Morning sickness Emojis & Symbols

⠀⠀⣞⠙⡆⠀⠀⢀⡀
⠀⣀⡈⣟⣁⡀⡼⠉⡇
⣞⠉⠉⠉⠉⠉⡇⠀⡇⠀⠀⠀⠀⣀⣤⠶⠤⢤⡀
⢿⠉⠉⠉⠉⠉⡇⠀⡇⠀⠀⠀⣸⠅⠀⠀⠀⠈⠙⡆
⢸⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⢹⡞⠓⠛⢲⣀⣤⠟⠀⢀⣀
⠸⡇⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠳⣄⣀⣀⡤⠏⣠⠞⠉⠉⠙⠦⣄
⠀⡇⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠈⠁⠀⢸⠁⠀⡆⠀⠀⠀⠈⠓⢦⣀
⠀⠹⣄⣀⣀⢀⣇⡀⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⠈⢧⡀⣧⣀⣸⡇⠀⠀⠀⠈⠳⢤⡀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠳⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠉⠉⠉⠉⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢲⡀
⠀⠀⠀⡇⠀⠀⠀⠀⠶⠶⡤⠶⠶⠶⠶⠓⠶⠶⠶⠶⠶⠶⠶⠺⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⠃
⠀⠀⠀⡇⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⢀⡤⠶⣾⠉
⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⢀⣴⡏⠀⠀⠛⠒⠒⠒⠒⠒⠒⢦
⠀⠀⠀⠇⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠛⠛⠛⠛⠛⠛⠛⠛⠉


⠀⠀⠆⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⡀⠀⡀⠀⡀⢀⢀⠀⠀⠀⠀⢀⠀⠀⠀⡀⡀⡀⢀⠀⠀⢀
⣀⣀⣀⣀⣀⣀⣀⣀⣅⣀⣀⣂⣀⣀⣐⣐⣈⣑⣠⣀⣁⣀⣀⣑⣀⣀⣃⣀⣀⣘⣘⣃⣸⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⣀⣀⠀⡠⠊⠉⠉⠁⠒⠒⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡁⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⢠⡤⡠⡼⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢰⡏⠉⠉⠉⠉⠀⠀⠀⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡈⠀⠀⠀⠀⣠⡅⠀⠀⠨⠃⠀⡇⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠐⢠⡀⢰⠋⠈⠀⠀⠂⠘⠁⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠒⠒⠒⠒⠒⠒⠒⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⢀⣀⡀⠀⠀⠀⠼⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠁⢸⠓⠲⠀⠀⠀⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⢈⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⢀⣀⠀⠠⢸⠞⠁⠘⢀⡲⣜⡁⣀⣀⡀⠀⠀⠀⠀⠀⣀⡀⠀⠀⢀⡰⢶⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠐⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠑⠉⠈⠒⠒⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠛⠛⠛⠶⣲⡶⢒⡒⢒⡖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠄⠀⠀⢀⠀⠀⠀⠀⠀⠲⣄⠀⠤⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⢀⢬⠤⢤⣶⠏
⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣬⡼⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠢⠀⠀⠀⠀⠀⢀⠇⠀⠈⠇⠀⠀⠀⠀⠀⠀⠀⠀⠑⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠧⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⢄⡀⠀⠀⠀⠀⠀⠀⢤⡔⠉⠀⠀⠀⠃⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠈⢳⠆⠀⠀⠀⠀⠀⠀⠀⠉⠈⡃
⠀⠀⣀⣠⠔⠚⠓⠦⢾⠛⠛⠚⠛⠓⠂⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠈⠄⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣀
⠀⣀⣀⣀⣀⣀⣀⣀⣀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠘⠦⠈⠙⠳⣦⠀⠀⠀⣞⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠓⠓⠒⠒⠒⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠒⠒⠒⠒⠒⠒⠒⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⣤⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠟⠁⠀⣀⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠀⠀⠀⠀⠉⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣅⣀⣈⣿⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠀⠉⠉⠉⠉⠉⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠋⠙⠛⠶⣄⠀⠻⣄⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠙⣧⠀⠈⠛⠶⠦⠶⠶⠛⠁⠀⠘⢶⣄⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠰⣆⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠘⢶⡀⢀⡀⠙⢷⡄⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠈⣷⠀⢹⡆⠀⠹⣆⠀⠀⠀⠀⢸⡇⠀⠀⠀⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠹⠂⠀⠛⠀⠀⢹⡆⠀⠀⠀⠘⡇⠀⠀⠀⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣷⠀⠀⠀⠘⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⢶⣄⠀⠀⣿⠀⠀⠀⠠⡇⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⣾⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠰⣤⡀⢀⣴⠟⠁⠀⠀⠀⠀⠙⠷⣤⣀⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣥⣤⣤⣤⣤⣤⣬⡇⠀⠀⠀⣿⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠻⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄⠀⠈⠛⠶⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⣀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠗⠶⠶⠶⠶⠶⠶⠆⠀⠀⠀⠀⠲⠶⠶⠶⢾
⠀⣠⠶⠚⠛⠛⠛⠛⠛⠛⠛⠛⠛⠂⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠙⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠾


⠀⠀⠀⠀⢠⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤
⠀⠀⠀⠀⠘⠀⠘⠉⠉⠉⠉⠉⠉⠁⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠃⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢀⠄⢄⠀⡀⢤⠄⢀⡀⠀⡄⡀⠀⠀⢠⠤⠀⠀⠄⠀⠤⡄⢀⠄⡀⡠⠤⡀⠀⢀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⢠⠀⡅⠐⠀⠦⠴⠀⡇⡧⢀⠀⢸⠀⠀⠀⠑⡄⠀⡇⠸⠒⡁⢇⠀⡄⠘⠣⠀⡇
⣶⣶⡶⠶⠶⠶⢶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣷⣾⣷⣾⣾⣷⣾⣿⣿⣷⣿⣿⣿⣿⣷⣾⣿⣷⣾⣷⣾⣶⣷⣾⣿⣷⣿⣶⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⢀⡀⠈⠁⠒⠂⠠⠤⠄⢀⣀⣀⣠⠤⠤⠄⢀⣀⠤⠤⠤⠴⣂⡈⠁⠀⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠶⡋⠉⠩⠐⠛⠛⠛⠁⠀⠀⠶⠀⠀⠈⠁⠙⠴⢤⣀⣀⠀⠤⠄
⠀⠀⠀⠐⠚⠀⠀⠐⠂⡠⠞⠋⠁⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⢄
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣦⡀
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⢡⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄
⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣣⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦
⠀⣼⠃⠀⠀⠠⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉⠈⠳⢤⣀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⢠⡅⠀⠀⠀⠀⠀⠀⠀⣠⠞⢩⡴⠆⠀⠀⠀⠀⠀⠈⠙⠓⠲⠶⠶⠤⠤⠤⠤⢄⣀⣀⡀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⡌⠀⠀⠀⢀⠄⠀⡠⠊⠀⢠⣀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠉⣑⠖⠤⣀
⡇⠀⠀⠀⠁⢀⠞⠁⠀⠀⠞⠀⠀⠀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⡀⠀⠀⢳⠀⠈⠓⢦⡀
⡇⠀⠀⢰⠒⠉⠀⠀⠀⠀⢦⡀⠀⠴⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠁⠀⢀⡘⠀⠀⠀⠀⠉⠖⡄
⠃⠒⠂⠛⣤⡀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⢀⣤⠛⠐⠒
⢰⠀⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡌
⠀⡆⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠁⠀⠀⠀⢰
⠀⠸⡄⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣅⣤⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠰⠀⢠⡇
⠀⠀⢲⡀⠀⠀⠀⠈⢆⠀⠀⠀⠀⢀⠴⣶⠿⡿⠿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣿⡶⠦⣀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢀⠞
⠀⠀⠀⢣⠀⠀⠀⠀⠈⠳⡀⠀⠘⠁⠀⠀⠀⠀⡐⠉⠁⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠈⠁⠀⢀⠜⠁⠀⠀⠀⠀⡜
⠀⠀⠀⠀⢣⡀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠉⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠳⡀⠀⠀⠀⠀⠀⠈⠳⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠞⠁⠀⠀⠀⠀⠀⢠⠞
⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠈⠙⠂⠤⠤⢀⣀⠀⠀⣀⡀⠤⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⡰⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠳⣤⠴⠤⠠⠐⠒⠒⠒⠒⠒⠒⢒⣿⠀⠀⣷⡐⠒⠒⠒⠒⠒⠒⠂⠠⠤⠤⣤⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⡿⠉⠒⠂⠉⢿⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⢠⣦⡀⠀⠀⢀⣴⡄⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⢀⢏⡼⠃⠀⠀⠘⢧⡹⡀⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⢊⠁⢎⡇⠀⠀⠀⠀⠀⠀⢸⡵⠈⡑⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⠟⠓⢾⠃⠀⠀⠀⠀⠀⠀⠘⡷⠚⠻⠖⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠤⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢿⠈⠙⠋⠉⡿⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣃⠀⠀⣘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠂⠠⣇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⣧⣶⣶⣾⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣶⣶⣶⣶⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠈⠳⡀⢠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⣁⠴⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠃⠀⢰⠗⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠠⣯⡈⢠⡴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡎⠀⢹⡦⠀⠀⠀⠀⠀⡘⠉⢲
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⣴⡶⠶⣧⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠴⠃⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⠔⠉⠠⣀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠈⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠤⠀⠀⠶⣄⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠐⠂⠀⢀⠂⠀⠀⠀⠑⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠠⠤⠂⠀⠀⢀⡀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠄⠀⠠⠄⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠆⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠙⠓⠄⠀⠑⠆⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⢀⣤⠀⠀⠀⠀⠀⠀⠈⡄
⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠃⠤⠠⠄⠐⠀⡇⠀⠀⠀⠀⠀⠀⠀⢆
⠀⠀⠀⠀⠀⠀⠀⠁⠁⠀⠁⠒⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⢂⠀⠤⠀⠀⠀⣶⢳⠀⠀⠀⠀⠀⠀⠀⢸
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣰⣧⣤⣤⣭⣭⣼⣤⣤⣬⣭⣥⣥⣨⣄⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠛⠛⠛⠻⢷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠹⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡶⠀⣀⡀⠀⠀⣀⣴⡿⠻⢷⣶⣤⣦⠀⢻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠃⠀⣿⡟⠿⠿⠛⠉⠀⠀⠀⠀⢸⣿⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⡇⠀⣀⣀⣀⣀⣀⣀⠀⢸⣿⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⢸⣿⠿⠛⠛⢻⣿⠛⠛⠿⣿⡇⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢀⣿⡏⠀⠀⠀⣸⣿⠀⠀⠀⢹⣿⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣴⡿⢿⣷⣦⣀⣴⡿⢿⣦⣀⣴⣾⡿⢿⣆⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⠟⠀⠀⠉⣻⡿⣿⣤⣤⣿⢿⣟⠉⠀⠀⠻⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠁⠀⠀⢠⣾⠟⠀⠀⠙⠋⠀⠀⠻⣷⡄⠀⠀⠈⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠋⠀⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠙⣷⣄
⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠈⠻⣧⡀
⠀⠀⠀⠀⠀⠀⣿⠋⠀⠀⢀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⡀⠀⠀⠙⣿
⠀⠀⠀⠀⠀⠀⠻⣷⣤⣴⡿⠛⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠙⢿⣦⣤⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠈⠉⠉⠀⠀⢀⡠⠴⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⡜⠁⠀⠀⠀⢀⡤⠚⠉⠀⠀⠀⠀⠙⢄⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⢰⠁⠀⠀⣀⠔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠸⡆⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⢳⡆⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠒⠛⣏⠉⠉⠁⠨⠻⣄⠀⠀⣠⠴⢚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠴⠚⠉⠀⠀⠀⠀⠘⢆⠀⡆⠀⠀⠈⢳⣎⣀⠤⢾⠀⠀⠀⣀⡠⠂⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡇⠀⠀⠀⠃⠘⠙⠢⣜⡖⠒⠋⠉⠁⡀⠀⡆⠀⠀⠀⠀⠀⠀⢀
⠀⠀⡠⠒⠁⠀⠀⠀⢣⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⡀⠀⠙⡗⠦⣄⢀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠋
⡰⠋⠀⠀⠀⣀⡴⠒⠀⢀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠲⢤⠤⠴⠊⠀⠀⠀⠘⣆⠀⢸⠁⠒⡇⠄
⠳⣄⠀⠀⠈⠁⠢⣀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢘⡆⣼⠀⠀⡇
⠀⠀⠙⢦⣀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠑⢄⢀⠔⠋⠱⡇⠀⠀⢻
⠀⠀⠀⠀⠈⠓⢤⣀⠀⠀⠈⠙⢦⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⣠⠴⠞⠀⠀⠡⡀⠀⠀⠇⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀⠀⠈⠉⠀⠀⠈⠉⠸⢦⣄⠀⠘⢦⡀⠀⠀⠀⠐⣄⠀⠀⠀⠀⣻
⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠈⠓⠦⣀⡀⠀⠀⠀⠀⠲⠭⢿⠀⠀⠈⣧⠀⠀⠀⠀⠈⠣⣄⠀⣠⠏
⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠠⠀⠀⠀⠉⠁⠂⠀⠐⠺⠏⠁⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠀⠀⢧⣤⣀⡀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⢰⠀⠀⠉⠙⠲⢤⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠈⠙⠲⠤⠤⠤⠤
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠠⢾⡅⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⣴⣶⠀⠀⣭⡰⠀⠀⠀⢀⣤⡀⠂⠀⠀⠀⠀⠀⣶⣶
⠀⠀⠀⠀⣴⣿⣿⣷⡄⠀⠀⠀⠀⢀⣶⣿⣿⣶⡄⠉⠊⠀⠀⣰⣾⣿⣿⣦⠀⠀⠀⠀⣶⣿⣿⣶⡀⠀⠀⠀⠀⠀⢀⣤⣄
⠀⠀⠀⠀⢿⣿⣿⣿⣿⠀⠀⠀⠀⠘⢻⣿⣿⡟⡇⠀⠀⠀⠀⠻⣿⣿⣿⠟⠀⠀⠀⠀⢿⣿⣿⡟⠃⠀⢀⣤⣾⡿⠞⠻⠋
⠀⠀⠀⠀⠀⣿⣿⡇⠛⠀⠀⠀⠀⠀⢸⣿⣿⡇⠃⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠸⣿⣿⡇⠀⠐⣇
⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠈⣿⡷⠀⠀⣿⡀
⠀⠀⠀⠀⠀⣿⢿⡇⠀⠀⠀⠀⠀⠀⠸⣿⢿⡇⠀⠀⠀⠀⠀⠀⢿⠿⣿⠀⠀⠀⠀⠀⠸⡿⢿⠇⠀⠀⠀⣾⠟⠀⠀⢠⣿⠧⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⠀⠀⣾⣿⣟⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⣠⡀
⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⠀⠀⠀⠀⣾⣿⣿⣯⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⢀⡀⣴⣶⡀⠀⠀⠈⠘⠿⣟
⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠏⠀⠀⠀⠀⠛⣿⣿⡿⠀⠐⢚⡀⠀⠀⠀⠀⠀⣰⣿⠇⠙⠋⠀⠀⠀⠀⠀⣼⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣶⡆⣿⣿⣧⣤⡄⠀⠀⢰⣶⡶⣿⣿⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣾⣿⢿⣿⠃⠀⠀⢸⣿⣷⣾⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠀⠀⠀⠀⠀⠀⠛⠙⠋⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠛⠘⠟⠀⠀⠀⠘⠛⠛⠛⠃⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠒⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠂⠀⠂⠀⠀⠐⠀⠂⠂⠂⠀⠀⠀⠀⠀⠀⠐⠐⠐⠂
⠀⠀⠀⠀⠀⣠⣶⡄⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀
⠀⠀⠀⠀⢀⣬⣷⣅⣀⠀⠀⠀⠀⢀⣬⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⣀⣀⠻⠟⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⢾⣿⣿⣿⠉⠀⠀⠀⠀⣿⣿⣿⣿⠉⠁⠀⠀⠀⡀⢀⣠⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷
⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠠⠟⣿⣿⣿⠀⠀⠀⠀⠀⢻⣾⣿⣿⣿⣷⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⢸⠀⢿⣿⣿⡜⡟⠛⠛⠛⠛⣿⠁⠀⠀⠀⠀⣾⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⣸⣉⣹⣿⣿⡇⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠿⣿⣿⠿
⠀⠀⠀⠀⠀⠙⠉⠋⠀⠀⠀⠀⠀⠀⠙⠉⠋⠀⠀⠀⠀⠀⠉⠀⠈⠋⠙⠀⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠉⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠉⠁⠀⢀⣠⠤⠶⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⡎⠀⠀⠀⠀⣠⠞⠉⠀⠀⠀⠀⠈⢆⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢸⠀⠀⢀⡴⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢸⡄⡰⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣀⣀⣀⣀⣻⡅⠀⠀⠀⠀⠀⣀⣠⡤⠤⠤⠤⠤⠄⠀⠀⠀⠀⠀⠘⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠋⠉⢳⡀⠀⡀⠈⠙⣦⡀⣠⠖⠋⠁⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢠⠖⠚⠉⠀⠀⠀⠀⠀⠀⠳⡀⡇⠀⠀⢀⠟⣦⣖⠛⡀⢀⣠⠤⠴⠁⠀⡐⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⢀⠄⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣇⠀⠀⠘⠀⠁⠈⠓⠿⣍⡀⠀⠀⡆⠀⡇⠀⠀⠀⠀⠀⢀⠜
⠀⡠⠊⠀⠀⠀⢀⣀⠣⢀⠂⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⢀⠔⠀⠀⠹⡍⠒⢠⡇⣀⡇⠀⠀⠀⠀⠀⠁
⣎⠀⠀⠀⠰⢞⠉⠀⢀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠉⠁⢀⠀⠀⠀⠹⡄⢸⠀⠀⡏
⠈⠓⢤⡀⠀⠀⠁⠢⣜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⢀⡴⢣⣸⠀⠀⣷
⠀⠀⠀⠙⠲⣄⡀⠀⠀⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠈⠲⠋⠀⠀⡇⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠙⠲⣄⠀⠀⠈⠙⠒⠒⠒⠒⠂⢄⣀⠀⠀⢯⡀⠀⠀⠀⠀⡀⠀⠁⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢄⡀⠀⠀⠀⠀⠀⢤⣾⡗⠀⠀⢳⡀⠀⠀⠀⠈⢦⡀⠀⢀⡏
⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠉⠑⠂⠤⢀⠠⢶⠒⠋⠀⠀⢀⡇⠀⠀⠀⠀⠀⠈⠒⠊
⠀⠀⠀⠀⠰⣅⣀⠀⠀⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⡄⠈⠉⠓⠲⢤⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠈⠓⠢⠤⠤⠠⠤
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠄⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⢾⡅⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠄⠀⠄⠀⠀⠀⠀⠠⠀⠀⠀⠄⠄⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄⠠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠚⠛⠛⠛⠓⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠶⠤⠤⠤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠐⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⢈⡿⢦⣤⣀⡀⠀⠀⠀⠀⣀⣠⡤⠞⠋⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⢀⣠⠞⠁⠀⠀⠉⠉⠛⠛⠛⢿⣉⠁⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡷⠶⠶⣶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⡶⠶⠶⣟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⣿⣤⠶⠖⠲⠶⠀⠀⢀⠀⠀⠰⠶⠒⠶⢦⣼⡇⠀⠀⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⣻⠟⠀⠀⠀⢀⡴⠶⣾⠋⢻⣄⠀⠀⠀⠀⠀⠈⢿⡛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣸⠃⢠⡇⠀⡿⠉⣻⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣀⠀⠀⢀⡿⠀⣼⠁⢸⠇⢀⡿⢦⡀⠀⠀⠀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⣷⠀⣸⠃⢠⡏⠀⡟⠀⢸⠁⣸⠃⣀⣤⠾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⣀⡟⠀⠺⠁⢰⠇⢀⡏⢀⡿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠘⠿⠃⠀⠀⠀⠀⠀⠘⠁⣸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠙⠶⢶⣤⣤⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠖⠛⠛⠉⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⢀⡴⠛⠁⠀⠈⠉⠙⠛⠓⠶⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡀
⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⢀⡤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠼⠃⠀⠀⠀⠀⠀⠰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠇



⣇⢘⡇⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⢀

⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢸⠀⢱⢸⠀⢹⠀⡘⢃⠀⡇⡗⢸⠀⠀⡇⠀⠀⠨⣁⠀⠙⠀⣎⣰⢠⠂⠈⡆⣢⡜⠀⡇
⣀⣀⣀⣀⣀⣀⣀⣀⣧⣤⣸⣤⣎⣸⣀⣸⣠⣉⣈⣄⣧⣌⣸⣤⣤⣧⣤⣀⣤⣬⣀⣤⣀⣇⣨⣌⣧⣤⣃⣥⣘⣤⣦⣄⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣤⣀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣬⠷⠎⠛⠶⣤⣈⢻⡶⣄⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣚⣉⣀⣀⣀⡀⠀⠀⠀⠉⠳⣇⠘⢾⢻⣰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⢋⣭⡿⠛⠋⠉⠁⣠⣴⠶⢦⣤⣀⠀⠘⢸⢿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣵⠶⣾⣟⠛⠒⠏⣠⣤⣄⠈⣻⣧⠀⢀⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠉⠀⠀⡿⠉⠛⠇⢶⠟⠋⡁⠀⢻⣿⠇⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⡇⢳⡇⢸⠀⠱⣠⠃⠄⢹⣿⣼⢔⡫⣳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⣼⢳⠌⡀⢀⡿⣄⠀⣾⣿⢱⡧⡤⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣚⡒⢋⣪⠏⠸⠄⠉⡐⢿⡿⣉⣘⡔⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣭⣛⣻⣽⣶⡿⠛⣢⡈⢡⣰⣇⠈⠩⢽⣥⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣉⠙⠛⠓⠶⠤⠭⠽⠶⠚⠁⠘⣆⢧⠹⢍⣻⣟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢛⡦⠀⠈⠁⠬⠂⠀⠁⣀⣸⡼⡦⡄⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠛⠛⠉⠁⠀⢠⢲⠄⢀⣴⢫⠝⣸⡇⡇⠉⠁⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠑⢝⣉⣄⡀⠀⣀⠀⠀⣡⡀⣼⣿⡹⠤⢫⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠟⢁⡾⠁⡼⢩⡇⢸⡏⠳⠛⣏⣷⣳⠞⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⢀⡱⠀⣴⠋⡴⢰⡇⣼⠁⢸⡇⠈⠀⠘⠷⠶⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠈⡆⣸⠁⠸⢧⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠷⣬⣴⠏

⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠶⠟⠛⠛⠛⠛⠻⠶⢶⣤⡀
⠀⠀⠀⢀⣤⠾⠋⠁⠀⠀⠀⠀⠀⠀⢀⠤⡀⠀⠀⠈⠙⢷⣄
⠀⠀⣠⡟⠁⢀⣠⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⠹⣦
⠀⣰⡏⣀⠀⠈⠓⠁⠀⠀⠀⠀⠀⠀⠀⠁⠁⢞⡱⠀⠀⠀⠀⢹⣇
⢠⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠚⣿⡀
⣼⡟⠀⠀⠀⠀⠀⢀⣀⠀⠀⢈⠀⢈⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⣿⣧⠤⠄⠂⠀⡐⠁⠀⢱⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⢻⡇
⣿⠐⠀⠀⠀⠀⠐⠠⠤⠊⠀⣀⠀⠸⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⣿⡤⠤⠄⠂⠀⠀⠀⠀⠴⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⡰⠀⠀⣾⣇
⢹⡇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠑⢄⠀⠀⠀⢌⢘⠀⠀⠀⢠⡿⠈⠁
⠸⣧⠀⠀⠀⠀⠀⠀⠀⡯⠤⠐⠂⠈⠘⡇⠀⠀⠈⠉⠀⠀⠀⣼⡻⡀
⠀⣿⡀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⢸⠀⢀⣄⣠⡀⠀⢰⡟⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⢸⣇⠀⣆⠀⠀⠀⢸⡄⠀⠀⠀⢀⣀⡆⠀⠰⠗⠾⠀⢀⣿⠀⢰⠇⠀⠀⢀⢀⡀⠀⡴⢦⠀⠀⣠⠞⠉⣉⡇
⠀⠀⣿⡀⢸⡀⠀⠀⣆⢳⡀⠀⠀⢘⡿⠀⠀⠀⠀⠀⠀⢸⡗⣷⠊⠀⠀⠀⠈⠚⢁⡼⠃⢨⠇⠰⠷⣚⣋⣁⠀⠀⢀
⠀⠀⢸⡗⢺⡏⣁⠀⠘⠶⣭⣻⡿⠟⣀⣠⣤⣤⣤⣤⣤⣿⣯⣃⣀⣀⣀⣠⠤⠖⠋⠀⢠⡾⠖⠊⣉⠁⠀⢈⡷⠀⠉⠠⠀⠀⠀⠀⡠⠐⡢
⠀⠀⢸⡟⢹⠇⡠⢄⠀⠀⠀⠀⣰⣿⣏⡭⠭⣝⣫⠉⠉⠉⠉⠉⠉⠉⠀⢀⠀⠀⠀⠀⠀⣀⣀⣠⡤⠴⠖⠛⠓⠚⠋⣉⣉⡽⠆⠀⣉⣀⣀
⠀⠀⣿⠁⠈⠀⠃⠜⠀⠀⠀⢠⣿⠿⠟⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢦⠀⠚⠯⣡⣲⣈
⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡭⠭⠁⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠶⠶⠶⣶⣒⡋⠀⠀⠀⠀⠈⠉
⠀⡿⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⣿⣍⡍⠡⠭⠅⠀⠀⠀⠈⠁⠀⠀⠀⠀⢀⠉⡉⠉⠀⠒⠂⠂⠠⠄⣀⠀⠀⠀⠀⠀⠀⠉⠙⢲⡄⢀⠀⡄
⢸⡇⠀⠀⠀⢠⠃⠀⠙⠄⠀⡀⣿⣏⢉⣉⣭⣿⣿⣿⣿⣿⣿⣿⡛⠳⠶⠬⣾⣁⡀⠀⠀⠀⣄⣀⣀⣀⣹⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠉
⣿⠁⠀⠀⠀⠈⠢⠤⠔⠀⣇⢨⠹⣿⣿⠟⠋⠁⠀⠀⠠⠄⣈⣙⢻⡆⠀⠀⠀⠀⠉⠙⠢⢄⡀⢹⡄⠉⠀⠀⠲⣒⠒⠲⡄
⣿⠀⠀⠀⠀⠀⠀⠀⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀⠈⠙⣷⠀⠀⠤⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠈⠑⠒⠊
⢿⡄⠀⠀⠀⠀⠀⠈⠦⠜⠀⠀⠀⠀⠀⠀⠀⠠⠒⢀⠀⠙⠀⠀⠀⣿⠀⠀⠀⠀⠂
⠸⣧⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⢀⠀⠀⠀⠀⠀⣿
⠀⠹⣦⣤⡽⣦⠤⠤⠄⠀⠐⠀⠠⣀⠶⣂⠀⠀⠉⠁⠀⠀⠀⠀⣰⡏
⠀⠀⠘⢷⣤⣬⠷⢦⡒⠂⠀⠀⠀⠨⠷⠙⠂⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠈⠛⠷⢦⣬⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣴⠾⠛⠁
⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣥⣤⣤⣄⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠟⣛⡛⠿⢋⣴⣾⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣏⢸⣿⣿⣶⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⢂⣹⣿⣿⣿⣿⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢫⣾⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣍⡛⠿⠿⣿⡿⠿⠿⢡⣾⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠿⠿⠿⠿⠿⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣛⢿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⢋⣵⣾⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠹⣷⡘⢿⣿⣷⣽⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⢡⣿⣿⣿⠟⣩⣍⡛⣿⣿⣆⠀⠀⠀⠀⠹⣿⣿⣷⣌⢻⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠏⣼⣿⣿⡗⢸⣿⣿⠀⠀⠀⠀⠀⠘⠿⣿⠿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⣰⣿⣿⣿⢡⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⢰⣿⣿⣿⢃⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢡⣿⣿⣿⣷⣬⣙⡛⠿⣿⠀⠀⣶⣿⠿⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣦⡙⠿⢿⣿⣿⣿⣿⣷⠈⠀⢠⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣬⣍⡛⠿⢋⡀⠀⣈⠙⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠈⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣄⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⣀⡀⣸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣄⣀⣀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆⡀⠀⠀⣾⡟⢻⣏⠻⣿⡿⣿⣿⣦⣀⢀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣄⡘⣿⡄⢻⣇⠘⢿⣌⢿⣯⠻⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⡌⢿⣆⠈⢿⣆⠹⣷⡈⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠘⣿⡄⠈⣿⡆⠘⣿⡄⠹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⢹⣧⠀⠸⣿⠀⠸⣿⡀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠈⣿⡄⠀⢻⡇⠀⢹⣧⠀⠹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠇⠀⠻⠇⠀⠸⠗⠀⠈⠿⠀⠀⠿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣶⣶⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠟⠁⠈⠛⠛⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⠿⠛⠁⠠⢤⣀⣀⠀⠻⠿⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡁⣠⣞⠀⠀⠀⠀⠰⠆⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⣇⠀⠈⠁⠀⡖⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢽⡄⠀⠀⣀⣷⠶⢂⡴⠲⣄⢠⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣦⣰⠃⠈⠙⠧⡴⠙⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣯⣿⣄⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⡿⠃⠈⠑⢦⣤⡀⠀⠀⠈⠻⣿⣿⣿⣿⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠟⠀⠀⠀⣰⣿⣿⣿⣶⣄⠀⠀⠀⠙⢿⣿⣯⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠋⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣷⣄⡀⠀⠀⠙⣿⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡁⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠋⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠛⠛⣻⡗⠀⠚⠶⠶⢦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠋⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⡀
⠀⠀⣴⠛⠛⠻⣶⠟⠛⠳⣶⡟⠋⢹⡗⠀⠀⠾⠿⣿⡿⢦⡀⠀⠀⠀⣤⣀⣤⠀⠈⠙⢷⣄⠀⣀⣀⣠⣄⣀⡀
⠀⢸⣇⠀⠀⠀⢤⣄⠀⠀⠉⠀⠀⣾⣥⣤⡀⢀⣼⠋⠀⠈⣷⠀⠀⢻⡏⠉⢹⡟⠀⠀⠀⣹⡿⠋⠁⠀⠀⠈⠉⠻⣦⡀
⣴⠟⠉⢻⡆⠀⠀⣹⠿⠛⠀⠀⠀⠀⢠⣟⣴⠟⠁⠀⠀⣼⠃⠀⠀⠉⣿⠶⣿⠋⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⢻⣦⡄⠸⠃⠘⣿⠉⠀⠀⠀⠀⠀⢠⣿⡟⠁⠀⠀⠀⢀⡿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣤⡴⠶⠶⠞⠛⠶⠶⠶⣤⣼⡇
⣿⡁⠀⠀⢀⣠⡟⠀⠀⠀⠀⠀⠀⠛⠋⠀⣰⡟⠰⠶⠟⠡⣿⠀⠀⠀⠀⠀⠀⣠⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠷⣦⡀
⢈⡿⠃⠀⢹⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣆⠀⠀⠀⣠⡟⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⣠⡿⠀⠀⠺⣇⠀⠀⠀⣠⡴⠶⠶⣶⠶⠾⠋⠀⠀⠀⠀⣿⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠈⢷⡄
⢿⡀⠀⣤⠀⠉⠀⠘⠻⣟⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⠞⠋⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⣼⣧⠀⠀⠀⠀⠀⠈⢿⡀
⠈⠛⠛⠛⠳⠺⠒⢦⣀⣹⡄⠀⠀⠀⢰⣶⣤⡾⠋⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⢀⣼⠏⠹⣄⠀⠀⠀⠀⠀⠘⣧
⢀⡄⠀⠀⠀⠀⠀⠀⠉⢻⣇⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⣀⣴⠟⠁⠀⠀⣀⣴⠟⠁⠀⠀⠙⢧⡀⠀⠀⠀⠀⣿
⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠆⠀⠀⢀⣤⠶⠟⠋⢀⣀⣤⡶⠟⠉⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⣿
⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠈⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡴⠋⣁⣤⡶⠞⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦⡀⣿
⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣧⣄⠀⠀⠀⠀⠈⣿⣿⡷⠟⠉⣀⣴⠶⠶⠶⠶⠆⠀⠀⠀⠀⠴⠶⠶⠶⢶⣄⡀⠀⠈⢻⣿
⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠁⠀⠀⠀⠀⣠⣾⡟⠀⠀⠘⠋⢀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⡈⠛⠀⠀⠀⣿⣦
⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠈⠁⡀⠀⠀⠀⠋⠹⣿⠟⠉⠀⠀⠀⠀⠀⠈⠙⢿⡿⠋⠋⠀⠀⠀⣶⠀⣸
⠀⠀⠀⠀⠀⠀⠈⣿⠆⠀⠀⣦⣀⣀⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⢀⡿
⠀⠀⠀⠀⠀⠀⣼⠇⠀⢴⣴⠟⠉⠉⠙⣷⡴⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡼⠃
⠀⠀⠀⠀⠀⠀⣿⠀⠀⣠⣿⠀⠀⠀⠀⣸⣇⠀⠀⣴⡶⠶⠶⠶⠛⠛⠉⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢴⣤⣴⠄⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁
⠀⠀⠀⠀⠀⠀⢻⡆⠀⠉⠙⣷⣤⣤⣾⠋⠉⠀⢠⡿⠀⠀⢀⣀⡀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⠀⠻⣤⡀⠀⠉⠀⠀⠉⠀⠀⣠⡟⠁⢠⡾⠋⠉⠙⢷⡄⠀⠀⠹⣦⡀⠀⠀⠀⠰⠶⠖⠛⠛⠶⠖⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣤⣤⣤⠶⠟⠉⠀⠀⢸⡇⠀⠀⠀⢨⡷⠀⠀⠀⢸⡟⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⡴⠟⠁⠀⠀⠀⢸⡇⠀⠙⠳⣤⡀⠀⠀⠀⢀⣠⡾⠋⠁⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠈⠙⠳⠶⠶⠛⠉⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣿⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣽⣄⣀⣀⣀⣀
⣿⣿⣋⣉⣉⡉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠀⠳⡙⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⣤⡀⠀⣤⠠⠄⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⣀⡛⠁⠀⠉⠀⠀⠀⠀⢀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⡀⠠⠠⣄⡠⢤⡀⠴⠆⡠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠤⠄⣀⡀⠤⠐⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢥⡐⠀⠀⠀⠀⠀⠀⠈⠐⠀⠀⠒⡠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢼⣍⠙⠒⠒⠒⠒⠒⠀⠀⠀⠈⢀⡧⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡆⠑⠢⢄⣀⣀⣀⣀⣀⠠⠀⢨⢁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢷⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⡞⢈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢖⠢⡴⡂⠀⠀⠀⠀⠀⠀⠀⠀⢰⡅⢸⡀⠤⠐⡂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⡂⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡁⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠁⠰⣤⣀⠀⠀⠀⠀⠀⠀⠰⠀⢹⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⢸⠧⡀⠀⠁⠉⠉⠉⠉⠉⠁⠀⠠⠁⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠆⠀⠀⠀⠀⡇⠙⠢⣄⠀⠀⠀⠀⠀⡤⠂⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠸⠀⠀⠀⠀⢸⠁⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢐⠀⠀⠀⠀⠘⡂⠀⢸⠇⠀⠀⠀⢸⠀⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢸⠀⠀⠀⠀⢸⠀⠀⠀⡌⠀⠀⠀⠀⢀⣀⣠⡄⠠⡀⠖
⠀⠀⠀⠀⢠⠠⠀⠄⠀⠀⠉⠁⠀⠀⢀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⢸⠀⠀⢰⠀⠀⠀⡈⠉⠈⢳⠄⣠⠄⠁⠀⠠⡀
⠀⠀⠀⣀⡌⠀⠀⠀⠀⠢⣀⣄⠀⠀⠈⢀⡀⠠⠀⢀⣀⣈⡤⠈⠀⠀⠀⠀⠀⠙⠄⣨⠀⠠⠤⡘⠢⠐⠈⠀⠀⡊⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡀⠀⠛⠒⠒⠈⠉⠒⠒⠀⠀⠀⣀⣖⣁⣈⠁⠈⠁⠀⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠐⠛⠛⠁⠀⢠⣴⣠⣭⣤⡤⠠⠝⠀⠀⠀⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⠾⠿⠿⠿⠿⠿⠿⠷⣶⣦⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢷⣦⣄
⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠁⠀⠀⠀⢀⣀⣤⣤⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣦⡀
⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⣀⣴⡾⠟⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⣠⣾⠏⠀⠀⠀⣠⣾⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄
⠀⠀⣰⡿⠃⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣆
⠀⢰⣿⠁⠀⠀⢰⡿⠃⠀⠀⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆
⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⣶⠶⠶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠙⢿⣆⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠹⣷⡄⠀⠀⠀⠀⠀⣿⣆⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣦⡀⠀⣰⣿⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⣘⣿⣶⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣿⣃⠀⠀⠀⠀⣰⡿⠋
⠀⠀⠀⠀⠈⠻⣷⣴⡾⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣶⣦⣾⠟⠁
⠀⠀⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠻⣷⣤⣤⣴⣶⠆⠀⠀⠀⢀⣤⡀⠀⠀⠀⢀⡀⠀⠀⠀⠘⢿⣿⣶⣦⣤⣴⡾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⢿⣦⣤⣤⣶⡿⠛⠿⣶⣶⣶⠿⠿⣶⣤⣤⣴⣾⠏⠀⠈⠉
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣾⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⠿⣿⣿⠋⠁
⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆
⠀⠀⢸⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣦⣾⡿⠀⠀⢻⣿⡀
⠀⠀⢸⣿⣿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⣿⣦⠀⠀⠈⢿⣷
⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⠀⠀⠀⠘⣿⣇
⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆
⠀⠀⢸⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣽⣿⡄
⠀⠀⢸⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠛⠛⠛⠛⠃
⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣶⣶⣿⣿⠀⢰⣶⣶⣶⣦⣤⣀
⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟⠉⠀⠀⠀⠀⠀⢀⣀⡀⠉⠉⠛⠿⣿⣦⣀
⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠸⠿⠿⢿⣷⣦⣄⠈⠙⢿⣧⡀
⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣤⣤⣤⣤⠀⢠⣤⣤⣄⡀⠙⢿⣷⣄⠀⢻⣿⡄
⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⣻⣿⠀⠈⠉⠙⠻⣿⣦⡀⠙⣿⣆⠀⢻⣿⡀
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠈⢿⣷⠀⢹⣿⡀⠈⣿⡇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠘⠛⠃⠀⣿⡇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢠⣶⡄⠀⠿⠇
⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⡇⠀⣤⡄
⠀⠀⠀⠀⣿⣷⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⡇⠀⣿⡇
⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠁⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⡾⠿⠿⠿⠛⠻⠿⠿⠿⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠋⢀⣤⣴⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⣦⣄⠈⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⢰⡿⠋⠁⠀⠉⠛⢿⠆⠀⠀⠀⠀⠀⠀⠀⠀⢾⠟⠋⠁⠀⠈⠻⢷⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠿⢷⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣶⡾⠇⠀⠀⠀⠀⠸⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⢈⣩⣿⡿⠗⠀⠀⠀⠀⠀⠀⠀⠐⠿⣿⣯⣉⡀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠰⠾⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⡷⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⣶⠿⠿⠿⢷⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠉⠻⢷⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⣴⡿⢃⣤⣶⠿⠿⠿⠿⠿⠿⠿⢷⣦⣄⠻⣷⡀⠀⠀⠀⠀⠀⠀⢰⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⢸⣿⢡⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣆⢹⣷⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣧⡀⠀⠀⠀⠈⠛⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠟⠋⠀⠀⠀⠀⣠⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⢀⣴⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⡀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⣀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣠⣴⣶⡄⢀⣤⣤⣄⠀⣀⣀⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠹⣷⡾⠏⠈⢿⣶⡿⠋⠉⠁



⢀⣀⡀⣀⡀⠀⣀⣀⢀⡀⡀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⡀⠀⢀⣀
⣿⣿⠿⠻⡿⠛⠿⢿⠿⢻⡿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⠙⠛⠛⠛⠛⠛⠛⠿⣿⣶⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡄⠚⠿⠟⠛⠛⠿⠿⠶⣦⣤⡀⠀⠀⠀⠈⠙⢿⣿⡻⠿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡶⠏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣦⣄⠀⠀⠀⠀⠹⣷⣄⠈⠙⠿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢿⣧⡀⠀⠀⠀⠈⢻⣦⠀⠀⠉⢿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⢠⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⣶⠆⠀⠀⠀⠀⠀⢰⣦⣤⣤⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⣶⠎⠉⢻⣿⣿⣷⠀⠀⠀⠀⠀⠀⣸⣿⣿⡏⠈⠙⠛⠳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⢼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠀⠀⠀⠀⠀⠀⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⢀⣤⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⠀⠀⠀⠀⠀⠀⠈⠻⠿⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣄⠀⠀⠀⠀⢠⣶⡶⠶⣷⣦⣀⠀⠀⢀⣠⡶⣶⣦⣀⠀⠀⢀⣠⣾⣿⠛⠿⠀⠀⠀⢀⡾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣀⠀⠀⠀⠀⠀⠀⠙⠿⣶⣶⠟⠋⠀⠀⠙⠻⣷⣶⠞⠋⠀⠿⠀⠀⠀⣀⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣦⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣴⡾⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣷⣦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡴⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠿⣿⠿⠿⠿⠿⠟⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⢷⣤⡀
⠀⠀⠀⠀⢀⣀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠰⠾⠋⠀⠀⠀⠀⠙⠻⢶⣆⠀⠀⠀⠠⠄⠀⢤⣤⠄⢀⣤⣤⣤⡄⢀⡄⣠⣀
⠀⠀⠀⠠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠶⠶⣶⡶⠶⢶⣶⡶⠶⣶⣶⢶⣶⣤⣤⣾⠃⣠⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣧
⠀⠀⠀⠀⠙⢃⣤⣤⡄⠙⠛⠛⠷⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⠁⠀⢰⣶⠤⣾⠟⠛⠛⠛⠛⠃⢤⣶⣄⣠⣶⣦
⠀⠀⡾⠟⢿⣷⡀⠉⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡏⠀⠿⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⢹⣷
⠀⢠⡄⠀⠀⢻⡿⠿⣶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⣠⣤⣄⡀⠚⠓⢿⡇⠀⠀⢸⣿
⠀⠘⣧⡄⠀⢸⡇⠀⠈⠛⠛⠛⠋⢀⣴⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠶⠶⠶⠶⢶⡶⠖⠀⠋⠀⠀⣉⠙⠁⣠⡀⢸⣆⠀⢀⣼⠛
⠀⠀⠉⠻⠶⣿⣿⣆⡀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠷⠀⠙⠁⣸⣿⠷⠞⠉
⠀⠀⠀⠀⠀⢼⡇⠈⢻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢠⣾⣿⠁⠀⢶⣦
⠀⠀⠀⠀⠀⠈⣷⡄⠀⠘⠻⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠎⠁⢰⣶⠉⠀⣸⣿
⠀⠀⠀⠀⠀⠀⣿⡷⠀⠀⠀⠀⠙⠛⢷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⠚⠋⠀⢀⠀⢼⡇⠀⠀⢸⡿
⠀⠀⠀⠀⠀⢸⣿⢧⡀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⣦⣴⣶⣶⣤⣠⣶⣶⣦⣤⣶⣶⣿⠛⣿⣶⠞⠛⠁⠀⠀⠀⠀⢸⠀⢸⡇⠀⢠⣾⠃
⠀⠀⠀⠀⠀⢸⡇⢸⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠿⠟⠛⠛⠛⠛⠛⠿⠛⠻⠗⠛⠉⠀⠀⠀⠀⠀⠀⠀⢸⣷⡟⠃⠀⢻⣯
⠀⠀⠀⠀⠀⢸⣷⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢺⣿
⠀⠀⠀⠀⠀⢸⣿⠘⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⢻⡇⠀⠀⢸⡿
⣀⣀⡀⠀⠀⠸⣟⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⠈⠀⠀⠰⡟⠁
⣿⠟⠻⣶⣶⣤⣉⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⢠⣿⠀⠀⠀⠀⠀⢀⣀⣤⣶⡆
⠀⣷⡄⠀⠈⠛⠻⣷⣦⢼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⣿⡇⠀⠀⢸⡏⠀⢠⣤⣤⠞⠛⠋
⠀⢻⣧⠀⠀⠀⢺⡏⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢿⠁⣠⣤⡄⠻⠟⠁⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠀⣿⡇⠀⠀⢸⡿⠀⠙⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⡘⠛⠉⠉⠹⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⢿⣧⠀⠀⠀⣀⣠⡄⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠈⣿⡆⢀⣼⣿⣁⡀⢈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⣿⡇⢀⣁⣉⣿⣄⡀⠀⠀⠀⠀⠀⠀⣴⡏
⠀⠀⠀⢻⣷⣿⠛⠉⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠀⣿⡆⠘⠛⠉⠉⢻⡿⠀⠀⠀⠀⠀⢀⡿⠃
⠀⠀⠀⠈⣿⣿⡆⠀⠀⠀⠀⠸⣷⣆⠛⢣⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣦⡜⠁⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⢻⣿⣷⡀⠀⠀⠀⠀⠀⠙⠿⣧⣤⣴⡟⠛⠛⢀⣀⣠⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⠚⠀⠀⠀⢠⡀⢹⡇⠀⠀⠀⠀⠀⣀⠟
⠀⠀⠀⠀⠸⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠿⠿⠿⠿⠿⢯⣉⣉⣭⣥⣤⣤⡶⠶⠿⠿⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⣿⠂
⠀⠀⠀⠀⠀⣿⡏⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⣰⡏⠀⠀⠀⠀⠀⠀⣴⠏
⠀⠀⠀⠀⠀⢹⣷⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠏⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠈⢿⡇⠀⠈⠻⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⠟⠁⠀⠀⠀⠀⠀⠀⢀⣾⠃
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠙⠻⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠈⠛⢿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾
⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢀⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⢀⣠⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⣤⡀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⣿⡀⠀⠀⠀⣿⡇
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣤⣤⣼⣷⣀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⢰⣏⣀⣀⠰⠶⠶⠶⠶⠿⠛⠷⠶⠿⣦⡀
⣀⣴⠶⠋⠉⠉⠉⠀⠀⠈⠉⣉⣿⣿⡿⢷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣿⠂⠀⢿⣿⣏⣁⣀⣀⣀⣀⣀⣀⣀⣠⣴⠶⠋⠁
⣙⣷⣶⣶⣶⣶⣶⣶⣶⣤⣍⣉⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡙⢉⣉⣉⣉⣉⠉⢉⣉⣀⣀⣀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡿⠛⠋⠈⠟⠛⠛⠛⠛⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⢿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣿⣿⣿⢿⢿⣿⣿⣿⣶⣶⣦⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠿⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠿⢿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣄
⠀⠀⠀⠀⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆
⠀⠀⠀⠀⠀⠀⢰⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡆
⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⣶⣤⣤⣄⣠⣤⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣤⣄⣠⣤⣤⣦⠀⠀⠀⠀⢿⣷
⠀⠀⠀⠀⠀⢰⣿⠇⠀⠀⠀⠀⠉⠙⠛⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠸⣿⡆
⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⣶⣶⣶⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣶⣶⠀⠀⠀⠀⠀⠀⣿⣧
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⢀⣠⣤⣴⣾⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣷⣦⣤⣄⡀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠈⠛⠋⠉⠉⠉⠉⠉⠉⠀⢀⣠⣤⣴⣶⣶⣤⣄⡀⠀⠀⠉⠉⠉⠉⠉⠉⠙⠛⠁⠀⠀⠀⠀⣿⡿
⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠇
⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠟⠉⠉⠉⢉⡉⠛⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣄⡀⠀⠀⢀⣴⣶⣶⣾⣿⠀⢠⡄⠀⠈⠁⠀⣿⣿⣶⣶⣶⡄⠀⠀⠀⢀⣠⣴⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣶⣾⣿⡁⠀⠉⠙⠀⠀⠀⠀⢰⡆⠀⠋⠉⠀⢀⣿⣿⣦⣶⣾⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⡉⠈⠀⠀⠀⠛⠂⠀⠀⠀⠀⠀⠀⠰⠖⠀⠀⠁⢉⣙⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⢿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣿⣿⣿⣿⡿⠿⠿⠿⠛⠁



⠀⠀⡀⠀⢀⠀⡀
⣿⣏⢩⣟⡛⣛⣛⡛⣛⣛⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣰⣆⠀⢠⡀⠀⢀⢀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡄⠀⠀⠀⠀⢠⠀⠀⢠⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠀⣸⣿⣿⣷⣼⣿⣸⣺⣾⣻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⢀⣼⣧⠀⣸⠀⠀⣾⣿⣿⣷⡄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⣿⣿⣿⣿⣿⣿⣿⣿⣽⡿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡺⣿⡇⠀⡏⠀⢰⣿⣿⣿⡟⣇⣇⡀
⠀⠀⠀⠀⠀⢀⡀⠀⠀⡇⠀⠼⣿⣿⣿⣿⣿⣿⣿⣶⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⢆⣿⠅⢀⠀⠀⣸⣿⣷⣿⡇⣿⣿⠇
⠀⠀⠀⠀⠀⣸⡇⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣼⣿⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⡇⡀
⠀⠀⠀⠀⢠⡿⠲⡄⣀⣀⠀⢀⣤⣀⣀⡀⠀⣀⠤⠓⠒⠂⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⡀⠀⣼⣿⣿⣿⣿⣿⣿⣿⢹⡇
⠀⠀⠀⠀⣽⣧⣤⡇⣧⣀⣾⣿⣿⣿⣿⣿⠀⡇⠀⠀⠀⠀⡀⣀⠀⠁⠀⠠⠄⣀⠀⠀⢘⣿⣿⣿⡇⠀⠁⣸⣿⣿⣿⣿⣿⣿⣿⣿⣼⡇
⢀⣀⣤⡶⢿⣿⣿⣷⣿⣿⣿⡿⠛⠿⠿⣿⣧⣷⣤⡀⠀⠀⠈⠻⣷⣤⠀⠀⠀⠀⠉⠒⢸⣿⣿⣿⠇⠆⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧
⠈⢱⡤⢤⣥⣭⣭⣽⡿⠉⢻⣷⣟⣦⣴⣹⣿⣿⣮⣳⣶⣶⡀⢁⠈⠙⢿⡧⡀⠀⠀⠀⠈⢿⣿⣿⣿⣾⠛⠋⠉⠁⠈⠈⢀⠈⠛⠛⢿⣿⡇
⠀⣼⡇⠀⡖⠒⢺⣿⣧⣯⡿⠛⠿⢿⣿⣿⣿⣿⣿⣿⡋⠛⣛⣛⣙⣷⣾⣿⣇⠀⠀⠀⠀⢸⣿⣿⣿⣟⠀⣠⣦⠼⠂⠙⢶⡷⢶⣒⣞⣉⣇
⢀⣿⡇⠀⣇⣀⣀⣉⣛⣉⣀⣀⣀⡀⣿⣛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣿⣄⠀⠀⠀⠈⣿⣿⣿⣿⣾⠟⠁⠀⠀⢠⣿⣿⣿⡿⡿⠿⣿
⢘⣿⡇⠀⠆⠀⠀⠐⠆⠀⠰⠀⠀⠰⣷⠖⠲⠞⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⣿⣿⣿⣿⣇⠀⠀⠀⡄⣾⣿⣿⣳⣿⣿⣿⣦
⠀⣿⡇⠀⠀⠀⠰⣆⠂⠀⠀⠀⠀⠀⣯⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢠⣿⣿⣿⣿⢿⠂⠀⡇⠀⣿⣿⣷⣿⣿⣿⣿⡿
⣠⣿⡇⠀⡀⣀⢀⣀⣀⠀⠀⠀⠀⣘⣟⡀⣀⣀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡯⡄⠀⠀⢸⣿⣿⣿⣟⣸⡷⣾⡅⠃⣿⡟⣿⣿⣿⣿⣿⡇
⠟⣿⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⢀⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡗⡇⠀⠀⢀⣿⣿⣿⣿⣹⡷⣏⣷⣴⣿⣽⣿⣿⣿⣿⣿⡇
⠈⣿⠃⠀⠃⠀⢀⡤⠀⠀⠀⠀⠀⠠⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⡿⣿⢿⣿⡇⡷⠀⠀⠘⣿⣿⢻⣿⣿⣃⣯⣿⣿⣿⣿⣿⣿⣿⣿⡿⡅
⠰⣿⡆⠀⡄⠀⠀⠉⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣧⠀⠀⢰⣿⣿⣿⣷⣶⣶⣶⣦⣭⣽⢛⣛⣉⣽⣿⣷⡇
⠘⣿⡇⠀⠓⠐⠒⠒⠒⠒⠒⠂⠐⢲⣿⠒⠒⠆⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⢉⣀⣠⣤⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⡁
⢠⣿⡇⠀⣴⣶⣶⣦⣴⣤⣶⣶⣷⣿⣽⣷⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣼⣿⣿⡄
⠈⢿⣧⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣭⠉⠉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠿⢿⠻⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣇⣿⣾⣿⡿⣿⣿
⠀⠀⠈⠛⠉⠫⠿⢟⠻⠿⠿⡿⠿⠦⣤⣤⣾⣿⣿⣿⣿⣿⣟⣋⣱⣦⣴⡿⢿⣿⣿⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣿⠿⢿⠿⢿⣶⣷⡀⠂
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣁⣉⣈⣁⣀⣀⣀⣀⣀⣈⣉⣉⣉⣉⣀⣀⣀⣀⣀⣁⣀⣀⣀⣀⣈⣉⣀⣀⣀⣀⣉⣉⣛⣛⣇⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣉⣉⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⡄⠒⠒⡎⠹⡉⠑⢖⠂⠤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠁⠀⠱⡀⢣⡈⠢⣈⠑⠒⠈⠐⠂⠉⠢⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠈⠢⠍⣐⡀⠬⠭⠉⠉⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⡄⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡱⢄⠂⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⢰⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣂⠇
⣀⠔⠂⠉⡡⠤⢐⡢⢨⡿⠦⡼⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⣲⢶⠖⣒⠒⠂⠤⠤⣀
⠀⠀⢀⠡⠒⢈⠄⠊⠁⠠⠅⠖⠃⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠇⡏⢏⠛⠤⡒⠨⢅⡒⠄⠀⠑
⠀⠈⠀⠀⠞⠁⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⡜⠀⠁⠉⠀⠀⠀⠑⢤⠈⠑⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⠀⠘⠤⣀⠀⠀⠀⠀⣀⠤⠊⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢄⡀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⣀⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⡦⢤⠤⡤⢤⠒⠂⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⡆⠀⠉⠀⠈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⢀⠃⠀⠀⠀⠀⡌⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣼⠀⢘⣀⣀⣀⣀⣀⡀⠀⡷⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠁⠀⠀⡆⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣇⢀⣰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⡀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠛⠛⠛⠛⠛⠛⠛⠛⠻⠷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣶⡄⠀⠀⣿⠀⠀⣠⣴⣶⠶⠶⠶⠶⣶⣤⠀⠨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣯⡀⠀⠀⣿⠀⣼⠏⠀⠀⠀⠀⠀⠀⠀⠹⣧⢸⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠀⠈⠻⠆⠀⢿⣴⡏⠀⢶⣄⡀⠀⠀⣠⣴⠆⠙⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠉⣿⣦⣴⣶⠄⠀⠈⣿⡀⠀⠾⠛⠁⠀⠈⠙⠿⠆⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⢘⣿⠂⠀⠀⠀⣴⠟⠻⢶⣤⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣰⡟⠁⠀⠀⠈⣿⣄⠀⡀⢸⡏⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠙⠛⠀⠀⠀⠀⠀⠀⢹⡟⠻⣾⣇⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠇⠀⣀⣤⣤⣤⣤⣤⣤⣾⣧⡀⠀⢿⣄⠀⠀⠀⢀⣹⣧⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠉⢁⠀⠀⠀⠀⠀⠈⠻⢶⣬⣿⣦⣤⡾⠛⠉⠹⣧⡈⠉⠙⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⢠⡶⠟⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠘⣷⡀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀⠀⠀⠀⠈⢿⣄⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄⠀⠀⠀⠈⠻⣆⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠹⣦⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠹⣷⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀⠀⠀⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠆⠀⠀⠀⠀⠘⠿





⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⡟⠙⠛⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠉⠉⠒⠒⠈⠀⠉⠓⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡖⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⣀⠀⠀⠤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠤⠂⠀⠀⠤⢄⠀⠀⠉⠑⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐
⠀⠀⠀⠀⠀⠀⠀⢀⠔⣀⡠⠤⠒⠈⠈⡆⠀⠀⠀⡀⠉⠀⢄⠀⠀⠀⠈⠲⡄
⠀⠀⠀⠀⠀⢀⠔⢡⠎⣁⠀⠀⠀⠀⠀⡁⠀⡀⢸⠇⠀⠀⠀⠐⢄⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⢠⠂⠀⡇⠀⠀⠈⣹⣃⠖⠉⠁⠈⡇⠈⠀⠀⠀⠀⠀⠀⡣⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⠀⠆⠀⢀⠱⣄⡀⢀⣈⡭⡄⠀⠀⠀⡇⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⡗⢄⣀⠤⠊⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠐⠺⣄⠀⠀⠀⠀⠀⠌⠁
⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⢸⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠑⠄⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠒⠂
⠀⠀⠀⠀⠀⠀⣤⣶⠟⠉⠒⠢⢄⣀⠀⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠉⠛⠀⠀⠀⠀⠀⠀⠉⠒⠦⣄⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠠⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡇⠀⡄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡗⠒⠒⠣⢦⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠶⣧⣠⣤⡤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠈⠃⠐⠼⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣔⣒⣀⠒⠶⠶⠶⠦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣺⣽⠟⢉⣩⣤⣤⣤⣤⣤⣬⣿⣒⠂⠀⠀⠀⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠟⠯⠛⠁⠢⢴⡿⠟⠙⣓⡚⢓⠛⡛⠳⠮⢤⣀⣄⡐⠻⡢⣄
⠀⠀⠀⠀⠀⠀⠀⢀⢔⡵⡫⠂⣰⡆⢴⣆⣤⣤⣈⠛⠿⢛⠉⠁⢀⣅⢀⡀⠀⠈⠙⠻⣦⣌⠐⠕⢄
⠀⠀⠀⠀⠀⠀⣠⣿⢿⠏⠠⣺⠟⣡⠀⠸⠟⠉⣤⢶⣳⣬⡛⢿⠿⣶⣦⣬⣉⠒⢦⡀⠈⠻⣷⣄⠲⡡⢀
⠀⠀⠀⠀⠀⣰⣳⠋⠁⢀⡼⢁⠞⡱⠃⡨⢤⣼⡾⠛⠉⠀⠀⠀⠀⠀⠀⠉⠛⢷⣦⣙⢾⡀⡈⢿⣷⣔⡹⣷⡀
⠀⠀⠀⠀⢰⢳⡏⢀⢠⡿⢠⢃⠠⠀⠐⣁⡈⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢴⣄⢩⣍⡈⠛⠻⠎⢻⢳⡀
⠀⠀⠀⠀⣿⢿⠇⠆⡟⠁⠋⢁⡄⡸⢰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠞⣆⢻⡟⣦⣶⠀⠈⣏⣧
⠀⠀⠀⠀⣿⡞⢠⠁⠀⠁⠠⣿⢣⠃⣿⡇⣀⡤⡄⠀⠀⠀⠀⡠⣄⣀⣀⣃⡀⠄⠀⠀⢸⡘⡈⠗⢇⡀⣴⢻⢸⣿⡀
⠀⠀⠀⣶⣿⡇⡀⢸⣠⡆⣄⣈⠘⢢⠟⠋⠁⢀⠇⠀⠀⠀⡜⠀⢿⣿⣶⠏⡘⠀⠀⠀⠈⠓⠐⣿⢹⠆⣿⠸⢸⣿⡇
⠀⠀⠀⣿⣿⡇⣷⠈⢿⡇⡇⢻⠞⠁⠀⠀⢀⠎⠀⠀⠀⠀⣇⠀⠀⠀⣠⠜⡤⠊⠙⠀⡘⢠⠰⣿⠈⡄⡿⢀⢹⣿⡇
⠀⠀⠀⢻⢿⠀⢸⣇⠸⣟⢰⣸⡄⠀⠀⠀⢇⠀⠀⠀⠀⠀⠈⠙⠋⠉⠀⣜⣠⣄⡸⡰⢃⠃⣦⠁⠘⠄⠁⡈⣸⣻⠃
⠀⠀⠀⠸⣾⡇⠈⢏⡆⢿⣖⠗⣷⡀⠀⠀⠈⠷⢄⠀⠀⠶⠮⣥⣦⠀⠀⠈⠉⣩⡞⠁⢃⣼⣿⠃⠈⠀⢠⢡⠇⡿
⠀⠀⠀⠀⢿⣿⣆⠘⣺⡜⢿⢆⠻⡷⠀⠀⠀⠀⠀⠉⠒⠦⠤⢤⡤⠤⠤⢶⠻⠗⢀⡀⠾⠙⠁⠞⠀⠐⣿⠏⡼⠃
⠀⠀⠀⠀⠈⢻⣎⢆⠱⡹⣎⠻⣧⣿⠀⠀⠀⠀⠀⠀⢀⡠⠤⢶⡲⢤⣴⣋⣤⠴⣪⡵⡣⢦⠄⠀⠀⠠⢊⡾⠁
⠀⠀⠀⠀⠀⠀⠛⢯⣧⡙⢿⢧⡈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡤⣤⣤⠴⠾⣋⠤⠖⢁⠔⡹⢋⡴⡫⠂
⠀⠀⠀⠀⠀⠀⠀⠪⡻⣟⠎⠳⣝⡻⡆⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⢀⠷⠾⠋⣀⠤⣚⡵⢊⠕⣫⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡷⣤⡀⠙⢳⠀⠀⠀⠀⢸⠍⢉⣳⣄⣀⣴⣛⡤⢄⣠⣶⠟⢉⣪⡴⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⡻⣶⣧⠀⠀⠀⠈⣗⣒⡲⠞⠒⠒⢒⣉⣉⣥⣴⡾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⢷⡀⠀⠀⢸⣽⡿⠿⠟⠛⠛⠛⠙⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣵⣄⡀⠀⢀⣥⣤⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡏⢙⡉⠁⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠟⢿⣾⣿⣀⣀⣀⣠⣈⣛⡶⣶⣾⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⢟⣿⣿⣿⠃⢠⣾⣿⣿⣿⣿⠏⡏⢀⡍⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⡟⠀⣼⣿⠃⠸⣿⣿⠇⠀⠁⣤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣧⣴⠏⢹⡸⠏⠹⣿⡄⠾⠶⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣬⡏⠀⠀⢸⣷⠀⣶⠈⠛⠄⠀⠹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⣿⡄⢻⡇⡄⠀⠀⠀⡇⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⣿⣿⡿⠀⢿⠀⡆⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡹⣿⣿⣿⣟⣿⣿⣿⣇⠀⠀⠀⣿⣿⠃⠀⣾⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⣿⣿⣿⣿⣿⣿⡀⠀⠀⢸⣏⣀⡀⠛⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣌⣙⡿⣿⠿⠿⠀⠀⠀⢸⣿⣿⡿⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⠿⠙⣾⣴⣦⣶⣤⣿⣿⣿⣏⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡿⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠛⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⠀⠀⠀⠀⠈⠛⢿⣿⣭⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡁⠀⠀⢀⠀⠀⠀⠀⢻⣿⠁⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠅⠀⠀⠀⠀⠀⠀⢀⣾⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣀⣤⣄⠀⠀⠀⠹⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣯⠀⠀⠀⠀⢸⣿⣿⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⢀⣾⡿⠇
⠀⠀⢠⣄⣀⣀⣀⣀⣀⡠⠤⠀⠀⡀⣀⠀⢸⡗⠀⠐⠿⠟⠁
⠀⠀⠘⠛⠻⠛⠿⠿⢿⣿⣿⣿⣿⣿⣾⣷⢿⣿⣾⣿⡒⠃⣐⠟⠀⠠⠚⠿⠓⣒⠒⠒⠒⠖⠲⠦⠤⠄
⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠉⠉⠉⠟⠻⠷⠻⠿⠿⣧⣗⣋⠉⠓⠂

⣶⣶⡶⠶⠶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣶⣶⣶⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⠟⢿⣿⡿⠛⠋⠉⢁⣤⣤⣤⣤⣭⣉⠙⠛⠿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣏⡉⠛⠁⠠⣿⣿⣧⠀⠀⠀⠈⠛⠛⠛⠛⠿⠿⠁⢠⣶⡄⠙⠻⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠂⢀⣀⡈⢻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠈⠻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣤⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀⠀⠙⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠛⠻⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡿⣿⣿⡄⠀⠸⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣿⡿⠟⠉⠀⢸⣿⣧⠀⠀⢻⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣿⣿⣿⣿⠿⠟⠛⠉⠀⠀⠀⠀⠀⢿⣿⡆⠀⢸⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣴⣶⣿⣿⠿⠟⠛⢛⣉⣉⠉⠁⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢸⣿⣧⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⠁⠀⣴⣾⣿⣿⣿⡿⠇⠀⠀⠀⠀⠸⢿⣿⣿⣿⣷⣦⠀⠈⣿⣿⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⡀⠀⠈⠉⠁⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⠉⠁⠀⠀⣿⣿⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢻⣿⡇⠀⠀⠀⠀⢿⠿⠀⠀⠀⠀⠀⠀⠀⠀⠿⡿⠀⠀⠀⠀⢸⣿⡿⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠈⢿⣿⣆⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⠈⢻⣿⣦⡀⠀⠀⠀⠸⣿⡿⠿⣿⡷⠀⠀⠀⠀⣰⣾⣿⠟⠁⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣷⣤⣤⣤⣤⣤⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣥⣤⣤⣤⣤⣾⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠛⠛⠛⠛⠻⢿⣿⣶⣤⣤⣀⣀⣤⣤⣶⣿⣿⠟⠛⠛⠛⠛⠛⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣿⣿⣿⡿⠿⠿⢿⣿⣿⣿⣿⣷⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠛⠉⠁⠀⢿⣿⡇⠀⠀⢸⣿⡟⠀⠈⠉⠛⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠁⠀⠀⠀⠀⠀⠘⢿⣿⣦⣴⣿⡿⠃⠀⠀⠀⠀⠀⠈⠻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⣾⣷⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⣤⣤⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⣿⣿⡀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣶⣶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⡿⠟⢻⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠀⠰⣤⣤⣿⠟⠋⠉⠁⠀⠀⠈⠻⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡷⠀⠀⢨⡟⠐⠢⠄⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡇⠀⠒⠶⢤⣤⣤⣤⣄⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠁⠀⠀⠀⡋⢠⡄⠀⠀⠀⠈⠁⠒⠀⢸⣿⣿⣿⣇⠀⠀⠀⠀⠈⠁⢀⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠰⠤⠈⠀⠚⠉⢉⣿⣿⡀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⡟⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡿⠷⠀⠀⠀⠻⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢠⣤⣀⡀⠀⠀⠙⢿⣿⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠂⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢀⢀⠀⠀⢀⡀⠀⠀⠀⣴⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠾⠃⠀⢀⡏⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠿⢿⣿⣿⣿⣿
⠀⠀⠀⠀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿
⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿
⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿
⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⡀
⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠃
⠀⠀⠀⠀⠀⠉⠛⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⣀⠀⠀⠠⠀⢂⠐⠒⠀⠀⠀⠐⠀⠀⠀⢀⣆⠄⠀⠀⡀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⡬⠀⠀⠀⡽⢻⡽⢾⠽⣧⡠⠈⠀⠀⢀⣊⠋⠀⢀⣮⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠈⡐⠀⠀⠀⠀⠀⠀⢀⠉⠁⠘⠀⠠⠀⠀⠀⠙⣙⠦⠜⠻⣿⣿⢶⡆⠰⢀⢀
⠀⠀⠀⠀⠀⠄⠀⠂⠀⠄⡤⠇⠀⠀⠀⠁⠢⠀⣤⢑⡀⠀⢤⠀⠀⠀⢶⣦⣄⠀⠀⠀⠀⡁⠘⠷⣧⣌⣌⣴⣤⣀
⠄⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠲⠤⠠⠤⠀⠀⠀⠂⢄⠀⢠⣀⢀⠉⠀⠀⠀⠀⠇⠀⠀⠀⡰⠙⢿⣿⣿⣿
⠀⠠⡀⠀⡀⠀⠀⠀⠀⠠⢥⣀⡀⠀⠀⠀⠀⠀⠴⠤⢀⠀⠈⠐⢕⡌⠹⠛⠀⠀⡀⠀⠁⠀⡠⠈⠉⠀⠀⠀⠀⠉⠁
⠀⠀⠀⠁⡇⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⡠⠖⣡⠛⡂⠔⠁⠀⠀⠀⠔⠁
⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠲⠇⠃⡠⠀⠀⠀⢀⠊
⠀⠀⠀⠀⠀⠑⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⢀⡞⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⡀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠐⠐⠲⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣾⣯⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⢿⠟⢻⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⠀⣄⣠⡉⠻⢧⢈⠻⢿⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⢰⢤⠄⠀⠀⠀⠈⠓⠄⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠘⠷⠒⢰⣿⣿⣿⣿⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠋⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⠉⠻⢿⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠷⠀⡠⠀⠀⠀⠀⢠⣾⣿⣿⡿⠃⠀⠀⠀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⡰⠎⠀⠀⠠⢂⣾⣿⠟⣿⠟⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠏⠀⠀⠀⠀⢠⣾⡿⠋⡼⠃⠀⠀⠀⠀⠀⠀⠀⠈⢄
⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠁⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠤⠀⠰⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠚⠷⠶⠚⠛⠓⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⡅⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣾⡀⠀⠀⠀⠀⣀⣀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣶⣶⣶⣶⣿⣿⠇
⣶⣶⣶⣶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⣤⣤⣴⣶⣠⣤⣶⣶⣾⣿⣿⣿⣿⣿⣿⣷⣶⣶⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠛⢻⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢁⡙⠛⠋⠀⠙⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠐⢸⣿⣿⣿⣿⡇⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡃
⠀⠀⣤⣭⣠⣀⣸⣿⣿⣿⣿⣷⣀⣄⡄⢀⣤⣄⣤⡤⠀⠀⢰⣶⣶⣾⣿⣿⣿⣿⣿⡗
⠉⠀⣤⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣟⡍⠂⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠸⠿⡿⣿⣿⠿⣿⡿⡿⢿⠿⢿⡟⠉⠀⠀⠀⠀⢠⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠿⠿⠛⠉⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠔⠊
⠀⠀⠀⠀⢀⣠⣶⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⢠⣀
⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡉⠙⢦
⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣧⡄⠀⠞⠉⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠠⠊
⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⢸⡛⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣄⡀
⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠈⠋⠀⠈⠻⠂⠀⠀⠀⠀⠀⢠⣤⣀⣴⣖⣋⣁⣀⣀⣉⣙⣒⣒⣤⣀⣤⡦
⠀⠀⠹⣿⣿⣿⣿⣿⣿⣏⡉⠀⠀⠀⠀⠀⢀⣠⠾⠀⠀⠀⠀⠀⠀⠀⠹⣯⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⠭⣭⡟
⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⠉⠠⡀⠀⠀⠀⠈⠛⠖⠀⠀⠀⠀⠀⢠⣤⣤⠬⠷⠦⠤⢤⣤⣤⣤⣤⡤⠶⠾⣧⣤⡤
⠀⠀⠀⠙⢿⣿⣿⣿⣿⡟⠀⠀⠈⠳⢦⣤⣤⣤⡴⠂⠀⠀⠀⠀⠀⠈⠉⣳⠖⣶⠖⠛⠋⡭⠶⠾⢗⣒⡭⠟⠁
⠀⠀⠀⠀⠀⠀⠉⠁⠀⢿⣄⣤⡤⠤⣤⣿⡄⣀⣄⠀⠀⠀⠀⠀⠀⠀⣼⠃⣼⠃⠀⢀⣠⣤⡤⠽⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣤⣀⡀⢀⣼⣿⣿⣿⣿⣿⠂⠀⠀⠀⣼⡇⣸⠇⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣦⡀⠉⠉⠛⠻⢿⣦⣄⡀⣰⡟⢠⡟⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠈⠙⢿⣟⢀⣿⠁⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⢻⣿⠃⠀⠀⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠟⠙⠻⣧⣀⠀⠀⠀⢀⣾⠃⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⡟⠁⠀⢀⣴⠏⠙⠷⣤⣠⡿⠁⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣤⡿⠁⠀⠀⠀⠈⠛⠀⠀⠀⠀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⣴⣶⣤⣄⣀⠀⠻⣿⡍⠛⢷⣦⣄⡀⠀⠀⠀⠀⢀⣼⡟⠁
⠀⠀⠀⠀⠀⠀⣾⡇⠀⠈⠙⠻⠿⣶⣿⣿⡄⠀⠈⠙⠛⠷⣦⣤⣠⣾⠟⠁
⠀⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠈⠙⢿⣧⠀⠀⠀⠀⠀⣾⣿⠉⠁
⠀⠀⠄⠀⠀⢸⣿⠀⠀⠀⣀⣠⠤⢶⣶⣾⠏⠀⠀⠀⠀⠀⣿⡏
⠀⠀⠀⠁⠀⠘⢿⣤⣶⣿⠿⠶⠛⣹⡿⠋⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠉⠉⢿⡄⠀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⢀⠀⠀⠀⡀⡄⣀⠀⠀⠀⣀⢀⣀⣀⠀⡀⠀⡀⣀⢀⡀⣀⡀⠀⠀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠋⠋⠁⠉⠈⠀⠁⠁⠀⠈⠈⠀⠈⠁⠈⠁⠉⠀⠋⠁⠙⠋⠈⠁⠉⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠤⠶⠒⠚⠋⠉⠉⠉⠉⠉⠓⠒⠤⣄⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠠⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠉⠲⢤⣠⠴⣒⠶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠝⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠊⢁⡴⠛⣀⡈⠓⠴⠒⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⣀⠥⠒⠋⠁⠱⡄⠀⠘⠢⣄⠀⢀⡤⡴⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⢸⠁⠀⠀⢠⣤⠀⣣⠠⢶⠐⣇⠉⠉⢼⡁⠀⠀⠀⠀⢸⣀⣀⣀
⠀⠀⠀⠀⠀⠀⣼⠁⣠⠤⡌⢇⠀⠀⠘⢿⣾⡁⠀⠀⢃⠈⠂⠀⠀⢉⡢⠄⠀⠀⠈⠀⠀⠈⠉⣙⡦
⠀⠀⠀⠀⠀⠀⡏⠘⣅⠀⠘⠈⣷⣤⣀⣸⠈⠀⠀⣀⠞⠀⠀⠀⠈⢹⠀⠀⠀⠀⣀⡤⠔⠚⠫⢍⣉⠉⠙⠓⠒⠲⢦⡄
⠀⠀⠀⠀⠀⠀⢻⠀⠈⠙⠀⡀⠂⠀⠀⠘⠷⠖⠚⠁⠀⠀⠀⠀⠀⠓⠒⡛⠛⠛⢣⡀⠀⠀⠀⢀⡜⠁⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠻⠦⠛⠆⠀⡇⠀⠀⡠⠋⠀⠀⠀⢀⡴⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠒⠤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⡗⠒⠤⠤⠤⠤⠚⠁⢠⠞⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡀⢨⠃⠘⠳⣄⢀⣀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⢀⠜⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡇⠀⠀⣧⣈⠉⠀⠁⠀⠀⠘⡏⣇⠀⠀⠀⡼⠁⠀⠀⠀⣰⠋⢀⡤⢤⣳⢹⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⣀⣠⠇⠈⠉⠓⢢⢄⡀⡼⠁⡸⡄⠀⢸⡇⠀⠀⠀⠐⠧⠚⣡⠞⠳⣄⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⢻⡇⠑⠃⠸⡄⠀⠓⠦⠤⡤⠤⠖⠋⠁⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢠⡀⠀⢀⡂⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢾⡀⡀⠸⢦⣶⣺⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⡀⡀⢘⣇⡀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟⡖⠖⠚⢿⣋⣏⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⡼⠋⠁⠀⣡⠄⡬⠗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⡀⡀⣀⣱⣤⣵⣤⣀⣀⣀⣱⣄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⣴⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠶⢶⣚⣿⣿⣿⣿⣿⣿⣶⣤⣈⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣍⡓⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣭⣿⣿⣿⣿⠿⣿⣿⣿⣯⣭⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣶⣿⣿⣿⣿⣋⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠿⠿⠿⠿⢿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣶⣶⣶⣶⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣿⣿⡿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣠⣾⣿⣿⣷⣄⣤⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣿⣿⣷⣽⣿⣿⣯⣾⣿⣿⣿⣿⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⠏⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠹⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁


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

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⢾⢻⡟⣦⢴⡄⠀⠀⠀⠀⠀⣀⡼⠉⣷⠀⠀⠀⢀⡠⠶⠶⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣌⠁⠀⠀⣾⠁⠀⠀⢠⠖⢾⠁⡾⠉⠁⠀⠀⢸⣏⣵⠶⣄⢸⡇⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⢻⡀⠀⠀⠈⡗⢸⢸⣇⣀⣀⣀⠀⠀⠉⠁⠀⢹⠀⣿⠉⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠳⣄⣠⠞⠛⠈⠉⠀⠀⠀⠉⠙⠛⠶⢤⣀⡟⣰⢃⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠈⠁⠀⠀⠀⠠⢒⠒⡀⠀⠀⠀⣀⣀⡉⠀⠙⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠤⣈⡠⠃⠀⠀⠀⡁⠂⡱⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⣧⣠⡤⠤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⢀⠤⡆⠀⠀⠡⠤⠋⠈⠉⡓⠂⣄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣈⡹⣦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠔⠥⠴⠁⠀⠀⠀⠀⢀⣀⠀⠈⠉⠀⡟⢆⠀⠀⠀⣾⠉⠁⠈⢳⡖⡀⣣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠀⠀⠌⠀⠀⠀⠠⠊⠀⠧⡠⠁⠀⠑⡄⠀⠀⠈⠉⠆⠀⠀⢸⠀⠀⠀⠈⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠸⠀⠀⠀⠐⠋⠀⠀⠈⠒⠤⠐⠈⠁⠀⠀⠒⢄⢰⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⢀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⡀⠀⠀⠹⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠤⠁⠀⢠⠇⢀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⠀⠀⠀⠀⠀⠀⠘⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⠀⠀⢹⡇⢰⡋⠱⠄⠀⠀⠀⢇⠀⠈⡇⠀⠀⠀⠀⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠉⠳⣄⣸⠃⠀⠁⠈⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠿⢦⡀
⠀⠀⣀⣤⠤⢤⣄⡤⠖⠒⠶⣾⠀⠀⡠⢤⠀⠀⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣄⠀⢳⣀⡴⣦
⠀⡞⠁⠀⠀⠀⠀⠀⠀⢀⠀⠘⠀⠀⠐⠚⠀⠀⠀⠒⠠⠤⠤⢄⠀⠀⠀⠀⠀⢖⣲⠀⠀⠀⠀⠀⢀⡞⠁⢨⡇⢨⣰⠞⠁
⠀⣧⡀⠀⠀⠆⠀⠀⠀⠈⠒⠊⠀⠀⠀⡌⠀⠀⠀⠀⠘⢄⠄⠀⠦⠂⠉⠁⠐⠠⢀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠉⠁⠀⠀⣠⠴⢤⡀
⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠑⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⢀⡠⠏⠀⠀⠀⣀⠀⠀⠛⠲⠾⠇
⢧⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⢹⠛⠋⠉⠀⠀⢠⡖⠻⣉⡉⢻⡆
⠈⠳⢦⣀⡀⢀⡀⠀⠀⠀⡆⠈⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⢄⠀⢀⠠⠛⢦⠀⠀⢀⣤⢤⣻⡆⠀⡴⠚
⠀⠀⠀⠈⠉⠉⡷⠄⠀⠀⠉⢀⠜⠀⠀⠀⡀⠠⡀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢸⠆⢨⡷⠙⠛⠁
⠀⠀⠀⠀⠀⣼⢱⠂⢀⠋⠁⠀⠀⣨⠀⠀⠃⠀⡀⠀⠚⠡⠀⠀⠀⠠⠠⠀⠀⢀⣀⣠⠔⠋⠀⠀⠈⠲⠖⠃
⠀⠀⠀⠀⠀⠹⣄⠈⠀⠀⠀⢀⣴⡅⠁⠀⠀⠀⠀⠀⣀⡌⠀⠀⠀⠀⠀⠀⣰⠟⠁
⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠛⠋⠁⠙⠶⣤⣤⣤⡴⠚⠉⠓⠦⢤⣤⠤⠖⠛⠁
⣿⣿⠟⠛⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⡀
⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂
⠁⠀⠀⢀⠀⠀⠀⢀⣠⣴⠚⠁⠀⠀⠀⢀⠀⢀⡀⠀⠀⠀⢀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠁⢸⠏⠀⠀⠀⠈⠈⠁⠀⠀⠀⠠
⠀⠀⠀⠀⢀⣤⣄⣤⣶⣶⣶⣶⣾⣧⡀⠀⡀⠸⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠂⣰⣷⣦
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⠇⠀⠀⠙⢳⣾⣿⣤⡟⢿⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⣾⡏
⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠀⠚⠁⠀⠀⠙⢻⡉⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣽⡇
⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣄⠀⠀⠀⠀⠉⠁⣶⡶⠦⠀⠘⢳⡛⠁⢀⡀⠀⠈⠁⠐⣶⠷⠿⠿⠟
⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⠿⠓⡤⣄⢀⠀⠐⠋⠀⠀⠀⠀⠀⠈⠀⠉⠀⠀⠀⠤⠀⠈⢿⠉⠁
⠀⠀⠀⠀⠘⠛⡯⣿⣿⠃⠀⠀⠈⠻⢟⡆⠀⠀⠠⠞
⠀⠀⠀⠀⠀⠠⠂⠿⠃⡠⠀⠀⠐⢲⡞
⠀⠀⠀⠀⠀⠀⠀⢤⣼⡇⠀⠀⠠⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠚⣷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠂⠀⠀⠀⠀⣠⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠒⢀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠁⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠤⠀⣀⠀⠀⠀⠀⢀⠀⠈⠢⠄⠀⣀⣀⡀⠜
⠀⠀⠀⠀⠀⡀⠂⠩⠓⠈⠥⢀⠇⠀⠀⢻⣿⠶⠂⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠂⠀⠈⠉⠂⠀⠀⠀⠀⠈⠙⠀⠀⠀⠀⠀⠀⠀⠀⠰⢾⣿⠃
⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⣀⣤⣤⣾⣷⣴⣦⣠⣦⣠⣴⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⣿⣿⡿⣿⠟⠙⠛⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⠟⠉⠉⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣆⠀⠄⡀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠟⠛⠋⠛⠀⠀⠀⠀⠀⢿⠗⠀⠀⠀⠈⠁⠂⠀⡀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⡈⠀⠘⠻⠀⠀⠀⠀⡄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠁⡰
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⡀⠀⠀⠀⠈⠀⢀⠁⠀⢠⣆⣀⣀⡀⢀⣀⡀⠀⡁⠀⠀⠔
⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠀⢂⠀⠀⢀⠀⠆⠀⠀⠀⠙⠋⠉⠛⠛⢩⠃⡀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣅⠴⣄⠴⠶⠒⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣀⠜⠉⠉⠙⠒⠒⠒⠒⠚⠉⠀⠀⠈⢢⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠉⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣀⡰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢄⡀⠀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡞⠉⠳⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⣀⣠⡤⢶⡋⠀⠙⠲⠤⠤⠷⢦⡀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠉⢉⡟⠀⠀⠀⢻⡀⢧⠀⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀⠀⠈⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣀⡴⠋⠀⠀⠀⠀⠈⢷⠈⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣻⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡟⠛⠲⢄⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠉⠲⣄⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⣸⣀⣀⣀⠀⢀⣠⡼⠋⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢧⡀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠀⠀⠎⠁⠀⠈⠉⠉⠉⠀⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠈⠉⠈⠉⠉⠁⠈⠱⠀⠀⠀⠀⠀⠠⣄⣠⣤⣤⠴⠶⠶⠶⠶⠞⠛⠛⠓⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠛⠶⢤⣄⡀⠀⠀⣀⣀⣠⡇⠀⠀⠀⠀⠀⠀⠈⣏⠠⠄⠀⠀⠀⠀⠀⠀⠀⠠⠈⢈⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠂⠉⠙⡛⠛⡉⣡⠜⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠓⠚⠒⠒⠚⠓⠒⠒⠊⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣜⠃⠀⠀⠀⠀⢀⣊⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⢸⡇⠀⠀⣰⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢶⣦⠀⠙⢷⡄⠸⠷⠀⢼⠟⠀⠀⢀⣠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⣿⡇⠀⠀⣀⣤⣤⣄⠀⠀⠀⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⢠⡾⠋⠉⣈⣹⣷⣄⠀⠀⢀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⣿⢷⣾⠟⠛⠙⠛⣿⠀⠀⢸⣟⠀⢹⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⠿⠷⠿⢷⣶⠄⠀⠀⠀⠀⠀⠀⠀⠻⢷⣤⣤⣾⠟⠀⠀⠈⠛⠻⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⣴⡶⣦⡀⠀⠀⠀⠁⢀⣤⡶⠶⢶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⣼⡟⢠⡿⠁⠀⠀⠀⠀⣼⡏⠀⠀⠀⠙⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⠀⠀⣼⡟⢠⡿⠁⠀⠀⠀⠀⠀⠸⣷⣾⠟⠻⣷⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⠀⣼⡟⢠⡿⠁⠀⠀⠀⠀⠀⠀⣠⡿⠃⠀⣠⡿⠀⠀⠙⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⣾⡟⢠⡿⠁⠀⠀⠀⠀⠀⢀⣼⠟⠁⣀⣼⣿⡁⠀⠀⠀⠀⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⣀⣀⣀⣀⣿⣿⣠⣿⣁⣀⣀⣀⣀⣀⣴⠿⢁⣠⣾⣟⣁⠙⣷⣄⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⠉⠉⣿⣯⣭⣭⣭⣭⣭⣽⣿⣿⣥⣾⣿⣯⣭⣭⣿⠇⠈⢻⣦⣠⣴⡾⠟⠛⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣽⠏⠁⠀⠀⢠⣿⠉⠁⠀⠀⢠⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡿⠋⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⣤⣤⣤⣤⣤⣤⣤⣶⠾⠛⠉⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⢠⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⠉⠉⠉⢹⡏⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⣾⣇⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠻⠿⠷⢶⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣤⣤⣤⣤⣿⣤⣤⣤⣤⣽⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣽⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⢶⣶⣶⣶⣶⡶⠶⠶⠿⠟⠛⠛⠋⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠋⠉⠓⠤⠠⠒⠒⠒⠛⠓⢦⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠦⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⢄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡽⠶⢚⣋⣩⠍⠐⠦⣀⣀⡀⠀⠭⠉⠛⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠊⠁⠀⣈⡩⠅⢦⠀⠀⠀⠀⠉⠑⠢⣄⡀⠀⠀⠀⠈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⣁⡤⠖⠚⠉⠀⠀⠀⢸⠀⠀⠀⠀⣠⡆⠀⠀⠙⠢⣀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⣠⠞⢁⡾⣁⡀⡀⠀⠀⠀⠀⠀⣸⢀⡀⡀⠀⢻⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧
⠀⠀⠀⠀⠀⠀⣴⠃⠀⡼⠀⠀⠀⠉⢉⡷⠖⡦⠚⠉⠉⠉⡷⠀⠸⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⣸⠃⠀⠀⢹⡀⠀⠀⠀⠘⠟⡞⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋
⠀⠀⠀⠀⢀⡇⡴⠛⠲⡄⠙⠲⠤⠤⠴⢺⡇⠛⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢀⡎
⠀⠀⠀⠀⢸⡇⢧⠀⠀⠹⠀⠀⠀⠀⠀⠸⡘⠦⡤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠀⠀⠀⠈⣇⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠒⠚⠉⠉⠙⠚⢤⠀⠀⠀⠀⠀⠀⢀⡼⠉⠁
⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢦⣵⣶⢦⠀⠈⡇⠀⠀⠀⠀⠀⣼
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⣀⠀⠀⠀⠀⣀⡴⠓⠦⠖⠒⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢲⣶⣶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠉⠉⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣤⡾⡟⠋⠀⠉⠒⠦⢤⣀⠀⠀⠀⠀⠀⠀⠀⡜
⠀⠀⠀⠀⠀⠀⠀⠘⠿⠷⠃⠀⠀⠀⠀⠀⠀⠈⠉⠒⠦⣄⡀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣝⠒⠋⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⡀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢱⠼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡀⣿⠀⢀⡄⠇⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⢤⣀⣉⡇⣄⢠⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠈⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣎⣉⣋⣻⣋⣾⡶⣖⠲⠾⠶⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠈⠁⠉⠓⠿⠴⠇

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠻⡆
⠀⠀⠀⠀⠀⠀⣞⢉⠳⣄⠀⠀⢀⣀⡀⢀⣀⢴⠊⠈⢼⡁
⠀⠀⠀⠀⠀⠀⠈⣳⠀⠈⣿⣶⣇⠢⣿⣷⣶⠚⡀⠁⠠⢹⠀⠀⠀⠀⠀⣀⢤⡀
⡴⠲⣄⡀⠀⠀⠸⣅⠁⠠⣩⣾⡿⠉⠙⣿⣟⠤⣄⣰⠤⣮⣀⣀⠤⠔⡊⠀⢀⡏
⢧⠒⠀⠍⢲⠤⣤⠼⠬⢚⢗⡼⠁⣀⣀⡈⠫⣷⢮⣄⠄⣁⣴⣞⣩⢻⠆⠀⠘⡆
⢨⠗⠂⢴⣿⣿⠦⣬⣔⣹⣿⣡⡼⠿⠿⠽⠷⠾⠿⠒⠊⠉⠁⠀⠈⢻⠀⠐⢰⠁
⠹⢴⠀⠨⡏⠀⠀⠀⠀⠀⠀⣀⠤⢴⡖⢶⣤⣴⣶⠶⣦⠀⠀⠀⠀⢸⡀⢁⡼
⠀⢸⣠⡤⡇⠀⣄⡴⠴⣶⡮⣋⡃⠁⢶⣷⣄⠉⢻⠿⠏⢹⣦⣤⠀⠀⡇⠋
⠀⠀⠁⠀⣿⡟⠁⠀⣼⡟⢀⣿⡇⠠⢦⠛⠃⠀⣸⣾⡇⢿⣧⣽⠀⠀⢳
⠀⠀⠀⠀⡇⣷⣠⠼⡟⣻⢤⠉⠀⠀⠀⠀⠀⠀⠙⠛⣷⣎⣷⠁⠀⠀⢸
⠀⠀⠀⠀⡇⠘⣷⣾⣵⡏⣚⡇⠀⠴⠒⢀⡠⠴⠚⠋⠉⠉⠉⠉⠙⠓⠺⣄⡀
⠀⠀⠀⢀⠅⠀⢳⣴⣠⣍⢽⣀⣀⡴⠊⠁⠀⠀⠀⠀⡤⣤⠤⡴⢾⡯⡭⠉⠉⠉⠉⠓⠦⠤⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⢸⠀⠀⢸⣿⠋⣁⣀⡜⠁⠀⠀⠀⠀⠀⠀⢠⣟⣿⣥⣿⡙⣿⡇⠀⣀⣀⣀⣤⠤⠤⠬⠿⠓⠒⠒⠒⠒⠲⠖⠋⣖
⠀⠀⠀⢸⠀⠀⢾⣻⣟⢿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢠⢔⠢⣤⡭⠿⠛⠋⠉⠉⠀⢀⢤⣀⡠⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⢸⣀⣀⣀⡙⢮⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣧⣀⠈⠁⡠⠞⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⢺⣿⠏⠉⠙⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⣄⡤⠒⢦⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠤⠲⡄⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣄⣀⡴⣯⣷⡄⠀⠀⠀⢀⣀⣀⣤⣤⡤⠴⠶⠶⠒⠒⠶⠶⠶⣶⡼⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠉⡷⣴⠞⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠖⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠂⠀⠉⠉⠀⠀⠒⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⢢⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⢃⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠠⠀⠀⢸⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⢀⡤⠂⠐⠠⢄⠀⠀⠀⠀⠀⠀⢀⠆
⠀⢠⠀⠄⠀⠆⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⠀⠀⠀⢠⣿⡇⠀⠀⠀⢀⠉⠒⠄⣀⡠⠔⠊
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⠀⢃⠀⠀⠈⢟⠉⠀⠀⠀⠀⠁⠢⡀
⠀⢀⠀⢄⠀⠊⠘⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠈⠁⠀⠀⠢⡀⠀⠀⠙⠓⠀⠀⠀⠀⠀⠈⠂
⠰⠁⠀⠀⠑⠀⠀⢀⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠠⣀⡠⡄⠀⠀⠈⠢⢄⣀⠀⠀⢀⠸⠄
⡆⠀⠀⠀⠀⠃⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠐⢄⡀⠈⠀⠡⠴⠠⡒⠤⠢⠀⠉⠉⠀⠀⢀⠀⠀⠀⠀⢁
⡇⠀⡀⠀⠀⣀⠀⠰⠠⠇⠀⠀⠀⠀⡀⡀⠀⠀⠤⠀⢄⠀⠀⠀⠀⠀⠀⣀⡨⢄⠀⢄⠈⠁⠠⢉⠏⠐⠬⠀⢀⡠⠂⠀⠀⠀⢸⠀⠀⠀⠀⠘⠀⠠⡀
⠃⠀⠀⠀⠀⢨⣀⣀⠤⠄⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡠⠚⠁⠀⠀⠑⠠⡈⢃⠀⠀⠀⢠⠀⠈⠇⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠢⣌⠁
⠀⠉⠀⠈⠉⠁⡀⠘⡖⠒⠒⠒⠢⡀⠀⠀⠀⠀⠈⠀⠀⡀⠀⠀⠈⠀⠀⠀⢀⠤⡀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠥
⠀⠀⠀⠀⠀⠀⠁⠀⠑⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠉⠀⠀⠀⠑⠤⠠⠔⠃⠀⠈⠀⠀⠀⠀⠀⠀⡐⠀⢀⠜⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠘⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁⠁⠀⠀⠀⠀⠀⠢⠤⡀⠀⢀⠀⠀⠀⠀⠀⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡒⠉⠁⠀⡀⠀⠀⠈⠠⠔⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠤⠀⠄⡀⠀⠀⠀⠀⠀⠀⡀⠙⠢
⣄⣤⣀⣠⣠⣄⣄⣤⣄⣄⣤⣠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⣤⣤⣤⣌⣰⣤⣔⣡⣄⣨⣤⣬⣭
⣿⣛⣛⣛⣻⣫⣟⣛⣟⣛⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⣯⣯⣯⣭⣿⣯⣭⣯⣯⣽⣿

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⣼⣿⣿⣿⣦⣠⣤⣤⣶⣶⣦⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⢻⣿⣿⣿⠟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⠈⡍⠁⠀⣸⣿⡇⠉⠉⠛⠿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢠⡁⠀⢀⣿⣿⠁⠀⠀⠀⢀⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⡇⠀⠀⠀⠀⢪⠄⢠⣾⣿⠇⠀⠀⠀⠀⠸⣿⣿⣷⣶⣶⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠘⠿⠿⠿⠇⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⢀⠠⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠂⠈⢡⠟⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠀⠠⢀⣀⠤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⡀⠀⣀⠀⢸⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⡀⢀⡌⠀⠀⠐⠶⠄⡀⠒⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠑⣄⢑⠦⡷⠇⠐⡶⢝⠓⠢⠀⠀⢰⡞⠀⠀⠀⠀⠀⠀⠀⠠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⠥⢀⠉⢴⢬⢀⠀⡂⠈⠀⡠⠘⢃⠀⠀⠀⠀⠀⠀⢾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⡀⢸⠆⠈⢢⠄⠀⠲⠈⠁⠇⠀⠦⣃⡄⢹⡄⠀⠀⠀⠗⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠃⠄⠀⠂⢏⠀⠈⠀⠀⠊⠀⠀⡀⠀⢀⠄⠡⠀⠰⠎⠀⠀⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⣎⣠⠦⠄⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠰⠄⠀⠈⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡲⠖⠙⠠⢀⣀⣀⣀⣀⡤⢐⠥⢄⡀⠄⢀⡀⢀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣞⣀⠿⡢⣀⠈⠀⡀⡄⠁⠀⠄⠀⠈⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠠⠇⠀⢀⣉⠱⠃⠀⠠⢶⡶⠈⠇⠀⠀⡀⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⡀⢠⡐⢲⢒⣔⣀⠀⣅⠀⠉⠁⠀⠀⠀⠀⠠⠒⠉⠱⠰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠂⠀⠀⠀⠀⢉⠁⠀⠀⠉⠙⠒⠫⠠⡈⠀⠸⢉⡓⠒⠒⢿⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠁⠏⡒⠁⠀⠤⣀⡱
⠀⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠄⠀⠀⠈⢂⠀⠀⠀⠃
⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠀⠀⠁⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢸⠀⠀⠀⡀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢸⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠀⠰⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠁

⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠀⠉⠉⠉⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⢀⠀⠁⠖⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢄
⠀⠀⠀⠀⡀⠄⠂⠀⠀⠀⠀⠀⠀⠄⠈⠁⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⣀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⢀⡐⠁⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠘
⠀⠀⡠⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠀⠀⢀⣠⠔⠋⠀⠀⠀⠀⠀⡠⠐⠁⠀⠀⠀⠀⠀⡄⠀⠀⢠
⠀⠈⠀⠀⠀⠀⠀⠈⠆⠐⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠉⠀⠠⠀⡀⠠⠄⠂⠁⠀⠀⡀⠀⠀⠀⠀⠀⠇⠀⢈⠆
⡌⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⡆⠀⠀⠐⠀⠀⠈
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⡈⠇⠀⠀⠁
⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠒⠠⠄⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢈⠄⠄
⠀⠀⠐⠠⡀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠂⠀⠀⠀⠛⠄⢠⢊⠂
⠀⠀⠀⠀⡀⠀⠀⢀⡌⠀⠊⠀⠲⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠒⠈⠀⢀⠀⢀⡔⠀⡊
⠀⠀⠀⠐⠤⠄⠂⠀⠃⣠⠀⠀⠀⠀⠀⠑⡦⡀⠀⡀⠀⠀⠀⠀⠈⠆⠀⠀⠀⠱⠁⢀⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠀⠀⠀⠀⠀⠠⠁⠈⠀⠀⠀⠈⢁⠟⠣⡁⠀⠀⠀⠀⠀⢀⠂⡘
⠀⠀⠀⠀⣀⠀⠀⠀⢀⡴⠠⠄⣀⠒⠒⠁⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢠⠄⢰⠂⠐
⠀⢀⠀⠘⡅⠀⠀⠠⠂⠀⠀⠀⠀⢀⠀⠀⠀⠀⠆⠀⠀⢠⠀⡄⠊⠁⠁⠀⠈⠆⠈⠑⢄
⠀⢇⠀⢰⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠀⣀⡈⠀⢀⠀⢈⠀⠀⢘
⠀⠘⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠁⠀⠀⠀⠁⠀⠂⠂⠈⠂⠀⠂⠈⠂
⠀⠀⠀⠀⠀⠧⢄⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠁⠂⠀⠤⠀⠀⠣⠌⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠈⠒⠒⠀⠀⠐⠦⠄⠀⠀⠀⠀⠆⢄⠀⣐⠄
⠀⠀⠀⠀⠀⠀⠀⠑⢄⠀⠀⠀⠀⠀⠀⠐⢀⠀⢀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢠⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⢇⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠄⠀⠠⠀⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠑⠠⠀⠀⠀⠀⢨⠁⠀⠁⠀⠒⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠁⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠠⠀⠀⠠⠞⠄⡀⠀⠀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢀⡘⠠⠀⡈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⡧⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣰⣾⠶⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡆⠀⢻⣶⡖⣀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡇⠀⠀⠀⢹⣅⣿⠀⠀⠀⠀⣀⡴⠻⣿⣿⣿⣿⡿⣟⣻⣷⣌⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣼⡇⠼⢁⠀⠀⠀⠈⠙⠿⣿⡆⠈⠋⠀⠿⠉⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣷⣶⣿⠀⠀⠀⠀⠀⠀⠈⠙⠶⣽⡳⠄⠀⠘⣟⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⡀⠀⠀⢸⡈⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣾⣷⣤⣴⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⡇⠸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣿⣿⠿⣿⣿⣿⣿⣾⣿⣿⣿⣟⠒⣂⡀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠰⠟⠉⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⠀⢸⣿⣧⣿⣿⣿⣿⣿⣿⢀⡀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢸⣧⠁⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⡿⡟⢿⢷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣾⣿⣿⡿⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠈⠉⠛⠿⢿⣿⣿⣷⣖⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⡿⠀⠀⠀⠀⠀⢠⡾⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠁⠀⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⠁⠀⠀⠀⠀⡐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢰
⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣼⣿⣿⠁⠀⠀⠀⠀⢸⠀⠀⠀⡀⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢨
⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⣶⣄⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠻⠿⠿⠀⠀⠀⠀⠀⠀⠙⢿⣥⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣿⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣤⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠯⠃⠀⠀⣀⡀
⠀⠀⢀⡀⢠⣤⣤⣶⣶⣦⣼⣷⣍⣴⣶⣲⣶⡖⠒⢂⣀⣤⣤⣤⣤⣤⣤⠖⠁⠈⣳⣶⡿⢟
⠀⠀⠀⠉⠉⠁⠉⠉⠉⠉⠁⠁⠀⠀⠀⠉⠉⠉⠁⠉⠉⠉⠉⠙⠉⠛⠛⠛⠛⠛⠉⠁

⣶⣷⡶⠶⡶⠶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣿⣧⣤⣤⣤⣀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠰⢊⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣍⡳⡄
⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇
⠀⠀⣷⣤⣤⣤⣤⠶⢦⠶⣴⢶⡶⣶⣶⣶⣶⠃⡇⠀⠀⣀⣤⣤⡀
⠀⠀⡏⠉⠉⠉⠉⣿⠍⣿⠉⣿⢹⡇⠀⠀⣨⠧⠗⠛⠉⠉⠀⠀⠉⠛⢦⣄
⠀⠀⡇⠀⠀⠀⠀⣿⠀⡿⠨⣿⢸⡇⡠⠋⠀⠀⠀⠀⢀⣀⣀⣀⢄⡀⠀⠈⢳⣄
⠀⠀⡇⢀⣤⠴⠶⠛⠛⠛⠛⠻⠿⠛⠛⠛⠁⣴⡆⠈⢵⢄⣄⣡⡍⠊⠳⡄⠀⠙⣆
⠀⢠⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣬⣷⡞⠉⠀⠀⢀⡠⠏⠙⣟⠀⠀⢟⡀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⣀⣀⢸⠀⠀⠀⠙⠲⢄⣬⡇⠀⠠⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠙⣿⡇⠀⠠⣾⠁⠠⣤⣯⢁⡀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡟⠀⢺⠇⠀⠀⠀⠀⠀⢨⣧⣿⡁⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⢿⠿⣆⣹⣢⣤⡀⠐⠺⢃⡼⢹⡯⡍⠙⢒⠦⣼⢤⡀
⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣤⢿⠝⢛⠯⠳⣄⣋⡽⢶⣿⠬⣉⠙⠛⢦⡿⠚⠛⠁⠉⠲⡄⠀⠀⠀⠀⢀
⠀⠘⢆⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠃⠀⠀⢻⡗⡄⠀⠁⠀⠈⠉⢱⣯⡩⣴⠞⠁⠂⠀⠀⠀⠀⣿⡤⠖⠋⠉⠉⠙⠃
⠀⠀⠈⢣⡘⣆⠀⠀⠀⠀⠀⠀⣠⢾⠷⠖⠶⢶⣦⣹⡦⣀⣀⣠⣤⣤⣖⡋⠴⠋⠉⠙⣲⣄⣠⡄⠊⣁⡤⠴⠶⠶⠶⠦⡄
⠀⠀⠀⠀⠙⢮⡳⢄⡀⠀⠀⣸⠁⠀⠀⠀⠀⠈⠕⠎⠛⣻⠦⠤⠎⠴⢵⠖⠀⣀⢀⣴⠩⣉⡤⠖⠋⠁
⠀⢀⠀⠀⠀⠀⠉⠓⠯⣓⣲⡇⠀⠀⠀⠀⢀⠄⠀⢠⣞⣁⡀⣀⣀⣀⣼⣾⡚⠭⠵⠀⠀⠁
⠀⠈⠛⠶⠤⣤⠤⠤⠤⠤⣤⡽⠦⣤⣴⡶⠶⠒⣒⣺⡿⠿⠟⠛⠋⠉⠁⠀⠀⠀⠀⣀⠤⠂
⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠁⢀⡤⠀⣠⠴⠚⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣢⡵⣀⠴⠂
⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⣠⢋⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡶⠴⠊⠿⠖⠋⠁
⠀⠀⠀⠀⠀⢠⠏⠀⠀⡰⣡⠋
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠛⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣎⠀⢰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠄⠀⠘⣷⡀⢀⣠⣴⣾⡿⠿⠿⣶⣦⣤⡀⠀⠀⢀⡼⠋⠘⠂
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⡟⠀⠀⠀⢠⠂⠀⠀⠀⠀⢈⣿⣿⣿⡋⠉⠀⠀⠀⠈⣿⣿⣿⣶⡞⠉
⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⠀⠀⠀⠈⠳⠤⣤⣄⣠⣾⣿⣭⣿⣿⣷⣦⣴⡾⠿⠛⣿⣿⣿⣷⡄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠃⠀⠀⠀⠀⡀⢀⠀⢠⣿⡟⣩⣤⣤⠀⠁⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⣀⣀⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠠⠀⠀⢠⣿⠯⠁⣩⣥⣄⠀⠀⣺⣶⣿⡿⣿⣽⣿⣿⣿⣿⣟⠉⠉⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⡀⠀⠀⣰⣿⡟⠀⢸⠋⠻⢟⡧⠐⡿⢻⣿⠤⠼⣿⣟⣿⣿⣿⣿⠀⠀⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⣴⠿⠁⠀⠀⠀⣛⠛⠛⠀⠀⠻⡌⠁⠀⣀⡼⣩⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⠀⠀⢀⣼⡏⠀⠀⠀⠀⠀⠀⢾⣿⣶⣶⣶⡎⢹⣿⠋⠈⠁⠘⣿⣿⣿⣿⡀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⡀⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⣀⣤⣽⣿⣯⣭⣀⠀⠀⠀⠀⠀⠀⣽⣿⣿⣿⣷⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣦⣾⣿⠟⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣷⣆⡦⣄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⡿⠀⠀⠀⢀⣾⣿⠟⠛⠻⣿⣿⣿⣿⣿⣿⣿⣷⡙⣆⠀⠈⣿⣿⣿⣿⣿⣿⠉⠉⠙⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⣿⣿⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⡆⠀⢸⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠸⣿⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⣇⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⢰⣿⠀⠐⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⢹⣿⡄⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⡟⣸⡏⠀⢰⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⠙⢿⣄⡀⢀⣼⣿⣿⣿⣿⣿⣿⡟⣴⡟⠀⢰⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢀⣼⣧⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠉⠛⠿⠿⡿⠿⠿⠿⠛⡫⠶⠛⢁⣰⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⣴⣿⠟⠉⠻⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠈⢿⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⠹⢿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠙⢿⣷⣦⣄⡀⠀⠀⠀⢀⣀⣠⣤⣴⣶⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⣼⣿⡿⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣆⠀⠀⠀⠀⠀⠀⢸⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣄⣀⢀⣀⣤⣾⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠉⠀⠈⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣼⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠁⠀⠀⠀⣠⣴⣶⣶⣾⣿⣿⣿⣶⣶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠛⠋⠉

⠀⡇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⠤⠤⣄⣀⡠
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠒⠒⠒⠀⠈⠉⠁
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠠⠦⠀⠙⠋⠑⠲⠶⣄⡀
⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⣄
⠀⠉⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠈⠑⠆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⡀⢠⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢤⣤⣄⣀
⠀⡧⠻⡄⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠉⠛⢧⡘⠃⢤⣄⡀
⠀⡁⠀⠘⢧⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠀⠀⠀⠀⠀⠙⢦⡀⠀⠉⠓⢢⣄⡀
⠀⠃⠀⠀⠀⠙⣄⠀⠀⠀⠀⠀⢿⡆⠀⢀⡀⠀⠙⠁⠐⠀⠀⠀⡀⣠⡀⠀⠀⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀⠈⠙⠳⢤⡀
⠀⡇⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠻⣦⡿⠟⢀⠀⠀⠀⣀⠔⠁⠀⣼⡇⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡄⠀⠀⠀⠀⠀⠀⠉⠳⢦⡀
⠀⡇⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠈⠙⠶⣤⣀⣀⡠⠁⠀⢠⣿⣽⣧⠤⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⣤⡀⠐⠊⠁⠀⠀⠉⠉⠁⠀⢠⡟⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠐
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⡀⠀⠁
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠾⠂⢳⠎
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣊⠀⣀⠠⠈
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢩⡉
⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠆
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⢂
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⡈
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⠇
⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⡌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡞⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠞⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⣀⠀⠉⠀⠉⠀⠀⠀⠸⠃⠠⠄⠀⠀⠶⣀⡀⠙⠁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠄⠀⠀⠦⣄⡀⠀⠀⠀⣀⠀⠀⠤⠀⠀⠀⠀⠀⠀⣀⡀⠀⠟⠛⠀⠀⣈⠀⣤⡐⠒⠲⠾⠇⠀⠀⠀⠀⠀⠀⠀⠈⠿⠖⣂⣠⣤⡄
⠀⠀⠀⠀⠈⠁⢀⡈⠛⠩⡄⠀⡀⠀⠀⠤⡀⠀⠀⠈⠁⠀⠀⠀⠀⠘⢋⡄⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠉⠁⠀⠀⠈⠛⠂⠀⠀⠀⣅⠀⠁⠀⠘⠆⠐⠉⠈⠉⠉⠉⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣠⣦⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⡟⠛⠛⠛⢿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡇⠀⠶⠀⣿⣿⣀⣸⣛⣀⣾⣆⣾⣦⣌⣿⣿⣞⣀⣿⣖⣹⣿⣅⣺⣿⢿⣂⣾⣇⣸⣷⣀⣻⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿