⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⣷⣮⣥⣤⣤⡷⠀⠀⣠⣼⡿⠿⠛⠛⠛⠻⠿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣶⠛⠉⠀⠀⠀⠀⠀⠀⠈⠙⢷⣶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⡖⠚⢿⣿⠛⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡼⠋⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⣸⡧⠀⠀⠀⢰⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣟⢿⠟⠃⠙⢷⡀⠀⠀⠀
⠀⠀⠀⠀⣠⠞⠉⢀⣤⡀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⠁⠀⠀⠀⢠⣿⡵⠀⠀⠀
⠀⠀⢀⡾⠁⢠⡶⠋⠀⠈⠐⠁⢀⠻⣧⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡋⠀⢀⣀⡀⠘⠻⣷⡀⠀⠀
⠀⠀⣾⠁⢀⡿⠁⠀⠀⣠⣤⠶⠟⠒⠾⠿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⡿⠁⠈⠉⠈⠻⣦⡀⠈⢿⡄⠀
⠀⢰⡇⠀⣸⠇⣀⣴⠟⠋⠀⢀⡠⠄⠀⠀⠤⠽⣿⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⣿⣿⣛⣛⠓⠶⣦⡀⢿⣿⡄⠘⣿⡀
⠀⢸⠁⠀⣿⣼⠟⠁⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⢈⡉⠻⢷⣦⣤⡀⠀⣰⣾⢟⣥⡾⢟⣫⣝⡉⠛⠳⢿⣿⡈⣿⡇⠀⢸⡇
⠀⣿⠀⠀⣿⡏⠀⠀⠀⠁⠀⠀⠀⢀⣠⡴⣾⣿⢟⣿⣛⡛⠛⠚⠻⢿⣿⣿⡷⠛⠁⣴⣟⣹⡿⠻⣧⠀⠀⠈⢻⣿⡇⠀⢸⣷
⢸⣿⠀⠀⣿⠁⠀⠀⠀⠀⠀⢀⣴⠟⣩⡿⠋⣾⠋⢹⡿⠛⣦⡀⠀⠀⢹⡇⠀⠀⠠⣿⣟⣻⣤⣤⣿⠇⠀⢀⣼⢿⡇⠀⢸⡏
⢸⣿⠀⠀⣿⡇⠀⠀⠠⠶⠾⣿⡵⠟⠋⠀⠠⣿⣶⠛⣧⣤⣼⡇⠀⢀⣼⣃⣀⠀⠀⢹⣿⡧⠿⠿⠿⢶⣶⣿⣿⣿⡇⠀⢸⡇
⢸⣿⠀⠀⢿⡇⠀⠀⠀⠀⠀⠙⠳⣦⣄⡀⠀⢻⣿⣧⣽⣿⡿⠟⠚⠋⠀⠉⠉⠛⠛⠋⠉⠀⠀⣀⣴⡞⠋⢻⣧⣿⠀⠀⣼⡇
⢸⣿⠀⠀⢸⣷⠀⠀⠀⣠⠴⠶⠤⠤⠭⠽⣿⣾⣛⣛⣉⣀⣀⣀⣀⣀⣀⣀⣀⣀⡤⠤⠶⠶⠛⠋⠁⢀⣠⣿⣿⡿⠀⠀⣿⠁
⠘⣿⠀⠀⠈⣿⡀⠀⢸⣧⠀⠀⢠⣤⣀⣀⣀⠀⠀⠀⠀⠈⠉⠉⠉⠉⠁⠀⢀⣀⣀⣀⣤⡤⠶⠞⠛⠋⣿⠟⣿⠇⠀⢸⡟⠀
⠀⣿⡀⠀⠀⢿⡇⠀⠈⠻⠷⢦⣄⣀⣈⡉⠉⠛⠛⠛⠒⠶⠶⠶⠚⠛⠛⠛⠋⠉⠉⢉⣀⣀⣀⣀⣠⣴⣿⠟⠁⠀⢠⡿⠁⠀
⠀⢹⡇⠀⠀⠘⣿⣦⡀⠀⠀⠀⠀⠈⠉⠙⠛⠛⠷⠶⠶⠶⠶⠶⠶⠶⠶⠶⠖⠛⠛⠛⠉⠉⠀⠀⠀⣸⡃⠀⠀⣠⠟⠀⠀⠀
⠀⠸⣷⠀⠀⠀⠘⢿⣿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⡴⠾⢻⣷⣤⠞⠉⠀⠀⠀⠀
⠀⠀⠸⣦⠀⠀⠀⠀⢹⣿⣿⣿⠷⣶⣤⣤⣤⣄⣠⣄⣠⣤⣤⣤⣤⣤⣴⣶⠶⠶⠿⠛⠛⠉⠁⠀⠀⠸⣿⣇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣹⣧⡀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣷⣄⠀⠀⠀⠀
⠀⠀⠀⣿⣿⣿⣦⣤⣼⣿⣿⡇⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⢀⣠⣀⡀⠀⠀⠀⠈⢻⣆⠀⠀⠀