⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠴⠒⠂⠀⠀⠀⠒⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢄⠀⠀⠀⢯⠙⡻⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⢀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⡄⠀⠈⠚⠁⠀⠀ ⠀⡠⠤⠤⡔⠉⠀⢱⠀⠀⡎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀ ⢸⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠇⠀⢀⣀⡀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀ ⠈⠓⢤⣀⠀⠀⢀⡜⠀⡟⠀⠀⠀⠀⠀⣠⡤⠔⠚⠉⠠⡄⣆⢱⠀⠈⠙⠲⣄⠀⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠁⠘⠀⠀⢹⠀⠀⠀⠀⠀⢰⢡⠂⠀⠀⠀⠁⠈⠉⠀⠀⠀⠀⠈⡆⠘⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⢠⡤⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢃⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⠞⠙⣆⠀⠰⢄⣤⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡾⢤⡞⠉⠢⣄⠀⠀⠀⠀⠉⠁⠒⠒⠒⠒⠒⠤⣔⡾⠃⠀⢸⠁⠈⠒⠀⢢ ⠀⠀⠀⠀⠀⠀⠀⢸⣥⡼⡤⢶⡖⢿⠷⣦⣄⣀⡀⠀⠀⢀⣀⣠⠤⠚⠁⠀⠀⠀⠀⢳⠀⣀⡤⠊ ⠀⠀⠀⠀⢀⠔⠊⠉⠓⣺⡥⢾⠀⠘⠿⣦⣤⣼⠈⢻⠭⠅⣈⣇⡀⠀⠀⠀⠀⠀⡀⠀⠉⠁⠀⠀ ⠀⠀⠀⠀⢘⣦⡤⠖⠋⠁⠀⠘⢦⡀⠀⠀⡜⠋⠳⣼⠀⠀⠀⠀⠹⣦⡀⠀⠠⢼⣉⡦⠀⠀⠀⠀ ⠀⠀⠀⡴⠁⠀⠈⠲⣄⠀⠀⠀⠀⠉⠐⠲⠼⠶⠚⠁⠀⠀⠀⢀⡶⠛⠁⠀⠐⢦⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⢧⠀⠀⢀⡠⠞⣆⠀⠀⠀⠀⣀⣀⣀⣀⠀⠀⣀⣀⣷⡏⠀⢀⡴⠒⠲⣌⡇⣠⢦⡀⠀⠀ ⠀⠀⠀⠘⡖⠒⠉⠀⠀⠙⣇⣷⢠⠎⠉⠀⠀⠀⠀⢀⣤⣄⠙⣧⠀⢺⡀⠀⠀⣸⢰⠈⠛⠁⠀⠀ ⠀⠀⠀⠀⠸⡄⠀⠀⢀⡴⠛⣇⢸⣤⣶⣿⣿⣿⣿⡆⣿⣧⠀⣿⡀⠀⠉⠉⠉⠀⠸⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢳⠶⠚⠁⠀⠀⠈⣾⡟⣿⣿⣿⣿⣿⡧⠿⠟⠒⠛⡇⠀⠀⠀⠀⢆⡀⠀⠉⢢⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⡀⠀⠀⢀⡴⢹⡷⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠘⠤⡀⠀⠀⠀⠈⢳⣶⢾⣧⠀ ⠀⠀⠀⠀⠀⠀⡇⢷⡒⠊⠁⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣄⡈⠑⠢⠤⠖⢿⡙⠇⢙⠀ ⠀⠀⠀⠀⠀⠀⢳⢸⠑⢄⣀⡠⠋⠀⠀⠀⠀⠀⢀⣀⣀⣀⡴⠶⠤⣀⠉⣆⡀⠀⠘⡆⢻⠉⠉⠀ ⠀⠀⠀⠀⠀⠀⠸⡘⣇⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⢸⡀⠀⠉⠁⠈⠉⠉⠉⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣻⠀⠀⠀⡀⠸⠈⢄⢀⣀⣠⣀⠀⠀⠀⢀⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡷⢤⣀⠈⠂⠊⢂⣯⣫⣂⣏⣿⡭⡶⣶⡿⣽⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⡸⠀⢀⡴⠋⣹⠋⠹⣙⠿⣿⡿⣿⡖⣺⣿⠛⢶⢧⣀⠤⣠⡄⣦⠀⣀⣀⣺⡇ ⠀⠀⠀⠀⠀⠀⢠⡧⠔⢫⡥⠞⠁⠀⠀⡙⡲⢯⣧⡾⠟⠋⠉⠀⠁⠘⡇⠀⠀⠀⠀⠙⡆⠁⢿⣿ ⠀⠀⠀⠀⠀⠀⢸⠚⠉⠉⠀⠀⠀⠀⠀⠀⠏⡿⡞⡞⡇⢕⠒⠒⠂⠒⢣⠉⠉⠉⠐⠀⠂⠛⡶⠄ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⡟⣿⣿⡞⡶⠾⠤⣤⣀⣸⡄⡄⠀⠀⠀⠀⠈⡆⢸ ⠀⠀⠀⠀⠀⠀⠈⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⢹⢿⢿⣧⡐⠀⠀⠀⠀⡇⠉⠉⠛⠫⠉⠛⠓⠞ ⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⢾⠕⠂⠁⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠘⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠁⠂⠕⢾⠑⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀⠀⠀⠀⠀ ⠞⠓⠛⠉⠫⠛⠉⠉⡇⠀⠀⠀⠀⡐⣧⢿⢿⢹⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀ ⢸⡆⠈⠀⠀⠀⠀⡄⡄⣸⣀⣤⠤⠾⡶⡞⣿⣿⡟⢘⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀ ⠄⡶⠛⠂⠀⠐⠉⠉⠉⢣⠒⠂⠒⠒⢕⡇⡞⡞⡿⠏⠀⠀⠀⠀⠀⠀⠉⠉⠚⢸⠀⠀⠀⠀⠀⠀ ⣿⢿⠁⡆⠙⠀⠀⠀⠀⡇⠘⠁⠀⠉⠋⠟⡾⣧⢯⡲⡙⠀⠀⠁⠞⡥⢫⠔⡧⢠⠀⠀⠀⠀⠀⠀ ⡇⣺⣀⣀⠀⣦⡄⣠⠤⣀⢧⢶⠛⣿⣺⡖⣿⡿⣿⠿⣙⠹⠋⣹⠋⡴⢀⠀⡸⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣽⡿⣶⡶⡭⣿⣏⣂⣫⣯⢂⠊⠂⠈⣀⢤⡷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡽⢀⠀⠀⠀⣀⣠⣀⢀⢄⠈⠸⡀⠀⠀⠀⣻⠈⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠉⠉⠈⠁⠉⠀⡀⢸⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠉⠉⠈⠀⣇⡘⠸⠀⠀⠀⠀⠀⠀ ⠀⠉⠉⢻⡆⠘⠀⡀⣆⠉⣀⠤⠶⡴⣀⣀⣀⢀⠀⠀⠀⠀⠀⠋⡠⣀⢄⠑⢸⢳⠀⠀⠀⠀⠀⠀ ⠀⢙⠇⡙⢿⠖⠤⠢⠑⡈⣄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⢸⠀⠁⠊⡒⢷⡇⠀⠀⠀⠀⠀⠀ ⠀⣧⢾⣶⢳⠈⠀⠀⠀⡀⠤⠘⠀⠀⠀⠀⠀⠀⠁⠉⠛⠛⡷⢹⡴⢀⠀⠀⡀⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⢢⠉⠀⡀⢆⠀⠀⠀⠀⡇⠛⠒⠟⠿⡧⣿⣿⣿⣿⣿⡟⣾⠈⠀⠀⠁⠚⠶⢳⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⠸⠀⠉⠉⠉⠀⡀⣿⠀⣧⣿⡆⣿⣿⣿⣿⣶⣤⢸⣇⠛⡴⢀⠀⠀⡄⠸⠀⠀⠀⠀ ⠀⠀⠁⠛⠈⢰⣸⠀⠀⡀⢺⠀⣧⠙⣄⣤⢀⠀⠀⠀⠀⠉⠎⢠⣷⣇⠙⠀⠀⠉⠒⡖⠘⠀⠀⠀ ⠀⠀⡀⢦⣠⡇⣌⠲⠒⡴⢀⠀⡏⣷⣀⣀⠀⠀⣀⣀⣀⣀⠀⠀⠀⠀⣆⠞⡠⢀⠀⠀⢧⠀⠀⠀ ⠀⠀⠀⠀⠀⠋⢦⠐⠀⠁⠛⡶⢀⠀⠀⠀⠁⠚⠶⠼⠲⠐⠉⠀⠀⠀⠀⣄⠲⠈⠀⠁⡴⠀⠀⠀ ⠀⠀⠀⠀⡦⣉⢼⠠⠀⡀⣦⠹⠀⠀⠀⠀⣼⠳⠋⡜⠀⠀⡀⢦⠘⠀⠁⠋⠖⡤⣦⢘⠀⠀⠀⠀ ⠀⠀⠁⠉⠀⡀⠀⠀⠀⠀⠀⡀⣇⣈⠅⠭⢻⠈⣼⣤⣦⠿⠘⠀⢾⡥⣺⠓⠉⠊⠔⢀⠀⠀⠀⠀ ⠊⡤⣀⠀⢳⠀⠀⠀⠀⠁⠚⠤⣠⣀⢀⠀⠀⡀⣀⣄⣦⠷⢿⡖⢶⡤⡼⣥⢸⠀⠀⠀⠀⠀⠀⠀ ⢢⠀⠒⠈⠁⢸⠀⠃⡾⣔⠤⠒⠒⠒⠒⠒⠁⠉⠀⠀⠀⠀⣄⠢⠉⡞⢤⡾⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡀⣀⠀⠏⣾⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠦⣤⢄⠰⠀⣆⠙⠞⢠⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠇⢃⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠷⡤⢠⠀⠀⡇⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⡆⠈⠀⠀⠀⠀⠉⠈⠁⠀⠀⠀⠂⢡⢰⠀⠀⠀⠀⠀⢹⠀⠀⠘⠁⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢸⠀⣄⠲⠙⠈⠀⢱⣆⡄⠠⠉⠚⠔⡤⣠⠀⠀⠀⠀⠀⡟⠀⡜⢀⠀⠀⣀⢤⠓⠈ ⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⡀⣀⢀⠀⠇⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢸⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⡄⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡎⠀⠀⢱⠀⠉⡔⠤⠤⡠⠀ ⠀⠀⠁⠚⠈⠀⡄⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡜⢀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀ ⠀⠀⡻⠙⢯⠀⠀⠀⢄⠓⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠞⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢄⠢⠒⠀⠀⠀⠂⠒⠴⣠⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀