⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣃⠀⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠊⠦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠏⠀⠀⠀⠀⠀⠀⠠⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢠⢴⣛⢷⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠁⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣼⢣⣟⣎⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠊⠁⠐⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢣⣟⣧⣿⣼⣣⣿⣂⢀⢤⡠⣲⣂⡐⣆⡀⡀⠀⠀⢀⡠⠦⠔⠒⠉⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠻⣿⣛⣟⡻⣽⣳⠿⣿⣾⣷⣿⡍⠀⠝⠉⠈⠣⣈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠙⢯⡞⣽⡇⠀⠀⢠⡿⢿⠿⣦⡠⡀⠀⠢⠤⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⡤⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣾⡼⠛⢾⡤⣀⣀⣀⣀⢀⡸⣿⣄⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠋⣛⡿⠿⠘⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠸⣅⠉⠉⠈⠉⠉⠀⠿⠻⠃⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣮⣖⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⣸⠙⠠⡧⠐⠒⢖⡶⠓⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠳⣨⢙⠷⢤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⠁⠀⠀⠈⠢⠄⢐⡤⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠅⠀⠜⣿⣆⠫⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡀⠹⠀⠀⠀⠀⠰⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠎⠀⠀⠀⠀⢹⣀⣶⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⢀⣢⢀⢀⣄⣄⣀⣠⣀⠀⠀⠀⠰⠴⠴⠤⠆⣼⡀⠀⠀⠀⠼⠋⢱⢪⠻⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠄⠂⠢⠀⠀⣻⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡾⢿⣿⠆⠐⠈⠀⠀⠀⠈⠁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠠⡁⠄⠀⠠⠈⢿⣿⡆⠲⠦⠦⠾⠰⠤⠀⣤⣴⣿⡟⠃⠀⠆⠀⠀⠀⠀⠀⠀⠀⠂⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠦⠁⠀⠀⠑⢪⠟⠀⠀⠀⠀⢐⠑⠞⠛⠉⠋⠁⠀⠀⡀⠀⣠⠀⠀⢀⣀⠚⠀⠐⣽⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢅⠈⠀⠀⠀⠃⡇⣀⠀⠀⠈⢠⠸⠖⠒⠒⠲⢒⠶⠃⠀⠛⠠⡀⠦⢀⣀⠀⠘⡗⠀⣀⠫⡂⠐⠂⠐⣢⣀⢀ ⠀⠀⠀⠀⠀⠀⠀⠑⠈⠀⠀⠀⠈⠙⠄⠶⠀⠀⠰⠄⠠⠀⡀⣸⠁⠀⠌⠠⠰⠐⠀⠀⠀⠠⡀⢠⠐⠢⡀⠐⠊⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⣀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⢀⠀⠶⠿⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⢀⠁⠀⠂⠄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⠉⠀⠀⠂⠀⠤⠀⠀⠀⠀⠀⠀⠀⠤⠀⠀⠀⠀⢀⡀⠀⠀⠀⢠⠄⠀⠛⠁⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠈⠐⠓⠋⠃⠛⢱⠆⠁⠐⠋⠩⠸⠓⠂⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠁⠀⡄⠀⠀⠀⢠⣠⠤⠄⡀⠀⢀⠄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⠶⠶⠰⠶⠰⠖⠀⠀⠀⠀⡰⠃⠀⠀⠀⠉⣩⠃⠀

⠀⠃⣩⠉⠀⠀⠀⠃⡰⠀⠀⠀⠀⠖⠰⠶⠰⠶⠶⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠄⢀⠀⡀⠄⠤⣠⢠⠀⠀⠀⡄⠀⠁⠒⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠂⠓⠸⠩⠋⠐⠁⠆⢱⠛⠃⠋⠓⠐⠈⠉⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠀⠀⠁⠛⠀⠄⢠⠀⠀⠀⡀⢀⠀⠀⠀⠀⠤⠀⠀⠀⠀⠀⠀⠀⠤⠀⠂⠀⠀⠉⠄⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠂⠀⠁⢀⡨⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠶⠀⢀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢠⣀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠊⠐⡀⠢⠐⢠⡀⠠⠀⠀⠀⠐⠰⠠⠌⠀⠁⣸⡀⠀⠠⠄⠰⠀⠀⠶⠄⠙⠈⠀⠀⠀⠈⠑⠀⠀⠀⠀⠀⠀⠀ ⢀⣀⣢⠐⠂⠐⡂⠫⣀⠀⡗⠘⠀⣀⢀⠦⡀⠠⠛⠀⠃⠶⢒⠲⠒⠒⠖⠸⢠⠈⠀⠀⣀⡇⠃⠀⠀⠀⠈⢅⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⣽⠐⠀⠚⣀⢀⠀⠀⣠⠀⡀⠀⠀⠁⠋⠉⠛⠞⠑⢐⠀⠀⠀⠀⠟⢪⠑⠀⠀⠁⠦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⢀⠀⠂⠀⠀⠀⠀⠀⠀⠀⠆⠀⠃⡟⣿⣴⣤⠀⠤⠰⠾⠦⠦⠲⡆⣿⢿⠈⠠⠀⠄⡁⠠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠁⠈⠀⠀⠀⠈⠐⠆⣿⢿⡾⣤⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣷⣿⣻⠀⠀⠢⠂⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠻⢪⢱⠋⠼⠀⠀⠀⡀⣼⠆⠤⠴⠴⠰⠀⠀⠀⣀⣠⣀⣄⣄⢀⢀⣢⢀⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⣶⣀⢹⠀⠀⠀⠀⠎⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠰⠀⠀⠀⠀⠹⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡅⠫⣆⣿⠜⠀⠅⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠄⡤⢐⠄⠢⠈⠀⠀⠁⡞⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⠷⢙⣨⠳⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢂⠓⡶⢖⠒⠐⡧⠠⠙⣸⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⣖⣮⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠃⠻⠿⠀⠉⠉⠈⠉⠉⣅⠸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠃⠛⠘⠿⡿⣛⠋⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⣿⡸⢀⣀⣀⣀⣀⡤⢾⠛⡼⣾⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠤⠢⠀⡀⡠⣦⠿⢿⡿⢠⠀⠀⡇⣽⡞⢯⠙⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⣈⠣⠈⠉⠝⠀⡍⣿⣷⣾⣿⠿⣳⣽⡻⣟⣛⣿⠻ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠘⠀⠀⠉⠒⠔⠦⡠⢀⠀⠀⡀⡀⣆⡐⣂⣲⡠⢤⢀⣂⣿⣣⣼⣿⣧⣟⢣ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠐⠁⠊⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣎⣟⢣⣼⣀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⠀⠀⠀⠀⠁⡴⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢷⣛⢴⢠⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠄⠠⠀⠀⠀⠀⠀⠀⠏⡠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠦⠊⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠏⠀⠀⠀⠀⠀⠀⠀⠀⣃⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀