Luigi mario kart Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠉⠍⠁⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⡀⠀⠀⠀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⡠⠐⠈⠉⠀⠉⠉⠁⠂⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⠒⢀⡠⠀⠀⡀⠀⣀⠈⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢸⠁⠀⢠⣷⡤⠤⠰⢧⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢙⠀⠀⠘⠿⠀⠀⠀⠀⠱⠀⠘⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣦⠇⠀⠒⡀⠀⠀⠀⡀⠠⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠀⢀⡀⠈⠀⠀⠁⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠁⠀⠘⠀⠀⠅⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⡼⡒⢄⠀⠠⠄⠤⢆⠀⢀⣀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⣠⠄⠙⠂⠀⠀⠀⠀⠈⠄⠂⠀⠀⠀⠀⠀⠊⠀⠀⠀⠈⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠠⠄⠆⠀⡀⠀⠁⠀⠀⠀⠀⠀⢀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠂⠐⠂⠀⡰⠒⠀⠀⠀⠶⢦⣌⠀⠈⣥⠠⢄⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢨⣀⡠⠐⠎⠀⠀⠐⠉⠃⠤⠸⣄⣠⠷⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠋⠑⢠⠤⠀⠃⠀⠀⠀⠀⠀⠀⠁⠀⢁⣀⡀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠲⢤⡁⠘⠀⠀⠔⢀⠀⠲⢀⡀⠀⠠⠀⠀⠀⠀⠀⠉⠀⢙⣤⠓⠀⠀⠀⠀⠀⠀⠒⢠
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠘⠀⠆⠀⢀⡤⠀⢬⡁⡰⡀⠀⡄⠙⠣⣤⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠘⢄⠓⠒⠒⠒⠐⠂⠓⠐⠺⣁⠄⠀⠀⠈⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⠀⢸⢠⠄⠀⠐⠀⠀⠀⠄⠆⣀⠀⢀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠁⠀⠀⠀⠰⢃⡀⠠⠤⠤⠤⠤⠤⠄⡀
⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⡠⠈⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠤⠄⠀⠠⢾⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄
⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠰⠖⠒⠀⠀⠀⠀⠀⢷⠀⠀⠀⠈⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢆⠀⠀⠀⠀⠰⠂⠂⠉⠉⠉⠑⢄⡀⠁
⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠀⠀⠘⠀⠀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⢘⡃⠀⠀⠀⠀⠀⠀⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⢀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠐⡀⢰⠀⠆⠠⣤⠆⠐⠀⢀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⣀⡀⡀⣀⢀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⡌⡀⢰⠚⠘⠂⣁⡁⠈⡀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⢢⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢠⠃⠀⣦⠄⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡦⡀⠁⠀⢀⠀⠀⢀⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢰⠀⠁⠀⠀⠀⠀⠀⠀⠀⢠⡅⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠀⠐⢠⠀⠈⠁⢰⢀⡄⢀⣁⢉⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢨⠀⢠⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠐⠣⡀⠁⠀⠈⠀⠒⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⠀⠀⠀⠀⠈⠐⠀⠐⠒⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠄⢀⡉⠀⠐⠒⠒⠒⠀⠀⠀⠀⠀⠒⠒⠀⠈⠀⣀⡀⠤⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⡰⠃
⠀⠀⠀⡠⠄⠤⢄⡀⠀⡠⠆⠐⠒⠄⣸⠀⠀⢰⠁
⠀⠀⠰⡁⠀⠀⠈⠉⠉⠑⠒⢄⠀⠀⢺⠀⠀⡏⠀⠀⢠⠞⠉⠉⠁⠢⠤⠤⣀⡀⠀⢀⡀
⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⠀⠀⠇⠀⠀⣞⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠁
⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠋⠉⠉⠀⠀⠀⠘⢄⠀⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢀⠔⣊⡉⠁⠈⠉⠢⡘
⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠰⢁⣺⡿⠛⠒⠲⠶⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⡄⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⡞⠁⠰⠷⠀⢠⡶⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠰⡀⠀⠀⢰⠃⣄⡀⠐⠁⠀⠈⠑⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠈⠢⣀⠘⡜⣿⣿⣧⡀⠀⠀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠈⠉⢳⣌⠙⠋⣉⠝⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⢍⠙⠉⠁⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠚⢢⠀⠀⠀⠘⣧⠀⠀⢀⡼⠦⠀⠤⠄⠒⠦⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⣠⠔⠚⠓⠜⠁⠠⠤⢄⡀⡄⠀⠀⠀⡷⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⢢⡀⠹⡞⠈⠲⣒⣡⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⣇⡰⠃⠰⢤⠤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠈⢢⠤⠾⠝⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠃⠀⠀⠀⠀⠀⠠⠆⠀⠐⠂⠴⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠉⠑⡄⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠩⢝⣓⢴⡁⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⣀⠀⢀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢤⠟⠋⠙⡛⢿⣢⡀⠀⢧⡀⠀⠀⠀⠀⠀⠀⠁⢰⢁⠘⠀⣈⠀⠉⠀⠈⡌⢠⠦⢆⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠼⢷⡇⠀⣴⡇⠉⡱⣄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠐⠉⠂⠀⠂⠘⠀⠂⠑⠀⠐⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⢋⠰⣎⢔⡉⢹⠃
⠀⢀⠤⠀⢄⠀⠀⠀⠀⠀⠀⠀⢿⣶⡶⣿⣿⡿⠃⢀⣈⣠⠞
⠀⠐⠀⠀⠀⠉⢦⡀⠀⠀⠀⠀⠀⠘⡜⢏⠏⠀⢀⠎⢫
⠀⠀⠈⠢⠀⠀⠁⠈⠙⡖⠂⠤⠄⠀⢈⣢⣀⣀⣬⡉⠉
⠀⠀⠊⣀⡀⠀⠀⠀⢀⠂⠀⠀⢀⠔⡽⠁⡴⠉⡴⠉⢢
⠀⠀⠀⠀⠈⠁⠈⠒⠉⠁⠉⠰⠣⣼⠓⡎⠀⢰⠁⠀⠀⠑⢄⠰⠉⠉⢂⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⠃⠀⣇⢀⡾⢻⣄⠀⡠⠄⠓⢤⣀⠈⠒⠒⠠⢤⠤⣴⣿⣅⡤⠉⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠈⠉⠀⠀⢸⡟⠀⠀⠀⠀⠊⠉⠐⠄⡀⠀⢠⣿⢢⣿⣇⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⣸⠚⢢⡀⠀⢀⠀⡀⠀⠀⢺⠀⠨⣟⣛⡏⠄⠀⡀⠀⠀⠀⠰⠒⠒⢄⠐⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⣄⡀⠀⠀⠀⢸⡄⠀⠈⠂⠀⠗⢶⣭⣿⠁⠚⢦⣄⠀⢀⡆⣀⠈⠀⡀⠀⠀⠘⢀⠀⢣⡤⠴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢇⠀⠀⠀⠀⣇⠀⠂⠄⢀⡀⠀⠀⠀⠈⠢⡀⠀⠑⡄⠀⠛⠁⠀⠀⠀⠀⠀⠀⠁⡈⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠸⡀⠀⠀⠀⠸⡀⠀⠂⠰⣧⠀⠴⡀⠀⠀⢱⠐⠀⡜⠋⠁⠀⠈⠁⠒⠠⠦⠄⠐⠚⠉⠀⠀⠀⠈⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠉⠢⠄⣀⣇⠀⠀⠀⠀⣣⡀⠀⠀⣿⡀⣿⡹⢟⠀⠀⡄⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢀⣀⡀⣸⠤⠖⠉⠀⠀⠉⢢⠈⠉⢻⠢⠄⠈⠀⡰⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⢹⣀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠂⠀⠚⠋⠁⠘⠢⠤⠤⠀⢀⣀⠀⠀⠀⠀⠀⢀⣀⠀⠤⠤⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠤⠴⠞⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⠄⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡧⠤⠖⠒⣀⣤⣤⡀⠀⠘⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⣠⡚⠁⡟⠁⠀⠉⠲⢄⣀⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⡯⠿⠠⢿⡆⢀⡀⠀⡎⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⡷⠋⢹⠀⢧⣀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⠤⢤⣼⡥⠔⠁⠀⠀⠱⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡷⠛⢝⢦⠉⠉⠉⠑⠺⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠉⠀⠀⠈⢆⡇⣀⡀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡜⢸⢸⠀⢧⣠⠴⣿⣯⣤⣏⠙⠂⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢚⠁⣠⠀⣗⠶⡃⡼⣉⣄⠀⠈⠳⡄⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡉⠿⣋⣀⣼⣟⣡⠞⡇⠀⣝⢣⡀⠀⠈⡧⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢁⣠⢖⣈⣁⠀⢀⢇⡴⠛⠲⡟⡆⢃⣀⣀⣇⠀⠇⡴⠒⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⡹⠊⠁⠀⠀⠀⠉⠻⡞⢮⡀⠀⠀⠀⠳⡎⠀⠀⠉⢾⡸⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠉⢢⡀⠀⠀⠘⡄⠀⠀⣼⠁⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⠀⠀⠈⡵⡶⠁⠀⠀⠀⠀⠀⢀⣀⠀⣠⠞⠀⠀⠀⠹⡀⠀⠀⠘⣄⢾⠃⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢀⠎⡜⠀⠀⠀⠀⠀⠀⣰⠃⠈⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⢸⡎⡠⢊⠞⠉⠉⠓⣲⠦
⠀⠀⠀⠀⠀⠀⢀⠴⠒⠒⠤⡀⠀⠀⠀⠀⠸⡀⠀⠀⣘⡞⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢰⠯⣁⡞⠀⠀⠀⣰⠁
⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠈⢑⠎⠙⠤⣀⡀⠀⠀⠀⣠⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⣌⠀⠀⡇⠀⠀⠀⡆⠀⢠
⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢲⠃⠀⠀⠀⠀⠀⠉⠉⠉⠀⡧⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⡜⠀⢀⠎⠀⠈⠉⡳⠲⡤⢄⣧⣠⠏
⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠈⠉⠑⠒⠦⠤⠄⠴⠤⠒⡏⠀⠀⠀⢰⠁⠀⡂
⠘⠓⠤⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠓⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡆⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠤⢄⣀⠀⠀⠀⠀⠱⢄⡀⠀⠀⠀⢀⣠⠔⠊⠀⠀⠀⠀⠀⠈⠉⠁⠒⠉⠉⠑⠒⢦⡑⠒⠦⠤⠥⠴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠤⢄⣀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⠤⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠙⡳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢀⢠⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⣨⣼⠚⠉⠉⠉⠙⣶
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠀⠀⠀⠀⣀⡴⣎⡥⡿⠛⣯⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢀⣀⣤⠞⠳⢤⡀⠀⠀⣼⣾⠤⠒⠒⢦⡀
⠀⠀⠀⠀⠀⠀⠹⣆⡀⣠⡏⠠⡀⠱⣄⢀⡇⣠⡁⠚⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢇⢧⠀⠙⠀⠈⠉⠀⠙⣿⣷⣶⣤⣤⠤⠞⠁
⠀⢠⠶⢲⢦⣀⠀⠀⠀⢨⠃⡙⠒⣦⣀⣀⡀⠀⠈⠉⢛⡿⠃⣀⣠⣴⣏⡇
⢠⠏⠀⢆⡀⠈⠳⢤⡀⠈⠉⠉⣿⠉⠁⠈⠉⠉⠓⠒⢿⠖⠚⢁⡂⠀⠀⢽⡄
⢾⠀⠔⠠⠼⠀⠀⠀⠙⢦⣀⣰⢷⡀⠀⣀⡀⠀⠀⠀⢸⠀⠀⠠⠅⠀⠀⢰⣗⣀⣀
⠈⠻⠦⣤⣀⣀⠀⠐⠕⠀⡿⢽⡇⢝⢦⣈⢉⡹⢟⢗⣻⣤⣄⡀⢀⡀⠀⣾⢿⣗⣬⣉⠒⢤⣀
⠀⠀⠀⠀⢸⣽⡹⠗⠚⠛⠳⢶⣇⠀⠢⢻⡉⠀⠈⠑⠒⠁⠀⠉⠉⠓⠊⠙⡏⠀⠈⠹⡍⠒⢌⠙⠦⣄
⠀⠀⠀⠀⡼⠋⠀⡠⢴⡦⢤⡀⠈⢦⠀⣾⡛⠛⠓⠒⠦⢤⡀⠀⠀⣀⠤⠤⠧⢄⡀⠀⣽⡄⠀⠉⠢⡈⠳
⠀⠀⠀⢰⠁⠀⣎⣀⢘⡃⣀⡹⡄⠀⣷⡯⠭⠭⠭⡙⠢⠤⢽⣀⠞⢁⠔⢒⠒⢤⠙⢮⣽⣽⣦⣤⣤⣽
⠀⠀⠀⢸⡀⠀⢏⠉⢨⡅⠈⢡⠃⠀⣿⡇⠀⠀⠀⠈⠑⠒⢺⣿⠀⡇⠤⠸⠀⠄⡇⢸⣿⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠳⡀⠈⠓⠬⠥⠒⠁⢀⣼⣼⣇⠀⠀⠀⠀⠀⠀⢸⣿⣄⠘⠦⠼⠤⠞⢁⣼⡏⠀⠀⠀⣠⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠐⠀⠒⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠂⠤⡀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠐⠈⢢⡀⠐⢀⠔⠂⠲⡤⠊⢱
⠀⠀⠀⠀⠀⠀⠀⡘⠈⠀⢀⠀⠀⢀⡙⠃⠸⠇⠑⡀⠙⠀⠀⡘⡀⠀⠸⠀⠀⠠⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠠⢀⠀⠀⡀⠠⡀⠄⠐⠃⠀⢀⠆⣤⠈⠓⠂⠐⡄
⠀⠀⠀⠀⠀⠀⠀⠰⠄⠐⠐⠀⡀⢅⡨⢀⡠⠃⡀⠀⡇⠀⠈⠀⠈⠀⠀⠤⠔⠃⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⢀⠀⠀⠀⠀⠀⠇⣀⠄⠀⠀⠀⠀⠂⣨⠋⠀⠀⠀⠀⠀⡠⠐⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠘⠢⢖⠤⠠⠐⠈⢑⠤⠀⢀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠁⠀⢀⠀⠀⠰⠊⠁⠉⣱⠀⠀⠠⠈
⠀⠀⠔⠀⠀⠀⣦⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠆⠀⠜⠄⣀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⡔⠐⠀⠀⠠⡀⠀⠀⠀⡐⠀⢀⡀⠀⠀⠀⠀⠀⠉⠂⠠⠐⠁⠀⠐
⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⢀⠀⠀⠈⡀⠀⠀⠀⡔⠁⠀⢀⠔
⠀⠀⠀⠀⠀⠁⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠈⡖⠀⠀⠈⡆⠀⠀⠀⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⡠⠐⠁⠀⠀⠠⠃⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠖⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⠀⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠁⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠉⣉⠤⡶⠚⠶⢀⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⣸⣣⢀⣦⠀⠀⠀⡘⠂⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠘⠄⠉⡆⢣⣀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⢠⡎⠤⠊⠀⠀⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠜⠋⢎⢋⠁⠈⠉⠛⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡆⠁⡄⡀⠀⢀⣬⠄⠤⠄⡀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⢴⠀⡃⢣⣈⠊⣵⠋⠉⠛⢦⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢒⠳⠞⡀⣱⡟⡩⠇⠀⢰⢇⠀⠀⢡⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⣀⠤⠎⣉⡀⠠⢁⠞⠳⢞⡆⣀⡀⣠⠀⠆⡄⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠝⠉⠀⠀⠀⠀⠙⡝⠠⡀⠀⠀⠱⡅⠀⠀⢱⡔⠀⠀⢀⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠄⠠⣀⡰⠃⠀⠀⠀⠀⠀⠀⠀⡨⠀⠈⢢⠀⠀⠘⡄⢀⡼⠁⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠐⡝⠀⠀⠀⠀⠀⡠⠒⠒⠊⠁⠀⠀⠀⢃⠀⠀⠐⣂⠁⠔⡡⠂⠤⢀⣀
⠀⠀⠀⠀⠀⠀⡠⠤⢄⡀⠀⠀⠀⠀⡆⠀⠀⣌⡌⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣵⡂⡴⠀⠀⠀⡜
⠀⠀⠀⢀⠄⠊⠀⠀⠀⠈⠢⢀⡀⠀⠈⢐⠖⠛⢄⡀⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢰⡁⠈⡅⠀⠀⢠⠀⢀
⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢐⠎⠀⠀⠀⠀⠈⠁⠀⠀⠆⠤⠀⢀⠀⠀⠀⠀⠀⡐⠀⡐⠁⠀⠈⡑⠲⠤⠸⠤⠎
⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⠈⠁⠒⠀⠐⠒⠈⠁⠀⠀⢰⠀⠠
⠀⠈⠀⠀⠒⠠⠄⠀⢀⠀⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⢀⠠⠊⠀⠉⠐⠂⠤⠄⠠⠤⠤⠀⡀⠄⠀⡀⢀⢀⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠠⠄⣀⠈⠐⠀⠀⠐⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⢀⠀⠀⠀⢀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠛⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠁⢀⡴⠋⠉⠙⢮⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⢸⠁⠀⠀⠀⢘⣯⣧⣠⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠘⣧⣤⠖⠛⣉⡁⠤⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⣠⣞⣉⣤⣾⣋⣡⣤⣄⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡏⠀⠀⠀⣠⠋⣰⠟⠋⠛⠀⠀⠉⣈⠛⣤⠴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠈⠀⠀⢀⣼⠓⠚⠉⢴⡁⠉⢂⠀⣨⡀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⣀⣀⡞⢱⡄⠀⠀⢻⣻⡆⠀⠀⢹⡾⠚⠛⠛⠳⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡾⠉⠉⠙⢦⠙⠲⣄⠈⠛⠵⠀⠀⠈⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢿⡌⠛⠞⠃⢠⣦⣄⣀⣠⣄⡀⠀⠀⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠐⠁⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⢶⠷⣆⠀⠀⠈⠛⣿⢛⣋⣤⠙⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⠘⣆⠀⠀⠀⠹⣄⡸⠃⣼⠃⠀⠀⠀⠀⣀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠻⠖⢻⡄⠀⠀⠀⢀⣠⡼⣣⠤⣤⠞⢶⡞⠉⢷⠋⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠾⠷⣤⢤⠤⠽⣥⣄⡏⠀⣿⠀⢸⣇⠀⡼⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠈⢳⡀⠈⠲⣄⠀⢰⣮⡻⣤⡞⠳⠞⠈⠋⠁⠀⢸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⢷⠀⠀⠈⢧⡈⠻⢷⡄⠙⣄⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠘⡇⠀⣠⡄⢻⡉⠉⣷⠠⠞⠶⡀⠀⠀⠚⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⡰⣰⣧⢘⠀⠀⢸⡃⠀⠸⣧⡇⠀⡷⠶⠚⢛⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⠋⠉⠀⠓⢤⡀⠀⢀⣾⡴⠃⠻⣄⠠⢔⣹⠃⠀⠀⠹⢮⣽⡇⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠛⡥⠀⠀⠀⠀⠀⠀⠙⣴⢻⡇⠀⠀⠀⠈⠙⠉⠁⠀⠀⠀⠀⠀⠀⣿⣤⡴⠋
⠀⠀⠀⢠⠖⠋⠁⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⣰⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⣵⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠛⠁⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠹⢄⠧⣄⠤⠶⠒⠛⢱⠃⠀⠀⣠⠜⠁⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⢀⠞⠁⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⠄⠀⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠋⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠻⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣀⡤⠚⠁⠀⠉⠓⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠓⠒⠂⠤⢄⡀⠀⠀⠀⡿⠒⠊⠉⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠳⠤⠴⣧⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒⠒⠚⠛⠿⠤⠶⣲⡶⠶⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢧⣆⣀⠤⠀⣤⣐⣢⠞⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡠⠤⠤⠤⢤⣄⣀⠀⠀⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⡠⠊⢹⠏⠉⠈⠑⠦⣀⢀⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⣘⡩⠦⢴⣷⠀⠀⠀⢀⠎⠁⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⢹⡤⠊⠃⠘⣄⢀⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣄⣀⣀⡜⣀⡤⠃⠀⠈⢫⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⢞⠫⡔⠒⠒⠒⠤⢴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠋⠀⠀⢱⢱⠀⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢊⠄⡆⡇⢠⠀⢀⣠⣼⣒⣒⡒⠠⡄⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮⡠⡎⢰⠀⢣⣀⡹⠁⡴⠛⠉⠉⠓⣄⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠜⢧⡴⠊⠑⣶⠕⢋⡷⢸⠀⡯⡇⠀⠀⠈⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⢀⡸⠓⠚⠋⢰⠋⣠⢬⣠⣷⡘⡄⠀⠀⠏⠉⡇⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⡎⠔⠚⠉⠙⠒⠶⣤⣼⠔⠁⠀⠈⠳⣇⡴⠒⠒⠲⣀⠃⡌⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡯⠊⠁⠀⠀⠀⠀⠀⠀⠘⡌⠑⢦⠀⠀⠀⠈⢣⠀⠀⠀⢸⡞⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠔⠒⠢⢄⣀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠑⡄⠀⠀⠀⢣⠀⢀⡟⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⣠⢊⠏⠀⠀⠀⠀⠀⠀⣠⠒⠤⠔⠊⠀⠀⠀⠀⠘⡄⠀⠀⠀⢶⢩⠃⣠⢊⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⢣⠃⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠘⣧⢞⣡⠋⠀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠉⠢⡀⠀⠀⠀⠀⠘⠄⡀⢠⣶⠁⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠸⠓⠂⡏⠀⠀⠀⢰⠁
⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠈⠒⠢⢤⣀⡀⠀⡼⠁⠈⠒⠠⠤⢤⡤⡤⠔⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣠⠷⠤⢀⣇⠀⠀⠀⢸⠀⢀
⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠒⠂⠤⢀⣀⡀⠀⠀⠀⠀⢀⠆⠀⣰⠁⠀⠀⠀⡜⠉⠖⠂⠼⠦⠊
⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠈⠉⠐⠒⠒⠚⠒⠉⠇⠀⠀⠀⠸⠀⠀⡄
⠈⠁⠃⠒⠠⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠉⠉⠒⠢⠤⢀⣀⠀⠀⣀⣀⠀⠀⠀⡃⠀⠀⠀⡆⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠢⠤⢄⣀⠀⠀⠀⠑⠤⢀⣀⢀⣀⡀⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠈⠑⠢⡉⠁⠒⠂⠶⠶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠢⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠢⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⢤⡀⠀⠀⠀⠀⠀⠀⢀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠴⠖⠒⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⠉⡀⠀⠉⠛⢷⣦⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⡴⠋⠉⠀⠉⠑⣄⢙⣷⣴⠾⠛⠋⠉⠉⠻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⠀⢸⠁⠀⠀⠀⠀⣠⣼⠟⠋⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠸⡄⠀⠀⣠⡾⠛⠁⠀⣠⠴⠂⠀⠀⠀⠀⣾⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠙⣦⡾⠋⠀⠀⣠⠞⠁⠀⡀⠀⠀⢀⣾⠏⠉⠉⠛⠿⣶⣤⡀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠉⣿⡆
⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⣠⣾⣡⣤⣴⣿⣿⣧⣠⡾⠃⠀⠀⠀⠀⠀⠀⠉⠛⢷⣤⡀⠀⠀⣠⡿⠋⠀⠀⢠⣿⣀⣤⣴⢶⣦⡄
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⡾⢡⣶⣶⣾⣯⡉⠀⠀⠘⠁⣀⠈⢻⡇⠀⠀⠀⠀⠀⠀⣴⠟⠛⠛⠿⣿⣦⣼⠟⠀⠀⡀⢠⣿⠿⠋⠁⠀⣀⣸⣧⡀
⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⣰⡟⠀⣿⠟⠁⣀⣄⣀⠀⠀⠀⣜⠉⠙⢆⣿⡀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠘⢿⣏⡀⠀⠀⠈⠻⣥⠀⣀⡴⠞⠋⠉⠉⣿
⠀⠀⠀⣠⡾⠻⠀⠀⠀⠀⢰⡿⠷⠟⠛⠀⣼⠁⠀⠈⢧⡀⠀⢻⣖⣄⣼⡾⠷⠶⢶⣤⡀⠀⠀⠙⣷⡀⠀⠀⠀⠈⠙⢦⠀⠀⠀⠈⠻⣏⠀⣀⣤⡶⠾⠿⣶
⠀⠀⠀⣿⠁⠀⠀⠀⠀⢠⣿⡀⠀⠀⠀⠀⢹⣠⢦⡀⠀⣧⠀⣨⡿⠋⠁⠀⠀⠀⠀⠙⢿⡄⠀⠀⢸⣷⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠻⠋⠁⠀⠀⣠⡿
⠀⠀⠀⢿⡄⠀⠀⠀⠀⣾⠋⢷⣄⠀⠀⠀⠈⢿⣿⡷⠀⣼⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣼⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛
⠀⠀⠀⠈⣿⣦⡀⣀⣴⣿⡄⠀⠉⠛⣶⡀⠀⠀⠙⠳⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⢸⡟⠈⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉
⠀⠀⠀⢸⣿⢉⣿⠋⠁⠈⠹⣦⡀⠀⣿⡇⢠⣿⣦⣄⣀⠀⠀⣤⣀⠀⠀⠀⠀⠀⣠⣾⣏⠀⠀⣸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⢸⡇⢸⡇⠀⠜⠛⠳⣬⠙⠛⠋⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣿⣿⣿⣿⡿⢀⣼⠏⠈⠻⣷⣄⠀⠀⠀⠀⠠⣤⣶⠾⠛⠉
⠀⠀⠀⢸⡇⠀⢿⡀⠀⠀⠋⠉⢷⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⣿⣿⣿⣿⡿⣣⡾⠁⠀⠀⠀⠈⠙⠷⣦⣤⣤⣤⣾⣿
⠀⠀⠀⢸⣷⠀⠈⠻⣦⣀⠀⠀⠀⠀⣀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣯⣥⣤⡬⠛⢻⣿⣴⠏⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠉⠉⢸⡿
⠀⠀⠀⠀⣿⡀⠀⠀⠈⠙⠛⠓⠻⣿⠉⢷⡄⠀⠀⠀⠈⣷⠶⠶⠶⢶⣾⠃⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⢻⣆⠀⠀⠀⠹⣆⠀⠀⣠⠏⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⣿⣀⣀⣴⣀⣿⡄⠀⠀⠀⠈⠙⠋⠁⢀⣴⣏⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠻⣧⠀⠀⠀⠀⠈⠉⠉⢉⣩⣼⣷⡀⠀⠀⠀⠀⠚⠛⣿⡅⠙⢷⣄⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⣀⣀⣠⣾⢿⡍⠀⠘⢿⡟⠛⠛⠚⠛⠛⠉⢻⡀⠀⠙⣷⡀⣠⡾⠁⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣟⠉⠙⢷⣤⣹⣆⠀⠀⠹⣆⠀⠀⠀⠀⠀⠈⢷⡀⠀⠈⢿⣿⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠀⠀⠀⣿⠉⢻⡶⠶⣦⣼⢧⣄⠀⠀⠀⠀⠈⢷⡀⢀⣠⣿⣧⠀⣠⣴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣴⠟⠀⠀⣿⠀⠸⣧⠀⠘⣷⣤⣶⠶⠟⠛⣧⣾⣁⣬⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣦⣤⣼⠏⠀⢰⡟⠀⠀⣿⣶⣶⡶⠶⠾⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠛⠛⠻⠶⠶⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠶⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢞⡋⡉⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⢠⢖⣹⡒⣽⣆⣤⣾⣟⢷⣤⣄⠀⠀⠀⣀⣴⠞⣶⠶⣦⣠⣤⣴⣏⣁⣞⠈⡆⠀⢹⣆
⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⢠⣸⣿⠿⠞⠛⠛⣒⣺⣇⠀⠙⣷⢀⣸⡏⠻⡀⠻⢀⡿⣷⣦⣤⣄⡉⠙⢶⡁⠀⠀⢻⡄
⠀⠀⠀⠀⠀⣼⠃⠀⠀⢀⠔⠊⠁⢀⡠⠔⣾⣿⠿⠟⠙⠛⣠⡿⠹⣇⡉⠂⠀⠀⠉⣠⡿⢿⣿⡆⠉⡓⢄⡑⠄⠀⠸⢷⣄
⠀⠀⠀⣠⡶⠏⠀⢀⣔⣁⡤⠔⢺⡅⠀⢸⡿⠷⠶⣤⣒⣺⡟⠁⠀⠈⠙⢦⣄⡀⢸⡃⠀⠀⠈⠀⠸⠃⢀⠭⠽⡄⠀⠀⣿
⠀⠀⢸⡏⢀⣀⣠⡏⠘⢄⡀⠀⠘⠟⠀⠈⠀⠀⠀⠈⣿⠋⠀⠀⠀⠀⠀⠈⠳⢶⡚⣷⢤⣤⠤⣤⡤⢤⠘⠦⢔⡋⠑⣶⠏
⠀⠀⠈⢷⡏⠀⢤⡙⢦⣰⠃⢸⠓⠶⠤⢄⣀⣀⣀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡌⠓⣖⡦⢤⡤⠞⠀⣀⠫⠀⣠⡟
⠀⠀⠀⠸⣧⡀⠠⠃⠀⠀⠀⠈⢹⣆⣀⣀⣉⣩⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠘⢮⠊⠀⢠⣏⣬⡿⠋⠁
⠀⠀⠀⠀⢈⣻⣿⡿⠿⣦⣄⡀⠈⢇⣡⣿⣿⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣷⠟⢩⢟⡿⠿⣤⣀⠀⠀⠀⠀⣀⣤⣄⡀
⠀⠀⣴⠶⠿⣍⡀⢀⡤⠞⠉⡏⠙⢿⣉⡿⢻⣦⣤⡾⠛⠻⢷⣄⠀⠀⠀⠀⠀⠀⠀⣼⢻⠉⡲⢧⣸⠘⢄⡀⠉⢹⠟⠛⠻⠍⠨⠔⢛
⢠⡾⢋⠀⠀⠀⢹⡟⠀⠀⢠⠇⡔⠉⠳⡀⠘⡏⣿⠀⠀⠀⢸⢻⡇⠀⠀⠀⠀⠀⠀⣿⠋⠘⢦⡠⠛⢦⣈⣿⠶⣞⣀⠀⠘⠃⠀⢈⣩
⣿⡀⠋⠼⠃⢀⠀⣯⡉⠉⠁⠀⠑⠤⠞⠁⠀⢸⡏⠀⠀⢀⢏⣿⠃⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⣿⠀⠉⠙⠶⣄⠘⣿⠋⠉
⠘⢷⣄⣀⠀⣻⠞⠋⢹⢷⡄⠀⠀⠀⠀⠀⣠⣾⣅⠀⢀⢾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⣀⡴⠿⢦⡀⠀⠀⠙⠷⠟
⠀⠀⠈⢹⡟⡇⠀⠀⠀⢸⣧⣤⣤⣤⡶⠟⠋⠈⠙⠛⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠽⠋⣻⠭⠄⠀⢸⣷
⠀⠀⠀⣿⢹⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⢀⣾⡏
⠀⠀⠀⠹⢿⣆⣀⣀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣶⣾⣷⣶⣶⣿⠟
⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠰⠊⠠⢈⠑⠀⠀⠀⠈⠂
⠀⠀⠀⢴⠀⠐⠒⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠬⢤⣀⣠⠁⠆⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⢸⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⢀⡈⠉⠓⠾⡀⡀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⢀⣤⣤⠉⠐⢢⣀⣉⠢⡀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡾⢋⠙⠀⠀⠾⠛⠻⣷⡀⠢⡀⠀⠀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠌⣷⠀⢀⠐⢀⣂⡘⠃⠂⠰⡄⠀⠀⠈⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠓⠛⠾⣿⠀⠀⠀⣼⣿⡆⠀⠀⢀⠙⢀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⣻⠟⠀⠀⡠⠂⠠⠊⠀⠈⢢⡜
⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⡀⠀⡆⠀⠉⠄⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠘⠄⠊⣠⣄⠂⠀⢨
⠀⠀⠀⠀⠀⠀⢀⠆⠠⢀⠈⠱⣄⠀⠀⠈⡀⠀⠀⠀⠈⣶⣤⣀⣠⣤⣶⣿⣶⣿⣿⣿⠀⠀⠀⠀⠡⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⢸⡄⢀⠀⠰⡀⠈⣦⠀⠀⠑⡀⠀⡀⠀⢿⣿⣿⡿⠋⠛⢿⣿⣿⠿⠃⠀⠀⢀⣀⡀⢀⠰⠃
⠀⠀⠀⠀⠀⠀⠘⡀⠀⠈⠢⠘⠁⠀⠀⠀⠔⠈⠁⠀⠀⠀⠂⠘⡀⠙⠏⠐⢂⠃⠀⠀⠀⢀⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠡⡀⠈⠒⠁⠀⠀⠀⠀⡄⠀⣀⠨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠈⠂⢠⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠀⠀⢀⡘⠀⠀⣀⡤⠒⡠⠋⠀⢂⠴⠋⠀⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠂⠀⠀⠀⠀⠐⠉⠁⠤⡾⠉⢀⠄⠀⠀⡐⠁⠀⠀⠀⠁⠀⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⢀⡐⠀⠀⠦⠀⢠⠎⠀⠀⠀⠀⠁⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠊⠀⠁⠰⠀⠀⠈⡠⠂⢢⠀⢀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⢡⡀⠀⢀⠃⠀⠀⠂⡄⠀⢀⠀⠻⡈⠄⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠴⠇⠤⠈⠀⠀⠀⠠⡀⠒⢊⠔⠀⠀⠘⢦⠀⠀⠤⠂⠀⠀⠀⠀⠲⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⠱⠆⠀⠀⠀⠀⠀⢀⡀⠶⠉⠉⠐⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⠀⠀⠀⠀⠁⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠁⠊⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠘⠢⡀⠀⠀⠀⠋⠀⠒⠀⠠⠤⠴⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠈⠄⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠈⠐⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠄⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠁⠀⠈⠂⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠉⠐⠀⠤⠴⠀⠀⠀⠀⢀⡀⠠⠤⠄⠰⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⢀⣀⡀⠀⠀⢀⡐⠖⢀⣀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠉⠉⠀⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠚⠶⠂⠄⠀⠀⠀⠀⠀⠠⢀⠎⠀⠀⠀⠀⠀⢀⠀⣄⢀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠁⠛⠙⠙⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡫⠀⠀⠠⣀⠀⠉⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⢰⡷⠛⣧⠈⠀⠀⠀⠀⠑⢄⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠛⣉⣉⣉⣉⣱⣗⠲⠤⣄⡀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠐⠈⢩⡿⢿⠉⠉⡉⠈⠙⠒⠊⠉⡶⢤⣀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠦⠤⠴⡈⢨⡇⠐⣷⡆⠀⠀⢠⡎⠀⡸⠁⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠐⠉⠉⠋⠀⠹⠯⠄⣠⡄⠳⠴⠁⠘⠁⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡀⠀⠀⠀⢀⣴⣷⣿⡏⠁⠀⠀⠀⣠⢴⣏⠑⠂⠶⠖⠉⢉⣢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⣶⣶⣿⡿⠛⣻⡇⠀⢀⣠⠞⠓⠾⣄⣸⠓⠦⣔⠒⠉⠙⠁⢐⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⣀⣤⡠⠛⠉⠉⠁⠈⠀⠈⠳⡀⠀⠈⢿⡲⣄⠀⢳⡎⠀⢀⣮⣩⣟⡁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠀⢿⠞⢛⡉⢌⠀⠄⠀⠀⠀⠀⠀⠀⠀⣷⠞⠃⢸⣷⠀⡀⢸⣇⠀⢸⢀⡟⣨⢷
⠀⠀⠀⠀⠀⢀⣠⢤⣮⠵⠤⢤⣇⠉⠀⠈⢻⠄⣀⠀⠀⠀⠀⠀⣴⣿⠓⠶⠎⢹⡇⠃⡸⠉⠵⢺⣿⡿⠥⢧⡀
⠀⠀⠀⠀⠄⠀⠀⠸⡧⠤⠤⣀⠈⢶⣗⠒⣺⠶⠋⠉⠙⠲⢤⡞⠉⠛⠂⠀⠀⢸⡿⢰⣏⡺⠻⠟⠁⠀⠀⠀⠈⠑⢦⡀
⠀⠀⠀⢰⠀⠀⠀⢸⠂⠀⠒⠎⢣⢸⡿⠻⡟⠠⢭⣀⠲⡀⠈⢧⠀⠀⠀⠀⠀⣼⢣⣏⠹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠠⠘⡀⠀⠀⢹⢉⠁⠐⠠⢤⡟⠀⢠⡅⠀⠀⠀⠀⠘⡆⢸⠀⢠⡄⢀⣼⢡⣿⠟⠀⡀⠀⠀⠀⠀⠀⠀⠀⣴⣶
⠀⠀⠀⠀⠀⠠⣠⠋⢯⣍⠀⢤⡞⠀⢠⠛⠛⠀⠤⣀⠀⠀⣿⢸⣄⣾⣷⡿⠟⠋⡠⠶⠶⠤⡀⠀⠀⠀⠀⠀⠰⣿⠟⡌
⠀⠀⠀⠀⠀⠀⢘⡦⣄⠀⠉⠘⠣⢤⣌⡉⠀⢲⣤⣌⠧⠶⠿⠛⠁⠀⠀⠀⠐⠺⠖⠒⠒⠂⠉⠀⢀⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠸⡔⢇⣈⡿⢦⣢⣤⣄⡉⠉⠉⢁⠀⡤⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠉⠀⠀⠀⠀⠈⠀⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣄⡀⠀⠇⣀⡹⣉⠽⠏⣠⠧⠾⠀⠀⠀⠀⠀⢰⣹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠶⠶⠷⠤⠐⠁⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⡛⢓⢦⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠙⣤⢋⠁⠀⢘⡆⠀⠀⠀⠀⠀⡠⢒⠤⢄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣱⣥⠗⠚⠑⣼⠁⠀⠀⢰⠐⠞⠁⠊⠜⢉⠂⠚⢹⠉⡆⠀⠀⣀⣀⠀⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢰⡻⠁⠀⣆⢠⠟⠉⠉⣆⠀⠇⠠⠀⡀⠀⠋⢹⠔⠘⠀⠥⢤⣘⠀⠀⠙⢯⣦⡄⡙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠸⢄⣀⡀⠙⠀⣀⢀⣠⡇⠀⣏⠀⠀⢀⡔⠉⢡⠀⠀⠀⣠⣚⣙⣤⠲⠬⣦⠻⡕⠁⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡴⠉⡐⠤⠃⠹⣿⡿⢿⢻⢁⠜⠉⠑⡦⠚⠀⠀⠀⢧⣀⢠⡎⠀⠈⠳⢀⡤⠉⢳⢇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⣤⠴⡦⣄⠈⠀⢙⣼⠋⠀⠀⡴⠁⠀⠀⠀⠀⠀⡇⢰⣷⣄⣀⣀⠘⠁⠂⠘⢾⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⠤⡄⠧⠼⣳⠒⡏⠘⡄⠀⠺⡀⠀⠀⠀⠀⠀⠀⢸⡘⣌⢩⣿⢿⡟⠋⡼⠉⡩⢇⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠣⣤⠀⢉⠀⣱⠔⠋⢏⠲⠅⠀⠈⠒⠤⠍⢆⠀⠀⠀⣠⠀⣈⠭⡙⣌⠀⠐⠀⠀⠉⠉⠃⣠⠧⠊
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⣅⢀⡤⠚⡷⠀⠀⠀⠀⠀⠀⠘⡆⠀⡰⠉⠋⠁⠀⡼⠋⢍⡝⠋⠉⠙⢿⡉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠪⠤⠲⠤⣤⢤⠞⠋⢻⠀⠀⠀⠀⠀⠀⠀⠀⡇⢰⠃⠀⠀⠀⣠⠦⠦⣞⣄⡗⢦⣀⠖⠉⠓⠂⢉⡵⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠼⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠘⡄⠀⠀⢰⣡⠤⢤⡈⠃⡇⢠⡞⠀⡀⠀⠈⠓⢂⣉⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢳⠀⠉⠒⢦⡤⡀⠀⠀⠀⡏⠀⠀⣧⠀⢀⣜⢀⣀⡀⢌⣾⡁⠀⠉⠉⠉⠑⠒⠒⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢕⣄⡉⠒⠚⣁⢇⡇⠀⠀⠀⡇⠀⠀⠸⡀⠀⢿⠁⠀⠀⠠⣻⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠓⠊⣸⠀⠀⠀⢸⠃⠀⠀⠀⢣⠀⠈⢂⡀⠤⠔⣻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠒⠲⢤⡀⢞⠀⠀⠀⠀⠸⣅⠀⢀⡱⠦⡖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠉⠙⢕⡄⠙⣾⠀⠀⠀⠀⠀⠸⡉⠉⠀⠀⢏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⢎⡆⠸⡄⠀⠀⠀⠀⠀⠱⢄⣀⡠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⣻⣠⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣄⠸⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢾⡆⠛⠂⢀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⢶⣤⡀⠀⢀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠋⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠐⠈⠂⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠸⠀⢀⠀⠀⠀⡀⠔⠊⠉⡉⠀⠀⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠂⠀⠁⠈⢀⠕⠀⠲⠄⠄⠂⢠⠊⠁⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠁⠐⠇⠀⠀⠀⠐⡆⠀⠁⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢀⠀⠀⠀⢀⡷⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⠄⠤⢘⡀⣀⡀⠀⢠⠐⠢⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⢸⠁⢰⠀⠀⠀⠀⠀⢸⠀⠊⡀⡠⠀⡀⠀⡀⠈⠁⠢⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠂⠠⠄⡎⢁⠇⠀⠀⠃⠀⠀⡌⠐⠀⠀⠀⠀⠀⠀⠀⠀⠑⣀⠄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠈⠀⠀⠈⠀⠀⡼⠀⠙⠒⠤⠤⠤⢤⢀⣀⡠⠔⠊⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠤⢤⡤⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⣋⡉⠉⠛⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⡕⣵⡴⣦⠑⡄⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠛⠛⠓⠶⠼⣧⡇⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⣉⣒⣦⣤⣾⡗⢤⡀⠀⠀⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⡾⠿⠅⠀⢘⣉⡙⠫⣄⣹⣄⠀⠈⠋⠓⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣧⣀⣦⠀⠂⢰⣿⠀⠀⣠⠞⢣⡀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠉⠛⠀⠰⢬⣟⣄⠸⡇⢠⢊⡉⠙⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⢀⣠⣶⣶⣿⡿⠋⠀⠙⠁⠾⠂⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡻⠿⠿⣿⣋⡽⠆⠀⠀⠀⣠⡤⢴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠷⠦⣄⡈⠑⠂⢀⣠⠴⢾⠷⣤⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠂⠁⠀⣈⣙⣳⠾⣝⢮⣳⠚⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠛⢳⡀⢀⠀⡾⠁⠀⠙⢦⡼⠚⠁⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠙⢿⡘⣧⣀⠀⠀⠀⠀⠀⠀⣠⢆⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣶⣶⠟⠉⠉⠉⣿⣦⣤⣤⡴⠞⠷⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠈⠛⠒⠋⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠉⢷⡀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠾⠷⠤⣄⡀⣠⠇⠀⠀⣀⣤⠴⠶⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠉⢹⡶⠚⠟⠁⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⠀⠀⠀⠀⣀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢭⣍⣭⣭⠥⠤⠤⢿⡒⣦⠤⠤⠤⠤⠤⠶⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠒⠒⠚⠛⠁

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⢤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡄⠤⡴⠋⠀⠀⠀⠀⠙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⠑⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠤⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠙⠆⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠚⠧⢄⡀⠀⠀⠑⢄⠀⠀⠀⠀⠀⢠⢤⠀⢹⡆⠀⠀⠀⣄⡀⠀⠀⣀⡴⢻⢲⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠧⢤⣴⠂⠒⢭⣂⣄⡀⢈⣷⠴⠖⠒⠒⠾⢦⣟⠡⡇⠀⠀⠀⠀⠀⠍⢉⡗⠁⠁⡏
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⣀⡏⠀⠀⠀⠙⢂⡀⣤⠐⢈⡽⠋⠀⢀⠔⠂⠂⢄⠀⠈⠻⣜⣦⣀⣀⠀⠀⢲⠛⢁⡠⠤⠬⠇
⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠈⠈⢽⠒⠒⠲⠶⠎⠀⠀⢠⡞⠀⠀⠀⠇⠀⠀⠀⢈⠀⠀⠀⢸⣆⠀⠁⠀⡀⠈⠳⠫⠀⠀⡴⠚⡳⣆⣠⠤⠶⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠋⣀⣀⢀⡀⣈⣻⠍⠀⠀⠀⠀⠀⢸⡄⡀⠀⠂⠈⠀⠀⠀⠉⠀⠒⢄⡼⡣⠃⠀⢀⠈⠀⠀⢰⣤⠴⣁⡴⠋⠁⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⡔⠛⢻⠅⢦⡀⠀⠀⠀⠁⠐⢀⡞⡷⠶⠶⣞⠋⠉⠉⣍⠉⠋⢛⡯⡖⠰⣉⣊⠀⠀⠀⢧⠀⡎⠀⣀⣄⡀⢤⡄⠀⠀⠉⠘⢇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠌⠁⠀⠀⠀⠀⡇⢀⣀⣀⠄⠒⠚⢧⣳⠆⠘⠟⠀⠀⠀⠋⠀⠀⢸⣿⠁⠀⢙⡆⠙⡄⠀⢻⡋⠀⡌⠀⠀⠀⠀⠀⠁⠠⠀⠀⣸
⠀⢠⠊⢻⡀⠠⠒⠒⡶⡞⠀⠀⠐⣀⠉⢿⣩⠝⠓⠢⢄⠀⠀⠹⡄⠁⢰⠀⠀⠀⠀⠀⠀⡸⠷⣄⣠⠟⠉⠉⠘⡄⠀⢳⠤⠀⡀⠐⠀⠛⠠⢶⡴⠓⠊⠁
⠀⢸⠀⠀⠙⠂⠀⠀⠫⣅⡐⠀⠈⠀⠀⠐⠁⠀⠀⠀⠀⢱⡴⠊⠉⠒⢦⣓⠀⠀⢀⡤⠺⣅⢠⠖⠁⢀⠤⠒⡲⠚⠀⠈⢀⠀⠁⡀⢁⠀⠀⠀⢱
⠀⠀⠱⢄⠀⠀⢠⢀⣀⡈⠣⣀⡀⠀⠀⠀⠀⠀⣠⡴⠚⠋⠑⢄⠀⡀⠸⠈⢙⡉⠁⠠⡀⢻⡼⠀⠀⠎⠀⠀⠀⠀⠀⠀⠁⢠⢄⠘⠈⠓⠢⠔⠃
⠀⠀⠀⠈⢄⡀⣸⠃⠈⠳⡄⠀⠉⠢⢤⣄⣠⡴⠋⠀⠀⠀⠀⠘⣿⠔⢣⡀⠀⠀⠀⠀⠙⠻⡄⠀⡸⠀⠀⠀⡴⢀⠄⠀⡀⠀⠈⣇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠳⢄⣀⠀⢠⠏⠀⠠⡀⠈⠉⡇⠀⡘⣆⠀⠁⠀⠀⢀⠄⠀⠀⠘⣄⡇⠀⠀⢐⡄⠄⠀⠘⡵⢣⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡏⠉⠙⡇⢌⠢⣉⣲⡞⣁⠴⢡⠁⠀⠀⢰⠋⠉⢦⠀⠀⠀⠘⣧⠀⠀⠸⠱⡀⢀⡤⢃⠎⠀⠀⠻⠶⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⣀⣠⠞⠒⠕⠊⠁⠈⠁⠀⠈⡧⠤⠴⢻⠀⠀⠀⡇⠀⠀⠀⠈⢷⡀⠀⣧⠈⠉⢔⠀⣠⡀⠀⠀⠀⠚⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⠴⠋⠀⠀⠀⢀⡀⠀⠀⠀⠀⢻⡀⢸⠂⠀⠀⠀⠀⠈⠣⣄⣈⠲⢤⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠚⠉⠉⠙⠲⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠏⡦⠜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣠⣭⣭⣀⣒⣴⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣷⣦⠀⣠⣴⣶⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣼⡿⢟⣛⣯⣭⣭⣽⣛⡱⢾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠟⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⣠⣤⣤⣾⣿⣿⣿⣿⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣽⣭⣭⣭⣝⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⢼⣿⣿⢟⣫⣽⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠻⠿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀
⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣮⡝⠛⠛⠛⠛⠛⠛⠛⠓
⠀⠀⠀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⠂⠀⠀⠀⠀⠀⣴⣶⣶⣶⣶⠂⠀⠀⠀⠀⢀⣶⣶⣶⣀⣀
⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⣿⣿⣿⣷⣶⡶⠀⠀⢀⣼⣿⣿⣿⣿⣇⣀⣀⡀⠀⠀⠚⠛⢻⣿⡿⠋⠀⠀⣠⣦
⠀⠀⠀⣰⣿⡿⠀⠀⠀⠈⠉⠉⣽⣿⠏⠀⠀⠀⠾⠿⠿⠿⢿⣿⣿⣿⠟⠁⠀⠀⠀⢀⣾⠟⠁⠀⠀⣼⣿⡟
⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠋⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠘⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⢀⡀⠀⠀⠀⢀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⢀⣴⣿⡇⠀⠀⠀⣼⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⠀⠀⣼⠟⠁⠀⠀⣠⣾⡀⠀⠀⠀⠀⣰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣼⠋⠀⠀⠀⣼⣿⣿⠁⠀⠀⠀⠀⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠙⠿⠋




⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⡟⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠀⠀⠀⠀⠊⢸⣷⣶⣦⣤⣤⣄⡶⣞⣷⠸⣷⣜⣿⣿⣿⡆
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⡠⣀⠄⠀⠀⠀⢿⣿⡿⣿⢿⠁⡅⡿⢻⡆⢿⣯⢿⠿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⡅⡊⠊⠀⠀⠀⠀⠀⠛⠀⣡⣼⠀⠀⡆⣼⢣⡘⣿⡷⣀⢺⡏⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠂⣿⠁⠀⡄⣣⢇⣾⡧⢸⣿⠗⢸⡃⡄⠈⡛⠂⠀⡴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⠀⠀⠀⠀⠈⠀⠁⠆⢋⠀⣿⡇⠘⡉⠒⠻⠿⢥⡆⠓⡤⠂⠐⢩⡷⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠂⠀⣼⣯⣇⢰⣿⣗⣱⣶⡆⢠⠎⠀⠀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡏⢸⢠⡿⢻⡞⢟⡧⡝⠛⠄
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠐⠀⣿⣻⡇⡆⢘⠰⠛⠁⠿⠃⠀⠁⣼⠖
⠀⠀⠗⢆⠠⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢀⣿⠾⠁⠀⠨⡊⠁⠊⠰⠀⠀⠀⠈
⠀⠀⠀⠏⠀⠀⠀⠉⣿⣷⣶⣶⣻⣵⣦⡤⢤⡤⠀⠀⠀⡂⢉⡴⠋⠘⠉⠀⠄⡀⠀⠀⢠⠀⠠⠀⠀⢀
⠀⠀⠀⠐⠀⠀⠀⠀⣿⣿⣿⠫⣾⣿⢃⠀⢈⡄⢀⡠⠎⡔⠈⠀⠀⠀⠄⠎⣠⣜⠳⣷⢸⣄⡄⠀⠀⠂
⠀⠀⠀⢸⠀⠀⠀⠀⠹⠺⢛⡄⢿⢿⡠⠜⠋⠃⠀⠀⢀⠀⠀⠀⠀⠀⠀⢰⣿⣽⣷⣌⢻⣇⣵⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⣗⠋⠈⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠐⡫⠘⠁⢹⡄⢻⣿⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠅⠀⢠⠀⠀⠁⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⢿⡀⢿⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⠀⡁⠀⠁⢃⢘⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈⠈⠀⠀⣀⠔⠀⣾⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸⢀⠔⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘


⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠒⠀⠀⠀⠀⠀⡴⠃⠀⠀⡄⠀⠀⠀⢠⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠛⠁
⠀⠀⠀⠀⡠⠀⠀⠀⠀⣠⣷⣤⠤⣤⣤⣶⣧⣰⣄⣀⡠⠔⠀⠀⠀⠀⠀⠀⠀⠒⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠔⡀
⠀⠀⢀⣾⡇⢠⠎⠀⠘⠛⠻⠁⠰⢿⣿⢿⣿⣯⠀⠀⠁⠠⠤⠀⣀⠀⠀⠀⠠⣤⡄⠀⠀⢀⠀⠀⠀⣀⠤⠂⠀⠀⠀⠁⠉⠛⡛⠉⠀⠀⠀⢀⠐⠄
⠀⠀⠀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠿⢟⣿⣶⣶⣶⡾⠋⠈⠉⠠⣄⠀⠀⠀⠀⠀⠀⠈⠁⠒⠀⠀⠀⠠⠀⠀⠀⠀⠰⡍⠓⠲⠶⠚⠁⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣔⣵⡾⣿⣿⣿⣿⠿⣶⣤⣠⣠⠉⠙⠛⠁⠀⠀⡰⠀⢤⣤⡤⠤⠀⠳⣅⡀⠀⠀⢀⡈⠻⣶⣶⣾⡿⠃
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠈⠈⠁⠞⠔⠋⠁⠀⠑⢦⣌⣒⣭⣽⣇⠀⠀⢶⣄⣀⣀⣤⣮⣿⠛⣻⣟⣤⣿⣿⡿⠋⠀⣀⡄
⠀⠀⠀⠞⠀⢲⣄⣉⣂⠀⡀⠀⠈⠃⠄⠀⢀⡀⠀⢀⠀⠀⠀⠀⠀⠀⣰⣶⢿⣿⠿⢛⣿⣿⣿⣷⡖⣹⣿⣟⡿⠋⠱⠁⠉⢀⣼⠟⢋⡀⠀⠀⠁
⠀⠀⠀⠀⠂⠁⣄⠀⠀⠀⠳⠆⠀⠐⠀⢠⡘⠉⠉⢉⠀⠀⡀⠀⠀⠈⢙⠁⠀⣴⡂⠊⢛⣿⡿⢋⣾⣯⣿⡟⠁⠀⠀⠀⠀⠈⢀⡔⠁⡰⠚⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⢰⣆⠀⠰⣄⠀⠉⣓⡈⠁⢀⣌⢷⣤⢤⣶⡽⠂⡴⠛⡁⣰⣼⠟⣴⣿⡿⠟⠋⠀⠀⣴⡅⠀⠀⣰⣯⡀⠊⠀⠀⢀⠞⠁
⠀⠀⠘⣿⣷⣶⣆⣀⡴⠂⠀⠙⠛⠟⣹⣿⣿⣿⣿⣿⣿⣿⣷⣾⢫⡥⠀⠀⢀⢀⣰⣿⣧⡶⣠⢿⡃⠀⣠⣤⡾⢟⡖⠀⠀⢑⣏⠀⠀⠀⠀⠁⣠⠆
⠀⠀⠀⢋⡿⣯⠟⣵⠾⣠⡔⡡⢂⣼⣿⣿⠟⢻⣿⠿⣿⣿⣟⣽⣋⠠⢀⡴⢇⣭⣿⣿⢋⣴⡣⠈⣠⠊⠿⣩⣶⣿⡷⠀⢴⡿⠋⠀⠀⠀⢠⠞⠁
⠀⠀⠀⠋⠀⢀⠞⢃⡿⠋⠀⢰⡾⣻⡿⠂⢠⡔⠂⠀⠀⠁⠭⠨⣻⡆⢈⣴⣿⣿⣿⣡⣿⣿⡿⡿⠛⠀⠘⠛⢻⠟⠂⠠⠍
⠀⠀⠀⠀⠀⣀⡰⠋⠐⠀⠀⠊⠀⠉⠀⠀⠀⢀⣊⠐⢛⣄⣤⣾⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⣚⢞⣁⡀⠀⡐⠀⢠⡜⡁⠈⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⠀⠛⡀⠀⢠⡄⠀⠀⠀⠀⠀⣀⣾⣿⣷⣟⣴⣿⣿⣿⣯⣭⣿⣿⠟⣿⣿⣷⣖⣠⣥⣹⠞⡀⠈⠀⠀⠾⠻⠃⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⢀⠚⠿⠿⠁⠀⠀⠀⡠⠊⠁⠁⣰⣿⣿⣿⣿⣷⣽⣯⣼⣿⡿⠃⠾⢿⣿⢯⠿⢿⡿⣿⣿⣅⢠⠄⠀⠈⣀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠟⢻⣿⣷⣿⡿⣛⢿⣿⣿⣿⡟⣡⡞⣡⡯⠀⠈⠈⠉⠉⢱⣶⣴⣦⣿⣿⣿⣿⣷⣶⣶⣖⠃
⠀⠀⠀⢀⠂⠀⠀⢰⡇⠀⠀⠠⠀⠀⠀⠀⠠⡾⠿⢋⠜⠙⠁⣼⣿⣿⣏⣸⣿⡿⢈⣦⣾⣥⣤⣤⣴⡿⠟⣋⣩⣿⣿⣿⣿⣿⣿⣿⣯⣷⠀⠁
⠀⠀⠀⡤⠊⠀⠀⢼⣇⠀⠈⣆⢠⠀⠀⠀⠀⠀⠜⠃⠀⢀⣾⣾⣿⣿⣿⣿⣿⣧⣿⠛⡁⠾⢿⣿⣫⣵⣾⣿⣿⢟⣿⡛⣩⣷⣧⣍⣙⣷⣶⡄
⠀⠀⠀⠟⠀⠀⠀⣿⣟⠂⢼⡿⣿⡂⠀⠀⢀⡀⠀⠀⠀⢺⣿⣿⣭⣭⣽⣿⣿⡿⣡⠌⠑⠠⠘⠿⢻⣿⣿⣿⣁⣙⣻⣿⣿⣿⡏⠻⣿⣿⣟⣦
⠀⠀⠀⠀⠀⠀⢹⣿⣿⣦⣸⣿⣿⡇⢰⡄⣾⡆⠀⠀⠰⠃⢾⣿⣿⣿⣿⣟⡿⠈⠁⣀⠄⠀⠀⠀⠀⠀⠸⢿⠿⣿⣿⣿⣦⣼⡰⣿⣿⣷⣿⠁
⠀⠀⠀⡀⠀⠠⢾⣿⣿⢿⣿⢫⣿⣇⣸⣟⣿⣟⠀⠀⣀⢀⣐⣫⣽⣭⣩⣭⣤⣉⠛⢁⣀⣀⡀⠀⠀⠀⢀⡘⡀⡟⠃⠉⠿⢁⠔⠙⠛⠋⣁⣀⣀
⠀⠀⠀⣿⣾⣿⣿⣿⣿⣾⣿⢟⣿⣻⡧⣿⣿⢾⣾⣿⣿⣿⠿⡟⣿⣿⠟⢻⠻⣻⣶⢃⣿⣧⠻⢶⣿⣧⣿⣿⣿⣿⣿⣧⣥⣧⣶⡷⠘⢿⣿⣿⣿⡆
⠀⠀⠀⣉⣍⣵⣾⡿⣧⣌⣵⢿⣿⣟⣡⣿⣿⣷⣙⣉⠁⣤⡤⠄⡀⠀⠀⠀⠀⠀⠀⠈⠁⠁⠀⠀⠉⠉⠉⠉⠙⡇⠁⢹⡇⠉⠉⠀⠀⠈⠛⠛⠛⠁
⠀⠀⠀⡽⠿⠟⠿⡛⠒⠙⠛⠻⠉⠬⠽⠷⠼⠿⣦⣬⣅⡀⠀⠀⠐⠛⠛⠛⠛⠻⠿⠛⠓⠈⠀⠀⠒⠂⠀⠈⠀⣿⡀⢸⡇⠠⠀⢴⣤⡤⠤⢤⡤
⠀⠀⠀⣷⣴⣶⣶⣶⡶⣶⣦⣤⣴⣦⣤⢀⣀⠀⠀⠉⠉⠉⠋⠉⠒⠐⠒⢴⣤⣤⣤⣄⠀⠀⠀⠀⠀⠤⠤⠶⠖⠚⠷⠚⠻⢿⣿⣿⣿⡿⣿⣿⣷
⠀⠀⠀⡻⠓⠚⠉⠋⠀⠀⠈⠁⠐⠒⠛⠛⠛⠛⠻⠿⣶⣶⣶⣤⣶⣶⣾⣿⣿⣿⣿⣿⣷⣽⣿⣾⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠴⠿⢿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣿⡄⣿⠀⣿⡄⣿⣻⢸⡇⡟⣷⠀⢸⣿⠃⢸⣧⢸⣟⡇⢻⠋⠀⢸⠈⣿⠁⡟⠁⣿⡀⣾⢰⡟⠇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⢸⡿⡇⣿⣯⢸⡇⡇⣿⠀⢸⣿⡄⣿⢿⢸⣿⡅⢸⠀⠀⢸⠀⣿⠀⣏⠁⣿⣷⢿⢠⣝⡆
⠀⠀⠀⠀⠀⠀⠀⠉⠈⠈⠈⠀⠁⠉⠈⠈⠁⠉⠁⠀⠈⠁⠁⠁⠈⠈⠁⠁⠈⠀⠀⠈⠀⠉⠀⠉⠁⠉⠈⠈⠀⠉⢡⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠙⠳⣄⠀⠀⠀⠀⣴⠚⠉⠛⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⣀⣠⣿⡀⠀⠀⢀⣿⣄⣀⣠⣾⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠱⠠⠈⠛⠁⠀⠀⠈⠛⠡⠀⠌⠛⠁
⠀⠀⠀⠀⣀⣤⣀⣀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⢰⣿⢟⡭⢭⣿⣿⠀⠀⠀⠀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣼⣆⠀⠀⠀⠀⠀⡼⠗⠀⣤⡖⣤
⠀⠀⠈⣿⣿⡼⢭⣾⡿⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠀⠀⠀⠀⠀⠀⣿⣿⢀⠀⠀⠀⠀⢠⡄⣀⡀
⠀⠀⠀⠙⠛⠿⣿⠟⠀⠀⠀⠐⢿⣷⣼⣴⣿⠷⠀⠀⠀⠐⢿⣾⣷⡶⠀⠀⠀⠀⠒⠤⠞⠙⠿⣍⠄⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⣾⣧⡀⠀⠀⠀⠀⣠⣴⣿⡁⠀⠀⠀⠀⢀⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⣰⣿⣷⡄
⠀⠀⠈⠻⣿⣹⣿⣿⠟⠀⠀⠈⠙⢿⣿⣿⠆⠀⠀⠀⣿⣿⣿⣫⣽⣿⣿⠀⠀⠀⠀⠀⣿⣧⣼⣇⠀⠀⠀⠀⣤⢀
⠀⠀⠀⢀⣿⠿⠿⣿⠀⠀⠀⠀⠀⢸⠟⠁⠀⠀⠀⠀⠈⠛⠿⠿⠿⠛⠟⠀⠀⠀⠀⠈⠹⣿⡿⠋⠁⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠰⡓⢆⠒⣓⠀⣠⠀⠀⡆⣶⢰⡂⠀⣄⠀⣎⢰⡢⢞⠂⢀⡀⠰⡷⢶⡆⣖⠀⢠⡀⢰⡆⡞⠒⡃⠀⣀⠀⡜⡆⡶⢰
⠀⠀⠐⠂⠘⠀⠚⠀⠀⠀⠐⠃⠃⠘⠂⠀⠀⠀⠓⠘⠀⠒⠁⠀⠀⠐⠀⠈⠃⠓⠀⠀⠀⠘⠀⠓⠈⠀⠀⠀⠀⠑⠃⠛⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⠀⠀⠀⠀⠐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢻⣇⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣤⣤⣽⣿⣾⣿⣧⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⠟⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠻⢿⣿⣿⣿⣿⡟⣿⣧⣀⣀⣼⣿⡇
⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠁⣠⣶⣦⡀⠘⣿⣿⣿⣿⣿⣿⡏⠀⣠⣶⣤⠀⢻⣿⣿⣿⣇⢸⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠈⠛⠿⣾⡇⠀⠀⠀⢸⣿⡇⠀⢿⣿⣿⠇⠀⣿⣿⣿⣿⣿⣿⡄⠀⢿⣿⣿⠇⢸⣿⣿⠙⣿⡆⢿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣄⡀⠉⠁⣀⣼⣿⣿⣿⣿⣿⣿⣷⣄⡀⠉⠁⣠⣾⣿⡟⢰⣿⣇⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠉⢠⣾⣿⡿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⡏⠀⠀⢀⣀⣤⣄
⠀⠠⠤⢤⣤⠤⠶⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⠇⠀⠀⠀⠉⠙⠛⠻⠶⠦⠤⠤⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⢀⣶⡄⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⣼⡇⢰⠀⠀⠀⠀⣼⣿⡏⢸⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢻⡇⠀⠀⠀⠀⠀⢰⣿⡇⠘⡆⠀⠀⢰⣿⣿⠁⢸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⣿⣿⠀⠀⠀⠀⠀⣼⣿⠁⠀⡇⠀⠀⣿⣿⡏⠀⢸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣽⣿⠀⠀⠀⠀⢰⣿⣿⠀⠀⣇⠀⣰⣿⡿⠀⠀⣿⡟⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠀⠀⠀⠀⣸⣿⣿⠀⠀⢿⢠⣿⣿⠁⠀⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⢸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡿⠀⠀⢸⣿⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢡⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠥⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠤⢀⠔⠉⠐⠄⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠐⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⡠⠁⠈⠔⡠⢂⠂⡀
⠀⠀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⢀⠀⠀⠨⠂⠄⠀⡠⠠⠂⠀⠀⠠⠊⠀⠀⠀⢀⠔⡡⡀⠁⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣀⡀⠀⣀⠀⠀⠀⠀⢀⢀⠁⠈⠈⠈⠉⡠⠁
⠀⠀⠀⠀⠀⠀⠃⢠⠀⡠⠀⠴⠀⠀⠖⠀⠰⠂⢀⠄⠀⠀⡐⠁⢀⠟⠉⠐⠁⠀⠤⠂⠀⠀⠀⡄⣠
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠁⠀⠠⠂⠠⠀⠰⠀⠀⠃⡔⢀⠊⠀⠀⠠⠮⠄⠀⢲⣂⠀⡰⠂⠀⢈⡀⠀⠚
⠀⠀⠀⠀⠀⠘⠀⠀⠀⡔⠀⢀⠀⢠⠀⠀⡰⠂⠀⠰⠇⠒⠒⠒⠒⠀⠀⠀⠄⠀⠊⠠⠆⠀⠈⡠⠀⠐
⠀⠀⠀⠀⠀⠀⡌⠀⠀⡄⠀⠉⠀⠃⡤⠀⢀⠀⠀⠀⠰⠂⠠⠊⠀⠀⢀⠔⠁⠀⠀⢀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⢀⠀⠀⠐⢀⠀⠰⠁⡄⠀⠀⠊⠀⠸⠁⢀⠔⠁⠀⢀⠔⠁⡰⠀⡀⠀⠊⠀⠀⠈⠀⠊
⠀⠀⠀⠀⠀⠀⠀⡄⠀⠄⠀⠀⠘⠀⠈⠀⠠⠂⠀⠔⠁⠀⠀⠀⠀⢀⠀⠀⠈⠀⣀⠀⠋⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠈⠀⠀⢀⠀⠀⢠⠇⠀⠀⠄⡠⠂⠀⡀⠈⠀⠀⠀⠋⢀⠀⠀⠈⠁⠀⠜
⠀⠀⠀⠀⠀⠀⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠀⢠⣊⣀⡀⠀⠀⠀⠀⠊⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⢀⡨⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠊⠁⠀⡔⠀⠀⠀⠀⡠⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⠁⠀⡀⠀⠉⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⣰⡴⢶⡄⠑⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠼⠶⠛⠐⠒⠻⠤⠦⣀⡀⠀⠀⠘⠉⠉⠲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠤⢲⣶⡶⠖⠾⠛⠓⠦⣌⠱⠶⣄⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⣀⣀⣀⡛⠄⢳⡀⢰⣥⡀⠀⠀⢀⡴⠃⢹⠟⠉⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠱⠤⠿⠄⠘⣷⡆⠀⠀⠘⣆⣀⠎⢠⠇⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⠀⠀⠀⢈⣉⣴⡿⠂⠈⠁⠀⠀⢀⣰⠇⡀⢀⣀⡤⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⣀⣀⣠⣴⣿⣿⢿⡁⠀⠀⠀⢠⣞⣹⠟⢠⣄⡈⢁⣀⠠⠆⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠻⠟⠛⠫⣍⠤⠼⠇⠠⠐⠾⡉⠀⠉⠳⣴⣁⠈⠑⢤⡀⠀⠀⠀⠼⢿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢠⣀⣠⣴⠾⠷⠊⠀⠀⠀⠀⠀⠀⠀⠘⣆⢀⡀⢹⣏⠓⠀⠈⣿⠀⠀⡜⠳⡾⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠘⢏⠡⡄⠀⣆⡐⠀⠀⠀⠀⠀⠀⠀⠀⣼⡋⠀⢸⢿⡆⠀⢀⡿⠄⣀⣧⣞⣠⠎⠇
⠀⠀⠀⠀⠀⠀⠄⠒⣿⠞⠛⠒⠺⣄⢠⡀⠀⣟⠠⣆⢀⣀⠀⠀⢠⡿⣿⠉⠙⠋⠸⡇⡆⣸⢁⣐⣩⣿⠟⠓⠚⠣⢄⡀
⠀⠀⠀⠀⠂⠀⠀⠀⡿⠒⢒⠢⣄⠈⣿⣭⣩⣽⠋⡀⠀⠀⠙⢲⡉⠀⠈⠁⠀⠀⢀⡿⢰⣿⡬⠁⠚⠁⠀⠀⠀⠀⠀⠉⠳⡄
⠀⠀⠀⠐⠀⠀⠀⢰⣃⣀⠈⠙⠈⢆⣿⠋⢹⠇⠐⠒⠄⠑⢄⠀⢳⠀⠀⠀⠀⠀⣸⢡⣿⡀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠄⠀⠀⢈⣅⣀⠀⠁⠒⣼⠃⠀⡰⡄⠀⠀⠀⠀⠘⡆⢸⠀⢰⡆⣠⣾⣡⡾⠟⠁⠠⠀⠀⠀⠀⠀⠀⠀⢠⢾⣧⢀
⠀⠀⠀⠀⠀⠀⢤⠊⠰⢧⡀⠀⣲⠃⠀⣌⠉⠉⠀⠤⢄⠀⠀⡿⢸⣤⠾⠿⠿⠟⢉⡠⠞⠛⠲⢄⡀⠀⠀⠀⠀⠀⠸⡿⢃⠂
⠀⠀⠀⠀⠀⠀⠀⡱⢦⢀⡀⠀⠉⠒⠤⣁⣀⠀⣳⣦⠄⠷⠒⠟⠉⠀⠀⠀⠀⠀⠚⠓⠀⠀⠈⠈⠁⠀⢤⡀
⠀⠀⠀⠀⠀⠀⠘⢶⠻⣀⡸⠯⢔⣢⡤⣀⡀⠀⠀⣀⢠⡔⠚⠀⠀⠀⠀⠀⠀⢀⡀⠀⠘⠈⠀⠀⠀⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⢤⣀⠀⠈⢄⢀⠟⡩⠿⠃⡸⠇⠚⠀⠀⠀⠀⠀⢰⣫⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠲⠶⠾⠦⠤⠘⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢼⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⢠⣤⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠸⠏⣸⣿⣿⣿⡇⠀⠀⠀⠀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣀⠀⠀⠀⠀⠀⢠⣰⣿⣿⣿⣿⣇⠀⠀⣀⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢀⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣧⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣶⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣿⣿⣿⡇⠀⠀⢀⣤⠄⠀⠀⣿⣿⣿⣿⡇⠀⠀⠘⠠⠸⣿⣿⣿⣿⣿⡛⠛⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣶⣾⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⡀⠊⠀⠘⣿⣿⣿⣿⣷⡀
⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⠻⠿⠛⠃⠀⠀⢀⣿⣿⣿⣿⣿⠖⠋⠀⠀⠀⠀⠈⢻⣿⣻⣿⣷⣀
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣆⠀⠀⢀⣾⡄⢠⢿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢿⣷⢤⡤⠐⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠻⣿⣽⣿⣿⣦⡀⠀⠿⠃⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⢀⣴⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠙⠠⠦⣤⣽⣿⣿⣿⣿⣿⣇⠀⠀⢀⣴⣾⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠈⠛⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠈⠻⠋⠉⠙⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⠀⠤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠄⠀⠀⠀⠀⢰⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠋⠙⠛⠛⠷⢶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣄⠈⢻⣄⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⢋⣤⣌⠻⣧⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⡆⠀⢀⣤⡶⠛⠿⣿⣿⣿⣿⡘⠿⠟⣰⣿⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⣷⠀⢸⡏⢸⣿⡷⢸⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠻⢶⣤⣀⣀⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⣤⣿⡆⠘⢿⣦⣭⣥⡾⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⡁⢀⣀⣠⣶⣆⠀⠀⠀⢀⡀⠀⠀⠀⢰⣆⠀⠀⠀⣿⣇⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠻⣦⡀⠀⠈⢿⣄⠀⠀⠘⣿⣦⠀⠀⣿⢻⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣦⡀⠘⣿⣧⡀⠀⢹⡟⣧⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠾⠇⠙⢷⣤⣿⠘⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⢟⣛⡻⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡎⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⣶⣿⡷⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⡿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣗⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣱⣷⣿⣿⣿⣧⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣱⣿⣷⣿⣿⣿⣿⣟⣲⣭⣭⠍⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣟⣛⣵⣾⣿⢿⡿⣋⢿⣿⣿⣿⣿⡛⣵⣾⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣮⣟⣚⣛⣓⣻⣽⣾⣿⣷⣝⣻⠿⣷⣭⣶⡯⢹⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠋⠉⠑⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡴⠉⠀⠀⠀⠀⠀⡀⠄⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⢀⡀⠠⠤⠤⠤⣀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠒⢄⠀⡂⠙⠀⠒⠛⠻⠆⠀⠀⠈⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠠⠀⠀⠰⠀⠀⠀⢠⡆⠀⠀⠙⠀⠀⢀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⠦⣄⠀⠙⠁⢸⣇⠀⠉⠀⠒⠺⡔⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠒⠀⢈⠀⣀⡀⠤⣴⡥⢂⠉⠚⠂⠐⢬⠻⣿⣆⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣃⠀⠀⠀⡱⢊⠀⠀⡌⢨⡔⠁⠀⠀⠀⠀⠀⢱⠈⠛⠷⢶⡶⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠤⡶⡅⡆⢀⡜⠈⢠⡄⠀⠀⠀⢀⢀⣄⣜⠐⠉⠲⣏⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠁⠈⠐⢄⠀⡠⢥⡜⠉⠀⢩⠃⡼⠓⠊⠁⠉⠉⠀⣨⠛⠈⠉⠲⠆⠘⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠻⠀⠘⢇⠄⠂⠉⠙⠠⣄⡠⠚⠁⠀⣮⡡⠀⡄⠀⠀⢈⡀⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⡎⠀⠀⠀⠀⠀⠌⢿⣎⠀⠈⠾⠄⠀⠀⢀⠀⣸⠁⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⣀⣠⠔⠚⠓⢶⡀⠀⠀⢀⡀⠂⠈⠀⡀⠀⢠⠀⠠⡄⡀⠘⣹⢁⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣠⠊⠁⠰⠁⠀⠀⠀⠀⠹⡛⠶⠂⠀⠐⠀⠈⣠⠄⠸⠇⠀⢃⠀⢠⠉⠂⢀⣀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠫⠵⠺⡀⠀⠀⠀⠀⠀⠱⣄⡈⢀⠘⡆⠀⢡⠄⠀⠚⠀⠈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⢱⠈⢂⢀⠈⠈⢀⡀⠀⠀⠐⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠤⠀⠠⠔⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠁⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⢁⣀⠤⢄⣈⠑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠈⠢⡀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠀⠃⠠⢀⠀⠀⠣⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⠑⢄⠀⠀⢠⠃⠀⠀⢀⡀⠧⠀⠀⠀⠴⢇⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡀⠈⠢⡀⡆⠀⣠⠊⢁⠀⠤⠄⠀⠤⠄⢀⡉⠲⣄⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠔⠚⠶⠀⠀⠙⣇⢠⡧⠊⠁⣤⣄⠀⠀⠀⣠⣤⠀⠑⢬⣆⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡠⠔⢊⢙⠀⠀⠈⢿⢱⠀⠀⠀⠉⣣⡀⣰⠋⠁⠀⠀⠸⠙⡏⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⣐⠨⠔⠊⠀⠀⠀⠘⡞⢠⣀⢀⠏⠁⠀⠀⠙⢆⢀⣠⠐⣸⠁⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⢰⠘⢿⣿⣄⠀⠀⠀⢀⣾⣿⠟⠀⣥⡴⠃⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⡵⠀⠀⠀⠀⠀⠀⠀⠀⣆⠈⠻⠛⠿⠷⠿⠟⡛⣇⣠⣼⠃⠀⠀⠀⠙⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡒⡎⠀⠀⠀⠀⠀⠀⠀⠀⣶⠕⣋⠉⠭⠭⠭⠿⢠⣂⡐⠺⣄⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠁⠀⠀⠀⠀⠀⠀⠀⠔⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢳⢶⡉⢣⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠌⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢣⠜⠀⡴⠓⠂⠀⠀⠀⠀⠐⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠁⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⡌⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⢢⢤⡅⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣯⡾⡽⠁⠀⠀⠀⠀⠀⠀⠀⡜⢰⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⢆⠹⣶⠀⡀⠀⠀⠀⠀⡀⣦⣹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⣰⠁⡄⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠰⠈⢆⣯⢸⠀⠀⠀⠀⠀⠀⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠜⠀⠀⠀⠀⠀⠀⢀⡤⠾⠇⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⠾⢿⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⣀⠄⠚⠛⠣⢼⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⡤⠘⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⢊⡀⣀⠠⣴⣂⠁⠀⠀⠀⠀⠀⢸⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠇⠀⠀⠀⠀⠀⠀⣀⠤
⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⢠⠀⠈⠉⠁⠉⠀⠐⠒⠒⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠒⠒⠒⠀⠈⠀⠈⠁⠀⠰⠀⢸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠛⠉⠉⠉⠙⠶⠖⠋⠉⠉⠙⠒⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠒⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠒⠛⠲⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣀⡀⣀⣀⡀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣐⡢⠀⠀⠀⠀⠀⠈⠏⢒⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡖⠁⠀⠀⠀⠀⠀⠀⠀⠚⠓⠒⠭⠶⠖⠠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡯⠤⢀⣀⠀⢀⣀⣀⣠⡄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣔⣰⡠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠒⠒⠋⠉⠀⠀⠉⠳⣞⣡⣖⣠⠖⠳⢴⣠⢖⣰⣦⠾⠛⠉⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⣰⠃⠈⠁⠀⢀⡤⠚⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⢰⠃⠀⠀⢀⡴⢋⠗⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠰⠿⠶⢞⡶⠂⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⢠⡯⠴⠒⡾⠃⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⣠⠖⠉⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣠⢞⡵⢋⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢠⣾⠗⠉⠀⠀⠀⠀⠀⠀⠀⢀⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠰⠃⠀⠀⠀⠀⠀⢀⠆⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣀
⣟⣛⣻⣛⣟⣟⣿⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣛⣛⣟⣻⣛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠟⠋⠁⠀⠀⠈⠙⠻⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⢠⡄⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⣦⡀⠀⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠀⢠⡿⠀⣠⣶⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠻⣶⣄⠀⠸⣷⠀⠀⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣦⣤⣿⠇⢸⣿⠁⣾⣿⣷⠈⣿⣿⣿⣿⣿⣿⢡⣾⣿⣦⠘⣿⡇⠀⣿⣧⣶⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⡿⠀⠸⣿⣆⠙⠛⠋⣠⣿⣿⣿⣿⣿⣿⣄⠛⠛⢋⣸⣿⡇⠀⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠙⠻⠿⠿⠿⠟⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠋⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣄
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣀
⠀⠀⠀⠀⣠⣴⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⣄
⠀⠀⠀⢸⣿⡟⠁⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⢙⣿⡇
⠀⠀⠀⠈⠻⣿⣷⣶⣶⣶⣶⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣷⣶⣶⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⣰⣿⠃⠀⠀⠀⠀⢀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠀⠀⠀⠀⠘⣿⡄⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⣠⣿⣿⠀⠀⠀⠀⠀⣸⣇⠀⠀⠀⠀⢠⣿⣿⣄⠀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⣀⣴⣾⡿⢻⣿⡀⠀⠀⠀⢠⣿⣿⡄⠀⠀⠀⢸⣿⡏⠻⣷⣦⣀⡀⢠⣿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠿⠟⠋⠀⠸⣿⡇⠀⠀⣠⣿⡏⢹⣿⡄⠀⠀⣸⣿⠁⠀⠈⠙⠛⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣦⣶⣿⠟⠀⠀⠻⣿⣶⣴⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠁⠀⠀⠀⠀⠈⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣀⣀⣀⡄⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣧⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣤⡀⠀⠀⠀⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⢠⣿⣿⡟⠋⠀⣀⡀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⢠⣿⣿⣿⣧⠀⣿⣿⣿⣿⣿⣿⡿⠋⣀⠹⣿⣿⣸⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣄⠀⠻⠿⠿⠋⢠⣿⣿⣿⣿⣿⣿⢁⣾⣿⡆⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣤⣤⣤⣶⣿⣿⣿⣿⣿⣿⣿⡈⠻⠟⣼⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠿⠿⣿⣿⣿⣿⣷⣶⣾⣿⡿
⠀⠢⢤⣄⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣨⠽⢿⠿⠛⠛⠋
⠀⠀⠀⠀⠈⠉⠉⠙⢛⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣴⣾⣿⡟⠉⠁
⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⠀⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠈⠛⠛⠛⠁⠀⠀⠀⢀⣠⣤⣴⣤⡄⢿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠟⢻⣿⣿⣿⡟⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣤⣀⡂⢦
⠀⠀⠀⠀⠒⠛⠋⠉⠀⠀⢀⣾⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠊⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣿⣿⣿⣿⣿⣿⡟⢣⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⢙⣿⣿⣿⡿⠿⣫⣽⣾⣿⣿⣿⣿⣿⡟⠉⢈⣡⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠿⠛⣱⣿⣿⣿⣿⣿⣿⣿⠿⢋⣡⣴⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢛⣿⣿⣿⡿⠛⠛⢱⣾⣿⠿⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⠶⠿⠿⠿⠿⠷⠶⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠹⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠿⠿⢷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⣠⣶⠟⠛⠉⠉⠉⠉⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⣠⣾⠿⠷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠹⠟⠉⠉⠛⢿⣆
⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠛⢷⡄⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⣠⣴⠿⠛⠁⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡶⠿⢟⣿⣶⠀⠀⠀⠀⢀⣤⣤⣤⣴⠿⠋
⠀⠀⠀⠀⠀⠀⠈⠻⣶⣤⣀⣀⣐⣿⡅⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⣸⡏⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⢻⣦⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣸⡏⠀⠀⠸⣿⣿⣦⣄⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠀⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⣀⣼⠿⣷⣿⠃⣀⣤⣄⠀⢀⣿⣿⡶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠻⣿⡿⠿⠶⠶⠶⠾⠟⠋⠁⠀⠈⠿⠾⠛⢹⡿⠀⣸⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡄⠀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠛⠛⠿⠷⠿⠿⠆⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⢀⣀⡀⢀⣿⠁⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣽⣿⣆⠀⠀⠀⢠⣿⠉⠻⣾⠏⠀⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣄⠀⢠⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⣸⡏⠀⡀⠀⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⢻⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣱⣿⡿⣷⣄⣼⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣌⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⠁⠀⠙⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⣿⣧⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡆⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⢀⣠⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄⠀⠀⠀⠀⢸⣿⠃⠀⠀⠙⣉⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡷⠀⠀⠀⠀⢿⠏⠀⠀⠀⠀⠉⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠉⠀⠀⢀⣀⡙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⡞⣡⡴⡏⣾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠂⠏⠀⠀⢀⣤⣬⡧⠧⠤⣥⡯⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⣠⠏⠀⠀⠀⣀⡤⠲⠭⠟⠟⠉⠟⢻⡛⠉⢂⣉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢑⣄⣟⣦⠎⢭⢙⠀⣠⢀⡀⠸⠀⢰⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣉⠀⠤⣽⠀⢺⠏⠛⢱⣿⣿⣷⠀⠀⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⢧⠀⣀⡌⢳⠶⢆⠀⢠⢿⣿⣿⣷⣶⣶⣿⣿⠁
⠀⠀⠀⠀⣀⡠⠤⠤⠧⣼⣡⠞⣡⠴⠚⠓⠈⠓⣦⡆⠀⠙⠛⠙⠛⣫⠧⡤
⠀⠀⣠⠞⠁⠀⠀⠀⠀⢰⢣⠎⠀⠀⢡⠜⡭⠒⠛⠚⢷⠒⠀⣫⠽⠆⠬⣙⡳⣄
⠀⢠⠃⢀⣄⠀⠀⠀⠀⡏⠘⢆⡀⢠⡇⠈⠀⠀⠀⠒⢤⡇⣝⣀⠀⠀⠀⠘⢹⠈⡖⢄
⠀⡞⠀⡏⢸⠀⠀⠀⠀⣇⠀⠀⢸⠋⠙⢦⣀⠀⠐⣦⢼⠒⣶⣁⠄⠀⠀⢀⡼⠜⠀⠘⡆
⠀⡇⠀⠣⠊⣀⡠⠤⠤⢼⡦⠤⠼⢦⣀⠀⡴⢉⠒⢫⣙⠀⣏⠼⣄⠔⠊⢻⠀⠀⠀⢸⠁
⠀⠸⡄⠀⣞⠁⠐⠶⡶⠋⠀⠀⠀⠀⠈⢳⠁⣄⠤⣀⣸⠀⡇⣆⡂⡄⢀⡼⠛⠊⠒⠓⠦⣀
⠀⠀⠈⠒⠬⠵⠶⢴⠃⠈⡇⠀⠀⠀⠀⢸⡇⣿⠤⠤⠞⠒⠳⠶⠶⠧⢇⡀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠒⠁⠀⠀⠀⠀⢸⠋⢁⡠⠖⠒⡖⠒⡒⠀⣄⣀⡸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣄⠀⠀⠀⠀⠀⢀⠏⠉⠉⠒⠢⠀⠁⠀⠧⠄⠉⠉⢣⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠒⠒⠁⠀⠁⠀⠠⠀⠀⠀⠀⠀⠀⠠⠤⠚⠲⠤⠤⠔⠚

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠉⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⣠⣤⡶⠶⠶⣶⣶⣶⣶⣶⣶⣶⡶⠶⠶⠶⣦⣄⡀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⣰⣿⢣⣾⣷⣆⠘⣿⣿⣿⣿⣿⡟⣱⣶⣶⣄⠸⣿⣿⡄⠀⠀⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢰⣿⣿⠸⣿⣿⡿⠀⣿⣿⣿⣿⣿⡇⢻⣿⣿⡟⢀⣿⣿⡇⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⣧⣌⣭⣤⣾⣿⣿⣿⣿⣿⣷⣤⣈⣁⣤⣾⣿⣿⡇⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⢿⣿
⣿⣏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿
⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿
⣿⣿⣿⣿⣿⣶⣶⣶⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⠀⠀⠀⠀⢰⣿⣿⡆⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⣿⣿⡆⠀⠀⠀⠀⠀⣸⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⡇⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢸⣿⣿⣄⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⣸⣿⣿⣿⣷⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿⣿⣆⠀⠀⣸⣿⣿⣿⣿⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣿⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⡆⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣦⡀⠀⠀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠛⠻⠿⠟⠻⠛⣿⡄⠀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⢸⡆⠸⣿⡀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⡀⣿⡄⢸⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠐⠠⢐⠁⢸⡇⢸⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⢠⡟⡆⠀⢠⡶⣦⠀⢸⡇⢸⡇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢸⣿⡇⠀⠘⣿⣿⠀⢸⡇⢸⣧⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠈⠿⠃⠄⠀⢿⠏⠐⢸⡇⢸⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠄⠐⠀⠀⠀⠀⢸⣇⢸⣿⡀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⣰⣗⠀⠀⠀⢰⣆⠀⠈⣿⠈⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠉⠙⠻⠷⠿⠛⠙⠃⠄⢿⡄⢻⣿⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠈⣿⣧⠈⠛⠿⣶⣦⣤⣤⣤⣤⣴⠶⣦⡀⠀⢰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠘⣿⣧⠀⠀⠀⠄⠉⠉⠉⠁⣠⡟⠉⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⢰⣶⡆⠀⠀⠀⠀⡀⠹⣆⠘⣿⣷⣄⣀⣀⣀⣀⣤⣶⠟⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⣠⣿⠿⣿⡄⠠⠀⠀⠀⠀⠙⢧⡈⠻⣿⣿⠛⠛⠛⠉⠁⠀⢀⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠂⢀⣴⡿⠃⠀⠹⣿⣄⠀⠄⠀⠀⠀⠈⠻⣦⡈⠻⣷⣄⡀⠀⠀⠘⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋⠀⠀⡀⠀⠈⠻⣷⣤⡀⠀⠀⠀⠀⠈⠛⠶⠌⠙⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢿⣯⣉⣀⠀⠀⠁⠀⠀⠀⠀⣀⣀⣤⣶⠿⠛⠉⠀⠀⣠⠞⠙⠀⠀⠀⠈⠻⢿⣶⣤⣀⡀⠀⠀⠀⠀⠈⠀⠀⠉⠛⠻⠿⢻⣿⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⠿⠿⠛⠛⠋⠉⠀⠀⠀⣠⡴⠛⠁⠀⠀⠀⠀⠠⠀⠀⠀⠈⠉⠛⠻⠿⠶⣶⣶⣤⣤⣤⣤⣴⡶⠶⠟⠋⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠒⠤⢄⣀⡀⠀⠀⠀⠀⠀⣀⣀⣠⠤⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠤⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠒⠒⠒⠒⠒⠒⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠕⠀⠀⣀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⣿⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠀⢶⠆⠀⠙⠀⠳⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠃⠀⣶⣴⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⣉⠈⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠄⠀⠀⣦⣶⠾⠇⠀⠀⠀⠈⢀⣀⣀⡀⠀⢀⡔⠻⣧⢨⠀⢿⠻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⢱⣾⣤⠆⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠉⠉⠘⠰⠶⠊⠈⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠰⠀⠀⠀⣿⣁⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢿⣿⠉⠁⠂⠀⣀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠂
⠀⠐⠁⠀⠀⠀⠀⡀⠀⠉⠀⠀⠀⢁⡐⠀⡸⠛⠓⠀⡀⠀⠉⠲⢄⡀⠀⠀⠀⠀⠀⡀
⠀⡄⠀⠀⠀⠀⠀⢨⠿⠖⠀⠀⢀⣠⣍⠀⠐⡀⢀⣴⣿⡖⣄⠀⠀⠈⠐⢤⡀
⠀⠀⠊⠀⠀⠀⢆⠹⠶⠀⡤⠊⠁⠀⠀⠉⠦⡘⠛⠵⢉⣿⣿⣶⢤⡀⠀⠀⠈⠐⠄
⠀⠀⢀⣠⡄⠀⣤⣶⣾⣷⡇⠀⠀⠀⡠⠀⠀⠨⠀⠐⠛⠻⠞⠠⠄⠚⠢⠄
⢀⠔⠏⠈⡍⠈⠀⢹⠞⠁⠀⠀⠐⢯⠀⠀⣠⠔⡾⠷⣌⢀
⣿⣆⠀⠀⠁⠀⠘⡁⠀⠀⠀⡰⠊⢛⠾⠋⠁⠉⠀⠒⠛⠃
⢿⡏⢒⡂⠀⠀⢨⣤⠑⠂⠀⢀⠀⠀⠁⠀⠂⠀⢀⠂⠀⠀⠀⠀⠀⠀⣀
⠈⠻⣮⣙⣦⣈⢈⣥⣥⣄⡰⢀⡀⠀⠀⠂⠀⠂⠁⠐⠂⡀⡀
⠀⠀⠀⠉⠛⠛⠛⠋⠉⠈⢿⡔⠀⠶⠀⠀⠀⠉⠁⣀⣴⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⡦⣬⣭⣽⡶⠿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠈⢿⣿⡏⠻⣿⣿⠟⢹⣿⠋⢸⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠘⠇⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⡴⠒⠲⢤⡀⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣞⠥⠠⢝⣿⡠⠄⠄⠀⢳⣤⡀⠀⠈⠡⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠶⠦⢤⣿⠁⠀⡄⠀⡏⠀⠀⠀⠐⠀⠂⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠉⠢⢀⠀⡃⠀⠈⠀⠀⣀⠘⣴⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠷⠒⠈⠉⠁⠉⠉⠣⡀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⡀⢿⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣾⣤⡈⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⡷⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⡿⠁⠈⡣⠀⠀⠀⠀⠀⢀⡞⠁⠈⠀⠎⢈⠷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠀⢀⣀⡴⠛⠉⢿⣧⣀⡔⠁⠀⠀⢀⣠⠔⠛⣧⣄⠀⠀⠀⠀⢰⠇⠀⢀⣀⠒⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠉⠀⣰⠞⠛⡟⠻⠏⠈⠉⠉⠉⠉⠀⠀⠀⠀⠁⠱⡄⠀⣰⠋⢀⣴⡿⠉⢹⡶⣌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⠯⡀⢰⣥⣼⠁⠀⠀⢠⡀⠀⠈⠀⠀⠀⠀⢸⣧⡜⣿⠀⣾⡅⠀⠀⡘⠀⡸⠻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⢻⠀⡈⠉⠁⠈⠀⠀⠊⠀⠉⠀⠀⡐⠃⣀⠠⠄⣻⠁⣸⢿⡟⠁⠀⠀⠀⠠⠁⠀⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣆⠀⢢⠋⠁⠓⢄⡀⠀⠀⠃⠐⡖⠈⠀⠄⠀⠀⠀⠈⢣⠟⠀⡏⠀⠀⣠⡄⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠈⢦⡂⠀⠀⢀⠎⣳⡤⠀⢀⠔⢀⠀⠀⠀⠀⢲⢀⡠⠋⠀⠀⢹⡤⠠⡈⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢇⠀⠀⠀⠀⠉⠒⠤⠎⣰⣟⣶⣆⡁⢀⣀⣀⠀⣀⣀⠾⠋⠀⠀⠀⠐⠋⠀⣴⣧⣤⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡇⠀⠓⡴⢊⣝⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⠀⠀⠀⠀⠀⠐⡲⣾⡏⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠰⣸⢎⡠⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡆⠀⠀⢠⠄⠀⠀⢸⡇⠀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠂⠐⠐⠂⠐⠀⠂⠀⠀⠠⢀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠄⠁⠀⠈⡈⠴⠀⠀⡸⢧⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣭⡢⠀⠀⠀⠀⣢⣥⡢⠀⠁⢄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡼⠳⡄⢻⡄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢿⡿⢃⠃⠀⠀⠸⣿⣿⠟⠀⠀⠘⢀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠓⠖⠁⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡋⠹⣾⢷⡄⠀⠀⠀⠀⠀⠀⠈⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠛⠓⠒⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢀⡀⣤⡘⠻⣯⡀⠀⠀⠈⠉⠀⠀⠀⠀⢀⡤⣀⠀⣀⣠⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠷⠈⢡⠄⠈⠻⠷⠶⠤⣤⣀⣀⣰⣢⠤⠷⣌⣿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡶⠶⠇⠀⠀⠉⠁⠀⢦⣤⡤⠴⠾⠛⠉⣽⠋⠀⢀⣀⡈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⣷⡀⠀⠙⠳⣄⠀⠀⠘⢷⣤⠖⢡⣤⠙⡶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠃⠀⠀⢀⡼⠉⠛⠲⠖⠋⠁⠀⠀⠀⠸⣧⣆⠈⢉⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⠤⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣷⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⡿⠟⠋⢉⣀⣤⣤⡄⠀⠈⠉⠛⠿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠟⠉⣠⡶⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⣶⣶⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠋⣠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠉⠉⠛⠻⠿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣾⡿⠁⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠿⠛⠋⠉⠁⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡄
⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃
⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏
⠀⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⣀⣀⠀⠀⠀⠀⠀⣀⣾⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣶⣤⣤⣤⣤⣤⣶⣿⠿⢿⣷⣦⣤⣀⣀⣀⣀⣀⣠⣤⣶⣾⣷⣦⣄⣀⠀⠉⠉⠀⣀⣠⣴⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⣋⡉⠀⠀⠀⠈⠉⠛⠛⠿⠿⠿⠿⠛⠛⠉⠁⠈⠙⠻⠿⠿⠿⠿⠿⠿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣆⠀⠀⠀⠀⠀⠀⣴⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠹⣿⣆⠀⠀⠀⢀⣾⡿⠛⣿⣧⠀⠀⠀⠀⠀⢀⡄⠀⢶⣿⣶⠆⢀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠹⣿⣆⠀⠀⣾⣿⠁⠀⠘⣿⡇⠀⠀⠀⣬⣿⣧⡀⠀⣿⠁⠀⣸⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠙⣿⣧⠀⢻⣿⣤⣀⣴⣿⠇⠀⠀⣤⡀⠀⠈⠻⣦⣿⣠⡾⠋⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠙⠛⠛⠛⠉⠀⠀⠀⢾⡿⠶⠶⠶⣿⣿⣿⡷⠶⠶⢿⣿⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣠⡾⠋⣿⠉⠻⣦⡀⣀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣤⣤⣤⣴⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣟⠀⠀⣿⡀⠀⢸⡿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠾⢿⠿⠆⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠤⠛⡩⠭⡉⠛⠣⡄⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠜⠐⣀⠀⠀⠀⠀⠘⣇⠡⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⢀⣰⠌⠀⠀⠀⠘⡄⣿⢰⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢃⢻⡄⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⢀⢒⠢⠀⠀⡐⠂⢌⠆⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢀⡎⢳⢈⢄⢡⠚⣦⠰⢸⡇⠂⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⣿⣿⠐⡆⢸⣷⣿⢰⢸⡇⡄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠿⠟⠈⠀⠸⣿⡏⠀⢸⡇⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀⠄⡉⠐⡘⠌⠆⠜⠘⢸⣇⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠄⣥⠑⢤⠡⡃⣮⡊⠼⠸⣿⢸⢸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢌⠘⠻⣦⣥⣥⣴⠞⠷⠈⠄⣿⡄⠈⣿⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠡⠊⠒⡪⠄⠨⣅⠐⢚⠀⠀⢀⢸⣇⢣⣹⡇⢌⠙⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠡⠁⠀⠀⠀⠊⠀⠀⠈⠀⠀⠀⠀⠆⢿⡀⡌⢿⡄⡀⠁⠀⠩⠝⣛⠛⣛⣛⠛⢉⣭⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠅⠀⠀⠀⠀⢀⣀⢀⣀⠀⠀⠀⠀⠈⡘⣷⠈⠎⢿⣄⢀⠀⠀⠀⠀⠀⠈⡔⢡⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢋⠀⢌⠀⠀⠀⢀⠀⠈⠃⣼⣿⠈⠀⠀⠀⠀⠲⠙⢧⡐⠄⠻⣦⣁⣑⣀⣐⣒⣥⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠕⠁⠁⠚⠀⠀⠀⠨⠖⢀⡼⠃⠘⣇⠐⠄⡀⠀⠂⠀⠈⠻⣄⠒⡘⢿⣍⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⢋⢔⡢⠄⠀⠀⠀⠀⠀⠀⠀⣡⠞⠁⠀⠀⠘⢧⡐⠡⠀⠀⠀⠑⠀⡈⠳⣄⡕⠙⠳⣄⡀
⠀⠀⠀⢀⣀⣠⣤⠴⠞⠋⠅⠂⠈⠀⠀⠀⠈⢠⡏⠠⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠙⢦⡀⠩⡂⠀⠀⠀⠁⠬⠙⠒⢵⢌⡛⠶⣤⣀
⠀⠀⠀⢿⣉⡀⠐⠂⢅⡀⠀⠁⠈⠀⠤⠤⢀⣂⣬⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢮⣀⡀⠄⣀⠀⠤⠱⠉⠀⠀⠁⠆⠍⡛⠶⠶⠶⣦
⠀⠀⠀⠀⠉⠙⠛⠳⠶⠶⠶⠶⠶⠶⠖⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠶⠦⣤⣥⣤⣤⣤⣤⣤⣬⣭⡤⠶⠞⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠈⠁⢉⠐⠢⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣦⠛⢻⡀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⠤⠄⣀⡀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⠞⠁⠉⣩⡀⢀⣉⠉⠹⢦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠘⡆⣠⣘⠏⠁⠉⢛⣠⡄⡜⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢆⠈⠻⢧⣤⣤⠾⠟⣁⢗⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣻⠦⠤⠤⢴⣂⠁⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢥⠊⠀⠀⠀⡄⢀⠐⠡⢀⡠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠒⠒⠾⠓⡾⠤⠦⠰⠀⠧⢼⣙⡟⢁⡈⠾⠒⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢀⠔⢻⠞⠐⠂⠐⠒⠂⠀⠐⠂⠽⡍⠁⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠉⠀⣁⠉⣝⠁⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣤⠤⢄⡘⠁⠈⠈⠉⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⣩⠖⡞⣀⣀⣀⡸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠘⠆⠀⠀⠺⣙⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣊⣴⣯⣤⣤⡟⠉⠈⡹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡗⢶⢧⠄⣤⣤⣬⣷⣌⣢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⢹⡦⠼⠥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢄⣈⡎⠀⠆⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⢰⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⡀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢾⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⡎⠀⠀⠈⠐⠁⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠈⠦⠊⠁⠀⠈⠃⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⡰⡀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⢀⢄⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠒⢄⡀⠀⠀⡠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⡀⠀⠀⢀⠠⠒⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠙⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣄⠀⠀⠀⠀⠈⣿⣿⣷⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠛⠛⢿⣿⣿⣦⡀⠀⠀⢿⣿⣿⣷⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⢀⣴⣤⠀⠹⣿⣿⣿⣿⣿⣿⡟⠀⣠⣶⣶⣦⡀⠙⣿⣿⣇⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠐⢤⡀⢠⣿⠀⢿⣿⣿⠀⢀⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⡇⠀⣿⣿⣿⠀⠀⢸⣿⣿⣿⣿⣄⣀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣆⠈⠛⠁⢀⣾⣿⣿⣿⣿⣿⣿⣧⡀⠈⠛⠛⠉⠀⣰⣿⣿⣿⠀⠀⠘⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣴⣶⣿⣿⣿⡿⠃⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⣸⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡿⠛⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠃⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠑⠢
⠀⠀⠐⠒⠒⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡟⠀⠠⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⣼⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⢾⡆⠀⠀⠀⠀⠀⠀⠀⣾⣧⠀⠀⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⣸⣿⣿⠀⢰⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⢀⣿⣿⣿⠀⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠛⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⣼⣿⣿⠃⣼⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡄⠀⠀⣠⣿⣿⠇⠀⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠁⠀⣰⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠃⠀⢹⣿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠾⠿⠿⠿⠿⢶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡶⠿⠿⠿⠿⢷⣶⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⣀⣠⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠉⠙⠛⠿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⢀⣴⡾⠟⠛⠉⠉⠙⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣹⣧⣤⣤⣀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⣀⣠⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⢀⣴⡿⠛⠋⠉⠉⠛⠻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⠉⠉⠉⠛⠿⣶⣄⠀⣀⣤⣶⣶⣶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠈⠛⣷⣄
⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⠛⠉⠀⠀⠀⠀⠉⠻⣷⣄⠀⠀⠀⠀⠀⠀⠈⢻⣧
⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣴⣶⣶⣶⣤⣄⠀⣿⡆
⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠉⠛⢿⣾⡇
⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⢰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠁⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡃
⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠾⠛⢿⣦
⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢻
⠀⠈⠙⠿⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⢉⣽⡟⠉⠉⠉⠉⣩⣿⠋⢿⣏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⢀⣼⣿⣥⣤⣬⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣃⣀⣀⣀⣀⣈⠉⠉⠉⢉⣿⠏⠉⠛⠿⠷⠶⠶⠶⠶⠶⠶⠶⠶⣶⣶⠶⠶⠶⠶⢶⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠐⠛⠛⠛⠛⠛⠛⢻⡿⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⠀⢠⣾⣿⣤⣤⣤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⣰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣁⣀⣀⣀⣀⣉⠉⠉⠉⣩⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠛⠛⣿⡏⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠁⠀⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⢀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠿⠿⠿⠿⠷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⣰⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠛⠛⠛⠛⠿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⣤⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠙⠻⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣄
⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⢀⣠⣴⡶⠶⢶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠉⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⢀⣤⣾⠿⠿⠿⠿⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠾⠿⠿⠿⢶⣤⡀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀
⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣶⡾⠟⠋⠉⠉⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⠙⣿⡄
⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠈⢻⣧⣠⣤⣤⣤⣄⡀⠘⣿⡀
⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠉⠀⠉⠙⠻⣷⣿⡇
⠀⢀⣼⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇
⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠈⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡀
⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣆
⠈⢻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠉⠛⠿⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣠⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿
⠀⠀⢀⣤⡾⠟⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⡾⠋
⠀⣴⡿⠋⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⡆⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣉⠉⠉
⠀⣿⡄⠀⠀⢀⣼⡏⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠉⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⢀⣤⣾⢿⡇
⠀⠙⠿⣶⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⢿⡇⠀⠀⠀⣠⣾⠟⠋⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠸⣿⡀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡾⠟⠉⠀⢸⡇⠀⠀⢰⣿⠁⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⢿⣷⠀⠀⠙⠻⠿⠿⠋⠀⠀⠀⠀⠀⠀⣴⣶⡀⠀⢸⣟⠀⠀⠀⠀⣿⠇⠀⠀⠘⣿⣄⣀⣠⣼⡟
⠀⠀⠀⠀⠀⠀⣠⣾⠟⠉⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡿⠋⣿⡇⠀⠘⢿⣦⣀⣠⣾⠟⠀⠀⠀⠀⠈⠙⠛⠛⠉
⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠁⠀⠀⣿⡇⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢿⣦⣄⣠⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢺⣇⠀⠀⠀⣰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣶⣾⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠋⠹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⢹⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣇⣀⣀⣀⣀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⢿⣿⣿⣿⣿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠀⠀⡤⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠘⣿⣿⣀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣾⣿⣿⣿⣿⡟
⢠⣾⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠃⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⢋⣽⣿⣿⠟⠁
⠸⣿⣿⢿⣿⣷⣶⣤⣤⣤⣤⣴⣶⣶⣾⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢴⣷⣦⡈⠉⣉⣀⣀⣀⣠⣴⣾⣿⣿⠟⠋
⠀⢻⣿⣶⣌⡙⠛⠻⠿⠿⠿⠿⠛⠛⠛⠉⠁⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⠿⠟⠛⠉
⠀⠀⠙⠻⣿⣿⣷⣦⣤⣄⣀⣀⣀⡀⡀⣀⣀⣠⣤⣾⣿⡿⢿⣿⣶⣄⡀⠀⠀⠀⠙⠻⣿⣿⣷⣦⣤⣀⣀⣀⣀⣤⣤⣶⣤
⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠀⠀⠙⠻⣿⣿⣷⣦⣄⣀⡀⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣾⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠋⠉⠉⠙⠓⢦⡀⠀⠀⠀⣠⠴⠶⠶⢤⡀⣠⠴⠚⠛⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣀⡀⠀⣀⣀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⠖⠚⠁⠀⠀⠀⠀⠙⠃⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠈⠙⠋⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠲⣄⡀
⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⣸⡧⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢻⡄
⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⡿
⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⣀⣴⠟⠁
⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠒⠚⠛⠉
⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠃
⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⢀⠀⠀⢀⣡⠞⠛⠓⠶⣾⠟⠁⠈⠙⠓⠶⠦⣤⣤⣤⣴⣶⠟⠛⠶⢦⣤⣤⠶⠞⠋
⠀⠀⠀⠀⠀⠙⠳⠶⠤⣤⡤⠶⠾⠛⠁⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⢀⣀⠀⠀⠀⠀⠀⠀⠠⠀⠛⠛⣻⠟⠁⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⡠⠂⠀⠴⠗⢚⡽⠃⠀⠀⠀⠀⠀⠀⠀⠠⣠⡾⠃⠀⠀⣠⠀⠀⠀⠀⠀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⢀⠜⠁⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢀⠴⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠁⠀⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⣥⡤⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⣀⠀⠀⠀⠀⠀⠀⠘⣩⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠖⠚⣹⠏⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⣰⠃⠀⠀⠀⣠⠾⠋⠀⠀⠀⢀⡔⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⣰⠃⠀⠀⣠⠾⠁⠀⠀⠀⠀⡠⠊⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣡⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠤⠤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠁⠀⢰⣀⡠⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⡌⠉⠡⠂⠀⠀⠀⠈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢀⣀⠀⠠⠤⣄⣀⣀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⣰⠐⠛⠙⠂⠀⠀⠋⠙⠋⠳⡄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⢉⠀⠀⠀⣾⠷⠀⠸⣷⠀⠀⠀⢈⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠈⠊⢰⣦⡇⠀⠀⠀⢈⣤⣶⠀⠊⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠆⣈⠙⠿⢦⣤⣴⠾⠟⠁⢀⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠈⢑⠶⣤⣄⣠⣔⣞⠥⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠀⠌⠔⠁⠀⠀⠀⠀⠈⠑⢈⡂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣃⡨⠓⢤⣆⡤⢆⠀⠰⠀⠀⠀⡀⠀⡏⢱⣧⠀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⡠⠒⠉⠐⡦⣄⣸⠥⠚⠒⠛⠒⠓⠒⠓⠚⠽⡁⢹⡁⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠐⡼⠇⠒⠂⠀⠉⠉⠉⠉⠉⠁⠐⠚⢾⠉⠢⡀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠉⠉⠉⠉⠹⠀⢀⣀⣀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⢋⣉⡉⠉⠉⠉⠑⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡧⢒⡤⠤⠤⠤⡤⠉⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡈⠁⠀⠈⠑⡤⢤⡒⠸⡄
⠀⠀⠀⠀⠀⣀⠔⢁⠴⠋⠀⠀⠀⠀⡀⢀⣠⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡴⠦⠴⠦⣴⠀⠉⠢⣌⠒⢄
⠀⠀⠀⡠⠮⠤⠶⠷⠶⠶⢶⠶⡒⢲⠹⠋⡙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⣼⠶⠖⠒⠞⠓⠀⠑⠂⢄
⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⡎⠀⠸⣍⣀⠴⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠵⠤⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠎⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⢰⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⢸⠀⢀⠤⠒⠒⠢⣄⠀⠠⠃⠀⠀⠀⠀⠀⢀⡠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⡀⠀⠀⠀⠀⠀⠈⠄⣀⠔⠈⠁⠒⡄
⠘⡀⢈⠀⠀⠀⠀⠀⠑⠁⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⢠
⠀⠑⡘⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢃⠂
⠀⠀⠘⠀⠳⠤⡀⠀⠀⠀⠀⠀⢀⠮⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠠⠄⠤⠀⠴⡀⠀⠀⠀⠀⢀⡠⠚⠐⠁
⠀⠀⠀⠀⠀⠀⠈⠁⠂⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠒⠈⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⡭⡉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡊⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠻⠤⠤⠤⠟⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡇⢰⣿⡆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠛⡁⢀⠛⠁⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠑⠚⠁⠀⡆⢹⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠹⡌⢆⠀⠉⣉⣉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠔⠁⠀⠀⠀⢠⠶⡀⠀⠀⠀⠈⠻⢭⣉⡀⠘⠋⠀⣼⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣏⠁⠀⠀⠀⣀⡠⠖⠁⠀⠈⠳⢤⣀⣀⠀⢀⣀⣩⠇⠀⠀⠘⠿⢿⣧
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣀⣉⣉⣉⣁⣀⣀⣀⣀⣀⣀⣀⣙⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢠⣄⠀⣀⡤⠴⠖⠒⠒⠒⠀⠭⢁⡀⠐⠒⠒⠰⠤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠂⠈⠓⠀⢀⡽⠉⡁⠀⠈⠁⠒⠠⢀⠀⠀⠀⠀⣉⡲⠶⠋⠁⡠⠚⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠅⠀⠈⠀⠀⠀⠀⠀⠀⣉⡢⢖⠉⠀⠀⠀⢀⠊⠀⡀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣰⠇⠰⣆⡀⠀⠀⠀⣠⠔⠚⠋⠢⢄⡀⠀⠀⠀⠀⡇⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⡂⠙⠆⡠⠊⢠⠖⠋⠉⠉⠢⣱⡀⡠⠴⠒⠓
⠀⠀⠀⠀⠀⠀⠀⠀⢰⢏⠃⠀⠀⠇⢠⢾⡁⢀⡎⠀⢀⠀⠄⣡⡔⡉⠀⠀⠑⢄⠀⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡜⢸⠀⠀⢀⠴⡏⢸⠀⠈⢇⡀⠉⠁⠠⠀⠢⡃⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢠⠃⢸⠀⡔⠁⠀⠀⠈⢇⠀⠈⢦⣀⣀⠛⠡⣤⠅⠀⢀
⠀⠀⠀⠀⠀⠀⠀⢸⠀⢘⡞⠀⠀⠀⠀⠀⡠⠛⡲⠫⠅⠒⢰⣮⠳⠦⢄⡀⠑⠦⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⢸⢀⠎⠁⢀⠤⠔⠒⠎⢀⠞⠀⠀⠐⢶⡆⠘⣺⠊⠲⡁⠀⠀⠀⠀⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠘⡾⢀⠞⠁⡀⠀⠀⡠⠋⠀⠀⠀⠸⡜⠛⠉⠸⢁⣀⣹⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠈⠢⡴⠁⠀⡀⠀⠀⠁⡇⣀⠠⠜⠉⢆⠈⠪⡹⡂⡀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⠞⠈⠢⡀⠑⣀⠀⠀⣥⠃⢀⠀⠀⠈⢧⠀⠑⢌⠻⢄⠽
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠈⠀⠈⠁⠀⠘⠀⠀⠑⠀⠀⠈⢧⠀⠀⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⡄⠀⠀⠐⢤⣀⠀⠀⠀⠀⠀⠀⠈⢧⠓⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠲⠴⠤⢤⣀⣀⣀⣈⣁⣠⠤⠤⠤⠖⠒⠚⠁⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⡠⣦⠔⠊⠀⠀⣠⠁⠢⡀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⡸⡄⠙⢄⣀⠔⠚⠁⠀⠀⠱⡀⠀⣀⠦⢠⠀⠀⠀⠀⠀⠀⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⢴⠊⠀⠈⡢⠤⠛⢀⣀⠤⠀⠀⠒⠁⡎⣠⠔⠚⣇⣀⣤⡀⠠⠂⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡢⡀⠈⠳⡀⠈⠣⠀⠀⢠⡀⠀⠀⠀⠐⠀⠙⠣⣀⠀⣤⠋⢀⠞⢀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠑⠠⠔⠃⠀⠘⠀⠀⠒⢀⠀⠠⠀⠀⢸⡴⢛⡶⠁⢀⣃⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠳⠶⠒⠚⠉⠉⠉⠉⠉⠉⠐⠒⠉⠀⠈⠂⠴⠶⠉⠩⠐⠋

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡿⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠨
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⠻⣿⠟⠿⠿⣷⣄
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢸⡎⠀⠀⠀⠀⠀⠈⢿⣧
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⠀⣾⠃⠀⠀⠀⠀⠀⠀⠈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠇⣿⣿⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⣿⡿⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⣿⡇⢸⡇⠀⢰⢶⡀⠀⢠⡶⡄⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⠀⢸⣾⠃⠀⢸⣿⡇⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⢸⡇⠀⠸⠿⠀⠀⠈⠿⠃⢸⣿⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⢀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠁⣼⠁⠀⢰⡆⠀⠀⠀⣰⣆⠈⣿⡇⠀⢀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣟⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⣿⡟⠀⡿⠀⠀⠋⠙⠻⠿⠟⠋⠉⠀⢹⣿⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡿⠁⠀⢠⣶⠶⢶⣤⣤⣴⣶⣶⡾⠿⠛⠁⣸⣿⠁⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠋⠀⠀⠀⠈⠙⢿⣆⠈⠉⠉⠁⠀⠀⠀⠀⣰⣿⠃⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣀⣀⣀⣀⣀⣾⡿⠃⣰⠏⠀⠀⠀⠀⠀⢰⣾⣇⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⢛⣿⣿⠟⢁⡼⠋⠀⠀⠀⠀⠀⢠⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⢁⣴⠟⠀⠀⠀⠀⠀⠐⣤⣿⣟⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⡀⠀⢀⣠⣴⡾⠟⠋⠀⠒⠋⠀⠀⠀⠀⠀⢀⣤⣾⡿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠠⣿⡟⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠙⠛⠷⢶⣶⣦⣤⣤⣶⣶⣶⠿⠿⠿⢛⣫⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣯⣿⣿⣿⢷⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡟⠁⠀⠀⠻⣷⡙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿⠋⠀⠀⠀⠀⠀⠘⣷⡄⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⠘⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⢏⣿⣥⣴⣶⣶⣶⣶⣶⣦⣤⡀⠈⢿⡆⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⡿⣫⣍⢻⣿⣿⠟⣩⣍⠻⣿⣧⠘⣿⡀⢘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣇⠛⢋⣸⣿⣿⣄⠛⠟⣠⣿⡿⠀⢹⣷⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠻⠿⠿⠿⠿⠿⠿⢿⣿⡿⠿⠁⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿⠶⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣭⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⢻⡆⠀⢠⣄⠀⠀⠀⣤⠀⠀⣼⡏⠀⠀⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠘⣿⡀⠈⣿⡄⠀⢀⣿⠃⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣽⣧⠀⢹⣧⠀⣼⣿⣴⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢻⣧⣼⣿⣰⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢫⡤⣆⠘⣿⣿⣿⣶⣄⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠉⠉⠉⡽⠿⠿⠿⠿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⠀⢠⡖⢢⠀⠀⣼⣿⠏⠉⠁⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠀⠀⠈⠿⠂⠀⠀⠙⠟⠀⠀⣠⡁⢾⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣴⢶⠆⠀⠀⠀⠀⢼⡏⠀⢈⠟⠀⠀⠀⠀⢀⠀⠐⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⢛⣉⣭⡶⠀⠀⣀⣤⣶⣾⣿⣶⣦⡀⡀⠀⢀⣴⣿⣷⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠢⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⣼⣿⠿⠿⠒⣋⠁⢰⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⢁⣴⣶⡿⠿⣷⣦⣄⠩⢻⣿⡿⢻⣽⣿⣿⣿⡇⣿⠏⠀⣴⣿⣿⠇⢠⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⠗⠠⣿⠏⠀⠀⠀⠀⠙⣿⡆⠀⣷⣿⣷⣿⣿⣯⣾⠇⣿⡄⣼⡿⠉⠉⣁⣩⣭⣥⣤⣀
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣴⣻⢿⠿⡫⠀⣼⣿⠟⣡⡄⣀⠀⢶⣤⣝⠃⠀⣿⣿⣿⣿⣿⠿⠟⠀⠀⠠⣿⠀⠀⢰⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⢀⣴⣿⣿⣿⣿⡿⣻⠯⣄⠙⠁⢰⣿⣿⢠⠏⠷⢻⢀⣾⣿⣇⠀⣼⣿⣿⡿⣫⣶⣿⣿⣿⣷⣦⡉⠀⠀⠈⣿⣿⣿⣿⣿⢻⣿
⠀⠀⠀⣼⣿⣿⣿⣿⣏⠞⢡⡄⠈⠀⠀⠈⠿⣿⣧⣤⣀⣽⣾⣿⡿⣾⠀⣿⣿⢟⣼⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⣸⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⣿⣿⣿⣿⣿⠙⠀⢀⣴⣾⣿⣿⠀⠀⠈⣿⣿⡟⠉⠉⠀⢠⣿⠀⡿⠃⢾⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣴⣿⣿⣿⣿⣿⣿⡟
⠀⣸⣿⣿⣿⣿⣿⠏⠀⠀⣾⣿⣿⣿⠏⠂⠀⢸⣿⡿⠀⠀⠀⠀⣼⣿⠀⢠⣾⣿⣿⣿⣮⡻⣿⣿⣿⠟⣠⣬⣶⣾⣿⣿⣿⡛⣿⠃
⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⣿⣿⣿⣿⣼⠀⢀⣿⣿⠃⠀⠀⠀⢠⡿⠁⢀⣻⣿⣛⢿⣿⣿⣧⣿⡿⢡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⣿⣿⣿⣿⣿⣿⣧⣀⠀⣿⣿⣿⣿⡿⠀⣸⣿⠇⠀⠀⢀⡴⠋⠀⣤⣾⣿⣿⣾⣧⣿⣿⡿⠋⢠⣿⣿⣿⣿⣿⣿⡿⢋⣉⣉⠻⣷
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣙⠻⠿⠗⢠⣿⡟⠀⢀⠔⠁⠀⠀⢰⣿⣿⣿⣿⣿⡿⠿⢋⣠⣶⣿⣯⣟⢿⣿⣿⡏⡰⠉⠀⠈⢣⢸⡆
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠸⠿⠁⠀⠀⠀⠀⠀⠀⠸⠟⠛⠛⣉⣡⣤⣶⣿⣿⣿⣿⣿⣿⣿⣾⡝⠀⠀⠀⣄⡀⠀⠀⡇
⠀⠹⣟⢿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣠⣾⣿⣿⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠈⠁⠀⣸⠃
⠀⠀⠙⢷⣝⡻⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣻⣿⠟⣡⣦⣀⣀⣀⣀⣴⠏
⠀⠀⠀⠀⠙⢿⣾⣽⣻⠿⣁⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣿⠟⠁⠀⠉⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠙⠻⣿⡟⠀⠈⠀⠒⠒⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣛⣻⣿⣯⣽⣷⣿⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠠⠤⠠⠿⠿⠿⢿⣿⣿⣿⠿⠿⠿⠿⠿⠟⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⢉⡉⠉⠓⠢⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⡠⠖⠋⠉⠁⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣠⠼⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⣠⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⠲⢤⡀
⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠐⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⢛⠛⠛⠛⠛⠛⠛⠛⠛⠛⡛⠛⠛⠛⠛⡛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⢠⠇⠀⠀⠀⣰⠃⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠏⠀⠀⠀⠐⠃⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣄⠀⢰⡀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢆⣀⡼⠀⠀⠉⠛⠉


⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠓⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠓
⠀⠀⠀⠀⠀⠀⢰⡂⡖⠲⣰⠐⡖⢰⡄⢰⡢⠀⠀⣖⡀⠠⡂⠐⡖⢰⡢⡴⠒⡄⣤⠂⣖
⣤⣤⣤⣤⣤⣤⣤⣤⣷⣼⣼⣤⣧⣯⣽⣴⣼⣴⣤⣧⣤⣤⣼⣤⣧⣬⣵⣵⣴⣥⣭⣦⣧⣤⣤⣤⣤⣤⣤
⣿⣯⣤⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠈⠉⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⣬⡁⣠⣤⠈⢷⣣⡀
⡆⠠⡀⠀⠀⠈⠀⠀⠀⠁⠀⠀⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⢈⣿⡳⣜⢿⣎⢻⣷⣔⠽⢿⣄⢠
⠈⠢⣀⡐⠒⣋⠀⠀⠀⠀⠀⠀⢈⠐⠀⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣤⣶⣯⠛⡛⢎⢢⡹⣷⣝⢿⣯⣂⠻⣧
⠀⠀⠀⠈⠉⠀⠀⣤⡤⢤⠖⠀⠈⠑⠀⠀⠀⢀⠀⠀⠀⠀⣠⡀⢴⣶⣷⣝⡿⠋⠙⠳⠘⠀⠑⠙⠊⠉⠀⠙⠁
⠀⠀⠀⠐⠒⠒⠚⠁⠀⠀⠉⠓⠀⠀⢀⣀⣤⣼⣿⣶⠲⣿⣿⣿⣦⡹⠿⠻⠃⠀⠀⠀⣀⡀
⠀⣀⢀⠀⠀⢀⣀⡀⠀⠀⢀⣤⡰⣾⣷⡙⢿⣿⣿⣿⣷⡌⠣⠉⠈⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠈⣿⣿⣍⢿⣿⣿⣿⣿⣧⡻⣿⣮⣿⣿⡦⠻⣿⣿⣇⡈⠒⠐⠠⠤⠔⠀⠀⠐⠒⠈⠀⢀⠀⠀⣤⣀⠰⣝⢷⣗⠄
⠀⠀⠈⢿⣿⣦⠻⠟⠹⣿⣿⣿⣮⣿⣿⣿⣆⢲⣾⣿⣿⣿⣿⣿⡻⣷⣿⣿⣶⣦⡺⣿⣿⣟⢦⡻⣿⣷⡳⠌⠢⡉⠳
⠀⠀⠈⢲⣝⢿⣷⣿⣧⡹⣿⣿⣿⣷⣝⢿⣿⣷⡙⢿⣿⣿⣿⣿⣿⣮⡿⣿⣿⣿⡛⣈⣿⣿⣷⣕⢮⢿⣿⣦⡢⠈
⠀⠠⡙⣝⣿⣿⣿⣿⣿⣷⡹⣿⣿⣿⣿⣷⣿⣿⣷⡼⣿⣿⣿⣿⣿⣿⣿⣾⢿⣿⣿⣮⡻⣛⣿⣿⣯⣷⣝⠿⡿⡄
⠀⡝⢮⠺⣿⣿⣿⣿⣿⣏⠉⣼⣿⣿⣿⣿⣿⣿⣿⣿⣄⢭⣝⣛⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠻⣿⣿⣿⣷⡝⠞
⠀⠈⣿⣿⣟⢿⣿⣿⣿⣿⣷⣜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⣿⣿⣼⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣮⡻⡿⣦
⠀⠠⣜⢿⣿⣿⣿⣿⣿⣿⣿⣿⢆⣻⣿⣿⣿⣿⣿⣿⣿⣄⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡻⢿⠿⢯⡘⠌⠢
⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣽⣿⣿⣿⣿⣿⣿⣿⣿⣯⡻⡿⠟⡛⢮⢠⣧⠳⡀
⠀⠐⢠⡎⡙⡟⡝⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⡛⢯⡻⢷⢰⡆⣿⠀⣸⣿⣀⡈
⠀⠀⢐⢯⣿⢰⣿⣸⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡝⣿⣿⣿⣷⣿⣿⣿⡿⣿⣿⡏⣤⠁⡆⣼⣿⣿⢃⣼⣿⡇⠙
⠀⠀⠂⣼⣿⣵⣿⣏⠷⠈⠻⠿⠟⠍⠛⠟⠗⠙⠛⠉⠊⢛⠋⠛⣛⠛⠻⠿⠮⠙⠐⣿⢘⣷⣸⣿⣿⣿⣿⣿⣷⡄
⢠⣾⣷⣿⣿⣿⣿⣿⣶⣶⣦⣤⣾⣿⣶⣦⣶⣿⣷⣦⣔⢻⠿⣿⣿⣿⣷⣶⣶⣦⢸⣿⣿⣿⣿⣿⣾⣧⣿⣿⣿⣶⣦
⠀⠉⠋⠁⠀⢀⣈⣀⣉⣉⣋⣉⣉⣉⡙⠛⠋⠉⠉⠤⣤⠤⠀⠀⢤⣁⠤⠭⢙⣐⣿⣿⣿⣝⣿⣿⣿⣭⣽⢿⣿⣶⣍
⠀⠐⠀⠂⠢⠀⠐⠀⠀⠈⠓⠐⠒⠶⠒⠀⠀⠀⠃⠙⠛⠉⠛⠋⠁⠀⣀⣠⣬⣴⠼⠗⠒⠛⠛⠛⠛⠋⠛⠻⠿⠛⠫
⠀⠮⠙⠛⠻⠿⠿⠛⠛⠛⠛⠛⠓⠒⠒⠛⣀⡘⢛⣡⣛⠛⣻⡓⠁⠀⠀⠀⣀⣀⣠⣤⣤⡶⡶⠶⢶⠿⠛⢿⣶⠦⣜
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣠⣄⣒⣟⣿⣷⣻⣿⣿⣿⣿⣿⣿⣿⣟⣛⣋⣉⣉⣉⣁⣀⣀⣀⣠⣀⣀⣀⣀⣈⣀
⣿⣿⣉⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣠⣤⣤⡀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⢋⠤⢍⣿⣿⣿⣿⣿⣿⣷⣶⣾⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⠛⠻⠿⠿⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⣿⠟⢻⡏⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠟⠁⠘⡿⣷⣦⣯⣀⢈⣤⡜⢃⣿⣶⣶⣶⣤⣤⣀⡈⠛⠿⣿⣿⣯⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡿⠁⢀⡴⢚⣿⣾⣿⣿⡿⠟⣫⣔⡛⠛⠛⠻⠿⣿⣿⣿⣿⣷⡀⠈⠻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⡟⠀⠒⡡⠞⠉⣿⣿⣿⣷⡆⢀⠀⠀⠉⠓⠄⢀⣀⠀⠉⠛⢿⣿⣿⣦⡀⠈⢻⣿⣆
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⡟⠀⢀⢄⠆⠀⣠⣼⣿⣿⣿⣷⣼⣷⣷⣶⣿⡀⣿⣭⣙⠀⠀⠀⠙⢿⣿⣿⣄⠀⠙⣿⣧
⠀⠀⠀⠀⠀⡐⠁⢹⣿⣿⣿⠏⡟⠀⢀⣾⠃⠀⠘⣿⣿⣿⣿⣿⡿⢿⠛⠀⣀⠀⠀⠹⣿⣿⣿⣿⣿⣷⡄⢻⣿⣿⡆⠀⠘⣿⢆
⠀⠀⠀⠀⠀⠀⡀⣾⢇⡿⣿⠀⠀⠀⣾⣧⣶⣾⣿⣿⣿⣿⣟⡏⣴⡟⠉⠋⠀⠑⢀⣀⠘⢿⣿⣿⣿⣷⣿⣶⣿⣿⣷⠀⠀⠈⡎⠇
⠀⠀⠀⠀⠀⢰⣿⡏⠘⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣦⣤⣤⣶⣾⣿⣿⣷⣌⠻⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠁⢰⡀⠳
⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⣾⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠛⠛⠛⠉⠉⠉⠁⠀⠈⠙⢿⣿⣿⣿⣿⣿⡇⠀⠀⢸⡇⣷
⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣀⣀⣀⣤⣤⣤⣤⣤⣶⣶⣶⣿⣿⣿⣶⣄⠀⠻⣿⣿⠿⢻⣿⢸⢠⣾⡇⣿
⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠉⠁⢀⣼⡏⢸⣾⣿⣰⡏
⠀⠀⠀⠀⠀⠀⠛⢹⡄⠀⠀⢸⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⠿⠿⢿⣿⣦⡴⠛⠉⠀⣾⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢣⣤⢀⣸⣿⣤⣝⣻⣿⣿⣿⣿⣿⣿⣿⠟⣿⣿⠛⣿⣿⣍⢹⣿⣅⢰⣶⣶⡶⠦⠰⣶⣴⣴⠶⣤⣴⣿⣿⣿⡟
⠀⠀⠀⠀⠀⢀⣤⣾⣿⣵⣿⣿⣿⣿⣏⣉⠛⢿⡿⣥⣿⣿⣿⣿⣿⡏⠀⣿⣿⣿⣾⣿⣿⡀⠹⣿⣷⣶⠶⠈⠙⣿⣷⣾⠻⢿⣿⣿⠃
⠀⠀⢀⣠⣶⣿⡿⠛⣩⣿⣿⣿⠟⢉⣿⣿⣿⠟⣹⣿⡿⠀⣿⣿⣿⠁⢀⣿⣿⡀⠻⣿⣿⣧⠀⢹⣿⣿⣤⣀⣀⡈⠻⣿⣷⣤⡙⠻⣿⣦⣄
⠀⠐⠛⠛⠛⠁⠀⠚⠛⠛⠋⠀⠐⠛⠛⠛⠁⠘⠛⠛⠁⠀⠛⠛⠛⠀⠈⠛⠛⠀⠀⠙⠛⠛⠂⠀⠙⠛⠛⠛⠛⠙⠀⠈⠛⠛⠛⠂⠈⠙⠛⠃
⠀⠀⠀⠀⠀⠰⡿⣦⢰⡇⣾⣛⣛⠘⣧⠀⣼⠂⣟⣛⡃⢸⡟⢛⣷⠀⢰⠞⢛⣳⢀⡇⢻⡄⢠⡟⢸⣛⣛⠀⢸⡇⠀⢸⡆⣿⡛⣳⡆
⠀⠀⠀⠀⠀⠈⠇⠘⠿⠇⠿⠦⠤⠀⠸⠶⠃⠀⠷⠤⠄⠸⠏⠉⠷⠀⠘⠦⠬⠿⠀⠇⠀⠳⠟⠀⠸⠦⠤⠀⠘⠷⠤⠾⠁⠿⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡼⢆⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣦⣄⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣧⢿⡱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣷⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣤⣄⡀⠀⠼⣿⣿⣿⣿⣿⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠟⠻⠿⣿⣿⣿⣿⣄⠀⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⢀⣤⣄⠀⢻⣿⣿⣿⣿⣿⣿⡿⠁⢀⣤⣤⣄⠈⢻⣿⣿⣿⣄⣿⡜⠻⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⢸⣿⣿⠆⠀⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⢀⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡀⠙⠋⠀⣰⣿⣿⣿⣿⣿⣿⣷⡀⠈⠛⠛⠉⢀⣼⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠒⠒⠾⠿⠿⡿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣿⣿⡿⠟⠉⠀⣯⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠁⠀⢀⣤⣶⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣾⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠉⠙⠛⠻⠿⠿⠿⠮⠵
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣟⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⠀⢸⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⢸⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠀⠹⣿⣿⣿⣿⡟⢸⣿⣿⣿⡏⠀⠀⠸⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠇⠀⢿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠘⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⠶⠤⣄⠀⣠⠖⠋⠉⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠀⠹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠶⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠦⢄⡀
⠀⠀⠀⠀⠀⢀⠴⠊⠉⠉⠉⠳⢄⠀⣠⠴⠖⠒⠲⢤⡀⠀⠀⢠⠔⠚⠉⠙⠒⢤⠀⣀⠤⠶⠶⠿⣄
⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠀⠀⠙⢆⢰⠃⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣄⣀
⠀⡠⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦
⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠴⠋
⠀⠈⠓⠦⠤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁
⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⡰⠃⠀⠳⣄⡀⠀⢀⣠⠔⠙⠢⢤⣄⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠈⠢⢄⣀⣀⣠⠴⠊⠀⠑⠲⠤⠤⠖⠋⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⡤⣄⠀⠀⠀⠀⡴⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡴⠉⢦⠀⠀⠀⡼⠁⠘⡄⠀⠀⣸⠁⠀⢸⡄
⠀⠀⠀⢀⡴⡄⠀⠀⠀⠀⠀⠀⡼⠁⠈⣇⠀⠀⠀⠀⠀⡇⣹⠀⢰⠃⠀⠈⡇⠀⠀⠣⡀⣠⠇⠀⠀⢻⡀⠀⢠⠇
⠀⠀⠀⡞⠀⠸⡄⠀⢀⡀⠀⠀⡇⠀⠀⢸⠀⢀⡀⠀⠀⠈⠁⠀⠸⣄⡀⣠⠇⠀⠀⠀⠀⠀⠀⣀⠀⠀⠙⠚⠉
⠀⠀⠀⠳⣀⡴⠃⠀⣇⣳⠀⠀⠙⠦⠴⠋⣰⠋⢳⡀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢀⣄⠀⠀⢸⣉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⡄⠀⠀⠀⣇⠀⢀⡇⠀⠀⠀⠀⠀⡰⢆⠀⠀⢠⠎⠈⢧⠀⠀⠉
⠀⠀⠀⠀⠀⡰⢲⡀⠀⠀⠀⡏⠘⡆⠀⠀⠈⠓⠋⠀⣠⠶⡄⠀⠰⡇⢸⠆⠀⢸⠀⠀⢸
⠀⠀⠀⠀⢰⠁⠀⢳⠀⠀⠀⠓⠖⠁⠀⠀⠀⠀⠀⢰⠇⠀⢹⡀⠀⠉⠉⠀⠀⠀⠑⠒⠋⠀⢀⣤
⠀⠀⠀⠀⠸⣄⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣀⡸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⡇
⣤⣤⣤⣤⣤⣬⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼⣶⣥⣤⣤⣤⣤⣤⣤
⣿⣿⣤⣴⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⢀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠀⠀⠀⠀⢠⡀⠀⢶⡀⠀⠀⠀⠀⢠⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡄
⢙⡆⠀⠀⠐⠿⠀⠀⠸⡆⠀⠀⢸⡆⠀⠉⠀⠀⠀⠀⠸⠆⠀⠈⠀⠀⢰⣇⠀⠘⠞⠀⠀⠀⢸⡆⠀⠀⠀⠀⢣⡖⠀⠀⠀⠀⣷⠀⠀⠀⣘⣃
⠘⠁⡟⡄⠀⠀⢀⠀⠘⠇⠀⠀⠘⠃⠀⠀⠀⢸⡃⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⡶⡀⠘⠃⠀⠀⣀⠀⠀⠀⠀⢰⢣⠀⠉⠀⠀⠀⠘⠋
⠀⠀⠙⠁⠀⠀⣹⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⠃⠀⠀⠀⢀⢙⡀⠀⠀⠀⠈⠛⠀⠀⠀⠀⢀⡀⠀⠀⢠⢇
⢀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⣭⡄⠀⠀⠀⡀⠀⠀⣤⠀⠀⠘⠃⠀⠀⠀⠀⢠⢆⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⡀⠀⢰⠆⠀⠀⣥⠀⠀⠈⠿
⢨⡇⠀⠀⣾⡄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⣷⠀⠀⢸⠇⠀⠀⠀⠀⠀⣿⠀⠈⠾⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⢰⣹⠀⠘⠃⠀⠀⠉⠀⠀⠀⣤
⠈⠁⠀⠀⠙⠃⠀⠠⣿⡀⠀⠀⣿⡄⠀⠀⠉⠀⠀⠀⠀⢀⣀⣀⣀⣘⣿⡀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠘⣆⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠂
⠀⠀⢀⡀⠀⢀⡀⠀⠛⠁⠀⠀⠈⢀⡠⠤⣴⠶⣲⠆⣉⠥⣒⠨⠄⠂⠉⢏⠉⣍⠒⠒⠲⠦⢤⣤⣀⡀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⡟⡄⠀⠺
⠀⠀⢸⣽⠀⠸⠇⠀⠀⣀⣤⣖⠉⣡⢔⡯⠒⡩⣖⠭⢒⡩⠄⠂⠀⠀⠀⠎⠎⢒⠉⠄⣀⠀⠀⠀⠉⠛⠯⣭⣑⠒⠲⠤⣄⣀⠀⠀⠀⠿⠃⠀⠲⠃
⢀⡀⠀⠛⠀⠀⢀⡔⠚⠽⠂⢀⠞⢓⠥⣪⠕⣪⠔⣊⡥⠒⠀⠀⠀⠀⠀⠠⠸⡀⠯⣐⢀⠈⠐⠀⠀⠀⠀⠰⠙⢯⣔⠖⠀⠈⠙⠲⣤⡀⠀⠀⠀⣴⡀
⢨⡇⠀⠀⡠⠞⡁⠚⠁⠀⢠⠏⢊⠕⣪⠔⣫⠔⣪⠵⠚⠀⠀⠀⠀⠀⠀⠀⠀⢇⠨⢃⡀⠄⠀⠒⡀⠀⠀⠀⠀⠰⠙⣮⠔⣈⠥⢀⠀⠉⠲⣄⠀⠻⠃
⠀⠁⣠⠚⡐⠭⠀⠀⠀⢀⡯⢐⡵⢊⠔⣪⢔⠩⢒⠨⠄⠀⠀⠀⠀⠀⠀⠀⠄⢸⢈⡥⢒⠨⠥⠀⠐⠂⠀⠀⠀⠀⠠⠌⢯⠔⡨⠄⢒⡀⠀⢈⢧⡀
⠀⡔⣡⢱⡦⠛⢄⡀⠀⢸⠔⡣⢚⢕⡽⢊⠅⢊⠥⢒⡩⠀⢀⠀⠀⠀⠀⠀⡀⠸⢘⠩⠔⣒⠨⠭⢄⣀⣀⡀⠀⠀⠀⠐⡀⢯⠔⣈⠄⢒⠠⠄⢳⠱⡄
⣼⠋⠉⠉⠉⠉⠑⠪⢄⡇⢪⣖⡴⠥⠞⠓⠚⠋⠚⠛⠒⠛⠲⠮⣴⣠⠄⠀⠀⠀⡅⣂⠥⣒⣬⣝⣒⣖⣀⣉⣐⣂⣀⠤⠶⡈⣏⣴⡮⠑⠂⠉⠉⠙⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠳⢦⡀⣯⡶⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡇⠀⠀⠹⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⣽⠀⠀⠀⢸⢱⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢽⡀⠀⠀⡜⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡉⠛⠋⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋
⠀⠀⠀⠀⠀⠀⡠⢀⡠⢀⠠⢀⠤⢀⠤⢀⠠⢀⡠⢀⠀⣀⠀⡀⢀⡀⣀⠀⡀⠀⡀⢀⠀⡀⠀⠀⢀
⠀⠀⠀⠀⠉⠁⠐⠁⠚⠁⠊⠡⠖⠡⠔⠡⠔⢡⠔⡡⢊⡤⣊⠔⡩⠚⡡⢊⡠⣪⢔⡡⢊⠔⣉⠔⡩⢞⡤⣊⠔⡡⢂⠔⡠⢂⠴⣂⠔⡠⢂⡤⣠⠆⡀⣠⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢤⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠚⠉⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⢐⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠈⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⡀⠀⠠⠀⠀⠀⠃⠸⠀⠀⠀⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢴⡀⠀⠀⢀⡜⠀⠈⢀⠇⠀⠀⠀⠀⠀⢰⠁⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢇⠒⡭⠁⠀⠃⡘⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⢂
⠀⠀⠀⠀⠀⢀⠜⠁⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⢁
⠀⠀⠀⠀⢠⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⡎
⠀⠀⠀⠀⡆⠀⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⢜⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⠀⠀⠀⠂⠠⠀⠀⠀⠀⠀⢠⡷⠀⣴⠁
⠀⠀⠀⠀⢡⡀⠀⠀⡀⣶⠀⠀⠀⠀⠀⡠⣺⣿⣿⡄⠀⠀⠀⢀⠀⠀⠀⠀⠘⢷⣤⣀⡀⠀⠀⠀⠀⣀⣠⣼⠏⠔⠃
⠀⠀⠀⠀⢀⣙⠷⢦⣌⣹⣧⣤⣔⣡⡾⠧⠙⠛⠋⠹⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠉⠉⠙⠉⠉⠉⠉⠀⠀⠀⠀⠁
⠀⢀⠊⠉⠀⠀⠀⠀⠀⠈⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠙⠢⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠀⠀⠤⠂
⠀⠀⠙⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠊⢀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣅⠀⠀⠀⠀⠀⠑⠤⠀⠀⠠⠐⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⠀⠀⠀⠀⠀⠀⠀⣀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠛⠒⠴⠶⠶⠶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⢠⣤⡀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠊⠁⠀⠈⠻⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⢀⣀⣤⣶⡾⠟⠻⣷⡄⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡇⠀⠀⢀⣴⠾⠿⣿⣿⣿⡇⠺⠇⣸⣿⠀⠀⠙⠷⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣤⣄⢸⡇⠺⠇⣸⣿⣿⣿⣷⡿⠟⠁⠀⠀⠀⠀⠀⠈⠉⠉⠉⢙⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠉⣿⠈⠿⣷⣾⠿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣯⠁⠈⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣷⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⢀⠀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣠⣤⣰⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠀⣠⣶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣳⣿⣿⠟⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⢋⣱⣾⣿⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠸⣿⣆⠀⠉⢉⣬⣽⣶⣿⣿⣿⣿⡿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣌⣿⡿⠿⢻⣿⣿⡿⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣭⠹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠉⠉⠛⠓⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠘⢧⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡿⢫⣭⡻⣧⠈⢿⡅
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣦⠀⢀⣴⠞⡛⢿⣿⣿⣧⡙⠟⣣⣿⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⢹⡀⢸⡇⢿⡿⢈⣿⣿⣿⠿⠛⠉⠀⠀⠀⠈⠛⠶⣤⣤⡤⢤
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⣧⠈⠻⠶⠶⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣋⣀⣀⣤⣶⡀⠀⠀⢀⡀⠀⠀⠰⣆⠀⠀⢸⣷⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠈⢷⣄⠀⠈⢷⣄⠀⠀⢿⣧⠀⢸⡟⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣄⡘⣿⢦⣀⠘⣟⢧⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠀⠉⠓⠟⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠊⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠐⠒⠄⡀
⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⠈⡀⠀⡀⠀⡀⠀⠀⠀⢁⠀⠀⠀⠀⠀⠀⠀⡠⠘⠂⠉⠐⢀
⠀⠀⠀⢀⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠑⠀⠀⢀⠤⢄⣠⠤⢄⡔
⠀⢀⠊⢀⡈⠀⠀⠀⠄⢀⡄⠄⠒⢒⠹⠛⡛⠛⠛⠔⣛⠠⠄⡀⠁⠀⠀⠁
⠀⠀⠒⠒⠒⠀⠀⠒⠂⠀⠀⠀⠔⠁⠀⠀⠈⡄⠀⠀⠀⠉⠢⡀⠀⠁⠂⠄⣀⠀⠀⠀⠀⠈⠈⣂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠐⢅⠀⠀⠀⠑⠢⡀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⣀⠀⠀⠄⢀⠀⠤⠄⠀⠄⠈⢣⡀⠄⠂⠉⠉⠂⠀⠀⠀⠀⠀⠁
⠀⠀⠉⠀⠀⠀⠀⠴⠐⠀⠉⠄⠋⠀⠀⠈⣇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⢀⢀⢀⢀⢂⠀⠀⠀⠀⠠⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠐⣿⠐⠐⢒⠀⢀⠀⢀⠀⠒⢒⠒⠒⠒⠀⢀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡖⢀⠀⣽⠀⠀⠎⢀⡍⠀⠄⠀⢀⡍⠀⡀⠁⠠⠏⠀⠌⡔⠰⠁⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⠀⠀⠆⠀⢠⠀⢀⠃⠀⢀⡂⠸⠁⢀⠄⠀⣐⠀⡴⠀⠠⠆⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡔⠀⠀⡼⡀⠈⠀⢀⠈⠀⠀⠀⠘⠠⠀⠁⠀⣠⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠀⠃⠀⡼⠀⠎⠀⠋⢀⠆⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⠊
⠀⠀⠠⠀⠀⠀⠀⢀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠂⡂⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠁