⠀⠀⠀⠀⠀⢀⣠⡶⠖⠛⠉⠉⠉⠉⠉⠛⠲⣦⣄⠀⠀⠀
⠀⠀⠀⠀⣤⠖⠋⠁⠀⠀⠀⠀⢀⣴⣿⠛⠙⠛⢷⣤⣈⢿⠀⠀
⠀⠀⣴⠋⠀⠀⠀⠀⣀⣤⣶⠶⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⣿⠀
⢀⡟⣠⣶⠖⠛⠉⢁⣠⣴⣶⢶⡄⠀⠺⣯⣭⣭⣭⣿⠿⠗⢸⡆
⣾⠀⠀⠀⣴⣞⣉⣈⣿⡿⠛⠁⠀⠀⠀⠀⣻⣦⠶⠛⠉⠙⢿⡇
⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⠶⠛⠉⠀⠀⠀⠀⠀⡶⢻⠁
⣿⠀⠀⠀⠀⠀⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⣿⠀
⠘⣆⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⣼⠃⠀
⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠛⣦⣀⠀⠀⠀⠀⣠⡶⠋⣼⠃⠀⠀
⠀⠀⠈⠛⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠉⠛⠛⠶⣤⣿⣿⣴⣶⠛⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢸⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⢸⠀⠀⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⢸⡆⠀⠀⠀⠀⠘⢶⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠻⡄⠀⠀⠀
⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⣀⣿⣀⣀⣀⣀⣀⣀⡀⢹⣦⣤⠄
⢀⣤⣶⣿⣿⣷⣶⠟⠛⠉⠀⠀⢸⡄⠀⠀⠉⠙⠛⠿⣿⣿⣦⢻
⠀⣸⠃⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠘⣿⠀⠀

⣥⣌⠹⡆⠀⢀⠈⣷⡏⣽⣿⣾⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⡿⢋⣥
⣿⣿⢣⠃⢠⣿⢘⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⢃⢺⣿
⡛⢋⠎⢀⣼⠏⠀⠀⢀⠈⣩⣁⣩⣿⣍⣁⣀⡀⠀⣿⣿⣷⠈⢆⠙
⠛⠉⠀⣸⣟⢿⡟⠉⣁⡈⠙⣿⣿⣿⢏⣉⣉⡙⠻⣿⣿⣿⡆⠈⠉
⠀⠀⣠⣿⣯⣨⠀⢸⡿⢹⡆⢹⣿⡟⢿⠏⣻⣿⠀⣿⣿⣿⢀⠀⠀
⠀⣴⣿⡽⣿⡿⠦⠈⠉⢉⠁⠀⠀⠀⠈⠙⠋⠉⠤⢿⣿⢻⣿⣧⠀
⠰⣿⣿⣿⣟⣾⣷⣶⣦⣶⣤⣀⡀⢀⣥⣶⣶⣶⣾⣷⣿⢿⣿⣿⠇
⠀⠹⡿⢿⣷⢿⣾⣿⣿⣿⣿⣿⣷⣿⣿⣿⣿⣿⣾⡷⣿⡟⠿⠟⠀
⠀⠀⠀⢸⠿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣅⠀⠀⠀
⠀⠀⠀⢸⠀⠀⢀⠈⠉⠚⠛⠿⠏⠛⠛⠛⠛⢋⡉⠍⠐⣿⠀⠀⠀
⠀⠀⠀⠨⣦⣄⡘⣘⢻⠎⠶⠶⠁⠶⠾⠰⠞⠛⡃⣠⣴⠈⠀⠀⠀
⣤⠀⠀⠈⢮⣿⡷⣿⣿⣿⣷⣾⡆⣴⣿⣿⣿⣿⣽⣿⡇⠁⠀⣤⣤
⢿⣦⡄⠀⠀⠈⠈⠓⠻⣿⣟⣻⣿⢿⣿⣿⡟⠛⠁⢨⠀⠀⢰⣿⡿