⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡠⠔⠊⠉⣐⣂⠀⠀⠒⢄⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠄⢀⠖⠁⠀⢀⡤⠚⠉⠀⠙⠄⢀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢁⠀⠀⠀⠘⣠⠂⠀⠀⠀⠀⠈⠳⡀⠘⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⠤⠄⠀⠀⠀⠀⢀⣮⠖⠋⠈⠓⢦⠀⠀⡀⠐⡀⠱⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⢀⡴⣿⡀⠀⠀⠀⠀⠘⢠⠀⢏⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⢠⠘⡀⠀⠀⡾⠀⠤⠤⠤⠤⠠⠄⠀⢸⠀⠘⣆⠘⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⠀⠀⡘⣠⠇⠀⢰⠃⢈⠀⣄⠀⠀⠀⡖⢀⢸⠀⠀⠈⠓⠤⠀⠈⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⠀⣀⠀⡅⠃⠀⠀⡞⠀⢸⡀⠘⠀⠀⠀⡷⢸⠸⡄⠀⠀⠀⠀⠒⠒⠆⠈⠆⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡸⠠⠀⠱⠳⠀⠘⣇⠀⠀⢣⠀⠀⣇⠀⠀⠀⣇⢱⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠉⠐⠠⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⢀⣃⠇⠀⠀⡠⠀⠀⠸⡄⠀⠈⣧⡄⠙⠀⠀⠀⠸⡎⡆⠀⠀⠀⠀⣠⠀⠀⠁⣀⠜⢂⠤⠀⠀⠉⠐⣂⠠⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠈⠉⠀⠀⠰⠡⠂⠀⢠⢳⡀⠰⢤⡐⣀⣀⡤⠄⠀⢹⠐⠀⠀⢀⡞⠁⠀⢀⠜⠀⡠⠋⠀⠐⢊⠄⠀⠀⠉⠀⣄⡐⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⣀⠀⠀⠀⣠⠦⠀⠄⢘⠈⣇⠀⠀⠀⠀⠁⠀⠀⠀⠀⢧⡀⠀⣾⠁⠀⢠⠃⠀⡜⠁⠀⢀⠰⠁⠀⠁⣠⣴⠆⠀⠈⠒⢸⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⢹⠀⠀⢔⠅⠀⢸⠀⢸⠀⢹⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠹⢰⠇⠀⢀⡞⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⠰⡡⢀⢴⡤⠠⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠘⠂⢀⡔⠈⠀⢀⠀⡇⠘⡄⣸⠀⠀⠀⠀⠀⢀⠀⣂⡀⠤⢠⠸⡀⢠⣞⠀⠀⠀⠀⠀⡞⠀⠀⠀⢀⠔⠙⡵⠋⠸⡁⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⠀⡜⡜⠜⠁⠀⠀⡿⠤⢻⡝⢦⠀⢀⠈⠉⠉⠉⠁⠀⠀⠈⠁⢀⡏⠉⠁⠒⠂⠀⠀⠃⠀⠀⠀⠀⢠⡞⢁⠀⠀⢳⠀⠀⠈⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡎⠘⣔⠣⠀⢀⠀⠀⠀⠁⢯⠀⢲⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠸⠀⠀⠘⡘⡀⠀⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠄⠀⡀
⠀⠀⠀⡼⢤⠈⠢⡀⠠⡇⠀⠀⠀⢸⡆⢨⢆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢳⡀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⡁⠀⢁⡀
⠀⠀⠀⡇⢸⠀⣶⣝⢦⣰⣀⠀⠀⠘⡇⠿⣌⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢨⠀⠀⠀⠀⠀⠀⠀⠀⠠⡄⠘⢸⣇⠀⠀⢰⡀⠀⠀⠀⠀⣀⠠⠄⠋⠄⠁⣠⠔⣟⡓
⠀⠀⠀⠀⢸⠀⡟⣿⠀⠳⣆⠑⡄⠀⢇⠀⣀⠔⠊⠉⠉⠉⠲⢤⣀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠘⠃⠀⠀⢧⠀⡀⠐⠁⠀⡠⠀⢀⠴⠀⢠⢇⠏⠀
⠀⠀⠀⠀⢸⠀⣷⡽⠀⡀⠸⡆⢠⠀⢸⡀⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡄⠀⠀⠀⠀⠀⠉⠀⢀⠀⠁⡀⠜⠁⠈⣀⡞⠁⠀⠀
⠀⠀⠸⠀⢻⠀⠿⠄⠀⠃⠀⢻⠈⠁⠘⡇⢸⣻⡆⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠈⡼⠀⢀⠱⡘⡀⠀⠰⠈⢀⠀⠊⠀⠀⣠⠴⠁⠀⠀⠀⠀
⠀⠀⠀⠀⢸⠀⠀⠀⠘⠀⠀⠈⢧⣄⠀⢹⡀⢿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⡴⢁⡴⠃⠒⠉⣀⡀⠀⠐⠁⠀⠀⣀⠴⠃⠀⠀⠀⠀⠀⠀
⠀⠀⠸⠀⠈⡆⠀⠀⠀⠀⠀⠀⠘⡇⠉⢳⡃⠘⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣣⠄⡀⢠⣄⠀⠀⠀⢁⡎⠀⣠⠔⠋⠀⠹⠀⢀⢀⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢰⠀⢰⡅⠀⢠⡀⠀⠀⠀⠀⠘⢮⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⢟⡡⡎⠀⢸⠏⡦⡀⠀⠈⢀⡜⠁⢀⠤⠀⠙⣧⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡠⡈⠐⡄⠀⠓⢤⡀⠀⠀⠀⠀⠀⠸⠀⠝⠒⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠖⢯⣀⠀⣻⡇⠀⠸⡼⣣⠿⡆⠀⠈⠀⠀⣀⠄⠀⠀⢸⡀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⡁⡇⡂⠠⠀⠤⠄⠀⠀⠀⠀⠀⢀⣇⠘⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⣠⠞⢄⠀⠙⢾⠗⢃⠀⢠⠗⠁⠀⡇⠀⠀⠐⠋⠀⠀⠀⠀⢸⠁⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠃⢁⢉⠀⢤⣄⠀⠀⠀⠀⠀⢨⡄⠀⠹⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⠁⠀⠀⢑⠴⠛⠀⠀⠉⠁⡠⡴⣫⠍⠀⠀⠀⠀⠀⠀⠀⠀⡘⠐⣳⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡮⠄⠀⡨⢀⠛⢢⠀⠀⠀⡼⢄⣆⡀⠈⣳⣆⠀⠀⠀⠀⠀⣠⠶⠛⠁⠀⠀⢀⡔⠃⠀⠀⠀⠀⠀⠀⠙⡞⠭⢣⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢀⢷⠀⠀⠆⡸⠀⡼⠀⠀⢸⠇⢹⠘⡇⢠⠁⠈⣉⠈⠁⠈⠉⠉⠓⢄⠀⣀⠔⠉⠀⢀⡀⠀⠀⣀⣀⣀⠀⠇⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⢰⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⢸⡘⠀⠰⠰⠁⢠⡃⠀⢠⠊⢀⡔⢸⢻⡧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣓⠿⠟⠀⠅⠀⣇⠸⠄⣿⠹⠀⠐⢚⠀⣘⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⠁⠀⡆⠀⠀⡖⠀⠀⡁⢀⣴⠃⠠⣼⢋⠇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠒⠒⠙⠷⡓⠀⠘⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⢀⡇⠀⠀⠁⠀⠘⠀⠀⡼⠁⣼⠏⠀⡴⠁⠊⣆⠈⠢⣔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⣤⡀⠘⢂⣠⠏⠀⠀⠀⠀⠀⠀⡇⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠸⠀⢸⠀⠀⠂⠀⡌⢀⡘⠘⠀⠞⠀⠀⠊⣈⠲⣄⠀⠀⣀⠔⠻⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡍⣭⣀⡉⣀⠀⠀⠀⠀⠀⢀⠁⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠁⡄⠀⡎⠀⠈⠑⠀⠀⡌⠀⡀⠀⠀⠀⢀⠞⠁⢀⣼⠉⢹⠁⠀⠀⣰⠟⢓⣦⣄⠀⠀⠀⢤⡄⠀⠀⠈⠑⠶⠬⢍⣀⡄⣼⠀⠀⠀⠀⠀⣸⠠⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠃⠀⣸⠁⠀⠀⠀⠀⢸⠀⠀⣧⡄⠀⣰⠋⠀⠀⠚⠇⢀⣾⠀⠀⣰⠏⠀⠘⠛⠛⠁⢤⠀⠀⠀⠀⠀⠀⠀⠘⠠⠀⣸⢀⠋⠀⡄⠀⠀⠀⡇⠈⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡕⠀⡈⠀⠐⠀⡎⠀⡰⠉⠇⣰⠃⠀⠀⠀⡀⠀⣸⠇⠀⢀⠏⠀⠀⠀⠀⠀⠀⠀⣰⠀⣦⣤⣄⡀⠀⠀⠀⠀⡇⠚⠒⠚⠁⠀⠀⢸⡇⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠸⠀⢸⡅⠀⡇⠀⠄⠀⠓⠚⠀⡗⡰⠃⡀⠀⢀⠜⠀⢰⠏⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠉⠿⠛⠁⠀⢉⠹⣾⠁⠀⠀⠀⠀⠀⠀⡼⠓⢈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠆⠈⢹⠏⠀⠀⡄⠓⠺⣇⠀⡽⠁⠜⠁⣰⠟⠀⣰⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀
⠀⠀⠀⡜⠀⠀⠀⠘⡌⢀⣾⠟⣡⠎⡰⡞⢁⡤⠖⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠖⠀⠀⠀⠀⠀⠀⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠧⠀⣄⠀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀