⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣦⣠⣴⣶⣤⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢸⣟⣾⡽⣯⣷⣟⣾⠂⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠻⣳⣿⣻⢾⡽⠊⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⣦⣄⡀⠀⢀⣠⣶⠁⠀⠀⠀⠀⠀⠀⣤⣰⣦⣿⣤⣶⠀
⠀⢿⣿⣿⡛⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⣽⠿⡿⡿⡿⢿⠀
⠀⢸⡟⡍⢁⢩⢻⠇⠀⠀⠀⠀⠀⠀⠀⠳⣤⡔⢗⣤⡾⠀
⠀⠀⢚⡶⠾⣶⡷⠀⠀⠀⠀⠀⠀⠀⠐⠟⣿⠛⠙⢻⡟⠂
⠀⠀⠨⣀⠀⣐⠛⠁⠀⠀⠀⠀⠀⠀⠀⠨⣃⠂⠲⣚⠇⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⢸⣏⣩⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣠⠶⠛⠋⠉⠉⠉⠙⠓⠶⢭⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠛⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢦⣄⣀⣀⣀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⢀⠀⠀⣤⡄⠀⠀⠀⠀⠀⠀⢿⡶⢱⡀⠀⠀⠉⠉⠉⠙⣦⠄
⠀⢀⢀⣠⠴⠞⠁⠀⠀⠀⡼⠀⠴⢿⠃⠀⠐⠤⠶⠼⠀⠸⠤⢃⣇⡀⠀⠀⠀⠀⠀⣿⠀
⢠⣴⠋⠀⠀⠀⠀⠀⠀⣰⡳⣍⣒⣈⠀⠀⢀⣀⣀⣀⣠⠤⢶⠿⣄⠙⠲⠦⠤⠴⠞⠁⠀
⠈⠻⣄⠀⠀⠀⢀⣠⠞⠁⢀⣤⣽⠉⠙⠋⠉⠉⠁⠀⠈⢳⡸⣆⣹⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠈⠙⠛⠛⠋⠁⠀⠀⢿⠁⠣⠀⠀⢸⡀⡄⠀⡀⠀⡘⠀⣽⠋⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠒⠒⠳⠴⠓⠳⠶⠓⠒⠳⠺⠃

⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠛⠛⢻⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣰⡟⠀⠀⣠⣴⠶⠿⠶⢦⡀⠀⠀⠀⠀
⠀⠀⠀⡀⣼⠇⠀⢠⡾⠋⠀⠀⠀⠀⠈⢻⡄⠀⠀⠀
⠀⠀⢸⠉⢻⣤⡾⠛⣧⡀⠀⠀⠀⣠⡄⠈⣿⠀⠀⠀
⠀⢠⣾⠛⣻⠤⣟⠓⣯⠛⠛⠛⠛⠉⠀⠀⣿⡆⠀⠀
⢠⡟⠈⠙⠁⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⠀⠸⣧⠀⠀
⢸⠁⠀⣠⣤⡶⠶⠶⠶⠦⣤⣀⠀⠀⠀⠀⠀⠘⣇⠀
⠹⣇⣼⠉⣾⣿⠀⠀⠀⠀⠀⠉⠳⣦⡀⠀⠀⠀⣿⡀
⠀⠙⢿⣄⠈⠁⠀⣶⢦⠀⠀⢰⣿⡎⢷⡀⠀⣠⡟⠁
⠀⠀⢸⣏⠛⠶⣬⣿⣓⣣⢤⣌⣉⣡⣾⣥⠾⠋⠀⠀
⠀⠀⠀⠻⣦⣼⠻⣴⠛⠳⣆⠈⠋⠉⣹⡷⠀⠀⠀⠀
⠀⠀⠀⠀⠈⣿⣸⣇⣸⡞⠉⠛⠛⠻⡿⠲⡄⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡿⡭⣹⡄⠀⠀⠀⢰⣧⣠⠏⠀⠀⠀
⠀⠀⠀⠀⠀⠺⠦⢼⣉⣁⣀⣀⣀⣾⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀

⠠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠈⠋⣴⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡶⠆
⠀⢐⣿⣿⣷⣧⡤⡀⠀⠀⢀⠔⠁⠑⢤⣰⣦⣿⡎⠄⠀
⠀⢈⣿⣿⣿⣿⣿⣲⣶⡤⠁⠐⠀⣉⢸⣿⣿⣿⢛⠀⠀
⠀⠘⣻⣿⣿⣿⣿⣿⠛⠛⣦⣤⣀⣰⠋⡘⡉⡍⠒⢠⡀
⠀⠀⢹⣿⣿⣿⣿⣵⡆⢰⣾⣿⣿⣿⣷⠱⠻⠁⡄⡶⠁
⠀⠀⢘⣿⠟⠏⠈⠙⠶⠿⠛⠙⠛⣿⣿⣷⡀⠃⠞⠁⠀
⠀⠀⠠⢿⠀⢿⠇⠀⠀⠀⠀⢰⣶⠈⣿⡿⡩⠁⠀⠀⠀
⠀⠀⠀⠙⠢⢀⠀⠀⠴⡅⠀⠈⠁⡠⡛⠁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡄⠚⠷⡇⠀⢶⣶⡶⠿⠷⡄⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠠⠒⠠⠄⠐⠂⠀⠲⠑⡀⠀⠠⣦⡂⠀⠀⠀
⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⡤⠄⠮⠋⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠐⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀