Algae Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⢰⠏⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣅⠀⠀⠞⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠀⡀⠘⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⣆⠀⠀⢸⡄⠀⡘⠀⣰⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⡄⠀⢸⣷⢀⡇⣰⢏⠂⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠠⡇⠀⠈⣿⣿⡿⢉⠃⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠸⣿⢁⠎⠀⠀⠀⠀⠀⢸⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢹⡇⠸⡇⠀⠀⠀⠃⠸⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠰⠁⢀⡗⠀⠀⢸⠀⡇⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⣠⠇⠀⡘⠁⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣶⡏⠀⡸⠁⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠁⣰⣷⡀⠀⠀⠀⠀⠸⠀⠆⠀⠀⠀⠀⣿⣯⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⢹⠝⣧⠀⠀⠀⠀⠀⡀⢸⡄⠀⠀⠀⢻⡎⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡘⣷⣤⣧⠀⠀⠀⠀⠃⠘⣷⠀⠀⠀⠈⡄⠀⠰⠛⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⢡⠫⠉⣆⠀⠀⠀⠀⠀⢸⢳⡀⠀⠀⢁⠀⠀⠰⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⢇⠀⠘⠆⠀⠀⠀⠀⡹⠀⢣⠀⠀⢸⣀⡀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⡇⠁⠰⠀⠀⠐⠀⡇⠀⠈⠀⠀⢸⠉⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣷⠈⢸⡆⢀⠀⣸⠁⠀⠀⠀⠀⢸⡀⠀⠸⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⣾⡇⠄⠀⣿⠀⠀⠀⠀⠀⠆⠃⡐⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣼⣇⣿⣿⠀⠀⡀⠀⠀⠐⢀⣞⠊⡔⠀⠈⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠠⠀⠀⢸⡿⢋⡞⠀⢀⣤⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⠀⢠⠄⢀⠀⡀⣾⢣⡼⢁⡔⣩⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠘⣿⡀⠀⠀⠺⠀⠀⣿⠙⣴⠏⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡸⣧⠀⠒⠀⡆⠀⣿⡿⣽⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣿⣧⠀⠀⢸⡳⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⢷⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠨⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢿⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁

⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠉⠉⠉⠉⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣾⣿⣿⣿⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢣⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠉⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⡇⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⢳⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢧⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠳⡀⠀⠑⢄⠀⠀⠀⠀⠀⠀⡠⠃⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠘⣆⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠑⢦⡀⣀⠤⠊⠀⢀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠈⢆⠀⠀⠀⠀⢰⢡⠀⠀⠀⠀⠀⠀⠀⠀⠑⣤⠤⠒⠉⠀⠀⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠳⡀⠀⡠⠃⣸⠀⠀⠀⠀⠀⠀⣠⠔⠉⠀⠀⠀⣀⡠⠴⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢈⠖⠁⣰⠃⠀⠀⠀⠀⢠⠊⠀⠀⣠⠴⠚⠋⠙⣄⠀⠘⣆⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⠱⣀⠔⠁⢀⠜⢇⠀⠀⠀⠀⡰⠁⢀⡔⠋⠀⠀⠀⠀⠀⠘⡆⠀⢹⡄⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⢀⠖⠁⢀⡴⠁⠀⠀⠳⡀⠀⢠⠃⢀⠎⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⣸⠁⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⠀⡰⠁⠀⢠⠋⠑⣄⠀⠀⠀⠱⡀⠸⠀⡞⠀⠀⠀⠀⣀⡠⠔⠊⠁⢀⡴⠃⠀⠀⡆⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡆⠀⠀⠀⢰⠁⠀⢀⡇⠀⠀⠈⠳⣄⠀⠀⢱⡇⢠⠃⢀⠴⠚⠉⣁⣠⠤⠀⠂⠁⠀⠀⠀⡼⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠹⡄⠀⠀⢸⠀⠀⠘⡅⠀⠀⠀⠀⠈⢣⡀⠀⡇⡸⣰⠃⣠⠖⠋⠁⠀⠀⠀⠀⣀⣀⠴⠊⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠙⢦⡀⠈⢆⠀⠀⠱⡀⢀⣀⣀⣀⠀⠹⡄⡇⣧⡇⡜⢁⡤⠒⠋⠉⠉⠉⠉⠁⢀⣀⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠙⠢⣌⠢⡀⠀⠜⠁⠀⠀⠈⠑⢦⠸⡇⣿⠸⢰⠋⣠⠤⢒⣒⣒⣒⡉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄⠀⠀⠉⠛⠏⠀⠀⣠⢶⡒⢦⡀⢣⡇⣿⢿⢇⡞⡵⠊⣁⣤⣤⣀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠂⠀⠀⠂⠙⠳⠖⠋⠀⢀⡜⢷⣄⡑⢄⠱⢸⣧⣿⣾⣾⡘⡠⠊⠀⠀⠀⠀⠙⢦⡀⢃
⠀⠀⠀⠀⠀⠀⢀⡮⠂⠀⠀⠀⠈⠉⠒⠒⠀⠐⠊⠁⠈⠓⣕⡈⢮⡄⢸⢻⡿⣿⡗⣼⠁⠀⠀⠀⠀⠀⠀⠀⠱⡈⡄
⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠃⠟⠘⢃⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠘⠢⠤⠤⠂⠀⠘⠂⠤⠤⠤⠤⠐⠁⠐⠠⠄⠂⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠑⠀⠀⠀⠈⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠂⠄⡄
⠀⠀⠀⠀⠀⠀⠀⠁⡀⠐⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠐
⠀⠀⠀⠀⠀⠀⢂⠀⠀⠠⠈⠀⠀⠄⠀⠄⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠦⠀⠞⠱⣎⡅
⠀⠀⠀⠀⠀⠀⠀⠂⠐⠐⢄⡀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠠⠂⠀⠈⢠⣯⠋⠀⠀⠀⠀⠀⠄⠀⠀⠀⣀
⠀⠀⠀⠀⠈⠢⠀⠀⢁⢠⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⡀⠐⠄⠀⠀⠀⠀⢆⠀⠐⠂⢀⠌⠰⠒⡄⠀⣠⠤⢊⠠⢀⣀⡀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠚⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⢁⡠⠈⡄⠀⡀⠁⠉⡀⠈⠀⠣⠀⠈⠢⢡⠊⠀⡔⡡⢨⠙⠈⠃⠈⠜⠑⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⡀⠀⠆⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣀⠐⠕⠆⠤⡁⠀⢠⡆⡆⠃⡀⡆⡄⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⡀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠠⣢⠉⡄⠀⡐⠀⠀⢱⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⡘⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠁⠛⠁⠠⡀⢠⢰⠀⠀⢃⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠪⣁⠈⡶⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⡄


⣶⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣧⣭⣷⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣼⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠖⠒⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠘⡆⠀⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠄⠀⣾⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢳⡷⡆⢾⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⢂⡜⠁⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⣧⡇⣿⣿⢺⡏⢻⣆⠀⠀⠀⠀⠀⢠⡞⠓⠀⢘⡶⠖⢄⢼⠀⠀⢠⠞⢡⢤⣀⠀⠀⠀⠀⠀⠀⣴⣼⣆⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⢀⢿⣄⠀⣿⣇⡏⣿⡜⣧⢠⡾⠀⢀⡴⠀⠀⠘⣆⡀⠄⢸⣷⡄⠂⡼⡆⢠⡏⠘⠀⣠⡿⠀⠀⠀⠀⠀⠀⣿⢼⡇⢀⣴⠛⠁
⠀⠀⠀⠀⠀⠀⠘⢦⣽⢀⣿⡜⣯⣼⢃⣏⡟⠁⠀⣼⠁⠀⠀⠀⠀⠉⠙⠺⣧⠙⣄⠈⠃⡼⢁⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⣿⢹⣥⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠻⢖⢹⢿⠛⢻⢹⣿⣧⠀⠘⡇⠀⠀⠀⠀⠀⡴⠒⠀⣿⠉⢺⠀⢠⡷⠧⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣟⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠙⣦⡙⠿⢎⢿⣻⣍⣽⣯⣀⡼⠃⠀⠀⠀⠀⠀⠛⠦⠄⢻⣶⣿⢀⡞⣣⠞⠛⢁⣀⡀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢑⢌⣻⠷⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡒⠰⡟⢿⡆⣼⠁⠂⠐⢂⣸⠇⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⣿⡳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠉⠒⠿⣾⡷⢗⠂⠈⠩⣍⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠀⠀⠀⣿⣦⠀⠀⣠⣴⠆
⠀⠀⠀⠀⠀⢴⡀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⡿⠁⠉⠛⠛⠋⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡏⠀⡰⠛⠁
⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣭⠐⡂⠀⠀⠀⠀⠀⠀⢸⡄⣇⡇⢠⡧⠂
⠀⠀⠀⠀⠀⠀⢘⡗⢦⡞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⢘⡃⠀⠀⠀⠀⢀⠀⢸⣷⡸⣧⣟⠁
⠀⠀⠀⠀⠀⡆⣸⠓⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠂⠀⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡝⠀⠦⠀⡀⠀⠀⠀⢼⣄⠀⢏⢓⢫⢿⡀
⠀⠀⠀⠀⠈⢿⡛⡀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠘⡇⠀⡇⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡓⢠⡝⢠⣎⡅⠀⠀⠀⠈⠻⡱⡌⣶⢸⣸⠇⠀⠀⣤⡀
⠀⠀⣀⠀⠀⠈⣿⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⢹⢸⠘⡸⠁⠀⡤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡆⠘⣆⡗⠸⠅⠀⠀⠀⠀⠀⠘⣟⣿⢸⢟⡠⠀⠐⠽⠃
⠀⠀⠙⢲⡄⢠⢸⡇⢾⠉⠁⠀⠀⠀⠀⠀⠀⠀⠘⢆⢱⡇⢀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠑⣶⣿⢀⡓⠀⠀⠀⠀⠀⠀⣶⣿⣿⡏⣺⡹⠁
⠀⠀⠀⠀⠉⠳⣄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡷⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⢸⠈⠁⠀⠀⠀⠀⠀⠀⠻⢥⣹⣷⣿⡇
⠀⠂⠀⠀⠀⠀⢹⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡛⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠁⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠏⠀⠀⠘⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⠁⠟⣀⢰⡻⡄⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢏⢁⢾⣿⣺⠖⠟⢀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⣀⣴⡄⠀⠀⠘⠶⠿⢾⣿⡼⢰⠀⠸⡆⣠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢷⣬⡟⣿⡞⠒⣷⡇⠀⢱⣿⢇⡆⠠⣾⠟⢘⣀⡀⢠⠀⠀⠀⠠⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣿⣧⡀⠀⣴⡄⠀⠀⠀⠀⠙⢊⠹⢿⣽⡅⢅⡿⡗⢀⣾⠏⠉⡤⢀⡿⡶⠿⠃⠔⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⢀⠼⣿⡟⣦⣠⣟⡧⣀⠀⠀⠀⠀⣀⡁⠈⢻⠻⣿⡤⠀⣿⡾⣧⡤⢶⠏⠐⠀⠐⠂
⠀⠀⠠⠲⠦⠀⠀⠀⠀⠀⠀⢹⠈⣵⡲⣄⣤⡀⠀⠀⣷⣹⣷⣿⣿⣏⡶⠉⠀⠀⠀⠀⠙⠃⠀⠈⠃⢈⡳⣏⢿⣟⡉⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⢥⣬⣿⣥⣭⣻⣷⣤⣿⣿⡾⠶⠋⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠸⡿⣿⠁⢰⡋⠛⢳
⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣹⠿⡿⣯⣿⠛⡇⠀⠀⣠⣤⣿⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠉⠉⠁
⣲⠂⠀⠃⠁⠆⠀⢠⠀⠀⠀⠀⠈⠛⠧⠋⠁⠀⢘⣾⣷⡎⠀⣠⡼⣿⣿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⢰⡀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣸⣿⣥⣤⣷⣷⣿⢯⣠⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠖
⡀⠀⠀⢀⣿⡆⡀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢎⠀⣿⣿⣟⢻⣟⣙⣿⣟⣳⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣤⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠃⠀⠂⠐⢸⠁⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⣿⡿⠋⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⣗⢾⡶⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠂⠅⢄⣸⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠻⡇⣰⠘⡃⣡
⠀⠀⠀⡐⣸⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡙⣾⣫⣿⠳⠏
⠀⠀⠀⠁⣿⠀⠆⠀⠀⠫⠭⠇⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⡸⢿⡏⠐⢠⡠⣋⣖⡶
⠀⠀⠀⠠⠼⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣄⣯⠁⣠⠖⣛⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠼⢿⡁⠊
⠀⠀⠀⠀⠀⠀⠯⠽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣣⠀⠀⠀⣞⣗⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅
⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⢰⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢯⢿⣵⣀⣶⡿⣭⠂⠀⢀⡤⣄⡀⠀⠀⠀⠀⠀⠀⠋
⠀⠀⠀⠀⠀⠀⢸⡻⡄⢀⣿⡿⣞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⡿⣿⣿⣉⠁⠀⠀⠸⠄⣀⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠻⣭⠻⣿⣿⣿⣿⢩⠃⠀⠀⢀⠀⣠⣴⡞⢳⠀⠀⠀⠀⠀⠑⢺⣿⡁⢀⣬⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⣀
⠀⠀⠀⠲⠀⠀⠈⠛⢫⣟⣿⣻⣾⡆⣠⣴⡟⢛⣷⡟⣀⣧⡀⠀⠀⠀⠀⠀⠰⣿⣵⣿⠹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⣿⡀⢠⡆
⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⢩⣻⣿⣛⣽⣿⡿⢿⣽⣏⡉⠉⠀⠀⠀⠀⠀⠀⢀⣿⡟⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⣿⢿⡿⡟
⡦⠀⠀⠈⢿⣿⣿⣿⣆⠀⠈⢷⣿⣿⡼⠁⠙⢻⣛⡿⠗⠀⠀⠀⠀⠀⠀⠀⠈⣿⠉⠁⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡄⠀⠀⢸⣿⢿⠋⠁
⠀⠀⠀⠀⠠⡈⢹⣿⣭⣽⣄⠸⣿⡟⣧⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠚⠝⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠊⠁⠀⠰⣜⣿⡉
⠀⠀⠀⢀⡼⢼⣿⡿⢿⣿⣿⣿⣿⡟⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣷⣿⠃
⠀⠀⠀⠀⠉⠉⠉⠓⠚⠓⠶⣿⣿⢱⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿

⠀⠀⠀⠀⠀⢠⡀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢀⢰⡇⣀⡇⡆⡆⡄
⠀⠀⣀⠀⠇⣀⠱⡇⡰⠂⡀⢠⡄⠀⠀⠀⠀⠀⢃⣘⡇⣖⣾⠀⠀⠀⠀⠀⠀⠈⡳⣜⠸⣧⠸⡞⠀⣷⠀⡟⠉
⠀⠰⠮⣀⡷⠻⡀⡷⠃⡼⠷⠃⠀⠀⠀⠀⢦⢀⡊⢧⡄⣛⠋⢀⡄⠀⠀⠀⠀⢠⡉⠙⢧⡇⣆⢷⣦⢫⣜⠒⡁⡄
⠀⠀⣀⠘⢠⠀⢃⢋⠶⣣⣦⠤⠀⠀⠀⠀⠘⢆⢧⡀⢣⠏⣰⡏⠀⠀⠀⠀⠀⠬⢇⣷⠈⣧⢏⣸⢳⢺⢋⣞⣼⡿⠁
⠀⠀⠈⠋⠋⠳⢆⡂⠉⠈⠉⠁⠀⠀⠀⠀⠀⠈⠙⠳⣦⠴⠋⠀⠀⠀⠀⠀⠀⠨⠦⣵⣄⣻⠀⡏⣼⣟⣭⡧
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠓⠬⠷⠷⠯⠟⠂⠀⠀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⢀⡀⠀⣸⡇⠀⠀⠀⠀⣀⠀⠀⠀⢀⡤⠶⠀⠖⠶⠴⠀⠶⠰⠆⠲⠔⠧⠐⠂⠚⠃⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⢸⡇⠀⣉⢃⠀⠀⠀⠀⣿⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⣾⠐
⠀⠀⠀⣾⠀⡍⠈⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⣀⣀⡀⠀⢀⡀⠀⠀⠀⡠⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠃⢀⣯⠀⠀⢀
⠀⠀⢀⡍⢰⡷⡟⠀⠀⠀⣮⡸⠀⠀⠀⣴⡀⠈⠉⠀⠉⠀⠀⠀⠀⠀⠁⠀⣐⣒⣶⠎⠀⠀⠀⠀⠀⠀⠀⡌⢸⠃⠀⢸
⠀⠀⢠⡷⢠⡟⡃⠀⢠⡞⡶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡆⢸⠀⠆
⠀⠀⢠⡾⠸⡬⡇⢰⢛⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⣰⠖⠀⠄⠠⣤⡀⠀⠀⠸⠀⠀⡇⢸⢸
⠀⠀⣠⠃⠀⣾⠇⢸⣋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣈⣁⠐⠂⠈⠀⣀⠉⠠⡤⠉⠉⠁⠀⠀⠀⠀⠀⡇⡆⡀⡈⢸
⠀⠀⠸⠇⠀⠙⠀⠘⡏⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠐⠚⠛⠷⠀⠘⠒⠂⠀⠀⠀⠀⠀⠀⠀⡇⢇⠁⡇⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⠃⠉⠸
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣷⣾⣭⣭⣭⣭⣬⣭⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠖⠒⠒⢒⣋⣭⣭⡭⢟⣡⣤⣤⡴⠖⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⡴⠉⢡⣾⡋⠛⠛⠛⢉⡷⠋⠀⠉⣀⡠⠤⡤⠤⠤⠤⠤⢤⠤⠤⠤⠤⠤⠤⣀⡀
⠀⠀⠀⠀⠀⠀⠰⡇⠀⠞⠉⠀⠀⠀⡠⠋⠀⣠⠖⠋
⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⢀⡴⠋⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⢀⣾⠁⠀⢀⣸⢧⣄⣀⣀⣤⡴⠶⠒⠓⠒⠒⠚⠉⠉⠙⠁
⠀⠀⠀⠀⠀⠀⠀⣧⡀⢀⣼⠇⣴⠞⢛⡟⠘⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣇⣼⣟⡾⠃⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⣴⠛⡁⢸⣷⡠⠋⠀⢀⣤⣴⠖⠒⠒⠒⠒⠋⠉⠉⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠰⣿⠀⢁⣾⣿⡇⣰⡾⠋⠉
⠀⠀⠀⠀⠀⠀⠀⢻⡄⢿⣯⣿⣷⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣧⢹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠃



⠀⢀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢡⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢸⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠂⡞⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⡇⠀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠀⠀⠀⠇⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠃⠀⠃⢸⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⡇⠀⡀⠀⠀⡐⡐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠈⠰⠀⠀⠀⠀⠀⠀⠘⡀⡀⡌⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⢰⡇⠀⢠⠀⡴⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⡄⠀⡇⠀⠀⠀⠀⠀⠀⢁⡧⠁⠀⠀⠀⢀⠌⢀⠀⠀⠀⠀⢀⢃⠁⠀⠈⡄⠇⡀
⠀⠀⠀⠀⠀⠀⠀⢠⢹⠘⡀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⡠⢂⢆⠂⠀⠀⠀⢀⠊⠌⠀⠀⢰⠁⢘
⠀⠀⠀⠀⠀⠀⠀⠰⠈⠀⠃⠀⠀⠀⣧⠆⠀⠀⠀⠀⢀⠜⠀⠀⢀⠔⣉⠔⡡⠂⠀⠀⠀⠀⠆⡘⠀⠀⠀⢠⠜⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢆⠂⠀⠀⠀⠀⡿⠀⠀⠀⠀⠠⠊⠀⣠⠴⢑⠨⠔⠉⠀⠀⠀⠀⠀⡈⠰⠀⠀⠀⠀⡬⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠰⠃⠀⠀⠀⡐⠁⣠⠾⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠁⠀⠀⠀⠀⠃⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⢠⠁⠀⠀⠀⠌⢀⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠆⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠧⡀⠀⠀⠌⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠘⢀⠄⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠈⠂⣴⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣀⢢⠀⠠⠄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⢠⢣⠂⠠⠁⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢠⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡈⡀⠀⣼⡏⢠⡡⡡⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⣀⣀⠂⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠱⣀⡿⣰⡗
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠂⠈⠀⠀⠀⠁⠢⣔⣠⡤⠀⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠒⠋⠉⠝⠛⢄
⠀⠀⠀⠀⠀⠀⠀⢌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣦⡄⠀⠀⠈⠆⠀⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠈⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠂⠀⠤⠤⠤⠤⠄⠒⠺⠟⠀⠀⠠⠄⠊⠀⠀⠀⠀⠀⠑⠒⠀⠀⠀⠐⠒⠂

⠀⠀⠀⠀⠀⢀⣰⣀⡠⠀⠀⠀⠀⠀⢀⠤⠄⣀⠙⡄⠀⡀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄
⠀⠀⠀⠀⢰⢅⠘⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⣠⡍⣧⡤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡀⠀⠀⠀⢠⣿⣿⣿⡿⠛⡉⠙⠲⠄
⠀⠀⠲⠦⣼⣧⡥⠃⠀⠀⠀⠀⠀⠀⢀⡀⣀⡈⠔⡏⠈⡄⠀⠀⠀⠀⠰⣶⡶⢀⣀⣠⠸⠃⠀⠀⠀⠀⠉⠉⠉⢤⣀⣀⣀⣠
⠀⠀⠀⠈⠪⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤
⠀⠀⠀⠀⠀⣸⣟⣄⠀⠀⠀⠀⠀⠀⢠⡀⣤⠀⢻⠏⠀⠀⠀⠀⠀⠀⢸⣟⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣤⣽⣯⣤
⠀⠀⠀⠀⡰⠏⠀⢻⡆⠀⠀⠀⠀⠀⠈⢻⡏⠰⠻⠇⣦⠆⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣽⡇⠀⠀⠀⠀⠀⢸⣿⡏⢹⣿⠃
⠀⠀⠀⠀⠛⢷⣤⡞⠀⠀⠀⠀⠀⠀⠀⢸⠻⣆⠀⠰⢿⠀⠀⠀⠀⠀⢸⣿⣿⣷⣾⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣪⣕⣿⡄
⠀⠀⠀⠀⠶⠶⠟⠗⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠁

⠀⠀⠀⠀⡐⣂⡤⠠⠄⠀⠀⠀⠀⠀⠀⢠⠀⣴⣦⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⢘⡱⠉⠀⠀⠁⣚⣤⠀⠀⠀⠀⠘⢦⡱⡌⢡⢎⡵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡐⠿⠿⠷⠂
⠀⠀⠦⢠⠀⠀⠀⠀⡐⠂⠀⠀⠀⠀⠀⠀⠉⣆⢰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣶⣄⠀⠄
⠀⠀⠀⢩⡄⠤⢐⠰⠈⠁⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⠿⠟⠛
⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⣀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⢰⢀
⠀⠀⠀⣄⠀⠈⠛⠻⣷⣤⢘⡇⠀⠀⠀⠀⠀⣃⠀⢠⠀⣸⠈⠇⠀⠀⢀⡔⠀⡀⠀⠀⠀⠀⠀⣃⠀⡞⢠⠃⠘⠂⢀
⠀⠀⠀⠘⢲⡧⠀⠘⠇⣸⢿⠀⠀⠀⠀⠀⠀⠈⣇⠈⡆⠛⠀⠇⠀⣠⠎⢀⠞⠁⠀⠀⢠⠀⠱⣤⣄⠇⢢⠀⢀⣴⣎
⠀⠀⢃⡀⠈⡄⢼⢰⣇⡾⣸⣠⠞⠀⠀⠀⢳⡄⢸⢀⣁⠘⡆⠇⢰⠃⢰⠏⠀⠀⠀⢀⠈⢧⠀⠙⡸⢈⣷⡀⡏⢀⣼⠃
⠀⠀⠀⠉⢣⠙⠈⣤⡿⠁⠃⢧⠀⠀⠀⠀⠀⡅⢨⡸⠹⠀⣼⠆⡴⠀⡾⠀⠀⠀⠀⠈⠳⢾⡄⠆⢳⣈⡀⠣⠛⣏
⠀⠀⠀⣄⠈⣤⡻⣾⣿⠀⣴⢸⡇⠀⠀⠰⣤⠣⢀⢡⡞⢦⣕⣟⢁⡔⡑⠃⠀⠀⠀⠀⠀⣧⠸⣿⣯⣿⣁⣸⢀⣼
⠀⠀⠀⠈⠢⣌⠉⢿⣿⢿⢻⡋⠀⠀⠀⠀⠀⠉⠛⠻⣟⣾⢼⡿⢮⠴⠃⠀⠀⠀⠀⠀⠀⢸⠀⠺⣿⣾⢅⡎⠉⠁
⠀⠀⠀⠀⠀⠈⠉⠻⠛⠛⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠊

⠀⠀⠀⠆⠀⠀⠀⠀⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣰⡆
⠀⠀⠀⢀⠀⠠⠄⢀⡇⠻⠀⠀⠀⣠⠂⢀⠀⠀⢄⠀⡈⠛⠶⣿⣄⠀⡇⠀⠀⠀⠀⠀⣿⡟⠉⡇⠀⣰⠀⢰⠀⠀⢀⡠
⠀⠀⠀⠀⢳⠀⣷⠸⠃⢼⠀⢀⡴⠋⣰⠋⠀⠀⠘⠦⣧⡀⠀⡟⢨⣿⠁⠀⠀⠰⣄⣰⡀⣥⢰⢀⡴⠃⡴⠃⢀⡴⠈
⠀⠀⠰⣄⠈⡇⢨⡀⢷⢸⠀⡞⡀⡼⠁⠀⠀⢰⠀⠀⣅⢰⠀⣆⣸⢸⢁⡔⠁⠀⠙⢿⣆⠘⣨⠿⡆⠸⡆⢰⠟⠁⡄
⠀⠀⠀⣈⠀⣕⠟⡇⢠⡦⢠⡜⢱⠇⠀⠀⠀⠀⠙⢂⡙⠈⢤⣽⠃⠏⢿⠀⠀⠀⠀⢸⡄⢲⣿⡄⢸⡄⣱⡇⡀⠐⠁
⠀⠈⢦⡹⢄⠙⣤⢳⣜⢶⡋⣫⢊⠖⠀⠀⠀⠀⠀⠈⢃⡸⢸⣿⠄⣠⠈⡇⠀⠀⠀⠀⠳⣀⢿⡻⣯⢃⡻⢹⡇
⠀⠀⠀⠩⣗⡻⣿⣲⣩⣿⡿⣭⠾⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣿⣖⡋⡞⠁⠀⠀⠀⠀⠀⠈⠛⠑⢿⣿⡥⠚⠁
⠀⠀⠀⠀⠀⠈⠒⠻⠷⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛

⠀⠙⠓⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠙⠟⠃⠀⠀⠁⠀⢀⢀⣀⡀⠀⠈⢿⣿⣇
⠓⠈⠀⠀⠈⣁⣀⠀⠀⠀⠀⠀⠀⢀⣠⡼⠀⠀⠀⠀⠀⠀⠀⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠛⠁⠠⠀⢆⣬⠌⢠⣿⡟⠉⠹⡏⠀⠀⢀⡙⠃
⠀⠓⠲⠀⠀⠉⠙⠁⠀⠀⠀⠀⠀⢨⣀⣠⠄⠀⠀⠀⠀⠀⠀⠀⡈⠰⠀⢀⢀⠀⡀⠀⠂⠀⠀⢀⡤⠋⣵⡿⢟⠏⠐⡓⠁⡈⢁⣴⣿⣟⢀⣰⣤⡆⠀⠀⠀⢷⣿
⠀⠀⠘⣆⠀⠀⠤⢤⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⠂⠉⠀⠀⠀⠀⠀⠀⢀⡎⢈⠀⠀⠀⠀⠐⣿⡹⠶⣧⣄⣿⣿⣿⣷⣄⣀⠙⣴⠀⣠⣿⣿
⠀⠀⠀⠀⣄⡀⣀⠀⣀⣐⢉⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠈⠁⠠⠄⠀⡖⠛⠲⡶⣝⣿⣿⣿⡿⠛⢻⣿⣿⣿⣿⣿⠿⠟
⠀⠀⠀⠀⠈⠉⡁⠚⢉⡍⠲⠦⠶⠆⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠴⠀⡀⢰⣶⣿⣶⣄⠀⠛⠉⠻⡿⢿⣿⣶⠿⠿⢉⡍⠷⠋
⠀⠆⠀⠀⠀⠘⠿⠖⠉⢁⢀⡜⢀⣀⠄⢁⠀⠀⠛⠢⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣴⡆⢸⣿⣿⣦⣿⣍⢻⡿⡃⢤⡀⣌⡐⠚⠉⠣⠞⠁⠀⠆⢠⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣠⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⢷⡀⣼⠓⢟⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠻⡶⢫⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠛⠁⢠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠂⠀⣈⣩⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⣾⠀⠀⠀⠿⠒⠚⠛⣻⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠀⣴⠁⣠⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡉⢿⣦⠀⠀⣸⠃⠀⠀⣰⠖⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡘⠿⠃⣴⠯⢴⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠹⣷⣀⡟⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡷⠀⣠⠶⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠈⠛⠃⠀⣼⣁⣤⠤⠶⢶⡆⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣼⠁⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠈⣀⣤⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⢾⠙⣆⣼⢃⡼⠃⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢿⡶⣤⡀⠀⠀⠀⢸⠁⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠙⠁⠘⠛⠋⣹⠃⠀⠀⠀⠀⠀⣀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣌⠻⣆⠀⠀⢸⡄⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢦⡄⠀⢿⠀⢀⡾⠛⠛⠉⠀⠀⣀⣤⣄⣰⡏⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣌⠳⢤⣸⠇⠀⢸⠃⣀⣠⡴⠞⣻⠀⠀⠀⠀⠀⠹⣆⠹⣤⡟⠀⡾⠁⠀⠀⠀⠀⣴⠋⠀⠈⠛⠃⠀⠀⠷⠶⠟⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠁⠀⠀⠙⠋⠉⣡⡴⠞⠁⠀⠀⠀⠀⠀⠀⠈⢳⡌⠀⠀⠉⢛⡇⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⣾⠋⠁⠀⠀⠀⠀⠀⠀⣠⣤⣀⠀⣰⠇⠀⣠⡶⠛⠁⠀⠀⠀⣀⣹⣄⠀⠀⠄⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣿⠀⠀⠐⣿⠀⠀⠀⠀⠀⠀⠀⠰⡏⠀⠘⢻⠏⠀⢠⡟⠀⠀⠀⠀⢰⠏⠉⠉⠛⠀⠀⠀⠀⠀⠚⠿⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠙⠯⣝⠓⢦⣄⠀⣿⠀⠈⠀⣿⠀⠀⢀⣠⣄⠀⢀⣀⣿⠀⠀⡿⠀⠀⡌⠉⣳⠀⠀⠀⠘⣇⠀⠀⠀⠀⢰⠃⠺⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣬⡙⠋⠀⠀⠀⣿⣠⡴⠛⣡⣿⠀⡟⠀⠀⠀⠀⣧⠀⠀⢃⢠⡏⠀⠀⠀⠀⢘⣆⠀⠀⠀⡘⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠉⠁⣰⠞⠋⠀⠀⣇⠀⠀⠀⠀⢹⡆⠀⠘⡄⢹⡆⠀⣼⠋⠉⠛⠂⠀⡔⠀⠀⠘⠻⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⣾⠁⠀⢀⡶⠛⠻⠀⠀⠀⢸⠀⢿⡀⠀⠸⣸⡆⠀⢻⠀⠀⠀⢀⡜⠁⢀⡀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡇⠀⠀⠘⣷⠀⠀⠀⠀⠀⢸⠀⢸⡇⠀⠀⢿⠀⠀⢸⡇⠀⢀⡞⠀⠀⣠⡴⠟⠋
⢀⡴⠒⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠈⣧⠀⠀⢠⡿⠧⠀⠠⠄⠀⠈⠀⠀⣷⠀⠀⠸⠗⢻⣦⡇⠀⠈⠀⠀⠘⣯
⢸⠃⠀⠀⠘⣆⣠⠖⢶⣄⠀⠀⠀⠀⠀⣾⠀⠀⠀⠈⠳⢤⣸⣇⠀⠀⠀⠀⠀⢠⠀⢠⡟⠀⢀⣤⠶⢛⡟⠁⠀⠀⠀⢀⣴⠟
⠸⣇⠀⠀⠀⠘⠋⠀⠀⢹⡄⣠⡶⣤⡀⠸⣦⡀⠀⠀⠀⠀⠈⠛⢦⣄⠀⠀⢠⠆⢀⡾⠁⣠⠟⢁⡴⠛⢀⡴⠃⣠⡶⠛⠁
⠀⣹⡷⠀⠀⠀⠀⠀⠀⠈⣿⠏⠀⠀⢳⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀⠹⣆⠀⢋⡴⠋⠀⣰⣯⠶⡾⠁⢠⢎⣴⠟⠁
⣼⠁⠀⠀⠀⠀⠀⠐⠠⣀⡀⠀⠀⠀⠸⣇⣴⠞⣧⠈⢳⡀⠀⠠⡀⠀⠸⣦⡿⠁⠈⢱⡏⣿⠀⠁⠀⠁⡾⠁
⠙⠶⣤⣀⣀⣀⣀⠀⠀⠀⠘⡀⠀⠀⠀⠙⠁⠀⢸⠀⠈⢷⡀⠀⢱⠀⠀⢿⠀⠀⠀⣿⠀⣸⠀⠀⡄⢘⡇
⠀⠀⠀⠈⠉⠉⣿⠃⠀⠀⠀⠰⣀⠀⠀⠀⠀⠀⢸⡇⠀⠸⡇⠀⠀⠇⠀⢸⠀⢰⠀⣿⣴⠏⠀⡜⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠻⣄⡀⠀⠀⠀⠀⠈⠉⠒⠠⣀⠘⣷⡀⠀⣿⠀⠀⠸⠀⢸⣄⠈⠀⢹⣇⡠⠊⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢻⡇⠀⠀⠀⠀⠀⠁⢌⠙⠲⠿⣤⣤⣄⡀⠀⠾⢤⠀⢀⡿⠀⠀⣀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠶⠶⢶⡄⠀⠈⠒⠦⠤⠤⣀⣉⣳⣶⣈⣠⣿⠷⠖⠛⠉
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣙⣳⣶⣶⣾⣿⣟⣛⣛⣛⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡏⠙⠋⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢸⡇⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣿⢠⣧⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⢇⣿⡿⢀⣧⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠰⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢺⣿⣿⣿⠇⣼⣿⡇
⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠠⡀⠂⢀⠀⠀⠀⠀⠀⡀⠀⢠⠀⠀⠀⠀⢠⠀⠀⢀⡞⠀⣸⣿⡌⡿⢸⣿⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠦⠄⠀⢸⠀⡄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⡇⢰⣿⠿⣷⠾⠂⢿⣿⣿⠀⡇⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠰⢀⡀⠄⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⢸⣷⣸⣿⠀⣽⡀⣀⣾⣿⡟⣼⠇⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢪⡵⠶⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠘⣿⠀⢸⣿⣿⣿⡀⠉⡤⣉⡽⠋⣼⣿⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠐⠂⠠⠘⠂⠀⠐⠀⠀⠀⢀⠆⠀⠀⠀⠀⣿⠀⢸⣿⣿⡇⣧⡄⠄⠉⠁⠀⣿⣿⢀⣿⣿⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⢂⣀⠀⠀⠠⡄⢈⠠⠊⠀⠀⠀⠀⠀⣿⡄⢸⣿⡿⢁⣀⠐⢰⡦⠀⢀⣹⣿⣾⠟⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⡄⠀⠀⠒⠀⢀⠀⠀⠀⠁⠄⠀⠀⠀⠀⠀⠀⠀⢿⣷⣿⣿⣷⠘⠛⠌⠀⣠⠾⠛⣻⣿⠃⠀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠄⠀⠂⣠⡰⠄⠀⢀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠈⠻⢿⣧⡈⠳⣶⢀⠛⠃⣠⡾⠛⠁⠀⢀⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠄⠀⠡⡀⠋⠀⠀⠄⠂⡁⠤⠊⠀⠀⠀⠀⠀⠀⠘⢿⡙⢢⣤⠈⢰⡾⠉⠀⣠⣤⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠈⠘⠁⢀⠀⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⠉⠐⠃⠀⣴⠿⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠴⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⣀⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⡄⠀⢸⡆⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢸⠇⠀⢸⡇⠀⠀⠀⠀⠀⣾⠁⠀⠀⢸⠀⠀⠀⣿⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⢸⠀⠀⠀⣗⣼⠇⠀⠀⠀⠀⠀⢠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣿⠀⢀⡿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⠀⢀⣿⡟⠀⠀⠀⠀⠀⣴⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⣿⡇⣼⠃⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⠀⢰⣿⡇⠀⠀⠀⢀⡾⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⢿⠸⣿⡀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⢸⠀⠀⢸⡟⣇⠀⠀⠀⣼⠇⣼
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⣇⠈⠳⣦⣀⠀⠀⠀⠀⢻⡄⠀⠀⠈⡄⠀⢸⡇⢿⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⣴⡆⠀⠀⠀⢸⡇⠀⠀⠀⣄⠀⠹⣆⠀⠈⠉⠛⠶⠦⣤⣬⣷⡀⠀⠀⢇⠀⢸⡇⠸⣇⠀⠀⣿⠀⠀⠻⣆
⠀⢠⣾⡿⠀⠀⠀⠀⠀⣿⠀⠀⠀⢱⡀⠀⠈⢷⣄⠀⠀⠀⠀⠀⠀⠀⠉⠉⠑⠺⠦⣼⣇⠀⠹⡄⠀⠸⣇⠀⠀⠙⢷⡀
⢠⡟⢸⡇⠀⠀⠀⠀⠀⠹⣇⠀⠀⠈⣧⠀⠀⠈⢿⣷⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠹⣆⠀⢹⣆⠀⠀⠈⢿⡀
⣸⠀⢺⡁⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠘⢇⠀⠀⠈⠻⣌⠙⠛⠛⠷⠶⣦⡤⢤⣄⡀⠀⠀⡀⠘⣆⠙⣧⡀⢻⡄⠀⠀⠀⢷
⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠈⢧⠀⠀⠀⠙⢷⣄⠀⠀⠀⢸⡆⠀⠈⣿⣦⠀⠀⠀⢹⡀⠈⠻⣄⣷⠀⠀⠀⢸⡄
⣿⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠱⡄⠀⠀⠀⠹⣦⠀⠀⠈⣷⠀⠀⠇⢹⡆⠀⠀⢸⡇⠀⠀⠘⢻⡇⠀⠀⣸⠃
⢸⡆⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠈⠹⢦⣄⠀⠈⢢⡀⠀⠀⠘⣧⠀⠀⣿⠀⠀⠀⣸⠇⠀⠀⣼⣿⣄⠀⠀⢠⠃⠀⢀⣿⣄
⠀⢻⡄⠀⠀⠈⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⣀⠙⠄⠀⠀⢸⣧⠀⣿⠀⠀⢠⡿⠀⠀⢠⡟⠈⢻⣧⣴⠋⠀⠀⡾⠀⠘⢷⡀
⠀⠀⠹⣦⡀⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⠀⠀⠀⣿⣤⡏⢀⣰⡟⠁⠀⣰⣟⣠⣴⠿⠋⠀⠀⣠⠞⠁⠀⠀⠘⡇
⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠉⠳⠦⣤⣤⣤⣀⣀⣀⣀⡀⠈⢷⠀⠀⢹⣿⣴⠿⠋⢀⣴⠾⠛⠉⠉⠀⠀⣀⡴⢾⡇⠐⠂⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠙⠳⢦⣄⡀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠛⠳⣾⣇⣴⠿⠋⠁⣠⠞⠉⠀⠀⣀⣄⠤⠶⠿⠧⠴⠞⠁⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠶⢤⣄⣀⠀⠀⢀⠀⠀⢈⡿⠃⠀⢀⣾⢋⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⡄⠑⣄⠸⡇⠀⢠⣿⣱⠟⠉⠀⠀⢀⣠⠴⠚⠛⠳⣶⠶⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠶⠶⠛⠛⠛⠛⠛⠛⠛⠓⢾⣶⣧⠀⢸⣿⣁⡴⠾⠗⠚⠋⠁⠀⠀⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠋⠓⠲⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣆⣼⠟⠓⠒⠒⠲⠶⠦⣄⠀⠀⠒⠂⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⢶⡄⠀⠀⠀⠀⠀⠀⠀⠈⢿⡇⠀⠀⠀⠀⠀⠀⠀⠸⣇⣀⣤⣤⣴⣶⢾⣦⣤⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠉⠉⢷⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠃⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⣤⡀⠀⠀⠀⠙⣄⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠙⢦⡀⠀⠀⣠⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠶⠶⣦⣤⣤⣈⣀⣀⣀⣀⣠⣿⣿⠟⠉⠀⠙⠷⠶⢶⣦⣤⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⢀⣤⡴⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⢁⣀⠠⠤⠶⠋⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠂⠤⠴⢏⣀⣭⡴⠆⠀⠀⠲
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⡾⠋⠿⢉⣾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠂⠀⣼⠖⠢⠀⠀⠙⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠁⠘⠁⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢠⠅⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠛⣀⣤⣶⠶⢞⡁⠘⠁⠀⠀⠀⠀⢀⠈⠀⣏⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡲⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠀⠉⠉⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠁⠈⠧⣠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢀⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⡋⠄⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠙⠛⢁⡤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣸⣿⡄⣁⣀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠋⠀⢠⡤⣀⠴⠁⠀⠀⠀⠀⠐⣄⣰⠉⠈⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⢠⡟⠁⠀⠀⠀⠁⠀⠀⠀⢩⠠⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢠⡞⢹⠖⠃⠞⠃⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⡞⢧⡍⠐⠀⠀⠀⠀⠀⠀⠈⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠓⠀⠘⡀⢀⠄⠀⢠⣶⠒⢀⠀⠈⠀⠀⢡⣴⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣄⣸⠃⠉⣠⣴⠞⠛⠉⠉⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠺⠻⢷⣿⣟⣠⠆⡿⠟⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠙⠃⢀⡀⠐⢫⢡⠈⠁⠤⠓⠒⠄⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠃⡴⠿⠿⣷⠶⠦⠀⠀⣤⢀⡖⠈⠀⠀⠀⠐⠶
⠀⠀⠀⠀⠀⠀⠀⠀⣇⠐⠑⠀⢀⠂⠀⠀⠀⠀⣀⠀⠶
⠀⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠀⠀⠀⠀⠀⠄⠀⠀⡈⠀⠀⢀⣄⡠⠖⠒
⠀⠀⠀⠀⠀⢀⣰⣿⠆⠠⠖⠛⠋⠁⢀⠂⠀⡃⠠⠀⠀⠀⠀⠀⠀⠀⣾⠇⠂⠀⠊
⠀⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⣀⠀⠈⠀⠀⢀⣀⣠⣴⣁⠀⡀⢀⠈⠃
⠀⠀⠀⠀⠀⠈⠀⠀⠀⣴⡖⠐⠉⠀⠘⢠⠞⠀⠀⣠⣜⡯⠉⠁⠀⡄⠴⠖⠒⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⣠⣤⠀⡰⠀⡔⠀⣾⠀⠈⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⢶⡄⠀⡄⠰⠟⠁⠀⠀⠂⠀⣸⠏⠀⠀⠀⠀⢁⡠
⠀⠀⠀⠀⠀⠀⢀⠀⠰⠟⠀⠀⠀⠂⠀⠀⠐⠁⠀⠐⠀⠁⠀⠠⠄⠀⠉⠁
⠀⠀⠀⠀⠀⠠⡄⠙⢀⠀⠀⠁⠀⠀⣠⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⡀⠠⡀⠈⠀⢸⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⡈⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣩⣿⣩⣭⣯⣥⣍⣿⣿⣉⣩⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣯⣭⣽⣿⣿⣿⣭⣭⣭⣽⣯⣭

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢄⣠⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠈⢳⠉⢩⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠀⠀⠀⠀⠀⠈⡇⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡒⠎⠷⢺⡀⠀⠀⠀⠀⠈⢁⣀⠀⠀⠀⠀⠀⠀⣿⢹⣠⢴⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠤⡈⠑⢦⡀⠀⠀⠘⠚⠀⠀⠀⠀⣀⠀⢸⢈⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣆⠹⡀⠀⣀⠀⠀⠀⠀⠀⢹⢧⡼⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡤⣀⢸⡇⣧⡼⣹⠀⠀⠀⠀⠀⠈⡆⠁⢸⠥⣶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢤⠀⠈⣠⠃⣠⡄⠀⠀⠀⢰⠃⢀⡤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣄⠇⠀⣇⠜⡱⠁⠀⣤⠀⡜⢀⡞⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠑⡄⠀⢠⠊⠀⠀⠀⡇⠛⠀⡼⢞⠝
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠟⠤⠤⣼⠀⡏⡠⡿⠀⠀⡇⡐⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡋⠙⠀⠀⠀⣼⣹⠀⠛⡱⠃⢀⡜⠀⡠⣫⣠⠖⢻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠸⠼⠉⠀⡜⠁⢠⠞⡀⡰⢱⠃⠁⠢⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⠁⠀⠀⠀⠀⣠⠀⠀⡇⡰⠃⠀⣴⡵⠇⡀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠘⢿⡀⢸⠟⡡⣠⣎⡞⠀⠀⠀⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⡉⠀⠀⠀⠀⡰⢁⡏⣠⡾⠋⠨⠀⠠⡔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⣧⡾⢞⢋⣀⣀⠤⠴⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠚⠒⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⣴
⠀⠀⠀⠀⠀⠀⣰⣿⣙⣆⡀⠀⠀⠀⠀⠠⣤⠀⣴⡆⠀⢸⡿⠃⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣆⣀⣀
⠀⠀⠀⠀⠀⢠⡿⠃⠉⢻⣷⠀⠀⠀⠀⠀⠹⣷⣿⠃⢠⡟⣿⠀⣤⢀⡀⠀⢀⣾⣿⣿⣿⣿⡿⢋⡉⠉⣙⠲⡀
⠀⠀⠀⠀⢰⠮⣅⡀⠀⢸⡿⠀⠀⠀⠀⠀⠀⢹⣿⣄⠈⠀⠙⠀⣻⠟⠀⠀⠀⠙⠛⠛⠋⢁⠠⠀⠀⠄⠀⢀⠇
⠀⠀⠀⠀⠀⠉⠺⠧⣒⣟⠀⠀⠀⠀⠀⠀⠀⢸⡏⢻⣆⠀⠀⡼⢻⡇⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠶⠶⠞⠋
⠀⠀⠀⠀⠰⠶⠶⠾⠿⠿⠆⠀⠀⠀⠀⠀⠀⠘⠁⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣰⢝⢤⡀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⠀⠀⣤⡀⢰⣿⣷⠀⢠⡄
⠀⠀⠀⠀⠀⢀⣔⢞⢻⡶⢷⣽⣤⠄⠀⢸⣗⣒⣿⣿⣯⣽⣿⣿⣿⣿⣿⠀⠀⠈⢷⡌⠳⣌⠙⢉⣴⠋⣴⠟
⠀⠀⠀⠀⠀⢸⠢⡑⢍⣷⠀⠀⠀⠀⠀⢸⡿⠶⣿⣿⣿⣿⣧⣾⣟⣻⣿⠀⠀⠀⠀⠙⢦⢙⡁⣙⢡⡞⠁
⠀⠀⠴⡶⣤⣼⣏⣪⣢⠟⠀⠀⠀⠀⠀⢸⡯⠭⣿⣿⣟⣛⡿⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢸⡇⢿
⠀⠀⠀⠙⢮⡢⣿⠉⠁⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠿⠿⠿⠿⠿⠧⠴⠿⠀⠀⠀⠀⠀⠀⢸⡇⣾
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉
⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⣠⣾⣦⠀⠀⠀⠀⠀⢀⠤⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢠⣶⣾⣿⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠿⣿⣿⡿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡄⠀⠁⠁
⠀⠀⠀⠀⢸⣿⣿⠉⣹⣿⡇⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⣄⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄
⠀⠀⠀⠀⢸⣿⡖⣩⡒⣿⡇⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣧⣀⠜⠀⠀⠀⠰⣶⣶⣶⠆⣀⣀⣈⡀⠿⠃
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠟⠛⠋⠀⠀⠀⠀⠀⠀⠈⠉⠁⢸⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠤⠀⠀⠀⠀⠀⠀⢠⠤⡂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢤⠆⣠⡀
⠀⠀⠀⠀⠀⠀⠰⣋⡁⠀⠀⡀⠀⠀⠀⠀⠀⠛⢃⠘⡀⠀⠀⠀⠀⢤⠈⢉⠃⠀⠀⠀⠀⠀⠀⠀⡀⢼⡂⠈⠿⡿⠧⣄⣤⣀
⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⡀⠸⠶⣮⣀⠀⠀⠀⠈⠒⠉⠀⠀⠀⠃⠀⠀⠀⠀⠁⠃⢻⠄⠚⠀⣨⣯⢿⡛⠂
⠀⠀⠀⠀⠀⠀⠀⡤⠀⢀⠞⠂⠀⠀⠀⠀⠀⠑⡶⠉⢉⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠀⠀⠀⢥⣿⠿⣙⡄⡼⠃⠐
⠀⠀⠀⠀⠀⠸⠈⣀⠀⢀⠀⠀⠤⢺⣱⠂⠀⣸⠀⡰⢡⡴⡤⡀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢰⠌⠒⠓⠀⠐⠁⣄⣼⢧⢤⠄
⠀⠀⢀⣀⠲⠞⠋⠁⠀⠀⠀⠀⠀⠈⠈⠙⠀⠻⣸⡷⢀⠟⠛⢿⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠠⠌⠍⠀⠀⠑⠆⠀⢴⡯⢀⡀
⠀⡐⠀⠁⠄⠁⢀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢱⡻⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⠄⡄⠀⠀⠘⣀⣴⠪⠄⠚
⠀⠀⢀⠀⠠⠃⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠐⢀⣱⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟
⠀⠀⠀⠀⠀⠀⠀⡠⠎⠀⠀⢠⣠⢀⠆⠄⠀⠀⠀⠀⠀⠲⠀⠀⠀⢠⠀⣤⠀⠀⡇⡤⠀⠀⠀⠀⢀⡠⠄⠀⠀⠐
⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⠀⢤⠽⡿⠄⠀⠀⡀⠀⠀⠀⠲⠀⠤⠀⠀⠊⠀⠀⠰⠀⠃⠠⠀⠂⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⢐⠃⠀⠁⠢⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⠀⡀⠀⠀⠀⠀⠠⠀⠰⡇⠠
⠀⠀⠀⠀⠀⠀⠀⠠⣓⢆⠀⡀⠈⢈⠁⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⡀⢺⠞⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠐⢁⠘⢡⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠠⠀⠀⠓⣀⡤⠀⣴⠴
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⢪⣢⡄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡆⠀⠠⠀⠀⠀⠀⠀⠀⠘⠅⠀⠀⠀⠀⠀⡉⣗⢰⠱⠷
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠃⢁⠀⠅⠀⠀⠀⠀⠀⡁⡀⠀⠀⠀⠀⠀⠄⢰⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠈⣄⠇⡿⠂⠀⣀
⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢾⡿⠀⠀⠀⠁⠄⠀⢠⠾⠂⢀⣀⡧⠀⠀⣤⡇⠀⠀⠀⠀⠀⠀⠓⡸⠈⠀⠤⠁
⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⣼⡆⠀⠀⠀⠀⠤⠄⢘⡀⡔⠀⠀⠀⠀⠐⠻⠁⠀⠀⠀⠀⠀⠀⠀⠀⡸
⠀⠀⠀⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁

⠀⠀⠀⠀⠀⣰⠉⠡⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠤⡁⠀⠀⠀⡀
⠀⠀⠰⡀⢀⡷⠂⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠓⠃
⠀⠀⠀⠜⢿⡀⠀⠀⠈⠪⢁⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⡀⠀⠀⢀
⠀⠀⠘⠀⠤⣏⠓⠲⠠⠤⠤⠀⠀⠀⠀⠀⠀⠀⠐⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠠⠀⠈
⠀⠀⠀⠀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠛⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠭⠅⠀⠐⠂⠤⢄⣖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠢⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⢠⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠨⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡀⢀⡀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢰⡦
⠀⠀⠀⠀⠐⠢⠀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢀⠀⠀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠕⠪⠅
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⣀⡤⠄⠀⠀⠀⠀⠀⠀⢤⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢀⣄⡀
⠀⠀⠀⠀⠀⢰⠥⠀⠀⠠⠀⠀⠀⠀⠀⠉⠆⡁⡀⠀⠀⠀⠆⢀⠌⠀⠀⡀⠀⠀⠀⠤⢰⣧⠘⣻⠟⣦⣴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠄⠠⣄⣛⡟⡶⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⠘⠀⠁⢠⣺⣿⠍⢠⠄
⠀⠀⠀⠀⢀⠄⠊⠀⠈⠀⢀⢠⣤⡀⠀⡜⠁⣔⣃⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠈⡀⣄⠄⠈⡹⠋⢐⣇⠉
⠀⠀⠀⠠⣴⠆⠂⠀⠀⠀⠀⠰⠙⠢⠀⠏⣾⡀⣿⠿⣶⠀⠀⠀⠀⠀⠷⠀⠀⠀⢀⠒⠃⠀⠦⠀⠀⣼⠋⠉⠉
⠀⡀⠉⠁⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⣾⠏⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢂⣩⠄⡁⠐⠄
⠀⠀⡀⠀⠖⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢠⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⡀⠀⠀⠀⠀⡄⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢀⡀⠠⠀⠀⠁⠀⠀⢠⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠘⣅⠀⠈⠀⠡⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⢠⣬⠁⠈
⠀⠀⠀⠀⠀⠀⠈⠛⠀⠔⠠⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢰⠈⣁⠀⣇⡀
⠀⠀⠀⠀⠀⠀⠀⡀⡠⣎⡁⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡙⣯⢠⣻⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡭⠿⠊⠀⡀
⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠁⠀⠀⠠⠀⠀⠔⠃⠀⡠⠆⠀⢠⣶⠀⠀⠀⠀⠀⠘⢠⢊⠀⠂
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⠀⠀⠀⠀⠒⢀⣥⠠⠁⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⡜
⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣤⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢾⡷
⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⢰⣶⠀⠀⠀⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠿
⠀⠀⠀⠀⢠⣤⡄⠀⠀⠀⠸⠿⠂⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣤⣄
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⢰⣶⠄⠀⠀⠀⠀⣴⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣷⣦⣤⣾⣿⣿⣦⠀⠀⠀⠀⠙⠻⠿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠿⢿⣿⣿⡿⠏
⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠾⢙⠿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢰⡇⠀⠀⠰⣿⠆⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠂
⠀⠀⠀⠀⠀⢰⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⢀⡆
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢰⣦⠀⠀⠀⢀⣀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠰⣿⣿⣷⠀⠀⢀⠀⠀⠐⠂⠀⠀⠀⣤⣤⣼⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢹⡿⠿⢿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠂⠀⠙⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣾⣿⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠛⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⣼⣿⣿⣿⠟⠛⠛⢿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⡿⢹⣿⣿⣿⠀⠀⠀⢠⣿⣿⣿⡏⠀⠀⠀⠈⣿⣿⣿⣧⠀⠀⠀⠀⢀⣾⣿⣿⡟⣻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠟⠁⢸⣿⣿⣿⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⣰⣿⣿⣿⠋⠀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣏⣀⣀⣸⣿⣿⣿⣄⣀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⣿⡿⠀⢀⣼⣿⣿⣿⣁⣀⣀⣿⣿⣿⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢿⣿⣿⣿⣄⡀⣀⣴⣿⣿⣿⠇⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⢻⣿⣿⣿⠋⠉⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠈⠋⠉⠉⠉⠉⠉⠙⣿⣿⣿⣿⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠿⠿⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⠿⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣶⡀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣇
⠀⠀⠀⠀⠀⡀⡆⠀⠀⠀⢀⣿⡇⠀⠀⠠⣄⡀⠀⠀⢦⡈⣿⣿⣗⡀⠀⠀⠀⠀⠀⠠⣼⣧⣺⣷⣿⣻⠆⠀⠀⠀⡆⠀⠀⢶⣼⡆⠀⠀⠀⣻⣿⡆
⠀⠀⠀⢠⠶⣧⣆⣿⠄⠀⠀⣿⠁⠀⢠⡄⠼⠁⠀⠀⢺⣿⣿⣿⡿⠆⠀⠀⡀⠀⠀⠐⠲⣟⣻⣿⣿⠵⠃⠀⢀⣾⠁⠀⠶⢾⣿⣧⡀⠀⢠⣿⡿⠁
⠀⠀⠐⢯⣿⣽⣿⣻⡄⠀⠀⠘⠄⠀⠀⠀⠼⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⢰⡜⣿⣸⠃⠀⠸⣿⣿⣇
⠀⠀⠀⠀⠉⠛⠉⠉⠀⠀⠀⠀⠀⢠⡟⠀⣘⠛⠁⠶⠀⠀⠀⣀⠀⢀⠀⢿⡀⠀⣠⠃⠀⠀⢄⣀⠀⠀⠀⣼⡟⢠⡀⠀⠀⠉⠉⠁⠀⠀⠈⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣠⡌⢁⣀⠒⠀⠀⢸⠿⠇⠈⢳⡄⣿⠀⠻⣄⡀⠀⠀⠉⢳⣄⠀⣿⡇⠈⣷⠀⠀⣠⡴⠚⠁⠀⠀⠘⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⣒⠀⠀⠀⢀⡤⠚⠃⠀⠈⠀⠀⣠⣾⠋⣿⡄⣤⠾⠃⠀⠀⠀⠀⢹⡇⣿⡗⠀⢹⡆⣼⡏
⠀⠀⠀⠀⠀⣦⣤⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠁⠀⠀⣀⡀⠙⣧⠸⠫⠖⣫⡤⣤⡤⠀⠀⠀⠸⡇⠉⠀⠀⢸⡇⡿⠁⠀⠀⡀⢻⣀⣦
⠀⠀⢀⣬⣿⣿⣿⣿⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣤⠽⠿⠾⣯⡭⠖⠒⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⡼⢙⠆⣫⣅⠸⢀
⠀⠀⢠⡶⣿⣿⣿⣿⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡌⠑⢠⣶⡀⠄
⠀⠀⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⢠⣶⣀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢤⣀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠘⠂⢃⢹⢜⣠⠁⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⣶⣿⣿⡀⠀⠀⠀⠀⠀⠂⠀⡀⠀⢀⠀⢀⠀⡀⠀⠀⠀⠤⠆⠀⠀⠀⠀⠀⠀⡀⢠⣾⠇⠀⠀⠀⠈⠈⠿⠁
⠀⠀⠀⠀⡞⢁⣶⡄⠀⠀⠹⢿⣿⣿⣿⠿⠃⠀⠀⠀⠐⠀⠀⠁⠀⠈⠀⠈⠀⠁⠈⠀⠁⠁⠀⠀⠀⠀⠀⠀⠸⣷⣸⣏⣴⠖⠀⠀⠀⠀⠀⠀⣰⣆
⠀⠀⢠⢀⠓⡋⡼⣧⠄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠂⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠠⠾⠻⠿⠗⠂⠀⠀⠀⠀⠀⠈⠻⠟
⠀⠀⢈⢋⣱⣩⠙⠯⡴⠃⠀⠀⠀⢀⣶⠀⠀⠀⣀⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠹⣧
⠀⠀⠸⡆⣉⣹⣶⡷⠒⠀⠀⠀⠀⠘⣿⡆⠀⠀⢿⣿⡿⠁⠀⢀⣀⣤⣀⠀⠀⠀⠸⣶⢸⣷⠆⠀⠀⠀⢸⣿⡆⠀⠀⢀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠙⠙⠁⠀⠀⠀⢀⡆⣸⣿⠇⠀⠀⠀⢿⠃⠀⠀⣿⣿⣿⡿⠃⢀⣀⡘⣿⣻⣿⣶⣶⡄⠀⢸⣿⡂⠀⢠⡟⠀⠀⠀⠈⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣇⣿⣿⡆⠀⠀⠀⠀⠀⡀⠀⠙⠋⠙⣧⠀⠀⠙⠉⠟⠿⠿⠏⠙⠀⠀⠸⣿⣧⠀⢸⣷⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⢀⡴⠊⠀⠀⠀⢿⣿⢹⣿⡟⠀⠀⠀⠀⠀⣧⡄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⢰⣿⣿⡁⣾⡏⠀⠀⢠⣤⣄⠀⠀⣴⠞⠁
⠀⠀⠀⠀⢀⣼⣿⡤⠆⠀⠀⢺⣿⠈⣿⡟⠀⠀⠀⠀⢠⣾⣷⡀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠈⠋⠀⠀⢸⣿⣿⢹⣿⣇⠀⠀⠸⠛⠟⢀⣠⠿
⠀⠀⢠⠀⣿⣧⡻⣤⢀⡀⠀⠈⠃⠀⠉⠀⠀⠀⠀⠀⠈⣿⠟⠁⠀⢀⠀⠀⢴⣾⠖⠀⠀⠀⠀⠀⠀⠀⠨⣿⡏⠀⢿⡿⠀⠀⠀⠀⠀⢿⣧⡀
⠀⠀⣿⡀⣸⡿⣳⠟⠸⣇⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⢰⡿⠀⠀⢀⢸⣤⠆⢾⢁⡶⢀⣤⠃⠀⠀⠀⠀⠀⠈⠀⠀⠘⠁⠀⠀⠀⠀⠀⢨⣿⠋⣤
⠀⠀⢸⡇⠹⣧⡘⠢⡄⠈⠃⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠈⠛⡵⡼⠘⣆⠁⠜⡹⢆⠖⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⢿⣄⠘⣷
⠀⠀⣼⢁⠀⣸⣣⡞⠁⣾⠀⠀⠀⠀⣴⣼⢿⡿⠗⢀⠀⠀⠀⠀⢀⣤⡸⠃⢠⡎⡃⡶⠷⢞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⢨⠟⣴⡏
⠀⠀⢿⡈⡷⡇⢿⡀⣀⡼⠃⠀⠀⠀⣿⣿⡧⠀⠰⠯⠄⠀⠀⠀⠀⠱⡎⠶⠛⠀⡇⡽⣰⡟⠋⠁⠀⠀⢠⣴⣶⣶⣄⠀⠀⠀⠀⠀⢸⡁⣿⠀⣹⠇
⠀⠀⠀⢡⠇⠙⠈⢻⠋⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣆⠓⣿⠧⠀⠀⠀⠀⠠⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠈⠛⠎⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠄⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⢻⣯⣧⢹⣷⠈⠀⣿⡾⢋⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⢸⣶⡖⢯⠡⣄⣑⠀⠀⠀⠀⠀⠀⠀⠀⠍⠀⢀⠃⠀⠀⠀⠀⠀⠀⠐⠙⣿⣧⣿⣯⣦⣿⡇⠰⠸⣷⠏⣹
⠀⠀⠀⠀⠀⠀⠀⣀⡸⠯⣉⡆⠀⠻⠯⢻⠦⠷⡄⢹⠎⠰⡄⠀⠀⠀⠀⠐⠚⠈⠁⠀⠀⠀⠀⠀⠀⠀⠁⢹⣿⡜⣿⡟⢿⣿⠀⠐⠜⠻⣿
⠀⠀⠀⠀⠀⠀⠄⠉⠁⢰⠞⢡⣤⠀⠀⡋⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⣿⣿⣿⣷⡈⢿⠆⠀⠀⠈⠉
⠀⠀⠀⠀⠠⡀⠀⠀⣨⣯⠀⣋⠉⠃⠀⢁⠠⠀⢀⢰⡀⢸⡇⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢷⣿⣿⡗⢾⡇
⠀⠀⠀⡀⠀⠈⠐⠀⠼⡃⠀⢹⡄⣀⠀⠀⠀⠀⢀⡽⠳⠴⠁⠀⠀⠀⠀⠁⢀⠂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠙⡦⠸⣻⣿⡗⢸⣇⠀⢰⣦
⠀⠀⢀⠙⠂⠀⠀⠘⠀⠀⠠⡋⠘⠁⠀⠙⢲⣀⠆⢠⡦⠔⠄⠀⠀⠀⠀⠂⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣍⢁⢸⡟⢒⠐⣿
⠀⠀⠙⢤⠀⠁⢢⠀⠀⠀⠙⣿⠤⡤⠀⠀⢙⡁⠐⠊⠁⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢫⣿⣿⠀⢺⡇⣙⡷⣿
⢀⡄⠀⠀⠈⠃⠈⠀⠀⠀⡀⠂⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣸⣿⡏⣄⣼⡗⣿⣽⣿⣾
⡌⠁⠀⠀⠀⠀⠁⠀⠀⢠⠁⢀⡨⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⡉⢉⣿⣿⣿⣿⣿⣥⡿⣸⡏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢇⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢸⠀⠀⠀⠀⠀⠈⢦⡀⠀⠀⠀⠀⠱⡀⠈⠦⡀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠘⡄⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠙⣄⠀⠈⠢⡀⠀⠀⠀⠀⡠⠂⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠹⡄⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠈⣢⡤⠖⠉⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠘⢄⠀⠀⠀⡸⢠⠃⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠀⠀⠀⣀⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠳⣄⠔⠀⡼⠀⠀⠀⠀⠀⡠⠊⠁⠀⢀⣀⠤⡖⠋⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⠀⠀⠀⢢⠀⠀⡠⠉⢀⡜⠀⠀⠀⠀⢀⠞⠀⢀⠔⠊⠁⠀⠀⠘⣆⠀⠸⡆⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⢀⡵⠈⢀⡴⠋⠙⢄⠀⠀⠀⠎⠀⡔⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡰⠋⠀⡰⢯⡀⠀⠀⠈⢦⠀⢸⠀⡼⠀⠀⠀⠀⠀⠀⣀⠴⠋⠀⣰⠃⠀⢠⢡
⠀⠀⠀⠀⠀⠀⠀⠀⢸⢡⠀⠀⠀⠀⡜⠀⠀⠸⠁⠀⠙⢦⡀⠀⠀⢇⡄⢀⠇⠀⣀⡤⠖⠚⠉⢀⡀⠄⠊⠁⠀⢀⡞⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠘⣆⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠑⣄⠀⠈⡇⢸⢠⠞⢁⡤⠖⠚⠉⠁⠀⠀⠀⢀⡠⠊⢀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⢆⠀⠀⢇⠀⠀⠸⠀⠀⠀⠀⠀⠈⢣⡀⡇⣇⡇⡴⠋⣀⠤⠤⠒⠒⠒⠒⠊⠉⠀⡠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠑⢦⣀⠢⡀⠀⠱⠐⠈⠉⠑⠢⣄⢳⡇⣿⢰⢡⠎⢁⣀⠤⠤⠤⠤⠶⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣀⠀⠈⠑⠺⣶⠁⠀⠀⣠⠤⢄⠈⢦⡃⣿⣷⡏⡔⡡⠒⠉⣉⡉⠉⠒⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠈⠑⠶⠤⠔⠁⠀⡠⢮⣀⠑⡄⠣⢸⣇⣿⣿⣾⡘⣠⠚⠉⠀⠉⠙⠢⡀⠱
⠀⠀⠀⠀⠀⠀⢀⡮⠀⠀⠀⠀⠐⠒⠤⠤⠤⠔⠊⠉⠲⣝⡕⢌⡀⢸⢿⡿⣿⡇⡷⠁⠀⠀⠀⠀⠀⠀⠘⠄⢃
⠀⠀⠀⠀⠀⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠃⡾⠘⢃⡿⠓⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠤⠤⠂⠀⠙⠤⠤⠤⠤⠄⠐⠀⠢⠤⠔

⠀⠀⠀⠀⠀⠦⡴⢶⣶⡶⣦⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠶⣠⠆
⠀⠀⠀⠀⠀⠀⢈⣹⠿⣏⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⡽⠊⠁
⠀⠀⠀⠀⢀⣴⣛⣒⣒⣒⣛⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⢶⣶⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⢶⣶⣦⣴⣶⣟⣲⣤
⠀⠀⠀⠀⠘⢯⣩⡭⠭⢭⣭⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣈⠭⠭⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣾⢻⣷⣿⣷⣿⣸⣯⣟⣢⣤
⠀⠀⠀⠀⠀⠀⣉⡿⠶⢯⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠼⢻⡿⣿⣟⣟⣉⣽⠋⣡⡟⢹
⠀⠀⠀⠀⠀⣾⢩⣿⣿⣿⣭⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣭⣭⣥⣝⡆⠀⠀⠀⠀⠀⠀⠀⠈⠻⣄⣈⣿⣼⡿⣟⡟⣿⣷⠋⢁⣼
⠀⠀⠀⠀⠀⠈⠳⢿⣛⣻⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⢶⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⢋⣦⡤⢾⢿⡞⠙⠚⠙⠋
⠀⠀⠀⠀⠀⠀⣠⠶⣭⣽⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢖⣙⣒⡒⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢧⣤⣾⡿⠁
⠀⠀⠀⠀⠀⠘⠙⠛⠛⠛⠛⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠐⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⢠⣶⣦⡀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⡰⠆⡀
⠀⠈⠛⠋⠀⠘⠛⠃⠀⠀⠀⠀⠀⠉⢰⣦⠘⠋⠀⠀⠀⠀⠀⠀⠛⠂⢾⣿⠆⠀⠀⠀⠀⠀⠀⠐⢗⣴⣿⣷⣚
⠀⠀⠀⠀⢶⡦⠀⠀⠀⠀⠀⠀⠀⢰⡎⠉⠌⠁⠀⠀⠀⠀⠀⠀⢠⣶⠄⠈⣶⠀⠀⠀⠀⠀⠀⠀⠰⠎⢻⠱⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠦⢴⡶⠀⠀⠀⠀⠀⠀⠀⢴⠄⠰⡆⠠⡶⠀⠀⠀⠀⠀⠀⢘⣄⢀⣍⠀⠀⠀⠀⠀⠀⢀⣄⠘⡛⢀⣄
⢠⠄⠀⠀⠠⡆⠀⠀⣤⠀⠀⠀⠀⣤⡀⣠⣦⢀⣤⠀⠀⠀⠀⠤⠠⡎⠁⠀⢱⡦⠠⠄⠀⠀⠀⠈⠉⠸⠿⠈⠁
⢾⡦⠀⠀⢴⡦⠀⠠⣾⠆⠀⠀⠀⣀⡀⢈⡁⠀⣀⠀⠀⠀⠀⠀⠀⢘⠗⠐⠗⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤
⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⠉⠀⠀⠀⠀⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛

⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⡌⠀⠠⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠙⢀⡀⠀⠀⠀⠀⠺⠁⠀⠀⢛
⠀⠰⠆⠀⠈⠑⠀⡄⠀⠀⠀⠀⠀⠁⠀⣀⠈⠰⠆⠀⠀⠀⠀⠀⠶⠀⠀⠘⠁⠀⠈⠀⠀⠀⠀⠀⠰⠆⢀⣠⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⣤⡄⠀⠈⠃⠀⠀⢠⡄⠀⠀⠀⠀⠀⠰⣿⠆⠀⠀⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⢿⡷
⠈⠀⠀⠀⣿⠆⠀⠀⠁⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⣀⡄⠁⠀⠀⠀⣤⣤⠀⣠⡄⠀⣤
⢀⠀⠀⢠⣦⠀⠀⢀⡀⠀⠀⢀⣤⡀⠘⠛⠃⢀⣤⡀⠀⠀⢰⡆⠀⠉⢀⣀⠈⠁⠠⣦⠀⠀⠉⠁⠀⢈⡁⠀⠉
⠛⠋⠀⠀⣶⡆⠀⠉⠁⠀⠀⠈⠛⠁⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠟
⣿⣿⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿