⠀⠀⠀⠃⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠆⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢷⣤⣬⣷⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠉⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⡀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢙⢿⣧⢄⣀⡀⣀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠈⠠⠀⠀⠀⣀⣤⠞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⠝⠳⠾⡿⢿⣋⠵⣿⣿⣛⣟⡿⣿⣿⡗⠖⠲⣤⡄⠂⡨⠊⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠟⠁⣄⣜⠛⠋⢈⡀⢻⣿⣿⡿⠁⣭⠓⠒⢢⢈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⠀⠀⠀⠀⢀⡔⠃⠈⠀⣀⣠⣀⡈⠃⢠⣄⣇⣁⠀⠋⢀⣀⡀⠐⠒⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠐⠀⠀⠀⣾⢥⣶⡆⠈⣟⣿⣿⣿⣆⠀⠹⡽⠃⢠⣾⣯⣿⢿⠂⠤⣬⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢷⠀⢹⠛⠋⣿⡰⣌⡙⠋⠑⣫⠀⠀⠀⠀⣿⠚⠛⢋⡪⣤⠞⠋⣻⠀⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠄⢻⣦⠀⣻⡚⣹⠕⢃⡀⠉⣷⣤⣼⣶⠎⠂⠈⣵⠀⠀⠀⠀⢸⠃⢁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣾⣁⡀⠐⢿⣇⠂⠀⠀⠀⠻⣿⣿⠟⠀⠈⠥⠈⣁⠀⠄⠠⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⣿⣧⡱⠄⢚⡿⡢⢀⢐⣶⣤⡾⠷⣀⣀⡀⠀⠠⠒⠀⠀⠒⢮⠀⠀⠀⠠⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣴⡿⢿⣿⣮⣀⠵⠼⠡⠢⠁⠀⠀⠀⠀⠀⠀⠈⢠⣄⢀⣠⡤⠏⠀⠑⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡾⡾⠀⠚⠻⣿⣿⡿⣵⡦⣤⣶⣶⣤⣶⣶⣶⣶⡶⠾⣾⠟⠉⠁⠀⠀⠘⠮⡀⠀⠀⠀⠀⠀⠀ ⠀⢀⠾⣹⠷⢄⠀⠜⠺⡯⣇⡛⠷⣿⣿⣿⣿⣿⣾⣿⣦⡤⣄⡀⠠⢀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀ ⠀⢸⠁⠉⠑⠢⢍⡉⠁⠐⠿⠿⣿⣿⣿⣿⣿⣿⠿⠻⠓⠒⠘⢷⣦⠼⣥⡍⠐⠂⠀⠈⣷⠀⠀⠀⠀⠠ ⠀⢼⣜⣞⠀⠀⡀⣫⣶⡄⠀⠀⠘⠿⣿⠟⠉⠉⢳⡤⠀⠈⠀⢺⠁⠀⠈⡆⠀⣤⣒⡀⠘⡄⠀⠀⠀⠀ ⠀⢸⠋⠐⠀⡀⠃⠀⠿⣿⣶⣾⠤⣠⣴⠀⠀⠀⠈⠀⠀⠀⠀⢈⠀⠀⠀⢠⡀⠜⠁⠀⠀⣾⠀⠀⠀⠀ ⠀⢸⡁⠐⠈⠀⠀⠀⠀⠈⠹⠁⠀⠈⣾⡆⠀⠀⠀⠀⢄⠀⠀⢘⠀⠀⠀⢸⠃⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠀⠀⢧⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠸⣧⠀⠀⠀⠀⠈⠂⠀⢸⢀⠀⠀⠁⢠⢄⠀⠀⠀⡏⠀⠀⠀⠀ ⠀⠀⢈⣗⠀⠀⠐⠡⠈⠀⠀⡠⠐⠀⠀⠈⠁⠀⠀⠀⢠⠀⠀⡺⠂⠀⠀⠀⠁⠰⡡⠄⡾⡀⠀⠀⠀⠀ ⠀⠀⠚⠹⣷⣄⠀⣷⠄⠀⡜⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⡀⠠⣀⠀⠀⠀⠀⢠⢀⠄⠉⢆⡀⠀⠀ ⠀⠀⠀⠀⣿⣻⣿⡪⣅⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⡡⠐⠉⢆⠀⡀⢀⢨⡟⡀⠐⠀⠙⢄⠀ ⠀⠀⠀⠀⢿⠈⠝⣇⠀⠙⣶⣄⣀⠀⣀⠀⢀⠀⠀⠀⠠⠤⠁⠀⠀⠐⠀⢣⣰⠃⠈⡇⠇⠀⠀⠀⠀⠁ ⠀⠀⠀⠀⢽⠓⠀⢾⡆⠀⠉⠻⢿⣷⣷⡀⠁⢀⠀⠀⠀⠀⣄⡠⠊⣤⣦⠈⠃⠁⠀⣇⠂⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠟⠀⣚⡇⠀⠀⠀⠀⠈⠉⠻⠶⣬⣖⣀⢰⣤⠿⠗⠛⠋⠁⠀⠀⠀⠀⡟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡏⡀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠆⠀⢰⠢⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⢸⢣⠄⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡾⣵⡆⠀⠀⢸⡄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡏⠉⠀⠀⠈⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣼⠃⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠄⠀⠀⠀⠀⠀⠀⣹⡶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠸⡀⡠⠀⠀⢀⠀⢠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⠁⠀⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡄⠀⠠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀