⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣹⣯⣦⠉⡏⠑⢶⣿⡝⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠟⠙⠀⠀⠀⠀⠀⠈⢓⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⣀⡀⣼⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡳⡀⢼⣿⢁⡧⣀⡿⠀⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣳⣤⠋⠉⠓⠒⠚⢈⡲⠚⠓⠒⠤⣀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠶⠦⠥⣄⠀⠀⠀⠀⠀⠀⢀⢀⡤⠚⠁⢹⡈⠆⠀⠀⠈⠁⢆⡀⡀⡀⠀⠈⢣⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠒⠤⢤⡉⠛⣦⠀⠀⠀⣰⡶⠟⠋⠐⠃⠈⠳⡀⠐⠀⠀⠀⠀⠀⠀⠘⠤⠀⢸⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢘⣆⠹⣧⣦⠞⢹⠀⠄⠀⠀⠀⢀⡠⠃⠀⠀⠀⠀⠠⠀⠀⠀⠀⢆⠀⡧⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢇⢹⠏⠀⠘⡆⠀⠀⠀⠈⠏⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠊⠀⠀⠀⢳⡀⢀⡠⠜⡜⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠣⡈⠈⠁⣠⡾⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠃⠀⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠂⠀⠀⠀⠀⢠⡞⠉⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠀⢰⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⠐⠀⠀⠀⠐⠿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠉⠀⡜⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡴⡔⠄⠀⠀⠀⠈⠻⡉⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⡴⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢎⣐⢄⠀⠀⠀⠀⠘⢿⣿⣷⣤⣀⠀⠀⠀⠀⠀⠌⠀⠸⣅⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⠿⢶⡄⠀⠀⠀⠀⠈⢙⣿⡇⠀⡀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠥⣄⠒⠀⢀⡸⠃⠠⡀⢢⠀⡄⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡋⢹⠟⠁⠀⠀⠱⢸⠀⠙⡲⢄⡀⠀⠀⠈⠢⣄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡘⠀⠀⠀⠀⠀⢸⣦⣼⠁⠀⠈⠑⢮⡐⢰⠈⠳⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀⢸⢏⡿⢾⣄⠀⠀⢠⠋⠙⠦⠤⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠘⡞⠀⠈⠓⠀⠀⡏⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣱⢤⡀⠀⠀⢀⡼⠹⣄⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠁⠀⠁⠄⠀⡟⠀⢀⡟⢀⠀⢸⡁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⢰⠃⠀⠈⣇⠤⠀⠀⠉⠑⠢⣄⠀⠀⠀
⠀⠀⠀⠀⡠⠄⠀⠀⠀⢰⠀⠀⠀⡠⠐⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⡀⠀⣸⠀⠀⠀⠈⠉⠛⠷⣄⡀⠀⠈⡆⠀⠀
⠀⠀⢀⡜⢀⣖⣲⠆⣠⣣⣤⠀⡴⢁⡜⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡗⠷⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠁⠀⠀
⠀⢀⠎⢠⠤⢤⠀⣰⠋⠐⠃⠚⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⡇⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢨⣿⡲⠿⡄⢓⣒⠉⢒⣒⠒⠂⠉⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡆⢁⡼⠹⠾⠯⠷⣿⣿⠿⠿⠭⠽⠿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⣀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠾⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⠤⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀