Melody bunny Emojis & Symbols

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⠿⠟⢿⣿⠟⠉⠉⠁⠀⠉⠙⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣧⠘⠁⠀⠀⣀⣤⣄⠒⠀⠀⠀⠀⠀⠀⠐⠂⠀⢉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⢏⢿⣿⣿⣿⣿⠃⠀⢀⣴⣾⣿⣿⣿⣧⣀⣤⣴⣶⣶⣶⣶⣶⣥⣀⡈⠹⠿⠏⠛⣛⣛⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠋⠁⠈⠀⢻⡿⣿⠃⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣴⣿⣿⣿⣿⣷⡝⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠙⠀⠀⠀⠀⠀⠀⠃⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠛⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠉⠀⠀⠈⠙⠻⣿⣿⣿⠛⠉⠙⣿⣿⣿⣿⣿⣿⣿⠀⠈⢿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⡇⠀⠈⢻⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⡿⠠⡤⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⣿⠀⠀⠀⠇⣿
⣿⡟⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⡿⠋⠈⢻⣿⣿⣿⣧⠈⠙⣡⣍⠙⠉⠁⠀⢀⡀⠀⠲⢶⣛⡙⢻⣿⣿⣿⣽⣿⡇⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡿⠀⠀⠀⠀⠙⢿⣿⣿⣦⡀⢀⠤⠒⠒⠲⡀⠈⠁⠀⠀⠉⠉⣡⠏⠈⠻⣿⣏⣿⡇⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡏⠀⠀⠀⠀⠘⣆⠆⠀⠉⠉⢻⣅⢀⣤⣄⠘⣿⣿⣇⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⠿⠛⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⡶⢿⣿⡿⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠘⣿⡿⡿⠃⠀⠀⠀⠀⢰⡇⠀⠀⠀⢀⠴⠛⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⢺⣶⣤⣄⠀⠀⠀⠀⠀⠜⢻⠀⠁⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠉⢿⡔⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠘⠿⢻⣿⣦⣤⣀⣀⡀⠀⠀⠹⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠐⠂⠠⠄⠀⠀⠀⠀⣠⣧⡀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠛⠲⠖⠠⢀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⡀⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⣇⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿
⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿
⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠈⠉⠉⠉⠉⠁⠐⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠆⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠈⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⡀⠈⠀⠀⠀⠉⠢⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⣮⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠋⠀⠈⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠐⠂⠄⠀⠈⠀⠒⠀⠀⠀⠐⠁⠀⠠⠐⠉⠀⢀⠂⠀⠀⠀⠀⠀⠀⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⠀⠀⠀⠀⠀⠑⢄⠀⢠⡀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⠀⠀⢠⣀⠴⠁⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣠⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠂⠀⠀⠐⠒⠂⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠇⠀⠀⠀⠐⠀⠀⠀⠘⠿⠇⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⡉⠉⠁⠀⠀⠀⠀⠀⠀⠈⠠⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀
⠀⠀⠀⠀⠀⠀⠀⢠⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠐⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠠⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⣰⠃⠠⠉⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠗⡀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠎⠀⠀⠀⢰⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠃⡀⠀⠁⠠⠀⠀⠀⠀⠀⠀⠀⠳⡀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠘⠤⠀⠀⠀⠀⠀⠀⠀⠘⠃⠀⠘⠂⠀⠤⠀⠀⠀⠀⠀⢠⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠤⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠖⣦⠀⠀⠀⡀⠀⠀⠀⠈⠁⠒⠦⠀⠀⠀⠀⠀⠆
⠀⠀⠀⠀⢀⡀⠀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠀⠀⠐⠌⠀⠀⠀⠀⠀⠄⠤⠄⡄⠀⠀⠀⠀⠈⠀⠔⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⢠⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠘⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⣤⠐⠂⡄⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⡘⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠈⠆
⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⡱⠄⠀⠀⠄⢁⠀⠀⠐⠁⠀⠀⠀⠀⠀⠈⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⠀⠁⠀⠀⠀⢠⠁⠀⠀⢘
⠀⠀⠀⠆⠀⠀⠀⠀⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠁⠀⠀⠀⠀⡠⠁⠀⠀⠀⢨
⡆⠁⠸⠆⠀⠀⠀⠀⠀⠀⠀⠲⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠋
⠣⡀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠘⠂⠄⠠⡀⠀⢀⡄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⠀⠀⠑⢢⡀⠀⠀⠀⠊⠀⠐⠤⠀⠀⠀⠀⠀⠀⡠
⠀⠈⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠠⠓⠀⠄⠀⣀⡀⠀⣀⣀⣠⣀⡀⠀⠀⠄⢚⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⡆⠀⠀⠀⠀⡄⠀⠀⠀⡬⠀⣀⣀⣹⠃⠐⠉⠂⠤⢤⡀⠀⢀⡄⠔⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⢰⠀⠀⠀⠀⠓⡀⠀⠀⡘⠀⠀⠀⠀⠄⠀⢁⠀⠈⠀⡇⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠉⠁⡄⠀⠀⠐⠒⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠠⠄⠐⠈⠉⠉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠐⠂⠄⠄⠤⡃⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⢀⠐⠀⠀⠤⠀⢀⣀⠀⠀⠀⠘⠀⠀⠀⠀⢀⢀⠀⠀⢠⠀⠀⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⢀⠠⠀⢀⠒⡀⠈⠀⠀⠀⠀⠀⠀⠀⠁⠄⠀⠀⠀⢀⡜⡄⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⠀⠀⠈⡔⠂⠀⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠁⠀⠀⠁⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⢀⡀⠀⠀⠀⠐⠀⠀⠀⡐⠁⠀⢀⠔⠂⠀⠀⠁⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠉⠆⠀⠐⠐⢂⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠌⠢⠀⠀⠀⠀⠀⠔⠁⠀⠀⠀⡇⠀⠀⠰⠀⠀⡠⠀⠀⢀⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡆⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣀⡀⠀⠀⢀⡀⠠⠤⠘⣄⠀⠀⠀⠀⠀⠀⡐⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠈⠀⠈⠀⢀⠼⠐⠈⠀⠀⠀⠀⠈⠁⠐⠂⠈⠁⠀⠀⠀⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠁⠒⠒⠒⠒⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢀⣀⣀⣀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠛⠁⠀⠀⠀⠈⠳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡀⠤⠤⠄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠊⠁⠀⠀⠀⠀⠀⠉⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⠀⠀⠀⡠⠒⠒⠲⣇⡠⠤⠤⢄⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡇⠀⠀⣀⠀⣀⠀⠀⢀⠆⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⡗⠀⠐⡁⠀⢀⠂⠀⢮⡀⠀⠀⠀⠳⢄⡀⠀⠀⠀⠀⠀⣀⠴⠋⠀⠀⠀⠀⢠⠃
⠀⠀⠀⠀⠀⣰⡄⠀⠀⠀⣉⠀⠀⠀⢀⠇⠀⠀⠀⠀⠀⠈⠉⠁⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠘⡀
⠀⠀⠀⢀⠜⠁⠈⠐⠒⠉⠀⠉⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠀⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡
⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠤⠤⠄⠀⠀⠤⠤⠤⠤⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁
⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠔⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⢠⠀⠀⠀⠀⢀⠔⠁⣰⣾⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢
⠀⠀⠘⡄⠀⠀⠀⡈⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡆⠀⠐⡀⠀⠀⠀⠀⢠
⠀⠀⠀⠘⠄⠀⠀⡇⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⢰⠉⠉⡢⠀⠀⠀⠀⠀⢻⣿⣿⠇⠀⠀⡇⠀⠀⠀⢀⠆
⠀⠀⠀⠀⠈⠢⡀⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⡇⠀⠀⡠⠊
⠀⠀⠀⠀⠀⠀⠀⠐⠵⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢁⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠽⠒⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠚⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢴⠁⠀⠀⠀⠀⠀⠀⠀⢈⠇⠀⠀⠐⡆⠀⠀⠀⠉⠀⠀⠈⢲⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢢⠤⣀⡀⠀⠀⠀⡜⠀⠀⠀⠀⠘⡄⠀⠀⠀⣀⡠⠒⠙⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠈⠉⠁⠊⠀⠀⠀⠀⠀⠀⠱⠄⠒⠉⠁⠀⢀⠀⠀⠳⢄
⠀⠀⠀⠀⠀⠀⠀⡘⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⡠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠢⢄⣀⡠⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠐⠒⠲⠄⢀⠋⣦⠄⠈⠓⠂⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣌⠀⠀⠀⠀⠀⠀⠀⠀⠟⠁⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⢀⡴⡀⠀⠀⠀⠀⠀⣠⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠒⠒⠉⠁⠀⠈⠓⠒⠒⠒⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠶⠶⠶⠶⠶⠶⠶⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠉⠉⠉⠙⠻⢿⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⢀⣠⡾⠏
⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⠀⠀⠀⢸⡿⠛⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠰⣿⣦⣤⣀⣀
⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠈⠉⠙⠻⢶⣤⡀
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⢷⣦⣤⣀⣀⣀⣀⣤⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⣿⡀⠀⢀⣤⣞⠉⠁⠀⢿⡉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠘⣷⠴⠋⠀⠈⣦⠠⠤⢼⠉⢻⡦⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣄⡀⠈⢿⡄
⠀⠀⠀⠀⠀⢀⠼⣁⠀⠀⠀⢠⡧⠤⣤⣾⣀⡏⠀⠀⠀⠀⣠⡴⠞⠋⠉⠀⠀⠀⠀⣴⣶⣬⠙⢦⡘⣷⠀⠀⠀⣴⡠⠾⢄
⠀⠀⠀⠀⢠⠏⠀⠈⡛⠓⣶⠊⠀⠀⠀⠀⠈⠀⠀⢀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⡇⠀⢿⣿⠀⠀⢠⠀⠈⠣⡈⢳⡀
⠀⠀⠀⠀⠀⢦⣤⣠⡇⣠⡇⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⢸⣿⠀⣠⠃⠑⠆⠀⠙⠉⠛
⠀⠀⠀⠀⠀⢸⣿⡄⣀⣀⣷⠀⠀⠀⠀⠀⠀⣼⠃⣠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣏⠖⣁⣤⠄⠚⠉⠙⠓
⠀⠀⠀⠀⠀⠘⣿⠟⠉⠀⠁⠀⠀⠀⠀⠀⢰⠇⢰⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⢤⡴⠗⣀⠉⠐⣿⡙⠂⠉⠲⡄
⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠛⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠈⢧⠀⠀⢠⡏⠙⠒⠤⠤⠕
⠀⠀⠀⠀⠀⣠⡾⠻⣷⣄⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠃⠀⠀⢀⡞⠀⠀⣼⠁
⠀⢀⣤⠶⠛⢅⠀⠀⠈⠙⢷⣤⣀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⣀⣠⡞⢩⡏⠀⠀⣠⠋⠹⣄⡼⠃
⠀⣏⠀⠀⠀⠸⡆⠀⢀⡤⠀⠈⠿⣛⠳⠶⣶⡶⠦⣿⡿⠶⠖⠛⠋⢩⡜⠀⣸⠃⠀⡰⠃⠀⠀⢹⡄
⠀⠹⣆⠀⣀⠔⠀⠀⡎⠀⠀⠀⠀⠈⡆⠀⠈⢀⣀⡾⠀⠀⠀⠀⠀⠀⠀⣠⠿⠖⠋⠁⠀⠀⠀⠀⣧⣀⣤⠶⠛⠛⠳⣆
⠀⠀⠈⠻⣧⣀⠀⠀⠘⠦⠄⠀⠤⠞⠀⠀⠀⠀⢿⣅⣀⣀⣀⣤⣤⠶⠋⠁⠀⠀⠀⠀⠀⠀⠀⣠⡿⢤⣄⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠙⠓⠶⣤⣄⣀⣀⡀⠀⠀⠀⣠⠴⠶⠶⣿⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠈⣧⠀⠀⠀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡼⠋⠉⠉⠉⠉⢻⠇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⣼
⠀⠀⠀⠀⠀⠀⣯⠀⢀⡤⣄⡀⢀⣠⣤⡟⠉⠛⠓⠚⠛⠻⢦⣄⣠⢤⣀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡷⣤⣤⡴⠏
⠀⠀⠀⠀⠀⠀⠘⢷⠛⠀⠉⠙⠟⠉⠈⠙⠀⠀⠀⠀⠀⠀⢴⠿⠇⠈⠉⠀⠛⣦⣄⡀⠀⠀⠀⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠶⠦⠴⠞⠁

⡿⠋⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠙
⠁⠀⢠⣶⢶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣴⠶⠾⠿⠶⢶⣤⡀
⠀⠀⢸⣧⣠⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠉⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⠟⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣤⣀⣀⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡄
⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠶⠶⠶⠶⢤⣤⣀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠆⠀⠀⠀⠀⠀⢀⣤⠶⠛⠋⠁⠀⠀⠀⠀⠀⢠⣶⣤⡉⠳⣄⠀⢻⡇
⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⠀⠹⣇⢸⡇
⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠀⠀⣿⣿⠁
⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠀⠀⠀⣰⡟⠀⣠⣶⣄⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠀⠀⠀⢠⣿⠃
⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⢠⡿⠀⠀⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⣰⠟⠁
⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡀⠀⠀⠀⠀⢸⡇⠀⠀⠙⠿⠟⠁⠀⠀⠀⠀⠀⠀⠠⠐⠁⠀⣀⣴⠟⠛⣷⡀
⠀⠀⢿⣦⣀⠀⠀⣀⣤⡾⠛⠁⠙⢷⣄⡀⢀⣀⣼⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⠋⠁⠀⠀⣸⡇
⠀⠀⠀⠈⠙⠛⠛⠋⠉⠀⠀⠀⠀⠀⠉⢻⡟⠁⠀⠈⢳⣄⡀⠀⠀⠀⣀⣀⣤⣴⡶⠟⠛⣧⠀⣾⠀⣦⣤⠴⠛
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠈⠉⠉⠛⠻⣿⡋⠉⠁⣿⠀⠀⠀⠘⢷⣇⣴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠶⠴⠶⣆⣀⡀⠀⠀⠈⠻⣦⣰⡇⠀⠀⠀⠀⢸⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢉⡿⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠉⠙⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣤⣼⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣇⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⠉⠉⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⠀⠉⠙⢳⡄⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠶⢤⣤⣄⣀⣀⣀⣰⠟⠋⠀⠀⠀⠀⠀⠀⠀⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠟⠛⠿⠿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⣠⠞⠛⠻⣦⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⠿⠿⢿⣿⡏⠀⣾⠃⠀⠀⠀⠘⣇⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡏⠀⠀⠀⠀⠈⣿⠾⠷⣤⣠⣤⡀⠘⢷⣄⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠰⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣦⡀⠀⣠⣴⣏⠀⠀⣹⡇⠀⠀⠀⠀⣿⠆⠈⠛⠶⣤⣄⣀⣀⣤⣴⠟⠁⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⠂⠉⠀⠙⢷⡞⠻⢦⣄⣀⣀⣴⠟⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣧⡀⠀⠀⣠⡾⠁⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡟⠈⠛⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⠤⠶⠶⠶⠶⠶⠶⢦⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠞⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠳⢦⣀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣧⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⢠⣶⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣷⡀⠀⢻⡄⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⡄⠀⠀⠀⠀⢰⡏⠀⠀⠀⣿⣿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⠀⠀⣿⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⡄⠀⠀⠀⢾⡇⠀⠀⠀⢿⣿⡿⠃⠀⠀⠀⠀⠀⠀⡞⠉⠙⡆⠀⠀⠀⠀⠀⠹⣿⡿⠃⠀⢀⣿⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣦⡀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢃⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣶⣄⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠂⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⡴⢶⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡙⢻⡿⠛⠛⠛⠛⠋⠉⠉⠉⢹⡏⢻⡉⢀⡀⣸⠇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣠⡟⠁⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠶⣤⣤⣀⣀⠀⡀⣀⡀⣸⡏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠉⠛⢿⣍⣉⣉⣉⣀⣤⣴⣶⣴⣧⢠⣤⣤⣄⣠⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢩⠴⠞⠛⠃⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⢹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣷⣦⣤⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠛⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⣿⣿⣿⣿⣿⣿⣿⡟⠛⠁⠀⠀⠀⠈⠺⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠂
⣿⣿⣿⣿⣿⣿⣿⡷⠉⠀⠀⠀⢀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⢀
⣿⣿⣿⣿⡿⣿⣿⠁⢀⡀⠀⠀⠀⠀⢸⡇⠀⣿⣿⣿⣿
⣿⣿⣿⣿⡅⢞⣉⠃⠀⣿⣫⣶⡀⠀⠀⢙⣄⣸⣿⣿⣿⠀⠀⠀⠀⠀⠔⠀⠀⠀⠀⡀
⣿⣿⣿⣿⣿⣾⣿⡄⢀⣿⣿⣿⣷⣶⣶⣤⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠈⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⣸⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣸⡇⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⠴⠶⠶⠶⠞⠛⠋⠉⠉⠉⠉⠉⠙⠛⠳⢦⣤⣀⠈⢹⡇⠀⢀⣤⠶⠛⠋⠉⠉⠉⠉⢳⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠳⠾⢿⣥⣀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⢀⣴⠾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⣀⣠⡴⠛
⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣤⡀
⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀
⠀⠻⣦⡀⠀⠀⢀⣀⣠⣴⢾⡏⠁⠀⠀⢀⣠⡤⠶⠒⠚⠛⠛⠛⠛⠛⠓⠲⠶⢤⣤⣀⠀⠀⠀⠀⠉⠛⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠈⠉⠙⠛⠉⠉⠁⠀⠈⣷⠀⠀⣴⠟⢁⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄⠀⠀⠀⠀⣾⣿⠟⠶⢦⣤⣤⣤⣤⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⣼⠃⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣦⠀⠙⣧⠀⢀⣼⣳⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⣤⣭⣉⡀⡴⢶⠀⠀⡖⠛⢲⠀⠀⠀⠀⠘⠿⠟⠀⠀⣿⣤⠾⣿⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠈⠻⣿⣤⣷⣄⠈⠛⠁⢀⣀⣀⣀⣀⣀⣤⡴⠾⢿⡁⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⢀⠀⠀⠀⠈⣿⠛⢿⡏⠁⠈⠉⠉⠉⠀⠀⣠⡼⠛⠿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⣿⣧⣀⢀⣠⣿⠤⠼⣇⠀⠀⣠⣶⠶⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠉⠉⢧⣹⡖⠒⠚⠛⠉⢩⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠠⠬⠝⠉⠁⠀⠀⠀⣼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠐⠒⠂⠐⠠⢂⡆⢀⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠙⠛⠛⠒⠒⠒⠒⠒⠚⠲⠺⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠉⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠹⣆⠀⠀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢹⣤⠞⠁⠀⠀⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⣸⠃⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⣟⠀⠀⠀⣰⠂⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠈⠒⠖⠚⠁⠀⠀⠀⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⡀⠀⠄⠀⢀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⢰⣦⠀⠀⠀⠀⠀⠀⣬⡒⡄⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠒⢈⡁⠀⠀⠀⠀⠀⠀⠛⠃⠈⣄⡴⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣉⢋⣰⠄⠀⠈⢦⠀⢘⠒⢲⠆⢤⠀⠒⠊⠐⢾⡉⠀⠀⡠⠐⠂⠠⡀
⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⡠⠦⠤⠤⠶⢄⠼⢓⣛⡐⠈⠑⠚⠉⣹⡋⠀⣀⣠⡅⠀⠚⢻⠃
⠀⢠⠞⠁⠀⠉⠉⠉⠉⢐⡾⠓⠰⢦⡀⠀⣤⠀⠀⠀⣤⣤⣀⡀⠀⠑⠒⣂⣒⠊⣁⡀⢀⠀⢰⡏⠀⠀⢘⡀⠤⡄⠀⠄
⠀⡇⠀⠀⠀⠀⠀⠀⢠⢋⠴⠀⠠⠰⠷⢀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸⡥⠟⠀⠀⣆⠀⠰⡉⠁⣠⢤⡄⠈⢀
⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠆⢦⠇⠀⠒⠙⡄⠃⠀⠀⠀⠀⠀⡇⠀⢐⠀⠀⠀⠀⡸⠀⠀⠀⠀⠁⠀⢘⠁⠘⡑⡝⠰⠅⠈⡀
⠀⠤⢄⡀⠀⠀⠀⠀⠗⠀⢏⠂⣀⠀⠀⣠⠇⠁⠀⠀⠀⠀⣠⣶⡄⣺⠀⢀⣴⣿⣧⠀⠁⣤⢠⡃⠀⠈⡿⠀⢈⡀⠀⡠⠏⠠⠄⢤⠐
⠀⠀⠀⠀⠉⠒⢦⠤⣧⠀⠀⠋⠉⠁⠹⢄⠀⡄⠀⠀⠄⡰⣿⠋⣻⣿⣿⠿⣴⣿⣤⣽⠆⡬⣾⡇⠀⡀⠑⠀⡌⠁⠈⠤⠐⠀⠀⢢⣑⠂
⠀⠀⠀⠀⠀⠐⠂⠀⢺⡄⠀⠀⠀⠀⠀⠘⠂⢡⠰⠁⠈⠧⣿⣿⣿⢉⣿⣦⣾⣛⠿⠋⠀⢠⡨⠁⠀⠈⠖⠘⠻⠆⠠⠂⢀⣄⠀⠀⡨
⠀⠀⠀⠀⠀⠀⠀⡀⢠⠘⢄⠀⠀⠀⠀⠀⣀⢂⠀⠀⠀⠀⠈⠉⠙⡟⠛⠋⠙⡅⠀⠀⠀⢲⣴⠀⠀⠚⠃⢀⢠⠀⠀⠔⡻⠖⠂
⠀⠀⠀⠠⠂⠈⠳⣄⡸⠀⠈⠳⠤⠤⣤⠴⠩⠄⠈⠀⠀⠐⠀⠀⠀⠣⠠⠤⠐⠃⠀⠀⠠⠀⠀⠰⠄⠸⠶⠘⠘⠲⠌⢳⡄
⠀⠀⠀⠐⢤⢤⡠⠃⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⠄

⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠈⢀⣀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢡⣀⣀⣠
⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠔⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⠂⠋⠁⠉⠀⠀⠀⠀⠀⠀⠁⢀
⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠈
⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢀⠀⠀⠀⠠⠊⠀⠀⠀⠀⠀⠀⠀⠈⠂
⠀⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠
⠀⠀⠈⠓⢠⠀⢀⠄⠄⠀⣢⠚⠉⠀⠀⠀⠀⠈⠙⠂⡄⠀⠠⠠⠀⢠⠐⠋⠁⠀⠀⠀⠀⠉⠓⢠⠀⢀⠄⠄⠀⡄⠚⠉
⠀⠀⠀⠀⢀⡍⠀⠀⠀⠈⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈⣹⠀⠀⠀⠀⢉⡉⠀⠀⠀⠀⠀⠀⠀⠀⢉⡇⠀⠀⠀⠈⡍⠁
⠀⠀⠀⠀⠀⠠⠀⢀⠀⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡠

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠉⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠙⠑⢢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⡀⣀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⢣⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠑⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠐⠀⠀⠀⠈⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢨⡞⠁⠀⠈⢣
⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠂⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠘⡄⠀⠀⠘⣇⠀⠀⠀⢸⡄
⠀⠀⡀⡴⠄⠴⠀⠘⠑⠒⠒⠀⠆⠀⠀⠀⠀⠀⠘⠂⠀⠄⠀⠃⠒⠒⠀⠤⡀⠀⠀⠀⠀⠀⠛⠁⢱⠶⠾⠿⠳⠿⠿⢅
⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⡼⢇⣀⠄⠜⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⡀⠀⠐⠂⠀⠀⠐⠂⠠⡀⠀⠀⠀⠀⠀⢀⠀⠀⠒⠀⠀⠐⠒⠀⢀⠀⠈⠀⠀⡇⢀⡤⠖⠒⠊⠉⠉⠐⠒⠦⡄
⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠄⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⣇⠏⠀⡖⣦⠀⠀⠀⢰⣻⡆⠘⣄
⠀⠀⠠⣀⠀⠀⠀⠀⠀⠀⠀⣀⠴⠈⠀⠀⠀⠠⢄⡀⠀⠀⠀⠀⠀⠀⢀⡤⠔⠁⠀⠀⠘⠧⣀⠛⠋⠀⠀⠀⠈⠛⣁⠼⠋
⠀⠀⠀⠀⠸⠥⠀⠁⠁⠠⠵⠀⠀⠀⠀⠀⠀⠀⠀⡀⠧⠄⠉⠉⠀⠼⠄⠀⠀⠀⠀⠀⠀⠀⠀⠸⡿⠛⠉⠛⠻⠧⢀
⠀⠀⠀⠀⠐⠃⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠃⠀⠀⠀⠀⠃⠈
⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠛⠛⠛⠶⠶⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣄⡀⠀⠀⠀⠀⣀⣤⡴⠶⠶⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣀⠀⠀⢀⣀⡔⢢⡀⢀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⢠⡀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠷⡈⠃⠈⢀⠜⠒⣾⡇⠀⠀⠀⠀⠀⠀⣠⡿⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠀⡚⠀⣎⠐⠋⢻⢷⣄⣀⣀⣀⣤⠾⠋⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⡀⠱⠂⠀⢄⣙⡆⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠸⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠉⣀⢾⢀⠷⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⢀⣠⡴⠶⠒⠛⠛⠛⠓⠲⠶⢤⣄⣀⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢀⡴⠋⣡⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇⠀⣼⠁⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣧⠀⢹⡄⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⣠⠤⢤⣀⠀⠀⠀⠀⠀⠙⢧⣿⡄⠀⠉⠁⠀⠀⠀⠸⣭⠗⠀⠀⠀⠘⠻⠋⠀⢸⡇⣰⠟
⠀⠀⠀⠀⠀⠀⠀⣇⡎⠙⢪⣧⡀⠀⠀⠀⠀⠀⠙⠻⠶⣤⣄⣀⣀⠀⠘⠲⠒⠀⠀⠀⠀⢀⣀⣴⠿⠛⠁⠀⠀⠀⣜⢹⣦⠶⢶⡀
⠀⡴⢚⣛⣒⠦⣀⢹⣷⣄⡀⠙⣷⡀⠀⠀⠀⠀⠀⠀⠀⢰⡞⠋⣹⠋⠙⠛⢻⠛⠛⠛⠛⢿⣅⠀⠀⠀⠀⠀⠀⣴⡋⢰⡇⠀⢀⡿⠟⠋⡇⣠⠔⠚⠉⠉⠓⠦⡀
⢸⢱⡇⠀⠈⠑⣌⠋⠀⠀⠉⠳⢿⡇⠀⠀⠀⠀⢀⣤⣤⣈⣷⠞⠁⠀⠀⠀⠘⣧⣤⠤⢴⣾⠁⠀⠀⠀⠀⣠⢞⣡⠈⡆⢉⠩⠥⡀⠀⡟⣴⠃⠀⠀⠀⠀⠀⠀⢹
⠸⡎⢇⠀⠀⠀⣸⠀⠀⠀⠀⢀⠚⢳⡄⠀⠀⠀⢾⠀⠀⠉⢸⠀⠀⢠⡞⠉⠙⠖⠉⠉⢑⣬⠢⠀⠀⠀⠘⢇⡈⠉⢼⡶⠀⣠⡄⠹⢸⢁⡇⠀⠀⠀⢠⠀⠀⠀⢸
⠀⠹⣌⠦⣀⢸⣏⠀⠀⠻⠀⠨⠆⠾⠀⠀⠀⠀⠈⠓⠶⠶⠾⡆⠀⠈⢧⣀⣀⣀⣤⠴⠛⠧⠣⢧⡀⠀⠀⠀⢙⣦⣕⣂⣀⠈⠀⠘⢺⣾⠀⠀⠀⠀⢸⠓⠶⠒⠋
⠀⠀⠈⠳⠬⣭⣭⠤⢤⣤⠴⡂⠀⠀⢐⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⠀⠀⠘⣡⣍⠀⣠⢤⠉⢌⡨⠇⠀⢾⣛⢋⡝⠀⠀⠉⠉⠻⣟⣉⣸⠀⠀⠀⠀⢸⠂
⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠮⣑⣠⠂⠁⠀⠀⠀⠀⠀⠀⢀⡖⠒⠏⠀⠀⠂⠓⠊⠡⠈⠉⠀⠀⢹⠀⠀⠀⠉⠉⢻⠀⠀⠀⠐⢲⣤⡥⠼⠀⠀⠀⠀⡼
⡔⠀⡂⠀⠀⡤⠒⢺⠀⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⢤⣀⠀⠀⠀⠀⢰⡄⠀⠀⢀⣀⠼⠀⠀⠀⠀⢀⡬⠷⠂⠀⠀⢠⡧⢄⣀⣀⣤⠴⠊
⠱⢼⣭⡦⠞⠀⠀⠀⠳⣄⠺⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⢤⣠⠾⠛⠒⠉⠉⠀⠀⠀⠀⠀⠀⠈⠳⢤⣀⢀⣰⣫⠗

⠀⠀⠀⠀⠀⠀⢀⡀⡀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠘⢄⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⢀⢀⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠠⠀⠀⠀⠀⠈
⠀⠀⠀⡉⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠒⠒⠒⠒⠤⢤⣀⠀⢠⠞⠁⠀⠀⠀⠙⡄⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⢹⠇⠀⠀⠀⢀⠀⠀⢹⠀⠠
⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠙⠲⠤⢄⣀⣀⣀⠀⠘⢦⣀⣠⠴⠋⠀⠀⢸⡆
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡤⠤⠤⢬⣀⣀⣀⡀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⢀
⠀⠀⠀⢀⠤⠦⠭⠭⠤⠦⡦⢤⡀⠀⠀⠀⠀⠈⢩⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⣨⠀⠠⣂⠐⣆⡠⠂⢀⣇⣀⠀⠀⠀⠀⣼⠀⠀⢀⠤⠒⠒⠒⠒⠒⠢⢤⡀⠀⠀⢸⠦⢤⡀
⠀⠀⠀⣘⡀⠁⠒⠉⠺⠃⢀⠃⠀⡀⡟⠲⠀⠐⢻⡀⡔⢱⣿⠀⠀⠀⠀⠀⠀⣶⡎⢢⠀⢸⠀⠀⠈⢢
⠀⠀⠋⢐⡁⢜⡀⣀⡡⢧⡠⠰⡀⢠⡡⣊⢁⡁⡽⡓⢧⣀⢃⢀⠀⠀⠁⠀⠀⠈⠁⣸⡠⠋⠀⠀⠀⠘⡆
⠀⠀⠀⠈⡓⣻⠂⣀⣗⡴⡄⡐⠁⣸⢄⣤⡀⣠⠔⠓⠒⠉⠉⠑⣼⠒⡖⠒⠒⢚⡏⠉⠀⠀⡀⠀⠀⠀⡇
⠀⠀⡀⠀⠁⠀⠉⠁⠀⠀⠂⠓⠤⣀⢤⡇⠀⢦⡐⢀⠤⢆⠁⣰⡁⠀⠘⠒⡋⠉⠦⣄⠔⠉⢀⡀⠀⢰⠃
⠀⠀⠀⠉⠒⠢⠤⢀⣀⡀⠀⣀⡀⠀⠣⠵⠤⠘⠛⠚⠢⢼⠍⠊⡥⠂⠀⠀⠈⡦⠤⡎⠀⢠⠋⠀⠀⡸
⠀⠀⠀⢀⢀⣀⢀⡠⠤⠬⣩⡈⢙⡖⠤⠤⠄⣀⣀⡀⠀⣹⠑⢨⠇⠄⠀⡴⠋⠀⠠⠇⠀⠸⠀⠀⡠⠃
⠀⢀⡌⠉⠀⠀⣉⡀⠀⠀⠐⡉⠁⠈⠒⢦⠀⠀⠀⠀⠉⠙⠒⠺⢄⣀⡤⠧⠤⢀⣀⣀⠀⢀⡠⠊
⠀⠀⠆⡀⠀⠒⠚⢷⠀⠀⠈⠅⠀⠈⠁⡸
⠀⠀⠱⡐⠄⣤⢐⡄⠉⠫⢕⡂⡤⠐⠚⣤
⠀⠀⠀⠈⠪⢧⣛⡁⠄⠄⠠⠜⣻⣄⡀⠹
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠈⠁⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢟⣻⣭⣿⣶⣶⣶⣶⣾⣯⣭⣛⣻⢷⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣏⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣝⡻⣷⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣶⠿⣟⣛⣧⣭⣿⣭⣭⣟⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣝⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡾⢟⣻⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣎⣷⣙⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣝⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⡾⢟⣫⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣓⣎⣟⣿⣿⣾⣶⣶⣭⣽⣻⠿⣿⣿⣿⣿⣿⣮⢿⣦
⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⣟⣭⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⢟⣿⣿⣿⡟⣿⣉⣷⢸⡶⣬⣯⣼⣷⡿⣿⣿⣶⣭⡻⣿⣿⣿⣧⢿⣇
⠀⠀⠀⠀⠀⢀⣴⢿⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣛⡽⣴⣿⣿⣿⣿⣗⣛⣭⢫⣾⣼⢪⣿⡱⣹⠿⣰⣏⣫⣍⣽⣎⠟⣽⢿⡟⣿
⠀⠀⠀⠀⣴⡿⣡⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣟⣯⣷⣿⡟⣼⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣥⣝⣋⢿⣿⢺⣇⣽⡝⣿⡋⣿⠿⣠⢻⡇⣿⠃
⠀⠀⠀⢰⣿⢹⣿⣿⣿⣿⣿⠿⣟⣯⣽⡾⠿⠛⠉⢰⣿⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣵⣾⣝⣟⡻⢿⢇⣯⣞⣼⡟
⠀⠀⠀⠀⠻⢷⣿⣭⣽⣷⡶⠿⠛⠋⠁⠀⠀⠀⠀⢸⡏⣿⣿⣿⣿⣿⣿⡿⣫⣶⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⢿⣿⣿⣿⣿⣿⣴⣿⣿⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢧⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠿⠿⠿⣿⣿⣿⡿⣛⡻⣿⣿⣏⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣜⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢃⢿⢏⣾⣿⣿⣿⣵⣿⢷⣿⣿⣟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣮⣻⢿⣿⣿⡿⢟⣛⡛⣿⣿⠸⣣⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣹⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣿⣷⢭⣵⣿⣿⢟⣽⣿⣿⣿⡟⣭⣹⣿⣿⣿⣿⣿⣿⡿⣣⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢸⣷⣍⣿⣿⣟⣵⣿⣿⣿⣿⣿⣇⣿⡏⣿⣿⣿⣿⡿⣟⣵⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡫⣾⣿⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣭⣭⣽⣷⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣜⣫⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⣿⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣾⣿⢟⣯⣮⣝⣛⡿⠿⠿⠿⣿⣿⡫⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣷⡾⠟⠋⠉⠙⠛⠛⠿⠿⣷⡹⣿⣷⣹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣝⠿⣣⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠟⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⠀⠀⠀⢀⠠⠐⠈⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠀⠀⠀⠈⠢⡠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁
⠀⠀⣀⣠⣄⣠⣴⣦⣤⣤⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⠠⠊
⢀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢀⡠⠚⠀⠀⠀⠀⠀⠠⠀⡀⠀⠔⠁⠀⣀⠤⠂⠁
⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢦
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠙⠿⠿⢻⣿⣿⣿⣿⣿⣿⣿⣿⣄⣀⣀⠀⠀⠀⠀⡇⠀⠀⢀⠤⠒⠈⠀⠀⠀⠉⠁⠒⠠⢀⠀⠀⠀⠀⠀⡆
⠀⠀⠀⠀⠙⠛⠛⠛⠉⠉⠉⠛⠛⠉⠁⠀⠀⠀⠀⢃⠀⠀⠂⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⣤⡉⢆⠀⠀⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⢄⣆⠀⠀⠀⠀⠀⡃⢘⠀⠀⠀⠛⠃⠈⠄⣠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡦⠀⠄⠀⡀⣀⣀⣀⢀⡀⠠⠞⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠙⠋⡂⠠⠚⠀⠱⠤⠤⡔⠳⠂⢐⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⠈⢡⠀⠀⠀⠀⠀⠀⢏⡁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠅⠠⠀⡖⢣⠔⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠄⠀⠠⠊⠀⠂⠒⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠴⠤⢤⡀
⠀⠀⠀⢠⠤⢤⣄⣀⣀⣀⣠⣤⠞⠀⠀⠹⡏⠉⠀⠘⡆⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠤⠤⠤⠤⡴⠋⠀⠀⠀⠀⠀⠙⡄
⠀⠀⠀⡏⠀⠀⠀⠈⠁⠀⠀⢸⠀⠀⣯⡟⠉⠙⣖⠛⠓⣆⠀⠀⢀⠴⠊⠉⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⢀⡔⠀⢻
⠀⠀⠀⣧⡄⠀⠀⠀⠀⠀⠀⠈⠲⠴⠞⠧⣀⡴⠯⠃⢀⡏⠀⢰⠃⠀⠀⢰⡋⢉⣖⠋⢲⠀⢧⡀⠀⠀⣀⡴⠋⠀⠀⢸
⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠖⠋⣧⠀⠘⢦⣀⣀⣰⠃⠣⠼⠃⡏⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠈⠳⡀
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠒⢻⠉⠉⠀⠀⠉⠙⢲⠞⠲⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄
⠐⠒⠚⡏⠁⠀⠀⣾⠆⠀⠀⠀⣀⡀⠀⠀⠘⠟⠀⠀⠀⡿⠒⠂⠀⠀⠀⠀⣾⠀⠀⣀⠤⠒⠚⠉⠉⠉⠑⠒⠢⢄⠀⠀⠀⠀⡇
⠀⠀⠔⠻⣍⢀⠀⠀⠀⠀⠀⠈⠒⠋⠀⠀⠀⠀⢀⡤⣾⣓⡤⠀⠀⠀⠀⠀⢻⠀⡜⠁⣾⡆⠀⠀⢀⠀⠀⠀⣤⠆⠙⡄⠀⢰⠇
⠀⠀⠀⠔⠊⠓⢦⣄⣀⣀⢀⠀⠀⣀⣀⣀⣤⠴⠺⡄⠀⠀⢹⡄⠀⠀⠀⠀⢨⢧⣣⡀⠉⠀⠀⢀⣛⣋⠀⠀⠈⠁⡰⢃⣤⠋
⠀⠀⠀⢀⣴⡚⠉⡴⠁⠈⢯⣉⠉⣉⡼⠃⠈⢧⡀⠘⢆⣀⠞⠀⠀⠀⠀⢰⡋⠀⠉⠛⣷⠦⢤⣤⣤⣤⠤⠤⡶⠟⠛⠁⠘⢦
⠀⠀⢠⠏⠀⠙⣾⠁⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⢧⠴⠊⠁⠀⠀⠀⠀⠀⠀⠓⠒⠋⠙⠻⣄⡴⠁⠀⠹⣤⠜⠳⢶⣛⣲⡤⠞
⠀⠀⠘⢧⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⢳⠀⢹
⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⣀⣠⣀⣀⣀⣀⣀⣠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢰⠉⠙⠂⠀⠀⠀⡼⠒⠋
⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠋⠀⠑⢤⡀⠀⢀⡜⠁
⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠤⠴⠛⠦⠤⠤⠤⠴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠛⠛⠦⠞

⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⣾⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣠⣤⣿⣿⠃
⠀⠀⠈⢹⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⢸⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⣀⣀⣠⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁
⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢠⣄⠀⣤⣌⣿⣿⣿⠟⠿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⢩⣿⣿⣿⣿⣿⡿⢿⣿⣷⣬⡉⣀⣨⣿⡿⠛⠁⠀⠀⡀⠙⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡿⠋⠀⠀⠀⠉⠙⠛⠻⠟⠉⠀⠀⢠⣴⣾⣷⡄⠈⢻⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⡇⠀⠀⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠃⠀⢀⡶⠞⠓⠲⠄⠀⠀⣤⡄⠀⠀⠀⠈⠉⠉⠀⠀⠀⣸⡟
⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡄⠀⠀⠀⠀⠀⠀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⡀⠀⠀⠠⠤⠄⠀⠀⠀⠺⡿⠉⠀⠀⠀⠀⠀⢢⣞⣡⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢌⣿⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡸⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠊⠉⠁⡀⠀⠀⠀⣸⣶⣶⠶⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⢀⠿⠋⠁⠀⠀⠉⢟⣣⡀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢘⣿⣿⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠋⠻⢷⡿⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⢀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠒⡀⠀⠀⠠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⠂⠀⠈⠒⠊

⠀⠀⠀⣀⣤⣤⣤⣀⣀
⠀⢠⡟⠉⠀⠀⠀⠉⠙⠛⠶⣤⣀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⡀
⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣭⣳⣦⣴⠾⠛⠉⢉⡽⠋⠀⠀⠹⣷⢦⣀
⠀⠸⣇⠀⠀⠀⠀⠀⠀⢰⠏⠀⠈⠉⠻⢿⣷⡄⠀⡾⠁⠀⢀⣀⡀⢹⡆⠉⠳⣄
⠀⠀⠘⢷⣄⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⢾⠇⠀⠀⣟⢩⡟⠋⠉⠻⣦⡽⠷⠶⣤⡀
⠀⠀⠀⠀⠙⠳⣤⣀⠀⢹⡶⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠙⣿⠀⠀⠀⠀⣹⣦⡀⠀⠈⡷
⠀⠀⠀⠀⠀⠀⠀⠉⢛⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠶⣟⠛⢧⣄⣀⣴⣯⣼⠇⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠈⠉⢷⡀⠀⢀⣰⠟⠶⣄⡀
⠀⠀⠀⠀⠀⢀⣀⣀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣦⡀⠙⠛⠛⠁⠀⠀⠈⠛⢶⣄
⠀⠀⠀⠀⠀⠈⠉⠈⣿⠉⠁⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠙⠳⢦⣄⡀⠀⠀⠀⠀⠀⣈⡷
⠀⠀⠀⠀⠀⠀⠠⠶⠿⡗⠂⠀⠀⠉⠁⠀⠀⠀⢠⠴⢤⡀⠀⠀⠀⠻⠃⠀⠀⠀⢼⣿⣿⡟⠒⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣶⠂⠀⠀⠀⠀⠀⠀⠈⠓⠚⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠈⣻⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⠉⠓⠆
⠀⠀⠀⠀⠀⠀⠀⣰⡾⠻⠟⢿⣍⣿⠛⠻⣶⡶⠶⠤⠤⢤⣤⣴⠶⠶⣿⡋⣿⠿⠾⢷⣄
⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠈⣿⠇⠀⠀⠹⣧⣀⠀⠀⢀⣼⠏⠀⠀⠘⣿⠇⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⢰⡟⠀⠀⠀⠀⠈⠙⠛⠛⠛⠁⠀⠀⠀⠀⢻⡇⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠶⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡶⠶⠟⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠉⠙⠛⠛⠛⠿⠶⢶⡶⠾⠟⠛⠛⠛⠛⠉⠉⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣤⣀⣀⣀⣀⣸⣷⣀⣀⣀⣀⣀⣤⡾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠋⠉⠉⠉⠉⠉⠉⠁

⠀⠀⠀⠀⠀⠀⣼⠁⢀⣴⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣯⢿⣿⣿⣿⣿⣿⠉⣥⡀⢙⡣⡀⠀⠀⠀⠀⢹⡀
⠀⠀⠀⠀⠀⠀⢿⢆⣾⣿⣿⣿⣿⡟⣁⠀⢧⢙⣿⣿⢿⣿⣿⣿⣾⣿⣿⣿⣿⣿⠀⠛⠃⠘⠃⣻⣤⣀⡀⢀⣸⡇
⠀⠀⠀⠀⠀⢀⠌⣾⣿⣿⣿⣿⣿⣿⣮⣀⣼⠿⠃⢀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⢾⠆⢀⣘⠏⡘⠛⣽⣏⣀⠰⣷
⠀⠀⠀⠀⠀⢸⢸⣿⣿⣿⣿⣏⠀⣀⡬⣥⡄⡶⢳⡟⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢤⡀⠀⢙⣿⣧⡄⣛⢾⣏⠀⣤
⠀⠀⠀⠀⠀⠸⡌⣿⣿⣿⣿⣿⣆⠻⠷⢟⣙⣋⣋⠉⠀⣿⣿⣿⣿⣿⡿⢟⡿⠋⠉⠉⠉⠉⠉⠉⠻⣿⣿⣦⣉⣠⡉
⠀⠀⠀⠀⠀⠀⠱⡘⣿⣿⣿⣿⣿⣦⣠⣾⣿⣿⣿⣿⣿⣿⡿⢟⣉⣥⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠘⣿⠁
⠀⠀⠀⠀⠀⠀⢀⠧⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠾⡷⢸
⠀⠀⠀⠀⠀⠐⣁⣴⣦⣤⣭⣭⣭⣽⣿⣾⣿⣿⣿⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠆⣠⣼⡆
⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⢠⣾⣿⣿⣿⣻⣿⣿⡿⠿⠛⠛⠃⣴⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⣦⡀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠈⠉⢩⣩⢻⡟⠋⠉⠛⠒⠲⠀⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠶⠶⠶⢿⣿⠟
⠀⠀⠀⠀⠈⣻⣟⣷⣠⣤⣤⣤⠤⠤⠈⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠙⠛⠋⠀⢠⣤⣤⣤⣼⣿⣀
⠀⠀⠀⠀⢨⣿⣯⣿⣇⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⢈⣽⣿⠋⠉
⠀⠀⠀⠀⠸⢾⣿⣿⣿⣶⡞⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣿⠿⣧⡄
⠀⠀⠀⠀⠀⢩⣿⣿⡿⡏⠻⣷⣦⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⣾⣿⣿⠟⡑⡁
⠀⠀⠀⠀⠀⠈⠛⣿⢗⣿⠀⠘⢿⣿⣿⣿⣿⣿⣶⣶⣶⣴⣦⣶⣴⣤⣴⣶⣶⣿⣿⣿⣿⣿⣿⣿⣇⡣⢬⠄
⠀⠀⠀⠀⠀⠀⠀⣶⣛⣥⣷⡀⠀⠻⣿⣿⣿⣿⡿⠛⠻⣍⡉⠛⠛⠛⣻⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡆
⠀⠀⠀⠀⠀⢠⢺⣿⣿⣿⣿⣿⣄⠀⠈⠻⣿⣿⣿⣄⠀⠀⠉⠉⣳⡏⠁⠀⣼⣿⣿⠟⢁⣼⣿⣿⣿⡿⢿⣿⣦
⠀⠀⠀⠀⠀⠀⣿⣿⣿⡋⢿⣿⣿⣷⣄⡀⠈⠻⢿⣿⣦⠀⠀⢨⣿⣿⠆⢀⣾⡿⠃⣠⣾⣿⣿⣿⣿⣧⣼⣿⣿
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣦⣀⠀⠙⣿⣶⣤⣤⣬⣥⣤⣾⠋⣠⣾⣿⣿⣟⣿⣿⣿⣿⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣤⡈⠻⣿⣿⣿⣿⡿⢁⣾⣿⣿⣿⣿⣟⣻⣿⣿⣿⣿⣧⣤
⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡘⣿⣿⡟⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃

⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠤⠄⡀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣤⣀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠑⢶⡟⠁⢀⠠⠤⢄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣇⣠⣤⣤⣤⣬⣄⡀⠀⠀⠀⠀⠱⠊⠀⠀⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣡⠄⢬⣿⣿⡂⢲⡀⡆⢇⠀⠀⣀⠔⠁⡸
⠀⠀⠀⠀⠀⠀⣴⣶⣤⣤⡌⣿⣿⣿⠟⠋⠛⠷⣶⡾⠟⠻⠃⠜⠁⠃⠀⠉⠉⠀⠀⠀⢇⠀⡠⠠
⠀⠀⠀⠀⠀⡈⠉⠹⠿⣿⣧⣿⣿⠃⠠⣷⡄⠀⠈⠀⢠⡇⡔⠊⠁⠀⠀⠉⠐⠠⡀⠀⠈⠋⠀⠜⢓
⠀⠀⠀⠀⠀⠙⠛⠶⣬⣝⣹⣿⣿⣄⠀⠀⠀⠀⠘⠀⠀⢻⠀⠉⠀⠰⠄⠀⢾⠆⠘⠀⣰⠀⠡⠀⢉⠇
⠀⠀⠀⠀⠀⡔⠉⠠⠃⠈⠀⣠⠿⠿⠓⠲⠤⠤⠬⢴⣖⠁⠑⣤⠤⢀⣀⣀⣀⣠⠼⠴⠁⠁⠉⢦⠶⠄⡀
⠀⠀⠀⠀⠀⠑⠰⣄⣀⢀⠰⠀⠀⠀⠀⡢⠄⣀⡀⠀⠀⣙⠁⢀⠉⠁⠀⠑⠂⠐⠊⠀⢀⠀⠀⠀⠀⡀⢘
⠀⠀⠀⠀⠀⠀⠀⡅⢀⠦⢀⣀⠝⠂⠉⠀⠀⠀⠀⠀⠀⠀⠁⠒⠐⠒⠒⠒⠪⠠⠤⡤⠊⠑⠠⠍⡎⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠑⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⠊⠁⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠐⠂⠤⣀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⣰⠁
⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠉⢣⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁
⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠀⠀⠀⠀⠀⠈⡆⠀⠀⣀⠤⠖⠋⠁
⠀⠀⠀⠀⠀⢀⡜⠀⠀⠀⠳⣄⠀⠀⠀⢀⡟⠉⢙⡖⠀⢲⡀
⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⠀⠀⠉⠑⠈⢡⠛⠀⢧⡼⠀⢞
⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠚⠦⠤⠼⡄
⠀⠀⢠⡇⠀⠀⠀⠀⠀⢀⡠⠔⠒⠈⠉⠉⠀⢒⡢⢄⠀⠀⣟
⠀⠀⠘⡇⠀⠀⠀⡰⢪⣥⡄⠀⠀⠀⠀⠀⠀⣿⣿⡆⠱⠀⡏
⠀⠀⠀⠹⡄⠀⢸⠁⠻⣿⠇⠀⠀⠰⠶⠀⠀⠈⠋⠁⣨⠜⠁
⠀⠀⠀⠀⠈⠒⠼⣄⣀⣀⣀⣀⣀⡈⣈⣀⡴⠒⣲⡾⣅⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⡉⠀⣨⠧⢤⠋⠀⡀⢹⣀⠀⡏
⠀⠀⠀⠀⠀⠀⢀⠴⠦⣸⣍⠉⢁⣀⣠⡃⠠⠁⠄⠈⡻⠁
⠀⠀⠀⠀⠀⠀⢇⠀⢀⡏⠀⠉⠉⠀⠀⠈⠁⠒⡖⠉⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠈⠑⠚⢇⡀⠀⠀⠀⠀⠀⠀⢰⠀⠀⡘⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠸⡦⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠲⠤⣄⣀⡴⠃⠠⠚⠀⠀⠀⠣⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⠊⠁⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠁⠐⠂⣄⡀⠤⠤⠠⠤⢼⡀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⡇⠀⠀⣀⠀⣀⠀⠀⠑⠦⡀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢪⢄⠀⡤⣵⠀⠀⠀⠈⢦⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠰⠆⠀⠀⠀⢀⠠⠬⠳⣶⣼⠅⠂⠐⢄⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢡⣄⡀⠀⠀⠀⠀⢠⣾⡇⢡⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⣿⠇⠀⠠⢠⠀⠈⠛⠃⢘⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠄⡀⠘⢄⠀⠀⠀⠈⠐⠁⠀⣀⡠⠚⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢢⣬⠍⢍⠃⠐⢒⣀⠀⠈⡗⢨⠶⣁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⢁⠧⠀⢠⡱⠊⠁⠀⠈⠞⢻⠜⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠫⠑⣤⠊⠁⠀⠀⠀⠀⠀⢀⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠒⠾⠃⠀⠀⢰⡆⠀⠀⠙⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠄⡀⠤⠊⠑⠂⠄⠐⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠿⠛⠛⠛⠛⠿⣿⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⣷⣦⣤⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡇⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠉⠉⠀⠀⠀⠈⠉⠻⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣶⡶⠶⠿⠿⠿⠷⠶⠶⣦⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡶⠿⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⣠⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣸⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠇⠀⠀⠀⠀⢸⣷
⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⢀⣴⠶⠶⣦⣄⠀⠀⠀⣴⠟⠉⠉⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡿⠃⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢻⡷⠿⠿⣯⣀⣀⠀⣸⡿⣧⣀⠀⠀⠀⣀⣤⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠰⣿⡀
⠀⠀⠀⠀⠀⠀⢻⣧⣀⠀⠀⠀⠀⠀⢻⣦⠠⠶⢿⣇⠀⠀⣸⡟⠉⠀⠙⣷⠈⠙⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠷⠶⠶⠿⢿⠇⠀⠀⠀⣿⠷⠟⠻⣦⣀⠀⣀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣤⣤⡾⠋⠀⠀⠀⠈⠙⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠁⠀⠀⠀⠀⠀⠀⣀⣠⣤⡴⠶⠶⠶⠶⠶⠶⠶⢶⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⣠⡴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⡾⠋⠀⣴⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣷⣆⠀⠙⣧⡀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢀⣿⠁⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢸⣿⣿⣿⠀⠀⠈⣷⠀⠀⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠸⣿⠀⠀⠘⠿⠿⠃⠀⠀⠀⠀⢰⡋⠉⡣⠀⠀⠀⠀⠛⠿⠟⠀⠀⢀⣿⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣽⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠃⣠⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣿⣦⣴⣶⡶⠶⠶⠶⠶⠶⠶⠶⠶⠶⣶⣦⣀⣠⣤⣶⣾⡿⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡏⠻⣦⣀⠀⠀⠀⠀⢀⣠⠾⠋⣿⠋⠉⠉⠉⠹⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠟⠛⠻⣦⡙⡟⠳⠞⢳⢛⣥⡶⣦⣿⡦⣤⣄⣠⣤⣼⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⢸⡗⠙⠦⠴⢋⡿⠁⠀⠀⠹⡿⠛⠉⠉⢨⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣤⣴⣿⣧⣤⣤⣤⣴⣿⣄⠀⢀⣤⡄⠀⢀⣠⣾⠁⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠋⠁⠈⣿⠋⠀⠉⢻⣏⠛⠋⠉⠙⠛⠛⠉⢻⡟⠋⠛⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠘⣷⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⣸⢿⣇⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠾⠛⠛⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣀⣴⣿⠟⢻⣆⡀⢀⣀⣤⡶⠟⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠉⠛⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠶⢦⣄⠀⣠⡤⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠘⠟⠁⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠖⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠳⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣄⣀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣰⡶⠛⠉⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⣠⣶⣦⣤⣄⣹⣷⠞⠛⠻⣯⡉⣉⣉⣉⣉⣉⣹⣧⣴⠾⠟⠛⠛⣷⡀
⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠈⠉⣿⠃⢀⡀⠀⠈⢿⡛⠛⠛⠛⠛⠛⠋⠀⠀⠀⠀⠀⠘⣷
⠀⠀⠀⠀⠀⢀⣼⣧⣤⣄⡴⠚⠛⠻⣏⢹⡆⠀⠈⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⡏⠀⠀⣠⣾⡁⠀⠀⠀⣽⠋⠀⠀⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯
⠀⠀⠀⠀⠀⢻⡀⠀⠿⡼⢷⣤⣤⠶⠋⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⣿⣦⣀⣠⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡆
⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣧⣤⣤⣄
⠀⠀⠘⠛⠛⢻⡟⠛⠂⠀⠀⠀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⢸⡇
⠀⠀⠀⢀⣠⣼⣷⡤⠀⠀⠀⠀⠻⠟⠀⠀⠀⠀⢀⡤⠤⡀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠐⢲⣿⠷⠦⠄⢀⣴⠶⠛⠲⣦
⠀⠀⠀⠀⠀⠀⠹⣧⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⠔⠃⠀⠀⠀⠀⠀⠀⠀⠀⠶⣤⣾⡁⠀⠀⣴⠏⠀⠀⠀⣀⢸⡇
⠀⠀⠀⠀⢠⡴⠞⠛⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠋⠈⠙⠳⠤⣟⠀⢀⣀⣴⢏⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠶⣦⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣶⣾⣿⣋⠁⠀⠀⠀⠀⣠⡶⣫⣤⣍⣭⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⣀⣀⣶⣤⡾⢋⡟⠉⠉⣿⠉⠉⠉⠉⠉⠁⣿⠀⠀⢹⣆⢙⣷⠶⠦⣤⡾⣫⡾⠋
⠀⠀⠀⠀⠀⢀⡾⠋⠉⠀⠈⢛⡿⠁⠀⠀⠛⠛⠛⠛⠛⠛⠛⠋⠀⠀⠀⢹⣿⠁⠀⠀⠘⡿⠋⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⣠⡴⢦⣤⠶⢦⡄⠀⠀⠀⣾⠁⠀⠀⠀⣰⠇⠀⠀⠀⣸⡏
⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⢰⡏⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⣿⠀⠀⠀⠹⢦⣄⣠⡴⠋⠀⠀⢀⣸⡛⣻⣇⡀
⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⣾⠁⠀⠀⠀⠀⠈⠻⣄⡀⠀⣀⣼⠃⠀⠀⠀⠀⠀⠈⣷⠀⠀⢀⡶⠛⠉⠙⠉⠉⣙⣳⣦
⠀⠀⠀⠀⠀⠀⠀⠙⠛⢻⡏⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⣼⣧⡴⠞⠛⠳⠾⠋⠙⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣶⢤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡤⠶⠶⠶⠞⠛⣻⡟⠁⠀⠘⢻⡾⠻⠛⠛⠛⠛⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⡀⠀⠀⠀⠀⣀⣽⣇⣀⣀⣀⣀⣠⣤⡾⠏⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠛⠋⠩⠭⠩⣉⣉⣉⣉⠀⢀⣀⣀⣀⡄⠄⠤⠛⠛⠛⠛⠛⠛⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⠶⢤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⣠⠋⠀⠀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠲⢤⡴⠞⠉⢳⡄⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣤⠤⢤⣤⣄⣤⡴⠶⢶⠇⢀⡤⣬⠷⠦⣤⠶⠓⢦⠀⠀⢀⡏⠀⠀⠀⠀⠀⣸⠁
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡀⠈⠳⣇⠀⠀⣽⣳⠀⣸⠀⡞⠙⣆⣀⡤⣄⣠⠴⠛⠋⠉⠛⠢⡀
⠀⠀⠘⣧⡄⠀⠀⠀⠀⠀⠀⠀⠙⠚⠋⠉⠙⠛⠧⣥⡴⢷⣴⡁⢹⣅⡹⠄⡞⠁⠀⠀⠀⠀⠀⠀⣷
⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠉⠁⠀⠳⠴⢇⠀⠀⠀⠀⣠⠀⢠⡇
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⡆⡼⢀⡤⠴⠶⠤⢤⣀⠀⠀⠙⠛⠛⠉⠁⠀⣞
⠀⠤⠖⢿⠒⠀⠀⠸⡷⠀⠀⠀⣠⠲⡄⠀⠀⠀⠀⣷⠃⣾⡿⠀⠀⠀⠈⠙⠢⣄⠀⠀⠀⠀⠀⢹
⠀⠀⠠⠼⢷⡁⣀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢀⣹⣆⠈⠀⠀⡠⡀⠀⠀⠀⣈⠱⡄⠀⠀⠀⢸
⠀⠀⠀⢀⡴⠛⠳⢦⣤⣀⣀⣀⣠⠖⠛⠛⠚⠛⣏⣅⡈⠳⣄⢀⣊⡁⠀⠀⢸⡿⠀⢸⠀⠀⢀⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠁⠘⣦⡀⠀⠀⠀⢸⣆⠙⣏⠉⠉⠉⠉⠳⣄⣀⣀⣠⠞⣀⡤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠉⠙⠛⠛⠉⢻⣩⡏⠓⠦⣄⣀⣀⣀⣹⠏⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠺⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣇⠀⠀⠀⠀⠀⠀⠘⢦⡔⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠶⢤⣤⣄⣀⣀⣠⣤⡴⠚⠁⠘⣦⠀⢀⠀⠀⠀⠀⠀⣇⢀⡼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⢷⠀⠀⠀⠀⠀⢻⠀⠀⣠⠇⢀⠜⠀⠀⠀⠀⢸⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠚⠳⠦⠤⠴⠶⠋⠀⠀⠑⠒⠾⣄⣠⣤⠤⠤⠞

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠷⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠞⠉⠁⠈⠙⣧⡀⢀⣀⣀⣠⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠉⠻⢦⣤⣤⣤⣤⣤⣤⣠⡾⠃⠀⠀⣀⣀⠀⠸⣿⠛⠉⠉⠁⠀⠹⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠈⣽⠃⠀⠀⣾⠉⣩⡷⠚⠛⠳⣦⡀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠻⢶⡏⠀⠀⠀⠀⠈⢿⠛⠻⠶⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⢦⣤⣤⣼⣧⠀⠀⠀⠀⢀⡿⢶⡄⠀⠈⣿⠄
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠦⣤⠶⠿⣥⣴⠇⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣦⡀⠀⠀⣠⣴⡏
⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠹⣷
⠀⠀⢠⣤⣤⣤⣾⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣰⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣷⣀
⠀⠀⠀⠀⠶⠶⢿⣟⠓⠀⠀⠀⠀⠘⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠛⠛⢹⡟⠉⠙⠛⠂
⠀⠀⠀⠀⠀⢀⣀⣿⣤⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠋⠓⣦⠀⠀⠀⠀⠀⠀⠸⠿⠟⠀⠀⠀⠀⠀⢠⣄⣼⣇
⠀⠀⠀⠐⠚⠋⠉⠉⠻⣦⡀⠀⠀⢀⡴⠶⡄⠀⠀⠀⠀⠉⠓⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠉⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⠏⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⣾⣯⣀
⠀⠀⠀⠀⠀⣀⣤⡤⠤⠴⣤⣾⣥⣴⣿⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠁⠀⠙⠳⡦
⠀⠀⠀⠀⠸⣿⣤⣀⣀⣼⠋⠀⠀⠀⠀⠀⠉⠛⠿⣿⡛⠶⠶⠶⠶⠶⢤⣤⣤⣤⡴⢶⣶⡶⠛⠛⠉
⠀⠀⠀⠀⠀⢻⡀⠀⠹⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡟⠶⢦⣤⣤⣀⣀⣤⡤⠶⠛⠉⠹⣆
⠀⠀⠀⠀⠀⠈⣿⢙⢙⡻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⡠⢤⠀⠀⠀⠀⠸⣉⡵⠘⢷⡀
⠀⠀⠀⠀⠀⠀⢹⡌⠚⣡⡌⠙⣶⣤⣀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠀⠓⠘⠀⠀⠀⣀⠀⠀⠀⠀⠀⢳⣄
⠀⠀⠀⠀⠀⠀⢀⣷⣤⣉⣁⣴⣏⡾⠉⠛⢓⠶⠶⠶⠛⠁⡖⢲⠀⠀⠀⠀⠀⠸⣈⠇⠀⠀⠀⢠⠒⣽⣦
⠀⠀⠀⠀⠀⠠⣟⠙⠷⠶⠶⠞⢙⡧⠀⠰⣉⡵⠀⠀⠀⠀⠈⠉⠀⢀⡠⡀⠀⠀⠀⠀⠀⠀⠀⠈⠒⠁⠘⢧⡀
⠀⠀⠀⠀⠀⠀⠉⠛⠳⠶⣶⣶⣿⣆⠀⠀⠀⠀⠀⢔⠓⡄⠀⠀⠀⠘⠦⠞⠀⠀⠀⡠⠲⡄⢀⣀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣷⠦⠴⠞⠻⣮⣉⣀⣠⠾⣦⣀⠀⢀⣴⠿⣦⣈⣚⣵⠏⠉⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠁⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠉⠉⠉⠀⠀⠀⢨⣿⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣾⣿⣤⡶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠞⠛⠛⠛⠛⠛⠳⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣆
⠀⠀⠀⠀⠀⠀⣠⡶⠞⠛⠛⠛⠶⣴⣟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⠀⠉⠳⣆⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⣠⡼⠋
⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀⠀⢀⡿⠛⠛⠛⠛⠋⠉
⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠚⠳⠶⢦⣤⣀
⠀⠀⠀⠀⢸⡄⠀⠀⠀⢶⣄⡀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠉⠻⢦⡀
⠀⠀⠀⠀⠘⣧⠀⠀⢀⡴⠛⠉⢻⠓⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦
⠀⠀⠀⠀⠀⢹⡦⠞⠁⠙⣄⠠⢼⡟⣲⠄⠀⠀⠀⠀⠀⣀⣀⣤⡤⢤⣤⣄⡀⠹⣇
⠀⠀⠀⠀⣠⠚⣀⡀⠀⢰⠧⠤⠶⢤⡇⠀⠀⢀⣠⠖⠋⠉⠀⠀⠀⢰⣶⣦⠙⢦⣻⠀⠀⠀⢦⣚⠦⡀
⠀⠀⠀⠀⠃⠀⢨⠉⡽⠁⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠃⠈⣿⠂⠀⠼⡀⠈⢠⠥⣄
⠀⠀⠀⠀⢹⣷⠚⠐⢣⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⣄⠞⢀⠈⠤⠤⡌
⠀⠀⠀⠀⠸⣿⠖⠋⠛⠀⠀⠀⠀⢠⡏⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀⣀⣀⡠⠆⢙⠊⢵⠺⠉⠢⡄
⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⢸⠀⠘⠿⠟⠀⠀⠀⠀⠀⠀⢰⠏⠀⠙⢇⠁⠀⡞⠑⠢⠤⠼
⠀⠀⠀⢀⡤⠞⠻⣦⡀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⣠⡜⠀⠀⢠⡎⠀⣰⠃
⢀⡴⠚⠉⢣⠀⠀⠈⠙⠶⣤⣄⣀⡀⠘⢢⣄⣀⣀⣀⡤⢴⡏⢸⠃⠀⡰⠃⠘⣶⠃
⠘⣧⠀⠀⡨⠀⢀⠊⠁⠀⠙⢎⠉⠛⡉⢉⡟⠉⠉⠀⠀⠋⢀⣾⣠⠔⠁⠀⠀⢹⡀⢀⣠⠤⢤⣄
⠀⠈⠳⣎⡀⠀⠈⢦⡀⠀⣠⠆⠀⠀⢈⣾⣀⠀⣀⣀⣠⠴⠋⠁⠀⠀⠀⠀⠀⣸⣯⣉⠁⠀⠀⢸
⠀⠀⠀⠈⠙⠲⠦⣤⣀⣀⣀⠀⠀⣠⠴⠶⢽⡏⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⣧⠀⠀⣸
⠀⠀⠀⠀⠀⠀⣠⠴⠋⠀⠉⠉⢹⡇⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡇⠀⠀⡏
⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⢸⢷⣄⣀⣸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⣰⠇
⠀⠀⠀⠀⠀⢳⣤⠎⠷⠦⡴⠛⠿⠄⠀⠀⠀⠈⣙⣶⠏⠷⠋⣦⡀⠀⠀⠀⠀⠀⢰⠏⠉⠉⠉
⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠛⠲⢤⣤⡤⠏

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠖⠉⠀⠀⠀⠀⠀⠈⠓⢄
⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠔⠒⠒⠛⠋⠉⠙⠛⠒⣲⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⢀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢳
⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠘⡇
⢀⡏⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡤⢤⡴⠒⠒⢾⡄⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⡇
⠈⣆⠀⠀⠀⢰⡃⣠⠤⢽⠀⠈⠀⢠⣗⣒⡦⣸⠉⠲⠤⠤⠴⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀
⠀⠈⠢⢤⣀⣀⣓⣬⡽⠟⢳⠦⠔⢯⠉⢻⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠓⡶⠞⠀⠀⠘⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⠤⠤⠤⠤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⡀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⢀⡞⠁⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠙⣆⠀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⢀⡤⣄⠀⠸⡄⠀⣼⠀⠀⢸⣿⡿⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⣿⣿⠆⠀⠀⢸⠀⠀⠀⢀⡞
⠀⠀⢠⠖⠚⠀⠈⡇⠀⠹⣄⠸⡀⠀⠀⠉⠁⠀⠀⠀⠺⢤⠽⠀⠀⠀⠀⠈⠉⠀⠀⠀⡼⠀⠀⡠⠊
⠀⠀⠈⠢⣄⣀⣠⠃⠀⠀⠈⠳⣝⣦⣀⣀⣀⣀⣀⣈⣓⣒⣒⣉⣀⡀⠀⠀⠀⢀⣠⣮⠤⠒⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡩⠟⡏⠲⣄⠀⣀⢀⡀⣀⠴⠋⢹⠒⠒⠚⠻⣅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠞⠉⠙⢦⢻⡉⢉⡝⢁⡤⠤⢼⣢⣤⡤⠤⡞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⢈⡇⠙⠋⢀⡎⠀⠀⠀⠉⠀⠁⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⢤⠴⠚⢫⡭⠭⢭⡱⣄⣀⡠⢤⡤⠴⢮⡤⠶⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⢯⠀⠀⠀⠘⠆⠀⠀⠀⠀⠀⠀⢣⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⡼⡄⠀⠀⠀⠀⠀⠀⠀⢀⡠⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⣀⡤⠞⠁⠙⢦⣀⣀⣠⠤⠖⠋⠉

⠀⠀⣀⣤⣶⣶⣿⣷⣶⣶⣶⣦⣄⡀
⠀⣼⡿⠋⠁⠀⠀⠀⠀⠀⠈⠉⠛⠿⣷⣦⣀
⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣄
⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⡀
⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦
⠀⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣄⣀⣀
⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⣀⣠⣴⡶⠿⠛⠛⠉⠉⠉⠛⠛⢿⣦⣄
⠀⠀⠀⠈⠻⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠈⠛⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣦⣄⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠄⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⠾⠻⠶⣦⣌⣻⣿⠿⠿⠿⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠏⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠙⠛⠁⠀⠀⠀⠀⣻⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠋⠀⠀⠀⠀⠀⠀⠸⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⢀⠎⠁⠉⠲⠀⠀⠀⣠⡿⢿⣷⣄⠀⠀⠀⠀⠀⣀⣤⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠐⢆⣀⣀⡴⠁⠀⠀⠛⢷⣄⠙⠻⠿⣷⣶⣾⡿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠉⢉⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦
⠀⠀⠀⠀⠀⠀⣠⣿⣿⣦⣀⣀⣀⣤⣾⠟⠿⣶⣤⣤⣤⡾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀
⠀⠀⠀⠀⠀⢠⣿⠏⠀⠉⠛⠛⠛⠉⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⣠⣴⠾⠟⠛⠉⠉⠉⠉⠉⠉⠉⠉⠛⠛⠛⠿⢶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⣿⡇⠀⠀⣠⡿⠋⠁⢀⣴⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢷⣦⣄
⠀⠀⠀⠀⠀⢿⣧⠀⢰⡟⠁⠀⢀⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⡄
⠀⠀⠀⠀⠀⠘⣿⡄⢻⡇⠀⠀⠈⢿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠘⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⣤⡀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡆⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⣀⣼⠇⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡇⠀⠀⠸⣷⠀⠀⠀⠀⠀⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣦⣤⣤⣄⣀⠀⠀⠀⠀⢶⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠿⠋⠀⠀⠀⢀⣿⠀⠀⠀⠀⢠⣾⠟
⠀⠀⠀⠀⠀⠀⢀⣤⣄⡰⠋⠹⣯⣀⠀⠀⠈⠙⠲⣄⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⢀⣤⣾⠟⠋
⠀⠀⠀⠀⠀⠀⠻⣄⠈⠁⠀⠀⣀⡾⠀⠀⠀⠀⠀⠈⢿⣷⣶⣦⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣷⣾⠿⠋⠁
⠀⠀⠀⠀⠀⠀⡠⠋⠀⠀⠀⠀⢙⡆⠀⠀⠀⠀⠀⠀⠈⢧⠀⠉⠉⢻⣿⠟⠛⠿⠿⠿⣿⣿⡿⠿⠿⠿⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠻⡶⢦⠀⡞⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢸⣷⠿⠛⠿⣿⣇⠀⠀⠀⠀⠈⣿⣷
⠀⠀⠀⠀⠀⠀⠀⢥⠈⠉⠀⠀⠀⠐⠂⠀⠀⠺⠀⠀⠀⣿⠁⠀⠀⠀⠈⣿⣦⣴⣶⣾⣿⣿⠋
⠀⠀⠀⠀⠀⠀⠀⢈⣧⣄⠀⠲⠀⠀⢀⡀⠀⠀⣄⠀⠀⣿⡀⠀⠀⠀⠀⠉⠉⠉⠀⠀⣾⡏⠀⢀⣀⡀
⠀⠀⠀⠀⠀⠀⢀⣿⠋⠉⠓⢦⣄⣀⣈⡀⣀⣀⣠⡴⠞⠙⠻⠷⢶⣶⣿⣀⣀⣀⣤⣾⣿⣷⡾⠛⠛⠛⠿⣶⡀
⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⣽⡏⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠋⠁⠈⣿⡄⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⣿⠇
⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣀⠀⠀⣠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⢻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠛⠛⠟⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣦⣄⣀⣨⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣶⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉⠻⢷⣤⣤⣤⣤⣴⣶⠾⠿⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣾⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⢀⣾⣿⣧⣤⣤⣤⣄⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣴⣶⣶⣶⣶⣤⣤⣄⣸⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠙⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢀⣴⣿⣿⣿⣿⣿⣿⠋⠉⠀⢀⡌⢻⣿⣿⣿⣿⣿⣿⣿⡍
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⣿⣇⠸⠇⠀⠈⢁⣾⣿⠟⠉⠙⢿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⢿⣿⣷⣶⣴⣼⣼⠟⠁⠀⠀⠀⡀⠹⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠉⢨⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠈⠉⠛⠛⠁⠀⠀⢀⣠⣾⠗⠀⠙⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⠃⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠀⠀⠀⢹⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠈⠉⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠀⠀⠀⠘⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡇⠀⠀⠈⢿⣿⡿⠀⠀⠀⢀⡤⡀⠀⠀⠈⠁⠀⠀⠀⢰⣿⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⡀⠀⠀⠀⠉⠀⠀⠀⠀⠈⠓⠁⠀⠀⠀⠀⠀⠀⢠⣾⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⡠⠰⠆⠀⠀⢀⣠⣾⣿⣏⣀⠀⠀⣠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣿⣶⣤⣀⡀⠀⠀⢀⣀⣀⣠⣤⣶⣿⣿⣿⣿⣿⡿⠿⠛⠤⠼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠉⢯⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡖⣾⣿⠿⠟⠛⠛⣿⣿⣿⣿⠟⠁⠈⠛⠿⢿⣿⠀⠀⠈⣇⠹⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⡟⠁⠀⠀⠀⠀⢘⣿⠟⠁⠀⠀⠀⠀⠀⣾⠉⢹⠀⠀⠈⢧⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⢏⣀⠗⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠸⡆⠘⣧⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣶⠆⠀⠀⢹⡶⠶⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣀⣀⣤⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣟⠁⠀⠀⠀⠸⣇⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⠉⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⠛⠻⣷⣤⣤⣤⣴⡿⠟⠒⣿⡋⠀⠀⠀⠀⠀⠀⢀⡴⢦⡀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⢸⡇⠈⣷⠀⠀⠀⠀⠀⠈⠉⠛⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠀⠀⢸⡇⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⣠⡟⠀⠀⠀⠀⠙⠓⠶⠶⢤⣤⣤⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⣀⣤⡴⠶⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⢀⡴⠖⠛⠉⠉⠉⠛⠓⠶⢦⣤⣀
⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⢦⣄
⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀
⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄
⠀⠀⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠻⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠀⢀⣀⣤⠶⠚⠛⠉⠉⠉⠉⠙⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠉⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠈⠙⠳⣤⣀⣀⢀⣀⣀⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡗⠀⠀⠀⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠛⠉⠛⠻⢦⣀⡼⠟⠛⠉⠛⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⢀⣤⣭⣀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⢰⡏⠀⠀⠙⣧⠀⠀⢠⡾⠉⢷⣄⡀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠘⢧⣀⣀⣴⠃⠀⠀⠈⠙⢦⡀⠈⠙⠶⠶⠤⠴⠶⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠉⠉⡀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠛⢷⣀⠀⠀⠀⣀⡴⠟⠛⠦⣄⣀⣀⡴⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠉⠛⠛⠛⠉⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣤⣤⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⣀⣤⠶⠛⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠉⠛⠓⠶⢦⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⡾⠋⠀⠀⣀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢰⡏⠀⠀⠀⣼⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣿⠀⠀⠀⠀⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⣿⠀⠀⠀⠀⠈⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⠀⠀⠙⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠉⠉⢱⡆⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠇⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⢠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠑⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡿⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⣰⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣽⡷⠶⠖⠶⠶⣤⡀⠀⠀⠀⠙⠦⠤⠤⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣠⡾⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠻⢶⡞⠁⠈⠷⢶⡄⠀⠀⠀⠙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⢀⣤⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣦⠀⠀⠀⠀⣤⡾⠃⠀⠀⠀⠀⠀⠹⣷⠶⠶⢦⣤⣤⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣯⣴⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢀⣀⣈⣷⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⢀⣀⣘⣏⠉⠉⠙⠛⠓⠒⢶⡖⠶⠶⠒⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡾⣧⢀⡿⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣹⠟⠋⠉⠙⠻⣄⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠙⠋⠀⠀⠀⠘⠃⠀⠀⠘⠃⠀⠀⢸⠃⠀⠀⠀⠀⠀⢻⣤⣤⡴⠶⠟⢻⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣧⡀⠀⠲⠀⠀⢀⣀⠀⠀⣠⡀⠀⢸⣆⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⢀⡟⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠙⠷⣦⣤⣀⣀⣀⣀⣀⣠⣤⠾⠋⠙⠳⢦⣤⣴⣧⣀⡀⢀⣀⣴⠞⣧⡶⠛⠉⠉⠙⠳⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⠋⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠘⣧⠀⠀⠀⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀⢀⣰⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠳⠶⠶⠶⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⠒⠚⠛⣧⡀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠴⠶⠛⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠶⠶⠖⠚⠛⠛⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⡀⢀⣀⣤⣴⠶⠶⠶⠶⢦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢷⣦⣀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⠶⠶⣬⣻⣿⣶⠶⢶⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⣉⡁⠀⠀⠀⢸⣷⡀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠋⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⡟⠉⠉⡧⠀⠀⣾⡛⠿⣦⣤⣤⣤⣤⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋⠀⠀⠙⠲⠚⠃⠀⠀⠈⢷⡀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣦⣀⣀⣤⡶⠟⠷⢶⣶⣶⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⢀⣠⣴⣶⠶⠶⢶⣶⣶⣶⣶⣦⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢠⡾⠋⠁⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠻⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⢰⡟⠀⠀⣸⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⢻⡇⠀⠀⠹⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣶⡌⠻⣦⠀⠀⠀⠀⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠑⠆⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠘⣧⠀⠀⠀⠀⠀⣸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣷⣤⣀⣀⣀⡀⠀⠀⠀⢤⡉⠉⡀⠀⠀⠀⠀⠀⠀⠙⠻⠟⠁⠀⠀⢹⡆⠀⠀⢀⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣴⠟⣿⣋⠉⠉⠙⢶⣄⡀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⣀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣅⠉⠀⠀⢀⣽⠃⠀⠀⠀⠙⢿⡿⢷⣶⣦⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣿⠿⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⢀⣨⡇⠀⠄⠀⠈⠑⠈⢧⣀⣀⣹⣿⡟⠉⠉⠙⠻⣿⣟⠋⠉⠉⠀⠀⠀⠀⠀⠀⠐⠒⠒⠒⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡿⢤⡴⠋⢉⡀⠀⠀⠀⠘⠳⠀⣼⠟⠉⠉⠙⣷⣀⣀⣠⣴⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡀⠀⠀⠈⠁⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠈⠙⠛⠛⢻⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡷⣦⣈⠁⠀⠀⠀⠉⢁⣰⣿⡿⣦⣤⣤⣄⡀⠀⣀⣴⣿⣿⣷⡿⠿⠿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠉⢻⡿⠿⠞⠛⠋⠉⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠉⢻⡇⠀⠀⠀⠀⢻⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠀⠀⠀⠀⢸⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣀⣀⣀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡟⠛⠋⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣄⣠⣼⣿⣄⠀⠀⠀⠀⠀⠀⣀⣠⣤⣴⣶⣾⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠛⠻⣷⣶⣴⣶⡾⠿⠟⠛⠋⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠉⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠱⡀⣀⠤⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡀⠀⡟⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡵⠀⢄⡠⠆⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠱⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⢤⠀⠀⠀⢀⡄⠀⢀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⢉⠀⠄⡀⡀⠀⠡⡖⠊
⠀⠀⠀⠀⠀⢀⠠⠀⠄⠀⢀⣄⣀⠀⡐⠀⠚⠀⠃⠅⠁⠀⠘⠁⠀⡆⠀⠉
⠀⠀⠀⠀⠀⡌⠀⠀⠀⠀⠀⢀⠐⢂⠨⠀⠀⠀⡇⠀⠈⠁⢸⠜⠉⠅⠀⠈⡠⢄
⠀⠀⠀⠀⠀⠀⢀⠀⠀⠐⠰⢈⡀⢀⡄⠀⠀⢀⠆⣀⢀⠄⠊⠀⡄⠀⠀⡆⢈⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠕⢲⡀⠀⠀⠐⠀⠠⠀⢂⠀⠀⠀⠀⠀⠅⢘⠇⠀⠀⠦⢀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⡄⡀⠀⠀⠀⢒⠀⢩⠀⠀⠲⠀⢈⡠⠄⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠄⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⠿⠷⣶⣄⠀⠀⢀⣠⣴⣶⣿⣿⣿⣷⣆
⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣾⡟⠁⠀⠀⠀⠈⠻⣷⣾⣿⠿⠛⠋⠉⠀⠀⠹⣿⣇
⠀⠀⠀⠀⠀⠀⠀⣾⣿⠋⠉⠉⠉⠛⠻⠿⣿⣷⣶⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠙⣿⡅⠀⠀⠀⠀⠀⠀⠀⢿⣿⡀
⠀⠀⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠉⠉⠉⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⢀⣴⡾⢷⣶⣴⣿⣷⣶⣦⣄⠀⢀⣀⣠⣼⣿⣇⡀
⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⣏⠀⣼⡿⠋⠀⠀⠀⠉⢻⣿⡟⠛⠉⠉⠉⠙⢿⣦
⠀⠀⠀⠀⠀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡅⠀⠀⠀⠈⠻⣿⣿⠃⠀⠀⠀⠀⠀⠀⣿⣷⣶⣄⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⠸⣿⣷⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⣀⠀⢀⣀⣨⣿⣧⡀⠀⠀⠀⠀⣰⣿⠃⣸⣿⠀⠀⠀⣸⡿
⠀⠀⠀⠀⠀⠀⠀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠉⠙⠿⣶⣶⣶⣾⡟⠻⠿⠟⠃⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣄⡀⠀⠀⣀⣼⣿⣇
⠀⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⠿⠿⠟⠋⢻⣿⡄
⠀⠀⠀⠀⠀⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣇⣀⣀⣀⡀
⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⣿⠿⠿⠻⠿
⢀⣀⣠⣤⣴⣿⣿⣤⣤⣄⠀⠀⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿
⠛⠛⠋⠉⠉⢿⣿⠉⠉⠉⠀⠀⠀⠀⠀⢸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⣤⣴⣿⣧⣤⣀⣀
⠀⠀⠀⠀⠀⠸⣿⣇⣀⣀⠀⠀⠀⠀⠀⠸⢿⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠀⠀⠉⣿⣿⠛⠉⠛⠛⠃
⠀⠀⠀⣠⣴⣶⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⡁⠀⣹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣰⣿⡏
⠀⠀⠀⠉⠉⠀⠀⠹⣿⣦⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡿⠋⠀⠈⠉⠛⠛⠂
⠀⠀⠀⠀⠀⣤⣾⠿⠋⠁⠉⠻⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⠟⠉
⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣿⣶⣦⣤⣤⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣤⣤⣤⣶⣾⣿⣿⠿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⡿⠟⠋⣽⣿⠟⠛⠛⠻⣿⡿⠿⠿⠿⠿⠿⠿⠿⣿⡟⠛⠛⠛⣿⣿⡛⠿⣷⣦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣾⣿⡟⠁⠀⢀⣼⡿⠃⠀⠀⠀⠀⠙⣷⣤⣀⠀⠀⢀⣠⣾⠟⠀⠀⠀⠀⠈⢿⣷⡄⠀⠉⢛⣿⣷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⣾⡿⠛⠋⠉⠻⣿⣦⣠⣾⡟⠁⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠻⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⢻⣿⣦⣴⡿⠛⠉⠛⠛⢿⣷⡀
⠀⠀⠀⠀⠀⠀⢠⣿⡇⠀⠀⠀⠀⠘⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣯⠀⠀⠀⠀⠀⢨⣿⡇
⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⢀⣾⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣷⡀⠀⠀⠀⠀⣿⣷
⠀⠀⠀⠀⠀⠀⠘⢿⣧⣄⠀⣰⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣄⠀⢀⣰⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⡿⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⣶⣶⣶⣶⣶⣿⠿⠻⣿⣦⣄⡀⠀⠀⠀⠀⢀⣀⣴⣿⡿⠿⣿⣷⣶⣶⣶⣶⣾⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡍⠉⠉⠀⠀⠀⠀⠀⠙⠛⠿⠿⢿⣿⣿⠿⠿⠛⠁⠀⠀⠀⠀⠉⠉⠉⢩⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⡿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⡿⠿⠟⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠐⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠄⠀⠀⠀⠢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣀⣀⠠⠀⠀⡀⢑⠀⠠⠠⠀⠀⠀⠚⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠔⠀⠒⠂⠘⠀⠤⠀⠀⠀⠀⠧⠀⠠⢇⠁⠆⠁
⠀⠊⠀⠀⠀⠀⠀⠀⣉⠀⠀⣀⠀⠠⠀⠐⠂⠀⠄⠀⠀⠀⠀⠀⠄⠄⠀⠄⠀⢀⠐⠀⢀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡢⠄⠤⢄⠐⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠀⠊⠀⠠⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⣀⢐⠘⠉⠀⠀⠀⠀⠂⠀⡀⠀⠄⠒⠀⠱⢾⠇⠀⠀⠂⢀⠁⠀⠀⠠⠄⠔⠂
⠀⠀⠀⠀⢀⠂⠰⠀⠈⠉⠀⠀⠀⠠⢠⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠇⠀⠁⠀⡆⠄⢀⠂⠀⠀⠲⡀
⠀⠀⠀⠀⠉⠀⠀⠃⠀⠀⠀⠀⠀⣰⠈⠂⠀⠀⠤⢀⠠⠀⠤⠂⠉⠠⡄⠆⠀⠠⠀⡅⠁⢡⢸⡗
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⢀⡀⢨⣐⠀⠀⠀⠐⠁⠖⠐⠰⠀⠀⠨⠉⠁⠀⢠⡀⡿⠤⠈⢮
⠀⠀⠀⢠⢠⠄⠉⠁⠀⡀⠀⠀⠈⠠⠠⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠀⠁⠈⠉⠠⠜⠢
⠀⠀⠀⠀⠀⠁⠀⠀⠁
⠀⠀⠀⠀⠀⠀⢠⠀⠀⠠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠠⠠
⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠠⠀⠀⠈
⠀⠀⠀⠀⠀⠐⠀⠠⠄⠐⠀⠀⠀⠀⢀⠄⠄⠀⠀⠀⠀⠄⠂⠀⠀⠀⠀⢀⠀⠀⠀⠈⠠⢰
⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣾⣿⡇
⠀⠀⠈⠻⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣶⣿⣿⣿⣿⣿⣿⡏⠉
⠀⠀⠀⠀⣿⣿⣿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣀⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠈⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢰⣦⠀⢰⣦⣹⣿⣿⡿⠛⠻⢿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠿⣿⣿⣿⣬⡉⡄⣄⣽⣿⠟⠋⠀⠀⠀⡀⠈⢻⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠉⠙⠛⠿⠿⠋⠁⠀⠀⣀⣴⣾⣷⡤⠀⠹⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⠀⠀⢸⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠀⢰⣤⠶⠦⣤⡀⠀⠀⢀⣀⠀⠀⠀⠀⠙⠛⠛⠃⠀⠀⠀⣿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡇⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠛⠁⠀⠀⠀⠀⠀⢀⡴⢋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⡄⠂⠉⠀⠀⠀⠄⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⢘⣿⡶⠧⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⢰⠾⡇⠀⠀⠀⠀⠀⢀⠀⠀⣀⣀⣠⣤⣦⠀⠀⠀⠀⠘⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⣼⣿⡿⠟⠻⢿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠛⠉⠀⠀⠀⠀⠈⠏⠷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⢀⣀⣠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⣻⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠋⠛⢿⣾⡿⠁⠙
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠈⠐⠒⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠐⢤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢃⡂⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢀⡸⢀⠬⡁⢹
⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠣⢕⣆⠁⡆⠀⠀⠀⠀⠀⣀⣀⠘⢤⡘⠒⣁⣨⠂
⠀⠀⠀⢰⠃⠠⡈⠙⣆⠀⠀⠀⠉⠀⠀⠀⠀⢀⠔⠋⠁⠈⠑⢄⠑⠚⠹⣆⣀⣀⡠⠤⠎⠉⢆⡀
⠀⠀⠀⣸⠴⠦⢴⡀⢸⣀⣀⣀⣀⣀⡤⠴⢶⠃⠀⠀⠀⠀⠀⠈⢆⠀⣰⠝⠉⠀⢣⠀⣏⣱⠀⣸
⠀⠀⡘⠁⢀⠠⠤⢿⠙⢫⡭⠛⠉⠀⠀⠀⡏⠀⠀⠀⣰⠃⠀⠀⠘⣶⠃⠀⠀⠀⠘⠦⠴⢤⡼⠁
⠀⠀⡇⠈⠀⠀⢀⠾⣤⠋⠀⠀⠀⠀⣀⠴⠛⠤⠤⠚⠁⠀⠀⠀⠀⠈⢦⣠⡤⠤⣤⡀⠀⢀⣀⣀⣀
⠀⠀⠈⠓⠲⠲⡉⠀⠿⣄⣀⡤⠔⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⠤⠐⠻⢞⣁⣀⠀⠈⠓⡄
⠀⠀⠀⠀⢀⠴⠛⠓⠲⣏⠀⠀⠘⡇⢀⢤⡒⠒⠒⠒⠒⠒⠢⢄⡀⠀⠀⣼⠁⡀⢤⠞⠙⡈⠙⢢⢀⡼⠁
⠀⠀⠀⠀⢸⡀⢀⣰⠤⢬⠒⠢⢤⡑⢇⡸⠟⠀⠀⡀⠀⠀⠸⣿⠘⣄⠴⢧⣀⣀⢸⣄⠀⠰⠀⢐⠏
⠀⠀⠀⠀⠀⢳⠋⡀⣠⠉⢻⠤⡀⠙⣶⣫⡳⢲⡒⣢⠤⠀⠒⢶⡉⢁⣀⣀⣼⣹⠯⠼⠤⢄⣀⠞
⠀⠀⠀⠀⢀⣸⣸⣙⡏⢆⣼⡀⠀⣀⣏⣀⡕⠛⠓⡲⠚⠚⠉⡹⠀⣤⢗⠖⠋⠀⠀⠀⠀⠀⠈⠳⡀
⠀⠀⢠⠞⠁⠀⠂⠀⠉⢻⠭⠽⣉⣁⡔⠙⡦⠒⠤⠈⠑⠚⠉⢹⠉⢦⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱
⠀⠀⠃⠀⠀⠄⠀⠀⡔⠋⡤⠤⡉⢙⣿⠀⠑⣄⠀⠀⠀⠀⣠⠾⣤⠻⡇⠀⠀⠄⠀⠀⠀⠀⠀⠀⠘⡄
⠀⠘⠀⠀⠀⠀⠀⠀⠙⡆⠑⣚⠀⡾⠙⠤⠤⠚⠣⣠⠔⠉⠀⠀⢨⠦⡷⠒⢦⠀⠀⠀⣠⠴⠒⠢⢴⠁
⠀⠠⠀⠀⠀⠀⠀⠀⠀⠉⠋⢩⠋⡇⠈⠀⠀⠀⠐⠀⠀⠀⠀⠀⢣⠀⡖⢢⠈⢻⣦⡞⢀⣀⠂⠀⢸
⠀⠀⡄⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⡇⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠳⣤⢌⠁⡰⠋⢀⡞⢍⡀⠉⢳⡋
⠀⠀⠘⠦⠤⠤⠤⠖⠊⠁⠀⠀⠀⢳⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⡴⠁⠀⣿⠀⡐⠹⡄⠀⠀⠄⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⣠⠔⠋⠀⠀⠀⠹⣄⣀⡤⠗⠦⣄⣀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠴⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⠿⠃
⢀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡄⠀⠀⠀⠀⠀⣀⣴⣾⣿⣿⣧
⢻⣿⣿⣿⣤⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⣾⣿⣿⣷⠀⠀⢀⣴⣾⣿⣿⣿⣿⣿⣿
⠀⠉⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣄⠀⠀⠀⠛⢻⣿⣉⣀⡀⠀⠀⠀⠀⠈⣿⠋⢉⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣾⣿⣄⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠛⠙⠛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁
⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⣿⣿⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⡿⠀⠀⠀⣿⠆⣸⣿⣿⣿⣿⣿⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡄⢠⠀⡀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠋⠉⠀⠀⠉⠛⠿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠻⣿⣿⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⣈⣳⣦⣄⡀⠀⠀⠀⠀⠉⠛⠿⠿⠟⠉⠀⠀⣠⣴⣯⠻⣿⣿⠇
⠀⠀⠀⠀⠀⠀⢀⣀⣨⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⢨⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⡇⠀⢿⣿
⠀⠀⠲⠾⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠘⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⣠⠤⣄⠈⢿⣿⡿⠃⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⢀⣄⠀⠀⠀⠙⠒⠋⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣯⠙⠲⠶⣶⠟⠀⠀⠀⠀⢀⣼⠟⠀⠀⣠⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠻⣿⣿⣿⣿⣿⣿⣷⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⣦⠞⠁⠀⠀⣀⣠⡶⠟⠁⠀⣠⡴⠿⣤⢧⡴⢦⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣦⣤⣴⣶⣿⣿⣿⣤⡶⠶⠟⠛⠉⠀⠀⠀⣼⠋⠀⠀⢀⣼⠿⣴⡇
⠀⢠⣶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠿⠟⣩⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣴⠶⣦⠀⠀⠀⠀⠘⣧⠀⣠⡴⠟⠁⠀⣿⣍
⠀⢸⣿⣿⣿⣦⡀⠀⢀⣠⣤⣴⣟⠉⠀⠀⠀⠘⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠻⠶⠞⠀⠀⠀⠀⠀⣹⣾⡋⠀⠀⢀⣴⠟⠉
⠀⢾⠿⣿⣿⣯⣠⣴⣿⣿⡿⢿⣿⡧⠀⠀⠀⠀⠀⠀⠀⠸⠟⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿⣆⣀⠀⠀⠀⢀⣴⠞⠁⠈⠙⠛⠛⠛⠁
⠀⠀⠀⠈⠻⠿⠿⠟⠋⢸⡇⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠛⠛⠛⠿⣿⣿⡍⠛⣦⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⡿⢦⣤⣀⡀⠈⠻⣷⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠋⠀⠀⠀⠉⢻⣤⣀⣀⣠⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⢿⡛⠁⠀⠀⠀⠀⢀⣴⠟⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠳⣄⠀⠀⠶⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢦⣤⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⣀⡀⠀⢀⣀⣀⣀⣀⣠⡴⠟

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠁⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⢰⣤⣀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠁⠙⢧⠀⠀⠀⠀⠀⠀⡽⡟⠀⠀⠀⠀⠀⠒⠿⣿⡿⢆⣠⣾⣿
⠀⠀⠀⠀⠀⠀⠀⢀⣤⡤⠀⠀⠀⠀⣰⣌⡄⠠⣤⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢀⠘⠙⡟⢳⡀
⡀⠀⠀⠀⠀⠀⠀⠀⠟⠛⠀⠀⠀⠀⣿⡿⠓⠚⠛⠻⢿⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⣶⣿⣷⡤
⣤⣤⣤⠤⢠⡀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⣁⣄⡀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠂⠘⢿⣿⡇
⣿⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠘⠛⠏
⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣷⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢀⡀⢰⡄⠀⠀⠀⠀⠀⣀⣤⣀
⠁⠀⣴⣿⣿⣷⣄⠀⠀⠀⠀⠀⠙⣿⡿⠧⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⡷⠆⠀⠀⠀⢸⣿⣿⣿
⠀⠀⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣀⣤⣾⣿⣿⣿
⠀⠀⠈⡿⠿⣿⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⡜⠃⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⣿⣿⣿⣿⡷⠆
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠈⠁⠈⠛⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟
⠀⠀⢠⣼⣆⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣤⣤⣶⣶⣶⣶⣶⣶⣶⣤⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠘⠛⢯⠈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠗
⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿
⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠉⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟
⠀⠀⠀⠀⠀⠀⠈⠛⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⣠⣤⠀⠀⣠⣤⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⡁
⠀⠀⠀⠀⠀⠀⠀⢼⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⠛⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠈⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⢿⣿⣿⣿⣾⣷⣿⣿⣿⣿⠿⠻⠿⣿⣿⣿⣿⣿⣿⣄⡀
⠀⠀⠀⠀⠆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⠟⠉⡀⠀⠀⠀⠀⠀⠉⠙⠛⠿⠿⠛⠉⠀⠀⠀⡀⠈⢻⣿⣿⣿⣿⣿⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡏⠀⠀⣿⣷⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣿⡇⠀⠀⢿⣿⣿⡟⠁⠉
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠹⣿⣿⣿⣿⠀⠀⠘⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡟⠀⠀⣾⣿⡿⠁
⠀⢠⣀⣀⡿⡀⠀⠀⠀⠀⣼⣿⣿⣿⣇⠀⠀⠈⠉⠁⠀⠀⠀⠀⠸⡍⠆⠀⠀⠀⠀⠈⠉⠀⠀⣰⡿⠋
⠀⠀⠹⣿⡇⠀⠀⠀⠀⠀⠈⠻⠛⠻⢿⣦⣀⠀⠀⠀⠀⠀⢀⣼⣷⣶⣾⣠⡀⠀⠀⢀⣠⣴⠞⠋⠀⠀⠀⠀⠀⠀⠘⣡⡤
⠀⠀⠘⠛⠹⠆⠀⠀⠀⠀⣴⠛⣦⣤⣶⣾⣿⣿⣿⣶⣶⣶⠋⠀⠀⠈⣧⠀⠘⣿⣿⣿⣥⣀⣠⡞⢷⡀⠀⠀⠀⠀⠰⣿⣧
⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠙⠛⠉⠙⠛⠛⠛⣿⣿⣿⣿⣿⠄⠀⠀⣠⣏⠀⠀⠛⢿⣿⣿⡿⠟⠓⠚⠀⠀⠀⠀⠀⠀⣾⣿
⠀⠀⠀⡀⠀⠀⠀⢹⣿⣿⣿⠃⠀⠀⣼⠓⣾⣿⣿⠿⠛⠁⠀⢀⡼⠁⠈⢷⠀⠀⠀⣻⠀⠀⠀⠀⠀⣠⡶⢀⡀⠀⠠⠏⠁
⠀⠀⣾⣿⡶⠂⠀⢸⣿⣿⣿⣦⣀⢀⣸⡗⠋⠈⠓⠶⠶⠶⠖⠋⠀⠀⠀⠈⠓⢶⡞⠁⠀⠀⠀⠀⠀⠚⠳⠀⠁
⠀⠀⠁⠙⠂⠀⠀⠀⠀⠉⠻⣿⣿⣿⡿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠀⢀
⠺⣷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠉⣹⡆⠀⢸⣷⣶⠃
⣾⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠙⠳⡄⠀⠀⠙⣶⠛⢿⠟⠂
⠿⠿⠿⠦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢀⣠⠏⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠲⠤⠤⠤⣤⣤⡴⠊⠉⠉⠉⠑⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⡟⠃

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⣠⣴⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠉⠛⢷⣶⣿⠟⠉⠀⠀⠹⣿⡄
⠀⠀⠀⠀⢀⣠⣤⣤⣀⣀⡀⠀⠀⢀⣀⣤⣤⣴⣶⣾⡏⠀⠀⠀⣀⡀⣻⣧⣀⣀⠀⢀⣀⣿⣷⣄⡀
⠀⠀⠀⢠⣿⠟⠛⠛⠛⠛⠿⢿⣿⠿⠟⠛⠋⠉⠉⣿⠀⠀⢠⡿⠛⣿⠟⠉⠉⠛⢿⡟⠉⠉⠉⠙⣷
⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠈⠿⣾⣇⠀⠀⠀⠀⢸⡟⢿⡆⠀⢀⣿
⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣦⣀⣀⣤⣼⠿⣦⣄⣀⣴⡿⠷⠟⠃⠀⣼⡏
⠀⠀⠀⠈⣿⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠉⠉⠉⠻⣦⣤⣤⡾⢿⣷⡀
⠀⠀⠀⠀⣸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⣿⣧⣤⣤⣤
⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠟⢻⣿⠁
⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣷⠀⠀⠀⠀⢠⣼⣿⣤⣤⣤
⠀⠀⠀⢸⣿⣄⣀⡀⠀⠀⠀⢠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⠟⠀⠀⠀⠀⠀⣹⡿⠁
⠰⠶⠿⠛⢿⣿⠉⠁⠀⠀⠀⠸⣿⡿⠀⠀⠀⠀⠀⠀⣴⠟⢷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣿⣷⣤⣄⡀
⠀⠀⠀⠀⢈⣿⣦⡶⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠷⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⠋⠀⠉⠉⠁
⠀⠀⠀⠾⠛⠉⠻⣷⣄⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⡟⠙⠻⠿⣷⣆
⠀⠀⠀⠀⠀⠀⣠⣿⠿⣿⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣴⣶⠿⠟⢻⣿⡀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠾⠋⠀⠀⢀⣭⣿⣿⣿⣿⣿⣿⣿⠿⠿⠿⠿⠿⠟⢻⣿⠉⠙⣿⣄⠀⠀⠹⣿⣄⠀⠀⣠⣿⠃
⠀⠀⠀⠀⠀⢀⣤⣶⣾⣿⣏⠁⣴⡿⠁⠀⠸⣷⡀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠘⢿⣦⠀⠀⠙⣿⣦⣾⠿⠃
⠀⠀⠀⠀⠀⣿⡏⠀⠀⠙⣿⣿⣿⣿⣿⣶⣦⣈⠻⠷⣶⣶⠾⠟⠋⣠⣶⣶⣿⣿⣿⣷⣶⠿⠛⠋⠁
⠀⠀⠀⠀⠀⣿⡇⠀⢀⣴⡿⠋⠀⠀⠀⠀⠙⢿⣧⡀⠀⠀⠀⢠⣾⠟⠁⠀⠀⠀⠀⠙⢿⣦⡀
⠀⠀⠀⠀⠀⠻⣷⣄⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⠀⠀⢀⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷
⠀⠀⠀⠀⠀⠀⠈⢹⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠀⠀⠘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⡀⠀⠀⠀⠀⠀⢀⣼⣿⣁⣀⣀⣀⣸⣿⣄⠀⠀⠀⠀⠀⠀⢠⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⣦⣄⣀⣤⣴⣿⠿⠟⠛⠛⠛⠛⠛⠻⠿⣷⣦⣤⣤⣤⣾⠿⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡏⠉⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⡄⠀⠀⠀⣀⡀⣀⡀⠀⠀⠀⠀⣠⠿⠚⡅⢀⡤⠤⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣅⣀⣿⡀⢠⠚⠡⣤⡀⣹⠂⠀⠀⠈⣷⠀⠀⡇⢸⠀⠰⣶⠈⣱⠀⠀⠀⠀⠀⢀⡤⠶⠦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⢀⠀⢠⠏⠀⠱⡘⢤⣀⡀⠈⠉⠳⡀⠀⠀⣿⠀⠀⠳⠚⢳⣄⠈⠛⡅⠀⠀⠀⠰⡏⠉⠀⣰⢆⣨⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠟⠉⠳⣠⠞⠉⠙⢮⡓⣄⠀⠙⠚⠁⠙⠛⣀⠶⠁⠀⠀⠈⠳⠶⠛⠦⣈⣛⣀⡠⠇⠀⠀⠀⡴⠁⢀⡶⣉⣏⠁
⠀⠀⠀⠀⠀⠀⣀⣀⡘⠢⣄⠀⠙⢶⠳⣄⠀⠉⢻⢦⣠⠜⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠀⢠⢞⡔⠉⠀⣨⠷⠒⡄
⠀⠀⠀⠀⠀⡞⠁⠈⢉⡆⠈⠳⡄⠀⠱⣌⠳⠤⠞⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⠛⠛⠛⢶⣄⠀⠀⠀⠀⠀⠀⢀⠋⠀⠠⡋⢸⠀⠀⠎⢹⡆⠀⢸
⠀⠀⠀⠀⡼⢁⡴⣏⠁⠀⠀⠀⠘⢦⣀⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠓⠶⠚⠁⠈⢧⡈⠒⠋⠀⣠⡿⠒⢤⡀
⠀⠀⣠⠞⢠⣟⠀⠈⠓⠦⠤⡀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢛⡿⠛⠁⠀⣠⣞⡀
⠀⠰⣇⠀⢸⠉⠓⢦⣀⠀⠀⢙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⣀⡰⠛⢦⠀⢈⠆
⠀⠀⠘⠲⠞⠀⠀⠀⠈⠛⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠙⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⣀⣴⠞⠋⠉⠉⠉⠉⠛⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠋⡆⢀⡴⠶⠶⢦⣿⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣾⣭⣾⣅⠀⠀⠀⡿⠋⠉⢳⣄⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⢀⡤⣴⡉⠃⡸⠿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠈⠉⠳⣄⠀⠀⠀⠀⠀⢹⡇⢸⡇⠀⠀⠀⠀⠀⠀⠀⢠⡾⠀⠀⠀⣿⠀⠀⠀⠀⢠⠋⠀⠸⣁⣀⠀⣴⡦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠲⣏⠀⠘⣧⣀⠀⠀⠀⣀⣠⡴⠟⠀⠀⠀⢀⣿⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠉⣸⠗⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⡿⠂⠀⠀⠀⣀⠀⠀⠀⠀⣸⠆⠀⠀⠉⠛⠛⠛⠋⠉⠀⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠘⢌⣴⡄⠀⢀⡴⢃⠴⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣤⡀⠀⣠⡟⢶⣤⣤⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠈⢻⡀⠉⣀⠀⣤⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠙⠛⠉⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠙⠳⠯⡀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⣠⡴⠖⠋⠉⠉⠉⠁⠈⠉⠉⠉⠙⠲⠦⣤⡀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⢀⠻⡙⢦⡍⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢠⠞⠁⣴⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡉⠳⣄⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠈⠚⠉⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⢠⡏⠀⢸⣿⣿⠇⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⣿⣿⡆⠈⢷⡀⠀⠀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆⠸⡇⠀⠀⠉⠉⠀⠀⠀⠀⠘⢭⡹⠂⠀⠀⠀⠀⠿⠿⠃⠀⢸⡇⠀⢠⡟
⠀⠀⠀⠀⢀⣀⡀⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣃⣴⠏
⠀⠀⠀⠀⢸⠋⠳⠄⠀⡟⠉⠓⣄⠀⠀⠀⠀⠀⠀⠈⠙⠛⢶⣤⠴⠲⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠟⠋
⠀⠀⠀⠀⠀⠋⣤⠴⠒⠋⠀⠀⣸⡄⠀⠀⠀⠀⠀⠀⠀⠀⣛⠀⠀⠀⢹⣿⣋⣉⣛⣛⣛⡛⢻⡻⡋⠻⣄
⠀⠀⠀⠀⠀⠴⣦⠀⠀⠀⠀⠀⢁⠇⠀⠀⠀⠀⠀⠀⠀⣼⠋⠀⠀⣤⠞⠉⠉⠉⠉⠉⠉⠉⠉⠛⢧⡀⠘⢧⢄
⠀⠀⠀⠀⠀⠀⠀⢑⡶⠀⠀⢶⠉⠀⠀⠀⠀⠀⠀⠀⠀⣥⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣾⣭⠟⢷⡀
⠀⠀⢀⡆⠤⠀⠴⣏⠀⠀⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⣸⠃
⠀⠀⢢⡤⠛⣢⠔⠚⠾⠓⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢯⠉
⠀⠀⠈⠒⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⡟⠢⠶⢦⣠⣤⣀⣠⣤⣀⡰⢦⣀⡴⠖⠖⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣠⠴⠚⣒⣉⣺⣏⣁⣀⣈⡀⢰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡷⢮⣉⣀⣀⣿⠴⠶⠶⠦⣭⣻⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠶⠬⠭⠽⣿⠦⣄⣀⣠⠴⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠤⠤⠤⠤⢤⡠⡄⠀⠀⠀⠀⠀⠀⠈⠓⠲⠶⡶⠏⢅⠀⡤⡄⠀⠀⠀⠀⠀⢀⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠧⠴⠖⠰⠦⣠⡄⠰⠦⢤⣀⣤⠤⢄⠀⠀⠡⠀⢸⠆⢀⣇⠦⢾⡠⢤⠤⢤⠤⢷⠀⣧⠤⡤⢤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⡇⢸⡇⠘⡇⠘⢧⢾⡀⠀⡰⠀⢈⡻⠄⢹⠀⢺⡅⠰⡖⣇⠀⢿⠀⢿⠄⡉⠺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠊⠀⠀⠳⠀⠛⠔⠉⠒⠀⠊⠀⠈⠃⠀⠈⠁⠐⠉⠃⠊⠑⠐⠁⠈⠂⠚⠂⠛⠂⠥⠚

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢿⠟⠉⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⢉⡛⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⢀⣴⣾⣿⣆⠀⠀⢀⣀⣀⣀⣀⡀⠃⠘⠿⢿⡿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⡟⠋⠊⢻⣿⣿⠟⠀⢀⣼⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣶⣤⣂⣤⣴⣶⣾⣝⣿⢿⣿⣿⣿⣿⣿
⣿⣿⠿⠋⠀⠀⠀⠈⠿⠉⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠹⢿⣿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠉⠉⠛⠻⢿⣿⣿⡿⠛⠻⣿⣿⣿⣿⣿⣿⡇⠀⢿⣿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠙⠋⠀⠀⠀⠘⢿⣿⣿⣿⣿⣿⠀⠈⠿⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣾⣿⣿⣿⣿⡡⢤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⣿⣿⣿⣿⣿⡇⠀⠀⠛⣿
⣿⡇⠀⠀⠀⠀⠀⠀⣠⣿⣿⡟⠋⠘⢿⣿⣿⣿⡈⠈⢡⢭⠉⠉⠀⠀⣀⠀⠘⢶⣚⡝⢻⣿⣿⣯⣿⣿⠇⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠸⣿⣿⡟⠀⠀⠀⠀⠙⣿⣿⣷⣄⣀⡐⠀⠀⠲⡀⠉⠀⠀⣈⣉⡠⠋⠀⠹⣿⡼⣿⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⡜⠁⠀⠀⠙⣦⣠⣶⣦⢸⣿⣿⡄⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠿⠟⠋⠙⣿⣿⣿⡇⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⣿⣿⣿⡿⠛⠛⠛⠁⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⣹⡏⠙⠀⠀⠀⠀⠀⢻⡀⠀⠀⢀⠜⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⢸⣿⣿⡶⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠰⢷⡄⡀⠴⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⣀⠀⠀⠀⠀⠀⠸⣄⣀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠁⠈⠻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠒⠠⠠⠄⠀⠀⠀⢀⣴⣌⠀⠀⠀⠠⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠙⠓⠲⠀⠄⣀⣀⣀⣀⠀⠀⠀⠀⠀⡀⣾
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⣿⣿
⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿
⣿⣿⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣿⣿⣿⣿
⣿⣿⣿⣿⣷⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣀⠀⠀⠀⠀⠀⢀⣀
⠀⠀⠀⠀⠀⠀⢠⣶⣶⣶⣤⣄⡀⠀⠀⠀⣀⣀⣀⣠⡿⠋⠁⠈⠙⢷⣤⣶⠾⠛⠛⠛⣷⡀
⠀⠀⠀⠀⠀⢠⣿⠃⠀⠀⠈⠉⠛⠿⠟⠛⠛⠛⢻⡿⠀⠀⠀⣠⣤⣈⣿⣀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⣇⣼⠟⠉⠉⠻⣶⠾⠿⠿⣿⡄
⠀⠀⠀⠀⠀⢸⣷⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣄⣀⣀⣨⣿⠀⠀⠀⠀⣿⢦⡀⠀⠈⣿
⠀⠀⠀⠀⠀⢠⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠙⠷⣦⣴⡾⠧⠾⠁⠀⣰⡟
⠀⠀⠀⠀⠀⣾⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣄⣀⣤⠾⢿⣇
⠀⠀⠀⠀⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠈⣿⡀
⠀⢀⣀⣤⣼⣿⣤⣤⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠲⠛⣿⠟⠛⠛⠃
⠀⠈⠉⠁⠘⣿⡀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⠀⣀⣠⣿⣄⣀⡀
⠀⠀⠀⢠⣴⢿⣿⠛⠁⠀⠀⠉⠁⠀⠀⠀⠀⠀⣴⣿⣷⡆⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⣽⡏⠉⠉⠉
⠀⠀⠀⠀⠀⠀⢹⣷⣴⠆⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣿⠿⣦⣄
⠀⠀⠀⠀⢤⠾⠋⠉⠛⢷⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠟⠁⠀⠀⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠶⣶⣶⣦⣤⣤⣤⣤⣴⣶⡶⠾⠟⠛⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣤⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠙⠳⣶⡿⠋⠁⠈⢿⣆
⠀⠀⠀⠀⠀⠀⣠⣴⣶⣦⣤⣤⣀⣤⣴⣶⡶⢿⡟⠀⢀⣤⣤⣼⡷⢤⣄⣤⠾⠿⢦⡀
⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠉⠉⠉⠀⠀⠀⢸⡇⠀⠸⣧⣾⠁⠀⠀⢹⡷⣤⠀⠈⡇
⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣄⣀⣤⡿⣦⣀⣠⣾⠷⠟⠀⣸⠇
⠀⠀⠀⠀⠀⠀⢻⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠈⠀⠙⠶⠴⠾⠻⣧
⠀⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⡷⠛⠛
⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⠀⠀⢀⣼⣧⣀⣀
⠀⠀⠀⠀⢀⣀⣿⣤⣄⠀⠀⠀⣴⣦⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠛⠛⠀⠀⠀⠈⣿⠏
⠀⠀⠀⠘⠋⠉⠹⣧⣀⡀⠀⠀⠛⠛⠀⠀⠀⠀⢸⣏⣹⠇⠀⠀⠀⠀⠀⠀⠀⢈⣿⠿⠷⠶⠄
⠀⠀⠀⠀⠀⢠⠶⠻⣿⣁⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠟⢿⣦⣄
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⢿⣦⣄⣀⡀⠀⠀⠀⠀⠀⣀⣀⣀⣤⣴⡶⠟⢻⣇⠀⠀⠀⢹⡇
⠀⠀⠀⠀⠀⠀⠀⠛⠁⢀⣤⡾⠟⣿⠟⢻⡿⠛⠛⠛⠛⠉⣿⠁⠙⣷⡀⠀⠻⣧⡀⣠⣾⠃
⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⠻⣦⣾⣯⣤⣄⡻⣦⣤⣠⣤⡾⠃⣀⣤⣬⣿⣄⣤⡿⠿⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣴⠟⠋⠉⠉⠙⢻⣆⠀⠁⠀⣠⡾⠋⠉⠈⠉⠻⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠹⣧⣼⡏⠀⠀⠀⠀⠀⠀⢻⡆⠀⢠⣿⠀⠀⠀⠀⠀⠀⠘⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⣠⣿⣀⣀⣀⢻⣆⠀⠀⠀⠀⠀⣠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢷⣤⣤⣤⡾⠟⠛⠛⠛⠛⠛⠻⠷⣦⣤⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠙⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠘⣧⠀⠀⢀⣠⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠘⣦⡾⠋⠀⠀⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣄⠀⠀⢠⡏⠀⠀⠀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⢸⠀⠀⠀⢀⡖⠀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠈⠳⠤⠖⠋⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⣀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⢀⢴⣭⠀⠀⠀⠀⠀⠈⢉⡒⢄⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡖⠤⡋⠀⠀⠀⠀⠀⠀⠘⠟⠈⠃⢀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠀⠀⢀⡄⠀⠀⢧⡀⢁⠖⠠⡤⢤⠄⠤⠒⠒⢶⣟⠉⠀⢀⠤⠤⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠉⠙⢁⠥⠠⡤⢼⣄⣨⣗⣚⡡⠚⠓⠒⠂⢘⡖⠉⠀⣀⣉⠀⠀⠒⢚
⠀⠀⢀⠖⠉⠉⠉⠉⠉⠛⠒⡲⠷⠤⢷⡀⠀⣭⠀⠀⠀⢀⣀⡀⠀⠈⠉⠤⠒⣒⠒⠊⠁⠁⠀⠀⣸⠀⠀⠀⢏⠠⢄⠀⢄
⠀⢀⡏⠀⠀⠀⠀⠀⠀⢠⢎⠤⠄⢀⡤⠧⠀⠀⣉⠀⠈⠉⠀⠀⣿⠉⠉⠉⠉⠉⠉⢉⣏⡽⠋⠉⢉⠀⠀⡐⠉⢀⡠⡤⡀⠁⠂
⠀⢸⠁⠀⠀⠀⠀⠀⠀⡸⠈⠂⢀⡖⠠⠄⠛⢄⠋⠀⠀⠀⠀⠀⡟⠀⠰⡀⠀⠀⠀⢸⡇⠀⠀⠀⠘⠀⠀⡊⠀⠟⢅⠮⣴⠀⢑
⠀⠀⣄⣀⠀⠀⠀⠀⠀⡷⠀⡖⠈⠁⠀⠀⢀⡞⠀⠀⠀⠀⠀⢀⡼⡀⢰⠁⠀⣠⠖⢫⡀⠀⢤⡐⠰⠀⠀⢱⢖⠀⡈⠈⢁⣰⠈⣀⢀⡄⠂
⠀⠀⠀⠀⠉⠓⠢⣤⣄⣇⡀⠀⠓⠋⠉⠙⣅⠉⡀⠀⠀⠀⢀⠎⠀⠈⠉⠓⠋⠁⠀⠀⠙⣦⣈⢡⣧⠀⢀⠚⠢⣈⠙⠒⢩⡄⠃⠐⠂⡘⢲⠐
⠀⠀⠀⠀⠀⠀⠠⠆⠀⢸⡄⠀⠀⠀⠀⠀⠘⠆⢹⣀⠟⠀⢫⡀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⠀⣠⡏⠀⠈⢳⠤⠟⡿⢀⡐⠃⢃⡀⠀⠁⡉
⠀⠀⠀⠀⠀⠀⠘⡄⠀⢸⠙⡄⠀⠀⠀⠀⠀⢸⢀⠀⠀⣀⠀⠉⠓⠒⣦⠄⠒⠒⣏⠁⠀⢀⠰⣄⡇⠀⠔⠺⢄⡀⣀⠀⢠⠰⣧⠈⠁
⠀⠀⠀⠀⢀⠔⠀⠣⡄⣸⠀⠈⠢⣄⣀⣀⣠⣺⣨⠕⠀⠀⢀⠀⠀⠀⢻⣀⣀⡠⠟⠀⠀⠀⠀⠉⠁⣄⣀⣤⠴⠋⠇⣔⢸⣀⠤⠍
⠀⠀⠀⠀⠱⣄⢠⡀⠽⠁⠀⠀⠀⠀⠀⠈⠒⠂⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⡐⠁⠀⠀⠀⠈⠀⠀⠈⠟⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠶⢦⣄⡀⣀⣀⣤⣤⣤⣤⣤⠞⠉⠉⠙⢶⣴⠶⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠈⠙⠉⠉⠀⠀⠀⢀⡟⠀⠀⣴⢶⡶⠛⠲⢦⡶⠿⠶⢦⣄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠳⣿⠀⠀⠀⢈⡷⣦⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠓⠒⠛⠦⣤⣤⠾⠷⠋⠀⢀⡿
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⣤⠞⠁
⠀⠀⠀⠀⠀⣤⣀⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣀⣤⡀
⠀⠀⠀⠀⠀⠀⠉⣿⠉⠁⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡄⠀⠀⠀⠉⣿⠉
⠀⠀⠀⠀⠀⠰⠶⢿⡟⠂⠀⠀⠈⠿⠃⠀⠀⠀⠀⣠⣄⡀⠀⠀⠀⠀⠻⠃⠀⠀⠀⢻⡿⠶⠶
⠀⠀⠀⠀⠀⠀⠀⣨⣿⣞⠃⠀⠀⠀⠀⠀⠀⠀⣈⣷⠶⢃⣀⠀⠀⠀⠀⠀⠀⠀⢳⣾⣅⡀
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠙⢷⣤⣀⣀⠀⢀⣠⣾⣿⣿⣿⣿⣿⣷⣀⣀⠀⢀⣠⡶⠋⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠉⠀⠉⢿⡏⠉⠀⠀⠀⠉⠉⠛⠿⣿⣿⡿⠟⠻⢶⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⡾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠻⣦⣀⣀⣠⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣄⠀⠀⠀⠀⠀⠀⣀⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠷⠶⠶⠾⠟⠋⠁

⣻⣿⠯⠿⠿⢿⣽⣿⣟⣻⠏⣀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣮⣈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇
⣀⣀⣀⣤⣤⣼⣾⣶⣤⢼⣿⡿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣴⣿⣿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠃
⣈⣉⣀⣀⣀⣀⠀⠈⠉⠉⠛⠳⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠾⠛⣩⠀⠀⠀⠉⠉⠙⢂⠀⢰⣿⠀⠀⠀⠀⠀⠀⢀⣀⠠⢄⣀⣤⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠾⠛⣓⠲⠶⠶⠤⠌⠁⣬⣭⣸⣿⠀⠀⠀⠀⡠⠊⠁⢀⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏
⣭⣀⣀⣀⣠⠀⠀⠀⠀⠀⠆⣸⡿⠀⠀⠀⢠⠁⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠛⠛⠿⣷⣆⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⢸⠀⣼⣿⡿⠋⠉⠉⠙⠻⢿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⢸⡇
⣴⣆⣠⠤⠤⢶⣶⣶⣶⣾⣶⣿⡇⠀⠀⠀⠈⣴⣿⡏⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠈⣿⣼⠦⠤⠐⠀⢾⡇
⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⡇⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⣀⡤⠤⠄⠀⢀⣿⠀⠀⠀⠀⠀⣸⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢹⣿⣆⠀⠀⠚⠛⠛⠒⠂⠀⠀⢀⡀⠀⠀⠁⠀⠀⠀⢠⣾⣿⡹⣩⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⡻⠿⠟⠛⠋⢹⣷⠀⠀⠀⠀⠈⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠻⠃⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⡆⠀⢀⣶⣿⣿⠀⠀⠀⠀⠀⠈⠻⣿⠀⠀⠀⠀⠀⣰⣶⣦⣤⣤⣶⣿⣷⣤⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣠⡏⠀⠀⠀⠀⠚⠛⠋⠉⠉⠉⠁⠁⠀⣀⣰⣶⣦⣶⣿⣿⣿⣿⣿⣿⣿⣿
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢀⣀⣀⣀⢠⣿⣿⣶⣶⣿⣶⣶⣤⣤⣤⣤⣤⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣣⡝⠿⣿⣿⡿⣿⣿⣿⡿⢿⣿⣿⢿⣿⡿⣿⢿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣶⡀⣀⣀
⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡷⣯⣝⣤⡗⡶⠧⣼⠿⢿⣥⣼⣶⣾⣥⡏⠀⠈⢴⣿⣾⣯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣀⡀

⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⡾⠉⠉⠉⠻⢦⡀⠀⠀⠀⣀⣠⣀⡀⠀⠀⠀⢻⣿⣀
⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠙⢦⣴⠋⠁⠀⠈⠙⢦⡀⠀⢸⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤
⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⠠⡇⠀⠀⠀⣷⠀⠈⢷⡀⢸⣿⣿⣿⣿⣿⣷⣀⣀⣀⣀⠀⠀⣠⣤⣶⣶⣿⣿⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡷⠦⣄⡜⣇⠀⠀⢠⡏⠀⠀⠈⠙⠺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⢻⡼⣉⣳⠞⠉⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠚⠀⠀⢀⣠⠤⠴⠶⠲⠦⠤⣀⠀⠈⣿⣿⢟⡋⠙⠻⢿⣿⠿⠿⣿⣿⣿⡟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⣠⢊⠁⠀⠀⠀⠀⠀⢾⣷⠈⢧⢠⣿⡇⢸⣿⠂⠀⠀⠀⢀⣤⡜⣿⣿⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⡇⠿⠗⢀⣀⡶⣂⠀⢠⠖⠒⠻⠛⠛⢣⡀⠀⠀⣄⣓⠀⠀⠛⠁⣾⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠙⠿⢦⣄⣏⠀⣹⡥⠴⢾⡀⠀⠀⠀⠀⣰⣿⣶⣦⣬⣥⣤⣤⠤⠞⣻⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⢠⠇⢀⣀⠴⠠⠔⠸⣅⣨⠇⠉⠻⡉⠙⠚⢲⠞⠒⠫⢽⠏⠉⠻⡿⠟⠻⡟⡏⠁⠈⠙⣿⣧
⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⡀⠀⡄⢹⣄⡀⠀⠙⠒⠶⡎⢳⠶⠒⠁⠀⢀⣰⡃⠁⠀⠀⠀⠀⠀⠀⠈⢻⣧
⠀⠀⠀⠀⠀⠀⢸⠁⢠⠂⣠⣇⡴⠧⠞⠻⡅⠉⠀⠀⠀⣠⠼⠥⠜⠦⣀⠀⠀⠀⠉⣹⠦⠔⠚⠓⠲⡤⠖⠒⠲⢽⡆
⠀⠀⠀⠀⠀⠀⠘⠒⠉⠋⠁⠀⠀⠀⠀⠀⠈⢦⣠⣴⣉⠏⠀⠀⠀⠀⢻⣙⣦⣄⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠤⠶⠶⠶⠶⢤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠋⠉⠁⠀⠀⠀⠀⠀⠉⠛⢦⡀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⣠⡴⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋
⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⣠⠶⠶⣦⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠴⠛⠁
⠀⠀⢀⣀⣀⣀⣀⣾⠁⢠⡾⠁⠀⠀⠈⢷⡸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⠴⠚⠉
⠀⡴⠋⠁⠀⠉⠙⢷⣄⣿⡁⠀⠀⠀⠀⣾⡇⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⢀⣠⡤⠶⠚⠋⠉
⠀⢷⡀⠀⠀⠀⢀⣾⠉⠀⠹⣿⠛⠃⠀⠈⠹⣦⠈⠻⣦⣀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠀⠀⠀⠹⢦⡀
⠀⠀⠙⢶⡄⠺⠋⠻⣦⣀⣴⣏⠀⠀⠀⠀⣸⡏⠀⠀⠀⠉⠙⠛⠻⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠻⣆
⠀⠀⠀⡟⠀⠀⠀⠀⢨⡟⠀⠈⠛⠶⠶⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧
⠀⠀⣼⠿⣦⣤⣤⡴⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀
⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷
⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠶⠛⠛⠛⠉⠉⠉⠉⠉⠉⠛⠛⠲⠶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠘⣇
⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢶⣄⠀⠀⠀⠀⠀⢻
⠸⡇⠀⠀⠀⠀⠀⠀⠀⢠⡶⠋⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠙⢧⡀⠀⠀⠀⢸⡆
⠀⣷⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⢠⣾⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡆⠀⠈⣷⠀⠀⠀⣸⠃
⠀⠘⣆⠀⠀⠀⠀⢠⡟⠀⠀⠀⢸⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⢸⡆⠀⢠⡟
⠀⠀⠘⣦⠀⠀⠀⢸⡇⠀⠀⠀⠘⠿⠿⠋⠀⠀⠀⠀⠀⠀⠰⣏⠀⣨⠇⠀⠀⠀⠀⠀⠈⠻⠿⠃⠀⠀⣼⠃⢠⡞⠁
⠀⠀⠀⠈⠳⣄⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠉⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⢋⡴⠋
⠀⠀⠀⠀⠀⠈⠛⢦⣈⣳⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⣿⡋
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠿⢶⣄⣀⡀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣠⣤⠶⠾⣿⠿⠿⠿⠿⠿⢿⣿⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣏⢉⣿⠟⠛⠛⠉⠉⠉⠉⠉⠉⢹⡏⢻⡄⣀⠤⠬⡇⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⠟⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⡶⠦⣤⣤⣀⣀⣀⣀⣀⣀⣸⡇⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢨
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠉⠻⢿⣍⣉⣉⣉⣀⣤⣴⣶⣴⣧⣠⣤⣤⣤⠤⣤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⢩⡴⠞⠛⠏⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠛⠙⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠴⠖⠋⠳⠤⢄⣀⣀⣀⣀⡠⠤⠴⠒⠒⠛⠉⠉⠉⠉⠉

⠀⠀⠀⠀⠤⠄⠀⠀⠀⠤⠀⠀⠀⠀⠀⠄⠀⠠⠤⠀⠤⠄⠀⠀⠀⠠⠄⠀⠀⠤⠄⠄⠤⠠⠤⠀⠤⠄⠤⠠⠄⠀⠀⠐
⠀⠀⠀⠂⠒⠀⠐⠐⠀⠄⠀⠀⠀⠐⠂⠒⠂⠐⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠐⠀⠐⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠁⠃⠂
⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠂⠀⠀⠀⠀⠀⣤⡤
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⠀⣴⣴⠀⠀⠀⠀⣀⣀⠀⠀⢀⣀⡀⣀⢀⣈⡉⠀⠀⠀⠀⠀⠙⠛
⠀⠀⠀⠀⠀⠀⠸⠿⠆⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠸⠿⠿⢃⡀⠛⠛⠃
⠀⠀⡄⠀⠀⠀⢠⠀⠉⠈⠉⠀⠀⠀⠂⠀⠀⠀⠀⢀⠂⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⡇⠀⠀⠠⠃⠀⠀⠀⠀⠆⠤⠀⠀⠀⢀⠀⢀⢄⠤⠨⠀⠀⠑⠆⠀⠀⠀⠀⠀⠀⣈⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠠
⠀⠀⡇⠀⠄⠀⠀⠀⠈⠠⠀⠀⠀⠀⢤⡀⠀⠂⠨⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡄⠀⠁⠀⠀⠰⠞⣠⠀⠀⠀⠀⠈⠰
⠀⠀⠁⠀⠀⠀⠀⢠⠤⠄⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠄⠀⠉⠈⠠⠀⠀⠀⠀⢠⠠⠄

⠀⠀⠀⠀⠀⠈⠉⠀⢁⣀⠁⠁⠉⠈⠈⠀⠁⠈⠘⠀⠀⠀⠀⠀⠀⠈⠈⠀⠈⠀⠉⠉⠃⠂⠀⡉⡁⠈⠉⠈⠀⠉⠁
⠀⠀⠀⠀⠈⢀⠁⠀⠀⡉⡁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠆⠂⠄
⠀⠀⠆⠀⠀⠈⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⣠⢼
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⠄⠀⠛⠋⠀⠀⠀⠀⠤⠦⢀⠰⠶⠂⠤⢀⡀⠀⠀⠀⠈⠉⠉⠀⠉⠉
⠀⠀⣤⡤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠆
⠀⠀⠛⠛⠃⠶⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠰⠀⠀⠀⠀⠀⠂⠈⠀⠛⠀⠀⠀⠀⢀⠀⢀⢍⡰⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠴⠄⢤⠀⠀⠀⠀⠀⠀⠀⢀⠄⡃⠍⠃⠀⠀⠀⡄⠀⠀⠀⠌⠀⠠⠄⠰⠀⠀⠀⠨⢂⣃⠄
⠀⠀⠀⠀⠀⠀⠈⠀⠤⡂⠀⠀⡀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠂⠀⠀⠀⠁⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠁⠈⠁⠀⠀⠈⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠢⠄⠂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄

⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣄⠀⣀⣠⣤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠈⠛⠚⠛⠋⠋⠉⣽⠋⠁⢀⢹⡏⠉⠀⠀⠘⡆
⠀⠀⠀⠀⠀⠰⠀⠀⢸⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁⢰⡟⣻⠿⠿⢤⡀⠀⠀⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣚⣿⡇⠦⣠⡄⣿⣟⠛⠛⠓⣦
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢿⣑⢄⣬⣴⣯⣸⡇⠀⢠⠟
⠀⠀⠀⠀⠀⢀⣀⣀⣏⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠙⣿⡈⠁⠀⣴⠋
⠀⠀⠀⠀⠀⠀⠀⢀⣿⡀⠀⠀⠀⣾⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡇⠘⠿⢶⣿⡷⠶⠂
⠀⠀⠀⠀⠀⠐⠒⠋⠘⣦⠀⠀⠀⠘⠁⠀⠀⠀⠠⡂⢰⠀⠀⠀⠀⠙⠁⠀⠀⠰⣿⠧⢄⣀
⠀⠀⠀⠀⠀⠀⠀⡠⠊⠉⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⠾⢧⣀⠀⠀⠀⠒
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣽⣶⠶⢤⣤⣄⣀⣀⣀⣀⣀⣤⣤⢤⡶⣟⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⢀⡴⠚⠻⣟⠛⠉⢠⡟⠀⠀⠹⡋⠀⠀⠀⠈⢹⠏⠀⠀⢿⡈⠙⢲⣦⣤⣄
⠀⠀⠀⠀⠀⢸⡇⠀⠀⠸⣯⣦⡾⠀⢀⣤⣀⠉⠛⠦⠖⠛⠁⠀⣀⡀⠘⣇⣴⣶⡟⠀⢈⣇
⠀⠀⠀⠀⢰⡏⠀⠀⠀⢸⢿⡿⠁⠀⢯⣀⡼⠀⠀⠀⠀⠀⠀⡎⠀⣹⠀⢹⣿⠃⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠘⣇⠀⢀⠠⢀⡞⢁⡴⠞⠛⠛⠳⣤⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⢻⡄⢀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠘⡳⣾⣦⣾⣠⡟⠀⠀⠀⠀⠀⠈⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⣀⣀⡴⠋
⠀⠀⠀⠀⠀⠉⠀⠀⢉⠍⣿⠀⠀⠀⠀⠀⠀⠀⢸⡆⢠⣄⠀⢀⡀⣰⣟⣀⣴⣼⣏
⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⣿⠀⠀⠀⠀⠀⠀⠀⢸⣧⠞⢛⣷⠞⠛⠋⠉⠙⢻⡀
⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠻⣶⣄⡰⠀⠀⠀⢀⣾⣏⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁
⠀⠀⠀⠠⠊⠀⠀⠀⠀⠐⠀⠙⠿⣧⣶⣴⠶⠛⠀⠙⠶⠦⠤⠤⠤⠶⠶⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠚⠛⠛⠓⠲⢶⡏⠀⢀⣼⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢴⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⢀⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠷⠴⠛⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⠀⠀⠀⠀⢀⠀⠀⢀⣀⡀⠶⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠛⠃⣞⠅⠀⡹⠀⠀⠀⢀⣾⡟⠋⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣄⣀⠀⠀⠀⠈⠉⠉⠀⣀⣴⣾⣿⣿⣷⣄⣤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⣾⣿⣿⣿⣿⣿⣿⣧⣤⣴⣿⣿⣿⣿⣿⣿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣀⣿⠿⠛⠻⢿⣿⣿⣿⠋⡉⢻⣿⣿⣿⣿⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⠁⠀⠀⠀⠀⢻⣿⣿⣇⣰⣿⣿⣿⡿⠿⢿⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠘⠉⠙⠛⠛⠛⠉⠁⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⣤⣶⡄⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣤⣤⣤⣤⣤⣤⣤⣿⠄

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠞⠛⠛⠳⠶⣄⡀⠀⠀⢀⣠⠖⠋⠉⠁⠀⠈⠙⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠀⠀⠀⠀⠈⢻⣄⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠋⠉⠙⠛⠳⢦⣀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⠀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢶⡀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠙⢶⣄⡀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⠐⠿⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠽⢤⡴⠒⠒⢢⠈⠉⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠤⠄⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡱⠀⠀⠄⠀⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⣀⣀⡴⠒⠢⠔⠋⠀⠀⠀⢀⣠⠤⠴⠒⠒⠛⠛⠛⠓⠒⠲⠤⣄⠀⠀⠀⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣶⡌⠙⣆⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⢀⡴⢋⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⠇⠀⠸⡆⣸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⡼⠁⢸⣿⣿⠀⠀⠀⠀⠀⢆⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣷⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⡇⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠲⢦⡖⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢲⡾⢷⣦⣤⣤⣤⣤⣤⡴⠶⠲⠿⣿⠉⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣉⠁⠀⠀⢹⡁⡴⠋⠀⠈⢷⠀⠀⠀⣈⣷⣀⡀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⢦⣴⠋⠉⣇⢀⠀⣀⠘⣷⡛⠉⠁⠈⠻⠶⢧⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠈⡇⠀⠈⠉⠓⠛⠉⠁⠙⠲⣤⣄⠀⠀⠀⣈⡧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢄⡀⢀⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠙⠦⣤⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠠⢴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⢷⠀⠀⠀⠀⠀⠀⠀⠀⣸⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢤⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠖⠒⠲⠶⠒⠖⠞⠁

⠒⠒⢤⣀⢰⡏⣼⣧⡔⠠⣪⡍⢿⣯⠃⠾⣱⢛⣷⡊⣧⢰⡛⠞⣿⢠⡟⠉⠉⣷⠤⣤⡤⠤⠤⢬⣭⣉⣉⣉⣭⡭⢭⡍⠩⢛⣉⠉⣉
⠆⠶⠎⠈⣿⢦⠟⡍⣳⣶⣫⠊⠛⠙⣇⠛⢠⠞⢇⠰⢹⡄⠱⡴⠃⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⣯⣿⣄⠀⠀⣿⠀⠀⠉⠀⠙
⠀⠀⠀⠀⢿⣮⢎⢼⠏⠟⠷⣽⣶⣼⠗⡰⡁⠛⣠⣆⣠⡿⣤⡀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⢿⣿⣿⣛⣳⣶⣟⣮⠛⠖⠆

⠘⠛⠁⢸⠘⣧⠈⣰⢟⡖⢒⡈⢽⢚⠛⣝⣽⣴⡷⠶⣯⣾⣶⣻⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⣏⣿⣿⣻⣟⣯⣿⢠⡀⣀⣀
⠀⠀⠀⣠⣀⣘⢾⡡⢋⠰⣈⢕⣸⠗⠋⠉⠀⠀⠀⠀⣠⣾⣿⠿⠿⣶⠓⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠳⣿⣿⡿⠀⠀⠀⠁
⢀⠀⠜⣧⠉⣹⡟⣰⣻⣢⣿⠏⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠃⠠⠠⢸⡆⠀⠀⠀⠀⠀⠀⠚⠉⠙⠳⣄⠀⠀⠀⠀⠀⢹⡇⠓⠂⠺
⠋⠀⡠⠹⣧⡟⣿⠾⡱⢱⡟⠀⢀⣤⠴⠶⠦⠀⢀⠸⣿⣿⡇⠀⢀⣼⠃⠀⢪⡀⣡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣶⣤⢀⣰
⠤⣺⠔⠓⠄⠀⢻⡴⡁⣹⡇⠀⠛⠀⠀⠀⠀⢀⢐⡴⠛⢻⣧⣤⣾⠋⠀⣤⡄⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢦⣴⢏⢉⠀⠁⠀⠉
⠛⠑⠒⢒⠚⠓⠠⣿⣾⣡⢻⡀⠀⠀⠀⠀⠀⠘⢽⡇⠀⢀⣿⣿⣿⣧⡀⠈⢄⠔⠁⠀⠀⠀⠀⠀⠀⠀⠈⠛⣦⣠⠟⡟⠘⠘⠛⠁⠘
⠏⠾⠇⠘⠀⠐⠠⠺⠬⣽⣿⣷⣄⣀⡀⠀⠀⢀⣀⣏⠛⠛⠉⠉⢻⣿⣿⣷⣦⣄⣀⣀⠀⠀⠀⠀⠀⣘⣷⡴⠛⠻⡹⠹⠆⢦⠆⠆⠠
⢤⠀⠆⢠⡀⠶⠔⠀⡎⢸⣿⣿⣏⣽⡿⠿⠛⠉⠉⠀⠀⠀⢀⣠⠞⠭⠉⠛⠿⢿⣿⣿⣿⣿⡟⠛⣿⣿⣿⡇⠀⠈⠓⠤⠤⠤⠤⠤⢄
⢴⢀⡀⠀⡀⣄⠀⢠⢖⣢⡟⠉⠉⠀⠀⠀⠀⠀⣀⣠⣤⣶⣋⡁⠈⡀⠀⠀⠒⠀⠀⠉⠭⢙⣿⣿⣿⣿⣿⣧⠀⠈⠀⠀⢀⡶⢶⡞⢶
⢉⣘⡃⡀⡁⠀⣤⠾⣟⣿⠁⠀⠀⣀⣠⣤⠶⠛⠉⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⡶⢶⡆⠀⠈⣷⠀⢠⡟
⣯⣭⣯⣧⣭⣤⣧⣴⣿⣿⣤⣤⣬⣭⣥⣤⣤⣴⣤⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣾⣧⣴⣤⣼⣷⣿⣤

⠀⠀⠀⣠⠖⠊⠉⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⣰⠟⠁⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⡾⠒⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠻⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠆⠀⠀⠉⠉⠀⠀⠀⠀⢀⡀⠀⡀⠘⣉⠂⠀⠀⠀⡀⠀⡀
⠀⠀⠀⠉⠓⠲⢄⡀⠀⣾⣩⣶⠀⡠⣾⠉⢁⡔⠀⠀⡜⠀⣾⣙⣴⠀⡠⠀⠀⠀⠀⢀⡔⠔⠻⡇⢺⡇⣾⠟⢀⣴⠰⠺⡧⢺⡏⣴⠟⠁
⠀⠀⠀⠀⠀⠀⣨⡇⠈⠈⠉⠙⠈⠀⢹⡶⠃⠀⠀⢀⠃⠘⠀⠉⠙⠊⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠁⠉⠂⠈⠉⠀⠀⠀⠈⠁⠘⠒⠊
⠀⠀⣤⠄⡠⠜⠉⠀⠀⠀⠀⠀⠀⠐⠟⠁⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣀⡀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠏⠀⠀⠙⣿⣿⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡿⠻⠶⢄⡠⠦⠾⣿⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⡷⣄⣤⠋⢣⣀⣠⣿⣿⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣷⡀⠠⢦⡄⠉⣼⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⡏⠀⠀⠀⢺⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⡇⢀⡀⢀⡸⣿⣿⣿⣿⣷⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⢸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠙⠛⠛⠋⠉⠙⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⠿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣉⣉⠀⠀⡄⠀⠀⠀⠀⡰⠁⠄⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠋⠀⠀⠀⠀⢠⠀⠀⠀⠔⠁⠀⠀⠀⠀⢀⡁⠂⢁⠀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠈⠀⠀⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠠⠗⠀⠀⠀⠀⠣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⣀⣀⡸⠀⠀⠀⠀⠀⠀⠘⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡤⠄⠂⠛⠻⣿⣟⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠠⡎⠀⢀⠤⠒⢠⣿⣿⣿⣿⣿⣧⣀⡀⠀⠀⠀⠀⡠⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠈⠁⠃⣀⠋⠀⢲⣿⣿⣿⣿⣿⣇⠀⠈⠁⠢⠆⢀⡔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⡜⢀⠀⠀⠙⢿⣿⣿⣿⠟⠀⠁⠢⡀⠀⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠙⠟⠡⠀⠀⢀⡌⠇⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⢀⠃⠀⠀⠈⠀⡀⣀⣳⣀⡠⢀⣴⠀⡇⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⡁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠛⡇⠀⠀⠀⠀⠀⡈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⠑⠒⠀⠀⠀⠐⠂⠻⠛⠟⠛⠛⠉⠀⡇⠀⠀⠀⠀⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⡠⠁⠀⡇⠀⠀⠀⠐⠳⡆⠴⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠅⢀⣀⣀⡀⠀⠐⠂⠀⠀⢇⡀⢀⣀⡠⠌


⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠈⠀⠆⠀⡀⠀⡄⢀⠠⠀⠀⠄⠰

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣶⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡾⠿⠿⢷⣦⣄⣠⣶⣿⠿⠛⠉⠉⠻⣿⣆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⠋⠀⠀⠀⠀⠘⢿⣿⠋⠁⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣄⣀⡀⠀⠀⣀⣠⣤⣶⣶⣾⣿⣿⣿⠃⠀⠀⠀⢀⣀⣀⣀⣹⣧⣤⣤⣀⠀⣀⣤⣤⣿⣷⣦⣄
⠀⠀⠀⠀⠀⣰⣿⠟⠉⠉⠉⠙⠛⠻⠿⣿⣿⡿⠟⠛⠋⠉⠉⠀⢸⡟⠀⠀⠀⢰⣿⠋⣹⡿⠋⠉⠀⠉⠻⣿⡟⠉⠁⠀⠀⠈⢿⡆
⠀⠀⠀⠀⢠⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠸⣿⣤⣿⠁⠀⠀⠀⠀⠀⢹⡿⢷⣦⠀⠀⠀⢸⡇
⠀⠀⠀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠉⣿⣧⠀⠀⠀⠀⢀⣿⣇⣠⡿⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠘⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⢶⣶⣶⡶⠟⠋⠙⠷⣶⣶⡶⣿⣏⠉⠉⠀⠀⢀⣾⣏
⠀⠀⠀⠀⠀⠹⣿⣶⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⣤⣤⣴⡿⠛⣿⣇
⠀⠀⠀⠀⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢸⣿⣄⣀⣤⣤⣤
⠀⠀⠀⠀⠀⢰⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣴⡾⣿⣿⠛⠉⠉⠉
⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿
⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣷⠀⠀⠀⠀⠀⠠⣶⣿⣿⣶⣶⠶⠦
⠀⠀⠀⠀⠀⢸⣿⣀⣀⡀⠀⠀⠀⠀⠀⣠⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠋⠀⠀⠀⠀⠀⠀⢀⣿⡏
⠀⣠⣶⣾⡿⠿⣿⡟⠛⠋⠀⠀⠀⠀⠀⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⣠⣶⠶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣼⣿⣅⣀⡀
⠀⠉⠁⠀⠀⠀⢻⣿⡀⠀⠀⠀⠀⠀⠀⠈⠙⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣀⣼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⠛⠛⠛⠿⠷
⠀⠀⠀⠀⠀⣀⣤⣿⣿⣟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣁⣀⡀
⠀⠀⠀⠀⠘⠋⠉⠀⠙⢿⣦⣄⣴⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⡿⠁⠀⠙⠛⠛⢿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⢿⣿⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣶⡿⠟⢻⣿⣄⠀⠀⠀⠀⠀⠈⢿⡇
⠀⠀⠀⠀⠀⠀⢀⣼⠟⠉⠀⠀⠉⠛⠛⣿⣿⣿⣶⣶⣶⣤⣤⣤⣤⣴⣶⣶⣶⣶⣿⢿⣿⡟⠛⠻⣿⣄⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⣾⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡾⠿⠛⢉⣿⡟⠉⠉⢻⣟⠉⠉⠉⠉⠉⠀⠀⠀⢠⣿⠁⠀⠀⠙⣿⣆⠀⠀⠀⠹⣿⣦⠀⠀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠿⠟⢿⣷⡀⢀⣾⡟⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⣘⣿⣷⡾⠟⠉
⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠈⢻⣿⣿⣿⡿⠿⢿⣷⣦⣄⠙⠻⠷⠶⠶⠶⠿⠛⠁⢀⣤⣶⡿⠿⠿⢿⣿⣷⣶⠿⠟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⣠⣿⠟⠋⠀⠀⠀⠀⠀⠙⢿⣷⡄⠀⠀⠀⠀⠀⢀⣴⡿⠋⠀⠀⠀⠀⠀⠈⠙⢿⣶⡀
⠀⠀⠀⠀⠀⠀⠀⢿⣧⠀⠀⣼⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡄⠀⠀⠀⠀⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠀⠀⠸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠀⠀⠀⠀⠀⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣦⡀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⣶⣶⣶⣶⣶⣶⣿⣿⣦⣀⠀⠀⠀⠀⠀⢀⣤⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣶⣤⣤⣶⣶⠿⠟⠋⠉⠉⠀⠀⠀⠀⠀⠈⠉⠉⠛⠿⢿⣷⣶⣶⣾⠿⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⢠⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⢐⡇⠵⡀⠀⠀⠀⠀⠀⠀⠏⠑⡄⠀⠀⠀⠀⠀⢀⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⡀⢸⡈⢦⠀⢠⣤⣤⣤⣬⣥⣀⣧⡔⠒⢀⡶⢦⡤⣼⣀⣧⡤⠖⢂⠴⠀⡎⠘⣂⠀⣀⣠⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⣠⢀⡭⠿⣿⣄⣸⣧⢼⣛⣸⠷⣼⡏⠈⣽⡄⠖⠛⠶⠤⢶⣏⠀⢹⣦⣶⣧⡤⢄⣸⣆⣹⣿⠟⠋⡱⠎⠻⣆
⠀⠀⠀⠀⠀⠀⠀⢀⣾⠁⠀⠙⠳⠄⢀⣼⠉⠈⣧⣾⢻⡁⢰⠉⣙⣿⣍⣙⣤⠶⣀⣠⣏⣙⣿⡋⢙⣿⠛⣷⣠⣝⠁⢙⣦⠠⠞⠁⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⣼⣉⣻⣿⣍⣿⠀⢹⡿⣿⠿⢿⡛⠉⠻⠀⢻⠋⠙⢛⣛⠛⠿⢿⡀⠸⣿⣽⡿⢿⣿⢧⡀⠀⠀⠀⠀⠹⣧
⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⢀⣻⣯⠙⣀⡈⣿⠓⢻⣏⣰⣶⠾⠏⠰⢶⡦⢼⡶⠛⢉⣴⣛⣀⣻⠗⠺⣏⣁⡰⠎⠛⢦⡹⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠈⠉⠀⠈⠉⡽⠿⣦⡼⠻⣅⠉⠑⠚⠳⢿⣄⢠⣷⠛⠋⠀⠉⣩⠟⢦⡴⠛⣯⡁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠈⣿
⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣸⠃⠐⠤⡈⠷⠀⠀⣏⢀⡙⢧⣈⠹⣆⠀⠀⡇⢀⠆⠙⠦⣄⢹⡄⠀⠀⠀⠀⢀⠀⠀⠀⣸⠇
⠀⠀⠀⠀⠀⠀⠀⠙⢷⣴⠟⠀⠀⠀⠀⠀⠀⠚⠚⠁⠀⠀⠀⠈⠃⠀⢤⡻⠌⠁⠀⠉⠙⠾⠁⠐⠓⠋⠀⠀⠀⠀⠛⠁⠀⠀⠀⠀⠈⢳⣤⡾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄
⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇
⠀⠀⠶⠶⢶⣦⣤⣼⣇⣀⣀⠀⠀⠀⠀⠀⠀⣤⡤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡴⣤⡤⠀⠀⠀⠀⠀⠀⢀⣀⣸⣧⣤⣴⡶⠶⠦
⠀⠀⠀⠀⠀⠀⠀⢹⡏⠉⠉⠁⠀⠀⠀⠀⠀⢸⣷⣼⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⣿⡇⠀⠀⠀⠀⠀⠈⠉⠉⢹⡏
⠀⠀⠀⠀⠀⢀⣀⣼⣧⣤⣤⠄⠀⠀⠀⠀⠀⠈⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠙⠿⠟⠀⠀⠀⠀⠀⠀⠠⣤⣤⣾⣧⣀⡀
⠀⠀⠀⠠⠞⠋⠉⠉⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠉⠉⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠏⠉⠉⠙⠳
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣦⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢦⣴⣏
⠀⠀⠀⠀⢀⣤⠶⠿⠛⠋⠙⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠉⠙⠛⠿⢶⣄
⠀⠀⠀⠀⠋⠁⠀⠀⠀⠀⠀⠀⠈⠻⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠛⠁⠀⠀⠀⠀⠀⠀⠈⠓
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠌⠻⣿⣶⣶⣤⣤⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣶⣶⣿⠟⢡⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣇⠀⠀⠈⢿⣷⡄⠈⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠋⠉⠉⠉⠁⣠⣾⡟⠀⠀⢀⣹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣮⣷⣄⠀⠘⢿⡻⣦⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣴⢟⡿⠁⢀⡴⣿⣿⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠈⠛⢿⣷⡄⠈⠛⠛⠛⠛⠛⢛⣛⣻⣦⣄⣠⣶⣟⣛⡛⠛⠛⠛⠓⠋⠀⣠⣿⡿⠋⠁⠘⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠁⠀⠀⠀⠀⠙⢿⣦⡀⢤⠖⠛⠛⠉⠉⠉⠉⠛⠋⠉⠉⠉⠉⠛⠛⠲⣤⣀⣾⡿⠋⠀⠀⠀⠀⠘⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⣿⠁⠀⠀⠀⠀⠀⠀⠀⠙⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠈⣰⠿⢦⡄⣠⡾⢳⡇⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⣠⠿⣿⡖⠒⣦⣄⢀⣠⣿⡶⠜⠻⠛⠑⢶⣟⣀⡀⣠⡴⠒⣺⣿⢿⣄⠀⠀⠀⠀⠀⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⣤⣀⣠⣤⣾⣿⡾⠟⠛⠉⠻⣿⣭⣭⣽⣿⣶⣦⣶⣶⣿⣯⣭⣭⣿⠟⠉⠙⠻⢿⣿⣶⣤⣀⣠⣤⡴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣽⡿⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⢿⣯⣄⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡯⣭⣥⡉⠹⣇⡀⠀⠀⠂⢀⣠⣤⡶⠶⠶⣄⡀⠀⠀⠀⠀⣀⣠⠶⠶⣤⣤⣄⡀⠀⠐⠀⠀⣼⠋⢁⡭⣭⣗⣦⣄
⠀⠀⠀⠀⠀⠀⢀⣾⣫⣽⣶⣶⣾⣷⡀⠘⠳⠶⠛⠛⠋⣁⣠⠤⠤⠴⣌⠙⠷⣤⣴⠞⢉⣤⠴⠦⠤⣄⣈⠉⠛⠳⠶⠞⠁⢠⣿⣶⣶⣾⣭⣹⣷
⠀⠀⠀⠀⠀⠀⠸⠟⠻⠿⠿⠿⣿⣿⡻⠦⢤⣴⣶⣾⣿⠿⠿⠿⠶⣦⣜⠷⣄⠀⢀⣠⠾⣡⣶⠶⠾⠶⠾⣿⣶⣶⣤⡤⠶⢻⣿⣿⠾⠿⠿⠟⠿⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡾⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠙⢷⣭⣍⣯⣽⡾⠋⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⣶⡟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⣤⡴⠶⠾⠛⠻⠶⣤⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⣤⠶⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠁


⣶⣶⣶⣶⣶⣶⣶⣶⡶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶
⣿⣉⣙⣋⣙⣉⣛⣉⣡⣉⣙⣋⣋⣉⣉⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣯⣭⣤⣤⣭⣥⣼⣿⣿⣭⣭⣭⣭⣭⣭⣭⣭⣭⣭⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠛⠛⠛⠛⠛⠻⣶⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡶⠶⠶⣶⣤⣄⡀⠀⠀⣠⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⠟⠉⠀⠀⠀⠀⠀⠀⠉⠛⢷⣾⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⠟⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⢀⣠⣴⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⣀⣀⣀⣠⣶⠟⣋⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠘⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠉⠉⠉⠻⠷⠞⠉⠉⠉⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⠀⠀⠀⠀⠀⠈⠻⢷⣤⣀⠀⠀⠀⠀⠀⣠⡿⣧⡀⠀⠀⡴⠂⠲⡄⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⢀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⠶⣶⠶⠿⠋⣠⡾⠋⠀⠀⢧⡀⣠⠇⠀⠺⣧
⠀⠀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⠀⣠⣄⠀⠀⠀⠀⢸⣧
⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠷⠾⠛⠉⠙⠳⢶⣤⠶⠟⢻⣧
⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡴⠶⠟⠛⠛⠋⠉⠉⠉⠙⠛⠛⠷⣦⣄⠀⠀⠀⢸⣷
⠀⠀⠀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⠾⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣶⣤⠀⠙⢷⡄⠀⢸⣿
⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠈⣿⠀⣼⡇
⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀⠀⢠⡾⠁⢠⣾⣿⣆⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠈⠛⠛⠀⠀⠀⣿⣴⡟
⠀⠀⠀⠀⢻⣇⠀⠀⠀⠀⢀⡿⠀⠀⢸⣿⣿⣿⠀⠀⠀⠀⠀⠀⢞⣉⣹⠆⠀⠀⠀⠀⠀⠀⠀⢀⣼⡿⠋
⠀⠀⠀⠀⠀⠻⣧⡀⠀⠀⢸⣇⠀⠀⠈⠛⠛⠃⠀⠀⠀⠀⠀⠀⣄⣀⣠⠖⠀⠀⢀⣠⡤⢤⣴⣿⡋
⠀⠀⠀⠀⠀⠀⠈⠻⣶⣄⡀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡖⠋⠀⠀⣤⠼⠇⠙⣤⠖⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⢿⣷⣶⣤⣤⣤⣤⣤⣴⣶⣶⣶⡿⠟⠛⣻⠏⠀⠀⠀⠀⠙⡶⠀⠀⠀⠲⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠉⠁⠀⠀⢰⣿⠶⠶⣴⡏⠀⠀⠀⠀⠀⠈⠳⠶⡄⠀⣤⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡷⣶⣤⣤⣿⠁⠀⠀⠈⣿⠀⠀⠂⠀⠀⠖⠀⠀⠈⠋⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣀⢸⣷⡀⠀⠀⠁⣀⠀⠀⣠⣿⡀⠠⠄⠀⠠⠀⠀⠂⣠⢼⣇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠈⠙⣿⠟⠻⢶⣦⣶⠿⠛⠋⠉⠀⠉⠓⠲⠦⠤⠶⣶⠋⠁⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⢠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣀⠀⠀⣸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⣰⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠷⠶⣦⣤⣄⣀⣀⠀⠀⠀⠀⣀⣼⢷⣤⣴⠾⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠛⠛⠋

⠀⠀⠀⠀⣀⣀⣀⡀⣀⠀⠀⡀⠀⡀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⢀⢠⢀⣀⡈⣁⡁⠉⣈⡁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠈⠀⠈⠁⠙⠀⠓⠐⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠰⢀⠀⠁⠀⠉⠁⠀⠉⠉⠂⠀⠁⠘⠀⠀⠀⠀⠀⠀⠐⠆⠀⠀⠀⠀⠀⠀⠈⡁⠉⠈⠀⠂⠈⠀⠒⠂⠐⠀⠒⠒⠠⠀⠀⠀⠀⠀⣀⠀⢀⡀⠀⠁
⠀⠀⢸⠀⠈⠍⠄⠈⠀⠓⠂⠒⠒⠂⠂⠂⠀⠀⠀⠀⡀⠤⠒⠈⠀⢙⠒⠄⠀⠀⠈⠁⠀⠒⠃⠀⠀⠐⠈⠀⠀⠀⠰⠀⠀⠀⠀⠀⠃⡀⠀⠠⠀⠌⡁
⠀⠀⢰⠀⠀⠀⠀⠈⠀⠈⠂⠀⠀⠲⠆⠄⠀⠀⠀⠀⠁⠴⠀⠉⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠀⠄⠤⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁
⠀⠀⠸⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⢠⠀⠘⣿⠓⠸⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⢀⣀⡀⠀⠀⠀⠀⢀⣤⡄⢠⣤⡀⠀⠀⢀⡀⢠⡄⣤⢁⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄
⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⡀⠱⠾⠇⠀⠀⠀⠀⠈⠛⠡⠘⠃⠁⠀⠠⠈⠅⡀⣠⠒⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡘⠁⠀⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠘⠄⠠⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠤⠀⢀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠂⡀⠀⠀⠂⠰⠈⠀⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂
⠀⠀⠀⠀⠘⠀⠀⢠⠀⠀⠀⠀⢀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠰⠀⠀⠠⠄⠺⠧⠀⠠⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠢⠈⠠⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⢀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⣄⠀⠀⠀⢠⠴⡆⠀⠀⠀⠀⠀⢀⡀⠀⠂
⠀⠀⠀⠀⠀⠀⠀⡎⠁⡠⠀⢀⡅⢸⠆⠀⠀⠀⠀⠀⠁⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⠠⠄⠀⣴⠠⠇⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠀⢠⠀⠀⠀⠀⠀⠈⢂⠗⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠂⠀⡀⠀⢀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠛⠀⣘⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢠⣇⣰⠁⢀⠄
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠀⠀⠀⠀⠄⠆
⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⠀⠀⠀⠀⠀⠀⣀⠐⠜⠂⢠⠤⠔
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⢀⣤⣤⠀⠀⠀⠄⠈⠁⣀⡤⠀⠀⠀⣄⠂
⠀⠀⠀⠀⠀⠀⠀⣤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⣤⣤⠈⠛⠋⠀⠈⠀⠀⠰⠞⠉⠀⣀⠠⠉⠀⠀⠀⢠⡀⠀⠀⠄
⠀⠀⠀⠀⠤⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠉⢀⡀⡰⠄⠙⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⢀⡀⢀⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠉⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠛⠛⠛⠛⠳⢦⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⠀⠘⢷⡶⠖⠒⠒⠒⠲⠶⠶⢤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⢠⡀⠀⠀⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⣧⣠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢠⣟⠀⠈⢻⣤⣤⡴⠋⠙⣦⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⠁⠀⠀⠀⠀⠀⠀⠉⠓⠲⠖⠚⢋⡞⠀⠒⢿⠀⢈⡷⠄⢰⠃⠀⠀⠀⣠⡾
⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠧⣤⡤⠏⠉⠻⣄⠀⢸⠟⠛⠛⠋⠉
⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⠤⢤⣤⣀⣀⠀⠀⠀⠀⠈⠻⣏
⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⢀⡴⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⣄⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⣰⠋⢀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠈⢳⡀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡀⠀⣿⠀⠈⠻⠟⠀⠀⠀⣴⢲⡄⠀⠀⠈⠻⠋⠀⢸⢇⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣌⣧⣄⠀⠀⠀⣀⣀⣲⣭⣒⣀⣀⣀⣀⣀⣴⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠟⠛⠛⢻⠛⢦⡀⠀⠀⠀⣠⠼⢻⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡦⠤⢤⣾⠶⠒⢭⠂⠀⡘⣵⠋⠉⢻⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⢉⠀⠀⣸⣇⣉⣠⣽⣄⣀⡼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⢙⡟⠉⠉⠉⠉⠉⡟⠉⠉⢻⠉⠙⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⠀⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣺⠻⡶⣞⣷⣄⡀⠀⠀⠀⠀⠀⣼⣇⠀⠀⠀⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠳⠤⠽⡇⣷⠟⠈⡟⠉⢙⠲⢤⡤⢼⠋⡟⠶⣤⡞⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠤⡾⠁⡆⠀⠇⠀⢿⠀⢰⠀⠈⢸⠀⡶⡘⣧⣀⣀
⠀⠀⢀⣠⠴⣒⡉⡉⠁⠀⣰⠃⡸⠀⢠⠀⠀⠀⠀⢸⠀⢠⢸⠀⡇⢳⣙⣧⣌⡉⠑⠢⢤⡀
⢀⡴⠋⡞⠉⠁⠉⠙⢦⠀⠳⠴⠧⡀⣸⠀⠀⣆⣀⣸⠀⠈⠘⣠⠿⠞⠉⠁⠀⠙⠂⠀⠀⠉⠲⡄
⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣃⣀⡴⠋⠀⠈⢧⣴⣤⠏⠀⠀⠀⣠⡴⠦⠲⣤⡀⠀⠀⣳
⠘⣦⡀⠀⠀⠀⠀⢠⠴⠛⠋⠱⣆⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠁⢀⡴⠃
⠀⠀⠙⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⠤⠖⠉
⠀⠀⠀⠀⠀⠈⠉⠓⠒⠢⠤⠤⠤⠀⡀⠀⢀⣀⣀⣀⣀⣤⣤⠤⠤⠄⠒⠚⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⡿⠟⠛⠛⠛⠿⣿⣷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡿⠃⠀⠀⠀⠀⠀⢀⣈⣻⣿⣷⠀⠀⢀⣠⣤⣴⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠁⠀⠀⠀⠀⢀⣴⠟⠉⠉⠛⢿⣧⣾⠟⠛⠉⠀⠙⣿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠿⠿⠷⣶⣦⣤⣀⣿⣿⣦⣶⣶⣶⣶⣿⠃⠀⠀⢀⣀⡀⢻⣇⡀⠀⠀⠀⠀⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠈⠉⠛⠋⠉⠁⠀⠀⠀⢸⡏⠀⠀⣴⡟⢻⣿⠟⠛⠛⠿⣶⡶⠟⠛⠛⠻⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠹⢷⣾⡇⠀⠀⠀⠀⢹⣷⣶⡄⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣤⣀⣀⣤⣿⣷⣄⡀⣀⣠⣿⣧⣾⠇⠀⢰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠉⠛⠛⠻⣧⡉⠀⢀⣰⣿⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠉⢹⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣿⡶⠶⠶⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⡀⠀⠀⠀⠀⠉⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣿⣦⢤⠄⠀⠀⠀⢀⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⠀⠀⠀⠀⠀⢶⣿⡷⠶⠶⠄
⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⢻⣇⠀⠀⠀⠀⠀⠘⢿⡿⠀⠀⠀⠀⠀⠀⢀⡤⠶⣤⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣿⣶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢦⡤⢾⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠷⣦⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠻⣦⣤⡤⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⣤⣤⣤⣿⠛⣻⡆⠀⠀⠀⠀⠀⠀⢀⣠⣾⠟⠁⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡾⠛⠛⢷⣦⣤⣤⣤⣀⣀⣾⣏⣁⡀⠀⠈⠉⠛⠰⠿⣧⣤⣀⣀⣤⣤⣶⣿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠉⠀⠀⠀⣰⡿⠋⠀⠈⠙⣿⡏⠉⢹⡟⠀⢀⣠⣄⠀⠀⠀⠉⣿⡟⠁⠀⠈⠙⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⣼⡇⠀⠘⠛⠛⠛⠉⠻⣦⡀⢰⣶⣿⠇⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠉⠻⠛⣽⡏⠀⠀⠀⠀⠀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠻⣷⣄⠀⠀⢀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⣄⡀⢀⣠⣼⠟⢷⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠈⠙⠛⠛⢻⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⡟⠛⠛⠋⠁⠀⠈⢿⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⢀⣠⣶⢿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣿⣿⣏⣁⣈⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⣠⣾⠟⠛⠋⠉⠉⠉⠙⠛⠻⢿⣆⡀⠀⠀⠀⢀⣠⣾⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⠿⠿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⠿⠶⠾⠟⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢯⡀⣈⠇⠀⠀⡞⠁⢹⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⡅⠀⠀⠀⣹⡖⢊⣀⣀⣤⡤⠢⣄
⠀⠀⠀⠀⠀⠀⠀⣠⣶⠶⢶⣤⣄⣀⠀⠀⠀⣀⣀⣀⣀⡜⠀⢱⣀⡤⠊⠀⢸⡛⠉⠉⢙⣄⣀⠜
⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⠀⠉⠙⠻⠛⠛⠛⠛⠋⢹⠁⠀⠀⠉⠀⠀⠀⠀⢣⡤⠚⢩⠻⣇
⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⣿
⠀⠀⠀⠀⠀⠀⢸⣧⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠲⠤⣀⣀⠀⠀⠀⣸⠃⠀⣿
⠀⠀⠀⠀⠀⠀⢠⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠐⣿⡀
⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧
⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣿⣤⣤⣤⡀
⠀⠀⣀⣤⣤⣾⣷⠤⡄⠀⠀⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠈⠉⣹⡇
⠀⠀⠀⠀⠀⠘⣷⠀⠀⠀⠀⠀⢿⡿⠁⠀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⢸⣿⠇⠀⠀⠀⠀⠲⣿⠷⠦⡤
⠀⠀⠀⠀⠤⠶⠿⣿⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣉⣉⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⣹⣷⣶⡃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠛⠛⠶⡦
⠀⠀⠀⠀⠀⠰⠟⠉⠀⠙⠻⢷⣦⣤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⡶⠟⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⡶⠛⢉⡿⠛⠛⣿⠿⠿⠿⠿⠿⣿⠟⠛⠛⠋⠉⢉⣷⣄
⠀⠀⠀⠀⠀⠀⠀⣴⠟⠛⠛⢷⣴⠟⠀⠀⠀⠿⢶⣶⠶⠒⠉⠀⢀⣐⠦⢀⣴⣧⡞⠛⠛⢷⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⡴⠛⠒⠂⣋⠨⡉⢀⠀⠀⡠⢰⠌⢚⡡⠒⠁⠈⢿⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⢿⣄⢀⠎⠀⠀⠀⠀⠹⠔⠁⠲⠚⣋⡩⠔⠚⠁⠀⠀⠀⠀⠈⢇⠀⢀⣼⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢯⡤⠤⠤⠀⠀⠐⠂⠒⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡶⠦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠴⣾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠉⠉⠓⠒⠒⢲⡖⠒⠒⠊⠉⠁⠀⠀⢀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⣀⣾⠏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠷⠶⠶⠶⠾⠛⠻⠷⠶⠶⠶⠿⠛⠋⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠈⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⠈⢳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⣀⣀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⠀⢻⣀⣴⠟⠉⠉⠉⠻⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⣾⠀⠀⠀⠀⢀⡀⠀⠘⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⠆⠀⢿⡀⠀⠀⣠⠞⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠁⠀⠀⠀⠙⠛⠋⠁⠀⠀⠀⠀⠈⢷⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⢀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢻
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⡔⣤⡀⠀⠀⠀⠀⠀⠀⠉⣐⢤⡀⠀⠀⠀⢸⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⣬⡀⠻⠃⠀⠀⠀⠀⠀⠀⠀⣿⡇⠙⡀⠀⣠⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⣤⠤⠀⠀⠀⠀⡇⠀⠓⣄⣀⡀⠂⠀⠀⠀⣀⡠⣀⣠⡶⠞⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠶⠄⡴⠾⠀⠀⠀⢸⠃⠀⣦⡀⣨⠃⢸⣇⢀⣀⣀⣀⣹⡶⠀⠀⢠⠂⠈⢁⣀⣠
⠀⠀⠀⢀⡀⣀⣀⣀⣀⣀⠀⠀⢀⠀⠀⠀⠀⠀⠀⡞⠓⠒⠒⠚⠳⠄⠚⠬⢭⣌⠁⠀⠉⠁⢀⡼⠇⠀⠠⠤⠴⡄⠀⠉⢉⡆
⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠈⣩⠟⠙⠐⠶⡅⠀⠨⡆⠀⠤⠀⣠⣤⣤⢄⡀⠀⠀⠃⢉⣉⡉⢃⣀⡀⢀⡀⠀⣸⠁⠀⠀⠀⣃⠐⠢⡄⠀⢆
⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⡜⡡⠤⠀⢀⠠⠵⠆⡀⠀⡇⠀⠀⠀⠀⠀⢘⡇⠀⠀⠀⠀⠀⠀⠀⢸⣅⡼⠁⠀⠈⡄⠀⠀⡇⠉⠀⡤⣤⠄⠈⠁⠂
⠀⠃⠀⠀⠀⠀⠀⠀⠀⢸⠀⢱⠀⣀⠗⠀⠤⠚⢧⠘⠁⠀⠀⠀⠀⠀⢸⠇⠀⠰⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⢠⠁⠀⠀⠋⠀⠟⢨⡲⠥⡇⠀⠓
⠀⣀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠦⠙⠀⠀⠀⠄⢸⠃⡆⠀⠀⠀⠀⠀⢈⣤⠀⢰⠃⠀⠀⣠⣾⡏⠀⠐⢠⠠⢀⠆⠀⠘⢲⠦⠈⠐⠃⠂⠀⡰⠈⠀⠀⣀⠠
⠀⠈⠉⠒⠢⠤⣀⡀⠀⢰⠀⠈⠱⡤⠶⠦⠠⡖⠛⠀⠃⠀⠀⠀⠀⢠⣿⡾⣷⣾⣦⣴⡏⣹⣿⠛⢢⡀⠚⠗⣸⡄⢀⡀⠼⡀⠀⠲⠄⠠⠋⠁⠈⠉⢀⡙⢤⡀⢀
⠀⠀⠀⠀⠀⠀⢀⡙⠋⢻⡇⠈⠀⠀⠀⠀⠀⠙⣦⠐⡇⢀⡤⠀⣴⠛⣿⣤⣼⡿⣿⡟⠙⣿⣿⣷⣿⠏⠘⠛⢻⠁⠀⠰⣀⠀⣸⣆⡀⠀⣙⠀⠀⠀⠀⠸⠢⠄
⠀⠀⠀⠀⠀⠀⠈⠁⠀⠈⠷⡀⠀⠀⠀⠀⠀⠀⠈⠄⠶⠜⠃⠀⠈⠻⢿⣿⣿⣄⣼⣿⣿⣿⡡⠛⠁⠀⠀⠦⠞⠀⠀⢀⡘⠀⠉⠛⠁⠐⠅⢠⡖⠄⠀⠠⠖
⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠆⠹⣄⠀⠀⠀⠀⠀⠀⡄⣥⢀⠠⠤⢀⠀⠀⠈⠉⠟⠉⠉⠁⠙⡄⠀⠀⠠⠈⢣⣆⠀⠀⠉⠉⠂⣄⣦⠐⢒⡊⢉⠿⢉
⠀⠀⠀⠀⡴⠊⠈⠱⣆⢰⠄⠀⠈⠳⢤⣤⣤⡤⢞⠡⠄⠎⠀⠀⢀⠂⠀⠀⠀⠹⢀⣤⡄⠒⠁⠀⠀⠀⠎⠀⠀⠢⠄⠸⠶⠆⠋⠛⠲⡄⠱⣤⠀⢠
⠀⠀⠀⠀⠢⣀⣀⣀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠑⠋⠐⠈
⠀⠀⠀⠀⠀⠃⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠉⠉⠉⠙⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⠈⢳⣤⣤⣤⣤⢤⣤⣤⣄⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⣀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠲⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⢸⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⣿⠀⢀⣀⡀⠬⣙⠦⣤⣤⡤⠞⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢋⡤⡟⠑⠃⠈⣇⣀⢸⡀⠀⠀⠀⠀⠀⠀⠈⠛⠲⢤⣤⣀⣀⣀⣀⣀⣀⡴⣇
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⢏⠀⡼⢲⡤⠞⠤⢬⣋⡼⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣄⠈⠉⠉⠉⠀⠀⠸⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⢀⣾⢙⠲⡎⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⢿
⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠉⠁⠙⠁⠀⠀⠀⠀⠀⢀⣀⣀⣠⣤⣀⣀⣀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⣇⢸⠀⠀⠀⠀⠀⠀⣠⠶⠛⠉⠁⠀⠀⠀⠀⠀⠉⣙⡳⢤⡀⣀⣾⠀⠀⠀⠀⠀⠀⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠀⢿⠸⣆⠀⠀⠀⢠⠞⢡⣶⡄⠀⠀⠀⠀⠀⠀⠀⠠⣿⣷⢠⡿⠋⢪⢳⠀⠀⠀⢀⣴⡪⠭⡑⡄
⠀⠀⠀⠀⠀⠀⠀⠀⣸⡧⠼⢦⡀⠀⣿⠀⠸⣿⠇⠀⠀⠀⣔⣒⡄⠀⠀⠙⠁⡼⠃⠀⠀⢇⣇⢀⣠⣮⠊⠀⠀⢸⢸
⠀⠀⠀⠀⠀⢀⡴⠛⠁⠀⠀⠀⠙⣶⢿⣤⣀⣀⠀⠀⠀⠐⣂⣔⣋⣠⣤⣶⠚⡇⡇⠀⢠⠋⠁⠉⠉⣇⡀⠀⠀⢸⠸
⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠈⢰⣏⡉⠉⠉⠉⢩⠏⠉⠉⠹⡄⢀⣈⣳⠘⢌⡲⠃⠀⠀⠀⠀⠨⣃⣀⣴⡣⣇
⠀⠀⠀⣰⢃⣀⣀⡀⠀⠀⠀⢀⡴⠖⠲⣿⡙⠳⠦⠴⢯⣄⠀⠀⠀⢹⡋⠀⠙⣧⡀⢧⣃⣤⠀⠶⠀⢀⠏⠉⠉⠀⣸⣆
⠀⠀⠀⡏⠉⠁⠈⠙⠆⠀⠀⢸⠀⠀⢰⠏⠙⢶⡄⠀⠀⢻⠁⠒⠒⢼⠳⢦⠞⠁⠈⠓⣼⣿⣏⢫⡉⡁⡠⠒⠉⠽⢷⡿⢶
⠀⠀⠀⡇⠀⠀⠀⠀⢀⡀⠀⣸⢦⣀⣸⡀⠀⠀⢹⠶⢾⣿⣶⣶⠶⠾⢶⡾⠿⠿⠿⠿⢭⣍⠀⢀⡏⠈⠉⠓⠤⠤⠼⠙⡏
⠀⠀⠀⡇⠀⠀⠀⠀⠈⣇⡼⠁⠀⠀⠀⣙⣦⡀⠀⠓⠉⠀⠀⠀⠀⡄⠠⣧⠤⡤⠀⠀⠀⠉⠉⠁⢻⡀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⣧⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠙⡆⠀⠀⠀⠀⠀⠀⢧⠀⠙⡆⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⢰⡇
⠀⠀⠀⢿⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣀⡀⠀⠀⠀⢨⡧⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⢸⠃
⠀⠀⠀⢸⡄⠀⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡿
⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠈⠳⢤⣤⣠⡤⠟⠶⠤⠴⠶⠶⠶⠶⠖⠒⠒⠒⠒⠛⠛⠛⠛⠛⠛⠓⠒⠒⠶⠶⠶⠒⠋⠳⣤⣀⣠⡴⠋

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⡀⠀⠀⠀⠀⡀⠀⢀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠄⠂⠀⠀⠀⠀⠀⠑⢄⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠀⠂⠒⠠⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⠄⠄⠒⠐⠀⠢⠄
⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠱⠀⠀⠀⠀⠀⠂⠀⢀⠑⠀⡀⠀⠀⠀⣀⠀⠀⢀⠄⠊⣀⠀⠀⠐⠀⠀⠈⠐⠆⠀⠀⠀⡀⢀⠀⡀
⠀⠀⠀⠀⠐⠰⠁⡐⠀⠀⢘⠀⠀⠀⠀⠀⠀⠀⠈⠁⠠⡀⢀⠆⠉⠀⢓⠀⣀⠔⠈⠁⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⢁⠀⠉
⠀⠀⠀⠀⠀⠀⡠⠁⡀⠀⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠊⠂⠁⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⢀⠀⠈⠁⠂
⠀⠀⠀⠀⠀⠀⠠⠊⠠⠒⠸⠁⠀⠀⠀⠀⠀⠀⠀⠔⠀⠂⠀⠀⠀⠀⠀⠀⠲⠀⠢⠀⠀⠀⠀⠀⠀⠀⠈⠇⠂⠄⠑
⠀⠀⠀⠀⠀⠀⠀⠃⠐⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠀⠆⢐
⠀⠀⠀⠀⠀⢀⠀⡁⠐⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⢀⡄⠈⢀⠌⠁⠈⠡⡀⠐⢠⡀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠂⠈⠀⡀
⠀⠀⠀⠀⠐⠁⠀⠐⠆⠠⡀⠰⠀⠀⠀⠀⠀⠠⠐⠀⢠⠐⠀⠀⠀⠀⠀⠀⠀⡀⠈⠂⠄⠀⠀⠀⠀⠀⠆⢀⠄⠰⠀⠀⠈⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠐⡀⠡⠠⠐⠂⠁⠠⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠢⠤⠈⠐⠢⠠⠌⢀⠂⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠢⠜⢀⡈⠋⡀⠄⠒⠀⠉⠀⠀⠀⠀⠀⠀⠉⠀⠒⠠⢀⠉⢁⡂⠣⠔⢁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠆⠀⠀⠔⢁⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠈⠢⠀⠀⠰⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠦⡀
⠀⠀⠈⠂⠀⠀⠀⠀⠂⠀⠈⠢⡀⠀⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠘⠀⠀⠀⠀⠀⠄⠀⠂⠀⠀⠀⢀⠔⠁⠈⠐⠀⠀⠀⠀⠐
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⢢⣀⠀⠀⠀⠀⢀⡀⢀⠁⠈⠀⢀⡀⠀⠀⠀⠀⣀⡔⠀⠂⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠙⢁⡀⠉⠀⠑⣯⣿⠊⠀⠉⢄⡈⠃⠄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠁⠀⠀⠀⠀⢀⡿⢗⡀⠀⠀⠀⠀⠈⢀⡸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠑⠠⠄⠠⢄⠂⠁⠀⠀⠈⠐⡠⠄⠀⠄⠂⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⡀⠈⠡⠀⠀⠀⠀⠀⠀⠁⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠌⠑⣤⠤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠉⣣⣄⢈⢄⡀⠀⠂⠀⠀⠐⠂⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠐⠀⢀⡠⡀⣠⡊⠁⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠈⠥⢴⡉⠻⡀⢁⠄⠀⠀⠀⢀⠄⡀⠀⠀⣀⠠⠀⠀⠀⠀⠰⡀⢀⠛⢉⡦⠌⠁⢠⠅
⠀⠀⠀⠀⢀⠀⡀⢀⠀⠈⠀⠄⣈⠀⠴⢌⡁⠀⠀⠀⠀⢠⢀⡀⡯⢹⢀⡀⡄⠀⠀⠀⠀⢈⡠⠦⠀⣀⠠⠐⠁⠀⡀⠀⠀⡀
⠀⠀⠀⠀⠀⠉⠀⠉⠀⠀⠀⠀⠀⠂⠂⠀⠌⠀⠒⠀⠤⠀⢦⢠⠄⠨⠄⡴⠀⠤⠀⠐⠀⡡⠀⠐⠀⠀⠀⠀⠀⠀⠉⠁⠉⡀
⠀⠀⠀⠀⠀⠁⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠑⠀⠀⠐⠀⠀⠂⠀⠀⠊⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠈
⠀⠀⠀⠀⠔⠈⠰⠒⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠒⠆⠁⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠁

⡏⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉
⡇⠀⠀⠀⠀⠀⢀⠠⠤⢀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠀⠤⡀
⡇⠀⠀⠀⠀⠀⡆⠀⠀⠀⠑⠄⠀⠀⠀⠀⡰⠁⠀⠀⠀⠰
⡇⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠈⠄⠀⠀⡐⠀⠀⠀⠀⠀⠰
⡇⠀⠀⠀⠀⠀⠐⡀⠀⠀⠀⠀⠈⡄⠠⠁
⡇⠀⠀⠀⠀⠀⠀⢐⡀⡀⠀⡀⠀⢐⡐⠀⠀⠀⠀⠀⡐
⡇⠀⠀⠀⠀⠀⢰⠁⠉⠀⠀⠠⡀⠀⠃⠀⠀⠀⠀⡜
⡇⠀⠀⠀⠀⠀⠀⠒⠀⠀⡈⢀⠄⠀⠀⠀⠀⠀⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⡇⠀⠀⠀⣖⢆⢠⠉⠒⠂⠁⡀⠤⠀⠀⠠⠄⡀⠀⠀⠀⠁⠀⠀⠀⡠⠀⠀⠀⢺⣡⠟⢚⣙⣂
⡇⠀⠀⠀⠀⡀⢾⠀⢆⠐⣥⡀⠀⠀⠀⠀⢠⣦⡐⠄⠀⠀⠀⠀⠀⢱⠀⠀⠀⠘⣿⣋⣉⣉⠉⢹⡀
⡇⠀⠀⠀⠀⠁⢂⠁⣾⠘⠿⠃⠀⠀⠄⠀⠈⠛⠃⢸⡠⠁⠀⠀⠀⠈⠂⠐⠁⠀⠀⠀⠀⠈⠉⠛⠃
⡇⠀⠀⠀⠀⠌⣠⢼⣏⣢⠤⠀⡀⣀⣀⡀⠠⠤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠠⢄⠠⠄
⡇⠀⠀⠀⠀⠀⠇⠀⣈⠀⢑⡄⠀⠊⠀⠢⠀⠤⠓⠤⠠⠀⠀⠀⠀⠀⠂⠁⠀⢀⡁⠀⠈⠐⠄
⡇⠀⠀⠀⠀⠀⠀⠛⠁⠀⠈⡀⠀⠀⠀⠀⠀⢼⠀⠀⠔⠀⠀⠀⠀⡉⠀⠀⠐⢺⡿⠒⠀⠁⠈
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⡆⠀⠀⠠⡀⠁⠀⠀⠀⠀⠀⡓⠀⠀⠄⠀⠀⠠⠄⠀⠒
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢀⢀⡠⠇⢀⣀⡀⠂⠀⠀⠀⠀⠀⠀⢁⠀⠀⠐⠖⠴⠆⠀⠀⢉
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣨⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠰⢤⠃
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠄⡀⠀⠀⠀⠀⠀⠀⡀⠤⠂⠀⠀⠀⡆⢀⣀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠂⠀⠀⠀⠀⠠⢄⠀⠀⠀⠀⢠⠀⣜⡠⣸⠃
⡇⠀⠀⠀⠀⢰⣤⢀⣀⠟⡘⣇⡄⠴⣶⠀⠀⠀⡄⠀⠠⠂⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⠀⡈⠸⡋⠉⠉
⡇⠀⠀⠀⢀⣬⣥⡼⠍⠚⠛⠈⠵⣦⢵⣄⡀⠀⠈⠰⠁⠀⠀⠀⠀⣄⠀⠀⡴⠀⠀⠀⠀⠘⠂⡐
⡇⠀⠀⠀⠈⠣⡈⢀⡀⡀⠀⠠⣀⣀⣨⠊⠁⠀⠀⠆⠀⠀⢔⣈⠀⠀⠛⠚⠁⢉⣀⠀⠀⠀⣴⢶⡇
⡇⠀⠀⠀⠀⠀⠉⠀⠙⠦⠤⠔⠁⠀⠉⠀⠀⠀⠀⠐⣀⠀⠸⡿⠃⠀⢀⠀⠀⢻⡿⠀⠄⢘⡰⢂⡷
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⡤⣀⠀⠀⠀⠈⠀⢀⢠⡴⢾⠖⠻⠁
⡇⠀⠀⠀⠀⠀⠀⡠⠐⠃⠈⠁⠘⠓⢠⠀⠀⠀⠀⠐⠙⠗⠐⣦⣀⡈⠍⢉⡀⡠⡀⣰⢏⣦⡔
⡇⠀⠀⠀⠀⠀⠄⠀⠀⠠⢴⣷⠄⠀⠀⠰⠀⠀⠀⠀⠀⢀⠀⠗⠉⠀⠀⠀⠙⠉⠁⠠⡄⠛⠄
⡇⠀⠀⠀⠀⠀⠠⠀⠀⡀⡀⢁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠘⠠⡆⠀⠀⢀⠀⠀⠀⣗⠐⡁⠒⠂
⡇⠀⠀⠀⠀⠰⠴⠀⡀⠀⢠⡔⢀⢀⠀⠰⠶⠀⠀⠀⠀⠀⡔⠁⠀⠀⢸⠀⠀⠀⠰
⡇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠁⠑⠂⠀⠊

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠈⠀⠈⢂

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠊⠁⠈⠑⠄
⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⣷⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠊⠀⠀⠀⠀⠀⠈⠄
⠀⠀⠀⠀⣰⣾⣿⣿⡿⣿⢿⠿⡿⠿⣿⣿⣄⠀⠀⠀⠀⠀⡰⠉⠘⢥⠀⢂⠀⠀⢀⠔⠀⠀⣄
⠀⠀⠀⣰⣿⣿⣿⣿⣾⣷⣾⣷⣿⣷⣿⣿⣿⣧⠀⠀⠀⢀⠘⠄⠢⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⢿⣿⣿⣿⣛⣿⣿⣿⣿⣿⣻⣟⣿⣻⣿⠀⠀⠀⠀⠀⠀⢀⡀⠄⠀⠐⠒⠂⠀⠠⢀⠀⠀⢰
⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣿⣿⡿⠀⠀⠀⠠⡀⠀⠀⢸⠇⠀⠀⡀⠀⠀⢾⠇⠱⠀⡘
⠀⠀⠀⠀⠙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⡿⠁⠀⠀⠀⠀⠈⠂⠦⣄⠀⡀⠀⢢⠀⡀⢀⣀⠼
⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⣿⠿⠟⠉⠀⠀⠀⠀⠀⠀⠀⢀⠸⠄⡀⢀⠜⠣⡄⠘⠀⠱⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠀⢀⠎⠀⠀⠀⠀⠈⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⣀⠠⠋⠆⠀⠠⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡂⠀⠄⢠⠀⠀⠀⢠⠠⠀⠠⢀⠀⠀⠀⠀⠰⠀⡄⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡀⢀⠀⣄⠀⢀⠀⠀⡀⠀⠀⡀⠀⢀⠀⡀⢀⡀⠀⠀⢰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠠⠤⠤⠤⠤⡌⠀⣠⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠎
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢀⠇⡰⠁
⠀⠀⠀⢰⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⡿⠃⣸⡜⠁
⠀⠀⠀⠀⠘⣿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣿⣿⣿⠁⢀⠟
⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣷⣀⣀⣀⣀⣀⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⡟⣋⢉⢻⣿⣿⣿⣿⠏
⠀⠀⠀⠀⠀⠀⢉⣿⣿⠟⠛⠻⠿⢷⣥⣮⡾⠿⠿⣿⡀
⠀⠀⠀⠀⠀⠀⢸⣿⡏⠀⠀⣤⣀⡀⠈⠉⣀⣤⡆⢹⡇
⠀⠀⠀⠀⠀⠀⠸⣿⣧⠀⠀⢿⣿⠇⢀⣀⠻⠿⠇⢸⠇
⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⡽⣮⠀⢀⡠⠋
⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣷⣦⣤⣤⣽⣷⣶⣿⣄⢀
⠀⠀⠀⠀⠀⠀⠐⢯⡟⠉⢹⣿⡿⠟⠛⠿⣿⣉⡉⣯⠇

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡶⢶⣦⣄⡀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠿⠛⠻⠿⠶⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠉⠻⣦⣀⣠⣴⠾⠛⠋⠉⠁⠈⠹⣧
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠈⠙⠻⢶⣄⣀⣤⣤⣤⣶⠶⠶⣾⡟⠀⠀⠀⠀⠀⠀⠀⠘⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⢀⣤⣶⣤⣤⣿⡷⢶⣦⣄⠀⢀⣀⣀⣀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⢸⣏⢠⡾⠋⠀⠀⠀⠀⠙⣿⡟⠉⠉⠉⠉⠛⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⠙⢿⡇⠀⠀⠀⠀⠀⠀⢹⣧⡀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⠶⠶⣶⡶⠾⠻⣧⡀⠀⠀⠀⠀⣠⡿⠉⣿⡄⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣶⣤⣤⣾⠿⠷⡶⠟⠁⠀⠀⢀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣤⣀⠀⠀⣀⣤⡾⣷
⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠁⠀⣿⡄
⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇
⠀⠀⠀⠀⠀⢀⣀⣿⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠶⠿⠟⣿⡟⠛⠻⠿⠷
⠀⠀⠺⠿⠛⠛⠛⣿⡛⠉⠉⠁⠀⠀⠀⠀⢰⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃
⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⠀⠀⠀⠀⠀⠀⠠⣤⣶⣿⣤⣤⣀⣀
⠀⠀⠀⠀⠀⠀⣀⣼⣷⡶⠿⠃⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⡶⠛⠛⠻⢦⡀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⠀⠈⠉⠉
⠀⠀⠀⠀⠀⠛⠋⠁⠹⣧⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣤⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣄⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣹⣧⣶⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⠟⠿⣶⣤⣀
⠀⠀⠀⠀⠀⠀⢀⣴⡾⠟⠛⢷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠃⠀⠀⠀⠉⠛⠃
⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠈⠛⢷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⠾⠛⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⢶⣤⣤⣤⣄⣀⣀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣶⠶⠿⠛⠋⠉

⠀⠀⠀⠀⠀⡠⠄⠒⠒⠒⠂⠠⠀⡀
⠀⠀⠀⢀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠂⢄⡀
⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⢄⠀⠀⠀⠀⠀⠀⣀⠠⠀⠒⠒⠒⠠⢀
⠀⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀⢀⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠡⡀
⠀⠀⠀⠀⠀⠈⠒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠠⢀⠤⠀⠠⠤⠂⠀⠂⠄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⠀⠀⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠀⠀⠀⠀⠔⠂⠬⠤⠀⠸⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⢃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡀⠀⠀⠈⣄⠀⠀⠀⡘⠀⠑⠄⣀⣀⡀⠄⠂⠁⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠃⠀⠁⠢⠂⠉⠐⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⣀⠤⠐⠒⠂⠀⠀⠀⠐⠒⠒⠀⠤⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠈⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⡀⠀⠀⠀⠀⠀⢸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⢀⠂⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⣆⠀⠈⢆⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠈⠀⠀⠹⠿⠋⠀⠀⠀⠀⠄⠂⡄⠀⠀⠀⠀⢿⣿⠏⠀⠀⠈⠀⠀⠀⡰⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢴⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠀⢀⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠄⣀⡀⠀⠀⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⣀⡀⠴⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠈⠉⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠤⠄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠁⠀⠀⠀⠈
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⡀⠄⠀⠠⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠤⠤⠀⣀⠀⢀⡀⠀⠠⠌⠀⢀⣀⡈⣅⡀⠀⡀⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠆⠒⠀⠒⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⢆⣠⠉⠀⠀⠹⠄⡀⠈⡆⠠⠒⢄⠀⡠⠤⣠⠊⠀⠀⠀⠀⠀⠀⠘
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠘⠢⠀⢀⡴⠀⠃⢀⠋⠆⠰⠎⠈⡤⢠⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠠⠀⠙⠊⠠⠄⠉⠘⢄⠸⡀⠀⠀⠀⠀⠠⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⡌⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠒⠂⠉⠀⠀⠀⠡
⠀⠀⠀⠀⠀⠀⠀⠀⡀⣧⠀⠀⠀⠀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠉⢀⠀⠀⠀⠈⠉⠐⠠⢀⠀⠀⠀⠀⠀⠀⠁⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⣀⠀⠀⠀⠁⠂⠀⠀⠀⠠⠀⠄⠀⠀⠀⠀⠀⠀⣾⠀⠈⡠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠉⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⢦⡀⠀⠀⠀⢀⠀⠀⠀⠠⠀⠀⠀⠱
⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠈⠐⠠⢤⣀⣀⣀⣀⢀⡀⠀⢤⡄⠒⠉⢀⣀⠀⠁⠢⣄⡀⢁⠀⠀⠀⠀⠈⠀⠀⡠⠀⠀⡠⠁
⠀⠀⣍⡠⠦⢀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠁⠀⠃⠀⠀⠠⠁⠀⠀⠀⠉⢈⠁⠀⠑⠢⡁⠀⠀⠀⠈⠁⠒⠒⠲⣦⣌⡀⠆⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀
⠀⢠⠮⡁⢒⠁⠀⠀⠀⠀⠀⠀⠀⢀⡠⠖⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⣢⠀⢄⠀⠈⢂⡀⠀⠀⠀⠀⠀⠰⡾⠦⢀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆
⠀⠘⠤⠉⠀⠀⠀⠂⠐⡀⢀⡄⠀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠂⠐⠂⠑⢄⠀⠈⠉⠁⠀⠉⠀⠀⠁⠀⠊⠀⠀⠀⢱⠊⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⣡⠄
⠀⠀⣲⡆⠤⠃⠀⢃⣐⡀⠀⠤⠔⠀⠐⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠂⠀⠀⠀⠁⢄⠀⠀⠀⠀⠀⠲⠄⣀⠠⠂⠀⠀⠀⢀⠉⠉⠈⠇⠀⡀⢐⠟⠁
⠀⠀⠈⠀⠀⠀⠰⠤⡅⣜⡂⠀⠀⠀⠀⠈⡀⠈⠻⠀⠐⠒⠒⠂⠐⠃⠀⠀⠀⠀⠀⠀⠀⣀⠇⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⣡⢶⣁⠀⠀⠁⠸⠗
⠀⠀⠛⠐⠄⠀⠀⠴⠓⠆⠀⢀⠀⠀⡀⠀⠁⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢊⠀⠀⠀⠀⠀⠀⡠⠖⠁⠀⢀⠀⡀⠀⠀⠰⠛⠀⠀⠀⠀⠚⠑
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠖⠠⠃⠀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠀⠤⢄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠀⠀⠀⠀⠘⠂⠐⠠
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠋⢙⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⢂⣁⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠰⢈⡃⠯⠁⠀⡀⢀⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⢋⡐⢀⠃⠐⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⡶⠀⠃⠀⠀⢈⠀⠠⠠⡃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠴⠁⠰⠄⡄⠀⠀⠀⠀⠁⠀⠀⠀⠀⠐⠴⡇⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠀⠉⠁⠐⢄⠀⠀⠀⠈⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⢬⠀⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠎⠀⠀⠀⡀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠀⠈⡄
⠀⠀⠀⠀⠀⠀⠰⠂⠀⢂⡀⣀⡀⠀⠀⠀⠀⠀⠐⠀⠠⠄⠀⠀⠀⠀⠀⠀⡀⠁⠀⠀⠀⠀⠀⢀⠄⠈⠁⠀⠀⠀⠄⠰⡁
⠀⠀⠀⠀⠀⢀⡠⠀⢀⣀⠁⠀⠈⡆⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢀⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢲⠀⠈⠁⡁⠀⠀⠀⠀⠀⠀⠀⡠⠤⡠⠒⢂⡀
⠀⠀⠀⠀⠠⠁⠀⢌⠀⡠⠀⢀⠔⠁⠀⠀⠀⣀⠀⠀⠀⠈⠀⠈⠁⠠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠲⠎⠀⠈⠀⠀⠀⠀⠐⠉⠁
⠀⠀⠀⠀⠈⠂⢠⣄⠀⠀⠀⡀⠀⠀⠀⠄⠉⠀⠁⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃
⠀⠀⠀⠀⠀⠀⠘⠀⠁⠐⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠄

⠀⠀⠀⠀⠀⢤⣤⠀⠠⣤⠀⢤⡤⠀⠀⣤⣤⣤⠀⢠⣤⠀⢤⣤⠀⠀⣤⠀⢠⣤⠀⠀⠤⠤⠤⠤⢰⢤⠀⣤⣤⣤⡀⡄⡄⢠⣤⠀⠀⢠⣤⣤
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⢸⡇⠀⠀⣿⣿⣿⠀⢸⣿⠀⣻⣿⠀⠀⡗⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠉⠉⠳⠆⡇⡇⢸⣿⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⢸⡇⠀⠀⣿⣿⣿⠀⢸⣿⠀⣿⡿⠀⠀⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢀⢿⠀⠀⠀⠠⠀⠀⠁⢸⣿⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⢸⡇⠀⠀⣿⣿⣿⠀⢸⣿⠀⠉⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢠⢜⡃⠀⡤⠀⠀⠀⠀⠀⠀⠙⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⢸⡇⠀⠀⣿⣿⣿⠀⢸⠟⠀⠀⠀⢰⠀⠀⠀⠀⡀⠀⠀⢀⠀⠀⠨⡎⠐⢐⠀⣀⠀⠂⠀⠀⠀⠀⠀⠀⢸⣿⣿
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⢸⡇⠀⠀⣿⣿⣿⠀⠘⠀⠀⠀⠁⠀⠀⠀⠈⠀⡇⡐⠀⢊⣖⣠⠤⡾⢳⡴⣲⠟⠂⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⢸⡇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠀⠁⡆⠀⠀⢆⠀⢸⡅⠀⣯⠀⡀⠀⢸⡗⠋⠑⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡏
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⢸⡇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠐⠀⢳⡄⡀⠀⢀⡎⠱⣡⠞⢷⡋⢉⡥⠗⠀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⢸⡇⠀⠀⣿⣿⣿⠀⠀⠀⠀⠐⢢⣴⡁⢸⣤⠮⠖⠳⠥⣄⢺⡟⠉⠀⠀⠀⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⢼⡇⠀⠀⣿⣿⣾⠀⠀⠀⡀⠀⠈⠂⠽⣟⣻⣀⠤⣀⠀⢠⡼⠇⡴⠊⠀⠀⠀⢀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⢸⣷⡏⠀⣿⣿⣿⠄⠀⠀⣄⠀⠀⠀⠀⠘⢮⣷⣘⣷⣶⣿⡷⡟⠛⠶⢶⣶⣶⣿⣿⣿⣥⣄⡀⠀⠀⠀⠀⢸⡗
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⢸⡟⣧⣖⣿⣿⣿⣀⠐⠀⣯⠀⠀⠀⢳⣀⠀⠀⠈⠁⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠘⠠⡉⠛⢿⣷⣄⡀⠀⣾⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⢼⡇⠈⠉⣿⣿⡻⢯⣽⣿⣧⣤⣤⣠⡏⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠹⣿⣷⣼⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⢸⡇⠀⠀⣿⣿⣿⠀⢸⣽⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠎⠀⠀⠀⢿⣿⣿⣿⡇
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⢸⡇⠀⠀⣿⣿⢿⠀⢸⣿⣾⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⣿⣿⣿⡧
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⢸⡇⠀⠀⣿⣿⣯⠀⢸⣿⣿⠋⣁⣀⣤⣤⡴⠶⠶⠾⠟⠛⠛⠛⠛⠛⠛⣛⠛⠛⠛⠛⠛⠛⠛⠶⢾⣿⣿⣿⣦⣤⡄
⠀⠀⠀⠀⠀⢸⣿⠀⠀⣿⠀⢸⡇⠀⠀⠿⠛⠁⣠⣾⣿⠿⠛⠋⣉⣁⣤⣤⡶⠶⠶⠟⠛⠛⠛⢛⣛⣛⣛⣛⣛⣛⣛⣛⠛⠛⠛⠛⠛⠿⠿⠷⠶⡄
⠀⠀⠀⠀⠀⠸⠻⠀⠀⠻⠀⠸⠇⠀⠀⠤⠶⠟⠋⠁⠤⠶⠾⠛⠋⠉⠠⠤⠴⠶⠶⠾⠛⠛⠛⠛⠛⠛⠉⠉⠉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠻⠶⠶⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣸⣿⡿⠟
⢠⣴⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣦⡀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣧⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡇
⢻⣿⣿⣿⣶⣦⣤⣤⣤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡆⠀⠀⠀⠀⠀⠼⣿⣿⣿⠀⠀⣀⣴⣿⣿⣿⣿⣿⣿⡇
⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⠀⠀⣈⣋⣹⣧⣤⣀⣀⣀⣀⡀⠀⣼⡏⢈⣤⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷
⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠉⠀⠀⠀⠉⠻⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋
⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⣠⡀⠀⠀⣠⡀⢸⣿⣿⣿⣿⣿⣏⠁
⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠛⠁⠀⠀⠙⢋⣼⣿⣿⣿⣿⣿⣿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⠛⠛⠿⣿⣿⣿⣴⣦⣦⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⠠⣄⡀⠀⠀⠀⠀⠉⠻⠿⣿⣿⣿⠿⠋⠁⠀⢈⡿⣿⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⢲⣾⣿⣷⣦⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⣤⣾⣿⡟⠈⣿⣿
⠀⠀⣤⣤⣤⣶⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⢸⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⣿⣿⣿⡇⠀⣹⡟
⠀⠀⠀⠀⠈⠉⠛⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠙⠛⠋⠀⠀⠀⢀⠀⠀⠀⠸⢯⠿⠀⠈⠉⠉⠀⢠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡳⢤⣤⣤⡴⠂⠀⠀⠀⠀⣠⡿⠁⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠿⣿⣿⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣤⠞⠁⠀⠀⢀⣤⡾⠋⠀⢀⣠⣿⣹⣆⣤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣦⣤⣤⣄⣀⣤⣴⣾⣿⣧⣤⣤⡶⠾⠛⠁⠀⠀⣴⠋⠁⠈⢉⣼⣦⣽
⠀⢠⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣿⡿⢋⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣀⡤⢤⠀⠀⠀⠀⠰⡇⠀⢀⣴⠟⠁⢰⣟⢳
⠀⢸⣿⣿⣷⣄⠀⠀⢀⣀⣠⣴⠛⠉⠁⠀⠐⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠦⠼⠁⠀⠀⠀⠀⣻⣶⠛⠁⠀⢀⣴⠟⠉
⠀⢿⠿⣿⣿⣍⣠⣾⣿⣿⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢹⠿⠛⠻⢿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⣠⠾⠋⠉⠛⠳⠞⠋⠁
⠀⠀⠀⠈⠻⠿⠿⠟⠁⣿⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠟⠛⠛⠻⢿⣿⣏⠛⢶⣴⠞⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠷⢤⣄⣀⠀⠙⢿⡄⢈⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠞⠁⠀⠀⠈⠙⣧⣄⣀⣠⡾⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⢿⡋⠀⠀⠀⠀⢀⣠⠞⠉⠈⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠳⣄⠀⠰⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⢦⣾⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣤⣀⣀⣀⣠⣤⣤⣤⡴⠞⠃

⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢀⡴⠋⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠉⠢⣠⠎⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄
⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⣠⠜⠁⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⡼⠀⠀⢲⡀⠀⠀⠀⡇⠀⢀⠞⠁⠀⠀⠀⠀⠀⠀⠀⠠⠄
⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠙⢤⣀⡠⠃⠀⠣⣄
⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣
⠀⠀⠀⠀⡎⠀⠀⠀⠀⢀⡠⠤⠄⠒⠠⠤⢄⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠒⡄
⠀⠀⠀⠀⢣⠀⠀⢀⠞⣥⡄⠀⠀⠀⠀⠀⣶⡝⣆⣏⠀⠀⠀⠀⠄⠄⠀⠀⠀⠠⠃⠀⢠⡃⠀⢀⠤⡤⡀
⠀⠀⠀⠀⠈⠣⣄⢸⡀⠛⠁⠀⠀⠂⠂⠀⢈⡠⠿⢤⡗⡲⠈⠀⠄⠀⠁⠒⣆⣘⡠⠊⠁⠈⠙⠅⠀⠀⡷
⠀⠀⠀⠀⠀⠀⠀⣝⠛⠒⠤⠤⡤⢤⠒⡸⠷⢛⠄⢠⢃⠁⠐⠀⠀⠂⠀⠴⡁⢒⣧⡀⠀⠀⠀⠅⠀⢠⡃
⠀⠀⠀⠀⠄⠀⢀⣈⣱⠦⢤⡴⠋⠛⠛⣤⢴⠋⠀⠘⠺⠚⠒⡤⠬⣤⠐⠀⠈⣹⡗⠈⣒⣰⢶⡴⠖⠣⠑
⠀⠀⠀⠀⠀⠀⣏⣷⡏⠀⠀⠉⠉⡷⠔⠗⠒⠉⠒⢁⠀⠀⠊⠀⠀⠀⠷⡄⠀⣩⠙⠒⠉⠉⡠⠰⢂⢈⡎⠁
⠀⠀⠀⠀⡄⠀⡿⠀⡇⠀⠀⠀⠀⣇⠀⠄⠀⠐⠲⠁⠀⠀⠣⠤⡇⣘⠄⠠⠀⢡⠔⠀⠄⠂⠀⠀⠐⠸
⠀⠀⠀⡐⡏⠉⣅⠀⡻⡀⠀⠀⢸⠈⢦⠁⠂⠀⠂⠁⠀⠉⢐⠪⢰⣉⡈⠀⠃⢋⠆⠀⠠⠀⠀⠀⠀⡇
⠀⠀⠀⠙⠛⢫⡄⠀⠐⠓⠢⠤⠤⠧⠼⡀⠀⠀⠀⠀⠀⠈⡁⠠⠀⠈⠬⠟⠌⠛⠀⠄⠀⠌⠀⠀⣸⡅
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⠂⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠔⢅⡉⠂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠆⢀⠓⠢⠤⠤⠤⣄⠀⠀⠀⢀⠀⡀⠀⢀⡜⠉⣄⢉⠐
⠀⠀⠀⠀⣆⡛⠃⣢⠀⠀⠀⠀⠀⠀⠀⠒⠒⠁⠀⠀⠀⠀⠀⠀⠉⠒⠢⢇⠀⡴⠒⠉⠀⠀⠉⡀⠰⡀⠄
⠀⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠤⠃⠀⠀⠀⠀⠠⠑⠀⠈

⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⣀⣤⣶⣶⣶⣶⣶⣶⣶⣤⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⢈⡟⠛⠛⠉⠉⠉⠀⠀⠀⠙⣿⣄⡀
⡇⠀⠀⠀⠀⠀⠀⡀⠀⠀⣀⢀⠀⠀⣀⢀⢀⡀⡀⡀⠀⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠸⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠘⠁⠸
⡇⠀⠀⠀⠀⠀⠉⠉⠉⠛⠉⠈⠈⠋⠉⠉⠈⠉⠁⠁⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠁
⡇⠀⠀⠒⠚⠃⠘⠒⠓⠛⠚⠃⠙⠓⠘⠙⠒⠃⠛⠀⠒⠛⠒⠒⠒⠁⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⢀⠀⡀⠀⠈⠁⡀⠤⠐⠀⢀
⡇⠀⠀⠀⠠⢰⠰⠀⠰⠰⠒⠰⠲⢴⠀⠆⠄⠒⠆⠀⠆⠆⠆⠆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠁⠀⠀⠀⠀⢠⡀
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠈⠀⠐⠂⣄⢲⣾⣧⠀⢧⠀⠈⠁⠂
⡇⠀⠀⠀⠀⠀⠀⢀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣆⣀⣀⣀⣀⣀⣀⣀⣀⣔⣁⣈⣶⣙⣿⣀⣉⣃⣀⣀⣀⣀
⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⠒⡒⠒⠒⠒⠒⠒⠒⠒⠂⠒⠒⠒⠒⠒⠒⠚⠛⠒⠒⠒⠒⢒⠒⠒⠒⠒⠒⠒⢲⣶⡶⠾⠓⠒⠒⢲
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠐⠀⠀⠀⠀⠠⠐⣀⣤⣤⣴⣶⣶⣴⣶⣄⠀⠠
⡇⠀⠀⠀⠀⠀⠀⢀⡀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠁⠀⣤⣾⣿⡿⠟⠋⠉⠀⠘⢿⣿⣷
⡇⠀⠀⠀⠀⠀⠐⠈⠁⠀⡤⠔⠀⠀⠀⠀⠀⠀⠀⠀⠡⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠈⣟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡀⠀⠀⠀⠰
⡇⠀⠀⠀⠀⠀⠖⠓⢉⢀⡀⠤⠦⠀⠀⠀⠀⠀⠀⠀⠀⠑⡀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⢀
⡇⠀⠀⠀⠀⠀⠀⠠⠀⠁⡀⣠⠄⠀⠀⠀⢠⡄⠤⠢⠃⠀⠐⡀⠀⡃⠀⠀⠀⠀⠡⡀⠀⠀⠀⢀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣶⡆⠻⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠘⠈⠀⢄⡤⠄⠂⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣄⢠⣾⣿⣿⡀⣿
⡃⠀⠀⠀⠀⢀⣄⠀⠖⠊⠁⠀⠀⡀⣄⡤⣴⡆⠀⠀⠀⠀⠀⠀⠁⡄⠀⠀⠀⠀⠀⠐⠀⠀⠀⠘⠂⣿⡆⠀⠀⢀⠠⣤⡀⠀⢯⠈⠉⠉⠛⠛⠿
⠀⠀⠖⠚⠉⠁⠀⠀⠀⠀⣤⠸⠾⠥⠙⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⠀⠀⠀⡦⠀⡀⠀⠀⠀⠀⠻⠇⠀⠠⠘⢄⡿⣿⡆⠼
⠆⠀⠀⠀⠀⠀⠀⠄⠠⠠⠤⠀⠤⠄⠤⠀⠄⠤⠄⠀⠀⠀⠀⠀⠠⡆⡦⠠⠤⠤⠤⠀⠷⠀⠤⠤⠠⠤⠄⡴⠤⠤⠌⠦⠄⠤⠤⠤⠠⠤⠤⠤⢠
⠁⠀⠀⠀⠀⠀⠀⠀⢀⣿⠇⠠⠀⠀⠈⡁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⡏⠉⠉⠄⠊⢁⡀⠄⠋⣹⣯⣍⣹⡉⠁⠉⣉⡈⢀⣹⣿⣻⣿⡿⢿⡿⣿
⡄⠀⠀⠀⠐⠂⠉⠀⠀⡟⠀⣀⣠⠔⠉⠀⠀⠀⠡⡀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⣈⡀⢀⡶⠋⠳⡽⣻⣿⣷⣿⣿⣿⠿⣿⣿⣿⣼⣁⢳⠘⠦⠾
⡇⠀⠀⡀⠀⠀⠀⣀⣤⣿⠯⠁⠀⠀⠀⠠⠔⠒⠀⠑⡀⠀⠀⠀⠀⡀⡇⠀⢹⢹⠉⡙⡆⢓⣴⢶⣿⠿⠿⠛⡍⣅⣀⣬⣼⣿⣿⣿⡉⣁⡢⠴⠶
⡆⠐⠁⠀⣠⣶⠿⠛⢋⣁⠠⠀⢂⢉⡁⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠃⡇⠀⠈⠈⠙⣉⣿⠋⠀⢀⣿⢠⠶⠒⢿⠹⣇⣤⡤⠿⣼⢙⡆⣿⣇⢀⡠
⡇⠀⠐⠈⠻⠁⠀⠋⠁⠤⠔⠊⠉⣁⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠁⡇⠀⠀⠘⡄⠘⢿⣷⠀⠅⠘⠃⠐⢓⣉⣤⣤⣄⣤⡐⣽⣾⢧⡙⣉⣡⣤
⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡁⠠⡤⠀⠒⠀⠀⠀⠀⠀⠀⠄⠀⠀⠇⠀⠀⠀⠈⠢⠄⠉⢠⡴⣾⡆⠀⣾⣧⠀⠀⠀⣹⣿⣇⡿⣠⣿⣧⠟⣿
⡇⠀⠀⠀⠀⠀⠀⠀⠀⠆⠂⠙⠀⣀⠄⠰⠂⠈⢉⣀⠀⠀⠀⠈⠄⠃⠀⠀⠀⠀⠀⠀⠀⡠⠊⢇⡻⣷⡀⠙⠛⠰⠞⠋⢁⣿⣿⣾⣿⣿⣿⣮⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠂⠉⢉⣉⠄⠰⠂⠈⠁⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⣿⡇⠀⠀⢲⠀⣿⣧⡉⣿⣾⣷⣿⣿⣿⣻
⠀⠀⠀⠀⠀⠀⠀⠀⠠⠔⠚⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠉⠃⠀⠄⠈⠳⠋⠻⠏⢿⠀⠀⠈⠉⠙⠛

⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡶⠾⠷⢦⣄⠀⢀⣠⣴⣶⣶⣶⡄
⠀⠀⠀⠀⠀⠀⠀⣼⡿⠛⠛⠛⠿⣷⣶⣤⣀⣤⣤⣤⣤⣤⣤⣤⣾⠋⠀⠀⠀⠀⠻⣾⠿⠛⠉⠀⠀⠙⣿⡄
⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠉⠉⠉⠉⠉⣿⠃⠀⠀⢀⣤⣤⣀⣻⣆⣀⠀⠀⠀⠀⢿⡇
⠀⠀⠀⠀⠀⠀⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠀⣿⠁⣼⠟⠉⠉⠙⢷⣶⠶⠿⠿⠿⣦⡀
⠀⠀⠀⠀⠀⠀⢸⣷⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀⠀⠙⢿⡏⠀⠀⠀⠀⢈⣿⣦⡄⠀⠀⢸⡇
⠀⠀⠀⠀⠀⠀⢈⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣦⣤⣴⠾⢿⣄⡀⠀⣀⣼⣏⣸⡟⠀⠀⣼⠃
⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⢻⣍⠉⠉⠀⢀⣼⠏
⠀⠀⠀⠀⠀⣸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣶⠶⠟⢿⡇
⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷
⠀⣠⣤⣤⣴⣿⣦⣤⡄⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠰⠾⢻⣿⠛⠛⠛⠛
⠀⠈⠀⠀⠀⢿⡇⠀⠀⠀⠀⠀⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⣸⣿
⠀⠀⠀⢀⣀⣼⣿⣶⠦⠀⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⣠⠶⠶⣄⠀⠀⠀⠀⠀⠈⠛⠋⠀⠀⠀⠀⠀⠙⣿⡟⠛⠷⠆
⠀⠀⠀⠉⠉⠁⠹⣷⡀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢤⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⣼⡟
⠀⠀⠀⠀⠀⢀⣠⣾⢿⣿⣉⣠⣴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⠟⠻⢷⣦⡀
⠀⠀⠀⠀⠰⠟⠋⠀⠀⣉⣻⡏⠀⠀⢹⠞⠻⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡾⠟⠁⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⠉⠁⢀⡤⡀⠀⠀⣸⣷⣦⣤⣤⣤⣤⣤⣤⣤⣤⣶⡶⣾⣿⣿⣛⠉
⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⣀⠀⠸⠤⠇⠀⠘⣿⡸⣯⠀⠀⠉⠉⠁⠀⢨⣿⠀⠀⠈⣿⡌⠛⣿⣦⣀
⠀⠀⠀⠀⠀⠀⠀⢀⣼⠿⣿⠀⠀⢀⣄⠀⢀⣼⠇⠹⣷⣄⣀⣀⣀⣠⡾⠃⠀⠀⠀⠘⣿⣴⡟⠉⠛⠻⣷⡄
⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠙⠷⠶⣿⣟⠻⣿⡁⠀⠀⠀⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⢸⣿⣦⠘⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣄⣀⣼⠏⠙⣷⣈⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣀⣠⣼⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡏⠁⠀⠀⠈⠉⠉⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠷⠶⣶⣶⣦⣤⣤⣤⣤⣤⣼⣿⣤⣤⣤⣤⣤⣤⣤⣶⡶⠾⢿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⣼⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣦⣤⣤⣤⣤⣤⣤⣾⣿⣤⣤⣤⣄⣤⣤⣤⣶⡿⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠀⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠠

⠀⠀⠀⠀⠀⠀⠀⡠⠖⠒⠲⢤⡀⠀⠀⠀⠀⠀⣀⠤⠒⠋⠉⠉⠉⢳⡀
⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠀⠀⠙⢦⡀⣠⠔⠋⠁⠀⠀⠀⠀⠀⠀⣸⠁
⠀⠀⠀⠀⠀⣸⠁⠀⢀⠀⠀⠀⠀⠀⢻⠁⠀⠀⠀⠀⠀⠀⠀⣀⠔⠁⣀⣀⠴⠒⠒⠤⠒⠒⠢⣀⣀⡀
⠀⠀⠀⠀⠀⡏⠀⠀⠈⠣⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣀⠴⠚⠁⢠⠋⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧
⠀⠀⠔⠲⡊⠓⠀⡆⠐⡄⠈⠓⠒⠚⠉⠀⠀⢴⡒⠉⠁⠀⢀⡔⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢢
⠀⢀⠦⣂⡱⠂⠪⣁⠶⢣⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀
⠀⠘⢰⠞⠀⠀⠀⠈⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⢀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷
⠀⠀⣼⠀⠀⠀⢀⡤⠔⠒⠊⠉⠉⠓⠒⠢⢄⡀⠀⠀⢸⡀⢣⠞⠀⡄⠀⠀⣠⢄⡴⠦⠤⢦⣀⣀⠀⠀⢠⡀⠲⡃
⠀⠀⢿⠀⠀⡔⢡⣶⡄⠀⠀⠀⠀⠀⠀⢰⣶⡝⢦⠀⣸⠁⡏⠀⡸⠁⣸⢋⣥⠀⠀⠀⠀⠀⢠⣌⠒⣆⠀⢧⡀⢹
⠀⠀⠘⢦⡐⡇⠈⠛⠁⠀⠀⠠⠕⠀⠀⠈⠛⠁⣸⡴⠃⠀⠈⠉⠳⠬⣕⢌⡛⠀⠀⠀⠀⠀⠈⣋⡴⣫⠤⠞⠉⠁
⠀⠀⠀⠀⠙⠛⢦⣤⣤⣀⣀⣀⣀⣀⣠⣤⣤⠞⠋⠀⠀⠀⠀⠀⠀⠀⢈⡭⠟⠉⠑⠒⠒⠈⠉⠀⠙⢥
⠀⠀⠀⠀⢀⣘⡷⢤⣀⣀⡞⠀⠀⠙⣤⡤⠾⣁⡀⣀⠤⠀⠀⢄⣀⣠⠊⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⣀
⠀⠀⠀⢼⠙⠁⣠⡴⠂⠀⠀⠀⠀⠀⠀⡧⣀⡀⡶⢩⢦⠄⠠⡠⣍⣾⠦⠤⣇⠀⠀⠀⠀⠀⠈⠒⠤⡶⠧⡄⠁
⠀⠀⠀⢸⡉⠉⡟⠀⠀⠀⠀⠀⠀⠀⡸⠁⠀⢸⣿⢩⣬⣤⣤⣥⢤⢿⡆⠀⢱⠄⠀⠀⠀⠀⠀⠀⠀⡇⠀⡱
⠀⠀⠀⠀⠉⠉⢳⡀⠀⠀⠀⠀⡄⢸⡅⠀⠀⠀⠣⡀⠀⠀⠀⠀⢀⡰⠁⠀⠸⡀⠀⢆⠀⠀⠀⠀⡰⠓⠊
⠀⠀⠀⠀⠀⠀⠀⠧⣀⠀⠀⠀⢳⠈⡧⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠘⡒⢚⡖⠢⡴⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠤⠤⢄⣀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⠉⠁⠀⠀⠈⠑⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠈⠙⠲⣄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⢠⠚⠳⠒⠒⢆⠀⠀⠀⠀⠀⠀⠀⠑⢄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡀⠠⠤⠤⢄⡼⠀⠀⠀⠀⠈⠓⠤⠤⡀⠀⠀⠀⠀⠈⢣⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⡤⠂⠀⠀⠀⠈⠀⠀⠀⠀⠀⠑⠢⠠⣄⠀⠀⣄⠀⠀⡸⠄⠀⠀⠀⠀⠀⢱⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⢀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠀⠀⠀⠈⠁⠘⠢⢄⠠⠇⠀⠀⠀⠀⠀⠀⠀⢣
⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⡀⠀⢠⠎⣉⠠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆
⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠐⠁⢰⠃⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⣡
⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⢀⠇⠀⠀⠀⠰⡀⢀⡠⠲⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠑⠢⠤⠤⠜⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠄⣠⠂⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⡎
⠀⠀⠀⠀⠀⠀⠀⠀⠱⣄⠀⠀⢀⡗⠀⠀⠀⠀⠀⠠⠤⠄⠀⠀⠈⠐⠒⠉⠀⠀⠀⠀⠀⠀⠤⠤⠀⠀⠀⠀⠀⠀⢸⠑⠦⠤⠤⠊
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠁⡇⠀⠀⠀⠀⢀⣤⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⠀⠀⠀⠀⠀⣸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⡇⠀⠀⠀⣰⣿⣿⣟⢉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣁⣸⣷⡀⠀⠀⠀⠌⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⢱⠀⠀⠀⣿⢹⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢹⡇⠀⠀⠀⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠘⣆⠀⠀⢈⡆⡛⠛⡋⠌⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⢌⡛⠛⡁⣆⠀⠀⢀⠗⠀⠀⢸⠄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠉⡳⢄⣀⣘⢦⡀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢏⣀⣀⢴⣃⢂
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠤⠊⠑⠨⠙⠲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡠⠴⠊⠥⠐⠉⠢⠌
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⠝⠓⣒⣒⠒⠒⠒⠒⣒⣒⠚⠻⢍⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠛⠁⠀⡜⠀⠀⣹⠊⠙⣏⠀⠀⢱⠀⠀⠉⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠊⠣⢄⡐⢱⡀⠀⣨⠦⠴⢏⠀⠀⡸⢂⡠⠊⠑⢢
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡃⠀⠀⡼⠀⠀⠙⠊⠀⠀⠀⠀⠉⠚⠁⠈⢧⠀⠀⢹
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢷⠚⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠣⢄⣐⠂⠠⠀⠀⠈⠡⠀⠠⠄⢀⣀⡧⠞
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠈⠭⠭⣱⠖⠲⣌⠭⠭⠁⢺
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⢀⡇⠀⠀⢡⡀⠀⠀⠘⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠶⠶⠚⠀⠀⠀⠈⠓⠶⠶⠚

⠀⠀⢀⣀⣤⣤⣀⠀⣠⣤⣤⣀⡀⣠⠀⠀⠀⡀⠀⢀⣄⡀⠀⢀⣤⣴⣶⣶⣦⣄⡀⠀⠀⡀⠄⠀⠀⠀⠀⠀⢀⣄⡀⢀⢠⡄
⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⢸⣷⣿⠀⠀⠀⠉⠻⠟⣴⣿⡿⠋⣭⣭⣟⣿⣿⡄⢲⣿⣷⡷⢃⣴⣾⣿⣿⣿⣿⣿⣧⡁⠄⠀⠀⠀⣶⢀⡇⠆
⠀⠀⣿⣿⣿⢛⡻⢿⣿⢛⣿⣿⡿⠈⠍⣹⡆⢠⠀⡄⠀⢰⣿⣿⣷⣿⣟⠻⡏⣬⢻⣿⠸⠿⠿⢱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⢰⣷⣤⣤⣾⣿⣦⣤⣴⡆
⠀⠸⣿⣿⠟⠉⠁⢠⡌⠉⠉⣭⣴⣿⣿⡟⢡⠄⢠⣀⢠⠘⠿⣛⣛⣛⠅⠀⠀⠿⡸⡿⣸⣿⡟⣹⣽⠿⢿⡿⢿⣟⠻⠟⢿⣿⣿⡸⣿⣿⣿⣇⣸⣿⣿⣿⠇
⠀⠀⣄⢠⡀⠀⡀⢄⡀⠀⡰⠘⠛⠙⢿⡛⠀⠀⠙⠋⠾⠁⠀⣭⡍⠉⠀⠀⠀⠀⠃⠀⣛⣛⣈⠛⠓⢐⣓⡐⠀⣡⣾⣿⡇⣛⣉⠁⢼⣿⣿⣿⣿⣿⣿⣿
⠀⠈⢁⣶⡶⣦⣥⣦⣴⣆⢀⠐⠗⠀⠘⠛⠀⠀⠀⠀⠀⠀⠘⠉⢱⢁⠀⠀⠀⠀⠠⠀⠻⢿⣿⣿⣶⣿⣿⣿⢸⣿⣿⡋⢼⣿⣿⣶⠸⣛⣭⣭⣭⣝⡻⠷
⠀⢀⣼⣿⠟⣻⠿⠳⣿⣿⠘⠁⢠⠀⡀⠀⠀⢠⡀⠀⠀⠀⠐⢂⠈⠿⣷⣶⣔⢰⣾⡗⠀⣀⠺⣿⣿⣿⣿⣿⡜⠛⠛⣿⡆⣰⣶⣥⣾⣿⣿⣿⣿⣿⣿⣿⡦
⠀⠈⢿⡇⠀⠉⠛⠀⢸⡿⠿⠂⠃⢤⣶⠌⠒⢠⣶⣦⣠⣴⣿⣿⠗⠀⠈⠋⠉⢤⡌⣀⠀⣿⣷⡈⣀⡉⣹⣿⡗⣀⡀⠀⠾⣯⣶⣿⣿⡟⡛⠿⢿⣿⣿⣿⣧
⠀⠀⢘⣃⣀⣀⢀⣤⣤⠤⢄⠀⣀⣼⣷⣀⣀⡘⢻⣿⣿⣿⣯⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⠰⡉⠁⠛⠁⠀⡀⠘⠟⠻⣍⣟⣡⣤⡀⣽⣿⣿⠃
⠀⠀⣇⠀⠉⠁⠸⣿⣿⣷⣿⡆⢈⡙⡟⢉⠀⠉⢆⠛⠋⠉⡿⡇⢠⠆⠀⠀⠀⢧⠄⠀⠀⠀⠘⣿⣿⣿⣷⡀⠐⠀⢰⡷⣯⠈⡽⣀⠐⠯⠍⠉⠑⠿⠀⠁
⠀⠀⠇⠀⠀⠀⠀⠀⠀⠈⠉⡦⠉⣉⣧⠉⠃⢀⡞⣠⡤⢥⠀⠁⠩⠀⠀⠀⠰⠀⠀⠀⠀⠀⢀⡠⢀⣛⠿⠁⠀⠀⣴⣶⣶⣿⡀⢋⡛⣄⡒⣂⡒⣡⣦⣤⡀
⠀⢨⠟⠢⢨⡄⠰⠆⣀⣀⠠⠏⠠⠍⣙⠿⠿⣿⣷⠰⠒⢒⣠⡖⣰⣾⣿⣷⣶⣂⡀⠀⡁⢄⠀⠀⠉⠉⢀⣴⣄⠀⠙⣿⣿⣿⣿⡾⢃⣼⣿⣿⣿⣿⣿⡿⠟
⠀⠁⠆⣀⣀⣰⣶⣿⣿⣿⣷⣦⣀⣠⠽⣿⣿⣦⣶⢶⣶⣿⣿⡇⣿⣿⣿⣿⣿⣿⢛⠀⠹⡆⠀⠀⠀⠀⠀⠛⠻⣿⡇⠹⡿⢿⣿⢿⣌⠻⣿⣿⣿⡿⠿⣷
⠀⠀⠀⠋⠉⠉⠛⠛⠛⠿⣿⣿⠉⠀⠀⠉⣿⠿⠿⡼⠟⠻⣿⡄⡿⣿⡟⢩⡭⢵⠀⠀⠀⠈⢂⠀⠀⠀⡀⠀⠠⠀⠰⠀⣹⣶⠁⣷⣭⣥⣶⣦⣭⣡⣶
⠀⠀⠀⣿⣀⡀⠄⠀⠀⠀⠀⠙⢛⣀⣴⣦⡉⠀⠀⠀⠀⠋⠞⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢠⡄⢀⣀⠀⣀⡀⢠⠁⠀⠻⠟⠀⠸⢵⣿⣟⣿⣿⣿⣿⣤⡀
⠀⠀⣴⣿⣿⣿⣦⣄⠀⣀⣤⡾⠛⢿⣿⣿⣧⠀⢛⣋⣙⠃⠀⠀⠀⠀⠀⠀⠀⠀⠑⠢⣦⣼⣷⠀⢈⣿⣿⣿⣿⢁⠾⠛⠛⠖⠛⠿⢷⠹⣿⣿⣿⣿⣿⠛⠁
⠀⠀⠙⠿⢋⠀⠈⡁⢛⣛⠿⢧⣠⢜⠣⠀⣿⡅⠘⠻⠟⠀⠀⠠⠀⠀⠀⣤⠀⠀⠸⣷⣶⣬⠙⢂⣩⣭⣍⠛⣡⠻⢦⣤⣴⣷⣤⣤⣾⣧⢹⣿⣿⠿⡿
⠀⠀⠀⠀⠁⠀⠀⠀⠿⣿⣤⡅⣶⣌⡳⣶⣶⣶⣤⣤⣄⣤⣦⡄⠀⠀⠀⠀⠀⠀⠀⣈⣥⣤⣾⣿⣿⣿⣿⣻⣿⣿⠇⢿⣿⣿⣿⣿⣿⠟⣘⣥⣶⣿⣶⡄
⠀⠀⠈⠁⠐⣰⡳⣤⣄⠘⢛⣁⣫⣴⣶⣙⢿⣿⡟⣭⡍⠛⠉⠀⠁⠀⠀⢀⡀⢀⠀⣿⣿⣿⢿⣿⠻⠟⢻⡏⠘⠀⠀⢀⣿⣿⣿⣿⢥⡾⠟⣵⣶⡝⢿⡇
⠀⠀⠀⡛⠋⢡⠤⠘⣵⣶⣿⣿⣿⣿⣿⣿⡆⣿⠀⠉⠀⠀⠀⡉⠉⠀⠙⣿⣿⣤⣧⠘⠿⣿⣯⠈⠃⠀⠌⠹⠿⠟⡡⠀⣶⡀⣍⢣⣾⢃⣤⣿⣿⣷⠸⣿⣆
⠀⠀⢰⣷⣶⣶⣆⠀⠙⢻⣿⣿⣿⢛⡛⣿⠟⠀⠀⠀⠀⠀⢐⠁⠀⠀⠀⠀⠉⠙⠋⠀⠀⠈⠉⠈⠁⠉⠀⠀⠀⡄⠉⠉⢿⣿⣧⣤⠛⣙⡻⣿⣿⣿⡘⢿⡿
⠀⠀⢸⣿⡟⣩⠃⣼⣿⣮⣭⣭⣭⣈⠑⠋⠀⢀⠀⠀⠁⠀⠘⣦⠈⣀⡰⠂⠀⠀⡼⠀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⡙⢹⠄⠉⣤⢹⣿⡿⢿⣧⠁
⠀⠀⢿⢋⡁⠀⣼⡿⢿⣿⣿⣿⢋⣤⠀⠀⠀⠀⠈⠀⠀⣀⣴⡆⣿⣦⠾⠶⢿⡯⠀⠈⢻⣾⠿⠁⠀⠀⠰⠀⠀⣀⣀⠀⠁⡀⢀⠚⠀⠿⣶⡿⡅⠀⠈⠙
⠀⠀⢠⣴⣦⣄⠋⡀⢀⡸⠟⣿⣆⠻⠷⣶⣶⠰⣿⡶⣩⣍⣋⣁⣥⣲⡯⣩⡲⡶⣦⠀⠘⢋⣀⣤⣤⡀⢶⣼⣷⣿⣟⣿⣹⣿⣌⠠⣴⠿⡎⠳⣀⠒⠃
⠀⠀⠈⢶⣶⣤⣤⣴⣦⡀⠈⡛⠿⢠⣤⣾⣿⣷⡆⣴⣿⣿⣯⣿⣩⣕⣚⣧⡷⣮⠉⣶⣿⣿⣿⣿⣿⣿⡇⢿⣿⠟⠛⠻⣿⣷⣺⣷⡘⠟⠧⢀⣿⣿⣦
⠀⠀⢠⣿⣿⣿⣿⣿⣿⡇⠈⢻⣦⠚⠓⢀⠉⡿⣿⡆⠹⠿⢿⣿⡿⠃⠉⢹⣾⣵⠃⣼⣿⣿⣿⣿⣿⣿⣿⣷⠁⠀⠀⠀⢸⣿⣿⣿⣥⢺⣿⣿⣿⣿⠿
⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⣀⡿⡃⠀⠲⠖⠶⠶⡏⠀⠠⢴⡈⠉⡍⠉⠓⢾⣷⡞⠘⢿⣿⣿⣿⣿⣿⣿⠍⡉⢲⣄⣀⡠⠎⠿⢛⡛⠿⢈⣩⡟⠀⢤⣶⡄
⠀⠀⠀⣹⣿⠿⠿⣿⡟⠉⢹⡀⠿⡦⠀⠀⠀⠀⠀⢠⣄⠋⠼⠀⢤⣀⣀⣈⡏⠀⠈⠛⣿⣿⣿⣿⣿⣿⠐⠛⠛⠋⠹⠓⢃⣾⣿⣿⣁⣰⣿⣧⣤⣿⣿⡷
⠀⠀⠀⠙⠛⠀⠀⠘⠀⠀⠉⠉⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠈⠛⠁⠉⠛⠁⠀⠀⠋⠁⠀⠈⠀⠉⠛⠿⠟⠿⠿⠟⠻⠟⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⣿⣶⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠟⠋⠁⠀⠀⠀⠈⠙⠿⣿⣦⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣘⣿⣷⠀⠀⠀⠀⠀⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⣄⣀⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⢀⣴⡿⠛⠛⢿⣿⣇⣤⣶⣾⡿⠿⣿⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⠋⠉⠙⠛⠿⢿⣿⣿⣷⣶⣶⣶⣿⣿⣿⣿⠋⠀⠀⠀⠀⠹⣿⠛⠉⠁⠀⠀⠘⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⣿⠇⠀⠀⣴⡿⢷⣦⣿⣷⣦⣄⢀⣀⣀⣿⣷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠘⣿⣤⣿⠋⠀⠀⠈⢻⣿⡋⠉⠉⠙⢿⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⣀⣀⣈⣹⣿⡀⠀⠀⠀⣰⡿⢻⣷⠀⠀⣼⡏
⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠛⠋⠙⠿⣶⣶⣾⡟⠿⠿⠋⠀⣠⡿⠁
⠀⠀⠀⠀⠀⠀⠀⢠⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣀⣠⣶⣿⡇
⠀⠀⠀⠀⠀⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⢹⣿
⠀⠀⠀⢀⣀⣀⣀⣿⣧⣀⣀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⠷⠶⠿⠶
⠀⠀⠀⠙⠛⠛⠉⢻⣿⠉⠛⠀⠀⠀⢀⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡄⠀⠀⠀⠀⠀⢸⣿
⠀⠀⠀⠀⠀⠀⣀⣸⣿⣦⣤⡄⠀⠀⠀⠻⠿⠃⠀⠀⠀⠀⠀⣠⣴⣶⣤⡀⠀⠀⠀⠀⠘⠻⠟⠁⠀⠀⠀⠀⠻⣿⡿⠷⠶⡶
⠀⠀⠀⠀⠀⠚⠛⠋⠙⣿⣄⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣧⣤⣽⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⣼⣿⠁
⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣟⣡⣴⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⡿⠻⢷⣦⣄
⠀⠀⠀⠀⠀⠀⠰⠿⠛⠁⠀⣈⣻⣿⠁⠀⢹⡿⠿⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣿⠟⠋⠀⠀⠀⠈⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠉⠉⢠⡴⣤⠀⠀⣠⣿⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⠾⢿⣿⣿⣏⡉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⣤⡄⠘⠷⠞⠁⠘⢿⡇⣿⣇⠀⠀⠀⠀⠀⢠⣿⠃⠀⠈⢿⣇⠙⣿⣷⣤⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡟⣿⡇⠀⢀⣶⣄⣀⣼⠇⠘⢿⣶⣤⣤⣤⣴⡿⠋⠀⠀⠀⠈⢿⣿⠟⠉⠉⠛⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠈⠛⠿⠿⣿⡉⢻⣧⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⢀⣿⣿⣄⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⠀⠀⢀⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣷⣶⡾⠟⠀⠻⣷⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣷⣶⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣯⣀⣀⣀⣀⣀⡀⠀⠀⠀⢠⣶⡀⠀⠀⠀⠀⢀⣀⣀⣀⣤⣿⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠛⠛⠛⠻⠿⠿⠿⠿⢻⣿⠿⠿⠿⠿⠿⠿⠟⠛⠛⠉⢹⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡏
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣦⣄⣀⣀⣀⣀⣀⣀⣸⣿⣄⣀⣀⣀⣀⣀⣀⣠⣴⣿⠟
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠿⠿⠿⠛⠛⠛⠛⠛⠻⠿⠿⠟⠛⠛⠉