⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣟⡕⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⢻⠙⢄⠑⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣯⡭⠀⡈⢦⡈⢗⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠒⠒⠒⢀⠠⠤⢀⣠⡔⣞⢻⣏⢎⣤⢌⣱⡄⠹⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣏⡢⡀⠀⢠⣶⢿⠋⢑⢄⢄⡈⢙⡔⡴⣂⣐⣦⣸⢊⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣜⣠⣊⣱⣏⡎⠘⠀⠩⢆⢱⡉⢦⠀⠀⠱⡄⢘⣿⡦⢵⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⣿⢸⣷⠐⠀⠀⢸⢸⣳⣌⢷⡀⢦⠓⣿⣁⢿⣴⣿⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⢸⢳⣆⢃⠀⢾⡿⡁⣈⠙⠇⠀⡇⡟⢸⡇⡎⣸⡟⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⡾⣾⠛⣮⣸⠊⠘⢟⣿⣿⢇⣀⡇⢻⢿⡷⣽⣡⣧⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣣⣿⣿⡄⠀⠀⠈⠚⠈⣸⣼⡰⠏⣘⡷⠉⣯⣿⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣽⣷⠓⠁⡀⠀⠀⠀⠀⠉⣿⡖⣰⣽⣥⣾⢻⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣶⡽⣯⡀⠀⢠⡀⠀⠀⢀⢼⡼⣿⣿⠿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠴⣲⣰⢤⡈⡿⢿⣿⣶⣤⣄⣠⣔⢁⣀⣃⣉⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡀⡀⠀⢺⣧⣾⣶⡋⣌⣾⡄⠉⢛⡀⣉⣀⡱⠕⠛⠋⠻⡛⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣰⠊⠈⠈⠢⡀⠈⠉⠹⢞⠏⠪⣱⠎⠀⠀⠀⠈⢷⠀⠀⠀⠀⠰⡈⠑⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠒⠢⡀ ⠀⠀⠀⠀⠀⠩⣶⣤⣠⠆⠚⢇⠀⠀⠀⠱⢀⠃⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠃⠀⢸⡌⡆⠀⠀⢀⣀⣀⠀⠀⠀⠀⠀⢧ ⠀⠀⠀⠀⠀⠀⠀⠘⠳⡏⠀⢸⠀⠀⠀⢀⠏⠀⠀⠀⢀⢴⠎⣸⠁⠀⠀⠀⠀⠀⠀⢸⢇⣷⠊⠉⢁⠜⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠈⡆⠀⢠⡾⠦⣀⢀⢔⠕⠁⢀⡟⠉⢀⠄⠀⠀⡀⠀⣾⣾⡿⣟⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠇⠀⠀⢡⢠⠃⠸⠒⣽⣶⡊⠀⠀⣸⢃⠔⠋⠀⠀⢰⠁⣿⡿⣿⣟⠋⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠨⠁⠀⡔⡁⢠⣾⣏⣹⣿⣿⣶⡶⣶⣶⣶⣷⣾⡿⠿⢛⡛⠯⠤⢄⠀⠀⠀⠑⠄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⢠⡏⠠⠎⢰⠀⠀⠀⠀⠀⠀⠈⠙⠣⡴⠿⡿⠿⡟⡷⠊⠁⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠀⠟⠔⠁⢀⢼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠪⡗⣀⡸⠁⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⡰⠉⡓⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⠁⠀⠀⠀⠀⠀⠀⠼⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠑⠊⠀⢀⠏⢣⡄⠀⠀⠀⠀⠀⠀⠀⠀⡠⠤⢜⢀⠤⢄⡀⠀⡠⠠⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡸⠀⡄⣊⢄⠀⠀⠀⠀⠀⠀⢸⠀⠀⢀⠧⡀⠀⡇⠀⠀⡘⠀⠀⠀⠀⠀⠀⠀⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠒⠉⠁⣂⣍⡾⢑⠢⡈⠀⡇⠢⠀⠀⠀⠀⠀⠀⢑⠔⢇⠈⡘⢔⠁⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⢈⠴⠟⢫⠃⣼⡇⠚⠀⠱⣼⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠙⣹⠀⠀⡇⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⡠⠊⠀⠀⡰⡡⠊⡟⣃⡀⡠⠒⡇⠀⠀⠀⠀⠀⠀⠀⠀⡝⠂⡔⣿⠒⠚⠀⠀⠀⠀⣷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠁⣒⡆⠀⡠⠋⠀⠀⠁⣇⢀⠤⠒⠃⠀⠀⠀⠀⠀⠀⠀⡔⠀⡔⠀⠃⢣⠀⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⠤⠂⠉⠀⠷⠯⠀⢀⠀⠀⣜⠀⠁⠀⢀⡄⠀⠀⠀⠀⠀⡠⠊⡠⠊⢀⢰⡆⡀⠑⢀⠀⠀⠀⢸⠑⢢⠄⡀⠀⠀⠀⠀ ⡔⠁⠒⢄⠀⠀⠀⠀⠀⠀⠱⡼⠃⡠⠂⠀⠀⡇⠀⠀⠀⣐⡨⠐⠉⠠⠒⠁⡜⢡⠈⠢⡀⠑⠆⠤⠜⠀⠀⠉⠪⡑⢄⠀⠀ ⠰⡀⢀⠤⠓⡀⠀⠀⠀⠀⠀⡠⠚⠁⠀⠀⠀⠘⠒⠀⠉⡰⠁⠀⠀⠀⠀⢸⠇⡜⡆⠀⠀⠑⢌⠄⠀⠀⠀⠀⠀⠀⡔⠀⠀ ⣠⠞⠁⠀⠱⡘⣄⡀⠀⢀⡮⣤⣀⠀⠀⠀⠀⠀⠀⠀⡔⠁⠀⠀⠀⠀⠀⡟⠄⢡⢱⠀⠀⠀⠀⠉⢆⠀⢀⡤⠐⠋⠲⣄⡀