⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣖⣶⣬⣟⣿⣽⣿⣷⣐⣶⣒⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣼⣿⣿⣿⣿⣿⣿⣟⣻⣿⣾⣿⣿⣿⣿⣾⣿⣿⣶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣷⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣽⣿⣿⣿⣿⣿⣿⡿⠋⠀⠈⠉⠉⠛⠟⠿⣿⣟⣻⣿⣿⣿⣿⣿⣿⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢺⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⡿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠋⠀⠀⣠⣤⣤⣤⣄⣀⡀⡀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡿⣿⣿⠃⠀⠠⠀⣘⣭⣥⣭⣽⣛⠿⡿⠆⢠⣶⣿⣶⣾⣶⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠻⢀⣷⣿⠇⠀⠀⠀⠈⠉⠙⠛⣛⡿⣿⠦⠀⠀⢼⣿⣿⣿⣷⡃⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠈⠀⠘⠋⠉⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣆⠀⠘⠳⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢤⡔⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣤⠤⡀⢀⡄⠀⠀⠀⢀⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡅⡄⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⣴⣿⣷⣴⣶⠀⠀⠀⠀⡜⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⢷⠀⠀⠀⠀⠀⠀⠸⠟⢿⡽⠾⡄⠒⠙⠯⣿⠇⠀⡼⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⢶⣲⣠⠏⠀⠪⣧⡀⠀⠀⠀⠀⠠⠄⠀⠈⠡⣅⣀⠀⠀⠀⢀⡼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠙⢯⡀⠀⠀⠙⢿⣶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⡤⠚⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠉⠻⣟⡻⡶⢶⣤⣤⣄⣀⢀⣤⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡤⠐⠒⢚⡋⠁⠀⡌⢀⠀⠀⠀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠈⠓⠄⠁⠀⠀⢸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠉⡤⡝⠈⢆⡀⠀⠀⠀⠀⠀⠀⡙⡄⠀⠀⠀⠀⠀⠀⠀⢡⡺⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢆⠈⢫⣄⠀⠀⠀⠀⠀⠠⡜⡆⠀⠀⠀⠀⠀⠀⡌⠉⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠠⠀⠀⠀⠀⢳⠄⠈⣁⠀⠀⢠⢼⣿⣿⣷⠀⠀⠀⠀⠀⠸⣇⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠀⠀⢤⢤⣄⣀⠀⠀⠄⠀⠳⡀⣰⣟⣾⢻⣿⣿⡀⠀⠀⠀⠀⠀⢸⣧⣼⠞⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢣⣾⠄⣛⢿⢺⣶⣶⢌⣆⠀⠙⡻⣿⡗⢩⡿⣟⢃⠀⠀⠀⠀⠀⠸⣿⣙⡅⡂⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠁⠀⡟⢹⣶⣇⠙⠄⡬⠰⣤⡸⠿⠃⠚⡟⢻⠫⣧⠀⠀⠀⠀⠀⣿⢻⡟⣄⢻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⢀⢰⡇⡀⣰⡿⡀⢰⠆⠉⠁⠈⢐⠀⢰⣣⣼⡇⠘⠷⣄⠀⠀⠀⣹⠈⣾⣌⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠠⡵⡷⠿⢿⡕⢾⠚⠋⠊⠃⠈⡒⡂⠀⠠⡀⠀⠈⢻⢟⡄⠘⡌⠓⠤⠴⠙⡆⣿⣯⣾⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠎⠀⠀⠐⠁⣀⠀⢀⣴⡀⠂⣄⠀⠱⡀⠀⢿⣷⡐⡜⡄⠀⠀⠀⣿⣿⡿⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠢⢦⠀⠰⠆⠐⡒⠚⠡⠬⠻⠷⡗⡄⠀⠀⠀⢀⣷⡾⣣⠀⠀⢸⢿⢧⡄⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢁⠀⠀⠈⠴⠆⠀⣴⣷⠄⠀⢼⠔⠷⠻⣄⠶⡬⠄⡸⣻⣿⡟⢇⠀⢸⣍⣿⢳⠘⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⡤⠀⠀⠈⢂⢼⡿⠈⠀⠀⠀⠀⠀⠀⢞⠦⠻⠅⡀⣀⢹⣿⡼⣄⣿⢾⢿⢸⠀⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⣠⣗⢞⡀⠀⣼⢾⡽⡄⠀⠀⠀⠀⠀⠀⠈⢃⠀⠀⠀⠉⠛⠹⣿⣾⣥⠁⠛⡞⠀⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⠹⢳⡺⠁⡠⢻⠉⠀⢧⠰⣦⠀⠀⠀⠀⠀⠘⢠⣀⡀⠘⠀⣄⠻⣿⣷⡑⣧⡆⣰⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⣰⣷⣰⣧⡼⣠⢸⡀⠟⠓⢦⡀⢀⠀⡦⠀⠈⢠⣤⡈⠙⡑⢸⣿⢻⠃⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠺⣌⡏⣹⣿⠀⡿⠏⠀⠀⠀⠀⣿⠜⠐⠁⠀⠐⠙⠃⠑⠀⠀⢰⣀⢼⠀⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢃⠈⠇⢹⠇⠀⠀⢀⡎⠁⠀⠀⠀⠀⠀⠀⠀⢐⠇⠀⠀⠠⠀⢀⣼⣯⡾⡆⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡈⠀⠀⠈⡐⠀⢀⠎⠃⠀⠀⠀⠀⠀⢌⡀⠀⠀⠀⠂⠀⠀⠀⣈⠿⠇⣿⣧⣙⡀⠀⠀⠀⠀⠀⠀⠀