⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣴⡀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢤⡾⡿⠉⠉⠈⠻⣦⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢐⣿⡙⠀⠀⠀⠀⠐⢻⡖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣴⢾⡷⣾⢿⣻⣟⣾⢷⣤⡤⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣺⠯⠁⠀⠀⠀⠀⠀⠉⢿⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⢿⣻⡾⣽⢯⠿⡽⠻⣽⠾⣯⡿⣾⡽⣿⣆⡀⠀⠀⠀⠀ ⠀⠀⠀⣀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠺⣧⠄⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⣽⣻⢷⠛⠁⠀⠀⠀⠀⠀⠀⠀⠉⠳⠟⣷⣯⣷⣆⠀⠀⠀ ⠀⠀⠀⣹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠠⢿⡄⠀⠀⠀⠀⠀⠀⠀⣾⢯⣿⡽⡯⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⣻⣾⢦⡀⠀ ⠀⠀⠠⣿⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣯⡄⠀⠀⠀⠀⠀⣸⣟⡿⣾⡽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣞⡿⣦⠀ ⠀⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⠀⣿⣽⣻⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣟⣧⠂ ⠀⠀⣼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣦⠀⠀⠀⠀⠀⣾⣷⣻⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡷⣯⢿⡀ ⠀⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⠀⠀⠀⠀⠀⠸⣷⣟⣾⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⡽⣏⠀ ⠀⠃⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢫⡇⠃⠀⠀⠀⠀⠐⣿⣾⣽⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣯⣿⠃⠀ ⠀⢸⣇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⣿⠀⠀⠀⠀⠀⠀⢹⣞⡷⣿⢶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣿⢷⣻⡎⠁⠀ ⢀⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠆⠀⠀⠀⠀⠀⠀⠩⣿⢯⣟⣿⣦⢦⣄⣀⠀⠀⠀⢀⣠⣠⣶⢿⣻⢾⡻⠃⠀⠀⠀ ⠘⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡆⠀⠀⠀⠀⠀⠀⠀⠈⠋⠿⣾⡽⣯⣟⡾⣟⣿⣻⢯⣿⡽⣾⣻⠯⠋⠀⠀⠀⠀⠀ ⠀⣿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢽⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠙⣿⣽⢾⣯⡿⠊⠋⠁⠁⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣿⢾⣻⣞⣷⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣼⡟⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢯⣟⡿⣾⣽⣳⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡇⠜⣷⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⣯⢿⡽⣷⢯⣟⡮⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢼⡇⠀⠨⢿⣅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⢿⣽⣻⢿⣽⣻⡽⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀ ⢾⡇⠀⠀⠀⠝⢷⣄⠄⠀⠀⠀⠀⠀⠀⠀⣼⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣽⣻⣞⣯⡿⡾⣽⣻⢷⣟⡀⠀⠀⠀⠀⠀⠀⠀ ⣾⡇⠀⠀⠀⠀⠀⠫⠻⣦⣄⡀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣳⣯⢷⣻⣽⣻⡇⠹⣯⢿⣞⢆⠀⠀⠀⠀⠀⠀⠀ ⣻⡇⠀⠀⠀⠀⠀⠀⠀⠁⠫⢻⢶⣥⣀⠀⣿⣅⣠⣤⣤⣤⣴⡶⣞⣶⡿⣿⣻⢷⡯⠗⣿⣳⣯⡇⠈⣟⣯⡿⣏⠀⠀⠀⠀⠀⠀⠀ ⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢛⡷⣯⣟⡹⢟⣾⣳⢿⣯⠷⡟⠷⠻⠉⠁⠀⣿⣳⣯⡇⠀⢸⢯⣟⣿⣃⠀⠀⠀⠀⠀⠀ ⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠂⠋⠛⡷⢯⣽⣀⢀⠀⠀⠀⠀⠀⠀⠀⣿⣳⣟⡆⠀⠈⣿⣻⢾⣭⠀⠀⠀⠀⠀⠀ ⠘⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡏⡀⠀⠀⠀⠈⠈⠙⢻⢶⣤⣀⠀⡀⠀⠀⣿⣳⣯⢷⡀⠀⢺⡽⣯⣷⠇⠀⠀⠀⠀⠀ ⠀⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠻⢶⣤⣈⠿⣷⢯⣿⢦⠀⠘⣿⣽⢾⡇⠀⠀⠀⠀⠀ ⢰⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢨⣽⣻⢶⣭⣛⠷⡀⢀⣻⣬⣽⣛⢀⠀⠀⠀⠀ ⠀⢿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣻⢷⣾⣽⣛⠷⣮⣝⡿⣿⣽⢧⠀⠀⠀⠀ ⠀⡸⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣟⣷⢯⣯⢳⣟⡿⣿⣳⣿⣷⣷⢿⡓⠀⠀⠀⠀ ⠀⢠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣟⡾⣿⡁⠀⢿⡽⣷⢷⢻⣿⡡⠀⠀⠀⠀⠀⠀ ⠀⠀⢹⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣾⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⢯⣟⡷⠀⠀⠹⣿⡽⣿⢸⡿⣧⡄⠀⠀⠀⠀⠀ ⠀⠀⠛⣷⠄⠀⠀⠀⠀⠀⠀⠀⠀⣠⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢼⣯⣟⣯⡅⠀⠀⠀⢿⣽⣻⣼⡧⢿⡄⠀⠀⠀⠀⠀ ⠀⠀⠠⢸⡟⠀⠀⠀⠀⠀⠀⠀⢀⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣧⣟⣧⠀⠀⠀⠀⢿⣻⣟⣿⣇⡼⣧⠄⠀⠀⠀⠀ ⠀⠀⠀⠉⣿⠁⠀⠀⠀⠀⠀⠀⣀⣿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣾⣽⠣⠀⠀⠀⠀⢘⣷⣻⡏⣿⡵⢿⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠚⣯⠂⠀⠀⠀⠀⠠⣼⠧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣟⡷⣯⠇⠀⠀⠀⠀⠈⣯⣷⢷⢻⡤⣼⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠽⣧⣀⠀⠀⣔⣾⡋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⡾⣿⣍⠀⠀⠀⠀⠀⠀⢸⣯⢿⣾⣧⣸⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠹⠻⠟⠏⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡽⣷⡛⠀⠀⠀⠀⠀⠀⠸⣟⣯⣇⣿⣱⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⢿⣽⡁⠀⠀⠀⠀⠀⠀⠀⢿⣽⣻⢮⠛⠑⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣯⡿⡾⠁⠀⠀⠀⠀⠀⠀⠀⢿⣳⡿⣯⡆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢷⣻⡿⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⡽⣯⡅⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣻⡽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡽⣯⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡿⣽⠅⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣽⢷⠟⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⣶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣿⣿⣿⡿⠟⠋⠛⠛⠿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⣿⣿⡟⠉⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡿⠿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣷⣶⣿⣶⡶⠟⠛⠿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⡄⠀⢀⣠⣤⠤⢼⡄⠀⠀⠀⠀⠘⢻⣿⣿⣿⠈⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⣿⣿⣧⡀⠸⠟⠀⠀⠘⠁⠀⠀⠀⠀⠀⣸⠿⣿⣯⣀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢿⣿⣿⣷⣄⡀⠀⢸⣇⠀⠀⠀⠀⣠⠎⠁⠀⠘⠿⠟⠓⠚⠉⠀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠻⣿⣿⣿⣿⣷⣦⣼⣦⣤⣤⣶⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠙⠿⠿⣿⣿⣿⣿⣿⣿⡿⠿⠒⣲⣦⣄⡀⠀⠀⣀⣀⣀⢀⣸⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡇⢠⣿⣿⣏⠿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢠⠴⠢⠴⠉⠣⣄⡀⠀⠀⠀⢸⣿⣿⣿⠁⢸⣿⣿⣿⠀⠙⢿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡴⠁⠀⠀⠀⠀⠀⠀⠈⢣⠀⢀⣿⣿⣿⡟⠀⠈⣿⣿⣿⡇⠀⠀⠹⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⡁⠀⠀⠀⠀⠀⠀⠀⠀⠸⣠⣾⣿⡟⠁⠉⠒⢾⣿⣿⣿⠁⠀⠀⠀⠈⢿⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⠋⠉⠱⠀⠀⣠⠊⠉⣱⣶⣿⣿⣿⡀⠀⠀⠀⠀⠉⠉⠁⢣⠀⠀⣠⣴⣾⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡰⢁⣠⣴⣾⣿⣿⣿⣿⡿⠋⠙⢆⠀⠀⠀⠀⠀⠀⢈⣴⣿⣿⣿⣿⡿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢰⠁⢾⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⣼⣿⣿⡿⠛⠁⠀⢻⣿⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠦⣈⣙⣋⣩⠀⠀⠀⠀⠀⠀⠀⠀⣨⣦⣤⣤⣤⣾⡿⠛⠁⠀⠀⠀⠀⠘⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣦ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⡿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣯⣇⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠛⣻⡇⢠⠀⢀⣤⣤⣤⣶⢞⣯⣭⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣠⠞⣽⡿⠖⣿⣷⣿⣿⣾⢿⡿⡿⢿⣿⢿⣾⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⣧⡀⠀⠀⠀⠈⠻⣦⡀⠀⣇⣿⣽⣵⡆⠼⡿⢻⡟⣋⡄⢸⠀⢠⠞⣡⣏⣽⣿⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢻⣿⡿⣿⣳⣶⣶⣿⣿⡄⣿⣧⣿⡉⣇⡄⠔⡟⢷⡿⠃⠸⣷⢃⢠⢷⣯⠿⠛⠻⣾⣻⣿⡿⣶⣤⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣿⣷⣿⣿⣿⣿⣿⣿⣿⣿⢻⣟⣌⣡⣴⣁⣼⣵⣴⣶⣿⣿⡟⠀⡁⢍⣛⡻⢿⣿⡻⠛⠛⠒⠫⠓⢦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⢈⣿⢟⣿⣿⢸⠀⣹⣿⣿⡿⠿⠛⠛⠛⠛⠿⢿⣿⣿⣷⣍⣻⣦⡛⠛⠷⢀⣠⠷⠛⠋⠉⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣯⣯⣅⡤⣾⠯⠤⠤⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢟⣿⣿⣿⡺⣿⣯⣻⣿⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣇⠈⣿⣿⣾⣷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢃⡾⢹⢿⣿⣿⡙⠙⢮⡙⠿⣿⣷⡤⠀⠀⠀⠀⠀⠀⠀⠀⠸⡟⣿⣷⣿⡟⢿⣎⠻⣦⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣼⠁⢸⣾⣏⣿⣷⣤⣬⣻⣄⠀⠁⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⣧⣽⣾⣋⢻⣿⣯⣈⢿⣿⣄⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠈⣿⢻⣿⡿⠿⢿⣿⣿⣷⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⣿⢻⢿⣿⡿⢟⠻⡝⠛⣻⡿⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠹⡎⢷⣿⣻⣟⣆⠙⠻⢿⣷⣄⡀⠀⠀⠀⠀⢀⡤⣾⣷⣿⣿⣾⣯⣷⣼⡿⠉⠉⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠓⠀⢻⡿⡟⢿⣦⡀⠀⠀⢀⡉⣀⣤⢴⣾⣿⣾⣟⠋⣹⣽⣻⡙⣌⢻⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⣷⣾⣿⠯⠿⠿⠿⢿⣿⡿⣿⠟⠣⣭⣭⣴⣾⣿⣿⣷⣿⣿⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣲⣿⣿⣤⣿⣿⣿⣷⣶⣿⣿⣿⠿⠋⣿⠃⠹⣿⠁⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢼⣿⠛⠉⢻⣿⠿⠙⣿⠿⣿⣿⢿⣧⠀⠁⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⣭⠳⡄⠛⣿⡆⢠⣿⠀⢻⡏⣼⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⡿⣶⣿⣶⣧⠈⣹⢧⣿⠇⣀⣾⢱⣿⡏⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣷⣷⠘⠳⡝⢻⣾⡏⢡⣿⣞⣽⣿⣯⡿⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠛⢿⣦⡄⣽⣿⣿⣴⡟⢡⣿⣿⣷⣿⣿⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣤⣈⡇⡹⣿⣯⡤⣼⢁⡍⣼⡿⢿⣿⣿⡟⢃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠉⠻⢧⣾⣿⠻⢴⢇⣼⣾⡟⠁⠀⢻⣿⣧⣾⣹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣦⣤⣴⣿⣄⢀⠈⣺⣷⣿⡄⠀⠀⢸⢿⣿⣄⣨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣷⢸⣌⣿⣿⠈⢿⣿⣶⢟⣿⣿⣷⠀⠀⢠⣾⣿⣻⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢞⣿⢸⢹⣿⣿⡟⢆⠘⣧⡽⣾⡿⢿⣿⣇⢠⣿⡏⣿⢹⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣼⣯⣼⣿⣿⢿⣆⠀⢳⡏⠁⣾⣧⠸⣿⣿⣾⣿⢻⣿⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣴⣶⣤⣤⣤⣄⣀⠀⢀⣴⢿⣿⣼⣿⢿⣿⣉⢸⠙⢷⡀⡧⠂⠇⢹⣓⢼⡟⣿⡿⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡀⠀⠿⠿⠿⠿⣯⣹⠿⡿⢏⣥⣶⣿⠟⠁⢸⡿⠙⣿⣄⠀⠈⠛⠀⠀⣰⣯⢸⡇⢿⣷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣷⣤⣀⣠⣴⠚⢉⣀⣀⣽⣾⣿⣿⠃⠀⠀⠘⣧⢰⡟⠛⢷⣄⡀⢠⣴⡁⢸⣼⠀⢸⡘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣻⣻⣿⣿⡿⢟⣿⣷⢾⣿⠟⠁⠀⠀⠀⠀⢹⣾⣀⠀⠀⠉⢫⠊⣼⢠⣼⣿⠁⠘⠃⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠘⢿⣿⣿⣶⣿⣍⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢿⡝⣦⣄⣀⠘⣦⠉⢸⣿⣿⡗⢦⣄⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠉⠉⠛⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡻⡌⠉⠓⢺⣶⢾⣿⣾⡇⢠⡿⢻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⣅⣴⡏⢷⣽⣾⣿⢸⡇⢉⡀⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠟⣿⣇⣈⣿⢯⣿⣾⣿⣾⡿⠛⢿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⢸⠟⣿⡿⣾⣿⣿⣅⠈⠁⠐⣦⣻⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠘⠀⡈⣿⣷⣿⡦⣤⣄⣘⣿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⡄⣀⣦⣤⢨⡟⣽⣷⠤⢠⠉⢙⣿⣸⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⡞⢿⣿⣺⢿⡟⣿⣡⡿⠖⢚⣉⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⢠⣿⠀⢙⡝⣸⠁⢻⣿⠐⣦⣈⣻⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⠷⣿⡷⣿⠀⠀⢿⣶⣼⣿⡿⠻⣿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢈⡃⠀⠈⠁⣿⠀⠀⠈⢿⡋⠙⢷⣤⣀⢻⣦⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠀⠉⠲⣤⣠⣽⡆⠀⠀⠈⢷⡀⠘⣦⣍⣿⡟⣷⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣎⠙⣿⣿⠀⠀⠀⠈⣿⣦⣿⣟⠉⠁⡟⠿⣷⣤⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣄⠀⠀⣿⣷⣿⣿⡄⠀⠀⠀⠸⣏⢀⣤⠀⠀⠀⣠⣶⣿⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠈⢷⣼⡏⠙⢿⠻⣷⠀⠀⠀⠀⢻⡟⢏⠆⡼⠀⠟⢹⢻⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠀⠈⢿⡇⠀⠀⢴⢿⣧⠀⠀⠀⠀⢷⣼⣰⡃⠀⣠⣿⣾⣧⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠘⣆⡀⠀⡌⣹⣶⣾⣼⡿⠀⠀⠀⠀⠸⣧⡋⠉⠉⠉⠉⠈⢿⣆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⣯⠙⢶⣇⡈⢀⣽⠏⠀⠀⠀⠀⠀⠀⠹⣿⣶⣤⣀⣖⣾⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠉⠙⣿⡆⠀⡿⣻⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠉⠉⣻⡿⢹⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣇⢠⣶⣡⣧⠶⠿⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣆⠀⡿⢆⣿⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣏⠁⠀⠀⣨⣷⣄⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣆⠃⣸⠏⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠛⠓⣠⣾⠿⢿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠓⠋⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢰⠟⡏⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠰⣏⣴⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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