⠀⣁⠀⠁⢀⢀⠀⠉⠀⠈⠁⠀⠀⠀⠉⠁⢁⣀⠈⠁⠀⢉⡀⠉⠀⢀⣠⡀⠁⠀⠁⢀⣨⡈⠁⣀⡀⣀⡀⡀⢀⢀⢀⠀⣀⣀⣀⣀⠉⠁⠈⠀⠀⠁⠈⠉⠀⠈⠀⠀⠀⠀⠀⠉⠉⡀⡀⠀⠀⠀⠀⠁⠀⠉⡀⠀⠀⠀⠀⠀⠉⠈⢁⣄⠀⣀⣉⠉⠉⠁⠀⠈⠀⠈⠀⠈⠁⠀⠉⠀⠀⠀⣀⣀⠈⠁⠈⢀⡀⡀⠀⠀⢁⡀⠀⠀⠈ ⠀⣿⣧⣤⣼⣿⢠⣶⠟⣶⣼⣶⡄⣼⡟⠀⢸⣿⣤⡿⠋⣿⣇⣵⡾⠷⣿⣧⣴⡟⠗⢸⣿⠃⠀⣿⡇⣼⢿⡇⣾⡇⣿⡇⢿⡇⢸⣿⠀⠘⣾⡄⣰⡟⣶⡾⠻⣦⣸⣾⠀⢸⣶⠀⠀⣿⡷⢿⣦⣀⣶⠟⣷⣄⣿⡇⣿⡶⠿⣶⡄⠀⢸⣿⣾⣟⠀⣠⡾⠿⣶⣘⣷⡀⣿⡆⣸⡗⠿⣛⣷⣄⣸⡏⣴⣾⠳⢆⣿⣇⣾⠞⢹⣿⠀⠀⠀ ⠀⣿⡇⠀⢸⣿⠸⣿⣛⣛⡃⠹⣧⡿⠀⠀⢸⣿⠻⣷⣀⣿⡏⢿⣇⣠⣿⡇⣙⣻⣷⢠⣭⡄⠀⠸⣿⡿⠘⣷⣿⠀⣿⡇⢼⡇⢸⣿⠀⠀⠸⣷⣿⠁⢿⣇⣠⣿⠛⣿⣄⣼⣿⠀⠀⣿⡇⢸⣿⠸⣿⣛⣛⡃⣿⡇⣿⣇⣀⣿⠇⠀⢸⣿⠙⢿⣄⢻⣇⣀⣿⠇⢻⣿⠏⣷⣿⠁⣾⣋⣽⡇⢹⡏⢈⣛⣿⡾⣿⡟⣷⣄⢸⣿⠀⠀⢸ ⠀⠉⠁⠀⠈⠉⠀⠈⠉⠉⠀⣤⡿⠃⠀⠀⠈⠉⠀⠉⠉⠉⠁⠈⠉⠉⠉⠁⠉⠉⠁⠈⠉⠁⠀⠀⠉⠁⠀⠉⠁⠀⠉⠁⠈⠁⠈⠉⠀⠀⣤⣿⠃⠀⠈⠉⠉⠁⠀⠉⠉⠉⠉⠀⠀⠉⠁⠈⠉⠀⠈⠉⠉⠁⠉⠁⣿⡏⠉⠉⠀⠀⠈⠉⠀⠈⠉⠁⠉⠉⠁⠀⠈⠉⠀⠉⠁⠀⠉⠉⠉⠁⠈⠁⠈⠉⠉⠀⠉⠁⠈⠉⠈⠉⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡤⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⡗⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠺⣛⣿⣦⢼⣷⠿⣷⡄⠺⣛⣿⣦⢸⣿⢹⣷⢀⣿⠻⠿⣿⡿⣰⡾⣻⣶⡀⠘⢿⡿⠓⣿⡷⢻⣷⢠⣶⢻⣷⡆⠀⢸⣷⠞⢿⣦⣾⣷⠿⣰⡾⠛⣷⡤⣿⡷⠻⣷⣤⣿⣇⣶⢟⢻⣦⣿⡷⢻⣷⠾⣿⡦⠙⣋⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⣿⣏⣽⡇⢸⣿⠀⣿⡇⣿⣏⣽⡇⢸⣿⠀⢿⣾⡏⢠⣾⣋⣠⢻⣯⣛⣻⠁⠀⢸⣷⡀⣿⡇⢰⣿⠙⣿⣟⣙⡏⠀⢸⣿⣀⣸⡿⢹⣿⠀⢻⣧⣀⣿⠟⣿⣧⣠⣿⠓⣿⡟⢿⣟⣋⡛⢹⡇⠈⣿⠀⢾⡇⠀⣽⣥⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠈⠉⠈⠁⠈⠉⠀⠉⠁⠈⠉⠈⠁⠈⠉⢠⣼⠟⠀⠈⠉⠉⠉⠀⠉⠉⠉⠀⠀⠀⠉⠁⠉⠁⠈⠉⠀⠈⠉⠉⠁⠀⢸⣿⠉⠉⠀⠈⠉⠀⠀⠉⠉⠁⠀⠉⠈⠉⠁⠀⠉⠁⠀⠉⠉⠁⠈⠁⠀⠉⠀⠉⠁⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠋⠉⠉⠉⠉⠉⠛⠳⢦⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠛⠋⠉⠈⠐⠻⣟⣛⣽⣿⣻⠟⣉⣤⣐⡲⣶⣭⣵⣐⡦⠀⠐⠀⠺⣟⠲⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠐⠺⠿⠷⣶⣶⣶⣶⣶⣶⣛⣻⣛⣛⣽⣙⣿⣿⣷⣶⣶⣶⣶⣿⠿⠿⠿⠟⠛⠗⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣽⡍⣻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⢀⠂⠀⠛⢙⣛⡿⠿⠟⠛⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠡⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡿⢵⣦⣽⡷⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣧⡳⠇⠀⠨⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⢽⣞⣻⣢⠠⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡴⡻⣟⡽⠿⠂⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣛⣭⠷⡟⠛⢸⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡘⠿⠛⠈⠀⠀⣼⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡨⠙⠛⠉⠀⠀⣸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⡤⣤⣖⡃⠠⠤⠤⠤⠰⡿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⡿⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣀⣤⠤⠖⡚⠓⠒⢒⣒⣒⠤⢿⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠘⣟⠉⠉⠉⠉⠉⠉⠈⠈⢹⡆⢳⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣿⣿⣷⣄⠀⠀⠀⠀⠀⢻⡉⠉⠉⠉⠉⠉⠉⠉⠉⡏⠸⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠸⡅⠀⠀⠀⠀⠀⠀⠀⠀⡇⣤⢻⣿⣿⠀⠀⠀⠀⠀⠀⢀⣾⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣦⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⢸⢱⣝⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⣹⣀⡀⠀⠀⠀⠀⠀⠀⣇⣿⣿⣿⣿⠀⠀⠀⠀⠀⢠⣿⣿⣿⡟⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⡀⢽⣿⣿⣿⣧⠀⠀⠀⠀⢨⣆⣀⣀⣀⠀⠀⠀⠀⢸⢸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⠿⠛⠁⠀⠀⠀⠀⢯⢹⣿⣿⡟⠀⠀⠀⠀⢀⣿⣿⣿⡟⠀⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠈⢀⡀⠤⢸⠸⣿⣿⣿⡄⠀⠀⠀⠈⠿⡟⠛⠉⠀⠀⠀⠀⢸⡈⢿⢿⢿⠁⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⣀⡀⠀⠀⡀⠀⢸⠀⠀⠁⡣⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠄⡁⠌⡐⣀⢦⡟⠀⠸⣿⣿⣷⠀⠀⠀⠀⠀⢹⠦⢀⣀⡀⠀⠀⣀⡇⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠉⠉⠙⠒⠚⠃⠀⠀⡇⠀⠀⠀⠀⢸⣿⣿⠁⠀⠀⠀⢳⡀⠀⠀⠀⡒⠀⠀⠀⠄⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⡀⢂⠥⢒⡨⣡⠵⣸⠞⠀⠀⠀⠹⣿⣿⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠉⠉⠉⠃⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠃⠀⠀⠀⠀⢸⡿⠃⠀⠀⠀⠀⠀⠙⢄⣇⠰⡌⠴⠌⠥⡐⡀⠢⠤⣀⠀⡀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢀⠀⡀⠀⠀⡀⢠⠤⣀⣂⠖⣌⡲⣍⡶⣬⢯⣞⣭⢷⣭⠟⠋⠀⠀⠀⠀⠀⠙⢿⠆⠀⠀⠀⠀⠸⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⠀⠀⠀⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⣞⣻⣻⣶⣧⣽⣍⣳⣦⡳⣴⣙⡖⣦⢢⡤⣄⡖⣤⢢⣒⣆⢦⣌⣦⣲⣔⣮⣼⣾⣵⣾⣽⣾⣿⣾⣷⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠀⠀⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣶⣾⣗⣀⠀⠀⠀⣀⣄⣴⣃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣠⣬⣽⣿⣿⣿⣿⣿⣿⣿⣿⣍⣉⠉⠉⠉⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠉⠉⢉⣭⣿⣿⣿⣿⣿⣿⣿⣿⣭⣤⣤⣤⣤⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⢀⣴⣾⣿⣧⡶⣄⣀⢀⣀⢤⣶⣯⣀⡀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠚⠋⠉⠈⠉⠉⠉⠁⢿⣿⢿⣿⡳⠤⠀⠀⠒⠒⠛⠛⠛⠛⠛⠛⠿⠿⠿⠿⠿⠟⠛⠛⠛⠛⠉⠙⠛⠻⠟⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠛⠋⠉⠉⠉⠛⠛⠛⠛⠛⠛⠛⠛⠏⠉⠉⠉⠉⠉⠛⠂⠀⠀⠀⠀⠊⠉⠁⠀⠀⠀⠀⠀⠸⣿⡻⢿⣟⡓⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠉⠛⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠀⠈⠁⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⣀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠁⠀⠁⠀⢀⠁⢂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠈⠀⠀⠀⢀⡀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⢲⣖⢶⡔⣲⣴⡆⣶⢴⡶⠀⢰⡶⣶⣷⣤⡖⣦⣴⣶⣶⣷⢴⡶⣦⢶⣴⣖⣲⠺⢴⣲⡆⢀⡖⠶⡶⢦⣖⡦⡴⢺⡇⣷⣾⡗⠀⣰⡶⢴⣷⡴⣶⢦⡖⣿⠀⠰⡶⣶⢴⡦⣶⢰⡶⣶⣷⢤⡗⢶⣤⣖⣦⣶⠖⠀⠀⠀⠀⢸ ⠀⠀⠠⠄⠤⠀⠤⠀⠠⠄⠀⠀⠤⠁⠄⠀⠢⠤⠀⠄⠤⠁⠄⠀⠤⠄⠄⠠⠀⠤⠠⠄⠀⠀⠀⠀⠀⣀⡟⠀⠙⠚⠈⠓⠛⠚⠓⠀⠘⠓⠛⠘⠊⠓⠋⠘⠓⠓⠙⠘⠓⠛⠘⢣⣸⠁⠀⠙⠚⠁⠈⠛⠒⠛⠈⠓⠃⠙⠛⠓⠛⠘⠓⠀⠘⠓⠙⠚⠓⠛⠈⠛⠛⠀⠘⠓⠛⠊⠓⠛⠚⠓⠛⠘⠒⠓⠋⠈⠓⠒⠛⠂⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⣀⡀⢀⣀⠀⢀⣀⢀⣀⠀⡀⣀⠀⢀⡀⡏⢀⣀⣠⠀⣀⣀⢀⣀⠀⣿⢀⠀⣿⠀⣀⡀⣀⣀⢠⡀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⢿⡅⣾⢭⣗⡏⠉⣿⠈⡇⣿⢹⡇⣿⠉⡇⠀⣿⠉⣧⣿⠁⣏⢉⡇⣿⠉⡇⣿⢸⢭⠧⣿⢹⡏⣿⠘⠋⠀⠀⠀⠀⠀⠀⠀⠀⣿⢸⡷⡦⣴⣶⠄⢸⡗⡷⢶⢰⡶⣴⣲⢤⣶⡄⠐⡶⣶⣶⢶⡦⣶⢶⠶⡦⣿⢶⣤⣶⡦⣶⢶⣶⡀⢠⡖⣆⣶⢶⡄⠠⡟⢺⢲⣦⣔⣶⠀⢹⠶⣦⣖⣦⣴⠲⣿⡴⠂⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠲⠋⠙⠒⠂⠛⠷⠻⠾⠓⠟⠘⠇⠛⠞⠇⢀⣯⠺⠃⠛⠀⠙⠾⠃⠛⠾⠃⠛⠘⠒⠆⠛⠘⠃⠚⠸⠏⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠓⠛⠙⠚⠁⠘⠓⠛⠛⠛⠛⠘⠛⠈⠓⠃⠐⠛⠛⠊⠛⠓⠛⠚⠛⠃⠛⠊⠈⠓⠛⠛⠘⠚⠁⠈⠓⠋⠛⠛⠃⠀⠛⠚⠚⠋⠙⠚⠀⠙⠚⠁⠛⠓⠙⠒⠛⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⡀⠀⠀⡀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⢀⣶⡀⣇⣀⠀⡇⣀⣀⢀⣈⡇⠀⣀⣀⡀⣀⣀⢀⣀⡀⣟⣀⡀⣿⢀⣠⡀⣀⣀⣀⣀⠀⡀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⢀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⣀⠀⠀⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⣿⠀⡏⢸⠃⡇⣿⠉⣏⢈⡇⠀⣿⠈⣷⣿⠉⣏⢈⡇⣏⠈⡇⣿⢾⠦⠷⣿⢸⡇⣻⠈⡁⠀⢸⡗⣿⢶⣴⣶⣦⠠⡖⣦⢶⡔⢶⠚⣦⣾⢰⡶⣐⣶⣿⠓⣟⣶⢲⣴⡶⣶⠀⢰⡖⡖⣶⣴⡳⣦⣶⣶⢼⡗⡿⢶⢤⠟⣶⡾⣶⣲⢔⣶⣴⡶⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠙⠓⠃⠘⠃⠃⠛⠀⠙⠛⠃⠀⣿⠛⠁⠛⠀⠙⠛⠁⠛⠛⠁⠛⠈⠛⠃⠛⠘⠃⠛⠈⠃⠀⠈⠃⠙⠘⠊⠛⠋⠀⠙⠃⠋⠙⣻⠟⠁⠛⠘⠃⠙⠙⠈⠃⠛⠘⠚⠙⠓⠙⠀⠘⠓⠓⠙⠈⠛⠑⠙⠙⠈⠃⠙⠘⠺⢠⡼⠃⠉⠛⠘⠉⠛⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⣠⣤⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⣀⡀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⠀⠀⠀⠀⢀⣤⡄⠀⠀⢀⣠⡀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⣿⣟⣠⣤⡀⠀⣠⣤⣄⡀⢸⣿⠠⣤⣠⣤⣄⡀⠀⠀⣿⡇⣴⡿⠋⠀⣠⣤⣤⡀⢤⣤⠀⣤⡄⢀⣤⢤⣤⣤⣄⣀⢸⣿⢀⣠⣤⣤⢰⣿⣇⣠⣤⢬⣽⡍⠀⢠⣿⣯⡤⢀⣠⣤⣄⡀⠀⠀⢀⣤⣤⣠⡤⠀⣠⣤⣄⡀⣼⣿⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⣿⣿⠉⣿⡗⢿⣿⣴⣽⡿⢿⣿⠀⣿⡏⠈⣿⣷⠀⠀⣿⡿⢻⣷⡀⣾⣿⠀⢹⣿⠼⣿⣴⡿⣷⣼⡟⢠⣵⠶⣿⡇⢽⣿⠘⠿⣷⣬⣰⣿⣿⣿⡁⠀⣿⡇⠀⠈⣿⡇⠈⣿⡏⠀⢻⣿⢠⠠⣿⡏⠀⣿⡷⣿⣿⢶⣽⣿⢼⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠿⠿⠀⠿⠷⠈⠻⠶⠶⠆⠸⠿⠀⣿⡷⠶⠟⠃⠀⠀⠿⠇⠀⠻⠷⠌⠻⠶⠾⠋⠀⠹⠿⠁⠹⠿⠁⠘⠿⠶⠻⠇⠸⠿⠈⠶⠾⠟⠈⠿⠇⠹⠿⠴⠿⠇⠀⠀⠹⠿⠖⠙⠿⠶⠟⠃⠀⠀⠙⠿⠖⣿⡇⠈⠻⠶⠶⠇⠘⠿⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⢠⣤⣤⣄⢠⣤⠀⣠⣤⠀⣤⡄⣠⣤⣤⣀⢀⣤⣤⡤⠀⣠⣤⣤⣀⢠⣤⣠⣤⣄⣠⣤⣄⡀⣠⣤⣤⡀⠀⠀⣼⣿⣭⢀⣤⣤⣤⡀⢠⣤⣠⣤⣼⣿⣤⣤⣤⣤⣤⣄⡠⣭⣵⣼⣿⣤⢀⣠⣤⣤⡀⠀⠀⣠⣤⣤⢠⣤⠀⣠⣄⠀⣤⡤⣤⣤⣤⡀⠀⣠⣤⣄⣤⢄⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⣤⡶⠿⣿⠋⢿⣇⣿⣿⣸⡿⢸⣿⠶⠾⢿⠛⠿⣶⣤⣾⣿⠀⢸⣿⠹⣿⡇⢸⣿⠁⢹⣿⢿⣿⠶⠾⠿⠆⠀⢸⣿⠀⣿⡏⠀⢹⣿⢻⣿⠋⠁⢾⣿⠀⢸⣿⠁⢹⣿⠀⣿⡇⢸⣿⠀⣾⡿⠶⠿⠿⠀⠘⠻⢷⣦⡀⢿⣇⣿⣿⣰⡿⢠⣴⠶⢿⣿⢿⣿⠁⢸⣿⠐⠻⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠻⠷⠞⠿⠂⠘⠿⠇⠘⠿⠃⠀⠛⠷⠶⠟⠸⠶⠾⠋⠈⠻⠷⠿⠋⠀⠿⠇⠸⠿⠀⠸⠿⠀⠛⠿⠶⠟⠀⠀⠸⠿⠀⠘⠻⠶⠟⠃⠸⠿⠀⠀⠘⠿⠿⠸⠿⠀⠸⠿⠀⠿⠇⠘⠿⠿⠈⠻⠷⠾⠃⠀⠐⠷⠶⠟⠁⠘⠿⠃⠸⠿⠃⠘⠻⠶⠻⠿⠈⡛⠻⢻⣿⠀⠻⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸