⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⣶⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⠛⠛⠉⠉⠉⠉⠛⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠺⠶⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣇⠀⢀⡀⠀⠀⠀⠀⢀⣀⣀⣌⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⢣⣿⠆⢀⡀⠀⠀⠀⠀⠈⠉⢉⡺⣿⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣿⣾⡿⣻⣿⣿⡷⠇⠀⠀⣴⣿⣿⣿⣿⢿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⣿⣿⡏⣾⣿⣿⣯⣿⣶⠾⠻⣿⣿⣽⣿⣿⣿⣿⣿⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣻⣿⣿⢁⣙⡋⠉⠉⣿⡇⠀⠀⣺⣿⡯⠻⠛⠛⣿⣿⢉⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡽⡏⠁⠀⣴⢿⣏⣥⣄⣠⣤⣽⡿⠆⠀⠀⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣇⣿⢰⣿⣤⣶⣾⡿⢿⡿⢿⣿⣶⣦⣌⢢⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣄⣻⣿⣿⣯⣉⡉⣉⣉⣩⣿⣿⣿⣼⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⡋⠠⣤⣤⣤⣴⡾⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣦⡀⠿⠃⣀⣴⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣀⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣼⠏⠙⢿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠉⣿⣿⣿⣿⠛⡗⠶⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⣾⠻⣿⡟⣿⠀⠀⠀⠀⠈⠛⢉⣠⡝⠋⠉⠀⠀⠀⢻⣯⣿⠇⣼⢃⡆⠀⠈⠙⡶⢤⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡤⠞⠋⢳⡘⣧⡹⣿⡹⡇⠀⠀⠀⠀⠀⠚⠛⠀⠀⠀⠀⠀⠀⣼⣿⠏⣰⠋⡜⠀⠀⠀⠀⡇⢸⢸⣷⣤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⢻⠛⡇⠀⠀⠀⠳⣌⢷⡌⢷⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⣿⠏⣴⠋⠐⠁⡀⠀⠀⠀⡇⢸⢸⣿⢹⣯⣻⣷⣦⣤⡀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⠘⡇⢹⠀⠀⠀⠀⠙⢦⡙⢦⣍⡻⠶⣤⣀⣀⠀⠀⠀⣀⣴⣾⡿⢛⣥⠞⡡⠀⠰⣿⡿⣿⡆⠀⠀⢸⠈⣯⠲⣏⠉⢻⣾⣿⡿⣦⡀⠀⠀
⠀⠀⠀⠀⣀⣴⣾⣿⣿⠟⢻⠀⣷⢸⠀⠀⠀⠀⠀⠀⠈⠓⢮⣙⠳⠦⣌⣙⣛⣳⣞⣛⣋⡥⠶⠋⠥⠛⠀⢠⣤⣭⣟⡟⣀⣀⡀⢸⡄⢿⠀⠀⠀⠈⢹⣿⡀⠬⣿⣄⠀
⢀⣠⣶⣿⣿⣿⡉⠉⠀⠀⢸⠀⣿⠸⠀⠀⠀⠀⠀⠀⢀⡤⠄⠈⠙⢒⢦⢀⢈⣉⡉⡁⠀⢀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠻⠿⡛⠛⠈⡇⢸⠀⠀⠀⠀⢸⡟⠳⢆⢈⣿⣄