⢻⣷⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⣰⠏⠀⢸⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠈⢿⣿⣿⡇
⠸⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⡼⠁⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠈⣧⠈⢿⣿⣿
⠀⠛⢿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⢠⠆⢀⡞⠁⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⢃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢆⠈⠛⠋
⠀⣀⠀⣹⠃⠀⠀⠀⠀⠀⠀⠀⠀⡎⢠⡞⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠈⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀
⠀⢁⣠⠇⠀⠀⠀⠀⠀⠀⠀⠀⡜⣠⠟⠀⠀⣀⣀⣀⣀⣹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠂⠀⠀⠈⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀
⣴⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⣼⣱⠿⠖⠋⠉⠉⠉⠉⠉⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢀⣀⣀⣀⣣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀
⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠋⠉⠉⠉⠉⠉⠛⣄⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⢸⣇
⣿⠁⠀⠀⠀⠀⠀⠀⠀⣰⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⢻⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⣿⣸⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⣿
⠃⠀⠀⠀⠀⠀⠀⠀⢠⠇⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠈⣧⠘⡄⠀⠀⠀⠀⠀⠀⠀⡇⢰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⢠⡟⢠⡇⠀⠀⠀⣀⣀⡀⠀⠀⠀⠀⠀⢾⡇⠘⣆⢳⠀⡆⠀⠀⠀⠀⢸⠃⣸⢸⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⠀⠀⣸⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⢠⡿⠁⢸⣥⣤⣶⣾⣿⣿⣿⣿⣿⣷⣶⣄⡀⠀⠀⠈⠂⠳⠃⢀⡀⠀⡼⠎⠀⠃⠘⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⡏⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣠⡿⠁⠀⢸⠼⣿⠛⠋⠁⢰⣿⣿⣿⡏⢹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⣰⡟⠀⠀⠀⠀⠀⠈⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣤⣴⣶⣶⣶⣦⣤⣀⡀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⢰
⠀⠀⠀⣴⡿⠁⠀⠀⠀⢸⡀⠀⠀⠀⢠⣸⣿⡿⠿⠻⠿⠟⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡶⠛⠛⠉⠉⠉⠉⠙⠛⠿⠿⢿⣿⣶⣤⣠⠀⠀⠀⠀⠀⠀⠈
⠀⢠⣾⣿⡇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⡇⠀⠀⠀⠀⠀⠀⡆
⣴⣿⠏⣿⢷⠀⠀⠀⠀⣇⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡧
⡟⠁⠀⣿⢸⣧⠀⠀⠀⢻⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠀⠀⠀⢀⣾⣼⣿
⠀⠀⠀⣿⢸⠀⢣⠀⠀⢸⣎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡼⠃⠀⠀⣠⣾⡿⠋⣿
⠀⠀⠀⣿⢸⠀⠀⢢⠀⠀⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠚⠁⠉⠀⠀⠁
⠀⠀⠀⣿⣸⠄⠀⠀⠳⡀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⣿⠁⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠐⢄⠹⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠠⠀⢀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀⠀⠀⠀⢀
⠀⠀⠀⣿⢻⠀⠀⠀⠀⠀⠀⠁⢻⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠀⠀⠀⠀⠀⠀⠀⠀⡘
⠀⠀⠀⣹⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠁
⠀⠀⠀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠾⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠈⠀
⠀⠀⠀⠋⣿⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣟⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡇⢹⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣿⣿⣷⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠘⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠷⣦⣄⣀⣀⣠⣤⣴⣶⣿⣿⣿⣿⣿⣿⣿⠿⣿⣿⣛⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰
⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣿⣿⣿⣿⣿⣿⢻⣿⣿⣿⣿⡄⠈⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠁⢠⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢧⢸⣿⣿⣿⣿⣿⡌⣿⣿⣿⣿⣇⣀⠀⠀⠉⠛⠿⠿⠿⠟⠋⠁⠀⠀⠀⣾⣿⣿⣿⣿⣿⣿⣿⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠈⣎⣿⣿⣿⣿⣿⡇⢹⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⢀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀