⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠒⡀⠀⠀⠀⠀⢸⣶⣄⠀⠀⠀⠈⠉⠉⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠟⣻⣿⡿⠟⠋⠁⠀⢀⣤⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠒⢄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠞⠀⠠⠳⣄⠀⠀⠀⠹⠿⠿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠐⠘⠋⠁⠀⢀⣠⢴⣶⡎⠿⠿⠿⠀⠀⠀⠀⠀⠀⣠⡞⠀⠀⠣⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠈⠀⢈⠀⠀⠀⠈⠀⡁⠂⠁⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⣿⣷⢹⣯⠀⠀⠄⠀⡒⠀⠂⡀⡄⠈⠃⠠⠀⠀⠀⢰⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠈⠀⣠⠄⠀⠀⠀⢠⣤⣤⢤⠀⠈⠁⠀⠀⠀⠀⠀⠰⢦⣤⡦⡄⡤⠀⠀⠀⠀⠀⠀⠈⢟⢘⣰⡄⢉⣀⣐⠒⠒⠀⠐⠂⠒⠢⣀⠀⠅⡄⠀⠿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡃⠀⠀⠀⠀⣿⣿⣿⣾⢀⠀⡀⠀⠀⠀⠀⣿⠀⠂⣍⠠⢀⡀⠀⡀⣆⠀⠀⠀⢠⣾⣮⡝⢿⣷⢹⣶⠀⠀⠀⠀⠀⠀⠀⢘⡈⠐⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡏⡿⠈⠀⠀⠀⠀⠀⢸⣿⣶⡀⠉⠁⠉⠁⠀⢿⣿⠀⠀⠀⠈⠛⠿⢿⣼⡍⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⡆⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⠍⣼⣧⢢⣀⣠⠆⢀⠸⠇⠀⠀⠀⠀⠀⠀⠀⠙⣡⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠃⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣝⠢⣭⠉⣡⡥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⢰⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡈⢿⣟⠀⠿⣿⠏⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢸⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡦⡉⣶⡘⢡⣾⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⢸⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠂⢴⣾⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣋⠅⠉⠋⠍⢘⠿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⠈⢩⣥⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣶⣾⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠰⣤⡀⠚⢁⣐⡛⣘⡛⠴⡄⠀⠺⠆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣿⣿⡋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠒⠚⠋⠩⡄⣠⣯⣄⣀⠰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢠⣼⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣷⡶⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣆⠐⠒⠋⢐⣂⡨⠭⠍⠓⠁⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠘⣿⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣦⠀⠈⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⠟⣫⣥⡀⠛⠋⡐⢂⣉⡐⠶⠶⠶⢮⣝⢻⡁⠀⠀⠀⠀⠀⠀⠀⢻⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠉⠀⠀⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠋⠄⣠⠖⣡⣾⣿⣿⣿⣿⣿⣿⣷⣌⠷⣄⠀⠀⠀⠀⠀⠀⠀⠘⠸⠛⠿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀