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

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

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

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

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

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