⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠒⢢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠁⡇⠀⡌⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠇⠸⠁⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⢤⡀⡠⠐⠂⠉⠄⠀⠀⠠⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡤⠚⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡩⠂⣆⠏⣮⠃⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠉⢛⠣⣁⠀⠀⢰⡳⢀⠔⠊⠉⠙⡆⠀⠀⠀⠀⠀⠀⠀⣀⡀⢀ ⠀⠀⠀⠀⠣⡌⠻⢄⡈⡱⠁⠀⠀⠀⢀⢉⠱⠀⠀⠀⡠⠐⠉⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣱⢢⢌⣇⣠⠀⢀⡀⠘⡁⠀⠀⡠⠊⠀⡀⠤⠒⠂⢸ ⠀⠀⠀⠀⠀⡔⠹⠊⠀⠀⠀⠧⠚⠦⡉⠁⢠⠊⡠⠐⠉⠀⠀⠀⢀⠃ ⠀⠀⠀⠀⠀⡝⠁⠀⣀⡄⠀⠀⠀⠀⢈⣷⡧⠊⠀⠀⠀⠀⠀⢀⡎⠀ ⠀⠀⠀⠀⠀⠉⠒⠊⠑⢽⠀⠀⠀⠠⡇⣋⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⠀⠀⢀⡴⠕⢻⢌⠉⠉⠉⠉⡩⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠼⣅⣀⠤⢮⣀⡠⠃⠀⠉⠂⠤⠊⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⡿⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⡍⠀ ⠻⡟⢿ ⠀⠀⠀⠀ ⢿⣿⠟⠉⠀⠀ ⢹⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣆ ⚞•⚟ ⡜⠀⠀⠀⠀ ⠀ ⠈⣡ ⚞•⚟ ⣧⣀⣀⣀⠀⠀⠀ ⠀⠀⠀⣀⣤⣴⡒⠁⠑⠠⠤⠘⣹⣿⣿⣷⣶⣤⠌⠊⠁⠸⡑⠠⠠⠤ ⠃⡘⠀⠀⠈⠉⠹⡀ ⠀⣼⣿⣿⣿⣿⣿⣶⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠉⠒⠀⠚⠈⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠫⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉⠀⠀⠀⠈⠓⠿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠋⠁⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⢯⢿⣿⠀⠀⠀⠀⠀⠀⢉⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⢿⠀ ⚞•⚟ ⢐⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠿⡇⠀ ⚞•⚟ ⠀⡛⠀⠀⠀ ⠀⠀⠀⠀⠀⠀ ⠀⠀⠀ ⢸⢶⠀⠀⠀⠀⢀⣌⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⡠⢼⡀⠀⠀⠀⠀ ⣰⠛⢲⠒⠢⠤⠤⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣤⣶⡞⠉⠀⠉⠠⠤⠴⠊⣸⣿⣿⣿⣿⣿⣷⣄⠔⠉⠀⠀⠸⡈⠒⠤⠠⠄⠁⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣦⣄⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠙⠢⠤⠄⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⣤⣾⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣸⣿⡿⢿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⡍⠀⠈⠻⡟⢿⣇⠀⠀⠀⠀⠀⢿⣿⣿⠟⠉⠀⠀⢹⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⣿⡅⠀⠀ ⠀⠀⣼⠀⠀⠀⠀⠀ ⣾⡿⠀⠀⠀⠀ ⠀⡼⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⣆⠄⠀⠀ ⠀⡜⠀⠀⠀⠀⠀⠀⠀⠈⣡⠀⠀⠀⠀⢠⣧⣀⣀⣀⠀⠀⠀ ⠀⠀⠀⣀⣤⣴⡒⠁⠑⠠⠤⠘⣹⣿⣿⣷⣶⣤⠌⠊⠁⠸⡑⠠⠠⠤⠃⡘⠀⠀⠈⠉⠹⡀ ⠀⣼⣿⣿⣿⣿⣿⣶⣤⣤⣤⣾⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠉⠒⠀⠚⠈⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⡯⠍⠳⡄⢀⡴⠊⠉⠉⠳⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠁⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⡀⠀⠀⠀⠀⠀⠶⠀⠀⠀⠀⣤⠀⠀⠀⠈⠳⠿⠖⠲⢶⣄⠀⠀ ⠀⠈⣇⠀⠀⠈⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀ ⠀⠀⡿⠀⠀⠀⠀⠀⠉⠉⠓⠓⠛⠛⠋⠉⠁⠀⠀⠀⠀⠀⠀⣸⠇⠀ ⠀⠀⣻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣺⠃⠀⠀ ⠀⡼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⡁⠀⠀ ⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡀⠀ ⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡄ ⠹⣆⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣰⠇ ⠀⠈⠓⠿⠥⢦⣤⣤⣤⣤⣤⣤⣄⣀⣀⣀⣠⣤⣤⠤⠤⡬⠶⠚⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⠿⠫⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⠉⠀⠀⠀⠈⠓⠿⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⡿⠋⠁⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠁⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠈⢯⢿⣿⠀⠀⠀⠀⠀⠀⢉⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⠀⠀⠀⠀⠀⠀⢐⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⡇⠀⠀⠀⠀⠀⠀⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢶⠀⠀⠀⠀⢀⣌⣀⣀⡀⠀⠀⠀⠀⠀⠀⣀⡠⢼⡀⠀⠀⠀⠀⣰⠛⢲⠒⠢⠤⠤⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣠⣤⣶⡞⠉⠀⠉⠠⠤⠴⠊⣸⣿⣿⣿⣿⣿⣷⣄⠔⠉⠀⠀⠸⡈⠒⠤⠠⠄⠁⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣾⣿⣿⣿⣿⣿⣦⣄⣀⣀⣀⣠⣴⣿⣿⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠙⠢⠤⠄⠤⠒⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢀⣴⠾⣿⠷⢶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠿⠟⣁⣠⣤⣤⣤⣦⣾⣏⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⣯⣴⠟⠋⠁⠀⠀⠀⠀⠀⠉⠙⠻⣦⣄⠀⠀⢿⣆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⡾⠋⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢙⣳⣴⠿⠋⢷⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⢀⡴⣾⣵⡛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣤⡿⠃⠀⠀⠀⠀⠀⠀⣠⣴⣤⡀⠀⠀⠀⠀⠀⠀⠀⣴⣞⣽⣤⣴⣿⣿⠟⠓⠒⣶⣀⣤⣶⣶⡆⠀⠀⠀⠀⠀ ⠀⠀⢠⡟⣿⠃⠀⠀⠀⠀⠀⠀⡾⠃⠀⠘⣷⠀⠀⠀⠀⠀⠀⠀⢹⣾⣿⣿⣿⡿⣦⣀⣤⣴⣿⣿⣿⣿⣯⣤⣤⣀⡀⠀⠀ ⠀⠀⣿⣷⡏⠀⠀⠀⠀⠀⠀⢸⡇⠀⣠⡀⣿⠀⠀⠀⠀⢀⡀⣀⣾⣿⣿⣿⣿⣿⣿⠋⣿⣿⣿⡿⠛⠀⠒⠿⡿⣭⣥⣀⠀ ⠀⠀⣿⣾⠁⠀⠀⠀⠀⠀⠀⢸⡇⠀⢿⡟⣿⣠⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠘⣿⣏⣤⣤⣤⣄⠀⠻⢿⣍⠉⠁ ⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠸⣧⡀⣀⣼⠇⠉⠛⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⢹⣿⠁⠀⠉⠙⠛⠛⠛⠛⠛⠀ ⠀⠀⣾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠋⠁⠀⠀⠀⠀⢀⡿⠹⢫⣿⣿⣿⣿⠃⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣼⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⣀⣤⢿⣿⣿⣿⠀⠀⠀⢀⣴⠿⢧⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⡃⠀⠉⠉⠛⠉⠁⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠛⠁⠀⢹⡛⢛⣖⣾⣛⣿⣧⣚⣋⣥⠟⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢳⣥⣀⣀⣀⣀⣤⠶⠟⠛⠀⣹⣦⣤⣤⡶⠶⠟⠋⠁⠀⠀⠀⠀⠈⠻⢦⣭⣭⣭⠶⠏⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⢮⣭⣭⣥⣤⡴⠶⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀