⠀⠈⠀⠀⠀⠀⠀⠀⠀⣦⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢁⠽⠃⠀⠀⠈⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣱⣿⣷⣄⡐⠀⠀⠀⠀⠂⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠆⣤⣀⠀⠀⠀⢰⣦⣿⡟⣿⣿⣿⣀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢢⣸⢻⡿⠀⠀⢰⡇⢫⣇⡈⢳⣾⣙⣇⢐⠀⢀⡰⠈⠀⠀⣶⣠⠀⠀⠀⠀
⠀⠀⠀⠻⠈⠛⠇⠀⡀⠁⠘⣼⣿⣿⣯⠹⢿⣿⡁⠞⠀⠀⠀⠈⠛⠛⠀⠀⠀⠀
⠀⠀⢀⠀⠀⠂⠀⠀⣻⣖⠸⣧⣿⡍⢻⡄⢀⣿⣿⣧⡲⠀⠀⠀⠀⠐⠀⠠⠂⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠙⠀⠁⢻⢸⡇⢹⣷⣿⣹⣫⣞⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⡆⠐⠀⢸⣈⣿⣿⣿⣿⣿⣿⣇⢿⣏⠦⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⣇⣠⣧⣿⡏⣽⡿⣶⣯⢿⣽⣿⠄⠺⡶⠁⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠂⠉⠀⠀⡰⣵⡿⠘⣻⢏⠟⠚⣶⢰⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣌⠀⣠⣴⣄⡵⢤⡼⠟⠓⣄⠧⢀⣌⢿⢷⡾⣿⢃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣿⠿⠻⣺⠣⠄⠜⠟⣿⡀⢿⣿⢿⡏⢠⣿⣰⣎⠘⣦⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢩⣀⣤⡯⣿⣷⣶⣤⣌⡉⣓⠒⠛⡃⠀⠰⡯⡍⠀⡏⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣿⣴⣁⠈⠋⢻⡉⠹⠉⠉⣻⣾⣧⠃⠀⢹⣏⠀⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢴⠏⡟⠿⣿⣿⣿⣿⣿⣷⣶⣿⣾⡟⠉⢀⠸⡯⠽⡷⠀⠀⠀⠀
⠤⡀⠀⠀⠀⣤⣾⡿⢀⢠⡼⠷⡿⠿⠿⢷⣬⡙⣿⡇⠀⠘⠲⠏⠁⡏⠀⠀⠀⠀
⠳⢿⣷⣴⣛⣤⣿⠳⠾⣄⠀⠀⠀⠀⠀⠀⢽⣿⣿⠃⠀⣠⣞⣾⢠⠇⠀⠀⠀⠀
⠀⠀⢻⣿⣿⣿⣿⣷⡀⠠⠤⠀⠒⠒⣀⣀⢈⢱⠠⡆⣴⢻⣼⣿⢸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠉⢻⣮⣳⠀⠠⠀⢨⣍⡙⡽⡛⣾⢶⡇⠀⢨⣿⡿⠋⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⢷⣯⣧⠄⠠⣠⣙⠚⠠⣿⣿⣋⡇⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢷⣶⡿⠉⢰⣶⢾⣿⣿⠟⡢⣄⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⣾⡟⢭⢼⡟⣾⣿⣟⣿⣿⡟⠀⠂⢲⡿⢦⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠁⢜⢻⠎⣿⡟⠿⡟⢧⡀⠀⠀⠀⠉⢻⣲⣄⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⡄⢿⣭⣿⠢⡈⢂⠈⠙⠦⣄⡀⠉⠚⢿⣧⣦⣀
⠀⠀⡀⠀⠀⠀⠀⠀⢰⢤⡀⣔⡟⠀⠹⣿⣦⠗⠺⡆⢀⠀⠈⠴⠺⣄⣾⣿⣿⡿
⠀⠀⠘⢷⡢⢄⠀⢑⡝⣿⣻⣿⣗⠚⠩⣻⣿⡤⡗⡧⠂⢀⣀⠀⠀⠐⠀⠀⠉⠻
⠀⠀⠀⠀⠣⠀⠠⣿⣂⣷⣿⣷⣐⡤⣀⣿⣿⣿⣹⣧⣷⠌⢉⠉⣹⠗⠒⠂⠀⠠
⠀⠀⠀⠀⠀⠀⠀⠙⠛⠘⠹⠁⠀⠀⢉⣕⣿⣯⠸⣧⣸⣿⣬⠿⠻⠷⠂⠀⠀⠀