⢀⣀⡤⣤⣶⣦⡄⠀⢀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡎⣿⣿⡟⣿⣿⣾⡟⡂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠝⠂⠐⠢⠙⠻⣿⣯⣥⡾⢇⣶⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠐⣄⠀⠀⠩⣶⣭⣾⡗
⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⣯⡀⠀⠀⣷⣶⣿⠀⠀
⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀⢸⠘⠁⠀
⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⢀⡜⣿⠀⠀⠀⠘⣰
⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠋⠀⠀⠀⠀⡿⠀
⠀⢸⠇⠀⠀⠀⠈⠓⠄⢀⡼⠃⡴⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀
⠀⢸⠀⠀⠀⠀⠀⠀⠘⡎⣀⠈⠁⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠷⢦⣀⠀⢀⡤⠞⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠈⠳⠤⠟⢏⠁⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠈⠳⢄⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠤⠤⠖⠋⠀

⢀⣀⡤⣤⣶⣦⡄⠀⢀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡎⣿⣿⡟⣿⣿⣾⡟⡂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠝⠂⠐⠢⠙⠻⣿⣯⣥⡾⢇⣶⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠐⣄⠀⠀⠩⣶⣭⣾⡗
⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⣯⡀⠀⠀⣷⣶⣿⠀⠀
⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀⢸⠘⠁⠀
⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⢀⡜⣿⠀⠀⠀⠘⣰
⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠋⠀⠀⠀⠀⡿⠀
⠀⢸⠇⠀⠀⠀⠈⠓⠄⢀⡼⠃⡴⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀
⠀⢸⠀⠀⠀⠀⠀⠀⠘⡎⣀⠈⠁⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠷⢦⣀⠀⢀⡤⠞⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠈⠳⠤⠟⢏⠁⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠈⠳⢄⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠤⠤⠖⠋⠀

⢀⣀⡤⣤⣶⣦⡄⠀⢀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡎⣿⣿⡟⣿⣿⣾⡟⡂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠝⠂⠐⠢⠙⠻⣿⣯⣥⡾⢇⣶⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠐⣄⠀⠀⠩⣶⣭⣾⡗
⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⣯⡀⠀⠀⣷⣶⣿⠀⠀
⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀⢸⠘⠁⠀
⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⢀⡜⣿⠀⠀⠀⠘⣰
⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠋⠀⠀⠀⠀⡿⠀
⠀⢸⠇⠀⠀⠀⠈⠓⠄⢀⡼⠃⡴⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀
⠀⢸⠀⠀⠀⠀⠀⠀⠘⡎⣀⠈⠁⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠷⢦⣀⠀⢀⡤⠞⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠈⠳⠤⠟⢏⠁⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠈⠳⢄⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠤⠤⠖⠋⠀

⢀⣀⡤⣤⣶⣦⡄⠀⢀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡎⣿⣿⡟⣿⣿⣾⡟⡂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠝⠂⠐⠢⠙⠻⣿⣯⣥⡾⢇⣶⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠐⣄⠀⠀⠩⣶⣭⣾⡗
⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⣯⡀⠀⠀⣷⣶⣿⠀⠀
⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀⢸⠘⠁⠀
⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⢀⡜⣿⠀⠀⠀⠘⣰
⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠋⠀⠀⠀⠀⡿⠀
⠀⢸⠇⠀⠀⠀⠈⠓⠄⢀⡼⠃⡴⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀
⠀⢸⠀⠀⠀⠀⠀⠀⠘⡎⣀⠈⠁⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠷⢦⣀⠀⢀⡤⠞⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠈⠳⠤⠟⢏⠁⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠈⠳⢄⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠤⠤⠖⠋⠀

⢀⣀⡤⣤⣶⣦⡄⠀⢀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡎⣿⣿⡟⣿⣿⣾⡟⡂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠝⠂⠐⠢⠙⠻⣿⣯⣥⡾⢇⣶⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠐⣄⠀⠀⠩⣶⣭⣾⡗
⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⣯⡀⠀⠀⣷⣶⣿⠀⠀
⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀⢸⠘⠁⠀
⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⢀⡜⣿⠀⠀⠀⠘⣰
⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠋⠀⠀⠀⠀⡿⠀
⠀⢸⠇⠀⠀⠀⠈⠓⠄⢀⡼⠃⡴⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀
⠀⢸⠀⠀⠀⠀⠀⠀⠘⡎⣀⠈⠁⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠷⢦⣀⠀⢀⡤⠞⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠈⠳⠤⠟⢏⠁⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠈⠳⢄⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠤⠤⠖⠋⠀

⢀⣀⡤⣤⣶⣦⡄⠀⢀⡀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⡎⣿⣿⡟⣿⣿⣾⡟⡂⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠝⠂⠐⠢⠙⠻⣿⣯⣥⡾⢇⣶⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡾⠁⠀⠀⠀⠐⣄⠀⠀⠩⣶⣭⣾⡗
⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⠀⠀⣯⡀⠀⠀⣷⣶⣿⠀⠀
⠀⠀⠀⠀⠀⡴⠃⠀⠀⠀⠀⠀⠀⠀⣽⡇⠀⠀⢸⠘⠁⠀
⠀⠀⠀⢀⡾⠁⠀⠀⠀⠀⠀⠀⢀⡜⣿⠀⠀⠀⠘⣰
⠀⠀⡴⠋⠀⠀⠀⠀⠀⠀⠀⣰⠏⠀⠋⠀⠀⠀⠀⡿⠀
⠀⢸⠇⠀⠀⠀⠈⠓⠄⢀⡼⠃⡴⠋⠀⠀⠀⠀⠀⣿⠀⠀⠀
⠀⢸⠀⠀⠀⠀⠀⠀⠘⡎⣀⠈⠁⠀⠀⠀⠀⠀⠀⢸
⠀⢸⠷⢦⣀⠀⢀⡤⠞⣴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧
⠀⠈⠳⠤⠟⢏⠁⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠈⠳⢄⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠙⢧⡀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠲⠤⠤⠤⠤⠖⠋⠀