⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠛⠳⠦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠈⠙⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠔⠒⠒⠋⠉⠉⠉⠁⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠑⢄⣀⠀⢠⡀⢠⡔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣹⣶⣅⣀⢀⣼⠗⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠶⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠲⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⢀⡀⠀⠂⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠸⣄⠘⡇⠀⠀⠀⠀⠀⠀⡸⢃⡆⠀⡄⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠛⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄⠀⠀⠀⠀⡌⠀⢿⠀⢰⡄⠀⠀⠀⠀⣠⠃⠿⠀⠀⠀⡄⠸⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠇⠀⠀⠀⣌⠀⠀⠀⠀⠀⠰⡀⠀⠀⡰⠀⠀⠀⠀⠀⠀⢱⡆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠑⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⠀⢀⡸⡇⠀⠀⠀⣿⡆⠀⠘⠦⠞⠀⠀⠀⠀⣰⣦⠀⠈⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠓⠀⠀⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⣇⡜⠁⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠉⠁⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣦⣤⠤⠄⠐
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⢀⠇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⢀⣀⣀⢀⡏⠀⣀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⢸⡇⠀⠀⠃⡀⠻⣄⣤⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⢁⠂⠀⠀⠀⠀⠀⢀⠀⣴⠀⠀⣷⡀⢀⣀⣀⡀
⠀⠀⠀⠀⠻⡄⠀⠀⠱⠄⠘⠃⠆⠀⠀⡙⡶⠆⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣶⠖⣸⣧⢶⡀⢀⡰⢛⡔⣡⡤⠈⠀⠀⠀⢠⠟⠁
⠀⠀⠀⠀⠀⠘⠣⡀⠀⠀⠀⠀⠀⠐⠂⠸⠛⠢⣤⢿⡾⢀⡻⢏⣻⠋⢉⣫⡄⠙⠋⡦⠞⠁⠛⠀⠓⠋⠀⠀⠀⠈⠀⠀⠀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⡀⠀⠀⠀⠀⣀⠤⠘⡷⠸⠇⣠⡿⣧⠀⠀⢸⡇⠺⠁⠀⠈⠦⣀⠀⠀⠀⠀⠀⠀⠠⠄⠊
⠀⠀⠀⠀⣀⢤⠤⠐⠒⠒⠂⠉⢁⡀⠤⠟⠋⠁⠀⡌⢀⠟⢢⠟⠀⢽⠓⠤⣾⠃⢀⠀⠀⠀⠀⠈⠙⠲⠖⡒⠒⠠⠤⠄⢀⡀
⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣴⠀⠀⡾⠇⠀⠀⢠⣧⠐⠋⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢉⡄⠀⠀⠀⠈⠁⠒⠦⣤⡀
⠀⠀⠀⠀⠀⠉⠑⠂⣀⠀⠀⣠⠙⢡⠀⠀⠀⢰⠁⠀⣰⠃⠀⠀⠀⠀⢱⡄⠀⠀⠀⢱⠀⠀⠀⠀⠀⢀⠴⠋⡑⠀⠀⠀⠀⠀⢀⣠⡤⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣶⣄⠉⠲⣰⠇⠀⠘⠃⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠘⣤⣀⣀⠶⠊⣁⡰⢯⠁⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢀⡼⠋⠈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠈⠀⠉⠈⠳⡄⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⣡⠔⠃⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⢦⡈⠣
⠀⠀⠀⠀⠀⠀⠀⠴⠦⠚⠁⠀⠀⡠⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠈⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⢄⡀
⠀⠀⠀⠀⠀⠀⢀⣤⡁⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠈⠙⠳⠦⢀⣀
⠀⠀⠀⢀⡤⠞⠋⠉⠀⢠⡇⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀⠦⠄⣀⡀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠁⡿
⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⢣⠀⠀⣀⠔⠋⠀⠹⣆⠀⠀⠀⠀⠀⣠⠋⠹⣄⠀⠀⠀⠀⢀⠃⠀⠀⠈⠙⠛⠂⠴⠀⠀⠀⠀⢀⡠⠛
⠀⠛⣤⣀⠀⠀⠀⠀⠀⠀⠸⣦⠊⠁⠀⠀⠀⠀⠙⡄⠀⠀⣠⠞⠁⠀⠀⠈⢳⣄⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊
⠀⠀⠀⠉⠓⠂⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡜⠁⠀⠀⠀⠀⠀⠀⠘⠳⡞⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠶⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠉⢰⡶⠶⠄⢀⣀⠀⠠⠴⠶⠦⠐⠀⠀⠀⠀⠙⠋⢻⡋⠁⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠞⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠛⠳⠦⣀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠈⠙⠦⣄⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠈⠙⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣤⠔⠒⠒⠋⠉⠉⠉⠁⠀⠀⣸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠑⢄⣀⠀⢠⡀⢠⡔⠒⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⣹⣶⣅⣀⢀⣼⠗⠶⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠠⠶⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠲⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡶⠎⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠢⣄⠀⠀⠀⠀⠀⠀⠀⠇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠸
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣄⠀⠀⠰
⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⢠⡆⠀⠀⠀⠀⠀⠀⢀⡀⠀⠂⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⣀⠃
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠁⠀⠀⠀⠀⠀⠀⠸⣄⠘⡇⠀⠀⠀⠀⠀⠀⡸⢃⡆⠀⡄⠀⢸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⠛⢄
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⡄⠀⠀⠀⠀⡌⠀⢿⠀⢰⡄⠀⠀⠀⠀⣠⠃⠿⠀⠀⠀⡄⠸⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠈⠲⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢸⣾⠇⠀⠀⠀⣌⠀⠀⠀⠀⠀⠰⡀⠀⠀⡰⠀⠀⠀⠀⠀⠀⢱⡆⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠑⣆
⠀⠀⠀⠀⠀⠀⠀⠀⢸⠁⢀⠀⢀⡸⡇⠀⠀⠀⣿⡆⠀⠘⠦⠞⠀⠀⠀⠀⣰⣦⠀⠈⠃⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠈⠓⠀⠀⠤⣤⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⢸⣇⡜⠁⡇⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⢀⡠⠔⠒⠉
⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠂⠉⠁⠀⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⢀⣦⣤⠤⠄⠐
⠀⠀⠀⠀⠀⠀⠀⢠⠎⠀⠀⠀⠀⢀⠇⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠁⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠀⠀⠱⡀
⠀⠀⠀⢀⣀⣀⢀⡏⠀⣀⠀⠀⠀⡈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣡⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓
⠀⠀⠀⢸⡇⠀⠀⠃⡀⠻⣄⣤⠀⠐⢀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠉⢁⠂⠀⠀⠀⠀⠀⢀⠀⣴⠀⠀⣷⡀⢀⣀⣀⡀
⠀⠀⠀⠀⠻⡄⠀⠀⠱⠄⠘⠃⠆⠀⠀⡙⡶⠆⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣶⠖⣸⣧⢶⡀⢀⡰⢛⡔⣡⡤⠈⠀⠀⠀⢠⠟⠁
⠀⠀⠀⠀⠀⠘⠣⡀⠀⠀⠀⠀⠀⠐⠂⠸⠛⠢⣤⢿⡾⢀⡻⢏⣻⠋⢉⣫⡄⠙⠋⡦⠞⠁⠛⠀⠓⠋⠀⠀⠀⠈⠀⠀⠀⡠⠔⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠄⣀⡀⠀⠀⠀⠀⣀⠤⠘⡷⠸⠇⣠⡿⣧⠀⠀⢸⡇⠺⠁⠀⠈⠦⣀⠀⠀⠀⠀⠀⠀⠠⠄⠊
⠀⠀⠀⠀⣀⢤⠤⠐⠒⠒⠂⠉⢁⡀⠤⠟⠋⠁⠀⡌⢀⠟⢢⠟⠀⢽⠓⠤⣾⠃⢀⠀⠀⠀⠀⠈⠙⠲⠖⡒⠒⠠⠤⠄⢀⡀
⠀⠀⠀⠘⢧⡀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⣴⠀⠀⡾⠇⠀⠀⢠⣧⠐⠋⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⢉⡄⠀⠀⠀⠈⠁⠒⠦⣤⡀
⠀⠀⠀⠀⠀⠉⠑⠂⣀⠀⠀⣠⠙⢡⠀⠀⠀⢰⠁⠀⣰⠃⠀⠀⠀⠀⢱⡄⠀⠀⠀⢱⠀⠀⠀⠀⠀⢀⠴⠋⡑⠀⠀⠀⠀⠀⢀⣠⡤⠛⠃
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣶⣄⠉⠲⣰⠇⠀⠘⠃⠀⠀⠀⠀⠀⠘⠃⠀⠀⠀⠘⣤⣀⣀⠶⠊⣁⡰⢯⠁⠀⠉⠉⠉⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠋⢀⡼⠋⠈⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡀⠈⠀⠉⠈⠳⡄⠳⣄
⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⣡⠔⠃⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠈⢦⡈⠣
⠀⠀⠀⠀⠀⠀⠀⠴⠦⠚⠁⠀⠀⡠⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡀⠀⠀⠀⠀⠀⠀⠈⠀⠶
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠢⡀
⠀⠀⠀⠀⠀⠀⠀⠀⢀⠖⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣁⢄⡀
⠀⠀⠀⠀⠀⠀⢀⣤⡁⢤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠀⠈⠙⠳⠦⢀⣀
⠀⠀⠀⢀⡤⠞⠋⠉⠀⢠⡇⠀⠀⠀⠀⢀⣠⡄⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⡀⠦⠄⣀⡀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠁⡿
⠀⢀⡴⠋⠀⠀⠀⠀⠀⠈⢣⠀⠀⣀⠔⠋⠀⠹⣆⠀⠀⠀⠀⠀⣠⠋⠹⣄⠀⠀⠀⠀⢀⠃⠀⠀⠈⠙⠛⠂⠴⠀⠀⠀⠀⢀⡠⠛
⠀⠛⣤⣀⠀⠀⠀⠀⠀⠀⠸⣦⠊⠁⠀⠀⠀⠀⠙⡄⠀⠀⣠⠞⠁⠀⠀⠈⢳⣄⠀⢠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊
⠀⠀⠀⠉⠓⠂⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣦⡜⠁⠀⠀⠀⠀⠀⠀⠘⠳⡞⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠊⠁
⠀⠀⠀⠀⠀⠀⠀⠈⠉⠐⠶⢄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠶⠋⠁
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡟⠉⢰⡶⠶⠄⢀⣀⠀⠠⠴⠶⠦⠐⠀⠀⠀⠀⠙⠋⢻⡋⠁⢹⡆
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣏⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⠀⠈⣧
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠸⡇
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡀⠀⣷
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢡⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⡀⠙⡄
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⡼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠞⠃
