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

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