⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢻⡆
⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣦⣤⣴⡟⠀⠀⢿⣶⣤⣤⣴⠾⣿
⠀⠀⠀⢀⣴⠟⠋⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀
⠀⠀⢠⡿⠁⠀⢀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠈⠛⠛⠀⠀⢶⡤⣿⣀⣀
⠀⢀⣿⠁⢠⡾⠛⠉⠀⠀⠉⠻⣦⣀⡴⠞⠛⠛⠛⠷⣦⣀⡾⡒⠤
⠀⢸⡇⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠸⣇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿ ⠀⠀
⠀⠀⢻⡄⠹⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣤⣀⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢻⡆
⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣦⣤⣴⡟⠀⠀⢿⣶⣤⣤⣴⠾⣿
⠀⠀⠀⢀⣴⠟⠋⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀
⠀⠀⢠⡿⠁⠀⢀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠈⠛⠛⠀⠀⢶⡤⣿⣀⣀
⠀⢀⣿⠁⢠⡾⠛⠉⠀⠀⠉⠻⣦⣀⡴⠞⠛⠛⠛⠷⣦⣀⡾⡒⠤
⠀⢸⡇⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠸⣇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿ ⠀⠀
⠀⠀⢻⡄⠹⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣤⣀⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢻⡆
⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣦⣤⣴⡟⠀⠀⢿⣶⣤⣤⣴⠾⣿
⠀⠀⠀⢀⣴⠟⠋⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀
⠀⠀⢠⡿⠁⠀⢀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠈⠛⠛⠀⠀⢶⡤⣿⣀⣀
⠀⢀⣿⠁⢠⡾⠛⠉⠀⠀⠉⠻⣦⣀⡴⠞⠛⠛⠛⠷⣦⣀⡾⡒⠤
⠀⢸⡇⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠸⣇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿ ⠀⠀
⠀⠀⢻⡄⠹⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣤⣀⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢻⡆
⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣦⣤⣴⡟⠀⠀⢿⣶⣤⣤⣴⠾⣿
⠀⠀⠀⢀⣴⠟⠋⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀
⠀⠀⢠⡿⠁⠀⢀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠈⠛⠛⠀⠀⢶⡤⣿⣀⣀
⠀⢀⣿⠁⢠⡾⠛⠉⠀⠀⠉⠻⣦⣀⡴⠞⠛⠛⠛⠷⣦⣀⡾⡒⠤
⠀⢸⡇⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠸⣇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿ ⠀⠀
⠀⠀⢻⡄⠹⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣤⣀⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢻⡆
⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣦⣤⣴⡟⠀⠀⢿⣶⣤⣤⣴⠾⣿
⠀⠀⠀⢀⣴⠟⠋⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀
⠀⠀⢠⡿⠁⠀⢀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠈⠛⠛⠀⠀⢶⡤⣿⣀⣀
⠀⢀⣿⠁⢠⡾⠛⠉⠀⠀⠉⠻⣦⣀⡴⠞⠛⠛⠛⠷⣦⣀⡾⡒⠤
⠀⢸⡇⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠸⣇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿ ⠀⠀
⠀⠀⢻⡄⠹⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣤⣀⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⢻⡆
⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣦⣤⣴⡟⠀⠀⢿⣶⣤⣤⣴⠾⣿
⠀⠀⠀⢀⣴⠟⠋⠁⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⠀
⠀⠀⢠⡿⠁⠀⢀⣀⣤⣤⣀⡀⠀⠀⠀⠀⠈⠛⠛⠀⠀⢶⡤⣿⣀⣀
⠀⢀⣿⠁⢠⡾⠛⠉⠀⠀⠉⠻⣦⣀⡴⠞⠛⠛⠛⠷⣦⣀⡾⡒⠤
⠀⢸⡇⠀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠘⠋⠀⠀⠀⠀⠀⠀⠘⣿
⠀⠸⣇⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿ ⠀⠀
⠀⠀⢻⡄⠹⣆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟
⠀⠀⠀⠀⠻⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠋
⠀⠀⠀⠀⠀⠈⠻⣶⣄⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣶⣤⣀⣤⡾⠟⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉