⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣯⣏⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠺⠧⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⣳⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢒⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠴⠉⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣙⣳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⣤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢬⡭⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⣖⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣯⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢿⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⣤⣷⣶⣶⣴⣴⣦⣶⣠⣰⡄⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⣖⠁⠀⠀⠀⠀⠀⠀⠀⢠⢄⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣇⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⡔⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣿⡋⠀⠀⠀⠀⠀⠀⠀⢀⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣷⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⣦⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣽⠋⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣼⣻⣿⣿⣿⣿⣽⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢟⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣤⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣽⣿⣽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠸⡟⣶⣄⠀ ⠀⠀⠀⠀⠀⠀⠀⣶⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣻⣿⡛⣎⠹⣿⣟⢋⣉⣻⣿⣿⣿⣿⣿⣿⣿⣿⣆⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠹⠾⡃⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣿⣿⣿⠃⠓⠙⠂⠈⢹⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡠⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣾⡖ ⠀⠀⠀⠀⠀⠰⣻⡡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣻⣿⣿⣿⡟⣿⣿⣦⠀⠀⠀⠀⠀⠻⠿⠙⠀⠀⢘⣟⣇⠿⣿⣿⣿⣿⣿⣕⡘⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷ ⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⣿⣿⡟⢿⡿⠯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⢊⣠⣿⣿⡿⣿⣿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙ ⠀⠀⠀⢦⣼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠘⢿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⡿⠡⣼⣿⠟⠘⠁⠁⠛⢿⣷⡆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣾⣧⣵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠘⢙⣧⣷⠟⠁⠀⠀⠀⠀⠀⠀⠙⣿⣇⢰⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢳⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣿⣿⣿⡄⠀⠀⠀⠾⠷⠄⠉⠁⠀⠀⠀⠀⢉⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⢛⣻⣾⣇⢃⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⣫⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⢿⣿⣿⣿⣆⠀⠀⠀⣠⣤⣐⣒⣦⣤⣤⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣾⣿⣿⣿⣮⣿⣧⠀⠀⠀⠀⠀⠀⢴⣤⡰ ⠀⡠⠒⠈⠉⠁⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣾⣿⣿⣾⣿⣿⣿⣿⣷⡀⠐⢻⡿⠿⠿⣿⡟⡏⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣦⣄⠈⠛⢿⡉⠛⠛⣻⣷⣶⡄⠀⡆⡄⣾⣇⠀ ⢴⣧⣤⣤⣶⣤⣑⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⢠⢸⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣦⠀⠳⢤⣰⡿⠋⠀⠀⠀⣀⣤⣂⡀⠀⠀⢈⣻⢿⣿⣧⣄⡐⣬⠵⠖⠻⣿⠛⣿⣿⣿⢳⣿⡿⠇ ⠉⠡⡀⢻⠪⣽⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠸⡊⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣧⣶⣦⠘⢻⣿⣿⣿⣿⡏⠈⠻⣶⡂⠈⢆⠹⡿⣷⠛⠊⠀⠀ ⠀⠀⢈⣟⡳⣨⣇⣤⡶⠀⠠⠀⠀⠀⢠⠀⠀⠀⢃⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠙⠒⠀⠀⠒⠉⠀⠘⣿⣿⡟⢛⡗⡲⢾⢿⣟⣯⣩⣟⣢⢴⡺⣍⠆⡨⢋⠔⠁⠀⠀⠀⠀ ⡀⠀⠀⠋⠉⠹⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⣿⣿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⡻⠋⠐⠫⢊⢔⠝⣋⢞⡼⣣⢦⡜⡀⠘⢮⣩⠕⠋⠀⠀⠀⠀⠀⠀ ⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡿⣿⠛⠻⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠐⠡⠂⠱⠃⠰⢁⠿⠀⠁⠂⠆⢧⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠟⣼⣿⣿⣾⣿⠿⢿⣿⣿⣦⣀⠀⠀⠈⢇⣀⣀⡀⡀⠀⠁⠐⠃⠰⠁⠈⠀⠀⠀⢸⠀⠀⠈⠁⠒⠤⣀⠀⠀⠀ ⠀⠀⠙⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⣷⣿⠛⠛⣿⣿⣤⠀⠿⣿⡻⢿⣿⣶⣦⣶⣽⣏⡟⠛⠻⡿⣲⢶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢄⠀ ⠀⠀⢀⡜⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣻⣿⣿⣿⣿⣄⢠⣾⣤⣾⣧⣤⣽⣿⣶⣾⣿⣿⣿⣿⡏⠀⠰⢱⠡⠣⠟⠰⠅⣏⣹⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑ ⠀⢀⡞⠀⠀⢁⡘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⢏⡫⡻⠿⣳⢿⢿⢿⡿⠛⢟⠿⡿⢟⣿⣿⡿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠉⠩⡅⠀⠀⠀⣀⣤⣶⣶⡶⣦ ⢠⡎⠀⣠⣾⣿⠗⠈⣄⠀⠀⠀⠀⠀⠀⠀⠀⡄⡘⣿⣿⣷⣶⣮⣶⣬⣤⣦⣴⣤⢵⣄⡃⢕⣽⢻⡏⡯⣲⣟⣿⡄⠂⠀⠀⠀⠀⠀⣠⢦⣶⢜⢴⣴⢟⠛⠛⠛⠛⠛⠉⠀⡼⢛⡿ ⣭⣾⣿⡿⠋⡄⡠⢠⠘⠀⠀⠀⠀⠀⠀⠀⢣⡱⡅⠹⣿⣿⣿⣿⣽⣿⣿⣿⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⡇⠀⠰⠀⠀⠀⢠⣿⡿⡏⡞⡏⣵⣅⠀⠀⠀⠀⠀⢀⣼⠃⠈⠁ ⡏⣿⣏⣄⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠑⠈⢆⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣴⣧⡀⠀⠀⠀⢸⠁⠧⠷⠙⠘⠻⢻⣿⡦⡀⠀⠀⡼⠁⠀⠀⠀ ⡇⠇⣿⣿⠲⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⡄⣴⠟⠁⠀⠀⢸ ⣇⢹⠟⠁⣤⠃⡨⠙⠙⠶⠒⠲⢖⠗⠖⠂⠶⠢⠖⡕⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠛⠁⢀⣼⣸⢰⢠⠀⠀⠀⢀⠀⠄⠆⠢⠀⠈⢹⣿⢏⠀⠀⠀⠀⠸ ⣿⣼⠀⠠⢂⠔⠀⠀⠀⣦⣤⣤⣤⣤⡤⠤⠄⠄⢔⠻⣏⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠋⠀⢿⠟⣿⣿⠇⠀⠀⠈⣣⣭⠏⡎⡆⢀⡸⠀⠀⠀⠀⠀⢰⠀⡞⡡⠊⠀⠀⠀⠀⠀ ⢻⢁⡴⢢⢈⠀⠀⠀⠀⠛⠙⠋⠀⠀⠈⠀⠀⠀⠀⠀⣹⡯⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡰⢤⣿⡅⣿⡟⠀⠀⠀⠀⠈⠑⠃⠠⢃⡈⠁⠀⠀⠀⠀⠀⠀⠣⡪⠀⠀⠀⠀⠀⠀⠀ ⠠⣸⢠⢳⢋⡾⣰⠴⡶⢠⠔⠰⠀⠀⠀⠀⠀⢀⢠⡌⢹⢿⡜⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡉⠀⠉⢃⣿⠁⠀⠀⠀⡀⠀⠀⠀⠃⠀⢁⠀⠀⠀⣀⣀⣤⢴⡪⣶⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠀⠆⡀⠌⠃⠸⠀⠂⠀⠀⠀⠀⢀⢀⢤⠊⣿⡄⠈⡟⣿⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣦⣤⣼⡿⠀⠀⠀⠀⡱⢼⣾⡶⡖⣾⠿⣾⣻⣯⡿⣙⠮⣳⠼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣆⠁⠀⠀⠀⠀⠀⠀⢰⣠⡜⡞⡎⢎⠊⠈⣇⠀⠰⡸⣽⣿⣿⣿⣿⣿⣿⣿⣿⢿⡁⠿⠿⣿⠃⠀⠀⠀⠀⠸⣷⣿⣴⣾⡇⠂⠻⠙⢮⣻⠬⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠐⢀⢸⡆⠀⠀⠀⠀⠀⠀⠈⠈⠉⠀⠀⢀⠔⠁⣿⠀⠀⢡⢫⢻⣿⣿⣿⣿⣿⣿⣿⣏⠃⠀⣰⣿⠀⠀⠀⠀⠀⠀⠀⢹⠛⠧⢠⡤⠤⠒⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀ ⠀⠀⢸⢆⠑⠤⣠⣄⠀⠀⠀⠀⣀⣀⡤⠔⠉⠀⠀⢸⡇⠀⠘⡌⡻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠈⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⠀⠀ ⠀⠀⠈⡆⠑⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢃⢡⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠸⡈⡾⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠡⡀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠇⢰⢻⣿⢿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠏⣢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀ ⠀⠀⠄⠑⡄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⢰⠈⡞⣿⢾⡕⢿⠉⠉⠉⢉⣿⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡙⡑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀