Это было сложнее чем показалось в начале.
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⡀⠀⠲⣶⣤⣀⡙⠷⢦⣤⣛⡷⢦⣤⣶⣦⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡆⠀⠀⠀⠀⠐⠶⣦⣤⣀⡈⠉⠛⠻⢶⣦⣌⣉⠛⠿⢶⣦⣉⡛⠿⡾⢝⡛⠿⡿⢟⡿⣿⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣈⠉⠙⠻⠶⢦⣄⡀⠉⠋⠑⠢⢀⠀⠈⠙⠂⠀⣀⠙⠀⠀⣀⠙⠂⠀⠈⠀⠉⠋⠛⠲⢦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⠈⠙⠁⢠⡄⠀⠀⢸⠀⠀⠀⣿⠀⠀⢠⡏⠀⠀⢸⠇⠀⠀⣴⠀⠀⠀⡀⠉⠛⠒⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⡶⢾⣛⡛⠿⠿⠛⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⢹⡄⠀⠀⣿⠀⠀⢸⡇⠀⠀⢸⡄⠀⠀⣿⠀⠀⢸⡇⠀⠀⣿⠀⠀⢰⡏⠀⠀⣼⠃⠀⢀⣤⠀⠉⠛⢂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⡶⣞⣛⠿⠭⠛⠂⣉⣩⣤⣶⣶⠿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⣧⠀⠀⢿⡄⠀⠸⣧⠀⠀⢸⡇⠀⢰⡏⠀⠀⣾⠀⠀⢰⡇⠀⠀⣾⠁⠀⢰⡏⠀⠀⣼⠃⠀⢀⡶⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠛⠛⠉⣉⣀⣤⣤⣶⠶⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⡄⠀⠀⠀⠀⠀⢸⡄⠀⢸⡇⠀⠀⣿⠀⠀⢸⡇⠀⢸⡇⠀⠀⣿⠀⠀⣼⠁⠀⢸⠇⠀⢀⡟⠀⠀⣼⠇⠀⢀⡾⠁⠀⢠⡶⠀⠙⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠐⠾⠟⠛⠋⣉⣀⣤⣤⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣇⠀⠀⢠⣶⣿⣸⣇⠀⠈⣿⠀⠀⢿⠀⠀⢸⡇⠀⢸⡇⠀⢰⡇⠀⢀⡟⠀⢀⡿⠀⠀⣼⠁⠀⣸⠏⠀⢀⡾⠁⠀⣠⠟⠀⠀⣴⠆⠙⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⢰⣶⡾⠿⠛⠛⠉⠁⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⡄⢐⣟⣿⣿⣿⣿⡄⠀⢻⡄⠀⢸⡆⠀⢸⡇⠀⢸⡇⠀⢸⡇⠀⢸⠇⠀⣸⠇⠀⢰⠇⠀⢰⡏⠀⢀⡾⠁⠀⣰⠏⠀⢠⡾⠃⠀⣠⡶⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⡾⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣧⢰⣿⣿⣿⣿⣿⣇⠀⢸⡇⠀⢸⡇⠀⢸⡇⠀⢸⡇⠀⣼⠀⠀⣿⠀⢠⡟⠀⢀⡟⠀⢠⡟⠀⢀⡾⠁⠀⣼⠃⠀⣰⠟⠀⢀⡼⠋⠀⢀⣤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠘⠛⠋⢉⣀⣤⣤⣶⠿⢿⣷⣿⣿⣿⣿⣿⣿⣽⣽⣻⣿⡆⢻⡎⣿⣿⣿⣿⣿⣿⡀⠀⣿⠀⠈⡇⠀⢸⡇⠀⢸⠀⠀⣿⠀⢰⡇⠀⣸⠃⠀⡼⠀⢠⡟⠀⢀⡞⠁⢀⡼⠁⢀⡼⠋⠀⣰⠟⠁⢀⣴⠟⠁⠀⢀⣵⣆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠾⠟⠛⠋⠉⠀⠀⢘⣿⣿⣟⣿⣿⣿⣿⣷⣧⣯⣧⣿⣷⠘⣷⢿⣿⣿⣿⣿⣿⣇⠀⢹⡆⠀⣿⠀⢸⡇⠀⢸⠀⢰⡇⠀⣼⠁⢠⡏⠀⢰⠃⢀⡾⠁⢀⡞⠁⢀⡞⠁⢠⡞⠁⢀⡾⠋⠀⣴⠟⠁⠀⣠⣾⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⣠⣤⣤⣶⠾⠟⠛⢻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣽⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⡀⠸⡇⠀⢹⠀⢸⡇⠀⣿⠀⢸⡇⢀⡏⠀⣼⠁⢠⡏⠀⣼⠃⢀⡞⠀⢠⠟⠀⣰⠏⠀⣰⠟⠀⣠⡾⠃⢀⣤⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠉⢉⣠⣤⣤⣶⠾⠟⣿⣿⡿⣿⣿⣿⣿⣿⣷⣧⣇⣿⣿⣾⣿⢿⣿⣿⣿⣿⣿⣇⠀⣿⠀⢸⡇⠸⡇⠀⣿⠀⣼⠁⢸⠇⢰⡏⠀⡜⠀⣼⠃⢠⡞⠀⣰⠋⢀⡼⠃⢠⡾⠁⢠⡾⠋⢀⣴⣿⣿⣿⡿⠛⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠘⠛⠋⣉⣠⣤⣴⣶⢿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⡆⢸⡇⠀⡇⠀⡟⠀⣿⠀⡿⠀⣾⠁⣸⠃⣸⠇⢠⡞⠀⡰⠃⣠⠞⠀⣴⠋⢀⡴⠋⢀⣴⣿⣿⣿⡿⠋⠀⠀⠘⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠙⠛⠛⠋⠉⠀⢀⣘⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣧⠀⣇⠀⣧⠀⡇⢰⡇⢰⡇⢸⡇⢰⠇⣰⡏⢠⡞⢀⡼⠁⣴⠋⣠⠞⢁⣴⠟⢁⣴⣿⣿⣿⢿⣯⣤⣀⣀⡀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⣤⣤⣶⡾⠿⠛⠛⢻⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⡀⣿⠀⣿⢸⡇⢸⡇⣼⠁⣿⢀⡟⢰⡟⢠⡟⢀⡞⢡⡞⢁⡴⠋⣠⠞⣡⣼⣿⣿⣿⢟⣵⣿⣿⣛⣒⡦⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⢈⣡⣤⣤⣶⠿⠿⠛⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⡇⢻⡀⣿⢸⡇⣾⢁⡏⢸⡇⣼⢡⡟⢠⡟⢠⠏⣰⠏⣠⠟⣡⡾⣡⣾⣿⣿⡿⢋⡽⣽⣿⣿⣗⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠉⠉⠀⢀⣀⣤⣤⣽⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣷⢸⡇⣿⢸⡇⣿⣸⢇⡿⣸⢇⡾⢡⡟⣰⢋⡼⢃⡼⢃⡼⣫⣾⣿⣿⡿⠿⠴⢯⣿⣿⣟⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠰⠾⠿⠛⠋⢉⣡⣬⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⣼⡇⣿⣼⣷⡏⣿⣸⢧⣏⣾⢡⡏⡼⣣⠞⣵⢏⣴⣯⣾⣿⣿⡿⢋⡴⠯⢭⣿⣟⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⢴⣶⠿⠿⠛⢋⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣿⣿⣿⣧⣟⣾⣽⢳⣟⣾⣵⢫⣞⣵⣿⣿⣿⣿⠿⢫⡯⠯⠭⢽⣽⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⣤⣶⡾⠿⠟⠛⠉⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣵⣯⣿⣿⣿⣿⡿⠯⡴⠯⠭⠭⢭⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠈⠁⣀⣠⣤⣴⡶⢿⣿⣿⣹⣿⣿⣯⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⣴⣿⠽⠭⢭⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠘⠛⠛⢉⣉⣤⣤⣶⠿⠛⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣿⣿⢿⠭⢭⠝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⠀⠀⠀⠀⠘⠿⠛⠋⠉⠁⣀⣀⣤⣼⣿⣿⣷⣧⣯⣯⣿⣟⣟⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣶⣿⣿⡭⠭⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⡀⠀⠀⠀⠀⢠⣴⣶⠾⠿⠛⢋⣁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠙⠏⠋⠻⢿⣿⣿⣿⣿⠋⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⢀⣡⣤⣶⡶⠿⠛⠋⣉⣸⣿⣿⣿⣷⣧⣧⣯⣏⣏⣿⣿⢿⣿⣿⣿⣿⣿⠿⠛⢹⣿⣿⣦⣤⣾⣿⣿⣿⣿⣦⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⢀⣉⣩⣤⠴⠶⠛⠛⠉⠉⠀⠀⠀⠀⠈⠉⠛⠛⠛⠿⠿⢧⣿⠿⠛⠉⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠴⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣤⣀⡀⠀⠲⣶⣤⣀⡙⠷⢦⣤⣛⡷⢦⣤⣶⣦⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⡆⠀⠀⠀⠀⠐⠶⣦⣤⣀⡈⠉⠛⠻⢶⣦⣌⣉⠛⠿⢶⣦⣉⡛⠿⡾⢝⡛⠿⡿⢟⡿⣿⣶⣶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣾⣿⣿⣿⣿⣿⣷⣶⣶⣤⣄⣈⠉⠙⠻⠶⢦⣄⡀⠉⠋⠑⠢⢀⠀⠈⠙⠂⠀⣀⠙⠀⠀⣀⠙⠂⠀⠈⠀⠉⠋⠛⠲⢦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⡀⠀⠈⠙⠁⢠⡄⠀⠀⢸⠀⠀⠀⣿⠀⠀⢠⡏⠀⠀⢸⠇⠀⠀⣴⠀⠀⠀⡀⠉⠛⠒⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣴⡶⢾⣛⡛⠿⠿⠛⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠋⠁⢹⡄⠀⠀⣿⠀⠀⢸⡇⠀⠀⢸⡄⠀⠀⣿⠀⠀⢸⡇⠀⠀⣿⠀⠀⢰⡏⠀⠀⣼⠃⠀⢀⣤⠀⠉⠛⢂⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⡶⣞⣛⠿⠭⠛⠂⣉⣩⣤⣶⣶⠿⠟⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠘⣧⠀⠀⢿⡄⠀⠸⣧⠀⠀⢸⡇⠀⢰⡏⠀⠀⣾⠀⠀⢰⡇⠀⠀⣾⠁⠀⢰⡏⠀⠀⣼⠃⠀⢀⡶⠀⠈⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠛⠛⠉⣉⣀⣤⣤⣶⠶⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢹⡄⠀⠀⠀⠀⠀⢸⡄⠀⢸⡇⠀⠀⣿⠀⠀⢸⡇⠀⢸⡇⠀⠀⣿⠀⠀⣼⠁⠀⢸⠇⠀⢀⡟⠀⠀⣼⠇⠀⢀⡾⠁⠀⢠⡶⠀⠙⠓⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠐⠾⠟⠛⠋⣉⣀⣤⣤⣶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣇⠀⠀⢠⣶⣿⣸⣇⠀⠈⣿⠀⠀⢿⠀⠀⢸⡇⠀⢸⡇⠀⢰⡇⠀⢀⡟⠀⢀⡿⠀⠀⣼⠁⠀⣸⠏⠀⢀⡾⠁⠀⣠⠟⠀⠀⣴⠆⠙⠒⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠘⣿⡀⠀⠀⠀⠀⢰⣶⡾⠿⠛⠛⠉⠁⠀⢈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⢻⡄⢐⣟⣿⣿⣿⣿⡄⠀⢻⡄⠀⢸⡆⠀⢸⡇⠀⢸⡇⠀⢸⡇⠀⢸⠇⠀⣸⠇⠀⢰⠇⠀⢰⡏⠀⢀⡾⠁⠀⣰⠏⠀⢠⡾⠃⠀⣠⡶⠀⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣶⡾⠟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠘⣧⢰⣿⣿⣿⣿⣿⣇⠀⢸⡇⠀⢸⡇⠀⢸⡇⠀⢸⡇⠀⣼⠀⠀⣿⠀⢠⡟⠀⢀⡟⠀⢠⡟⠀⢀⡾⠁⠀⣼⠃⠀⣰⠟⠀⢀⡼⠋⠀⢀⣤⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠘⠛⠋⢉⣀⣤⣤⣶⠿⢿⣷⣿⣿⣿⣿⣿⣿⣽⣽⣻⣿⡆⢻⡎⣿⣿⣿⣿⣿⣿⡀⠀⣿⠀⠈⡇⠀⢸⡇⠀⢸⠀⠀⣿⠀⢰⡇⠀⣸⠃⠀⡼⠀⢠⡟⠀⢀⡞⠁⢀⡼⠁⢀⡼⠋⠀⣰⠟⠁⢀⣴⠟⠁⠀⢀⣵⣆⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠾⠟⠛⠋⠉⠀⠀⢘⣿⣿⣟⣿⣿⣿⣿⣷⣧⣯⣧⣿⣷⠘⣷⢿⣿⣿⣿⣿⣿⣇⠀⢹⡆⠀⣿⠀⢸⡇⠀⢸⠀⢰⡇⠀⣼⠁⢠⡏⠀⢰⠃⢀⡾⠁⢀⡞⠁⢀⡞⠁⢠⡞⠁⢀⡾⠋⠀⣴⠟⠁⠀⣠⣾⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣇⠀⠀⠀⠀⠀⣠⣤⣤⣶⠾⠟⠛⢻⣿⣿⣻⣿⣿⣿⣿⣿⣿⣽⣿⣿⡇⢻⣿⣿⣿⣿⣿⣿⣿⡀⠸⡇⠀⢹⠀⢸⡇⠀⣿⠀⢸⡇⢀⡏⠀⣼⠁⢠⡏⠀⣼⠃⢀⡞⠀⢠⠟⠀⣰⠏⠀⣰⠟⠀⣠⡾⠃⢀⣤⣾⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⡀⠀⠀⠀⠀⠉⢉⣠⣤⣤⣶⠾⠟⣿⣿⡿⣿⣿⣿⣿⣿⣷⣧⣇⣿⣿⣾⣿⢿⣿⣿⣿⣿⣿⣇⠀⣿⠀⢸⡇⠸⡇⠀⣿⠀⣼⠁⢸⠇⢰⡏⠀⡜⠀⣼⠃⢠⡞⠀⣰⠋⢀⡼⠃⢠⡾⠁⢠⡾⠋⢀⣴⣿⣿⣿⡿⠛⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣇⠀⠀⠀⠀⠘⠛⠋⣉⣠⣤⣴⣶⢿⣿⣷⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢸⡆⢸⡇⠀⡇⠀⡟⠀⣿⠀⡿⠀⣾⠁⣸⠃⣸⠇⢠⡞⠀⡰⠃⣠⠞⠀⣴⠋⢀⡴⠋⢀⣴⣿⣿⣿⡿⠋⠀⠀⠘⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠙⠛⠛⠋⠉⠀⢀⣘⣿⣿⣾⣿⣿⣿⣿⣿⣿⣷⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⠘⣧⠀⣇⠀⣧⠀⡇⢰⡇⢰⡇⢸⡇⢰⠇⣰⡏⢠⡞⢀⡼⠁⣴⠋⣠⠞⢁⣴⠟⢁⣴⣿⣿⣿⢿⣯⣤⣀⣀⡀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⣤⣤⣶⡾⠿⠛⠛⢻⣿⣯⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡀⢿⡀⣿⠀⣿⢸⡇⢸⡇⣼⠁⣿⢀⡟⢰⡟⢠⡟⢀⡞⢡⡞⢁⡴⠋⣠⠞⣡⣼⣿⣿⣿⢟⣵⣿⣿⣛⣒⡦⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠀⠀⢈⣡⣤⣤⣶⠿⠿⠛⣿⣿⡽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢸⡇⢻⡀⣿⢸⡇⣾⢁⡏⢸⡇⣼⢡⡟⢠⡟⢠⠏⣰⠏⣠⠟⣡⡾⣡⣾⣿⣿⡿⢋⡽⣽⣿⣿⣗⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣷⠀⠀⠀⠀⠀⠉⠉⠀⢀⣀⣤⣤⣽⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡌⣷⢸⡇⣿⢸⡇⣿⣸⢇⡿⣸⢇⡾⢡⡟⣰⢋⡼⢃⡼⢃⡼⣫⣾⣿⣿⡿⠿⠴⢯⣿⣿⣟⡗⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡇⠀⠀⠀⠀⠰⠾⠿⠛⠋⢉⣡⣬⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣇⢻⣼⡇⣿⣼⣷⡏⣿⣸⢧⣏⣾⢡⡏⡼⣣⠞⣵⢏⣴⣯⣾⣿⣿⡿⢋⡴⠯⢭⣿⣟⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⡆⠀⠀⠀⠀⢴⣶⠿⠿⠛⢋⣉⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣼⣿⣷⣿⣿⣿⣿⣧⣟⣾⣽⢳⣟⣾⣵⢫⣞⣵⣿⣿⣿⣿⠿⢫⡯⠯⠭⢽⣽⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⣤⣶⡾⠿⠟⠛⠉⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⣵⣯⣿⣿⣿⣿⡿⠯⡴⠯⠭⠭⢭⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀⠀⠈⠁⣀⣠⣤⣴⡶⢿⣿⣿⣹⣿⣿⣯⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢉⣴⣿⠽⠭⢭⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠘⠛⠛⢉⣉⣤⣤⣶⠿⠛⣿⣿⣿⣽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣛⣿⣿⢿⠭⢭⠝⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣇⠀⠀⠀⠀⠘⠿⠛⠋⠉⠁⣀⣀⣤⣼⣿⣿⣷⣧⣯⣯⣿⣟⣟⣿⣿⣿⣿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣋⣶⣿⣿⡭⠭⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⣿⡀⠀⠀⠀⠀⢠⣴⣶⠾⠿⠛⢋⣁⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢻⠙⠏⠋⠻⢿⣿⣿⣿⣿⠋⠀⠈⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⠀⠀⠀⠀⢀⣡⣤⣶⡶⠿⠛⠋⣉⣸⣿⣿⣿⣷⣧⣧⣯⣏⣏⣿⣿⢿⣿⣿⣿⣿⣿⠿⠛⢹⣿⣿⣦⣤⣾⣿⣿⣿⣿⣦⠀⠀⡀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡄⠀⠀⠀⢀⣉⣩⣤⠴⠶⠛⠛⠉⠉⠀⠀⠀⠀⠈⠉⠛⠛⠛⠿⠿⢧⣿⠿⠛⠉⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠷⠴⠒⠚⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
