Cursed Dot Art

⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠤⠤⠤⠖⠒⠶⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⣠⠞⠉⠉⠀⠀⠀⠀⠀⠀⠀⣀⠀⠉⠙⠲⢤⣀⠀⠀⠀⢀⠀⠀⠀ ⠀⠘⣿⣉⣿⣿⣿⣷⣤⣀⡴⠃⠀⠀⠀⠀⢀⣠⠶⠛⠛⠛⠶⣤⣀⣀⣠⣶⣾⢿⣦⣠⣾⣿⣷⡆ ⠀⠀⠙⠛⠛⠛⠛⠋⢹⡟⡁⠀⠀⠀⠀⠀⣸⣷⣿⣿⣿⣿⣷⣶⡎⠉⠙⣿⣿⣿⣿⡿⠿⣿⣿⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⡧⠇⠀⠀⠀⠀⣸⣿⠏⠉⢀⣤⣤⡄⠙⢿⡀⢠⣿⢋⣥⡽⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⣿⡖⡄⠀⠀⠀⠀⣿⠇⠀⢰⣿⣿⣿⣿⡄⢸⣧⢸⡇⢸⣿⣿⣷⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⡁⠀⠀⠀⠀⢻⣧⠀⠈⠻⠿⠿⠋⢀⣿⡇⢸⣇⠸⠟⣁⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⣆⡀⠀⠀⠀⠛⣿⣶⣶⣶⣶⣾⣿⠿⠃⠈⣿⣿⣿⡿⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣼⣄⠀⠀⢈⣿⣿⣦⣀⠀⠀⠀⡉⠉⠉⠉⠉⠁⣴⣾⣿⡏⠀⣼⣁⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⡾⠿⠿⠿⠾⠛⠛⠛⠛⠛⠳⠶⣾⠁⠀⠀⠀⠀⠀⠛⠿⠋⠀⡾⠷⠛⠉⠛⠃⠀⠀ ⠒⠒⠿⣿⣯⣤⣤⣤⣄⣀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠙⢿⣿⣿⣿⣿⣿⣿⠻⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⢿⡄⠀⠈⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⣀⡤⠤⠔⠒⠲⣾⣿⣽⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⢀⣀⣴⠞⠁⠀⠀⠀⠀⠀⠀⠙⠻⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣿⡍⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠿⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣰⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠤⠤⠤⠤⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⠔⠊⠀⠀⠀⠀⡠⣄⠀⠀⠉⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⢣⠀⠀⠀⠀⠀⠸⣷⡿⠃⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡜⠿⢏⡀⣈⣀⣀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡇⠀⠀⠀⠹⡀⢶⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⢄⠀⠀⠀⠱⢇⡹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣑⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢⡹⢳⡀⠀⠘⠄⠀⠀⠀⠀⠀ ⣀⡆⡂⠉⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⢼⠰⠁⠀⠀⠈⢂⠀⠀⠀⠀ ⢾⣭⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⠀⠀⠀⠀⠀⠀⠀⠡⡀⠀⠀ ⠀⠀⠀⠉⠉⠀⠐⠒⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⣂⠀⠂⠈⢀⠤⠐⠒⠂⠤⢀⡀⠀⠀⠀⣀⡜⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣩⡇⠀⠀⠀⠀⠀⠀⠀⠀⠉⢧⡠⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢑⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⡋⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡤⠖⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⠳⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠚⠁⠀⠀⠀⠠⣤⣶⡀⣠⢀⣦⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠉⠀⠀⠀⠀⠀⠀⠀⠹⣯⣷⣰⣿⣿⣯⢃⣽⣷⠀⠈⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣫⣤⡶⠀⠀⠀⠀⠀⠀⠀⠠⢾⠉⠀⠀⠀⠀⠀⢀⣀⣀⠤⠼⡘⣿⠟⠁⠈⣿⣾⢟⡁⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⠊⢁⣠⣞⣉⣠⣤⠄⠀⠀⠀⠀⠀⢀⣈⣷⠀⢀⣠⠴⠚⣉⣁⣀⣀⣀⡀⠈⣀⣈⣁⡚⠃⠈⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠚⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠐⢦⡀⠈⢿⣤⣿⣧⣤⣤⣤⣤⣤⣦⡶⣶⣶⣶⣤⣤⣬⣙⠓⠂⢤⣦⡀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣿⡟⠘⢿⣿⣿⠟⠻⢿⣿⣿⣄⠀⠀⠀⠀⢉⣿⣿⣦⣤⡀⢳⡄⢠⡇⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠦⠀⠀⣿⠀⠀⣀⣿⡆⠀⠀⢀⡈⠻⣿⣿⡀⣠⣶⡿⠿⠛⢿⣿⣿⣿⣷⡾⠁⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⣧⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⢀⣾⡃⢀⡀⠈⠉⠙⠲⠶⣿⣇⣠⡾⠉⠀⠈⠹⣾⠀⠀⢸⡿⠁⣿⠟⣁⣰⠟⢈⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⠏⠸⣧⡀⠀⠀⠙⠦⣀⠀⠀⠀⠀⢀⣀⢴⡟⠋⢳⣶⣿⣿⣷⣿⣷⡄⢀⣠⣄⠖⠀⢀⡏⠀⠀⠀⠀⠀⠘⠤⠖⠛⠀⠸⣿⣠⡟⣧⡀⠈⣅⣉⠖⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡟⠀⠀⠘⠻⣦⣄⠀⠀⠈⠛⢢⡴⠒⠋⠁⠸⣧⠀⠸⣿⠛⠿⢿⣿⢿⣿⣿⣿⣿⣷⣄⣼⠁⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⣨⣿⢀⡼⠓⠚⢩⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡁⠀⠀⠀⠀⠈⠙⠛⠓⠒⢶⣏⠀⠀⠀⠀⠀⠙⠳⢾⣿⠀⠀⢸⡿⠀⠛⠛⠉⠙⢿⣿⣿⣦⣤⣀⡀⢀⢀⣴⣶⣿⣿⣷⣾⣿⣿⡟⠀⠀⠀⠈⣿⣿⡃⠀⠀⠀⠀⠀⡠⠂ ⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⠏⠙⠋⠛⣶⣤⣤⣤⣿⣦⡀⢾⣷⣀⠀⠀⠀⠀⠠⡭⠀⠀⠈⠙⠛⠛⠛⠿⠟⠛⢻⣿⣟⠉⠋⠈⠛⠛⢲⡾⣿⣿⣍⡛⠓⢒⣲⣿⣤⡆ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠶⠚⠉⠀⢀⣤⠞⠋⠙⠙⢷⣦⡀⠉⠳⠤⣀⣀⣀⡀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠐⢺⣿⠿⣧⡀⠀⠀⠀⠀⠀⠈⢻⣎⣉⡿⠋⠉⠀⣼⡇ ⠐⣿⡀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⠁⠀⠀⠀⣰⠞⠁⠀⠀⠀⠀⠈⢿⣿⣶⣄⠀⠈⠉⠉⠉⠳⣶⣦⣄⣀⣀⣀⣀⠠⠴⠋⠀⣠⠏⠉⠀⠀⠀⠀⠀⠀⠀⠿⡇⠀⠰⢠⣀⣾⠀ ⠀⢹⢧⠀⡀⠀⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠈⠿⡙⢿⣿⡄⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠀⠀⠀⢀⡴⠋⠀⠀⠀⢀⣤⣀⣤⠞⠀⠀⠁⣤⢸⣿⣿⠃⠀ ⠀⠘⣿⠀⠀⠱⣤⠄⠉⠁⠀⠀⠀⠀⠀⠀⠘⠣⣄⣀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠙⠻⠶⣦⣤⣤⣤⣤⣤⣀⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⢰⣿⡿⠁⠀⠀⠀⠀⣿⣿⡿⠁⠀⠀ ⠀⠀⠹⣷⡦⡀⠈⢿⣷⣦⣤⣀⠀⠀⠀⠀⠀⠀⢿⣿⣄⠀⠀⠀⠀⠀⠀⠘⢧⣄⠀⠀⠀⢀⣠⣌⣗⠈⠙⠛⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⣼⣿⠃⠀⢀⣠⡴⠞⠛⠉⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠳⢤⣈⠻⣿⣶⣿⡻⢦⣄⠀⠀⢰⣶⣿⣿⣷⣷⣤⣄⠀⠀⠀⠀⠈⠙⠛⠛⠋⠀⠀⠉⢻⣛⠛⠋⠁⠀⠀⠀⠀⠀⠀⣀⣾⣿⣿⣿⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠙⠾⠿⣿⣿⣷⣯⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⠙⢷⣄⠀⠀⠀⠀⣀⣴⣾⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⢸⣿⡟⠻⠿⢿⣿⣿⣿⣷⣝⢶⣾⣿⡄⠀⠀⣠⣶⡷⠟⠉⣀⠈⠛⠻⠶⢶⣿⣿⣿⣿⣿⣿⣿⡟⠀⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠷⣦⣀⠀⠙⠿⣏⠛⢿⣷⠾⢿⣿⡓⠒⠚⠁⠀⠀⠀⣹⡀⠀⢀⣀⣠⣶⣯⡶⢺⣿⡿⢻⣡⠔⠛⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣷⣄⠉⠛⠲⢤⣬⡑⠸⡝⢷⡄⠘⢿⠳⢶⣤⡤⠔⠒⣿⡿⠋⠉⠉⠉⠛⣿⣡⣾⣿⢡⣿⣿⣠⣾⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡋⢷⡙⠻⢷⣦⣤⣈⢿⣄⠀⣷⡙⠦⣌⡛⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⣀⣀⣿⣿⣽⣧⠈⣿⣿⠿⢛⣿⣻⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣦⣍⣀⡀⠀⠀⠙⢿⣿⠀⢿⠻⣦⣈⣿⣆⣀⣀⣀⣀⣸⡷⣀⣤⢾⠿⢿⢿⣿⢿⣏⣼⣿⣷⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣷⣶⣶⣤⣿⣧⣸⣆⣈⡙⣿⡉⠉⠉⢉⣹⣿⣿⣏⣆⣀⣀⣼⣿⣿⠿⡟⠉⠉⠹⡿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⣿⣿⡟⠛⠿⠉⠙⢻⣿⣿⣯⣿⣿⣿⣾⣯⣿⣿⣿⣿⣿⣟⣹⣿⣯⣿⢉⡛⠀⠀⢀⣠⡾⢟⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠻⠿⣄⠈⠉⢁⠀⠀⠠⢶⣾⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⣇⠰⠛⢋⡥⠀⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠘⢿⣦⣀⠀⠀⠀⠀⠀⠀⣹⣟⣻⠛⠛⠛⠿⢿⣿⣿⣿⣿⣿⠿⠿⠯⠟⢹⣗⡿⢀⣼⠟⠁⠀⠠⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⡇⠀⠀⠀⠈⢿⡆⠑⣦⣀⡀⠤⣀⠘⠷⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⠛⣻⡿⠋⠀⠀⢣⣶⣶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠛⣶⡬⠹⠦⠤⠀⠀⠀⠀⠀⠠⠴⠶⠶⠛⠉⠉⠀⢀⣶⣿⣧⣶⣶⣶⠾⠟⢉⣄⣀⣀⡀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠖⠒⠒⠒⠒⠒⠒⠦⠤⠤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠖⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⢤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⢤⣄⡀⠀⠀⠀⠀⠀⠀⠈⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⠀⣼⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣫⠞⢳⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡾⣽⣿⣤⡾⠁⠀⠀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠉⣿⣿⡿⠃⠀⠀⠀⠈⠀⠀⠀⠀⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⡇⠀⠉⠉⠀⠠⢤⣤⣴⣶⠒⠒⠒⠒⠛⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⢀⣶⣦⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡀⠀⣹⣿⢛⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣼⠏⠚⠏⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠻⢦⣄⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⡿⡞⢉⣏⠉⠁⠀⠀⠀⠈⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠛⣡⠙⠋⢻⣶⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣀⡤⠶⠚⠉⠉⠀⠀⠀⠻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠛⠟⠉⢨⡎⠈⣾⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡿⠚⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⠚⠀⣶⣿⠀⡸⠟⠀⠀⠀⠀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣯⡭⢡⣶⠚⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠉⠹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀⠀⠀⠀⠀ ⢸⣏⣳⣀⠙⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀⠀ ⠀⠸⠿⠷⠤⢤⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣆⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠙⠛⠛⠓⠒⠒⠾⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠊⠀⠀⠀⠀⠀⠀⢠⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⡀⡀⠀⠀⠀⠀⠀⠀⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢮⡓⠖⠀⠀⠒⠊⠀⠀⠀⠀⠀⣀⣤⠴⠖⠒⠒⠒⠶⠦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡾⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠤⣄⣀⣀⣀⣀⣤⣴⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠲⠤⠤⠤⢤⣤⣤⡤⠴⠞⠛⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⣍⢩⣭⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠄⣄⠠⣤⣿⡆⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣻⡈⢯⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣻⡀⠹⡏⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠳⠼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣤⡟⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⣀⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣀⡀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⣿⠟⡡⢫⣿⣟⣿⠏⠈⢏⠙⣿⣿⣿⣿⣷⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⣟⣿⣿⠏⣰⢡⣿⣿⢟⣸⠀⡀⠈⡆⠈⢿⣿⣾⣿⣿⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⣾⣏⣽⣟⣾⣿⡏⢀⣧⣿⣿⠏⡜⡇⠀⠘⢆⠈⡄⠈⣿⣿⣿⣿⣿⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⣿⣿⡟⣾⣿⣿⠀⢸⢿⣿⣿⡄⢰⠁⠀⠀⠀⢧⠘⡄⢸⣿⣿⣿⣿⣿⣴⠀⠀ ⠀⠀⠀⠀⠀⣿⣿⡿⠁⠋⣸⢿⠔⢻⡿⣿⠋⠀⡞⠀⠀⠀⠀⠀⠀⠘⢾⣿⣿⣿⣿⣿⣿⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⠇⠀⣀⣿⣠⣔⠉⠠⠃⠀⢰⠃⠀⢀⣀⣤⣤⣆⠀⣼⢿⣿⣿⣿⣿⣾⡀⠀ ⠀⠀⠀⠀⢾⣿⠏⣴⣿⠟⠛⠿⣿⣿⣆⠀⠀⠈⠀⣶⣿⠿⠛⠛⠻⣷⣴⠀⢹⣿⣿⣿⡿⠵⠀ ⠀⠀⠀⠀⢸⣿⠀⣿⣇⢸⣿⣿⠎⣿⣿⠀⠀⠀⢸⣿⡏⣠⣶⣶⡀⢸⣿⠀⠀⣿⣿⣿⣿⠀⠀ ⠠⠤⠤⠤⢼⣿⡄⠘⣿⣦⣭⣽⣿⡿⠟⠀⠀⠀⠸⣿⣿⣼⣿⣟⣽⣿⠏⠀⢰⣿⣿⣿⣿⡘⠀ ⠀⠀⠀⠀⢸⣿⣧⠀⠈⠻⣿⠿⠋⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⠟⠁⠀⢀⣿⣿⣿⣿⣿⡇⠀ ⠀⠀⠀⠀⢸⣿⣿⡦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⢀⣰⣿⣿⣿⣿⣿⣿⠇⠀ ⠀⠀⠀⠀⢻⣿⣿⣧⠀⠀⠀⠀⠀⠀⣠⣤⣤⣤⡀⠀⠀⠀⠀⣰⡶⢻⣿⣿⣿⣿⣿⣿⣿⣧⠀ ⠀⠀⠀⠀⣾⣿⣿⣿⣷⢦⡀⠀⠀⠀⠻⠟⠛⠿⠙⠂⠀⣠⠞⣉⡴⣫⣿⣿⣿⣿⣿⣿⣿⡇⡆ ⠀⠀⠀⢠⣸⣿⣿⣿⣿⣄⠙⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⣡⡾⢋⣼⣿⣿⣿⣿⣿⣿⣿⣿⣧⠇ ⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣦⡈⠻⣦⣄⣠⣄⣀⣠⣿⠟⠁⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣦⡈⠙⠛⠛⢛⣉⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣦⣙⣛⣋⣠⡶⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠈⠉⠉⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡇⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⣿⣿⡟⣿⣿⣿⣿⣿⣿⣿⡇⡇⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⣿⣿⡷⣿⣿⣿⣿⣿⣿⣿⣧⡅⠀⠀ ⠀⠀⠀⢠⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣧⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣷⡄⠀ ⠀⠀⠀⠀⣿⢻⣿⣿⣿⣿⣿⣿⡿⠛⠾⣿⣧⡀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⡄ ⠰⡀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈⠹⢷⣤⣤⠴⠟⠛⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡹⡇ ⠀⠑⡄⠀⣿⡇⣽⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠙⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡿⢷⢃⢙⡇ ⠀⠀⠀⠀⠘⠧⢿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡇⠘⢿⡾⠻

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⢀⠀⠀⠀⠙⠛⠿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣶⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⠷⠒⢦⣀⡴⠋⠁⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢹⠁⠀⠀⠀⠀⠀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⢠⡇⢠⡄⠀⢀⣈⠀⢠⡄⠀⣰⡆⣸⣿⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣦⣾⣿⣿⣧⣾⣿⣿⣷⣾⣿⣷⣿⣿⣿⣿⣷⡿⠃⠀⠀⠀⣴⡆⠀⠀⠀⠀⠘⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠼⢻⠿⠿⣿⢿⣿⠿⠿⠿⡿⣿⡿⠿⠿⠿⠿⠿⡟⠁⠀⠀⠀⠘⡟⠳⡄⠀⠀⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢤⡀⡰⠋⢀⡎⠀⠀⠘⣆⠉⠀⠀⠀⢱⡌⠁⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⢳⡀⠘⣆⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⢠⠖⠛⠻⣄⠀⠙⢷⠀⠸⡅⠀⠀⠀⠈⠳⠄⣀⠠⠞⠙⠢⢄⣀⣀⠴⠃⠀⠀⠀⠀⠀⠀⢠⠃⠀⡿⠁⠀⣠⠏ ⠀⠀⠀⢀⡖⠋⠻⣆⠀⠀⠹⡄⢀⡈⠀⠀⡇⠀⠀⠀⠀⢠⠗⠉⠉⠉⠉⠉⠒⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢡⣤⣠⠏⠀ ⠀⣠⠶⠼⣇⡀⠀⠹⣶⠀⠀⢻⣯⠑⢄⠀⢹⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠠⠀⠂⠙⢦⡀⠀⠀⠀⠀⠀⠀⡏⠀⡰⠁⣿⠏⠀⠀ ⢰⣿⣄⠀⠈⢷⡀⠀⠹⣷⣠⠤⢿⣧⢮⡆⠈⡆⠀⡼⠈⠀⣀⣼⣶⣒⡖⢲⣦⣄⠀⠐⢝⣆⠀⠀⠀⠀⢸⠁⠸⣹⣾⠟⠀⠀⣰ ⢸⣿⣿⣿⣄⣈⠻⣦⣔⠛⣿⣇⡀⡛⢷⣗⣠⡇⠀⢗⢒⠏⠁⢀⢀⣀⠀⠀⠀⠀⠉⠑⣺⣿⠀⠀⠀⠀⢸⠠⣮⡿⠋⢀⣴⡾⠃ ⠸⡏⢻⣿⣿⣿⣧⣹⣿⣆⠘⣿⣗⠐⡀⠀⠀⡇⠀⠈⡆⠀⠀⣀⣐⠚⠀⠀⡀⠀⢤⡺⠟⠁⠀⠀⠀⠀⢸⠀⠀⠀⠠⣾⡟⠁⣠ ⠀⠿⠯⠄⠀⠈⠙⠻⠿⠿⡦⠈⠻⢦⠜⠒⠒⢧⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡼⠒⠉⠱⡶⠟⠀⡴⠿

⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠉⠢⠁⣌⣠⠶⠛⠉⠁⠀⠀⠀⠀⠀⠈⠉⠙⠻⢶⣤⣀⣀⠀⢀⡠⢄⠀ ⠀⠀⠀⢣⠀⣼⠟⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠣⠀⠑⠊⢀⠏⠀ ⠀⢀⡀⢠⣿⠃⠀⠀⠀⠤⠤⠞⠁⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠑⣦⡤⠊⠀⠀ ⢋⢀⢃⣿⠷⠒⢉⣿⣿⣿⢷⠶⣦⠀⠀⠀⠙⠦⣄⣀⡀⠀⠀⠀⠀⠘⣿⡀⠀⠀ ⠀⠁⡸⡿⡄⠀⠈⣿⣿⠧⣀⣠⡟⢰⢶⠶⠶⣶⣤⣤⣀⡀⠀⠀⠀⠀⢹⡇⠀⠀ ⠀⠀⢸⡇⠳⡀⠀⠘⢿⣷⢋⠜⠁⠸⡙⣄⣠⠿⣿⣿⣿⣿⠏⢲⠀⠀⢸⣇⠔⡄ ⢸⠑⠁⣥⠐⡍⠂⠤⠔⠛⠁⠀⠀⠀⠳⣿⣿⣿⡿⠟⣛⠏⡠⠋⠀⢠⠀⠁⡰⠃ ⠈⠢⠎⢿⡄⠈⠔⠁⠀⠀⠘⠒⠒⠜⠀⠈⠛⠻⠦⡞⠒⢋⠀⠲⠀⢠⣦⠔⠁⠀ ⠀⠀⠀⠈⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠙⠄⠀⠃⠀⡰⡻⠁⣀⠁⠀ ⠀⠀⠀⠀⠀⠹⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣞⠙⢄⠊⢠⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⠻⢶⣤⣄⣀⣀⣀⣀⣀⣀⣠⣤⡶⠟⠋⠈⢆⠀⢠⠊⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠛⠛⠉⠉⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠙⠲⣄⣠⡶⠛⢶⠀⣰⠃⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠛⠛⢿⡛⠛⠶⠦⢴⣷⣾⣆⡀⠀⣼⡟⠀⠀⢸⣷⠃⠀⠀⢳⢠⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠈⠉⠛⠻⠿⣦⣤⣀⢸⡇⠀⠀⠀⠸⠋⢸⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣼⠋⣼⡷⠀⠀⣀⠀⠘⣧⠀⠀⠀⠀⣀⣤⡶⢦⣄⣸⡏⠙⠻⣷⣤⡀⠀⠀⢀⣼⠟⠋⠉⠹⣆⠀⠀⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢰⡇⠀⠉⠀⠀⢿⠟⠀⢰⡇⠀⠀⠀⣴⡟⠁⣤⡀⠘⣿⡇⠀⠀⠀⠉⠻⢷⣴⡟⠁⠀⠀⠀⢠⣟⡠⠚⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⢀⣰⡟⠀⠀⠀⠀⠻⣧⡀⠉⠀⣠⡿⠁⠀⣠⣶⠶⢿⡛⠙⢿⣄⠀⠀⣠⣿⠁⠀⣸⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠛⠶⣤⣤⣤⠶⠟⠋⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠋⠀⠀⣾⠋⠀⣤⡀⠈⣧⠀⠹⣷⣴⠟⠁⠀⣰⣃⣠⣤⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠦⣴⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠈⠛⠁⣠⡿⠀⠀⠸⣿⡀⠀⠈⠉⣠⠞⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠶⠞⠋⠀⠀⠀⠀⢻⡇⠀⢠⣞⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣴⠛⢷⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠈⠳⢄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⢀⣾⡏⠀⢸⡆⠀⠀⠀⠀⠀⠀⠠⣉⣶⣶⡖⠃⠀⠀⢠⣿⢳⡒⠒⠒⠒⠚⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣷⡀⠀⠀⠀⠙⠷⣤⣤⠇⠀⠀⠀⠀⠀⢀⡾⠟⠙⠢⠀⠀⠀⢠⣾⣯⣀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡉⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡀⠴⠒⠚⠋⣩⣿⣶⣤⣖⣿⣿⣿⣿⡿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠟⠋⠈⢻⣄⠀⠀⢀⣠⣴⣶⣶⣿⣓⡒⠦⣄ ⣀⣰⡞⢋⣽⣿⣩⠿⠻⣧⣽⣿⣿⣿⣿⣷⣄⠉⠛⠛⠷⠶⢶⣶⣶⣶⣶⣶⣿⡿⠛⠉⠀⠀⠀⢀⣼⣿⣇⡞⢹⠟⣿⠶⢤⣀⠀⠀⠶⠠ ⠀⠉⢡⣿⣥⠟⠻⣄⣠⡼⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠉⠻⣿⣿⡿⠉⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣠⠟⣳⣯⣄⡼⠉⢻⣦⠀⠀ ⠀⠀⠘⢿⣿⣦⣠⠟⢿⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠈⠋⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣟⣶⣯⣠⡿⠛⣶⣏⡼⠇⠀ ⠀⠀⠀⠀⠙⣿⣿⣴⣛⡽⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⢠⣶⣿⣿⣿⣿⣿⣿⣿⣿⠻⣧⣠⡟⠛⣾⣯⣾⡛⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⠛⠉⠀⠀⠹⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠙⠛⠿⠷⠿⠟⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⢀⠀⠀⠀⢰⡆⠙⢿⣿⣿⣿⣇⠀⠀⣠⠞⠋⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣟⠁⠀⠀⠀⠀⢀⣴⣿⣷⣄⠀⢸⣇⢀⣤⡿⠋⠀⠙⠷⠤⢿⣶⡚⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠻⢷⣶⣤⣴⣿⣿⣿⣿⣿⣷⣾⡿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠉⠉⠉⠉⠉⠉⠁⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢿⣿⣿⣿⣿⡿⠇⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣻⣿⡷⣞⣿⡽⣿⣯⡽⣾⣟⡾⣽⡿⣟⣾⣟⣽⣻⣷⣟⢷⣻⢿⣯⣟⣽⣻⢾⣿⣟⢯⣷⣟⢯⣽⢿⣾⡿⣯⣷⣟⣯⢿⣷⢯⣷⢯⣿⡷⣽⣾⣻⣷⣾⣟⣳⣿⣯⣟⢷⣻⣽⡿⣟⣯⢾⣿⣯⣷⣟⣷⣟⡽⣻⣾⣽⢿⣽⣻⢿⣷⡽⣿⣟⡾⣻⣽⢿⣻⣾⣽⣻⢿⣯⣿⠒⡿⣿⡹⢿⣟⣿⣿⣧⢻⠉⡇⣿⢿⡻⣿⣯⣾⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢾⣻⣾⣽⢾⣿⢯⣾⣟⣯⢿⣷⣯⣞⡿⣟⣯⡿⣟⣷⡿⣯⣟⡾⣻⢿⣯⡿⣟⢷⣻⣿⣯⣟⣯⡷⢿⣯⢾⣽⣿⡾⣽⡿⣳⣾⣽⢿⣻⣿⡿⣿⣿⣶⣿⣿⣻⣽⢾⣻⣿⢯⣿⣞⡿⣯⣟⢾⣿⣯⣳⣿⡷⣟⢾⣿⣯⣞⡿⣟⡾⣻⣷⡽⢿⣷⣟⣯⡽⢿⣷⣯⣞⡿⣟⣯⣾⡟⣻⣼⣉⣤⣿⣿⣿⣿⣿⢙⡄⣤⣶⣶⣴⠀⢀⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣳⣿⣟⣽⢿⣽⣾⣟⣯⡾⣽⣻⣽⢿⣽⢿⣯⡿⣯⡿⣳⢿⣯⣽⡾⢿⣯⡾⣻⣽⡿⢾⣻⣷⣽⡿⣳⣿⣟⢾⣽⣿⡿⣿⣿⣾⣿⣶⣤⣄⡀⠂⠐⠀⣦⣿⣽⣿⣻⢷⣻⢿⣷⣯⣟⡷⣟⢾⣽⣿⡷⣯⢿⣯⢷⣾⣟⣻⢿⣷⣟⣻⣷⡿⣯⣞⢿⣯⣟⣽⣻⣽⢿⣽⣻⣿⣳⣿⣞⣿⣿⣌⣿⢻⣿⣿⣿⢻⡿⡿⣿⡿⢿⠙⡌⣿⣿⣿⣿⣿⣿⣿⡟⣿ ⣽⣾⡿⣞⡿⣟⡾⣽⣻⣷⣟⣽⡿⣯⣟⡽⣾⣟⢯⣷⡽⣿⢯⣻⣽⣾⣟⢾⣿⣟⣯⡷⣟⣽⣾⡿⣞⣿⡽⢿⣿⣿⣷⣴⣢⣄⢀⠒⠂⢀⡂⠄⠀⡀⠀⠠⡀⣶⣿⣿⣻⣽⡿⣯⣞⡿⣯⢷⣽⣻⣿⣿⣷⣿⣿⣻⣷⣻⢾⣻⣾⡿⣟⣯⡿⣳⣽⣾⣟⢯⣷⢯⣾⡿⣯⣟⡽⣿⡽⣾⣻⣽⣿⢾⣿⣬⣷⣾⣄⣠⣄⣤⣤⣤⣿⣼⡶⣿⣿⡘⣟⣿⣿⣿⣿ ⣾⣟⣾⣟⣻⢾⣽⣾⣟⣻⣽⡾⢿⣽⢾⣻⣿⣯⣟⣷⡿⣯⣟⢯⣷⣯⢿⣷⣟⡷⣯⣷⣟⡾⣽⣾⣟⢾⣻⣿⣿⢀⠠⠀⠡⠀⢂⠀⢀⠀⠈⠐⠠⠀⠀⠄⠀⡀⣆⡿⣯⣷⢿⣻⣿⢿⣿⣿⣾⣿⣶⣛⣥⠲⣿⣾⣻⢿⣷⣯⣟⢷⣻⣷⡿⣯⣟⣽⣻⣷⣽⢿⣷⣯⣟⢾⣻⣾⡿⣯⢷⣿⢯⣷⣯⣿⣷⣿⢻⠟⣷⣿⣿⣿⣿⣰⠉⡀⣅⣹⣿⣿⣿⢿⡿ ⣽⣾⣟⢾⣻⣿⣳⣾⣽⡿⣟⣯⢷⣻⣿⣳⢿⣷⡿⣯⡷⢾⣻⣾⣽⢾⣻⣿⣳⣿⣞⣿⢯⣾⣟⣯⢿⣯⣳⣿⣿⢌⠈⡀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⣀⣷⣯⣶⣞⣟⣧⢟⣣⢶⣛⢦⡛⣬⡹⣿⣷⣯⡾⣻⣷⡾⣽⣻⣾⡿⣟⢯⣻⣽⣾⡿⣟⣽⣻⢿⣯⣷⣟⢾⣽⣿⡽⣾⣻⣷⡾⣽⣿⣿⣿⡁⣟⣻⣟⣈⡿⣿⣿⡐⣤⣷⣿⣹⣆⣿ ⣾⣽⢿⣽⣾⡿⣯⣷⣟⢯⣻⣽⣿⡷⣞⣿⡽⣾⡿⣟⣾⣟⣻⣽⣾⣟⣾⡽⣿⡷⣯⣟⢾⣿⣯⣟⢯⣷⣯⣳⣿⢻⠀⠄⠀⠀⠂⠀⡀⠀⠀⠀⠠⡀⠀⠀⠀⠈⠀⠀⠀⣆⣿⢭⣳⢮⡝⣱⡼⡛⣥⠞⣏⠄⣿⣿⣯⣟⣯⣻⣷⣯⡿⣞⢿⣽⣻⢿⣯⣷⣟⡾⣻⢿⣯⣟⣯⢾⣽⣾⡿⣟⣯⣟⣾⣟⣳⣿⣿⣿⠻⣛⣉⣥⣿⣤⣷⣿⠛⠛⡛⣏⣶⠅⣿ ⣿⣟⣯⡷⣯⢾⣽⣿⡾⣻⢿⣯⣳⣾⣽⢿⣻⣷⣻⢾⣿⣟⢯⣷⣯⢿⣷⣯⣟⣾⣟⢯⣽⢿⣾⡽⣿⣯⣞⣿⣯⣻⠄⠂⡈⠁⠀⠄⠀⢀⠀⠐⠀⠀⠁⠀⠀⠀⠀⠀⠠⠀⡀⣷⢫⣵⡞⡭⡜⠳⣡⠷⢎⣈⣿⣿⢷⣻⢿⣷⣯⢷⣻⣽⢿⣾⣟⡷⣟⣽⢿⣯⢾⣻⣽⢿⣿⣷⣾⣷⢿⣽⣻⢾⣿⣯⣳⣿⣿⣿⣿⣿⣿⣼⣄⣷⠘⣇⣾⣴⣿⣠⠉⡻⣧ ⢾⣻⣿⣯⣳⣿⣞⢿⣯⣽⡿⣟⣷⣯⣻⢾⣽⣾⡿⣟⢷⣻⣿⣳⣿⡷⣽⣻⢿⣷⣯⣟⣯⡷⣟⣽⡾⣻⣽⢿⣾⣿⢸⢀⠂⠁⠀⠠⡁⠀⠐⠀⠐⡀⠀⠈⠀⠀⠀⠈⠀⠀⠀⠀⣄⣻⢮⣚⡝⢣⣱⡼⢳⢂⣿⣿⣻⣽⡾⣻⣽⣿⡷⣟⢷⣽⣾⣻⣽⡿⣞⢿⣷⢯⣿⣿⣌⠠⠀⠀⣧⣿⡷⣟⢿⣾⣿⣿⣿⣿⣿⣿⣿⢿⠿⠻⠛⡖⣶⢿⡉⠟⣿⣿⡘ ⣾⣻⢾⣽⣿⡷⣯⢷⣻⣷⡽⣻⣿⢯⣻⣿⣳⣽⣿⡽⣾⡿⣞⣿⡽⣾⡿⣟⡷⣽⢾⣻⣾⣽⢾⣻⣿⢷⣯⢿⣯⣷⣿⡙⠂⠀⠠⡁⠄⡂⠄⠃⠀⠠⠁⠀⠁⠀⢀⠀⠂⠀⠀⠀⠀⡄⣧⢟⣫⣕⡮⡟⢃⢠⣿⣟⡿⣳⣿⣟⣯⡾⣽⣻⣿⡷⣯⢿⣷⢯⣷⣞⣿⢯⣿⣾⢀⠈⠀⠂⢁⣿⣯⣿⢑⡤⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⡿⣿⣿⢿⡿⣿⣿ ⣿⣯⣟⣯⣟⣻⣷⣽⣻⣽⣻⣷⡽⢿⣽⡿⣳⣽⢾⣻⣿⣯⣟⢷⣻⣽⣿⡽⣿⡾⣽⣾⣟⣻⣷⣽⡿⣯⣟⢯⣷⣯⣿⡞⠈⡀⠰⢂⡀⠘⢈⠡⡈⠄⠂⠁⠈⠡⠋⠉⠀⠀⠀⠀⠀⠈⠀⣏⣿⡻⢿⣝⠩⢦⡇⣿⡽⣾⣟⡽⣻⣷⣻⢾⣽⣻⣿⡷⣽⣻⣷⣯⢿⣯⣷⣽⠂⠀⡔⠦⡶⣿⣿⣼⠂⡌⠧⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣻⢷⣽⣻⢷⣻⣾⣟⡷⣯⣟⣯⡿⣯⡷⣟⣯⣟⣯⢷⣻⣷⡽⣾⡿⣯⣟⡾⢿⣽⣻⣿⢷⣽⣾⡿⣟⢯⣻⣾⣻⣷⣟⢿⠀⢈⡐⠜⢂⠍⡈⠱⠚⢩⠴⢫⡱⢸⢦⡘⣰⢽⠊⠱⠛⠟⣿⣿⣷⣷⣾⣿⠿⣉⡵⣿⣟⣯⢿⣷⣟⣯⡾⣽⣾⣟⡽⣿⡷⣟⣾⣟⡷⣟⣾⣿⠹⠀⠀⢀⠠⠄⢂⡄⠀⠠⢏⡧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣽⣻⣾⡽⣿⡽⣾⣟⣾⣟⡽⣻⢷⣽⣻⣷⣞⡿⣟⣯⣳⣿⡷⣯⢷⣻⢿⣯⢷⣻⣷⡽⣿⡷⣯⢾⣻⢾⣻⣿⣞⣻⣿⣿⢡⠌⠏⠋⢥⠳⣌⡹⠶⣊⡵⢎⡱⡜⢎⡑⢦⡘⠟⣿⣿⣿⣾⣰⠲⠃⣄⣧⣿⢿⡻⣽⣿⢿⣯⣽⡿⣳⣿⣟⣯⣽⡿⣳⣿⡷⣟⣻⣾⡿⣟⣯⣿⠻⠀⠀⠀⠀⠁⠉⠉⡋⠝⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣾⡿⣟⣯⣟⡷⣯⢾⣿⢯⣾⣟⣯⡿⣞⣻⣷⢾⣻⣽⣿⡽⣻⣽⣿⣞⡿⣟⣷⣟⣯⡾⣻⣽⢿⣽⣾⣟⢾⣻⣽⢿⣿⣾⣣⡜⣙⠷⣩⠶⣎⡙⢮⣍⡲⢍⡢⠜⢏⡡⢜⠣⣤⣷⣾⢲⡄⣠⢀⠀⠀⠀⣄⣶⣿⡿⣗⣿⢿⣽⣻⣿⣞⡿⣽⡿⣟⣾⡿⣯⡽⢾⣽⢿⣾⣟⢯⣿⣿⠿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣽⢾⣿⢯⣻⣽⢾⣿⢯⣷⣟⣯⣞⡽⣾⣟⣻⣽⢿⣷⢯⣻⣷⡽⢿⣯⢷⣻⣿⡷⣯⣟⢷⣻⣽⡾⣽⢿⣷⣞⡿⣿⣷⡔⢫⡴⡛⢥⡳⢮⣙⠶⢎⣙⠦⢋⢤⡜⠓⢢⡔⢠⣀⠀⠀⠀⠁⠀⠠⠀⡀⢣⠈⠀⣄⣦⣻⡽⣶⣿⣟⡷⣯⢷⣻⣽⡿⣟⢷⣽⣻⣾⣻⢷⣽⣻⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣾⣽⢾⣻⢾⣽⣿⢯⣷⣯⡿⣳⣽⣾⣟⣻⢷⣻⣽⣻⣾⡽⣿⡽⣻⣽⣾⣟⡽⣾⣟⡾⣻⢿⣳⣿⣯⣞⣻⣿⣿⣾⣙⡴⢛⣥⠞⣣⠧⢎⣑⡽⢎⡘⢲⠤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠋⡿⢿⠫⠀⠀⠃⠋⠻⠈⠀⡀⣦⣿⣯⣿⣿⣞⣿⡽⣾⣟⡾⣻⣽⡿⣞⣽⣿⣞⡿⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣽⣻⣿⣯⣟⣯⡷⣟⣷⢯⣻⣾⣟⣯⢷⣻⣾⡿⣟⢯⣷⣟⢯⣾⡿⣟⣯⢷⣻⣷⢿⣯⢷⣻⣷⢯⣾⣟⣿⣾⣹⢦⡛⣌⠳⢭⡝⢪⢶⡤⣠⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣆⣿⣿⢰⠀⠀⡀⣿⣿⣨⢀⠈⠀⠀⣤⣳⣾⣿⢿⣳⣿⢷⣽⣻⣽⡾⣽⣻⢿⣯⣽⡿⣟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣾⣟⡽⢿⣾⣟⣯⣳⣿⢯⣻⣽⣻⣽⣿⢯⣷⣟⡽⣿⣯⣞⢿⣽⢾⣻⣾⣽⣻⣿⡷⣟⣾⣟⣻⣷⣟⣿⣿⢭⡹⢶⠴⣠⢠⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠠⣇⢤⠀⠀⠀⠀⠀⠀⠀⣄⣷⣿⣿⡽⣾⡿⣟⡾⣽⣾⣟⡽⢿⣷⢯⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⢯⣿⡷⣟⣳⣽⣾⡿⣟⢯⣷⢯⣷⡽⣿⣯⣟⡾⢿⣯⣟⢷⣻⣽⣾⣟⣻⢷⣻⣾⡿⣟⢷⣻⣾⣿⣹⣙⣀⠂⠐⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⢃⡀⠲⠀⠀⠀⠀⠀⠈⠀⠀⠀⡄⣧⣻⣿⣳⢿⣯⣟⣷⣞⡿⣳⣿⣞⡿⣟⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣟⡷⣯⣳⣾⣟⣯⢷⣻⣽⣾⣟⣻⣽⡿⣳⢿⣯⣟⣯⡽⣾⡿⣟⣯⢿⣳⣿⢯⣷⣟⡽⣾⡿⣟⣷⣯⣽⣿⢿⠷⡛⢉⠬⠂⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⢣⡈⠐⠀⠀⠀⡀⠑⠋⠛⡟⠿⣾⣟⢿⣷⣯⡾⣽⡾⣽⣾⣻⣾⡿⣟⣽⡾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣽⡾⣽⣻⣾⣽⣻⣽⣾⡿⣟⣯⣳⢿⣯⣟⣯⡿⣳⢿⣯⣞⣿⢯⣷⢯⣻⣽⢾⣽⣾⣟⡷⣯⢷⣻⣽⢾⣻⣾⡽⣾⣻⣷⣿⢯⠾⠻⡛⢌⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣆⡉⠿⠷⡯⣿⣯⣷⣽⣻⣷⣟⣯⡿⣳⣽⣾⣟⣾⣟⣯⢷⣽⣻⢷⣻⣽⢾⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣾⣽⣻⢿⣷⣟⡾⣟⣯⢷⣻⣽⣾⡿⣟⢯⣷⡽⣿⡽⣾⣟⢾⣽⣾⣟⡽⣻⣿⣯⣟⣯⣳⣾⣽⡿⣯⣟⣯⣟⣯⣟⣷⣯⡿⣯⣟⣯⣿⣽⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠆⣽⣿⣻⢿⣳⣾⣽⡿⣟⣯⡾⣽⡿⣯⣟⣯⢷⣽⣻⣽⣾⡿⣟⣯⡿⣞⣿⢯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣽⣻⢿⣳⣾⡿⣟⣯⣟⣷⡾⣟⣯⢷⣻⣽⣾⡿⣟⡾⣽⢿⣾⣟⣯⢷⣻⢾⣻⢿⣯⣳⣽⣿⣞⣻⢷⣾⣟⡾⣽⡾⣻⢿⣷⢯⣻⣽⢾⣿⣻⠦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⡌⣿⣻⢿⣳⣿⣟⣯⣞⡿⣯⣞⣽⡿⢷⣻⣽⣾⡿⣟⡷⣽⢾⣻⣽⡿⣞⢿⣯⣟⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣻⢿⣳⣿⣟⢷⣻⣽⡾⣻⣽⣻⣽⣾⡿⣟⣯⣳⢿⣯⣟⢯⣾⣟⣳⣿⢯⣽⣻⢾⣽⣾⣟⡽⣾⣟⣻⣷⢿⣯⣟⣷⣞⡿⣯⣞⡿⣟⣯⣳⣿⢻⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡷⣿⣞⡿⣯⣞⡽⣾⣟⢷⣻⣽⣾⡽⣿⡾⣟⣯⢷⣻⣾⡽⣿⣞⣻⢷⣽⣻⢷⣻⣽⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣽⡿⣯⣟⡷⣯⡿⣳⣽⢿⣾⣟⡷⣯⢷⣻⣽⣾⡿⣟⢯⣷⣟⣯⣻⢷⣻⣷⡽⣾⣟⣯⢷⣻⣷⣽⡿⣯⡽⢿⣻⣽⣿⣞⢿⣯⢷⣻⣽⣾⣟⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⣆⡿⣿⣯⢷⣻⣽⣾⣟⣻⣷⡾⣟⣯⣻⢷⣽⣻⣽⣾⡿⣟⣯⡷⣟⣽⣻⣷⡽⣾⡿⣟⢯⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⡾⣽⡾⣻⣽⡿⣯⣞⡿⣟⣯⣳⣽⣾⡿⣟⣯⢷⣻⣽⣾⡿⣟⡾⣽⣻⣾⡽⣿⣞⣻⣽⣻⣾⡿⣟⢯⣷⡽⢿⣯⡿⣟⢷⣯⣻⢷⣻⣽⢿⣯⣿⠙⢁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⡍⣿⢿⣯⣻⢷⣻⣽⢾⣻⣿⣯⣞⢿⣯⣳⣽⡿⣞⣽⢾⣻⣽⣻⣽⡿⣳⣿⡷⣯⣳⢿⣳⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣷⣦ ⢿⣯⣟⣷⢯⣷⢯⣻⣷⣟⡷⣯⣳⣾⣟⢷⣯⣳⣿⡷⣟⣯⣳⢿⣯⣟⢯⣷⣯⡷⣟⣯⣟⢯⣷⢯⣻⣽⣾⡿⣞⢿⣯⡽⣿⣞⡽⣾⡿⣟⢯⣷⣟⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⣏⣿⣯⣟⡷⣯⡷⣟⣾⣟⢯⣻⣽⢿⣷⣯⣟⡷⣯⣟⣷⣯⣟⡷⣯⡽⣿⡷⣯⣟⣯⡿⣯⣟⡽⣻⣿⣷⣯⣿⣷⣻⣾⣽⣿⣿⣷⣿⣾⢓⠀⠠⠀⠀ ⣻⣽⡾⣻⣽⣾⣟⡾⣽⣻⣽⣻⣽⣾⣟⣻⣽⣾⡿⣯⡽⣿⣯⡽⢾⣻⣿⣯⣞⣽⣻⢷⣻⣽⣾⣟⡽⣻⣾⢿⣯⢷⣻⣽⡿⣯⣟⣯⢷⣻⣽⣿⡷⣟⣿⠘⠀⠀⠀⠀⠀⠀⠀⠀⢀⠦⠀⠉⠉⠛⠛⡿⣷⣟⡷⣯⣟⣯⢷⣯⣳⢿⣯⡷⣞⣻⢿⣯⣳⣽⡾⣻⢿⣳⣿⢯⣽⣻⣷⣞⡿⣟⢯⣻⢷⣻⢾⣽⣻⣾⡽⣿⡽⣾⣻⢷⣻⣽⣿⣏⠠⠐⠃⠿⣶ ⣻⣷⣟⢷⣯⣽⢾⣿⣞⡿⣟⢯⣻⣾⢿⣯⡽⣿⢯⣻⣽⡿⢷⣯⣽⣻⢾⣻⣽⣾⡽⣾⡿⣟⣯⢷⣻⢿⣷⢯⣷⣯⣟⡷⣟⢯⣻⣽⣿⡷⣯⡷⣽⡾⣿⢿⡄⠤⠑⠀⠉⡉⠏⠛⠿⠿⣯⣷⣟⣽⣿⣯⣽⣻⣽⢾⣻⣿⣯⣟⣯⡾⣟⣷⣯⣟⢯⣷⣯⣟⣯⢿⣳⣿⢯⣷⡽⣻⣽⣾⣟⢯⣷⡽⣿⡷⣯⣟⢷⣯⣳⢿⣳⣿⣟⣯⣞⡿⣯⢻⣩⠐⣆⠀⠀ ⣾⣽⣻⣽⢾⣻⣽⢿⣽⣻⢾⣻⢿⣯⣟⢯⣷⡽⢿⣯⡽⣻⣽⢾⣻⢾⣽⢿⣷⣯⣟⣯⢷⣻⣽⣾⣟⡽⣻⣽⣾⣟⡷⣯⣟⢯⣽⡿⣳⣾⣟⣽⡾⣽⣾⣟⢿⠿⡿⣷⣾⣽⣻⣽⣾⡿⣟⣯⡷⣟⢯⣾⣟⡽⣾⣟⣻⢷⣻⢿⣯⣟⣯⣻⢷⣻⣽⣿⣞⡿⢯⣻⣷⢯⣷⣯⣟⡷⣟⣽⣻⣷⣯⡿⣞⣻⢾⣽⣻⣽⣾⡿⣯⡽⢿⣻⣽⢾⣿⢻⣿⡱⠀⠀⠀ ⣿⣞⡿⣟⣯⢷⣻⣽⡿⢷⣯⢷⣻⢷⣻⣽⣾⡿⣟⢯⣷⢯⣻⣽⣾⣟⣯⡷⣻⢷⣽⣻⣾⡿⣟⣷⢯⣾⡿⣯⣞⣽⣾⣟⢯⣻⣷⡽⣿⣞⣽⡾⣽⣻⣽⢿⣷⢯⣻⣽⣿⣞⡿⣟⣯⢷⣻⣷⣯⣞⢿⣯⢷⣻⣷⣽⡿⣯⣟⡷⣟⢯⣷⡽⣾⡿⣟⢯⣷⣟⢯⣽⣻⣿⣳⣽⡿⣯⣟⡷⣟⣯⣟⡷⣟⣯⣟⣯⡷⣟⣷⢯⣾⣟⡽⢾⣻⣷⣟⣿⣛⠻⠛⠛⠈ ⢿⣯⢷⣻⣽⣾⣟⡽⣻⣽⣻⣽⣻⣾⡽⣾⣟⢾⣻⣿⣯⣞⡽⣾⣟⣳⣽⣿⡷⣽⡾⢿⣯⢾⣻⣽⢿⣯⢿⣳⣽⣾⣟⣳⢿⣯⣳⣽⡿⣯⣟⣽⣻⢷⣽⣻⣾⣟⡽⣻⢷⣯⢷⣻⣽⣾⣟⣯⢷⣯⢿⣷⣯⡷⣽⡾⢿⣯⡽⣾⡿⣟⣾⡽⣿⢯⣽⣻⣷⢯⣾⡿⣟⡷⣯⣞⢿⣯⡽⣿⡾⣽⡾⣽⣻⢷⣻⣽⣾⡿⣯⢷⣯⢿⣳⣿⣞⣿⣿⣿⣿⣿⣿⣿⣿ ⣻⣽⣾⡿⣟⣯⢷⣽⡿⣳⢾⣽⢿⣯⣟⣯⢾⣽⣻⢾⣻⣽⣾⣟⣽⣻⣷⡽⣾⡿⣯⣞⢿⣯⢷⣽⣻⢷⣻⣽⣻⣽⣿⣯⡾⣟⣻⣷⡽⢿⣽⡾⣻⣷⡽⢿⣯⢿⣳⣽⣻⣾⣻⢷⣻⣽⣻⣽⣾⣟⡽⣻⣽⣿⡷⣯⢷⣻⣾⣟⣳⢿⣯⣟⢯⣿⡷⣟⣯⢷⣯⢷⣻⣽⢾⣿⢯⣽⣻⢾⣽⣻⣽⣾⡽⣾⡿⣟⣷⢯⣷⣯⣟⡷⣯⡿⣞⣿⣿⣿⣿⣿⣿⣿⣿ ⢾⣻⣽⣻⢾⣽⣿⡽⣻⣽⣿⣞⡿⣳⢿⣯⣟⣯⡷⣟⢾⣽⣿⣞⡿⣟⣯⡽⣿⢯⣻⣽⢿⣽⣻⣷⡽⣾⡿⣟⢯⣷⡽⢿⣷⣯⡽⣾⡿⣟⡷⣯⣻⣷⡿⣯⣞⡿⣯⣟⢯⣷⣟⣯⡾⣽⡿⣞⣿⢯⣾⣟⡽⣻⣽⣻⣾⡿⣟⣯⣽⡿⢯⣾⣟⡷⣯⡷⣯⣳⣽⣿⡷⣟⣯⢷⣻⣽⡿⣟⣯⡷⣟⣽⣻⣷⢾⣽⣻⣽⣿⣞⡿⣯⣟⡷⣞⣿⣿⣿⣝⣹⢦⡜⣳ ⣽⢿⣷⢯⣷⣞⡿⣞⡿⣟⢯⣷⣟⣯⡽⢿⣽⣻⣷⢯⣷⣟⡷⣟⣻⢷⣻⣽⡾⢿⣯⡿⣞⡿⣟⣯⡷⣯⢷⣻⣷⣽⡾⣻⣽⢾⣻⣾⣽⡾⣻⢷⣻⣾⡽⢿⣽⣻⢷⣻⣽⣾⡿⣟⣯⣟⢷⣯⢷⣻⣽⢿⣯⡿⣳⢿⣷⢯⣻⣽⡾⢿⣯⣟⣯⣳⣿⣳⣽⣻⣾⡽⣾⡿⣟⣯⡿⣞⡿⢯⣽⣻⣽⡿⣞⣻⣷⣞⡿⣟⢯⣷⢯⣷⡽⣾⣟⣳⣿⣿⣿⣿⣿⣿⣿ ⣽⣻⣽⣻⣽⣿⣯⣞⢿⣯⣟⣯⡷⢿⣯⣟⡷⣟⣯⣟⣯⡿⣯⣞⡽⣾⡿⣟⣯⢷⣻⢷⣯⢷⣻⣽⣾⣟⣯⣳⣿⡷⣯⢷⣻⣽⢿⣾⣟⣯⣻⣷⢯⣷⣯⣞⡿⣟⣯⡾⣟⣷⢯⣻⣷⡽⣻⣽⣾⡿⣟⢯⣷⡽⣿⡷⣯⣞⡽⣾⣟⣻⢷⣻⣽⣾⡿⣯⣟⢯⣾⣟⣯⢷⣽⣻⢷⣯⢷⣽⡿⢯⣽⡿⣞⣻⣷⣞⢿⣯⣟⣯⣟⣯⡽⣾⣟⣯⣿⣿⣿⣿⡻⣛⣿ ⣽⡿⣟⢯⣷⡽⢿⣽⣻⢷⣻⣾⣽⡿⣟⡷⣯⡿⣳⢾⣻⢷⣻⣽⣾⣟⢾⣻⣿⣯⣞⣻⣷⣽⡿⣳⣾⣟⣳⣿⡷⣯⣟⣯⡾⣽⡿⣟⣳⢾⣽⣻⣾⣽⢾⣽⣻⢿⣯⣟⣯⣳⣽⡾⣻⣽⡿⣞⣿⢯⣻⣷⣽⡿⣳⣽⣻⣽⣾⣟⢾⣻⣾⡽⣾⣟⢾⣻⢿⣳⣽⣻⣽⣾⡿⣟⣳⣾⣽⡿⢯⣽⡿⢯⣽⣻⣽⣿⢯⣻⢷⣻⢷⣽⡿⣯⣟⢯⣿⣿⣿⣿⣿⣿⣿ ⣽⡿⢷⣯⣽⡿⣞⡿⣟⣯⡾⣟⣽⡿⣞⣻⢿⣳⣿⣟⣯⣻⢷⣻⣾⢿⣯⣳⢿⣯⣟⣯⣽⡿⣳⣿⣞⣽⣾⡿⣯⣟⡽⣾⣟⣻⢷⣯⣳⣿⣟⢯⣾⣟⣯⣻⢷⣻⢿⣯⣟⣯⣟⣯⢷⣻⢾⣿⢯⣷⡽⣿⡽⣻⣽⣻⢷⣻⣾⢿⣯⢷⣽⣻⣾⢿⣯⢷⣻⣽⣻⢷⣻⣾⢿⣯⣳⣿⣟⢯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣻⣷⡽⣾⡿⢯⣻⢷⣻⣿⣿⣿⣿⣿⣿⣿ ⣾⡿⣳⢿⣷⢯⣷⣟⢯⣷⣟⣯⡽⢿⣯⣽⡿⣯⡽⢿⣯⡽⣿⢯⣽⢿⣯⣽⡿⣟⢯⣷⡽⣻⣾⡽⣾⣟⣯⣳⢿⣯⡽⣿⢯⣽⣻⣿⣯⣞⡽⢿⣽⣻⣽⡾⣻⢾⣻⢷⣾⣟⡿⣟⣷⢯⣽⢿⣯⣽⡿⢯⣽⡿⣯⡽⣿⢯⣽⢿⣯⣽⡿⢯⣽⢿⣯⣽⡿⣯⡽⣿⢯⣽⢿⣯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣽⡿⣯⡽⣿⢯⣽⡿⣯⡽⣿⣿⣿⣿⣿⣿⣿ ⣿⣟⣯⡷⣯⣟⣯⡷⣟⣯⡽⢿⣯⡽⢿⣯⡽⢿⣯⡽⢿⣯⡽⢿⣯⡽⢿⣯⡽⢿⣯⣻⣽⡿⣟⣯⣟⣯⣟⣯⡽⢿⣯⡽⢿⣯⡽⢾⣻⣽⣻⢿⣯⡿⣻⣿⢿⣿⣿⣻⣿⣿⣤⣿⣻⣽⡿⢯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣽⡿⢯⣷⣿⣿⣿⣿⣿ ⢿⣯⣟⣯⣟⡿⣾⣾⣷⣶⣷⣶⣶⣷⣶⣾⣶⣾⣶⣾⣷⣶⣾⣷⣶⣷⣶⣷⣶⣶⣾⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣲⣶⣖⣶⢶⡶⢶⣶⠶⢶⡶⣴⢀⠀⡀⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣿⡿⣽⡿⣿⣿ ⣻⢷⣿⣶⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣦⣿⣯⣿ ⣻⣿⣰⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠋⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠋⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿ ⣿⣞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠘⠀⠙⠋⠛⠈⠀⠉⠛⠙⠀⠀⠀⠀⠀⠁⣿⣼⢠⠃⠛⠀⠃⠙⠀⠃⠙⠀⠀⠀⠋⠘⠀⠃⠈⠃⠛⠈⠀⠛⠀⠀⠃⠙⠀⠋⠘⠀⠀⠀⠀⠋⠙⠋⠙⠀⠀⠉⠛⠙⠈⠀⠁⡿⣸⢠⠀⠀⠀⠋⠛⠈⠀⠛⠀⠛⠈⠀⠛⠈⠀⠀⠀⠛⠈⠋⠘⠃⠙⠀⠀⠛⠘⠀⠛⠈⠀⠀⠀⠁⠛⠈⠀⠀⠀⠀⠀⠀⠀⠀⡀⣿ ⣿⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⢼⡅⣿⠣⣏⣾⠀⣠⣀⣧⣿⠀⠀⠀⠀⡟⣾⣿⠈⡇⣿⠀⡇⣿⠀⡷⣺⠀⠀⠀⣿⢼⠀⣿⢼⡀⣧⢻⠄⣿⢰⠁⣿⣿⠋⣿⣿⠈⠀⠀⠀⣿⣼⡀⣿⢺⡇⣿⣀⣄⣿⠠⡟⣾⣿⠈⠀⠀⠀⡀⣷⣸⠆⣿⢈⣿⢸⠀⣿⢸⠀⠀⠀⣿⢘⣿⢸⡇⣿⠀⠇⣿⢻⡟⣿⢿⠀⠀⠀⡀⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⢿⣹⠀⠀⠀⠀⠀⠀⠀⠀⠃⡿⣿⣹⡀⣷⢻⣿⠘⠀⠿⠻⡿⣴⠀⠀⠀⡇⣾⢀⣇⢿⡄⣷⠻⣞⣿⠛⣿⢼⠀⠀⠀⣆⣿⠛⣿⣸⠓⡟⢿⡐⣿⠠⡷⢸⣆⣿⢰⣦⢻⠀⠀⠀⣷⣸⠀⣷⢸⡀⣷⠿⠟⣴⢧⣾⠀⣦⢻⠀⠀⠀⠓⡿⣿⠆⣿⠀⣶⢿⡛⣿⢸⠀⠀⠀⣿⠘⣷⢸⡆⣿⠂⣿⢐⣧⣿⡀⣿⢸⠀⠀⠄⣿⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣽⢺⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⡀⢀⠀⠀⢀⠀⡀⢀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⡷⣸⠀⣆⣰⠀⣿⠀⡀⠀⠀⢀⠀⠀⢀⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⢀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⣆⣰⠀⢾⠀⠀⢀⠀⣿⢰⠀⠀⠀⣿⠰⣷⣰⠆⢻⠀⢀⠀⡀⢀⠀⡀⠀⠀⠀⠀⢿⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣾⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⣯ ⣿⣯⢻⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠧⣿ ⢿⣻⣾⣿⠻⠙⠁⠀⠀⠁⠀⠀⠀⠀⠁⠀⠉⠀⠀⠀⠈⠀⠈⠈⠁⠈⠀⠁⠀⠀⠀⠈⠁⠀⠈⠀⠀⠀⠈⠁⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠁⠀⠁⠀⠁⠀⠀⠀⠀⠀⠁⠈⠀⠈⠀⠁⠀⠁⠁⠀⠈⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠈⠁⠀⠈⠈⠁⠀⠀⠀⠈⠁⠀⠀⠁⠉⠙⠯⡟⣳⣿ ⣃⣄⣖⣭⣥⣾⣿⣿⣯⣻⣽⣾⣽⣾⣻⣷⣟⣯⣽⣿⣯⣷⣟⣯⣳⣽⣾⣻⣽⣾⣽⣾⣻⣽⣿⣯⣽⣿⣯⣳⣽⣿⣯⣽⣿⣯⣽⣿⣯⣽⣾⣽⣾⣽⣾⣻⣽⣿⣯⣽⣾⣻⣽⣾⣽⣾⣽⣾⣻⣷⣯⣞⣻⣷⣽⣾⠿⠳⡝⠉⠤⠘⠢⡑⠌⠠⠜⠃⠡⠔⠊⠡⠔⠊⢡⠆⡈⠑⠢⠌⠑⠢⠌⠑⠢⠌⠑⠢⠌⣑⣦⣮⣷⣿⣟⣻⣽⣿⣯⣽⣻⣷⡾⣻⣿ ⠤⡑⠤⠐⡩⠆⢂⡄⣢⣄⣦⣶⣶⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣷⣶⣾⣷⣾⣷⣷⣶⣾⣷⣶⣾⣷⣾⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣷⣶⣿⣶⣿⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣾⣷⣶⣿⣷⢾⣿⣷⣾⡿⣷⣾⣿⣶⣿⣷⠾⢿⠛⡘⢆⡀⠰⡐⠢⢄⡐⠢⢄⠰⢆⡄⠐⢢⡄⠐⢢⡄⠐⢢⡄⠐⢢⡄⠒⢂⡐⢒⡠⣔⣦⣶⣾⣷⣿⣟⣻⣽⢾⣿ ⡐⠢⣉⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣄⣠ ⡐⢎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠉⠀⠙⠙⠋⠈⠁⠛⠈⠀⠙⠙⠙⠀⠀⠀⠀⠉⠋⠙⠈⠁⠛⠀⠋⠙⠀⠃⠛⠈⠁⠛⠀⠋⠘⠀⠀⠀⠁⠉⠛⠉⠀⠋⠙⠁⠛⠀⠃⠘⠁⠙⠀⠁⠙⠁⠛⠈⠀⠋⠙⠀⠋⠘⠀⠁⠛⠘⠀⠀⠀⠀⠋⠙⠉⠈⠁⠛⠀⠋⠘⠀⠛⠀⠋⠈⠀⠛⠈⠋⠘⠀⠃⠛⠀⠃⠛⠀⠁⠙⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢷⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⢺⡆⣿⠓⣏⣿⠀⣇⣿⠆⣿⡻⣉⢀⠀⠀⠁⡿⣚⣟⣿⠆⣿⠘⣀⣿⢸⡀⣇⢿⡀⣿⠘⣿⣸⠀⠀⠀⡟⣞⡛⣿⢺⣧⢻⡀⣆⢿⡿⣽⡇⣿⠀⡇⣿⡃⣿⠰⠃⣿⣿⠋⣾⣿⠈⡀⣧⢿⠀⠀⠀⠇⢻⣳⣟⢿⡇⣿⠰⣄⣷⠟⣿⢈⣿⢸⠀⣿⢘⣿⢸⠀⡟⣿⢹⣟⣿⠸⠀⣅⣿⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣻⢼⠀⠀⠀⠀⠀⠀⠀⠀⠂⠿⣷⢽⡀⣷⢻⣟⠈⠃⡟⣿⠘⠳⡟⣿⠠⠀⠀⡄⣧⢻⡟⣶⡁⣿⠰⠛⣿⢻⠓⡟⢿⡘⣿⠐⣿⢸⠀⠀⠀⣆⣿⠛⣿⢰⣏⢾⠀⠟⣼⣧⣻⡄⣷⠿⡿⣿⠆⣿⠠⡟⣼⡆⣿⢰⣧⣸⠓⡟⣿⠘⠀⠀⡀⣷⠻⡟⣰⠇⣿⠰⠃⡾⣥⣿⢈⣶⢿⠞⣿⠰⣷⣸⠇⣾⣀⣷⣼⡄⣿⠂⠛⣿⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢾⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⡀⢀⠀⠀⡄⣼⠀⡀⣀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠄⣿⠰⠀⣶⢠⠀⣆⣼⠀⡿⠀⣷⢸⠀⠀⠀⠀⠀⡀⠀⠀⡗⢼⠀⣀⠀⡇⣾⠀⡀⢀⠀⢀⠂⣿⠀⡀⠀⠀⣀⠀⠀⢀⠀⣄⣼⠀⠀⠀⠀⠀⠀⢀⠀⡆⣿⠠⡀⢀⠀⣿⠰⠀⣀⠀⡀⠀⡗⠸⠀⢀⠀⡀⢀⠀⢀⠀⣀⣼⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤ ⣽⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣞⡽⢫⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣽⡷⣛⢷⠻⠈⠈⠁⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠁⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠁⠀⠀⠁⠀⠈⠀⠀⠈⠀⠀⠈⠀⠀⠈⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠈⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣻⣯⡝⣻⢯⣽⣟⢯⡽⡻⢯⡽⢟⢯⡹⢿⢫⣽⡻⢯⡹⢿⢫⣽⡻⢯⡽⡟⢯⣝⠿⣏⠽⡻⢯⡽⢟⢯⡹⢿⢫⣽⠟⢯⡹⢿⢫⣽⠿⢯⡽⠿⢯⡿⢟⣻⡿⢟⣻⡿⢟⣻⡿⢟⣻⡿⢟⣻⡿⢟⣻⡿⢟⣻⡿⢟⣹⠾⣋⡱⢞⣍⡳⢎⣋⡱⢮⠝⣣⡜⠫⢱⢮⡝⢣⡜⢫⡱⠼⢛⣣⢜⢫⠱⢮⠝⣣⠜⢫⡱⢞⡍⠳⠈⠙⠡⠌⠉⠁⠌⠉⠡⠌⠉⠁