⢀⣠⣤⣤⣤⣀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣄⡀⠀⠀⠀⠀⠀
⠀⠀⣠⣿⠿⠛⠛⠛⠛⠛⢿⣷⣤⣾⠿⠛⠛⠙⠛⠛⠿⠗⠀⠀⠀⠀
⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠙⡿⠁⠀⢀⣤⣀⠀⠀⢀⣤⣶⡆⠀⠀
⢸⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀
⠸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿⣿⣿⣧⣄⠀
⠀⢹⣿⠀⣿⣷⣄⣀⣤⡄⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⠷
⠀⠀⣁⣤⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠘⠛⠛⠛⠻⣿⣿⣿⠋⠉⠀⠀
⠀⠘⠻⢿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠹⣿⡟⠀⠀⠀⠀
⠀⠀⠀⠀⢹⣿⠟⢙⠛⠛⠀⠀⠀⠀⠀⣀⣴⡿⠓⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⠁⠀⠈⠻⢿⣦⣄⠀⣠⣾⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀

⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠉⠉⠉⠉⠛⠒⠦⡤⠤⣄⡀⠀⠀
⠀⠀⠀⣀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⣆⠀
⠀⣰⠛⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠘⣇
⢠⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⢛⣠⣄⡀⠈⢧⠹
⣼⢀⡏⠀⠠⠶⠖⠒⠀⡀⠀⣠⣀⣰⠀⠀⠰⣿⣿⣿⣿⠀⢸⠀
⣿⢸⡇⣤⣶⣶⣦⠀⠀⠈⠉⣀⣀⣀⣀⡀⢀⠴⠋⠉⠉⠛⢯⡀
⡟⠘⣿⠻⠿⠿⠛⠀⠀⢠⠞⠁⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⣿
⠇⠀⠈⢷⣦⣀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠇⠀⠀⠀⠈⠉⢹⡏⠀⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠏
⠇⠀⠀⠀⠀⠀⣿⠁⠀⠙⠛⠛⠓⠢⢤⣤⣤⣤⣴⡾⠛⠙⢧⠀
⠻⢦⣤⡤⠴⠚⡇⠀⠀⠀⠀⠀⠀⠀⢀⡿⠿⠿⠟⠁⠀⠀⢸⡆

⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠉⠉⠉⠉⠛⠒⠦⡤⠤⣄⡀⠀⠀
⠀⠀⠀⣀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⣆⠀
⠀⣰⠛⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠘⣇
⢠⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⢛⣠⣄⡀⠈⢧⠹
⣼⢀⡏⠀⠠⠶⠖⠒⠀⡀⠀⣠⣀⣰⠀⠀⠰⣿⣿⣿⣿⠀⢸⠀
⣿⢸⡇⣤⣶⣶⣦⠀⠀⠈⠉⣀⣀⣀⣀⡀⢀⠴⠋⠉⠉⠛⢯⡀
⡟⠘⣿⠻⠿⠿⠛⠀⠀⢠⠞⠁⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⣿
⠇⠀⠈⢷⣦⣀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠇⠀⠀⠀⠈⠉⢹⡏⠀⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠏
⠇⠀⠀⠀⠀⠀⣿⠁⠀⠙⠛⠛⠓⠢⢤⣤⣤⣤⣴⡾⠛⠙⢧⠀
⠻⢦⣤⡤⠴⠚⡇⠀⠀⠀⠀⠀⠀⠀⢀⡿⠿⠿⠟⠁⠀⠀⢸⡆

⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠉⠉⠉⠉⠛⠒⠦⡤⠤⣄⡀⠀⠀
⠀⠀⠀⣀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⣆⠀
⠀⣰⠛⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠘⣇
⢠⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⢛⣠⣄⡀⠈⢧⠹
⣼⢀⡏⠀⠠⠶⠖⠒⠀⡀⠀⣠⣀⣰⠀⠀⠰⣿⣿⣿⣿⠀⢸⠀
⣿⢸⡇⣤⣶⣶⣦⠀⠀⠈⠉⣀⣀⣀⣀⡀⢀⠴⠋⠉⠉⠛⢯⡀
⡟⠘⣿⠻⠿⠿⠛⠀⠀⢠⠞⠁⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⣿
⠇⠀⠈⢷⣦⣀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠇⠀⠀⠀⠈⠉⢹⡏⠀⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠏
⠇⠀⠀⠀⠀⠀⣿⠁⠀⠙⠛⠛⠓⠢⢤⣤⣤⣤⣴⡾⠛⠙⢧⠀
⠻⢦⣤⡤⠴⠚⡇⠀⠀⠀⠀⠀⠀⠀⢀⡿⠿⠿⠟⠁⠀⠀⢸⡆

⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠉⠉⠉⠉⠛⠒⠦⡤⠤⣄⡀⠀⠀
⠀⠀⠀⣀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⣆⠀
⠀⣰⠛⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠘⣇
⢠⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⢛⣠⣄⡀⠈⢧⠹
⣼⢀⡏⠀⠠⠶⠖⠒⠀⡀⠀⣠⣀⣰⠀⠀⠰⣿⣿⣿⣿⠀⢸⠀
⣿⢸⡇⣤⣶⣶⣦⠀⠀⠈⠉⣀⣀⣀⣀⡀⢀⠴⠋⠉⠉⠛⢯⡀
⡟⠘⣿⠻⠿⠿⠛⠀⠀⢠⠞⠁⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⣿
⠇⠀⠈⢷⣦⣀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠇⠀⠀⠀⠈⠉⢹⡏⠀⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠏
⠇⠀⠀⠀⠀⠀⣿⠁⠀⠙⠛⠛⠓⠢⢤⣤⣤⣤⣴⡾⠛⠙⢧⠀
⠻⢦⣤⡤⠴⠚⡇⠀⠀⠀⠀⠀⠀⠀⢀⡿⠿⠿⠟⠁⠀⠀⢸⡆

⠀⠀⠀⠀⠀⠀⣀⡤⠖⠛⠉⠉⠉⠉⠉⠛⠒⠦⡤⠤⣄⡀⠀⠀
⠀⠀⠀⣀⣠⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⣆⠀
⠀⣰⠛⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠘⣇
⢠⡇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠛⢛⣠⣄⡀⠈⢧⠹
⣼⢀⡏⠀⠠⠶⠖⠒⠀⡀⠀⣠⣀⣰⠀⠀⠰⣿⣿⣿⣿⠀⢸⠀
⣿⢸⡇⣤⣶⣶⣦⠀⠀⠈⠉⣀⣀⣀⣀⡀⢀⠴⠋⠉⠉⠛⢯⡀
⡟⠘⣿⠻⠿⠿⠛⠀⠀⢠⠞⠁⠀⠀⠈⠙⠋⠀⠀⠀⠀⠀⠀⣿
⠇⠀⠈⢷⣦⣀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿
⠇⠀⠀⠀⠈⠉⢹⡏⠀⢹⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⠏
⠇⠀⠀⠀⠀⠀⣿⠁⠀⠙⠛⠛⠓⠢⢤⣤⣤⣤⣴⡾⠛⠙⢧⠀
⠻⢦⣤⡤⠴⠚⡇⠀⠀⠀⠀⠀⠀⠀⢀⡿⠿⠿⠟⠁⠀⠀⢸⡆