⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣠⣤⣤⣤⣤⣤⣤⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣿⣿⡻⢛⡻⠟⠛⠛⠛⠛⠫⠝⣛⡍⠛⣿⣿⣷⣿⣿⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⠿⠛⠣⠊⠁⠀⠀⠀⠀⠀⠐⠀⠀⠈⠐⠄⠈⠉⠛⠿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⡿⠋⡀⠔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢄⠀⠀⠀⠀⠙⢿⣿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⢀⠎⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣠⣄⠀⢀⠈⠄⠀⠀⠹⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⠃⢀⠀⡴⠟⢚⣉⣛⠓⠒⠒⠢⠤⠴⠖⠚⠉⣉⡤⠤⢼⡙⠷⡅⠀⠈⢢⠄⠠⡽⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⢋⠏⡟⠇⢸⢁⠊⣳⡶⠬⣍⠺⢆⡀⠀⢠⣤⠴⣋⠵⠶⠷⡆⠙⠀⠇⠀⠄⢸⣰⠀⠀⢹⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⣼⢀⣀⠀⠈⠸⠸⡛⡇⠀⢘⣫⡆⣿⠀⢀⡇⢸⡄⠀⠀⢺⡿⡜⢰⡆⠈⠀⠘⣻⠀⠀⠈⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⡏⠸⢸⠀⠾⡄⢧⠹⠧⢤⡿⠻⡼⠛⠀⠈⠱⣌⡻⠤⠤⢛⣱⢱⡿⠁⠀⠀⠀⢣⠀⠀⠀⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣇⡇⠈⡟⠠⠀⠹⣌⡟⠚⠒⠒⠋⠁⠀⠀⠀⠀⠀⠈⠑⠋⣡⣾⠟⠀⠀⠀⠀⠈⢹⠀⢸⡴⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣤⡇⠁⠀⠀⠈⠙⠶⣄⠀⠰⠶⡦⠀⣤⣾⠗⠀⡴⠞⠋⠀⠀⠀⠀⠀⠠⠀⣹⢀⣮⠆⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠫⠇⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠈⠀⠀⠀⡇⠀⠀⠤⠀⠀⢀⠈⠀⠰⢿⢚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠈⠀⠀⢿⠀⠀⠀⠀⠀⠀⠀⠠⠁⠈⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠂⢀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢸⡄⠀⠀⡀⠀⠀⢁⠂⠀⢰⠀⠀⠀⠀⢰⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⠂⠁⢄⠀⠀⠀⢣⠀⠱⣀⣀⡰⠶⢂⣀⡖⠃⢸⠉⢠⠎⠁⡀⠀⠈⠀⠁⠘⠂⠤⠀⡀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⢒⠀⠡⡀⠀⠂⠁⠠⠐⠀⠀⠀⠘⣧⡄⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⡄⠖⠃⠀⠀⠀⠀⡀⠀⢀⠄⠠⠁⠂⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⠐⠀⠀⠀⠀⠀⠀⠀⠀⠐⡆⠀⠀⠀⢹⣷⣴⣤⣤⣤⣤⣴⣾⣿⠇⠀⣬⠀⠀⠀⠀⠀⠀⢀⠌⠀⠀⠁⠀⠈⠄⠀⠀⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠁⠀⠀⡰⠁⠀⢀⠄⠈⠒⢠⠔⠝⠀⠀⠀⠀⠀⠍⠉⠉⠉⠉⠉⣁⠀⠄⠈⢀⠠⠀⠀⠄⢘⡀⠄⠀⠐⠀⠀⠂⠀⠀⠀⠂⠐⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⢀⠛⡀⠀⠊⢀⠄⢔⠱⡐⠂⡔⢁⠀⢁⠤⠠⢤⠤⡤⠎⣔⣀⣤⣀⣀⣀⣀⡠⠬⠅⢀⠀⣀⡄⠀⣇⠈⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⢰⠀⠀⢀⠈⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⢉⠄⠠⠀⢀⠀⠀⠀⠀⡠⠊⠀⣤⠄⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡦⠕⠁⡠⠂⠠⡚⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠠⠀⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠁⠀⢘⡈⠳⠀⠀⠀⠀⠀⠀⠰⠁⣰⢺⣍⣣⠢⠍⢲⢉⡉⢤⢚⣒⢤⠐⠒⢆⢀⠴⢆⡯⠤⠤⢔⡀⠀⠀⠚⢘⠄⠀⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⠚⠀⠀⠁⠀⠁⠀⠀⠀⠀⠀⠐⠀⠁⠀⠣⡚⡣⠇⣰⡂⡌⢰⡔⡙⠸⢟⢸⠀⣍⢲⠃⣿⠃⣷⠀⡗⠎⠀⠄⠀⠀⣱⠀⠂⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⡂⠄⠀⢠⠁⢠⢀⠓⠄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠠⢦⠆⠆⠀⠀⠀⠀⢀⠀⠀⢀⡘⠠⡌⠀⠀⠀⠃⠀⠨⠆⠉⠈⠀⠐⠈⠒⠎⠉⠲⠒⠁⠑⠤⡀⠙⣴⠃⠀⠀⢀⡄⠀⠁⠀⠀⠀⠡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⢸⠀⠄⡌⠀⢸⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠈⠂⠐⠨⢀⠀⠈⠑⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⢀⡀⠀⠀⠀⠀⠀⢠⣀⣀⠀⠇⠁⠀⢀⠅⠀⢈⠌⠀⡠⠀⠔⠉⠀⠀⡇⠀⠙⠉⣄⠀⠀ ⠀⠀⠀⠀⠀⠄⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠢⢈⠢⠘⠐⠂⢠⡄⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢂⠓⡂⠀⠐⠐⠆⠀⠀⠀⠀⢤⠀⠀⠀⠄⡐⠃⢀⠊⠁⠀⢠⠎⠀⢠⠁⣈⠀⡞⠒⠀⠀ ⠀⠀⠀⡀⠀⠀⠀⠀⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠀⠀⢀⠘⠀⠀⠀⠀⠀⠀⡆⠀⠀⢁⡀⠍⠉⠉⠉⠉⠉⠙⠉⠁⠉⠀⠀⠁⠀⠀⢸⡀⠀⠀⢸⠀⠀⠀⠀⠐⠀⡅⠀⠀⠀⠎⠀⠀⠈⠀⠀⠈⠀⠀⠀⠀ ⠀⠀⡐⠀⠀⠠⠀⢶⠀⠀⠀⠀⢈⠠⠀⠠⠀⠀⣠⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠰⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡄⡀⠀⠂⠀⠐⣁⠢⠐⠀⠀⠀⠤⢀⠀⠀⠄⠄⠀⠰⠀ ⠀⠐⠀⠀⠀⠀⠐⡼⠀⠀⠀⠀⠘⠐⠀⠀⢰⠀⡈⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠊⠒⠀⠀⠀⠀⠀⢸⢀⡀⠀⠀⠀⠀⠴⠀⠀⡆⠀⠀⠀⠇⠀⠐⠠⠐⠁⠀⠀⠀⠀⠈⠀⠀⠀⢈⠉⠲⡄⡀⠂⠀ ⠀⠀⠀⠀⠀⡸⠊⠇⠀⠀⠀⠀⠀⠀⠀⠁⠈⠀⠱⡀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⢀⠀⠀⠄⠀⠀⡀⠀⠀⠀⠀⠠⠀⠀⠀⢀⠀⠠⣈⠳⡇ ⠀⠀⠀⠀⠉⠀⠈⠀⠀⠀⠀⠂⠀⠀⢀⠁⢡⠀⢢⢡⠀⠃⠀⠀⠀⠀⠀⣀⡀⠀⠀⠀⠋⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠀⠀⠘⠀⠄⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠅⣀⠀⠀⠁ ⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⢀⠔⠁⠀⠀⠁⠆⢡⢱⠀⠀⠀⠀⠀⠀⠀⠐⠠⠄⠀⠀⢉⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⡰⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠂⠄⠀⠀⠀⠀⢂ ⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⢀⡇⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⠀⡇⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⣘ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠂⠀⠐⠀⠀⠈⠀⠈⡇⠸⡀⠈⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠐⠀⠀⠄⠈⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠈ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⡄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⢠⠀⠠⠀⠈⠂⠀⠀⠀⠠⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀