⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⡀⠤⠀⣀⢠⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠒⠤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⢀⡤⠒⣀⢀⠀⠐⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡆⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⡰⠋⠀⡴⠉⢠⠊⠀⡎⢀⡄⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⡴⢁⠄⡞⠀⢀⡇⡔⠁⡇⡔⡇⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀ ⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠃⡎⢸⠇⢠⠇⣿⠁⠀⢣⡇⢧⢀⣦⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢣⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⢰⢁⠗⠀⡏⠀⢿⡀⠀⠈⠺⠌⣇⢧⢱⠀⣸⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀ ⢰⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⢀⠇⢸⢸⡀⡆⡇⠀⠀⠉⠀⠀⠀⠀⠈⠃⠓⢇⢹⣣⠄⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀ ⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⠀⠸⡸⡟⢜⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣼⢺⢹⣇⠀⢸⠀⡄⠀⠀⠀⠀⠀⠀⢠⡟⠀⠀⠀⠀ ⠿⠀⠀⠀⠀⠀⠀⠀⠀⢀⡎⢀⠀⠀⢣⣇⢐⣽⣦⣄⠀⠀⠀⠠⢴⡶⠛⠛⠓⣾⡎⢸⣀⢨⠀⡇⠀⠀⠀⠀⠀⠀⠀⠹⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⡌⡇⢸⢄⣀⡞⡏⡟⠁⢠⠭⢷⡀⠀⠀⠈⢡⢦⢤⠀⠁⢻⡮⡟⡈⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠱⣜⢢⠧⠸⡇⢸⣦⡀⠙⢧⣧⠇⡶⣆⠀⠘⠯⠴⠃⠀⣠⡿⣡⠓⠁⢀⡎⠀⠀⠀⠀⢀⣰⢠⠇⠀⠀⠀ ⠂⠀⠀⠀⠀⠀⠀⣀⠀⠀⢀⡸⣰⠀⠹⡮⣷⣵⣠⣂⡤⠞⠁⠹⢦⣀⣜⣘⣐⣻⠟⢋⠏⢀⡠⢊⠴⠀⠀⠀⠀⠈⡟⠉⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⡤⣾⡴⠃⠀⠀⠉⢸⡘⣇⠉⣒⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠒⠮⡵⠎⠠⠒⠁⠀⠀⠀⠀⠀⠖⠳⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⠀⡏⠀⠀⠀⠀⠀⠀⠉⡉⢉⣿⡀⣍⣓⣲⠤⣄⣀⣂⣠⡤⠤⢆⠔⢉⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⢦⣀⠀ ⠀⠀⠀⠀⢸⠀⡇⢀⣀⡤⠤⡴⠒⠒⢳⣞⠏⠣⢯⡝⠋⢰⢉⣩⣽⠏⠁⢠⠎⢀⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄ ⠀⠀⠀⡠⣌⢸⡇⠈⢆⠀⠘⠊⠀⠀⠀⠻⡀⠀⠀⠀⠀⢎⣼⡗⣁⣀⣀⣈⣢⣾⢾⡄⠀⠀⠀⠀⠀⠀⠀⣄⡄⠀⠀⠀⡀⠀⢺⠁ ⠀⠀⠀⡇⡇⢸⢀⠀⠘⣆⠀⠀⠀⠀⠀⠀⢳⡀⠀⣤⣴⣿⢿⠉⠁⣀⣴⢯⣾⣱⡿⠀⡀⠀⠀⠀⠀⢀⣾⣿⡿⢆⣀⠴⡇⠀⡼⠀ ⠀⣠⠊⡗⣃⡼⣏⣇⠀⠘⣆⠀⠀⠀⠀⠀⠀⢷⣀⣿⣗⢟⠇⣀⣶⡿⡷⣷⣿⣶⠶⡱⠃⠀⣰⠀⠀⣿⠁⠀⠀⠈⣗⣸⡡⠞⠁⠀ ⣴⣹⢌⠏⡟⢺⠋⠘⡆⠀⠘⣆⠀⠀⠀⠀⠀⠈⢧⠀⠻⣿⢶⣻⣟⡯⠞⣛⠍⠲⡚⠲⢲⠚⠁⠝⠒⠚⠒⠀⠀⠀⢸⣣⠀⠀⠀⠀ ⣟⢫⣎⢰⣷⣸⠀⣤⢧⠀⠀⠘⣆⠀⢠⣖⣎⣭⢭⠉⠉⠉⠛⠧⣄⠓⠉⠀⢀⡴⠋⢀⡇⠀⡌⠀⠀⠀⠀⠀⠀⠀⠈⡇⣧⠀⠀⠀ ⠈⠉⠛⡎⠀⢳⠜⠁⠈⢧⢀⣰⠙⣆⠀⢯⣧⠤⠤⠤⠀⠀⠀⠀⠈⠱⡒⠚⠉⠀⠀⢸⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⡏⠁⠀⠀⠀ ⠀⠀⠀⠹⣶⡼⡆⠀⠀⠈⢻⡿⣷⣾⣆⠀⠙⠲⠶⣖⣂⣀⡀⠀⠀⠀⠈⠢⢄⡀⠀⠙⢠⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀⠀ ⠀⠀⠀⠀⠋⠀⢸⠀⠀⠀⠀⠙⢿⣷⡟⡦⠒⠒⢚⠟⠁⠉⠉⠒⣄⠀⠀⠀⠀⠈⠑⠢⢬⣶⣶⣶⢷⣲⣶⢦⣤⣀⠀⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠲⠂⢸⠀⠀⠀⠀⠀⠀⠙⠳⡿⠁⢀⠎⠀⡄⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠉⠻⣟⣛⡛⠛⠚⠧⣿⢻⠟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⡇⠀⠈⠀⣼⡇⠀⠀⠀⢮⠠⡵⣄⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣶⣄⠀⢹⠂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⠀⡇⢰⡀⠀⠀⠸⢀⡇⠈⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣸⣧⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠹⢄⡀⠀⠀⢀⡴⠋⣧⠀⠀⣸⠃⠀⠱⡄⠀⠀⡞⠀⠀⠀⠙⢆⠀⠀⠀⠀⠀⠀⠀⠀⣠⡟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠑⠚⠉⠀⠀⡟⣄⡴⠁⠀⠀⠀⠈⠢⡼⠁⠀⠀⠀⠀⠈⠓⢄⣀⠀⠀⣀⣠⠜⠹⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀