⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀ ⠀⠀⠀⣠⠞⡷⠀⠀⠀⠀⠀
⣶⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⡾⢷⡘⣷⠀⠀⠀⠀⠀
⠈⣿⣾⠊⠳⣦⡀⠀⠀⠀⠀⠀⠀⡴⠶⢦⣠⣤⡀⠀⠀⢠⡾⠋⠀⠀⠹⣇⠀⠀⠀⠀⠀
⠀⢨⠇⠀⠀⠀⠙⢦⡀⠀⠀⠀⢸⡇⠀⠈⠁⣨⠇⢀⡴⠋⠀⠀⠀⣽⣀⠹⡆⠀⠀⠀⠀
⠀⡾⠀⠀⠀⠀⠈⣌⠻⣆⣀⣤⣤⣷⣄⣠⣤⣤⣴⡟⠀⠀⠀⠀⠀⡟⢹⡄⢻⠀⠀⠀⠀
⢰⢇⠀⠀⠀⠀⠀⠈⡲⠋⠁⠀⢀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢁⣟⡀⢸⡄⠀⠀⠀
⢸⠸⠀⠀⠀⣀⢔⡿⠀⠀⠀⣰⠋⠀⣸⣾⢀⡀⠀⠀⠀⠀⠀⣰⠏⠈⣡⠗⢸⣤⠀⠀⠀
⢸⡀⠫⣶⡿⠛⠋⠀⠀⠄⡼⠃⠀⠀⣿⡇⠘⣿⢄⠀⠀⠀⠀⠛⠦⣄⣻⡲⠸⣸⠁⠀⠀
⠈⣧⠀⠙⣿⡾⠋⠀⠀⡼⠁⠀⠀⢸⢻⣇⠀⢻⣯⣓⣤⡀⠀⠀⠀⢨⠁⠀⠰⢯⡄⠀⠀
⢀⣨⣧⢰⣽⠁⢀⡠⣿⠁⠀⠀⠀⣸⠸⣿⠀⠈⢯⣿⡆⠀⠀⠀⠀⠀⠓⢿⣾⠋⠀⠀⠀
⠘⢦⣀⢸⡇⡄⢉⢶⡇⠀⠀⠀⠀⣿⠀⢷⢇⠀⠈⢯⡻⣴⣄⠀⠀⠠⣼⡆⡇⠀⠀⠀⠀
⠀⠀⠈⢹⡇⠁⡜⢸⢀⣠⣤⣀⠀⢻⠀⠈⣿⠶⠶⢬⣷⣍⠳⣟⡦⡸⣾⡃⢳⡀⠀⠀⠀
⠀⠀⠀⠀⠻⣤⣠⡿⠋⡠⢾⠿⣦⣼⡄⢸⠁⠀⣠⠾⣿⣿⣦⡈⠙⣿⡟⣬⣪⣳⡦⠀⠀
⠀⠀⠀⠀⣼⣟⣋⠀⠈⠐⠿⣿⢿⡎⡝⠺⡁⠀⠁⠿⣿⠽⠁⢛⣺⡟⠀⡏⣇⠀⠀⠀⠀
⠀⠀⠀⢰⡇⠀⠛⠶⢶⣤⣤⣒⢁⢿⠃⠀⠈⠒⠢⢤⣀⠶⠾⠋⠁⠀⢸⡟⠙⢦⣤⡤⠀
⠀⠀⠀⠈⢧⡀⠁⣤⢤⡾⠋⠁⠈⠉⠀⠀⠀⠀⠀⠀⠉⣩⠟⠀⠀⣠⠏⠀⢠⣤⠾⠁⠀
⠀⠀⠀⢠⣤⡽⠳⣾⣯⠿⣦⡀⠀⢠⡤⠄⠀⠀⢀⣤⢾⡯⠴⠖⠚⣡⡴⠀⡼⠀⠀⠀⠀
⠀⠀⠀⠀⠉⠛⢻⠀⠙⠀⠀⠉⠓⢦⣤⣠⡤⠞⠋⠀⢸⡷⠶⣒⣯⣟⣥⡞⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠘⣆⡀⣷⠦⠤⠴⠖⢿⣏⣠⠦⣤⠖⠞⣿⣋⣵⠟⠉⠀⣷⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠛⠾⣷⠶⠶⠤⣤⠟⠁⠀⠀⠀⠀⣰⠟⠁⠀⠀⠶⣊⡙⢶⡄⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡕⠲⣾⡟⠀⠀⠀⠀⢠⡞⠁⠀⠀⣀⣠⠴⠂⠉⠙⠓⣲⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⢅⡢⠝⢧⡀⠀⠀⣰⠏⠀⣀⡴⡚⠙⠀⠀⠀⣠⡴⠋⠁⠀
⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠹⢳⣦⣄⡈⢻⡄⣸⢋⣤⢞⠕⠁⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠘⠻⠦⣤⣀⠀⠀⠈⠙⠽⢷⡿⢿⣿⠊⠁⠀⢀⡤⠞⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠲⢤⣄⡀⣿⣷⠀⣿⣇⣠⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡿⢤⣹⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⡇⠀⠸⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⠀⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡇⠀⠀⢹⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠘⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀