⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣢⡴⡤⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⢫⡜⣯⢿⡾⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠔⣒⡄⠀⠀⠀⡼⣞⠛⠎⠉⡹⠚⡿⡽⡇⠄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠂⠀⡀⢒⣢⣴⣦⣜⡼⣭⢿⡄⠀⠀⢿⣎⣄⣄⠀⢠⣴⢴⡳⣇⣄⣐⠀⠀⠀⠀⠀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠔⣐⣢⢢⡜⠉⠈⠚⢷⣾⣷⣽⣯⡞⠀⠀⠸⡪⡚⠁⡀⡈⠛⣅⣾⢽⡎⠁⠀⢀⢜⣩⣾⣝⣿⣿⣿⣆⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣾⣻⣵⣿⠃⡀⠠⢊⣼⣿⣿⢺⣿⡇⡇⠢⠀⠀⠗⢀⡄⠠⠪⠘⣽⡿⣸⡤⣤⣲⣞⣿⡿⣿⣿⣿⣿⣿⣿⣾⣦⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣳⣾⣿⣠⣤⠀⠉⠁⢸⣿⣿⣟⡧⠁⠀⡄⠫⠐⠢⠀⠘⡎⠊⢿⢞⡑⠁⣿⣿⡟⠿⠿⠿⠻⣿⣿⣿⣿⣿⣿⡅⠑⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣾⣟⡿⣿⡗⣅⠀⠀⢀⢼⣿⢿⣟⡇⠀⢠⠠⠠⠁⠉⠡⠹⣰⣦⡿⣯⡇⠀⢛⣿⢻⣇⠀⠘⣿⣿⣿⡟⢿⠿⠛⠂⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⠌⣿⣯⢿⣖⣿⣱⣏⠅⡠⠉⣟⡎⠁⠊⡆⡈⠀⠁⠀⠂⠀⣧⣿⣞⡾⠗⢸⠀⢿⣏⢡⡁⠄⠄⡠⡸⢿⣶⣂⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠰⠶⢁⣴⣾⢿⣿⣿⣿⣽⣿⣷⣤⣤⣿⣠⣴⣾⡷⡇⣥⣴⠀⢀⣤⣽⣎⣯⣿⢦⡅⢦⡾⢏⣌⠈⣾⡏⢠⠎⣽⠇⣅⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⡀⠀⠘⠿⣿⣿⣿⣥⣤⠹⠋⢩⢿⣿⣿⣇⡁⡀⠸⡄⠸⣻⣽⣿⣿⣭⢸⠀⠈⣠⠎⣿⠿⠟⠶⠶⠾⠏⣤⣻⠆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣵⡒⠀⢀⣄⠙⠣⡐⠠⠀⠤⠀⢸⣿⣿⣿⡁⠇⠀⣡⡀⢳⠧⡿⡟⠁⢸⠀⠀⠣⠀⠜⢤⣠⣤⣄⢄⠀⠈⢥⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣶⣃⢀⢿⣮⢷⠀⠈⢄⡁⡠⣇⣠⠊⠉⣿⣬⣱⠀⠈⣟⡟⣷⣽⠁⠀⣤⠀⡔⠀⠀⢀⣓⣵⡵⡰⠂⠀⡨⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⢢⠄⠀⢄⣪⡾⣷⣻⢸⢯⡞⣧⢻⣷⡀⠩⠀⠀⡸⡄⠀⢹⢺⣷⠱⣠⣿⣞⢧⣿⠐⣴⢔⢇⠐⡀⠀⢜⠀⠀⠁⠀⠀⠠⠁⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠁⠩⠾⣿⡽⠷⢿⣯⢷⣻⣭⢟⣳⡽⣟⣷⡲⣖⣿⣖⠞⠦⢿⣊⡁⠈⡻⠟⠁⠀⣸⣧⡸⠀⠠⠒⠃⢃⠁⠀⠀⠀⠸⠀⠀⠰⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢢⢀⣠⢫⣿⣷⣳⡞⣯⢟⣷⣫⢷⣹⣛⣗⠁⠰⠔⠀⠈⠱⡔⣨⣎⣀⣾⢽⡷⣳⢢⠆⢠⠀⠌⢀⠁⠀⠄⠊⡀⠀⠰⠘⠀⠀⠀⣀⠀⢀⠀ ⠀⠀⠀⠀⢤⣤⡮⣽⣽⣣⡧⢼⣽⢫⣞⡷⣿⣟⡯⣟⢮⡽⢶⣤⣤⣄⡀⢸⠍⠧⡓⡌⢳⣿⢟⠐⠚⠓⠒⠶⢤⣄⡁⠂⠀⠡⠀⠀⠑⡩⢁⣇⠠⣅⠂⢁ ⠀⠀⠀⠀⠀⠈⡩⠉⠉⢈⠜⣶⣯⡟⣾⣹⢿⣿⡵⣯⡿⠜⠷⠷⠾⠙⠋⠉⠁⠀⠈⠁⠉⢠⠁⠀⠀⠀⠀⠀⠀⠀⠙⣦⣪⠠⡴⢂⣮⢕⢛⣙⣩⠂⠀⡸ ⠀⠀⠀⠀⠀⠀⠉⠀⠀⢰⢱⠘⠳⣻⣽⠙⣯⠗⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠤⢀⣀⢰⠀⠀⠀⢀⠔⡩⠒⠉⠀⠉⠀⠀⠀⠀⠈⠉⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡜⡸⣴⠟⠛⠳⢭⣱⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠂⠠⠐⠃⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡡⣁⠀⠀⠈⢏⡹⠀⠀⠀⠀⠀⠀⠘⠞⠀⠘⠞⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀