⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣤⣶⢄⡿⢿⣭⣁⠴⡤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠤⡀⠰⠁⠀⠀⠀⠀⠀⠉⠓⢦⡀⠉⠛⢮⡊⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢄⠈⠋⠐⠒⡦⢤⣀⡀⠀⠀⠀⠈⢢⡀⠀⢳⡀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠑⠁⠐⠜⠉⠒⢄⡀⠀⠀⠱⡀⣈⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢠⢤⡀⠀⠀⠀⠀⠀⣀⣄⡉⠢⡀⠀⢳⠑⢦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢈⠍⠁⢖⠂⡤⡀⠸⡟⢀⣤⠄⡲⠂⠩⡙⢧⡌⢡⠒⠁⠲⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣇⠈⠤⠠⠜⠒⠛⠧⠜⠳⠬⠟⠉⠣⠄⠤⢁⣹⠉⠹⣀⢀⣠⠃⠀⠀⠀⠀⠀⠀⠀ ⣠⠴⠒⠲⢦⣄⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⠀⠀⠘⣀⠜⢷⡀⠀⠀⠀⠀⠙⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠦⣄⡀⠀⠀⠐⢳⠀⠀⠀⢀⡾⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢢⡀⠐⠚⡇⠀⠀⡾⠃⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢣⠀⠀⣷⠀⢸⠃⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠺⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡄⠀⣿⠀⡿⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢱⠀⢸⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢇⠈⢿⡇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠃⠀⠀⠀⠰⡀⠀⠀⠀⡆⠀⠀⠀⢠⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⢳⠀⠀⠀⡇⠀⠀⠀⠎⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⠤⠤⣕⣀⣄⢇⣀⣀⠞⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⡟⣷⠀⠀⣀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢧⠀⠀⠀⡏⠎⡇⢠⢒⡆⡶⠢⡶⠢⢰⠀⢰⠀⡇⠀⠀⣇⡀⡶⠢⢨⠀⢔⠌⡋⢡⢤⣄⢀⠤⣠⠀⢔⠄ ⠀⠀⠈⣇⠀⠀⠃⠀⠘⠈⠒⠂⠘⠀⠘⠀⠀⠉⡎⠀⠀⠑⠒⠘⠘⠘⠀⠀⠃⠐⠊⠘⠀⠃⠃⠃⠑⠊⠃⠐⠊ ⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣤⣶⢄⡿⢿⣭⣁⠴⡤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠤⡀⠰⠁⠀⠀⠀⠀⠀⠉⠓⢦⡀⠉⠛⢮⡊⢂⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢄⠈⠋⠐⠒⡦⢤⣀⡀⠀⠀⠀⠈⢢⡀⠀⢳⡀⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠑⠁⠐⠜⠉⠒⢄⡀⠀⠀⠱⡀⣈⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⢠⢤⡀⠀⠀⠀⠀⠀⣀⣄⡉⠢⡀⠀⢳⠑⢦⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⢈⠍⠁⢖⠂⡤⡀⠸⡟⢀⣤⠄⡲⠂⠩⡙⢧⡌⢡⠒⠁⠲⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣇⠈⠤⠠⠜⠒⠛⠧⠜⠳⠬⠟⠉⠣⠄⠤⢁⣹⠉⠹⣀⢀⣠⠃ ⣠⠴⠒⠲⢦⣄⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠈⠀⠀⠀⠀⠀ ⡇⠀⠀⠘⣀⠜⢷⡀⠀⠀⠀⠀⠙⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠦⣄⡀⠀⠀⠐⢳⠀⠀⠀⢀⡾⢁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⢢⡀⠐⠚⡇⠀⠀⡾⠃⠀⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⡉⠘⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢣⠀⠀⣷⠀⢸⠃⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠐⠺⡆⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⡄⠀⣿⠀⡿⠀⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⡈⢳⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢱⠀⢸⣰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢇⠈⢿⡇⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠃⠀⠀⠀⠰⡀⠀⠀⠀⡆⠀⠀⠀⢠⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣀⠀⠀⠀⠀⢳⠀⠀⠀⡇⠀⠀⠀⠎⠀⢀⡴⠃⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠒⠠⠤⠤⣕⣀⣄⢇⣀⣀⠞⠒⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣀⡤⠶⠭⠿⠖⢦⣄⣸⣿⣿⣿⡆⠀⠀⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣐⡷⣏⠥⣒⣂⢢⠢⣠⣀⡤⠙⠛⠁⠀⠀⣼⣿⡗⠀⠀⠀⠀ ⠀⠀⠀⣠⠟⠀⠘⠿⠿⠶⠷⠾⠉⢻⡅⠀⠀⠀⠀⠀⣧⣿⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣴⣦⣤⣤⣤⣿⢿⣄⠀⠀⠀⠀ ⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠉⢷⣄⠀⠀⠀⠙⣷⡴⠶⣦ ⠀⠀⢱⡀⠀⠉⠉⠀⠀⠀⠀⠛⠃⠀⢠⣇⢠⡿⣇⣀⣀⣠⣤⠿⠞⠛⠋ ⣠⠾⠋⠙⣶⣤⣤⣤⣤⣤⣀⣠⣤⣾⣿⣴⣯⠛⠿⣗⣯⡀⠀⠀⠀⠀⠀ ⠛⠒⠛⠉⠉⠀⠀⠀⣴⠟⢃⡴⠛⠋⠀⠀⠈⠻⣖⡀⠈⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀