⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣀⠀⢀⠔⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠤⡄⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⠀⣿⡤⡤⣒⣒⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⢹⣷⣄⡰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⣿⣿⣌⢀⡀⡸⠉⠑⠢⢄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠈⣿⣿⣿⣦⣵⣄⢀⡠⠠⠄⠀⠀⢀⡠⠀⠀⠀⠀⠀⣾⡇⠀⢻⣿⣶⣶⠊⠁⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⡄⠀⢻⣿⣿⣿⣿⠋⠁⣠⣶⣆⠀⣾⣿⣿⠀⠀⠀⠀⢰⣿⡇⠀⠸⣿⣿⣿⣆⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢱⡀⠘⣿⣿⡟⠋⠓⠚⡉⠀⠙⢤⣹⡿⠛⢆⣀⣀⣠⠞⠛⠃⠀⠀⢻⣿⣿⣿⣆⠀⡀⠀⢀⣤⣃⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡠⠚⠉⣧⢀⡼⠋⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⡄⠀⠉⠁⠀⢠⠃⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠑⢄⠀⣿⠟⠀⠀⡎⠀⠀⠸⡇⠀⠀⠀⠀⠀⡐⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⣄⡴⢦⣀⠟⣆⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡽⠃⠀⠀⢰⠇⠀⠀⡼⢳⠀⠀⠀⠀⢀⠇⢳⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡾⠁⠀⠀⠀⣾⠀⠀⣸⠁⠈⣇⠀⠀⠀⢸⠀⠈⢧⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡼⠁⣠⡄⠀⠀⡏⠀⢰⠃⠀⠀⠘⢦⢦⣤⣾⠤⠖⠊⠳⡀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣡⢞⡏⠀⠀⢸⣇⣠⡯⠔⠃⠀⠀⠈⠳⣀⡇⠀⣀⣀⣀⣹⣦⡀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠟⠁⢸⠇⠀⠀⢸⡇⡽⠀⠀⣀⠀⠀⠀⠀⠚⠋⠉⠉⠹⣿⣿⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⢸⣿⠗⠚⢻⣿⠀⠀⠀⠀⠀⠠⢤⠶⠶⠛⠛⠀⠀⢸⠀⠀⠀⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⢿⣀⣀⡼⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠂⠀⠀⢸⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⡀⠀⠀⠀⠀⣿⠠⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡤⠀⠀⠀⠀⢀⠇⠀⢀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⢰⡿⠋⠁⠈⠉⠀⠀⠀⠀⠀⡜⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⢺⡄⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⢀⠀⠀⠀⡠⠀⠀⠀⠀⡜⣡⠞⢡⠇⠀⠀⠀⠀⢀⡄⠀⠀⣸⡆⠀⠀⢸⡇⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠈⠻⢦⣄⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠼⠋⠁⣀⡞⠀⠀⠀⠀⢀⣾⡇⠀⢠⡏⠙⣆⠀⠈⢧⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠉⠓⢦⣄⡀⠀⠀⠀⠀⣀⣠⣴⣖⣿⡿⠀⠀⠀⠀⣠⠞⡾⠀⣠⠟⠀⠀⠈⠓⢦⣸⣆⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⢀⣀⡤⠤⠴⡾⠽⠿⠿⠿⣿⡿⠛⣋⢥⡾⠁⠀⠀⣠⣾⣥⣼⣣⣾⣃⣀⡀⠤⢤⠀⠀⠈⠙⠃⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡏⠀⢀⣰⣷⠞⠉⠢⢄⡀⠐⠮⡑⢶⣶⣒⢻⡇⢸⣡⢟⣀⣤⣶⠟⣉⠤⠒⠛⠷⣼⠒⠤⣄⣀⣸⣄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣞⣠⡴⠚⢸⠏⠀⠀⠀⢀⡈⠑⠂⠬⣺⢷⣼⣿⣡⣾⣿⣯⣥⡞⢁⠜⠁⠀⠀⠀⠀⠈⢣⠀⠈⡕⡎⠀⢱⠀⠀⡠⠤
⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⠛⠉⠁⠀⢠⠏⠀⠀⠀⣠⠋⠉⠙⢛⣿⠟⣾⣋⠀⠀⠀⠀⠀⢀⣇⠎⠀⠀⠀⠀⠀⠀⠀⠀⠳⢺⢰⠀⠀⢸⠀⢰⠁⠀


⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀