Lolipop Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠐⠒⠒⢍⠉⠉⠉⠉⠐⠂⠠⢄⡀⠀⠀⠀⠀⠀⢀⡀⠤⠦⡐⠒⠒⠒⢦⠠⠄⢀
⠀⠀⠀⠀⠀⣀⠔⠉⠑⠢⢄⡀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠈⠑⡤⣀⠔⠊⠀⠀⠀⠀⠈⠢⡀⠀⠀⠡⡀⠀⠈⠐⠤⡀
⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⡇⠈⠢⡀⠀⠀⠀⠀⠀⠀⠘⠄⠀⠀⠁⠀⠀⠀⠀⠈⠲⠄
⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⡆⠀⠀⠀⠀⠀⠀⠇⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢸⠀⠀⠀⠀⠀⠀⠈⢢⡀
⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⢀⠃⠘⡦⢄⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠇⠑⡀
⢀⠁⡠⠔⠒⠈⠉⠉⠁⠐⠢⢄⡀⠀⠀⠘⠀⡆⠀⠀⠀⠀⡰⠁⠀⢀⠎⠀⠀⢱⡀⠑⢄⠀⠀⠀⡇⠀⡖⠀⠀⠀⠀⠀⠀⡜⠀⠀⢡
⡜⠁⠀⠀⠀⣀⠠⠄⠐⠒⠀⠤⢈⡢⣀⣠⡜⠀⠀⢀⡠⠊⠀⢀⡠⠂⠀⠀⠀⠀⡏⠒⢌⢢⠀⠠⢀⠎⠀⠀⠀⠀⠀⡠⠊⠀⠀⢠⠊
⡇⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⣘⠀⠀⢱⣐⣊⣁⡀⠄⠒⠁⠀⠀⠀⠀⠀⠀⡇⠀⣀⠋⠉⢳⠁⠀⠀⠀⣀⠤⠊⠀⠀⢀⠔⠁
⣧⠊⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⢩⠊⠑⡶⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠔⠉⠢⡤⠚⠣⠀⣀⣁⣀⣀⠀⠄⠚⠁
⠘⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠠⠁⠀⠀⢠⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⢃⠀⠀⠀⠀⠀⠀⠐⠀⠀⠂⠀⠀⠀⠀⢃⠀⠑⠢⢀⡀⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⡀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠈⠉⠉⠉⠉⢀⠏⠀⠀⠀⠀⠰⡀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⢀⣀⣀⣀⡔⠋⠀⠀⠀⠀⠀⠀⠱⡀⠀⠀⠑⠤⣀⡀⠀⠀⠀⢠⠊
⠀⠀⠀⠀⠀⠑⢄⡀⠠⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⡁⠀⠸⠀⠀⠀⠀⠀⠀⠀⠈⠢⣀⠀⠀⠀⠀⠉⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠳⠄⣀⡈⢢⡀⠀⠀⢀⣀⠠⠤⠐⠈⠀⠀⠈⠒⠄⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢒⠤⠄⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⡅⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠀⠖⠒⠒⠒⠒⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠸⠀⠀⠀⠀⠀⠀⠀⠇⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡄⠀⠀⠀⠀⠀⠸⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠃⠀⠀⠀⠀⠀⠆⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢰⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠂⠀⠀⠸⠀⢠⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣤⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⠉⠉⠀⠀⠀⠀⠉⠉⠛⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⣀⣠⡤⠤⠤⢤⣀⣀⠀⠀⠀⠉⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⡠⠖⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠲⣄⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⢠⠎⠀⠀⠀⠀⣠⠤⠤⠤⠤⣄⡀⠀⠀⠀⠙⣄⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⢠⠃⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠙⢢⡀⠀⠀⠈⢆⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⡞⠀⠀⠀⣼⠁⠀⠀⢠⠔⠒⠲⣄⠀⠀⢱⡀⠀⠀⢸⡄⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⢣⠀⠀⠀⣇⠀⠀⠀⣿⠀⠀⠀⠈⡆⠀⠀⡇⠀⠀⠀⡇⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠘⡄⠀⠀⠘⢆⡀⠀⠈⠀⠀⠀⣰⠃⠀⢠⡇⠀⠀⢰⠇⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠙⣄⠀⠀⠀⠙⠒⠦⠤⠖⠚⠁⠀⢀⡞⠀⠀⠀⡼⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠈⠓⢤⣀⡀⠀⠀⠀⠀⣀⣠⠔⠋⠀⠀⠀⡰⠃⢀⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⣠⠞⠁⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⢊⣡⣴⠟⠁⠀⠀⡀⠄⠂⠒⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⢶⣶⣶⣾⣿⡷⢶⡟⠛⣿⡀⠀⠀⠀⠊⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠘⣧⠀⡰⠁⠀⠀⠀⢀⠔⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠠⠄⣀⡈⢿⡄⠹⣷⠁⠀⠀⠀⠀⠁⠀⠀⠀⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡸⡗⠐⠉⡈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠂⠀⠂⠈⠉⠀⠀⠸⣄⡀⢾⡆⠤⠀⠀⠀⠀⠀⠠⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⢀⠊⠹⣧⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⣀⠔⠁⠀⠀⢹⣆⠈⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠈⠀⠀⠀⠀⠀⠀⢻⡆⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠉⠉⠉⠉⠉⠉⠉⠛⠛⠿⢿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⢀⣴⢟⣿⣿⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⣰⡿⢣⣾⣿⣿⣿⡿⠋⠀⠀⠀⠀⢀⣠⣤⣶⣶⣿⣿⣿⣶⣶⣦⣤⣀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⡀
⠀⠀⠀⣼⠏⣰⣿⣿⣿⡿⠋⠀⠀⠀⢀⣠⣾⣿⣿⣿⣿⡿⠿⠿⠛⠿⠿⠿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠈⢻⣿⣿⣿⣄
⠀⢀⣾⠏⣰⣿⣿⣿⡟⠁⠀⠀⠀⣰⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣷⣄⠀⠀⠀⠀⠹⣿⣿⣿⣆
⠀⣼⡏⢠⣿⣿⣿⡿⠁⠀⠀⠀⣼⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠀⠀⠀⠀⠘⣿⣿⣿⡆
⢠⡿⠀⣾⣿⣿⣿⠁⠀⠀⠀⣸⣿⣿⣿⠏⠀⠀⠀⢀⣤⣶⣿⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠹⣿⣷⠀⠀⠀⠀⢹⣿⣿⣿
⣼⡇⠀⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⢠⣾⣿⣿⣿⠟⠛⠛⢿⣿⣷⡀⠀⠀⠀⠀⠀⢹⣿⣇⠀⠀⠀⠀⣿⣿⣿
⣿⠀⠀⣿⣿⣿⣧⠀⠀⠀⠠⣿⣿⣿⣧⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠙⣿⣷⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢸⣿⣿
⣿⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⣿⣿⣿⣿⡀⠀⠀⠀⠻⣿⣿⡿⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠸⣿⣿
⣿⡄⠀⢹⣿⣿⣿⡄⠀⠀⠀⠸⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠁⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢀⣿⣿
⢸⣇⠀⠈⢿⣿⣿⣿⡀⠀⠀⠀⠙⣿⣿⣿⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠃⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⢸⣿⣿
⠈⣿⡀⠀⠘⢿⣿⣿⣷⡀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣷⣶⣤⣤⣴⣶⣿⣿⠟⠁⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⠀⠀⣸⣿⡿
⠀⠸⣧⠀⠀⠈⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⡿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⣠⣿⡿⠃⠀⠀⠀⠀⢀⣿⣿⠃
⠀⠀⠹⣧⡀⠀⠀⠻⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠟⠁⠀⠀⠀⠀⠀⣼⣿⠃
⠀⠀⠀⠙⣷⡄⠀⠀⠈⠻⢿⣿⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠟⠁⠀⠀⠀⠀⠀⢀⣼⡿⠃
⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⠿⠋⠁⠀⠀⠀⠀⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠘⠿⣦⣀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⠿⠿⠿⠿⠟⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣦⣤⣄⣀⣀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⠾⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠻⠿⠿⡿⠛⠛⢻⡏⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⣀⣀⡾⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠖⠛⠛⠉⠉⠉⠉⠉⠙⠛⠒⠦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⣤⠴⠶⠛⠛⠛⠛⠛⠓⠶⢦⣄⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⣤⠞⠉⣀⣤⠶⠖⠚⠛⠒⠲⠶⢦⣄⡈⠙⠶⣄⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⣠⠞⢁⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠈⠳⣄⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⡼⠁⢠⠞⠁⠀⠀⠀⣀⡤⠖⠒⠚⠒⠲⢤⣀⠀⠀⠈⢳⡄⠘⣦⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⣾⠁⣰⠏⠀⠀⠀⢠⡞⠉⣀⠴⠒⠒⠲⢦⡀⠙⢷⡀⠀⠀⢻⡄⠸⡇⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⢸⡇⢠⡟⠀⠀⠀⢠⡟⠀⡼⢃⡞⠛⡆⠀⠀⠙⣇⠀⣷⠀⠀⠈⡇⠀⣿⠀⠀⠀⠀⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠁⢸⡇⠀⠀⠀⢸⠁⢸⠁⣿⠀⣼⠃⠀⠀⢀⡿⠀⣿⠀⠀⢠⡇⠀⡿⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⡆⢸⡇⠀⠀⠀⢸⡀⢸⠀⠻⣄⠈⠳⢤⠴⠞⠁⣰⠃⠀⠀⣼⠃⢰⠇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠘⣇⠀⣷⠀⠀⠀⠘⣧⠀⢳⡄⠈⠳⠤⣤⠤⠴⠚⠁⠀⢀⡼⠃⢠⠟⠀⠀⠀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠹⡄⠘⢧⠀⠀⠀⠘⢧⡀⠙⠳⢄⣀⣀⠀⢀⣀⣠⠴⠋⢀⡴⠋⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠹⣆⠈⠳⣄⠀⠀⠀⠙⠳⢤⣀⡉⠉⠉⠉⠉⣁⣤⠶⠋⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⠈⠳⣄⠈⠳⣤⡀⠀⠀⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⣠⡴⠞⠛⣧⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠈⠳⢦⣀⠉⠳⠶⢤⣤⣤⣀⣀⣤⣤⠴⠶⠛⢁⣠⡴⠞⠁⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⡀⠀⠀⠉⠙⠲⢤⣤⣄⣀⣀⣀⣀⣤⣤⠴⠒⠋⠁⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⠉⠛⠒⠦⢤⣀⠀⠀⠀⠉⠉⠉⠁⣀⣠⠤⠖⠛⠋⠉⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⣀⣀⣉⡙⢳⡞⠛⠓⣶⠛⣉⣁⣀⡀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⠁⠀⠀⠀⠀⠈⠀⠀⠉⢻⣄⠀⢀⣼⠉⠉⠀⠈⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⢤⣤⡤⠴⠶⠶⠖⢸⠟⢉⡿⣏⠙⣿⠒⠶⠶⠶⠤⣤⣤⠴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣾⠁⢹⡄⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠋⠀⢀⡼⣇⠀⢨⡿⡄⠀⠈⠳⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⠞⠀⣿⠀⢸⡇⠙⠦⠤⠖⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣀⢠⠀⣀⠀⠀⢠⣀⣀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⢂⠠⠴⠶⠶⠬⢌⣀⣙⣛⣀⣡⡤⠤⠶⠤⠌⡑⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣔⠕⣠⢞⣡⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣦⣍⡑⡄⢀⡠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢠⡇⣰⡿⣻⣵⣷⣴⣴⣾⣿⣷⢭⣥⣭⣤⣶⣾⣿⣤⣴⣬⣙⢳⣾⣆⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⢰⣿⣤⡿⣛⢫⡥⠭⢛⠴⠒⠲⢩⠵⠚⠒⢝⠉⠭⠻⢟⣻⣷⡌⣿⡄⢸⡔⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢐⠆⣾⣿⡯⠉⡁⠀⡀⠀⣨⠀⠀⠀⢸⠀⠀⠀⢰⡀⠀⢀⠀⠈⠻⣿⣜⣷⠘⣂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠠⢭⢰⣿⣿⣹⣀⣷⣤⣷⣶⣿⣶⣶⣶⣾⣷⣶⣶⣾⣷⣶⣿⣴⣇⣠⢘⣿⣿⡆⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠈⠐⠶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣯⣽⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⡇⢀⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠈⣖⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣼⣖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠶⠇⢸⣿⣿⢛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⠿⣿⣿⡇⢨⣭
⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠈⡿⣿⢠⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢳⠻⣿⣿⡇⠬⠤
⠀⠀⠀⠀⠀⠀⠀⠈⢀⣷⡀⣇⣿⡖⢒⣻⣿⡿⠋⠉⠀⠉⠻⣿⣿⠟⠃⠁⠀⠉⢻⣿⣗⡒⢷⣿⣿⡇⣾⡦⠄
⠀⠀⠀⠀⠀⠀⠀⠈⠼⠿⠇⢿⣿⡄⢠⠾⣿⠃⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠈⣿⣿⡀⢸⣿⣿⢠⣛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠸⣿⣷⠏⠀⣿⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⢿⠏⣿⣿⣿⡇⠼⣿⠟⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⡀⢻⣿⣷⣷⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣬⢟⣾⠟⢸⣷⣤⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⣴⢆⢹⣷⣿⣶⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⢛⣿⣿⠟⢰⣷⣌⠉⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡠⠋⠀⢿⣿⣷⣿⣷⣤⣆⣤⢀⡄⢀⡠⣌⣤⣶⣾⣷⣿⣿⡷⢠⣿⡙⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠘⠀⠙⠻⢿⣯⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠿⠻⢋⠰⣦⠙⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⡰⢀⣌⠁⡻⣿⢿⣿⣿⣿⣿⡿⢁⡀⠄⠂⠛⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠰⠁⡌⠓⢤⡡⠄⠋⠔⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⣶⠾⠷⢶⣄⡀⠀⠀⣀⡴⠞⡓⠲⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠑⠋⠀⠀⠀⠀⠈⠉⠛⠛⠉⠀⠀⠉⠛⠓⠮⣝⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⢀⣠⣤⣤⣿⣦⣄⣀⠀⠀⣠⣾⣥⡤⠶⢦⣤⣄⡀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢀⣤⡾⠟⠋⠁⠀⠀⠉⠉⠙⠛⠛⠉⠉⠀⠀⠀⢀⣾⣿⣿⣷⣶⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⣇⣠⣤⣶⣿⣿⣄⠀⣰⣦⣤⣤⣄⣠⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⠟⠉⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠻⣇⠀⠀⠙⢿⣿⣿⠿⠟⠛⠉⠉⠉⠁⠈⠉⠻⣿⣟⠛⠛⠛⠻⢿⡿⠃⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠙⣦⡀⠘⢹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠈⢳⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⢻⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣦⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠇⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡳⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⢦⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡐⠳⣶⣤⣤⣤⣤⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠦⢬⣭⠥⠖⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠖⠂
⠀⠀⠀⠀⠀⠌⠀⠀⡀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠴⠓⠁⠀⠀⠀⠀⣀⡤⢴⠒⡖⣲⢦⣀
⠀⠀⠀⠀⠀⠀⢠⣞⡍⠱⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢂⣀⡀⠤⠊⠀⠀⠀⠀⠀⢠⠺⡅⠃⢰⠀⠀⠁⠈⡘⢹⢦
⠀⠀⠀⠀⠐⠀⠈⠙⠁⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣏⠂⠱⠀⠀⠀⠀⠀⠐⢀⠊⡼⡇
⠀⠀⠀⠀⠀⠘⠒⠐⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢸⡢⡠⠀⠀⠀⠀⠀⠀⠀⠀⠈⢘⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠈⠀⠀⠠⢤⠄⠁⠀⠀⠀⠀⠀⠙⠦⣬⠁⢀⡠⣤⢄⡀⣤⠔⠛
⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢰⡍⠀⠀⠤⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠿⣤⣶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠐⣦⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠐⠂⢡⠀⠀⠀⠀⠠⠂⠄⠈⠀⠀⠜⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⡀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⣐⣰⢁⠀⡈⠡⠔⠩⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀⠀⠀⠀⠀⠀⠘⠈⠁⠒⢠⠃⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⠀⠀⠳⣄⠀⠀⡀⢐⠀⠀⠀⠀⠀⠀⠀⠀⣓⡔⠀⠀⠀⠀⠀⠀⠒⠤⠀⠒⠁
⠀⠀⠀⠀⠀⠒⠂⠀⠁⠀⠀⠀⡅⠀⠀⠈⠠⠆⠙⠛⠁⠀⠀⠀⠀⠀⠀⠈⠐⠈⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠄⠀⠀⢀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠘⠋⠇⡀
⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⣠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠓⠒⠀⠑⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢐
⠀⠀⠀⠀⠀⠈⠀⠀⢀⢷⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠪⠥⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠐⡀⡀⠀⠀⠂⠀⠀⠄⠀⠀⠰⡙
⠀⠀⠀⠀⠀⠀⠀⠘⣠⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠘⡆⠀⠀⠀⡀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠂⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⡀⠈⠡⠤⢠⠆⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠐⡀⡇⠰⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠒⠎⡄⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠀⠀⠀⠙⠒⠂⠂⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠀⠀⢀⢤⣤⣤⢤⣤⣀⢀⡀⠀⠀⠠⠌⠐⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⡀
⠀⠀⠀⠀⠀⠀⠸⠟⠁⠁⠀⠀⠈⠓⠇⠀⠀⠀⠀⠀⠀⠀⠈⠐⠂⠀⠀⠀⠀⢀⠀⡰⠊⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠸
⠀⠀⠀⠀⢀⠆⠀⠀⠀⠀⠀⠀⠀⠂⠠⡆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀⢁⠜⠁⠀⠀⠁
⠀⠀⠐⡵⢋⠞⠡⠄⣀⢀⠀⣀⠀⡄⢢⡘⢮⡳⠀⠀⠀⠀⠀⠀⠀⡀⠀⠼⠠⠇⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⢡⠏⢀⠉⠐⠃⢈⠀⠸⠀⢠⠀⢱⣌⡇⠀⠀⠀⠀⠀⠀⠀⠈⠘⢸⠸⠀⠀⢀⠄⡠⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⠜
⠀⠀⠀⠀⠳⢾⡀⢼⠀⢸⠀⠠⡄⠀⣧⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢻⡇⠀⣀⠔⠁⠀⠀⠀⠀⠈⠀⢔⠢
⠀⠀⠀⠀⠀⠀⠑⠚⠐⠚⠀⠐⠃⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠺⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠦⠆

⠀⢐⡀⠀⣂⠀⠀⠀⠄⠀⠀⠀⢜⠀⠀⠆⠀⠀⠀⢤⢀⠠⡀⠀⠀⣠⣤⣶⣶⣶⣶⣶⣶⣤⠀⠀⠀⠠⠄⠄⣠⢀⠄⡀
⠠⠈⠂⠐⣈⠂⠀⡄⠂⠄⠀⠁⠉⠀⠂⡥⠆⠑⣈⢰⣇⡠⠋⠢⡀⣿⣰⣧⣝⣀⣇⣷⣅⣿⢀⠔⠀⠀⡤⠀⠠⡄⠀⢠⡔
⠀⡀⢀⠀⠄⠄⡀⢔⢊⠌⠀⡨⣀⠀⠀⠰⠀⠰⠢⢓⠀⢳⡄⠐⠀⠙⠛⠛⢻⡿⢛⡛⠛⠁⢨⠀⡳⠆⠀⣼⡄⢡⣶⡄⠁⢳⡇
⠀⠁⠁⠂⠀⠸⠅⠃⠀⡂⢀⠦⢀⠀⠁⢉⠀⠀⠾⠂⢠⠂⠀⡠⠊⠖⠀⡀⠈⠀⢠⡄⠀⠈⠀⠁⠠⠘⠠⣀⠔⠢⣀⠄⠁⠤
⠀⡠⢂⠅⠰⢈⢐⠀⡨⠇⣀⠪⠂⠁⢀⠰⢁⠀⠀⠠⠂⢰⡁⠄⠀⠀⠀⢧⢀⠀⡇⢩⠀⡞⢰
⠠⠠⠠⢐⠀⠂⠂⠂⠰⠃⠀⠄⠡⠂⠂⠀⠠⠃⠠⠄⠠⠊⠧⠤⠤⠀⠂⠈⠄⠀⠀⢸⠀⠇⢸⠀⡀⡤⠀⠠⡢⠀⠀⢰⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠡⡀⠐⢖⠂⠡⠀⠁⠀⠀⠔⠀⠈⠀⠀⠈⣹⡄⠀⠀⠐⠤⠘⠀⡄⢼⠀⠀⠈⢀⠀⠀⠀⢀⠅⠘⢂
⢀⠄⠀⢠⢀⠀⠀⣉⣂⠐⠻⠲⡶⠲⡶⠆⠀⠰⢆⠂⢒⠶⡀⠁⡁⠈⠁⡀⠀⡐⠈⠀⠁⢀⠀⠀⠀⣄⠀⢠⠀⠀⠌⠈⡀
⢀⣤⣤⣄⡏⢄⢾⣿⣿⠀⠀⠀⠹⠜⡀⠈⠤⠂⠈⠳⠎⠀⠈⠒⠀⠀⠂⠂⠀⠀⠀⠀⠀⢀⠀⠀⣄⠈⠘⠈⠑⠠⠆⠀⠀⠠⠘
⠀⢿⣿⡟⠀⠀⠈⠋⠙⢆⠀⠀⠀⢀⢆⠀⠀⠠⠀⢀⠀⠲⠲⠒⠒⠒⠖⡤⢄⠀⠀⠀⠀⠞⠉⠀⠐⠄⠀⠀⠆⠀⠀⠀⣀⡀
⠀⠀⢖⠀⠀⠀⡠⠒⡀⠘⠣⢀⠠⠼⠸⠄⢀⠀⠀⡞⠀⢀⠀⢀⠐⠀⡆⠀⢘⠆⠘⠋⠁⠀⠀⠀⡀⠈⢆⠈⠀⠀⠃⡀⠉
⠀⠂⠛⠑⠀⠀⠅⠀⠀⢂⠀⠔⡀⠀⠀⠀⢰⡀⠀⡁⢈⠁⠄⠁⠈⠀⠁⠀⠀⠀⠀⠀⢢⡀⠀⠀⡀⡀⠀⠁⠀⠈⠂⠁⠀⠐
⠀⠀⠀⢰⡄⠸⡀⠀⠀⡘⢸⠠⠄⣁⠀⡀⠡⢸⠀⢃⢄⠀⠐⠐⠢⠀⠠⠄⢀⠇⠀⠀⠀⠀⠀⠤⠀⠸⠄⠀⠀⡀⠈⠁⠈⠂
⠈⡐⢠⠃⠱⡀⢡⠀⢀⠀⡸⣀⠀⠀⠀⠀⢐⠸⠀⠀⠘⠀⠤⠤⠤⠤⠄⠐⠁⠀⠰⠆⢰⣶⠞⠉⠁⠀⠙⢶⣶⠀⠀⠐⠈⠄⠁
⠀⠀⠎⠀⠀⠰⠀⠉⠈⠀⣈⠂⢩⠄⠀⠬⠀⠊⠀⣄⠀⠀⠀⢀⠀⠢⠉⠁⢐⠀⣀⠀⠀⠙⠀⠀⠀⠀⠀⢸⠁⢀⠠⠀⠒⢐⠢
⠀⢸⢀⡀⣀⠀⢇⠀⣸⠀⠉⠀⠙⠁⠀⠀⣠⠊⡀⠊⡀⣀⡂⠘⡬⢄⣲⠅⠈⡀⠓⠁⠀⠈⢀⡀⠀⠀⣠⠊⠀⢀⠘⠂⢒⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠇⢠⠀⢀⢐⠀⠀⡰⠁⠀⠀⢠⡅⠃⠀⠀⠀⠀⠀⡀⢀⠅⠀⠴⠢⠀⣤⣬⣷⣯⣤⣇⠀⠀⠑⠀⠐⢂⠁
⠀⢀⡀⠙⢋⢄⠀⠈⠢⠈⠈⠈⠀⠀⠐⠧⠐⠂⠉⢀⡀⡀⠀⠀⠀⠉⠐⠒⠁⠐⡿⠠⡤⠤⡄⡉⠉⣉⣉⣀⣀⢀⠀⠠⠄⠺⠃
⢀⢮⣈⠻⠧⣔⠢⡄⠐⠠⠀⠀⠀⢀⠆⢀⠀⢠⠞⠁⠀⠰⠞⠉⠁⠀⠀⠀⠂⡀⠀⢠⣀⣀⡃⠀⠀⠀⠀⣰⠀⠀⠀⡀
⠘⠉⠀⠤⠀⠐⠀⠅⠐⠀⠊⠀⠈⢂⣀⡈⠀⠐⠀⠁⠂⢐⠆⠼⠀⠷⠀⠀⠀⠁⠀⠀⠀⠈⠁⠁⠈⠁⠈⠁⠉⠀⠁
⠈⠢⡀⠀⠀⣀⠤⠀⠚⠒⠀⠀⠂⠀⠙⠀⠀⠃⠒⠀⠀⠌⢸⠀⣇⠀⠍⠀⠀⠀⠘⠄⢱⠀⢉⠀⠀⠎⠂⠰⡰⢢⠚⠁
⠀⡠⠬⠉⠀⠀⢄⠀⢀⢆⠀⠀⠀⠀⠀⠀⠀⠄⠘⠀⠌⠀⠀⠲⠀⢀⠃⠀⠀⠀⠀⠀⠈⠀⠀⠂⠐⠃⠀⠊⠀⠐⠂⠀⠈
⠀⠀⠀⡖⠲⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣰⣰⡌⢄⡸⠀⠀⡂⢀⠀⢀⠂⡂⠀⠚⠈⠇⢹⠈⠐⠄⠀⠡⠀⢡⠋
⠀⠒⠀⠀⠀⠀⠚⠀⠁⠂⠤⠁⠁⠀⠈⠉⠈⠒⠒⠒⠒⠒⠀⠂⠀⠁⠀⠑⠀⠈⠂⠘⠑⠃⠐⠂⠐⠁⠊⠐⠒⠀⠀⠀⠂⠚

⠀⠀⠀⢀⢀
⠀⠀⠊⠉⠳⢄⠈⠙⠋⠉⠉⠀⠁⠀⣁⠨⠜⠋⠁⠀⠀⠀⠀⣠⠀⠤⠈⣀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⡀
⠀⠀⠤⡀⠀⠀⠀⠀⠀⠀⡀⠴⠒⠋⠁⠀⢀⠐⠊⠈⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠈⢃⣀⣀⣀⡴⠏
⠀⠀⠀⠈⠐⠠⠖⠋⠀⠉⠀⢀⡀⣀⠀⠀⠀⠈⠁⠀⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠂⠀⠚⠁
⠀⠠⢀⣀⠠⠀⠀⡀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⡠⠂⠛⠂⠃
⠀⠀⠀⠀⡠⠴⡄⠤⠠⢨⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⣀⠀⠀⢀⢠⠀⠀⠀⠀⠀⠀⠸⠁⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠃⠀⢅⠀⠀⡄⠀⠀⠀⡤⢀⡄⡄⡄⡀⠀⠀⠀⠀⠀⠘⠦⠀⠠⣔⣰
⠀⠀⠰⡀⠠⠆⠠⠤⠴⠊⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠉⠉⠋⠁⠉⠀⠁⠉⠙⠁⠀⠀⠀⠀⠀⡀⠀⠀⠈⠁
⠀⠀⠀⠀⡀⠀⠐⠒⠂⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠁⢀⡞
⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⠀⠀⠀⠀⢆⠀⠀⢠⠅
⠀⠀⠀⠀⢀⠐⠒⠂⠄⠀⠀⠀⠈⡄⠀⠄⡀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠐⠀⠀⠀⠈⡀⠀⠀⠀⠐⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔
⠀⠀⠐⠄⠀⠀⠀⠀⠔⠀⠀⠀⠀⡄⠀⠀⡀⠀⠀⠀⠀⢀⡴⠞⠁⢠⣀⣀⣠⠤⠖⠒⠲⠶⠶⠶⠄⠀⠉⡑
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠒⠀⠀⠈⠀⠀⠀⠀⠉⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠈⠁

⣿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠉⠳⣄⠀⣠⠶⠛⠉⠉⠙⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠹⠟⠁⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠀⠀⣀⣤⣤⣀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⣠⠞⠁⣠⣶⠋⠁⠀⠀⠉⠳⠦⠤⠶⠚⠉⠁⠀⠉⠛⢦⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⢀⡴⠞⢁⣴⣿⣿⣿⣿⣿⣷⣀⠀⠀⣀⣤⡀⠀⠀⠀⣠⣤⣀⠈⣧⠀⠀⠀⠀⠙⢦⡀⠀⠀⢸
⣿⠀⠀⠐⢿⡀⠰⣿⣿⣿⣿⡿⠟⠉⠀⠉⠙⣻⠿⠛⠙⠲⠶⠚⠁⠀⠉⠉⠙⠳⢦⣤⡄⠀⠀⣹⡆⠀⢸
⣿⠀⠀⠀⠀⠹⣆⠘⣿⡿⠋⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⢀⡼⠋⠀⠀⢸
⣿⠀⠀⠀⠀⠀⢸⣶⠋⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⢀⡴⠋⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⣼⠁⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⢠⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⢀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡧⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠙⠳⢦⣤⣀⣀⣀⣀⣤⠴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣼

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠔⠽⣿⣷⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⣀⣀⣀⣤⡙⢛⣷⣶⣶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠒⠂⠋⠉⠑⢒⡒⠒⠓⣶⠀⢂⡒⠘⢽⣿⣿⣿⣆⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⡴⠻⠉⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠞⠛⢓⣛⣫⣽⣿⣿⣿⣿⣽⣭⡿⠷⣦⢤⡀
⠀⠀⠀⠀⠀⢠⠖⠀⠄⠠⢄⠽⠠⠦⠤⠼⠬⣥⠬⣿⣿⣽⣿⠭⠿⠿⢿⣿⣟⣽⣿⣿⣷⣮⣄⣙⠋⠙⢷⣄⡀
⠀⠀⠀⠀⣰⠋⠁⠠⢤⣤⣀⣆⣀⣐⣀⣄⢤⣤⠠⠤⠤⢤⣴⣶⣶⣶⣿⠿⣾⣿⡷⣿⣿⣿⣿⣿⣷⣦⣄⠙⠻⣤⡀
⠀⠀⠀⢀⠎⠀⠂⠉⢁⣈⣈⣁⣀⣉⣁⣈⣉⣙⣏⣉⣉⣉⣉⣭⡤⠤⢶⣶⣿⡿⠗⣿⣿⣿⣿⣿⣿⡧⠀⠀⠀⢸⣷⣄
⠀⠀⠀⢠⠀⠀⢌⠐⠒⠂⠐⠳⠒⠒⠒⠒⠒⠲⠗⠒⠒⠒⠖⠛⢛⣋⣉⣯⣿⢷⣫⣿⣿⠛⠛⢿⣿⣻⠓⠂⠀⠐⠉⢻⡆
⠀⠀⠀⠘⢀⡠⢼⣒⣒⣉⣭⣭⣭⣭⣭⣭⣭⣭⣭⣬⢭⣭⡭⢽⠿⠿⢿⣟⣯⡥⣶⣿⣷⣦⣛⣿⣿⣖⠲⠤⠀⠀⠀⠀⢻⡄
⠀⠀⠀⢀⠀⠂⠹⢯⣀⡠⠤⠌⣃⠀⠀⠀⠠⠠⠟⠂⠀⠀⠒⢒⣚⣻⣿⠿⢷⣾⣿⣿⡿⣿⣿⣿⣿⣉⠄⣒⠀⠄⣀⠀⠘⡙
⠀⠀⠀⢨⠀⡄⠈⠻⡄⠀⣀⡠⠄⠀⠀⠀⠀⠀⣚⣉⣀⣉⣭⣥⣼⣗⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠈⣀⠀⠀⠀⢈⡓⢱
⠀⠀⠀⠀⣅⠋⠘⠑⢨⡥⠤⠐⠂⣐⣀⣀⠈⠭⠭⣥⣀⣖⣾⣿⣯⣾⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⡛⠛⠷⢮⣍⡒⠀⡀⠉⠹
⠀⠀⠀⠀⢨⡀⠼⠂⣀⠴⠒⠈⣉⣠⡤⠤⠶⣒⣺⣻⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣭⣈⡁⠂⠤⡙⠳⢬⣑⠀⠂
⠀⠀⠀⠀⠀⠉⡼⠋⣠⡴⠚⣁⣭⠴⢒⡻⠭⣵⣶⣿⣿⣿⢿⣿⣿⣿⣿⣽⣭⣿⣿⣟⣿⣿⣿⡍⠉⠉⠛⠛⠶⣤⡑⠢⣙⠻⠃
⠀⠀⠀⠀⠀⠀⠐⢾⠁⡠⠚⣁⠴⣚⡽⣶⣿⣿⠿⠛⠉⣱⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠂⠤⢈⡒⠤⣀⠉⠛⢷⣄⡑⢠
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢅⡼⣡⠞⣡⣮⢞⠁⢀⠀⢀⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣁⠀⠀⠈⠹⢷⣮⡛⠦⣄⡉⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⣼⢵⠁⠈⠔⡁⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⠉⠋⠙⣶⣤⣀⠠⢉⠛⣷⣬⡙⠖⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⡀⠀⢐⢿⣿⣿⢿⣿⣿⣿⣿⠿⢿⣿⣿⣟⠋⠉⢷⠦⣄⠀⠙⠛⢿⣦⣁⠀⠈⠻⢦⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⣾⡄⠹⣿⢸⣿⣿⣿⣿⣻⣿⣶⠬⠉⠁⠀⠀⠀⠀⠙⢶⣄⠀⠉⠛⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠄⡀⢿⣿⡆⠟⣾⣿⣿⣿⣿⣿⡿⠗⠠⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⠀⢘⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⡅⢸⣿⣿⢠⣿⣿⣿⣿⣿⣿⡗⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣈⠊⠿⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡃⢸⣿⣿⣼⣿⣿⣿⣿⣯⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⡀⠛⡷⡀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣞⠻⣿⣿⣿⣿⡿⣿⡧⡉⠢⡀⠀⢢⡀⠀⢠⡀⠀⠳⣄⠀⠸⢓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠈⣿⣿⣷⡙⣮⠳⡙⠄⠈⢆⠀⠹⣆⠀⢹⣄⠀⠘⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠏⠉⠛⢿⡜⣧⢹⡈⢆⠈⢧⠀⠸⣧⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠱⢸⣎⡇⠘⣇⢸⡇⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡶⠾⠟⠛⠛⠛⠻⠶⣦⣄
⠀⠀⠀⠀⣀⠀⠀⠀⢀⣀⣤⣴⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣦⡀⠀⣀⣤⣴⡶⠶⠶⢶⣦⣤⣀
⠀⠀⠀⢸⣿⡛⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠿⠋⠉⠀⠀⠀⠀⠀⠀⠉⠛⠷⣦⣀
⠀⠀⠀⠀⣿⣿⣷⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣄
⠀⠀⠀⠀⢻⡏⣿⣿⣿⣿⣿⣿⣶⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀
⠀⠀⠀⠀⠘⣿⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⣀⣀⣠⣿⠉⠉⠉⠉⠉⢹⣿⠛⠛⠷⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄
⠀⠀⠀⠀⠀⢻⡇⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⡀⠀⠀⣿⡇⠀⠀⠀⠀⢨⣿⠻⠷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣷⡆
⠀⠀⠀⠀⠀⠘⣿⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣤⣤⣾⣿⣦⣤⣤⣭⣽⣿⣶⣦⣤⣀⡀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⢹⣇⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⢾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⣹⣿⠿⠛⠉⠉⠀⠀⠉⠉⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢡⣾⠋
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⡿⠛⠁⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣬⡿⠟⠋⠁⠀⠀⠀⣰⡿⠃
⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⠛⠋⠁⠀⠀⠀⠀⠀⣠⣾⠋
⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⠀⢀⣤⡾⠋⠁
⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⢀⣀⣤⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠿⠿⠿⠟⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⠶⠶⠶⠶⠶⠟⠛⠉

⠀⠀⠀⠀⢀⣶⠖
⠀⠀⠀⠀⠈⠁


⠀⠀⠀⠀⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⣠⣶
⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠃⠀⠀⠀⣀⣀⣀⣴⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠶⠿⠟⠋⠀⠀⠀⠀⢠⣖
⠀⠀⠀⣈⣿⣁⠀⠀⠰⣤⠉⠀⠰⣿⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠘⠿⠿⠿⣿⣇⠀⠀⠘⠀⣆⣀⠠⠀⣤⡄⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿
⠀⠀⠰⠟⠉⢹⡇⠀⠀⠀⠀⠀⣼⠁⢸⡏⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⣿⠀⡀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠉⠃⡈⠻⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣦⢀
⠀⠀⠀⠀⢀⠀⠀⣴⣤⣤⡀⠀⣿⣠⣤⡀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠛⠂⠀⠀⠀⠀⢙⠇⠀⠀⠀⠀⠀⠀⢳⡆⠀⠀⣀⡀⠀⠀⠀⠀⠀⢠⣿⣿⣿
⠀⠀⠀⣠⣷⣦⣄⡘⢿⠿⢷⠀⣿⣿⣿⠏⡀⠀⠀⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠐⣿⡇⠀⠀⠀⠀⠀⠀⣬⣁⣴⡿⠋⠁⠀⠀⠀⠀⠀⠸⣿⠄⣿
⠀⢠⣴⢛⡛⠛⠛⠁⠀⠀⢀⡀⠉⣶⣤⣶⣷⣤⡀⠙⢿⣧⡀⠀⠀⠿⠀⢸⣦⠀⣴⣦⣼⣃⠀⠀⠀⠀⠀⠀⠛⣙⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠛
⠘⣿⣿⣾⡏⢀⠀⠀⠀⠀⠀⠃⠀⠉⠘⠛⠉⠁⠀⠀⠀⠈⠻⠞⢿⡗⠀⠀⠋⣀⣿⣿⠟⠛⠻⣦⠀⠀⠀⠀⠘⣿⡦⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢰
⠠⣿⣿⣿⡿⠛⠛⠀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⡄⢷⠀⠀⠀⠀⠘⠀⠀⠀⠀⣿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠛⢿⡗⠀⠀⠀⠿⣿⣆⣰⣜
⠀⠀⠉⠻⠀⠀⠀⠀⠀⠰⣾⣿⡇⠀⠀⠀⠀⠀⠀⡀⣧⠀⠀⠀⠀⠀⠀⠀⢠⣾⠀⠀⠀⠤⠀⡀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠠⠬⡙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠋⠙⠃⠀⠀⠶⠂⠀⣠⣷⣼⠇⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘
⢸⣶⢦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⣠⣾⣿⠟⠃⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢶⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠘
⢸⡁⠀⠀⠁⠀⣀⣠⣤⣤⣀⠀⠀⠀⢀⣿⣿⣿⡟⠀⠀⠀⠀⠀⣼⠃⠀⠀⣤⠀⠐⠀⠀⠀⠉⠀⠀⠀⠀⠀⢀⠛⠃⠀⢶⡄⠀⠀⠀⠀⠀⣰⣆
⢸⣷⡀⠀⠀⠀⣽⣿⣿⣗⠀⠀⠀⠀⠸⠛⣿⡟⠀⠀⠀⠀⠀⠀⠈⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠶⠆⠈⠁⠀⠀⠀⠀⠸⣿⣿⡆
⠈⢹⣷⡆⠀⠀⠿⣿⣿⣿⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡇
⢀⣾⡁⠀⠀⠀⠀⠘⢻⣿⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠒
⢸⣟⢁⣌⣅⠀⠀⠀⠈⠻⢷⣦⢴⣿⣸⠀⠀⠀⠀⠀⣠⣶⣦⡀⠀⠀⠀⠀⠀⠶⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⢟⠁⠇⠀⢸⣷⠀⠀⠀⠀⠀⠀⠀⠋⠁
⢈⣉⠉⠻⢿⡇⠀⠀⠀⠀⠀⠀⠘⠋⣩⡄⠀⣀⡠⠘⠉⠀⣹⣿⠿⠿⠗⣀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠐⣷⠀⠘⢠⠄⠀⢈⣿⣂⠀⠀⠀⠀⠀⠀⠐
⠸⠿⣿⣦⣀⣾⡀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠉⠀⠀⠀⢠⣿⠀⠀⠀⠀⣿⠀⠀⠀⠀⠃⠀⠀⠀⠉⠆⢩⡄⠀⠀⠀⠀⠙⠉⠛⠂⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠹⣿⢻⣧⠀⠀⠀⠀⠠⣤⣄⠀⢾⠁⠀⠀⠀⠀⠈⣥⡀⢀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⡇⢰⣶⣶⣷⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⡿⢸⡇⠀⠀⠀⠀⠀⠀⢹⣷⣾⠇⠀⠀⠀⠀⠀⣿⣷⡈⠀⠀⠀⠀⠀⠀⣰⣶⣿⣿⣿⣍⣛⡛⣧⠟⠉⠛⠿⢿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠹
⠠⠀⠀⢀⡄⠀⢀⡀⢀⣀⣀⣀⠀⠀⣼⡿⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⣴⠏⠉⠈⠉⠻⣿⡿⠛⠿⠃⠀⠀⠀⠀⢹⣏⣽⡆
⠀⠀⠀⣼⣣⣶⣾⣿⣿⣿⣿⣿⣷⡶⠈⡅⠀⠀⠀⠀⠀⠀⠀⠈⢁⣄⣤⠀⠀⠀⣿⠀⠀⠀⠀⠀⢿⣿⣠⣤⠀⠀⠀⠀⠀⠀⣁⣀⡴⣶
⠀⠠⢾⡿⠿⠿⠿⠿⡿⠿⠟⠋⠁⠙⠰⠀⠀⠀⠀⠀⠀⠀⢾⢿⠿⠿⠿⢶⡦⡤⠏⠀⠀⠀⠀⠀⠸⠹⡿⣿⠀⠀⠀⠀⠀⠈⠉⠻⣧⢷⠀⠀⠀⠀⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠤⠶⢒⡒⣛⣛⢋⠉⣉⠙⣦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⠉⣶⣶⣴⣦⢸⣿⠃⢹⡇⠘⢾⡟⢠⡟⠉⠉⠉⢛⣲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⠋⠁⢸⡄⣟⠁⠛⠹⠆⠉⠓⢀⣁⣑⣛⣁⣸⣇⣀⣀⣀⣙⣳⣄
⠀⠀⠀⠀⠀⠀⠀⠠⡄⢀⠀⠛⣻⠂⢀⣸⣧⣤⠤⠶⠶⠚⠛⠉⠉⠉⠉⠉⠉⠉⡁⠀⠀⠀⠀⠉⠉⢁⣀⣴⠊⠀⢀⠴
⠀⠀⠀⠀⠀⠀⢰⢸⡇⢴⠀⢰⣧⠖⠋⠁⠀⠀⠀⠀⠀⠀⢀⣀⣤⢺⡇⠀⠀⠀⣿⡷⢲⣒⡶⣶⣻⠛⢆⣿⠀⣀⢸⣯
⠀⠀⠀⠀⢀⣀⣸⣸⣇⣿⠀⠈⠁⠀⠀⡶⣶⠲⡖⢲⢺⣿⣿⡇⠸⣮⢿⠀⠀⠀⠛⢀⡘⠟⠀⠈⠛⠀⠀⠁⠀⣿⢸⣿⢀⣶⣆
⠀⢀⡞⠩⠁⣀⡈⣉⣁⠉⠍⠙⢦⡀⠀⠯⡏⠐⡷⢾⠀⠿⠛⠇⠀⠁⣀⠀⣀⠀⢀⣼⡅⠀⢾⡆⠀⠰⣿⡆⠀⣿⡜⠋⠀⠈⠀⣀⡀
⠀⠀⡇⣤⣤⣴⢶⢠⡶⣄⣶⣦⢈⡇⠀⠀⠀⢀⠀⣤⠀⠀⠀⠀⢷⢴⠻⠔⣇⠀⣼⠽⡇⠀⣟⢳⡀⢀⣯⡿⣄⠙⢁⢠⣿⣆⡆⠘⠁
⠀⠀⢻⣇⠻⠿⢾⣼⠧⠿⠃⣿⣼⠃⠀⠀⢀⣸⣿⣿⣽⣃⠀⠀⠘⠄⠑⣒⠋⠘⠳⠛⠃⢸⣯⢈⣧⠸⠷⠿⠛⠀⠈⢳⣻⠯⠂
⠀⢠⠼⢯⣔⣆⣈⣩⣄⣀⣺⠴⠛⠑⣆⢏⣉⣩⣿⣧⠤⢼⡇⠈⣏⣧⣼⣹⠀⠀⢠⢒⠤⢠⡬⠉⡁⠀⣀⣀⠀⢀⡤⠠⡁⠀⢴⣤⠄
⠀⢸⠈⣀⠀⣠⡀⣰⣦⠀⣠⡀⢠⣄⢹⠈⡇⠀⣿⡇⠀⣸⠀⢺⡿⣿⣿⠿⡿⠀⠜⠬⠗⠠⠽⠖⠁⢸⡁⠈⠳⠏⠀⢀⡇⣀⠈⠁
⠀⠘⡟⢹⣾⠇⣿⣿⢸⣸⡏⢧⣾⠘⡾⠃⣇⠀⣿⣷⣀⡏⠀⠘⣷⠀⢐⢿⡇⠰⠀⠀⣠⡴⠲⣄⠀⠘⠧⣄⠀⠀⢀⡼⠁⣿⣿⠟
⠀⠀⣧⣠⢉⠠⡙⠇⡀⣙⣂⢬⡗⢔⡿⠀⢈⡅⢠⡀⢀⣀⡀⠀⠻⠼⠿⠾⠃⠀⢀⣠⡟⠀⠀⢸⣇⡤⢄⠀⠉⢷⡟⠁⠀⠈⣁⡀
⠀⠀⠛⠬⣏⣙⣙⣋⣹⡥⠽⠖⠚⠉⠀⠀⠘⢦⣾⣷⣯⡴⠃⢀⣤⢀⣀⠀⢀⣰⣋⠸⡇⠀⠀⢸⡏⠀⢸⡇⠀⠸⣅⠀⢠⠞⠁⠀⠉
⣀⠞⢦⡄⣀⠀⣀⣤⡤⡄⠀⡀⠀⢿⡷⠀⡏⠉⣿⠀⣿⠁⢹⣾⣿⣿⠟⣰⠏⠀⠉⣷⢳⣀⣠⣾⡞⠋⠉⢳⡄⠀⢸⡆⡏
⢨⡶⠼⠆⢹⡽⠛⠛⠉⠃⣸⣽⢠⣏⣷⠀⢻⠀⢿⢀⡯⠀⣼⢸⣿⢹⠇⣿⠀⠀⠀⣿⡏⠉⣷⣼⠁⠀⠀⢸⠇⢀⡾⠁⢹⣄⣀⣠⠼
⢠⣄⡄⠀⠀⠀⠴⣿⡆⠀⠧⠿⢀⠌⡄⠀⠘⠲⠺⠞⠓⠒⠋⠘⠛⠚⠀⠘⠦⣤⠞⣿⠀⠀⣿⡿⢄⣀⣠⠟⠀⠀⠀⠀⡾⠉⢠⣤⣤
⠚⢶⠛⠠⠴⣱⠴⢋⡀⣰⣆⢻⡿⠀⡗⣠⡀⠀⠀⠀⣀⢤⡎⣳⣀⠀⠀⠀⠀⢩⠀⡻⣄⣠⠏⡀⠘⢋⡴⠊⠉⠑⢦⠀⢇⠀⠮⣿⠿
⠴⠆⢀⣀⡉⠋⠀⠈⠙⠾⠋⠁⠀⢀⣔⣛⣓⣄⠀⢴⡙⠦⠟⠗⣚⣳⠀⠤⠀⠀⠄⢃⠘⠉⠠⠁⠌⢸⠀⠀⠀⠀⠈⡇⠈⡆⢀⣁
⠀⠀⣿⠁⡭⠉⠉⣉⣷⡆⠀⠀⢠⡗⠢⠗⡒⢚⡇⢸⣸⣿⢻⢫⣿⠇⠀⡿⡄⠀⠀⠱⣄⢀⢀⠊⠀⠸⣄⠀⠀⣀⡾⠁⣠⠇⠺⠿⠂
⠀⠀⣿⣀⣠⣴⠞⠛⣩⡿⡵⠀⢪⣤⣑⣭⣤⡭⣼⠀⠛⠛⠛⠛⠋⡤⠀⠛⠳⠤⡀⠀⠸⡶⠁⠀⠀⣠⠟⠛⠉⠁⣤⡀⠁⣤⣤⡄
⠀⠀⠈⠙⣯⣄⡴⢞⡥⠚⣁⢀⠈⢿⣿⣿⣶⣧⠏⢀⢀⣴⡄⠀⢺⡁⠀⠀⠀⠀⣈⠇⢰⣧⠀⠀⠀⡇⠀⣴⣶⠀⠉⢁⡄⠘⠋
⠀⠀⠀⠸⣯⠵⠚⠉⠀⠠⣻⣟⠄⠀⠀⠀⠀⠀⠀⢹⠾⡿⣿⠃⠀⠹⡟⡟⣿⣿⣿⠀⠸⠁⠀⠀⠀⢸⠀⠈⠈⢀⣽⡁⡷⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣈⣉⣉⣁⣀⣀⣀⣧⣿⣟⣛⣛⣀⣀⣀⣀⣀⣴⣃⣀⣀⣀⣈⣉⣉⣃⣀⣀⣀⣀
⣿⣿⠛⡿⢛⠻⢻⡿⣻⢿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠂⣤⡤⣀⡀
⠀⠀⠀⠀⡈⠘⢄⠠⢔⡲⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡞⠓⢺⣅⠀⠏⣷⣰⠉⢲
⠘⠯⠭⣉⠁⡷⡆⣰⠋⠀⠀⠀⣰⢹⣭⡭⠷⠦⢙⣶⣶⣶⠆⠀⠀⠀⣀⣀⠠⢤⣀⠀⠘⢯⡿⣿⠇⢰⢻⡁⠠⣁⣿⣿⣆⠘⡇
⠀⠀⠀⡜⣠⠖⠢⡘⣆⠀⠀⠈⠻⣇⣛⣛⣋⠉⣈⠿⠋⠀⠀⢀⠴⠿⠤⣍⢢⡀⣿⠈⢢⡀⠉⢿⡇⠘⣗⠀⢘⢠⡅⠙⢿⣶⣿⣄
⠀⠀⠈⠚⠁⠀⠀⠙⠚⠃⠀⠀⠀⠘⠛⠒⠂⠉⠀⠀⠀⠀⠀⢮⣿⣿⣷⣮⣿⣧⣇⡠⠏⠁⠀⠈⠋⠙⣯⠀⣰⣰⣀⡴⠶⠻⠿⣿⡧
⠀⠀⠀⣀⢤⠴⠶⡶⡤⣤⡀⠀⠀⠀⠀⠀⠀⢀⠠⡄⠤⢤⠠⠀⠀⠉⠙⢫⠞⠻⣟⠒⠒⡏⠀⠀⠀⠀⠈⠋⠉⠉⠁⢠⡴⠶⢤⡀
⠀⣴⠻⠹⠀⠀⡄⠀⢀⠃⠞⣳⣄⠀⠀⡠⠊⠣⡀⢣⡀⣹⠀⠇⠀⠀⠀⠘⠣⣧⠈⠹⠞⠀⠀⠀⠀⢀⡄⠀⠀⠀⡠⣿⢏⠢⠡⢹⡄
⠈⡎⢂⠁⠃⠀⢀⠀⠈⠈⡰⠡⢋⠆⡐⠙⠢⣤⠟⠉⡏⢻⢆⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⣸⣷⠀⠀⠀⡇⡈⠘⡄⡂⠆⣧
⠀⠘⢆⢢⢠⣠⢘⠀⠀⠐⠐⡡⠋⠀⡗⠲⠴⡟⢒⣶⡷⣯⠤⡇⠀⠀⣰⠇⡢⠀⠄⡁⠨⢳⡄⠀⠀⡯⠰⡄⠀⠀⢻⢁⠀⠀⠀⠀⢻
⠀⠀⠀⠳⣕⢷⣿⣾⠌⣠⠊⠀⠀⠀⠘⢦⠒⢛⠥⣮⢶⠛⣤⠇⠀⠀⣥⠊⣠⠎⡔⢠⠁⡅⡇⠀⣘⣋⠉⢵⠀⠀⠸⡼⡠⡀⠀⠀⡿
⠀⠀⠀⠈⠛⠛⠛⠛⠛⠛⠀⠀⠀⠀⠀⠈⠙⠻⠤⠧⠜⠛⠁⠀⠀⠀⠋⣴⠃⣼⠁⣾⠀⣇⡿⠀⠫⣤⣺⣿⡷⠀⠀⢿⡵⣣⢇⢢⡇
⠀⠀⠀⠀⣠⡤⣀⢤⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠒⠛⠴⠟⠒⠉⠁⠀⠀⠸⠿⠋⠁⠀⠀⠈⠻⣵⣯⠞
⠀⠀⡄⠊⠀⢳⡀⠈⢁⡆⠙⢦⠀⠀⠀⠀⠀⣀⣤⣤⣀⠀⠀⠻⣟⠛⠒⠚⠳⠲⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⣼⣀⣀⣠⡜⢋⠓⠺⢀⠠⠈⢳⣄⠀⠀⡼⣛⣫⡈⠛⣷⣄⠀⠀⠉⢢⡀⢀⠀⠃⠈⠙⠦⣄⠀⠀⠀⠀⠀⢴⣾⣿⣿⢧⣄
⠀⢱⠀⠏⣇⡼⣟⡖⠈⢹⠶⠛⠉⣿⠀⠀⡏⣴⣾⣿⣮⡟⣿⣆⠀⠀⠀⠙⠒⠒⠓⠒⠒⠒⠚⠓⠀⠀⠀⣠⡾⣿⣛⣫⣤⠛⠙⡦⡀
⠀⠘⣦⠚⠙⠑⡎⠉⠺⡇⢠⠀⣆⢺⠀⠀⢣⡻⣿⣿⣿⣿⡿⠛⠀⣀⠤⢤⠞⠛⠙⣟⠓⠦⣄⣀⠀⢠⢞⡙⠀⠈⠀⠀⠀⠐⡜⡄⢽
⠀⠀⠈⠙⠲⠶⠧⠖⠲⠶⠚⠒⠛⠛⠁⠀⠀⠙⠚⠛⠋⠉⠀⠀⢰⡡⠊⠀⢂⠀⠀⠘⣄⠳⣈⡟⠀⠸⡕⢡⢀⠁⠃⡛⡈⡁⡐⡜⣼
⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣯⣔⣚⠉⠓⢔⠄⡄⠈⣳⠋⠀⠀⠀⠘⠧⣼⢐⡃⡃⡇⢡⣱⡴⠋
⠀⠀⠀⣴⣿⣿⣛⡷⡄⠀⠀⢀⣀⣀⣀⣀⣠⣄⣀⣀⣀⣀⣀⠈⠳⣝⣛⢛⣿⣚⣷⠤⠾⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠛⠉⠁
⠀⢠⢚⢝⡉⠀⢉⣶⡿⡆⠀⡟⡩⠋⡥⠼⣧⡈⠉⢀⣴⣦⡌⢷⡀⠈⠈⠉⠀⠉⠀⠀⠀⠰⡒⡖⡲⠉⡟⠉⢹⠖⠘⠳⢦⣄
⠀⣇⢏⢮⠸⣼⣿⡿⣿⠁⢠⡋⢰⠺⢷⡄⠈⠻⣦⠈⢿⣿⣿⡎⣧⠀⠀⠀⢀⡖⠒⠦⣄⠀⠘⢶⠃⢀⠀⠀⠀⠀⢐⠈⠀⢘⢆
⠀⠈⠲⢽⣽⣿⣫⡞⠁⠀⢈⣶⡛⠳⣆⠙⠷⣄⠙⣦⢸⣿⣿⣧⣽⠀⠀⣀⡼⠅⠀⠀⠠⠛⣄⠈⠛⣇⠀⢠⠀⠀⡄⠀⠀⠀⢸
⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠘⢏⠙⠶⢌⣙⡓⢮⣿⣌⢣⣻⣿⣯⠏⠀⢸⠙⠌⠀⠀⠀⠀⠄⢹⠀⠀⠈⠛⣇⠀⠐⠀⠀⠀⠀⠈⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢤⣭⣭⣴⣍⣰⣇⠉⣿⡟⠀⠀⠈⠣⣀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠘⢶⣄⡀⠀⠀⠠⠀⢛⣨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠚⠓⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠀⠀⠀⠈⠉⠙⠓⠋⠉⠀⠀⠀⠉⠙⠲⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠖⠉⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠉⠲⡄
⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⣀⣠⠴⠒⢿⠉⠉⠁⠙⡏⠀⠉⠉⡿⠒⠢⣄⣀⠀⠀⠀⠘⢦
⠀⠀⠀⠀⢀⡞⠁⠀⢀⡴⠊⠉⢃⠀⠀⢘⣄⢀⣀⣠⣇⣀⡀⣠⠃⠀⠀⡘⠉⠑⢦⡀⠀⠈⢳⡀
⠀⠀⠀⠀⡞⠀⢀⣴⠃⢡⠀⣀⣼⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣧⡀⠀⡌⠙⣦⡀⠀⢳
⠀⠀⠀⢸⠁⢠⡫⠈⣤⣴⣿⡿⠿⠛⠛⠛⠛⠿⢿⣿⣿⣿⠿⠛⠛⠛⠛⠿⢿⣿⣦⣴⠀⠿⡄⠘⡇
⠀⠀⠀⢸⠀⣿⣱⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠁⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣦⣿⠀⡇
⠀⠀⠀⠸⡄⠈⠻⣍⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣩⠟⠁⢠⠇
⠀⠀⠀⠀⢳⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⡞
⠀⠀⠀⠀⠀⠱⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣠⠎
⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠦⣤⣤⣀⣀⣀⣀⣤⣤⠴⠞⠋

⠀⠀⠀⠀⠀⠀⢀⠀⢀⣱⣴⣴⢛⣋⠐⠒⠢
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡿⣿⣿⠿⣭⡉⠉
⠀⠀⠀⠀⠀⠀⠀⡟⠈⣾⡗⣌⣷⡈⠙⠈⠀⠀⢀⣰⣿⠋⣓⠀⣠⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠘⠶⢻⡇⠈⢻⠙⠠⠀⠀⠀⡾⠁⢻⣷⡌⠸⢳⠏⣦⠈⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢄⠑⢤⡀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⣀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠑⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠎⠉⠠⢄⠀⠀⠀⠀⠉⠒⠦⢄⡀⠀⠈⠑⠦⡀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠓⠺⡞⠛⠛⠒⠂⠀⠀⠀⠀⠀⠀⠈⠑⠠⣀⠀⠈⠓⢄⡀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠑⢦⣀⠀⠙⢶⠀⠾⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⢐⠤⡹⣧⣠⣄⡈⠶⣬⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⣀⡤⠖⠋⠉⣀⠀⠚⢑⠻⣮⡾⠛⠓⠾⣧⡘⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠟⣹⢀⣴⠡⠜⡉⣤⣦⣾⣷⣿⣿⣿⣶⣄⠺⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠖⠟⠳⠿⠿⠾⠷⠷⠛⠁⠁⠀⠀⠐⠀⠐⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⡬⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠤⣁⡃⠀⠀⠀⠀⠀⢱⠚⠂⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡆⠺⡀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠂⠀⠀⠁⠀⡀⠀⠀⣀⣀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⢀⠠⠀⠀⠐⠀⠑⢄⠈⠂
⠀⠀⠀⠀⠀⢀⠀⢤⠤⠤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠔⢁⠄⠀⠈⠀⠀⠄⠀⠀⠠⠀⠔⠀⠀⢸⢀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢫⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡠⢂⡄⠀⢈⣨⡄⠉⠛⢄⠀⠀⠀⠀⢀⡀⠀⠀⠰⠀⠀⠀⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣐⢀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⡀⠀⠀⠈⠀⣀⡣⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠈⠀⠀⠀⠠⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠐⠞⠉
⠀⠀⢀⠂⠁⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠁⠈⡆⠀⡠
⠀⠀⡀⠁⠈⠀⠐⠀⠀⢳⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠄⠀⠀⠀⡯⡊⢀⠴⠁⠀⡀
⢸⡂⠧⠀⠀⠀⠀⠀⠀⢄⠁⠠⡄⠀⠀⠀⠗⢄⠀⢀⡀⠀⠀⠊⢀⡌⡀⠀⠀⠀⠀⢀⠇⠀⠁⠀⠈⠀⠀⡀
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⢀⠀⠀⡀⠔⠑⠐⣦⣤⠀⠘⡀⠐⠁⠀⠀⠀⡠⠊⠉⠀⠐⠀⠀⠒⡤⠅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠃⠀⠀⠀⠀⠀⠀⠀⢑⠶⠀⡀⠃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠄⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢻⡄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷

⠀⠀⠀⣠⣴⣶⣶⣶⣤⡀⠀⠀⠀⣠⣴⣶⣶⣶⣤⡀⠀⠀⢀⣠⣶⣶⣶⣶⣄⡀⠀⠀⢀⣤⣶⣶⣶⣦⣄⠀⠀⠀⢀⣤⣶⣶⣶⣦⣄
⠀⠀⣼⣟⠙⣿⣿⣟⠙⣿⡆⢀⣾⡟⢙⣿⣿⡟⢙⣿⡄⢀⣾⡏⢹⣿⣿⡏⢹⣷⡀⢠⣿⡋⢻⣿⣿⡋⢻⣷⡀⢰⣿⠋⢻⣿⣿⠋⣻⣧
⠀⠀⣿⣿⢿⣿⣿⣿⢿⣿⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣛⣿
⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠇⠀⢿⣯⡻⣿⣿⣿⣳⣿⠃⠈⢿⣯⣯⣿⣿⣿⣽⡿⠁⠘⣿⣿⣵⣾⣷⣿⣿⡿⠀⠸⣿⣿⣷⣷⣷⣝⣿⡟
⠀⠀⠀⠙⠻⠿⠿⠿⠛⠁⠀⠀⠀⠙⠻⠿⠿⠿⠋⠁⠀⠀⠀⠙⠻⠿⠿⠟⠋⠀⠀⠀⠈⠙⠿⠿⠿⠟⠋⠀⠀⠀⠈⠛⠿⠿⠿⠟⠋




⣿⣿⠟⠛⠛⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⢀⡔⠘⠊⠓⢦⠀⠀⠀⠀⡠⠐⠒⠠⢀⠀⠀⠀⢀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠂⠐⠢⡀⠀⠀⠀⠀⢠⠪⠤⡌⠉⢳⡀
⠀⠀⣾⠀⠀⠀⠀⠈⡇⠀⠀⣜⠀⠀⠀⠀⠀⠂⠀⠀⡇⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠅⠀⠀⠀⠀⢨⡄⠀⠀⠀⡏⠄⡀⠄⡔⠈⡇
⠀⠀⠘⣄⡀⠀⢀⣰⠃⠀⠀⢻⡀⠀⠀⠀⢀⠆⠀⠀⢳⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⣴⠃⠀⠀⠀⠀⠤⣤⣀⣴⠖⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠉⢻⠉⠀⠀⠀⠀⠀⠙⠓⠶⢾⠋⠀⠀⠀⠘⡅⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⡽⠛⠛⠋⠁⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⢠⠺⢭⣇⢹⢳⡄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⢹⡀⠀⠀⢀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⢟⡫⢾⣿⣟⣁⡄
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠛⠶⣶⠊⠀⠀⠀⠀⢰⠏⠀⡐⠉⢈⠁⠢⠀⠀⠀⠰⠁⢀⣤⢶⣤⡀⠘⢄⣟⣧⣙⠾⠁
⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣀⠄⠢⢤⡀⠀⠉⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⢀⠀⠀⣀⠀⠄⠀⢾⡗⠀⢳⠀⠀⠀⠀⣿⣿⣿⣯⢷⠀⠀⠈⠉⢧
⠀⢀⣶⠛⣓⢦⡀⠀⠀⠀⠰⠁⠀⠀⠀⢱⡀⠀⠀⡤⠤⠤⠀⠀⠀⢷⠀⢰⠉⠀⠀⠈⠂⠀⠣⣄⣀⣠⡾⠀⠀⠀⠀⣿⣯⣽⣿⣿⠀⠀⠀⠀⢸⡄
⠀⠘⠛⠃⣓⣉⣡⠀⠀⠀⡄⠀⠀⠀⠀⠀⡇⠀⣾⠰⠁⢀⠚⢂⠀⠘⠆⢰⠀⠀⠀⠀⡄⠀⠀⠀⠉⠉⢳⡄⠀⠀⠀⢻⣿⢿⣥⣭⡀⠀⠀⠀⠈⡧
⠀⠘⣛⠋⢩⣏⣠⡆⠀⠀⢣⠀⠀⠀⠀⢠⠃⠀⢻⣤⢌⠈⡶⠾⠀⠀⠀⠸⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠻⡆⠀⠀⢹⣿⡟⣿⢿⠇
⠀⠀⠛⢏⢃⣠⣤⡅⠀⠀⠀⠢⣀⢀⡠⠊⠀⠀⠀⣹⠿⠷⠟⠁⠀⠀⠀⢀⠀⠀⠀⠀⡔⠀⢀⠤⠶⠶⢤⡀⠙⠆⠀⠀⠙⢿⠟⠋⠀⢀⡠⠤⠄⡀
⠀⠀⠀⠙⢿⠦⠊⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢰⠇⠀⠀⣠⢠⣤⢄⠀⠀⠲⢄⡀⠔⠁⢠⠓⠒⠤⠤⢀⣱⠀⠀⠀⠀⠀⢸⠀⠀⢰⠏⠀⠀⠀⠈⢂
⠀⠀⠀⠀⠸⡄⠀⣠⠖⠒⠠⠀⠀⡆⠀⠀⠀⢠⡏⠀⢀⢾⡼⣁⡽⠚⡇⠀⠀⠀⡇⠀⠀⢸⣆⠂⠠⠄⣀⡌⠀⠀⠀⠀⠀⢸⡆⠀⢸⡄⠀⠀⠀⠀⡸
⠀⠀⠀⠀⠀⡇⠰⡏⠀⠀⠀⠱⠀⡅⠀⠀⠀⠈⠀⠀⠸⡘⠃⢼⣙⣾⠃⠀⠀⠀⡇⠀⠀⣀⢙⠳⠶⠺⣏⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠙⢦⣤⠤⠒⠁
⠀⠀⠀⠀⠀⢳⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⣴⠯⠉⠓⠄⠙⠛⠻⡟⠁⠀⠀⠀⠀⡇⢀⡎⠀⠀⠀⡀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜
⠀⠀⠀⠀⠀⠉⠀⠟⡄⠀⠀⠀⡇⠀⠀⢸⡷⠐⠺⠣⠖⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠇⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠈⠫⣦⡤⠜⠀⠀⠀⣿⠃⠀⠀⣠⠃⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡱⠀⠀⠀⠠⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⣿⡟⢰⣎⡙⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⢿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣀⣠⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢐⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⢄⣀⠀⠀⠀⠀⣀⡠⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠒⠉⠀⠀⠀⠀⠀⠈⠑⠦⠔⠊⠁⠀⠀⠀⠀⠀⠙⠢⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠤⠒⠉⠀⠈⠑⠒⠤⢄⣀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⢻⠻⣿⣿⣿⣿⣭⣁⣈⣻⠉⠉⠉⠉⡏⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⢸⠈⠉⠉⢉⣋⣉⣭⣽⣿⣿⣿⠟⢩⠏
⠀⠀⠀⠀⠀⠀⠀⢳⡈⠻⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣷⣤⣤⣤⣤⣤⣼⣤⣤⣤⣤⣶⣶⣾⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀⠀⠈⠻⣿⣿⣿⠟⠋⠉⠉⠉⠙⢻⡿⠛⠋⠉⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⠟⠁⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⢨⠏⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡠⢬⡿⠁⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢠⠃⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠀⡰⠋⠀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡠⠊⠀⠀⠀⣠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠉⠀⠀⠀⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢀⠔⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢃⡠⠔⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠒⠒⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠚⠉⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⠋⠉⠉⠉⠁⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⠞⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣄⣀⣀⠀⠀⠀⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠐⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠈⠑⠲⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠲⠦⠤⠄⠀⠀⣀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠙⠢⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠀⠉⠓⠶⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠈⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠓⠒⠀⠀⠀⣠⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡀⣀⡤⠶⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠉⠉⠀⣀⣿⣤⣤⣄⠀⠀⠠⢄⣀⠀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠄⠀⠈⠷⣤⣄⠀⠈⠉⠁⠀⣠⠤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⢓⠐⠒⠘⢖⠀⠀⢙⡟⣠⠶⢲⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠧⠀⠀⠤⠳⣰⠟⣰⢋⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠰⡀⠀⠀⠑⣄⣠⡞⠃⣠⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢀⠀⠐⡄⠀⠀⠀⠙⠶⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⢠⡈⢃⠀⠙⠂⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢣⡈⠳⠐⠒⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢠⡀⠙⠁⢉⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠰⡄⠈⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠑⢦⠈⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣧⡴⠋

⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣿⣿⣿⣿⣿⣿⣽⣏⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠘⠋⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⣥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢚⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠟⠉⠉⠀⠀⠀⢁⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠁⠐⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⢀⢀⠠⠀⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⢀⠀⠀⠀⠐⠀⠀⠑⠈⢀⠀⠠⠀⠀⡤⢘⠢⠀⠀⠰
⠀⡘⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢟⠃⠃⡀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠠
⠀⠙⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⢄⠂⠀⠀⠀⠀⠀⠀⠑⠀⠄⠀⠀⠄
⠀⠴⠦⣖⠀⠀⢀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢦⠀⠀⠀⠀⠁⠀⠀⠀⠀⠚⠿⠁⠀⠀⠀⠀⠠⠀⠀⠀⠀⣀⡄
⠀⠀⠀⠈⠣⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⢀⡀⠀⠈⠀⠈⠀⠂⠁
⠀⡆⢐⠀⠈⠀⠤⠀⠐⠀⠋⠀⡄⠂⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠘⠟⠁⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠂⡀⠀⢠⡀⠀⡄⠐⢀⠀⠀⠀⡐⠌⢿⠀⠀⠀⠀⠀⠀⠀⠀⠰⢀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠈⠀⠀⠀⠀⠈⠏⢂⡈⠀⠀⡠⠀⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠤⠈⠀⠀⠀⠀⠀⠀⠀⢴⠀⠀⠀⠠⡀⠀⠀⡀
⠀⢀⠀⢀⠀⠀⠀⠈⠁⠀⠀⠀⠁⠀⢀⠄⠁⠐⠄⡄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡄⠊⠁
⠀⠀⡈⠉⠀⠀⠀⠀⠑⣄⠀⠀⠰⠀⡋⠀⠀⠀⡀⠐⠐⠁⠀⣐⠾⠛⠁⠀⢀⡀⠄⠀⢦⠢⣄⠀⣠⢀⠈⠈⠀⡄⠈⠓
⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠈⠑⠚⠓⠒⠂⠛⠀⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⠶⠶⠶⠤⠀⠀⠀⠀⠀⢀⠈⣜⡿⠿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⣠⣞⡽⠟⠯⠴⣶⢶⣦⣤⣀⢶⣶⡄⠀⣿⣻⣿⠁⠀⠀⠉⠙⢿⡇
⠀⠀⠀⠀⢰⣯⠟⠁⢀⣤⠶⠶⠤⠤⣈⡙⢷⣝⠇⠀⢹⣿⡟⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⢠⣿⠏⡠⠖⠋⠀⠀⠀⠀⠀⠀⠙⠄⢻⣆⠀⠸⣿⡇
⠀⠀⠀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⣿⠁⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢨⡟⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡇⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⣀⣤⡤⠶⠒⢂⣭⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠀⠀⠇⠀⣠⠆⠀⠀⠀⠀⣨⣴⠞⣋⠡⠐⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠉⠉⡑⢀⢢⡏⠀⠀⠀⠀⣰⠟⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣸⣷⣿⣷⣄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣟⣿⣿⣿⡙⣿⣿⣿⣛⣶⣆⠀⠀⢠⠄⠀⠀⢀⣠⡤⠴⠶⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣏⠀⠀⣸⣠⣤⠭⠖⠒⠒⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣶⡿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠟⠙⢿⣿⣿⣿⣿⣿⣿⠗⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠛⠋⠉⠡⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠙⠿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠈⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠸⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣷⣦⣿⣿⣆⠀⠀⠀⠀⠀⢀⣙⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⡿⠿⣋⠉⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠁⠀⠀⠀⠉⠒⢄⡀⠀⠀⠀⠀⠀⢻⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠋⠑⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠇⠀⠀⠀⠀⠈⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⣀⣴⣿⡿⠋
⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⣿⣿⣧⣄⠀⠀⠀⠀⠀⠀⠀⣀⣠⣷⣾⣿⠟⠋
⠀⣿⣿⣿⡉⠉⠀⠀⠀⠀⠉⢹⣿⣿⣿⣷⣶⣶⣶⣾⣿⣿⠿⠟⠋
⠀⠀⠙⣿⣿⡄⠀⠀⠀⠀⠀⠈⣿⣿⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⢸⣿⣇⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠈⠻⣿⣿⣿⣷⣦⡀⣸⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠛⠛⠛⠶⢤⣀⠀⠀⢀⣠⡴⠞⠛⠛⠛⠓⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠂⠀⠀⠀⠀⠈⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠀⠀⠈⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠈⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⠀⠀⡄⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⢀⣠⡴⠒⠒⠚⡏⠉⠉⠒⠒⠒⠲⠒⠒⠋⠉⠉⢹⠉⠑⠲⢇⣀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⢀⣤⣾⣿⣿⣧⣤⣄⣠⡇⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⢸⣀⣀⣠⣾⣾⣷⣶⣄⡀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⣠⣶⣿⣿⣿⡿⠟⠛⠛⠛⠿⠿⢷⣶⣤⣤⣤⣾⣧⣤⣤⣴⣶⡿⠿⠛⠛⠉⠉⠉⠛⠿⣿⣶⣦⣉⠄⠀⠙⠷⣄
⠀⠀⠀⠀⠘⣇⠀⠠⢴⣾⣿⣿⣿⡿⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠙⣿⣿⣿⣿⣶⠄⡀⣹⠆
⠀⠀⠀⠀⠀⠸⣆⠀⠀⢻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠃⠁⢠⡟
⠀⠀⠀⠀⠀⠀⢹⡄⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⣾⣿⡿⠁⠀⠀⡾
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠘⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠿⠁⠂⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠘⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠇⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠈⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⢰⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣶⡸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠶⢦⣤⣤⣤⣤⣤⣤⠴⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⡀
⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⡠⠀⠀⠀⠀⢀⡦⢄
⠀⠀⠀⢸⠀⡸⠁⠙⢉⠇⠠⠀⣠⢐⠚⣓⠢⢀⠴⠂⠀⣴⢿⡭⠭⡻⣧⠀⡀⠀⠀⠇⢰⠙⠒⡉⡂
⠀⠀⠀⢸⣰⠁⠀⠀⣌⠀⠐⠄⡁⠬⣶⡟⠁⣇⡄⠀⠸⢟⡸⡀⠀⡀⣸⠀⠀⠒⠊⢊⠓⠘⠉⢏⡿
⠀⠀⠀⢀⠏⠀⠀⠀⠘⡄⠀⠀⠉⢄⡀⢀⡜⠁⡂⠁⡄⠑⢯⢮⣯⠾⠋⡀⡀⠀⠀⠈⠦⠀⠠⠼⠃
⠀⠀⠀⠈⠉⠉⠉⠉⡉⢁⠀⡀⢠⣤⣄⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⡤⡌⣳⡁⢸⠂⡒⠄⠀⠀⠀⠒⡱
⠀⠀⠀⠀⠀⡲⢠⡀⠂⠠⠃⢱⡟⣷⡎⡆⠐⠂⢰⠀⢰⠅⠀⠀⠀⠈⠁⠉⠁⢸⠀⡃⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠄⢵⠐⠃⠀⣀⢀⢀⢉⡒⠊⠀⠀⠀⠈⠀⠀⡀⠀⡀⢀⠀⡀⠀⠀⠀⠰⠥⠤⠤⠤⠤⠤⠱
⠀⠀⠀⠀⠀⠀⠤⣸⣆⠹⢯⣟⡿⠃⠀⠀⠀⠀⠀⠀⠈⠀⠇⠑⠈⠠⠥⠀⠀⠀⠀⠀⢀⠰⠄⡀
⠀⠀⠀⠀⠀⢀⣀⡈⣁⡀⠀⠀⠀⡀⠀⠀⠙⠰⠁⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠈⡍⣔⠁⠀⠀⠈⡴⡆
⠀⠀⠀⠀⡊⠁⠀⠀⠀⣈⠄⢀⠙⢋⡇⠀⠳⠀⣉⣀⣀⠈⢸⢓⣲⢀⢨⣿⣔⡁⠀⢿⠀⣴⣶⡀⠃⣤
⠀⠀⠀⠀⠀⠁⠉⠉⠉⠁⠀⠸⠤⠼⠆⠀⠀⠂⠡⣀⡠⠒⠉⠉⡀⠘⠿⠟⠉⠀⢁⠀⠈⠛⠞⠁⡀⠽
⠀⠀⠀⢸⡑⢒⠒⠠⢂⡄⠀⠰⢪⢍⢢⠀⠀⢶⠀⡀⠀⠀⠀⡼⣁⣥⠀⠀⠐⠉⠂⠉⢢⣀⣀⡜⠁
⠀⠀⠀⠘⠁⠀⠒⠒⠂⠝⠀⠰⢌⡈⠜⠐⠟⠀⠐⠘⠀⠀⠀⠀⠃⠔⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁

⠈⣤⡄⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⡀⢀⣴⡄⠀⠀⠀⠀⠀⣀
⠖⠠⠀⠀⠀⠀⠀⠀⣿⠁⠀⡀⠄⠀⣤⢠⡀⠀⠀⠀⠉⠁⠀⢀⣤⣤⣾⠟⠃⠄⡀⠀⠀⡀⢰⠏⠛⠉⠀⠀⠀⣼⣾⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠟⠛⠇⠀⠉⠀⢠⠃⠟⠁⠀⠀⠆⠀⠀⢰⡇⠀⠀⠙⣧⠀⠀⠉⠓⠘⠏⠀⠀⠀⠀⠀⠀⢰⣏⣠⣶⣿
⢺⡏⠀⠀⠀⠀⠀⠀⣾⣷⣶⣶⣆⢸⣶⣦⡀⢀⠀⠀⠀⠀⠈⠁⠀⡀⢀⣍⠀⠀⠀⠀⡹⠀⣤⠶⠀⠀⠀⠀⣿⢻⡟
⠘⠁⠀⠀⠀⠀⣠⢾⡿⠛⠋⠁⢙⣿⣭⣥⣿⡿⠿⢷⡀⠀⠀⠀⠀⢠⣿⡟⠀⠀⠀⠀⢻⡿⠇⠀⠀⠀⠀⠀⠻⠘⠃
⠀⠀⠀⠀⢀⣀⡛⠚⠃⠀⠀⠀⠈⠉⢨⣿⠁⠀⠀⠀⢹⠀⠀⠀⠀⠸⠟⠃⠀⠀⠀⠀⠘⠟⣀⣤⣶⣶⣦⣴⣄⡀⣦
⢀⡄⠀⠀⢀⣇⣿⠛⠂⠀⠀⠀⠀⣿⣿⢻⠀⠀⠀⠀⢸⣠⣤⣼⣷⣷⣶⡄⠀⠀⠀⠀⠀⣇⠝⠛⠿⣿⣿⣿⣿⣿⣿⣦⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢋⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠉⢑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠚⠉⣆⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⣧⡟⡡⣼⣆⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⠃⠀⠀⠀⣥⡀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡞⠄⢁⠘⣹⣄
⠀⠀⠀⠀⠀⠀⠀⣠⠖⢩⠏⢀⠜⠉⢻⣮⣞⡵⠞⠀⠀⠀⢀⠔⠊⠉⠀⠀⠈⠡⣄⣀⣀⠤⠃⠀⠀⠀⣠⠲⢉⠑⠈⡁⠃⢦⣰⣠⡥⠟
⠀⠀⠀⠀⠀⠀⣾⠃⡰⠁⡰⠃⢀⠔⢹⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠞⠍⡈⠰⢈⠐⠂⡁⣺
⠀⠀⠀⠀⠀⣸⠃⡰⠁⡜⠁⡠⠋⣰⡟⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⣮⠁⡂⠄⢈⠰⢈⠁⣢⠏
⠀⢀⡤⢒⣶⠿⣤⠃⡜⠀⡰⢁⡾⠋⠀⠀⠀⡠⠔⠒⠚⠆⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⢀⡴⠲⢒⠳⡂⠄⡁⠐⢨⣐⡾⠋
⠀⠘⢎⡥⠊⣸⢹⠏⠙⠛⠉⠁⠀⠀⠀⠀⠀⠧⣀⠀⠀⠀⡟⠙⠛⠋⠉⠀⠀⠀⠀⠀⠸⢅⡐⠠⠀⢼⠉⠛⠛⠉⠁
⠀⠀⠀⠣⢴⢃⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⡄⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⣄⣃⡟
⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⠶⢦⣄⡀⢀⣠⣴⠶⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠉⠛⠛⠉⠀⠀⠀⠀⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⣠⣤⠶⠟⠛⠉⠉⠉⠉⠛⠳⠶⣤⣄⡀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⣴⠟⣁⣠⣤⡶⠟⠋⠁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠉⠛⠳⢦⣤⣀⡈⢳⣄⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠻⣿⣿⣏⣩⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣍⣹⣿⣿⠏⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠻⣿⣿⣿⣿⠿⠟⠛⠛⠻⠿⢿⣿⣿⡿⠛⠉⠉⠉⠉⠉⠛⠿⣿⣿⠟⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠹⣿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣴⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠘⢿⣟⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠙⢷⣌⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠈⠙⠻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣄⡀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠳⠶⠶⠶⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠶⠖⠛⠛⠋⠁




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

⠀⠀⢀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠈⡃⢄⠀⠸⣧⠯⠃⠀⠀⢀⣀⣐⠀⠉⠁⠀⠀⠐⠀⠠⢀⠀⠀⠐⠻⡟⠂⠀⠀⠀⠀⠐
⠀⠐⢤⠃⠀⢀⠔⡅⠀⠀⠐⣋⠤⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⢀⣀⣂⣀⠀⣴⠆⠾⠇
⠀⠀⠀⢀⠔⢁⠢⡇⠀⠀⠀⠀⢀⡀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠈⠽⠒⠅
⠀⢀⡔⠁⢌⢢⢳⡇⠀⢹⡃⠀⣸⠁⠀⠀⠀⢀⠀⠀⠀⠀⠀⠁⠈⠀⠤⠑⡄⠀⠀⠀⠀⣤⡞⠀⠹⠆⠬
⠀⠫⣉⠉⠚⢦⣻⠁⠀⡈⠳⠎⢸⣀⠄⡟⢃⡠⢧⣀⠀⠀⠀⠀⠀⠀⠘⠀⢀⡠⠒⠀⠋⠀⠑⢲⠊
⠀⠀⠈⠉⠓⠒⠛⠀⠀⡷⠴⢶⣺⢅⡜⠀⠀⠹⢪⠋⣹⠒⠶⠤⢤⠴⠶⡊⠟⣄⠴⠄⠈⠁⠲⠉⠀⢠⠄
⠀⠀⢀⣀⣀⡀⢀⣀⠀⠫⠻⣷⣮⡟⢠⢒⡒⢄⠀⠉⠀⠃⠰⠢⠌⠦⠆⠈⠃⠈⠀⠀⠀⢀⡈⠀⠀⠈⠂
⠀⠀⠙⢄⠀⢠⡋⠶⠥⡀⠀⠀⣀⠀⢧⡇⠈⢪⡄⣰⠞⠉⢢⠀⠀⢤⠀⠀⢰⠠⠂⠀⡠⢊⢁⠝⠑⠒
⠀⠀⣀⠀⠑⢼⢢⣔⠀⠉⠳⣄⣈⣯⠚⠿⣄⠌⣷⡟⠀⣀⠎⠀⠒⠈⣁⣠⠤⠒⠂⠀⠀⠁⠃⠔
⠀⡰⢤⡂⠐⣢⠉⠈⢳⡉⣉⠽⡏⠉⡑⠲⢬⡟⢙⣶⣚⣉⠙⢧⠀⣸⠑⠀⡗⠀⢀⠀⠀⡠⠀⠀⠀⠠⡀
⠀⠰⠔⠄⢀⡽⡄⠀⠀⠻⠴⡞⠁⠀⢦⠀⢠⠀⢀⡀⢀⡰⠀⠀⠀⢇⢀⡔⠱⢄⡜⠀⢠⠁⠀⠀⠀⠀⠄
⠀⠀⢀⣀⣸⢀⠇⢀⠀⠀⠀⢹⠀⠀⡆⠀⢸⠀⠀⠀⢠⠀⠀⠀⠀⡨⠉⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢠
⠀⠀⢘⢒⠢⡿⠤⠒⡃⠀⠀⢸⠀⠀⡇⠀⢸⠀⠃⠀⡆⠀⠀⠀⠴⡇⠀⠀⠀⢠⡼⠤⢀⡆⠄⠤⠒⠁
⠀⢀⣸⠂⠈⠑⠎⢸⠀⠀⢿⡛⣏⠀⠉⠉⠉⠘⠒⠒⠃⠀⢠⡤⠐⠀⠤⠶⠂⠀⠀⠀⠙⠂
⠀⠘⠤⣑⣦⣤⣔⡃⠴⠀⡰⠉⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⡇⠃⡰⡟⣭⣕⡄⢯⡟⠀⠀⠀⢀⣸⠙⣳⠆
⠀⠀⠀⠈⣒⣒⡉⠀⠀⠀⠀⠀⠴⡀⠀⠀⠢⡁⢀⡀⢀⣀⢧⣆⠘⠷⢝⠿⠃⢀⠀⠂⠀⡠⠢⡀⢙
⠀⠀⢠⠊⡉⢳⣹⣀⠠⠰⣷⠄⠣⡁⠠⠀⢠⣌⠀⠲⠟⠉⠀⠉⠑⠒⠀⠀⠀⠀⠀⠀⢀⡫⠒⣠⠏
⠀⠀⠈⠦⣑⣊⣁⣀⠤⠒⠉⠀⠀⠈⠢⠘⠋⠈⠀⠈⠀⠈⠀⢠⡀⢢⠘⢑⡀⠀⠀⠀⢏⣋⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠁⠁⠊⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠈⠒⠒⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠁⡀⡀⠐⠈⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠈⠉⠀⠀⠀⠀⡠⠈⠈⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠐⠀⡠⢅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠈⠀⠀⠀⠁⠤⠤⠠⠄⠀⠀⠀⢀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠁⠀⠀⠀⠀⠀⠈⢀⠀⠀⠆⠀⡰⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⣈⡂⠤⣀⣈⠀⠀⠀⡀⠈⠀⠀⠀⡊⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡈⠓⠀⠀⠄⠄⢀⢀⣱⠀⢠⠴⠁⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠈⠤⠀⠰⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠈⠂⠀⠀⠀⠀⠄⠀⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⡀⠀⠈⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠐⣹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⢂⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠐⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⡀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠠⢀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠐⢸⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣣⣊⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣛⣟⣛⣻⣟⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⡟⣫⣴⣶⣶⣬⡻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠉⠛⠦⡄
⣿⣿⣿⣿⣿⣿⡟⣼⣿⣀⣿⣅⣽⣿⡸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣼⠁⠰⠷⠀⠿⠀⠹⡆
⣿⣿⣿⣿⣿⣿⣇⢻⣇⠻⠿⠟⣡⣿⢡⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⢻⠀⢧⣄⣀⣤⠇⢠⠇
⣿⣿⣿⣿⣿⣿⣿⣦⣙⠿⠿⠿⢟⣡⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠳⣄⣈⣉⣀⡴⠋
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠸⡄⠀⠀⢠⡆⠀⠀⢷⣀⣀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠈⠳⢄⣀⣀⣀⠀⠀⠀⠀⢧⠀⠀⠀⠀⢧⠀⠀⠀⠓⠒⢠⡄⢸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⢠⣦⣤⣭⠉⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠁⠒⢶⣾⡿⣼⣿⠤⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⢀⣤⣽⣿⣿⠋⠀⠠⡇⠀⠘⠲⣄⡀⠉⠓⣆⠀⡀⣠⣿⡇⠿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠠⡌⣿⣿⣿⣿⠀⢤⠀⠑⣄⠀⠀⢸⡇⠀⢠⣿⣿⢡⣿⣿⡧⠔⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢹⣮⣿⣿⣿⠀⢠⡆⠀⢸⡇⠀⢿⣷⡆⣿⣿⣿⣤⠉⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⣈⣻⣿⣿⠇⠀⣾⣇⠀⠈⢷⡄⠘⣿⣇⠻⣿⣿⣽⡷⠊
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⢼⣿⣿⡿⠋⢠⡀⣼⣿⠂⠀⢠⡇⠀⢸⡿⢠⠈⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⢠⣶⣼⡿⠿⠟⠋⡴⢀⡜⠠⣿⣏⠀⢀⣾⠁⢠⡿⠁⣠⣾⣿⣻⠄
⠀⠀⠀⠀⠀⠀⠀⠀⡾⢠⡟⠋⠀⢠⠄⡗⠰⡃⠀⢸⠀⣿⠹⠀⢸⣧⡀⢸⣇⢠⡿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⡰⠃⠋⠀⠀⣇⢸⣆⣻⣢⠟⡤⠿⠶⠿⠧⣤⣾⡿⢃⣤⣿⠸⣧⣤⣤
⠀⠀⠀⠀⠀⢀⠊⠀⠀⢠⢸⣧⠿⠊⠉⠉⠀⠀⠀⠀⠀⠒⠒⠒⠈⠽⢿⣿⣿⠶⠿⠛⠛⠁
⠀⠀⠀⠀⠀⣧⣤⣴⣶⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⡤⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⣰⣾⣿⡿⠋⠁⢀⣠⣶⣿⠿⠟⠛⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⢀⣾⣿⣿⢋⣀⠤⠴⠿⣿⣯⣥⣤⣶⣶⣶⣶⣶⣶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⣼⣿⣿⠟⠋⢁⣤⣶⣿⣿⡿⠿⠟⠛⠿⢿⣀⡀⠉⠉⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⣿⡇⢀⣿⠟⠁⢀⣴⣿⣿⣟⣭⣤⣤⣤⣤⣤⣤⣤⣬⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣿⣇⣼⡏⠀⢀⣾⣿⡿⠿⠿⢿⣿⣿⣿⣿⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠹⡟⣿⠀⠀⢸⡟⠁⠀⣠⡄⠀⢨⣿⣿⣿⣷⠈⢳⡌⠙⠋⢿⡆⠈⠛⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⠘⣿⡆⠀⠸⠀⢠⣾⣿⡇⠀⢸⣿⣿⣿⣿⠀⠈⣿⣦⡀⠀⣷⡄⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣄⠀⠀⠻⠀⢿⣷⡀⠀⠀⢸⣿⡆⠘⣷⣼⣿⡿⣻⠏⠀⢠⣿⡿⢿⣆⡹⣿⣦⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣤⡀⠀⠘⣿⣷⡀⠀⠈⢿⣿⣄⣈⣛⣛⡁⢁⣠⣴⣿⢿⣧⠈⢻⣿⠈⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⣷⣦⡈⠻⣿⣦⣄⠀⠈⠛⠻⢿⣿⣿⣿⡿⠟⣁⠘⣿⡇⢸⣿⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠙⠛⠛⠷⠈⠛⠿⣿⣶⣤⣄⣀⣀⣀⣤⣴⣾⡇⠀⣿⡇⢻⣿⡆⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⢶⣶⣶⣶⣶⣿⠿⠋⢙⣿⡿⠛⠉⢩⣿⣿⠃⢸⡿⠁⢸⣿⡇⠰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠩⣭⣉⣉⣠⣤⣾⠿⠋⠀⢀⣴⣿⣿⣿⣿⡿⠁⢀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⢀⣀⣤⣽⣿⣿⣿⣿⠟⠁⢀⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⢀⡴⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡿⠿⠛⠛⠛⠉⠉⠀⠀⠈⠁


















⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣿⠋⠉⠉⠉⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡶⠶⠶⠶⠶⠶⢦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠋⠀⠀⠀⣀⡤⠴⠖⠒⠒⠒⠦⢤⣀⡀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⣄⠀⠀⠈⢻⣆
⠀⠀⠀⠀⠀⠀⢠⡟⠁⠀⠀⡰⠋⠀⠀⠀⢀⡠⠴⠒⠒⠲⠤⣄⠀⠀⠀⠈⠱⡄⠀⠀⢻⣆
⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⣸⠁⠀⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠘⡄⠀⠀⣿⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⡼⠀⠀⠀⢀⠖⠒⠒⢦⡀⠀⠈⣆⠀⠀⠀⢱⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⡇⠀⠀⠀⣇⠀⠀⠀⢸⠀⠀⠀⠀⢷⠀⠀⢸⠀⠀⠀⢸⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⡀⠀⠀⠘⢆⠀⠀⠈⠀⠀⠀⢀⡇⠀⠀⣸⠀⠀⠀⢸⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠳⡄⠀⠀⠀⠙⠲⠤⠤⠤⠖⠋⠀⠀⣰⠃⠀⠀⠀⡏⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠈⠲⣄⡀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⡼⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠉⠙⠒⠒⠒⠒⠋⠉⠀⠀⠀⠀⣠⠞⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⣁⣤⠾⠋⠀⠀⢀⡠⠄⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠷⣦⣤⣤⣤⣤⣤⣴⣚⣭⣥⡶⢿⡏⠁⠀⠀⢀⠔⠁⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⢻⣆⠈⢿⡀⠀⠠⠀⠀⠀⠀⠀⡰⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⢻⡄⠘⣷⡀⠁⠀⠀⠀⠀⠈⠀⠀⠁⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⠈⠁⠒⠨⣿⣄⡸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡀⠀⡀⠀⠠⠄⠂⠙⡄⠀⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠽⣶⠈⢹⣇⠁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠹⣧⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⢀⠤⠊⠀⠀⠀⠀⢹⣆⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣀⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡗

⠀⠀⠀⠀⣠⡄⠐⠀⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⣤⠀⠀⠀⣶⠀⠀⠀⡀
⠀⠀⠀⠀⠉⠀⠀⠀⠈⠂⢀⡄⠀⠀⠀⢠⠀⠀⠀⠿⠀⠀⠀⠀⠈⠓⠀⠀⠘⣿⣦⣾⡏⠀⠀⣠⣡⣄
⠀⠀⠀⠀⣠⣄⠀⠀⢡⠀⣾⣇⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢻⣿⣿⠃⠀⠀⠙⠿⠁⠀⠀⡒⠄
⠀⠀⠀⣰⣿⣿⡀⠀⠀⠀⠈⠉⠀⣴⣶⣶⠀⠀⢸⣿⡇⠀⠀⠰⢿⣿⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⡆
⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⣿⡏⣿⡇⠀⠈⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⣿⡇
⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣿⡇⠀⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⢹⡇
⠀⠀⠀⠀⠀⢄⠀⠀⠤⠀⠀⢀⠀⢻⠀⢹⡇⠀⠻⠛⣇⠀⠀⠀⡀⡀⠀⠀⢀⠀⠀⠀⢀⡀⠀⣀⠀⡀⠀⠟⠀⠸⠇

⣶⣶⡶⣶⠶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⡰⢄⠈⠀⠀⢀⠀⠀⠅⠑⢶⣦⣄⣀⠀⠀⠀⠀⠀⠈⠀⠀⠰⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⣁⣀⡴⠖⢾⡟⠀⢀⠀⠀⢀⢀⡄
⠀⠀⠀⠃⠦⠈⢱⠚⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠶⠈⠡⠈⢲⣶⠄⣠⠠⣤⡀⢠⡤⣀⣀⣀⢀⠄⣀⣤⠀⠄⠰⡶⠒⠄⠉⠏⠁⢀⠀⠀⠀⠈⠀⠐⠲⠖⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠈⠀⠛⠀⠀⠀⠈⠟⠁⠁⠀⠙⠁⠀⠚⠂⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣈⠻⣤⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⣀⡸⠟⠀⠀⠀⠀⠀⠀⣶
⠀⠀⠀⠀⠀⠠⠉⠀⠀⠀⠀⠀⠁⠀⠀⠊⠀⠈⠓⠖⠒⡀⠤⢤⠀⠀⢀⣀⠀⠀⢌⡀⢀⠀⠀⣠⠶⠤⡤⢀⠀⠰⠛⠀⠸⠁⠉⠉⠀⠅⠀⠀⠀⠈⠁⠀⠀⡏⡆
⠀⠀⠀⠀⠀⠀⢠⠄⠀⠀⠤⠀⠠⡖⢆⠀⠰⣴⡄⠀⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠶⠈⠀⠀⠀⠃⠀⠀⠀⡀⠀⠈⠀⠀⠀⠀⣀⠈⠀⠀⠈⠀⠀⠀⢱⣃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠽⠁⠀⠀⠀⠁⠀⠀⠀⠺⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠘⢶⡄⠀⠀⢀⣀⠀⢀⡈⠰⠆⠀⠀⠀⠁
⠀⠀⢤⣴⠾⠶⠶⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠆⠀⠐⠀⠀⠘⣛⢂⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢺⠂⠄⠈⠁⡀⠈⠈⠒⢀⣀⠀⠰⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⣤⠀⠀⠀⠀⢸⡅⠀⠀⠀⠀⠀⠁⠈⡀⠀⠀⠈⠁⠀⠀⠆⠁⠀⠐⠦⡈⠉⢠⠀⠀⠀⠉
⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠠⠀⠈⠁⠀⠀⠀⢀⡰⠒⠇⠀⠰⠂⠀⡀⠀⢀⠀⠈⡧⢀⠀⠀⣀⠈⠉⠁⠀⠀⠀⣃⡦⠀⢀⠇⠐⠀⠀⠀⠺⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠈⠋⠀⠀⠀⠀⣀⣷⣄⢈⡧⠀⣧⠈⡷⡀⢨⣦⣀⠀⠀⠀⣠⡝⠀⠀⠀⠀⢀⠤⠈⠀⢠⡦⠀⢀⠀⠘⠛⠅
⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠈⢀⠊⠀⠀⠀⠀⠀⠀⠒⠈⠀⠐⠣⡾⢀⡨⠉⡍⢛⡍⣯⠉⡍⡈⢺⠀⠀⠁⠛⠀⠀⠀⠘⡐⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⢤⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠀⣇⡘⡄⢀⢁⠉⡍⣀⢠⢀⡁⣸⠀⠀⠀⣀⡀⠀⢀⠟⠀⠀⠀⠰⠆⠘⠇⡀⢀⠀⡀⠌
⠀⠀⠀⠀⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣘⣋⡶⣀⠏⡇⠀⢿⡜⠙⠇⠘⢿⣟⠃⢙⠛⡆⠀⠉⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠆⣁⠘⠀⠀⡀
⠀⠀⢀⠀⠀⠀⠀⠀⠉⠀⠸⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⡟⠘⠃⢀⠻⠃⢀⠓⠀⠘⠀⠐⠎⠁⠆⠉⠰⡧⠀⠀⠠⠀⠀⠂⠀⠀⠀⠀⢀⠀⠀⠀⣀
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢆⠂⠀⠀⡀⠀⠘⠋⠀⢀⠘⠁⠀⠘⠁⠀⠀⠖⠀⠛⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⢢⣶⠱⠀⢿⠎⠀⣀⢠
⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⢘⢥⠀⡛⠩⣀⠀⠀⠀⠈⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⣣⣾⠃⠀⠀⠀⠸⢛⠄⠀⠀⠶⠃⠚⠛⢠⣤⣿⠂⠁
⠀⠀⠀⠀⡀⠀⠄⠀⢀⠀⠀⠀⡠⣤⠀⠀⠀⠀⠘⣞⠀⣟⠢⠤⡉⣀⠒⠀⠀⠀⣀⠤⠤⠤⠐⠒⠀⠀⣈⠔⠀⡀⠀⠀⠀⠀⠀⠀⠚⠠⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠁⠀⠀⠈⠇⠀⠘⠛⠁⠀⠀⠀⡀⠀⠉⠀⢨⠙⠲⢤⣄⣀⣀⡀⠀⠀⠀⢀⡀⠠⠄⠒⠋⣀⠄⠨⢁⣀⠀⠀⠀⠀⢀⣀⠂
⠀⠀⠀⢠⣊⣅⡰⢄⡀⠀⠂⠀⠀⠀⠀⠀⠀⠛⢋⠉⠉⠀⠑⠢⠤⠄⢈⣉⣉⡉⠉⠉⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⠀⠀⢀⠀⠀⠉⠀⡀⠀⠀⠀⠄⠀⡄⠠
⠀⠀⠀⠘⠉⠞⠀⠙⢍⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠠⠄⠀⣰⣆⠀⡀⠀⠀⠀⠀⠠⠊⠀⠰⣤⠶⢎⡛⣠⣀⢠⡄⠀⠀⢈⠀⠈⠱⠀⠀⠠⡄⢸⠀⡇⢀⠆
⠀⠀⢠⡄⠀⠀⠀⠀⠀⠘⠌⡆⠀⠀⠈⠀⠀⠀⠀⢹⠀⠀⠀⠘⠳⠦⠴⠁⣁⣀⣴⣄⠀⠐⠀⠀⢬⣻⢨⣻⣯⢹⣶⢃⡢⠀⠠⠀⠁⢨⠀⠀⠀⡇⢸⠀⣇⢸
⠀⠀⠀⠀⠀⠈⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠾⠿⡧⣥⢿⣼⡇⠀⠐⠐⠒⠐⠀⠀⠀⠁⠈⠀⠁⠈
⠀⠀⠀⠀⠠⠤⠀⠛⠠⠤⠤⠀⠀⠈⠑⣄⡀⠐⠀⠉⠁⠀⠁⠘⠈⠁⠀⠀⠀⠀⠀⠀⠁⠀⡀⠀⠀⠀⠀⠀⠁⢻⠶⠜⠃⠀⠰⣤⠖⡩⡀⠀⢴⣤⠀⠀⠠⠈⠓
⠀⠀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⢑⠑⡇⠀⠀⠁⣀⠀⢀⡤
⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠉⠀⠀⠀⠀⠾⢗⠀⠀⢤⡀⠀⠀⠀⠀⠄⡀⢸⣦⠀⠀⠈⠀⠀⡅⠀⠀⢀⠀⠑⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠙⠛⠉⠀⠒⠀⠀⠀⠄⠀⠀⠀⠀⠈⠙⠀⠀⠀⡐⠿⠁⠈⠋⠀⠀⠠⠀⠰⠀⠀⠀⠈⠀⠀⡀⠇
⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠄⠀⠀⠠⠠⠄⠤⠀⠄⠀⠠⠀⠴⠤⠀⠐⠀⠀⠙⠿⠂⠀⠀⠀⠀⠀⠀⠀⢂⡟⠁⠀⠀⠀⠀⠀⠀⣠⣄⠀⠀⠀⠀⠀⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡀⠀⠀⢀⣠⣴⠂⠈⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠾⠛⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠐⣡⠊⠀⣀⣴⣿⣿⣿⣷⣤⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠉⠀⠀⠀⠀⣠⣼⠟
⠀⠀⠀⠀⠀⠀⠀⢀⠜⠀⣠⣾⣿⣿⣿⣍⠛⠿⣿⡏⠀⠀⠀⠀⠀⠀⠀⢀⠴⢋⡡⠄⠀⠀⣀⣤⣶⡶⠛⠉
⠀⠀⠀⠀⠀⠀⣠⠃⢀⣼⣿⣿⣿⣿⣭⡭⣤⣼⡏⠀⠀⠀⠀⠀⠀⠀⢀⠥⠚⠁⣀⣤⣶⣿⣿⣿⠟
⠀⠀⠀⠀⢀⡴⠁⣴⣿⣿⣿⣿⣿⣏⡉⣡⣌⣿⠁⠀⠀⠀⠀⣀⠄⠊⢁⣠⣶⣿⣿⣿⣿⣛⡿⠃
⠀⠀⠀⡠⠊⣠⣾⣿⣿⣿⣿⣿⡟⠛⣛⣀⣹⡏⠀⠀⣀⠔⠊⢀⣴⣾⣿⣿⣿⣿⣿⣿⣻⣿⠁
⠀⢀⡜⢁⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⠎⠙⣿⣧⡴⠊⢁⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⡟
⢰⡟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣽⣿⣿⠀⠲⣾⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣛⣫⡿⠁
⠀⠱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡙⢷⣾⣿⣿⡄⠀⠘⢿⣿⠋⣤⡤⠈⣿⣿⣿⢿⣿⣿⡇
⠀⠀⠀⠻⢿⣿⣿⣿⣿⣿⣿⣿⣋⣤⣶⣾⣿⡇⠀⠀⠀⠉⠳⣄⣁⣠⣿⣿⣿⠷⠘⣿⡇
⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⡿⠿⢿⣿⣿⣿⣯⡹⣆⠀⠀⠀⠀⢹⣿⣿⣿⠿⠿⠿⠷⣮⡁
⠀⠀⠀⠀⠀⠀⠀⢹⡿⠋⠀⠀⠀⠈⠁⠈⢻⡇⠈⡆⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⢰⡀⠀⠀⠀⠀⠀⠀⢀⣀⡄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡖⣀⠀⠀⠀⠀⢹⣇⠀⣧⠀⠀⠀⠀⠀⠀⢼⠿⠷⠆⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠛⠋⠀⠀⠀⠀⠀⢿⡄⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣿⣇⡘⠀⠀⠀⠀⣿⣶⣶⡆⠐⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣿⠁⡀⠀⠀⠀⢙⣽⣿⣷⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣏⣰⣡⣤⣤⣶⣿⣿⣿⣿⣇⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⣾⡿⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⢰⣿⠇⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⣇⢀⣠⣿⡿⡀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⢀
⣿⣿⣿⣻⣴⣠⠾⠀⠄⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⠀⣼⣿
⣿⣿⣿⣿⣿⣿⣿⣦⣄⣰⣌⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣧⡄⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠐⡅⠈⠀⠐⠀⣀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⠐⠝
⣤⣤⣤⣴⡿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠈⠉⠐⠂⠀⠌⠳⠀⠀⠀⠀⠀⠀⠀⠐⠂
⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⣀⣀⣄
⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠿
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠤⢤⣄⡀⠀⢠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠚⠀⠠⣌⠹⣷⣧⡞⠁⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣆⣄⡀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⢸⡘⢋⣴⣬⣦⢹⡆⣹⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠈⢻⣿⣦⠄⠂⠀⠀⠀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠉⠛⣿⢏⡾⠃⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⣄⢢⡀⣹⣦⣀⣠⣿⣿⣾⣛⣁⣠⡴⠏
⠠⡄⠀⠀⠀⠀⠀⠀⠀⠈⠙⡛⠋⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠛⠉⠛⠿⠛⠛⠉
⠀⢇⠑⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⡀⠄
⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⣾⡧⢀⡀
⠀⠙⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⡀⠀⠈⠀⠀⠀⠀⠸⠏⠀⢸⡿⢦⣄
⠀⠘⣦⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣧⠀⠀⠀⢰⡀⠀⠈⡄⢈⣄⡽⠶
⠀⠀⠘⢟⣀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⢀⣀⣿⡗⠠⠖⠛⠋
⠀⠈⠉⠉⢿⣧⣤⣴⠞⠉⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣿⠿⠃
⠀⠀⠀⠀⠈⠙⠛⣿⣤⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢀⡴⠀⢊
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠼⠁⠀⠁⢀⡀
⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢰⣦⠤⡄⠀⡀⠀⠀⠀⠀⠀⠀⠑⠒⠶⠦⠴⠾⢿⣷⣦⡤⠀⠀⢀⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡎⠀⣠⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣍⡉⠝⠉⠁
⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣾⣿⠀⠀⠀⠀⠐⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡿⠌⠑⠄⠀⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿

⠀⠀⠀⠀⠀⢀⠠⠄⠀⢠⢄⡀⡚⠑⠀⠂⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠠⣀⡀
⠀⣂⠳⣠⡴⢯⡁⠀⣈⠆⠀⢙⡤⠞⠀⢰⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢀⠃⠴⠙⡌⠄⢉⠁⠉⢳⠆⠀⡆
⡠⠊⠀⠀⢀⠝⠻⠀⠀⠠⣀⠇⣷⢴⠈⡡⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠊⢀⡈⣣⠀⢸⠀⢸⡄⣈⡿⢗⡔⠊
⠣⠀⠖⠣⡈⢑⣔⡌⡈⢂⢐⡶⠙⠢⠤⠃⠀⠀⣠⠄⠰⠒⣒⡲⠂⠤⢄⠀⠉⣟⡴⠈⠁⠁⠋⠁⠉⠉⠉
⠀⠀⠀⠀⠈⠁⠀⠉⠒⠊⠁⠀⠀⠀⠀⠀⠀⠘⠂⠬⠄⣋⣉⣉⣑⡍⠴⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⣀
⠀⠀⠀⠀⢀⡠⠊⠁⠀⠀⠉⠢⡀⠀⠀⠀⠀⠘⠀⣐⠀⠀⣀⠀⢀⣇⠜⠁⠀⠀⠀⠀⠀⠀⠠⠎⠀⠀⢠⠒⡋⢂
⠀⠀⠀⢀⡀⠣⡀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠔⠀⠀⠆⠈⠀⢎⡀
⠀⠀⠀⠀⡓⢄⡈⠢⠄⣀⢀⣀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠂⠠⠄⣀⠀⠀⠀⠀⠀⢆⠠⠀⠀⠀⠤⠜⡀⠁
⠀⠀⠀⠀⠘⢄⡈⠀⠂⠠⠀⡴⠊⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⡀⠀⠠⠖⠉⠀⠀⠉⠰⠆⠀⠀⠙⠠⠠⣠⠶⠊⣑⡢
⠀⠀⠀⠀⠀⡸⠈⠗⠒⠒⠉⠀⠀⠀⠀⠀⣀⣈⠓⢆⠀⠀⠀⠀⠁⠀⠲⠄⠀⠂⠀⠀⡸⠀⠀⠀⠀⠐⠂⠑⠂⠐⡄
⠀⠀⠀⠀⢠⠃⡌⠀⠀⠀⠀⠀⣀⠤⠒⠉⠀⠀⠀⡀⠛⠶⠄⣀⣀⠤⣄⠀⢸⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐
⠀⠀⠀⢠⠃⡘⠀⠀⠀⠀⠀⠀⠣⢄⡂⣄⣀⣀⠬⠄⣀⡀⣀⠐⠉⠂⢈⡄⠈⠁⠀⠀⢀⡠⠴⠲⠶⢤⡀⠀⠀⠀⠂
⠀⠀⠀⠁⠴⠁⠀⠀⠀⠀⠀⠀⠑⠤⣈⡀⢀⡅⠀⠀⣇⡀⢀⡁⢀⠜⠚⠀⠀⠀⢀⠞⠁⠀⢀⣀⡀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⡀⠉⠀⠀⠀⠀⠀⠀⡟⢀⣀⠔⢁⣄⢹⠃⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣦⠀⠢⡀⠀⠀⠀⠀⠀⢧⡀⢸⡀⡨⠶⠚⠠⣀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠐⠂⠛⢍⢂⠀⢱⡄⠀⡃⠀⠀⠀⠀⠀⠀⠑⠯⣙⣦⡤⠴⠞⢁
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠤⣒⠈⠁⠀⠀⠑⡀⠀⢀⣦⠴⠋⠉⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠱⡀
⠀⠀⠀⠀⠑⡒⠠⠤⠀⠑⠄⠑⠠⣀⡠⠴⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠘⢆
⠀⠀⠀⡏⠀⣈⣒⡖⠊⠤⠤⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣶⣶⣤⣤⣤⣤⣤⣤⣤⣴⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠟⠋⠉⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠈⠉⠛⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⠀⢀⣀⣤⣴⣶⠿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠿⢷⣶⣤⣄⣀⠀⠀⠈⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⣰⡿⢃⣠⣴⣾⣟⣛⣉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣙⣻⣿⣶⣤⣀⠻⣷⡀
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠷⣶⣶⣶⣶⣶⣶⣶⡶⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⡄
⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⣿⡿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡿⣿⡟
⠀⠀⠀⠀⠀⠀⠹⣿⡄⠉⠙⠛⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠛⠉⠁⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⢀⣼⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣼⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣶⣶⣶⣶⣶⡾⠿⠛⠉

⠀⠀⠀⠀⠀⣠⣶⣦⡀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⡀⢻⡅⠈⢇⡴⠛⠻⡷⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣶⣦⣄⡀
⠀⠀⠀⠈⣛⣓⣚⣓⡰⢦⣴⣚⣵⣶⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠟⠻⢿⠿⠛⠿⠷
⠀⠀⠀⠀⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢹⣿⣿⣿⡇⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⡀⣀⢀⣀⡄
⠀⠀⠀⠀⠘⣿⣿⣿⡇⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣦⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠛⢠⣶⣶⣄
⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿
⠀⠀⠀⠀⣠⡝⠒⠶⠶⠶⠶⠶⠖⠒⣄⡀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⣌⠙⠟⠁
⠀⠀⠀⠘⠿⢿⣷⣶⣦⣤⣤⣴⣶⡿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠁⢻⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇
⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⠇
⠀⠀⠀⠈⠉⠙⠗⠲⠶⠶⠶⠶⠲⠖⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠉
⠀⠀⠀⠀⠀⠀⠐


⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢸⠘⠀⠇⡇
⠀⠀⠀⠀⠀⠈⠉⠂⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣶⣶⣶⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⡀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣭⣭⣭⣭⣭⣭⣭⣭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡓⠂⠀⢠⡿⡀
⠀⠀⠀⠰⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⠠⢦⣉⣉⣠⣿⣿⣷
⠀⠀⠀⠀⠀⠀⢀⣴⣤⠀⢰⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠀⠻⢦⣬⣭⣭⣿⣿⣷⡦
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⠀⠀⠀⠀⠀⠀⠈⠳⠦⢤⣤⣤⠾⠉⠉

⠀⠀⠀⠀⠀⠀⢀⣔⠒⢢⠀⠀⠀⠀⠀⠀⠀⢀⣰⣦⠀⠀⠀⠀⠀⠀⣀⠤⣠⣀⢀⠀⠀⠀⠀⣠⣴⠀⢤⣄⣀
⠀⠀⣘⣷⡄⢰⠉⣠⠒⠚⠢⠀⠔⠒⠢⡀⣴⣿⣯⣼⡁⠀⠀⠀⠀⢰⣿⣾⡛⠟⢷⡀⠀⠀⢰⡇⠸⣆⠀⡽⠿⢷
⠀⣾⣛⢧⣿⠜⣲⠧⠀⢀⣐⠆⠆⠀⠤⡇⢿⣯⣿⣿⢁⣤⠀⠀⢰⡸⣿⣽⣇⣉⣬⣷⠀⠀⢺⣿⣦⡈⠉⣳⣾⣿
⠀⢸⣿⡿⡟⠀⠙⣷⣾⣴⠋⠀⢴⣶⡶⠁⠘⣿⣳⡟⢛⣉⣀⣀⣸⠀⠻⣿⣯⣿⣼⠏⠀⠀⢸⣿⣿⣻⣷⣿⣿⡟
⠀⠘⣿⣿⠃⠀⠀⢿⣻⡍⠀⠀⠘⡝⠁⠀⠀⢿⣿⠇⠀⢿⣭⣼⠃⠀⠀⣠⣿⢹⣀⠀⠀⠀⠀⣇⠀⠈⡉⠈⣿
⠀⠀⢹⡇⠀⠀⠀⠈⣭⠃⢀⠀⠀⠑⠀⠀⠀⢸⣻⠀⠀⢸⣗⣿⠀⠀⠀⠉⠁⠈⢉⣴⠖⠂⠀⠻⣄⡀⣀⣠⡿
⠀⠀⢈⠁⠀⠀⣀⣀⡙⠀⣿⢯⣿⠀⡞⢻⡆⢀⣭⣤⣀⠀⠃⠃⠀⠀⠀⠀⠀⠀⣿⣿⡄⠀⣨⣄⠀⠈⠉
⠀⠀⠈⠀⡄⢠⣿⣿⣽⡄⣿⣾⡟⠀⡃⢸⡇⣾⡏⢹⣿⣇⠀⠀⠀⠀⠀⠀⢀⡀⠸⣷⢦⣤⠿⠿⠿⠿⠿⠿⣶⡄
⠀⠀⠀⠀⢡⢸⣿⣿⡇⡁⣿⣽⣿⠀⡆⢸⡇⣿⡇⢈⣿⣿⠀⠀⠀⠀⠀⠀⢙⣇⣤⣶⣭⣁⡄
⠰⡟⠀⢬⣿⣾⣿⣿⡇⡅⣿⣿⣿⠀⡇⢸⡇⠻⣧⣠⣿⠏⢀⣀⣠⢤⣄⠀⢈⢻⣿⣿⣯⣿⠧⠄⣶⠀⠀⡀⡴⡄
⠀⠉⠉⠋⠉⠘⠻⠿⠓⠀⠙⠛⡏⠀⠳⠾⠃⠀⠀⠈⠀⣼⣿⣥⣿⣿⣿⠢⣀⣼⢀⣀⣘⣿⠀⣦⢸⣦⣶⣶⣶⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⣿⣿⣿⠇⠀⠈⣻⠿⠿⣿⠁⠀⢸⣯⣻⣸⣟⢻⡬⡀
⠀⠊⠁⠉⢳⠀⢠⠖⠒⢤⡀⡠⠒⠒⢦⢀⡴⠒⠒⢆⢹⣶⣾⣿⣬⣿⡆⠀⠀⠉⡀⣠⠃⠀⠀⠘⣿⣷⠿⣿⢿⣿⠇
⠀⣷⠀⣀⣼⠆⣗⠀⠀⢰⠇⣷⠀⢀⣸⠘⣆⠀⣠⣾⠰⣟⠀⠀⢹⣯⠁⠀⠀⢞⡓⣻⡄⠀⠀⠀⠈⣿⢿⢻⣿⡇
⠀⠈⠉⠉⠉⠀⠈⠁⠉⠉⠀⠈⠉⠉⠀⠀⠈⠈⠉⠀⠀⠈⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠡⠂⠘⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠂⠀⠀⠑⠀⠑⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠆⠀⢂⡕⠉⠉⠑⡤⡑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠈⠀⢀⠤⠂⠁⠀⠀⠀⡠⠁⠸⠂⠑⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⡠⠐⠈⠀⠀⢀⡀⠄⠐⠈⠠⠂⢀⠥⡔⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡓⢁⠀⠠⠶⠠⠬⠄⠒⠀⠈⢉⠰⠂⠁⢀⢆⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠔⠉⢀⠤⠂⠁⠀⠀⢀⠤⠐⠈⠀⢀⠠⠐⠁⡈⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⡠⠊⢁⠀⠠⠐⠈⢁⠀⠠⠐⠂⠁⠀⠀⢀⠴⠄⠒⠛⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⢀⠔⠁⡀⠄⠂⠁⠀⠀⠀⣀⡀⠤⠀⠀⠁⠀⠀⡠⠊⠀⠑⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠬⠔⠉⠀⢠⣊⠀⠀⢀⠀⣀⢀⡄⠀⠁⠀⠀⠀⠄⠀⣀⡀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡄⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠠⠤⠤⠄⠀⠀⠀⠀⠀⠀⠠⠄⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠄⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠢⠀⠠⡤⠀⢄⣄⠀⣀⡀⠀⠄⣤⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠢⣀⠈⠙⠢⢀⡀⠀⠠⠒⠂⢤⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠓⠲⣀⠉⠉⠑⡠⠤⠊⢁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠢⢤⠄⠑⠒⠄⢀⣀⠄⢚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⣀⠀⣈⠰⠤⢄⠈⠈⡡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡁⠈⠑⠠⣀⡀⠠⠈⠉⢐⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⠑⠌⡉⠀⠉⡀⠖⠮⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠚⠛⠃⠀⠒⠂⠉
⣿⣿⣻⣻⣛⣟⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣛⣛⣿⣿⣛⣻⣛⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⡴⢦⡴⠶⣤⡴⠲⠲⠶⠶⣤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠋⠉⠹⣿⠇⠀⠀⠀⣿⠇⠀⠀⠀⠀⢹⠍⠁⠈⠁⠉⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⢲⣿⡏⠁⠀⠀⠀⣿⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⠿⠟⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⢸⣿⠁⠀⠀⠀⠀⢸⡆⢀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠃⠀⠀⠀⠈⣧⣄⡀
⠀⠀⠀⠀⠀⣠⠴⣾⡇⠀⠀⠘⡌⠀⠀⠀⠀⠀⢸⠀⠈⠃⠀⠈⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⠇⠂⠀⠀⠀⣸⠿⠿⠉⢷⡀
⠀⠀⠀⠀⢰⡇⠀⠹⣧⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡀⠀⠀⠀⠈⡧⠀⠀⠀⣸⡀⠈⠀⠀⡼⠃⠀⠀⠀⠀⡟
⠀⠀⠀⢀⣯⠀⠀⠀⢱⠀⠀⠀⡀⢱⠀⠀⠀⠀⠀⣧⠄⠀⠀⠘⡇⠀⠀⠀⢸⡇⠀⠀⠀⡿⠁⠀⠐⣾⠓⠀⠀⠀⠀⣼⡿⢦
⠀⠀⢠⣟⠉⢦⠀⠀⠀⢣⠀⠀⠀⠘⡂⠀⠀⠀⠀⢸⡄⠀⠀⠀⡅⠀⠀⠀⢸⠀⠀⠀⣰⠀⠀⠀⢰⠉⠀⠀⠀⠀⠼⠋⠀⢈⡇
⠀⠀⢸⡇⠀⠈⢲⣄⠀⠠⢦⠀⠀⠀⠱⡀⠀⠀⠀⠈⣡⠀⠀⠀⣧⠀⠀⠀⣾⠀⠀⢀⠏⠀⠀⢠⠇⠀⠀⠀⢀⡜⠀⠀⢀⣼⣷⡄
⠀⠀⢨⢧⡀⠄⠲⡿⣆⠀⠉⢧⠀⠀⠀⢷⣖⠀⠀⠀⡏⡆⠀⠀⡿⠀⠀⢀⢿⠀⠀⡜⠂⠀⢀⣞⠀⠀⠀⢀⡜⠀⠀⢠⠎⠀⢀⡇
⠀⠀⠸⡆⠘⢄⠄⠈⠻⡆⠀⠀⢳⡆⠀⠘⣿⠀⠀⠀⢇⠃⠀⠀⠁⠀⠀⢸⠂⠀⣠⡇⠀⠀⡟⠄⠀⠂⢀⡞⠀⠀⡴⠃⠀⡠⠎⡇
⠀⠀⠀⣿⠳⣾⢷⡀⠀⠙⢶⣄⠀⢿⠀⠀⢹⠀⠀⠀⠸⡀⠀⠀⡀⠀⠀⣿⠀⠀⡿⠁⠀⣼⠇⠀⠀⡠⡣⠄⢀⠞⠀⣰⣯⠕⣾⠁
⠀⠀⠀⠘⣷⣈⣷⡙⢦⠀⠀⢿⣆⠀⢣⡀⠀⢧⠀⠀⠀⡇⠀⠀⠁⠀⠀⡏⠀⣸⠁⠀⣰⠏⠀⢠⡞⠁⢀⡴⢅⡠⣪⣞⣵⢴⠋
⠀⠀⠀⠀⠙⢮⡻⣝⢮⡳⣤⠀⠹⣆⠀⠹⡄⠈⡆⠀⠀⢣⣠⢀⢠⡤⢴⣁⢀⡧⠀⢰⠹⠀⢀⡏⠀⣠⢞⡱⣫⣺⠖⣫⡷⠋
⠀⠀⠀⠀⠀⠀⢹⣚⢷⣝⣮⡣⣄⠘⢷⡄⢹⣤⢿⠁⠁⠸⡅⠸⣂⠀⡾⠀⡼⠛⢲⣿⣀⣠⠋⢠⢞⡕⣫⢞⣩⢶⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠉⠳⣬⡿⠿⣮⣢⣌⠿⣦⠙⡄⢣⠀⠀⡇⠰⠁⢠⠇⢠⡇⢀⡾⠉⡵⢷⣶⣗⣡⣎⣪⠭⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⡶⣭⣻⢷⣬⠳⡘⣌⢇⠀⢿⢸⡇⢸⢀⣾⢀⣾⢀⣼⣵⣿⣿⣿⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠻⠷⢽⠿⢿⣦⡹⣞⢞⣆⢹⠸⣇⡏⢈⡟⣾⣫⣾⣿⣿⣿⠇⣡⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢲⣮⡟⣁⡀⠀⡿⣿⣯⣿⡌⡄⣹⡟⣾⡼⣱⣿⡟⠉⢡⣴⡏⢁⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠶⠤⠽⠋⠉⠙⠳⠦⢌⣿⣿⣇⣿⣴⣿⣾⡟⢡⣷⠖⢚⣿⣛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠾⠷⠖⠶⠾⠗⠒⠒⠋⠉⠻⠿⠿⠟⠓⠛⠛⠛⠒⠿⠿⠶⠚

⣿⣿⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠦⠤⣄
⠀⠀⢀⠔⢀⠀⠀⣴⠛⢢⠀⠀⠀⠀⠀⡈⠀⠀⠀⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠯⢊⡔⠀⢹⣦⡀⠀⠀⠀⠐⠣⠄⢶⡦⡀⡀⠓⣆
⠀⠀⡾⢀⠈⠁⠚⠉⢢⡜⢣⠀⠀⠀⠀⡧⠈⠠⣾⣿⣿⠁⠀⠀⢀⢀⠖⡠⢘⠢⢰⡄⠀⠀⠀⠀⢸⢇⣦⣿⣾⣭⣻⣻⡇⠀⠀⠀⡇⠔⢥⢲⢸⣠⠆⣠⢹
⠀⠀⣧⠐⢀⣀⣠⣀⠘⢻⡿⠀⠀⠀⠀⠙⠾⣶⣿⠿⠋⠀⠀⠀⠂⠃⢀⣸⣆⠀⣒⢍⡆⠀⠀⠀⠘⣿⣟⡛⣻⢿⣽⣷⠃⠀⠀⠀⢆⠀⢰⡀⢤⡿⠈⠥⣻
⠀⠀⠈⢢⠚⠁⠀⣀⢀⠜⢁⣀⣒⠲⣦⡳⣆⣄⠀⠀⠀⠀⠀⢄⠀⠠⢭⣿⣿⣶⠘⢦⡿⠀⠀⠀⠀⠈⠙⠯⢷⡷⠟⠋⠀⠀⠀⠀⠀⠠⣕⠤⢄⣀⡀⠞⠁
⠀⠀⠀⠀⠈⠈⠋⠉⠁⢀⡼⣛⣩⣙⡎⣷⢹⡸⣦⠀⠀⠀⠀⠠⣀⠂⠐⠛⠿⡨⢸⡾⠇⠀⠀⠀⠀⠀⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡞⡵⡰⣾⣟⡥⢟⣵⣿⠀⠀⠀⠀⠀⠘⠊⠶⢄⡼⠷⠞⠁⠀⠀⢀⡀⣀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢼⠰⡿⣜⢮⣉⣹⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣤⣈⡻⣄⢸⢿⣄⣀⠘⠀⠀⠀⢀⠠⡄⢤⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠝⢮⣳⠮⠟⠋⠀⠀⠀⠀⢀⣲⣤⡀⠀⠀⠀⢀⠞⣠⣤⣭⣝⢻⡜⣿⢇⡿⡄⠀⠀⠶⠶⡶⢤⠿⣦⣻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⢀⣼⣽⣿⣿⣷⠀⠀⠀⠈⠗⢁⡴⣲⣺⣿⣿⣫⢞⣱⡇⠀⠀⠴⢛⣛⣺⣶⡛⢧⠾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠐⣤⣤⣼⣿⣿⣿⣿⡿⠀⠀⠀⠈⣳⡟⣸⡇⣟⠾⠭⠶⢟⣫⡅⠀⠰⡀⢿⣢⢻⣯⣷⠛⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠈⢣⡸⣇⠻⣽⣿⣿⡿⠏⠀⠀⠀⠹⢦⣽⣾⣯⣵⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⡏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠈⠉⠓⠲⠶⠖⠚⠋⠁⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⣠⡄⠀⠱⠦⢄⡀⠀⠀⠀⣀⣠⣴⠂⠰⠶⢀⠀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⣠⡔⠈⠀⠁⠀⢠⡀⠀⠀⠀⠙⠁⠀⠀⠀⠳⠈⠀⢢⠑⢦⡀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⣴⣿⣿⣶⣾⣀⣀⣨⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⣀⣨⣷⣶⣿⣄⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⣴⣿⣿⣿⠿⠟⠛⠻⠿⠿⢿⣷⣶⣶⣿⣿⣷⣶⣿⣿⡿⠿⠿⠿⢿⣿⣿⣷⠄⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠘⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⢹⡿⠃⠀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⢨⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⡀⠀⠀⠀⠀⠀⢀⣀⡤⠞⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠉⠉



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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠤⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢧⣠⡿⠁⣠⣽⠛⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢚⡁⣸⣿⣿⣵⠀⣀⡀⣀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠛⠃⠰⠋⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣺⡟⢋⣠⠼⢿⣿⣾⣿⢗⠝⠋⠁⠀⠀⠀⢀⠴⠿⠿⢛⠁⠀⠠⠖⠟⠉⣧⠐⠎⠓⠀⠀⠒⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠋⡄⡶⣷⣿⣿⣿⣿⢧⡀⠂⠄⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⢰⠁⠀⡘⢧⠀⠀⠀⠀⠀⠀⣠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⣥⠟⢹⡿⢹⠉⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡀⠀⠀⠀⠐⠃⠈⠆⠀⠀⡄⠀⠀⣧⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⢼⣧⠌⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⣡⠀⠀⢹⡀⠀⡀⠁⢰⠃⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠉⠀⠀⠀⠉⠁⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⣧⠀⡀⠀⡞⠀⠠
⠀⠀⠀⠀⠀⠀⢀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠁⢠⠃
⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸
⠀⠀⠀⣰⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢼⠦⣄⣀⣠⢿⠀⣿
⠀⠠⣴⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠜⠓⠀⠾⢊⡴⢂⣉⣿⡄⣿⡀
⢀⣈⣽⣿⣷⣷⣤⠄⡀⠀⣠⡀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡰⠚⢙⠣⣃⠁⠚⣉⡐⢂⣔⣿⣿⣿⣷⠦⠄
⠀⢴⣿⣾⡿⠽⣿⡧⢹⣿⣿⣿⣿⡤⠀⡼⠙⠁⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣶⣿⣤⣴⣶⣮⣭⣥⣿⣿⣿⢿⣿⣿⢿⡟⠋
⠀⢸⣿⡟⠀⣀⡀⣸⣿⣿⠿⣯⠝⠂⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠉⠻⠯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣤⣭⢿⣄⠙⠆
⠀⣞⠏⠀⠉⠙⣿⠛⢉⡃⠈⠈⣀⠀⠀⡅⡀⢨⠀⠀⠀⠀⠀⠀⠀⢈⣉⣰⣾⡿⣽⣛⣉⡻⠦⠚⠛⠉⠉⠉⠉⠀⠹⣄
⠚⠁⠀⠀⠀⠀⠠⠀⠉⠀⠄⠠⢅⠀⠀⣧⡇⡈⠀⠀⠀⠐⠛⠙⠷⠿⠯⠶⠶⣿⣇⡱⠯⠻⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣧⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣉⡭⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢁⡑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣀⠀⠀⠀⠀⠀⠀⣠⣚⢢⠀⠀⠀⠀⠀⣷⣤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⢧⠀⠀⠀⠀⢀⠼⣁⣪⠉⠀⠀⠀⠀⠶⠿⣿⠿⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠻⠀⠀⠀⠀⠁⠀⠀⠀⠀⣠⡛⢄⠈⠁⠀⠀⠀⠀⠀⠀⠀⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣵⠃⠀⠀⠀⠀⠀⠀⣠⣜⠣⠙⠋⠀⠀⠠⠒⠂⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⡙⡅⠀⠀⠀⠀⠀⠀⠀⠛⠁⠙⠁⠀⠀⠀⠐⠄⠠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠞⠀⠀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣱⠀⠀⠀⠑⠊⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡧⠄⠀⠀⠀⠀⡠⠢⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠈⠈⠃⠀⠀⠀⠀⠀⠀⠈⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡂⣣⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠠⡀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠢⣀⡀⠀⠀⠠⢄⠚⠈⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣄⠀⠈⠒⡤⠂⢄⠀⠀⠀⠀⠀⠀⣶⢑⣈⡄⠛⠁⠀⠀⠀⠀⣥⠐⠺⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠉⠢⡀⠀⢄⣀⣴⠀⠀⠀⢴⡙⣄⣨⠜⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡤⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⢙⣄⠀⠀⠀⠑⢶⡑⣤⡥⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄⢠⣾⠉⠨⠿⠁⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⡿⠁⠀⠀⣰⣿⣿⣷⣄⠀⢠⣶⡷⡉⠀⠀⠀⠀⡊⠀⢐⠀⠀⠀⠀⠤⣾⠇⠀⠙⠁
⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⠀⣠⣾⣿⣿⣿⠿⠋⠉⠢⡀⠀⠈⢆⠀⠀⠀⠈⠀⠁
⠀⠀⠀⠀⠀⠀⣼⡟⠀⢀⣴⣿⣿⡿⠟⠁⠀⠀⣀⣤⣾⣷⣦⣤⠇
⠀⠀⠀⠀⠀⣸⡟⠀⣴⣿⣿⠟⠋⠀⢀⣠⣴⣿⣿⠿⠟⠋⠉
⠀⠀⠀⠀⢰⠟⣠⣾⡿⠛⢁⣠⣴⣾⡿⠟⠛⠉
⠀⠀⠀⢠⢏⣼⠟⣋⣤⡶⠟⠛⠉
⠀⠀⢀⣿⡿⠷⠛⠉
⠀⠀⠈⠁

⡿⢿⠿⠿⡿⠻⢿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⢿⣿⣿⡿⣿⣿⢿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⠶⠶⠶⠶⠶⢶⣶⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⢀⣠⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦
⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠹⣧⡀
⠀⠀⠀⠀⠀⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⣠⣶⣦⠀⠀⠀⠾⠟⠛⠉⠉⠉⠉⠉⠉⠛⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⢰⡿⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢹⣇⠀⠀⠀⢀⣿⠁⠀⣸⡇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠈⣿⡀⠀⢀⣾⠃⠀⠀⣿⣇⣤⣤⣶⡶⠿⠟⠛⠋⠉⠉⣹⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠹⣧⣠⡿⠃⠀⠀⠈⠛⠉⠉⠀⠀⠀⠀⣀⣠⣤⡶⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⣀⣀⠀⢀⣀⣀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⢿⣿⣋⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⠶⢶⣶⣶⣤⣴⣶⣶⠶⠾⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠒⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣮⠁⠀⠀⠀⠀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢴⣴⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⡿⢻⠻⣌⠀⠀⢀⠰⣾⠃⠀⠀⢀⣠⠤⢤⣀⠀⠀⠀⠀⣛⣛⣯⣟⣋⣬⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠩⣤⣁⣤⣄⢠⣦⣐⡎⠀⠀⣴⣯⣬⠁⠀⠈⣧⠀⠀⣿⣿⣟⣭⣭⣿⡿⣻⡦
⠀⠀⢀⡴⠖⠛⠲⣤⡀⢛⣿⡏⠙⢉⣹⡿⠁⡴⠏⠁⠀⣀⡵⠶⠴⢿⣀⠀⢾⣿⣶⣤⣿⣶⣾⡉⠁⠀⢀⡿⣦⣀
⠀⢠⡏⠀⠀⠁⠀⢈⣷⠈⡿⣿⡿⣿⣿⠇⢰⡝⠂⠀⣼⠇⠀⠀⠀⠀⢈⡄⠸⣯⣏⣻⡟⢋⣿⡏⠀⠰⣏⣆⢻⣿⢳⡀
⠀⠈⢏⠀⠀⠀⣠⣬⣟⠀⢹⣿⡷⣾⢿⠀⠈⢹⢲⡴⣯⡀⢀⠀⠀⠀⠠⣾⠀⢹⣿⣟⣛⣿⡿⠀⠴⣴⠿⠼⣿⢘⣿⣧⡄
⠀⠀⢋⡀⢀⢠⣀⢢⡼⠀⠸⣿⡷⢮⣿⠀⠀⠺⣼⣗⠀⠣⣠⡀⠤⠤⢶⡋⠀⠀⣿⢹⣿⣿⡇⠀⠼⣯⣾⣱⠚⣜⣿⣹⠃
⠀⠀⢠⡾⣷⡾⡿⡾⠀⠀⠀⠛⠓⠚⠃⠀⠀⠀⠈⢿⣿⣶⣶⣦⣴⡻⠉⠀⠀⠀⢽⢾⣤⣿⠃⠀⠀⢻⣿⣿⣾⣛⣿⡿
⠀⠀⠀⠜⣧⣻⠓⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⣧⠃⠀⠀⠀⠀⢸⣿⣩⣿⠀⠀⠀⠘⣟⣿⣹⣯⣽⠇
⠀⠀⠀⢸⣶⢋⡣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠻⣖⡏⠀⠀⠀⠀⠀⠀⣿⣻⡿⠀⠀⠀⠀⢻⣿⣙⣯⣿
⠀⠀⠀⠈⡟⣩⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⣻⣽⣩⠁⠀⠀⠀⠀⠀⠀⠹⢿⠇⠀⠀⠀⠀⠈⣿⡟⣿⠇
⠀⠀⠀⠀⠙⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⣴⡖⠛⠛⠛⠛⢶⣶⠶⠦⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣤⢴⣶⡞⠉⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠉⢻⣶⠶⢦⣄
⠀⠀⠀⠀⢀⣠⣴⠁⠀⠀⠈⢿⡄⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⣸⡇⠀⠀⠉⠳⣦
⠀⠀⠀⣰⠋⠀⠹⣆⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⢹⡆⠀⠀⠀⠈⣧⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⡷⢦⣄
⠀⠀⣰⠛⣆⠀⠀⢹⣆⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⣧⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⣴⠏⠀⠀⠈⠻⣄
⠀⠀⣿⠀⠸⣆⠀⠀⢿⡄⠀⠀⠀⠸⣷⠀⠀⠀⠀⣿⠀⠀⠀⠀⡿⠀⠀⠀⣿⠁⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⢿⠀⠀⢻⡄⠀⠘⣷⠀⠀⠀⠀⢻⡆⠀⠀⠀⣿⠀⠀⠀⢰⡇⠀⠀⢰⡏⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⢀⣴⣿⢷⡀
⠀⠀⠸⡆⠀⠀⢿⡀⠀⢻⡆⠀⠀⠀⢸⣇⠀⠀⠀⣿⠀⠀⠀⣾⠀⠀⠀⣿⠁⠀⢀⣼⠃⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠙⣆
⠀⠀⠀⢳⡀⠀⠈⣧⠀⠸⣇⠀⠀⠀⠀⣿⠀⠀⢠⡇⠀⠀⣸⠃⠀⠀⣼⠃⠀⢀⣾⠃⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠈⢧⠀⠀⠸⡆⠀⣿⠀⠀⠀⢀⡇⠀⠀⣼⠁⠀⢰⠏⠀⠀⣼⠃⠀⢀⡾⠁⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⣠⣾⣇
⠀⠀⠀⠀⠘⣧⠀⠀⢻⡀⢿⠀⠀⠀⢸⠇⠀⢠⡇⠀⢠⠏⠀⠀⣼⠃⠀⢠⡿⠁⠀⠀⣠⠟⠁⠀⠀⠀⠀⢀⣠⡶⠛⠉⠀⠘⣦
⠀⠀⠀⠀⠀⠸⣆⠀⠈⡇⢸⠀⠀⠀⣾⠀⠀⡾⠀⢠⠏⠀⢀⡼⠃⠀⢠⡿⠁⠀⢠⡾⠁⠀⠀⠀⢀⣠⣶⠟⠉⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠹⡆⠀⢿⢸⠀⠀⢀⡏⠀⢰⠇⢀⡞⠀⢀⡼⠁⠀⣰⡟⠁⠀⣰⠏⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⠀⠀⠀⣀⣤⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠹⡄⢸⣾⠀⠀⢸⠃⠀⡟⢀⡞⠀⢠⡞⠁⠀⣰⡟⠀⢀⡼⠁⠀⠀⢀⣴⠟⠁⠀⠀⠀⣀⣤⡴⠾⠛⠋⠉⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣷⠘⣿⠀⠀⡿⠀⣸⢁⡞⠀⣠⠏⠀⠀⣼⠏⠀⢠⠟⠀⠀⢀⣴⠟⠁⠀⢀⣠⡴⠞⠋⠁⠀⠀⠀⠀⣀⣠⡏
⠀⠀⠀⠀⠀⣠⠞⠋⠈⣇⣿⠀⢰⡇⢠⠇⡼⠀⡴⠃⠀⢀⣼⠃⢀⣴⠋⠀⢀⣴⠟⠁⠀⣠⠶⠋⠁⠀⠀⣀⣤⡴⠶⠞⠛⠛⣿⠁
⠀⠀⠀⠀⠀⠻⡀⠀⠀⢸⣽⠀⢸⠇⡞⡼⢁⡾⠁⠀⣠⡾⠁⣠⡞⠁⠀⣠⠟⠁⢀⡴⠋⠁⢀⣠⡴⠞⠛⠉⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠘⢦⡀⠈⣿⡇⢸⣼⣱⢣⡞⠀⢀⣴⠋⢀⣼⠋⠀⣠⠞⠁⣠⠖⠉⣀⡴⠞⠋⠁⠀⣀⣀⣤⣤⣶⡶⠶⢾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⢻⣷⢸⣿⣧⡟⠀⣠⠞⢁⣴⠟⠁⣠⠞⢁⡤⠚⣡⠴⢛⣁⡤⠴⠖⠛⠋⠉⠉⠁⠀⠀⠀⢀⡬
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣾⣿⡿⢀⡜⣁⡴⠛⢁⡤⠞⣡⣴⣫⢔⡫⠔⣚⣉⣀⣀⣤⣤⣤⣤⡤⠶⠶⠶⠖⠛⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣷⠿⠚⣉⡤⠖⣫⣴⣞⣻⡽⠾⣿⠟⠋⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠾⢿⣵⠶⠟⠛⠋⠉⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠓⠲⠤⣼⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢥
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⢊⢓⠀⠀⠐⣂⠂⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠠⠁⠀⠀⠨⡢⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⡀⠜⣾⠁⠀⠐⡐⠈⠛⠂⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠄⣀⡆⠀⠧⢘⣿⣠⠤⠤⠄⠀⢀⠌⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣬⣀⠀⣼⣿⠁⡎⣰⣿⠊⡑⢀⡀⠔⠊
⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠄⠤⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠠⣈⡛⠻⣿⣿⣧⣜⣰⣿⠇⡼⢠⣿⠕⡀
⠀⠀⠀⠀⣀⣴⣾⠫⡑⣶⣙⣛⣫⡴⢆⡥⡀⢀⡀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢾⣷⣦⣌⣱⣿⢯⣝⣻⣿⣿⣶⣥⣿⡟
⠀⠀⣠⣾⡿⢛⡵⣷⡿⢶⣛⣛⣃⣶⣯⣟⠾⣕⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠑⠶⡢⠬⣉⢻⣿⣿⣶⣧⣟⡟⠲⢍⣿⡿⠿⣷⣦⡄
⠀⣴⡿⣟⣵⣻⢾⣵⢮⠿⣛⠛⢋⡽⣻⠻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⣤⣿⡟⢶⢯⣿⡿⢿⣿⡾⣿⣙⠒⠦⠍⠃
⢰⣿⣝⢪⡿⢯⡾⢭⡴⡻⣍⠓⠋⢝⡳⣽⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⢿⣿⣾⣿⣙⡟⣼⣿⣛⠻⢿⣷⠤
⣿⣿⡏⢷⠀⣦⡄⣀⠘⢍⠈⣩⢕⢦⡱⠛⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠂⠀⠀⠉⢣⠇⣼⣿⢛⠿⣿⣿⣧⣌⣁⠂
⣿⡏⣧⡾⣃⣿⢃⢿⠳⢎⠠⠏⢁⢸⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⢴⣿⠃⡞⢰⣿⠏⠉⠛⠻⠓⠁
⢹⣿⣻⢧⣫⡹⣝⣮⡷⡵⣂⣛⣥⢕⡽⣻⡇⠀⠐⠒⠒⠒⠒⠂⠀⠀⠐⠒⠒⠒⠒⢲⠂⡘⠉⡗⠨⠤⠿⠭⠀⠂⠁
⠀⢻⢿⣎⢳⡹⢾⣫⢏⡾⢻⡟⣢⣳⣟⡵⣻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⡜
⠀⠈⠳⡿⣷⣭⡳⡽⣋⡶⠟⠻⢟⣙⣽⢞⣵⣿⣿⣦⢀⠀⠀⠀⠀⠀⠀⡀⠔⠊⠀⢀⠃⡐
⠀⠀⠀⠉⠨⡛⠿⣿⣯⣿⣿⣿⣷⣽⣾⢿⣻⡿⠟⠁⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠂⠉⠀⠀⠀⠈⠡⠖⠏⠙⡀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⢀⠂⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⡀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠈⢀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠐⠀⠀⠀⠀⡇⢸⠀⠀⠀⡐⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢡⠀⠀⠀⡇⢸⠀⠀⡐⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢃⠀⠀⡇⢸⠀⠰⠁⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢣⠀⡇⢸⢀⠀⡐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠂⡇⢸⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⡇⢸⢀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⡇⢸
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣥⣶⣥⣾⣬⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡞⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢸⠇⢀⠀⠀⠀⠙⠲⠶⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠚⠛⠛⠛⠛⠻⠈⠀⠏⠀⠀⣀⡠⠀⠀⢀⡈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⢁⠤⠒⠋⣉⠽⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣈⣉⣤⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠈⢁⡀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⢻⡉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠻⣄⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠘⠷⣄⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠴⠾⠦⠀⠀⠀⠀⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⢩⡟
⠀⠀⠀⠀⠀⠀⣠⠞⠋⣁⡤⠖⠒⢂⡀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠦⣤⣤⣴⠋
⠀⠀⠀⠀⠀⢼⡃⠀⠀⠁⠀⠀⠀⠉⠀⢠⠀⠀⢀⣀⣀⣀⣀⣀⣤⠶⠋
⠀⠀⠀⠀⠀⠀⠙⢶⣄⣀⣀⡀⠀⠀⠀⡞⢀⠄⠀⢿⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⢷⡀⠀⠀⣸⠀⡆⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⣏⣸⠁⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⡈⠁⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⠁

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠍⠙⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢯⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣤⠀⠖⠡⠙⠛⠳⢽⣶⣄⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠴⠣⠀⢃⠘⠂⠀⠈⣿⠁⠀⠀⠘⣿⣠⠀⠁⢯⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡰⣻⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠠⣸⣿⣷⡀⠀⠀⡼⠡⠇⠀⠀⠇⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⣏⢷⣠⠛⣰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠘⢠⡏⣿⣻⣷⠀⠀⠇⠀⠀⠁⢠⢀⡀⠀⠀⠀⠀⠛⠀⠦⠌⣉⠻⢼⣏⣴⣣⡴⢦⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡿⠀⠹⡟⠃⠀⠈⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⣩⡵⢈⣿⣶⣤⡙⣦⣤⣁⠀⠈⣿⠂⢀⠠⢒⠚⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢴⠶⢾⡏⠠⠞⠈⢿⡈⢻⣸⣇⣙⣧⣴⣼⣿⡏⠶⢭⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣼⡀⠁⠀⠀⠘⣷⠀⠉⠉⠁⡰⢋⣴⣿⣿⣧⠘⡇⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠹⠆⠀⠀⣟⡤⠋⣸⠛⠟⠘⠷⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠁⠀⢠⡏⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢉⣉⠁⠀⠀⡁⢀⡀⠀⠀⠀⠉⠉⠉⠉⢙⠃⠀⠀⠠⠤⠄⠀⠀⠀⠉⠉⠁⠐⠒⠠⠀⠀⠀⠀⠹⡇⠀⢾⠆⣾⢰⠚⠈⠉⡉⠈⠠⠤⠸⠋
⠀⠀⠀⠠⣤⡀⠘⠛⠻⠶⡶⣡⢤⣴⣷⣶⠀⠀⠀⠀⠀⣤⣤⣤⣤⠀⠀⠤⠈⠙⠁⢀⠀⠠⢀⣀⡀⠐⠒⠠⠄⠈⣷⡀⠐⢀⡟⠀⡛⠂⠀⠀⠀⠠⠿⠛⠃
⠀⠀⠀⠀⢴⣟⣩⣤⣶⣆⢀⡤⠀⠀⠈⠉⠁⢀⠀⠀⠀⠀⠀⠀⠛⠀⢤⣶⣆⣥⣄⣀⢀⢀⠀⠀⠀⠁⠀⠀⠙⠃⢙⠈⠂⢸⠃⠀⠶⠶⠶⠒⠂
⠀⠀⠀⠀⢠⣶⣤⡀⠀⠈⠸⣇⠀⠀⢴⣶⣶⣯⣤⣿⢠⢣⣶⡤⠄⡄⠀⠀⠛⠋⠉⠉⠀⠀⠤⠶⠶⣧⣶⣤⣠⣀⢈⠀⢄⣉⠀⢀⠀⣀⡀⢀⣤
⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠴⡦⡴⠴⠆⢦⡄⢀⠀⣤⢀⣀⡈⠀⠈⠀⠀⠃⢠⠟⠛⠉⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠃⠈⠁⠉⠉⠁⠀⠀⣦⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠔⣧⣤⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠁⠶⠶⠶⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠺⠿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣷⡾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⣠⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣒⠀⠀⠉⠀⠀⠀⠀⠀⠉⠉⣹⠖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠠⠿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠰⠆


⣿⣿⡿⠻⠟⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⡂⠀⢀⡀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠅⠀⠀⢀⠀⠀⠀⠀⠀⠀⠘⡿⠂⠀⠀⠀⠀⣶⠆⠀⠀⠀⠀⠰⣶
⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠐⠀⠀⠀⠈⠁⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠰⠆⠀⠀⠠
⠀⠀⠅⠀⠀⠀⠀⣶⡶⠸⡆⠀⣸⡀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⢀⠀⠀⢦⡀⠀⢻⠟⠀⠙⢦⣽⣥⠾⠁⠀⣦⠀⢀⣇⠀⢰⠆⠀⣦⠀⢀⣆⠀⠀⠀⢠⡄⠀⣠⣇⠀⣾⠀⠀⢰⣀⠀⠀⣀⠀⡀⠀⠀⢀⣄⠀⢀⡆
⠀⠈⠀⣀⣻⣋⣠⠏⠀⠀⠀⢸⣿⣿⠀⠀⠀⠘⢦⣙⣟⣤⠟⠀⠀⠘⢦⣙⣟⣠⣄⡀⠀⠹⣦⣙⣯⡴⠃⠀⠀⣙⣿⣤⠴⠋⠀⠙⠶⣤⣘⣟⣠⠞⠁
⠀⠀⢸⡍⣿⣿⠀⠀⠀⠀⢀⣼⠋⠻⣄⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⢀⣿⣿⡇⠀⠙⠂⠀⠀⢹⣿⡇⠀⠀⣞⠹⣿⣧⠀⠀⠀⠀⠀⢰⣿⣿⡇⢀⡀
⠀⠀⠀⠙⣿⣿⠀⠀⠀⢠⡾⠁⠀⠀⠙⣧⠀⠀⠀⣿⢻⡅⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⢸⡟⡇⠀⠀⠙⠀⣿⠻⣆⠀⠀⠀⠀⣿⣿⣿⡇⠀⠁
⠀⠀⠀⠀⣿⣿⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⣿⢸⠇⠀⠀⠀⠀⠀⣿⢸⡇⠀⠀⠀⠀⠀⢸⡇⡇⠀⠀⠀⠀⣿⠀⣿⠀⠀⠀⠀⢸⡿⡏
⠀⠀⠀⠀⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠘⠁⠀⠀⠀⠀⠀⠛⠘⠃⠀⠀⠀⠀⠀⠘⠃⠃⠀⠀⠀⠘⠃⠘⠋⠀⠀⠀⠀⠘⠋⠃

⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠻⡿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣆⠀⠐⠀⠀⠐⠠⠌
⠀⠀⠀⠀⢠⡾⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣠⣽⣵⣄⣀⣠⠖⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠙⣿⢋⡿⠋⠙⠁⠀⠀⠀⠀⠀⢐⣯⣽⡛⣿⡏⠛⠁⢠⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠠⠀⠀⠳⠀⠘⠀⢰⡃
⠀⠀⠀⠀⠀⠀⣿⡌⢿⡄⠀⠀⠀⠀⠀⠀⠀⠈⠻⣾⣿⠛⢷⣄⠀⠠⠄⠃⠀⠀⠀⠀⠀⠀⠐⠀⠀⣿⡄⠄⠀⣠⣤⡀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⣿⠁⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⢠⡟⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣼⡀⠀⢈⣻⡆⠘⢿⣿⣿⣿⣷⡿⠁⠀⠂⠉
⠀⠀⠀⠀⠀⠘⠋⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠀⠟⠁⠀⠀⠀⠀⣾⣿⡄⠀⠀⣾⣿⣇⠀⠀⡌⠻⣷⣶⣸⣿⣿⣏⣀⡀⠀⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠘⠿⣦⣤⡻⢿⣋⣠⡄⢟⢆⢸⡿⣿⣻⡟⣿⣿⣿⠀⠀⢀⣠⣾⠇
⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠐⢿⣿⣿⣿⣿⡏⢸⣿⣿⣿⣿⣯⡿⣧⣬⣭⣥⣴⡶⠟⠋
⠀⠀⠀⣠⣧⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⣴⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣷⣶⣿⣿⣟⣯⣴⣮⣥⣼⣿⢿⣿⠀⣿⣿⣿⣿⡀
⠀⠀⠀⢙⣛⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⢛⣛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⢸⣿⣻⣷⣸⣿⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⣧
⠀⠀⠀⢸⣿⡷⠶⠶⠾⠀⠀⠸⠶⠶⢶⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⢸⣿⠙⣿⣹⣿⣿⣿⣿⢸⣿⢸⣿⣿⣿⣿⣿⡄
⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢈⣽⡿⠿⣿⣿⣿⢸⣿⢸⣿⢹⣿⢻⣿⠟⠘⠿⠘⢛⣿⠟⣿⡏⠁
⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠾⣿⡿⠿⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⢸⣿⠁⠉⢸⣿⢸⣿⢸⣿⢸⣿⠀⠀⠀⠀⠀⣿⡇⣿⡇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠐⠿⠋⠀⠀⠀⢸⣿⠀⠀⠈⠉⠀⠉⢸⣿⢸⣿⠀⠀⠀⠀⠐⠿⠃⠿⠃
⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇⠀⠀⠀⠀⠀⠀⠸⠿⠘⠿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠔⣩⣴⣶⣶⣶⣍⡲⡄⠀⠀⠀⠀⣠⢞⣭⣶⣶⣶⣭⣑⢦⡀⠀⠀⠀⠀⣠⢞⣭⣶⣶⣶⣬⣑⢦⡀
⠀⠀⠀⠀⠀⠀⢰⢣⣾⣿⠻⣿⣿⠟⣿⣿⡜⡆⠀⠀⡼⣱⣿⡟⢻⣿⣿⠻⣿⣧⢳⡀⠀⠀⡼⣱⣿⡟⢻⣿⣿⠻⣿⣧⢳⡀
⠀⠀⠀⠀⠀⠀⣾⢸⣿⣿⣶⣿⣿⣶⣿⣿⡇⣿⠀⠀⡇⣿⣿⣷⣼⣿⣿⣴⣿⣿⡏⡇⠀⠀⡇⣿⣿⣷⣾⣿⣿⣶⣿⣿⡏⡇
⠀⠀⠀⠀⠀⠀⠸⡜⣿⣯⡻⠿⡿⢟⣽⣿⢇⡏⠀⠀⢧⢻⣿⣟⣛⣛⣛⣛⣿⡿⣹⠃⠀⠀⢧⢻⣿⢋⣵⣶⣶⣝⣿⡿⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠙⢮⡻⠿⣷⣾⠿⢟⡵⠋⠀⠀⠀⠈⠳⣝⠿⣿⣿⣿⠿⣛⡵⠃⠀⠀⠀⠈⠳⣝⠿⣿⣿⣿⠿⣛⡵⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠒⠒⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⠒⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠒⠋⠁





⣶⣶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠬⡄⠤⡵⠆⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣀⠘⢡⠒⠛⣦⣀⠀⠀⢇⠈⠂⠋⢀⠇⠀⠀⠐⠀⠀⠶⢃⠀⠀⠀⠀⡀⠀⠀⠁
⠀⠀⠀⠀⠻⣤⠛⠒⢲⣄⠀⠀⠀⡄⢀⠈⢒⡃⠺⡤⠀⡹⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⠀⠀⠈⠊⢦⠀⠀⠴⠟⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠈⠑⠪⡄⢠⢗⡹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠁⠈
⠀⠀⠀⠀⠠⣤⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈⠁⠀⠙⠁⠀⠀⠀⠀⠀⡌⠀⠠⠈⠂⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⣀⣄
⠀⠀⠀⠀⡿⠦⢀⢀⡀⢀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠨⠉⠑⠀⠂⠀⠀⠀⠈⢣⡤⢊⡀⣦⡀
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠐⠀⠂⠀⠀⠀⣀⠀⠀⠀⠙⠚⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠀⠀⠀⢀⡊⠁
⠀⠀⠀⠀⠈⠀⣀⡤⠀⢄⠀⠠⠤⠀⣀⠀⢰⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⣶⡤⢤⢀⢸⡄
⠀⠀⠀⠀⠈⠈⠁⠐⠯⠀⣶⣲⠀⠀⠀⣐⡹⣇⠈⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⢀⣲⢂⢀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠈⠀⠉⢡⠁⠀⠀⠀⠀⢀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⢀⣤⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠃⠀⢋⡲⠰
⠀⠀⠀⠀⠀⠄⠀⠀⠀⢀⠀⠀⢰⣶⠀⠀⠀⠀⠀⠀⠀⠲⡄⠀⠀⠀⠀⠆⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠁⢠⣀⣤⡤⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠈⣈⡀⠀⢀⠀⠀⠀⠀⠒⢻⠆⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠚⠈⠁⠀⠀⠀⠀⠘⢩⣽⣿⠋⠀⠀⡄⡈⠀⠀⠀⠀⠀⠐⠂⡀⠀⢸
⠀⠀⠀⠀⠀⠄⠠⢖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢀⠀⠁⠀⠀⠠⠄⠀⠠⠜⠁⠀⠀⣀⠐⢀
⠀⠀⠀⢺⡀⠀⠏⠈⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠈⠃⠈
⠀⠀⠀⠀⣧⠔⠖⠚⠀⠀⠀⠀⠀⠀⠀⢀⣴⠇⠀⠀⠀⠀⠀⠠⢆⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⡤⠊⠁⠀⠀⠀⠀⠀⠀⠐⠾⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⠀⠐⠃⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣏⢙⣧⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠾⣀⢀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠞⠛⠋⠉⠉⠉⠙⠛⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⢀⣀⡤⠤⠤⠤⣄⣀⠀⠀⠈⠻⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠏⠀⠀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠈⠉⠲⣄⠀⠈⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢀⡞⠀⠀⠀⡠⠖⠒⠛⠒⠲⢄⠀⠀⠈⠳⡀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⡼⠀⠀⢀⠎⠀⠀⢀⣠⣀⡀⠀⠱⡄⠀⠀⢱⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⡏⠀⠀⠙⡄⠀⢹⠀⠀⠀⡆⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠱⡀⠀⠘⢆⠀⠀⠁⠀⠀⢠⠃⠀⣸⠀⠀⢀⠃⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠳⡄⠀⠀⠙⠒⠢⠐⠚⠁⠀⣠⠃⠀⠀⡼⠀⣰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠈⠓⠤⢄⣀⣀⣀⡠⠴⠊⠁⠀⢀⡴⠁⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠊⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣄⣀⣠⣤⣤⣖⣮⣥⢶⡟⠁⠀⠀⠐⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠙⣧⠈⢷⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠤⠀⢀⠘⣧⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠻⠒⠉⢌⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢷⡄⠺⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⢻⡄⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠄⠊⠀⠀⠀⠀⢷⡀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠛⠛⠳⢦⣄⣀⣤⠶⠛⠛⠛⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢦⣄⡀
⠀⠀⠀⠀⣀⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⣦⣄⡀
⢀⣠⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⠶⣤⣤⣀
⣿⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣽⣦⣄⣠⣴⣿⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣤⡤⢿
⢸⡇⠈⠉⠛⠻⣿⡟⠛⠛⠛⠛⣿⠋⠉⠉⠀⠀⠈⣿⠀⠈⠉⠙⠛⠛⣶⠶⠶⠶⠶⠶⢶⣶⠚⠛⢛⣿⠋⣩⡿⠋⠀⠀⣾
⠀⢿⡀⠀⠀⠀⠙⢿⣷⣶⠶⠶⠻⣦⣤⣤⣤⣤⣼⣿⣦⣀⣀⣀⣀⣠⡿⠷⠶⢶⣶⡶⠟⠉⠛⠛⠋⢁⡾⠋⠀⠀⠀⢠⡟
⠀⠘⣷⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠻⢦⣄⠀⣀⡴⠋⠀⠀⠀⠀⠀⣾⠁
⠀⠀⠘⣧⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠟⠋⠀⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠘⣧⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋
⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⡾⠃
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⣴⠟⠁
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⣴⠞⠁
⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣃⣠⠴⠛⠁
⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠋⠁
⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢦⣤⣄⣀⣀⣀⣀⣠⣤⣤⡴⠶⠛⠉
⣶⣶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠆⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡊⠀⠐⠀⠀⠀⢀⠀⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⢀⠌⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⡈⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄⣀⠀⠀⠀⠀⠀⠀⠁⠘⠘⠒⠓⠒⠒⠈⠋⠀⠀⠀⠀⠀⠘⠀⠀⠀⠐⠾
⠀⡠⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢄
⢨⠄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠢⠤⡀⠀⠀⠀⠘⢢⣤⣠⢤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠈⢄⡀⠀⠀⠠⠐⢦⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁
⠀⠀⠹⠂⠓⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⢀⠠⠔⠉⠰⠄⠀⠀⠀⠀⠈⠓⢶⠀⠁⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴
⠀⠀⠀⠀⠘⠁⠀⠀⢀⣰⠂⠀⠀⠀⠀⠀⠐⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⠀⠀⠀⠀⠀⠐⠀⠁⠈⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢐⠂⣤⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁
⣿⣿⢟⠿⡟⠿⢿⠟⣿⢿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣆
⠀⠀⠀⠀⠀⠀⣠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋
⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⢀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠸⠿
⠀⠀⠀⠀⢸⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡄
⣴⣦⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣸⣿⠁⠀⣀⣀⣀⣀⣀
⣿⣿⠀⠀⠈⣿⣇⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠀⠀⠀⠀⠀⢀⣿⣿⣿⡿⠿⠿⠿⠿⠿⢿⣿⣶⣦⣀
⢹⣿⡄⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠈⠻⣿⣷⣤⣤⣤⣤⣴⣾⡿⠛⠀⠀⠀⠀⠀⢀⣾⡿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣦⣄
⠈⣿⣧⠀⠀⠀⠙⣿⣧⡀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⣠⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣷⡄
⠀⠘⣿⣧⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠟⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣆
⠀⠀⠙⣿⣧⡀⠀⠀⠀⠈⠻⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⡿⠋⠁⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆
⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠉⠛⠿⠿⣿⣿⣿⣶⣿⣿⡿⠿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿
⠀⠀⠀⠀⠀⠉⠻⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⠀⠈⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣷⣦⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠿⠿⣿⣿⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠿⠛⠛⠛⠻⢿⣷⣦⡀⠀⠀⠀⠀⠀⢀⣾⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡇⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⡄⠀⠀⠀⢀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⡄⠀⠀⠀⠀⠈⢻⣿⣄⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡄⠀⠀⠀⠀⠀⠙⢿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣶⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠿⠿⠿⠿⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣶⣤
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣽⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⢿⠟⠿⠙⠯⠹⠯⠻⢟⡻⢶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡿⠏⠣⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠁⠋⡝⠷⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠟⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠃⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡽⢳⣄
⠀⠀⠀⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣷⡀
⠀⠀⠀⠀⠀⢀⡏⠁⠀⠀⠀⠀⢀⣠⣴⣶⡶⡾⣶⢶⣶⣤⣀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷⡀
⠀⠀⠀⠀⢀⣿⠉⠁⠀⠀⣠⣾⡟⠿⠙⠀⠀⠀⠈⠉⠘⠻⢿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⢸⡏⠁⠀⢀⣼⠿⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⣾⠒⠀⠀⣾⡯⠁⠀⢀⣀⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡀
⠀⠀⠀⠀⢿⡄⠀⢰⣿⠄⢠⣾⠟⠋⠉⠉⠘⠙⢻⣧⡄⠀⠀⠀⠀⠀⢈⢾⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣿⡇
⠀⠀⠀⠀⢸⣟⠀⢸⣿⢠⣿⣡⡶⣶⠶⣶⡄⠄⠀⠙⣿⡄⠀⠀⠀⠀⠀⢺⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠈⢿⡆⠀⣿⣼⣿⣿⣿⣿⣦⣽⣿⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠁
⠀⠀⠀⠀⠀⠈⢷⣄⠘⣿⣿⣿⣿⣿⣟⣰⡿⠀⠀⢠⣿⠁⠀⠀⠀⠀⣘⣿⣿⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠹⣷⣌⡻⢿⣿⣿⡛⢉⣀⣤⣼⡿⠁⠀⠀⠀⠠⢠⣼⠟⠛⠻⠶⠶⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣍⠙⠛⠛⠛⠋⠁⠀⠀⢠⡀⣠⣽⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠷⣷⣦⣤⣦⣶⣦⣶⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠋⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠈⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⣰⠃⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢠⡟⠀⠀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠾⠿⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣶⣼⣿⠀⠸⠃⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⠉⠁⠀⠀⠀⠀⠀⠈⠛⠁⠀⠀⢸⠃⠀⠀⠀⢀⣠⡤⠖⠀⠀⠀⢀⣀⡀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠋⠁⠀⣠⡤⠶⠛⠋⠉⣹⠆⠀⠀⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠁⣀⣠⡤⠶⠛⠁⢀⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣇⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣤⣴⡾⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠘⠏⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠛⠛⠛⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠉⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢷⣦⣄⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣤⣄⣀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⣷⣀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⡟
⠀⠀⠀⢀⣠⣴⡶⠿⠛⠛⠋⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠁
⠀⢀⣴⡿⠋⠁⠀⣀⣤⠶⠖⠚⠋⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢶⣦⣤⣤⣤⣤⣾⠏
⢀⡿⠋⠀⠀⠠⠞⠉⠀⠀⠀⠀⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣭⡿⠟⠁
⢻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⠀⠀⠀⣤⣄⣀⣀⣀⣀⣤⣤⣶⠾⠛⠉
⠀⠙⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⡔⠀⠀⢹⣿⠉⠛⠋⠉⠉⠁
⠀⠀⠀⠈⠛⠿⠷⢶⣶⣶⣦⣄⠀⠀⠀⢰⠇⠀⣸⠃⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⠀⠀⠀⠀⢀⡟⠀⢰⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⢸⡇⠀⣼⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠘⣧⣼⠃⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⣼⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣦⣄⣾⠟
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣿⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣏⣈⣉⣉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢒⣶⣿⣶⡂⠀⠀⢤⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢹⠏⢻⠉⠉⠷⠈⡿⠋⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠘⠀⠈⠐⡀⠀⠈⠀⠀⠀⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣲⣾⢿⠓⠀⠀⠀⠀⢠⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⢠⡀⠀⠀⠀⠀⣆⡀⣠⣷⣴⣦⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣴⣶⣽⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠑⠒⠓⠒⠉⠏⠉⠍⠉⢉⡙⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠒⠂⠂⣉⣁⣀⣤⡴⠒⠚⠀⠀⢠⢤⠖⠂⠁
⠀⠀⠀⠀⠀⢀⣀⣀⣢⣤⠤⠶⠶⠶⠾⠿⠟⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠀⠀⠈⠑⣶⣤⢤⠈⠁
⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⡤⠤⠤⠤⠤⠤⠤⠤⠤⠶⠶⠾⠿⠛⠛⠉⢀⡸⠀⠀⠀⠀⠀⣀⠔
⠀⠀⣀⠀⠤⠤⢄⡠⠤⠶⠞⣛⣩⣭⣤⠶⠶⡶⡶⠶⠶⢶⢦⣤⣤⣤⣤⣤⠤⢤⡶⢞⣉⣦⠀⣀⠠⠔⠈⠠
⠠⠠⠀⠒⠒⠒⠒⠚⠛⠉⠉⠉⠀⣀⣀⣀⡤⠤⠒⠒⠴⠒⠉⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠉⠀⣦⣤⣤⣶⠖⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢉⣡⠤⠂⠀⠀⣀⡠⠤⠐⠀⠘⠇⠀⠀⠀⠀⠀⡠⢎⣤⡷⢖⣸⡟⢈⣩⡁
⠀⠀⠀⠀⠀⠉⠉⠉⠁⠚⠛⠉⠉⠀⠠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠈⣑⡫⠔⠋⠀⠉⠁⠈⠉⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⡀
⠀⠀⠀⠀⠤⠜⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢤⣴⠂⣶⠆⣤⠤⢀
⠀⠀⢀⠀⠀⢠⣶⡶⢐⣀⡀⠀⠀⠀⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡞⣿⡜⣿⡄⣿⢰⣿⢠⡾⢉⡶⡄
⠀⠀⠀⡅⠀⣿⠋⡾⣽⣿⣿⡦⡇⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⡽⣿⣽⣷⣿⡇⣿⣼⠇⣾⢡⡟⣱⠿⡆
⠀⠀⠉⠇⠈⣿⣾⣗⢿⣿⡿⢣⠃⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣿⡿⢸⢣⢟⡾⣡⢞⣩
⠀⠀⠐⠶⠛⠛⠳⢉⠀⠀⠀⠁⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷⣿⣿⣿⣿⣿⣿⢇⣏⢏⣮⣞⣵⣯⣶
⠀⠀⠀⠀⠀⠀⠀⠈⠑⠀⠃⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣹⠏⣜⣻⠿⠛⠋⠁
⠀⠀⠠⣠⣤⣶⣦⣀⣀⣤⣤⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⣠⣿⣯
⠀⠀⠀⠙⢿⣟⠛⠛⠛⠛⠙⡋⢩⣙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠶⠽⠿⠿⠿⠿⠿⠿⠿⠆
⠀⠀⠀⠀⠀⠈⠙⠿⣩⠩⠉⡭⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣢⣄
⠀⠀⠀⠀⠀⢰⣶⡄⠀⠀⠀⠀⠀⠀⠀⣈⠁⣽⡄⠀⠀⠲⢦⣤⣤⣀⣀⣸⣿⣄⣀⣤⣤⣀⠔⠂⠀⢠⣿⣯⣿⣶⡄
⠀⠀⠀⠀⠀⣾⣏⣻⡀⠀⠀⠀⠀⠀⢠⡿⠘⠙⣷⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⣸⣿⣿⢿⡻⣿⡆
⠀⠀⠀⠀⣸⣿⣿⣧⣧⡀⠀⠀⠀⠀⣠⠀⣼⢢⣿⡆⠀⠀⠀⠀⠀⢀⣾⡿⠻⣿⣧⡀⠀⠀⠀⠀⠀⣿⣿⣏⡅⢎⡿⣿
⠀⠀⠀⢀⣿⣿⣿⠛⠼⣳⠀⠀⠀⢠⡿⠑⠈⢂⣿⡇⠀⠀⠀⠀⢠⡿⠛⠀⠀⠈⠻⣷⡀⠀⠀⠀⠀⣿⣿⡷⠜⡡⢞⡿
⠀⠀⠀⣼⣿⣿⣷⠛⡲⣿⡆⠀⠀⠨⠀⡀⠆⡿⢁⣷⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠈⠳⠀⠀⠀⠀⢹⣿⣿⣣⢑⢹⡇
⠀⠀⣰⣿⣿⣿⣁⣼⠳⣄⣿⠀⠀⢈⣀⠦⠻⣹⡯⡯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣬⠹
⠀⢠⣿⣿⣿⣿⣧⡄⠻⣀⢽⠆⠀⠈⠄⣘⢴⣿⡗⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣟⡷
⠀⢸⣿⣿⣿⡗⠒⢉⠗⠜⠺⡄⠀⠀⠠⠟⣿⣿⡷⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛
⠀⠀⠙⠋⠿⣿⡷⠺⡷⠚⠓⠁⠀⠀⠀⢰⣿⠿⠇
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠶⠞⠛⠛⠛⠛⠛⠛⠛⠶⠶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠚⠉⠁⠀⠀⠀⠀⠈⠉⠓⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⣄⠀⠀⠀⠀⠀⠀⠀⠈⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠉⠀⠀⠈⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⢰⡆⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠓⠶⠛⠁⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⣀⣀⣀⣠⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠏⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋⠀⠀⠀⠀⠀⠀⢀⣴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠈⣻⣿⡳⠶⠶⠶⣤⣤⡴⠶⠶⠶⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⣠⡾⠃⠈⠻⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⣠⡾⠋⠀⠀⠀⠀⠀⠉⠻⠶⣤⣀⣀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠶⠞⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠀⢀⡶⠋
⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⡴⠋
⠀⠀⠀⢀⣴⠟⠁⢀⣴⠟⠁
⠀⠀⣴⠟⠁⢀⣴⠟⠁
⢠⡞⠁⠀⣴⠟⠁
⣿⣀⣤⠞⠁