⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⣍⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠘⠙⢧⠸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠁⢻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⢠⠀⣸⣧⣄⡼⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠀⠘⠲⣿⣛⡉⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣿⣿⡋⠀⢠⢶⣿⣿⡁⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣶⣿⣿⣿⣿⣿⣿⣷⡀⠀⢸⣿⣿⣁⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣀⣀⣀⣤⣤⣴⣶⣶⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⡀⠉⠉⠀⠀⢹⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢰⣾⣿⠛⠋⠻⠿⣿⠛⠛⠛⠿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣄⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⣿⣿⣦⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠟⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠈⠻⣿⣽⠄⠀⠀⢿⣦⣷⣷⡆⠀⣿⣿⣿⣿⣿⣿⠀⠀⠘⠿⡿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠻⢷⣤⣤⣉⣉⣉⣽⡇⠀⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠈⠀⡾⠛⣇⠀⣿⣿⣿⣿⠀⠀⠀⣀⣀⣀⣀⣀⣤⣤⣴⣶⣶⣿⣿⣿⣷⣿⣆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠉⠻⢷⣄⡘⠛⢃⣾⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠇⣀⡠⠞⣻⣿⣿⣿⣶⣾⣿⣿⣿⣯⣿⢿⣛⣻⣯⣿⣿⣿⣟⣛⣿⣿⣿⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣿⣿⣿⣿⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠚⠛⢹⣿⠿⡿⢉⠸⣿⡛⢿⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠎⣿⣿⣿⣿⣿⡟⠛⠻⣍⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠇⡄⠀⠈⠃⣀⣀⣈⣷⣾⣿⣶⣷⣶⠭⣏⣙⣿⣿⣿⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣿⣯⣿⣿⣮⡻⣶⠚⠉⠀⠀⠀⢠⣶⣶⠆⠀⠀⠀⠀⠀⠀⣰⣟⣸⣷⣀⠀⢸⡏⠹⣿⣿⣿⣿⣿⣿⣥⣴⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠹⣿⣿⣿⣿⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠙⠈⣿⣿⣙⡷⣚⣿⣾⣿⡿⣿⣿⣟⠫⠿⠿⠽⠿⣿⣿⣿⣿⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⡀⠛⢿⠿⣯⣀⣀⠀⠀⠀⠀⠀⠀⠾⠛⠉⠀⠀⠀⠀⠀⠀⠻⠧⢬⡇⠈⠛⠻⢷⣍⣿⣿⠛⠵⠶⠚⠇⠘⣿⣿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡤⠴⢒⣠⠴⠞⢳⡀⠀⠀⠀⠀⠘⢷⡄⢀⣀⡀⠀⠀⠀⣀⣠⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠘⡇⠐⠮⣳⣦⣠⣤⣰⣮⠿⢿⣿⣿⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠋⠀⠀⠀⣀⣳⡀⠀⠀⠀⠀⠀⠉⠈⡿⢿⣟⠛⠋⠛⠁⠀⠀⠀⠀⠀⠀⡤⢺⠀⠀⠀⠀⠀⢷⠦⣀⣀⡉⢻⣾⣿⣿⠀⠀⠈⠙⠻⠦⠤⣄
⠀⠀⠀⠀⠀⠀⠀⠞⠁⠀⠀⠀⣠⡾⠙⣿⣇⠀⠀⠀⠀⠀⠀⢠⣇⢀⡙⠛⢦⡀⠀⠀⠀⠀⠀⢠⣾⣧⣿⣀⠀⠀⠀⠀⠘⡆⠈⠉⠀⠈⣿⣿⣿⠀⠀⢠⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠋⠁⠀⠀⢹⡏⠀⠀⠀⠀⠀⢀⠎⠉⠉⠓⠲⢤⡙⢦⡀⠀⠀⠀⠀⠬⠅⣹⠏⠙⠗⠦⠤⣄⣽⡀⠀⠀⢀⣿⣿⣿⠀⠀⣸⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⣰⠁⠘⠦⣄⡀⠀⠀⠉⠓⠲⠤⢤⣀⣀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⠀⠀⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀⡗⢤⡀⠀⠀⠉⠓⠀⠀⠀⠀⡆⠀⠀⠘⡆⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⣿⣄⢰⠇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢰⡿⠀⠀⠀⠀⠀⡸⢡⡀⠉⠓⠦⣄⡀⠀⠀⠀⢀⡇⠀⠀⠀⠙⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⢏⡾⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢠⠏⠀⠀⠀⠀⠀⢰⠃⠈⡇⠀⠀⠀⠀⠉⠑⠲⢤⣼⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⢠⠞⠀⠀⠀⠀⠀⠀⡞⢰⡀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⢿⡇⢀⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⢠⡞⠀⠀⠀⠀⠀⠀⢰⠃⠀⢧⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⢸⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡸⠀⢠⡟⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠘⡆⢃⠀⢄⠀⠀⠀⠀⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣿⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⠇⣰⡟⠀⠀⠀⠀⠀⠀⠀⣸⠁⠀⠀⠀⢳⢸⠀⠀⠳⣄⠀⠀⠀⠈⠻⢷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠉⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣜⣴⠏⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠈⣿⡇⠀⠀⠈⠳⣤⣀⠀⠀⠀⠉⠉⠓⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⡇⠀⠀⠀⠀⠀⠀