠⣏⠀⣰⢿⡇⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⣿⢷⡀⢈⣧
⠀⠀⣾⢻⣇⣸⣾⡇⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⣿⣾⣀⡿⢻
⠀⠀⠸⣦⡙⡏⣿⡗⠀⠸⠷⠶⠶⣶⠶⠶⠶⠶⠶⠶⣶⠶⠶⠶⠶⠶⠶⠶⠶⣶⠶⠶⠶⠶⠶⠶⡶⠶⠶⠾⠃⠀⠸⣿⣿⡟⣡⡟
⠀⠀⠀⠈⠙⠻⠟⠁⠀⠀⠀⠀⠀⠻⣦⣤⣀⣀⣤⣴⠟⠀⠀⠀⠀⠀⠀⠀⠀⠿⣤⣄⣀⣀⣤⡴⠇⠀⠀⠀⠀⠀⠀⠙⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠀⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠏⠙⠛⠋⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠙⠞⠋⠻⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣤⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⣄⠀⠀⠀⠀⢈⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣠⡴⠟⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠳⣤⣀⣠⡾⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠴⠾⠡⠤⠄⡀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠛⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠂⠈⠀⠒⠂⠄⡀⢀⡠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⡄⠀⠀⠀⠀⠀⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣀⠀⠀⠀⣀⡀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠒⠂⠉⠉⠙⠛⢦⡀⠈⠛⢿⣦⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠈⠉⠀⢀⣀⣀⣀⡤⠇⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⢀⣤⠤⣤⠴⣯⠤⢄⣀⠔⠛⢦⡀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⢀⡞⠀⢀⡇⣸⢀⣀⠀⣇⣄⠀⠀⢻⡀⠀⠀⢷
⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⢸⠃⠀⢸⠇⣿⠸⡿⠀⡝⠿⠀⢠⠞⠉⠉⠁⠘⣆
⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠸⡄⠀⠀⢧⠀⠀⠈⢳⣤⣤⡴⠀⢻⡀
⠀⠀⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠷⣄⠀⢸⠀⠀⠈⠲⠴⠋⠳⠤⠔⠁⣰⠆⣱⡀⠈⣧
⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠈⢳⣿⠀⠀⠀⠀⠀⢠⠒⢲⠒⢶⠉⢤⠈⠇⠀⢹⢦⣀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠶⠖⢦⣄
⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⢳⠎⡼⠀⠀⠀⠀⠀⠘⣆⠘⠀⠈⢣⠀⠙⠆⠀⠀⠀⠹⣆⡤⠖⠛⠉⠁⠀⠀⠀⠀⠀⠀⠈⢧⡀
⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⢸⠀⢡⠀⠀⠀⠀⠀⠀⠀⠙⠳⠄⠠⠵⢊⡼⢀⠆⠀⢰⠇⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣡⠖⠁⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠈⠢⣀⢨⠗⠒⢂⣶⡦⠤⠤⠒⠊⠉⣀⡤⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠷⣄⡀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣶⠁⠀⠀⡠⠞⢹⣤⣀⣸⢭⠲⡶⠶⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠉⠀⠀⢈⠷⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠐⠄⠀⠚⠁⠀⠉⠢⣀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠸⣤⠀⠀⠠⠆⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⢦⡀⠀⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⠀⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠑⠀⡀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠈⠀⠒⠀⠤⠄⠀⣀⣀⣀⠀⠠⠤⠄⠒⠂⠈⠁⠀⠀⠀⠀⣠⠴⠒⠋⠑⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⢠⢾⠁⠀⠀⠀⠈⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣄⠀⠀⠀⠀⠀⠀⠀⢷⣄
⠀⠀⠀⠀⠀⠀⠀⣿⣤⠙⠢⠄⣀⡀⢠⡞⠉⠛⠳⠶⣤⣤⣤⣤⣤⣤⣤⣤⡴⠶⠚⠋⠁⠀⠙⣦⣀⣀⣀⠤⠔⠂⢁⣼⡀
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⣀⡤⠶⠚⠁⢁⡀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣳⠀⠀⠀⠀⠀⠐⠤⣀⡀
⠴⣆⣉⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣄⡀⠀⠀⠀⢀⣀⠠⠬⠭⠴
⠀⠀⠉⠈⠒⢤⣠⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠚⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠱⡀⠀⠀⠀⠀⠀⢀⣀⠤⠄⠒⠒⠂⠉⠉⠉⠉⠉⠁⠒⠒⠂⠤⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⢣⠀⣀⠤⠐⢊⣁⠤⠤⠒⠒⠀⠉⠉⠉⠉⠉⠉⠉⠐⠒⠲⠤⢄⣀⠉⠐⠀⣀
⠀⠀⢀⠤⠤⠄⠒⠒⠒⠉⠀⠀⠀⠀⠀⠙⠓⠒⠺⠥⠤⣤⠤⠤⠐⠒⠒⠒⠒⠂⠤⠤⠄⣀⡀⠀⠀⠀⠀⠉⠒⢦⠤⠭⠆
⠀⠀⠀⠳⣄⠀⠀⠀⠢⠤⠆⢄⣄⠄⠦⠤⠂⠀⠀⢁⣤⠫⠀⠀⠀⠠⠤⠤⠄⣀⡀⠀⠀⠀⠈⠑⠒⠤⡀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠥⠄⠐⠒⠒⠒⠀⠤⠤⢀⡀⠈⠉⠒⠤⣀⠀⠀⠀⠈⠑⡖⠒⠈
⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠲⢄⡈⠑⠦⡀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⡸⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡈⢒⠉⠁
⠀⠀⠀⠀⠀⠀⡇⠀⢀⡠⠖⠉⠈⠑⠦⣀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠺
⠀⠀⠀⠀⠀⠈⠓⠚⠁⠀⠀⠀⠀⠀⠀⠀⠑⠒⠃


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠋⢛⣛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀⣀⡤⠀⢀⣀⡤⠤⠄⡤⠤⠀⠠⠴⠒⠢⠒⢤
⠀⠀⠀⠀⠀⠀⢀⠔⠉⡁⠀⠀⠀⠀⠀⠀⠀⡀⢰⡄⣄⠀⠰⠄⠓⠸⠀⠐⠸⡇
⠀⠀⠀⢀⠄⠐⠁⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠹⠁⠀⠀⠑⢆⠀⠀⠀⠀⠀⠀⠐⡄
⠀⣀⠴⠋⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⢢⠀⠀⠀⠀⢃⠀⠗⠈⢢
⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⢀⠀⡂⠀⠀⠀⠘⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠈⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠠⡀⠀⢀⣦⡵⣶⡄⠂⠀⣀⠔⢻⠀⠀⠀⠀⠀⠀⡠⠄⠤⠀⡔⢀⠁
⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢰⠀⢀⡀⠐⠤⠠⠟⠀⠉⠠⠐⠚⠁⣀⠸⠀⠀⠀⡠⠀⠈⠁⠈⠢⠀⠃⢎
⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢻⣶⣤⣤⣤⠤⢤⡴⠖⠚⠉⠀⠀⢣⠀⠜⠀⠐⠀⠀⠀⠀⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣇⣀⣸⣷⣤⠜⠀⠀⠀⠸⠀⠯⠀⠠⠀⠠⠀⠀⠒⠋⠀⡹
⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢸⡀⠣⡤⠤⠐⠀⠠⠀⠀⠀⢈⠇
⠀⠀⠀⠀⠀⠀⠀⠱⡀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠿⠿⠿⠿⠿⢿⣷⡀⠀⠂⢸⠤⢤⠑⠂⡤⢤⠔⠒⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⡄⠢⡀⠀⠀⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⢀⣿⠇⠀⠁⢀⢰⠒⠒⣋⠡⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠸⠀⠀⢰⠀⠀⡁⠀⠀⠀⠀⠀⠀⡀⢀⣰⢯⠅⠠⠂⠁⢱⠤⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⡇⠀⠀⠈⡤⠤⢥⡀⠤⠴⢆⡀⠊⢁⠜⡀⡈⠑⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⢲⢲⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⣁⡐⠀⢰⡶⠖⠟⠛⢐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠐⠿⢸⣦⣤⠀⠐⢀⣤⣴⠶⠐⠛⠋⠁⠀⠀⣀⣠⠤⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⣸⠸⠀⠀⠀⠀⠈⠁⠀⣀⣀⠤⠴⡖⠋⠉⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠙⣗⠒⠲⠒⠚⠙⠁⠀⠀⠀⠙⡖⠲⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⣹⠢⠤⢤⠐⠊⠀⠀⠀⠀⠀⡇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣠⣸⠀⠀⡇⠨⠀⠀⠀⠀⠀⠀⠀⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄⠀⠀⠀⠀⠀⢀⣴⣤⣧⣄⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⣠⡀⢀⣀⡀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣯⣿⡆⠀⠀⠉⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠙⠛⠛⠋

⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢠⣀
⠀⠀⠀⠀⠀⡶⠇⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀
⠀⠀⠀⠀⠈⠁⠈⠀⢸⡀⠙⠲⢊⡟⠀⠀⠀⠀⠀⢠⠏⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠓⡄⠀⠀⠀⠀⠀⡩⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⡸⢃⡀⠀⣈⡳⣄⠀⠀⠀⠀⡏⠀⠀⠀⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠘⣄⣀⣀⣀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠙⣴⠁⠀⠈⠀⠀⠀⠀⡇⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⡤⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠱⡀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠁⢳⠀⡠⠒⠠⢷
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠐⡹⢿⠆⠀⠀⠀⠙⢦⣀⠀⠀⠀⢈⡓⠴⠄⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⢀⣠⠋⢸⠀⠀⠀⠈⠁⣀⣴⣶⣶⣦⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⣤⡾⠿⠛⠲⢤⡀⠀⠀⠐⢠⣜⡄
⠀⠀⠀⠀⠀⠎⣁⠀⠀⠈⣡⠛⠀⣠⡾⢋⠁⡨⠋⢙⣧⣄⠀⠀⠀⠀⠀⠀⣠⡴⠛⠉⠁⠐⠂⠀⠀⠻⣄⠀⠈⠜
⠀⠀⠀⠀⠀⠀⢸⣁⠴⢤⡇⢠⣾⢋⠔⠠⢊⠔⠊⡕⠁⢉⢷⣄⠀⠀⣠⡾⠋⠠⠄⢀⣀⠀⠀⠀⠀⠀⣸⣧
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠁⣾⠣⢁⢾⠊⠁⢀⠎⠀⡠⢃⡴⠻⣦⠀⢻⡇⠀⠀⠀⠀⢀⣈⠉⣩⠗⠛⣿⡿⠀⢀⡴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡅⢸⠀⠠⡀⠸⠀⠀⠃⡎⢀⣾⠋⣠⡾⠻⠀⠉⠀⣀⡀⣀⡍⠀⠀⢰⣿⠃⠒⣌⣀⡑⠂
⠀⠀⠀⠀⠀⠠⡀⢠⣃⡀⠈⣿⠡⡈⠄⠰⡀⠘⢄⠀⢧⢧⠸⣇⠀⠹⣧⡔⠛⡃⠁⠉⠀⠀⠀⠀⠀⣼⠋⠀⠀⠋⠉⠃
⠀⠀⠀⠀⠀⠒⣸⠛⢤⡀⠀⠈⠳⣌⠢⡑⠄⡐⠀⡑⢄⠑⢷⡌⣷⡄⢘⣷⠠⠴⣄⣀⡀⠀⠀⣠⡾⠃⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠳⣌⡀⠀⠐⠨⡂⢌⠢⣼⠋⢰⣿⠁⠑⡄⠈⣣⡤⠚⠋⠁⠀⠀⠀⠀⠐⣠⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠙⠳⢤⣀⡀⠝⠲⣽⣷⢸⠟⣄⣰⠾⠋⠁⠀⠀⠀⠐⡦⢄⣀⣀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢡⠀⠀⠀⠀⠀⠈⠙⠻⣦⣼⣯⣿⡴⠋⠁⠀⠀⠀⠀⠀⠀⢀⡟⡀⢀⡙⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⣋⠀⠈⢡⠛⠀⠀⠀⠀⠀⠀⠈⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠱⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣧⠋⠰⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⡔⠃⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⠜⣃⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠹⡍⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠛⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠀⢣
⠀⠀⠀⠀⠀⠀⠀⡅⢀⠐⡀⠈⢆⠀⢀⠄⠐⢄
⠀⠀⠀⡠⠂⠐⢄⠃⣀⣀⡠⠁⠘⢤⠂⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠄⠀⠀⠀⢀⠈⠋⠁⠐⡠⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠁⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⣷⠃⢀⡀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⢰⠀⣀⡇⠀⣀⡀⠀⠀⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠛⠃⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠟⠟⢃⠀⠛⠃⠀⠀⠘⠄⠀⠸⠄⠀⢰⠀⠀⢀⠀⠀⠀⢠⣮⣀⣳⣆⠀⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢰⠀⠀⠀⠘⣆⠀⢰⠀⠈⡆⠀⣘⠀⠀⠀⡜⠀⠈⠻⠾⠟⠻⡿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⢸⠀⠀⢠⠄⠈⠓⠂⠋⠉⠁⠀⠄⠈⠂⢼⠁⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠇⢐⠒⠚⠉⠉⠀⠀⠀⠀⢀⣀⠀⠀⠀⠄⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⢡⠀⠀⠀⢴⠶⠐⠄⠉⠁⠀⠀⠀⠀⠄⠀⢰⠆⠀⠀⠀⠀⠀⠀⠈⢦⡇
⠀⠀⠀⠀⢀⠀⣤⠁⣀⢀⡀⠀⢈⡇⠀⠦⠀⠀⠀⠀⠀⠄⠀⠀⡀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠑⡄
⠀⢀⡤⠒⠈⠐⠂⠉⡹⢳⡁⠊⠁⠈⡀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠁⠀⢀⡄⠀⠢⣀⠀⠀⠀⠀⣤⠄⡄
⠀⡞⠠⡀⠀⢐⠀⠀⠙⣮⡴⠠⠀⢆⢀⠀⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠘⢁⣀⣀⠐⠂⠀⠘⠂⠀⠀⠀⠀⡄
⠀⠣⡐⠀⠀⠈⠂⢠⣔⠉⢻⣤⡀⠅⠒⠦⠒⡆⣀⠀⠲⡐⡂⠀⠀⠉⠈⠁⠀⠀⠀⡀⠀⣍⠀⠀⠀⠀⣰⠁
⠀⠀⠉⠂⠠⡄⠐⠉⠉⠁⠹⡄⠀⠀⠠⢘⠰⠏⠵⠶⠷⠯⢀⠀⢀⠀⠀⣀⢀⠀⠀⠐⠀⠀⠀⠀⠤⢶⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠽⠀⠀⠀⠈⠀⠠⠠⡄⠀⠠⠤⠘⢀⣠⠀⠈⠙⠒⣀⣀⣀⣀⡀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠁⠠⠠⠈⠁⠁⠀⡀⠀⠁⠒⠀⣉⠀⠄⠀⠁⡘⠀⠀⠀⢄⠀⠏⠀⠀⠩⠉⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠊⠁⠀⠩⠔⠂⠁⠡⠀⠀⠀⠠⠀⠀⠀⠘⠀⢆⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⢠⣤⣼⣤⠄⠀⠀⠀⠀⠀⠀⠀⢳⣾⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠂⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⣀⡀⠀⠀⠀⢀⣀⣀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠆⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠄⠀⠀⠀⢨⠀⠀⠀⢻⠀⢈⣰⣶⠶⠀⠐⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⢀⣀⣠⣤⣦⣴⠄⠀⠀⣻⡔⠋⢘⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠁⠀⠀⢠⣶⠀⠈⠀⠀⠀⠐⠤⠒⠉⠛⠳⠀⢄⡀⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠷⠆⠠⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⡐⢤⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢄⡀⠀⣠⠦⣀⣀⠀⣀⡅⠀⠘⢠⡇⠀⠀⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⢠⡤⠞⠁⠶⢄⠁⠀⠀⠀⠀⠸⠆⠁⠀⠶⠛⣦⡔⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⡷⠀⠠⠖⠢⡄⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⢱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠗⢲⢆⠘⢷⣾⠆⠀⠈⠀⣀⠀⠀⠀⢈⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣀⠛⡿⠓⠒⠁⠀⠀⠀⠊⣿⣅⠀⠀⠀⠑⠄⠀⢨⠤⠤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠁⠀⠀⢷⠀⠀⠀⢠⠛⣛⡀⠀⠀⠄⠀⢠⡌⠀⠀⠀⠀⠐⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠂⠀⠀⠀⢸⡇⠀⣠⠏⠳⣠⠃⠀⢀⡄⠀⠀⢰⠀⠀⠠⡀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⢠⠊⠶⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠀⠀⠀⠀⠀⢸⣧⣾⣁⠛⣠⡞⡀⠀⠃⠀⠀⠀⣸⠀⠀⠀⠿⠀⠀⠀⠈⢢⡀
⠀⢎⠑⠲⢄⠀⠈⢆⠈⢧⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠛⠉⢡⡶⡳⠊⠁⠀⢀⡴⠃⠀⡀⠀⠘⠀⠀⠀⠀⠀⠱
⠀⣀⡁⠒⣀⣉⠀⠘⠓⠀⠈⠑⢄⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠐⠈⠉⠁⠀⠀⠀⣠⠇⠀⠀⣤⠀⢰⡇⠀⠀⠀⠀⠀⠃
⠯⠀⠉⣉⣀⡷⠀⠸⠁⠀⠀⠀⠈⣅⡘⣄⠀⠀⠀⠀⠀⢀⣴⠞⠈⣧⣀⣀⠀⠀⠀⠀⢀⣀⣠⠋⠀⠀⠀⣺⠀⠈⡇⠀⠀⠀⠀⠀⠘
⠀⢤⠛⠉⣁⡴⠆⠀⠀⠀⠀⠀⣰⠋⠙⢮⡛⠢⠶⠶⠚⠋⠁⠠⠊⠀⠉⠉⠳⢄⣀⣀⠼⠉⠁⠀⠀⠀⠀⣿⠀⠀⡇
⠀⠈⠁⠀⡈⠀⠘⠉⠛⠛⠛⠋⠁⠙⢆⡀⠉⠓⠤⣀⡀⢀⠔⠁⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡇
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢆⣄⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⢀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⡠⠖⠁⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠅⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⡅⠀⠊⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠰⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡷⠀⠠⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⠀⠀⠶⡀⠀⠀⠀⠀⣀⠀⠐⠀⠁⢸⠄⠰⢆⠀⠀⠀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⠀⠐⠀⠀⠃⠀⠈⠀⠀⠀⠀⠀⠀⠀⣼⣦⠤⣷⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠀⠀⠀⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠉⠶⠢⠤⣤⢤⡤⠀⡠⠞⠿⡇⠀⠀⠀⠀⠆⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⢠⡋⠀⠀⠀⠀⡐⢀⠞⠱⠆⢠⡇⠀⠀⠀⠀⠘⠃⠎⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠈⠠⡀⠀⠀⠘⠁⢸⠀⠀⠀⠀⠙⠦⠤⠤⠤⠤⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠱⠆⠈⠑⢄⠘⢄⠈⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠁⠐⠂⠀⣤⡄⠀⠐⠂⠈⠉⠀⢀⣀⠀⠀⡼⠀⠀⠑⢠⣈⠶⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⠀⠀⠰⠃⠒⠀⢤⣴⣄⠉⢩⣅⣀⣤⡼⠄⠒⠊⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠒⠲⠾⢦⡀⠀⠀⠀⠉⠉⢉⠉⠁⠀⠀⠀⣠⠲⢶⠒⠒⠒⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⢀⠀⣀⣸⡀⢀⣤⠴⠈⠀⠀⠀⠓⠒⠓⠛⠃
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣦⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⡏⠁⠛⠙⠉⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⢀⣠⠤⠴⠞⣛⡓⡶⠶⠒⠲⠶⠒⠿⠔⠶⠖⠒⠒⠒⠛⠓⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠠⠄⠀⠀⠈⠀⡄⢀⠀⠀⠀⠀⡀⢰⠀⡄⠀⠀⠀⠀⠀⢠⠛⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⡸⠖⠓⠻⢄⠀⢀⡤⠃⠉⠙⠣⡀⠀⠀⠂⠀⠋⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⠁⠀⠎⠀⠀⠀⡀⠀⠱⡎⠀⠀⣀⣀⠀⠘⡄⠀⠀⠀⡄⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⢀⠀⠀⡰⢉⣌⠱⠀⠀⠀⠊⣤⣄⠡⠀⡇⠀⠀⢰⠁⠀⠀⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⡴⠒⠦⡤⠦⠾⠿⠗⢢⠗⢒⣚⠛⡿⠫⠉⡑⠀⠀⠀⠀⠂⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠘⢇⡀⠀⠈⠑⠤⣀⡴⠋⠑⢄⡀⠰⡅⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠉⠓⠲⣤⠤⠤⠀⠀⠀⠀⠉⢉⡩⠓⠒⠂⠀⠀⡇⠀⠀⠀⢰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐⠯⣤⣤⣤⣤⡤⠤⡔⠂⠁⠀⠀⡆⠀⠀⠀⡇⣰⣆⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⣧⣀⡿⢸⣄⣠⡇⠀⠀⠀⢀⡇⠀⠀⠀⡇⡿⠯⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣻⢿⢢⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠄⢸⠁⡄⠀⠘⢇⠀⠀⠀⠀⠲⡄
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡴⣞⡀⠌⠉⢸⠇⢀⠁⠀⢳⠀⢀⡤⠒⠖⠛⢉⠇⠀⠀⠀⠀⠀⢣⠀⠀⢈⠆⠀⠀⠀⡃⠥⠠⠒⣈⠇
⠀⠀⠀⠀⠀⠀⢰⣧⡘⣮⠴⣤⣤⣤⠟⠐⠀⠀⠀⠀⠳⡞⠀⠀⠀⣠⠋⠀⠀⠀⡀⢀⠄⠈⠳⣶⡙⡄⠀⠀⢸⠀⠀⠀⡛⣉⠬
⠀⠀⠀⠀⣀⠔⠋⣀⡿⢓⡴⢁⡤⢾⠀⠀⠀⠀⢀⠤⢄⡨⣥⣤⣭⡤⠤⠤⠀⠀⠀⠀⡀⣀⡠⠶⡷⡈⢆⡠⢀⠔⠒⠢⠍⠱
⠀⠀⢠⣮⢁⡤⠞⠉⡃⠋⠀⣋⡄⠘⣦⠶⠒⠂⠺⡀⠀⢩⠀⢐⠨⠄⠀⣴⠖⠒⠲⠖⡏⠉⠀⠀⣧⠙⢄⠔⠁
⠀⠀⠘⠛⠁⠀⠀⠀⡇⢀⠔⣡⣞⣠⢿⡀⣀⠀⠀⠳⡶⠚⠓⠚⠑⠦⠤⠞⠀⠀⠀⠀⢠⢀⣠⡶⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠣⡤⠞⠁⠈⠁⠈⡇⠺⠶⠶⠶⠀⠶⠶⠶⠶⠶⠀⠀⠶⠶⠶⠦⠀⠈⠉⠀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠦⢤⡤⠤⠤⡤⠤⢤⣤⣤⣤⣤⣄⣀⣀⣀⣀⣠⠴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⣄⣀⣠⡗⠀⠀⠀⠀⠀⠠⣇⠀⠀⣀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⡙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢶⣤⣷⣿⠄⠀⠀⠀⠀⠀⠀⠀⢈⣌⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠻⠟⠀⠀⠀⠀⠀⠀⣾⣵⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠉

⠀⠀⠀⠀⠠⠀⠠⠤⠀⠄⠀⠄⠀⠠⠄⠤⠀⠤⠀⠀⠠⠀⠀⠀⠀⠆⠤⠴⠤⠄⠀⠂⠠⠄⠀⠒⠀⠄
⠀⠀⠀⣤⣄⡀⢀⣤⣤⡀⢀⣄⠀⢀⡄⠀⣠⣤⣀⡠⣤⣤⢠⡤⠤⠀⢠⡆⠀⢠⡆⠀⣴⣶⡦⠀⠀⣦⠀⢴⠶⠶
⠀⠀⠀⣿⠈⣷⠀⣿⠄⠀⢸⣧⣤⣼⡇⣼⠋⢈⣿⠁⠀⣿⢸⡗⠀⠀⢸⡷⠶⢾⡇⢀⡷⢾⡷⠀⢸⡟⠀⢻⠃
⠀⠀⠀⣿⠀⢸⣷⡇⠀⣠⢸⡇⠀⢸⣷⡟⢠⡟⢹⠀⠀⣿⢸⡇⣤⠀⢸⡇⠀⢸⡇⢸⡇⢸⡇⠀⢸⡇⠀⣾⡇
⠀⠀⠀⣯⠀⣸⣿⡇⠀⠁⢸⡇⠀⢸⣿⣷⡟⠀⣿⠀⠀⣿⢸⡆⠂⠀⢸⡇⠀⢸⡇⣸⠃⢸⡇⠀⢸⡇⠀⣿⡇
⠀⠀⠀⣧⣴⠏⢸⡇⠀⠀⢸⡇⠀⢸⣧⣿⡀⣰⠏⣤⣰⡟⣸⣀⠀⠀⢸⡇⠀⢸⣇⣿⠀⠈⣿⠀⢸⣇⠀⣿⣇⡀
⠀⠀⠈⠋⠁⠀⠘⠛⠛⢀⠈⠃⠀⠘⠁⠈⠛⠉⠀⠉⠋⠀⠉⠉⠁⠀⠘⠃⠀⠀⠙⠃⠀⠀⠙⠓⠘⠛⠃⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⢦⠀⠈⣄⠀⠀⣈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠂⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠄⠂⠆⢀⡌⠉⠀⠀⠀⠒⠂⠴⢤⢠⡄⣤⠤⠴⠶⠤⠤⢠⡀⣀⠀⣄⠠⡄⠒⠚⠋⠉
⠀⠀⠀⠀⣤⣀⣀⡴⡖⢋⠁⠀⠀⠀⠀⠀⣄⡀⢸⣦⡀⢨⡀⠀⢸⣶⡄⠀⢷⠀⠀⢅⣰⠀⢨⣤⠀⠀⠰
⠀⠀⠀⠀⣿⢿⡭⠏⠁⠀⠀⠀⢀⠀⠀⠐⠙⠁⠘⠉⠀⠜⠻⠖⠚⠩⠀⠀⠸⠀⠀⢈⡇⠀⠈⠉⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠸⠌⠛⠺⡏⠀⠀⢀⡀⢀⢀⣤⣤⢠⣤⢠⡴⠄⠀⣦⣡⣶⢰⣿⡯⠀⡇⠀⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠰⡖⢦⣶⡟⠀⠘⣷⢾⣼⣵⣿⠀⢸⣿⡏⠀⠀⣿⠀⢻⣾⡇⢧⠀⡇⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢷⡼⠹⣧⠄⠀⠿⢸⢯⣯⡼⠠⡼⠡⠷⠆⠀⠻⠆⠸⠟⠁⠘⠃⠛⠃⠛⠛⠃
⠀⢀⡀⠀⢀⡀⡀⢀⠀⠰⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠂
⠀⠸⣿⠛⢻⡇⣧⢸⣿⣷⣰⡇⢳⡾⠁⣻⡿⢷⡼⣿⣭⠇⣶⢸⡿⣄⣿⠹⣷⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃
⠀⠀⣿⠄⠸⠷⠙⠟⠻⠇⠻⠧⠟⠙⣦⠷⢼⢺⡄⢿⠀⢧⡾⠿⠃⠙⠿⠀⠾⠻⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⢠⣤⣴⡄⠀⠀⣀⢠⣤⢀⣀⡀⣠⣤⡀⣀⠀⠀⣀⢀⠀⣀⣀⢠⡄⢀⣤⣄⢠⣤⡀⣤⣄
⠀⠀⠀⢸⡇⣿⢀⣿⣿⠻⣿⣿⠥⣿⣿⢶⠁⢹⣶⣶⣇⣿⡇⣷⢎⣸⡇⢸⡇⢼⣽⡶⡇⣿⢸⡇⠀⠀⠰⠆
⠀⠀⠀⠸⠇⠘⠿⠟⠿⢀⡛⠙⠶⠛⡟⢘⣃⡀⣛⠙⢘⠁⠛⠃⠘⠛⠷⠘⠷⠞⠛⠀⠟⠿⠾⠃⠀⢀⡀⠀⢀
⠀⠀⢨⣿⡁⣿⣦⢿⣷⣏⣹⣾⣷⡀⡿⣾⣉⡗⣿⠀⣸⠀⢛⡟⠛⣿⣤⣿⠀⢾⠂⠀⠀⠀⠀⠀⢀⠘⠁
⠀⠀⠘⣭⠃⣿⠀⠈⡿⢯⣽⢿⠏⠻⠏⢷⣤⠇⣿⡄⢿⠀⢸⡇⠀⣿⠀⣿⢀⣈⡷⠀⠀⢀⠀⠀⠚⠀⠰⠊
⠀⠀⠀⣉⣥⣭⡄⢠⡤⣄⢠⡴⠦⠤⣤⡤⠀⠐⣶⠖⢶⠀⠠⡄⢠⡄⢠⡶⠦⢹⣄⣶⠀⠈⣧⠀⠀⢀⣀⡀⡀
⠀⠀⠀⢹⡯⠈⣷⢸⡟⣧⠈⠳⣦⠀⣿⠀⠀⠀⣿⠃⢸⡀⠀⣧⢸⡇⠈⠳⡄⢸⡇⢿⠀⠀⠋⠀⠀⠠⠭⠄⢠⡀
⠀⠀⠀⠸⠇⠀⠿⠘⠇⠘⠒⠶⠋⠀⠻⠀⠀⠀⠿⠀⠸⠷⠆⠙⠛⠃⠛⠶⠃⠸⠃⠸⠃⠀⠀⠀⠀⠐⢦⢠⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⣀⣀⠀⢠⠀⠀⠀⠀⠘⡿⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⣤⢄⣠⣍⢈⢀⠄⡀⢀⣀⣨⠉⠁⠀⠀⠀⠀⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠀⠀⠉⠾⢧⠞⠺⠠⠄⠑⠐⠀⠇⠀⠀⠐⠦⠒⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⠟⠀⠳⠤⠤⣶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠓⢦⡀⠀⠀⠀⠠⡞⢡⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣼⣡⠴⠛⠓⠦⣝⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢰⠟⠁⠀⠀⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⢸⠈⡆⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠙⢆⠀⠀⠀⠀⢸⣤⣧⡀⠀⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡇⠈⠳⡤⠖⠋⠉⡴⠋⡇⠀⠀⠀⣸⠁⠀⠀⣰⢻⡄
⠀⠀⠀⠀⠀⠀⠀⣠⠴⠖⠒⠋⠉⠀⠀⠀⠀⠀⢀⡼⠁⠀⡇⠀⠀⢠⠟⢯⡛⠛⠁⠀⠳⠦⠤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠙⢿⡲⠤⣤⡀⠀⠀⠀⠀⠀⠘⠦⣄⡀⡇⠀⢀⡞⠀⠀⢹⠆⠀⠀⠀⡴⠚⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⢠⡏⠀⠀⣠⠖⠒⠶⠶⠤⠭⣷⣄⣸⠁⠀⣴⣫⠴⠚⠳⢄⡹⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⣼⠋⠁⠀⠀⠀⠀⢉⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢰⠇⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⢀⡞⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡼⠁⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⡏⣸⠁⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⣼⣱⢃⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⣰⣿⡵⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠋
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠈⠓⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠀⠀⠀⢈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢠⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠿⠀⣀⢈⡖⠠⣀⠀⠀⠀⠀⠀⢎⠛⠉⣬⢔⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢸⠀⢀⠠⢦⠈⢷⠀⠀⠀⠀⠘⡔⣃⠔⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠰⣎⠀⠀⡸⠤⠼⠄⡀⠀⠀⢰⢳⠇⢠⠒⠲⢤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣠⣄⣉⣉⣀⣀⣤⡾⠃⠀⠀⡀⡞⡴⢋⠠⠚⠰⢆⡄⢉⡍⢑⠒⠒⠦⠤⠤⣄⣀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠈⠻⣿⣿⣿⡿⠷⢤⡴⢣⢀⣳⡖⡐⠁⢀⣤⡄⡠⠓⠉⠉⠙⢶⠀⢰⣉⠅⡠⠔⣷⠀⠀⠀⠀⡸⠸⢔⡡⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠙⠤⣄⣤⠤⠊⠀⢸⣎⡽⢸⡉⠂⡈⠛⠛⠀⢼⣿⡆⠀⡘⠀⢀⡴⠂⢰⢓⠌⡆⢀⠀⢐⣁⠔⠀⢤⠼
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠤⠤⠞⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠀⣕⠦⠌⠈⠱⣀⢀⠉⠀⢞⠁⡠⠎⢴⠄⢈⡠⠀⠩⠄⠈⠀⠀⠀⠀⠐
⢀⠤⠐⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⡏⠇⢸⣉⣷⠲⣦⣤⣥⡾⠃⢊⠎⠀⡠⢺⢚⣅⠂⠔
⠸⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢠⣾⣿⣿⣿⣿⣿⠏⠀⠰⣉⡀⣎⣀⣈⡥⠃
⠀⠀⠉⠉⠒⠒⠶⢦⡤⠠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢜⠻⠇⠤⠤⠚⠡⠒⣠⠃⠧⠀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⠲⠐⢦⠬⣍⣉⣀⣈⢀⡇⠀⠁⠰
⠀⠀⠀⠀⠀⠀⣠⣤⢇⡈⠀⠐⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠗⣈⠙⠶⠏⣧⣄⠠⣤⡀⣍⢁⣈⣴⠇
⠀⠀⡀⠀⣀⣠⡇⠀⠢⡄⠀⠀⠀⠁⠨⠂⠀⢀⡀⠀⢀⣀⡀⢄⣠⡴⠴⠙⡏⠐⠓⣤⢤⣤⣈⣁⣇⣈⡥⠼
⠀⠸⡀⠀⠀⠀⠁⡀⠔⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⣀⠒⠒⠈⠁⢤⠀⣨⡞⠙⠦⣔⢇⠀⢠⣿⣄⣀⣠⠃⠀⣠⣤⡀
⠀⠀⠙⠦⣄⡀⠀⠑⢄⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠦⠤⠀⣀⣴⠾⠋⠀⠀⠀⠈⠮⣱⡿⣿⣿⡟⢾⠦⣜⣽⣿⣇
⠀⠀⠀⠀⠀⠉⠙⠓⠒⠛⠃⠉⣉⠜⠋⠒⠒⢦⣀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠃⠀⠙⠉⢹⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠀⠀⠀⠀⠀⠀⣈⡽⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡶⢋⡤⠤⡈⢢⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⠃⠸⡀⢀⡅⠀⠹⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡇⠀⠀⡠⢤⡀⠀⠀⠱⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⡺⠀⠀⠸⡀⢀⡽⠀⠀⠀⢻⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡇⠀⠀⠀⢈⣁⡀⠀⠀⠀⠈⢧⠄⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢨⠁⠀⠀⠀⣇⠀⢸⠀⠀⠀⠀⠘⣄⡦⠸⠤⠦⠘⠒⠓⠚⠂⠤⣀
⠀⠀⠀⠀⠀⠀⢀⡠⠾⠐⠒⠚⠒⠒⠚⠂⠼⠤⠼⠀⠀⠀⠀⠈⠉⠁⢀⡠⠤⠤⣄⡀⠀⠀⠀⠀⡀⠀⡔⠉⠙⡄⢸
⠀⠀⠀⠀⠀⠞⠁⡠⠤⡀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠒⣤⣀⠀⠀⢰⠁⠀⢀⣾⣿⣿⡆⠀⢰⠋⠉⢣⠘⠒⠚⢁⠎
⠀⠀⠀⠀⠘⡀⠸⣄⣀⡔⢰⠋⠙⡆⠀⠀⡜⠁⠀⢠⣿⣿⣿⣆⠀⢡⠀⠀⠸⣿⣿⣿⡿⠀⠀⠑⠒⠁⠀⠀⣠⠛⠂
⠀⠀⠀⠀⠀⠱⡄⠀⠁⠀⠈⠂⠐⠁⠀⠀⢣⠀⠀⠘⣿⣿⣿⡟⠀⠈⠢⣀⠀⠈⣻⠿⠁⠀⠀⠀⠀⠀⢀⡞⠍⠁
⠀⠀⠀⠀⠀⠀⠉⡢⣀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢄⣀⣈⡹⠟⠁⠦⡠⠃⠀⠈⠁⠀⠀⠀⠀⠀⠀⣀⠴⠁⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠚⢱⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⢱⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠘⢎⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠀⢈⠆⠀⠀⠈⢳⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡹⠀⠀⠀⢰⠉⠙⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⡴⠒⢢⠀⠀⠹⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠃⠀⠀⣀⡈⠒⠒⠁⠀⠀⠀⢠⠶⣄⠀⠀⠀⠀⠀⠣⠄⠔⢀⣀⠀⢱⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠀⠀⢸⠁⠈⡇⠀⠀⠀⢀⡔⠧⠀⠁⡹⠦⣄⠀⠀⠀⠀⢰⠁⠈⡣⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⡇⠀⣀⣌⡑⠊⠀⠀⠀⣠⡋⠁⠀⠀⠀⠀⠈⠁⠹⠲⣤⣀⠀⠑⠊⠁⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠰⡁⠀⡱⠀⠀⣠⠚⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠈⢉⣀⠴⡏⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⣿⣿⢛⢻⡛⡟⢻⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⣀⠤⠒⠢⢄⡠⠄⠒⠒⠤⣀⠤⠒⠉⠑⠤⠔⠉⠀⠀⠉⠉⠀⢨⠹⡀
⠀⠀⠀⠀⠀⠀⢸⠁⠀⣈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡴⢉⠇⠀⠀⢠⠋⠀⠉⠒⡄
⠀⠀⠀⠀⠀⠀⠀⡇⢰⠁⢸⢀⡀⠀⢰⠂⠀⠀⡀⠀⢀⣠⣧⣄⣀⣠⠂⠀⠑⠉⠀⠀⠀⡏⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠰⠁⠹⠤⠃⣠⢷⠶⠿⢯⡓⠚⡥⢊⡕⠊⠉⠉⠒⣍⠳⣄⡠⠀⠀⠀⠀⢱⠀⡞⢃⠀⠈⠓⠢
⠀⠀⠀⠀⠀⠀⢃⢠⠋⣆⡞⠁⡇⣴⣶⡄⢹⡞⠀⢸⠀⣶⣿⡿⠀⡸⠀⠈⢆⠀⠀⠀⢠⠃⡸⠀⡌⠀⠀⠀⡴
⠀⠀⠀⠀⠀⠀⡘⠘⠔⢹⠀⠀⠙⠿⠭⠖⢹⠀⠀⠈⠳⠬⣉⡤⠞⠁⠀⠀⢸⠀⠀⢀⠇⠀⠧⠔⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠇⠀⠀⢸⣄⡀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠘⡄⠀⠀⠀⡰⢦⠀⢸
⠀⠀⠀⠀⠀⢸⠄⠀⠐⡇⠀⠈⠑⠦⣀⠀⠀⠙⣄⠀⠀⠀⠀⠔⠀⠀⠀⠀⠁⠢⠀⢀⠇⠀⠀⠀⠣⠼⢀⠜
⠀⠀⠀⠀⢠⠁⠀⠀⠀⠙⢄⡀⠀⠀⠀⠉⠛⠛⠈⠑⠢⢤⡄⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⡠⡀⠀⠀⠀⡏
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠉⠒⠒⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢰⠁⡇⠀⠀⠀⢰
⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠎⣠⠃⠀⠀⡰⠃
⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢀⠀⡠⠉⠁⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠈⠉⢁⣀⠀⢰⠁
⠀⠀⠀⠀⠀⢈⠆⢈⠀⠐⠀⠌⠀⠀⠀⠀⡈⠈⠉⠁⠀⠀⠀⠀⠀⡴⠋⢣⠀⢸⠀⠀⠀⢎⡠⠃⡇
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡎⠀⡸⠀⠀⠀⣀⣀⡜
⠀⠀⠀⠀⢀⡸⡆⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠞⠀⢰⠁⠀⢀⠞⠁⠈⢆
⠀⠀⢠⠚⠁⠀⡄⠀⠁⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⡇⠀⢸⠀⢀⠎⠀⠀⠀⠈⡆
⠀⢠⠃⠘⠓⢄⡧⠈⢀⣀⣀⡀⠀⢀⣀⠤⣀⣀⠀⠀⣀⣀⡀⠀⠙⣋⡀⠀⢠⠂⢸⠀⠀⠀⠀⠀⡇
⠀⠈⠃⠀⠀⠈⠀⡴⠁⠤⠤⠬⠉⠉⠀⡲⢶⠦⠭⠭⠤⠤⠬⠽⠉⠀⠨⠥⢭⡥⢽⣦⣔⠀⢰⠞
⠀⠀⠀⢀⠀⠀⠀⢳⠀⠀⠀⠀⠀⢠⠞⠁⠉⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠁⠀⠐
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠤⠜⠀⠃⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠆

⠀⠀⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠂⡰⠂⠀⠀⠀⠀⠀⠀⠀⠐⠒⠐⠲⠂⠂⠂⠀⠀⠀⠐⠒⠒⠂⣢
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢹
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠁⠒⠒⠁⠄⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠂⠀⠀⠀⠐⠤⡀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠰⠡⠤⢄⠀⢠⠒⠈⠉⠀⢸⠀⠀⠀⠀⠀⠐⠀⠀⠀⠰⣿⣿⡄⠁⠀⠀⠀⢰⣾⣿⡆⠁⠀⠀⠀⠀⢼
⠀⠀⡇⠀⠀⠀⡏⠐⠉⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠆⠀⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⠀⠀⠀⠙⠛⠈⠀⠀⠀⠀⠀⣸
⠀⠀⡇⠀⠀⠴⠥⡀⢀⠄⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⡇⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡁⠁⠉⢨⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⢁⠀⠀⢀⡑⠆⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠐⠒⠒⠀⠄⢄⣀⣀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⢀⠠⠤⠀⠠⡤⢒⡭⠀⠤⣉⡢⠀⠈⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⣀⠔⠊⢹
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠴⢅⣠⠊⠁⡀⠤⠠⠮⠜⡁⠈⠢⡀⠈⡄⠀⠀⠀⠀⠉⠒⠲⠤⠀⢀⣀⣀⣀⣀⣠⠤⠀⠒⠉⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⠊⢀⡤⢲⠂⢲⡍⢦⠈⠀⠀⠀⠀⠀⠨⣶⣄⠱⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡅⢀⠎⠀⢸⠀⢘⢸⠓⠃⠀⠲⣦⠀⠀⠀⠀⡠⠛⠣⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠐⠚⠀⢀⠘⡀⠘⡼⠀⠀⠀⠁⠀⠀⠀⠀⠀⠣⣀⣠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⡀⡤⠐⠉⠉⠙⡄⠹⢆⡀⠀⠘⠧⣀⠀⠀⠀⢀⡠⡺⠁⠀⠀⣀⠤⢄⠐⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⢀⠤⠂⠁⠀⡇⠀⠀⠀⠀⠈⠢⣄⠙⠢⠤⠱⠤⠳⠄⠂⡡⠶⠄⠲⠊⠁⠀⠀⠈⢢⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⢀⠾⠁⠀⠀⠀⠀⠱⠀⣀⡤⢀⠀⠀⠀⠉⠐⠆⠒⠂⠐⠊⠁⠀⠀⠀⠀⡇⠀⠀⣀⠴⠊⡠⠔⠂⠀⠐⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⢀⠃⠈⢇⠀⠀⣀⡤⠒⠉⡐⠁⠐⠀⡀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠇⠒⠉⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠈⠱⡀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠈⠦⠠⠤⠓⠉⠠⠀⠀⡴⠠⠤⠄⠀⣀⡀⡐⠀⠀⠁⠀⠀⡐⠁⠉⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⢀⠎⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢌⡀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠬⠢⢄⡀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢀⡀⠤⠒⠈⠁⠀⠀⠀⣀⠨⠖⠀⢸
⠀⠀⡇⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⢀⠔⡛⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣀⠤⠐⠊⠁⠀⠀⠀⢀⡠⠄⠒⠉⣈⠆⠀⠀⢸
⠀⠀⡇⠀⠀⠀⢠⠎⡀⠀⠀⠀⢀⠔⢁⡔⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⠀⢀⡠⠄⠒⠉⣁⠠⣴⠌⠬⠁⠀⠀⠀⢸
⠀⠀⡇⠀⠀⠀⡁⠀⠈⢓⡤⠒⠁⣠⢎⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠤⠒⠈⢀⠠⣤⣂⠹⠓⠂⠁⠀⠀⠀⠀⠀⠀⢸
⠀⠂⡇⠀⠀⠀⠈⠉⠈⠁⠀⠀⠠⡁⠀⢈⡱⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠂⠣⠠⠀⠀⠀⠀⠀⠀⠠⠤⠠⠌⠁⠀⠠⠠⠤⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠄⠀⠀⠀⠤⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠜

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢀⡀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠘⠁⢀⣸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡇⣴⣿⠇⠘⠻⣷
⠀⠀⠀⠀⠀⠀⠀⢠⠁⠟⠁⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡠⠐⠢⡔⠉⠑⡄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠰⠀⠀⠀⠀⠀⢀⣐⠄
⢀⣀⢀⣀⣀⣠⣀⢸⡀⠸⣠⠴⠶⢛⡉⠛⠉⠒⣄⠐⠒⠒⡀
⠊⠏⠀⠀⢀⣀⠠⠴⡆⠀⠐⠒⠲⢆⠈⠀⠠⠞⣠⢗⢩⣑⡧⠐⢒⣄
⠨⣀⡤⠚⠉⠀⠀⠀⡇⠀⠀⠀⠀⠀⢃⠀⠀⠀⠓⣻⣓⣦⠶⠎⡷⠓⠒⠤⣀
⣴⠁⠀⠀⠀⠀⠠⣠⠇⠀⠀⠀⠀⠀⠊⠀⠀⠘⡒⠉⠉⠱⡀⣼⠀⠀⢃⣀⣈⠳⡀
⢸⡄⠀⠀⠀⠀⠀⠈⠛⠄⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢁⠈⠓⢚⠃⠀⣀⣉⡓⣄
⠀⠱⡄⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡠⠐⠭⠓⠉⠉⠀⠀⠈⠉⠳⡀
⠀⠀⡙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⢄⡠⠃⠀⡀⡀⠀⠀⠀⠀⠙⢄⠀⠁⠘⣆
⠀⢠⢁⢫⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢔⠕⠉⠀⠀⡞⠀⡇⠀⠀⠀⠀⠀⠀⡃⠀⠀⠘⡆
⠀⡏⢹⠀⡆⠂⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⡡⠋⠀⠀⠑⠚⠁⢰⡀⠀⠀⠀⣀⠤⠚⠁⠀⠀⠀⠧⢀⣀⡀
⠀⠀⠆⠀⠺⡜⡀⠀⠈⡇⠀⠀⠀⠀⠠⡱⠁⠀⠀⠀⠀⠀⠀⠀⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠈
⢼⣸⠀⠀⠀⠅⢁⠀⠀⣧⠀⠀⠀⢀⢁⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⡤⠚⣤
⠀⠀⠀⠀⠀⠫⠈⡄⠀⠸⡄⠀⠀⠈⠸⠀⠀⠀⡠⠢⡀⠀⡠⣄⠀⠈⠑⠲⡀⠀⠀⠀⠀⠀⡞⡴⠁⠀⠘
⠀⠀⠀⠀⠀⠀⢳⡻⡀⠀⠹⡄⠀⠀⡇⠀⠀⠐⠀⠀⢇⢈⠁⠀⡱⠚⢧⠀⡇⠀⠀⠀⢀⠎⢸⡀⠀⠀⠖
⠀⠀⠀⠀⠀⠠⣁⡍⢊⡑⡀⠘⢦⡀⢻⠀⠀⠀⠀⠀⠀⠉⢀⡜⠁⠀⠀⢻⠀⠀⣠⠖⠻⣄⣀⡼⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⡀⢄⠈⠛⠧⡀⠐⡀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠓⠉⠀⠀⠀⠀⠀⠉⠢⢵⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢍⠢⠀⠈⠒⠳⠄⠧⣀⢉⣦⡀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠴⠆⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣑⠄⠀⠀⢀⣈⠉⠤⠸⢦⣀⢀⡜⠉⠁⠀⠀⠀⠀⠘⠦⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡋⡋⠉⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠂⠒⠲⠴⣋⠉⠉⠉⠓⠢⣄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡤⠖⠊⠉⠉⣿⡀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⡞⣩⠔⠋⠉⠉⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⠀⠀⠀⠉⠓⢤⡀⠀⠀⣸⠿⠒⠋⠉⠉⠑⣄⣸⣄⣀⣠⠟⠁⠀⠀⠀⠀⣼⡷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣬⣙⡒⠤⠤⣀⣀⣙⣄⡞⠁⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⡇⠀⢀⣀⣀⣠⠾⠟⣚⣩⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢣⢿⠀⠉⠉⠒⠒⠢⠬⠭⢍⣉⣉⣉⣛⣛⣛⣛⣛⣛⣋⣉⣉⡉⠭⠥⠔⠒⠚⠉⠁⡟⢌⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢇⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⢎⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⢀⣸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢮⠛⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⣧⠸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢸⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⡄⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⡇⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠃⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡆⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢣⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢧⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠈⢦⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠈⠣⡘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢡⠎⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⠀⠀⠀⠙⢦⡙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⢋⠴⠃⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠉⠲⢌⡙⠲⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠤⠒⣋⡤⠞⠁⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠈⠙⠒⠦⠬⠭⣉⣉⣉⣉⣉⠭⠥⠤⠖⠒⠉⠁⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠦⠤⢄⣀⣀⣀⣀⣀⣀⣀⡠⡤⠴⠒⠊⠁



⡿⠉⢹⡟⠿⠻⠿⠟⠿⡛⠿⠻⠟⠿⠟⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⡿⣿⣿⣿⡿⣿⠿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⡀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢒⣻⣍⡙⢢⡀⢰⡖⣛⣋⣉⣉⡄⠈⢉⣀⣉⠻⠁⣭⡍⣧⠀⢀⡏⢩⣛⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⣼⠃⠀⠸⣿⠀⠣⡾⠀⣿⡋⠉⠙⠃⠀⠀⣿⣿⣧⠀⠉⣿⡜⢦⡼⠀⢸⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠰⣿⠀⠀⠀⠀⢀⡀⠀⠀⣿⡇⠀⠀⠀⠀⢠⣿⠀⣿⠀⠀⣿⣧⠀⠀⠀⢸⣿⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠙⠓⠒⠚⠉⠉⠙⣷⡄⣿⡇⠀⠀⠀⠀⢸⡟⠀⢿⡆⠀⣿⣿⡀⠀⠀⢸⡏⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣥⣀⠀⠀⠀⠀⠀⠀⣿⣧⣿⡇⠀⠀⠀⠀⣾⡇⠀⢸⡇⠀⣿⡟⣇⠀⠀⢸⡇⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢿⡏⠀⠀⠀⠀⠀⠀⣿⡇⢹⡿⠛⠃⠀⠀⣿⣇⣀⣸⣿⡀⣿⡇⢻⡄⠀⣸⢃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡈⠳⡀⠀⠀⠀⠀⣰⠟⠀⢸⣧⣤⣤⣴⠀⣿⡏⠉⢹⣿⠀⣿⡇⠈⠻⡶⢏⡼
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠁⠀⠀⠉⠐⠂⠉⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣋⣀⡀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⣀⡥⠤⣒⠒⠛⠛⠳⣦⡄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⠀⡀⣀⠀⠀⢀⣀⠀⠀⣀⡀⠀⢀⠀⢻⠀⡇⣶
⠀⠀⠀⠀⠀⠀⠀⠡⢤⠀⣏⠀⠀⠀⠀⢸⣿⡆⢀⡞⠹⡄⠿⠛⠛⡟⠛⠛⠱⡇⠈⣧⠀⠈⡇⠀⡞⠁⠁⠀⢸⡇⠈⠉⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣿⠀⠀⠀⠀⢸⣿⠃⣾⠁⠀⣧⠀⠀⠀⡇⠀⠀⠀⡇⠀⣿⡆⠀⡇⢠⡇⠀⠀⠀⢸⡇⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⠀⠀⢀⡰⠟⠁⢰⡇⠀⠀⣿⠀⠀⠀⡇⠀⠀⠀⡇⠀⣿⡇⠀⡇⠈⡇⠀⠀⠀⢸⠇⠀⢠⠏⠠
⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⣿⡤⠖⠉⠀⠀⠀⣸⠇⠀⠀⣿⠀⠀⠀⣧⠀⠀⠀⡇⠀⣿⠁⠀⡇⠀⡇⠀⠀⠀⢸⠀⣰⠏⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢻⡆⠀⠀⠀⠀⠀⣿⠖⠒⠋⣿⠉⠀⠀⣿⠀⠀⠀⣿⣰⠏⠀⠀⣧⠀⣧⠀⠀⠀⢸⣾⡁⢾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢸⡇⠀⠀⠀⠀⢠⣿⠀⠀⠀⣿⠀⠀⠀⣿⡀⠀⠀⣿⠳⠤⣤⡄⣿⠀⢿⡀⢀⡄⢸⠀⠹⡎⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠸⠿⠀⠀⠀⠀⠸⠟⠀⠀⠀⠛⠂⠀⠀⠙⠃⠀⠀⠉⠀⠀⠀⠀⠛⠂⠈⠉⠉⠀⠈⠀⣀⣉⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡤⠶⣶⠀⠤⢤⠤⠤⢤⣀⠀⠀⠀⠀⢀⣤⠀⠀⣤⠀⠀⢠⡶⠀⢰⡶⠶⠶⠶⠦⢤⣀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠲⡆⢸⠀⠀⠀⢹⣷⡀⠀⠀⣾⠹⡇⠀⢸⡆⠀⢸⡇⠀⢸⡇⠀⠀⠀⠀⠀⣿⡧⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⣿⡇⠀⢰⡇⠀⣿⠀⢸⣷⠀⠈⡇⠀⢸⡇⠀⠀⠀⠀⠀⣿⠃⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⢠⡟⠀⠀⣼⠃⠀⣿⠀⢸⠸⡄⠀⣷⠀⢸⡇⠀⠀⠀⠀⣰⠏⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⣀⠴⠋⠀⠀⠀⣿⠀⠀⣿⡀⢸⡆⢧⠀⣿⠀⢸⡇⠀⠀⠀⣰⠃⣰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⠟⠛⠛⠲⢦⣄⠀⣿⠀⠀⣿⡇⢸⡇⠸⡆⣿⠀⢸⠀⠀⢀⡜⢁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡄⠀⠀⠀⠀⣿⡇⣯⣤⣤⣿⣧⢸⡇⠀⢿⣿⠀⢸⠀⣠⠎⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣇⣀⣀⣀⣼⠟⠁⠏⠀⠀⠻⠇⠸⡷⠀⠘⠿⠀⠘⠔⢁⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠉⠉⠉⣀⣠⢤⣄⣀⣤⡤⠤⠤⠶⠶⠶⠶⠴⢤⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⢺⣍⣭⡓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⢄⣀⠀⠀⠀⠀⠀⠀⡰⠃⠀⡼⣿⣯⠀⠘⢄⣀⣤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⢀⠀⠀⠈⠓⠦⢤⠤⠤⠚⠁⡠⠄⢽⢣⠁⡀⠀⢴⢸⢀⠀⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⡠⠤⡖⠒⢠⡨⡍⡷⢁⠠⠀⡆⢏⠛⣺⠀⠈⠢⠀⠸⡘⡀⠀⢀⡤⠃
⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⡍⠡⢇⠈⠈⠃⠄⣣⣀⣀⣀⣁⣠⣤⠶⢷⠶⣶⡶⣶⢟⢿⣠⠋
⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⢰⡶⢾⣟⢿⢻⢻⣏⢻⢉⡏⢉⡇⢜⡏⢸⣆⠙⡇⢾⡮⢹⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢸⡯⠽⡾⢾⡜⢸⡔⢸⣸⣿⣍⣧⣿⣷⡾⣿⢗⠛⠺⠓⠛⠁⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡜⠳⠚⠛⢻⡿⠿⢿⣋⠉⠁⠀⡠⠚⠉⠁⠀⠈⠉⠉⠓⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠊⠁⠀⠀⠀⠀⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡄⠰⠜⠀⠃⠀⠀⠀⠀⠀⠢⢬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠘⠃⠀⣤⡁⠐⠿⠀⠐⣀⠀⠀⠀⡘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠈⠀⡠⠀⠀⠉⠀⠂⠄⠀⢴⡁⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠌⡒⠀⠀⠈⠀⠆⠀⠀⠀⠰⣌⣀⣀⠀⢤⠒⠋⠀⠀⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠀⠀⠀⠘⢿⣿⣦⣾⣿⡇⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡕⠀⠀⠀⠈⠃⠀⠙⠛⢛⣋⠅⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣖⣀⣀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣶⣤⣶⣶⣾⣿⣿⣿⣿⣿⣧⡄⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣴⢷⠈⣿⣿⡿⠿⠛⠛⠉⠉⠁⠈⠻⠟⠃⠤⠀⢻⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠰⠄⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⡿