⠀⠀⠀⠀⠀⠀⠀⣠⠶⣶⠁⢶⡒⢶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣤⣾⣿⣦⢿⡷⠖⣳⢤⣿⢻⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⠏⢼⣿⠟⢉⣴⡿⢋⣠⡈⠻⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⢸⡄⢀⠉⠚⣋⡉⠀⢿⣿⣶⠀⢹⣿⣆⠀⠀⠀⢠⡴⣄⠀⠸⣿⣇⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠈⣷⣿⡆⠞⣻⡿⠆⠸⡟⠋⠁⠀⢿⣿⠀⠀⠀⠀⢳⡛⢦⠀⢷⣼⡄⠀⢸⠛⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠙⣿⡆⠌⠛⠀⣀⣹⡶⠤⣄⠈⣇⠀⢰⣶⣄⠀⠻⣉⣷⣸⡤⢷⠀⡏⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠹⣿⣄⠀⠘⢠⣴⣾⣷⡄⠀⡿⣷⣤⣻⣏⠓⢦⣽⡏⠙⢃⡈⠛⠙⣯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢠⣤⡀⠀⠉⠳⣄⠈⢻⣿⣿⣷⡄⢣⡇⠹⢿⠈⠓⣤⡉⢥⣄⣬⣵⡶⠦⠸⣍⣙⢶⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⣶⣄⠀⠘⣿⣿⡄⠀⠀⠈⣷⣄⠛⠿⠟⣠⣾⣀⣀⢸⡀⠙⠋⠹⣌⠛⠛⠻⣿⢠⡆⣿⠙⠒⢶⡿⠿⣿⣷⣦⣄⡀⠀⠀
⠀⠈⠻⣿⣷⣄⠹⣟⣿⡄⠀⠀⣸⣿⠛⣶⣿⣿⣿⢿⡏⣩⢁⡄⠀⢠⡿⡰⢾⣷⣄⣤⢀⣜⣀⣀⡀⠁⠀⠈⠛⠿⠓⢿⣦⠀
⣶⣦⣄⠈⢻⣿⡷⣿⢿⠳⣄⡴⠿⠜⣾⡿⠿⢻⡿⣾⡿⣷⡟⢀⡴⢋⣠⠤⣤⣾⣿⣿⣟⡻⠿⡿⠟⣣⣴⣶⣦⣤⣤⣤⣿⣷
⠈⠻⢿⣿⡶⠿⠹⡧⢈⣥⣙⢷⡤⠴⠋⣠⢴⣋⡿⢿⣴⡟⡴⠋⡴⠋⢀⣤⣴⣤⣼⣿⢿⣏⠉⠙⠒⠭⣟⣿⣿⣿⣿⣿⡟⠋
⠀⠀⠀⠉⣳⠞⠓⣴⣿⣿⣿⡆⢀⣀⡞⠁⢸⠋⠀⢸⢿⠁⠉⠉⠠⠶⠞⣛⣻⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀
⢰⣶⣞⣽⣽⣿⡰⠛⣛⠛⠋⣠⣿⡟⣷⠀⣾⠆⣀⢼⠸⣤⣶⠖⠀⢐⣩⣽⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠈⠹⣌⢻⣷⣶⣿⡏⠉⡟⢰⣿⠆⠁⢸⠀⣷⣾⣵⣾⣿⣿⣿⣿⣿⣿⣿⣿⣏⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢀⣿⣬⣿⠿⠿⡇⣾⣧⣾⢿⠀⠀⡸⠀⣿⣻⢽⣿⣿⠿⢿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢀⡞⠳⣜⣀⣠⠾⣇⢻⣿⣿⢼⡀⠀⡇⠀⢸⠚⠋⢁⣠⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⢧⣤⣶⣿⣿⡟⣹⣿⣿⡿⠈⡇⠀⡇⠀⢸⠴⠚⡿⠟⢛⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⢸⡀⢀⣤⣿⣿⣿⣧⡟⠉⢻⣇⢳⠄⡇⠀⣼⠀⢠⢽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀