⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣀⣀⠀⠠⢄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠖⣀⣠⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠐⠈⣠⣤⣶⠾⠟⠛⠛⠛⢷⡌⢢⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⢡⣿⠛⠉⠀⠀⠀⠀⠀⠉⠙⠻⠿⣶⣤⣀⠀⠔⠁⣠⣶⠟⠋⠁⠀⠀⠀⠀⠀⠀⠈⢿⡈⠆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⢿⣦⣼⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠠ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⢹⠀⠀⠀⠀⣠⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡼⣄⣴⠶⢾⣟⡁⠙⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⢸⣯⠀⣾⠛⢻⣷⠿⣧⡀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣄⣈⠒⠀⠀⠀⢠⣿⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⣻⣧⣹⡿⠻⣶⣾⠏⢀⣿⠃⠀⣠⣴⠾⠟⠋⠉⠀⠀⠀⠀⠈⠉⠙⠻⠷⣦⣾⣷⡟⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⣿⡟⣷⣤⣴⡿⠛⠛⠁⣴⣾⡋⠁⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣿⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡃⠀⠈⠁⠀⠀⣠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⠃⠀⠀⠀⠀⣰⡿⠁⠀⣤⣤⣤⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣶⠶⠌⣿⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡀⣿⣅⠀⢀⡄⢠⣿⠁⠀⠀⠈⠉⠉⠛⠻⢷⣦⡀⠀⣀⡀⢀⣴⡿⠋⠀⠀⠀⠞⢿⣇⢱ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢃⢸⣿⠀⣤⡅⣸⣧⡶⣦⡶⠂⠀⠀⠀⠀⠀⢉⠕⠩⣶⡮⠉⢍⠀⡀⠀⠀⠀⠀⠘⣿⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢎⢿⣇⠘⡶⢸⡇⠀⠀⠀⠀⠀⠀⠀⠰⠂⢸⠰⢶⣤⣴⠿⢙⠈⠁⠀⠀⠀⢀⣰⡿⠰ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠨⠻⣦⡁⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠣⢀⣀⣀⠠⠊⠀⠀⣤⡶⠿⢿⣏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠙⣿⣦⠘⢿⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣾⠋⠀⠀⢀⣿⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣾⡃⣃⠀⠀⠈⠉⠛⡻⠿⠶⢶⣶⡶⢶⣶⠿⠿⠛⢛⣽⡿⠀⠀⢀⣾⠇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢤⣿⠛⣿⣦⣤⡄⢀⠀⠀⠀⢠⣾⠋⠀⠀⢻⣦⣤⡶⢟⠏⠀⠀⢀⣼⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠜⣿⠃⠀⠈⠈⠙⠛⠿⠷⠶⠾⠛⠀⠀⠀⠀⠀⠉⠀⠀⠁⢰⣆⣶⣿⠏⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡜⣰⠟⠀⠀⣠⣶⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣉⡅⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢱⣿⠀⠀⢰⣿⣿⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡏⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⣪⣾⢿⣤⣀⣼⠟⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡟⠘⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⢊⣴⣿⣡⡾⠋⠉⠁⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡴⣡⡾⢋⠙⢿⣄⠀⠀⠀⠀⢸⣧⣀⠀⠀⠀⠀⠀⢀⣀⣤⡾⠋⠄⠀⠠⠀⢿⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⢎⣼⠟⠴⠃⠀⠀⣹⡷⠀⠀⠀⢸⣟⠀⢀⡄⠀⣀⠀⠀⢸⣷⠀⠀⢀⠀⢠⡀⢸⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡰⣣⡿⡫⠀⢀⠄⢁⣽⠟⠁⠀⠀⠀⠈⠻⠶⣼⣧⣤⣿⣤⣤⣾⣿⣤⣤⣽⣷⠾⠷⠟⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⢞⣴⣟⠉⠀⢘⣡⣾⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡠⢱⣿⣓⣁⣤⣶⡟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⠉⠈⠙⠛⠉⠁⠒⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⢀⣀⠄⠐⠀⢰⠂⠁⠔⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡴⢁⣀⠄⠁⠀⠠⠐⠁⠐⠆⠐⢉⢢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠎⠃⢄⠇⠀⠀⠀⠀⠀⠀⠀⠀⠐⡸⠀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣤⣤⣾⣶⣶⣶⣶⣤⣶⣶⣶⣶⣶⣧⣤⣼⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠛⠉⣿⣿⣿⣿⣿⣿⡯⣽⣿⣿⣿⣿⣿⡏⠉⡇⠀⠀⠀⠐⡄⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⠀⠘⠻⠿⠿⠿⠋⠀⠈⠛⠿⠿⠿⠛⠀⢠⢁⡠⠐⠂⠈⠙⠃⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢑⢄⣀⣀⣤⣄⠀⠀⠀⢀⣤⣀⣀⣀⣴⣮⣮⣤⣤⣦⣴⣤⣤⣤⣤⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢘⣧⣿⣿⣿⣿⣷⣶⣶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡾⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⣻⠿⣿⡿⠋⣽⣍⠹⢿⣿⡿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠉⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠎⠁⠑⠄⡀⠀⠀⠀⠀⠀⠠⠐⠉⣠⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⡟⣿⣿⣿⣿⡿⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠊⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠺⢿⠿⡿⠇⠸⢿⣿⡿⠇⢀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠄⢀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠠⠄⡀⠀⠀⠀⠀⠀⠀⣀⠤⠐⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡸⡆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀