⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣤⣤⣴⣿⠟⠁⠀⠈⠛⠿⣿⣿⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣴⣶⣇⠀⢀⣴⣿⠟⠉⠉⠙⠛⠁⠀⠀⠀⠀⠀⠀⠀⠈⠉⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⡟⠙⢿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣿⡇⠀⠀⠀⠀⠀⢀⡴⠶⢦⣄⣀⣤⠾⠛⠛⣧⡀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⣇⠀⠀⠀⠀⣴⠋⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠻⣦⣤⡤⠶⠻⢿⣦⠀⠀⢻⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠉⢳⣶⢶⡿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⣿⠁⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣿⣄⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠄⠀⠀⠀⠀⢠⡼⠋⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⡿⠁⠀⢀⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⠠⣝⢦⡀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⠇⠀⠀⠘⣿⠇⠀⠀⢀⠎⠀⠀⠀⠘⠛⠛⠿⠆⠀⠀⠀⠀⠠⣝⢧⡳⡄⣸⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠀⠀⠀⠀⠀⠀⢠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢢⣜⢷⣽⣷⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡏⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠆⣹⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣇⠀⠀⠀⠀⠀⠀⠈⠛⠂⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣿⠀⠀⣾⣤⣀⣀⣀⢀⣀⣀⣀⡤⠔⠚⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣇⠀⠻⠳⢤⣈⣉⠉⠉⠀⣀⣀⣤⠖⠋⠟⠀⠀⠀⠀⠀⠀⢀⣀⣠⣾⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⣿⣆⠀⠀⠀⠈⠙⣛⣛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⢿⣧⡀⠀⠀⠈⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠙⠿⣿⣶⣦⣤⣤⣤⣤⣶⣶⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣍⣁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠋

⠀⠀⠀⠀⠀⠀⠀⠀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣄⠀⣠⠶⠲⠞⠁⠀⠙⠛⠳⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡟⠙⠛⠁⣀⣀⢀⡤⢤⠀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀ ⢠⡷⢄⣠⠊⠀⠀⠁⠀⡀⠑⠒⠈⢳⠀⢻⡆⠀⠀⠀⠀⠀⠀ ⠀⣷⠃⢠⡀⠀⠀⠀⠀⠈⠀⠀⠀⢎⠀⢸⡇⠀⠀⠀⠀⠀⠀ ⢠⡇⠀⠘⢁⡄⠀⠀⠉⠉⠀⠀⠀⣳⢧⣾⠃⠀⠀⠀⠀⠀⠀ ⢸⡇⠀⠀⠘⠆⠀⠀⢀⠀⠀⠀⠀⠁⢿⡏⠀⠀⠀⠀⠀⠀⠀ ⠈⣇⠸⢖⡀⠀⠐⣂⠹⡇⠀⠀⠀⣀⣼⠇⠀⠀⠀⠀⠀⠀⠀ ⠀⠹⣦⠀⠈⠭⠉⠀⠀⠀⠀⣠⡾⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠳⢦⣄⣀⣀⣠⡴⠞⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⠔⠉⠒⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠺⠤⠔⠁⠀⠀⢀⣀⠀⠀⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⢀⡰⠋⠉⠈⠉⠉⠳⠤⠔⢦⡈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⡜⠑⠂⠀⠀⠀⠀⠒⠄⠀⠀⣴⠃⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢰⠄⢀⠆⠀⠰⢦⠀⠀⠀⢽⣳⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠔⠋⢹⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠠⣏⠀⠀⠀⠀⠀⠀⠀⠕⢻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢠⡄⣀⣀⣀⠠⠴⣄⠀⠀⠀⠀⢈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⣠⣧⣀⠘⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡌⠉⠒⣦⠖⠒⠉⠉⠀⠀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢮⠀⢀⡀⠀⠙⡆⠘⣦⣤⣀⣀⣀⠀⠀⢀⣀⣀⣙⣦⡀⠀⠀⠀⠀⠀⠠⡾⠓⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⠉⠉⠉⠉⠚⡅⢀⡟⡄⠀⠈⠉⠉⠉⠉⠀⠀⠀⢸⠉⠳⢶⣤⣀⡤⠖⠁⢀⡞⠀⠈⠓⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⡗⠉⠓⠒⠲⡇⢸⢁⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⣀⣠⠴⠋⠀⠀⠀⠀⠀⠈⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⠶⢖⣒⣺⣵⣣⠊⠀⣀⣀⣀⡠⠤⠔⡿⠀⠀⠀⡞⠀⠀⠀⡞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⣇⠀⠀⠀⡇⠀⠀⠀⡇⠀⠀⠀⠀⢦⣄⣀⠀⠀⠀⠀⠀⠀⢙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠃⠀⠀⢸⠇⠀⠀⠀⠀⣿⣿⣿⠛⢲⡄⠀⠀⢀⣼⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢰⠀⠀⠀⢸⠀⠀⠀⠀⢰⣿⣿⡟⢀⡞⠀⢀⣠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠦⢄⣈⠀⠀⠀⢸⠀⠀⠀⠀⣼⣿⣿⣇⡎⣠⣴⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠈⠀⠀⠀⠈⠓⠒⠒⠚⠋⠉⢸⡿⢿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣸⡇⠀⠉⡹⠻⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠈⠉⠛⠒⠒⠒⠒⠚⣿⣿⣿⣿⣷⣀⣀⣙⣢⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠛⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣭⣁⢀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠋⠈

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢂⠄⠄⠠⠀⡑⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡑⡀⠀⠀⡀⠀⣆⡐⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⡅⠀⠀⠀⠀⠀⡇⣀⢃⠠⡀⠀⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⠒⠓⠄⢄⣀⠀⠀⠀⠱⡈⠂⠁⢀⡴⣉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠐⡥⠬⠁⡈⠆⠀⠀⠀⠀⢠⠑⠒⢂⡠⠃⠉⠂⢄⠀⠀⠀⠀⠀⠀ ⠀⠉⠒⠓⠢⠄⠒⠂⢸⠀⠸⠀⠘⠀⠀⣀⠀⠀⠀⠡⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⡄⠀⠀⣿⡏⡔⢀⣼⠃⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡐⠂⠀⠡⠠⠼⠿⣬⣶⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡗⠠⠤⠤⠤⣤⣴⡄⠨⡱⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠆