⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⣀⡈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠤⠢⢄⠀⠀⠀⠀⢷⡛⠉⠈⢿⡲⢲⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢼⠀⠀⢀⡇⠀⠀⠀⡜⠑⢤⣤⡿⡇⠆⠀⢠⠉⠂⢄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠲⣾⢟⢅⡀⠀⡸⠀⠢⡀⠀⠰⠁⠈⠒⠚⢖⠲⠁⡸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠦⠣⡀⠉⡇⠒⢢⠳⡠⠐⠤⠤⠀⣀⡬⠃⠜⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠒⠤⠔⠁⢀⡸⠤⣇⠀⡀⠯⠄⠊⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠋⠑⢄⠲⢟⠒⢂⠍⠒⡹⡄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠃⠀⢀⣠⣇⠔⠣⣀⠔⠁⠀⢣⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠈⠂⠞⠁⠀⠀⠀⠀⠛⠣⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠁⢀⡜⠀⠀⠀⠀⠀⠀⠀⠀⡞⠂⢘⠇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡜⢠⠊⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠲⡅⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠎⠈⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠳⣄⣈⢦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⠭⠵⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠀⠀⠀⠀⠀⠀ ⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⡿⠋⠀⠀⠀⠙⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⣠⣤⣴⢦⣸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠴⠦⢤⡀⠀⠀⠀⠀⠀⠀⠘⣷⡞⠛⠉⠁⠀⢻⣿⡒⡖⠲⡦⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡾⠁⠀⠀⠀⢹⣆⠀⠀⠀⠀⠀⠀⢘⣿⣆⠀⠀⠀⢠⣿⣷⠀⡼⠁⠀⠈⢙⠦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⣧⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⣰⠋⠀⠈⠑⢶⣶⣿⠿⡿⠀⢄⠀⠀⠀⡏⠀⠀⠙⠲⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠷⣴⣾⣿⠻⣇⠀⠀⠀⠀⢀⡇⠀⠰⣄⠀⠀⠀⠀⢰⠁⠀⠈⠑⠤⠰⠷⣦⢤⣴⠊⠀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⡉⠑⡌⠓⠶⠤⢤⣼⣁⠀⠀⠈⣣⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠹⣶⠃⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠾⠛⢦⡀⠀⠀⢩⠀⠉⠉⣲⠋⢧⡀⠒⠓⢲⠢⠤⠤⠤⣀⣠⠴⠋⢀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⣠⠞⠁⠀⠀⠹⣄⢀⡞⠀⠀⠀⠀⣸⠋⠀⣀⠼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠋⠁⠀⠀⢀⣴⠚⠉⠙⠳⠤⣀⡤⠚⠉⠉⣀⠀⠀⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⠀⠉⠢⡀⠓⢷⡒⠒⠒⠊⣁⠤⠒⠒⠈⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠈⢦⠀⠈⣢⡀⠊⠁⢀⡠⠒⠉⠻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢴⡇⠀⠀⠀⣀⡤⢶⣿⠴⠋⠀⢻⡄⣴⠁⠀⠀⠀⠀⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠋⠀⠓⠂⣴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠓⠛⢧⡀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣦⡀⠀⢀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠈⠒⢋⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡯⣀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⡗⠠⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⢄⣠⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣅⠉⠈⠙⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⢀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣆⡀⢀⣹⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡯⠒⠒⢠⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠚⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣷⣾⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⡶⣶⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣾⠛⠁⠀⠀⠀⠀⠛⣗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⠀⣄⣰⡀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⣀⣼⣾⡶⠿⠉⠹⡾⣿⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⠾⠛⠛⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⡇⠀⠀⠀⠀⠀⠸⣿⢯⢹⠏⠉⣻⠛⠳⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣼⠇⠀⠀⠀⠀⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣽⡆⠀⠀⠀⠀⢀⣧⢾⢸⠀⣰⠃⠀⠀⠀⠉⣻⢦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⢀⣿⠀⠀⠀⠀⠀⠀⠀⢰⡿⠁⠀⠉⠓⢦⣤⣤⣾⣞⠾⡎⠀⣯⠀⠀⠀⠀⡸⠁⠀⠈⠙⠳⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣷⣀⣀⣠⣤⣚⣻⡟⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⡀⠀⠀⠈⠙⠛⠛⠁⣼⠃⠀⠘⠣⣀⠀⠀⣧⣀⡀⠀⠀⣠⠤⠈⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠛⠻⢾⣿⣆⡉⢳⣄⠀⠀⠀⠀⠀⣸⡇⠀⠀⠙⢦⡀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠈⠉⠉⠋⠹⣏⠛⣿⠃⠀⠀⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠙⣆⠈⠙⠛⠶⠶⣤⣿⣀⡀⠀⠀⠀⣽⡆⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⠏⠀⢀⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⠾⠟⢷⣄⠀⠀⠀⠈⡇⠀⠉⠙⠓⣶⠏⣿⡄⠠⠒⠛⠒⡦⠤⣤⣤⣀⣀⡀⠀⣤⠴⠋⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠟⠀⠀⢀⡾⠋⠀⠈⠙⣦⡀⠀⠀⡇⠀⠀⠀⠀⠀⢨⣿⠟⠀⠀⣠⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠻⠦⣄⣠⡴⠋⠀⠀⠀⠀⢀⣨⡷⣄⢾⡁⠀⠀⠀⠀⣀⣜⣁⡤⠤⠔⠋⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⣀⣾⣏⡁⠀⠈⠉⠛⠒⢤⡴⠊⠁⠀⢀⣠⡤⠄⠀⠸⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠋⠀⠀⠉⠳⣄⠈⠺⢅⡒⠒⠒⠒⠉⢉⣀⠴⠖⠒⠆⢨⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠃⠀⠀⠀⠀⠀⠈⢦⡀⠀⠈⠳⣄⠀⠔⠋⠀⠀⢀⡤⠖⠓⢮⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠃⠀⠀⠀⠀⠀⠀⢀⡤⡇⢀⣴⠖⠻⣦⠀⠀⣠⠒⠉⠀⠀⠀⠈⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠟⣿⠀⠀⠀⢀⣠⠴⠞⠛⠿⠿⠋⠀⠀⠀⠹⡇⢾⣆⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠈⠛⠂⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⢧⡀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⠀⠀⠀⢰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣦⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠙⠳⠤⠴⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⠀⠀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠤⢄⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⡏⠓⢒⣾⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣁⣀⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⠉⠛⠛⠉⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⠀⠀⠉⠉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢾⣵⣦⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⢀⠀⠀⢀⣴⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣗⡶⢶⣞⣽⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣊⣉⣉⣛⣫⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⣤⣤⣤⣤⣤⣤⣤⣤⣦⣤⣴⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤ ⣿⣿⣿⠿⣿⣿⣿⣿⣻⣿⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⢿⠿⠿⠿⠿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣷⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠒⠲⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣤⠤⠶⠤⠤⢤⣤⡜⢨⡷⠋⠑⢦⡀⠀⠀⢈⠇⣀⡀⣰⢋⠟⣆ ⠀⠀⠀⠀⠀⠀⣀⣴⠶⠺⢿⣭⣉⠀⠀⠀⠀⠀⠀⠀⠀⣷⠄⠀⠹⡷⢤⣍⡉⣻⠏⡴⢩⡟⡡⢋⢞⣽ ⠀⠰⡄⠀⢠⡾⠋⠀⠀⠀⠀⠈⠉⠛⠲⢤⣄⡀⠀⠀⠀⢻⠀⢐⡻⣆⡈⠉⣸⠋⢹⠃⠸⡆⠀⢿⢎⡜ ⠰⡀⠘⣦⠸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠒⠤⣼⣆⠻⣿⣿⣥⠞⠁⠀⢸⠀⠀⠸⠀⢠⠏⠀ ⠀⠹⣆⠘⣷⣜⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠙⢷⡶⠞⠁⠀⠀⡀⠈⡇⠀⠀⣰⠋⠀⠀ ⠀⠀⠹⣷⣌⢯⠳⣍⢻⣿⡛⠛⠛⠻⣿⠛⠛⠛⠓⣷⠀⠀⠀⠀⠹⣦⣤⣤⣤⣧⣀⣷⠀⠈⠈⢧⠀⠀ ⠀⠰⣄⡘⢯⡻⣷⣌⠛⢿⡙⢦⣄⠀⣿⠀⠀⠀⢼⢹⠇⣠⢀⠀⡀⢈⡷⠀⠀⠀⠈⠙⢳⡄⠀⠈⣧⠀ ⠀⠀⠈⠻⣿⣿⣮⡙⠷⣄⠙⠢⣌⠓⢿⣇⣀⠀⠈⠿⢴⣧⣞⣠⢃⡞⠀⣀⣄⡀⠀⠀⠀⣷⠀⠀⠘⣇ ⠀⠀⠀⠀⠈⠛⢮⣝⠢⢌⡙⠲⠌⠑⠂⠈⠙⠛⠶⢦⣤⣄⣸⣧⣾⣄⢸⡅⣀⣿⠀⢀⣼⠇⠀⠀⢠⡇ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠶⢤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠿⠛⣿⣿⠟⠓⠚⠛⠷⣤⣀⣠⠞⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠓⠶⠶⠤⠤⠤⠤⠤⠴⠶⠚⠋⠉⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠖⠲⠦⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠙⠻⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢳⠀⣠⣤⡀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀⣠⣤⣄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣶⠶⠾⠟⠛⠻⠶⠶⠶⠶⢾⠁⣼⡟⣁⡀⠙⢷⣄⣀⡀⠀⢠⠟⢠⣴⡀⣴⢓⡜⢹⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡶⠿⢿⣯⣍⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⠀⠀⠚⣿⣆⣀⡀⠀⠉⣿⠏⣰⠏⣸⡿⢁⠞⢡⢏⣼⡀ ⠀⠀⡄⠀⠀⠀⣠⣾⠟⠁⠀⠀⠀⠀⠉⠛⠻⠶⣤⣀⡀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠠⢴⡧⠀⠸⠛⢁⡾⠛⢶⡟⠀⣿⡀⠋⣴⣧⠏⣹⠁ ⣄⠀⠹⣆⠀⢰⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠓⠶⣤⣀⠀⠀⠀⣧⠀⡶⣦⣝⡦⡆⣀⡼⠃⠀⢸⠀⠀⠉⣧⠀⠘⢋⡼⠋⠀ ⠙⣆⠀⠘⣷⡈⢻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠶⣿⣄⠓⠯⡝⣻⡾⠋⠀⠀⡀⢸⡄⠀⠀⠿⠀⢀⡾⠁⠀⠀ ⠀⠘⣷⡀⠙⣿⣦⡹⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡀⠀⠀⠈⠻⣷⠶⠾⠋⠀⠀⠀⢀⡇⠀⣷⠀⠀⠀⣰⡟⠁⠀⠀⠀ ⠀⠀⠘⣿⣦⡈⣯⡻⣦⡛⢿⣶⠾⠶⠶⠶⠶⢶⣶⠶⠶⠶⠶⠶⢾⡇⠀⠀⠀⠀⠘⢳⣄⠀⠀⠀⠀⢸⡇⠀⣿⡀⠀⠘⠉⢷⡀⠀⠀⠀ ⠀⢀⠀⠘⢷⡛⢮⣳⡌⠻⣮⣿⡳⣤⡀⠀⠀⠈⣿⡄⠀⠀⠀⢀⣼⣷⡀⠀⠀⠀⠀⠀⠙⢿⡟⠛⠛⠛⠛⠳⢿⣇⡀⠀⠀⠘⣷⠀⠀⠀ ⠀⠈⠳⣦⣌⠻⣆⠙⢿⣦⡀⠙⢿⣌⠛⢶⣄⡀⢿⡇⠀⠀⠀⢸⣅⡿⠀⣸⠂⡴⠀⡴⠀⣾⠃⠀⠀⠀⠀⠀⠀⠉⢿⡆⠀⠀⠘⣧⡀⠀ ⠀⠀⠀⠈⠻⣟⡾⣷⣄⠙⠻⣦⡀⠙⠳⣤⠈⠻⢾⣿⣄⠀⠀⠀⠻⠧⢴⣧⣴⣃⣴⠁⣼⠋⠀⣀⣤⣀⠀⠀⠀⠀⢈⣷⠀⠀⠀⢹⣧⠀ ⠀⠀⠀⠀⠀⠈⠻⣮⣙⠻⢦⣀⠉⠳⢤⣀⠙⠢⢄⠈⠙⠻⢷⣶⣤⣀⣀⠈⠉⢿⣇⣼⡇⠀⢸⠋⠀⢸⣧⠀⠀⢀⣾⠇⠀⠀⠀⢸⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⢦⣌⣙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠿⠿⢿⣿⣿⣷⣼⣧⣶⣿⣃⣠⣴⣟⡃⠀⠀⠀⢀⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠶⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣂⣹⣿⠿⠋⠉⠉⠁⠀⠉⠛⠷⢦⣴⠿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⠛⠲⠶⠶⣶⣦⣤⣤⣶⠶⠶⠖⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⣀⠀⠉⠲⡀⠀⢀⣀⠀ ⠀⠀⠀⢀⡤⢤⣒⠒⠉⠉⠉⠀⢅⠊⢦⣑⠒⡤⡣⡢⡢⣙⡆ ⠐⡄⢴⠁⠀⠀⠀⠉⠒⠢⠄⣀⢸⢠⣵⣌⡱⠉⠃⢳⠘⡲⠁ ⠱⡜⢮⡣⣄⣀⣀⣀⣀⣀⡀⡄⠉⠳⡝⠋⠀⡇⡇⠀⢔⠁⠀ ⠠⡙⡮⣮⠪⣗⢄⠈⡇⠀⢠⡧⠀⡀⡈⡆⠀⠓⠻⡄⠈⢆⠀ ⠀⠙⠻⡦⢕⠮⣑⠍⡻⢤⣀⡓⠳⡕⡔⢡⠐⡄⠀⡸⠀⢸⠀ ⠀⠀⠀⠈⠑⠫⢤⣀⡀⠀⠀⠉⠉⠉⢟⣿⠞⠓⠚⠥⢤⠞⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀