Cute stars Emojis & Symbols

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⠿⡄⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⣼⠀⠹⣄⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⢀⡏⠀⠀⠙⣆⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⢸⠃⢰⡆⠀⠘⢧⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡘⠋⠀⡿⠀⢸⠛⣆⠀⠈⢧⡀⠙⠋⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⢰⠇⠀⣿⠀⠈⢧⡀⠀⢳⡀⠀⢺⣿⡗⠀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⡄⠀⠤⠀⠐⠆⠀⠘⠃⠀⢀⣀⣠⡼⠀⠀⡿⠀⢸⣆⠳⡄⠀⠳⣄⣀⣀⠀⠀⠉⠁⠀⠚⠀⠰⠀⠀⢤⠀⠀⣤⡄
⠀⠀⢠⣾⣷⠀⠘⠋⢀⣀⣀⣠⣤⡤⠴⠶⠒⠒⠉⠉⠁⠀⠀⠀⠀⠀⡇⠀⢸⠛⣆⠙⣆⠀⠈⠀⠉⠉⠉⠙⠓⠒⠒⠶⠶⠦⠤⣤⣤⣄⡉⠀⠀⣾⣿⡆
⠀⠀⠈⠉⠁⢀⣀⠘⠯⣅⠀⠀⠀⢠⣤⠤⠤⠤⠶⠶⠖⠒⠒⠒⠒⠚⠃⢀⡎⠀⠹⣄⠈⠓⠒⠒⠲⠶⠶⠤⠤⠤⠤⣤⣤⠀⠀⠀⢀⡤⠟⢠⣄⠈⠉
⠀⠀⠀⠀⠀⠈⠉⠀⡀⠈⠓⢦⣀⠀⠉⠲⢤⣀⠀⠀⠻⢿⣗⡒⠒⠒⠒⠻⠃⠀⠀⠉⠙⠛⠓⢒⡶⠞⠂⠀⢀⡤⠖⠋⠀⣀⡴⠚⠉⢠⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠆⠀⠈⠓⢦⣀⠀⠈⠓⠦⣄⡀⠀⠉⠛⠲⢤⡀⠀⠀⠀⠀⢀⣤⠞⠉⣀⣤⠴⠚⠉⢀⣠⠶⠋⠁⣀⠐⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⢀⣄⠈⠙⠦⣄⠀⠀⠉⣳⠀⠀⢠⠞⠁⠀⣀⣄⡀⠈⢷⡀⠘⡏⠀⢠⡴⠚⢉⡀⠠⣶⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⢠⣤⡀⠈⡿⠀⢠⡏⠀⣠⠏⣠⠴⠚⠁⣀⡙⠲⢄⣳⡄⢷⠀⠘⡇⠀⢿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠃⢰⠁⠀⣼⠀⣰⠿⠋⠁⣀⡴⠛⠁⠉⠳⣄⠙⠛⢸⡄⠀⢻⠀⠀⣤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⡞⠀⣰⠇⠀⢀⡠⠔⠋⠁⢀⣠⠴⠳⡀⠈⠙⢦⡀⢷⠀⢸⡄⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⠀⢸⠃⢠⣯⠴⠚⠉⠀⣀⡤⠖⠋⢀⣤⡀⠈⢢⡀⠀⠙⢿⡆⠈⡇⠀⠘⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⡟⠀⠈⠁⢀⡤⠖⠋⠁⠠⣶⠄⠻⠿⠃⣀⠀⠙⠢⣀⠀⠁⠀⢻⠀⠐⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⢸⢃⣠⠴⠚⠉⢀⠀⠰⠆⠀⠀⠀⠀⠀⠀⠉⠀⢠⠀⠈⠳⣄⠀⠸⡆⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠗⠀⠛⠋⠀⠀⠤⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⠀⠈⠳⣄⣷⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄⠀⠿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢀⣀⠛⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⣴⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⡝⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣠⡽⠊⢳⡀
⠀⠀⠀⠀⠀⢀⣀⡴⡯⡻⣱⡶⣷⠯⣻⠯⣽⣿⣯⠟
⠀⠀⣤⠖⡻⡩⢷⣬⣽⣿⣾⣿⣿⣿⣷⢾⣾⣿⠋
⠀⠀⠈⠛⠮⣿⢿⣿⣿⣿⣿⣿⣿⣿⣇⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠈⠙⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣬⣉⡙⠛⠶⡢⣀⡿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣽⣿⣿⣿⣿⣯⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣡⣶⣶⣬⣿⣶⣄⠈⢪⢣⣀
⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⠟⠉⠀⠀⠉⠙⠛⠿⠇⢠⢴⠢⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⢹⡏⡇
⠀⠀⠀⠀⠀⠀⠀⠳⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠫⡅⠀⣧⢄⡀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⠗⣹⡇⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⣴⠋⠀⠈⠱⠿⣿⣿⣿⣿⣿⣿⣿⣿⣸⢸⣿⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠦⣀⠀⠀⠻⣿⣟⣛⣿⣿⣛⣻⣭⣟⡑⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢴⠁⠉⠉⠛⠛⢹⠉⠀⠀⠑⠾⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠈⠉⢹⡦⠄⠤⠷⢄⣀⠀⠀⢀⡵⠦⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣄⣉⣉⣸⡗⠒⠒⠒⠈⣹⠑⠲⠼⠧⢄⣀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠄⠀⠀⠀⠀⠀⠀⠐⣇⡠⠃⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⢀⣰⣆⠀⠀⠀⢸⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣋⡋⠹⡇⠻⡒⠚⢋⠽⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⡇⠀⠹⡀⠀⠀⠑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⣀⠜⠀⠀⠀⢇⠀⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠉⠛⠉

⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⡰⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⡀⠈⠀⡀
⠀⠐⢆⠀⠀⠀⠀⠀⠂⠀⠀⠘⢎⠘⠁⠈⠂⡺⠃⠀⠀⠐⠀⠄⠀⠁⠀⠀⠀⠀⠀⠠⢤⣤⣿⣦⣴⠒⠀⠀⠤⠀⠘⠀⠈⠁⠀⠄
⠀⠀⠀⠁⠀⠀⠀⠅⠀⠀⠀⠀⠀⡅⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠀⠀⠀⣽⠿⢿⡀⠀⠀⠀⠀⠀⠚⠀⠈⠂
⠀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠀⠀⠸⠀⠁⠈⠙⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠐

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⣴⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⡞⠿⡈⢜⡵⠂
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⠊⠿⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⡀⠀⠠⡇⣀⣀⣀⡀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⣀⣀⣄⠂⡀⡀⠀⠀⠀⠀⠀⠀⠻⠀⢀⡀
⠀⠀⠒⠒⠒⢲⠆⠙⠒⠒⠀⠀⠈⠛⢓⡟⢭⡄⠀⠀⠀⠀⠀⠐⢀⡀⠂⠀⠀⠀⠀⠀⠈⡹⢿⣶⡁⠀⠀⠀⠀⠀⠀⢀⠀⣶⠋
⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⢳⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠀⠈⠙⠂⠀⠀⠀⠀⠖⠉⠀⠺
⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢂⡀
⠀⠀⠀⠀⠀⠁⠀⠀⠀⠑⠀⢀⡀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⣠⢷⡀⠀⠀⠀⠀⠀⠠⠟⠃⠀⠛⠂⠄
⠀⠀⠀⠂⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠒⠲⠶⠞⡏⠉⠁⠒⠀⠀⠈⢻⣅⣀⣽⠛⠁⠀⠀⠀⢹⡆⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠸⠉⠀⠙⠀⠀⠀⠀⠀⠠⠐⠾⠿⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

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

⣿⣿⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠁⠀⠀⡈⢻⣿⣿⣿⠁⠀⠀⠀⠉⠀⠀⠀⠀⠀⠉⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠁⠀⠀⡈⢻
⠉⠙⠂⠓⠀⠀⠀⠀⠀⠀⠀⠈⠀⠋⢩⠉⠃⠀⠀⠀⠀⠀⠀⣀⠀⠀⠁⠘⠋⠉⠙⠂⠒⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⢩⠉⠃⠀⡀⠀⠀⠀⠀⣀⠀⠀⠁⠚
⠀⠀⠀⠀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄
⠀⠀⠀⠀⠠⢶⣾⣿⣷⡶⠀⠀⠀⠀⠀⢀⠀⠀⠀⠰⣶⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠠⢶⣾⣿⣷⡶⠀⠀⠀⠀⠀⢀⠀⠀⠀⠰⣶⣿⣿⣿⠂
⠀⣀⠀⠀⠀⢠⡿⠿⢿⡄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠸⠿⠿⣿⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢸⡿⠿⢿⡄⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠸⠿⠿⣷
⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠐⠃⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠃⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐
⣧⣀⣀⠀⠀⠀⠀⠈⠀⠀⢀⠀⢀⣠⣿⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣧⣀⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⣠⣿⣆⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⣿⣿⠃⠀⠀⠀⠀⡀⠀⠀⠀⠈⠻⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠉⠀⠘⢻⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠉⠀⠘⢻
⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠿⠛⠛⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠘⠛⠛⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠛⠛⠧⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠘
⠀⠀⠀⠀⠀⣤⠀⣄⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈
⠁⠀⠀⡀⠠⣤⣼⣿⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣷⣤⠄⠀⠀⠀⠈⠁⠀⠀⠀⠀⣤⣼⣿⣶⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣿⣷⣤⠄
⠀⠀⠀⠀⠀⠈⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⣻⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡁⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⣿⣿⣿⣏
⠂⠀⠀⣤⠀⠀⠀⠀⠈⠁⠀⠀⠀⠃⠀⠀⠠⠀⠀⠀⠉⠠⠀⠉⠀⠀⠀⠀⠀⠂⠀⠀⣄⠀⠀⠀⠀⠈⠁⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠉⠠⠀⠉
⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⡀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⣰⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡀⠀⠀⠀⠰
⣿⣿⠟⠀⠀⠀⠴⠀⠀⠀⠀⠀⠶⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠆⠀⠀⠲⣾⣿⣿⣿⠟⠀⠀⠀⠤⠀⠀⠀⠀⠀⠶⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠆⠀⠀⠲⣾
⠿⢿⡀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⢸⡿⠿⢿⡄⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠿⠿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣸
⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⢀⠀⠂
⠀⠀⠀⠂⠀⣀⣰⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣧⣤⡄⢀⠀⠀⠀⠀⠀⠀⠂⠀⣀⣰⣿⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⣧⣤⡀⢀
⠀⠀⠀⠀⠀⠙⣿⣿⣿⠋⠀⠀⠀⠀⠀⠰⠄⠀⠀⠈⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⣿⠋⠀⠀⠀⠀⠀⠰⠄⠀⠀⠈⢻⣿⣿⣿
⠀⠒⠀⠀⠀⠘⠋⠉⠙⠃⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠀⠀⢀⠀⠀⠀⠒⠀⠀⠀⠘⠋⠉⠙⠃⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠀⠀⢀
⡄⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⣴⡐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⣴⡀
⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣾⣿⣷⣶⠆⠀⠀⠀⠀⠀⠀⠤⠀⢠⣴⣾⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠠⣴⣾⣿⣷⣶⠆⠀⠀⠀⠀⠀⠀⠤⠀⢠⣤
⣿⣿⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠈⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠉⠀⠀⠀⠀⠀⠠⠀⠀⠀⠁⠈
⠀⠀⠀⠀⠀⠘⢠⣷⣀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣼⣆⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠚⢠⣷⣀⡀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⣼⣆
⠀⠀⠀⠂⠀⠻⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢠⠀⠚⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠂⠈⠻⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⢠⠀⠚⣿⣿⣿⡿⠃
⡀⠀⠀⠀⠀⠀⠛⠛⠻⠇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠿⠛⠛⠷⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠛⠛⠻⠇⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠿⠛⠛⠷
⡄⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠈⠀⠀⢀⠀⠈⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠀⠀⢀⠀⠈
⣿⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣦⣤⠀⠀⠈⠀⠀⠀⡀⠀⠀⣀⣤⣾⣿⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣦⣤⠄⠀⠈⠀⠀⠀⡀⠀⠀⣀⣤

⠀⠀⠀⢹⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠚⠻⠶⠶⣤⠀⠀⣀⣤⣤⣽⣦⡀⠀⠀⠐⠛⠻⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⡿⠟⠷⠀⠀⠀⠀⡀
⡶⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡷⠶⣴⠞⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣄⣠
⠃⠀⠀⠀⠀⠀⠀⠀⠠⣼⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠻⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠘⠷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⣿⣿⣿⣿
⣷⡀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⣄⢀⣀⠀⠀⠀⠀⠀⣰⣶⡀⠀⠀⠀⠀⢰⣄⣠⡤⠀⠀⢠⣾⣁⣀⡀⠀⣤⠶⠞⠛⠀⠀⠀⠀⠀⠐⠻⠿⣿⣿⣿⣿
⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⡀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⢴⣿⣿⣿⣇⠀⠀⠉⠉⠉⠉⠻⣴⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⠋
⠀⠀⠀⠀⠀⢸⡷⣄⡀⠀⠀⢀⣀⠀⠀⠀⠹⡟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠉
⠀⠀⠀⠀⠀⢸⡇⠈⠻⠞⠛⢹⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⢿⣦⣄
⠀⠀⢀⣤⠶⠋⠀⠀⠀⠀⠀⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣶⣶⡿⢻⣧⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⣸⡷⣾⡟⠁⠀⠀⠀⢀⣷⣧
⠀⠀⠉⠛⠶⢤⡄⠀⠀⠀⠀⠹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⢀⠀⣼⠿⠋⠀⠀⠀⠀⠀⢠⣄⣀⡀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⣷⢀⣴⠛⠛⠛⠛⠃⠀⠀⢠⣄⠀⠀⠀⠀⡾⠿⠛⢿⣿⠀⠀⠀⠀⠀⠀⠐⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⡀⠀⠀⠀⠀⠀⢹⠟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡄⠀⠀⠀⠀⠈⠟⠀⠀⠀⠀⢀
⣷⣶⣶⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⡀⠀⠀⠐⣶⣶⣶⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⣀⣼
⣀⣿⣏⠀⠀⠀⠀⠀⠀⠀⢤⣼⣷⡶⠀⠀⠀⠀⠀⠀⢀⣴⣷⣤⠀⠀⠀⠀⠀⠀⢸⡏⠻⢦⣤⣴⠶⢿⡇⠀⠀⠀⠈⣻⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠛⠿⣿
⠟⠻⠿⠄⠀⠀⠀⠀⠀⠀⠀⠿⠛⠇⠀⠀⠀⠀⠀⠀⠀⠽⠟⠷⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⢠⣿⣿⠿⣿⣿⡇⠀⠀⠀⠀⢀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠋⠀⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠈⠁⠀⠀⠈⠙⠃⠀⠀⠀⢲⣿⡷⠀⠀⠀⠉
⠀⠀⠀⠀⢰⣤⣆⠀⠀⠀⠀⠀⢀⣀⣀⣀⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⢶⡄⠀⠀⣠⣤⣤⣽⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⠀⠀⠀⠀⠈⠙⠁⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣶⣦⡄⠀⠀⢰⣷⡆⠀⠀⠀⠀⠈⢷⣀⣼⠋⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠘⡿⠁⠀⠀⠀⠀⠀⠀⠀⠽⢿⠃⠀⠀⠀⠠⣤⣴⢿⣆⡀
⢀⡾⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣧⣤⡿⠋
⠉⠁⠀⠙⠛⣶⠶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣤⡾⣷⣀⠀⠀⠀⠀⠀⢤⣾⣿⣶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠙⠃⠀⠀⠀⠀⠘⢿
⠂⠀⠀⠠⡟⠁⠀⠀⠀⠀⣰⣄⠀⠀⠀⠀⠀⢠⣄⣀⡄⠀⠀⠀⠀⢸⣷⣀⣼⡟⠋⠀⠀⠀⠀⠀⡿⠟⠿
⠶⠛⠳⢶⣧⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⣠⣿⣿⣧⡄⠀⠀⠀⠛⠉⠙⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⢀⡀⡀⠀⢀
⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣶⣤⣶⣿⡇⠀⠀⠀⠀⠀⠼⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣄⡀⣀⣴⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⢶⠆⠀⠀⠀⠀⢸⣿⠉⠁⠻⣷⣤⡀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠿⠆⠀⠀⠀⢸⣿⠿⢿⣿⡀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⢠⣤⣤⣾⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⣶⣤⣿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣄⣴⣿⣿⠦⠀⠀⠀⠀⠀⠘⠻⠋⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡏
⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡿⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⢀⣠
⣾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⣿⠷⣤⣀⣀⣤⣶⡇⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠙⢻
⠀⠉⠀⠀⢀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⣿⠀⠈⠉⠉⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠈⠿⠿⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⣀⣤⣿⣦⣤⠀⠀⠀⠐⠛⡟⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠀⣻⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⠃
⣿⣿⡿⠻⠟⠿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠶⠤⠤⢤⣤⣤⣤⣀⣀⡀
⠀⢀⣀⣤⡴⠶⠚⠛⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠳⠦⣄⡀
⣴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻
⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⢦⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⠆⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼
⠀⠹⣦⡀⠀⠀⠀⠀⠀⢀⠉⠒⠀⣠⠶⠶⣄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⡴⠶⢦⡀⠐⠋⢁⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠈⠻⢦⡀⠀⠀⠀⠈⠁⠀⣼⣧⣤⣤⣸⡆⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣮⣀⣤⣤⣿⡄⠀⠉⠀⠀⠀⢀⣴⠞⠁
⠀⠀⠀⠀⠀⠙⠷⣤⡀⠀⠀⠜⢿⣿⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⣿⣿⣿⠟⠀⠀⢀⣤⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠈⢙⡷⠀⠄⠀⠉⠙⠻⠿⠃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠻⠿⠛⠉⠁⣀⠄⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀
⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠖⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⣄⠀⠀⠀⠀⢀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣤⣤⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠶⠛⠁
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⢀⣸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠘⠀⠰⠀⠀⠅⠀⠀⠀⠀⠀⠀⠀⠒⡀
⠀⠀⠐⠒⢺⣿⣿⠒⠂⠀⠀⠀⠀⠀⠀⠚⠍⡋⡖⠁⠀⠀⠀⠀⠰⢦⡀⠀⠀⣠⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⢤⣿⡤⠶⠃
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠗⠁⠙⠂⠀⠀⠀⠀⠀⢀⡤⠖⠲⣤⠀⠀⠀⠀⠀⢐⠀⠐⠀⠀⡄⠀⠀⠀⠀⠀⢀⡸⠋⠓⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠰⠂⣀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀
⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⠀⠀⢠⣶⠀⠀⣶⠀⠠⠄⠀⠀⠀⢀⡀⠀⠀⠠⠀⠠⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⣤⡀⠘⣧⡶⠂
⠀⠀⠀⠀⢠⠀⠐⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⢠⣦⠀⠀⠀⠀⠀⠀⠀⠛⠃⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠈⠷⢂⣤⣀
⠀⠀⠀⠀⠀⠰⢠⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠠⠀⠂⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⠀⠁⠉
⠀⠀⢀⡀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢨⠀⣴⢄⡀⠰⠏⠀⠀⠀⠀⠀⠀⠈⡤⢐⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣉⡀⡀⠀⠀⠀⣀⣠⣿⣄⡀⠀⠀⢀⡔⠀⠀⠀⠀⢀⠸⡄⣀⡀
⠀⠀⠀⠀⠈⡤⢃⠄⠀⠀⠀⠀⠀⠂⠀⠀⠀⣠⣁⣀⠀⠀⠀⠀⠀⠛⣼⠋⢹⡯⠁⠀⠀⠀⠈⣿⣿⣿⠲⠶⠛⠉⠀⠀⠀⠀⠉⠄⣀⠠⠊
⠀⠀⠠⣖⠄⠈⠛⠀⠿⠂⠀⠀⠀⢀⠀⠀⠠⡁⠀⠀⠀⠀⠀⠀⠀⢀⣯⠟⠣⣷⠀⠀⠀⠀⠐⠋⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠰⠀⠉⠐⠦
⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠰⢀⠂⠀⠀⠒⠀⠀⠀⠀⠀⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠀⣀⡀
⠀⠀⣀⣸⣧⣠⠀⠀⡈⠀⡈⠁⠀⠀⠲⠂⠂⠀⠃⠠⠂⠀⠀⠀⠠⠤⣶⢖⣚⡚⠋⠀⠀⠀⢀⢀⢐⠀⡀⡀⠀⠀⠀⠀⠀⠐⠲⣾⣿⣿⡿⠋
⠀⠀⢉⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠀⠀⠀⠀⠀⠀⢠⣭⠉⠩⠷⡀⠀⠀⠀⠀⠨⠛⣓⠁⠀⠀⠀⠀⠀⠀⠀⠀⣾⠟⠻⣿⡀
⠀⠀⠈⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⢀
⠀⠀⠀⠀⠀⠀⠐⠁⠐⠇⠀⠀⠀⠀⠀⠀⠀⠈⠄⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⣀⣀⢸⡿⢀⣤⠄⠀⠀⠀⠀⠀⠁⠀⠀⠈
⠀⠀⠄⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⠀⠈⠡⠀⡀⠐⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣾⢻⣏⠉⠀⠀⠀⠀⠀⠈⢁⠀⢀
⠀⠀⠀⠀⡄⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠸⠃⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠡⢀⢀⡀⠀⠀⠀⠀⣤⡤⠉⠓⣰⡆
⠀⠀⢀⠀⠒⡨⠓⡀⠀⠀⠁⠀⠀⠀⠓⢶⠈⠘⢣⠼⠃⠀⠀⠀⠀⠀⡈⠀⠀⡀⠀⠀⠀⠀⠀⠉⢡⠀⠀⠀⠈⠀⠀⠀⠀⢀⣵⢀⠤⣄⣣⡀
⠀⠐⠊⠠⠉⠀⠘⠋⠁⡈⠀⠀⠀⠀⠀⣌⡵⠾⢽⡄⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠊⠄⠀⠀⠀⠀⠈⠛⠁⠀⠈⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⠿⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠏⠀⠀⠀⠙⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠁⠀⣠⡖⠀⠀⠈⢻⣷⡀⠀⠀⢀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠁⠀⣴⠟⠀⠀⠀⠀⠀⢻⣷⡀⠀⠈⠛⠁⠀⠀⢀⣴⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⠂⠀⢀⣾⡟⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⢾⣿⣿⣿⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣀⠀⠀⠀⠀⠸⠿⠁
⠀⠀⠀⣀⣀⣠⣤⣤⣶⣶⡾⠿⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⠿⢷⣶⣶⣦⣤⣤⣀⣀
⢠⣾⠿⠟⠛⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠻⢿⣶⡀
⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷
⠹⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠃
⠀⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠃
⠀⠀⠈⢻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠠⣿⣷⠀⠀⠀⣤⡀⠀⠀⠀⠀⠀⣠⡄⠀⠀⢼⣿⡆⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⢀⣶⣄
⢀⣠⣶⡀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠈⠀⠀⠀⠀⠹⣷⣤⣀⣀⣤⣴⠟⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⢿⣿⣿⣿⡿
⠈⢻⡟⠋⠀⠀⠀⠀⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠀⢿⠿⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⢠⣄
⠀⠀⢠⣄⠀⠀⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠈⠁
⢠⣶⣿⣿⣶⡄⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆
⠀⠈⢿⣿⠉⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⡿⠟⠛⠻⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⢠⣄
⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⢀⣠⣤⣶⠿⠟⠋⠁⠀⣠⡀⠀⠀⠈⠙⠻⢿⣶⣤⣀⡀⠀⠀⠀⣼⡟⠀⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣶⡿⠿⠛⠉⠀⠀⡀⠀⠀⠘⢿⡿⠃⠀⠀⠀⠀⠀⠈⠉⠛⠿⢷⣶⣾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣾⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣦

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣆⠀⠀⢀⡀⠀⠀⠀⣸⠇⠀⠀⣿⠀⠀⠀⠀⢀⡶⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⣷⡀⠀⢀⡿⠀⠀⠀⢹⡆⠀⠀⠀⡾⢁⣴⠋⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠙⢦⠘⠃⠀⣼⠃⠀⠀⠀⠀⣷⠀⠀⠀⠁⠘⠁⠚⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠶⠀⠀⢠⡏⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣠⣤⣤⠴⠚⠁⠀⠀⠀⠀⠀⠀⠈⠤⠤⠴⠶⠶⠶⠶⠚⠛⠛⠛⠋⠉⢉⣩⡽⠟⠋
⠀⠀⠰⢶⣾⡛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠁
⠀⠀⠀⠀⠉⠛⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠉⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣀⡈⠙⠳⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠁⠀⠀⠴⠞⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣙⣛⣃⡀⠉⢛⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣄⠀⠀⠀⠀⠘⠛⠛⠛⠶⠶⠶⠶⢤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠉⠉⢉⣤⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⢀⡙⠳⣦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠋⠀⣸⠇⠀⠀⠀⠀⠀⣠⡶⠠⣄⡀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠈⠉⠀⠀⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⢠⡟⠀⠀⠀⠀⣠⠞⣡⠄⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⣾⠁⠀⠀⣠⠞⣡⡾⢣⡾⣠⢰⣆⠀⠈⠛⢶⣄⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⣠⠞⠁⠴⠋⠀⠀⠀⣿⠀⠛⠀⠀⠀⠀⠈⠻⣦⣀⠀⢹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⡹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡞⢙⡆⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⡿⡼⠉⠹⡄⠀⠀⠀⢠⠶⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢳⡀⠀⠹⡄⠀⠀⣸⡦⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣉⣷⠀⠀⠀⠀⠀⠀⣼⠀⠀⢳⡀⠀⠹⣤⠞⠁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⡉⠓⠤⣄⡀⡼⡏⠀⠀⠀⢳⣠⠞⠁⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠉⠛⠃⠀⠀⠀⠀⠁⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⣀⣀⣀⣤⡤⠤⠴⠖⠒⠚⠻⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠟⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⢀⣀⣀⣀⣤⡤⠤⠴⠶⠒⠒⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠒⠲⠶⠤⠤⣤⣄⣀⣀⣀
⣞⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⢙
⠈⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊
⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣍⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣍⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊
⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠀⠀⠀⢀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠙⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢤⣀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⢀⣠⠴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠲⢤⣀⠀⠀⢷
⣤⣤⣤⣤⣤⣤⣤⣤⣬⣷⣾⣭⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣬⣽⣶⣯⣤⣤⣤⣤⣤⣤⣤⣤
⣿⣿⣁⣅⣅⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣴⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡀
⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣽⡛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆
⠀⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣷⠀⠈⠉⢉⠉⠀⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣁⣀⣈⠉⠉⠉⠉⠙⠛⠛⠛⡉⢉⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣀⣀⣀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠆⠛⠂⠄⠠⠄⠀⠀⠀⠨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏
⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⢀⣤⡀⠀⠀⠠⡀⢰⣤⣐⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡟⠀⠀⢀⣶⣿⡟⠁⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢠⣾⣿⡿⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⠏
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⠀⠀⠀⣾⣿⣿⣿⠃⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢰⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠙⠛⠛⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠉⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⡒⢒⣶⣦⣼⡇⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⡔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢉⣀⣤⣤⣤⣤⣀⡉⠻⣆⠀⠀⠀⠀⠀⠀⠀⠙⠂⠐⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣡⠞⠋⣽⣿⣿⣿⣿⣿⣿⣷⣌⣇⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⣿⢡⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣻⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠟⠋⡽⠳⠯⠭⣉⣋⠭⠽⠞⢏⠙⠻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⠀⡸⠁⠀⢀⣀⣀⣀⣀⡀⠀⠘⡆⠀⢹⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⡜⠣⠤⢤⠁⠀⠀⢠⠀⢹⠤⠤⠞⢢⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣥⣄⠀⢹⡗⠒⠺⣆⢀⡘⢺⠂⣺⠒⠒⢻⡉⠀⣠⣬⣆
⠀⠀⠀⠀⠀⠀⠀⢀⠴⡪⠁⠀⣹⠗⣿⢳⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⡏⣿⠺⣏⠀⠈⠕⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠻⢾⡶⠋⠉⠁⠀⢻⣼⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⣇⡟⠀⠈⠉⠙⢶⡷⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣀⣀⣠⡏⢧⣄⣀⣀⣤⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠈⠉⠈⢹⠁⠘⡍⠙⠋⠁⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠁⠒⠂⡏⠀⠀⢿⠐⠒⠈⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢸⠁⠀⠀⢸⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⣀⣀⣠⠞⠀⠀⠀⠀⠣⣀⣀⣀⠜

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

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⠟⠁⣠⣾⣿⣿⣿⣿⣿⣿⣟⠉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣤⣾⣿⣿⣿⣿⣿⡇⠀⢲⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿
⣿⣿⣿⣿⣿⣿⣴⣿⣿⣿⣿⣆⡀⠀⠙⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷
⣿⣿⣿⣿⣿⣿⣿⣿⡿⢿⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⢉⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡿⢿⡿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣟⣃⠀⠀⢿⣿⣿⣿⠏⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣤⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣉⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣧⣽⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣷⣠⣽⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⡟⠻⢿⣿⣿⣿⣿⣿⣷⣦⣄⣀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢻⣿⣿
⣿⣿⣿⣿⣿⣿⣷⣦⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠉⠉⠉⠉⠑⠒⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⢀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⢀⣤⣤⣤⣤⣀⡀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⡠⠀⠬⠀⠀⠱⠁⠀⠃⠀⠀⡠⣤⢼⠁⠀⠀⠀⠀⣴⠟⢉⣽⣿⣿⣿⣿⣷⣦⡀⢸
⠀⠀⠀⠀⠀⢂⡀⠀⠁⠀⠈⠀⠈⠂⠀⢘⡜⠉⢻⠀⠀⠀⠀⣼⠃⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶
⠀⠀⠀⠀⢀⠀⠀⠈⠀⠀⠀⠀⠀⠶⠤⢾⡇⠀⢸⡀⠀⠀⢰⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠁⠒⠈⠡⡀⣀⠠⠀⠀⠀⡰⠓⢴⠉⢣⡀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢫⠃
⠀⠀⠀⠀⠀⠀⠀⠀⣜⡗⠉⢣⠀⣠⠞⠁⠀⠀⠳⡀⠑⢄⠘⠿⣿⣿⣿⣿⣿⣿⣿⡿⢟⠕⠁⠀⢀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⢋⡽⣦⡀⠀⠀⠀⠈⠢⣄⠙⠲⠬⣙⣛⣿⣿⣯⠭⢞⣁⠀⢀⠤⠏⠀⣸⠤⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠑⢵⡢⠖⠋⠈⠃⠉⠀⠀⠀⠀⠀⠈⠙⠲⠤⣄⣀⣀⣠⠟⠚⡆⠀⠉⠻⠀⠀⠀⢱⣀⣀⣠⡃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠁⠉⠀⠀⢈
⠀⣀⣀⣀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠤⠤⡴⠞⢀⣀⠤⢆⠀⠀⣀⠀⠉⣹⠁
⢀⣿⠏⠀⠙⠒⠒⠋⠿⣷⣄⠀⢀⠠⣤⡀⢳⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠙⠉⠁⠀⠀⠀⠉⠉⠀⠉⠉⠁
⢸⣿⠀⠀⠀⠀⠀⢰⠀⠀⠀⣊⠄⠈⠀⠈⡿⠀⠀⠀⠀⠀⠀⠀⣠⠎
⣼⣿⠀⠀⠀⠠⡠⠈⡀⠀⠈⢇⠀⠀⣀⣔⠁⠀⠀⠀⠀⣀⡤⠚⢇
⣼⡏⠀⠀⡪⣳⠓⠧⣽⠖⠲⠒⠓⠋⠁⠈⣉⡿⠟⠛⠛⢿⡄⠀⢸
⣿⡇⠀⠀⠑⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠙⣄⠀⠀⠀⠈⢳⠆⠊
⣿⡇⠀⢀⡜⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠁⠀⠈⠓⠄⣀⣠⠊
⠙⠛⠒⠉⠀⠀⠀⠀⠀⠀⠀⢾⣷⡀⠀⠀⠀⠀⡴⢅⠶⠚
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣄⠀⠀⠀⠪⡽⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⡀⠀⠉⠈⢧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⡀⠀⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣶⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⠀⠀⠀⠴⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠄⠀⢀⡤⠒⠦⣄⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢀⣄⠀⠀⡠⠴⠦⢄⣠⠔⠉⠀⠀⠀⠀⠑⢦⣴⠤⣄⢀⠴⠲⢄⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⢳⡀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⣔⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠄
⠀⠀⠀⠀⠀⠀⠀⣏⠙⠒⠦⠤⣄⣀⣀⣀⣀⠀⡀⠀⢀⣀⣀⣀⣀⣀⣤⠤⠴⠒⠋⢹
⠀⠀⠀⠀⠀⠀⠀⢸⢀⠀⠀⠀⠀⠐⠀⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠐⠂⠀⠀⠐⢸
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠀⠀⢀⡤⠦⠀⠀⠀⠂⠀⠀⠀⠂⠀⠀⠖⠲⢤⠀⠘⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠋⣠⡤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣤⡖⢶⣄⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⣼⣿⣶⣿⣷⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠆⠀⢰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠘⠿⣿⡿⠋⠀⠀⠠⠤⠀⠀⠈⠛⠿⠿⠋⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠮⠭⠆⠀⠀⠀⢻⣶⣶⣿⠀⠀⠀⠐⠫⠌⠃⠀⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡞⢇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠐⠁⠀⠀⠀⠀⠀⠀⠀⢰⠁⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣄⣀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⢀⠁
⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠊⠀⠀⠙⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡗⠒⢤⠤⠤⠤⠤⠤⢤⠔⠒⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠁⠀⠀⠀⠀⠀⠀⠑⠚⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠄⣤⠔⠉⠉⠉⠑⢤⡄⠤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡿⡣⣴⣶⣶⣶⣶⣤⡻⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣻⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡗⡍⠁⠀⠀⠂⠀⠉⡛⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣮⡑⠒⠀⠐⠒⣩⣾⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠯⡉⠉⠙⠝⠫⠭⠉⠩⠭⠛⠙⠉⠉⣩⣝⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠈⠆⢹⡄⠁⡠⠤⠤⠤⠤⠤⠤⡄⣦⣸⠨⣿⣾⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠈⠠⣼⣧⠀⡂⠀⠀⠀⠀⠀⠀⡁⣾⣟⠀⢙⣿⣡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠈⣻⣿⠃⠀⠈⠖⠀⠤⠄⠐⠎⠀⢿⣿⠀⠩⣿⣮⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⣰⣾⣿⣿⢀⣾⡷⠠⣀⠀⢀⡠⢰⣿⣿⣿⣧⡀⠘⠽⣿⣟⡄
⠀⠀⠀⠀⠀⠀⣀⢌⡀⣀⣤⣿⡿⠙⣿⣿⠋⣄⣠⠉⠋⠋⢡⣀⡌⢻⣿⡟⠱⣀⠈⠸⢻⣯⠄
⠀⠀⠀⢀⡤⠐⠋⠑⣮⣿⣵⠗⠚⢉⣩⣿⣶⣦⣤⣤⣤⣤⣤⡴⢒⡋⠉⠉⠙⠲⠷⣄⢠⠖⠉⠓⠤⣄
⠀⠀⠀⣎⣴⠖⠂⢠⣿⠟⣁⣶⡻⢷⠿⠗⠤⠠⡴⠲⠖⠋⠑⠬⣻⢿⣿⣿⣷⣶⣤⣬⢿⡆⠀⠒⢶⣌⡆
⠀⠀⣔⣇⡱⣡⠆⡼⣁⠤⢐⣂⡹⡎⣆⠀⡄⡀⡀⢠⣀⣄⣄⡀⠈⠑⢯⡢⡀⢀⠀⠈⠳⡽⡄⢦⡱⣁⣗⡄
⠀⠀⠀⠘⠒⠻⣎⣞⣵⣫⡌⣶⣶⣷⣼⣿⠿⢿⢿⣛⠿⠭⠛⢧⠀⢠⣿⣿⣿⣾⣶⣴⣶⣧⣼⣾⡟⠚
⠀⠀⠀⠀⠀⠀⠹⣿⢿⣛⣃⡯⣽⣣⠵⠒⠚⠉⠉⠀⠀⠀⠀⠀⠑⠾⠿⠿⠛⠻⠭⢽⣛⣩⠿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠶⣶⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⢸⣿⣿⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡈⢻⣯⣿⣿⣿⣿⣿⣿⣿⣿⡗⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠘⢇⡽⢻⠿⠿⣿⠿⠻⣫⡿⠁⣿⣠⠀⠤⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠃⠀⢀⣞⠘⣿⡇⠙⠶⠖⢠⠀⢶⠟⠁⢸⣽⣿⣿⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣠⡞⡯⠀⣄⣀⣀⠀⠀⡘⣶⡘⠀⠀⡀⣼⣿⣿⢠⡄⠈⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢆⠀⠀⣰⣅⣽⠀⠀⠀⠀⠀⣤⠘⡇⢻⠃⠀⠀⠀⢀⢀⣿⣿⠁⢀⣼⠛⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠈⢫⣹⣿⡯⣍⣉⡁⢰⠇⠀⢹⣿⠃⠈⠉⠉⠉⢉⣿⣿⡶⠋⠁⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠖⢲⣻⣶⣿⠏⠀⢸⡍⠹⠃⠀⠀⠈⠁⢠⣦⣿⣿⣿⣿⣿⣿⠀⣀⣠⣤⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠉⣿⡟⠀⣧⡘⣧⠀⠀⠀⢀⣶⠀⠈⠡⢿⣿⣿⣿⣿⡇⣺⣭⣤⣬⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢀⡐⣿⠁⠀⠀⠹⢄⠀⠀⠀⢸⡷⠤⠐⢰⣿⣿⡿⠿⣿⠇⠘⠀⠀⢰⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⣀⠉⠁⠀⠀⠃⠀⣮⣿⡆⠀⠀⠒⠚⢻⣿⠿⠋⠀⣰⡟⠀⠈⠁⠐⢾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣉⢹⡈⠀⠀⢀⠀⣤⣿⣷⡁⢦⡀⠐⣴⠞⠁⣠⣴⣾⣿⣿⠀⣰⡷⠞⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠘⠃⠀⠀⠄⠤⠽⠻⠿⢷⣀⣏⢹⣧⣴⠞⠁⠀⠀⣠⢶⠀⠛⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⣹⡟⠁⣈⡉⣉⡉⠁⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⡍⠀⢠⣿⡧⣿⠁⠀⠀⠀⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⢘⣿⠀⠏⠀⠀⠙⠛⠛⠃⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠺⠏⠀⢠⠀⣀⣀⠀⣀⣀⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣳⣿⠀⠀⢈⡛⠻⠿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⣄⣐⣿⣿⢿⣆⠀⠀⠉⠉⠛⠛⢋⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡙⠻⣷⣶⣾⣿⠀⡄⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⡙⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣾⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⣽⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢿⣿⣿⠇⠀⠀⠀⠀⣶⣦⣤⣴⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⠿⠿⠛⠀⠀⠀⠀⠀⢸⣿⢿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠿⠿⠟⠃


⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠉⠉⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢰
⠀⠀⠀⢠⠔⠒⠒⠒⠒⠁⠀⠀⠀⠀⠀⠓⠒⠒⠒⠢⢄⠀⠀⠀⠀⠀⢀⠖⠉⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠑⢆
⠀⠀⠀⡇⠀⠀⠀⣴⣖⡄⠀⠀⠀⠀⠀⣴⣖⡄⠀⠀⠈⡆⠀⠀⠀⠀⠘⡄⠀⠀⠀⠾⣷⠄⢀⣀⡀⡀⠀⣾⡷⠀⠀⠀⡸
⠀⠀⠀⠘⠢⣀⠀⠘⠛⠁⠱⢄⣀⡴⠁⠘⠛⠁⢀⡠⠞⠀⠀⠀⠀⠀⠀⠈⠓⢄⡘⠛⠀⠀⠀⠀⠀⠀⠀⠀⠘⢛⠤⠊⠁
⠀⠀⠀⠀⠀⠈⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⠴⠢⣀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡀⠀⠀⣠⠔⠉⠑⢤⡀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠑⠤⠄⠊⠁⠀⠀⠈⠑⠠⠤⠚⠀⠀⠀⠀⢀⡀⢀⡀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠈⠁⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠒⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⢈⠆⠀⡄⠤⠤⢤⠀⠶⡁⠀⠀⠀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⣄⠚⠃⠀⠀⠙⠂⠒⠁⠀⠀⠚⢃⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⣀⠔⠊⠢⢄⠀⠀⠀⣠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠊⠁⠀⠀⠀⠀⠑⠒⠊⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣯
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⣿⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠀⠙⢛⣿⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢃⣠⡀⣿⣿⡿⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣷⣦⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣾⣿⣿⣿⠿⠿⠋⠀⠘⠿⠿⢿⣿⣿⣦⣀⣀⣀
⢀⣀⣀⡤⠠⣤⣴⣶⣶⡒⠃⠀⠛⢻⣿⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⠟⢿⣿⣿⣿⣷⡶⠶⠀⠤⢤⣤⣄⣀
⠀⠙⢿⣷⣤⣿⣿⣿⣿⣿⢀⣀⠰⣿⣿⣿⡿⠻⢿⣿⣿⣿⡇⠀⣀⡀⠀⣿⣿⣿⣿⣿⡦⢀⠠⣾⣿⣿⣿⣷⠄⠀⠀⣾⣿⣿⠟
⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣀⢰⣿⣿⣿⣶⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣶⣿⣶⣿⠟⠁
⠀⠀⠀⠀⠀⠙⢿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠙⠍⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣈⣿⣿⣿⣿⣿⡿⠉⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣿⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡁⠀⠀⠀⢉⣽⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠿⠿⠃⠀⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣀⡀⢿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠀⢀⣀⠀⢸⣿⣿⣿⣿⡋⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣶⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣄⣸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠋⠀⠙⣻⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣿⣿⣿⣟⠉⣿⣿⣿⣿⠿⠋⠉⠻⢿⣿⣿⢀⣀⡐⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣿⣿⣿⡿⠻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠻⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠆⣀⢰⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠗⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⣧

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⣀⣴⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⢻⣿⠟⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣶⣮⣽⣿⣶⣤⣄⣀⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿
⠀⠀⠀⠀⠴⠶⠶⠿⠿⠷⣶⣤⣴⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣦⣄⡀
⠀⠀⠀⠀⣀⣀⣠⠶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣆⣠⠄
⠀⠀⠘⠛⠛⠛⢛⣋⣩⣿⣿⣿⣿⣿⠿⢿⣿⣿⣿⣥⣤⣿⣿⣿⣿⣿⡙⢿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡷⠦
⠀⠀⠀⠺⠿⠿⢛⣻⣭⣭⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠈⠁
⠠⠶⠶⠶⠾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⢀⣸⠟⣋⡽⣿⣟⣋⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⣠⠟
⠀⠀⣀⣠⠤⠾⣿⡿⠋⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⢀⣀⡴⠋
⠒⠋⠁⠀⠀⠾⣯⣰⣿⣿⠿⢟⣛⢋⣭⣽⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⣰⣾⣿⣿⣧⣟⣣
⠀⠀⠀⠀⠀⢈⠿⢛⣭⣷⣟⣫⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⣠⣴⣿⣿⣿⣿⣿⣿⡷⠆
⠀⠀⠀⠀⣠⣴⣞⡫⠭⢟⣿⣿⣯⡿⢟⣿⢿⣯⣿⡿⠛⠉⠋⠈⣿⣿⣿⡿⠃⢀⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠈⠉⠁⠀⠀⢰⣿⣽⣿⠽⣶⡿⣧⠟⣫⣿⣿⣿⣿⣷⣄⠀⢉⣱⣶⣶⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠀⠀⠀⣠⡼⢿⡻⠞⠛⠁⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⢾⣯⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢸⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣥⡴⠋⣿⢿⣿⣿⣿⣿⣿⣿⡿⠃⠸⢿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠙⠳⠚⠳⠋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⣰⠋⣥⠉⣿⢁⣭⣿⡏⠉⢿⡏⣩⣹⡏⢹⡉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠀⠀⠀⠀⠀⠀⢰⣿⠀⡀⢺⣿⠠⣴⣿⢁⣁⠸⡇⢹⣿⡇⢈⠀⣿⡆
⠀⠀⠀⠀⠀⠀⠀⣠⣴⡏⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣶⣿⣶⣿⣶⣶⣿⣾⣿⣷⣷⣶⣾⣷⣾⣷⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠙⠋⠋⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⠛⠛⠛⢻⡟⢻⡟⢻⣿⡟⠻⣿⠛⠛⠛⢻⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠂⣾⣿⡇⠸⠇⢸⡿⠠⠄⢹⣿⡆⢸⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⠀⣿⣿⠅⣰⡆⢸⠇⣰⣦⡀⣿⡇⢸⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⡿⠛⣩⣽⣯⠉⣭⣽⡟⢹⣿⠏⣭⠉⢻⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣷⡤⢉⣿⣿⠀⣿⠋⣀⠀⣻⠀⣄⡒⠿⢿⣿⣿⣿⡿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣯⣴⣿⣿⣿⣴⣿⣶⣿⣶⣿⣶⣿⣿⣷⣶⡿⢻⡿⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⣿⣯⡼⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣏⣹⢿⢉⡽⣏⣹⠿⡭⠟⠻⣤⠾⠳⣾⡟⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠈⣿⡆⠀⠀⠀⣀⣀⣀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣾⠃⠀⠀⠀⠘⠿⠾⠿⠛⠛⠛⠉⣉⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣶⡿⠛⠛⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⣴⡿⣦⡀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⢠⡾⠋⠀⠙⢿⣦⡀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢀⣴⠟⠁⠀⠀⠀⠀⠙⠿⣦⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣷⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠏⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢶⣄⠀⢼⡟⢻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀⠀⠹⣆⠙⢧⡘⣿⡀⢻⣇⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡉⠛⢦⡄⢹⡇⠘⢿⣿⡇⠈⣿⣼⡿⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⣾⣿⡆⣼⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢻⣦⡈⠙⠻⠗⠀⠈⠻⠃⠀⢻⡿⠃⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⣧⣿⣿⣷⣿⢿⣷⠀⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⠛⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏
⠀⠀⠀⠀⠀⢾⣿⣶⣼⣷⡹⣿⡷⠻⠿⢸⣿⣾⠋⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢶⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠈⠻⣦⣙⠛⠃⠀⠀⠀⠀⠘⠻⢃⣼⠏⠀⠀⠀⠀⠀⣀⣄⡀⠀⣀⡀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⢰⡿⢿⣤⣿⢻⣧⣸⡿⣿⡀⠀⠀⠈⢿⡆⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⢸⡏⠀⠀⢀⠈⣿⡈⢿⣿⡀⣿⣿⡇⣿⠃⣠⣄⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⣠⣤⡀⢠⡿⢷⡄⢰⡿⣷⡄⣿⡇⠀⠀⣿⡻⢿⣷⠀⠉⠀⠘⠛⠀⣿⡿⢋⣽⠃⢸⡇⠀⠀⠀⣴⣶⣄⢈⣿⣷⠀⢀⣴⣦
⠀⠀⢀⣤⣄⣿⡉⣿⣸⡇⢸⣧⣿⠃⣿⠇⣿⠃⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⢸⡇⠀⠀⠀⣿⠈⣿⣼⡟⣿⠀⣾⠏⣿⠀⣠⣤
⠀⠀⢸⣏⠹⣿⣇⢹⣿⡇⠸⣿⡟⢰⡿⢀⣿⡀⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⢼⣷⣶⣦⡀⣿⡇⢻⣿⠇⣿⣰⡿⢠⣿⣿⢻⣿
⠀⠀⠀⢻⣦⠹⣿⠀⠙⠁⠀⠉⠁⢸⣷⡾⠛⣿⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⣾⣿⣦⡈⢻⣿⡇⠈⠛⠀⢿⡿⠁⠸⠿⢁⣿⠇
⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠉⣠⣾⡋⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢾⡏⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠏
⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⣠⡾⠋⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠘⣿⠀⠀⠀⠀⢸⣧⠀⠘⢿⡄⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇
⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⣾⠏⠀⠀⣿⡇⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⢸⣿⠀⠀⠈⠛⠷⣦⡄⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⢀⣿⠃⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⢿⣇
⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⢹⣷
⢀⡀⣀⣿⡏⢀⠀⣀⠀⣀⣀⢀⣿⡀⡀⢘⣿⣀⠀⣀⡀⠀⡀⢸⣿⣀⡀⣀⣀⣀⣀⣿⣇⣀⡀⠀⢘⣿⡀⣀⣀⠀⣀⢀⣻⣇⡀⣀⣀⣀⡀⣿⣆⡀⡀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⡀⣧⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣸⣇⣼⣀⣀⡀
⠀⠀⢀⣀⣤⣤⠶⠶⠾⠛⠛⠛⢋⣩⣍⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣉⣉⣉⠉⠉⠉⠉⠙⠛⠛⠶⠦⣤⣀
⣴⠞⠋⠉⠀⠀⠀⠀⠀⠀⠀⣰⠏⠉⠉⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠉⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢳
⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠈⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋
⠀⠀⠀⠀⠈⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⢈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠶⠶⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⠹⣅
⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⢠⡾
⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣤⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠞⠋
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡤⠤⠤⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⢤⣀⣀⡀
⢶⡒⠒⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠒⠒⠢⠤⠤⠤
⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠶⣶⣄⠀⠀⠀⠀⠀⠀⣠⣴⡶⠦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔
⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣴⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⣄⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁
⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠈⠻⠷⠟⠃⠀⠀⠀⠀⠀⠀⠙⠷⠾⠟⠁⠀⠀⠀⠀⠀⠀⡠⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⣀⡾⠀⠀⠀⠀⠀⠀⠀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠴⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠈⠑⠢⣄⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⠀⠸⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠲⢄⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣶⣾⣿⣿⣷⣦⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣇⣠⣤⣴⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠿⠛⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⣼⠿⠛⠋⠁
⠀⠀⢠⣦⡀⠀⠀⠠⣶⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⡦
⢤⣶⣿⣿⣿⣿⡗⢠⣿⣿⣿⣿⢋⣡⣤⣶⣶⣶⣶⣤⣍⡙⠿⡿⠋⣠⣾⣦⡀
⠀⢹⣿⣿⣿⣿⠀⣿⣿⠟⢻⣿⣿⣿⣿⣿⣿⣿⠛⢿⣿⡿⠂⡀⢺⣿⣿⣿⣷⡀
⠀⠘⠛⠉⣉⣉⠀⣿⠏⣰⣿⣿⣿⣿⠟⢋⣉⡉⢰⣄⠉⢠⣾⣿⣆⢹⣿⣿⣿⣧
⠀⠀⠀⢸⣿⣿⣿⡟⢰⣿⣿⣿⡿⢁⣾⣿⣿⠁⣿⣿⠷⠄⠙⣿⣿⡄⣿⣿⣿⣿⡄
⠀⠀⠀⢸⣿⣿⣿⡇⢸⣿⣿⣿⡇⢸⣿⣿⣇⣀⣥⣤⡆⢸⣿⣿⣿⡇⢸⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣇⠸⣿⣿⣿⣧⠘⢿⣿⣿⣿⣿⡿⢁⣾⣿⣿⣿⠃⣾⣿⣿⣿⠃
⠀⠀⠀⠈⣿⣿⣿⣿⡄⢻⣿⣿⣿⣷⣤⣉⣙⣋⣉⣴⣿⣿⣿⣿⠏⣰⣿⣿⣿⡿
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣆⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢋⣴⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⢀⣌⠻⠿⠿⣷⣦⣉⠛⠿⠿⢿⠿⠿⠿⠛⣁⣴⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⣤⣾⣿⣿⡖⢠⣿⣿⣿⣿⣶⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⡿⠋
⠀⠀⠀⠀⠈⣿⡿⠿⠇⠉⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁
⣶⣶⠶⠶⢶⣶⣶⣶⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⠤⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠢⢤⣀⣀⣀⡀
⣠⠤⠶⠒⠒⠛⠋⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠛⠓⠒⠲⠦⢤
⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴
⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣛⡆⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⢀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠈⠱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠁⠀⠀⠀⠀⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢀⡠⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⠀⠀⠈⡇
⣀⣀⣀⣀⣀⣀⣀⣀⣧⣴⣚⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⣲⣤⣇⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣉⣩⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣶⣶⣶⣶⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠈⠐⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⡿⠿⣿⣿⠿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⡀
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠿⣿⣿⡟⠁⠂⠀⠀⠀⢀⡈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢩⡍⠁⠀⠀⠈⢀⠀⢘⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄⣀⠀⠀⠙⠊⢋⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂
⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⢠⡄⠀⠀⠀⠀⠀⠀⠀⠉⠈⣇⢣⠀⠐⢦⡨⠏⠉⢍⣹⠆⠓⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇
⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣼⡄⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡜⠋⠂⠄⠀⠀⠀⠀⠙⠀⣀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⣇⢹⠀⠀⠀⠀⠀⢀⠀⠀⢠⠞⠀⠀⠀⠠⠂⠀⠀⠀⠈⡤⢸⢸⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢸⠀⠈⠀⠀⠀⠀⠀⠀⠀⡑⠢⢀⡴⠀⠀⠀⠀⠀⠀⢃⣀⣴⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠰⠀⠀⠀⠀⠀⠀⣀⢀⣠⠁⠀⡾⣿⣿⣿⣶⣶⣶⣾⣿⣿⣿⠾⠎⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣴⣓⣂⠀⠈⠁⠀⠀⣠⡎⢀⣸⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⠿⢿⣿⣿⣶⣦⣤⣿⡿⣯⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣞⠀⠀⠀⠉⠉⠻⣿⣩⠇⠒⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁
⠀⠀⠀⠀⠀⠀⠑⠄⠀⠀⠀⠀⠀⠀⠀⣾⠟⡿⢷⣶⣦⣤⣀⣀⣿⡿⡄⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⢰⠃⠀⠀⠉⠙⠛⢻⣟⣷⡃⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⡏⡇⡇⠘⣿⣿⣿⣿⣿⣿⠉⢷⡵⠚⠑⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠇⠃⠀⠑⠬⣧⣍⡁⠈⡱⡆⠉⠋⠉⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠟⠻⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⣤⣄⣀⣀⣀
⢀⣤⡶⠶⠾⠟⠛⠛⠛⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠛⠛⠛⠻⠷⠶⢶⣤
⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠖⠒⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⠈⢲⡿⠻⣄⠀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⢷⡀⠈⢳⠊⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠁
⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠒⢻⣷⣶⣽⠀⢀⠇⠀⠀⠀⠀⠀⠀⠀⠀⢿⣷⣮⣷⠀⣸⠓⠂⠀⠀⠀⠀⣠⣾⠟⠁
⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠙⠻⠿⠖⠋⠀⢳⠀⠀⠀⠀⠀⢰⡇⠈⠛⠿⠿⠒⠁⠀⠀⠀⠀⣠⣾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠷⢤⣤⣤⡤⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠜⠀⠀⠀⠀⠀⠀⠳⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠉⠉⠉⠉⠛⠷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⣀⣤⡶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣤⣀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣶⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣶⣶⣾⠏
⣿⣿⠛⠛⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠴⣆⣲⠴⠒⠒⠒⠶⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣡⣴⠞⠁⠀⠀⠀⠀⠀⠀⠙⢖⠒⠒⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⡆⡽⣹⣶⣶⣿⣷⣶⣦⣤⡀⠀⠘⡗⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠈⠘⢷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣌⣏⡀⠠⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢚⡶⢲⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠈⣬⣥⠗⡄⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⢴⠞⠙⠀⠈⠃⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡧⢰⣟⡏⠀⡿⠙⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣏⣿⠉⠉⠀⠀⠀⠀⠀⠀⠀⠋⠛⠿⣿⣿⣿⣿⣿⡿⠛⠀⠈⢩⠁⠐⠇⠀⠛⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢄⣤⣀⣤⣤⡀⢠⡦⠠⠀⠀⠀⠀⠈⠉⠉⠠⠊⠀⠀⠆⠨⠀⠀⠀⠈⢑⠿⠙⢷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡿⠁⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠁⠒⢄⠀⠀⠀⠀⠀⠘⡤⣾⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠈⠂⠖⠁⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⢙⠈⠓⢦⣀⣸⣶⡝⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠐⠇⠀⡀⢈⡿⠷⣶⣽⠀⠀⠀⠈⠉⠀⢠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⢦⣀⡀⠀⠀⠀⠀⠀⡇⠐⠰⠃⢡⣆⠀⣠⣿⢏⡀⠀⣠⡄⣠⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠙⠛⠁⠀⣄⣀⣼⠀⠀⣬⡄⢸⣏⠜⢉⡟⠀⠈⠙⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠈⠉⢛⣛⠿⠿⠂⢴⣃⣠⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠗⠀⠀⠀⠀⢀⠢⣄⣀⡀⣀⠄⠔⠂⠀⠀⢸⠍⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⣿⠏⢹⠄⠀⠀⠀⠠⠀⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⣠⣣⠇⠀⠈⢦⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢠⣾⡋⠀⠀⠀⠈⢧⠀⠀⡚⣰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠐⠒⠚⣿⠧⠙⠢⢤⡀⠀⠈⠳⡈⢁⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠁⠀⢶⣄⢠⠇⠀⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⣀⣠⣄⠐⠒⣣⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢧⣠⡴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⢻⡄⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣸⠃⠀⠈⠷⠖⠚⠛⢋⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⢯⣉⠉⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢳⡄⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣰⠟⢧⡀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⣀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢁⡾⠁⠀⠀⠙⢦⣹⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⣤⡄⣼⠛⣷⣾⢻⣇⣾⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠿⠋⠀⠀⠀⠀⠀⠀⠉⣴⠷⣆⠸⣏⠻⣆
⠀⠀⠀⠀⠀⠸⣏⢻⣿⠀⣿⡇⣾⣿⠇⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⢶⣄⠘⣷⡙⢷⣿⡄⢻⡆⣴⢶⡄
⠀⠀⠀⠀⠀⠀⢿⡌⠋⠀⠉⠀⠙⠋⣸⣏⣴⢶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢦⡈⠳⣾⡇⠈⠿⠇⠘⣿⠏⣸⠁⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠘⠛⣡⠞⣁⣀⣤⣤⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⠻⠿⠂⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⣠⣤⡀⢸⡿⣇
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢠⡞⣷⣾⡏⢻⡟⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⣦⠀⠀⠀⠀⠀⠀⢀⡟⢀⣤⣀⢻⡌⢻⣼⡇⣿
⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⣿⣴⣿⡜⣿⠸⡇⣿⣡⡶⣿⡆⠀⠀⠀⢀⣀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠘⣧⠘⢷⣝⢷⣿⡌⢿⡷⢸⣧⡞⢻⡆
⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⣸⠇⠻⣟⠃⠀⠀⠀⠻⢋⣼⠏⠀⣴⣤⡀⣾⠛⣧⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⢻⣶⡶⢿⣷⡍⠁⠀⠀⠈⠛⠀⣾
⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⢀⡟⠀⠀⢹⣇⠀⠀⠀⠀⣸⢧⡶⣤⣿⡜⣷⣿⡄⣿⡄⠀⠀⠀⢻⡆⠀⠀⠀⠀⠘⣯⠙⠛⠶⣦⠀⠀⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⣼⠁⠀⠀⢸⡟⠀⠀⠀⠀⣿⣀⡻⣎⠻⠟⠈⠻⠃⢹⣇⣴⠶⣦⠘⣷⠀⠀⠀⠀⠀⢻⡆⠀⠀⠘⢷⡀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⣸⡇⠀⠀⠀⢠⡟⢿⣙⠛⠃⠀⠀⠀⠀⠈⠉⢁⣴⠋⠀⢻⡆⠀⠀⠀⠀⠈⣿⡀⠀⠀⠈⣷⠀⠀⠀⠀⢻⡀
⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⢠⡿⠀⠀⠀⠀⢸⡇⠀⠉⠛⢷⣄⠀⠀⠀⠀⢰⡟⠁⠀⠀⠈⣿⡀⠀⠀⠀⠀⠘⣷⠀⠀⠀⢹⡇⠀⠀⠀⠘⣧
⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⢀⣾⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢻⡆⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠹⣧⠀⠀⠈⣿⡀⠀⠀⠀⠸⡇
⠀⣰⠏⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢀⡾⠁⠀⠀⠀⠀⣸⠇⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠹⣧⠀⠀⠸⣧⠀⠀⠀⠀⢹⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣴⣶⠶⠶⠶⠶⣶⡦⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡯⢄⡴⠋⢀⣀⣀⣀⣀⡀⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⣼⢫⣾⣿⣿⣿⣿⣭⡙⢷⡐⠄⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⣿⣾⣿⣿⣿⣿⣿⣿⣿⡆⣧⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢏⡶⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⡿⠂⢤⡐⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣸⠧⠊⠻⣿⣿⣿⣿⣿⣿⣿⠟⠁⠐⠺⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⡄⣉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⢸⡇⢰⡀⠀⠀⠀⠂⠀⡀⢀⡄⡀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⡀⢸⣿⣼⣷⣦⡄⠄⠂⢿⡀⠸⣧⣃⠹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡯⠀⠀⠀⣴⣠⢛⡄⠀⠀⠀⠀⢀⡀⠈⣧⡀⠀⠈⠉⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡆⠀⢀⡸⣿⡿⣟⢿⠀⠀⠀⠀⠦⠱⠄⢻⣷⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣟⣿⡵⢸⣯⢿⡃⢿⡿⠁⠀⠀⠀⠂⠀⢁⠨⠙⣇⠀⣀⠨⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠑⠎⢲⡎⠙⠯⢦⡐⠒⠒⠒⡶⠱⠞⠁⠚⢹⣟⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠸⠀⣼⠀⠀⠄⠰⡟⠉⠈⢡⠀⠠⠄⠀⣀⠀⣿⠞⠃⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⢠⠀⢀⡇⠀⠀⠀⠀⠛⠄⢠⡂⠸⠀⠀⠀⠀⠀⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠈⠁⢸⡂⠀⠀⠀⠀⡀⠀⠀⢳⣌⢀⣀⣀⠀⠆⠈⠑⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠒⠀⠀⢀⡄⠀⠀⠀⠀⢹⡄⠤⠖⠒⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣏⠀⢤⡤⠄⠀⠀⠀⠀⠀⠸⡇⢤⡄⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠦⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣛⣓⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡞⠛⢀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣷⣿⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠻⢷⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠙⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠘⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣠⣤⣤⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⢶⣶⣶⣶⣦⣤⣤⣤⣤⣀⣀⡀
⠀⠀⠀⢀⣀⣠⣤⣴⠶⠾⠿⠟⠛⠛⠋⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠷⢶⣦⣄⡀
⢀⣴⡾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⣦⡀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢠⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷
⣿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢶⣤⣈⣿⡾⠛⠻⣿⣷⡦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢴⣿⣿⠟⠛⢿⣏⣀⣤⠶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘
⠹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢈⡻⣿⣇⣀⣠⣿⡿⠁⠱⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠘⣿⣿⣀⣀⣼⣿⢏⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼
⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⡇⠙⠫⣉⣉⡹⠃⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠹⢍⣉⡉⠟⠁⡘⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⡿⠋
⠀⠀⠈⠛⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠙⠿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠒⠉⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠁⠒⠐⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠋⠙⠳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⢻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠃⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣦⣄⠀⠀⠀⠀⠀⠀⣠⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⢀⣀⣠⣶⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣤⣤⣤⡾⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠖⠒⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠀⠀⠈⠳⣄
⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⣀
⠀⠀⠀⠀⠀⠮⢤⣠⡄⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠞⠁⠉⠙⠒⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠒⠋⠀⠀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠤⣄⡆⠀⠀⠈⢄⡀⠀⠀⠀⠀⠀⠀⠀⠐⣄⠈⠆⠀⢀⣀⡤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣠⠏⠀⠀⠘⣇⠀⠀⠀⠀⠹⢥⣀⡀⠀⠀⠀⢡⠀⠘⠀⠀⣐⠯⢬⣲⡒⠚⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠰⢿⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⣀⡨⠧⠤⠀⠘⠀⠀⢠⠋⣼⠃⣠⠇⠈⢉⡴⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠉⡱⢼⣷⠞⠀⠀⠀⠀⢀⣠⡄⠈⠃⢄⡀⠠⠀⠀⠀⠈⠣⠬⠭⣅⠰⢎⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠞⠁⠀⠈⠀⠀⠀⠀⠀⢳⣀⠸⣄⠀⠀⠈⢱⠈⠰⠦⠤⣤⣀⣀⣈⠑⢤⡑⢤⡀
⠀⠀⠀⠀⠀⠀⠀⢀⠴⠊⠠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢳⠴⠚⠄⠀⠀⢸⠀⠀⠀⠀⣀⣀⣘⣏⡈⠉⠉⠂⠙⢦⡀
⠀⠀⠀⠀⢀⠠⠂⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡖⠂⠡⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣭⣑⠒⠒⠃
⠀⠀⠀⠰⠅⠀⠀⠐⠈⠀⠑⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠠⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠢⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠐⠀⠀⢀⣀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠈⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠚⡡⡄⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠖⠉⠒⠀⠀⢀⠀⣸⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⢠⠇⠸⣤⠤⣤⠀⠀⠀⠀⠀⠀⠀⢀⣠⡴⠚⠁⡈⠀⠀⠀⠀⠖⠁⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⢠⣄⢀⣀⣀⣀⡸⠒⣾⣀⣀⣀⢀⣈⣆⠀⣀⠠⣄⣒⣪⣡⢴⠗⠀⠒⠉⡀⢁⡀⠀⣠⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠾⠿⠧⠤⠤⠤⠠⠤⠤⠤⠧⠴⠷⠄⠀⠀⠀⠻⠟⢣⣼⠛⣛⡉⠅⠠⠆⠀⠈⠀⠊⠁⠌⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢁⠞⡰⠂⠐⠂⠐⠃⡀⠀⠐⠋⡰⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠒⠒⠛⠛⠛⠛⠻⠿⣷⣶⡶⠆⠀⠀⣿⠉⡘⢁⡘⢁⠊⢀⡘⣁⣘⣡⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⣶⣶⣖⠉⠉⠉⠁⠀⠀⠀⠀⠀⢠⡏⠉⢿⡿⡍⠉⠉⠉⠻⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⢀⣩⣭⣭⣤⡀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢀⣳⠘⢆⠀⠀⠀⣈⣳⠝⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢶⣭⡭⠷⠦⠤⢿⣎⣩⣤⠭⠶⠦⠬⠵⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠐⠆⠐⠂⠐⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠐⠐⠀⠀⠀⠀⠀⠀⠈⠐⠀⠂⠀⠀⠀⠂

⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠜
⠀⠀⠀⠀⠀⣠⣀⡠⣤⣤⣄⠰⠶⣄
⣴⣿⣽⣿⣿⣿⡿⢿⣿⣿⣿⠆⠀⠈⠳
⠈⠉⠉⠉⠉⢿⣦⣈⡿⠁⠉⠀⠀⣠⠴⠒⠀⠀⠀⠀⠀⠀⠀⡀⢻⡆⠀⣀
⠀⠀⠀⠀⠀⠀⠻⣿⡇⣀⣀⣀⠀⢀⣀⣴⣏⣀⠀⠀⠀⣀⢠⣇⣼⡇⠐⢹⣶⣤
⠀⠀⠀⠀⠀⠀⠀⠘⢷⡉⠉⠻⡟⠛⢿⣉⠉⠛⠛⠛⠛⠉⣸⠀⠀⡗⠇⠛⠻⠼⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀⠀⠂⢀⣙⠛⠿⠶⠿⠟⠀⡿⠀⠀⡇⠇⠀⢸⠀⢸⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⠾⠟⠳⠶⠿⠋⠀⠀⠀⠃⠀⠐⠉⠀⠀⠘⠧⠘⣟⢻⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠦⣼⠃⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠑⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡦⣄⣀⠀⠀⠀⠀⠀⣤⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢮⣿⣧⠀⠀⠀⠀⠉⠙⠿⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡄⠀⠀⠀⠀⠀⠀⠈⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠶⣤⠀⠀⠀⠀⠀⠀⣙⣿⣋⡀⠀⠀⠀⠀⠀⣰⠖⢦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⠴⣾⣤⠄⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⢦⣽⡶⠾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⣷⣄⣀⠀⠀⠀⠾⠁⠙⠂⠀⠀⠀⣀⣤⡟⠙⠂
⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⣀⣠⣤⠤⠤⠤⣤⣄⣀⠈⠁⠈⠧⠀⠀⠀⠀⠀⠀⣠⣤⣄
⠀⠀⢸⣍⣸⣧⣞⠀⠀⠀⠀⠀⣠⠖⠛⠉⠀⠀⠀⠀⠀⠀⠀⣹⠟⠶⣄⠀⠀⠀⠀⠀⠘⣦⣿⣀⡟
⠀⠀⠀⠉⠡⠟⠉⢿⠋⠁⣠⣞⠁⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⠏⠀⠀⠈⠳⣄⠀⠙⢻⡟⠙⠇⠉
⠀⠀⠀⠀⠀⠀⠀⠘⠃⣰⠟⢹⡇⠀⠀⠀⠀⠀⠻⠤⣤⡀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠸⠧⠶⠶⣄⡀⠀⠀⠀⠀⠻⠶⢦⡀⠀⠀⠀⠀⠘⣇
⣠⠖⣦⣸⣄⣠⠞⠀⢸⠁⠀⠀⠀⣀⣀⣨⡿⠀⠀⠀⠀⠀⢀⡾⠀⠀⣀⠀⠀⠀⣹⠀⠘⢦⣀⣼⣠⡖⢦
⠻⠶⠟⢹⠁⠉⠳⠄⢸⠀⠀⠀⣾⠉⠁⠀⠀⠀⠀⠀⢀⡴⠛⠀⠀⢸⡟⢧⡴⠞⢹⠂⠴⠋⠀⢹⠙⠧⠾
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⡾⠀⠀⠀⠀⡾⠀⠀⠀⠀⣾
⠀⠀⠀⠀⠀⠀⠀⢠⠄⢷⠀⠀⢀⡀⠈⠻⣆⠀⠀⠀⣇⠀⠀⠀⣼⠃⠀⠀⠀⣰⠃⢠⡀
⠀⠀⠀⣀⣐⣦⣠⠿⣤⡌⢷⡞⠋⠉⠳⢦⡿⠀⠀⠀⠹⣦⣤⠞⠁⠀⠀⣠⠞⠁⣤⠼⠧⣴⡇⣀⡀
⠀⠀⢸⣅⣹⡏⠷⠀⠀⠀⠀⠙⠶⣄⣀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⠶⠛⠁⠀⠀⠀⠀⠰⠏⣟⠉⣷
⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⣧⢀⡉⠙⠛⠛⠛⠛⠋⠉⠉⠁⢀⣀⣀⡗⠀⠀⠀⠀⠀⠀⠈⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠦⣤⡟⠉⠁⠀⠀⠀⢲⣄⣴⠆⠀⠀⠀⠈⠙⣧⡴⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⠛⢿⠙⠃⠀⠀⠀⠀⣀⣹⣇⡀⠀⠀⠀⠀⠚⣹⠟⢳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⠀⠀⠀⣩⠿⢯⡁⠀⠀⠀⠀⠀⠙⠶⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣤⠞

⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⡀
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣠⣾⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠹⣿⣿⣿⢉⣭⣿⣿⣿⣿⠿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⣽⣏⢻⣷⢦⠈⠉⠻⣿⠛⠭⠅⠀⠀⠈⣿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠿⣁⠺⢃⣼⣷⣿⣄⡀⠀⠈⠿⣄⠀⠀⢀⣶⣴⡏⣹⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⢀⣠⣾⣿⣿⣿⣿⠀⣀⠀⠀⠈⣁⠀⢼⣿⣿⠋⠉⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⣴⣿⡿⢿⣿⣿⣿⣿⣣⣽⢻⠀⣠⣼⣿⢿⣿⣟⠂⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢢⣴⣾⣿⣿⣄⣀⣿⣿⣿⡏⡹⣿⠟⠀⢬⣭⣁⠀⢙⣿⡅⠀⢸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠈⠉⢻⣾⣿⣿⣿⣿⣿⣿⣿⣛⠟⠒⠶⠛⠟⠋⢠⣾⣿⠀⣈⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠙⠿⢿⠿⣿⣿⣟⣿⠋⠀⠀⠰⠀⠀⠀⢰⣿⣿⠀⠉⣹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⢦⡔⢀⣴⡀⠘⠿⣟⣷⠀⣀⣀⡠⢀⣀⠀⢾⣇⣰⠀⠀⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠋⣀⣤⣰⡿⠿⠖⠐⠿⢀⣸⡿⣴⣾⣿⣿⡃⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⣤⣤⣀⡀⠈⢉⣀⣠⣿⣿⣿⣿⢿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠉⠛⢿⣿⣿⣿⣿⣿⣿⠶⣾⣿⠋⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠈⢻⣷⣶⡾⠟⠁⠀⢾⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠀⠀⠀⣾⣿⠉⣷⠀⠀⠀⣘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣓⠀⠀⠀⢈⣿⡄⢟⡀⠀⠀⢸⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⠀⠀⣀⣿⣿⡇⢸⡅⠀⠀⣸⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠈⢉⣻⣿⡇⢸⣿⣇⣀⣹⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠈⢽⣿⣇⠸⡏⠀⠉⠉⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠈⣽⣿⢸⡇⠀⠀⠲⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠠⣿⣿⢨⡅⠀⠀⢈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⣨⣿⢢⡄⠀⠀⣈⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⣀⣼⣿⣶⣄⡀⢀⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡋⠰⣿⣿⠿⣿⡏⠉⠹⣏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣀⣥⡾⠟⠁⠀⠙⢿⣄⣀⣉⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉
⣀⣀⣀⣀⣀⣄⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣿⣿⣿⡿⠟⠻⠿⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣏⣀⣀⣀⣤⣤⡀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⡤⠀⠐⠀⠈⠂⠀⡤⠀⠀⠀⢦⠆⠴⠁⠘⠄⢴⡶⠀⠀⠀⠄⠀⡀⢀⠂⠀⡀⠀⠄⠀⠀⣀⣀⣀⣾⣇⣀⣤⠄⠀⠀⢀⠀⠱⠆⠀⠞⠀⢀⡀
⠀⠀⠈⠢⠀⠀⠀⠀⠊⠀⠀⠀⠀⠀⠑⡄⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢻⣿⣿⡟⠁⠀⠀⠀⠉⠀⣰⠆⠀⢦
⠀⠀⠀⢠⡠⠐⠢⠄⡀⠀⠀⠀⠀⠀⡜⠠⠔⠢⢜⡄⠀⠀⠀⠀⠀⢀⠌⠃⠀⠈⢀⠀⠀⠀⠀⠀⢀⡿⠋⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣪⢂
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⡀⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠠⣼⣦⠄⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠁⡠⠂⠀⠀⠀⠺⢟⡳⣣⡵⣫⡞⠁
⠀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢈⡀⠂⠀⡄⠀⠀⠀⠀⠀⠀⠀⢠⠟⣟⡟⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠀⠂⠑⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⣀⣀⣠⣜⣓⡀⢤⣤⣀⡀⠀⠒⢦⣤⣘⣧⠾⠒⠓⠒⠀⠀⠀⠂⣐⠀⠘⡀⠘⠀⠀⠀⠀⠀⠺⢿⣿⣌⡝⠐⠁⠀⠀⠀⠁⠉⠀⠀⢉⣠⠞
⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠻⣧⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠐⢀⡞⠹⠻⢷⡀⠂⠀⠀⠀⠀⢀⡠⠄⠸⡇
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠠⠞⠁⠀⠀⠸⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠋⠀⠀⠈⠃

⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠒⣀
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⡑⠀⠀⢀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢿⡄⠀⠀⠀⠀⠀⢀⠠⠿⠋⠀⠘⠻⠆⠄
⠀⠀⠀⠰⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠁⠀⠀⠂⠀⠀⠀⠀⠀⠐⠦⠤⢤⠵⡞⠛⠒⠒⠀⠀⠀⠘⢿⡍⣀⢩⡿⠛⠀⠀⠀⠀⢻⡦⠀⠀⠀⢰⡿
⠀⠀⠀⠀⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣸⠟⠉⠛⠇⠀⠀⠀⠀⠀⢈⠡⣴⣾⡶⠌⠅
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠘⠁

⣿⣿⠀⠀⠀⠈⠀⠀⠀⠀⠈⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⢹⣿⣿⣿⠀⠀⠀⠈⠀⠀⠀⠀⠈⣻⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣀⢹
⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠰⠈⠁⠀⠀⠀⠀⠠⠄⠀⠀⠈⠉⠈⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠉⠰⠈⠁⠠⠀⠀⠀⠠⠄⠀⠀⠈
⠀⠀⠀⠀⢀⣠⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣦⣀⠀⠀⠀⠀⠀⠀⠐⠀⢀⣠⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣦⣀
⠀⠀⠀⠀⠙⣿⣿⣿⠁⠀⠀⠀⠀⠰⠀⠀⠈⢹⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⠁⠀⠀⠀⠀⠰⠀⠀⠈⢹⣿⣿⡏
⠀⠋⠀⠀⠀⠉⠉⠉⠀⠀⠤⠀⠀⠀⠀⠀⠀⠈⠁⠈⠉⠀⠀⠀⠀⠀⠉⠀⠀⠀⠉⠉⠉⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉
⣦⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣾⣌⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⣀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣀⣾⣌⣀⠀⠀⠀⠐
⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡏⠀⠀⠀⠀⠀⠈⠁⠀⠻⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⡏⠀⠀⠀⠀⠀⠈⠁⠈⠻
⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠛⠃⠀⠀⠀⠀⠀⠀⠀⠰⠀⠋⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠋⠙⠃⠀⠀⠀⠀⠀⠀⠀⠒
⠀⠀⠀⠀⠐⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡄⠀⠀⠀⠀⢠⠀⠀⠀⠀⠐⢀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡄
⠀⠀⠐⠀⠛⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⡄⠐⢿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠛⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⡄⠐⢿⣿⣿⡟
⠄⠀⢀⡀⠀⠛⠉⠛⠂⠀⠀⠶⠀⠀⠀⠀⠀⠘⠛⠛⠃⠀⠀⠀⠀⠄⠀⢀⠀⠀⠛⠉⠛⠂⠀⠀⠆⠀⠀⠀⠀⠀⠘⠛⠛⠃
⣆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢠⣆⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣤⡀⠀⠀⠠⠄
⣿⣿⠂⠀⠀⠰⠀⠀⠀⠀⠲⣾⣿⣿⡗⠀⠀⠀⠀⠰⠂⠀⠐⢶⣿⣿⣿⠂⠀⠀⠠⠀⠀⠀⠀⠲⣾⣿⣿⡗⠀⠀⠀⠀⠰⠆⠀⠐⢶
⠻⠿⠠⠄⠀⠀⠀⠀⠀⠀⠀⠺⢛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠒⠸⠿⠻⠿⠠⠄⠀⠀⠀⠀⠀⠀⠀⠺⢛⠻⠇⠀⠀⠀⠀⠀⠀⠀⠒⠸
⠀⠀⢀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⡀⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢠⡀⠁
⠀⠀⠀⠀⢴⣾⣿⣶⠆⠀⠀⠀⠀⢀⠀⠀⠠⢶⣿⣿⡶⠀⠀⠀⠀⠀⠀⠀⠀⢴⣾⣿⣶⠆⠀⠀⠀⠀⢀⠀⠀⠀⢶⣿⣿⡶
⠀⡤⠀⠀⠀⠿⠿⠿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠸⠛⠻⠧⠀⠀⠀⠀⠀⠄⠀⠀⠀⠿⠿⠿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠘⠟⠻⠧
⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠉⠀⣠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠉⠀⣠
⣿⣶⠄⠀⠀⠀⠀⠀⠀⠀⢤⣴⣿⣷⡦⠀⠀⠀⠀⠀⠠⠄⠀⣤⣾⣿⣶⠄⠀⠀⠀⠀⠀⠀⠀⢤⣴⣿⣷⡦⠀⠀⠀⠀⠀⠠⠄⠠⣤
⠿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠨⡿⠿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠿⢿⡇⠀⠀⠀⠀⠀⠀⠀⢀⠨
⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⢀⠀⣠⣴⣿⣦⡄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣿⣧⣤⠀⠀⠀⠘⠀⠀⢀⠀⣤⣴⣿⣦⠄⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⣧⣤
⠀⠀⠀⠀⠀⡿⠿⣿⡀⠀⠀⣀⠀⠀⠀⠃⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠿⣿⡀⠀⠀⡀⠀⠀⠀⠃⠀⢹⣿⣿⡇
⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠉
⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣤⣄⠀⠈⠁⠀⢀⡀⠀⢀⣀⣼⣷⣤⡄⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⣦⣄⠀⠈⠁⠀⢀⡀⠀⢀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠒⠉⠀⠀⠈⢀⡠⠤⢜⠒⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⣀⠀⡀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⠁⠀⠐⠊⠀⠑⠋⠀⠀⠰⡄⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠋⠀⠀⠈⠁⠀⠀⠠⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠄⠀⠠⠆⠀⠀⠲⠄⠀⠘⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡃⠀⠠⠊⠀⠑⠆⠀⠀⠀⠈⠆⠋⠶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠆⠀⣘⠃⠀⠀⠀⠱⠎⢷⠀⠀⠀⠀⠀⠀⠀⠀⠺⣧⠗⠀⡇⠀⡰⠀⠀⠀⠈⠢⠀⠀⣀⠜⠋⠓⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⢈⡄⠀⠀⠀⠘⠈⠁⣀⠗⠀⠀⡰⠉⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠧⡀⠇⠀⠁⠁⢀⢤⠁⠀⠀⠘⣥⢱⠰⠀⠘⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣥⡤⣀⠀⠀⠀⠰⠾⠃⢀⡠⠚⠀⠀⠀⠀⠀⠀⠀⠀⣴⢀⠈⡀⠐⠯⡴⠀⠀⡀⠀⠀⢀⡤⠆⣸⢯⠁⠀⠀⠇⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⠲⠖⢶⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⢸⡀⠄⠀⠀⠀⢧⡀⠉⠙⠫⠟⢀⡔⠁⡀⠀⢰⣦⢤⡾
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠻⣀⡸⢶⠆⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⣄⢦⠐⣠⠆⠈⠒⠤⠤⡖⠉⠀⠋⠀⠀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠊⠁⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⠄⣄⠀⠀⠀⠀⣀⣄⡀⢱⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣠⠔⠒⠚⠉⠉⢳⠀⡆⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⡠⠊⠁⠀⠉⠁⠀⠈⠑⠦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⢤⡀⢃⠀⣀⣀⡤⠤⠼⠆⢃⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⡄⠀⠀⠀⠀⠀⠀⢰⡄⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⡇⠀⠉⠉⠀⠀⠀⠀⠀⢸⠀⠀⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠘⡇⠘⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⢡⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣄⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠀⢀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢑⡶⢲⠒⠖⣰⠶⡒⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠠⠉⠉⠁⠀⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⠀⠀⢸⢛⠓⠲⠶⠤⠤⠤⠶⠚⣧⡤⠤⢟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢈⣀⣀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠚⠑⢲⠋⢸⠀⠀⠀⠀⠀⠀⠀⠀⣧⠁⡀⢠⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠈⠈⢹⠍⡁⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢻⠞⡁⠒⠘⠦⠃⠘⠀⠀⠀⣠⠀⠀⠀⠀⡇⠉⣰⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠋⠂⠀⠀⠀⡇⠐⠤⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⢸⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠈⡄⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣄⡀⠈⡇⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢇⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠁⠀⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⢠⡇⠀⠀⠸⡆⠠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⠀⠀⠀⡇⠀⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠉⡆⠀⠀⢰⡆⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⡇⠀⠀⡠⢓⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡁⠀⠀⢸⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠚⠉⠙⠯⢉⡑⠢⢤⡧⠔⣫⠔⠉⠈⠙⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⣤⣼⣄⠀⠀⡇⠀⠀⢸⠀⠀⠀⣧⣤⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠈⠑⠛⠒⠋⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠋⠁⠑⠦⣇⠀⠀⠈⡦⠞⠻⠻⠃⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡓⠢⠤⣀⣀⢀⣀⠄⣒⠤⠶⠶⠶⠶⠶⠾⠟⠀⠀⠀⠀⠀⠀⠀⠀⡦⢄⣀⢀⣀⣀⡠⠔⡿⠀⠀⠀⣷⢤⣀⣀⣀⣤⡤⢾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠢⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠀⠐⠒⠒⠋⠁⠀⠀⠀⠙⠒⠒⠀⠀⠀⠒⠋
⣿⣿⡿⠻⠟⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣷⣶⣶⣶⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣶⣶⣶⣶⣶⣦⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣟⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣥⡴⠶⠶⠶⠛⠛⠛⠶⠶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣛⣩⣴⠶⠞⠛⠛⠛⠛⠛⠻⠶⢶⣭⡛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠐⠿⠿⣷⣦⣌⠙⢷⡝⣦⠀⠀⠀⠀⠀⠀⠀⠈⣿⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣷⡈⢷⡸⣧⠀⠀⢀⣀⣤⣄⠀⢹⣿⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠸⣇⢹⡆⢰⣟⣩⠥⢿⡇⢸⣿⠀⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⣿⠈⣷⠘⣷⣔⣚⣻⡿⢸⣿⣰⣿⠉⣻⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣿⠀⠈⠉⠉⠁⠀⣿⡟⠛⣿⡗⠉⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⣿⠀⠀⠀⠀⠀⣼⡿⠁⠀⣿⡷⠦⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⢰⡟⠀⠀⠀⠀⣼⡿⠁⠀⠀⣿⣇⢀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢁⣾⠁⠀⠀⣠⣾⣟⠀⠀⠀⢠⣿⠇⢹⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣾⣧⣼⣧⣤⣶⢿⣿⣟⣻⣷⣦⣴⡿⠋⠲⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣏⠿⣿⣍⣉⣉⡉⡉⠉⠉⠉⠉⠉⠉⣉⣉⣉⣩⣴⣟⣡⡿⠁⠀⠈⠻⣿⣤⣼⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⣿⣦⠚⢿⣿⣍⠉⠉⠉⠛⠛⠛⠛⠋⠉⢉⡽⢿⣡⡾⠋⠀⣠⡴⠶⠛⣋⠿⣿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣫⡿⠈⠻⣷⣶⣛⣿⣷⣶⠾⠿⠿⠿⠿⠿⠿⢿⣿⣿⠋⠀⠀⠀⠹⣶⣋⣉⠤⠴⢛⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠛⠋⠀⠀⠀⠀⢹⣿⠿⠿⠶⠶⠛⣛⠛⠛⢛⡛⣿⠉⣿⡆⠀⣿⡄⠀⠘⢯⣤⠶⠞⠋⠉⣿⡆⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡆⢀⣿⡏⠀⠀⠀⠀⣀⠀⠸⣿⢰⣟⣿⠆⢺⣿⡇⠸⣿⡿⢻⡆⢿⡇⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⣾⡟⠛⢶⣄⡀⣸⣿⠀⠀⣿⡇⢉⣥⣤⣤⣤⣤⣤⣤⡀⠘⣧⢸⣿⠀⠀⠹⣷⣄⠀⠀⠀⠀⣀⣤⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⢉⣿⣿⡏⠀⠀⢹⣷⠘⣧⣀⣀⣀⣤⣤⣼⡇⠀⣿⢸⣿⡀⠀⠀⠘⢿⣦⣤⠶⠟⠋⠁⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⣶⣶⣾⣿⣿⢀⣠⣴⣾⠿⣷⣾⣯⣭⣭⣭⣥⣤⣤⣴⣾⣿⣿⣻⡿⢷⣶⣶⣿⣷⣦⠀⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⢠⣿⣿⠟⢿⣉⣵⣾⠟⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠈⠛⠿⣷⣾⣥⣤⣟⣻⣿⣶⣶⠿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣾⣶⠿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣛⠶⢦⣤⣤⣀⣀⣴⡿⠟⠛⠛⠛⠛⠛⣿⣧⣤⣤⣄⣠⣤⣤⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣿⡏⠉⠛⠳⠶⠾⠿⢿⣿⠁⠀⠀⠀⠀⠀⠀⣿⠟⠶⢦⣬⣭⣤⣴⣿⠁⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢁⣾⡿⠃⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀⠀⣿⡃⠀⠀⠀⠀⠀⠈⣿⣆⠉⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣶⣶⣦⣴⣶⣶⣶⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣶⣤⣤⣤⣤⣤⣬⣿⠇
⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁
⠀⢰
⠀⠘

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠏⠀⠈⢿⡄⠀⠀⠀⣀⣀⣀⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣠⡟⠀⠀⠀⠘⠻⠚⠛⠛⠋⠉⣩⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣏⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⣤⣄⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠀⢠⡾⠋⠹⣷⣄⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣴⠟⠀⠀⠀⠈⠛⢷⣄⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠙⠛⠀⠀⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣦⡀⢿⡍⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⢶⣄⠈⣷⡌⢿⣼⣷⠈⣷⢀⣴⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡙⠷⣼⣿⠀⠻⣿⠀⢸⣿⠇⣸⠃
⠀⠀⠀⠀⠀⠀⠰⣿⣷⣸⣿⣷⣼⣿⡆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡶⢾⣿⠆⠀⠁⠀⠀⠀⠀⠀⠉⢠⡟
⠀⠀⠀⠀⢰⣶⣦⣹⣎⢿⣿⠻⡿⢹⣧⡾⢻⡇⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣄⠀⠀⠀⠀⠀⠀⠀⢀⡟
⠀⠀⠀⠀⠀⠻⣮⣙⠛⠀⠁⠀⠀⠘⠛⣡⡟⠀⠀⢀⠀⢀⣤⡀⠀⣠⡀⠀⠈⢻⣆⠀⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠈⢹⣧⠀⠀⠀⠀⠀⢰⡏⠀⠀⢰⣟⢷⣼⡏⣿⣸⡟⣿⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⢐⣿⡀⠀⣀⣀⠀⣿⠁⠀⣠⣤⣿⡌⠻⠇⠸⣿⠃⣿⣠⣶⡄⢸⣷⠀⠀⠀⣀⠀⠸⣷⡀
⠀⠀⠀⠀⢰⡿⣆⣸⡏⣿⣰⡟⣻⡆⣿⠀⠀⠻⣯⡛⠛⠀⠀⠀⠀⠀⠛⠋⡼⠃⢸⣿⠀⠀⢸⡟⣷⣠⣿⣿⠀⣾⢿⡆⢀⡀
⠀⠀⣾⠻⣾⣇⢻⣿⡇⢿⣿⠁⣿⢸⣿⠀⠀⠀⠉⢷⡄⠀⠀⠀⠀⠀⢀⡼⠃⠀⢸⣿⣀⣀⢸⣇⢸⣿⡇⣿⣸⡇⣼⣧⢿⣿
⠀⠀⠘⣧⡹⣿⠈⠛⠃⠘⠋⢸⣧⣾⠿⡦⠀⠀⠀⠈⢻⡆⠀⠀⠀⢠⣞⠁⠀⠀⢸⣿⣍⠙⣷⣿⠈⠛⠀⢿⡟⠀⢿⢏⣾⠇
⠀⠀⠀⠘⢷⡀⠀⠀⠀⠀⠀⠀⠉⣠⣾⠁⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⣿⠀⠀⠀⢸⣯⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏
⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⣠⠞⠁⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠘⣿⠀⠀⠀⢸⣿⠀⠘⢷⣀⠀⠀⠀⠀⠀⠀⣼⠏
⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣼⡇⠀⠀⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠘⣿⠀⠀⠈⠙⠳⣶⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⣿⡆⠀⠀⠀⣿⡄⠀⠀⠀⠀⢿⡆⠀⠀⠀⠘⣿
⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⢹⣇
⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⣿⡇⠀⢸⣿⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠘⣿⠀⠀⠀⠘⣿⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⣿⡄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠟⠋⠀⠀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣯⣀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⣠⣄⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣷⣶⢄⡀⣠⠔⣀⣵⣾⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣟⣿⣿⣿⣿⠟⣡⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣗
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣎⠹⡿⠉⣿⣷⣿⣿⣿⣿⣿⣿⡟⠋⠉⠁⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠀⣧⢠⣌⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⢨⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⢻⣿⣿⣿⡿⢠⣧⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣬⣿⣿⣯⣴⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⢠⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⡃⡙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⣿⣿⣿⣿⣛⠻⣿⣿⣿⣧⣦⣷⣝⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣏⡛⠻⢿⣿⣷⣬⣻⣿⣿⣧⣭⣙⡛⠻⠯⠽⠿⠿⢛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢟⠿⠟⠋⠀⠀⠀⢽⣿⣿⣧⠹⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⡶⢂⠀⠀⠐⠘⢿⣿⡇⢉⠛⠛⠿⠿⣟⣛⡻⠿⠋⢻⡷
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣟⠻⠛⠟⢡⠃⣰⠀⠀⠁⠸⣿⣿⣽⡆⣠⡄⢄⣤⣆⢰⣶⢶⡈⠃⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⣛⣉⠉⠙⠓⠃⢰⠃⢰⢀⠀⠀⢿⣿⣿⡇⣿⣿⡝⠛⠋⠙⣿⡏⢛⠸⠀⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠉⠉⠉⠛⠀⡼⠏⠀⣿⣾⣿⠟⣾⣿⣿⡇⠀⣀⡀⢿⣇⣹⡀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠠⠿⡿⠋⠀⡿⠽⠋⠋⠉⠉⠁⠀⠙⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠈⠀⠀⠀⠀⣀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠚⠉⠁⠀⠀⠀⢠⣶⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣼⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢀⣠⣿⣶⣿⣼⡗⠀⠀⣠⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣸⠏⢻⡟⢡⣟⡿⠁⢠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⢸⡄⠀⠛⠀⣲⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠃⠀⠀⠀⡇⠀⢄⡽⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠠⡄⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⣠⠗⣰⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢋⡀⠤⢀⣠⠞⠁⣦⡟
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠘⣿⠉⠀⡄⣘⣃⣀⣉⣉
⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⢀⣿⣀⡄⠉⠿⠟⠻⢿⠟
⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢸⣿⣿⠇⠀⣲⣺⣶⡶
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠶⠺⠋⠀⠀⠀⢿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⠴⠖⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠉
⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠈
⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀
⣯⣿⣿⣿⣯⣽⣿⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣯⣭⣿⣯⣽⣭⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠛⠳⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣵⠞⠰⣜⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣥⠀⠀⠀⠙⣘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡙⠃⠀⠀⠀⠀⠹⠿⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠃⠀⠀⠀⠀⠀⠀⢸⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢡⣷⡀
⢀⣤⡤⢶⣶⡖⢿⣿⠟⠿⠿⠟⠻⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠟⠿⠿⠛⠿⠿⠛⣿⣷⠶⣶⠶⣤⣄
⣿⡀⢀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠀⣸
⠈⠳⣌⠳⠄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⣤⡀⠀⠀⠀⠀⠀⠀⣠⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢂⡴⠋
⠀⠀⠈⠳⣜⠳⡄⠀⠀⠀⠀⠀⠰⣧⣠⢿⡇⠀⠀⠀⠀⠀⠀⣧⣀⠼⡷⠀⠀⠀⠀⠀⢀⡴⣢⡴⠋
⠀⠀⠀⠀⠈⠻⢦⡳⠦⠀⠀⠀⠀⠉⠛⠊⠀⢀⡀⠀⠀⣀⠀⠈⠛⠂⠀⠀⠀⠀⣠⠶⣨⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠙⠷⣜⢷⠄⠀⠀⠀⠀⠀⠘⢧⣤⣴⠟⠀⠀⠀⠀⠀⠀⢴⢆⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣾⡆
⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢿⡆
⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⠀⠀⠀⠀⣠⡴⣈⣽⣔⡶⡄⠀⠀⠀⠀⠀⠀⠀⣮⣷
⠀⠀⠀⠀⠀⠀⠀⣼⢡⡄⠀⠀⠀⢠⡴⣂⡼⠞⠉⠀⠈⠛⢦⣝⠶⠄⡀⠀⠀⠀⢉⢻⡀
⠀⠀⠀⠀⠀⠀⠀⣿⠘⠇⠐⢚⣫⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣍⡓⠀⠶⠟⢸⡇
⣀⢀⣀⣀⣀⣀⣀⢻⣤⣶⠞⢋⣁⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣈⣙⠳⣶⣤⣼⢃⣀⣀⣀⡀⣀⣀
⣿⣟⣉⣉⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣠⣿⡿⠛⠙⢿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⡿⠿⠻⢿⣿⣦⣤⣤⣤⣤⣀⣀⣠⣾⣿⠿⠛⠛⢿⡿⠀⣴⠆⢸⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠁⠀⠀⠀⠀⢹⣿⠟⠛⠛⠻⣿⠿⠿⡟⠁⠀⣀⣀⣀⠁⠀⠁⢀⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⢠⣶⡆⠀⢰⠃⠀⣠⠆⢠⡿⠀⠀⢹⣦⠎⠁⠈⢻⠁⢰⠖⠻⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⡀⠀⠈⠟⠀⣠⠛⠀⠀⢁⡴⢿⡇⠀⠀⠈⣿⠀⠀⢶⣾⠀⢀⡤⠀⢹⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣴⡇⠀⠀⣀⡀⠈⠱⣦⣀⣀⣀⣼⠀⢠⣦⠀⠸⣆⡀⢀⣬⣀⣸⡇⠀⠈⠀⣹⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡇⠀⠀⡿⠛⢦⡀⠈⠛⠁⠀⡏⠀⢸⣿⣶⠚⢛⣿⣿⠋⢀⡉⢷⡀⠀⣠⣿⣿⡻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣷⣾⡇⠰⢸⣿⣦⣤⣤⢼⣇⣀⣼⠋⠉⠀⠘⠛⠃⠀⠋⢀⣾⡿⠋⡉⠹⣿⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠋⠁⡈⠁⠀⠘⠋⠀⣀⠙⢀⠄⠀⣼⣷⡆⠀⢠⣶⡆⠀⠖⠉⢻⡄⠰⠃⢰⣿⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠘⣷⠂⡀⢸⡄⠀⠛⠀⣿⠀⠀⠉⠈⡇⠀⠈⠈⡇⠀⢰⡆⠸⠇⢀⡀⢉⣻⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣾⣿⣄⣁⣼⣿⡶⠶⢿⣿⠦⠀⣠⣾⣿⣦⣤⣾⠷⠶⠻⢧⣀⣠⣾⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⣀⠉⢻⣿⣶⣤⣀⣀⣠⣾⡿⠘⠿⢋⡼⠁⠀⢀⡀⠀⢹⠁⢀⡀⢻⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣇⠀⠀⠇⠀⠈⠛⠀⠈⠟⠻⣿⡿⠃⠀⠀⣾⡇⠀⠀⠹⠁⢀⣾⣦⡈⠳⣾⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣦⣀⠀⠙⢧⡀⠀⠀⢀⡴⠋⠀⠀⠀⠀⢹⣷⡇⠀⢀⠀⠈⢻⠀⠛⠀⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⠉⠹⡇⠀⠈⣷⠀⠸⡿⢿⣷⠀⣠⣀⠀⠀⢻⡇⠀⢸⣇⠀⠀⠑⠒⠂⢹⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣀⠀⠀⢀⣴⣿⣆⠀⢀⣼⡟⣴⣿⣿⣿⣷⣾⣷⣶⣾⣿⣦⡀⠀⢀⣠⣾⣿⢿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣟⡗⠀⠉⠛⠛⠛⠛⠛⠿⣿⣿⣿⣿⣿⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠉⠉⠉⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⢸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⣀⠀⠀⠀⠀⢰⡟⠀⠀⠈⣿⠀⠀⠀⠀⠀⢠⡖⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⢸⣧⠀⠀⠀⣾⠃⠀⠀⠀⢻⡆⠀⠀⠀⢠⡿⠁⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⢻⡆⠀⢰⡟⠀⠀⠀⠀⠘⣷⠀⠀⠀⠘⠁⠾⠃⠰⠶⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠶⢶⣤⣄⡉⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠹⠆⠀⠀⠀⠀⢀⣀⣀⣀⣀⣤⣤⣤⣤⣶⣶⠶⠶⣾⣿⡿⠃
⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣤⣤⣶⡶⠶⠶⠶⠶⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠛⠋⠉⠉⠉⠉⠉⠀⠀⠀⠀⣀⣴⠾⠛⠁
⠀⠀⠀⠻⢿⣟⡉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠁
⠀⠀⠀⠀⠀⠉⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠋⠁⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠳⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⢠⣤⠶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠶⠶⠄⠉⠛⠶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⡁⠀⠀⠀⠀⠀⢤⣤⣤⣤⣤⣤⣤⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣴⣶⠶⠶⠶⠂⠀⢠⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⠰⣦⣄⡀⠀⠀⠀⠉⠉⠉⠉⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⢶⡄⠙⠻⢶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣶⠟⠁⠀⣸⡏⠀⠀⠀⠀⠀⢀⣠⠞⠋⠻⣦⣀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠟⠁⠀⠀⢠⡿⠀⠀⠀⠀⢀⣴⠟⣡⡖⡀⠀⠀⠉⠻⣦⣄⠀⠀⠀⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣾⠃⠀⠀⢀⣴⠟⢡⣾⠋⣼⢇⡄⢰⣄⠀⠀⠙⠻⣦⣀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⢀⣴⠟⠁⣴⠟⠁⠀⠁⢸⡇⠈⠿⠀⠀⠀⠀⠈⠙⢷⣤⡀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣵⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣾⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠄

⠀⠀⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠉⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣝⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢟⣩⠤⠤⠤⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠈⠃⠈⣻⣿⣿⣿⣿⣿⣿⡿⢃⠋⣀⣀⣀⣀⣬⣷⣭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⡏⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠐⣿⣿⣿⣿⡇⣹⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⢿⣿⣿⠃⠉⠠⣝⣿⣿⣿⣿⣿⣿⣿⡏⠃⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠀⠀⢀⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡌⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⢀⣿⣿⣭⠉⠹⢿⣿⡟⣿⣿⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢩⣿⣿⣿⡿⣦⠀⢶⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣻⣿⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣷⣿⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣘⣿⣿⣿⣿⣿⣿⣿⡷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⢷⣾⡿⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠿⣿⣿⣿⡇⢩⣷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⡟⢼⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠙⣷⡈⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡿⠁⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⡀⠀⠀⠀⠘⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⣿⠇⠈⠞⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⠈⠁⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣿⠀⠀⠀⣸⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⣼⡆⠀⣀⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣏⣿⠀⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣏⠃⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗⡇⠀⠸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⢸⣿⣿⣿⣿⣿⡏⣿⣿⣿⣿⡅⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⣿⣟⠿⠿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠀⣿⠟⠛⢶⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣧⠀⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣟⠀⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⢀⣿⣿⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡯⠈⣿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣷⣐⣿⣿⣇⣀⣦⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣶⣶⣶⣷⣶⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣛⣹⣿⣿⣿⣿⣿⠛⠛⠛⠛⠛⠛⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣤⣶⣾⣿⣿⣿⣿⣿⡿⢿⠯⠭⠭⠭⠭⠭⠥⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⠒⠛⠛⠛⠓⠒⠶⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⣠⠀⠀⠀⠀⠈⠳⣄⠈⠛⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠏⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⢻⡇⠀⠈⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣚⣓⣒⠒⣶⣦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⠀⠀⣰⡿⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣾⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢭⣭⣭⣩⣭⢽⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡇⠀⠀⣿⡇⠀⢰⠀⡄⢀⣤⣴⠛⠿⠛⠛⢻⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣸⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⠀⠀⣿⡅⠀⢸⣿⣷⡿⠛⠉⠁⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⡟⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣬⠿⡷⠀⠙⠷⠀⣼⣿⣿⠇⡞⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠀⢻⡀⠀⠀⠀⠁⣼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⠶⣾⣷⣶⣶⡆⣼⣿⣿⣷⡔⣇⡀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⢀⣠⠴⠖⠉⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣧⣾⠁⠈⠻⣿⠃⢿⣿⣿⣿⡇⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⢠⡾⠯⠴⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⠙⠇⠀⠀⣿⣀⣸⣿⣿⡟⠁⣀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⠷⠦⠤⠤⢤⣤⠤⣤⣤⠤⣤⡶⠶⠦⠤⣴⣶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⢀⣠⠴⠾⣭⣭⣭⣝⣋⣀⡀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢀⡿⡇⠀⢀⣼⢣⡟
⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⠶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠲⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢸⠀⠙⠛⠋⠀⠈⣧
⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⣦⡀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠀⣾⠞⠉
⠀⠀⠀⢀⡟⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠀⣸⠛⢦⣄⠀⣰⠏⠀⠀⠀⠀⣸⠃
⠀⠀⠀⣼⠳⢤⣀⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⣰⠏⠀⡼⠃⠀⠀⠙⢿⡅⠀⠀⠀⠀⢠⡏
⠀⢠⣴⡃⠀⠀⠈⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠛⢷⣤⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞
⠀⢀⡟⠛⠶⣤⣄⡀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⠈⠙⠶⣄⡀⠀⠀⠀⠀⠀⠀⣴⠋
⠀⣼⠁⠀⠀⠀⢈⡟⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⣤⣀⣀⣠⠞⠁
⢠⡇⠀⠀⠀⠀⠈⠁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁
⢸⡇⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃
⠈⠳⠦⣤⣤⣤⡤⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⣠⣾⠿⡿⠶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾
⠀⠀⠀⠀⢠⡾⠋⢀⡜⠁⠀⡼⠉⠙⠛⣿⣷⠒⠛⠻⣿⠿⣝⡻⣆
⠀⠀⠀⠀⠀⠀⠀⠞⠀⠀⠘⠃⠀⠀⠀⠇⠘⠆⠀⠀⠙⠀⠀⠙⠈⠃

⠀⣠⣶⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆
⠀⠹⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇
⠀⣠⣿⣿⡏⠁⠀⠀⠀⠀⠀⠀⢀⣤⣾⣿⣯⣀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⣿⣷⣤⡀
⢠⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣆
⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡆
⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⣿⡟⣿⣿⣿⣿⣿⣿⠛⣿⡇⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣾⣿⠃⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠟⠁
⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡇
⢸⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇
⠀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧
⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠰⣿⣿⡏⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⡟⢹⣿⣿
⢰⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⢰⣿⡿⠀⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⣿⣿⡆
⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⢸⣿⡟⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢸⣿⣧
⢸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣧⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠘⣿⡿
⣾⣿⣿⣧⣀⣀⠀⠀⠀⠀⠀⢘⣿⣿⣤⡘⣿⣿⡀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⠀⠀⢻⣿⡅⠀⠀⠀⠀⠀⠀⣠⣿⣿⠁⠀⣼⣿⡇
⣼⣿⣿⣿⣍⡉⠀⠀⠀⠀⠀⠘⠛⠉⠁⠀⣿⣿⣿⡶⠆⠀⠀⠀⠀⠻⠿⠀⠀⠀⠀⠰⠿⠟⠀⠀⠀⠀⠀⠛⠛⠿⠿⠀⠀⠀⠉⠋
⠈⠉⠉⠉⠉⠁
⢀⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡀
⢼⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣧
⠸⢿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⣿⡟
⠀⣾⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣷⣶⡄
⢰⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣇
⢈⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⢹⣿⡄⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠘⣿⣿⣹⣿⣿⣿⣿⣿⣿
⢸⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿
⠀⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⢿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡇
⠀⠸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡿⣿⣿⣿⠃
⠀⠀⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⢰⣿⣿⠇⢸⣿⣿
⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⣿⣿⡄⠸⣿⣿⡄⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢿⣿⣇⠀⠀⠀⠀⠀⠀⣸⣿⡿⠀⢸⣿⣿
⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣻⣿⡇⠀⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢸⣿⣿
⠀⠀⠀⣸⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⠇⠀⣿⣿⠁⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⣿⣿
⠀⠶⣾⣿⣿⣿⠀⠀⠀⠀⠀⣤⣼⣿⠿⠄⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠁⠀⠀⢸⣿⣿⣄⠀⠀⠀⠀⣾⣿⡇⠀⠀⢿⣿⣷⣄