⠀⠀⢀⡀⠀⠀⠀⠂⠀⠀⢆⣠⣶⣶⢄⠰⡶⡄⠀⠀⣀⡀⠀⠀⠀⠀⢀⠄⡂⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠁⢸⠀⠀⠀⢀⠀⠉⢿⣿⣿⣿⣠⣽⣠⠀⠈⠾⣗⡀⠀⠀⠀⡂⠀⡇⠸⣇⠀⠄⠠⠈⠀⡠⠐⠈⠐⡖⣀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⠄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠁⠀⠀⠀⠈⢀⡤⢴⣿⣿⣿⣿⢋⣼⣿⢴⣢⣸⠁⠠⢁⣴⢜⠄⠇⠀⣴⡟⠐⠮⢄⠇⡀⡘⠀⢰⠶⠉⡛⢣⡆⠂⠛⠀⢀⢤⡴⢠⣬⣾⠆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⠀⡀⢀⣴⣿⣆⣼⣿⠉⠁⠠⠈⢔⠻⠀⠀⢣⣥⠇⠀⠀⡈⡙⡇⠀⠸⡈⠹⢪⣰⣴⠿⡿⣬⢼⠀⠺⠟⠉⠉⠀⠀⢠⠽⠀⠐⢢⡝⠁⠀⠀⣠⣦⣤⡄⠀ ⠀⠀⠀⠀⠀⠈⠪⣻⠟⠁⠙⢃⣤⠁⠀⣀⠀⡤⢠⠒⠀⢡⡄⠀⠚⠉⢋⣤⢀⠀⠋⡩⡀⡸⣅⠀⠱⠀⡀⠀⠊⡇⠀⠄⣤⠆⠸⠩⠂⠀⡔⠉⠁⠦⠀⢘⣿⢁⣥⠀ ⠠⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⣴⣄⠂⠀⠸⠠⠄⠀⢀⠄⠀⠰⠄⠛⠀⠀⢺⣦⡈⠋⠎⠓⠀⠀⠀⡀⠠⡨⠅⠀⠉⠀⡄⠀⠀⠀⢀⡰⠈⠀⢀⣀⡀⡈⠉⠀⠀ ⠀⠀⠐⠃⠀⠀⠀⠀⠀⠀⠀⠊⢮⡄⠈⡦⠀⡁⠀⠀⢈⠁⢐⣂⡀⠀⠀⠀⠀⠐⣾⣧⠀⠀⠀⠀⠀⠀⢈⣾⣴⣆⠀⠀⠀⠀⠒⠒⠀⢸⠃⠀⠐⠂⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠆⠀⣠⡷⠁⠀⠻⠇⠁⠀⠀⠀⠀⠀⠄⠀⠀⠀⠘⠀⠀⠀⠀⠀⠋⢀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠸⠆⠀⠈⠙⡠⣴⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⡻⠔⠀⡀⠊⢂⢔⠀⠀⠐⠆⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡐⠀⠄⠀⠀⠀⢀⣀⠂⠀⠀⠙⠑⠂⣀⣶⣾⢢⢀⠀ ⠀⠀⣀⡀⠀⠀⡀⠀⠀⠀⡰⠀⣴⢀⠀⠀⢘⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢸⠒⢰⠂⠀⠀⢀⡀⢀⠂⠀⠀⠀⠀⠀⠀⠔⠀⠀⠀⣠⢰⠤⠛⠁⡠⣊⠀ ⠰⣶⣦⠄⠮⢀⠁⠂⠼⡜⠃⠀⠈⠁⠀⠀⡙⣅⠁⠀⠀⢀⠀⠀⠀⠀⠀⠖⢖⠋⣀⠀⢰⣁⣈⣛⠐⢒⢀⡴⠈⠠⠤⠺⢤⡀⠀⠂⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢀⠁ ⢀⣻⡏⠠⠁⢈⢉⠻⠀⠁⠀⠀⠀⠐⠂⠂⠊⠉⠀⠀⠀⢠⠀⠒⠂⠀⠀⠀⠀⠀⠋⠀⠺⠀⠀⠭⠀⠊⠈⠁⠀⢐⡤⣀⣈⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠈⠂ ⢈⠛⠷⠦⣄⡋⣉⡃⠆⠀⠀⠘⠀⠁⠀⠀⠈⢀⡀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠶⠀⣀⡀⠸⠀⠀⠀⠀⣮⡑⢂⣨⠕⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠡⠀⠀⠈⢩⠛⠻⠷⢼⡀⠰⠀⠀⢐⡀⠁⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡿⠀⠀⡀⢀⠀⠀⠀⠀⠀⠀⠈⡀⠄⠖⠂⡈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠂⠀⠀⠐⠼⠨⠟⠃⠀⠀⢴⠁⠀⠀⠀⠀⠤⠀⠀⠀⡀⠄⠀⠀⠀⠀⠀⡇⠀⡤⠐⢚⡦⢠⠀⠀⠀⠀⢰⡅⠀⠄⠀⢁⡀⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⠔⠉⢀⠄⠁⠊⡏⠀⠈⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠐⠂⡀⠁⠀⠀⠀⠀⠀⠃⠂⠀⢱⡫⣠⡔⠘⠔⠀⢺⣷⠣⢀⠄⢈⠁⠃⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⢀⣀⢠⣴⣥⠆⠉⠖⠭⠆⠀⠀⠀⠀⢠⠤⠀⠀⠀⠀⠀⠀⠀⠀⢰⠅⠙⢁⠀⣀⠀⠀⠈⠀⠗⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⢦⠆⠃⠀⠀⠀⠀⠀⠀⠀⡀⠙⢿⣿⠃⠠⡖⠀⠁⠀⠀⠀⠀⠐⣩⣴⣀⡤⡤⣠⠤⠤⡀⠈⠂⠀⠀⢈⠀⠈⠀⠀⠀⠀⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠠⢤⠀⠉⠛⠃⠀⠀⡀⠀⠀⠀⠈⢈⠱⠀⠀⠸⢯⠛⠉⠁⠀⠀⠀⠀⠀⠚⠣⠀⣷⡟⢐⡯⠉⠁⣿⠀⠐⣄⡀⠀⠂⠀⠀⠀⢀⢤⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠂⠀⢀⡀⠠⢀⡀⠀⠀⠀⠀⢀⠐⠑⠊⠀⠀⠀⠀⢘⠀⠀⠈⠉⠀⠀⠀⠀⠀⢀⠀⠁⠓⠨⠱⣶⢞⣵⢫⠜⠲⡄⣵⡔⠀⠀⠀⠀⠀⣃⣠⣤⣤⡄⠀⠀⠀⠀⠀ ⢀⣂⣐⣀⣐⡐⡀⠀⠀⠀⠂⠀⠀⠁⡀⢀⢺⠁⠀⠀⠈⠰⢆⠠⠄⠀⠀⠀⠀⠀⣦⣦⣀⠀⡑⡩⣈⠰⢛⠵⠐⠒⢳⣿⣿⡆⠀⠀⣀⠀⢨⣿⣿⣿⣿⣆⡀⠀⠲⠀ ⠀⠉⠛⠿⢿⣿⣿⣿⣿⣿⣶⣖⡒⠤⠀⠀⡀⣀⠀⠀⠀⠀⠀⠐⠂⠀⠀⠒⠀⣸⡁⣈⡖⢂⡲⠆⠐⠀⠀⠀⠀⠀⢿⣿⣿⣿⣆⢘⡿⣶⣓⣿⣿⣯⢿⣿⡿⠐⠀⠀ ⠀⠀⠀⠀⠀⠾⠿⠿⠿⠿⠿⠿⠿⠃⠀⠀⠃⠓⠃⠀⠀⠀⠀⠀⠄⠀⠀⠂⠄⠋⠂⠀⠹⠀⠓⠢⠀⠀⠸⠽⠀⠀⠸⠿⠿⠿⠿⠂⠻⠿⠿⠿⠿⠻⠷⠉⠘⠤⠈⠀