⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣶⡶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣠⣤⣶⣺⣿⣯⣽⣲⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣷⣟⣷⣿⣟⠻⣿⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢀⣠⣿⣽⣿⡟⢋⣠⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣻⣿⣿⣿⣿⣿⣿⣧⡐⡑⣿⣷⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠠⣿⣿⣿⣿⡿⣄⣾⣿⣧⣿⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠺⠿⢽⣿⣿⣷⣿⣟⠿⡞⢿⣿⡄⠀⠀⠀⠀
⠀⠀⠀⣼⢟⡷⣻⣟⣼⣿⡟⠋⠉⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣷⠹⡆⢹⣆⠹⣿⡆⠀⠀⠀⠀
⠀⠀⢠⣿⢿⡗⣹⢿⣽⠿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣯⣿⡌⣿⢤⡌⢷⡆⠀⠀⠀
⠀⢀⣎⣷⣷⠋⣽⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣧⠈⠂⡿⣾⣿⡄⠀⠀
⠀⣸⣿⣿⣯⢼⣛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡀⠀⠁⠸⡾⣿⡀⠀
⢀⡟⡸⢸⣃⣾⢼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣯⣻⡃⠀⣴⢣⣹⡇⠀
⢸⣿⠁⣾⣷⣿⣹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⡿⠁⢰⢱⠠⢹⣿⠀
⣼⢳⠘⣿⡆⣿⢴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⡁⠀⢰⡘⣧⣤⠻⠀
⢻⣴⣰⣿⡇⠙⠻⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣿⡿⠛⢛⠖⠶⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡇⠀⢸⡟⢻⣸⠀⠀
⢨⡷⠻⣟⣧⣤⣴⢿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠏⠁⠀⠈⠙⠛⣓⣿⣷⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣯⠟⡇⠏⢸⢏⠆⠋⢿
⠸⠁⠰⢸⣧⣿⡝⢾⣿⣿⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⡫⣄⠀⠀⠀⢀⢠⣾⣧⣼⠿⣿⣿⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⡿⢸⡷⠂⣼⠐⡟⠁
⢸⠂⢡⣾⡇⣿⠀⢘⣿⣜⣟⡾⡦⣄⡀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣵⣇⠀⣀⣴⢟⡿⣫⣿⣧⣻⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⡧⣿⠀⠀⣯⢄⠂
⠈⢀⠘⡏⣷⣻⠆⢸⣿⣿⣿⣯⣿⣿⣯⣳⣦⣤⣀⣀⡀⢸⣿⣿⣿⡼⣿⣵⡠⠟⢰⣿⣯⣿⣿⣿⣿⣿⣿⣿⣀⠹⣷⣄⣀⣀⣤⣤⣶⡿⣛⣹⣧⣿⣼⣸⣿⢀⡟
⠀⢸⣾⠷⣬⣿⣚⠻⣍⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣽⣿⣿⣿⡗⢺⣿⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠈⢸⣿⣿⣿⣿⣿⣷⠟⣧⣼⣿⣿⣿⡟⣆⠀⠁
⠀⢸⣿⣆⢸⠀⢹⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢈⠼⠛⠁⠉⠀⠈⠈⠻⣽⣿⣿⣿⣿⣿⣧⠀⢸⣿⣿⣿⣿⣿⣿⣶⣿⣿⣿⣿⣿⠁⠈⠟⡎
⠀⠸⣿⣧⡽⡆⡙⢻⣿⣿⣿⣿⣿⣿⣿⣽⣿⣿⣿⣿⣽⣿⣿⣿⡷⠖⠀⠀⢰⡶⠶⠶⣦⣬⡲⣿⢿⣿⣿⣿⣿⣿⣦⢸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢀⣸⠇
⠀⠀⣿⣯⣄⢱⠈⡚⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⢀⣰⠟⠁⠀⠀⠈⢻⣷⡿⡇⠘⠟⣿⡟⠛⠛⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⣾⠀⡟
⠀⠀⠘⡟⣏⡙⣆⢛⣻⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⠀⢀⡴⣸⠇⠀⠀⠀⠀⠀⠀⣿⣧⠃⠀⢠⣿⡏⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢀⣰⢿⣷⡿
⠀⠀⠀⢻⣻⡸⣾⡖⣤⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⢋⣸⡏⠀⠀⠀⠀⠀⠀⡞⣿⣏⢹⣾⣿⣿⠁⠀⠀⢨⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠈⣟⣿⣿⠁⠀
⠀⠀⠀⠘⡏⣧⠘⢧⠘⠂⢻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡞⠀⣾⣿⡇⠀⠀⠀⠀⠀⠀⣇⣧⣇⣿⣿⣿⡿⠀⠀⢘⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⢾⢿⣿⠋⠀⠀
⠀⠀⠀⠀⠹⣾⡇⠼⠐⠤⣈⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⠳⣾⣿⣿⡁⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠇⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⣸⢧⡿⠁⠀⠀⠀
⠀⠀⠀⠀⠀⢹⣿⡘⢇⡀⡀⠸⣿⣿⣟⣿⣿⡟⠋⠀⠁⠀⠀⠀⣿⣿⡇⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠁⢀⢀⣠⠟⠻⠿⠿⡿⠿⠿⠿⢿⣿⡏⠀⢰⡷⣹⠃⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢻⣿⠷⣷⡌⢓⣻⣿⣿⣿⣋⠀⠀⠀⠀⠀⠀⢰⣿⠙⣷⠀⠀⠀⠀⢀⣾⣿⣿⡿⠃⠀⠀⣈⣾⡟⠀⠀⠀⠀⠀⠀⠀⢀⣴⡿⠀⠀⡨⣰⠃⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠈⠹⣦⣌⢻⡄⠳⡽⣿⣿⡿⠇⠀⠀⠀⠀⠀⢸⣿⢧⣿⠀⠀⠀⠀⢩⣿⣿⠋⠀⠀⢒⣴⣿⣿⢧⠀⠀⠀⠀⠀⠀⠀⠘⣻⡥⠀⠈⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⢻⡘⢿⡻⡜⢷⣾⣿⣷⡀⠀⠀⠀⠀⠀⢸⢻⢡⢻⡆⠀⠀⠀⣸⠟⠁⠀⠀⣤⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⢀⡴⠧⡺⠖⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣤⣷⣿⡄⠺⣸⣿⣿⣦⣤⣀⠀⠀⢸⡧⠘⢸⣧⣤⠴⠛⠁⠀⢀⣴⣾⣿⣿⡿⠟⠛⠿⣧⠀⠀⠀⠀⢠⡎⢀⠞⠀⣴⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣸⣿⢶⣸⣿⣝⢷⣿⣿⣷⠀⠀⢇⢡⣿⠟⠁⠀⡠⣶⣴⣿⣿⣿⠟⠁⠀⠀⠀⠀⣻⣷⠀⠀⣰⢋⣼⢇⠀⣰⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢻⣍⣻⣯⡻⢾⣶⣿⡉⠉⠁⠀⠘⣿⣇⠀⠀⢈⣶⣿⣿⣿⣿⡟⠀⠀⠀⠀⢠⣗⣾⣿⠀⡴⣿⠞⠀⠁⡶⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣯⠛⢿⣦⡈⠛⣿⣦⣄⠀⢰⣿⣿⢀⣴⠿⢻⣿⣿⣿⡿⠀⠀⠀⠀⠀⣰⣿⣿⡿⣮⠜⠁⠄⢠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡧⡈⢀⠈⣻⣿⡃⢸⣿⣿⡿⠁⠀⠀⣿⠛⠓⢷⡄⠀⠀⠀⠀⢡⣼⢿⡴⠃⢄⡤⣴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⢿⣿⣦⡉⠙⢿⣿⣿⢻⣿⠁⠀⠀⠀⢻⡆⠀⠀⣧⠀⠀⠀⠀⣿⡿⠈⣐⠮⣷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣦⡸⢷⣿⣿⣿⣆⡖⢸⢠⠀⡇⠀⠀⠸⡆⢀⡤⠚⢉⣀⣾⡷⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣦⣉⠻⣿⣿⣷⣾⣹⡜⠃⠀⢀⣠⣻⠟⠋⠉⣠⠼⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣼⡝⢿⣯⣿⣷⡆⠀⠻⢿⠤⠯⠖⠋⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠟⠁⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣦⡀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣼⠟⢡⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣧⠙⢿⡄⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣴⡏⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡆⠈⣿⡄⠀⠀⠀⠀
⠀⠀⠀⢀⣴⡏⠃⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠁⣿⣄⠀⠀⠀
⠀⠀⢀⡾⠁⣇⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠇⠀⢠⡇⠹⣆⠀⠀
⠀⠀⢸⡁⠀⣿⠑⠀⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠀⠀⢩⡇⠀⢹⠀⠀
⠀⠀⢸⣧⡀⣿⣆⠀⠀⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠃⠀⢀⣼⠇⢠⣾⠀⠀
⠀⢠⠾⡇⠁⠘⣿⡉⠀⠀⠙⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠁⠀⠀⣹⡿⠀⠀⡿⢦⠀
⠀⡿⠀⢿⣆⠀⠱⣿⡆⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠟⠀⠀⠀⣾⣿⠁⢀⣼⠃⠘⡆
⠀⣿⡀⢈⢷⡀⠀⠱⡿⣦⣀⡀⢰⡹⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢣⠀⢀⣠⣾⡿⠁⠀⣠⠏⠀⢰⡇
⣴⢿⡄⠈⢯⢿⡖⠀⣿⢿⢷⣍⣈⣷⡈⠙⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⣰⡟⢀⣹⢿⣿⡇⠐⣺⣯⠇⠀⣸⢧
⣏⠈⢷⣄⠀⠳⣿⣦⣌⣻⣿⡏⠙⠻⣟⠀⠀⠈⠓⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠖⠋⠁⠀⢸⡿⠛⠉⢿⡿⢋⣠⣾⡿⠋⢀⣴⠏⠈
⠹⡄⠈⣿⣅⠀⠘⣿⣷⣍⢻⣇⣷⠄⠈⠳⣤⡀⠀⠀⠈⠳⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠀⠀⠀⣀⣴⠋⠀⢠⡇⣾⢋⣤⣿⡿⠁⢀⣽⠋⠀⡴
⠀⢻⠦⠹⣝⣷⡂⠈⣿⣿⠛⠻⣮⡃⠀⠀⣿⣿⡶⣄⣀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠞⠁⠀⢀⣀⡴⣾⣽⡿⠀⠀⣾⡿⠛⠻⣿⡟⠀⣲⣿⡽⠡⢾⠃
⠀⠈⣷⣄⠈⠳⣝⣧⡀⢿⣷⣀⠈⠙⠶⣄⡚⠽⣿⣿⡉⠙⠂⠀⠀⠹⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠁⠀⠀⠘⠋⣝⣿⣻⠕⣂⣴⠞⠉⠀⣠⣿⠇⣠⢾⡿⠋⢀⣰⡏⠀
⠀⠀⢸⠙⢯⣅⠀⢽⡯⣿⢷⣽⣂⠀⠀⣓⡯⣗⣾⣷⣄⡀⠀⠀⠀⠀⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⣀⣽⣿⣖⡿⣟⡋⠀⢀⣺⣷⢿⣻⣿⠉⢀⣩⠟⢹⠃⠀
⠀⠀⠈⢧⡀⠙⣿⣇⣉⠻⣿⡋⠉⠓⠶⡤⢭⣽⣿⡅⠀⠀⠀⠀⣴⠞⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢶⣄⠀⠀⠀⠀⣽⣿⣭⠥⠴⠖⠋⠉⣻⡿⢋⣁⣽⡟⠁⣠⠟⠀⠀
⠀⠀⠀⠘⣿⡂⠈⠓⢯⣷⣿⣿⣾⠤⠀⠩⠭⢽⣿⣦⡴⠀⠀⠀⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡇⠀⠀⠰⣦⣾⣿⠭⠭⠁⢀⣬⣾⣿⣷⣿⠟⠋⠀⣺⡿⠀⠀⠀
⠀⠀⠀⠀⠈⠛⢶⣤⠀⠈⠻⣿⣿⣿⠶⠶⠶⣒⣿⣿⡶⠀⡀⠀⠈⠙⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠞⠉⠀⠀⣄⠠⣼⣿⣖⡒⠲⠶⢾⣿⣿⡿⠉⠀⢠⣴⠾⠋⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠓⠒⣼⣟⡁⠀⠀⢀⣀⡭⣟⣿⣾⠁⠀⡀⠀⠀⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⣀⢀⢹⣿⣿⣿⣅⣀⠀⠀⠀⠘⣿⡔⠒⠋⠉⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣃⣴⠞⠋⠁⠈⣛⣽⣿⣶⣾⠃⠀⠀⠀⠹⡄⠀⠀⠀⠀⠀⠀⡼⠋⠀⢀⢀⢹⣾⣿⣿⢯⡋⠁⠉⠙⢶⣄⣻⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⣶⡀⢠⠞⠁⠉⣵⣿⣿⣦⣼⡀⠀⠀⠙⢦⡀⠀⠀⣠⠞⠁⠀⠀⣸⣾⣾⢿⢷⣍⠀⠙⢦⣀⣰⣼⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠻⢶⡏⠀⠀⡼⠁⢉⡿⠋⡽⠉⠉⠉⠓⠚⠉⠀⠀⠙⠒⠋⠉⠉⠹⡍⠿⣇⠁⠹⡆⠀⣈⢿⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⠭⠿⣧⣖⣼⡧⢦⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠢⢻⣔⣲⡿⢿⡽⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀