⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣰⠞⠛⠲⣦⣤⠤⠤⢴⠏⣦⣈⣷⣚⠉⠻⡄⠀⠀
⠀⠀⠀⣿⣀⠀⠈⠁⠀⠀⠀⢾⡀⢻⡿⠉⠉⣷⡞⠻⣦⠀
⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠈⠛⠛⠷⣤⣴⠿⠿⣠⡟⠀
⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⡶⢻⡄⠀
⠠⠤⡧⠤⠄⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣤⣄⠀⠋⢹⡏⠁
⠀⢀⣿⡤⠄⠘⠿⠁⠀⠠⣞⣻⠄⠀⠀⠻⠏⢀⡈⣽⠛⠃
⠀⠀⢈⡷⣶⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠿⠛⠂⠀
⠀⠀⠀⠀⠀⠉⠙⠛⠛⠓⠒⠒⠒⠚⠛⠛⠉⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⡛⠛⠛⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⠀⠀⠈⠀⠀⠀⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠉⠛⠃⠚⠛⡠⢂⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣤⠄⠀⠀⠀⠠⠊⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣤⠟⠁⠀⠀⠀⠀⣠⡞⠀
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⠍⠁⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠚⠁⠀⠀⠀⠄⠀⣠⠟
⠀⠀⢀⣴⠋⠀⠠⠞⠁⠀⠀⠀⠀⠀⢀⡾⠉
⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⣴⠻⠀
⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠈⠻⣿⡁⠀⠈⢷
⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢸⡅
⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡼⠀
⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⢠⣿⡴⠟
⠀⠀⠀⠀⠀⠈⠻⠶⣤⣤⡴⠾⠋⠀

⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⡛⠛⠛⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⠀⠀⠈⠀⠀⠀⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠉⠛⠃⠚⠛⡠⢂⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣤⠄⠀⠀⠀⠠⠊⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣤⠟⠁⠀⠀⠀⠀⣠⡞⠀
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⠍⠁⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠚⠁⠀⠀⠀⠄⠀⣠⠟
⠀⠀⢀⣴⠋⠀⠠⠞⠁⠀⠀⠀⠀⠀⢀⡾⠉
⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⣴⠻⠀
⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠈⠻⣿⡁⠀⠈⢷
⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢸⡅
⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡼⠀
⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⢠⣿⡴⠟
⠀⠀⠀⠀⠀⠈⠻⠶⣤⣤⡴⠾⠋⠀

⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⡛⠛⠛⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⠀⠀⠈⠀⠀⠀⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠉⠛⠃⠚⠛⡠⢂⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣤⠄⠀⠀⠀⠠⠊⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣤⠟⠁⠀⠀⠀⠀⣠⡞⠀
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⠍⠁⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠚⠁⠀⠀⠀⠄⠀⣠⠟
⠀⠀⢀⣴⠋⠀⠠⠞⠁⠀⠀⠀⠀⠀⢀⡾⠉
⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⣴⠻⠀
⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠈⠻⣿⡁⠀⠈⢷
⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢸⡅
⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡼⠀
⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⢠⣿⡴⠟
⠀⠀⠀⠀⠀⠈⠻⠶⣤⣤⡴⠾⠋⠀

⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⡛⠛⠛⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⠀⠀⠈⠀⠀⠀⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠉⠛⠃⠚⠛⡠⢂⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣤⠄⠀⠀⠀⠠⠊⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣤⠟⠁⠀⠀⠀⠀⣠⡞⠀
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⠍⠁⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠚⠁⠀⠀⠀⠄⠀⣠⠟
⠀⠀⢀⣴⠋⠀⠠⠞⠁⠀⠀⠀⠀⠀⢀⡾⠉
⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⣴⠻⠀
⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠈⠻⣿⡁⠀⠈⢷
⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢸⡅
⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡼⠀
⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⢠⣿⡴⠟
⠀⠀⠀⠀⠀⠈⠻⠶⣤⣤⡴⠾⠋⠀

⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠟⡛⠛⠛⢶⣦
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠶⠋⠀⠀⠀⠈⠀⠀⠀⠟⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⣀⠀⠀⠀⠀⠀⠀⠀⣀⣼⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠉⠛⠃⠚⠛⡠⢂⡿⠋
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣤⠄⠀⠀⠀⠠⠊⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⣤⠟⠁⠀⠀⠀⠀⣠⡞⠀
⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⢀⠍⠁⠀⠀⠀⠀⢀⡴⠋
⠀⠀⠀⠀⢀⡴⠋⠀⠀⠚⠁⠀⠀⠀⠄⠀⣠⠟
⠀⠀⢀⣴⠋⠀⠠⠞⠁⠀⠀⠀⠀⠀⢀⡾⠉
⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⢀⠀⠀⣴⠻⠀
⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠈⠻⣿⡁⠀⠈⢷
⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⢸⡅
⠀⠀⠀⠸⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⢀⡼⠀
⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⢠⣿⡴⠟
⠀⠀⠀⠀⠀⠈⠻⠶⣤⣤⡴⠾⠋⠀