⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢹⣿⡁⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠈⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⢖⡶⠀⠬⣪⢰⠠⣆⣺⠀ ⣿⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⡤⠒⠒⡆⠐⠒⡢⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠉⠉⠁⠀⠁ ⣿⠉⠈⠳⡄⠀⠀⠀⠀⢀⠔⠁⠈⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢜⠲⢃⡤⠤⠁⠀⠀⠠⢄⡐⢉⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠠⢱⠀⠀⠀⡐⠁⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣡⣾⠟⣧⣄⣀⣄⣀⣴⠾⠿⣆⢢⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠉⡄⠀⡼⠁⠀⠀⡀⡳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣥⣿⣁⣜⣰⠟⠀⢀⠭⠋⢠⣾⣿⣧⢺⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⢣⢀⠀⢰⢳⣰⠁⠀⠀⢰⡰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠹⠉⠙⢻⠁⢀⠰⡋⠀⠀⣸⡜⠉⣝⢺⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠈⡅⠀⠀⢨⠃⠀⠀⠠⡝⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣸⢆⠀⠈⡆⠙⠚⠂⠠⠞⢋⡇⠐⢛⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⣱⡀⠀⡎⣀⣀⡰⢲⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⢿⣄⠀⠱⡀⠀⠀⠀⢀⠞⢀⢜⡻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠁ ⣿⡄⢯⣿⡾⠀⠘⢯⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⢤⣵⡂⢲⢰⢡⣶⠕⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⣆⠀ ⣿⠈⠛⣿⡇⠀⠀⡙⣄⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠎⣏⣿⡟⢟⡷⣭⣣⣤⣎⡯⢶⡶⠺⡆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣟⠄⢈⢤ ⣿⠀⠀⢱⠃⠀⠰⢺⡏⠻⢄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢁⢿⢓⡀⠹⣾⡄⠀⣿⡇⢸⢃⡼⡘⠀⠃⡘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣀⣤⣲⣷⡃ ⣿⠀⠀⡄⠀⠀⠠⡌⣗⡁⠀⠣⠢⡀⠀⠀⠀⢀⠔⠋⠀⠀⢸⢸⠀⠈⠁⢹⣅⠀⡇⡄⣺⣋⡷⠁⢠⡸⠁⠘⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠿⣯⢿⣻⣽⠇ ⣿⠀⠀⡇⠀⠀⠃⡇⣹⢯⡀⠀⠀⠸⢤⠤⢔⠁⠀⠀⢀⡰⠊⡿⡏⠙⠊⢸⡿⠛⠭⣭⠓⠛⣧⢀⢘⡇⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⢀⡜⠚⠃⣄⡾⡿⠟⠃⠀ ⣿⠀⠀⡇⠀⠀⠀⡇⠋⡀⠙⢆⡀⠀⢈⣾⣪⡄⠀⡀⢀⣤⠔⣇⡇⠂⠆⠁⣧⠀⣰⠟⠳⠒⢯⡃⠸⡃⡀⠀⠀⠸⢆⣀⡀⣤⡴⢲⠋⠻⠧⣨⠿⠊⠁⠀⠀⠀ ⣿⠀⠀⢱⠀⠀⠐⡧⠀⡇⠀⠀⠳⣄⢸⣇⡟⡏⣠⡝⠋⠁⢀⣿⣧⣶⣮⡞⢻⡆⣿⡙⣛⠓⢾⣧⠇⠈⠻⡄⢀⣾⢻⠏⠉⠀⣲⠣⣫⠀⣨⠇⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠈⠣⣀⣰⢇⣸⠟⠀⠀⠀⠈⠻⠬⠧⠟⠉⠀⠀⠀⠘⡇⡿⣿⡝⣠⣾⣇⣏⣛⠿⠟⢿⡿⠀⠀⠀⠹⡞⣇⡷⠀⠄⣰⢋⠀⠀⣰⡎⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢽⠟⠺⢿⡋⡸⣿⢿⢻⢯⡖⣿⣦⢤⢤⠀⠀⠘⢿⣱⣖⣿⠋⠁⠃⠠⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠾⠀⣌⢂⠀⠀⠈⢛⣿⠠⠔⠛⣷⡟⠔⣁⢅⢇⠀⠀⠀⠀⠀⢸⡄⠀⣀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡧⡛⠴⢻⢓⢕⡄⠀⠀⠼⠙⣶⡶⠾⣿⡀⠈⠁⣸⡀⠀⠀⠀⠀⠀⠉⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠊⢅⠞⠓⠶⡷⢅⣀⠑⢅⠟⣦⣀⠀⠀⢰⢻⢦⣹⣷⡄⠙⠊⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⣋⠀⠀⢰⡽⠀⢀⡭⠭⣛⠂⠬⣶⣄⠀⠀⢸⣿⣿⣦⡀⠴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣮⠃⣿⠟⠒⣧⢤⣋⢤⣪⠞⠷⣄⢈⢲⢋⢗⣺⣿⢿⣿⣿⣢⡖⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣼⢣⣣⠀⠈⠀⠹⢿⣁⡀⡞⠫⡾⡎⠈⣷⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣿⠟⠋⠈⠙⠳⣤⣄⣀⡙⣝⡾⣕⣬⣺⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣽⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡻⠁⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀