⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⢖⣤⣭⣿⣟⣿⣭⣿⡿⣶⣦⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢰⣶⣶⣿⣿⣾⣶⡾⣿⢿⡿⣗⢶⣿⣶⡾⣿⣿⣿⣷⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⢻⣿⣿⣿⣿⣉⢧⣦⣷⣧⠻⣆⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⢻⣾⣿⣿⣿⣿⡏⣿⣽⠋⢻⢻⠻⣼⢷⣿⣿⣿⣿⣟⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⡗⣿⣿⢿⣿⢣⡿⢻⢸⣿⢠⣼⣿⡇⡟⣷⣷⣿⣿⣧⢿⡀⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡏⣿⣿⣿⣯⣾⢤⣿⢺⣿⢀⡿⡇⣿⣷⢿⣷⣿⣟⣿⣸⡇⣸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣻⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣾⣿⣾⣿⣿⣿⡟⣸⣿⣿⣿⣿⣿⣧⡇⣿⠇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⡿⣿⡿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣾⣻⣿⣧⣜⣿⣭⣿⣿⣴⢼⣧⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣿⡏⣿⣷⣿⣯⣿⣿⣿⡿⠿⠾⠟⢿⣾⣿⣿⡿⢻⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡿⣿⣿⣿⣿⣿⣻⣿⣿⠏⠀⠀⠀⠀⠈⠛⠛⠀⣼⢟⣧⣿⡞⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢸⣿⣿⣿⣿⡌⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⣟⣾⣿⣛⣷⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⣻⣿⣿⣿⣿⣶⡀⠀⠀⣀⣠⣤⠀⠀⣨⣿⣫⣿⣯⣿⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣽⣟⣿⣿⣿⣿⢿⣦⡤⣈⡉⢉⡤⠚⣿⣷⣿⣟⣽⣷⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣩⡿⢿⣿⣿⣾⣿⣿⣿⣿⣶⣦⠀⠀⠀⣠⣿⣿⣿⣾⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠸⠀⠈⠉⠉⠙⣿⡿⣟⣿⣿⣿⠀⠀⢀⣼⣿⣿⠏⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢢⡀⠀⠀⠘⠣⢹⣀⣉⡉⠁⠀⠜⠃⠛⠛⠓⠲⢦⡒⠒⢒⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢱⠀⠀⠀⠀⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣦⣐⡄⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⢳⡀⡄⠀⣿⠋⣀⠈⠓⣦⡀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⡇⠀⣰⣻⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⣸⡇⢁⣏⠙⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⡄⠆⢣⣄⣽⣿⣿⣿⣿⣿⣿⣾⣶⣧⣤⣤⣠⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣧⣠⣶⣿⣿⡿⠿⠿⠖⠛⠛⠛⠻⠿⠿⠿⠿⠿⢦⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⢸⢹⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠙⠿⣿⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢠⠇⠀⠀⡧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⡘⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢀⠇⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠰⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⡸⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⠀⠀⠈⠄⣹⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⡄⠀⣰⠃⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⡆⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⠀⠀⢰⠎⠀⡰⠃⠀⢀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇⢀⡀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡎⠀⠀⡜⢀⡜⠀⢀⡰⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⡸⡆⢇⠀⠑⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⠀⠀⠀⢡⠎⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠃⢱⠈⢆⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀
⠀⢠⣶⡖⠧⣤⣄⢠⠇⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⢣⠀⠀⠀⠠⠘⡄⠀⠀⠀⠀
⠀⢸⠟⠁⢀⣹⣿⣧⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠳⡀⠀⣠⢶⣿⣦⣄⠀⠀
⠀⡼⡀⢦⣿⣿⠟⣻⢳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⣴⠁⢸⣿⣿⣿⣷⡄
⣠⣿⣷⣬⣿⣿⠊⢀⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢧⠀⡞⣹⣿⣿⣿⠃
⣷⣿⣿⣿⡿⠁⠀⢸⣀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⡆
⢻⣿⣿⣿⣿⣄⠀⡟⠂⠉⠛⠛⠒⢶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⣄⣀⣀⡀⢱⣤⣾⠀⠀⢀⣻⣿⣿⣿⣿⡇
⠸⣿⣿⣿⣿⣿⡀⣵⠀⠀⠀⠀⠀⠐⠊⢽⡻⢿⣿⣷⣶⣶⣤⣤⣤⣤⣄⣰⣶⣾⡿⠋⠁⠀⠀⠀⠀⠉⠉⢹⣿⣿⣄⣴⣽⣿⣿⣿⣿⠿⠃
⠀⣿⣿⣿⣿⢿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀
⠀⠙⢿⣿⣿⡄⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀
⠀⠀⠀⢻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠀⠉⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠙⢿⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⣧⣐⣀⣤⣤⣤⣴⣶⣄⣤⢤⣄⣀⠀⠀⣧⢸⠀⠀⠀⣀⣀⣠⠤⣤⣤⣤⣄⣀⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢪⣯⠷⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣟⣸⣶⡾⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⢰⣶⣶⣿⣿⣾⣶⡾⣿⢿⡿⣗⢶⣿⣶⡾⣿⣿⣿⣷⣿⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡿⢻⣿⣿⣿⣿⣉⢧⣦⣷⣧⠻⣆⢿⣿⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡿⢻⣾⣿⣿⣿⣿⡏⣿⣽⠋⢻⢻⠻⣼⢷⣿⣿⣿⣿⣟⢿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢼⡗⣿⣿⢿⣿⢣⡿⢻⢸⣿⢠⣼⣿⡇⡟⣷⣷⣿⣿⣧⢿⡀⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡏⣿⣿⣿⣯⣾⢤⣿⢺⣿⢀⡿⡇⣿⣷⢿⣷⣿⣟⣿⣸⡇⣸⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢠⢾⣻⣿⣿⣿⣿⣿⣿⣿⣯⣾⣿⣾⣿⣾⣿⣿⣿⡟⣸⣿⣿⣿⣿⣿⣧⡇⣿⠇⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⡿⣿⡿⣿⡟⢿⣿⣿⣿⣿⣿⣿⣾⣻⣿⣧⣜⣿⣭⣿⣿⣴⢼⣧⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡧⣿⡏⣿⣷⣿⣯⣿⣿⣿⡿⠿⠾⠟⢿⣾⣿⣿⡿⢻⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⡿⣿⣿⣿⣿⣿⣻⣿⣿⠏⠀⠀⠀⠀⠈⠛⠛⠀⣼⢟⣧⣿⡞⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣇⢸⣿⣿⣿⣿⡌⠉⠁⠀⠀⠀⠀⠀⠀⠀⢀⣼⣟⣾⣿⣛⣷⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣼⣻⣿⣿⣿⣿⣶⡀⠀⠀⣀⣠⣤⠀⠀⣨⣿⣫⣿⣯⣿⣻⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣽⣟⣿⣿⣿⣿⢿⣦⡤⣈⡉⢉⡤⠚⣿⣷⣿⣟⣽⣷⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣩⡿⢿⣿⣿⣾⣿⣿⣿⣿⣶⣦⠀⠀⠀⣠⣿⣿⣿⣾⣿⠿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠸⠀⠈⠉⠉⠙⣿⡿⣟⣿⣿⣿⠀⠀⢀⣼⣿⣿⠏⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⢢⡀⠀⠀⠘⠣⢹⣀⣉⡉⠁⠀⠜⠃⠛⠛⠓⠲⢦⡒⠒⢒⡤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢱⠀⠀⠀⠀⣿⣷⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⣦⣐⡄⠈⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⢳⡀⡄⠀⣿⠋⣀⠈⠓⣦⡀⠀⠀⠀⠀⠀⠀⢀⣹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⡇⠀⣰⣻⣿⣿⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⣸⡇⢁⣏⠙⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⡄⠆⢣⣄⣽⣿⣿⣿⣿⣿⣿⣾⣶⣧⣤⣤⣠⣾⣿⣿⣿⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⣧⣠⣶⣿⣿⡿⠿⠿⠖⠛⠛⠛⠻⠿⠿⠿⠿⠿⢦⣾⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠀⠀⢸⢹⣿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠈⠙⠿⣿⠃⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠈⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⡇⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠈⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⢠⠇⠀⠀⡧⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⡘⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⠈⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢀⡞⠀⠀⠀⠀⢀⠇⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠰⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⠟⠁⠀⠀⠀⠀⡸⠀⠀⡌⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⢣⠀⠀⠈⠄⣹⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡎⠀⠀⠀⡄⠀⣰⠃⠀⢠⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠸⡆⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⠀⠀⢰⠎⠀⡰⠃⠀⢀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⡇⢀⡀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⡎⠀⠀⡜⢀⡜⠀⢀⡰⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠀⠀⠀⠀⠀⠀⠀⠀⡸⡆⢇⠀⠑⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢰⠀⠀⠀⢡⠎⠀⢠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠃⢱⠈⢆⠀⠀⠀⠀⠀⣆⠀⠀⠀⠀⠀
⠀⢠⣶⡖⠧⣤⣄⢠⠇⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠈⢣⠀⠀⠀⠠⠘⡄⠀⠀⠀⠀
⠀⢸⠟⠁⢀⣹⣿⣧⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠳⡀⠀⣠⢶⣿⣦⣄⠀⠀
⠀⡼⡀⢦⣿⣿⠟⣻⢳⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠘⣴⠁⢸⣿⣿⣿⣷⡄
⣠⣿⣷⣬⣿⣿⠊⢀⡇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⢧⠀⡞⣹⣿⣿⣿⠃
⣷⣿⣿⣿⡿⠁⠀⢸⣀⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢶⣿⣿⣿⣿⣿⡆
⢻⣿⣿⣿⣿⣄⠀⡟⠂⠉⠛⠛⠒⢶⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠄⣄⣀⣀⡀⢱⣤⣾⠀⠀⢀⣻⣿⣿⣿⣿⡇
⠸⣿⣿⣿⣿⣿⡀⣵⠀⠀⠀⠀⠀⠐⠊⢽⡻⢿⣿⣷⣶⣶⣤⣤⣤⣤⣄⣰⣶⣾⡿⠋⠁⠀⠀⠀⠀⠉⠉⢹⣿⣿⣄⣴⣽⣿⣿⣿⣿⠿⠃
⠀⣿⣿⣿⣿⢿⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣝⢿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣹⣿⣿⣿⣿⣿⣿⠟⠁⠀⠀
⠀⠙⢿⣿⣿⡄⠙⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠉⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀
⠀⠀⠀⢻⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠀⠉⢹⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠙⢿⣿⣽⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠛⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠉⣧⣐⣀⣤⣤⣤⣴⣶⣄⣤⢤⣄⣀⠀⠀⣧⢸⠀⠀⠀⣀⣀⣠⠤⣤⣤⣤⣄⣀⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢪⣯⠷⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣟⣸⣶⡾⠿⠿⠿⣿⣿⣿⣿⣿⣿⣿⠿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
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