⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠒⡩⡗⡦⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⣿⡗⡞⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠒⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡝⢱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣸⠁⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢰⡶⠦⣄⡼⡕⠀⠉⣷⡤⢴⢲⠃⠀⠀⠀⠀⠀ ⠀⠀⠸⣇⢿⣿⣟⣽⣿⣛⣽⡔⡧⣾⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠛⢿⣿⡆⠀⠀⣿⣉⡵⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣠⣴⡟⠻⡟⠉⢻⢆⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⣤⣎⠟⠋⠸⣿⠅⡃⠀⢠⡇⢾⣯⡆⠀⠀⠀⠀⠀ ⠰⠿⠁⠀⠀⢸⡗⣿⡇⠀⣾⠁⠀⠈⠚⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣾⡏⠛⠛⢯⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠿⠇⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣴⣦⡀⢸⣿⠀⣿⣠⣤⠀⣶⣴⣤⣴⣦⠀⢾⡇⢠⣤⣤⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣅⣸⣿⣼⣏⠀⣿⣿⡇⠀⣿⠙⣿⡯⢿⡇⣾⡇⢸⡏⠉⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠛⠁⠘⠛⠈⠛⠈⠛⠂⠛⠀⠛⠁⠘⠃⠘⠃⠘⠃⠀⠛⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡤⠶⠆⠐⣛⡿⠿⠖⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡟⠉⠁⢀⣤⠴⠛⢁⣠⡴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣷⣤⣄⣀⣀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠀⣀⣪⣥⠶⠟⠉⠁⠀⠀⠀⡴⠚⠲⣤⠤⠤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠋⠉⠉⠓⢲⣼⣟⠁⠀⠀⣿⠋⠛⢿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡾⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⡀⢱⣀⡀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⣀⠀⠀⠀⠀⠀⠀⣿⠉⠳⣄⣠⡇⣀⣉⣾⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡼⢻⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠃⠀⢿⡀⠙⢷⡾⠿⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣴⣿⣆⠀⠀⠀⠀⣰⣧⣨⣤⣾⢻⣿⣿⠋⢹⣧⠀⠀ ⠀⠀⠀⠀⠀⢀⡞⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣄⠀⠀⣙⡶⠼⠇⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⣀⣸⠟⢿⣿⣿⣯⠴⠚⠁⠘⣿⠁⢹⣶⡿⢧⣤⡾⠋⠀⠀ ⠀⠀⠀⠀⠀⡾⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣽⣿⠋⠉⠙⣆⠀⠀⢻⡏⠁⠀⠀⠀⠀⢀⢖⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⣾⠹⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠇⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡞⣼⠁⠀⠀⠀⠈⠳⠤⠾⠁⠀⠀⠀⠀⢰⢏⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⣿⡀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⢰⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣿⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠰⢿⣟⡻⣦⣾⠏⠀⠹⣶⣄⠀⠀⠀⠀ ⠀⢠⣴⣿⠌⠉⠀⠹⣷⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠠⣶⣤⡿⠟⠁⠀⠀⠀⠈⠛⢦⡀⢀⣀ ⢠⣿⣿⢤⡴⠋⠀⣠⣼⣿⣧⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⠫⠿⠛⠉⠐⢿⢦⡀⠀⠀⠀⠀⠀⣼⣿⡷⣄⠀⠀⠀⠀⠀⣴⢾⣿⣯⠀ ⢸⣿⣿⣿⠇⠀⠀⠻⣿⣿⣿⠀⠀⠀⣿⠙⠿⣟⠫⡤⠀⠀⠀⠠⣬⣽⠿⠟⢙⡇⠀⠀⢠⣿⣶⣶⡖⠀⠀⡶⢶⣾⣷⠀⠀⠀⠀⢰⣷⣽⣷⡟⠀⠀⠂⠀⣀⣻⣾⣿⣿⠀ ⠘⣿⣄⠀⠀⣿⡇⠀⠀⣽⠟⠀⠀⠀⠹⣄⠀⠸⠿⠿⠇⠀⠀⠦⣿⣿⠀⣀⡾⠁⠀⠀⠸⠿⠿⠞⠃⠀⠀⠻⠿⣿⡿⠀⠀⠀⠀⠸⣿⣼⣧⣤⣤⣤⣴⣶⣿⣿⣿⣿⣿⠀ ⠀⠈⢿⣦⡀⠈⠁⣠⣾⠋⠀⠀⠀⠀⠀⠈⠳⢤⣄⠀⠀⠀⠀⠀⣠⣿⠿⠋⠁⠀⠀⠀⠀⠘⢧⣀⡤⠶⢦⣄⣠⠟⠀⠀⠀⠀⠀⠀⠙⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀ ⠀⠀⠀⣿⡇⠀⠀⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⡼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣯⡽⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⢀⣾⠟⠛⠛⠛⠿⠿⢿⣿⣿⣧⠀⠀ ⠀⣠⣾⣿⠀⠀⠀⠸⡿⣦⡀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣐⣿⠏⠀⠈⢻⣤⣀⠀⠀⠀⠀⠀⢀⣾⣿⡄⠀⠀⠀⠀⠀⠀⢀⣿⣿⣧⠀ ⣰⣿⣷⡏⠀⠀⠀⠀⣧⢈⣳⡀⠀⠀⠀⠀⠀⢀⣾⣶⠀⠀⠀⢰⣿⣧⠀⠀⠀⠀⠀⠀⠀⠸⣿⠃⠀⠀⠀⠘⣧⡿⠃⠀⠀⠀⢠⣾⡏⣹⣇⠀⠀⠀⠀⣀⣤⣾⣿⣿⡟⢧ ⠁⠀⣿⡇⠀⠀⠀⠀⣿⠈⢷⣿⡆⠀⠀⠀⢀⣾⡿⡇⠀⠀⠀⠀⡟⣿⣧⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠻⠟⠁⢻⣿⣿⣷⣿⣿⣿⣿⣿⣿⠏⠁⠀ ⠀⠀⢻⣇⡶⠶⢶⣦⣿⠀⠀⠁⠀⠀⠀⠀⠈⠛⠀⡇⣠⠤⢤⣠⡇⠈⠉⠀⠀⠀⠀⠀⠀⠀⠈⣷⡶⠒⠲⣶⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⢿⣿⡿⠛⢿⣿⣿⠏⠁⠀⠀ ⠀⠀⠸⣿⡇⠀⠀⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡿⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡧⠀⠀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠇⠀⠀⠿⠿⠁⠀⠀⠀ ⠀⠀⠀⠉⠁⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠤⠴⣶⠦⢤⡀⣀⡀⠀⠀⠀⠀⠀ ⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠀⢠⣃⣠⠼⠤⠄⠼⠵⠦⣀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣶⡊⠭⠤⠤⠤⠄⠀⠒⠒⠚⠚⠛⠐ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⣺⠗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⢉⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡠⠊⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⠁⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣀⣀⠀⡰⠃⠀⠀⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡎⠁⠀⡻⠋⠁⠉⢳⠀⠈⠑⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⡇⠀⢀⡇⠀⠀⠀⢀⠀⠀⠀⠀⠙⡄⢀⣠⠤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⠒⠉⠈⠢⠤⠔⠊⠀⠀⠀⠀⠀⣿⠿⣎⣉⠤⠔⢷⠀⠀⠀⠀⠀⠀⠀ ⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢁⣰⠧⠤⠤⢲⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⢦⡀⠀⠀⠀⠀⠀⢀⣠⣾⠿⠧⠤⠵⠔⠒⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣨⢗⣶⠖⠒⠋⡏⠘⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣿⡿⠋⠉⠘⣄⠀⢰⣿⡆⠀⡀⣳⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠀⠀⠀⠀⠈⠑⢺⣿⡤⠚⠉⢹⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢀⣾⠇⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢨⣾⠟⢀⠢⡄⠀⠀⢠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣠⠴⠊⠻⡷⣴⠟⠁⠀⣠⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⡿⠁⠀⠀⠀⠈⠛⠓⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡘⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢰⠀⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢣⡀⠈⠉⠉⠉⠉⡖⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡇⠀⠀⠀⠀⠀⠳⢬⡥⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡀⢠⢖⠒⢦⠀⠀⠀⠀⠸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⢃⡇⠸⠇⡼⠀⠀⢐⠴⠛⡇⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠻⣟⠋⠀⠀⠀⣏⣠⡾⣇⡠⠔⠚⠉⠀⠉⠒⢤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠒⢺⡽⢽⣋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⢀⣠⣇⣀⡀⠀⠀⠀⠀⠀⠀⠨⣇⣷⠀⢀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠛⠉⠁⠀⠀⠈⠉⠙⠒⠒⠒⠚⠋⠉⠉⠁⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⠀⠀⠀⠤⣀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⡀⠠⠀⠀⠁⠀⠀⠀⠀⠀⠠⠂⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⢠⠆⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠠⠜⠁⠀⠀⡀⠤⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡂⠌⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⡿⣿⣿⣦⣄⡀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⣫⢟⣮⣿⣿⣿⣿⣿⣿⠷⣧⣒⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡏⣴⣦⠈⣞⣟⣻⣿⣿⣿⡏⢰⣶⡌⢻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡞⢯⠗⣬⣥⠾⢋⡼⣼⣿⣿⣿⣿⣦⣭⣴⣿⣿⣯⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣟⣲⣷⣬⣬⡾⣊⣃⣘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢘⠏⣭⠾⣞⣷⡿⠯⠽⢯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣨⣭⣝⣾⠛⣒⣺⣯⣛⠫⠥⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣡⠨⠭⡽⠿⢓⣓⣉⠴⠿⢭⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢨⠷⠚⠛⣉⣙⠛⠿⢶⠶⣖⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣌⡭⣴⣒⠒⠠⣬⣽⣝⢖⡤⠽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢘⢽⣽⣿⣿⢳⣷⢮⣜⣵⡺⢋⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠄⡞⢿⣿⣭⣟⡼⣻⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠈⢻⠱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡼⠁⠘⢟⡶⣽⡺⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠑⡐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢈⠌⠀⠀⠠⠘⠙⠾⢫⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠻⠟⡼⡡⠀⠀⠀⠀⠈⢄⡀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠒⠋⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠛⠻⠿⠿⠛⠛⠑⠀⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠁⠉⠁⠉⠉⠋⠚⠒⠒⠒⠙⠉⠈⠀⠀⠁⠉⠛⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⢀⠀⣷⣇⠨⠀⠀⠀⠀⠀⠀⡀⣀⣇⣠⢀⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⣋⢽⡽⢺⠒⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡀⢤⠒⠉⠀⠉⠚⠔⡠⣇⡾⣠⣏⠀⠀⠀⠋⣟⠻⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⡇⠛⠴⢐⠀⠀⡼⠇⠸⡇⢃⠈⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠸⠀⠀⠀⠀⢦⠒⢖⢠⡀⢸⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⡥⢬⠳⠀⠀⠀⠀⠀⡇⢠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⣤⡖⠉⠉⠉⠉⠈⡀⢣⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠑⠀⢰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢱⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⡇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⡘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠊⠒⠓⠛⠈⠀⠀⠀⠁⡿⣴⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠍⣠⠀⠁⠟⣴⡷⠻⠊⠴⣠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⢠⠀⠀⡄⠢⢀⠟⣾⢨⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠇⣾⢀⢀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠢⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡐⣍⣶⣢⣉⡀⠠⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢼⡲⣝⡻⣗⣾⣖⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢿⣳⣯⣷⣽⣿⣿⠇ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠸⢳⢿⣿⣿⢿⡃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣄⣤⣶⣿⣿⣿⢿⣏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢘⣿⣿⣿⣿⣿⣻⣿⣿⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣧⣿⣷⣿⣿⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣼⣿⣿⣿⣿⣿⣿⣿⣟⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡙⣿⣿⣿⣿⣿⡟⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⡯⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠿⣿⡟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠁⣻⡇⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀
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