⠀⠀⠀⠀⡀⠘⠀⠀⠊⠹⢢⠀⠊⡠⢁⠚⠔⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡷⣧⢠⡄⠂⡾⢿⢻⠊⣭⣧⢸⠁⢠⠀ ⠀⠀⠀⠀⠀⢃⠀⡁⡿⣿⠁⡜⠁⠞⣡⠔⢚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⢄⢸⠁⡇⠝⡣⡪⠬⣸⢱⡇⠀⠀ ⠀⠀⠁⠒⡤⣄⣚⣞⣴⢗⡴⠏⣰⠁⡻⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠆⡎⠈⣀⣇⣋⡗⢾⡇⠀⠀⠀ ⠊⠤⢀⠀⠀⠀⣧⣖⠣⣿⣽⡻⠇⣞⣈⠀⠋⡾⢀⠀⠀⠀⠁⠃⠍⠤⠤⣃⠻⠙⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⢆⠈⠈⠄⢪⡳⠛⢫⢹⠀⠀ ⠀⠀⠀⠀⠀⠀⡄⢿⡴⣤⣡⢟⣷⢀⠀⡞⣠⠀⠁⠁⠐⡠⠀⠀⠀⠀⠀⠀⡀⣄⣯⠘⠀⠀⠀⠁⢠⠀⠀⠀⠀⡄⢿⠈⠺⡻⠶⢷⣷⠈⠃ ⠀⠀⠀⠀⠀⠀⠀⣇⣽⠿⠽⢮⢣⢹⠔⢀⠀⠊⡤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣇⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⡀⢳⡀⠀⠀⡇⡼⢸⡇ ⠀⡀⠱⠀⠀⠀⠀⡁⣿⠿⡮⢣⡗⢠⠀⠃⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠌⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⠀⡧⢃⠁⡰ ⠀⠀⠀⢆⡜⠙⠆⣕⣷⢟⣽⢖⣾⠀⠚⢐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠟⣰⠀⠁⠟⢀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⡀⡇⡰⠀ ⠤⠑⠈⠀⡀⡣⠫⣄⠷⠘⢮⣻⢠⠆⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢀⠀⠏⣠⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠤⠀⡜⡰⠀⠀ ⠀⠀⡀⠤⠑⠈⢄⢕⠑⡎⣻⣧⠁⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠞⠷⣿⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⡏⡌⠀⠀⠀ ⠀⠀⠀⠀⠀⣄⠧⠑⢢⠈⢼⣿⣄⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠚⠓⠀⠸⠀⠀⢢⡠⠼⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠦⢹⠇⣿⢰⠀⠀⠎ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⡢⡏⢱⢱⢇⠸⠀⠀⠀⠀⠀⠀⠀⠂⡋⠛⢞⢔⠀⠀⠀⠃⡠⠀⠀⠊⠚⠈⠮⠮⠼⠾⣐⣀⡦⣶⣿⣇⠀⠀⠆⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⠈⣡⡧⠈⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠠⠀⠁⠛⣷⣵⠔⣌⢠⡀⣄⡑⣭⣫⠈⠀⡁⣟⠀⠃⢠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡞⣌⢰⠇⢰⠀⠀⠀⠀⠀⠀⠀⠀⠐⠤⣀⠈⠀⠀⠂⣣⡣⡵⢑⠗⣦⠀⠁⠹⠀⠀⠈⡀⠀⢀⡇⠀⡌⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢡⠇⡆⠀⠀⠈⠀⠀⠀⠀⠀⠀⠉⠔⣁⠛⠴⠚⠽⢜⢕⢞⢪⠣⢠⠀⣆⡙⢯⣖⠀⠀⠁⠔⡤⡦⢙⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⣯⡇⠁⠉⡟⢷⠀⠀⠁⠈⠒⡠⠁⠔⢇⣡⠊⣫⡳⡲⠕⡠⠞⢀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⡀⠰⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⡄⡿⡇⡾⢣⣼⡠⣉⠈⠂⠒⠤⢀⠏⠛⡾⡤⠷⢚⡊⡝⣹⠀⠈⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠁⠀⠀⡆⠀ ⠀⠀⠀⠀⠀⠈⠀⠑⠀⠀⠀⢀⡇⡇⣮⢀⡜⣁⣂⠄⠀⠀⠀⠀⠀⣾⣒⣫⢦⡈⢧⡻⣣⣧⢡⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⣹⢘⠀⠀⠀ ⠀⠀⠀⠀⠊⢈⠀⡇⠸⠀⠀⠀⡿⣸⠃⣼⡩⢒⠄⠠⣀⣀⠄⠑⠈⡹⣦⣗⢻⣀⡵⣇⣚⠘⣰⢿⠀⠎⠱⠤⠠⠂⠒⡏⠀⠀⣿⢻⠀⠁⢄ ⠳⠈⠁⠔⢎⢀⠀⡌⢾⠀⠍⡶⣡⡝⡴⣀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣦⠑⡇⣄⠹⡀⠰⠾⢏⠇⣠⠿⢀⡜⢿⠑⠈⠀⠀⠘⠀⣤⣠⠀⡄⠀ ⢇⢇⣿⡨⢀⠀⠎⢏⠛⡵⢂⠛⡶⣻⠴⠀⠀⠀⠄⡤⣀⣒⠲⠐⠀⠀⠀⣄⠑⡇⣛⡞⢋⢃⣱⠈⢇⠡⢃⣠⠸⡀⠢⠉⠆⠈⠀⠀⠃⢠⠀ ⠁⣤⠜⣁⣴⣡⣓⡿⢵⣮⢏⢞⡠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣎⢛⢰⣇⣀⣾⢸⠀⡸⡿⡇⢿⠀⠀⡀⢢⡈⠤⠅⢀⠀⠀ ⠀⡜⠃⢠⠊⠣⣵⢔⢎⡥⣸⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡙⣷⡎⡌⡀⠸⡆⢸⢢⠁⡎⡷⣦⠀⠀⠀⠀⡀⠢⠈⢡⠀⠀ ⠄⠀⡸⠎⢃⢢⠡⡴⠜⢕⠈⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣳⣼⢸⠀⢰⠀⢸⠈⡟⣁⣿⠀⠀⠀⠀⠀⠀⠀⡄⠘⢀⠀ ⠀⠇⠇⢁⢺⢁⡹⡿⡿⣸⢠⡟⠿⠽⡻⢸⠀⠊⠙⠓⠮⠁⠗⢨⠙⠈⠀⠀⠀⡆⣾⠀⠀⠀⠀⢠⢸⣧⡀⡇⠀⢸⠀⠀⠀⠀⠀⠀⡇⠀⠀ ⠀⠸⢸⡏⢡⡾⡼⣠⣿⣿⠷⢿⣿⣿⣋⢿⡺⡯⣾⢀⠁⡿⣷⣮⣤⣶⢿⡷⠿⠾⣷⠕⠫⠒⠓⠞⢠⡇⠰⠨⠀⢸⠀⠀⠀⠀⠀⠀⡄⠀⠀ ⠀⢆⠀⣸⡏⣾⢇⠃⡏⠡⣣⡄⣤⣥⣧⣴⠏⣻⠔⠀⡷⢣⢣⢈⠊⡫⢓⠵⣵⣛⡿⣡⠚⡯⢣⡏⡷⡆⢀⠀⢄⢘⠀⠀⠀⠀⠀⠀⡆⠘⠀ ⠀⠀⡇⢠⢹⢳⡟⡟⢫⡸⠰⢣⠃⢧⣸⠆⢂⢠⠀⡍⢱⢡⢡⡻⡵⢔⢋⢔⢇⣵⢟⣵⠴⢕⣜⣀⡆⢰⠀⡥⠠⡆⠈⠀⠀⠀⠀⠀⠀⡁⣉ ⠀⠀⡀⠃⣇⡆⢁⡞⣱⣧⣤⠾⣳⢨⠃⠰⢠⠀⠃⣝⡜⡄⢞⢩⡯⡞⢲⠞⢚⣡⡼⢀⠊⣿⢸⢸⠇⠀⠀⡍⠀⠀⢸⠀⠀⠀⠀⠀⠂⠨⠀ ⠀⠀⠀⡇⣇⢢⣩⠖⣯⡘⠘⢃⡎⡀⣷⠀⠀⠃⣟⡘⢸⡿⣠⠃⣼⠁⡿⡼⢎⣠⠀⠎⣼⣿⢠⢰⡇⠀⡧⢡⠉⠀⢸⠀⠀⠃⠈⠀⠃⣧⠀ ⠀⠃⠀⡇⣿⠘⣜⢷⡙⠖⢏⡏⢹⠀⠀⠀⠀⡌⢣⢁⡟⢠⠀⡞⠁⠡⣡⡗⠨⠁⠖⢧⢃⣸⡇⠘⡈⠀⢲⡟⣴⠃⢁⠀⠁⡱⣿⠹⠃⡭⢀ ⠀⡜⠤⠑⣾⢇⢃⠀⡀⢤⠗⢩⣼⡔⠸⠀⠀⠀⠀⡏⢸⠀⠆⢁⠮⢋⣴⣻⡿⢿⢧⣳⢠⠀⠸⢁⢨⢱⠀⣔⢁⡱⣰⠰⡌⡘⣿⣿⡜⠐⠀ ⡀⠀⠛⠀⢇⠹⢷⠹⠀⠀⠀⡀⣀⠤⠢⠒⠖⠉⠙⢻⢹⠋⢻⠶⣶⠴⣤⣀⡊⢻⣵⣴⠀⠎⠀⣷⣮⡚⢮⠌⡼⡌⠻⡄⢀⣿⣿⣿⢿⠛⠛ ⢰⠀⠅⠀⠀⣾⡹⡳⣖⠫⠙⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠝⣗⣠⡀⠀⠃⢠⠆⡛⢜⢯⢿⡙⣶⢻⣿⢻⡇⣿⣿⣿⣿⣿⣿