Aquatic plant Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠠⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠮⡀⠀⢀⢄⠂⡄⠁⡠⠒⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢦⢄⠘⣷⢡⣴⡡⣛⠀⢄⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠰⠼⢄⣤⠑⡀⠢⢤⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⢀⣂⡇⠐⠀⡠⠒⠂⠁
⠀⠀⠀⠀⠀⠀⠀⢋⡀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠢⡀⠐⠈⢛⠘⠩⠠⠐⠉
⠀⠀⠀⠀⠀⠀⡂⠈⢷⡎⡰⠉⠄⢊⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⢀⠀⠀⠼⠿⠦⠔⠃⠀⠤⠄
⠀⠀⠀⠀⠀⠀⠸⡀⠢⣽⡡⠬⢖⢋⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠉⠳⠴⡶⠤⢤⠖⡫⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠰⢤⣀⣦⠖⠜⡑⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠢⣤⢴⢠⡶⢆⠠⠀⠀⡠⠄
⠀⠀⠀⠀⠀⠀⠀⢀⡱⢤⡌⣦⢀⠐⠨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡂⠈⢦⣴⢃⠀⡠⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢁⠘⣡⣶⠁⠀⠄⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⣠⠁⠀⢢⠨⠐
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⢂⢨⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⡈⢠⣯⠀⠀⡁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢤⡀⠄⢙⠇⠠⢸⠊⠁⠀⠀⠀⠀⠀⠀⠀⡀⢈⠃⣼⠔⠀⡐⠂⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠡⣸⠗⠗⢓⠂⠀⠀⠀⠀⠀⠀⠀⠑⢄⠑⠳⠏⣀⠊⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠔⢀⣼⠁⠐⠀⠀⠀⠀⠀⠀⠀⠉⠐⢔⢆⠣⣿⢄⡀⠋
⠀⠀⠀⠀⠀⠀⠀⠄⠈⠠⣨⡅⢀⣠⠊⠀⠀⠀⠀⠀⠀⠃⠄⠈⢺⣞⠁⠀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⢄⠉⠃⢭⡄⢠⣤⠌⢀⠀⠀⠀⠘⢄⡀⢀⡜⠁⠀⢀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠰⢌⠄⢺⠀⣀⠠⠔⡁⠀⠀⠀⢖⠂⠈⢙⡃⠜⠉⠃⠆
⠀⠀⠀⠀⠀⠈⠂⢅⠈⠁⢈⣯⠀⠈⠐⠁⠀⣀⠀⠲⢱⣢⡿⠁⠚⠉⠁⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠛⠇⠀⠀⠀⠀⠀⠠⡀⢐⠣⣆⡤⢖⠋⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠸⣿⡄⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⢀⣤⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡆⢀⡄⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⣰⠟⠁⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠰⠆⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠄
⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⡏⣇⡂⡀⡃⠄⠀⠀⠀⠀⠀⠜⣶⡱⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡎
⠀⠰⢯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⡇⡟⡇⢱⠁⠀⠀⠀⠀⠀⠀⠀⣙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⢸⢀⡔⠁
⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⡀⠟⡇⡅⡇⡄⠀⠀⠀⠀⠀⠀⠀⢜⢰⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢀⣠⡤⠤⡀
⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⡀⠀⣄⠁⡇⠘⠂⠀⠀⠀⠀⠀⠀⠀⢈⡃⢐⣠⠀⢀⡀⠀⠀⠀⠐⠈⠻⣾⣷⢋⡠⠄
⠀⣴⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡟⠀⡇⠉⡇⠀⡀⠀⠀⠀⠀⠀⠀⠱⡙⠃⠀⠀⠈⠀⠀⠀⠀⠛⠙⢿⡷⠋
⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁




⠀⠀⠀⠀⡄⠀⢀
⠀⢀⠀⠀⡇⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴
⢀⠸⡄⠀⠁⠼⠃⢠⡞⠀⠀⠀⠀⢀⢠⠠⠁⠌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢂
⠈⣇⠁⠀⠅⢔⢠⣿⡾⠀⠀⠀⠀⠀⠀⢐⢀⠀⠀⠆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣀⣰⡈
⠀⢙⡈⠀⠘⡁⢚⠟⡃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠠⠂⠀⠀⡀⠀⠀⠀⠀⠀⢠⣴⣶⣶⣤⡀⠀⠀⠀⢠⣤⣤⡀⠀⠀⠀⠀⠠⢤⣿⢃⡠⠊
⠀⠈⣁⡰⢺⡶⠖⠋⠀⠀⠀⠀⠀⠤⡒⢔⠋⠀⠀⠂⠁⠀⠒⠁⠀⠀⠀⠀⠀⠀⠛⠻⠛⢛⣧⣧⣤⡶⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⣟
⠀⠀⠈⣣⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⡗⠀⠀⠄⠀⠒⣤⠀⠀⠀⠁⠀⠀⠰⢿⣿⢆⡈⢿⣿⣿⣗⣾⣿⣿⣿⣶⡄⠀⠀⠀⠩⢕⣷⣆
⠀⠀⠀⠬⠿⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠢⠀⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⠇⠀⠀⠀⠀⠻⠿⠿⣿⡿⠇⠀⠀⠀⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⠄⡀⠀⡄⠢⡁⠀⠔⠈⢀⡀⠜⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢀⠀⠑⠈⣄⠄⠇⠀⣰⠡⣤⠒⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢗⠢⢄⠹⡟⢰⣾⢅⠬⠡⠌⡒⢌⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠘⡕⡼⠀⣴⡀⠚⡀⠒⢬⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⢄⠠⡀⡎⢁⠆⠀⠀⠠⠄⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢀⠈⠐⠳⣧⠥⠤⠔⠓⠒⡲⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⠄⡠⠂⣡⡴⠷⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⢄⠑⠤⡀⠈⠀⣀⢀⠐⢉⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠘⡑⠤⠙⣽⡇⡘⠁⡠⠊⢁⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠢⡀⠈⠒⠲⠟⠺⠖⠋⢀⡠⠔⠒
⠀⠀⠀⠀⠀⠀⠀⠀⢬⠂⠠⣈⣿⣁⢄⡵⠪⠋⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠙⠱⣌⣦⡀⠴⣅⣠⠶⠣⠤⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡒⠒⠈⡁⣠⠀⡠⠪⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢔⡂⢉⠠⡀⢌⣅⡊⠐⠡⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠛⠲⢺⣋⠄⠠⠃⡀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⢻⠛⠁⢚⢉⠅⠊⠁⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠛⣮⡢⢿⠒⡀⠈⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢣⠑⠌⠫⢶⠯⠠⠀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣁⡘⢤⣾⡆⠠⢈⠄⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠈⠀⠊⠀⢀⢤⡩⠍⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠐⠢⡌⠉⡁⠐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠃⢀⣿⠁⢀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣿⡠⢈⢠⢤⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖⠄⠘⠋⡀⠤⢒⠀⠒⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠠⠌⡐⢠⣄⢀⠁⠡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠤⠤⡀⢇⢤⡧⠊⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠘⢤⠟⡫⠀⢀⠟⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠑⢄⠀⠀⠸⠥⡀⠉⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡢⠀⣰⢊⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠢⡑⡆⠡⣰⣧⡌⠀⠜⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠈⠺⠏⠡⠐⢂⡐⠃⠀⠀⠀⠀⠀⠀⠐⢆⡐⢄⠐⢼⣀⠏⠀⠉⡁⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⢄⡀⣴⠧⠀⠒⠇⠤⡄⠀⠀⠀⠀⠀⠄⠠⠠⠈⠄⢰⠜⠓⢂⢀⢈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢀⠀⠀⢲⡶⠀⣻⠶⠊⢀⠄⠀⠀⠀⠀⠈⠢⢕⢀⣘⡁⠀⠁⢀⠴⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⠀⣈⢺⡄⢈⡀⠤⢐⡁⠀⠀⠀⠀⠐⡀⠀⠀⠉⣛⠡⠄⠭⠉⡰⠂
⠀⠀⠀⠀⠀⠀⠀⠒⠅⡀⠀⠀⠐⡀⠟⡁⠠⠦⢀⠌⠀⠀⠀⠀⠰⡌⡂⠀⣰⡟⢁⠒⠒⠊⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠌⠁⠸⢷⡷⠡⠐⠁⠀⠀⠀⠙⢌⠢⠑⣈⣂⢻⠀⢁⢀⣤⠴⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠣⡐⠢⠠⣹⠾⠃⠡⠒⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠪⢻⣷⠥⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⡀⠀⠀⠈⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⢀⡒⢬⠀⠀⠀⢀
⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠠⠄⠀⠀⠠⢭⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⣧⣉⠇⠀⠀⢀⣌⡂⠀⠀⠀⠀⠂⣁
⠀⠀⠀⠀⠀⠰⠒⣀⠀⠀⠀⠀⠀⠤⠀⠀⢐⠂⠀⠀⠐⠖⠁⠀⠀⠀⠀⠀⢰⡀⢒⢀⠀⢾⣿⡁⠀⠀⠠⢵⠣⠄⠀⠠⠄⠀⢈⣁
⠀⠀⣂⣀⠀⢈⣩⣡⢀⡠⠠⠀⠀⠒⢄⠀⠤⠀⠀⠀⠘⠒⠀⢠⠤⢀⠀⡐⠒⠀⠀⠒⢠⡄⣠⠄⠀⠀⣉⠈⠀⠡⣦⣍⠀⠀⢀⣀
⠀⠀⠐⠒⠀⡤⠤⢴⣾⣌⠙⠀⢂⡙⢄⢰⣤⡓⢀⠀⢈⡁⠂⠐⢚⡭⢀⢈⡩⠥⠀⠈⠁⣿⠦⠈⡁⠀⠨⠀⠀⠐⠓⠖⠀⣀⠠⡀
⠀⠀⠀⠉⣹⣒⠒⠾⢧⢤⣓⠀⡉⠻⣿⡜⢣⠀⢒⡲⢀⡤⠉⠀⠚⡴⠬⣂⡴⠒⣂⡀⠀⠃⠶⠂⠀⣀⠂⠠⠀⠀⠈⠁⠴⡟⠲⠐
⠀⠀⠠⣜⠉⠓⢶⡣⣬⣶⣀⠈⠁⠀⣀⢉⠁⠀⠶⠄⠀⠀⣀⠀⢀⣤⡦⠠⠐⠉⢀⠄⠀⡀⢀⢀⡄⠡⠍⣀⠀⠀⠀⠀⠂⠈⠒
⠀⠀⣤⡈⠉⠂⠍⢀⣠⠊⠀⠀⠀⠀⣈⣉⠀⡑⠂⠀⠀⠀⠀⠠⢜⠧⡄⠀⠀⠀⠅⣠⠞⢁⣀⠀⠀⡤⠚⠍⠀⠷⠅⠀⠒
⠀⠀⠀⢩⠁⠒⠀⠀⠆⠄⠀⠀⢀⠀⠄⡘⠢⠥⠀⠀⠀⠀⠀⠀⠀⠒⠢⠀⠀⠀⠀⡀⠄⠎⠁⠀⠀⠂⠐⠀⠀⠄⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢙⢆⠀⠀⠀⠀⠀⠀⠀⡼⡁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢸⠈⡌⠣⡀⠀⠀⠀⢠⠞⠀⡇⠀⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡇⠀⠘⡄⠙⣄⢀⡔⠁⠀⣰⠃⣰⠃⠀⠀⠀⠀⠀⠀⣀⣴⠁⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠹⡄⠘⣾⠀⠀⣰⢃⡴⠃⠀⠀⠀⢀⣠⠴⠊⡽⠈⡆⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⡇⠀⠀⠀⢹⡀⠸⣆⢰⣷⠋⠀⠀⢀⡠⠖⣹⠃⠀⡼⠁⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡇⠀⠀⠀⠀⢣⠀⢹⡘⡏⠀⠀⣰⠋⠀⢰⣃⡤⠞⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡇⠀⠀⠀⠀⠘⡄⠀⣇⣷⢀⡜⠁⠀⠀⡏⢁⣠⠴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢸⠀⢳⠀⠀⠀⠀⠀⢱⠀⢸⣏⡞⠀⠀⠀⠀⡏⢉⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡶⢶⣒⡒⠲⢬⡆⠘⡇⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⠀⠀⡿⠓⠒⢤⡀⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠢⣕⢝⣄⢹⡀⠀⠀⠀⢸⠀⠀⡇⠀⠀⠀⠀⡴⡏⠒⠒⣚⠁⢂⡤⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⡖⠒⠒⣒⠒⠲⢤⣈⢺⣎⢦⣇⠀⠀⠀⢸⠀⢀⡇⠀⢀⡤⠊⢰⠛⠛⠛⠒⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠈⢛⢯⡉⠙⠳⣽⡌⢿⡄⠀⠀⡆⠀⣼⡠⠖⠉⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⢄⠁⢙⠦⣀⠘⡏⠛⢷⡀⣰⠁⣰⡏⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠦⣍⣒⣥⣮⣿⣿⡄⠀⠳⡗⠚⠁⠉⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠈⢦⡀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢸⠀⠀⠀⡼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣳⠈⡇⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇⢸⢀⣶⠀⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠇⢻⡆⢡⠀⢸⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⡆⡇⡀⢸⡾⢠⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡇⡇⠀⠀⠀⢣⢸⣇⢸⠀⢸⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⢀⠀⡇⡇⡇⣜⡇⢸⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⡀⡇⢫⠀⢸⠑⣼⠀⣿⢸⡶⣼⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢱⠘⢀⠇⡇⡇⣿⠁⡇⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢃⢣⠈⡆⠈⠳⡜⢧⠁⡼⡇⡿⡸⢀⡠⡄⠀⠀⠀⠀⠀⠀⠀⢸⢸⠀⣿⠀⠇⢴⢿⡸⢠⢃⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣎⢿⡆⢸⠀⠀⠈⡆⢠⢣⠃⢣⡧⢊⠔⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⣇⢸⣄⠇⣿⠀⡇⠸⠏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡙⠀⡇⠀⢠⢃⣮⠎⢀⡮⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣧⡘⣮⠻⡆⢹⢰⡇⡆⣆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢳⣠⠃⡜⠁⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡷⡵⡜⠃⢹⢸⠀⡼⡜⡽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⢠⠏⡜⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠮⣛⡀⣿⢸⠀⠟⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⣼⠠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣜⡤⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡇⠀⠀⠀⡀⢠⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡇⠀⡿⢿⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣷⢆⠀⠀⣿⠈⢆⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⠐⠈⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡏⣼⠀⠀⡇⡇⠸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⡇⢸⡄⠀⡇⢸⢸⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠠⠀⠀⠀⠀⠀⠁⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⡇⢸⠁⣠⠇⣼⡜⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠆⠀⠀⠀⠀⠀⠃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⢧⢸⠰⢁⡜⢹⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⠠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡸⢘⠈⢁⠎⢀⠎⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇⡸⣰⠁⢀⠜⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡱⡁⡇⡰⠃⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⡇⡷⠃⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣇⡜⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢻⣷⣠⡄⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢯⡀⡿⠁⠀⢸⣿⡀⢀⣀⣀⡿⡏⢰⣤⣟⡬⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡻⣿⠂⣼⢀⡭⠿⠟⠓⠲⠿⢏⡇⠻⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⢳⡙⠞⠁⡸⢤⡀⠀⠀⠀⠀⣼⣿⣉⠛⠁
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢥⡳⣬⠇⣰⠋⠉⠛⠃⢰⣦⠀⣸⢣⠟⣾⣣⡄⣶⢻⣤⣶⡆
⠀⠀⠀⠀⠀⠀⢀⣸⣏⠣⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⣴⣚⣁⣀⡐⣇⠀⢠⡶⣤⣸⡿⣤⠏⡞⠀⣿⢹⡥⠋⣘⣿⣥
⠀⠀⠀⠀⠀⠀⠘⠲⠖⠲⣅⠸⡄⢀⡶⡄⢀⣤⣀⠀⠉⣩⣄⠈⠹⣌⢧⠀⠉⠓⢮⣄⠀⢸⣷⣻⠿⠒⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠇⠙⠞⢸⡁⠈⣛⡿⠓⠚⠋⢧⡀⠀⠘⡎⢧⠀⠀⠀⢘⡇⡴⠋⠀⢀⣤⣶⠀⡶⣄⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣉⣉⠉⠓⣦⢉⣉⠉⣰⠚⠉⠳⢤⡙⠓⠦⠟⠸⣆⠰⢿⣚⠃⣧⢀⣠⠞⢻⣥⡄⣧⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠓⣿⠛⣫⠟⢋⣩⠇⠹⣄⠀⢠⡴⣣⠴⠶⠶⢤⣌⠳⡄⠈⣧⠛⣿⠞⠉⠉⠉⣰⠟⣛⡿
⠀⠀⠀⠀⠀⠀⠀⢙⡿⣻⡿⡇⢸⠁⠀⠻⠞⡧⣶⠚⠁⠀⠉⠁⢀⣠⡀⠀⢈⣳⠙⢦⣸⠀⡇⠀⠀⢠⣞⡷⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠙⠛⠀⠀⠀⠀⠓⠋⠀⠀⠀⠀⠀⢈⣿⠙⠒⠋⣉⣄⡀⠛⢰⠇⣴⣄⡞⢾⣤⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢭⣭⠉⣠⠖⠛⢷⡇⠀⢳⠀⣾⠀⡏⢋⡴⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣡⢶⢿⠀⠀⠀⠀⢀⡼⠀⠹⠴⠃⣞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠁⠘⣻⠖⠋⠉⠉⠻⡄⠀⠀⠀⠀⠘⣦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡇⠀⠀⢠⡴⠚⠛⢲⣄⣀⣴⠋⠉⠈⠙⣿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠿⣄⣀⣀⡤⠏⠁⠘⠶⠤⠶⠚⠁




⣿⣏⢹⣟⠻⣿⣛⠟⣻⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⢁⣴⠖⠂⠐⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦⣥⣵⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⠂⠈⠀⣠⠀⠈⠀⠄
⠀⠀⠀⠀⠀⢠⣿⠁⠀⠉⠂⡀⠻⣆⠀⠀⠀⠀⠀⠀⠀⢺⣽⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⣿⠀⠀⠂⡼⣇
⠀⠀⠀⢠⢇⣼⣿⡀⠀⠀⣄⠉⠖⢢⠀⠀⠀⠀⠀⠀⠀⡏⢝⣿⣽⣿⡄⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⢟⢠⢀⡀⣇⣿
⠀⠀⠀⡰⣿⣾⠯⠗⠖⢦⡐⠀⣿⡏⠀⠀⠀⠀⠀⠀⢸⡆⠐⣿⠇⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⡐⣁⢿⡟
⠀⠀⠀⠈⠉⠙⡱⣯⣋⠹⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⢸⣀⠠⢝⣳⠛⠏⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠈⡘⣷⠟⠁
⠀⠀⠀⠂⠄⠀⠚⠿⢛⣷⡞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠀⠘⢉⡽⠃⢐⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⠀⠈⢸⡟⠁
⠀⠀⠀⠀⠘⡆⡁⠐⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣁⠀⣿⡇
⠀⢀⠀⠀⠀⠀⡀⠐⢺⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠈⡇⢠
⠀⠐⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⢰⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⣵⢾⣿⣾⡽⡀
⠀⠀⣠⠖⠾⣷⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣦⣿⣯⣛⡛⢅⣾⣥⣄⡀
⠀⠸⠁⠤⠈⣹⢦⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⣽⣧⣿⣏⣻⣟⡹⢿⣯⣽⠝⢧⠀⢠⠀⡀
⠀⢸⡆⠈⣧⣾⠙⢓⡇⠀⠀⠀⠀⠀⠀⠀⠀⢨⠦⢟⢰⣥⡉⢻⡿⣽⠌⣿⣿⠗⠀⠀⠀⠀⠁
⠀⠀⠙⠾⢿⣾⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⢊⠘⣻⠇⠸⡇⠙⢷⣑⣸⠖⠃
⠀⠘⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⡀⠀⠀⢀⣰⣿⣶⠤
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣑⡓⢹⢇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣷⡆⠂⢰⣿⠿⠇⠀⠀⠀⠟⠹⠹⠂
⠀⠀⠀⠀⠀⠀⡦⠀⠀⠀⠀⠀⠀⠀⠀⡇⠐⠸⣗⣨⡆⠀⠀⠀⠀⠀⠀⠀⠠⠛⠉⡙⠀⠈⠁⢸⠀⠀⠀⠀⠀⠇⠀⠁
⠀⠀⠀⠀⠀⡰⠅⠀⠀⠀⠀⠀⠀⠀⢀⢹⡀⠘⣯⡾⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⠸⠀⠀⠀⠀⢰
⠀⠀⠀⠀⡐⡌⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⣰⣿⣴⠟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⡆⠀⠀⠀⡇
⠀⠀⠀⠐⢿⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⢘⠀⢀
⠀⠀⠀⠉⣛⣘⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⢀⠀⠻⠀⠆
⠀⠀⠀⠈⠉⠁⣄⣀⡀⠀⠀⢠⣾⣿⣿⣄⠴
⠀⠀⠀⠈⠓⡔⡜⠉⠀⠀⠀⢺⣿⣿⣱⣟⠀⠀⠀⠀⠀⠚⢓⣠⢤⣒⡶⠖⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⡖
⠀⠀⣉⡛⠆⡹⠁⠀⠀⠀⠀⠘⣿⣿⣾⠏⠀⠀⠀⠀⠀⢠⣶⣶⣿⣷⣟⣙⣦⠀⠀⠀⠀⠀⢠⣤⠿
⠀⢤⢬⡉⣿⠷⠚⠀⠀⠀⠀⠀⠈⠹⠁⠀⠀⠀⠀⢀⣤⣿⢿⣿⠿⢿⠉⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⣄
⠀⠀⠤⢤⢏⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠛⡁⠀⡞⠀⠈⢹⠀⠀⠀⠀⠀⠀⠀⠒⠒⠀⠉⢩⣾⡐⢆
⠀⠀⠐⠶⠞⠓⣷⢄⣀⣸⣀⡀⣤⡤⢠⡀⠀⠀⠀⠀⠈⠄⠸⠁⠐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠃⠁⠀⠁
⠀⠠⠄⠀⠀⣰⠋⠈⢿⠉⠛⠳⠤⠤⠞⠉⠐⠀⠀⠀⠀⠀⠰⠀⢠⠁⠀⠀⠀⠆⢀
⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠋⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⡀⠀⣖⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠄⠄
⠀⠀⠄⣊⣴⠇⣌⠳⠶⠟⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠤
⠲⠔⣠⡮⣭⡘⣯⡸⣼⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠂⠀⠀⠀⠀⢀⠐⠀⠀⠀⠀⠠⠄⡀⠀⡔⠔⡌⠀⠀⠀⡂
⠀⠛⠿⢽⣒⠲⢸⢣⣝⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠄⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢧⣴⣾⠷⣀⣡⣴
⠀⠀⠀⠀⠋⠓⠛⠛⠉⠀⠀⠀⠀⠀⢁⠰⠀⢹⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠚⠛⢿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⢠⡇⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⢀⠿⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠀⠀⠀⠀⠀⢀⠀⡀⠀⢠
⠀⠀⠹⠠⠷⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠐⡇⠀⠀⠀⠀⠀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⡈⠀⠀⠀⠀⠀⠈⡄⡁⠀⠃⢀
⠀⠀⠀⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⢸⠇⠀⠀⠀⠀⠀⢳⡿⠻⠇⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡰⡎⡔⠀⠀⠀⠀⠀⠘⠃⠀⠀⢡
⠀⠀⠀⡰⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⢈⠀⠉⠀⠀⠀⠀⠀⠀⠀⢘⣷⣤⣳⡁⠀⠀⠀⠀⠀⠀⢶⡇⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⢤⠁⠀⠀⠠⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⣀⠀⣤⠀⠠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠣⠀⠀⠂⡠⠁
⠀⠀⠀⠀⠈⠆⡼⠃⡴⠋⣑⠈⣅⡀⢠⡀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠉⠙⠀⠁⠀⠀⠀⠁
⠀⠀⠀⠉⠀⠀⠈⡉⡉⠘⢭⠷⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠆⠈⠢⡀⠀⡄⠀⢘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡉⠓⢀⠀⢠⡜⠁⠀⠀⢇⣤⡤⠆⠀⠠
⠀⠀⠀⠀⠀⠀⢀⣤⠠⣬⡃⣼⠲⣽⣾⡟⢷⣶⡼⠏⠀⠃⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠈⠻⠀⠈⢻⠀⠀⡿⠁⠀⢀⣧⡾⠉⠀⠀⠀⠀⠀⡀⣸⠆⠀⠁⣸⠆
⠀⠀⠀⠀⠀⠑⡂⠐⠚⠒⠀⠀⣇⠤⡞⠀⠀⡂⢀⣴⠚⠃⠀⠀⠀⠀⠀⠀⣼⠁⢻⡦⢄⠈⢰⡆
⠀⢠⠶⠒⠛⠓⠛⠲⠄⠄⣀⣀⣉⣙⣧⣤⣾⣍⣉⡀⠀⠀⣀⠄⠀⠀⠀⠀⢿⣠⢏⡀⠀⠀⣼⠃
⠀⠀⠈⠀⠀⠠⢀⠀⣀⣠⣠⡽⠋⠉⠀⠠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣼⣧⣴⡪
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⢀⣀⢠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⢠⠏⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⠈⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⢰⠏⠀⠀⠒⠀⠀⠀⠀⠀⠀⠐⠁⠘⠁⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⢰⠆⠀⠠⠃⠀⠀⠀⢤⡀⢦⢀⢊⠀⠴⠂⠀⠀⠈⠀⠀⠀⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⢀⠀⠸⣛⠻⣧⣾⡷⠟⠀⠀⠉⠁⠀⠀⠈⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢅⠀⠰⠁⠀⠀⠀⢈⠐⡋⠛⠇⠛⠶⢤⡀⠂⠈⠉⠙⠂⠂⠠⢄⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠈⠀⠀⠳⣄⣠⠐⠖⠉⠀⠀⠀⠀⠀⠀⠉⠀⢀⠀⠀⠀⠀⠀⠀⢘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⢸⡀⠀⠀⠈⠳⢥⣀⢀⣀⠠⠀⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠠⢀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠈⡇⠀⠀⠀⠀⠀⠈⣿⠟⠓⠲⠤⠤⠤⢤⣄⣀⠀⣄⠐⢄⣀⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡇⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⢀⡀⠀⠀⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠇⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⢈⡆⠀⠀⢀⣽
⣿⣏⢹⣟⠻⣿⢛⠟⣻⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠂⠐⢦⡀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠐⠀⠀⠈⡐⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠊⠀⠀⠀⠀⠀⡧⠀⠀⠀⠀⠀⢠⠀⠀⠀⠂⡀⠀⡐⠀⠀⠈⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠂⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⡘⢠⠀⠀⠀⠀⡾⠁⢀⠄⠀⠈⣳
⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠠⡀⠀⢀⠀⠀⠀⠀⢸⠀⠀⠀⣀⠀⠧⠶⠤⠤⣀⠘⠀⠠⠊⡠⠂⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⡀⠈⠆⠀⠠⡄⠀⠀⢀⠗⠋⠉⣠⡢⢐⠓⢘⡦⣮⢕⡖⠀⠀⠀⢀⠀⢀⡍⠀⠀⠀⢀⣀
⠀⠀⠀⠰⢢⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠘⠄⢰⠈⠀⠁⠈⡸⠃⠀⠈⠁⡀⠠⣪⢿⡇⠀⠀⢀⡠⠜⢀⠠⠄⠒⠉⠀⠀⢹
⠀⠀⠀⢐⠀⠡⠀⠣⣀⣀⠁⡀⠀⠀⠀⢠⠖⠂⠀⢀⠠⠀⠈⠀⠀⠀⠀⠔⠊⡵⡿⠀⢀⠴⢋⡠⠊⠁⠀⢀⣀⣤⢤⠾⠇⠀⠀⡆
⠀⠀⠐⡁⠀⠀⠈⠐⢌⠉⠛⠺⠤⡀⠀⢘⠀⢘⠤⠈⠀⠀⠀⠀⠀⠠⣢⠈⠀⣰⢁⡔⣡⠔⠉⠀⢀⢄⣢⡿⢿⠟⠁⠀⢀⣤⠞
⠀⠀⠀⠁⠀⠀⠐⠦⠀⠈⠢⢄⠀⠀⠈⠻⡄⠀⠀⠁⠀⠀⠐⢁⣠⠴⠟⠓⢛⣉⣈⣥⣭⣷⣶⠶⠛⣉⠕⠂⣀⣀⣴⡾⠟⠁
⠀⠀⠰⡀⠀⣀⣀⠀⠀⠀⠀⠀⠁⠢⣠⣦⣬⣓⠐⣒⡐⠒⣂⣉⣥⣴⠾⢛⠭⠓⡉⢋⡼⠋⣀⠔⠊⡀⡤⠞⢡⡾⣻⠊
⠀⠀⠀⠉⠙⠛⠛⠲⠾⠷⢄⠤⡦⢤⢤⣍⠙⣻⣿⣙⣛⡛⠻⠟⠋⠁⢉⠀⠀⢈⣴⣋⠔⠟⣡⣶⣯⣮⡮⠶⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠮⠤⢤⣼⣦⣀⣠⣤⣀⣭⠙⠻⠦⣭⢀⡠⠄⠘⢋⣴⠚⠉⠛⠋⠛⠁⠒⠀⠀⠒⠐⠒⠂⠲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠈⠛⠒⠒⠒⠒⠒⠂⠠⠤⠄⠐⠀⠒⠒⠒⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⣰⡿⡯⢿⣽⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⣼⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢈⣽⣿⣿⣿⣿⣿⣿⢹⣿⣿⣿⡟⢿⣥⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⣼⣾⣿⣿⣿⣏⣽⣿⣿⣿⣿⣿⣦⢸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣡⣾⣿⢿⣏⣼⡿⣿⣿⣿⣿⣷⣯⢻⣿⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⢁⡿⢋⣿⣿⠟⣿⣽⣿⣿⠹⣿⢿⣿⡟⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⢀⠞⠁⣾⠿⡏⢠⡿⢀⣿⢿⠀⢻⠀⣿⢳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠐⠉⢰⠃⠋⣀⣿⠏⡽⢀⡟⠀⠀⠡⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠰⠃⠀⠀⠃

⣶⡖⢲⡶⢶⣶⠶⡶⢶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⡠⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠸⣇⠀⠀⠀⠀⠀⢸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠙⢷⡄⠀⠀⠀⢸⡆⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⢻⡆⠀⠀⠀⢿⡀⣿⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⣿⠀⠀⠀⢸⡇⣿⣀⡼⠃⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣄⠀⠀⠀⠀⢹⠀⣧⠀⠀⠀⣸⠃⠈⠉⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⢹⡀⠀⠀⠀⢸⡄⣿⠀⢀⡼⠃⢀⣴⠞⠛⠁⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢧⠀⠀⠀⠘⣧⠘⣶⠟⠀⠀⣼⠁⠀⠀⠀⠘⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠑⢦⡀⠀⢹⡆⠋⠀⢀⣼⠃⠀⠀⠀⠀⢰⠀⢻⠀⠀⠀⠀⠀⣠⡴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠙⣆⠀⣿⠀⣠⡞⠁⠀⠀⠀⠀⢀⡜⠀⢸⡇⠀⠀⠀⠀⡏⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠘⠶⠟⢰⡏⠀⠀⠀⠀⣴⠛⠉⠀⣀⡾⠀⣠⣤⠀⠀⡇⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠈⠻⣦⠀⠀⢸⡇⠀⠀⠀⠀⣇⠀⣴⠞⣫⡴⠞⠁⣼⠀⠀⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠙⣷⠀⠀⠀⠀⠀⠸⣧⠀⢸⡇⠀⠀⠀⠀⢻⡄⠛⠛⠉⢀⣠⠾⠃⣀⡴⠃⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢸⡆⠀⠀⠀⠀⠀⣿⠀⠈⢷⡀⠀⠀⠀⠈⣷⠀⣠⡞⢋⣵⠾⠛⠉⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠶⣤⠀⠀⠘⣷⠀⠙⢦⡀⠀⠀⠀⠘⣧⠀⠈⢷⡄⠀⠀⠀⢹⡄⣿⢀⡿⠁⠀⣀⡤⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⣤⣤⠞⠀⠀⠀⢳⠀⠀⠀⠀⠈⢷⣄⠀⠹⣆⠀⠀⣼⠀⣿⠸⡇⠀⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⠀⠀⠀⢀⣀⣀⡀⠘⢧⠀⠀⠀⠀⠀⠹⣦⠀⢻⠀⣰⠏⠀⢸⡆⡇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣦⣴⠶⠟⠛⠉⠉⢿⡄⢸⡆⠀⠀⠀⠀⠀⢹⡇⢸⣧⡏⠀⠀⢸⣵⠇⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠈⣷⢸⡇⠀⠀⣀⣤⣤⣀⣇⠀⠛⠀⠀⣠⠟⠁⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠙⣷⠀⠀⣿⠀⠻⠶⠚⠉⠀⠈⠛⡇⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠻⣤⠾⠋⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⣠⠖⠚⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⡀⠀⣀⣀⣤⣴⠾⠋⠁⠀⠉⢳⡀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢛⣉⣉⣩⣤⣤⣤⣤⣤⣤⣈⣇⠀⠀⢸⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⠶⠶⠟⠛⠛⠉⠉⠉⠁⠀⠀⠀⠉⣉⣭⠿⠿⠛⠛⠛⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙⠛⠻⠷⢶⣤⣄⡀
⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠒⠲⠦⠤

⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⣤⠀⢀⡀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢰⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⣀⠠⠘⣼⢹⠁⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⣰⣀⡀⠀⠀⠀⡄
⠀⢠⡀⢨⠄⢰⡀⡠⢤⠀⢶⣄⠀⣿⡯⢀⡗⠀⠀⣿⠘⠳⣽⢘⣶⠞⠀⠀⠀⡁⠀⠀⡇⠐⠀⠀⢾⣿⣿⣷⠀⠀⣾⠅
⠀⠀⠰⡈⣇⠀⡥⠁⠎⠀⠘⣿⣿⡟⣀⣾⠇⠀⠀⢈⢾⣄⠉⣿⢃⡞⠀⠀⠀⢡⠀⢠⡷⠁⠀⠀⠈⠉⠋⠁⠀⢈⣧⡀
⠀⠀⠀⢅⡪⢤⡿⡠⠀⠀⠀⢿⣿⣯⣿⠃⠀⢠⡀⠀⠳⠬⣷⡿⠞⠋⠀⠀⠀⠀⠱⣞⢇⠀⠀⠀⠀⠀⠀⣀⠀⠈⠻⣖⡄
⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠈⠁⠉⠁⠀⠀⣸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠹⠼⠀⠀⠰⢰⡀⠀⣷⡁⠀⠨⡬⣞
⠀⠀⢲⣾⡄⠀⠀⣸⢁⡀⠀⣤⠀⠀⠀⣆⠀⣿⡿⠀⡀⠀⠀⠀⣀⠄⠀⢠⢀⠀⢀⠀⠀⠀⢠⢲⣼⣳⠂⠛⡢⢤⣀⢨⡷
⠀⠀⠸⡇⢷⠀⢷⣸⡸⡄⢸⠁⠀⠀⠀⣿⣾⣿⢃⣼⡇⠀⢐⠃⠌⠳⣤⣘⢺⠃⣠⠀⠄⠀⣎⢣⢻⣇⡂⠀⠀⠅⢸⡞⠂
⠀⠀⠀⠙⢮⣷⣼⡇⡇⢷⢸⡀⠀⠀⠀⠙⠿⠿⠟⠋⠀⠀⠀⠀⠈⠿⠾⣿⡷⠏⠁⠀⠀⠀⠈⠺⠿⠟⠁⠀⠀⠀⠋⠉
⠀⠀⠀⠀⠀⠙⢿⣧⣸⣾⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣇
⠀⠀⢀⠀⢀⠀⠀⠿⠛⠛⠁⠀⠀⠀⠀⠀⠰⠊⠝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⣼⣿⠀⣾⣿⡗⢰⣶
⠀⠀⣿⡆⣸⣧⣤⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠒⠋⠐⠑⠃⠃⠂⠘⠁⠚⠀⠃⠀⠀⠀⠀⠀⠀⣿⣿⡀⣿⣿⡇⣼⣿
⠀⢠⣿⠇⣿⡟⣷⠀⠀⠀⠀⢠⣄⡄⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣶⣌⢿⣧⢻⣿⡇⣿⡇⣠⣶
⠀⠈⣿⣆⣾⣿⡟⠀⠀⢸⣾⣿⣿⣷⣦⣾⣷⠃⠀⠀⠰⡀⠘⡄⠀⠆⠀⠀⠀⠀⣄⠾⣃⠀⠘⣿⣦⢻⡜⣿⢱⡿⣵⣿⠃
⠀⠀⢸⡟⢿⡟⣷⠀⠀⠀⢻⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠐⠄⡃⣾⠐⠀⠀⠀⢐⠢⠜⣳⡆⠀⠈⠙⠓⠅⠙⠫⠞⠛⠁
⠀⠀⠘⠇⢸⠿⠋⠀⠀⢴⣮⣿⣿⣿⣿⡿⠟⠁⠀⠀⠰⠀⠘⣇⣟⡤⠀⠀⠀⢈⣗⠰⢛⣁⠀⠀⠀⠀⢠
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠋⠀⠀⠀⠀⠀⠄⠂⠲⣿⣋⠔⠀⠀⠙⠾⠿⣧⠚⣫⡄⠈⢦⡀⠸⣧⠀⠀⣀⡤
⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⢠⡾⠀⠀⠀⠙⢶⣿⠗⠊⠀⠀⠀⠛⠃⠋⠀⠀⠀⠀⠘⣿⣆⠉⢀⣾⡏
⠀⠀⢀⡀⠀⡾⠀⡄⠀⠀⡆⠀⠀⢸⣯⢀⣿⡇⢀⠀⡀⠀⠀⣿⠀⠀⠘⡆⠀⢠⠀⠀⠀⡀⠀⠀⠀⠻⣿⡄⠈⠹⠇⢀⡀
⠀⠀⠸⡆⠀⠺⠀⣇⠀⢰⠀⠀⡆⠸⣿⡌⣿⣇⢹⡀⣽⠀⠀⠉⣀⣭⣷⣾⣆⣸⣰⢞⣋⡁⢠⣀⡀⠀⠈⠀⠀⢀⣾⡏
⠀⠀⠀⠹⣆⠨⠀⠇⠐⠃⠀⠀⠻⣧⠹⣷⡜⣿⣾⢣⡿⠀⠀⢀⠤⠖⣒⢾⣿⣿⣿⠶⢦⡀⠀⠈⠛⠀⠂⠀⡆⠀⠙
⠀⠀⠀⠀⠀⠛⠁⠉⠁⠀⠀⠀⠀⠘⢳⣌⢿⣹⡦⠛⠁⠀⠀⠀⠀⠈⠰⠋⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡀⣀⣀⡀⣴⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣈⣿⣟⣁⣀⣼⡇⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⢣⡾⠛⠉⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡟⢡⡟⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⡇⢸⡇⠀⣄⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣆⢷⠀⠈⠻⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⡜⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣟⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣺⣷⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⣴⢟⣿⣶⣃⣠⠀⠀⠀⠀⠀⠀⣰⣯⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡇⣼⢡⡞⣱⢟⣿⢷⣾⣁⡠⠀⣠⣾⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡞⣼⢣⣟⣼⢣⡞⣱⢏⡽⣻⢷⣾⣿⣿⡿⣫⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢯⣿⣽⣷⣿⣾⣷⣿⣾⣵⣯⣾⣵⣯⣿⣿⣿⣾⣷⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠟⢁⡯⠞⠛⠛⠛⠛⠛⠟⢿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠟⠉⠄⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣭⣶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠮⣻⣿⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⡠⢒⠒⠒⢦⣄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠁⣫⣿⣿⣿⣿⣗⡩⠙⢳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠨⡳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠠⢟⣿⣿⣿⣿⣟⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠱⡝⣧⠀⠀⠀⠀⠀⣀⠴⣺⣿⠃⠀⠀⢊⢿⣿⣿⣿⣯⣭⣽⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⣰⣯⠖⠛⢿⣮⣷⣄⠀⢀⠀⠀⢀⡿⢸⣧⠰⣤⡶⣛⡵⣿⣿⡏⠀⠀⠀⠀⡾⣿⣿⣿⣿⣿⣿⣟⣿⡧
⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠠⣿⣿⢿⣿⢇⣿⣿⣿⠀⠈⠀⠀⠈⣳⣤⣿⡆⢟⡾⣫⣾⣴⣿⠃⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⣀⣾⡃⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⡾⡷⠋⠀⠀⠀⠀⠀⠈⣿⣿⡟⣼⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⢾⣭⣍⣉⠙⠒⠶⢤⣄⡀⠈⠉⢉⠉⠀⢀⠀⠀⠀⠀⠀⠀⢰⣽⣿⠃⣿⣿⣻⣿⣿⣿⣿⣶⣤⡀⠀⣸⣿⣿⣿⣿⣾⠏
⠀⠀⠀⢀⣹⣿⣿⣿⣷⣦⣄⠈⡛⢦⡑⣤⣠⣀⠀⠀⠀⠈⠀⠀⢀⠞⣿⡟⣸⣿⣿⡿⣵⣿⣿⠿⠛⠉⢀⣰⣿⣿⣿⣿⠿⠁
⠀⠀⠀⠸⢭⣛⣛⣉⣉⣛⣛⣛⣦⣈⣿⣎⣿⣿⣆⡀⠐⣈⣀⢁⣡⣾⡟⣡⣿⣿⣿⣾⡿⠿⠿⠒⠀⠀⣼⣿⣿⠋⠁
⠀⠀⠀⠀⠀⠙⠻⠿⢯⣭⣍⣉⣿⣽⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⠟⣫⣴⣿⡿⠿⢻⠍⠄⠀⠀⢀⣠⣾⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⣿⣿⣿⣾⣯⣭⣭⣵⣶⣿⠿⠋⠀⠀⠀⠀⢀⣀⣠⣴⣿⣿⣿⣿⣿⠿⠛⠓⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠿⠿⠿⢿⣷⣶⣶⣿⡟⠻⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣽⣿⡄⠀⠈⠻⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⡦⠀⠀⠙⢿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣄
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⢀⣴⠞⠛⠛⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀
⠀⠀⢸⣇⣀⣠⠀⢀⣿⠃⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⡦
⠀⠀⠀⠈⢉⣡⡶⠟⠁⠰⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣦⣄⣘⣿⣿⡅
⠀⠀⠀⣴⡟⣩⣶⣶⣦⣄⣽⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⣼⡏⢰⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⢿⣿⠟⣵⠶⣦⣄
⠀⠀⣿⡄⠘⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠋⣿⡘⣧⡀⠈⣿
⠀⠀⠘⣷⣄⠙⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡿⠷⠦⠘⠷⠄⢁⣴⡟
⠀⠀⠀⠈⠙⠻⠾⠿⠿⠿⠷⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠶⠶⠶⠾⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠞⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⢀⣼⠇⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠶⠟⠛⢛⠛⠋⠁⠀⣿⣿⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⣴⣿⣿⣿⣿⣶⣤⣽⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠿⠿⠿⠿⠿⠟⠉⠛⠿⠿⠷⠶⠶⠶⠆
⠀⠀⠀⠀⠀⠀⢀⣤⠶⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⣠⣤⣶⣤⣤⣈⡁⠀⠀⢨⡷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠉⠉⠉⠙⠻⣦
⣾⡏⠀⠀⠀⢀⣉⡛⠓⠞⠛⠁⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠸⣷⣤⣴⡇⠀⠀⣹
⠹⢷⣄⣠⣶⣿⣿⣿⣿⣦⣄⠀⣿⣿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⢿⣿⣿⣃⣤⡾⠋
⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⠋⠁
⠀⠀⠀⣼⣿⣿⣿⡏⠉⢹⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⢹⣿⣿⣿⣧
⠀⢀⣴⡿⠋⠀⣿⠃⠀⣿⠋⠙⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠃⠀⢠⣾⣿⣿⣿⣿⣦
⠀⡿⠉⠀⠀⠀⢿⡄⢠⡏⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣄⡀⠘⢿⣿⣿⣿⣿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢺⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢀⡠⠤⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⡁⠀⠀⠀⠀⣰⠥⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⠂⣀⠔⠀⠀⠀⣠⠎⠁⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡸⠁⠀⠀⠀⠀⠀⡰⢡⠎⠀⠀⠀⠀⡰⢻⠀⢀⠤⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠇⠀⠀⠀⠀⠀⢠⡰⠁⠀⠀⠀⠀⠰⠁⠀⡔⢁⡴⠁⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⢃⡰⢾⠒⢩⢔⠜⠉⠀⠀⠀⠀⠀⢀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡄⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢀⠜⠀⠆⢰⠁⠆⠀⠀⠀⠀⠀⡠⢊⠔
⠀⠀⠀⠀⠀⠹⡦⡄⠀⠀⢃⢰⠀⠀⠀⠀⠀⡇⢣⠀⠀⠀⠀⠀⠸⢀⡌⠀⢠⠀⡜⠀⠀⠀⡠⠼⠋⠁
⠀⠀⠀⠀⠀⠀⠘⡌⡆⠀⠈⢻⣀⠀⠀⠀⠀⠀⢄⣣⡀⠀⠀⢀⡇⡏⠠⠀⢠⠋⠀⠀⠀⠊⡰⠃
⠀⠀⠀⠀⠀⠀⢀⠀⡇⠀⠀⠈⠦⡁⠄⠀⠀⠀⠀⠈⠑⡦⡄⠀⠃⢃⡰⢀⠆⡀⠀⢀⡤⠂⠁⠀⠀⠀⠀⠀⠀⠀⡼⠃
⠀⠀⠀⠀⠀⠀⠈⢠⠁⠀⠀⠀⠀⠈⠢⣱⠀⠀⠀⠀⢀⠖⣼⠎⠀⢨⠓⣼⠀⡇⠔⠉⠇⠀⣠⡴⠂⠀⠀⠀⢀⠜⡜
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡼⡀⠀⠀⠀⠀⢠⣟⠀⠀⠠⡄⡿⡸⡌⢀⠜⢔⠟⠉⠀⠀⢀⣤⡴⠋⠉
⠀⠀⠀⠀⠀⠀⠀⡟⣄⠀⠀⠀⠀⠀⠸⠀⢡⠀⠀⠀⢠⡸⡌⢃⠀⣠⢃⡧⢰⡴⢃⡞⠁⠀⠀⠀⡴⡱⠉
⠀⠀⠀⠀⠀⠀⠀⠈⢎⠲⢄⠀⠀⠀⠀⠑⢴⡀⠀⠀⠀⢹⠸⣀⠟⢡⣎⠔⡏⢠⠻⠀⠀⠀⠀⠀⢦⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠑⠠⣤⣀⣀⠈⠣⣄⡀⠀⠸⢀⡧⣦⡋⠤⠊⠀⢸⡘⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠈⠙⢦⢜⣌⢣⣦⢈⠜⠇⠀⠀⠀⠀⠘⢇⠀⠀⠀⠀⣠⠋⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠙⡎⣇⠎⡘⢀⡠⢤⠶⠚⢛⠟⠲⠖⠾⠭⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠺⠋⡜⠰⡡⠊⢀⠠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠘⠀⡄⢷⡡⢊⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⢴⣴⠟⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⣀⣀⠀⠀⢀⠀⠀⣼⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣷⡈⢧⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⢠⣿⡟⠀⢠⠏⠀⣰⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡘⣧⠀⠀⠀⠀⠈⣿⣿⡇⠀⠀⣸⣿⠇⢀⡟⠀⢰⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣧⢹⣆⠀⠀⠀⠀⠿⣿⠟⠀⢀⣿⣿⠀⣾⠁⢠⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⢻⣿⣯⣿⡀⠀⠀⠀⠀⢹⠀⠀⠸⣿⠇⣸⡏⠀⢻⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠈⢿⣿⢻⣿⣄⠀⠀⠀⢸⠀⠀⠀⠀⢰⣿⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⡄⣿⣿⡄⠀⡇⢸⡆⠀⠀⠀⣾⡇⠀⡼⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⢠⢸⣿⣷⠀⣇⢸⡇⠀⠀⢰⣿⠀⣸⢁⡔⣠⣴⠾⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢷⣦⡀⠀⠀⠈⣿⣆⠀⠀⡆⣿⣿⡇⣿⣾⡇⠀⠀⣿⡏⢰⢃⣾⣾⠟⢁⡴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⣿⣦⣤⣤⣼⣿⡄⠀⢠⢹⣿⣿⣿⠛⡇⠀⢸⣿⢡⣿⣿⡿⠃⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣎⠙⢻⣷⣦⡀⠸⣿⣿⣿⡇⡇⠀⣼⣿⣾⣿⡿⢡⣾⠏⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⣿⣧⠘⣿⣿⣿⡄⣿⣿⣿⡇⣧⢠⣿⣿⣿⡿⣡⣿⠃⠀⣠⣴⡾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⡘⣿⣧⢻⣷⠹⣿⣿⣿⣹⣿⣿⢸⣿⣿⣿⢵⣿⢁⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣾⣿⣿⣿⡆⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣷⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡌⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣷⣾⣿⣿⣷⣏⣿⣿⣿⣿⣯⣾⡏⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡇⣿⣿⣼⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣹⣿⣿⣧⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁⢀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⢠⡶⠛⠁⢠⡾⠛⠛⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠈⢷⡄⠀⣿⡁⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠞⠋⠁⠀⠀⠻⣆⠘⢷⣤⣠⣤⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⡶⠟⠋⠁⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠈⢿⣄⣀⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⢦⣤⣤⣤⡶⠛⠉⠉⠉⠉⠻⢶⣤⣤⣤⡶⠟⠋⠉⠉⠉⠛⠷⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣦⣤⣤⠞⠋⠉⠉⠻⢦⣤⣤⠾⠋⠉⠉⠛⢦⣤






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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⠶⠶⢦⣄⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⢀⣀⣀⠙⣧⠀⠀⠀⠀⠀⣸⣿⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⣏⠀⠉⢀⡿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣤⡀⠈⠓⠒⠛⠁⠀⠀⠀⠀⠀⠹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡿⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⢿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⣾⣿⣿⣿⣿⣿⣿⠁⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣷⣾⣿⣿⣿⣿⣿⠃⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣭⣿⣿⡿⠇⠀⣽⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠟⠛⠹⠿⠿⠿⠿⠷⠄⠀⠛⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⣴⠦⣄⡀⠀⠀⠀⠀⠀⢀⣴⠞⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠉⠉⠉⠉⠙⢶⡄
⠀⣸⡏⢠⠑⠽⠖⠛⠉⠉⠉⠛⠊⢰⡄⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⡿⣅⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣾⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⡇⢀⣠⠟
⠀⢱⠟⠀⢀⡀⠀⠀⠀⠀⠀⡤⢤⡄⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠸⡏⠉⠁
⠀⡏⠀⢸⠉⡝⣆⠀⠀⠀⠸⠀⢆⡏⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣄⣀⡀⠀⠈⢧⠀⠀⠀⠀⠀⠹⣄
⠀⣇⠀⠀⠓⠐⠃⠀⠀⡀⠀⠉⠉⠀⠀⠀⢠⡇⣀⣀⣀⡤⠶⠚⠉⠁⠀⠀⠀⠀⠀⠉⠓⢦⡈⢷⡀⠀⠀⠀⠀⠙⣦
⠀⠘⢦⡀⠀⠀⣀⣈⡱⢅⣀⠔⠀⠀⢀⡴⠋⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠹⣄⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠙⢲⠦⠤⠤⣄⡤⠖⠒⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣀⣀⡀⠀⠀⠘⡆⢹⡄⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⣼⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢹⡀⠀⠙⠢⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⢠⠇⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⢀⡞⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠛⠁⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⢈⠷⢤⡀⢢⣤⣤⣀⣠⠤⠖⢉⡴⠋⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⣠⠔⠙⠦⣄⣀⡀⣀⣀⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠘⠶⠤⠤⠾⣴⣰⣀⣡⠤⠖⠻⠶⠤⠤⠤⠴⠶⠖⠚⠛⠓⠒⠒⠛⠉⠁⠀⠀⠀⠀⠉⠉⠉⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣴⣭⣴⣭⣿⣵⣯⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⡿⠿⠛⠁⠀⠈⡻⢷⣦⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣀⣀⣀⣠⣀⣤⣶⡶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⠉⠉⠀⢀⣤⣴⡿⢿⣟⣿⣭⣷⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣁⣤⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠓⠈⣨⣶⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⢿⣿⡿⣬⢹⢿⣿⡿⠋⢋⣴⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣵⠿⠛⡟⠉⠀⠀⠑⢭⣦⠴⠟⡼⢡⣾⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣠⡿⠟⠛⠛⠛⠛⠒⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⣠⠖⠊⣩⠉⠂⣤⣤⡴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠟⠃⠀⠀⠀⠀⠀⠀⠸⡿⣆⠀⠀⠀⡀⠈⠢⠄⠀⠀⠐⠊⠀⠀⠊⢁⡠⠜⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⠛⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣷⣌⠲⣄⣠⡈⠲⠤⠤⠀⠀⠀⢀⣤⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⣶⣿⣿⣿⣿⡿⠃⠀⠀⢠⣴⣾⠿⣛⠛⠊⢉⣿⣿⠛⠳⠦⢬⣍⣙⣀⣠⣤⠶⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠈⠛⠿⣿⣿⣷⣶⣭⡾⠃⠀⠀⢀⣠⣴⣾⣯⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⢉⣀⣤⠶⠚⢿⣿⡿⠿⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠋⠁⠀⠀⠀⠈⢷⣇⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣤⣤⣄⣈⢹⣿⣷⡀⠀⠀⠀⠀⠀⢠⡟⠁⠀⢀⣀⣀⣠⣤⣤⣬⠻⣾⣶⣿⣷⢀⣀⡀⠀⡀
⠀⠀⢠⠊⠀⢀⢠⠻⣍⣀⠄⠈⠉⠒⠛⢿⣿⣦⡀⠀⠀⠀⢿⣀⣠⣼⣿⡿⠿⢛⣻⣿⠏⠀⢈⣹⣛⣧⡤⠥⠚⠇⠀⣢⠀⣢⡄
⠀⠀⠸⣇⢸⣬⣿⣷⣌⣻⣶⣤⣐⣲⠶⠦⠽⠿⣷⣦⣤⣀⢀⣿⣿⣿⣿⣋⣭⣽⣿⣿⡶⣛⣫⣭⡭⠁⢀⣀⡔⡼⢠⢇⡖⠉
⠀⠀⠀⠙⢌⢮⣝⣷⣽⣿⣿⣷⣌⡋⠙⠲⣦⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⠿⢧⣾⠿⢛⣉⣁⣈⣃⣩⣴⢟⣵⡋⠉
⠀⠀⠀⠀⠀⠉⠚⢿⢿⡟⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣭⣿⣿⣿⣿⣶⣿⣵⣿⣿⣿⣿⣟⡪⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠉⠋⠙⢿⣿⣷⣶⣦⣭⣽⣿⣿⣿⣭⡿⠿⠾⠟⠉⠉⠉⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⣀⣤⢤⣴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⣷⠀⠀⠀⠀⠀⢀⣾⡥⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣠⠃⠀⠀⠀⢀⣤⠛⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠀⠀⠀⠀⠀⠀⠀⠀⣰⢃⡴⠚⠁⠀⠀⠀⢠⣾⠁⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣹⠃⠀⠀⠀⠀⠀⠀⢠⡞⣱⠏⠀⠀⠀⠀⠀⢠⠟⣿⠀⢠⡴⢋⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢁⡟⠀⠀⠀⠀⠀⠀⠀⣼⡿⠃⠀⠀⠀⠀⠀⢠⡏⢀⣇⡼⠉⣠⠞⠀⣀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠏⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⠀⢸⣆⣼⣾⠖⠋⣡⢖⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⢸⠟⠁⡟⢀⡞⢱⡋⠀⠀⠀⠀⠀⠀⢀⡴⢞⡿⠃
⠀⠀⠀⠀⠀⠀⠲⣄⡀⠀⠀⠀⠀⡏⣧⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⢠⡏⠀⡼⠁⢸⡇⠈⡇⠀⠀⠀⠀⠀⢠⣯⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠙⣟⢦⡀⠀⠀⢧⣸⠂⠀⠀⠀⠀⠀⢸⡏⢷⡀⠀⠀⠀⠀⠀⣼⣠⣾⠁⠀⠸⣇⡾⠁⠀⠀⢀⡤⢞⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⣷⠀⠀⠈⢻⣄⡀⠀⠀⠀⠀⠀⠳⣌⣳⡀⠀⠀⠀⣀⡿⢿⠉⡇⠀⢠⣯⠀⠀⠀⢠⠋⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⣿⠀⠀⠀⠈⢯⡙⠢⡀⠀⠀⠀⠀⠀⠈⠛⣦⣄⡎⢠⡇⢸⡀⡇⠀⡏⣿⠀⠀⠀⣧⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣾⢠⡇⠀⠀⠀⠀⠀⠉⠳⣌⢣⡀⠀⠀⠀⠀⠀⢸⣎⣧⡞⠀⠀⣿⣄⢸⠀⣿⢀⣰⢾⠇⠀⠀⢀⣤⠄⠀⠀⠀⠀⠀⣠⢯⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡾⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡇⠀⠀⠀⠀⢠⡇⢸⡏⠀⠀⠀⣿⢘⣿⢠⣯⡞⠁⣼⠀⣠⣾⠟⠉⠀⠀⠀⠀⣀⣴⡵⠎
⠀⠀⠀⠀⠀⠀⠀⠀⢈⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⣇⠀⠀⠀⠀⢺⢠⣿⣇⠀⠀⠀⢻⢸⣏⡼⡿⢀⡼⣡⡿⠟⠁⠀⠀⠀⣠⣶⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⢸⡄⢸⡀⠀⠀⠀⠸⣼⣿⡎⢳⡀⢠⠞⣸⠟⢹⡷⠋⣠⠋⠀⠀⠀⠀⢀⡾⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡙⢦⡀⠀⠀⠀⠀⠀⠙⢮⣇⠀⠀⠀⠀⠘⡇⢿⢀⡷⠋⣴⣫⠴⡿⠀⣾⡿⠀⠀⠀⠀⠀⠘⣧⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡉⠳⣄⣀⣀⠀⠀⠈⢿⣀⠀⠀⠀⢈⡇⢸⣟⣴⡿⢛⣡⠞⠁⢰⣷⡇⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠚⠛⠛⠛⢦⣄⠙⢿⡳⣄⢸⢃⡞⣫⡞⠋⠉⠁⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠢⣷⡘⣿⠋⡼⢡⠇⠀⠀⠀⢀⣀⣀⣿⣇⠀⢀⣀⣀⡤⠞⣡⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⢧⢹⡼⢣⡟⢀⡴⣶⠿⠛⠋⢉⡿⠉⠛⠛⠛⠓⠚⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡟⢻⡿⢡⡏⣴⣻⠞⠁⣀⣠⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠘⡇⣾⢰⣿⢃⡴⢛⡥⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⣻⣿⢸⣿⡿⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣴⣶⣶⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣴⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠘⠻⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠈⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠟⠛⠋⠁⠀⠀⠀⠀⠀⠉⠛⠛⠿⠿⠛⠛⠉⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠟⠓

⣀⣀⣤⣴⣶⣿⣿⣿⣷⣶⣤⣄⣀⣀⣀⣠⣤⣶⣿⣿⣿⣿⣷⣦⣤⣀⣀⣀⣀⣤⣴⣶⣿⣿⣿⣿⣶⣤⣄⣀⣀⣀⣠⣤⣶⣿⣿⣿⣿⣶⣦⣤⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡿⠿⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠛⠛⠿⢿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡴⠶⠒⢲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠚⠋⠁⠀⠀⣠⣾⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡤⠶⠚⠋⠉⢀⡖⣛⢶⡄⢀⢀⣼⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠖⠛⠉⠀⠀⠀⠀⠀⠀⢸⣎⣿⢞⡴⢁⣾⣿⣿⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠚⠉⠀⠀⠀⣀⡤⠖⠀⠀⠀⠀⠀⠁⠀⢠⡾⢁⣾⣿⣿⠏⡾⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠉⠀⠀⠀⠀⣠⠶⠛⡏⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⣾⣿⣿⠏⡼⠁⣀⡴⠋⢀⡇
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⢁⠤⠀⠀⠀⠀⠀⣰⠏⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⣼⣿⣿⠿⠼⠛⠋⠉⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠈⣿⡉⠙⠛⠲⢤⣀⢀⡴⠞⢁⣴⠞⠁⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠀⠻⠞⠃⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⢸⣏⡀⠀⠀⣀⡼⠋⣠⡶⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⡁⠀⠀⠀⠀⠙⠦⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⢀⡼⠋⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⢀⣀⣀⣠⠴⢒⣩⠶⠋
⠀⠀⠀⠀⠀⠀⠀⢸⠇⣰⠋⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⣤⣤⡴⠞⠋⡀⠉⠉⣉⣉⣀⣴⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣿⡼⠃⣰⡟⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠶⠶⠶⠶⠶⠶⠶⠤⠌⠉⠛⠛⠳⠚⠋⢉⡽⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣸⠃⣸⡏⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣒⠛⢛⣉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⢀⣠⢾⡻⣄
⠀⠀⠀⠀⠀⠀⠀⡟⢰⣿⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠉⠛⠧⣤⡄⠀⢀⠀⠀⣀⠀⠀⠀⣠⡴⠛⠁⠠⠙⢮⡳⣄
⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⡷⠖⠋⠁⣀⡴⠚⠁⠉⠛⠚⠓⠚⠒⠾⣿⣧
⠀⠀⠀⠀⠀⠀⠀⣷⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⣀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠇
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⣠⡴⠛⠁⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠚⢁⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⣴⠛⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣴⠾⠛⠛⠲⠦⠀⢀⡤⠞⠋⠁⣿⠀⠀⠀⠀⠀⢀⣀⡴⠞⢁⡤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠗⠒⠀⠀⠀⣀⡴⢿⡤⢀⠀⢠⡟⠛⠛⠛⠛⠋⠉⠁⠐⠊⣁⣠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣛⣉⣁⣤⣴⣞⠋⠀⠀⠙⢧⢎⡼⠁⠀⠀⠀⠀⠀⠀⠐⠈⣉⣁⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⢸⠉⠳⣄⡀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠠⢠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⡄⢀⠙⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠹⣤⠷⠋⠀⠉⠓⠦⣄⡀⠀⠀⢀⣈⠉⠒⠒⠶⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣿⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠦⣤⣉⡙⠓⠒⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠺⠷

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣷⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⢛⣿⣿⣿⣿⣿⣿⣿⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⠿⠿⢿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⣿⣿⣿⡿⣧⣶⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠀⠀⠀⢘⣽⣿⣻⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠇⠀⢐⣒⡛⢏⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⢏⣀⠀⢸⣿⣵⣶⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢹⢁⣄⣼⣟⢿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⢈⡻⢹⣿⣷⣾⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠦⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢋⣢⡄⠸⣿⣼⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣤⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢸⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠸⢿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⢾⣿⡇⣿⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡗⣿⣿⡟⠻⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢹⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢀⣿⡟⢸⣿⣿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⡤⣤⣤⣀⣀⣀⠀⣀⣤⣶⣾⣵⣰⠀⠀⣀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠰⢾⣯⡻⣿⢿⣤⡶⠈⠻⣿⣭⣙⠻⠿⣿⣿⣿⣿⣇⠈⠀⠁⠐⢢⠙⠒⣀⡀
⠀⠀⠀⠀⠀⠀⠈⢻⣷⣍⠓⠄⠀⣠⡄⣼⣹⣿⣿⣶⣤⣙⠻⣿⣧⠀⠞⠓⠀⠘⠀⠒⢢⠳⠖⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣍⠀⠀⠀⠉⢜⣵⡿⡿⠿⢿⣿⣿⣿⣬⣛⢶⣄⣰⠋⠙⠢⢤⠤⠖⠛⠳⣀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣶⣶⣾⣿⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣮⡿⣿⣷⣦⠈⢲⠰⢀⠍⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣶⣶⣦⣭⣁⡀⠀⠀⠉⠛⢿⣿⣷⣞⣿⣿⠀⣦⣤⣀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣶⣦⣄⣀⠙⠻⣿⣿⣿⡆⠲⡄⢹⡇⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡠⠀⠀⠀⠻⠿⠟⠛⠀⠘⢿⣿⣿⣿⣿⡢⠘⢿⣿⣷⠀⣁⣬⣔⣊⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⡀⣴⠚⠲⣏⠙⡆⠀⠀⡇⠀⣈⠃⡀⠘⠊⢳⡀⠘⣿⡟⢈⡡⠴⠒⠆⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠬⣝⠢⣄⢈⣧⡘⢄⠐⠒⠊⣉⢹⠔⣉⡀⢈⡇⣼⡿⠡⠋⠠⣒⣚⡛⠋
⠀⠀⠀⠀⠀⠀⢀⠤⡘⢁⢤⡤⣙⢮⡣⠀⠉⠲⣅⣒⣠⠞⢀⣈⣁⣨⣼⣿⠟⠁⣀⠴⠋⣉⢄⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠀⠐⠥⣙⡲⠬⠁⠂⣀⣴⣾⣿⣿⣿⣿⣿⡁⠀⠤⠤⠤⣄⡈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⡴⠛⠉⠹⢻⣿⣿⣿⣿⡇⠀⠁⢀⡠⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⡄⠀⠀⠀⠀⠀⢀⣠⢪⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⢿⡀⠀⠀⣠⡴⠋⠑⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⣠⣴⣾⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠁
⠀⠻⢶⣟⣩⠀⠀⠀⠀⠃⠀⠀⠀⢠⣿⠿⣿⣿⣩⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠟⠉
⠀⠀⠀⠉⠺⠧⢤⣄⣀⡞⡀⠀⠀⢸⣿⠀⠀⢨⡟⠉⠳⣄⡀⠀⠀⢀⣀⣤⣤⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠃⠀⠀⢸⡟⠀⠀⢸⠁⠀⠀⠈⠛⢷⡾⠟⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠘⣧⡀⠀⠀⠀⠈⠙⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢀⣿⠛⢦⡀⠀⠀⠀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⣼⠇⠀⠀⠉⠳⣤⡀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠃⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠐⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡗⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⢠⣼⠇⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢀⠀⢠⡾⠋⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠔⠊⠀⠀⢀⣀⣀⣤⠂
⠀⠀⠀⠀⠀⠀⠀⢠⣯⣤⣤⠶⢤⣤⣠⡼⠃⠀⠀⠀⠀⠀⠀⠀⠑⠀⠠⠀⠠⠶⠚⠉⢈⣷⣌⡑⢆
⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⡀⢸⡇⠈⠻⣄⠁
⠀⠀⠀⠀⠀⡀⣴⣁⣀⣀⣀⡠⠤⠤⠤⠤⣔⣒⣒⣒⣶⣿⣿⠯⠭⠭⠽⠗⠒⠶⠾⢿⣭⣉⠲⢄⢹⡄
⠀⠀⠀⠀⠀⠈⠻⠷⢶⣶⠖⠚⠛⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⡄⠙⣷
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠘
⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠊

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

⠀⠀⠀⡀
⠀⠢⣄⠘⠄⠀⣿⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⡀
⠀⠀⢘⣦⠈⡀⠉⣤⢀⡎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⣦⢠⡄⠿⠀⠎⡴⠂
⠀⠀⠘⣿⣇⢡⠀⠟⡜⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣿⠊⠇⠀⡈⠎⣰⠇
⠀⢀⡀⢠⢸⡘⣐⣶⡟⠠⡀⠀⢀⡤⡀⠀⠀⢄⠀⠠⣀⡀⠀⡄⢀⡀⠀⡀⠐⡄⠀⣆⣸⣷⡄⢠⣇⣠⠉⠀⡀
⣦⣏⣽⣮⣷⣷⣿⣿⣽⣿⣷⡐⣿⣴⣵⣿⢳⣾⣆⣷⣿⣾⣼⣶⣏⢀⣿⣌⢷⣽⡈⣿⣯⣿⣿⣿⣿⣿⣷⣶⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣠⣶⣤⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡿⠉⢻⣿⠁⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⠟⠁⠀⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣦⣀⣀⣀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡇⢈⣼⠟⠛⠛⠓⠛⠀⢰⠏
⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠉⡀⠸⠿⠆⣀⣀⣀⠀⠀⠙
⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣇⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠷⣶⣶⣶⣜⡻⣿⡄⠀⢠⡀
⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⡀⢈⡉⠀⠈⠉⠈⠙⠛⠿⣮⣍⣀⣼⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⡁⠀⠀⠀⠀⠀⢠⣟⣿⣵⡟⢃
⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠷⠀⠀⣠⣀⣿⣿⠛⣳⡾
⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠂⠀⠀⠀⠈⠀⠀⠁⢸⣿⠿⠃
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠃
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣷⡄
⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⣿⣿⡿⢹⣿⣿⣿⣿⣿⣿⣿⠟⠿⠋⣾⣿⣿⣿⡏⠀⠀⠀⠀⡀⠁
⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢿⣿⣿⣿⡇⣿⣿⣿⣿⣿⠋⠀⠀⠀⢀⣴⣿⣿⣿⡿⠁⠀⠀⢀⣶
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⣿⣿⣿⣿⡇⣿⣿⣿⣿⠟⣂⠋⣰⣿⣿⡿⠿⠿⠛⣁⣀⡀⢀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⣿⣿⣿⣿⡇⢸⣿⣿⣿⠟⠁⢴⠿⡿⠏⠀⠀⠀⣰⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⠟⢁⡀⠀⠀⠉⠛⠛⠋⠁⣾⣿⣿⣿⣿⡇⣿⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡿⠋⣡⣴⣟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⣿⠁⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⠃⣸⣿⣿⢹⣷⣤⣄⠀⠀⠀⠀⠀⢹⣿⣿⣿⣇⠘⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠻⠛⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠃⠐⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠶⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄

⡠⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⢠⠖⠀⡀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⢘⢆⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⢀⠔
⠀⠀⣀⡄⠀⠀⠀⠀⢘⡆⠀⠀⠀⢠⠙⠀⠀⠀⡀⠀⠀⠀⠐⡝⠀⠀⠈⠠⢠⠉⠀⣀⣴⠀⠀⠀⠀⠀⣒⡀⠀⠀⠀⢠⠋⠀⠀⠀⢄⠀⠀⠀⠐⡙⠀⠀⠀⠀⣬
⠀⠉⠉⠑⣀⠀⠀⠀⠈⣑⡏⠠⡀⠓⡀⠀⠀⢀⠙⣀⠀⠀⠐⢒⣸⡋⠤⡈⢓⠀⠀⠁⠈⠁⡙⢀⡀⠈⢉⣸⡋⢀⡈⢒⠀⠀⠀⠀⠀⡁⠆⠀⠐⢂⣺⠉⢄⠘⢂
⡶⣔⡭⠊⠉⣳⠀⠀⠀⠹⠀⠀⠇⠀⠙⡦⣞⡕⠈⠉⡲⠀⠀⠀⠛⠀⠐⠏⠈⠹⠦⣞⠕⠈⠉⡶⠀⠀⠀⠟⠀⠰⠇⠈⢱⠴⣊⠕⠉⠉⡶⠀⠀⠈⠗⠀⠸⡇⠈
⠀⣣⠄⠀⢤⡷⠶⠂⠙⢀⠀⠴⠤⠀⠀⠘⡡⠈⠀⢵⡷⠖⠂⠙⣀⠀⠴⠤⠐⠀⢘⡤⠈⠀⣼⠶⠖⠀⠛⣀⠀⠶⠤⠀⠀⢘⡤⠁⠀⣼⠴⠖⠈⠓⣀⠀⠦⠄
⠀⠀⢴⣀⣼⡆⠀⠦⠀⣼⠄⠀⢠⣀⣀⠀⠀⣖⣀⣾⡄⠐⠄⠀⡽⠄⠀⢠⣀⡀⠀⠀⣞⣀⣶⡄⠐⠄⢀⡽⠀⠀⢠⣀⡀⠀⠀⣆⣀⣾⡀⠐⠄⢀⡧⠀⠀⢤⣀
⠀⠀⠛⠍⠀⠠⡤⠀⣬⣁⡄⠀⢄⣫⠀⠀⠀⢫⠙⠀⠡⡤⢀⣬⣠⡄⠀⢀⣣⠀⠀⠀⢫⠉⠀⢡⠄⢀⣬⣠⠄⠠⣈⣣⠀⠀⠀⠫⠃⠀⢠⠄⢀⣌⣠⠄⠠⣘⣇
⠠⡀⠓⠀⠀⠀⠀⠑⢉⠸⠁⣀⠄⢹⡃⠀⡈⠓⠀⠀⠀⠀⠀⢉⠺⠁⣠⠀⣙⠃⢠⡈⠓⠀⠀⠀⠈⠐⣍⠮⢁⣠⠈⣹⠁⢠⡈⠃⠀⠀⠀⠈⠀⡁⠎⢀⣠⠈⣹

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⠃
⣤⣀⠐⠛⠽⠿⢦⣤⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠇
⠛⠒⠀⠀⠀⠀⠀⠙⠷⠦⣈⣹⡯⣤⣶⣞⠓⠄⠀⠀⠄⢤⣄⠀⠀⠒⠛⠶⣄⠀⠀⠀⣴⣾⣿⣿⡟
⠀⢉⠉⡁⠀⠉⠁⠀⣉⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⣀⠀⠀⣨⠉⠂⠀⠀⠀⠌⠙⠛⣝⡻⠿⢿⣿⠿⢿⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢀⡠⠀⠒⠂⠀⠶⠶⠚⢷⣶⡭⠉⠂⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⠄⠘⠂⠀⠶⠀⠀⠀⠄⠀⠢⠀⢉⠒⠀⡦⢤⡶⢤⡐⠛⠛⠳⢦⡴⠤
⠀⠀⠀⠤⢤⣬⣁⣀⣠⣄⣈⠁⠈⠩⠷⠶⠶⣶⠤⠤⠐⠀⠀⠀⠀⢠⣴⣤⣀⡀⠀⠢⠤⠚⠋⢁⣀⣀⠀⠀⠀⠠⠶⠀⠀⠐⠄⠀⠀⠀⠐⠖⠀⠤
⡴⠦⢄⣀⡤⠌⠙⠛⠻⠦⠉⠓⠦⠄⠠⢦⣄⡁⠀⠶⢾⣿⣒⣒⡛⠋⠉⠁⠀⢀⣀⠀⠁⠒⠲⠟⠛⠛⠓⣶⣤⡤⠀⠀⠀⠀⠀⠀⠤⠶⠛⠓⠦⠠⣄
⣠⣀⣤⣴⣿⣷⣤⣤⣄⡛⠃⢀⣠⣤⣤⡀⠉⠛⠒⠀⠀⠈⠉⠉⠉⠉⠙⠿⠿⠿⠷⠶⠶⢦⣤⡄⠤⠄⠀⠀⠀⠶⠶⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠄
⠿⠿⠿⠿⢿⣿⣿⣿⣿⣿⠿⠟⠛⠿⠿⣟⠛⢛⣛⠳⠶⠄⠀⠀⠀⠀⠀⠀⣀⣠⣬⣁⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣀⣀⠀⣀⣠⡤⠶⠈⠀⢀⡀
⠀⣀⣤⣤⣤⣄⣀⣉⣁⣀⣀⠀⠀⢀⣀⠀⠈⠉⠀⣀⣀⣀⠠⠠⠖⠒⠀⠈⢉⣴⠤⢶⣦⡄⠀⠀⠀⣀⣀⣀⣠⣴⣶⠿⣟⣉⣭⣡⣤⠀⠀⠀⠉⠀⣠
⠀⣉⣽⣿⣿⡿⠛⠛⠛⠛⠛⠷⣄⣀⣀⠀⠀⠀⠉⠁⠈⠛⠗⠂⠀⠒⠒⠆⠀⠀⠀⠈⠀⠀⢀⣉⣉⣀⣀⡀⠀⠀⣀⣠⣼⣿⠁⠀⢀⣤⢤⣤⠴⠞⠋
⠀⠛⠿⠿⠿⠿⠿⠶⠶⣤⣤⣤⣈⣙⠛⠶⠤⠄⠉⠙⠛⠀⠀⠤⠤⠤⠖⠂⠀⠹⣦⣶⠶⠿⠯⠭⠀⠀⠠⠤⠭⠭⠍⠉⠁⢀⠀⠈⠀⠀⢀⣀⣀
⠀⣐⣒⠀⠦⣤⣄⣀⣀⣠⣼⠿⠛⠛⠛⠒⠒⠒⠒⠚⠛⣛⣳⣶⣤⣤⣴⣶⣶⡶⠶⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⢤⣤⣤⣤⣶⣶⣶⢾
⣿⣿⣿⠿⠶⣄⡀⠉⠉⣉⣁⡀⢀⣠⣤⣄⣉⠉⠀⠀⠈⠉⠉⠉⢉⣥⡶⠶⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡤⠄⠀⠀⢘⣛⠛⠋⢉⣉⣥⣌
⣤⣴⣶⣶⣶⣿⣿⡛⠛⠛⠛⠿⠛⠉⠉⠉⠉⢉⠛⠋⠉⠁⣀⣠⠀⠀⠴⢶⠶⠖⠛⠀⠀⢀⣀⡠⠼⠁⠀⠀⠀⠀⣠⠴⠶⠀⠀⠈⠙⠻⠿⠿⠿⠃⠈
⣿⣿⡿⠿⠿⠿⠟⠛⠻⠶⠶⠶⠒⠂⣠⠴⠚⠻⠿⠛⠒⠉⠉⠀⠈⠙⠂⠠⠖⠚⠋⠉⢋⣩⣥⢤⡤⠀⡀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠂⠀⢀⡄⠀⣠⣄⣠⣴⣾⣿⣿⣿⠗⢀⣀⣀⡀⠀⠀⣀⣀⡴⠋⠀⠠⠴⠂⠴⣾⣶⣦⠀⠀⠀⣹⣿⣿⣶⣦⣄
⠀⠀⢠⣤⣄⣀⣠⠔⠂⠀⣀⡀⠀⠉⠁⠀⠀⣈⡽⠟⠛⠛⠛⢉⣠⡾⠋⠀⢀⣠⠴⠛⠉⢙⣿⠟⠀⠀⠦⣄⠀⠈⠛⠋⠀⠀⠙⠛⠋⠉⠉⢉⣡⣄⣀
⠀⠰⠛⠉⠉⠉⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠛⠁⠠⠖⠂⠀⠈⠋⠉⠀⠀⠈⠉⠀⠀⠀⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠛⠂⠀⠀⠈⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠘⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠡⠀⡄⢿⠇⠀⡀⠀⠀⠀⠄⢸⣿⠀⡆⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠈⠀⠀⠀⢡⠰⡀⠀⢸⣿⠀⢸⠀⠀⢸⠃⠀⡇⡆⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡀⢻⣦⠀⢣⢡⡇⠈⣿⠆⢸⠀⡀⢸⠀⢠⠟⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢻⣧⠀⢻⢱⠀⠙⠀⢸⠀⡇⠀⢀⣾⢸⠀⡄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢂⠀⠙⡄⢸⢎⡆⠀⡆⠸⡆⢇⣇⡎⡎⢸⢀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⢧⠀⠰⡏⠘⣧⠀⢡⠀⡇⢸⡟⢀⡇⢸⢸⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠈⣆⠀⣧⠀⢹⡀⠸⡀⡇⢸⡇⢸⠀⣼⡇⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠘⣆⡏⣇⠀⣧⠀⣇⣇⣿⣿⡾⠀⣿⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠹⡇⠸⡄⢹⡆⢹⣿⢸⠀⣇⠀⣿⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠸⡄⠀⣷⡀⢳⠸⣧⠸⡇⢸⢸⠹⣼⡏⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⢳⠀⢏⢧⠘⡆⣿⣠⡇⡾⡸⠀⣿⠃⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢧⢸⠈⡆⢣⠁⢿⢿⡇⡇⠀⣿⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⠀⠂⠘⠘⠘⠸⠸⠃⠀⠈⠃⠀⠁

⠀⠀⠐⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣆
⠀⠀⠀⣿⡧⠀⠀⠀⠀⠀⢤⠄⠀⠀⢸⠆
⠀⠀⠀⡆⢢⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⡞⠂⠀⠀⠀⠀⠀⠀⢀⣠
⠀⠀⢰⣂⣸⡀⠀⠀⠀⣀⣸⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⠃⠀⠀⠀⠀⠀⠀⠈⠟⣡⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠉⠉⠉⠁⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⢠⣾⠋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣴⣦⠏
⠀⠀⢈⣿⣶⡛⠁⠀⠀⠀⠀⠀⠀⣶⣶⣷⣶⡄⠀⠀⠀⠀⠀⠀⢿⣿⣶⣿⣶⠀⠀⠀⠀⠀⠀⠀⣶⣿⣿⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⢀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣀
⢸⣉⠁⠀⠀⠀⢉⡁⠀⠀⠀⠀⢱⣀⣉⡆⠀⠀⠀⠀⠀⠀⢀⣿⣷⠛⠛⠏⣼⣦⠀⠀⠀⠀⢀⣤⣤⣴⣦⣤⣤⡀
⢸⣿⣿⣾⣾⣮⣿⡇⠀⠀⠀⡀⣸⠒⢒⣇⢀⠀⡀⡀⠀⠀⠀⠛⢁⣶⣦⣴⣌⠻⠃⠀⠀⠐⢷⡖⠒⢢⡔⠒⢲⣾⠂
⠀⠈⠉⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠀⠀⠀⠀⠀⠀⠙⠒⠁⠈⠒⠉

⠀⣠⣶⠊⠳⣦⡄
⠀⠉⠛⠀⠀⠉⠀⠀⠀⠀⠀⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠙⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠿⣿⣶⣶⣶⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡟⠁⠈⠿⠂

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣤⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠲⡀
⠀⠀⠀⠀⠀⠀⣤⣤⣼⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠣⡀⣀⣠⣤⣤⣤⣤⣤⡃⠀⣱
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣤⣤⣿⣿⠿⣿⣿⣿⡿⢿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⠟⠀⠈⠿⠿⠃⠀⠈⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡀⠀⠀⢀⣷⡀⠀⢀⣠⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣶⣾⣿⣤⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⡀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠲⣶⢠⣶⣶⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⢶⣶⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣼⣿⣿⣿⣿⠃⠀⢿⣿⣿⣿⣿⡟⠀⠀⠀⢄⠀⠱⡀⠁⠀⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⠀⠀⠸⣿⣿⣿⣿⠃⡀⠈⢦⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠛⠉⠀⠻⣿⣿⠟⠀⠀⠀⠙⠿⠿⠛⠄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠



⡿⠿⠿⠿⠟⠻⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣻⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠤⠴⠚⢉⡉⢻⢶⠆⠖⣻⡶⠖⠚⡉⠛⠚⣋⠉⠐⠛⠒⠒⡚⢉⡟
⠀⠀⠀⠀⠀⠀⢀⠀⣟⡋⠙⢦⢰⡖⠲⢄⢀⡀⠀⠀⠙⢿⡀⠦⢄⡙⠿⠸⠛⢣⣭⣅⠀⢞⣥⠄⠉⣁⡠⠤⠴⠖⠋⠀⡼⣁
⠀⠀⠀⣀⣤⡼⠉⠭⠍⠙⠂⠀⠙⠇⠱⢤⡉⠈⠿⠶⣄⠀⠘⢦⡈⠙⣦⠰⠓⠂⢸⡯⠰⠏⠐⠓⠤⣍⣉⠀⠀⠀⠈⠛⡛⠁
⠀⠀⢯⡁⠤⣤⡤⠤⣤⣬⡉⠙⢳⡤⢶⣒⢈⣭⣄⣒⡈⠷⠤⣀⡹⠼⣟⢘⡴⣶⠏⠀⠉⠛⠶⢒⡀⠈⣀⠀⠰⠖⠋⠙⠁
⠀⠀⠀⠙⠶⢤⣤⣉⠀⠨⣝⣆⣡⣴⠀⠀⠊⢀⣠⠤⠞⠉⠙⠒⢯⡂⡸⢯⡔⡱⠒⠲⠤⠽⠗⠲⠖⠒⠈⠉⠋⠁
⠀⠀⠀⠀⠀⠀⠸⢥⡤⢴⠶⣉⡽⢁⡴⠶⢶⣞⠶⠖⠲⣤⠴⣖⣒⣾⣿⡇⣟⣥⠭⠭⣝⠶⡚⠋⡙⠖⣛⣲⣻⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢖⣢⡽⠁⠠⠀⠤⣤⣤⠞⡱⢺⠋⠀⣰⠃⢟⣯⡀⠀⠀⠈⡇⢨⠑⠦⣈⠲⠻⣥⡌⠳⠠⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢀⣀⣒⣰⣉⠁⣧⣯⣤⣥⠏⣀⣼⣱⠀⡌⢿⡇⠀⠀⠀⣇⠸⠄⠀⢨⡑⢦⡤⢒⠚⠉⠅⠀⠽⣆⢀⣀
⠀⠀⠀⠀⠀⠀⠐⡶⢤⣀⣾⣀⡭⠞⠋⠀⠀⡶⢸⠋⠀⣠⢞⠉⡤⢃⢰⠱⣄⡈⠙⢣⠀⠘⢦⠞⣦⠀⡗⡀⠀⠘⠻⡶⢤⣀⠠⠬⠉⠉⠯⣤⠴⡻
⠀⠀⠀⠀⠀⠀⠀⠙⢦⣙⣛⣓⢶⣁⡾⣤⡴⠟⠃⠀⢈⡇⣪⡇⠀⠹⢸⠀⢀⠑⠀⣈⢣⡀⠀⠀⠈⢦⣁⡙⠂⢰⠶⣈⡲⢌⠉⠙⣀⣴⣴⣶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⡠⠞⠀⠹⢍⣳⡁⡎⢢⡀⠇⠰⠹⡍⠁⠀⠀⠀⠀⠀⠉⠙⢦⣱⡄⠉⠲⢭⣤⡭⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⢀⣵⠃⡇⠀⢷⠀⠀⡤⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⠀⠋⠈⢀⠇⣦⠘⢷⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⠀⠸⠀⢇⠀⣀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣇⠀⢀⣠⢴⠋⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢹⠈⢳⡼⠁⡸⣆⢹⣶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢯⢇⡇⢷⣼⡇⣼⡇⢾⢼⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣞⠾⣇⡟⣇⣶⡷⣳⠸⣾⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⡞⡇⢻⢈⣿⠏⣧⣏⢺⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠘⡇⣧⡟⣦⠈⢽⢰⣿⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄⡇⡏⠁⠞⠀⠀⠀⠸⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⡇⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡆⠀⠀⠀⠀⠀⠘⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⣄⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠘⡄⠀⠠⡀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⡇⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠘⡄⠀⢣⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⡇⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⠀⠀⠀⠀⠘⡄⠘⡆⠈⠟⠀⠀⢠⣦⠀⠀⠀⠀⠀⡇⠀⢸⣿⡇⠀⠀⡇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⢢⠀⢸⠀⠀⠀⠀⠀⠸⡄⢹⡄⢸⠀⠀⢸⣿⡆⠀⠀⡇⠀⡇⠀⠈⠟⠀⠀⢰⠇⡷⠈⢢⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢸⠀⠀⣿⣦⡀⠀⠹⡄⢣⠘⡄⠀⢸⣿⡇⠀⠀⡇⠀⡇⠀⢰⠀⠀⠀⢸⡴⡇⠀⢸⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⠸⣿⣷⡀⠀⢹⡈⣇⡇⠀⠀⣿⡇⠀⠀⣧⠀⡇⠀⢸⠀⠀⠀⡾⠀⡇⠀⢘⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠹⣿⣷⠀⠀⢳⡏⢸⠀⠀⠈⡇⠀⠀⣿⠀⣷⠀⢸⠀⠀⣼⡇⠀⡇⠀⡏⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢳⡀⠀⠙⢿⡇⠀⠀⣧⠀⡆⠀⠀⠀⠀⠀⢹⠀⢸⠀⢸⠀⡼⢹⠇⢰⡇⢠⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢷⡀⠀⠀⠡⠀⢰⠈⢇⢡⠀⠀⢸⡀⠀⢸⠀⠘⡆⡙⠸⠁⣾⠀⢸⠇⢸⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢣⠀⠀⠀⢂⢸⠀⠘⣾⡀⠀⠀⡇⠀⢸⠀⠀⣧⣿⠃⠀⡏⠀⢸⠀⡌⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠈⢇⠀⠀⠀⣿⠀⠀⢹⣧⠀⠀⢿⠀⢸⡀⠀⢸⡇⠀⢰⠇⠀⢸⠀⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠈⣆⠀⠀⣿⡄⠀⠀⢿⠀⠀⢸⡆⢸⡇⠀⣾⣇⠀⣸⠀⠀⡼⢸⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠄⠀⠘⣆⠀⣿⢹⡀⠀⠸⣧⠀⠀⣧⢸⡇⣸⢿⣿⡄⡿⠀⠀⣿⡿⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠹⣆⣿⠀⢧⠀⠀⣿⡄⠀⢻⣸⣧⡟⣸⠉⣿⠇⠀⢰⣿⡇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⠀⠀⠀⢻⣯⠀⠸⡇⠀⢹⣷⠀⢸⡟⣿⠃⣿⠀⢸⡄⠀⢸⣿⠃⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⣆⠀⠀⠀⣿⡀⠀⢻⡀⠘⣿⡆⠀⣿⡟⠀⣿⠀⡿⢳⠀⣸⣿⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⢹⡄⠀⠀⣿⣷⠀⠈⣧⠀⢿⢷⠀⢸⡇⠀⡟⢠⡇⠈⣇⣿⡇⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⢳⡀⠀⢻⠘⣆⠀⢹⡄⢸⢸⡆⢸⡇⢸⡇⢸⠃⠀⢹⣿⠁⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠈⢧⠀⢸⡄⠹⡄⠈⣧⠸⡇⣇⣿⣧⢸⡇⣾⠀⠀⣼⡟⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠘⣇⠀⡇⠀⢻⠀⢹⡀⡇⢿⡇⣿⣸⠀⡇⠀⠠⣿⡇⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠘⡆⠸⡀⠈⢇⠈⡇⢡⢸⡇⢹⡿⠐⠀⠀⠘⠸⢡⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠘⠀⠁⠀⠘⠀⢁⠈⠀⡇⠀⡁⠀⠀⠀⠁⠀⠈⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡤⠠⠀⠆⢀⠀⠂⠀⠀⠀⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢀⠂⠀⢀⠀⠲