⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠈⠀⠀⠀⠀⠀⠀⠁⠙⠛⠷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⢶⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⣀⠤⠒⠒⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⠀⠀⡠⠖⠉⠀⠀⠀⠀⠀⠀⠣⢄⡀⠀⠀⠀⠀⠀⠀⠀⢰⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⣀⠞⣴⠀⣶⣴⣤⡾⡛⠀⣿⣸⠀⢱⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣤⡶⠚⠛⠀⠀⠀⢸⠡⠤⠼⠟⠟⢉⡋⠉⠇⠀⠉⠟⠁⢀⠇⠀⠀⣠⣴⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⣾⣋⡁⠀⠀⠀⠀⠀⠀⢈⣓⣶⠭⠿⣿⣷⣬⣶⣶⠶⠶⠶⠴⠿⠶⠾⠿⠿⠀⠈⠛⠻⠿⣿⣷⣄⠀⠀⠀ ⠀⠀⠀⠈⠉⠉⠉⢉⣽⣿⣿⠿⠛⠉⠀⠀⠀⠈⠛⠿⠿⣿⠀⠀⠀⠀⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⣿⠿⠋⢁⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣧⣀⡀ ⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠈⠛⠃⠀⢀⣤⣀⣀⣀⣤⣤⣤⣤⡄⠀⠀⠀⠀⠀⠀⢀⣀⡤⣤⠶⠶⠞⠉⠙⣿⠀⠀ ⠀⠀⠀⣾⠥⠤⡤⣴⡦⠤⠤⢤⠤⠤⠤⠤⠤⠤⠤⠤⠤⣄⣀⣀⣀⣤⡴⢖⡞⠉⠉⠀⠀⣿⡀⠀⠀⠀⠀⢻⡆⠀ ⠀⠀⢸⡇⠀⠀⠀⢻⠀⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⢸⡇⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠸⣧⠀ ⠀⠀⣾⢡⣶⠀⠀⢸⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⣼⣧⣀⣀⣀⣀⣀⣿⡄⠀⠀⠀⠀⣿⠀ ⠀⠀⢻⢸⣇⣀⣀⣸⣇⡀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣼⣃⣀⣀⣀⣀⣀⣿⠀ ⠀⠀⢸⢸⠁⠀⠀⠀⣹⣇⠀⠸⣧⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⢧⣀⣀⣀⡤⠖⠋⠀⠀⠀⠀⠀⠀⠀⢸⠀ ⠀⠀⢸⡾⣄⣀⣠⡴⢟⣿⠀⠀⠈⠙⠓⠒⠒⠒⠒⠲⠶⠖⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠀ ⠀⠀⠀⣿⣤⣤⡴⠶⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠶⣄⡀⠀⠀⠀⠀⠀⠀⣸⠃⠀ ⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠉⠀⠀⠈⠹⡄⠀⠀⠀⠀⡴⠃⠀⠀ ⠀⠀⢀⣠⢽⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⢽⡄⠀⣠⠞⠁⠀⠀⠀ ⠰⡟⠉⠀⠈⣧⠈⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⢷⡴⠋⠀⠀⠀⠀⠀ ⠀⣷⡀⠀⠀⠹⣧⡀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⢀⡀⠀⠀⣀⡴⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⣆⠀⠀⠀⠈⢻⣬⣳⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣘⣏⡿⠶⠾⠭⠞⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠻⠶⣦⣤⡶⠦⠿⠗⠻⠤⢤⣤⣤⣤⠤⠤⠤⠶⠒⠒⠚⠛⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀