⠀⠀⡠⠔⠀⠀⠀⠀⠠⠀⠀⠀⠀⢠⠊⠀⢠⣶⣿⣿⡿⣿⣿⣿⣷⣄⣃⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⢀⡸⠃⠀⠀⠀⠀⠀⠀⠀⡠⠂⠀⠀⠀⠒⠤⡀⠀⠀⠀⠀ ⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⣴⣿⣿⣿⣿⡽⠟⠛⠋⠉⠉⠛⠧⣀⢰⡊⠉⠙⠒⣤⣄⡐⣋⣠⣤⣤⣤⣦⣄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠈⠀⠀⠀⠀ ⠀⠀⠀⡀⠀⠀⠀⠀⢀⠀⢀⡠⠀⠀⢰⣿⣿⡿⠟⠉⠀⠀⠀⠀⡠⠞⠉⠅⠈⠑⣣⠤⢄⡀⠀⠈⠛⢿⣿⡿⣿⢿⣿⣿⣿⣶⣄⢄⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⠀⠀⠀⢀⢸⡿⢋⡀⠀⠀⠀⠀⢀⠞⠀⠁⠀⠀⠀⡜⠉⠀⠀⠈⠑⢄⠀⠀⠉⢻⣭⡟⣼⡳⢯⣟⣿⣿⡓⡀⠀⠀⠀⠑⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⢈⡞⡡⠌⠁⠀⠀⠀⢠⠎⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⣿⣷⣿⣷⣾⣿⣹⢿⣷⡑⠢⠤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⢀⠔⢫⠈⠀⠀⠀⡠⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠈⠺⣿⣟⠿⣿⣿⣯⣻⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⡰⣡⠊⠁⢀⠔⠀⢀⢼⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠘⣾⣿⣿⣿⣿⣷⡟⣇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢤⢤⡤⠖⠉⠀⡜⡴⠁⠀⡰⠁⠀⢀⠃⢸⡆⠀⠙⡄⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⠀⠘⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⢛⡤⡴⢀⡜⡜⠀⠀⡰⢁⠀⢀⡎⠀⡄⠈⠢⣀⠈⠳⣄⡀⠀⠡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠸⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠠⢄⠀⠀⡴⢊⣠⢁⡎⠈⠀⠀⣼⠃⡌⠀⣸⡇⠀⡆⠀⠀⠈⠉⠀⠈⠪⣕⣦⠼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⢻⣿⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀ ⢀⠀⠐⢄⠋⠀⠀⡰⢻⠁⠀⡈⢰⢋⣆⣧⠀⡟⣇⠀⣇⠀⠀⠀⠀⠀⠀⢀⣴⣯⡆⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠀⢣⠀⠢⡀⠈⢙⣻⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀ ⠠⡕⢄⠀⠹⡀⡰⠁⣾⢠⠀⠁⣿⣸⣯⣧⣹⣧⣬⣆⠈⠂⠀⠀⠀⠀⡰⢹⡟⠈⠹⣆⠀⠀⠈⢠⠃⠀⠀⠀⢰⠆⠘⡄⠀⠻⣿⡏⢿⣿⣿⣿⣿⣷⣶⣤⣤⣴⡶ ⠀⠑⢜⠀⠀⢳⠃⢀⡏⢸⢀⠀⢻⣿⣿⣿⢿⣿⣿⣿⡆⠀⠀⠀⠀⡠⢣⣞⣥⣀⡀⢹⡂⠀⡄⡸⠀⠀⠀⠀⢸⠀⢠⢧⠀⠀⠙⢇⣸⠙⢿⣿⣿⣿⣿⣿⣿⣿⠃ ⠀⠀⠀⠁⠀⡆⢠⢚⠱⡸⡌⣆⠈⣿⣿⢸⠸⡹⢿⢿⡁⠀⢀⣠⡞⡡⠻⢛⡿⣿⣿⣾⣽⢬⢣⠃⠀⠀⠀⠀⣸⠀⡸⣄⣓⢢⢤⣼⡿⠟⠋⠙⠛⠿⠿⠟⠛⠁⠀ ⠀⠀⠀⠀⠁⣷⡇⠈⡄⠱⡵⣹⣦⡘⢿⠀⠉⠁⠐⠛⠒⠋⠉⠉⠁⠀⠀⢸⡻⣿⡟⢟⡿⣿⠃⢀⡜⠀⠀⡠⢻⢀⣷⠘⣯⣍⡟⢆⠱⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⡼⠙⢧⠀⠑⢄⠳⠈⢿⣿⣶⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠛⠊⢠⠋⠀⡸⠁⣠⠖⢁⣿⣾⣿⠀⢸⣎⠁⠀⠀⢣⠘⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠄⠊⠀⠀⠈⠃⠀⣰⣿⣄⠜⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⣫⢱⠖⢋⠟⠁⢀⣿⡟⣿⡏⠀⢸⣿⡆⠀⠀⢸⠀⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣿⣟⣻⣿⣾⡿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠴⠾⠿⣽⠷⠡⠊⢁⢀⣟⣽⡿⣏⡜⣠⣷⠟⢸⡇⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡾⣿⣰⡿⠋⠻⣿⣷⡹⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⢄⣀⠤⢚⠡⢂⣑⡶⢋⣼⣿⡿⢽⡯⢾⢛⣇⠀⠸⠇⢀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⠃⠀⠘⢯⠇⠀⠀⢨⣿⡇⣿⣿⣿⣦⣀⣀⣀⡀⠤⠤⠒⢺⣹⣛⣽⣿⣿⠿⡵⢫⣾⣡⣿⣧⣞⡼⠀⢺⠀⠀⢀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⡄⠀⠀⠘⠒⠂⢠⡾⣯⣷⢿⣿⣿⣿⣿⢿⣿⣥⡀⠆⢢⣼⣿⠿⣫⠝⣍⢲⢃⣾⣿⡿⣿⣛⡿⠃⢀⡞⠀⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣀⠤⠤⠤⡤⠤⢤⢴⣿⣹⡷⣯⣿⣿⣿⣿⡿⣿⣿⣿⣿⣾⣿⠟⣥⡛⡴⢋⢌⣠⣾⣿⣿⣧⣿⢏⣁⣴⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡞⠃⣠⢒⣩⢶⣒⡙⣂⠖⣠⣩⣭⣿⣾⣿⣿⣿⣿⣿⢿⣿⡗⣿⡏⣝⢢⡽⠒⢿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢐⣜⣥⢻⡬⠗⠚⠛⠉⠛⠿⠧⣿⣿⣿⠿⣿⠿⠿⢿⣿⣷⠸⡇⠻⣾⡇⠀⠀⠈⢙⡿⠟⠛⠋⠙⠻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀