⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠖⠒⠒⠒⠒⠦⠖⠒⠒⠒⠒⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢠⢀⡄⠀⠀⢠⠀⣇⠀⢦⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⠲⢄⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠉⡀⢀⡴⣲⡏⣼⠁⠀⠀⡞⠀⢹⡀⠘⣆⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠙⢆⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢀⢞⣴⢋⡜⣝⣼⠃⠀⠀⡼⠁⠀⢸⠳⣄⠈⢷⣄⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⢠⣾⣻⠗⣡⢾⡿⠁⠀⢀⡼⠁⠀⡰⠋⠀⠈⠑⠦⢽⣻⣗⡦⢽⣦⣄⡀⠀⠀⠀⠀⠀⠘⢦⡀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣼⠋⠉⠀⣩⠜⠁⠀⣠⠞⢁⣠⠔⠃⠀⠀⠀⠀⠀⠈⠉⠛⠃⠈⠉⠙⠓⠦⢄⡀⠀⠀⠀⠈⠣⣀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠐⠃⢀⡠⠞⠁⣀⡤⠞⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⠀⠀⠀⠈⠉⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠙⠛⠛⡿⠉⠁⡤⢒⣯⣭⣭⣓⢤⡀⠀⠀⡇⠀⠀⢳⠀⠀⢀⡴⣺⣭⣯⣭⡓⢢⡀⠈⢧⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡼⠁⠀⢞⢰⣿⣯⣿⣽⣿⠷⠃⠀⢸⡁⠀⠀⢹⡀⠀⠘⠿⣿⣏⣟⣺⣿⡆⢱⠀⠈⢧⠀⠀⠀⠀⠀⢀⣈⣓⡦⡄⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⠃⠀⠀⠀⢀⣉⣉⣉⡡⠔⠃⠀⣠⠞⠒⠉⠙⠂⠳⣄⠀⠙⠦⢍⣉⣉⣉⡀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠙⠛⠒⢒⡿⠀⠀⠀⠀⠀ ⠀⠀⢠⡄⠀⠀⠀⠀⢰⠇⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⢀⣬⣆⠀⢰⣦⣀⡈⠱⡄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⢠⡶⠭⢾⠃⠀⠀⠀⢀ ⠀⠀⠈⣟⠶⢤⣀⡤⠟⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠙⠤⠟⠋⠁⠀⠈⠉⠛⠤⠤⠃⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢀⣡ ⠀⣴⡤⣈⣲⣤⡄⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⢳ ⠀⣿⣙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⡰⠋⠀⠀⠀⣀⣠⣤⠤⢤⣶⣶⠶⣶⣶⡤⠤⣤⢤⣀⣀⠀⠀⠀⠈⢆⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⠔⣋⣠⠄⠀⠀⠀⢀⣾ ⠀⠹⣌⠙⠛⠂⠀⠀⠀⠀⠀⠀⠨⡇⠀⠀⠀⣸⠁⠀⢠⣴⣿⠓⡞⠉⠱⠏⠀⠀⠿⠁⠀⠈⠎⠉⢱⠚⢫⢽⡲⡀⠀⠈⡆⠀⠀⢠⡇⠀⠀⣀⠈⢉⣩⠔⠋⠀⢀⣰⣾⣿⣭ ⠀⠀⣜⣣⣄⡀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢰⡇⠀⢰⡟⡇⡸⠀⡄⠀⠀⠀⠀⠀⢤⠀⠀⠀⡀⠀⣀⠀⠸⠀⡷⣽⡆⠀⢳⠀⠀⢸⠀⢀⣤⣙⣻⠿⠀⢀⣶⣾⣿⣿⣿⣿⣿ ⠀⠀⠈⠓⢯⣄⡀⡀⠀⠀⠀⠀⠀⢹⡄⠀⠀⡇⠀⣿⡹⡹⣜⣲⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⠴⣠⢻⣷⠀⢸⠀⢀⡏⢀⡾⠉⠛⠲⣄⣾⣿⣿⣿⣿⠿⠟⠿⠿ ⠀⠀⠀⠀⠈⠿⣗⡃⠀⠀⠀⠀⠀⠘⣇⠀⠀⡇⠀⣿⣧⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣯⣾⣿⠀⡜⠀⣸⢃⡼⠃⠀⠀⠀⠙⢯⡉⠉⠋⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠻⣦⡀⠹⡄⠀⢳⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠃⢀⡿⠋⠀⠀⠀⠀⢰⡀⠈⠻⢦⡁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢹⡍⠓⢷⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢻⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠈⣇⠀⢸⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⡟⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢸⣇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣤⣏⠀⠀⠀⠀⠹⡆⠀⣇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⠇⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢀⡾⠈⠛⢆⠀⠀ ⠀⠀⠀⠀⢠⡶⠋⠁⠹⣆⠀⠀⠀⠀⠹⣄⢹⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣸⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣠⠟⠁⠀⠀⠈⢳⡀ ⠀⠀⠀⣴⠋⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠘⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡏⠀⠀⠀⠀⠈⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⢳ ⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⢷⠀⠀⠘⡟⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣹⠁⠀⢰⠇⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⢸⡀⠀⠀⣏⡀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣸⠀⠀⢸⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡇⠀⠀⢻⡀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⣄⡇⠀⠀⡾⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠸⣦⠔⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⢸⠇⠀⢠⡇⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢻⣀⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢄⠀⡿⠀⠀⢰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠸⡏⠀⡨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠘⣦⡇⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣏⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠹⡜⠀⡼⢿⣿⣿⣿⣿⣿⣿⠿⡏⠘⣄⡞⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣧⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠐⣄⠙⣶⡀⢸⠀⢈⠉⡍⠀⢡⠀⣅⣠⠟⡀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠈⢦⡈⠙⠫⠷⣶⣤⣖⣤⡾⠶⠋⢁⡴⠃⠀⠠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠈⠒⠤⣄⣀⣀⣀⣀⣀⡤⠔⠋⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⡀⠀⠀⠀⢀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡤⠤⠖⠒⠒⠒⠒⠦⠖⠒⠒⠒⠒⠦⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠊⠉⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⢠⢀⡄⠀⠀⢠⠀⣇⠀⢦⠀⠀⠸⡄⠀⠀⠀⠀⠀⠈⠲⢄⠈⠓⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡜⠉⡀⢀⡴⣲⡏⣼⠁⠀⠀⡞⠀⢹⡀⠘⣆⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠙⢆⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢀⢞⣴⢋⡜⣝⣼⠃⠀⠀⡼⠁⠀⢸⠳⣄⠈⢷⣄⡀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠈⠳⡀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⢠⣾⣻⠗⣡⢾⡿⠁⠀⢀⡼⠁⠀⡰⠋⠀⠈⠑⠦⢽⣻⣗⡦⢽⣦⣄⡀⠀⠀⠀⠀⠀⠘⢦⡀⠹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠇⠀⣼⠋⠉⠀⣩⠜⠁⠀⣠⠞⢁⣠⠔⠃⠀⠀⠀⠀⠀⠈⠉⠛⠃⠈⠉⠙⠓⠦⢄⡀⠀⠀⠀⠈⠣⣀⠱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠐⠃⢀⡠⠞⠁⣀⡤⠞⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⠀⠀⠀⠈⠉⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠁⠀⠀⠙⠛⠛⡿⠉⠁⡤⢒⣯⣭⣭⣓⢤⡀⠀⠀⡇⠀⠀⢳⠀⠀⢀⡴⣺⣭⣯⣭⡓⢢⡀⠈⢧⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡼⠁⠀⢞⢰⣿⣯⣿⣽⣿⠷⠃⠀⢸⡁⠀⠀⢹⡀⠀⠘⠿⣿⣏⣟⣺⣿⡆⢱⠀⠈⢧⠀⠀⠀⠀⠀⢀⣈⣓⡦⡄⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢰⠃⠀⠀⠀⢀⣉⣉⣉⡡⠔⠃⠀⣠⠞⠒⠉⠙⠂⠳⣄⠀⠙⠦⢍⣉⣉⣉⡀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠙⠛⠒⢒⡿⠀⠀⠀⠀⠀
⠀⠀⢠⡄⠀⠀⠀⠀⢰⠇⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠋⢀⣬⣆⠀⢰⣦⣀⡈⠱⡄⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⢠⡶⠭⢾⠃⠀⠀⠀⢀
⠀⠀⠈⣟⠶⢤⣀⡤⠟⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢀⡴⠊⠀⠙⠤⠟⠋⠁⠀⠈⠉⠛⠤⠤⠃⠀⠙⠦⡀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⢀⣡
⠀⣴⡤⣈⣲⣤⡄⠀⠀⠀⠀⠀⠀⡏⠀⠀⠀⠀⠀⢀⠔⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠲⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢀⠞⠁⠀⠀⠀⠀⢳
⠀⣿⣙⢄⡀⠀⠀⠀⠀⠀⠀⠀⠠⡇⠀⠀⠀⠀⡰⠋⠀⠀⠀⣀⣠⣤⠤⢤⣶⣶⠶⣶⣶⡤⠤⣤⢤⣀⣀⠀⠀⠀⠈⢆⠀⠀⠀⠀⡇⠀⠀⠀⠀⣠⠔⣋⣠⠄⠀⠀⠀⢀⣾
⠀⠹⣌⠙⠛⠂⠀⠀⠀⠀⠀⠀⠨⡇⠀⠀⠀⣸⠁⠀⢠⣴⣿⠓⡞⠉⠱⠏⠀⠀⠿⠁⠀⠈⠎⠉⢱⠚⢫⢽⡲⡀⠀⠈⡆⠀⠀⢠⡇⠀⠀⣀⠈⢉⣩⠔⠋⠀⢀⣰⣾⣿⣭
⠀⠀⣜⣣⣄⡀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⢰⡇⠀⢰⡟⡇⡸⠀⡄⠀⠀⠀⠀⠀⢤⠀⠀⠀⡀⠀⣀⠀⠸⠀⡷⣽⡆⠀⢳⠀⠀⢸⠀⢀⣤⣙⣻⠿⠀⢀⣶⣾⣿⣿⣿⣿⣿
⠀⠀⠈⠓⢯⣄⡀⡀⠀⠀⠀⠀⠀⢹⡄⠀⠀⡇⠀⣿⡹⡹⣜⣲⣿⣿⣿⣷⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡭⠴⣠⢻⣷⠀⢸⠀⢀⡏⢀⡾⠉⠛⠲⣄⣾⣿⣿⣿⣿⠿⠟⠿⠿
⠀⠀⠀⠀⠈⠿⣗⡃⠀⠀⠀⠀⠀⠘⣇⠀⠀⡇⠀⣿⣧⣵⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⣯⣾⣿⠀⡜⠀⣸⢃⡼⠃⠀⠀⠀⠙⢯⡉⠉⠋⠉⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠉⠛⠒⠒⠻⣦⡀⠹⡄⠀⢳⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠐⠃⢀⡿⠋⠀⠀⠀⠀⢰⡀⠈⠻⢦⡁⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⢹⡍⠓⢷⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⢻⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠁⠀⠈⣇⠀⢸⡄⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⡟⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⢸⣇⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣤⣏⠀⠀⠀⠀⠹⡆⠀⣇⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⢠⠇⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⢀⡾⠈⠛⢆⠀⠀
⠀⠀⠀⠀⢠⡶⠋⠁⠹⣆⠀⠀⠀⠀⠹⣄⢹⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⣸⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⣠⠟⠁⠀⠀⠈⢳⡀
⠀⠀⠀⣴⠋⠀⠀⠀⠀⠈⢷⣄⠀⠀⠀⠀⠘⡇⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⡏⠀⠀⠀⠀⠈⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⢳
⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀⠙⢷⣄⠀⠀⠀⢷⠀⠀⠘⡟⡛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣋⣹⠁⠀⢰⠇⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣄⡀⢸⡀⠀⠀⣏⡀⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⣸⠀⠀⢸⠀⠀⠀⠀⠀⢀⡴⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⡇⠀⠀⢻⡀⠠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠤⣄⡇⠀⠀⡾⠀⠀⠀⣠⠾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⠸⣦⠔⠛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⣀⢸⠇⠀⢠⡇⣀⡴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣸⠀⠀⠀⠀⠀⠹⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⢻⣀⠐⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢄⠀⡿⠀⠀⢰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣿⠀⠀⠀⠀⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠸⡏⠀⡨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡋⠘⣦⡇⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣏⠀⠀⠀⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠹⡜⠀⡼⢿⣿⣿⣿⣿⣿⣿⠿⡏⠘⣄⡞⠀⠀⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣧⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠐⣄⠙⣶⡀⢸⠀⢈⠉⡍⠀⢡⠀⣅⣠⠟⡀⠀⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⣷⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠈⢦⡈⠙⠫⠷⣶⣤⣖⣤⡾⠶⠋⢁⡴⠃⠀⠠⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡄⠀⠀⠀⠈⠒⠤⣄⣀⣀⣀⣀⣀⡤⠔⠋⠀⠀⠀⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢳⣀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⡀⡀⠀⠀⠀⢀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀