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