⠀⠀⠀⠀⠀⠀⠀⣀⡠⡔⠎⠓⢤⡄⡀⠀⠀⢀⣠⠔⠎⠱⢢⢄⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣠⠴⠋⣡⠴⠛⠉⠙⠶⣌⡳⡆⢰⣚⡴⠞⠉⡉⠓⠮⣌⠓⠦⡄⠀⠀⠀
⠀⣠⠞⡁⠒⠉⠄⠂⢄⡡⣌⢠⠈⡙⢽⠷⠉⢁⡄⣡⡄⣁⠂⠌⠙⢂⠉⢷⣀⠀
⢰⠁⢂⠐⡈⠐⣈⡴⠋⠉⠈⠉⢳⡀⢸⡇⢨⠞⠉⠁⠈⠓⢬⡀⢁⠂⠌⡀⢉⠆
⢸⡈⢄⠂⠄⠡⣾⠁⠀⠀⠀⠀⠀⠑⠾⠳⠎⠀⠀⠀⠀⠀⠈⡷⠀⠌⡐⢠⠃⠆
⢸⢌⠢⣁⠊⠄⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠿⠀⢒⠈⢆⡌⠃
⢸⡌⠲⢄⠣⡈⠌⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡞⠃⡈⢆⠩⢆⡜⡁
⢸⡜⡱⢊⠴⡁⢆⠠⢉⠳⢤⡀⠀⠀⠀⠀⠀⠀⣀⠴⢊⠡⠀⢆⠱⣈⠇⡎⡴⡁
⢸⡜⡳⣭⢖⣡⢎⣐⣂⣄⠂⡉⠱⢦⣀⣀⡶⠋⢁⠂⣄⣂⣍⢦⡱⣬⢞⡼⣱⠁
⠀⠀⠀⠀⠁⠀⠀⠀⠀⠉⠈⠛⠳⢆⣄⡻⣞⢠⡴⠞⠛⠉⠉⠀⠀⠀⠀⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠒⠒⠒⠦⣤⣀⣀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⡞⠁⢀⣤⣀⠀⠀⠀⠀⠀⠀⠉⠲⣤⠀
⠀⠀⠀⠀⢠⡤⠴⠚⠁⣰⣿⣿⣿⡆⠀⠀⣴⣶⣶⠄⠀⢻
⠀⠀⠀⡼⠁⠀⠀⠀⠀⠻⣿⣿⣿⠃⠀⣼⣿⣿⣿⠀⠀⠀⢷⡀
⠀⠀⣼⠁⠀⣤⣶⡄⠀⠀⠈⠉⠁⠀⠀⠈⠛⠊⠁⠀⠀⠀⠀⠙⢦
⠀⢠⡇⠀⢸⣿⣿⡿⡆⠀⠀⣴⣶⣶⣴⣶⣄⠀⠀⢠⣶⣿⣦⠀⠀⡄
⠀⢸⡇⠀⠀⠛⠙⠉⠀⣰⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⣿⣿⠀⠀⡇
⠀⠈⣇⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣷⣿⣷⡀⠀⠉⠉⠀⠀⣸⡟
⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⡻⠁
⠀⠀⣿⠀⠀⠀⠀⠀⠈⠛⠉⠁⠉⠁⠙⠻⠿⠟⠀⠀⠀⠀⠀⣾⠁
⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁
⠀⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢷⡀⠀⠀⠀⠀♥⠀⠀⠀⠀⣼⢧⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠃⢘⣷⣀⣀⣤⣤⣤⣄⣀⢸⡏⠈⢷⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣬⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠁⠀𝟗 ⢹⣿⡟⠀𝟔 ⠈⢻⣿⣿⣿⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣒⣺⣿⣿⣿⣿⣀⠀⣀⣼⠛⢷⣄⠀⢀⣼⣿⣿⣿⣿⣉⡁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⢺⣿⣿⣿⣿⣿⣿⣿⣿⡇⣿⣿⣿⣿⣿⣿⣿⣿⣿⠢

⠀⠀⢀⣀⠤⠿⢤⢖⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⡔⢩⠂⠀⠒⠗⠈⠀⠉⠢⠄⣀⠠⠤⠄⠒⢖⡒⢒⠂⠤⢄⠀⠀⠀⠀
⠇⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠀⠈⠈⡨⢀⠡⡪⠢⡀⠀
⠈⠒⠀⠤⠤⣄⡆⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠀⢕⠱⠀
⠀⠀⠀⠀⠀⠈⢳⣐⡐⠐⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠁⠇
⠀⠀⠀⠀⠀⠀⠀⠑⢤⢁⠀⠆⠀⠀⠀⠀⠀⢀⢰⠀⠀⠀⡀⢄⡜⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⡦⠄⡷⠢⠤⠤⠤⠤⢬⢈⡇⢠⣈⣰⠎⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣃⢸⡇⠀⠀⠀⠀⠀⠈⢪⢀⣺⡅⢈⠆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠶⡿⠤⠚⠁⠀⠀⠀⢀⣠⡤⢺⣥⠟⢡⠃⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀