⣿⣿⠟⣁⠤⠒⠉⠁⠀⠀⠀⠀⠀⠂⠂⠙⢿⣿⣿⣿⣿⣿⣿
⣿⢣⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿
⢧⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢰⡦⣠⡟⢿⣿⣿⣿
⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣼⡟⣿⢇⠸⣿⣿⣿
⠃⠀⠀⠀⢀⡄⠀⠀⠀⣄⠀⠀⣰⡄⠀⠀⠑⡹⢦⣄⠀⠀⠉⠛
⠀⠀⠀⠀⢸⣹⡄⣧⡀⢸⠆⠀⠐⢠⠀⠀⠀⠀♡
⠀⠀⠀⠀⢘⣿⣿⣿⣧⣿⣧⣴⣄⣠⣇⡀⣦ 𝒽𝒶𝓋𝑒
⠀⠀⠀⠀⠘⣿⠟⠉⡻⣿⣿⣿⣿⣿⣿⣿⡟ 𝒶
⡄⡀⠀⠀⠀⠉⠀⢤⣄⣹⣿⣿⣿⣿⣿⣿⠃ 𝓁𝑜𝓋𝑒𝓁𝓎
⣧⣷⡠⡀⠀⢀⣄⠀⠙⢿⣿⣿⣿⣿⡿⠃⠀ 𝒹𝒶𝓎
⣿⣿⣷⣿⣦⣾⣿⡀⠀⠀⠀⠀⠀⢉⣴⣶⣤⣀♡
⣿⣿⣿⣿⣿⣿⣿⡇⠀⢠⠀⠀⣴⣿⣿⣿⣿⣿⣿⣶⡄
⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡆⢸⣿⣿⣿⣿⣿⣿⣿⣿⠃
⣿⣿⣿⣿⣿⣿⣿⡇⠀⢸⡇⠘⣿⣿⣿⣿⣿⣿⣿⡙

⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀
⠰⣤⣾⣾⣿⣤⣠⣖⣀⢀⣰⣿⠋⠀⠀⢀⣾⡿⠿⢷⣀⠀⠀⠀
⢰⣿⡟⠏⠙⠛⢻⡿⡿⠟⠉⠉⠁⠉⠉⣿⡿⠓⠤⢀⣹⠀⠀⠀
⣨⣿⣷⣮⠀⠄⠄⡔⢁⣭⣤⡀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠢⣀⠀
⠀⠘⠛⣿⢷⣶⣴⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠁⠀⢠⢃⣀⠁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠘⣝⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠈⠢⢤⠀⠀⢀⠀⠀⠀⠀⢰⠀⣰⡀⠀⠀⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣊⣸⡿⠉⠑⡦⠀⣸⡟⠀⠙⡦⠀⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠸⠦⠚⠉⠀⠀⠀⠃⠛⠀

⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀
⠰⣤⣾⣾⣿⣤⣠⣖⣀⢀⣰⣿⠋⠀⠀⢀⣾⡿⠿⢷⣀⠀⠀⠀
⢰⣿⡟⠏⠙⠛⢻⡿⡿⠟⠉⠉⠁⠉⠉⣿⡿⠓⠤⢀⣹⠀⠀⠀
⣨⣿⣷⣮⠀⠄⠄⡔⢁⣭⣤⡀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠢⣀⠀
⠀⠘⠛⣿⢷⣶⣴⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠁⠀⢠⢃⣀⠁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠘⣝⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠈⠢⢤⠀⠀⢀⠀⠀⠀⠀⢰⠀⣰⡀⠀⠀⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣊⣸⡿⠉⠑⡦⠀⣸⡟⠀⠙⡦⠀⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠸⠦⠚⠉⠀⠀⠀⠃⠛⠀

⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀
⠰⣤⣾⣾⣿⣤⣠⣖⣀⢀⣰⣿⠋⠀⠀⢀⣾⡿⠿⢷⣀⠀⠀⠀
⢰⣿⡟⠏⠙⠛⢻⡿⡿⠟⠉⠉⠁⠉⠉⣿⡿⠓⠤⢀⣹⠀⠀⠀
⣨⣿⣷⣮⠀⠄⠄⡔⢁⣭⣤⡀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠢⣀⠀
⠀⠘⠛⣿⢷⣶⣴⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠁⠀⢠⢃⣀⠁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠘⣝⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠈⠢⢤⠀⠀⢀⠀⠀⠀⠀⢰⠀⣰⡀⠀⠀⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣊⣸⡿⠉⠑⡦⠀⣸⡟⠀⠙⡦⠀⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠸⠦⠚⠉⠀⠀⠀⠃⠛⠀

⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀
⠰⣤⣾⣾⣿⣤⣠⣖⣀⢀⣰⣿⠋⠀⠀⢀⣾⡿⠿⢷⣀⠀⠀⠀
⢰⣿⡟⠏⠙⠛⢻⡿⡿⠟⠉⠉⠁⠉⠉⣿⡿⠓⠤⢀⣹⠀⠀⠀
⣨⣿⣷⣮⠀⠄⠄⡔⢁⣭⣤⡀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠢⣀⠀
⠀⠘⠛⣿⢷⣶⣴⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠁⠀⢠⢃⣀⠁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠘⣝⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠈⠢⢤⠀⠀⢀⠀⠀⠀⠀⢰⠀⣰⡀⠀⠀⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣊⣸⡿⠉⠑⡦⠀⣸⡟⠀⠙⡦⠀⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠸⠦⠚⠉⠀⠀⠀⠃⠛⠀

⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣶⣶⣶⣶⣤⡀⠀⠀⠀⠀
⠰⣤⣾⣾⣿⣤⣠⣖⣀⢀⣰⣿⠋⠀⠀⢀⣾⡿⠿⢷⣀⠀⠀⠀
⢰⣿⡟⠏⠙⠛⢻⡿⡿⠟⠉⠉⠁⠉⠉⣿⡿⠓⠤⢀⣹⠀⠀⠀
⣨⣿⣷⣮⠀⠄⠄⡔⢁⣭⣤⡀⠀⠀⠀⠈⠀⠀⠀⠀⠈⠢⣀⠀
⠀⠘⠛⣿⢷⣶⣴⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷
⠀⠀⠀⠁⠀⢠⢃⣀⠁⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇
⠀⠀⠀⠀⠀⠘⣝⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇
⠀⠀⠀⠀⠀⠀⠈⠢⢤⠀⠀⢀⠀⠀⠀⠀⢰⠀⣰⡀⠀⠀⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣊⣸⡿⠉⠑⡦⠀⣸⡟⠀⠙⡦⠀⡇⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠋⠀⠀⠸⠦⠚⠉⠀⠀⠀⠃⠛⠀