⡀⠀⡸⠀⠉⠉⠁⢸⠁⠀⠀⠀⠀⠀⣿⣿⣇⢿⣿⣇⣼⣿⣣⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⠿⠯⣀⣀⡀⠀⠀⣀⡴⠿⣿⢿ ⢣⠀⡇⠀⠀⠀⢀⡏⠀⠀⠀⠀⠀⠀⢻⣿⣿⣦⡙⣿⢟⣵⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣿⣿⠟⠓⠦⢄⣀⣀⣀⣀⣠⣤⣤⣶⣿⡟ ⠘⡆⢱⡀⠀⠀⣹⠁⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⢸⣾⣿⠇⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⠟⠁⠀⠀⠀⠀⢀⣶⣼⣿⣿⣿⣿⡿⠏⠀ ⠀⠸⡄⢣⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠋⠀⠀⠀⠀⠀⠀⢀⣨⣿⣿⣿⣿⡿⠛⠀⠀⠀ ⡒⠤⣱⡈⢧⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⢿⣿⣿⣿⣟⠀⠀⠀⠀⠀⢀⣼⣿⠟⠁⠀⠀⠀⠀⠀⣠⢔⣿⣿⣿⣿⣿⡿⠀⠀⠀⡀⠀ ⠹⠲⢬⡑⠈⢷⣿⠀⠀⠀⠀⠀⠀⢰⣿⣿⡟⠀⢻⠿⣿⢿⠀⠀⠀⠀⡰⠛⠩⠃⠀⠀⠀⠀⠀⠀⠈⣠⠞⠛⠉⠠⣾⣿⡇⣀⣠⣾⣷⣟ ⠀⠀⠘⢎⢦⡀⠙⢇⠀⠀⠀⠀⠀⢸⣿⠋⠀⠀⠚⠀⠈⠈⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠛⣿⣿⣿⣿⣿⣿⣿⡿ ⠀⠀⠀⠈⠳⠳⠀⠈⠆⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⣿⣿⣿⣿⣿⣿⠃ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⢀⡤⠤⠤⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠺⢿⣿⣿⣿⣿⣿⡀ ⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⡰⠃⠀⠀⢀⣴⢩⢇⠀⠀⠀⢠⠞⠁⠀⠀⠀⠀⢙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢻⣷ ⠻⣿⣿⣿⠷⢶⣤⣤⠴⠊⠀⠀⠀⠀⣾⡇⣲⢻⡆⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿ ⠀⠈⢻⡆⠀⠈⣿⡀⠀⢠⡞⠲⡄⠀⠹⣜⢭⡾⠁⠀⡾⣠⣶⣶⣿⣿⣿⣿⣶⣶⣾⣿⣷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡿ ⣒⢦⠀⢳⡄⠀⠈⢿⠃⢻⠀⠀⠙⣦⠀⠈⣶⠁⠀⡰⣿⣿⡿⠛⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⢀⣼⣿⠟⠀ ⠀⠀⡇⠈⣧⠀⠀⠀⠻⢾⢀⣴⣾⣿⣆⠀⡇⢧⠀⠀⣿⡏⢀⡰⠛⣿⣿⡿⢟⣟⣽⡿⠤⠀⠀⠀⠀⠀⠀⠀⠠⠭⠤⠶⢚⣿⣿⡟⠀⠀ ⠀⢠⠁⠀⢻⡆⠀⠀⠠⢼⣿⣿⣇⡈⢻⡄⠓⠊⠀⠀⣿⡿⢯⡀⠀⠀⢀⣀⣿⣛⠭⣈⢣⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⠁⠀⠀ ⠀⠈⠀⠀⠀⠻⣄⡀⠀⠙⢿⣿⣿⣿⣿⡇⣄⣀⡤⠔⠿⠳⠖⠓⠒⠚⠛⠋⢣⢸⣤⣬⣷⢿⠃⢀⣀⡠⠀⠀⠀⠀⣠⣾⣿⣿⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⢷⡀⠀⢘⣿⠽⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⢧⠴⢾⢛⡄⠈⠧⠤⢤⣴⣶⣿⣿⣿⣿⣿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠿⣦⠞⢁⡔⠋⢁⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢸⠀⠀⠉⠀⠀⠚⢷⣶⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢢⡀⠀⢊⠀⠘⠒⠤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠤⠒⣶⣥⣤⣾⣿⣿⣿⡿⠟⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢄⠘⣄⠀⠀⠀⠘⠂⣀⠤⣤⠤⡤⠤⢤⣄⡀⠀⠀⠀⠀⢰⠁⠀⠀⣰⡿⠗⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡀⠀⠑⠈⠷⢄⡀⠀⡎⠀⢀⣌⢷⠗⡋⠁⠈⣱⠀⣀⣠⣐⣿⠀⡆⣰⣿⡆⣴⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡀⠴⠭⣚⢮⠧⠀⠀⠀⠀⠉⠓⠳⢤⡟⣡⠋⡔⢁⣠⢾⡷⠒⠚⠉⠀⠈⠒⣷⠃⣇⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⠤⣈⡁⠢⢝⡄⠀⠀⠀⠀⠀⠀⠀⠀⡇⠃⠀⢠⠋⠀⢸⠀⠀⠀⠀⠀⠀⢠⣃⡤⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠑⠺⢶⣶⣤⠴⠒⠦⢤⣀⠀⢇⠀⡀⡗⠀⢀⡏⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⢠⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣦⣄⡀⠨⠜⠻⣌⡗⡾⠈⠀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠚⢕⢦⡀⠀⠀⠀⠀⠀⢀⡤⠞⠉