⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡤⠄⢀⣠⣤⣄⣰⣤⣤⣤⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⡏⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣶⠶⣿⠷⣄⠀⠀⠀⠀⠴⠒⢫⣷⣖⡚⣻⣿⣿⣿⣿⣿⣿⣿⣷⣆⣀⣭⡽⢿⣂⡰⠀⠀⠀⠀⣠⡾⠋⠼⠟⠛⢻⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡿⣂⣀⣄⡘⢷⡄⠀⠀⠐⠬⠉⠘⠛⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠉⠥⠂⠀⠀⠀⣠⡿⠁⠀⠀⡰⢾⣶⡙⣶⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀ ⠀⠀⠀⠀⠀⣠⣾⣿⡟⢉⡼⡏⢧⡌⣿⠀⠀⠀⠀⠀⠀⣾⣿⣧⡈⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⢰⣻⠇⠀⣠⡼⠁⣿⢻⣝⢦⡛⣧⡀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣏⠴⣿⡇⣿⣾⡇⢸⡆⠀⠀⠀⠀⠀⣼⣿⣿⣿⣶⣤⣽⣿⣿⣿⣿⣏⢉⣿⡇⠀⠀⣀⣼⢣⣿⠏⢀⣴⢿⣃⣼⣿⡈⡟⢷⡿⣌⠻⣦⡀⠀⠀
⠀⠀⠀⠀⠀⣠⣿⣿⠿⣻⡏⣰⢹⣳⣿⣿⣷⡌⢷⣰⣀⠀⠀⠀⢿⣿⣿⣿⣿⣿⣿⣿⠿⠻⢿⣿⣿⠟⠃⠀⣰⣿⡟⣼⣯⣴⣿⠋⣸⣿⠁⣸⣷⣷⠈⣿⢟⣧⠀⠀⠀
⠀⠀⠀⢀⣼⣿⡿⢡⣴⣿⢂⣟⣾⡟⢻⡹⢿⡹⡞⣿⣿⣧⡀⠀⢸⣿⣿⣿⣿⠟⠋⠀⠀⠀⣼⣿⡿⡆⠀⣰⡟⣿⣿⠟⣿⡿⢡⣾⣿⡏⠀⣿⠹⣿⣆⢹⡀⡇⠀⠀⠀
⠀⠀⡠⣾⢏⠞⣾⡟⢡⣯⣿⠸⣷⠀⠸⣧⢸⡇⢹⣿⡿⣯⡻⣄⣿⣿⣿⣿⣿⣦⡀⠀⠀⢀⣼⣿⢳⣷⣰⢟⣼⠟⣡⣼⡿⢁⡾⠃⣹⠀⣸⣿⠀⣿⢻⣆⣷⢻⡆⠀⠀
⠀⠐⢹⣧⣾⣾⢁⡇⣼⠏⢻⡄⢹⣧⢀⣿⣎⣿⠀⣇⢳⣌⠳⣝⢿⣿⣧⣿⣿⠉⠛⠶⠶⠛⣿⣿⣿⣿⢋⡾⣣⣾⣋⡼⢁⣼⠃⢠⣿⢀⢿⠟⣶⣻⠀⣷⠈⣷⠀⠀
⠀⢠⣿⢫⡾⢸⢸⣇⢛⣆⠸⣿⡀⣿⣎⣿⣿⣿⣷⣸⡴⣿⣷⣜⣦⣽⣿⣿⣿⣧⣤⣤⣤⣤⣾⣿⣿⣧⣿⣷⣻⡟⢹⣧⣿⡏⣠⣾⣿⣾⡿⢀⣿⣾⠀⣿⣧⢸⡇⠀
⠀⢸⢇⣼⠃⡟⠈⣿⠀⢿⢂⣿⣷⣿⣿⣿⣇⠇⣹⣟⣇⣿⣿⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠿⣿⣱⣼⡏⢸⣷⣿⡿⢸⣿⠃⡾⣸⢿⠀⣿⡇⡽⣧⣿⡀
⢀⣿⣼⡏⢠⡇⠀⣿⡀⠸⣧⣿⠙⣿⣿⣿⢻⡜⣶⡿⣿⣿⠇⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⡇⡇⣿⣿⢻⣧⣻⣿⢰⠇⣿⠀⢰⣇⡇⠀⣿⠈⢿⡇
⢸⠿⣽⠁⢸⡇⠀⢹⣇⠀⣿⣿⣆⢹⠸⣿⣈⣧⢹⣿⣿⡏⢸⣾⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣧⠘⣷⣿⣿⢁⣿⣸⡿⣽⣾⠀⣿⢀⣼⣿⠁⠀⢸⡆⠀⠻
⠀⢠⡏⠀⣿⠇⠀⠀⣿⡀⠸⡿⣿⠈⠀⢹⣿⣿⡞⣿⣿⡇⠈⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡧⠀⣿⣿⡇⢸⣿⣿⠁⠹⣿⠀⣿⣼⡿⣿⠀⠀⢸⣷⠇⢸⠀
⠀⣸⠃⢸⣿⡆⠀⠀⣿⣧⠀⣧⢸⠀⠀⠈⠻⣿⣷⢹⣿⣿⣤⣼⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣾⣿⣿⣷⡿⢸⣿⠀⠀⠛⠀⣿⢷⢷⣿⠀⠀⣸⢿⣷⠘⠀
⢠⡏⢀⢼⣿⣇⠀⠀⣿⢿⠀⣿⠉⠀⠀⠀⠀⢹⣿⣿⣿⡿⠻⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⢻⡿⣿⣿⠇⠘⡏⠀⠀⠀⠀⣿⣾⣼⡇⠀⠀⣿⠸⡿⠀⠀
⢸⡇⠈⣿⢿⡏⠀⠀⣿⡈⣧⣿⠀⠀⠀⠀⠀⠈⠃⣿⣿⡇⠀⣧⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡟⠈⡇⣿⣿⠀⠀⠃⠀⠀⠀⠀⠸⡿⣿⡇⠀⠀⣿⠀⣷⠇⢹⡆⠀
⢸⠁⢰⡏⢸⣿⠀⠀⣿⠃⢻⣿⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⢸⣾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡯⠀⠀⣷⢻⣿⠀⠀⠀⠀⠀⠀⠀⠀⠿⣿⡇⠀⠀⣿⠀⢸⣧⢸⡇⠀
⢸⠀⢸⡇⠀⣿⡀⠀⣽⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀⠘⣿⡇⠀⠘⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣷⠄⢸⣇⠈⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡀⠀⣿⠀⠈⣿⣿⡇⠀
⢸⡅⣸⠃⠀⢸⣥⠀⣿⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⢠⢸⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡁⢀⡏⠀⠀⢸⣿⡇⠀
⠸⣇⡏⠀⠀⢸⣿⡆⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣷⠀⠈⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡇⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣧⢸⠇⠀⠀⠀⢻⡇⠀
⠀⢻⠃⠀⠀⠈⣿⣗⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡇⡆⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⠀⠀⠀⠀⠈⠁⠀
⠀⠈⠀⠀⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠂⠀⢻⠻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⠇⠀⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀