⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⠢⡀⠀⠀⠐ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⢀⡴⠢⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠈⠧⠴⠁⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⣠⣴⣶⡾⠛⡻⡷⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢀⣼⣿⠟⠁⠀⢀⣠⢔⡽⡿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢹⣿⣛⢤⠂⠰⣴⣷⡟⣡⠐⢽⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⣿⡿⣏⣴⣟⣯⢿⣽⣿⢽⣴⣿⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢻⣧⠿⢏⢈⢄⣱⣺⣿⣷⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠈⢻⣿⢋⣏⣾⣿⣿⣿⣿⣿⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⡄⠀⠀⠀⠀⠀⠀⠀⢐⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠙⢷⣿⣿⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠻⣄⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣏⢀⡀⣄⣽⣄⡀⠀⠀⠀⠀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⢾⣿⣿⡿⣿⣧⠀⠀⠀⠀⠀⠁⠀⠀⠐ ⠀⠀⠀⢀⡀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣷⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⣲⣿⣿⣿⣾⣿⣿⣿⣿⣷⠂⠀⠀⠀⠃⠀⠀⠀ ⠀⠀⠀⣀⡕⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⣿⣯⣿⣿⣿⣦⣀⣀⣀⡖⠀⠀⠀ ⠀⠀⡄⠀⠑⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣟⣿⣷⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⣿⣦⡀⠀⣆⠀⠀⠀ ⠀⠐⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡿⡿⢻⣟⣽⣿⣿⣿⣍⠁⠀⠀⠀⠀⠈⣱⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠉⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣾⣯⣴⠤⢾⢿⣿⣿⠿⠿⣿⡷⠂⠀⠀⠀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣧⡅⠀⠀⠀ ⠀⠄⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⢯⣿⣿⣿⣿⣿⣿⣿⣾⣿⣍⣀⣀⠀⡀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣯⣿⣿⡷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿⣟⣦⡀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠲⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢶⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢙⠺⠿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⣿⣿⣿⣿⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⠁⠀⠀⣴⣿⣿⣫⣿⣷⣾⣿⣿⣿⣿⣿⣽⣿⣿⢿⡞⠋⢝⣿⣿⣿⣧⠂⠀⠀ ⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣩⡽⡷⣞⣿⣿⣿⣿⣿⣶⣾⣯⡿⢿⣿⣿⠿⠿⠿⢿⣿⣿⣻⡿⠿⡽⣟⣳⠜⠉⠽⠿⣿⡇⠀⠀⠀ ⠘⠪⠟⠿⢶⣤⣠⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣾⠽⠾⠶⢛⣿⣿⣿⣿⡷⣿⣿⣟⡺⡿⠒⠒⠂⠀⣰⣿⣿⣿⡟⢃⠀⣹⠟⠁⠘⠐⠀⢐⠚⣏⠀⠀⢀ ⠀⠀⠀⠀⠄⠈⢻⣶⣤⣴⣶⠿⠿⠿⠛⠿⣷⣲⣤⣠⣶⣾⣿⣿⣟⡀⠀⣠⢀⢡⣿⣿⣿⣿⣿⣺⣿⣟⠀⣀⣠⣀⣠⣼⣿⣿⣿⣟⣵⣹⢛⣁⣠⠴⠢⡄⣶⣬⣿⠷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡁⠀⠀⠀⢀⡤⠤⢬⢹⣿⣿⣏⣽⣿⣿⣟⣁⣤⣠⠄⣂⣀⣾⢿⣿⣿⣿⣿⣯⢻⣿⡒⠚⠪⡍⢻⣿⣿⣿⣣⣿⡿⣋⣾⣉⣠⠀⠀⡀⡠⢀⣹⠀⠀⠀⠠ ⠀⠀⠀⠀⠀⠀⠺⡂⠀⠁⠀⠀⠀⠠⣿⠿⢉⢸⠿⠛⣛⣗⣻⡿⠟⡛⠞⣿⣿⣯⠿⣿⣩⣟⣛⣿⣿⣿⣿⣯⢿⣽⣿⣿⣽⣿⣯⡽⣻⣽⣉⠉⠭⠉⠉⠃⠀⠹⣿⢃⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠠⠂⠀⠀⢀⣠⣰⣾⣟⣴⡿⠇⡦⣖⣵⡿⣿⣿⣿⣽⣽⣿⣿⣾⡿⠾⢔⣗⣾⣿⣿⣿⣿⢽⣿⣿⣿⣿⢿⢿⣾⢶⣟⡿⢻⣳⣶⠾⠒⢀⠐⠐⣺⡠⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡆⠀⢠⢛⣾⣿⣧⣿⡿⣢⣮⣷⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣉⣅⣽⣽⣶⣿⣿⣿⣿⣿⣿⣿⣿⣾⣵⣿⣵⣿⣼⣯⣶⡞⠱⡷⣶⠒⠃⠈⠚⢿⠀⠀⠀⠀ ⠀⠀⢠⠔⢦⠀⠀⡏⠉⠡⠿⣿⣿⡏⣫⣿⣿⣿⣿⣿⣿⣿⡻⠿⠟⠻⠟⠉⠉⠉⠉⠉⠙⠛⠻⠷⣷⣾⣿⣿⣿⣿⣿⣿⣿⣿⢿⢟⣄⣀⣄⣅⣠⣀⠀⠀⢀⣨⣼⠂⠀⠀⠀ ⠀⠅⠘⠢⠾⠒⠒⡇⠀⠐⠒⠛⠚⠿⠿⣿⣿⣿⡿⠾⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⠀⠀⠀⠋⠋⢙⣿⡿⢟⢿⠿⠛⠟⡭⠙⠑⠉⠉⠉⠉⠉⠈⠁⠀⢺⡄⠀⠀⠀ ⠀⠀⠀⠄⠠⠄⠀⡇⠀⠠⠀⠠⠀⠀⠀⠩⠭⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠈⠓⠀⠀⠀⠀⠀⠀⠀⠐⠒⠂⠀⠀⠀⠀⠐⠒⢺⠁⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡮⠄⠀⠀⠸ ⠀⢀⣀⣀⣀⣀⣀⣇⣀⣀⢀⣀⣀⣀⣀⣀⣀⢀⠀⣀⡀⠀⠀⣀⢀⣀⣀⣀⣀⣀⡀⢠⣤⢤⣤⣤⠤⠤⠄⣄⣤⣤⣤⣀⣀⣀⣒⣂⣀⣀⣀⣲⣶⣶⣦⣤⣤⣭⣽⣷⣾⣶⣶