⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣻⣿⣶⣶⣿⣷⣾⣿⣶⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣾⣿⣿⣿⣿⣿⣿⡿⠿⠿⠿⠿⠿⢯⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠟⠋⠀⡀⠀⠀⠀⠀⠀⠀⢈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣾⡡⣠⡖⡼⣕⣀⣀⣀⠀⠁⠭⢂⣱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠚⣷⣿⣿⣿⣿⣿⣿⣿⣿⣉⣲⡿⢋⣩⣿⣿⣿⠶⢫⢿⣿⡛⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⢟⣿⢒⡯⡴⣿⣹⣿⠿⣟⣏⣦⠻⣿⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⡾⠙⡜⡺⢃⠿⠚⠉⠂⢈⣿⣧⣴⣾⣷⠽⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⢿⣿⣿⠏⢚⣿⣥⢟⡅⠀⡆⢠⠧⢿⢿⠿⢻⡛⢷⡌⡆⠀⠀⠀⠀⠀⢀⣀⠀⣀⣀⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣗⣍⡽⣿⣗⣿⣽⣻⠸⣽⡟⢬⣿⣿⣿⡶⡶⣶⣮⣫⠱⠀⠀⠀⠀⠀⡎⠀⡀⠀⠀⠀⠀⠈⠣⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡧⠿⣷⢵⢿⣏⢉⢤⡿⣗⢷⢟⠙⡻⢿⣬⣴⣥⣦⠿⢷⢰⠀⠀⠀⠀⢰⠁⠃⣀⠀⠀⠂⠀⠤⢀⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⣿⡗⡞⣾⣷⣁⠣⣲⡟⠘⣺⢶⢶⣎⠐⠿⠷⠶⢨⣖⠈⣾⠀⠀⠀⠀⠆⠀⢠⠏⠀⠙⠦⠤⢤⣀⡘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⢳⠘⣿⣿⣳⣿⢤⡐⢉⢌⣽⣯⣷⣽⣶⣾⣷⣿⣾⡾⠀⠀⠀⢰⠀⠀⠉⢀⣗⢄⢠⡀⠀⠈⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠘⠀⣿⢟⣿⣦⢛⡕⠃⠒⢨⠙⠘⣻⡿⢯⢿⣿⠟⠁⠀⣀⠠⠋⡄⠠⠀⠈⠛⢷⣹⣿⡻⠎⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⢱⡀⡠⣏⢻⣿⣰⣗⣖⡀⠀⠉⠍⢇⣴⣶⡟⠁⠀⠀⡜⠀⡀⠀⠹⣴⠠⣴⣷⣆⣷⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠹⡧⡀⠅⡕⠉⠙⢿⣿⣿⡥⠄⠔⠛⠹⢻⠁⠀⠀⢰⠑⠀⠀⠀⠀⠈⠳⣍⣹⢿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠇⠫⡣⠉⠒⠀⠀⠀⠐⢨⠿⢷⡀⠉⠲⣬⢸⠀⡠⠠⠃⡠⠀⠀⠀⠀⠀⠀⠑⢲⠊⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⠁⠉⠢⢗⢀⠇⠀⠀⠘⠈⠀⠀⠈⠧⠑⠀⢹⡎⢠⠇⠀⠰⠁⠀⠀⠀⠀⠀⠀⢀⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⣃⡠⠀⠀⠓⠀⠑⢄⡀⠠⢀⡀⠀⠁⠀⠀⠘⠀⢺⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠎⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠁⠀⢠⣽⠀⡇⡢⡈⠒⢄⡀⠀⠀⠀⠀⠀⡰⢃⠄⠂⠀⢌⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡎⠀⡠⠀⠀⠀⢸⣸⢀⢿⠀⠀⠉⢢⠈⠑⠢⢀⡰⠊⠊⠁⡠⠂⡜⠀⠀⠀⠀⠀⠀⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡔⠋⠁⠐⠈⠀⠀⣠⢔⣾⣅⡬⠴⣴⣶⣀⡀⠀⠀⠀⠘⡉⢀⠔⡩⢰⠑⠀⠀⠀⠀⢀⠄⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠊⠀⠠⠀⠀⢀⡴⢿⣿⠃⣾⣏⠝⣋⠽⠛⡩⠂⠀⠀⠔⣨⠔⠁⠀⢃⡵⢎⠀⠀⠀⢀⠂⡴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠁⠀⠀⠀⠀⠠⠋⠠⠋⣎⡄⠺⢛⠝⢁⡴⠉⠀⠀⠀⣠⠞⠁⠀⢀⠔⢍⡴⠁⠀⠀⢠⡃⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡌⠀⠀⠀⠀⠀⠀⢀⣇⢔⣧⠀⠀⢀⡔⠙⠀⠀⠀⡠⠜⠁⠀⠀⠐⠁⡠⠊⠀⠀⠀⢀⢖⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⠀⠀⠀⠀⠀⠀⠈⠛⠀⠉⠁⠀⢠⠋⠀⠀⠀⠒⠉⠀⠀⠀⠀⠀⢀⠜⠁⠠⠀⠀⢠⠊⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⠀⢉⠨⠐⠐⠀⠀⢡⢮⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⢀⢸⢿⠀⠀⠀⠀⢫⡀⠀⠀⠀⣀⠐⠀⠀⠀⠀⣀⢾⣏⡎⡟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠆⠀⠀⠀⠀⢠⣴⣴⣦⣲⣿⣮⣿⣯⣼⡄⠀⢦⡄⠀⣝⣅⠀⢀⣧⡄⠀⠀⢀⠔⠩⣿⣿⡆⠸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⣾⣿⣿⣽⡭⠽⠿⠟⠛⠻⢿⢦⣬⡿⢗⣛⣩⣷⣤⣋⣀⡠⣴⣅⠀⠀⢹⡻⠇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢰⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡆⣿⡆⠀⠐⠹⣿⣧⡀⠀⡭⣤⡀⡀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠃⣾⣿⣿⣿⣿⣿⣗⡬⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⡅⣿⣧⢀⡀⢀⠙⢿⣷⠀⡷⢸⢡⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠀⢸⣿⣿⣿⣿⡿⣿⣿⣿⢆⡀⡀⠀⠀⠀⠀⢠⣼⣿⣿⠃⣿⣿⠜⣄⠈⢧⢄⠹⣧⠡⠸⠸⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡆⢘⣿⣿⣿⣿⣷⣺⣿⣿⣯⣴⣶⣾⡎⠀⠀⢤⣿⣧⣏⠸⢸⣿⡇⣿⡖⢮⠺⠂⠻⣷⠀⠐⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡯⠂⣰⣿⣿⣿⡟⠀⢾⡿⡧⡀⣿⢤⢹⡾⡶⣿⡲⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⣸⡏⠃⠀⣾⣿⣿⣯⣿⠀⢸⣧⢿⣿⡺⣷⢸⡑⡇⡇⡇⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡄⣹⣿⣿⣿⣿⣿⣿⣹⡟⣸⣏⠀⠈⠀⣾⣿⣿⣏⣿⠀⢨⣟⣼⣿⠷⢿⣦⣇⣧⣷⣀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡇⠸⢿⣿⣟⣾⣿⣳⣿⢳⡏⣌⡀⢀⢗⣿⣿⣿⡇⣿⠄⠈⣿⠟⣧⢻⡜⣿⡄⠀⠀⠀⢈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠇⠘⣿⣽⣿⣿⢇⣿⡟⡿⠁⡺⠀⣜⣼⣿⣿⣿⡇⣹⡇⠀⢹⣃⣸⠰⣧⢿⣷⠀⠀⠀⠀⢱⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠸⢻⡟⣿⣿⣿⣾⢿⡿⠃⠈⠀⢀⣁⣿⣿⣿⣿⡇⣻⡇⡴⠸⣯⣻⡇⣟⢏⡗⠀⠀⠀⠊⠀⠈⠻⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⡾⠘⣿⣿⢻⣟⣾⠁⠀⠀⢸⣞⣿⣿⣿⣿⣿⣏⢹⡇⢻⡆⣽⣧⣿⠘⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠀⢸⣿⣿⣼⣷⡎⢠⠀⢀⣾⠇⣿⣿⣿⣿⣿⣯⢠⣷⢸⣧⢻⣿⢽⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⡯⣿⡿⢿⠀⣰⣀⡘⡇⠀⣿⣿⣿⣿⣿⣿⣼⣿⠈⣿⣽⣽⠭⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⣄⠀⠀⠀⠀