⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⣏⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡔⠁⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠒⠋⠉⣀⣀⡀⢬⣗⢂⣀⣀⡈⠉⠓⠦⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢈⠀⠀⠸⡄⠀⠀⠀⠀⠀⢀⠔⠋⠀⠀⣠⣴⣿⣿⣿⣿⡿⠿⣿⣿⣿⣿⣷⣤⡀⠀⠉⠲⢄⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢳⠀⠀⠀⠀⢀⠜⠁⠀⣠⣶⠿⠛⢿⡿⠿⠛⠉⠀⠀⠈⠛⠿⣿⣿⠉⠻⣷⣄⠀⠀⠱⡄⠀⠀⠀⠀⢰⠃⠀⠀⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡸⠀⠀⠀⠘⡆⠀⠀⢠⠋⠀⣠⡾⠛⠁⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⢤⠀⠀⢀⠀⠀⠀⠙⢷⡄⠀⠈⢆⠀⠀⢀⠏⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠙⢆⢠⠇⠀⣼⠏⠀⢀⠀⢀⠀⠀⣰⡇⠀⠀⠀⠀⡆⠘⡆⠀⠘⡄⠀⠀⠀⠀⠙⢦⠀⠈⢇⡠⠋⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠙⠒⣴⠁⠀⠀⡞⢀⡞⠀⢀⣿⡁⠀⠀⠀⠀⣇⠀⠇⠀⠀⠹⡄⠐⣆⠀⠀⠈⢳⠒⠋⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⣼⠀⡼⠀⠀⣸⣯⡇⠀⠀⠀⠈⣿⠀⢸⢠⠀⠀⢳⡀⠘⣆⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⣆⠀⠀⣷⡀⠀⢠⠇⠀⠀⢰⡇⢀⡇⠀⠀⣇⣧⡇⠀⠀⠀⠀⣿⠀⢸⡆⣧⠀⢸⣇⠀⢻⡄⠀⠀⠘⡇⠀⠀⠀⡀⠀⣠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⢳⣄⠈⠛⠶⡾⠀⠀⠀⣼⠀⣼⠁⡄⠀⣽⢿⡇⠀⠀⠀⠀⣟⠀⢸⣇⢸⠀⠸⣿⡄⠈⣧⠀⠀⠀⢱⣴⠶⢛⣡⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠉⠒⠦⡇⠀⠀⠀⣿⠀⣿⢀⡇⢤⡿⣾⡇⠀⠀⠀⡆⣿⠀⠤⣿⢼⠤⠤⣿⣧⡇⢿⡄⠀⠀⢸⠒⠋⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⡄⠀⠀⠀⡇⠀⠀⠀⣿⣼⡇⢸⡇⢀⡇⣿⣇⠀⠀⠀⠁⣿⡇⠀⡿⡆⡆⠀⣿⡟⣿⢸⡇⠀⠀⢸⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⣀⠤⡾⠁⠀⠀⣠⡇⠀⠀⢸⣏⠟⡇⣮⡇⢈⣇⣇⣿⡀⠀⠀⠐⣿⡇⢸⣇⣧⣧⠀⢹⢹⢼⡄⡇⠀⠀⢸⣧⡀⠀⠀⠻⠦⠤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠢⣄⡀⠤⠐⠛⣉⡇⠀⠀⢸⣽⣴⣷⡿⣿⣿⣿⣿⡯⠓⠒⠐⠒⠛⠓⢺⡿⣿⣿⣿⣿⡿⣷⡇⡇⠀⠀⢸⢤⣉⡒⠂⣀⣠⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣹⢉⠀⣷⠀⠀⠀⣿⡄⢯⣷⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⣿⢿⣿⡿⣿⡷⠃⢰⡇⠀⠀⢸⣆⠀⡈⢏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣾⠀⣿⡄⠀⢠⢻⡇⠀⠛⢿⣿⣿⠞⠁⠀⠀⠀⠀⠀⠀⠀⠘⠻⣶⣶⠋⠀⠀⣿⠁⡄⠀⣼⣾⠀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣏⠀⣿⣧⠀⢸⣾⣷⠀⠦⠴⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠳⠀⢠⡿⠀⠇⢠⣿⡇⡸⢃⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣽⡘⡄⠀⡇⢿⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⢋⡇⢸⠀⣾⣿⡴⠕⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣷⠀⢹⠘⡄⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠁⢸⢃⡏⢠⣿⣿⢿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣇⠘⣇⢣⠀⠘⢯⢝⠒⠤⢀⣀⡀⢂⣀⣀⠤⠔⢚⣟⡽⠀⠀⡏⢸⠇⣾⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣻⣿⣿⣿⠘⣆⠹⡈⡆⠀⠘⢾⡳⢤⡀⠀⠙⠻⠋⠀⢀⣠⣫⡿⠁⠀⢰⢁⡟⢸⠈⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣏⣆⠘⣆⢷⡹⡄⠀⠀⠹⢦⢬⣭⣤⡤⣤⣌⡽⢫⠞⠀⠀⢀⡏⣾⢣⠇⣰⣿⣿⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⢛⣯⡷⣜⣮⣷⣷⡀⠀⠀⠈⣾⣯⠔⠛⠓⣿⢘⠁⠀⠀⠀⣸⡼⣟⣎⡼⣵⣿⣿⢿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⣿⢻⣛⡏⡆⣨⣙⠿⣎⡻⠀⠀⢀⡇⠏⢳⣤⡞⢹⢸⠀⠀⠀⠐⢋⣠⠼⢻⠿⡹⣿⡿⣿⣿⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⠋⢹⠟⢦⣯⡃⢠⢃⣇⡍⣓⠂⢼⢡⣞⡁⠀⣨⢿⢸⠤⠄⠒⣚⡍⢷⢳⡘⣢⣣⣿⠞⠹⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡏⠀⠈⠁⠙⣿⢿⡛⡼⢸⡀⠋⢹⢿⢸⣀⠽⠫⣀⢸⢸⢸⡆⢿⠀⡃⠈⣆⣫⣿⡥⠇⠀⠀⣿⠿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠁⣇⠀⠀⠀⠀⠙⠚⠻⣓⣦⣽⣒⠺⢸⢸⠧⡀⠀⣠⢿⣿⡄⢣⣔⣾⠥⣶⠟⠐⠋⠀⠀⠀⠀⣸⢠⡸⠃⠀⠀⠀⠀⠀⠀