Grandmother Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠙⠓⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠶⠐⠒⠒⠒⠂⠸⠦⣀
⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⣰⢆⢀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⢀⡼⠁⠈⠣⡑⢄⠀⠀⠀⠈⢇
⠀⠀⠀⠀⠀⢨⡀⢀⢠⡶⠋⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠌⢠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⡄⠀⡇
⠀⠀⠀⠀⠀⣲⡸⠀⠀⡀⣀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠸⣀⡃
⠀⠀⠀⠀⡜⠹⡁⠀⠀⠀⠁⠀⠘⠁⠀⠀⠀⠁⠀⠀⠀⢹⠉⠂
⠀⠀⠀⠀⠘⠤⢧⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠧⠔⠃⠀⠀⠀⠀⠠⢖⣦⣠⠤⠤⠤⣤⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠁⠀⠀⠀⠀⠁⠀⣠⣔⠁⠀⠀⠀⠀⠀⠀⠀⡠⠊⢀⡀⠀⠀⠀⠀⠈⠂⠉⠲⡀
⠀⠀⠀⠀⠀⠀⠀⢀⡠⠜⠑⣖⠂⠒⠒⠐⠂⣫⠇⠀⠉⠲⢄⠀⠀⠀⠀⡜⡡⠒⠁⢣⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⢀⠔⠋⡇⠀⠀⢹⠑⠂⠀⠒⠊⠹⠀⠀⠀⠀⢀⠗⢄⡠⠲⠋⠀⠀⣀⠀⠑⢄⢸⡆⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⡴⠁⠀⠀⡇⠀⠀⠘⡀⠀⠀⠀⠀⡆⠀⠀⠀⠀⡌⠀⠈⢣⡀⠀⠀⠸⠟⠀⠀⠀⠉⠙⢆⠀⠀⠀⠀⢸
⠀⠀⢀⠎⠀⠀⠀⠀⠇⠀⠀⠀⡇⠀⠀⠀⠀⡇⠀⠀⠀⢲⡇⠀⠀⠀⢧⠀⠀⠀⠀⠐⠀⠀⢀⣶⡆⠑⠤⣀⢀⠆
⠀⠀⡌⠀⠀⠀⣀⣼⠀⠀⠀⠀⡇⠀⠀⠀⠀⢃⠀⠀⠀⠀⢡⠀⠀⠀⠸⣆⠀⠀⢈⠀⠠⠀⠀⠁⠀⠀⠰⣥⠊
⠀⠀⡇⠀⠀⠀⠏⢸⠀⠀⠀⢰⠀⠀⠒⠒⠀⠘⡄⠀⠀⠀⠨⡆⠀⠀⢨⣄⣑⠤⣀⠁⠀⠀⠀⠀⠀⣀⡀⡸
⠀⠀⠘⣤⡶⠚⠧⣸⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⢀⡁⠀⠀⡸⠈⢧⣀⠈⣟⠐⠒⠒⠊⠉
⠀⠀⠀⠘⢤⣄⡤⠻⠦⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⣀⠁⢀⡰⠁⠀⠀⠀⠉⠀⢳
⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠛⠲⡇⠣⡀⠀⠀⠀⡠⠊⠉⡇
⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡶⠻⢆⡈⠁⢲⠉⠁⠀⡰⠁
⠀⠀⠀⠀⠀⢸⠃⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⠉⠓⠚⠦⠔⢺⠁
⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⣷⣠⡑⢤⣀⡀⠀⢸
⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠢⣄⠀⠀⠀⡀⠀⠀⠀⢀⣠⡇⠇⠀⠉⠉⠛⠛⠛⢻
⠀⠀⠀⠀⠀⣼⠀⠘⡄⣀⣀⣀⣀⣀⣉⡀⠶⠤⠘⠊⠉⣀⣴⠀⠃⠀⠀⠀⣿⠀⠀⢸
⠀⠀⠀⠀⠀⣿⠀⠀⠧⢄⣀⣀⣀⣀⣀⣀⡠⠤⡔⠂⠉⠀⠸⠀⠀⠀⠀⠸⢳⠀⠀⢸
⠀⠀⠀⠀⠀⡏⠀⠀⢸⡀⠀⠀⠀⡇⠀⠀⠀⠀⢣⠀⠀⠀⡇⢈⠄⠀⠀⠼⠸⠀⠀⢸
⠀⠀⠀⠀⠀⡇⠀⠀⠈⢧⠀⠀⠀⠳⠀⠀⠀⠀⠈⢆⡀⠀⢇⠈⠇⠀⢀⡇⠀⢦⣤⣼⡄
⠀⠀⠀⠀⢀⡏⠀⠀⠀⡞⠲⢄⠀⡆⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠿⢉⠹⠇
⠀⠀⠀⠀⠈⠁⠀⠀⠀⠑⠢⠤⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠀⠂⠐⠂⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠄⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⢀⠀⠀⠀⠐⠈⠂⡁⠒⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⢂⠀⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⡀⠀⡀⠀⠀⠀⠀⠂⢀⣂⠀⡀⠀⠀⠈⡒⠁⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⡌⠀⢀⠊⠴⠂⠀⠀⠊⠀⠀⠀⢀⠀⠁⠀⢀⠠⠠⠌⢀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢨⠀⠠⠀⡠⠆⠀⠀⠀⠀⠀⠀⣈⡈⠀⡄⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢈⣤⠀⠀⠀⠀⠀⠀⠀⠿⠇⠀⡀⠀⠀⡐⠀⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡁⠀⠨⠛⠒⠂⠀⠀⠄⠀⠀⠈⠀⠀⠀⠀⠀⡗⠠⠐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⢱⠆⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⡠⠊⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢆⠁⠔⠱⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⢈⠃⡀⠒⠡⠒⠆⠀⠐⠊⢉⠀⠐⠆⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠀⠀⠀⢄⠀⠀⠄⠀⢠⠂⠔⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠈⠖⢃⡀⠠⣌⠙⠀⠀⠀⠀⠀⠑⠤⠀⠀⢀⠄⠦⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠔⠈⣄⠀⠀⠀⠉⠀⠁⠁⠀⠀⠀⠫⡢⣀⡀⠀⠀⠀⡀⠀⠀⠀⠉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⡰⠁⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⡀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢌⠀⠁⠀⠘⠃⡤⠊⠑⠠⢀⣀⣀⡀⠠⠤⠀⠀⠤⠤⠐⠋⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠠⠴⠀⠺⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠂⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⡰⠉⡄⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⡰⢁⠴⠃⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠈⠀⠀⠀⡀⠤⠒⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢠⠃⠙⡤⠂⠀⢀⣀⠀⠀⠀⠀⢀⣀⣀⡀⠠⠤⠐⠒⠈⢁⡄⠀⠛⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⢠⠃⠀⠀⠑⠒⠢⡤⠀⠤⢀⣠⣄⣀⣀⠤⣤⠄⠴⠒⠒⠉⠉⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⠁⡇⠀⠀⠀⠀⠀⠸⠤⠐⠊⠁
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣥⣤⣤⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⠿⠛⠛⠿⢶⣤⣶⠾⠟⠛⠻⠷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠉⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠈⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣾⣷⣠⣴⠾⠟⠛⠉⠉⠉⠉⠉⠉⠉⠙⠻⢷⣦⣄⣰⣿⣶⣶⣶⣤⣄
⠀⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠈⠙⢿⣦⡀
⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄
⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡶⠿⠛⠉⠀⠀⠀⠀⠈⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⣿⠇⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣤⣤⣤⡶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣦⡀⠀⠀⠀⠀⠀⠀⣿
⢿⣆⣴⠃⠀⠀⠀⣼⡟⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⠀⠀⢳⣀⣿
⢸⣿⠃⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⣀⣠⡄⠀⠀⠀⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⢻⣿
⣼⡇⠀⠀⠀⣰⡿⠁⠀⠀⠀⠛⠛⠛⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠛⠃⠀⠀⠀⠀⢻⣦⠀⠀⠀⠈⣿
⣿⡇⠀⠀⣼⣿⣀⣀⣀⣤⡾⢟⣛⢛⣛⢛⡻⣦⡀⠀⠀⠀⠀⠀⢀⣴⠟⢛⣛⢛⣛⠻⣶⣤⣀⣀⣀⣻⣷⡀⠀⠀⣿
⢻⣇⢠⠀⠈⠻⣿⡍⢻⡟⠀⠈⠀⣿⣿⡇⠈⢸⣷⣴⠾⠿⠷⣦⣾⠃⠀⣿⣿⣧⠀⠁⠈⣿⠟⢩⣿⠛⠁⠀⣦⢠⣿
⠈⢻⣾⡄⠀⠀⣿⠃⠈⣿⡀⠀⠀⠙⠛⠁⠀⢸⣿⠁⠀⠀⠀⠈⣿⡄⠀⠙⠛⠃⠀⠀⢠⣿⠀⠸⣷⠀⠀⢀⣿⡿⠃
⠀⠀⠙⢿⣄⡀⠹⠄⠀⠙⢷⣤⣀⣀⣀⣠⣴⠟⠻⣦⣄⣀⣠⣴⠟⠻⣦⣄⣀⣀⣀⣴⡿⠃⠀⡰⠃⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠙⠻⣦⣄⣀⠀⠀⠉⠉⠉⠉⠉⠀⣀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠉⠉⠉⠁⠀⠀⣀⣠⣴⡿⠋⠁
⠀⠀⠀⠀⠀⢠⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⡨⠛⠛⠶⠶⠶⠛⠛⠅⡀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠈⠿⣿⡿⠏⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠙⢿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡛⠿⢷⣶⣶⣶⣶⣶⣾⠿⢛⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣇⣀⠀⠀⠉⠉⠉⠀⠀⣀⣰⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣇⣀⣤⠀⢠⣄⣸⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠶⢾⣿⣿⣿⣿⣿⣿⣿⣿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⠿⠟⠛⠉⠉⠉⠛⠻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠛⠁⠀⠀⠀⣀⣠⣤⣤⣴⣾⣿⣷⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⣀⣴⣾⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣴⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣶⣶⣦⣄⡀⠈⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣄⡉⠛⢿⣦⡀⠀⠉⠻⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠿⠿⠿⣿⣿⣶⡀⠙⠧⠀⠀⠀⠈⠙⢿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⣰⣿⡟⠁⠀⠀⠀⠀⠈⠙⠿⡄⠀⠀⠀⢤⣀⠀⠀⠙⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣾⣿⠃⠀⠀⠀⠠⣤⣤⣴⣶⡿⠟⠋⠀⣰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⣶⣄⠙⢷⡄⠀⠀⢿⣷⡀
⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⢀⡀⠀⠈⠁⠀⠀⣀⣤⣾⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠘⣿⡄⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠙⣿⡿⠿⠿⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠘⣷⡀⠀⢹⣿
⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠰⢶⣶⣾⣿⠇⠀⠀⠀⠀⠀⠀⠦⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠀⠀⠘⣿⣧⠈⠿⠆⢸⣿
⠀⠀⠀⢠⣿⡟⠀⠀⠀⣀⣀⣀⣤⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢻⣷⡀⠀⠀⢀⣾⡿⠋⠉⠀⠀⠀⠀⢹⣿⣷⣄⡀⠈⢿⣷⡀
⠀⠀⠀⢸⣿⠁⠀⠀⠀⣿⡟⠛⢻⡿⠻⣦⣀⠀⠀⠀⠶⠶⣷⣶⣤⡀⠀⢻⣷⠀⠀⢸⡏⠀⣠⣶⣶⡤⠀⠀⠘⣿⡉⢻⡇⠀⠀⣿⣷
⠀⠀⠀⢹⣿⡀⠀⠀⠀⢸⣿⣄⣿⠇⠀⠀⠙⢷⣦⣀⣤⠤⠿⠿⠿⠷⠦⣼⣿⣀⣀⣸⣀⣨⡭⠿⠿⠷⠶⠶⢤⣿⣧⣼⡇⠀⠀⣼⣿
⠀⠀⠀⠘⣿⣧⡀⠀⠀⠈⢿⣿⣿⠀⠀⠀⠀⠀⠹⣏⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠉⠉⣿⠁⠀⠀⠀⠀⠀⠀⠀⢸⣿⠿⠁⠀⣰⣿⡟
⠀⠀⠀⠀⠈⠻⣿⣦⣄⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠦⢶⣶⡶⠚⢋⠀⠀⠀⠘⣿⠲⠶⠶⠴⠶⠶⠚⢻⡿⢀⣴⡿⠿⠋
⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣷⣶⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠛⠛⠻⠷⡶⠿⠛⢿⣷⡀⠀⠀⠀⠀⠀⣾⣷⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣄⠙⣿⣆⠀⠀⠀⠀⠀⠀⢠⣾⡟⠁⠀⣠⣴⣶⣶⣶⣦⣤⠀⢻⣧⠀⠀⠀⠀⣼⡟⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣾⣿⣦⡀⠀⠀⠀⠀⠸⣿⠀⠀⣴⣿⣋⣉⣉⣉⣹⡟⠀⢸⠏⠀⠀⢀⣾⡿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⢻⣷⣄⠀⠀⠀⠀⠙⠂⠀⠹⣿⣍⣉⣉⣉⣻⣇⠀⠀⠀⠀⣰⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠿⠋⠀⢀⣀⣼⣿⣷⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡟⠉⠀⢻⣿⣿⣷⣦⣴⣤⠀⠀⠀⠐⠶⠶⠶⠂⠀⣠⣾⡿⢻⣿⠇⠀⢹⣿⣶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⡇⠀⠀⠘⣿⡇⠉⠛⠻⢿⣷⣤⣀⣀⣀⣀⣀⣤⣾⡿⠋⠀⣼⡿⠀⠀⢸⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⡟⣿⣷⡀⠀⠀⠙⣿⣦⡀⠀⠀⠈⠛⠻⠿⠿⠿⠟⠛⠁⠀⢀⣼⡿⠃⠀⠀⣼⡇⠸⣿⣿⣿⣿⣿⣿⣿⣦⣀
⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⣿⣷⡀⠀⠀⠈⠻⢿⣶⣤⣀⣀⠀⠀⠀⢀⣀⣀⣤⣶⡿⠛⠀⠀⠀⢠⣿⠁⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢼⣿⣷⡀⠀⠀⠀⠀⠈⠛⠻⠿⠿⠿⢿⣿⠿⠟⠛⠁⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢸⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣤⣀⡀⠀⠀⠀⢀⣿⣿⣷⣄⠀⠀⢀⣠⣴⣿⣿⣿⡟⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠘⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⣀⣀⣀⣉⣉⡛⠛⢛⠛⡛⠛⠛⣀⣀⣀⣀⣀⣈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢛⣁⣀⣀⣀⣀⣀⡛⠛⢛⣛⣋⣉⣁⣀⣀⣀
⣿⣿⡿⠿⢿⡿⠿⠿⢿⢿⠿⢿⡿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣶⣶⣾⣷⣾⣿⣾⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠠⠔⠀⠐⠒⠒⠄⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠴⠆⠊⠉⠓⢆⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠁⠀⠀⠀⠀⠀⠈⡄⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠃⠀⢀⠀⠀⠀⠀⠀⠛⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⡰⠇⠀⠚⢉⣉⣀⠀⠀⠀⠰⠆⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⣀⡀⠀⠀⢠⠤⠞⠃⠀⠀⠀⠈⠃⠀⠰⣀⣀⣨⠂⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⢴⡾⣗⠤⠀⠀⠀⠀⠀⠀⢀⢄⣈⠩⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠋⠲⢜⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠙⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠈⢳⡈⠑⢦⡤⠤⠤⠤⠶⠒⣶⢛⡧⢒⡶⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠳⠀⠈⢧⠀⠀⠀⡴⠒⢾⣏⣰⡏⠀⠀⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⢠⡦⠞⣩⣿⣗⣮⣇⣰⠋⠁⠀⠀⠉⠉⣏⠲⠒⠶⠦⡄⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠰⣟⠀⠀⢻⡿⠋⠁⢘⣅⡀⠀⠀⠀⠀⢀⡟⠈⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠈⢳⡀⠀⠙⢶⣛⠉⢁⠿⣷⠲⢦⠶⠟⢀⠀⠀⠀⠀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠛⠲⢆⠀⠙⣳⣾⣤⠟⡆⠘⠶⠶⡏⠻⠟⣿⡋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⣄⠀⠀⠀⠀⢀⡴⠚⠶⠛⢉⣉⣼⣶⠷⠴⠶⠚⠁⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠈⢳⡎⠀⡔⠁⠀⠀⠀⠀⠈⢉⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢦⣈⠳⠦⠾⠳⢤⣀⠀⢀⣴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠈⣳⠦⣤⣤⣤⠼⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡈⠓⠦⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠴⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠉⠉⠉⠉⠙⠋⠉⠉⠉⠉⠁⠀⠀⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠉⠙⠳⡶⠶⠶⠤⠤⢴⠶⠶⠚⠛⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⡇⠀⠀⠀⠀⣸⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⢠⠛⡆⠀⠀⡸⢏⠀⠀⠀⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⢠⠎⢰⠁⠀⠀⢹⠈⢦⡀⠀⠀⠘⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠧⠠⠶⣫⢶⡼⠀⠀⠀⠈⢆⠤⣍⠒⠂⠘⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⣤⠤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠦⠤⠞⠁
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⣀⢀⡀⡀⡉⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉⠉⠉⡁⠈⠉⠉⠉⠑⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⢀⡴⠳⡀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⢠⠃⡀⠀⠀⠀⣠⠞⠁⠀⠱⣌⠢⣄⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⣎⠜⠀⢠⣔⡼⠋⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡏⠉⣠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠦⣀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠈⡇⢸⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠙⡆⢸
⠀⠀⠀⠀⠀⠀⡠⣷⠏⠀⠀⠐⢰⠆⠀⢀⡇⠀⠀⠀⠲⡶⠀⠀⠀⠱⣼⠤⡀
⠀⠀⠀⠀⠀⢸⡁⠸⡀⠀⠀⠀⠀⠀⠀⠹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⡤⢤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⠙⠶⢧⡀⠀⠀⠀⠀⡠⠀⠀⠀⠀⢆⠀⠀⠀⠀⢀⡼⠶⠚⠁⠀⠀⠀⠀⠀⠀⢀⡴⠋⣉⠤⠀⠀⠀⠀⠀⢉⡙⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⡀⠀⠀⠀⠀⠈⠁⠀⠈⠀⠀⣀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⠠⠊⠀⠀⠀⢀⣀⠀⠀⠀⠀⠉⠉⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠗⢲⣤⠤⠶⠶⠦⠤⠒⢺⡇⠈⠙⠲⢄⠀⠀⠀⠀⠀⠀⡼⢁⣠⠤⠒⠒⠉⠉⡸⠃⠀⠀⠀⠀⠀⠀⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⡏⠀⠀⠈⡷⠤⣀⣀⣀⡠⠔⠻⠁⠀⠀⠀⠀⠙⣦⡀⠀⣴⠋⠋⠁⠀⢀⣤⠀⠀⠰⢇⡴⢻⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⡇⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡰⠁⠙⣆⠹⣤⠀⠀⠀⠸⠟⠀⠀⠸⠏⠀⠈⣆⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⡇⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⢠⠃⠀⠀⠈⣷⢰⡀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣴⡻⢆⠸⠀⠀⠀⡞
⠀⠀⠀⢀⡞⠀⠀⠀⠀⢀⠇⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡀⠀⠀⠀⠸⡆⣧⡀⠀⠀⠠⣄⡀⠀⠀⠀⠋⠁⠈⢣⡀⢀⡾⠁
⠀⠀⠀⣼⠀⠀⠀⠠⣀⣼⠀⠀⠀⠀⢠⣇⣀⣀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⣼⠇⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻
⠀⠀⠀⣿⠀⠀⠀⠰⠏⢸⠀⠀⠀⠀⣸⠀⠀⠒⠒⠂⠀⠸⡄⠀⠀⠀⠀⢸⡄⠀⠀⠀⢽⠶⣶⠚⠉⠒⣤⣄⣀⣀⣀⣀⢤⡖⠒⠶⠋
⠀⠀⠀⠱⣄⣠⣴⢾⡄⢸⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⢨⠛⠀⠀⠀⡼⡄⢩⠳⠤⠄⠵⢄⠀⠀⠀⠀⢰⠀⠀⡜
⠀⠀⠀⠀⠹⣟⠁⠀⢈⣾⡀⣀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⣠⡎⡃⠀⣀⣼⠁⣦⠘⡗⠐⢢⠀⠈⣧⠀⠀⠀⡎⢀⡴⠁
⠀⠀⠀⠀⠀⠈⠛⢳⡏⢰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⢸⡇⠰⣄⢸⡆⠱⣤⡾⠊⠉⢹⠀⠀⠀⠓⠋
⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠉⢹⣷⣄⠈⠉⠛⠶⡏⠀⠀⢀⡾
⠀⠀⠀⠀⠀⠀⠀⣾⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠢⡶⠋⡇⠈⠑⠲⠤⢼⣹⣀⣤⡎
⠀⠀⠀⠀⠀⠀⠀⣿⠁⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡇⣀⠀⠀⠀⠀⠈⠑⢄⡙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠸⠋⠭⠭⣐⣛⡒⠢⠤⠄⢹⡆⠙⣆
⠀⠀⠀⠀⠀⠀⠀⣿⠀⢸⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣞⠒⠦⠤⠤⣀⣉⣉⡉⠓⠒⣿⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠸⠀⠀⠀⠀⠀⠈⠑⠢⠄⠈⠁⠒⣠⣤⣤⠴⠒⢻⠀⣿⠐⠒⠲⠤⠤⣄⣈⣉⣉⠁⣿⠀⠈⢣
⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⡗⠒⠀⠀⠀⠀⠐⠀⠒⠚⠋⠉⠉⢀⣀⡤⠖⢻⠀⠈⢹⠋⠓⠐⠶⠒⠦⢠⠌⠉⢿⠉⠉⠁
⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⢳⠶⠦⠤⢀⣀⣄⡀⠤⠤⠶⠒⡟⠉⠁⠀⠀⡇⠀⠀⢸⠀⠀⠀⡇⠀⠀⠈⣦⣀⡼
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⡄⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⢷⠀⠀⠀⢠⠇⠀⠀⢸⠆⠀⣠⠃⠀⠀⠸⣇⡼⠃
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢳⡄⠀⠀⠀⢼⠀⠀⠀⠀⠀⠘⢆⡀⠀⢸⡀⠀⠀⢸⣀⡀⠻⢄
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢨⠦⣀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠙⠒⠒⠃⠀⠀⠘⠧⠤⠴⠊
⠀⠀⠀⠀⠀⠀⠺⠇⠀⠀⠀⠱⣄⣀⣙⣦⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣤⠤⠤⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⣤⣤⡀⣴⠑⠂⠀⠀⠀⠀⠀⠀⢹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⢠⠞⢋⣿⠁⢠⣸⣧⡀⠀⠀⠈⢀⡀⠀⢶⣿⡷⢄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠁⠁⠀⠀⠈⠛⠻⠛⠉⢛⣻⠦⠅⣂⣌⠳⣌⣸⡇⠀⠀⠉⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣩⣔⣀⣀⣹⣿⣿⣿⣿⠀⠀⠀⠈⠜⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⣧⠀⠀⠀⠀⠀⠀⠀⢠⡿⠛⠛⠉⠙⠋⠻⠟⠟⠶⢮⣀⡀⠀⠀⣿⣽⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⢀⢽⣦⠀⠢⠄⠀⠄⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣧⢴⠇⢌⠙⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠄⣻⣿⣿⣶⣦⣴⡼⠃⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠑⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠘⠄⢰⢳⣿⣿⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⣀⠹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠙⣆⠰⠃⢰⣿⠃⢈⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⠀⠸⣧⠀⢠⢀⣿⡍⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⡀⠀⠀⠀⢸⣇⣼⠞⠛⠛⣍⣙⠟⠛⢶⣎⣀⣃⣴⠋⠻⢋⡭⠛⠛⠳⣦⡹⣧⠀⢉⠛⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡈⠀⠀⢀⣿⡿⣿⣤⣴⡶⠛⠛⠒⠃⢻⡏⠉⢹⡟⠘⠒⠛⠛⣶⣦⣤⣿⢿⣿⠀⣎⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣒⠚⣯⣬⡇⠻⣍⠀⠈⠀⠀⠀⣠⡾⠀⠀⠀⢷⣄⠀⠀⠈⠉⠀⣩⡿⣸⣏⣻⣞⡽⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⢻⣿⣷⡐⠈⠛⠛⠛⠛⢉⣥⠄⠀⠀⠀⠠⣌⠉⠛⠒⠒⠛⢁⠀⣾⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢼⣷⣄⡀⠀⠀⢀⠘⠙⠛⠛⠲⠞⠓⠉⠃⠀⠀⠀⢄⣀⣼⡯⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠈⡯⣰⠿⠈⠛⠤⣄⣤⣤⣠⣤⣤⣀⠄⠘⠿⠟⡆⢹⠃⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣄⡀⢀⠀⠀⠀⠀⠀⠄⢀⣀⠴⢫⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢿⣿⣯⡉⠛⠻⢷⣶⣶⠦⠐⠉⠀⠀⠀⢡⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠔⠊⠁⢀⠈⢿⣦⡈⠢⡀⠀⠀⠁⠀⠠⠀⠀⠀⡰⣿⢃⡿⣼⡷⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠒⠉⠉⠀⠀⣤⠀⠀⠈⠀⠈⢏⠻⣇⠀⠀⠀⠀⠀⠀⢀⡠⠊⣰⠃⠸⠁⠈⠾⠟⢯⢝⡲⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⢀⠊⠙⠻⢷⣄⠀⠀⠀⣠⣿⠞⠋⠱⣦⠃⠀⠀⠀⠀⠈⠈⠜⠆⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠗⠀⠀⢀⡀⠀⠀⠁⠀⢠⠀⠀⠙⠧⣠⡾⠋⠀⠀⠤⠀⠘⠁⠀⠛⠀⠀⠰⠀⠀⢀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⣤⠀⠀⠀⠀⠀⠀⡿⠀⠀⣀⠀⠀⢀⡄⠀⠀⠀⠓⢀⠀⠀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠶⠀⠀⠈⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣶⣦⣴⣶⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⠟⠛⠉⠙⠛⠻⠿⠿⠟⠛⠋⠉⠙⢻⣿⣿⣦⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣦⣄⣀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡇
⠀⠀⠀⠀⢀⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀
⠀⠀⠀⢠⣾⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡄
⠀⠀⢠⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⠶⠶⠾⠛⠙⠳⠶⢤⣤⣤⡤⠴⠶⠛⠛⠷⠶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿
⠀⠀⠀⢹⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠏
⠀⠀⢀⣾⣿⣿⡆⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷
⠀⢀⣾⣿⡟⠉⣿⣄⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⢀⣠⡟⠉⢻⣿⣧
⠀⢸⣿⣿⠀⠀⠀⠙⠻⠿⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠾⠟⠉⠀⠀⠀⣿⣿⡇
⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇
⠀⠈⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠂⣠⣾⠿⠛⠛⢛⣛⣛⣻⢷⣄⠀⠀⠀⠀⠀⢀⣴⣾⣛⣛⣛⠛⠛⠛⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡿
⠀⠀⣼⣿⣿⠀⠀⠀⠠⣄⣀⣀⣴⡿⠁⠀⣠⢶⣿⣿⣿⣯⠓⠙⢷⣦⠤⣤⣴⡟⠛⢹⣿⣿⣿⣿⢦⡀⠀⠘⣿⣦⣄⣀⣀⡀⠀⠀⠀⣿⣿⣧
⠀⢸⣿⣿⠁⠀⠀⠀⢘⣦⣽⣿⡿⣧⠀⠈⠁⠈⠙⠛⠛⠛⠂⠀⣸⡇⠈⠁⢻⡅⠀⠚⠟⠛⠛⠛⠀⠉⠀⢀⡿⣿⣟⣡⡾⠃⠀⠀⠀⠈⣿⣿⡇
⠀⠈⢿⣿⣷⣤⣤⣤⣭⣥⣼⣿⡇⠘⢧⡀⠀⠀⠰⠒⠛⠀⠀⣰⠏⠀⠀⠀⠈⢷⡀⠀⠀⠛⠛⠓⠀⠀⢀⠞⠀⣿⣿⣥⣤⣤⣤⣶⣤⣾⣿⡟
⠀⠀⠀⠙⢿⣿⣿⣿⢿⣿⣿⣿⡇⠀⠀⠙⠢⠄⠀⠀⣠⡴⠞⠁⠀⠀⠀⠀⠀⠀⠙⠲⢤⡄⠀⢠⡤⠖⠁⠀⠀⣿⣿⣿⣿⡟⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠙⢿⣿⣯⢿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡀⠀⠀⠀⠀⠀⠀⢀⡶⣄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣟⣼⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣿⣿⣿⣇⠀⠀⠀⠀⣀⣤⠞⠁⠀⠙⠻⢦⣤⣤⡶⠟⠋⠀⠈⠳⣦⣀⡀⠀⠀⠀⣼⣿⣿⣿⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢀⣽⣿⡀⠀⠀⠛⠋⠀⡀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢀⠈⠙⠛⠁⠀⢰⣿⣇⡀⣹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⡇⠀⠀⠀⠀⠀⠇⠀⠈⠉⠛⠛⠛⠛⠛⠛⠉⠁⠀⢸⠀⠀⠀⠀⠀⣼⣿⡿⠟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣦⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣠⣴⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡏⢹⣿⣿⣿⣿⣷⣶⣦⣤⣤⣴⣶⣾⣿⣿⣿⣿⡏⢿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⠿⠋⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠛⢿⣿⣿⣦⣄⡀
⠀⠀⠀⢀⣠⣴⣶⣿⣷⣾⣿⣿⣿⡋⠁⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠈⢙⣿⣿⣿⣿⣿⣷⣶⣦⣄⡀
⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠈⢙⣿⣿⣿⣿⣿⣿⠋⠁⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⠿⢿⣿⣿⣷⣤⡀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⣠⣾⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣦⣀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛
⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣍⡀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⣀⣄⠀⠀⢦
⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⢰⠋⠁⠀⠀⠻⣄⡄⠊⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⠀⠀⢀⠼⠤⠿⠿⡀⢰⡄
⠀⠀⠀⠀⠀⠀⠀⢘⢺⡶⠃⠀⠀⠀⠀⠀⠀⢹⡀⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠴⠂⠀⠀⠀⠀⠈⡇⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠛⡖⠣⠖⢦⠤⡴⠺⣜⢲⠟⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀⣧⣒⡶⢠⢠⡔⣖⣢⣧⢸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡳⠤⠴⠊⠀⣙⠦⠤⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠺⡏⠡⠄⣎⠀⡂⠈⠙⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠉⣀⣤⣀⠀⠂⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠖⠀⠠⠤⠀⠒⠘⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣧⠉⠉⠀⠀⠀⠉⠉⣾⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡤⣀⡀⠀⠐⣇
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠒⢄⠀⠀⣀⣠⠞⠉⠈⠙⢳⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠀⢀⢘⠛⠳⠦
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠉⠀⠀⠀⠀⠀⠑⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⠀⠈


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣿⣿⣿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠛⣉⣁⣀⣀⣀⣀⡀⠉⠙⠻⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣼⣿⣿⣾⣿⠿⠿⠟⠻⠿⠿⢿⣿⣶⣦⣄⡈⢻⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⡿⠿⠿⠿⠿⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣠⣴⣿⠟⠁⠀⠙⢿⣷⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏⠀⠀⠀⢀⣴⣿⠟⠋⠁⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⢿⣿⣷⣶⣦⣤⡀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠃⠀⠀⢠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣦⡀⠀⠀⠈⣿⣧
⠀⠀⠀⠀⠀⠀⢠⣶⣶⣾⣿⠏⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⠘⣿⣷⣴⣷⡄
⠀⠀⠀⠀⠀⠀⣼⣏⠉⠉⠁⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠉⠉⢹⣿
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠒⠛⠛⠓⠂⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠂⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⠀⠀⠀⢸⣿⡆⠀⠀⠀⠀⠀⣿⣿⣤⣤⣶⡾⠿⠿⠿⠿⠿⣶⣦⡀⠀⠀⠀⣠⣶⠿⠿⠿⠿⠿⠿⣶⣤⣤⣿⣿⠀⠀⠀⠀⠀⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣀⡀⣀⣴⣿⠋⠙⣿⠃⠀⠀⢰⣾⠿⠷⣆⠹⣿⣶⣶⣾⡟⢠⡾⠿⢷⣦⠀⠀⠈⣿⡏⠙⢿⣧⣀⢀⣀⣤⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡟⢿⣿⠁⠀⠀⢻⣦⠀⠀⠈⠁⠀⠀⠈⢠⣿⠁⠀⢿⣇⠈⠀⠀⠀⠉⠀⠀⢠⣿⠁⠀⠀⣹⣿⠿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⠀⠻⣷⡀⠀⠀⠹⢷⣦⣤⣤⣤⣤⣶⠟⠁⠀⠀⠈⠻⢷⣤⣤⣤⣤⣤⣾⠿⠃⠀⠀⣴⡿⠁⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣦⣜⢿⣦⠀⠀⠀⠀⠉⠉⠉⢀⠠⣆⠀⠀⠀⠀⢀⡶⣄⠉⠉⠉⠁⠀⡄⠀⣠⣾⣏⣤⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢉⣤⣿⣷⡐⢧⣀⣀⣀⡴⠋⠀⠙⠷⠶⠶⠶⠛⠁⠈⠳⣄⣀⣀⣴⠇⣴⣿⣧⡉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⣹⡇⠀⠉⠉⠁⠀⢠⣀⣀⣀⣀⣀⣀⣀⣀⣠⠀⠀⠉⠉⠀⢸⣿⠀⣹⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣧⡀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⣸⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠉⠛⠘⢷⣄⣀⠀⠀⢀⣀⣴⠟⠈⠉⠉⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠉⠀⠀⠀⠀⠀⢻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡟⢿⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⠿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣿⣿⡄⠻⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡿⠃⣼⣿⣿⣿⣿⣷⣦⣄⣀
⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡈⠻⢿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⠿⠋⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀
⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣈⣉⣉⣉⣉⣉⣀⠀⠀⣀⣈⣉⣉⣉⣉⣉⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠙⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⢷⣦⣴⡾⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠄⡰⠈⠉⠱⠀⠀⠀⠀⠀⣀⠤⠔⠊⠉⠉⠒⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⣠⠂⠀⠀⣠⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⣄⠀⠀⠀⠀⠀⠀⡄⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠀⠊⠁⢀⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀⠀⠐⠀⠀⠘⠃⠐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣄⠀⠁⠀⠀⠀⠠⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⡀⠀⢈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡁
⠀⠀⠀⠀⠀⠀⠠⠔⠒⠂⠀⠀⡀⠀⡏⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠶⠥⠤⡄⢠⠤⠬⠶⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠐⠄⣀⠀⣀⠔⠀⠀⡕⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⡗⢺⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⢮
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⡀⠀⠀⢀⡀⣀⣼⠀⠀⠀⠀⠀⠁⡇⢸⠈⠀⠀⠀⠀⠀⣧⡀⢀⠀⠀⠀⢀⡼⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⣎⡠⠋⠹⣤⢤⣤⡤⢤⣠⣇⣸⣤⡤⣤⣤⣤⣤⠇⠙⢌⣱⠀⢀⡜⠀⡄⠀⠉⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⠞⠁⠀⠀⠀⠀⢀⠔⠂⠀⠀⠀⠀⠐⠢⡀⠀⠀⠀⠀⠈⠳⡔⠋⠀⠀⠈⠂⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠘⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⡀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⣀⢀⡀⡠⢄⡀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠈⠠⣄⠀⠀⠀⠀⠑⠢⠤⠤⠤⠤⠔⠊⠀⠀⠀⠀⡠⠈⠁⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⢀⡠⣄⢀⡀⡀
⢀⠤⢧⡀⢸⠁⠀⡅⠀⠀⠀⠀⠀⣀⡇⠀⠀⠀⠀⠀⠈⠉⠒⠠⠄⣀⢀⡎⠑⠊⢱⡀⣀⠠⠄⠒⠉⠁⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⠀⠀⣈⠀⠈⡇⢀⡼⠤
⢰⡄⠀⡘⠈⠀⠀⠨⣄⣀⠀⠀⡞⠁⢣⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⡜⠀⢳⠀⠀⣀⣠⠅⠀⠀⠇⢃⡀⢠
⢧⣀⣀⣁⠀⢀⣀⡀⠀⠈⠙⠐⢧⣀⣈⢦⡀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⢀⡼⣁⣀⡼⠃⠋⠁⠀⢀⣀⡀⠀⣀⣀⣀
⠀⠀⠀⠈⠁⠉⠀⠉⠓⠦⣤⣀⡰⠉⡝⠀⠙⢦⣄⡀⠀⠀⠑⠦⣄⣀⠀⠀⢀⠀⠀⠀⢀⣠⠴⠊⠀⠀⢀⣠⠴⠋⠀⠫⠉⢆⣀⣤⠶⠚⠉⠀⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠁⠀⠘⠦⣀⡠⡎⠉⠛⠲⢦⠤⣤⣤⣭⣭⣭⣭⣭⣭⣤⡤⠤⡴⠖⠛⠉⢱⢄⣄⠴⠃⠀⠈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠙⠦⣀⠤⠻⡄⠀⠀⡰⡄⠀⠀⣠⢆⠀⠀⢠⠟⠤⡀⠴⠋⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠈⠉⠉⠁⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⢤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣤⡤⠄⠞
⢀⢀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⠟⠛⢛⣛⠒⠒⠒⠒⠒⠒⠒⠒⠒⣒⠛⢛⡛⠿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⣿⠟⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣤⣶⣦⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠠⠀⠀⠠⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠊⠀⠀⠀⡄⠀⠀⠀⠙⡔⠀⠀⠈⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡌⠀⡠⠀⡁⠀⠀⠀⠀⠀⠦⠀⢀⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢇⠀⠃⠀⠧⣀⠀⠘⠂⠃⠀⠀⠀⠀⢀⠀⠠⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠉⠆⠀⠀⠐⠠⢄⡀⢈⠀⠰⠂⣀⠀⠠⠆⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠙⠂⠒⠤⢤⠤⠂⠘⠃⡀⠀⠀⠀⠄⠀⠀⠀⢌
⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⠄⡀⠀⡈⡁⠔⠌⠤⠇
⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢀⡀⠀⠀⠀⠒⠊⠀⠀⠀⠘⠢
⠀⠀⠀⠀⠀⠀⠀⠇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠐⠄⣀⠀⠀⠀⠀⠀⠠⠚⡀⠱⡀
⠀⠀⠀⠀⠀⠀⢸⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢡
⠀⠀⠀⠀⠀⠀⢸⠀⣀⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⢁⠀⠁⠈⠂⠀⠀⠀⠀⠤⠐⠊⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠳⡌⠊⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡏⡅⠀⠀⠀⡈⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢐⠀⠇⠀⠀⠀⠇⠀⠀⠀⠀⠈⠑⠂⠒⠒⠒⠀⠂⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠀⠈⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠅⢰⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⠠⠀⠀⠐⠤⠀⠔⠀⠀⠀⠀⠀⠀⠀⠸⠰⠀⢸⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠐⠚⠄⠀⠀⠌⠒⠳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡌⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠒⠂⠀⠀⠂⠀⠀⠁⠀⠀⠀⠀⠀⠀⠉⠉⠁⠈⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⢋⣉⣉⣉⠛⠷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⣰⠞⢋⣩⣭⣍⠛⢦⠈⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⣧⡤⠷⠶⠞⠓⠒⠚⠒⠶⠶⠶⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠾⠛⢉⣡⠶⠁⣠⡴⠂⢀⡾⢤⣀⠙⠶⣤⡈⠻⣯⣝⡳⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣁⣤⡶⠛⣁⡴⠞⠉⢀⣴⠟⣠⢤⡉⠛⢦⣄⠉⠓⠦⣍⡛⠷⢮⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠻⠚⠛⣉⣡⠴⠚⠉⠀⣠⣴⠟⣡⡞⠁⠀⠙⠷⣤⣈⠛⠦⣄⡀⠉⠛⠲⠶⠤⠙⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠰⠶⠚⠛⠉⢀⣀⣤⡶⠟⣩⡴⠟⠁⠀⠀⠀⠀⠀⠈⠙⠳⢶⣤⣉⠛⠶⠦⣤⣤⣀⡈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣤⣤⣤⠶⠶⠞⢛⣩⣤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠈⠙⠛⠶⢦⣤⣄⣉⡀⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠇⠀⣠⣤⣤⠶⠶⠛⠋⢁⣀⣤⡴⠖⠂⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣄⡀⠀⠀⠀⠀⠉⠉⢹⣥⠶⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡾⠓⠦⢠⠀⠀⠀⠀⠀⠀⠘⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⣧⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣸⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢿⠀⠀⠀⠀⠀⠠⠟⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠳⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠛⠻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣸⡆⠀⠀⠀⠀⠀⠀⢀⣠⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣄⡀⠀⠀⠀⠀⠀⢀⡿⠒⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠉⠁⠙⠶⣤⣀⡀⠀⠀⠀⠀⠀⢀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⡛⠳⠶⢚⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠶⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠶⣤⣤⣄⣀⣀⣀⣤⣤⠶⠞⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⡈⠭⠭⢁⠢⢒⠩⠭⠭⡐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢡⠂⠀⠀⠀⠀⠑⠁⠀⠀⠀⠀⠡⠐
⠀⠀⠀⠀⢀⡀⠄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠇
⠀⢀⠄⠐⡡⠂⠉⠁⠢⡑⠄⠀⠀⠀⢀⡀⠐⡌⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⡐
⡐⡡⠊⠀⠀⠀⢀⠠⠄⠓⠀⠀⠀⠀⠒⠠⠅⡚⢦⡑⢄⠀⠀⠀⠀⠀⢀⠔⣡⢊⣀⠄⣂⠭⠀⠀⠀⠈⠭⢐⠂⠄⡀
⡇⡅⠀⢀⠤⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⢢⡑⠤⡀⡀⠔⡁⢀⠅⠐⠢⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠈⡂⠄
⠐⡌⡲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠹⡑⠤⠔⡘⡱⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢎⢢
⠰⢰⠀⠀⠀⠀⠀⣀⣀⠀⠤⠄⠀⠀⡀⠀⠀⠀⠀⠀⠀⢡⠡⠀⠰⠰⠀⠀⠀⠀⠀⠄⠀⠤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢃
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠒⠁⠐⢄⡀⠀⠀⠀⠀⠄⡀⡄⢀⣀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠤⠣⣠⠀⠀⠀⠀⠀⠸⠈
⡰⠸⠄⣤⡀⠬⠀⠀⠀⠠⠀⠀⠀⠀⠠⠀⠀⠀⣄⠀⠔⣐⠢⡙⢰⠁⠘⠛⢤⠋⢀⣀⣀⠂⠀⠀⠀⠀⠀⠀⠑⠇⠀⠀⠀⢀⢀
⡇⡁⠀⠀⠈⠇⠠⠋⠉⣑⠄⠀⠀⠀⢔⡉⠉⠳⠀⠛⠀⠀⠀⠐⠸⠀⠀⢀⠈⠀⠊⠀⣨⡁⠀⠀⠀⢀⠔⠒⢦⠀⢮⠌⠥⠈⢂
⠡⠰⡀⠀⠄⠀⠀⠀⠘⠛⠀⠀⠀⠀⠘⠛⠀⠀⠀⠀⠢⠀⠠⢁⢆⠣⡀⡁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠐⠷⠀⠈⠀⠀⠀⠀⠀⡰
⠀⠑⠀⠂⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⢒⠡⠂⠀⠑⢢⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠑⢀⠔⡡
⠀⠀⠀⠈⢆⢂⠀⠀⠀⠀⠐⠂⠀⠐⠂⠀⠀⠀⢀⠎⠌⠀⠀⠀⠀⠀⠀⠆⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⡭⠅⠊
⠀⠀⠀⠀⠀⠢⡑⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠣⠊⠀⠀⠀⠀⠀⠀⠀⠈⢢⡣⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢊⠎
⠀⠀⠀⠀⠀⠀⠈⠂⢅⡂⠤⠤⠤⠤⠄⣂⠡⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢑⠂⠤⠄⠀⠤⠄⢒⠡⠀⠁
⣶⣶⠶⣶⣶⣶⣶⣶⣶⣶⣾⣷⣶⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣶⣶⣾⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣴⣴⣶⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣾⣿⣿⣿⣷⣶⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⡿⠛⠋⠉⠉⠉⠙⠛⢿⣿⣷⣶⣶⣶⣶⣤⣀⣠⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠟⠛⠛⠛⠻⢿⣿⣿⠿⠿⢿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⡿⠿⠿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀
⠀⠀⠀⠀⢀⣾⣿⡿⠟⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣄⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷
⠀⠀⠀⢀⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠀⠀⠀⠀⠀⠀⠈⣿⣿⡆
⠀⠀⣠⣾⣿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣾⡃⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⣿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⡀
⠀⣼⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀⠰⣿⣇⠀⣿⡄⠀⠀⠀⠀⠀⠀⢀⣼⠃⣠⣿⣿⠏⠀⠀⠀⠀⠀⠀⢀⠈⢿⣿⣷⣦
⣸⣿⡿⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⣿⣦⣿⣿⣦⣀⠀⣀⣠⣤⣾⣷⣾⣿⠟⠁⠀⠀⠀⣀⣀⣤⡶⠃⠀⠀⠈⠻⣿⣷
⣿⣿⡇⠀⠀⠰⣇⠀⠀⠀⠻⣦⣄⣀⣀⣀⣀⣠⣤⠆⠈⠙⠻⠿⢿⣿⣿⣿⣿⣿⡿⠿⠟⠋⠉⠙⠛⠛⢿⣿⣯⣉⣁⣀⠀⠀⢸⡆⠀⢹⣿
⣿⣿⡇⠀⠀⠀⠙⢿⣶⣶⣶⣾⣿⠟⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⣉⡉⠉⢀⣠⣿⠃⠀⢸⣿
⠸⣿⣿⣄⠀⠀⠀⠀⠀⠉⢁⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠿⠿⠛⠁⠀⢀⣼⣿
⠀⢻⣿⡟⠃⠀⠀⠀⢀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡙⠳⠄⠀⠀⠴⢿⣿⣿
⠀⢸⣿⣧⠀⠀⠀⠀⠉⢹⣿⠁⠀⠀⣠⣶⣿⣿⣷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⠿⢿⣦⡄⠀⠀⢿⡏⠁⠀⠀⠀⠀⣸⣿⡟
⠀⠈⢿⣿⣧⡀⣿⣶⣤⣼⣷⣶⣶⣾⣿⠿⠶⢶⠶⠿⣿⣧⣄⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⢷⣶⠶⠶⢾⣿⣶⣶⣾⣧⣠⣴⣿⠀⣴⣿⣿⠃
⠀⠀⠀⠻⣿⣿⣾⣿⣿⣿⣿⣿⠟⠉⠀⣰⡾⢿⣿⣿⣦⡙⢻⣷⣤⣤⣤⣤⣴⡿⢋⣵⣾⣿⣿⠿⣶⡀⠈⠙⢿⣿⣿⣿⣿⣿⣾⣿⡿⠁
⠀⠀⠀⠀⠸⣿⣿⡝⠻⢿⣿⡟⠀⠀⠈⠁⠀⢿⣧⣿⠿⣿⡆⢿⣿⡿⢿⣿⣿⠁⣾⡟⢿⣼⣿⠆⠀⠉⠀⠀⢸⣿⣿⠟⢩⣿⣿⠏
⠀⠀⠀⠀⠀⠹⣿⣿⡄⠈⣿⣧⠀⠀⠀⠀⢦⣀⣉⣠⠄⠀⠀⣸⣿⠁⠀⢹⣿⠀⠉⠀⢨⣍⣀⣠⠆⠀⠀⠀⢸⣿⡇⢀⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⢹⣿⣄⠀⠀⠀⠀⠉⠉⠀⠀⠀⢀⣿⠃⠀⠀⠀⢿⣇⠀⠀⠀⠉⠉⠀⠀⠀⠀⢀⣿⡿⢀⣿⣿⠏
⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⢻⣿⣄⡀⠀⠀⠀⠀⠀⢀⣠⡾⠃⠀⠀⠀⠀⠀⠻⣦⣀⠀⠀⠀⠀⠀⠀⣀⣾⡿⠃⠘⢿⣿⡆
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣄⣀⣼⣯⠛⠿⠷⢶⣶⣶⠾⠟⠋⠰⢾⣶⣤⣠⣴⣾⠷⠈⠛⠿⠶⣶⣶⡶⠿⠟⣻⣧⣀⣠⣾⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠘⠿⢿⣿⣿⣿⣆⠠⣤⣤⣤⣤⣶⠏⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠈⢷⣦⣤⣤⣤⠴⢠⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⠀⠉⠉⠉⠀⠒⠶⣤⣤⣤⣤⣤⣤⣴⣤⡶⠖⠂⠈⠉⠉⠀⣰⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠈⢉⣉⣉⡉⠁⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⠛⠿⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠿⠟⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣷⣦⣤⣀⣀⣠⣤⣾⣿⠃⠀⢠⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⢀⣀⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⡇⠹⠀⠀⠈⢿⡏⠉⠛⠛⠋⠉⣿⠃⠀⠀⠘⢀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣀⡀
⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠘⢇⠀⠀⠀⠀⢸⠇⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠉⠉⠉⠛⠛⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠛⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⢿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⡿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣠⣴⡶⠶⠶⠶⡶⣶⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡾⠛⠋⠀⠀⠀⠀⠀⠀⠀⠈⠙⢳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⠀⠀⠀⠀⠀⢀⣀⣀⣰⢞⡽⢶⣝⣷⡀
⠀⠀⠀⠀⠀⠀⠀⣹⣿⣄⠀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠀⠀⠀⢀⣀⣼⣿⢷⣄⠀⠀⢠⣿⢭⣍⢻⣿⣀⣶⢹⣿⡷⢿⡛⣦⡀
⠀⠀⠀⠀⠀⠀⣸⠿⣿⡉⠙⠓⠶⢦⡴⠞⠛⣦⡛⠙⢳⡶⠛⠉⠁⣸⣿⡼⠃⠀⠀⣸⡇⠶⢏⣾⠷⣬⣵⢿⡙⣟⠲⠛⣸⣧⣤⣄
⠀⠀⠀⠀⠀⠀⠘⢷⣿⡇⠀⠈⢳⡀⠻⢦⡤⠟⠙⠦⠘⢃⠙⠀⢠⣿⠋⠁⠀⣾⠿⣿⡷⠒⠛⠁⠀⠀⠀⠀⠙⠛⠛⠛⠛⣿⡖⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⡀⠀⠳⢄⣀⠀⠀⠀⣀⡰⠋⠀⣠⡾⠏⠀⠀⣼⢟⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣿⣶⣻⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⣿⠿⢶⣤⣀⣀⣉⠉⣉⣀⣤⣴⡾⢿⣷⣄⠀⠀⣿⣼⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⣷⡀
⠀⠀⠀⠀⠀⠀⣠⠞⠃⢰⠇⠀⣾⠉⠉⢿⣏⣹⡏⠉⢹⣿⠀⠈⣿⠙⠷⣼⣏⣸⡏⠉⠛⠶⣄⣀⠀⠀⠀⠤⠄⢀⣀⠀⠀⠀⣀⣠⣿⣯⡟⠁
⠀⠀⠀⠀⢀⡾⠃⠀⠀⣾⠀⠀⠹⣶⣶⣾⢋⠉⠛⠲⣿⠁⠀⠀⢻⡇⠀⠈⠻⣿⡇⠀⠀⢀⣀⠉⢻⡛⠙⢷⣴⡋⢹⡷⠾⠛⠉⠀⣿⢉⣷
⠀⠀⠀⣰⡟⠁⠀⠀⢰⣿⠀⠀⠀⠀⠀⢻⣇⠀⠀⣼⠏⠀⠀⠀⠘⣿⠀⠀⠀⢸⣿⡀⠀⠈⢣⡀⠀⠙⠒⠋⠈⠛⠋⠁⢸⠋⠀⢠⡿⠛⠁
⠀⠀⣴⡟⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⢻⡄⢠⡟⠀⠀⠀⠀⠀⢹⡇⠀⢀⡼⠛⣿⣦⡀⠀⠙⠦⣀⣀⠀⢀⣀⡠⠔⠁⢀⣴⡿⠁
⠀⠀⠻⣧⣀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⣷⣼⠃⠀⠀⠀⠀⠀⠈⣿⣾⠋⢀⣾⠏⣿⠛⠳⠶⣤⣤⣌⣉⣉⣀⣠⣤⣴⣿⠛⢷⡄
⠀⠀⠀⢸⡿⠛⠶⢶⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣷⣾⠃⢠⣿⠀⠀⠀⠀⠹⢟⣫⠿⠋⠁⠀⠀⢹⣇⠈⢿⣄
⠀⠀⠀⢸⡇⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⠃⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⢻⣆
⠀⠀⠀⣾⠁⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⢸⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⢻⣆
⠀⠀⠀⣿⠀⠀⢠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⢸⡯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⢀⣿⡇
⠀⠀⠀⣿⠀⠀⢈⣿⡷⣤⣄⣀⣀⣀⡀⠀⠀⢸⣿⠀⡀⢀⣀⣠⣤⡶⠞⠋⣿⣷⣄⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡶⠟⢿⡄
⠀⠀⠀⣿⠀⠀⠈⡇⠀⠀⠀⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⣿⡾⠛⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠘⣿⡀
⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢻⡇
⠀⠀⠀⣿⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆⠀⢸⡇
⠀⠀⠀⢸⣇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣇⠀⢸⡇
⠀⠀⠀⠀⢿⡄⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣤⣠⣀⣀⣀⣀⣀⡀⠀⠀⣀⣀⣤⣴⣶⠿⢋⠻⣿⠀⣾⠃
⠀⠀⠀⠀⠈⠻⣤⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⣿⠉⠀⠉⣉⠉⠙⠙⠛⠛⠋⣉⠉⠁⠀⠘⡆⠛⠂⢻⣴⡿
⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⡟⠀⣠⡖⠙⠶⡄⠀⠀⣠⡌⠉⠶⢄⠀⠀⠘⠎⠛⠛⣿
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⢸⡇⠸⡄⠻⠟⢰⠇⠀⠀⣅⠸⣭⠆⠼⠂⠀⣀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡇⠈⠣⠴⠓⠊⠀⠀⠀⠨⣀⡴⠒⠂⡠⠴⠉⠶⡄⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣾⡇⠀⠀⠀⠀⡠⠶⣤⠴⢄⠀⠀⠀⢈⠆⠸⣽⠂⠜⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣏⠀⠀⠀⢈⡃⡴⠒⡄⠺⡀⠀⠀⠀⠂⠔⠒⠔⠂⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⢺⣅⡙⠛⢁⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠿⠃
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠻⠷⣤⣄⣀⣈⣑⣦⣶⣀⣀⣠⣤⣤⣤⣶⣶⣿⠋⠉
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⣯⠉⠉⠉⠉⠉⣻⡏⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⡀⠀⠀⠀⠀⣀⣀⣀⣠⣾⠇⠀⠀⠀⠀⣿⣄⣀⡀⠀⠀⢿⡇⠀⠀⠀⢀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⠶⠶⠶⠶⠶⢶⣶⣶⡾⠿⣿⠶⠚⠛⠛⠋⠉⠉⠉⠻⣦⠀⠀⢀⣴⣿⡋⠉⣙⣷⣆⣸⣇⣠⣶⣛⣋⣩⠟⢶⡄
⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠙⣷⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢠⡿⠁⠀⠉⠉⠉⠀⠸⣿⡿⠁⠀⠉⠉⠁⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⡟⢸⣷⣶⣦⣤⣤⣤⣴⠶⣿⡷⢤⣤⡤⣤⡤⠴⠶⢿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⡟⠶⠦⠤⠤⠤⠤⠴⠞⠛⢛⣿⣉⠙⠛⠛⢛⣛⣓⣒⣛⣉⣹⡷⠸⢧⣀⣠⣤⣤⠤⠤⠤⠿⠧⠤⠤⠤⠤⠴⠶⠚⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠲⠶⠶⠶⠶⠶⠶⠶⠞⠛⠉⠉⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡥⠄⠆⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠀⠀⠀⠀⠀⠀⠤⠄⣀⠀⠀⠙⣧⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠑⠀⠀⠀⢀⠠⠂⠀⢀⠀⠀⠈⡱⣄⠀⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⠡⠄⠒⠀⠈⠀⠀⠀⠀⠀⠑⢄⠠⠈⢪⢳⡳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠤⡀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠀⠀⠘⠢⣄⣀⣀⣀⠤⠊⠀⠀⠀⣠⠃⠀⠀⠠⡅⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠖⠒⠠⠄⡀⠀⠑⠠⣀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⠀⠀⠀⠀⢀⡀⠀⠲
⠀⠀⠀⠀⠀⠀⢈⡵⠋⠀⠀⠀⡀⠀⠀⠈⠢⠐⡡⣿⡉⣑⣶⠒⢲⣶⢒⠍⠢⠀⠀⠀⢢⠀⡀⠂⠛⢀⡀
⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⡟⠀⡏⠣⣀⣄⣉⣰⠃⡎⠀⢀⡦⠖⠂⠁⠀⠈⠑⡄⠀⠰⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢠⡇⠰⠁⠀⠀⠈⠉⠀⠐⢇⠀⡈⠀⠀⠀⠀⠀⠀⠀⠈⠦⣀⠈⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠒⢉⡰⠃⠇⠀⠀⠀⠁⠀⠀⠀⠀⡀⠁⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠠⠤⠒⢹⡦⣀⠀⠀⠑⠀⠀⠀⣄⠀⠀⠁⠀⠘⠣⡐⠄⡀⠀⡀⠜⠀⠀⢀⡴⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠂⠋⠀⢨⠠⠀⠀⠠⠀⠀⠀⠀⠠⡄⠀⠋⣀⠈⢢⠠⢀⢀⡀⠄⠐⠉⠀⠃
⠀⠀⠀⠀⢀⡀⠀⠀⠸⣀⢀⠃⠀⠀⠀⢘⣸⠦⠀⢀⠀⠄⢀⠒⠀⠀⠀⢀⣠⠇⠉⡀⠘⠀⠀⡃⠀⠀⠀⠤⣷⠭
⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠈⠤⠀⠐⠒⠉⢈⠆⠀⠀⠀⢐⡆⠀⠒⠚⠉⠁⠉⡢⠀⣄⠀⠀⠀⢣⠀⠀⠀⠀⠘⠃⠀⠀⠀⠈
⠀⠀⠐⠂⠄⠙⡆⠄⠠⠀⡈⠀⠀⣀⣴⣠⢞⠀⠀⠀⠀⠈⣀⢀⣀⡠⠠⠆⠊⠁⢘⡉⠉⠒⠒⠈⠀⡄⠠⠀⠀⠀⠀⠜⠁⠪⢀
⠀⠀⠈⠢⠄⡀⠉⣠⠀⠋⠉⠉⠉⠉⠀⠀⣈⠈⠀⠀⠀⠈⠀⠀⠀⢠⠤⠠⡀⠀⠀⠀⠈⠈⠁⠨⣀⠀⠀⢀⠀⣀⡠⠤⠀⠄⠂
⠀⡄⠀⠀⢂⠀⠀⠜⠀⣆⠘⠈⠑⠀⠈⠃⠁⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⢀⠐⠁⠉⠒⢖⠃⠀⠐⠋⠰⠄⠀⠐⠹⠃⠆⠢⠄
⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢸⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣇⠀⠀⠀⠀⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣠⡔⠋⠈⠀⠀⠀⠀⠴
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⡀⠀⠁⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠐⠊⠉⠉⠲⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⣊⣁⠀⢀⣉⣒⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢱⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⠀⠀⠀⠀⠀⠀⡞⠉⠉⠉⠀⠀⢸⡧⣿⠀⠀⠈⠉⠉⠙⡆⠀⠀⠀⠀⠀⠀⢼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⢠⠞⣩⠛⡇⠀⠀⠀⠀⠀⢘⡇⣟⠀⠀⠀⠀⠀⠀⡟⢫⡙⢦⠀⠀⢰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⣘⠖⠁⠀⠉⠉⠉⢉⡩⠙⠛⠃⠛⠛⠩⣉⠉⠉⠉⠁⠀⠑⢎⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠙⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⢤⠀⠀⠀⠀⠀⠳⣄⡀⠀⠀⠀⠀⣀⡴⠃⠀⠀⠀⠀⣰⠄⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⠀⠀⠀⠉⠂⠄⡀⠀⠀⠀⠈⠩⢉⠩⠉⠀⠀⠀⠀⡀⠄⠊⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠒⠸⡄⠀⠀⡼⠐⠂⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⠗⢤
⠀⠀⠀⠀⠀⠀⢀⡤⠖⠒⡇⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⡗⠒⠦⣄
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠘⡦⢤⡜⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⣤⠤⡞⠀⠀⠀⠈⠳⣄
⡠⠖⠉⠉⠁⠀⠠⡖⠉⠉⡟⠀⢰⡀⠀⠉⢳⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠋⠁⠀⣰⠀⠹⡏⠉⠑⡦⠀⠈⠉⠉⠑⠦
⠣⣤⠖⡻⠇⠀⣠⠇⠀⣰⠁⠀⠀⠙⠲⠖⢻⡀⠈⠉⢙⡟⠓⠲⠶⠶⠶⠶⠶⠶⠶⠶⠒⠚⣟⠉⠉⠀⣸⠓⠶⠚⠁⠀⠀⢱⡀⠀⢧⡀⠀⠿⡓⢦⡤
⠀⠈⠊⠀⠳⣄⡼⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠙⠂⠔⠊⠱⢄⣀⡠⠛⢄⣀⣀⠜⠣⣀⣀⠴⠉⠒⠄⠚⠁⠀⠀⠀⠀⠀⠀⠀⢇⠀⠸⣀⡴⠃⠈⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠤⢄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠴⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣷⣶⡶⠶⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠲⠶⣶⣶⣿⣿⣿⣿⣿⠇
⣿⣿⣿⡿⢿⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣠⣀⣤⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣾⣿⣿⠿⠿⠿⠿⣿⠿⠟⠛⣛⣛⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠉⣩⣴⠶⠛⠁⠀⠀⠀⠀⠈⠉⠉⠉⠛⠻⢶⣤⡈⠻⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⣿⡟⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠆⠙⢿⣿⣿⣿⣿⣧
⠀⠀⠀⢀⣠⣤⣼⣿⣇⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣧⡀
⠀⠀⢰⣿⠟⠉⠙⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠋⠀⠉⢻⣷
⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠀⠀⠀⠀⣸⣿
⢀⣴⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣷⣄⠀⠀⠀⠀⠀⣀⣤⣶⠶⠿⠿⢶⣤⡀⠀⠀⠀⠀⠀⠀⢴⣿⣿⣦
⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠈⠛⠿⠶⠶⠾⠟⠋⠁⠀⠀⠀⠀⠀⠙⣷⣄⠀⠀⠀⠀⠀⠀⠀⠈⢻
⢿⣷⡀⠀⠀⠀⠀⠙⠶⠶⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⠆⠀⠀⠀⠀⢀⣾
⢈⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿
⢸⣿⠉⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠙⣿
⠸⣿⣄⠀⠀⠀⢀⣤⣤⣶⡶⠾⠿⢛⣿⣿⠿⢶⣦⡄⠀⠀⣤⣶⠾⢿⣿⣿⠿⠿⠷⢶⣦⣤⣤⡀⠀⠀⠀⣸⣿
⠀⠙⣿⣶⡄⠀⠘⠿⣿⡏⠀⠀⡴⢿⣿⣿⣷⠀⢹⣿⣶⣶⣿⠁⢠⢿⣿⣿⡷⡄⠀⠀⣿⡷⠿⠃⠀⣠⣾⡿⠃
⠀⠀⠘⢿⣿⡆⠀⠀⢸⣧⠀⠘⠀⠈⠛⠛⠚⠁⢸⡏⠀⠀⣿⡀⠈⠚⠛⠋⠁⠸⠀⠀⣿⠇⠀⠀⣴⣿⡟⠁
⠀⠀⠀⠘⢿⣦⣀⠀⠀⠻⣦⡀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⠈⢷⣄⡀⠀⠀⠀⠀⢀⣼⠏⠀⢀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠙⣿⣇⠀⠀⠈⠛⠿⠷⠾⠟⠛⠁⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠾⠿⠛⠁⠀⠀⣾⣿⠋
⠀⠀⠀⠀⢠⣾⡟⢻⣦⠀⠀⠀⠀⠀⠀⠀⠜⠢⣄⠀⠀⠀⠀⣠⠞⢢⡀⠀⠀⠀⠀⠀⠀⣾⠟⢿⣷
⠀⠀⠀⠀⠸⣿⣷⣾⣿⡄⠀⠀⢀⠠⠐⠈⠀⠀⠈⠉⠛⠛⠉⠁⠀⠀⠈⠒⡤⠀⠀⠀⢸⣿⣶⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠉⠁⢹⣷⠀⠀⠀⠀⠉⠓⠠⠀⡀⣀⢀⣀⠀⠀⣀⠤⠒⠈⠀⠀⠀⢀⣿⠇⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⣦
⠀⠀⠀⠀⠀⣀⣠⣴⣶⣾⣿⣿⣿⣿⣿⣿⣎⠲⣤⣀⣀⣀⣀⡤⠖⣰⣿⣿⣿⣿⣿⣿⣷⣶⣤⣄⡀
⠀⠀⢀⠴⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⡀⠉⠉⠉⠁⢀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠓⠦⡀
⠀⠀⠁⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣧⣤⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⠋⠙⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⣿⣷⣶⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⡿⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⠿⠿⠛⢛⣉⣉⠉⠉⠙⠛⠉⣁⣤⣤⣤⣤⣤⣄⡈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠉⠀⣠⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢷⣤⠈⠻⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠙⢿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⣀⣤⣤⣾⣿⣇⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⣾⡿⠋⠉⠙⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋⠁⠈⠹⣿⡇
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠀⠀⠀⠀⢀⣿⡇
⠀⢀⣼⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⣶⣤⣀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣼⣿⣷⡀
⣼⣿⠟⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠟⠛⠿⣶⣤⣀⣀⣤⣴⡾⠟⠋⠉⠀⠀⠀⠉⠻⣷⡀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠻⣿
⣿⣇⠀⠀⠀⠀⠀⠀⣤⣀⣀⣀⣤⣶⠿⠋⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠹⣿⣦⡀⠀⠀⠀⠀⠀⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠃⠀⠀⠀⠀⢀⣴⣿
⢀⣿⣿⡿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣿⣿⣧
⢸⣿⠃⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⢹⣿
⠸⣿⣆⠀⠀⠀⠀⢀⣤⣤⣴⣶⠶⠾⠿⠿⣛⣿⡿⢷⣶⣤⠀⠀⠀⢠⣴⡾⠿⣿⣿⣿⠿⠿⠿⢶⣶⣤⣤⣄⠀⠀⠀⠀⠀⣼⣿
⠀⠙⣿⣷⣄⠀⠀⠸⣿⣾⣿⠁⠀⠀⡴⢿⣿⣿⣷⡀⠈⢻⣷⣦⣤⣿⠋⠀⣼⣿⣿⣿⡷⡄⠀⠀⠘⣿⣾⣿⠇⠀⢀⣤⣾⡿⠃
⠀⠀⠘⢿⣿⣧⡀⠀⠀⠸⣿⠀⠀⠂⠀⠘⠿⠿⢮⡇⠀⣸⡏⠉⠉⣿⡀⠀⠣⠾⠿⠿⠃⢨⡄⠀⢠⣿⠁⠀⠀⣠⣿⣿⠟⠁
⠀⠀⠀⠈⣿⣿⡁⠀⠀⠀⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡏⠀⠀⠀⢹⣿⡟
⠀⠀⠀⠀⠈⠻⣿⣶⡆⠀⠀⠻⢷⣤⣄⣀⣀⣤⣴⡾⠋⠀⠀⠀⠀⠀⠈⠛⢷⣦⣄⣀⣀⣠⣴⡾⠋⠀⠀⣴⣶⣿⠟
⠀⠀⠀⠀⠀⠀⣨⣿⣧⡀⠀⠀⠀⠈⠉⠉⠉⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠈⠉⠉⠉⠉⠁⠀⠀⠀⢀⣿⣿⣀
⠀⠀⠀⠀⠀⣾⣿⠋⠙⣿⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠲⣤⣀⣀⣀⣀⣤⠞⠉⠢⡀⠀⠀⠀⠀⠀⠀⢰⣿⠋⢻⣿⡆
⠀⠀⠀⠀⠀⠹⣿⣷⣾⣿⣇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠈⢃⠶⠀⠀⠀⠀⣾⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠉⠁⠘⣿⡄⠀⠀⠀⠀⠃⠙⠢⠄⢀⡀⠀⠀⠀⠀⠀⢀⡠⠤⠂⠈⠀⠀⠀⠀⣸⣿⠁⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⣿⣿⣿⣿⣿⣷⡀⣄⡀⠀⠀⠀⠀⠀⠀⢀⡠⢠⣿⣿⣿⣿⣿⣿⣷⣄⣀
⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠙⠶⢶⣦⣶⠶⠞⠋⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀
⠀⠀⡠⠔⠋⠉⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⡀⠀⠀⢀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠙⠢⡀
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣷⣾⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣤⣿⣿⣦⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⠛⠙⢿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣦⣤⣾⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⠿⠋⠁

⠀⠀⠀⠀⠀⣀⣤⣤⡤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠤⠠⠤
⠀⠀⠀⢀⣮⣴⡿⠷⠶⣤⡀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣁⡤⠤⠤⠄⡀⠀⠡
⠀⠀⠀⢸⡥⠤⠀⠠⢖⠮⢻⣤⣷⢄⣠⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠈⡄⠀⠤⣀⠄⢀⡀
⠀⠀⠀⠈⣇⢸⠀⠰⡀⡁⠸⠿⣿⣈⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠠⢤⠁⠸⠀⠀⠀⠉⢰⡄
⠀⠀⠀⠀⡇⠁⡈⢀⡈⠀⢠⣾⡯⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⠀⠀⡠⡊⠬⣧⠀⠀⠀⠠⡝
⠀⠀⠀⠀⠙⠲⢭⣉⣤⣶⠞⣿⠀⢸⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠂⠤⣀⣀⠤⠴⠃⡀⠀⢸⠀⠀⢠⡓
⠀⠀⠀⠠⣖⣶⣶⣭⣿⡴⠄⣸⠦⢼⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⢐⠒⠒⠈⣩⡄⠀⠀⡡⠠⡌⠀⠀⡮⠁
⠀⠀⠀⠀⠿⣿⣿⣿⣿⡤⠞⢋⣠⣾⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠸⢵⡠⠕⣴⣁⠤⠊⢀⡠⢁⣀⣠⡉
⠀⠀⣠⠞⠉⠁⠀⣿⣦⣶⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⢀⠧⠤⠐⣊⡉⠠⣤⠀⢚⡃
⠀⢰⠁⠀⠈⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⠀⢠⠥⢽⣩⠀⡀⠊⠀⠕⣺⠇
⠀⡻⣤⣄⣀⣤⣿⣿⡿⠿⠛⠛⠋⠉⢻⣿⣷⡀⣀⠀⠀⠀⠀⢘⢤⡀⠀⠀⠀⣿⠿⠭⠁⠐⠒⠀⠙⡀⠏⢆
⠘⠦⠷⡾⣭⣿⣿⣿⣶⣦⣤⣤⣶⣶⡿⠟⢻⣿⣿⠀⠀⠀⠀⠣⠤⠶⠍⣹⣉⠝⡔⠂⠀⠀⠀⠒⢈⠠⠒⣀⡩⠇
⠀⠀⠀⠳⢾⣿⣿⣯⣭⣙⣛⣋⣩⣥⣤⣶⣿⠟⠁⠀⠀⠀⠀⠀⠀⠐⠶⡙⠅⠰⠭⠀⠐⠂⠈⠩⠤⠐⠈⡠⠊
⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⠿⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠂⠠⠤⠤⠤⠤⠤⠄⠒⠉
⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⢶⡶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⢀
⠀⠀⠀⠀⠀⠠⠀⠀⢀⠀⠀⢍⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠔⠂⣀⠒⢂⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠐⢈⠀⡀⠀⠙⠂
⠀⠀⠀⠀⠰⠀⣔⠀⠒⠂⠀⠈⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢦
⠀⠀⠀⠀⠀⠂⠠⡀⠀⠣⠚⢁⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠽⠂⠑⠀⠨⠄⡑
⠀⠀⠀⠀⠀⠀⠀⢈⣱⡀⢐⣥⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⢼⢓⡠⠐⠰⢓⡆⠀⠄⡀
⠀⠀⠀⠀⢀⠔⠊⠁⠈⠉⠉⠀⠀⠈⠑⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢀⡀⢴⠷⠬⢀⡀⠙⠀⠢
⠀⠀⠀⠀⡄⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠑⡄⠀⠰⡄
⠀⠀⠀⠀⠃⢂⠀⠀⠀⠀⠀⠀⠀⠀⢠⢋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠠⠆⠀⠀⢸⠀⠀⠁
⠀⠀⠀⠀⡀⠈⢢⠀⠀⠀⠀⠀⠀⠀⢣⠘⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠀⠀⠀⠀⡘⠀⠀⣤
⠀⠀⠀⠀⡇⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⢣⠃⠀⠀⠀⠀⠀⢀⠔⠂⢄⠄⠀⠀⠀⠐⠤⢀⡧⣀⣀⣆
⠀⠀⠀⠀⠑⠠⠗⠤⠤⢤⣀⣀⣀⡀⠠⢮⠇⠀⠀⠀⠀⠰⣁⡀⠑⠌⠀⠀⠀⠀⠀⠀⠀⠐⠀⣰⠇
⠀⠀⠀⠀⠐⢴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⡀⠀⠀⠊⠁
⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠆
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢢⠀⠰⠅
⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠢⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠃⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢉⡒⠒⡖⠲⠒⠒⡋⠉⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⢀⠊⠀⠈⣀⡽⠰⣇⠈⠀⠙⣆⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠈⣀⠀⠈⠛⠀⠀⠰
⠀⠀⠀⠀⠀⠈⠑⠊⠀⠉⠀⠀⠈⠓⠒⠚⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠒⠀⠉
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠒⠉⠉⠉⠉⠉⠁⠐⠒⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠤⣤⠤⠤⠤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢴⡤⡇⠀⠀⠀⢠⠖⠉⠀⠀⠒⣂⢰⠀⠦⠄⠀⠈⠓⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠩⣐⠝⡜⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠐⠸⠉⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠊⠑⠢⠤⠭⠭⠭⠭⠟⢻⠀⠀⢰⠀⠀⠀⠈⠀⠀⡠⠤⠤⠄⠤⠄⠤⠤⠤⠤⢤⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣄⠀⠇⠀⠐⠛⠀⠀⠀⠈⠓⠀⠐⡆⢀⢼⠀⠀⠀⢰⠀⠀⡇⠀⠠⠖⠂⠀⠀⠐⠦⠀⠀⡆⢀⣇
⠀⡤⣲⢢⠀⠀⠀⠀⠀⡁⢸⣸⠀⠀⠀⠠⠆⠀⠀⠢⠀⠀⠀⢣⡄⠀⡇⠀⠀⡋⢹⣹⠓⠢⢤⡊⠑⡤⣴⠁⢢⠤⠒⢻⡹⠀⡇⠀⠀⠀⠀⠀⡔⢄⣄
⢞⣵⠋⣡⠧⣀⠀⣀⣀⠑⢼⠀⠀⠀⡠⣀⠀⠉⠁⢀⡠⠀⠀⠀⡧⠜⠀⠀⠀⠣⣨⠁⠀⠀⢀⠑⠚⠃⠚⠒⢅⡀⠀⠀⣃⡴⠣⡀⠀⠀⢀⡸⠉⠻⣮
⠀⠑⠚⠧⡀⠀⡱⠁⠨⠃⠌⡄⠀⠀⠀⠈⠋⠭⠝⠋⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠑⠖⠶⠁⠀⠀⠀⢀⡇⢀⠴⠍⡑⠲⡁⢀⡠⠖⠚
⠀⠀⠀⠀⠈⡱⠁⡰⠀⠀⠀⡨⠢⣄⣀⡀⠀⠒⠀⠀⣀⣠⠴⠓⢤⠤⠤⠄⡤⢠⡤⣼⠦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢞⠉⠀⠀⠀⠀⡄⣳⠁
⠀⠀⠀⠀⠀⠈⠒⠧⣀⠀⡜⠀⢸⢠⢡⠉⢹⡶⣟⠉⢱⠘⡀⡂⠈⢇⡠⡶⠋⠁⡰⠁⠀⠀⡏⢫⠐⠒⠒⢉⠟⢱⠀⠀⢣⠀⠀⢀⠜⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠁⠀⡄⠘⠈⠦⠜⣋⡙⠤⠊⠀⡇⠇⠀⠈⠁⠁⠀⢀⠃⠀⠀⠀⠧⣀⡉⢦⡶⣁⣀⠜⠀⠀⠀⡖⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⡇⡆⠀⠀⠀⣈⡀⠀⠀⠀⠃⢠⠀⠀⣧⣑⠤⢴⠀⠀⠀⠀⠀⠀⠀⢘⠁⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡇⡇⠀⠀⠀⢈⡀⠀⠀⠀⠀⢸⠀⢀⠃⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⡇⠇⠀⠀⠀⢈⡁⠀⠀⠀⡄⠘⠀⡘⠀⠀⠀⠀⡗⠂⠠⠤⠠⠤⠤⠤⠤⠤⠤⠤⠤⠐⠒⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⢁⢰⠀⠀⠀⠈⠁⠀⠀⠀⡇⡆⢠⠃⠀⠀⠀⠀⡑⠂⠤⠤⠤⠀⣀⣀⣀⡀⠠⠤⠤⠄⢞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⡼⠆⠤⠤⠤⠤⠤⠤⠰⡤⢻⠁⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⢸⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⢸⡄⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠜⠒⠒⣞⡓⠀⠚⠢⢄⠀⠀⠀⠀⠀⠀⠀⠈⠥⡉⣉⠉⡉⢉⡉⢉⡉⣩⡉⢉⣌⡇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣋⣶⣖⣚⣋⣙⣓⣲⣶⣙⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣵⣽⣾⣿⣋⣻⣿⣷⣼⣟⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⠟⠛⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠠⠂⠈⡉⠈⠈⢉⢢
⠀⠀⠀⠀⠀⡐⠀⢊⡤⠈⢀⠄⠄⠂⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠂⠈⠁⠈⠲⠄
⠀⠀⠀⠀⠀⡄⠀⡠⠄⢠⡥⠀⠐⣇⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠈⠉⠐⣀⠀⠄
⠀⠀⠀⠀⠀⢀⠘⠃⠀⠠⣄⡤⠄⠘⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⡠⡀⠀⣛⡀⠤
⠀⠀⠀⠀⠀⠀⠀⠑⠠⢀⡈⣀⠄⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⣁⣨⡀⠀⣈⢁⣆⡀
⠀⠀⠀⠀⠀⠀⠀⡀⠔⠾⣤⡤⠗⠂⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠏⠁⠊⢀⠌⠠⠏⠁⢀⡂⢄
⠀⠀⠀⠀⢀⠖⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠒⠛⡟⠚⠀⢄⠀⠀⠀⠃
⠀⠀⠀⠀⢸⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠰⠠⠀⠀⢳⠀⠀⢳
⠀⠀⠀⠀⢸⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⡰⠃⠀⠀⠀⡇⠀⠀⠆
⠀⠀⠀⠀⢸⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠘⡄⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⢀⠌⠀⠀⠈⠀⢀⠃⠀⠀⡆
⠀⠀⠀⠀⠸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⡜⠀⠀⠀⠀⠀⠀⠀⡠⠂⢀⡠⠀⠀⠀⠀⠰⢤⠀⢣⣀⣀⣰⢁
⠀⠀⠀⠀⢐⠄⣰⢇⣀⣀⣀⡀⠀⠀⠀⣀⣠⣣⠃⠀⠀⠀⠀⠀⠊⠀⠒⢄⠋⠀⠀⠀⠀⠀⠀⠉⠃⠆⣀⣽⠁
⠀⠀⠀⠀⠀⡀⡼⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⡷⠀⠀⠀⠀⠀⠀⠁⠛⠆⠂⠀⠀⠀⠀⠀⠀⠸⠀⠀⠰⠞⠉
⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡄
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣇⠀⠀⡸
⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⢹
⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠆⢀
⠀⠀⠀⠀⠘⠢⠤⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⡠⠞⠁⠀⠀⠀⠀⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⢀⣈⡉⠙⡓⠚⡋⠉⣉⡀⠀⠀⠀⠀⠀⠀⠀⡀⢰⠀⠀⠀⠀⠀⠀⡀⢀⣀⡀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⡰⠁⠀⠈⣉⡽⠀⣏⡉⠀⠀⠑⡄⠀⠀⠀⠀⠀⠑⠘⠀⠀⠀⠀⠀⢆⣀⠂⠈⠙⠂⠠⠐⡎
⠀⠀⠀⠀⠀⠀⠙⠒⠛⠐⠉⠀⠀⠈⠛⠒⠶⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠐⠒⠂⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣷⣾⣿⣿⣿⠿⠛⠛⢿⣿⣿⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣦⣴⣿⣿⣿⡿⢿⣿⣿⣿⠋⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⠿⢿⣿⣿⣿⡿⠁⠀⠀⢿⣿⠃⠀⠀⠀⠀⠸⠿⠛⠛⠛⠛⠛⠻⢿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠁⠀⠀⠸⣿⣿⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣙⣿⣿⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣿⣿⣿⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠛⠿⠿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣦⡀
⠀⠀⠀⢀⣴⣿⣿⣿⡿⠟⠛⠉⠉⠙⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⡄
⠀⠀⢠⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡄
⠀⢀⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣷
⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⢸⣧⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡆
⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣶⣤⣤⣤⣤⣿⠿⠿⡶⡶⠶⠛⠁⠀⠀⠀⠀⣠⠎⠀⠀⣠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇
⠀⢻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣶⣤⡾⠛⠉⠀⠀⠀⠀⠀⠈⠢⣄⣀⠀⠀⠀⢀⣠⣴⠞⠛⠲⣶⣿⡷⠋⠀⠀⠀⠀⠈⠛⢷⣦⣄⣿⣿⣿⡇
⠀⠘⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠋⠉⠀⠀⠀⠀⠈⢻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⠁
⠀⠀⠹⣿⣿⣿⣄⠀⠀⠀⠀⠀⢀⣠⣴⣿⡟⢀⣀⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣀⠈⣿⣿⠃⣀⡀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣦⣄⣀
⠀⠀⠀⣹⣿⣿⡟⠀⠀⠀⠀⢈⣉⣉⣛⣿⣿⣿⡿⠟⠛⠛⠿⢿⣿⣦⣀⣀⣠⣄⣀⣠⣶⣿⡿⠟⠛⠛⠻⢿⣿⣿⣿⣋⣉⣈⠁⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿
⠀⢠⣾⣿⣿⡟⠁⠀⠀⢰⣾⣿⣿⣿⣿⣿⡿⠁⠀⣠⡴⠶⢦⣄⠙⢿⣿⣿⣿⣿⣿⣿⡿⢋⣠⡴⠶⢦⣄⠀⠙⢿⣿⣿⣿⣿⣿⣷⡄⠀⠐⣶⣶⣶⣿⣿⣿⡿⠋
⠀⠀⠻⣿⣿⣿⣿⡇⠀⢸⣿⣿⣿⣿⣿⣿⠁⠀⠈⣱⢚⣿⣷⡌⠃⠈⣿⣿⠛⠻⣿⣿⠁⠞⣱⣿⣯⠳⡌⠂⠀⠈⣿⣿⣿⣿⣿⣿⠇⠀⠀⢈⣿⣿⣿⡟⠉
⣀⣀⣤⣾⣿⣿⡟⠁⠀⠀⠀⠉⠙⢿⣿⣿⡀⠐⠀⠉⠈⠻⠟⠃⠀⢠⣿⡿⠀⠀⣿⣿⡄⠀⠙⠿⠛⠀⠁⠀⠀⢠⣿⣿⡟⠉⠉⠐⣶⣶⣶⣿⣿⣿⠟
⠙⢿⣿⣿⣿⣿⣤⣤⣴⡆⠀⠀⠠⢾⣿⣿⣷⣄⠀⠀⠀⠀⠘⢉⣠⣿⡿⠃⠀⠀⠘⣿⣿⣄⡙⠒⠀⠀⠀⢀⣠⣿⣿⣿⡷⠆⠀⠀⢿⣿⣿⣿⣛⠁
⠀⠀⠉⠛⠿⢿⣿⣿⣿⣧⣀⠀⠰⠛⢻⡟⠿⣿⣿⣶⣶⣶⣾⣿⡿⣟⠁⠀⠀⠀⠀⢈⡛⢿⣿⣷⣶⣶⣾⣿⡿⠟⣿⢋⠛⠂⠀⠀⣠⣿⣿⣿⣿⣿⠗
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⡇⢧⠀⠀⠉⠉⠉⠉⠉⠁⡰⠧⣄⡀⠀⠀⣀⣠⠽⣆⠈⠉⠙⠉⠉⠁⠀⢀⡟⢸⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣇⠸⡇⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠈⠑⠋⠁⠀⠀⠈⢦⡀⠀⠀⠀⠀⠀⣾⠀⣿⣿⣿⡟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣆⣷⠀⠀⠀⠀⢻⡏⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⢻⡗⠀⠀⠀⠀⡟⣸⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣆⠀⠀⠀⢸⠀⠀⠈⠉⠉⠉⠙⠉⠉⠉⠉⠁⠀⠸⠁⠀⠀⠀⣸⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣶⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗⠦⠤⣀⣀⣀⣠⠤⠔⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣿⣿⣿⣿⡿⠟⠉

⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠤⠤⠤⢤⣄⣀⠀⠀⠀⠀⠀⢀⠖⠋⠉⠳⡄
⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⡔⠉⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠀⣀⡤⠼⠶⠖⠒⠒⠛⠲⢤⡀
⠀⠀⡴⠋⢻⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠳⡄⠀⣸⠀⠀⠀⢀⡄⠀⢀⢶⡀⠀⠀⣧⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄
⠀⠀⣇⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡀⡇⢀⣿⠀⣠⣶⣋⡤⠖⠉⠀⠳⢤⡀⣿⠀⠀⠀⠀⠀⣠⠶⣄⠀⠀⠀⠀⡇
⠀⠀⢻⠉⢿⠀⣠⣤⣠⠤⣄⣠⣄⢸⠏⢙⠇⢺⡈⢻⠉⠉⠀⠀⠀⠀⠀⠀⠀⣿⣟⡇⡴⠒⠒⠋⠁⠀⠈⠓⠲⢦⣀⣇
⠀⠀⠈⢑⡏⠀⠙⠛⠁⠀⠀⠛⠛⠈⣷⠉⠀⠀⡟⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣇⠘⡧⠀⣴⣤⠤⠤⣤⣤⡄⢸⠏⣸
⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⢸⡘⢆⠀⠀⠀⠀⠀⠀⠀⢀⡞⡼⠙⡇⠀⠙⠋⠀⠀⠈⠛⠁⠈⡟⠁
⠀⠀⠀⠀⠀⠙⠢⣄⣀⣀⣠⡤⢚⡁⠀⠀⠀⠀⠀⠣⣌⠓⠦⣄⣀⣀⡤⠖⢋⡰⠃⠀⠘⣄⠀⠀⠀⠀⠀⠀⢀⡼⠁
⠀⠀⠀⢠⠴⡞⠉⠉⠹⠦⠏⠙⢯⣬⠧⡀⠀⠀⠀⠀⣀⡽⠖⠿⠦⠿⠒⢾⣍⠀⠀⠀⠀⢈⣑⢦⡤⢤⡤⠖⠋
⠀⠀⡴⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⣇⠀⠙⢆⠀⣠⠞⠁⣹⠀⠀⠀⠀⠀⣇⠈⠳⡀⠀⣠⠯⣬⡟⠓⠚⢻⠛⠲⣄
⢀⡞⠀⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⢿⣧⣠⣼⠁⠀⠀⠀⠀⠀⠘⢦⢀⣽⣰⠃⠀⠀⡇⠀⠀⢸⠀⠀⠘⠆
⢾⡳⠤⣄⣼⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣠⠴⢚⡧⠀⠹⡀⠀⠀⠀⠀⠀⠀⡾⠙⢾⠃⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⠘⡄
⠀⣿⢳⢶⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣶⠚⣯⠀⠀⠀⢱⡀⠀⠀⠀⠀⡼⠁⠀⡟⠀⡄⠀⠀⡇⠀⠀⢸⠀⠀⢠⠀⢱
⠀⢿⢸⡘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⡇⢸⠀⠀⠀⠀⡇⣀⡀⣀⣠⣇⠀⢸⠁⣸⡇⠀⠀⡇⠀⠀⢸⠀⠀⢸⡇⠈⡇
⠀⠘⡄⢇⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⢸⢸⡇⠀⢀⡞⠀⠀⠀⠀⠀⠸⣄⡏⢀⡏⡇⠀⠀⡷⠒⠖⢾⠀⠀⢸⢹⠀⢻
⠀⠀⠹⡼⢾⡗⠲⠦⠤⣤⠤⠴⠶⢺⠀⠀⢸⡜⡇⠀⡾⠀⠀⠀⠀⠀⠀⠀⢸⠃⢸⢰⠃⠀⠀⡇⠀⠀⢸⠀⠀⢸⡇⡇⠘
⠀⠀⢰⡗⠚⡿⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣸⠃⡇⢠⡇⠀⠀⠀⠀⠀⠀⠀⣾⠀⡏⠈⢳⢤⣀⡇⠀⠀⢸⣀⣤⡞⠁⢹
⠀⠀⢸⡇⠀⡇⠀⠀⠀⣶⠀⠀⠀⢸⠀⠀⠈⠛⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⣷⢶⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⡶
⠀⠀⢸⡇⠀⡇⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢧⣼⠃⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠺⣄
⠀⠀⢸⡇⠀⡇⠀⠀⠀⣿⠀⠀⠀⢸⠀⠀⠀⠀⠀⢸⣅⡀⠀⠀⠀⠀⠀⠀⢀⣸⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⡇⠀⣧⠀⠀⠀⣿⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠙⡖⢤⣤⡤⠴⡞⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⡇⠀⢹⠀⠀⢠⣿⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡧⡇⢰⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢸⡇⠀⢸⠀⠀⢸⣿⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⡇⢸⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⢸⡇⠀⢸⠀⠀⢸⣿⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⡇⡇⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⢸⡇⠀⢸⠀⠀⢸⠏⠃⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⣷⡇⣼⠀⠀⠀⠀⠀⠀⠓⠒⡖⢶⣶⢲⡖⠚
⠀⠀⢸⡇⠀⣸⣄⣀⣸⠀⣇⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣿⡇⣏⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⡟⢸⠃
⠀⠀⢸⡇⣾⣡⣤⣤⡽⠀⢯⣤⣀⣉⣷⠀⠀⠀⠀⠀⢀⡴⣯⣾⠟⢷⣼⠷⡄⠀⠀⠀⠀⢀⣴⣣⣾⢷⣌⣷⡄
⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣭⣥⣤⣤⣤⣤⣤⣬⣯⣭⣤⣤⣤⣬⣭⣧⣤⣤⣤⣤⣾⣾⣭⣥⣤⣭⣷⣾⣤⣤⣤⣤
⣿⣿⣏⣉⣉⡉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⢀⣀⣤⡤⡀⢀⣴⡾⠿⠛⠛⠛⠛⠻⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠿⠛⠛⠻⡿⠟⠉⠀⠀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⣦⡝⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠶⢦⡀
⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⣷⣄⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣦⡀
⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠃⠈⠛⠿⠿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⢠⣿⠆⠀⠀⠀⠀⣶⡶⠿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠙⢿⣤⣀⡀⠀⠀⣠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠁⠀⢻⣦⣀⣀⣠⣴⡆⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣼⠟⠀⠀⢀⣤⠶⣛⣛⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣀⡀⠙⠛⠛⠋⢹⣇⠀⠀⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠀⣴⠀⠀⠀⢀⡼⠋⠀⠀⣰⡯⠖⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠦⠤⠭⠿⠷⢦⡀⠀⠈⢿⡄⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⣿⡇⠀⣶⠈⠀⠀⠀⠀⠁⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⣤⠈⣿
⠀⠀⠀⠀⠀⢹⣧⠀⢹⣇⢀⣀⣠⡶⢛⡟⣫⠟⠉⠉⠉⠉⠉⣶⣶⣶⣤⡾⠛⣻⠛⣻⠛⠛⠒⠒⠒⠒⢀⣀⣀⣀⣠⣿⠀⡿
⠀⠀⠀⠀⠀⠀⠻⢧⣸⣿⡿⠿⡟⠴⢋⠜⠋⠀⠀⠀⠀⠀⠀⢨⠁⠀⢸⡤⠞⣡⠞⠁⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⣿⣿⠐⠁
⠀⠀⠀⠀⠀⢀⣴⣶⠾⣿⣇⠀⢿⣤⣀⣀⣀⣀⣀⣀⣀⣀⣠⠏⠀⠀⠈⢿⣄⠁⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⣿⡿⠿⠿⣷⣆
⠀⠀⠀⠀⠀⣾⡟⢁⣀⣹⣿⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⢸⣿⣥⣦⠀⠘⣿⡇
⠀⠀⠀⠀⢰⣿⡇⠈⠻⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠟⠁⠀⢀⣿⡇
⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠏⠀⢀⣤⣿⠟
⠀⠀⠀⠀⠀⠈⠻⢿⣦⣤⠼⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⠀⠈⠉⠁⠀⠀⠰⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠶⠾⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⢠⡟⣀⣀⣀⣀⣀⣀⣀⡀⠈⢻⡄⠀⠀⠀⠀⠀⠀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣦⡀⠀⠀⠀⠀⢸⠁⠈⠛⠿⠿⠿⠟⠋⠁⠀⠀⠉⠀⠀⠀⠀⣠⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡾⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠒⠒⠒⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣰⡄⢤⣿⣷⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⣶⣤⣤⣤⣀⣤⣤⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣄⡀
⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣷⠋⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⢮⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣸⠿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣦⣴⣤⣄⣴⣶⣤⣢⣤⣴⣶⣦⣶⣶⣿⠿⠎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠽⠿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣶⣦⣴⣶⣿⣿⣿⣿⣶⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠉⠁⠀⠀⠈⠙⠻⠟⠋⠁⠀⠀⠈⠉⠻⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⠁⠀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀⠈⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⠿⠛⣉⣤⣶⣿⡿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠿⣿⣶⣌⠙⠿⣿⣷⣄
⠀⠀⠀⠀⠀⢀⣼⣿⠟⢁⣠⣾⣿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣷⡄⠈⠻⣿⣷⡀
⠀⠀⠀⠀⢀⣾⣿⠃⣰⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡄⠀⠘⣿⣷⡀
⠀⠀⠀⠀⣼⣿⢣⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠸⣿⣧
⠀⠀⠀⠀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⣿⡀
⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣀⠀⠀⠀⠋⠀⠀⠀⠀⢻⣿⡇
⠀⠀⠀⣸⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣾⡿⠿⠛⠛⠛⢿⣷⡀⠀⠀⠀⠀⠀⠀⢸⣿⣇
⠀⣰⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣿⡿⢿⣷⣶⣶⣶⣶⣿⡿⠿⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠻⣿⣷⣄
⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿
⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⢨⣿⣿⡄⠀⠀⠀⢤⣤⣴⣾⡿⠋⠀⣤⣤⣤⣤⣤⣤⣤⠀⠀⠀⠀⠀⢠⣤⣤⣤⣤⣤⣤⡤⠀⠙⠿⣷⣶⣤⡤⠀⠀⠀⢠⣿⣿
⣿⣿⠃⠀⠀⠀⠀⣄⣀⠁⢀⣠⣴⣶⣶⣶⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⣶⣶⣦⣤⣄⣀⠈⢀⣠⠀⠀⠀⠀⠙⣿
⢿⣿⡀⠀⠀⠀⠀⠙⣿⣿⣿⠟⠁⠀⣠⣶⣶⣶⡄⠀⠙⣷⣄⣀⣀⣠⣿⠋⠀⣴⣶⣶⣦⡀⠀⠈⠻⣿⣿⣿⠋⠀⠀⠀⠀⢀⣿
⠈⢿⣿⣶⣦⡄⢀⣴⣿⠿⣿⠀⠀⠀⠈⢻⣿⣅⡵⠀⠀⣹⡟⠛⠛⢿⡇⠀⠐⣿⣿⣅⡟⠁⠀⠀⠀⣿⡿⣿⣧⡀⠠⣴⣾⣿⡿
⠀⠀⣹⣿⠏⢀⣾⡿⠁⠀⢿⣆⠀⠀⠀⠘⠛⠛⠁⠀⢀⣿⠃⠀⠀⠘⣷⡀⠀⠙⠛⠛⠁⠀⠀⠀⣰⡿⠀⠈⢻⣿⡀⠹⣿⡏
⠀⠀⢿⣿⡀⠘⢿⣷⣤⡄⠈⢿⣦⣄⡀⠀⠀⢀⣀⣴⡿⠃⠀⠀⠀⠀⠘⢿⣦⣀⠀⠀⠀⢀⣠⣴⠟⠁⢠⣶⣼⣿⠃⢀⣿⡇
⠀⠀⠘⣿⣷⣄⣈⣟⠉⠀⠀⠀⠈⠙⠛⠿⠟⠛⠋⠉⠰⣦⡀⠀⠀⠀⣴⠆⠉⠛⠛⠻⠿⠛⠋⠁⠀⠀⠀⠉⣿⣁⣤⣾⣿⠃
⠀⠀⠀⠈⠛⠿⢿⣿⣦⣤⣰⡄⠀⠀⠀⠀⢀⠄⠀⠀⠀⠈⠛⠷⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⣾⣿⡿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣷⡀⠀⠀⠀⠀⡰⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠐⢆⠀⠀⠀⠀⢀⣾⣫⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣷⡄⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⣠⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠑⠀⠀⠀⠀⠀⠀⣠⣼⣿⠏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡏⠙⠳⢦⣤⣀⣀⣀⣀⣤⡶⠞⠋⢹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⡀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⢀⣾⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣯⣤⣿⠿⣦⣄⠀⠀⠀⠀⠀⠀⣀⣴⠿⣿⣄⣽⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⠻⣶⣶⣶⣶⡟⢻⣿⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣯⣈⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠿⠟⠛⠿⢶⣦⣴⡾⠿⠿⠿⠿⢶⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠉⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠉⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣿⣇⣀⣤⣶⠾⠟⠛⠛⠛⠛⠛⠛⠛⠛⠿⢷⣦⣄⡀⣸⣿⣤⣤⣤⣄⡀
⠀⠀⠀⠀⠀⣠⣾⠟⠋⠉⠀⠈⠉⠙⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠉⠁⠀⠉⠙⠻⢷⣦⡀
⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡄
⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠏⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⣴⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⠿⠋⠁⠀⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧
⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⢻
⣿⡇⢀⡄⠀⠀⠀⠀⣴⡶⠶⠿⠿⠿⠿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⢤⠀⢸
⢹⣷⡾⠁⠀⠀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠈⢷⣼
⢸⡿⠁⠀⠀⠀⣰⡿⠀⠀⠀⠀⣤⣤⣤⣤⣤⠶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠲⢦⣤⣤⣤⣤⡀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠈⣿
⣿⡇⠀⠀⠀⣴⡿⠁⠀⠀⠀⣀⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣀⡀⠀⠀⠀⠘⣿⣄⠀⠀⠀⢸
⣿⡇⠀⠀⠺⣿⣶⣶⣶⣶⡿⠋⠭⢟⣭⣭⠩⢝⢿⣆⠀⣀⣀⣀⠀⢀⣼⠟⢉⣽⣟⠻⠭⡙⢿⣶⣶⣶⣶⣾⡿⠇⠀⠀⢸
⠸⣧⣸⡄⠀⠈⢻⣧⠈⣿⡁⠀⠀⠸⣿⣿⡇⠀⠘⣿⡿⠛⠉⠛⠿⣾⡏⠀⠸⣿⣿⡇⠀⠀⠀⣿⠋⢰⣿⠋⠀⠀⢸⣀⣾
⠀⠹⣿⣧⠀⠀⢸⡏⠀⢸⣧⠀⠀⠀⠉⠉⠀⠀⣸⣿⠁⠀⠀⠀⠀⢹⣷⡀⠀⠈⠉⠀⠀⠀⣰⡟⠀⠈⣿⠀⠀⢀⣿⣿⠋
⠀⠀⠈⠻⣷⣄⡀⠳⠀⠀⠙⢷⣤⣤⣤⣤⣴⡾⠟⠙⠷⣤⣤⣤⡴⠟⠙⠷⣦⣤⣤⣤⣤⣾⠟⠁⠀⠴⠃⢀⣠⣾⠟⠁
⠀⠀⠀⠀⠈⠛⢿⣦⣤⣄⠀⠀⠈⠉⠉⠉⠀⠀⢄⣀⡀⠀⠀⠀⠀⣀⣀⡄⠀⠈⠉⠉⠁⠀⠀⠀⣠⣤⣶⠿⠋
⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠴⠛⠛⠻⠿⠟⠛⠛⠻⢄⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠻⢿⣿⠿⠉⠷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠙⢿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡛⠿⣷⣶⣶⣦⣤⣶⣶⡿⠟⢛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣇⠀⠀⠉⠉⠉⠉⠉⠁⠀⢀⣼⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣇⠀⣀⠀⠀⣄⣀⣾⣿⣿⣿⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷

⠀⠠⠤⠀⠠⠤⠀⠄⠤⠄⠀⠠⠄⠠⠤⠀⠀⢀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠠⠠⠤⠄⠀⠤⠄⠤⠀⠠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢇⣀⢀⠀⠤⠤⡖⠈⠁⠀⠈⠁⠢⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⠀⢀⣀⡇⠀⠤⠄⢀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⠀⠀⠀⢀⣀⠁⣀⣀⠀⢀⣄⡀⠀⣀⡷⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣥⢙⠉⠃⠐⠉⠋⠁⡁⠨⡈⡀⢁⠈⠠⠁⡜⡕
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡸⡀⠀⠀⠉⢠⠐⠀⠀⣒⡆⠀⠀⠀⢀⢇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠼⠂⠀⠀⠀⠀⢱⢎⠀⢀⠀⠀⠀⠉⢭⠗⠤⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠚⡎⡀⠀⠀⠈⢁⡎⡐⠀⠀⠀⠀⠀⠰⠀⡀⠀⠀⠈⠑⠂⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠆⠁⠀⠀⠇⠱⢄⠠⠀⠈⣠⠥⡀⠀⢀⠠⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠢
⠀⠀⠀⠀⠀⠀⢠⠔⠁⠀⢠⠀⠀⠀⠀⠀⠂⠝⠉⠥⣐⠪⠕⢶⠃⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠘⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⡴⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⡰⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢰⠀⢀⠔⠁⠀⠀⢀⠄⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡤⠐⠁⠀⠀⠀⡀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⢸⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠐⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⡀⠀⠐⠁⠀⠀⠀⠀⠀⠀⡰⢀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠤⠄⠀⠀⠀⠀⠀⠀⠀⠐⠊⢀⠀⠀⢀⡀⢠⠈⡄
⠀⠀⠀⠀⣇⡌⠀⠀⠀⠀⠀⠀⠀⡔⢀⠈⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠘⠊
⠀⠀⠀⠀⢏⣇⠀⠀⠀⠀⠀⣀⠜⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠉⠂⠄⠀⠀⣈⠔⠈⠀⠀⡀⡀⡀⠀⢀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⠤⠤⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠚⠉⠉⠀⠀⠀⠀⠀⠈⠉⠙⠢⢄⠀⠀⠀⠀⠀⠀⠀⢀⡤⢴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⢓⠒⢤⡀
⠀⠀⠀⠀⠀⠀⢀⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⠀⠀⠀⠀⠀⡏⠀⡼⠀⢀⣠⣄⠀⠀⠀⣠⣄⠀⠘⡄⠀⢣
⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢀⡴⠛⠒⠒⠒⠒⠒⠚⠙⠢⡀⠀⠀⠸⡄⠀⠀⠀⡠⢧⣴⣥⣤⣜⡩⣻⡤⠤⣴⣉⡫⣥⣤⣽⣤⡦⣄
⠀⠀⠀⠀⠀⢠⠇⠀⠀⢀⠏⠀⠴⠶⠦⠀⠀⠶⠲⠄⠀⢱⠀⠀⠀⢧⠀⠀⠀⡅⢸⢫⠀⠙⠓⠄⠾⠀⠀⠹⠤⠜⠛⠀⢸⠙⠀⢸
⠀⠀⠀⠀⠀⢸⠂⠀⡔⣼⠀⡤⠒⠁⢒⠀⠐⠊⠒⢦⠀⠘⣤⠲⡀⢾⠀⠀⠀⠙⢻⠀⠳⠤⣤⠶⣾⡶⢶⡶⢶⡦⠤⣤⠞⢸⠓⠁
⠀⠀⠀⠀⠀⠈⡇⠈⠧⢇⠀⠀⠀⠀⢁⣀⡀⠀⠀⠀⠀⠀⡸⠴⠀⡏⠀⠀⠀⠀⠘⡄⠀⠀⠸⣄⡈⢷⠾⣀⡠⠃⠀⠀⢀⡎
⠀⠀⠀⠀⠀⠀⠈⠢⣠⣈⣦⡀⠀⠀⠀⣤⡄⠀⠀⠀⠀⣴⣡⡠⠊⠀⠀⠀⠀⠀⠀⣈⣦⣀⠀⠀⠉⠉⠉⠁⠀⠀⢀⣤⠮⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠛⣶⠢⣀⣀⣀⡠⠖⣶⠛⠢⢄⡀⠀⠀⠀⠀⢀⠔⠉⠁⡏⠀⢹⡃⠒⢲⣶⠒⠚⡹⠁⠀⡇⠈⠑⠢⡀
⠀⠀⠀⠀⠀⠀⢀⡔⠁⠀⠀⠀⣿⠀⠈⢦⡴⠁⠀⣿⠀⠀⠀⠙⢦⡀⠀⡰⠁⠀⠀⠀⡇⠀⠀⠑⠊⠁⠀⠉⠒⠁⠀⠀⡇⠀⠀⠀⠘⣄
⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⡿⠖⠚⠉⠉⠓⠶⢿⠀⠀⠀⠀⠀⢳⡼⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢇⠀⠀⢠⠀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⡀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⡆⠀⢀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⢀⢟⠀⠀⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⢧⠀⠀⠀⢇
⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⡄⠀⠈⣗⠋⠸⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢸⠁⠳⡖⠒⡇
⠀⠀⠀⠀⢀⠁⠀⢸⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⣇⠀⠀⡟⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⢧⠀⢰
⠀⠀⠀⠀⢸⠀⠀⣿⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⣿⠀⠀⡇⠀⠀⡇⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸⠀⠀⠘⡄⢸
⠀⠀⠀⠀⠈⡀⢠⠻⣄⠀⠀⠀⣃⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⣠⣿⡆⠀⡇⠀⠀⣯⢓⣞⣦⠤⠤⠤⠤⠤⠤⠤⠤⢤⢾⣖⡪⢿⠀⠀⠀⡣⠘⡇
⠀⠀⠀⠀⠀⡏⣹⠀⢸⠉⠒⠢⠞⠀⠀⠀⠀⠀⠀⠷⠔⠒⠉⣷⣁⡷⠲⡇⠀⠀⠇⠀⠀⠉⠉⠐⠒⣒⣒⣒⠒⠈⠉⠉⠀⠀⡎⠀⢀⢮⠀⠀⢘
⠀⠀⠀⠀⠀⢧⡿⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣼⣿⣇⠃⠀⠀⢸⠀⠀⠀⠀⠀⢸⠁⠀⠈⡆⠀⠀⠀⠀⠀⡇⠀⢸⡞⠓⠒⠉
⠀⠀⠀⠀⠀⠈⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⠋⠀⠀⠀⢸⠀⠀⠀⠀⠀⡆⠀⠀⠀⢃⠀⠀⠀⠀⢠⠁⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠇⠀⠀⠀⢸⠀⠀⠀⠀⢸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢸⠀⠀⠀⠀⠈⡄⠀⠀⠀⡌⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡏⠀⠀⠀⣏⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⡇⠀⠀⠀⠀⠀⢡⠀⠀⢰⠁⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢒⣊⣀⢴⠀⠀⠀⡦⣀⣙⡒⣤⣀⠀⠀⠀⢀⡤⠐⠒⠒⠧⠤⢠⡇⠀⠀⠀⠀⠀⢸⡄⠤⠾⠐⠒⠂⢾⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⠤⠤⠀⠒⠊⠀⠀⠀⠑⠒⠀⠤⠤⠜⠀⠀⠀⠚⠤⠤⠤⠤⠤⠒⠚⠁⠀⠀⠀⠀⠀⠈⠓⠒⠤⠤⠤⠤⢼⡓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⣴⠿⠋⠉⠀⠁⠉⠉⠙⢳⣄
⠀⠀⠀⠀⠀⠀⣸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠀⠀⠀⢀⣀⣄⡀
⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⣠⡶⢶⣿⠋⣻⣿⣄⣤⣀
⠀⠀⠀⠀⢀⣾⣿⠓⠦⢤⣄⡤⠺⣥⠒⢦⡤⠒⠋⣿⣧⠇⠀⢀⡟⠽⢣⢿⣛⣵⡿⡷⠽⢻⣆⣀⡀
⠀⠀⠀⠀⠈⠳⢿⡄⠀⢣⡈⠣⠴⠋⠂⠘⡀⠃⢠⡿⠉⢀⣾⣻⡷⠒⠋⠀⠀⠀⠙⠛⠛⠛⢿⣻⡗⣀
⠀⠀⠀⠀⠀⠀⢈⣿⣦⣀⠑⠢⠤⠤⠀⠊⣀⣴⣟⠁⠀⣾⢽⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡃
⠀⠀⠀⠀⢀⡴⠋⣹⠉⣽⠛⢲⡖⣶⠒⢻⡟⠙⣿⠳⣤⣟⣿⠛⠢⣄⡀⠀⠀⢀⡀⠀⠀⠀⠀⢀⣸⣧⠟
⠀⠀⠀⣠⠞⠀⠀⡏⠀⠹⡶⣾⡋⠙⠓⣾⠁⠀⢹⡄⠈⠻⣿⡀⠀⢀⡍⠻⡋⢳⣶⣉⣱⢶⡋⠉⢸⣻⡇
⠀⠀⣴⠋⠀⠀⢸⡇⠀⠀⠀⠈⣧⠀⢸⠃⠀⠀⠈⣧⠀⠀⣸⣧⡀⠀⢢⡀⠈⠉⠀⠉⠁⡠⠁⢠⡟⠉
⠀⠸⣧⡀⠀⠀⣾⠁⠀⠀⠀⠀⠸⣇⡟⠀⠀⠀⠀⢹⣦⡞⢁⡾⣿⠶⣤⣌⣐⣒⣒⢒⣉⣠⣶⢿⡀
⠀⠀⢸⡿⠲⢶⡏⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠈⣿⣷⡾⠁⣿⠀⠀⠈⠻⣛⠿⠋⠉⠁⢹⡄⠻⣄
⠀⠀⢸⠇⠀⣸⠇⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⢸⡟⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠹⣆
⠀⠀⣾⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠀⠀⠀⢈⣧⠀⢀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢹⣆
⠀⠀⣿⠀⠀⣿⠧⣤⣀⣀⣀⡀⠀⣸⡆⣀⣀⣀⣤⠴⠛⢻⣦⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡶⠻⣇
⠀⠀⣿⠀⠀⣿⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢹⠟⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⢻⡄
⠀⠀⢿⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⢸⡇
⠀⠀⠸⡇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢸⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡇⢰⡇
⠀⠀⠀⢻⡄⣿⠀⠀⠀⠀⠀⠀⠀⠠⡄⠀⠀⠀⠀⠀⠀⢸⡇⣸⣦⠤⣤⣤⣤⣤⣤⣠⣤⠴⠶⠞⢋⡹⡇⣸⠃
⠀⠀⠀⠀⠙⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⢀⡴⣄⡀⠀⠀⡰⢢⡀⠀⠈⡤⠤⢿⠏
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠘⡇⣿⠰⡍⠷⢠⠇⠀⢈⠱⡦⠰⠀⢀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣷⣿⠀⠲⠚⠉⠀⠀⠀⠤⠂⠊⠔⡊⡐⠄⠀⢿
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠆⢉⡊⢡⠀⠀⠀⠁⣑⡁⠅⠀⢸⡆
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⠠⣋⡑⠚⣀⠇⠀⠀⠀⠀⠀⠀⣀⡼⠇
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢻⠙⠓⠦⣤⣤⣵⣶⣤⣤⡤⠴⠶⠶⣿⠋⠁
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⢹⡀⠀⠀⠀⣿⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠙⣷⣦⠤⠤⠤⣤⣤⣤⠾⣷⠤⠶⠖⠒⠛⠛⢯⡀⠀⢀⣼⡗⠓⢲⣄⣻⣀⣤⠖⢚⡳⢦⡀
⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠹⣶⠁⠀⠀⠀⠀⠀⠀⠀⣿⢠⡟⠀⠈⠉⠁⠘⣿⠋⠀⠁⠁⠀⠈⣷
⠀⠀⠀⠀⠀⣿⣤⣀⣀⣀⣀⣀⣠⡴⣿⠷⢤⣄⣀⣠⣀⡠⠴⣿⢸⡟⠛⠛⠛⣛⣛⣿⣛⠒⢒⢒⣚⣩⡿
⠀⠀⠀⠀⠀⠙⠷⠬⠭⠭⠭⠭⠤⠴⠟⠓⠒⠒⠒⠒⠒⠛⠛⠋⠀⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠹⠡

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋⠁⠀⠀⠀⠈⠉⠒⠒⠒⠒⠋⠉⠀⠀⠀⠈⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠀⠀⠀⠀⠀⠀⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⠀⠀⠙⠢⣄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣤⡀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢤⣀
⠀⠀⠀⠀⣠⣾⣥⣴⠚⠉⣀⣀⣤⣤⣤⣤⣤⣶⣶⣾⣿⣿⠿⠿⠿⣿⣷⣶⣶⣶⣿⡿⠿⠿⢿⣿⣷⣶⣶⣤⣤⣄⣀⣀⠀⠀⠈⢛⢲⣬⣷⣄
⠀⠀⠀⠀⠛⠉⠳⢤⡀⠀⠀⠀⠀⠀⠈⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠉⠁⠀⠀⠀⠁⢀⣠⠔⠋⠻
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⣀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣬⠴⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠶⠤⠤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⡤⠶⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠶⠚⠛⠉⠉⠉⠉⠉⠛⠛⠿⠿⠛⠛

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⢁⣄⣀⡀
⠀⠀⠀⠀⠀⠀⣰⠋⠳⣄⠀⠀⣠⠔⠁⠀⠀⠈⠑⠦⣄
⠀⠀⠀⠀⢀⡼⠁⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀
⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠦⢤⣀⡀
⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠲⠶⠤⠄⣰⣄
⠀⠀⠀⠀⠀⣹⣄⠀⠐⠦⣤⡀⢀⣠⠶⠛⠉⠉⠉⠀⠈⠉⠉⠙⠒⠒⠦⠤⢄⣀⣀⣀⠀⠀⠀⣀⣀⢤⡾⠉⠁
⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⣉⡤⠖⠉
⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠋⠁
⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠋⠁
⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠐⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠔⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠉⠛⠓⠒⠲⠒⠒⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠓⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⠤⣀⠀⠀⠀⠀⠀⠀⣀⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠙⠲⠤⠤⠒⠉⠀⠀⠀⠀⠀⠉⠓⠦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢤⣀
⠀⠀⠀⠀⢀⣀⡀⢀⣠⠤⠖⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⣀⣀⣀⡀
⠀⠀⠀⠀⠈⠛⢯⡀⠀⠀⣤⣀⣀⣀⠀⣀⠀⣀⢀⣀⣀⣠⣤⠤⠶⢆⡀⠀⠀⢀⣀⠤⠀⠤⠄⠠⠤⠤⠀⢠⣀⣀⣀⣀⣀⣀⠀⠀⣠⠼⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠳⢄⠀⠙⢦⡀⠀⠁⠀⠁⠈⠀⠈⠱⣄⠞⠈⠉⠲⣉⡉⠁⠀⠀⢦⡀⠀⠀⠀⠒⠀⠀⠀⠀⢀⠴⠋⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠀⠉⠺⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠖⠁⠀⣠⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴
⠀⠀⠀⠀⠀⠀⢈⣛⡶⠶⠶⠶⠶⠶⠾⠿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠈⠁⣀⣀⡀⠉
⠀⠀⠀⠀⠘⠁⠋⠀⠀⠀⠀⠈⠉⠀⠈⠀⠈⠉⠛⠃⠀⢠⠾⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠓
⠀⠀⠀⠀⠀⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠌⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⢲⣀⠀⢀⣶⡁⠀⠀⠀⠀⠀⡀⠀⠀⡈⠀⠀⠀⠀⣀⢀⠠
⠀⠀⠀⠀⠀⠀⠐⠀⣴⣚⣺⣚⣒⣗⣓⢓⣠⡤⠐⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠐⢗⢶⢲⠖⡇⡗⡶⢺⢺⡒⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠽⠭⠭⠯⠋⠋⠙⠋⠀⠀⠀⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠂⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐

⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣙⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣾⡿
⠀⠀⠀⢀⣤⣀⣾⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡇⠀⠀⡆⠀⠀⢰⡆⠀⢸⣀⠀⠀⠰⠟⠛⠉
⠀⠀⠀⠘⠿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣀⡁⠀⠀⠀⡠⠀⠀⠀⠀⢈⣈⠇
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠆⠂⠀⡀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣀⡀⠀⠀⠀⠁⠀⠦⠀⠁⠀⠀⣀⣀⠆⠀⣇⠀⠀⠣⢀⡀⠔⠁⠀⡸⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣄⠀⠀⠁⡀⠀⠔⠀⠀⡰⠃⠀⠀⠀⠈⠑⠒⢠⠄⠀⠤⠒⠊⠁⠀⠀⢰⣶⣾⣿⣿⣿⣿⣿⣷⣦
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠤⡄⢠⠤⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠙⡿⣿⣿⣿⣿⣿⣿⣿⣇⡀
⠀⠘⠲⢲⣴⣿⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⢰⣷⣾⡆⠀⠀⠀⠀⠀⠀⠀⣠⣮⣗⡶⠦⠤⢶⣲⣷⣦⠀⡈⠀⠘⠁⠀⠉⣭⠉⠉⢹⣿⣿⣷
⠀⠀⢀⣿⣿⣿⣿⣿⣿⠟⠉⢛⠛⢧⠀⢠⣦⡘⠿⠿⢃⣶⡄⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢰⡀⠠⡈⢁⠀⠁⠀⠀⠀⠻⢿⡁
⠀⠀⣼⣿⣿⣿⠿⢻⡉⠀⠀⠙⠀⢸⢠⣿⣿⣿⣷⣿⣿⣿⣿⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠑⢤⣇⠋⠀⠀⠀⢀⡠⠒⠚
⠀⠀⢹⣿⠇⠀⠀⠈⠁⢀⣁⡄⢀⣼⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠈⠙⠀⠂⠉⠉
⠀⠀⠀⠛⠶⣶⣄⣀⣀⡀⣡⢔⣫⣿⡟⠀⠛⢻⡿⣿⣿⣿⠈⢻⣿⣆⠀⠀⠀⣿⣿⣿⡀⠀⠛⠿⣿⡇⠀⠀⠀⠀⠐⡍⣆⢡⣼⠏⢂
⠀⠀⠀⠀⠀⠊⠁⠤⣆⠀⠀⠉⠙⠋⠀⢰⡶⠎⠉⠈⠛⣿⣶⣶⣿⣿⡆⠀⠀⣿⣿⣿⣿⣦⣄⡀⠀⠁⠀⠀⠀⠀⠀⠇⡬⠸⣿⡀⠌
⠀⠀⠀⠀⠀⠀⠘⣀⣼⠇⠀⠀⠂⠀⠀⢰⣿⣿⣿⣿⣿⣿⡟⠉⠉⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠂⠀⠀⠀⠀⡇⠀⠀⡜⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⠿⠿⠿⠷⠀⠀⠀⠀⠀⠀⠹⠿⠿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠂⠘⠒⠒⠚

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠉⠀⠀⠈⠉⠲⡤⠤⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠎⠀⠀⠀⠀⠀⣄⣀⣀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠚⠳⠤⣤⠤⠖⠂⠉⠀⠀⠀⠀⣄⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠀⠀⣠⠠⠖⠃⠀⠀⠀⠀⠓⠢⠸⡀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠴⡃⡔⢡⣬⡳⡤⣤⣮⣥⡉⢦⢋⠀⢠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢴⠉⠉⠳⠄⠠⢼⠀⠘⠧⠄⠤⠚⠉⠑⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢲⠒⡀⠀⠆⠀⠀⠀⠀⠰⠀⢀⠒⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢙⣦⣀⡀⠀⠀⢀⣀⣴⣊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠋⠀⢀⡏⢹⠁⠈⡹⠁⡆⠀⠉⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠠⠗⠂⠓⡔⠁⠒⠇⠀⡀⠀⠘⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠞⠁⠀⠀⡜⠀⠘⠣⠀⠈⠁⠀⠄⠂⠀⠱⡀⠀⠈⠓⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠜⠁⠀⠀⠀⣸⠀⠀⠀⠀⠁⠃⠙⠈⠀⠀⠀⠀⢱⠀⠀⠀⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣔⠀⠤⠀⠀⣰⠋⡶⠠⠄⠀⣀⡰⠆⢄⡀⠀⠤⠴⡉⢦⠀⢀⡠⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠈⣦⠓⠊⢁⠎⠑⠢⡄⠀⠠⣇⠁⡸⠀⠀⡄⠘⠱⡄⠉⠚⢤⠊⠈⠑⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡀⢺⣀⠃⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠈⣆⣸⢢⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠛⠖⠈⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠈⠰⠛⠓⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠺⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠶⠐⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⠲⠶⡶⠶⠶⢶⠶⠶⢶⠒⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠀⢀⡇⠀⠀⢨⡄⠀⢼⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠿⠦⠖⠒⢻⠀⠀⡌⠑⠺⠤⠿⠧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡁⠀⠀⢀⡀⣠⠾⠃⠀⠻⣦⡄⣀⠀⠀⠀⣱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠉⠉⠂⠉⠀⠀⠀⠀⠀⠀⠉⠀⠋⠉⠙⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠄⠂⠉⠉⠒⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡄⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⠀⠀⡠⠌⠛⠃⠑⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠈⠇⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠸⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠀⠀⠀⠀⠀⠀⣀⣠⣖⣉⡀⢀⣉⣲⣄⣀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠘⡆⠀⠀⠀⠀⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠂⠀⠀⠀⠀⠀⠚⠉⠀⠀⠀⠀⡗⢾⠀⠀⠀⠀⠉⡇⠀⠀⠀⠀⠀⠰⡁⠀⠃⠀⠀⠀⠀⠰⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⡠⣀⡆⠀⠀⠀⠀⠁⡇⢸⠈⠀⠀⠀⠀⣧⡠⢄⠀⠀⠀⡠⠃⠀⠸⠀⠀⠀⠀⠀⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢄⡀⢺⡴⠁⠲⠤⠤⠤⠤⠤⠇⠼⠤⠤⠤⠤⠴⠆⠘⢦⡇⠀⡰⠁⠀⠀⠀⡇⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠋⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠙⡉⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠈⠣⣄⣀⠀⠀⣀⣠⠜⠁⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢣
⠀⠀⣠⣄⠀⡀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠘⡀
⢀⠴⢅⡔⠋⠈⡆⠀⠀⠖⠙⡄⠀⠀⠀⠀⠠⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠄⡀⠀⠀⠀⢠⠋⠢⠀⠀⠀⠑⢠⣰⢶⡈
⡜⠀⢀⠌⠁⠀⠣⠤⠘⢇⡀⣱⣄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣠⠋⣀⡰⠓⢄⡀⣰⠁⡘⣋⢉
⠈⠒⠒⠶⠒⠦⣄⣀⢀⡞⠉⡃⠈⠳⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠁⢸⠉⢣⠀⠀⠉⠁⠀⠘⣁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠑⠦⠄⢾⠈⠉⠒⡖⠲⠤⠤⠤⠤⠤⠤⠤⠤⠔⢶⠚⠉⠁⡷⠠⠔⠋⠀⠈⢗⠒⠂⠉⠓⠤⠅⣀
⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠈⠓⠀⠚⠱⢄⣀⠜⠣⣀⣀⠜⠢⣀⡠⠊⠓⠀⠚⠁⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠈⠉⠉⢰⣶⣶⣶⣶⣶⣤⣤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣤⣤⣶⣶⣶⣶⣶⠎⠉⠉
⣶⣶⣷⠶⡶⠶⢶⣶⣾⣶⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢋⠔⠂⠀⠐⠈⠙⢆⡠⠔⢒⣀⣐⠢⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠒⠒⠒⠲⠴⠀⠁⠀⠀⠀⠀⠀⠈⠪⠀⠀⠀⠀⠀⠀⢈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⡤⠴⠤⣄
⠀⠀⠀⠀⠀⠀⠀⢀⡏⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠈⢣
⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⢀⠴⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠀⠑⡂⠀⠀⠀⠡⢢⠀⠀⠀⠀⠀⠀⠀⠀⠘⠢⡀
⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡣⢅⠀⣀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠢⣤⠀⠤⡊⠀⣀⠀⠀⡀⠀⠀⠀⠀⠀⢀⡀⠀⢀⠀⠀⠀⠐⠘⣄⡀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⣠⠊⠀⢀⣀⡀⠀⠀⠀⠀⠜⢁⣀⡀⠀⠁⢀⡠⠔⠉⢠⠋⠀⠀⠀⠺⡀
⠀⠀⠀⠀⠈⠳⡤⡄⠀⠀⠀⢀⢀⠂⠀⢈⠀⠀⠸⠿⠆⠀⠓⠒⢺⠀⠸⣿⠇⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠰⠒⠁⠀⠀⠈⠀⡀⠀⠀⢀⠔⠀⠀⠀⠢⡀⠀⠀⠀⡠⠃⠀⠀⠀⠈⠦⣀⠀⢀⡠⠃
⠀⠀⠀⠀⠀⠠⡠⠄⠀⣠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⡹⠁
⠀⠀⠀⠀⠀⠀⠈⠉⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⢀⠀⠀⠀⠀⠀⠀⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠠⠤⠔⠺⡁⠈⠂⠀⢣⠀⠀⠀⠀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣔⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠄⡀⠌⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠮⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠈⠑⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠐⠂⠠⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠉⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⢀⣇⡀⠤⠤⠀⣀⣃
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⢄⠀⠀⠀⡠⠒⠁⠀⠀⠀⠀⠀⠀⠈⠑⢄
⠀⠀⠀⠀⠀⠀⠀⢸⠀⡠⠊⠒⠒⠒⠀⠒⠒⠒⠒⠂⠘⢆⠀⠀⡇⠀⠎⠀⡠⠒⠒⠀⠀⠐⠒⠢⢄⡀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⢸⢰⠁⠀⠀⠞⠙⠂⠀⠀⠚⠙⠆⠀⠈⡆⢠⠃⠘⢀⠎⠀⠀⠀⢀⠜⢆⠀⠀⠀⠈⢢⠀⢠
⠀⠀⠀⠀⠀⠀⡎⠈⡇⠀⠠⠄⠊⠑⡄⠀⠀⠊⠒⢤⠀⠀⢣⠋⠙⢢⡄⠀⠀⢀⠴⣧⠀⠈⡷⢄⡀⠀⠀⡆⡘
⠀⠀⠀⠀⠀⠀⠱⠄⡇⠀⢀⠤⠠⠬⠄⠠⠤⠤⢤⡀⠀⠀⢨⢄⠜⠰⢳⠔⠺⢏⣈⣹⠁⠹⡉⢉⠿⠓⠒⡗⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢶⠥⠀⠤⠤⠴⠤⠤⠄⠠⠽⠆⢀⠎⠀⠀⠘⠲⡄⠀⠀⠀⣀⣀⣀⠈⠁⠀⠀⢀⠗⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡱⠦⣄⡀⠀⠀⠀⢀⣠⠤⢖⡁⠀⠀⠀⠀⠀⠘⢄⡀⠀⠀⠷⠆⠀⠀⢀⡠⠊
⠀⠀⠀⠀⠀⠀⢀⠤⠖⠁⠀⠰⣜⠬⠍⠀⠭⢋⠜⠀⠀⠈⠑⠤⣀⠀⢀⠔⠊⢩⠉⠢⡤⢠⠖⠉⡉⠑⠢⣀
⠀⠀⠀⠀⠀⡔⠁⠀⠃⡠⠲⡀⠀⠉⡱⠲⣍⠁⠀⠀⢀⠤⡀⡇⠀⠳⡇⠀⠀⠈⡀⣀⠵⠮⣀⢀⠀⠀⠀⢨⠑⡄
⠀⠀⠀⠀⠎⠀⠀⢰⢊⡔⠓⢌⠢⢊⡔⠑⠢⡑⠤⢊⠥⠒⢌⡃⠀⠀⠘⡄⠀⠀⠉⠀⠀⠀⠀⠉⠀⠀⠀⢸⠀⠈⡄
⠀⠀⠀⣜⠀⠀⠀⣼⢋⡔⡙⣌⠲⢊⡔⣑⢦⡈⠒⢁⣠⠒⣄⢹⡀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⣸

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠤⠾⠟⡀⠘⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠊⠀⠀⠀⠀⠀⠀⢠⡀⠸⠆⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⢀⡤⠄⠀⠐⠃⣀⣀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣦⠤⢤⡴⢶⠒⢢⠤⠰⢟⢻⣞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠛⠙⢥⠠⠙⠒⠀⠁⠀⣴⢻⣿⣿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣉⣭⠥⠭⢦⣀⠀⠀⠀⠈⠁⣷⠂⠐⠈⠀⠀⠀⢸⡏⢹⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡈⠁⠀⠀⠲⠏⠑⠻⠿⠛⠀⣯⣄⠀⠒⠆⠀⢀⡞⠀⠀⡼⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠅⢀⣤⠴⠏⠀⠀⠀⣠⠀⠀⢟⣭⣿⠆⠀⠀⣼⣅⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠁⠀⢀⡞⠀⠰⠃⠀⠘⢟⠟⢉⡀⡠⡾⢿⢿⡿⠃⠀⠀⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢋⡜⢦⠀⠀⣴⠎⠈⠀⠀⡿⠁⠀⢀⡀⠀⠀⢀⡞⠀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠈⢇⠈⣇⣴⠃⠀⠀⣠⡈⠁⠀⠀⠀⠱⢤⢰⣿⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⢸⣿⣿⠟⠣⢤⣄⣠⣠⣀⣀⣀⠀⠀⢸⢿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢈⣿⡿⠀⠀⠀⠈⠉⠙⠛⠛⢻⣷⠀⠀⠀⠹⣿⣦⣤⠤⠄⠔⠛⣛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡤⠀⠀⠀⣸⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣇⠀⠀⠀⠘⢿⣿⢿⣝⠻⢽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣌⣀⣼⣿⣿⡿⠷⣦⣀⡀⠀⢀⣀⡀⠀⣾⣿⡆⠀⠀⠀⠈⢧⠀⠱⣶⡖
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠤⠿⠿⠿⠟⣉⡀⠀⢸⣿⣿⣷⡿⠛⠛⣻⣿⣿⣿⣆⢀⣀⣀⣴⠆⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣾⣿⣿⣿⣿⣿⣷⣶⣾⣷⣶⣶⣤⣬⣥⣾⣿⠟⢹⠀⠀⠀⠙⢿⠉⠿⣿⣿⣿⣿⣿⣶⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠐⢯⣝⣛⢛⣿⣿⣿⢿⡿⡿⠿⠿⠿⣿⣟⣛⣿⣿⣿⣿⣠⠀⠀⠀⠀⠀⠘⠀⠀⠻⠛⢿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣧⡀⢉⡉⣉⡁⢉⣀⣬⣿⣿⣿⣿⢫⣿⣿⣿⣧⠤⠤⠄⠸⠿⣆⠀⡀⢀⣠⣾⣿⣿⣿⣿⡿⠿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠧⠤⣠⣥⣿⠾⠿⠿⠿⠟⠃⠀⠀⠀⠁⠀⠀⠀⠀⡠⢅⠀⠀⢠⠀⠀⠀⠲⣴⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⣤⣸⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⡀⠁⠀⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⣾⣷⣦⠀⢿⢿⣾⣷⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⣿⣿⣿⣿⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣤⠴⠒⠒⢤⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠞⠁⠀⠀⠀⠀⠀⠈⠉⠙⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠈⢇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠐⢊⣠⣀⣠⠤⠻⡄⢺⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⣠⠖⡤⠊⠀⣀⠀⠀⣠⣧⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⠄⠀⠀⠀⠀⠊⢸⡥⠤⡎⠾⠙⠉⢷⣹⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡄⣄⠀⠀⠀⣰⠋⠀⠀⠑⠒⣊⢀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⣀⠀⠀⠻⣔⣀⠀⠀⠀⠚⠡⠤⠌⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄⠀⠀⠀⠙⠦⠤⠴⡿⠈⠁⠠⢄⣀⠈⢉⡴⠃⠀⢀⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠚⠁⠀⠈⠣⡀⢀⣀⡠⠴⠺⣅⠀⠀⣴⡿⠩⣉⠉⠀⠀⡰⠋⠀⠈⠑⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣶⣄⠀⠀⠀⠀⠘⢯⡉⢇⠀⠀⠈⣙⡾⣍⠀⠀⣀⡽⡲⠊⠀⠀⠀⠀⢀⣴⡖⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣬⣿⣷⣄⠀⠀⠀⠀⠈⠒⠭⣒⣛⣁⣗⣂⣉⠭⠔⠋⠀⠀⠀⠀⢀⣴⣿⣯⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠛⠻⢿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠿⠋⠛⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡴⠞⠋⠻⢿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠒⠒⠒⠛⠉⠉





⣟⣿⣿⣻⣟⣟⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣿⣛⣻⣿⣟⣛⣛⣻⣟⣟⣻⣿⣿⣻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠉⠑⢄
⠀⠀⠀⠀⣀⠤⠔⠉⠁⠉⠀⠉⠉⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀⣀⣀⣀⣸⡀
⠀⠀⠀⡔⠁⠀⠀⠀⠀⡄⠀⢀⡰⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⡇⠀⠀⠀⠉⠓⢄
⠀⠀⢠⠃⠀⠐⢢⠄⠒⠉⠀⠙⠤⡜⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⠆
⠀⠀⢸⠀⠀⡔⠁⢠⠤⠀⠀⠰⠦⠈⢆⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠚⠉⠢⣀⣀
⠀⠀⠈⠙⣤⠃⠀⠀⣤⠀⠀⣤⠀⠀⠈⣄⠇⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠦⢴⣋⢉⡡⢄⢀⡠⢍⢀⣈⡦⠤⢦
⠀⠀⠈⢢⡁⠀⠀⠠⠀⠊⠙⢀⡤⠀⠀⢘⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣸⠂⠀⠈⡢⠼⠉⠆⠘⠁⠀⠑⢇⡸
⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠈⠀⠒⠀⠒⠀⠀⠀⢀⠏
⠀⠀⢀⢴⠞⠱⠦⠤⢄⣀⢀⡠⠤⠔⢚⠻⡢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⡵⢄⣀⠀⠀⠀⠀⠀⣀⡠⢮⣀
⠀⢀⠃⠇⠀⠀⢣⣀⠔⠙⠆⠙⠦⡠⠃⠀⠑⡈⠳⡠⣔⠊⠉⣩⡶⠊⠁⠉⠁⠉⠲⢪⡉⠉⢒⡤⠀⠀⣠⠊⠀⡜⠀⠀⠋⠣⡉⠀⣩⠏⢱⠀⠀⢣⠙⢆
⠀⡘⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠘⡌⠉⠈⢩⠁⠀⠀⡰⡄⠀⠀⢸⠉⠉⠉⠀⠀⡏⡇⠀⢀⡁⠀⠀⠑⠐⠚⠛⠓⠒⠃⠀⠀⠈⡄⠀⢣
⠀⠃⠘⠀⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠀⠀⠠⠆⠑⡤⠼⢄⠀⡜⡶⠒⢛⡀⢈⠓⠲⡜⡆⠀⠀⢀⠔⢑⠬⣂⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣀⢎
⢸⠀⢠⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠸⠀⠀⢱⣈⣧⠀⠘⠇⠀⠀⠬⠭⠀⠀⡜⠁⠀⣴⣁⡔⠁⠀⠀⠀⡧⠤⠤⠀⢀⣀⣀⡀⠀⠠⠤⠤⢴⠓⠒⠋
⣘⠀⣺⠸⡀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⠃⠀⠀⠈⠿⢏⣑⠖⢻⠒⢤⠄⢤⠔⠺⠓⠒⣆⡹⠿⠃⠀⠀⠀⠀⢱⠠⠤⠀⣀⣀⣀⣀⡀⠠⠤⠔⢾⡠⠅⣆
⣇⣀⡼⠀⠘⡉⠐⠒⠂⠀⠀⠐⠒⠂⢉⠁⠀⠀⠀⠀⠀⠀⠈⠑⡇⠀⠀⢹⠃⠀⠀⠷⠚⠁⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡧⣀⣼
⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠨⠄⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⢸
⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠑⠒⠒⠒⠒⠹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢡⠀⠀⢠⡄⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠠⣊⠀⠀⠀⠀⠀⠀⠀⢈⡦⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢸
⠀⠀⠀⠀⠀⠀⡠⠦⠀⠼⡧⠀⠼⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣲⢶⢶⡶⡶⣎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣓⡒⢒⡒⣒⠒⡂⢐⢒⡒⣲⠇⠀⠀⢸
⣀⣀⣀⣀⣀⣸⣷⣶⣶⣏⣹⣶⣶⣾⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣤⣭⣜⣧⣭⣤⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣻⣷⣿⣿⣛⣿⣿⣿⣟⣀⣀⣀⣀⣈
⣿⣿⡏⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢄⣀⡠⠤⣀⠀⠀⠀⠀⠀⢀⠄⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠄⠠⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣐⠒⠒⠒⠒⠒⣒⠐⠂⠀⠀⣀⣀⡀⠠⠤⠄⢀⣀⡀⠀⠀⠀⠀⠀⢀⠠⠀⠀⠄⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⣈⠉⠙⠉⢉⡠⠖⠀⠀⠀⠀⠀⠄⠈⠉⠙⠋⠉⠀⠀⠀⠀⠀⠚⠛⠲⠶⠶⠒⠛⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⢀⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣒⣒⠒⠒⠦⢄⣀⠀⠀⠀⠰⠉⠐⠊⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠂⠑⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠈⠉⠉⠉⠉⡀⠈⠀⠀⠀⠀⠈⠛⠫⠵⠶⣥⣤⠄⠀⠀⠀⠀⠤⠖⠄⠲⠂⠐⠦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠒⠒⠈⠁⠀⠀⠀⠀⠀⠀⠢⠄⣀⣀⣀⠤⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠠⢤⡄⠀⠀⠀⢀⠔⠉⠉⠉⠉⠢⡀⠀⠀⠀⠀⠄⠒⠉⠐⠂⠉⠒⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠤⠤⠤⠤⠖⠊⠀⠀⠀⠀⣁⣴⣬⣥⣬⣥⣦⡐⠀⠀⠈⠙⠫⢭⣉⣉⣉⣉⠭⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⡀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠐⢤⣀⣀⣀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣔⣒⣒⣒⣐⣦⡀⠀⠀⠀⠄⣀⡠⡀⠠⠬⠀⠒⣰⠂⠀⠀⠀⠈⢀⣀⣀⣀⡀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠻⠛⠋⠉⠉⠀⠀⠀⠀⠈⠛⠻⠶⠿⠿⠟⠁⠀⠀⠀⠀⠉⠉⠛⠛⠛⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠤⠄⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠤⢄⠠⠤⠂