⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⡸⠅⣀⠉⠓⠉⠉⢣⠄⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢧⣴⣴⡷⠚⢷⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⡁⣤⢠⠉⠢⠀⠀⣪⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⡴⠿⠯⢄⡉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠐⠀⢤⣼⣦⢇⠀⢀⢤⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣿⣀⣠⣤⣚⢃⠀⣀⣀⣀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡖⠊⣡⠚⠀⢀⣉⣯⡺⣪⢶⠗⢁⡀⣠⣀⣤⣦⣤⣶⣶⣶⣶⡦⠤⠖⠂⠀⠉⢉⣀⣤⣴⡶⠽⣛⣻⠿⠿⠿⠿⠿⣶⣦ ⠀⠀⠀⠀⠀⠀⢡⠀⠉⢆⠀⢸⢯⡟⠃⠁⠈⣿⣻⣫⣿⢿⣿⠿⠛⠋⠉⠉⠀⣠⠤⣢⣶⢶⠚⠟⠻⠯⣁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⢲⡟⠃⠱⣄⡰⣮⣿⠀⠀⢀⣼⣿⡿⠟⠋⠁⠀⠀⣀⣤⣶⢿⣻⣿⣿⡛⠻⣿⣿⣶⣼⠀⠀⠈⠁⠀⠒⠂⠄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡤⠓⠢⢄⣀⣉⣩⠯⢶⣺⠟⠋⠁⠀⣀⡤⣖⠿⣛⡽⠟⠻⣿⣿⣿⣿⣿⣿⣦⣝⡻⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢿⡉⠀⡀⠀⠀⠀⠘⢳⣶⠟⠁⣀⣤⣦⢞⣫⡽⠟⠉⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⣮⣇⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢣⡀⠱⣄⠀⢀⠜⠉⢠⣠⠟⣫⡵⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠜⠁⠈⡡⠊⣤⡦⣺⡵⣾⣿⣥⣤⣄⣀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣄⠀⠈⠻⣿⣿⣿⣿⣿⣿⣙⣿⡀⠀⠀⠀⠀⠀⢀⡀⠀ ⠀⠀⢠⣏⣀⢀⣠⣧⡫⢛⡵⠋⢸⣿⣿⣁⣈⣩⣛⡿⠆⠀⠀⢸⡟⣛⣩⣍⣀⡉⠻⠄⠀⢻⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⡠⠋⠀⠀ ⠀⠀⢠⢿⣽⡿⠋⠁⡠⠋⠀⠀⠘⢿⣿⠻⣿⣿⠿⢿⠇⠀⠀⠞⠿⢿⣿⣿⣿⡿⠂⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⡠⠎⠀⠀⠀⠀ ⠀⢠⢊⡾⠋⠀⢀⠞⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢰⡏⣟⣿⣿⣿⣿⡟⢀⡠⠎⠀⠀⠀⠀⠀⠀ ⠀⢁⠌⠀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣛⣡⣿⣿⣿⣿⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠊⠀⠀⠰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠛⠼⠿⠧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⢀⣤⣶⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⣺⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠻⣿⣭⣉⣻⡿⠃⠀⠀⠀⠀⠀⣸⣿⣿⣹⡿⣿⣿⣿⡟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⠢⢤⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣦⡀⠀⠈⠋⠉⠁⠀⠀⠀⠀⠀⠠⠚⢻⢿⣿⣿⠷⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠛⠂⠠⠤⢀⣀⡀⠀⠀⣼⡆⣸⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡏⢹⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣷⣟⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠉⠑⠋⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⢻⣿⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠞⠁⠀⠀⠀⠹⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣔⣉⢤⣀⠀⠠⣀⠀⠀⠈⣿⣿⠛⣿⣀⡀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⣾⠋⢨⣐⣩⣯⣽⠿⡓⢦⡁⠀⠀⠈⠻⡿⣿⡛⣿⣶⣄⠀⠀⠸⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⢻⣿⢖⣕⠿⠀⠀⠈⠋⢛⡛⡿⣦⠀⠀⠀⠈⠉⣿⣿⣿⣻⣷⣦⣴⣟⣿⡉⠛⣖⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣯⢳⡥⡟⡷⠂⠀⠀⠀⠀⢲⢙⣀⢿⣳⡄⠀⠀⠀⠘⠿⠿⣿⣻⣻⣿⢿⢟⣷⡄⣝⣾⡽⠷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣜⡞⣼⠈⠽⠃⠀⠀⠀⠀⡀⠿⢾⣿⡏⣿⡵⡄⠀⠀⠀⠀⠀⠹⣿⣿⣽⣧⡿⣿⡇⢿⣿⣟⣺⣟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⣯⣿⣿⡳⠀⠀⠀⠀⡀⣸⣿⡀⠀⢿⣿⣽⣿⣟⣦⣀⠀⠀⠀⠀⠀⠹⣿⡿⣷⣿⠀⠘⣿⣿⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣿⡸⢛⠙⢢⠀⠀⠠⣤⣷⡿⠟⣱⠀⠀⡿⠛⣯⣧⣿⣿⣷⣄⠀⠀⠀⠀⠈⠻⣿⠟⠀⠀⠘⣿⣯⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⣿⢲⠠⢯⣢⢰⢪⣿⢿⣷⣿⣜⣧⡈⠳⣾⡹⡟⣿⡝⠉⠻⣿⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣟⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⠁⠈⣿⡀⠈⠗⢍⣻⣾⣥⣽⡷⡚⠱⢁⠀⠀⠻⣷⡙⠀⠻⠲⠛⠛⠿⠿⢵⡦⣀⠀⠀⠀⠀⠀⠘⢿⡏⢿⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣟⢀⠃⢸⡟⠆⢐⣾⢋⡟⠿⠍⠈⢈⠑⢄⠑⢄⠀⠹⣧⡀⠀⠀⠀⠀⠀⠂⠲⠹⣼⣻⢦⡀⠀⠀⠀⠀⡇⣸⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡄⠀⠂⠀⢧⡘⠸⠚⠺⡗⢷⣱⠞⢬⡯⣀⠳⡰⡑⠀⢫⣄⡀⣀⣀⣄⣈⡱⢶⣆⣇⠹⢿⣵⣄⠀⠀⠀⠢⡜⣷⣵⣄⠀⠀⠀⠀⠀ ⠀⢰⠃⠀⠀⠄⠈⢿⠀⠀⠘⢧⡦⠟⠳⠶⠗⠈⢣⠈⢧⠀⢸⣯⠾⠟⠥⠿⠓⢌⠙⠖⣿⣿⣧⡻⣿⣵⣄⢰⢠⢡⡿⠻⢫⣣⠀⠀⠀⠀ ⠀⡌⠀⠀⠀⠘⠀⠘⣧⠀⠀⠉⠁⠐⢀⢀⠖⠀⠀⠱⡀⠳⡀⢇⠀⠀⠀⠀⠀⠀⠱⣄⠈⠫⣮⡾⣿⣿⣿⢻⣮⣾⣶⢿⣿⡼⠣⡀⠀⠀ ⠀⠁⠀⠀⠀⠀⢇⠀⠹⡷⣀⠂⡠⢀⠽⣷⡀⠀⠀⠀⠘⣄⠰⡈⠀⠀⠀⠀⠀⠀⠀⠈⠧⡀⠘⣿⣿⣯⣿⣿⣾⣾⣗⢸⣿⠲⠱⡇⠀⠀ ⠰⠀⠀⠀⠀⠀⠘⡄⠀⢹⣧⠞⣀⡼⠲⣏⠈⠀⠀⠀⠀⠈⢆⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠹⣿⢿⣿⣿⣿⢼⡿⣷⣿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⢧⢠⡟⡷⣴⡾⠆⠐⠀⠀⠀⠀⠈⢆⠹⡄⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡿⠼⡷⡾⣿⡿⣤⣾⢯⠁⠀⠀⠀⠀