⣀⣀⠀⠀⣀⡤⠶⠚⠛⠛⠛⠛⠻⠯⣿⣿⣦⣠⣤⣤⡀⠀⠀
⠵⠾⠷⣟⣥⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣾⡭⣿⠀⠀
⠀⠀⠀⢹⡟⡚⣎⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠀⠀
⠀⠀⠀⢸⣇⢣⣻⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀
⠀⠀⠀⣸⢒⣲⠟⠀⠀⠀⠀⣰⠀⠀⠀⢱⠀⠀⠀⠂⠀⠺⡆
⠀⠀⢀⡿⣹⡏⠀⠀⠀⠀⢠⠇⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⡇
⠀⢀⣼⠳⡿⠁⠀⠀⠀⠐⠁⠀⠀⣀⠜⢁⠀⠀⠀⠀⠀⢢⠇
⠀⣾⡷⠲⠁⢠⣼⠶⠒⢦⡄⠚⠋⢁⡴⠞⠲⣄⠀⠀⢀⡟⠀
⣆⢹⡀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⣾⠀⠀
⠘⣷⣷⣤⡄⠀⢻⡄⠀⢠⣤⣤⡝⠁⠀⣤⣤⣤⡆⠀⣿⠀⠀
⠲⠚⠋⠉⠳⢦⣸⣿⠛⠉⠀⠀⠈⠐⠉⠁⠀⠉⢳⣴⠇⠀⠀
⠀⠀⠀⠀⠀⠀⣹⠛⢀⣀⡀⠀⠀⠀⠀⠀⠀⢀⣀⣹⠀⠀⠀
⠀⠀⠀⠀⠀⣀⣗⠞⠋⠘⡇⠀⠀⠀⠀⠀⢠⠋⠀⣹⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠾⠶⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⣠⠀⠀⣠⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠿⡝⢲⠗⠛⣷⣿⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣄⣘⣛⣋⣠⡇⠈⠻⠦⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠿⢿⣷⣀⣒⣀⡽⠧⣴⢶⡇⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⡴⠟⠀⠀⠀⠹⡿⢿⣿⣶⠞⣻⡿⠷⠛⡛⣧⠀⠀
⣾⠿⠟⢲⣤⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠉⣴⡊⠙⠳⣄⠀⢹⣿⠀⠀
⢻⡖⠓⠫⠀⡿⠀⢀⣤⡄⠀⠀⠀⠀⠀⠀⢻⣅⠤⡄⠈⠑⡄⣿⡀⠀
⠀⢿⣤⣼⠷⠁⠀⠈⠋⠀⠓⠛⠶⠒⠀⠐⠿⢿⡤⠃⠀⠀⠘⠿⢷⠀
⠀⠀⠛⠷⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣬⣿⣦⣤⣤⣤⣤⣼⠃

⣿⣿⣿⠟⠁⠀⠀⠀⣶⠾⠛⠉⠉⠁⡌⠉⡉⠙⠶⢬⡡⣄⠀⠀
⣿⡿⠁⢀⢠⠀⠀⢰⠀⠀⢺⠀⡼⡼⡅⠀⠇⢀⠀⠠⢝⢷⡄⠀
⣿⠇⠀⠃⡌⠀⠀⠐⠠⠦⢸⡠⣄⠀⢠⢠⢠⠘⠆⣴⠀⠨⠛⡀
⡟⠀⡌⢰⡇⠀⠀⣰⣥⣀⣺⠆⠃⠀⠀⠚⠈⠦⠴⠅⠀⡄⠰⠁
⠃⢠⠀⢾⡇⠀⠀⠽⣙⣝⡏⠀⠀⠀⠀⠀⠠⣶⣶⢤⣇⣭⡆⠆
⢠⠀⠀⡜⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠛⠽⠀⠁⣿⣇⠀
⣄⡄⠀⣧⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀
⠀⢁⣀⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⢀⣟⣿⢹⠀
⠀⢀⣾⣿⣿⣇⡇⠸⡦⠄⢀⠀⠀⠀⠀⢀⣀⣤⣶⠋⠈⣿⢸⠀
⠦⣻⣿⣿⣿⣿⣇⠀⠇⠠⡄⣈⠀⠲⢾⣿⣿⣿⣿⡤⠤⣿⢸⠀
⠀⣼⣿⣿⣿⣿⣿⡄⢀⠀⠀⠀⠈⠉⠆⢹⣿⣿⣇⣊⠀⣿⠀⡄
⠐⠊⠀⠀⠀⠙⢾⢧⠀⠆⠀⠀⠨⡻⡖⠸⣿⣿⣇⠀⠀⣿⢠⡀
⠁⠀⠀⠀⠀⠂⠈⠚⢧⡐⡀⠀⠈⣀⣄⣏⡀⠈⠉⠢⠀⡟⠎⠀