Dog Dot Art

⠀⠀⠀⠀⠀⢀⣀⣤⣄⠀⢀⣀⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣴⣾⣿⣿⡿⠟⠋⠁⠀⠀⠀⠈⠉⠳⢦⡀⠀⠀⠀⠀⠀⠀ ⠀⢰⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣷⣄⠀⠀⠀ ⠀⠀⢿⣿⣿⠇⠀⠀⢼⣏⡥⠀⠀⠀⠀⢀⣀⡀⠀⠘⣿⣿⣷⡄⠀ ⠀⠀⢸⣿⠏⠀⠀⠀⠀⠉⢀⣤⣄⣀⠀⢺⣼⡗⠀⠀⣿⣿⣿⣿⡄ ⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⢹⣽⣿⣟⠇⠀⠀⠀⠀⠀⣿⣿⣿⡿⠃ ⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣀⣽⡏⠁⠀⠀⡰⠀⠀⠀⣿⣿⠏⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠸⣿⡏⠉⠀⠻⣶⣤⡶⠁⠀⠀⠀⠈⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢻⣇⠀⠀⣠⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢷⡾⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣤⡄⣿⡇⣴⡦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢙⣣⣴⣦⠛⣥⡄⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⣿⡆⠋⠁⠀⠀⠀⠀⣴⡆⢿⠇⣴⡶⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠛⠁⠀⠀⠀⠀⠀⠀⢉⣥⣶⣶⠉⣵⡆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⢿⣿⣿⣇⠉⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠤⠴⠤⠤⠤⠴⠠⠤⠤⠀⠖⠶⠖⠶⠐⠖⠤⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣶⣾⣿⣿⣿⣿⣷⣶⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣿⣿⣿⣶⣿⣿⣯⠉⠀⠀⠀⠉⠉⠉⠉⠙⠻⠿⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠛⠉⠉⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⢿⣿⣦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⡀⠀⠀⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠿⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧⣀⣴⣿⠇⠀⠀⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⣘⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣼⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⡿⠁⠀⠀⠀⠀⣠⣾⣿⣿⡀⠀⠀⠀⠀⠘⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⡇⠀⠀⠀⠀⠘⠻⢿⣿⠿⣷⣿⡆⠀⠀⠀⠀⠙⠻⣦⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠀⠀⠀⠀⠀⠀⠴⠾⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠀⠙⠻⢿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣿⡿⣿⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⣿⣷⣶⣤⣀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣿⡟⠀⠈⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡏⠉⠉⠛⣿⣆ ⠀⠀⠀⠀⠀⠀⣼⣿⣧⡀⠀⠀⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⣠⣶⣼⣿ ⠀⠀⠀⠀⠀⢰⣿⣿⣿⣷⡄⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠻⣿⣿⣿⣿⠇ ⠀⠀⠀⠀⠀⣾⣿⡏⠘⣿⣿⡄⠀⠀⠀⠀⠙⢷⣤⡀⠀⠀⠀⠀⠀⠀⢰⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣶⣶⣶⣶⣦⣄⣀⣨⣿⡿⠁⠀ ⠀⠀⠀⠀⣸⣿⣿⠁⠀⠘⣿⣿⡄⠀⠀⠀⠀⠀⠉⠻⣶⣤⣀⣀⣀⣴⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⣀⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣻⣿⡿⠁⠀⠀ ⠀⠀⠀⢠⣿⣿⡏⠀⠀⠀⠈⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠉⠛⠻⠿⠿⢿⣦⡀⠀⠀⠀⢀⣠⣴⣾⣿⣿⣿⣿⣛⣋⣉⠀⠀⠀⠀⣀⣴⣶⣿⣿⣿⣿⡿⠟⠁⠀⠀⠀ ⠀⠀⠀⣾⣿⡿⠀⠀⠀⠀⠀⠈⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣿⣶⣤⣀⠈⠉⠉⠐⡿⠟⠉⣉⣙⣛⣛⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⣸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠻⠿⠿⣶⠶⠾⢿⣿⣿⠛⠛⠛⠛⠛⠿⠿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣾⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣸⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣿⣿⣶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⣧⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⢿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣤⣄⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠶⠋⠉⠙⢿⣿⣿⣿⣄⠈⢻⣶⠤⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠏⠀⠀⠀⠀⠈⣿⠋⠉⠙⢧⡀⢿⡄⢸⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣾⣿⣷⣄⠀⠀⠀⠀⠀⠀⣴⣶⣶⡄⢸⡇⢸⡟⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡏⣉⢻⣿⠟⠋⠀⠀⠀⠀⠀⠀⠿⠒⠻⣧⢸⡇⣿⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡇⢻⡀⠻⡄⠀⣶⣿⣷⠀⠀⠀⣀⡀⠀⠈⠻⣧⢻⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣷⠸⣷⣄⣹⣆⣿⠋⠁⠀⠠⣿⣿⣟⠀⠀⢀⡿⠿⠿⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢿⣄⠀⠈⠉⠛⢷⢰⠆⠀⠀⠀⠛⣿⠗⣺⣿⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠛⢻⣶⣄⣸⠦⠤⠤⠤⠾⠥⠚⠹⣿⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻⣿⠋⠛⠀⠀⠀⠀⠀⠀⠀⠀⢈⣿⡄⠀⠀⠀⠀ ⠀⣠⢖⣢⠀⢀⠀⠀⢀⣴⣿⠁⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣧⠀⠀⠀⠀ ⣾⣿⠋⣠⣾⠛⠀⣴⡿⠛⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀ ⠈⠁⣰⡿⠁⢀⣾⠟⠁⠀⢻⣷⡄⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⡘⢿⡆⠀⠀⠀ ⠀⠀⣿⡇⠀⣼⠃⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠘⣿⠇⠀⠀⠀⠀⣠⣧⠈⢷⠀⠀⠀ ⠀⠀⣿⣇⢰⣿⠀⠀⠀⠀⠀⣿⣿⣿⡄⠀⠀⠀⡟⠀⠀⠀⣠⣴⣿⠃⠀⠘⡆⠀⠀ ⠀⠀⢹⣿⣾⣧⠀⠀⠀⠀⣸⣿⣿⣿⡇⠀⠀⠀⢹⣦⣴⣾⣿⢿⡿⠀⠀⠀⣧⠀⠀ ⠀⠀⠈⢻⣿⣿⣄⣼⣿⣶⣿⣿⣿⣿⣷⠀⠀⢀⣸⣿⡿⠟⠁⢸⠇⠀⢤⡾⠿⣦⡀ ⠀⠀⠀⠀⠙⢿⡟⠉⠉⠉⠁⠈⠻⡏⠀⠰⠶⠛⠋⢹⡄⠀⠀⠸⡄⢀⠀⢸⡔⣆⢳ ⠀⠀⠀⠀⠀⠀⠹⠤⠼⠤⠼⠷⠞⢷⣀⡀⠀⢰⠀⣦⣷⠀⠀⠀⠉⠙⠒⠚⠳⠞⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠉⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⣶⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⣿⡇⠀⠀⢀⣀⣀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠀⠀ ⠀⠀⠀⢀⣾⠏⠈⠙⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⠁⢿⣧⣶⠿⠛⠛⢩⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⠿⠛⢻⣇⠀ ⠀⠀⠀⣾⠋⠀⠀⠀⠀⠈⢿⣧⡀⠀⠀⠀⠀⠀⢀⣀⣠⣤⣿⠇⠀⠀⠀⠀⠀⠀⣴⣿⣃⣀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠟⠋⠀⠀⠀⠈⣿⡄ ⠀⠀⣸⡏⠀⠀⠀⠀⠀⠀⠀⠙⣷⣀⣠⣴⠾⠿⠛⠛⠉⣹⡟⠀⠀⠀⠀⠀⠀⠀⢉⣻⣿⠛⠻⠿⢶⣤⣄⣠⣾⠟⠃⠀⠀⠀⠀⠀⠀⢿⡇ ⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠻⠟⠋⠁⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⣴⣶⡶⠿⠟⠛⠋⠀⠀⠀⠀⠈⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧ ⠀⢀⣿⠀⠀⠀⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿ ⠀⢸⣿⠀⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠀⠀⠀⠀⣿ ⠀⢸⡇⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⢀⣴⣿⠿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣶⣶⣄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿ ⠀⣿⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠸⣟⢁⣴⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠋⣠⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿ ⠀⣿⠀⠀⠀⠀⣾⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣶⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿ ⢸⣿⠀⠀⠀⠀⣿⠃⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿ ⢸⡏⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⣿ ⢸⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢀⣿ ⣾⡇⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⢸⣿ ⠹⣿⣤⣀⣀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⣼⡇ ⠀⠈⠉⠙⠛⠛⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣤⣴⡾⠟⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡟⠟⣿⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⢿⣷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⡿⠿⠛⠁⠀⠙⢿⣿⣷⣶⣶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⡏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣾⠟⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠻⣷⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣴⡾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠙⠻⠷⢶⣶⣤⣄⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣴⣶⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠻⡛⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠓⠛⠓⠚⠛⠛⠛⠿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⡿⠋⣁⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠈⠙⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⢀⣾⣿⣭⣦⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠼⠿⠽⠿⠦⢸⣿⣿ ⠻⢛⠛⣻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿ ⣬⠟⣻⠿⣧⡇⠐⡄⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹ ⣵⣾⣧⣴⣿⠃⠀⢘⡄⠀⠀⢀⣴⣿⠩⠩⠛⠫⠉⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⢸ ⣿⣿⣿⣿⣿⣦⡰⠁⠀⢀⢤⣿⣿⣿⣷⣶⣿⣶⣶⣿⣿⣿⣆⢀⠀⠀⠀⣀⢀⣼ ⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⢸⡿⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⢹⣿⣿ ⢠⠟⣿⣿⣿⣿⣧⡀⠀⠀⠀⠹⣷⣶⣾⣿⣿⣿⣿⣯⣵⡾⠉⠀⠀⣀⣠⣿⣽⣿ ⡏⠀⣿⣿⣿⣿⣿⣿⡿⣦⣄⠀⣙⢿⢿⣿⣿⣿⣿⣿⠛⠀⢀⣤⠊⠹⣿⣿⣿⣿ ⠇⢀⣾⠋⠁⠀⠉⡸⠀⠁⢹⣷⣿⢠⣾⠟⣿⠋⣭⠀⢦⣀⠈⠉⠁⠀⠸⣿⣿⣿ ⡥⠞⠁⠀⠀⢀⠔⠀⠀⠀⠠⢿⣿⣿⣿⣿⣿⣽⣾⣷⣿⡿⠀⠀⠀⠀⠀⢻⠛⠙ ⠀⠀⠀⠀⠠⠂⠀⣰⠀⠀⠀⠀⢙⠻⣿⣿⣿⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠈⠀⠀ ⠀⠀⠀⢰⠁⠀⣰⣻⡄⠀⠀⠀⠀⠙⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⠊⢀⣼⣷⣿⡷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⠔⠁⢀⣽⠟⠉⠁⠀⠘⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡔⠀⠀⠀⠀⠀ ⠁⣀⣴⠏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣿⣿⠧⠀⢀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣄⢀⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡿⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⣀⣤⠖⠛⠉⠉⠉⠉⠉⠙⠒⠦⣿⣏⣀⠀⠀⠀⠀ ⠀⠀⣠⠞⠁⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢵⡄⠀⠀ ⠀⢰⣯⠀⠀⢀⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⣿⠀⠀ ⠀⠈⣇⢀⢠⠇⠀⣶⡶⠄⠀⠀⠀⢠⣶⡶⠀⠀⣸⣀⣼⠟⠀⠀ ⠀⠀⠙⠛⠾⡆⠀⠙⠛⠃⠀⠀⠀⠀⠙⠋⠀⠀⣹⠟⠁⠀⠀⠀ ⢀⡴⠚⠉⠛⢿⠀⠀⠀⠀⢿⣿⠆⠀⠀⠀⠀⢀⣿⠋⠉⠉⢳⡄ ⢾⡀⡄⠀⣄⡼⠻⢧⠤⣤⠤⠤⣤⣠⣦⣾⠶⠞⢿⣤⡄⣠⣀⡷ ⠈⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⡄⠀⠀⠀⠀⠀⣠⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⢱⠀⠀⢀⡴⠋⢸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠋⠀⠀⣸⡠⠔⠝⠀⠀⣸⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⡀⠴⠊⣁⠀⣀⠤⠒⠉⠀⡌⠀⠀⢀⠸⠀⠀⠀⠀⠀ ⢰⠒⠒⠒⠂⢀⡰⠕⡀⠀⠀⡀⠀⠀⠈⠁⡀⠀⠀⢠⢃⠀⠀⡘⡇⠀⠀⠀⠀⠀ ⢞⡒⠓⠈⠀⠀⣀⠀⠀⠋⠛⠘⠃⠀⠀⠀⠀⠉⠉⠉⠉⢂⢠⡼⠁⠀⠀⠀⠀⠀ ⣾⣺⡖⣶⢤⣄⣀⣀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⡶⢛⠁⠉⠳⣄⠀⠀⢀⠀ ⠏⠈⡞⠈⠉⠓⠻⡛⠟⣦⢀⠳⠀⠀⠀⠀⠀⠀⠀⢿⠏⢀⠀⠀⠀⠘⡦⢔⣏⡄ ⠀⠀⠀⠀⠀⠀⢀⡗⢊⡼⠀⡆⠀⠀⠀⠀⡆⣀⡬⠖⢲⠁⠀⠀⢀⡔⠁⡊⣰⠁ ⠀⠀⡀⠀⠀⢠⠊⣐⠟⠁⠊⠀⠀⠀⠤⢊⠌⠀⠀⠀⡘⠀⢀⡴⠋⢐⢈⠋⡼⠉ ⠀⠀⣧⡧⡴⡗⠟⠁⡀⠤⢄⠀⠀⠠⠠⠁⠀⠀⢀⠌⣀⡴⠉⠀⠢⠌⡠⠾⠶⠥ ⠀⠀⠘⠥⠩⠤⠒⠉⠀⠀⠐⢥⠑⡁⠀⠀⢀⣴⠜⢋⢈⠀⠅⣇⠴⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣯⠉⡐⠈⡥⠉⢻⢐⣪⠴⠊⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡠⠮⠘⢧⣉⣠⡤⢖⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⠴⠒⠉⠉⠉⠈⠉⠉⠑⠲⢤⡀⠀⠀⢀⡀⠀⠀ ⠀⠀⢀⡴⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡞⠉⣉⠳⡄ ⠀⢠⠎⠀⠀⠀⠀⠀⠀⢀⡖⠋⠉⠓⢤⠀⠀⠀⠀⠘⢎⢀⠇⡿ ⢀⣯⠄⠀⠀⠠⣤⡄⠀⢸⠀⠀⠀⠀⠀⢳⡀⠀⠀⠀⠈⣧⠴⠁ ⢸⡷⠀⠀⢀⢔⣮⣵⡲⡌⢇⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⢸⠀⠀ ⢸⡇⣇⣀⣸⢿⣿⣿⣿⠱⠈⠳⢤⣀⣀⡴⠃⠀⠀⠀⠀⢸⠀⠀ ⢸⣿⡏⡏⠉⠪⣿⠿⠵⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀ ⢸⣇⡼⢧⠀⠀⢘⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠀⠀⢀⠇⠀⠀ ⠀⢻⡻⢭⡷⠦⠟⠁⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⢀⡞⠀⠀⠀ ⠀⠀⠙⠢⣤⣀⡀⠀⢠⠀⠀⠀⠀⠀⠀⠈⣲⡄⠀⡯⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⠚⠉⠉⠛⣇⢸⠓⠒⠒⠛⣛⢃⠹⣤⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⢠⠔⠒⠉⣉⠍⠉⠉⠒⠲⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⠖⠁⠀⢀⣿⣖⠒⢤⠀⠀⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀ ⢀⡠⢴⣒⡀⠉⠉⠀⠀⠀⡞⠋⢻⣾⣧⠈⠀⠀⢀⠀⠀⢳⡀⠀⠀⠀⠀⠀ ⢘⣿⣷⠟⠀⠀⠀⠀⠀⠀⠁⠀⠀⠐⠚⠳⣤⣤⣾⡟⢦⣿⠀⠀⠀⠀⠀⠀ ⢸⣏⠀⠀⠀⠀⠀⠀⢄⠀⢱⣄⡀⠀⠀⢀⣿⣿⣟⣴⠀⠈⢢⠀⠀⠀⠀⠀ ⠘⢿⠐⢄⡀⠀⠀⠀⠀⠉⠙⠻⣿⣿⣿⣿⣿⣏⠁⣀⡇⠀⠀⢣⠀⠀⠀⠀ ⠀⠀⠈⠒⠬⣟⣂⣐⡒⠊⣠⣄⣟⣻⣿⣿⣿⣿⡶⠯⢿⠀⠀⣼⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⣹⡟⢷⡀⠋⠙⠉⠉⣽⠇⢳⣀⡟⠀⣴⣿⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⡌⡿⡀⠀⠀⠀⠀⢠⣏⡝⠀⣰⣿⣿⣧⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣸⣿⣿⣧⡇⢃⠀⠀⢀⠤⠼⡟⠀⢠⣿⠉⢰⢹⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣼⣿⣿⡟⠁⠘⠀⠀⣈⡤⡊⠀⡔⢋⣿⠀⢸⠀⢻⠀⠀ ⠀⠀⠀⠀⠀⠀⠚⣿⣿⣿⠇⠀⠀⠀⣠⠾⠑⠀⠀⠀⡞⡇⠀⠀⢃⢊⢆⠀ ⠀⠀⠀⠀⠀⠀⠀⣿⣿⡟⠀⠀⠀⠀⣞⡦⣴⠂⠀⣸⢰⡽⠀⣆⠀⢆⢻⡆ ⠀⠀⠀⠀⠀⠀⢰⣿⠉⠀⠀⠀⠀⠀⢡⣏⠏⠀⠀⠙⢼⠀⡄⣿⡄⢸⢸⠇ ⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠹⡄⡇⡂⠠⡸⣢⢸⣶⣽⣞⣾⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠿⣧⣧⣵⣷⡙⣿⣿⣿⡿⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣠⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣾⠿⠟⠛⠛⠛⠛⠿⣦⣄⠀⠀⢀⣤⣶⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣄⠀⠀⠀⢀⣴⠿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠙⢷⣴⡟⢢⡀⠈⠙⠿⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣀⣴⠟⠛⠻⢿⣦⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⣷⠀⠀⠀⠈⠛⠻⣶⣄⠀⠀ ⠀⠀⣠⣶⠶⠛⠋⠁⠀⢰⡗⠂⠘⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀⠀⠀⠀⠀⠙⣧⠀ ⠀⠀⢸⠁⠀⠀⠀⠀⠀⠸⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⠀⢸⡆⠀⠀⠀⠀⠀⠀⢿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣄⠀⠈⣷⡀⠀⠀⠀⠀⠀⢀⣾⠇ ⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠸⣿⡆⠀⠀⢀⡴⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⣼⢿⡍⠻⣧⠀⣿⣷⡀⠀⠀⠀⢀⡾⠃⠀ ⠀⠀⠀⢿⡄⠀⠀⠀⠀⠀⠀⢿⡇⠀⢠⡟⠻⣆⠙⣆⠀⠀⠀⠀⠀⠀⠀⣿⠀⢹⡄⢹⡇⠸⣿⣿⣄⣀⡴⠋⠀⠀⠀ ⠀⠀⠀⠘⣷⡀⠀⠀⠀⠀⠀⢸⡇⠀⣼⣧⠀⣽⡆⢹⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⠇⢸⡇⠀⢸⡏⠉⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠘⠻⣦⡀⠀⠀⠀⣸⠁⠀⢹⣿⣿⣿⠃⡼⠀⠀⠀⠀⠀⠀⠀⠘⣿⡏⣠⡿⠁⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠻⢦⡀⣠⣿⣧⡀⠈⢿⣿⣧⡴⠃⠀⠀⠀⠀⠀⠀⢀⣀⠀⠉⠉⠈⠳⣏⣠⡤⠤⣤⣀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠋⠀⠉⠻⣷⣄⣉⡉⠀⠀⠀⠀⣴⣾⣿⣿⡿⢿⣿⡆⠀⠀⠀⢸⡏⠀⠀⠀⠙⡇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠊⠑⠚⠻⣿⠁⠀⠀⠀⠀⢿⣿⣿⣀⡀⢀⣼⡇⠀⠀⢀⣾⠀⠀⠀⠀⢀⡏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⠹⣧⡀⠀⠀⠀⠘⠿⠿⠿⣛⡛⠉⢀⣠⣴⣿⠇⠀⠀⠀⠠⠾⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣘⣇⠀⠀⠀⠀⠀⠙⠻⠷⠶⠶⠶⠶⠶⠛⠛⠛⠛⠛⠛⠛⠁⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⡴⠚⠛⠛⢿⣦⡤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣤⣤⡀⠀⠀⠀⠀⠀⡟⠀⠀ ⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⠀⠈⢻⡁⠀⠀⠀⠀⠀⣀⣤⣶⣶⣾⣿⣿⠿⠟⠛⠛⠉⠉⠉⠉⢿⣷⣤⣀⣀⡼⠁⠀⠀ ⢠⠀⠀⠀⠀⢸⡀⠀⠀⠀⠀⠀⠈⣷⣤⣀⣀⣠⣶⣿⠛⠋⠉⡏⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠋⠀⠀⠀⠀ ⡟⣆⠀⠀⠀⢸⣧⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⣿⠟⡏⠀⠀⢰⡇⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣇⠘⣦⡀⠀⠘⣿⣆⠀⠀⠀⠀⠀⢀⣼⣿⡿⠁⢀⡇⠀⠀⢸⣧⠀⠸⢷⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠘⣦⡈⠛⠶⢤⣿⣿⡇⠀⠀⠀⠀⣾⡿⠛⠋⠙⣾⠀⠀⠀⠘⢛⡳⣄⢠⠙⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠛⠶⠦⣤⣤⣤⣤⣤⣀⣀⣀⣷⣤⣀⣾⣧⣸⣧⣀⣀⣶⡀⣧⣹⡾⢷⣾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠛⠛⠛⠋⠉⠈⠉⠛⠉⠙⠉⠉⠛⠛⠉⠛⠋⠙⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠏⣧⠀⠀⠀⠀⠀⠀⠀⢀⣤⢾⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⠀⢸⡇⠀⠀⠀⠀⢀⣠⠟⠁⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⠞⠋⠁⠀⠈⡇⠀⠀⢀⣴⣟⠁⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⠛⠁⠀⠀⠀⠀⢰⣇⣠⠾⠋⡰⠁⠀⠀⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠞⠉⠀⠀⠀⠀⢀⣠⡴⠟⠋⠀⠀⡼⠀⠀⠀⠀⢸⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠴⠖⠚⠛⠒⠒⠦⢄⣀⣤⠞⠋⠁⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⢸⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⡖⠒⠒⠒⠒⠲⠤⢤⡤⠤⣏⡠⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡾⠀⠀⠀⠀⠀⡆⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣇⠀⣀⣀⠀⡄⠀⠀⠐⠊⠉⠉⠓⣤⡀⣀⣤⡴⣤⡀⠀⠀⠀⠀⠀⠀⠢⢤⣀⣀⣀⣼⣧⣶⠇⠀⠀⠰⢡⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢯⣹⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⣀⣀⠈⠉⠈⠛⠓⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⢀⡤⣠⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣏⣳⣄⣀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠐⠒⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⡿⠞⠛⣦⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⡏⡯⣽⡿⢉⣿⣿⢷⣶⣦⣤⣤⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣟⠛⠧⡀⠀⠀⠀⠙⢿⣆⠀⠀⠀⠀⢀⡀⠀ ⣷⠁⠀⢧⡈⠙⠋⠛⠶⢧⣿⣯⣹⣿⠿⣦⠀⠀⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣿⣿⡑⠀⢹⠀⠀⠀⠀⠀⠹⣧⣀⣀⡴⡿⢀⡀ ⠈⠀⠀⠘⠇⠀⠀⠀⠀⠀⠀⠻⡄⠈⣹⠿⡇⠰⡄⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠹⡟⠁⢀⠏⠀⠀⠀⠀⠀⠀⣸⠏⠹⣦⠗⣻⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡷⠞⢁⣤⡇⠀⢸⡄⠀⠀⠀⠀⠀⠀⠘⡄⠀⠠⣤⣽⠶⠗⢰⠁⠀⠀⠀⠀⠀⢀⡼⠋⠀⡜⠁⢠⠃⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠞⢀⣰⣿⠟⠀⣰⠊⠀⠀⠀⠀⠀⠀⢀⡜⢠⠚⠉⠉⠀⠀⠀⣸⠆⠀⠀⠀⢀⣴⠟⠁⣀⠴⡷⠴⠛⡷⠤ ⠀⠀⠀⣀⠀⠀⠀⠀⠀⣠⠋⢀⣸⡻⠋⠀⠈⠀⠀⠀⠀⠀⠀⡠⠖⢉⡴⠃⠀⠀⠀⠀⠀⢠⠏⠀⠀⠀⣠⠞⠁⠀⣞⠁⢰⠃⢀⡾⠃⠀ ⠀⠀⠀⣿⣄⣦⡀⢠⢾⢧⣸⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⢀⠞⠁⠀⠀⠀⠀⠀⢠⠋⠀⢀⣴⠟⠁⠀⢰⠉⡿⠉⢁⣴⣏⣤⡴⠀ ⠀⠀⠀⠸⣿⣇⠻⣏⡻⠖⠋⠀⢀⡠⠖⠊⠛⠦⣄⣀⣀⠀⡸⠀⠊⠀⠀⠀⠀⠀⠀⣴⢁⣠⣴⠿⠋⣀⡀⠀⠘⠒⢁⣴⠞⠉⠋⠉⠉⠙ ⠀⠀⠀⠀⢻⣍⠉⠁⢀⣠⠴⠚⠉⠀⠀⠀⠀⠐⣯⠀⠀⢺⠁⠀⠀⠀⠀⠀⣠⣶⡴⠟⠋⠁⠀⠀⢸⠁⢸⠀⣠⡶⠋⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣦⣸⣦⡀⠀⢀⣠⠾⣿⣷⣤⡀⢰⠉⡷⠀⠈⣉⣵⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⡍⠀⢈⠉⠉⠠⠤⡄⠀⠉⣷⠈⢒⣡⡴⠞⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⡽⠛⣿⡄⠸⠇⠀⠀⠑⠃⣠⣴⣷⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠿⠒⠉⠉⠳⢤⣤⡤⠶⠞⠛⣩⣿⠍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣶⣿⣿⣿⣷⣦⡤⠴⠶⠟⠛⠛⠛⠿⠿⢶⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣴⣾⣿⣿⣿⣿⣿⣿⠿⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣾⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣻⣶⣶⣶⣤⡀⠀⠀⠀⠀⠀ ⠀⠀⠘⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⢀⣠⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣿⣿⣿⣦⡀⠀⠀⠀ ⠀⠀⠀⠹⣿⣿⣿⣿⣿⠃⠀⠀⠀⢠⣿⣿⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⣆⠀⠀ ⠀⠀⠀⠀⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠙⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⢰⡏⠙⣿⡆⠀⠀⠀⢸⣿⣿⣿⣿⣿⣧⡀ ⠀⠀⠀⠀⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣶⣶⣶⣦⣄⡀⠀⠘⢿⣿⡿⠇⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⣷ ⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⢻⣹⣿⣿⣿⡟⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⣿⣿⡟ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⠀⠈⠻⣿⣿⣿⠷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣷⣄⣀⣀⣀⣴⣿⣧⠀⠀⠀⠀⠀⠀⣠⠃⠀⠀⠀⠀⢸⣿⣿⡿⠃⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠿⠟⠋⠈⢿⣷⣤⣀⣀⣠⡶⠃⠀⠀⠀⠀⠀⠀⠻⠟⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⣏⠀⠀⠀⠀⠀⠉⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠀⠀⠀⠀⣼⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⣄⣀⣤⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣤⡀⣾⣿⣿⠀⣤⣤⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢿⣿⡇⠘⠛⠁⢸⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠈⣉⣤⣾⣿⣿⡆⠉⣴⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣾⣿⣿⣿⣿⣿⣿⡀⠻⠟⠃⠀⠀⠀⠀⠀⠀⠀⢀⣤⣄⢰⣿⣿⠇⣠⣴⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠙⠛⠻⢿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⠀⠛⡋⠀⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠙⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢈⣡⣴⣿⣿⣷⠀⢠⣶⣶⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣇⠘⠛⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⠿⢿⣿⣿⣿⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⡀⣀⣀⡀⣀⢀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠘⠛⠞⠛⠻⠟⠛⠛⠟⠻⠛⠐⠛⠛⠛⠃⠀⠘⠾⠳⠆⠊⠙⠚⠐⠈⠋⠀⠓⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⢀⣤⠾⠛⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣿⣿⣿⣧⡀⠀⠀⠻⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣦⣀⣤⡶⠾⠿⠛⠛⠛⠛⢉⠀⠈⠙⢿⡄⠀⠀⠙⣷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⡀⢠⣾⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⢨⠍⠛⠷⣦⡹⣄⠀⠀⠈⢿⣆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⡿⠛⠛⠉⢀⣿⣿⠟⢀⣠⠄⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠈⢻⣞⣷⡀⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠀⠀⠀⣀⢸⣿⠏⢠⣿⠃⠒⠲⢶⣤⡀⠀⠀⠀⣿⢀⣤⣄⠀⠈⣿⡌⠻⣦⡀⠀⠀⠻⣧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⠀⠀⢰⡇⢸⣿⠀⣿⡇⠀⠀⠀⠀⠈⠻⣦⡀⠀⢻⣿⣀⣿⣧⠀⢹⣧⣤⣿⣿⣶⣦⣤⣈⡻⣄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⠁⠀⠀⠀⢸⡇⠸⡇⠀⣿⡄⠀⡴⠿⣷⣄⠀⠘⣷⡀⠀⢻⣿⠿⣣⣴⠿⠿⣿⣿⣿⣿⣿⡏⠛⢿⣦⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⠃⠀⠀⠀⠀⢸⣧⠀⠀⠀⢿⣇⠀⣧⣀⣿⣿⡇⠀⢸⡇⠀⣀⣽⡿⠋⠀⠀⢀⣿⣿⣿⣿⡿⠀⠀⠈⣿⣷⢠ ⠀⠀⠀⠀⠀⠀⠀⠀⣼⠏⠀⠀⠀⠀⠀⠀⢿⡆⠀⠀⠈⢿⣆⠈⠻⠿⠟⠀⠀⣼⣡⡾⠛⣿⣧⣄⣤⣴⣿⣿⣿⣿⡿⠁⠀⠀⢀⣿⡏⣼ ⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀⠘⣷⠀⠀⢀⣴⣿⡷⠶⠶⠦⠤⢠⡿⠋⠀⠀⠻⠿⠿⠟⠛⢿⣿⣿⠟⠀⠀⠀⢀⣾⠟⠀⣿ ⠀⠀⠀⠀⠀⠀⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⠀⠀⠀⠀⠀⠀⠠⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⠀⠀⢀⣴⠟⠁⠀⢀⣿ ⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⡇⠀⠀⣀⣀⣠⣤⣀⡀⠀⠀⠀⢠⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⠀⣸⡿ ⠀⠀⠀⠀⠀⠀⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⣠⠾⠛⢿⣯⡉⠉⠁⠀⠀⠀⠀⠀⠀⠘⠿⠗⠀⠀⠀⣀⠴⣻⡏⠀⠀⠀⠀⢠⣿⠃ ⠀⠀⠀⠀⠀⠀⢸⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⠀⠀⠀⠀⠙⠿⣶⣤⣄⣀⡀⠀⠀⠀⠀⣀⣀⣤⡶⠛⢁⣴⠏⠀⠀⠀⠀⢀⣾⡏⠀ ⠀⠀⠀⠀⠀⠀⠀⢿⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣶⣤⣄⡀⠀⠀⠀⠉⠉⠙⠛⠛⠛⠛⠛⠉⠉⠀⣀⣴⡾⢳⣇⠀⠀⠀⢀⣾⡟⠀⠀ ⠀⣠⡀⠀⠀⠀⠀⠈⢿⣷⡀⠀⠀⠀⠀⠀⢀⣿⡇⠀⠉⠛⠻⠿⢶⣶⣤⣤⣤⣤⣤⣤⣤⣤⣤⣶⣿⣟⠁⠀⠈⣿⣆⣀⣠⣾⠟⠀⠀⠀ ⢰⣿⣇⠀⠀⠀⠀⠀⠈⢿⣷⣄⠀⠀⠀⠀⢸⣿⠃⠀⠀⠀⠀⠀⠀⣾⣿⣍⠉⠉⠉⠉⠉⠉⠉⣿⣼⣿⠀⠀⠀⠈⠻⠿⠟⠁⠀⠀⠀⠀ ⣿⠁⢿⠀⣄⠀⠀⠀⠀⠈⠻⣿⣦⡀⠀⢀⣿⡿⠀⠀⠀⠀⢀⣤⡾⢿⣹⡿⢿⣷⣶⣶⣶⣾⣿⢿⣏⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⠀⠸⣾⡿⣦⠀⠀⠀⠀⠀⠈⠻⢿⣷⣾⡿⠁⠀⠀⢀⣴⡿⠋⠀⠀⠙⠿⢾⣿⣤⣿⣧⣿⣿⣾⣟⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⡆⠀⠹⡇⢹⣇⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⢠⡾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⣽⠏⠁⠉⠹⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠸⣷⡀⠀⠁⠀⢻⡆⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⡀⠀⠀⢀⡇⢿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠻⣧⡀⠀⠀⠀⢳⣿⢻⣆⠀⠀⠀⢀⣤⡶⢿⡟⠀⠀⠀⠀⣴⠇⠀⠀⠀⠀⢀⡾⠁⠀⠈⠛⠶⢶⡏⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠹⣷⡀⠀⠀⠀⠛⠀⢻⣆⢀⣴⠟⠉⠀⠚⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⣼⡇⠀⠀⠀⠀⡿⣦⡿⢀⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⣦⡀⠀⠀⠀⠈⣿⡿⠁⠀⠀⠀⠀⠙⠶⣦⡀⢸⡇⠀⠀⠀⠀⠀⣿⡇⠀⠀⡀⢰⡇⠘⢡⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢿⣦⣀⠀⣼⡟⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣼⣇⠀⠀⠀⠀⠀⣿⣇⠀⠀⣷⠟⢀⣴⠟⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠻⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡄⠀⠀⠀⠀⢉⣻⣷⣤⣀⣴⡿⠁⠀⠙⣿⠷⠶⠶⠶⣶⣤⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⠀⠀⠀⠀⢀⣤⠴⠶⠶⠶⢶⣿⣸⡗⠀⠀⠔⠚⠋⠉⠉⢉⠙⠻⣧⡀⠀⠀⠀⠠⣄⡀⠘⢦⡉⢻⡆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣆⠀⠀⢠⠎⠀⠀⢦⡀⠀⠰⣌⠻⣷⣿⠀⠀⠀⢤⡀⠀⠈⢷⡄⣹⡇⠀⠀⠀⠀⠀⢹⡆⠀⣿⣼⡇⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣤⣿⠀⠀⠀⠀⢻⡆⠀⢻⡆⢹⣿⡀⠀⠀⠈⢿⡄⠀⢈⣷⣿⣷⣤⣤⣤⣤⣤⣾⣷⣾⠿⠋⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⢻⣷⣤⣤⣤⣾⣧⣤⣼⣷⡿⠛⢷⣤⣤⣤⣾⣷⣶⡾⠟⠁⠈⠉⠉⠙⡉⡉⢉⣁⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠤⠤⠴⠒⠒⠒⠶⠶⠶⠤⠤⠴⠶⠶⠤⠤⠤⠤⠤⠤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⢀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣈⠱⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠟⢁⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣷⡈⠛⢦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⡴⠻⠋⣺⣽⡿⠀⠀⠀⠀⣀⡀⠀⠀⠆⠀⠀⠀⠀⠀⠀⢠⣴⣦⣀⠀⠀⠀⠘⣿⣦⡀⠙⢷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣴⠟⠁⡠⣴⡇⡸⠁⠀⢠⣾⣿⣿⣿⣷⣠⠀⠀⠀⠀⠀⠀⠀⢼⣿⣿⣿⣿⣦⠀⠀⢸⠹⣷⣄⠀⠙⣿⡀⠀⠀⠀⠀ ⠀⠀⢰⡞⠉⠁⠀⠤⠊⢠⡿⢱⠇⠀⠐⢛⡿⠿⠿⢿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠈⢿⠛⣿⣿⠛⠁⠀⠹⡷⣿⡇⠳⢄⡈⠳⢶⣦⡀⠀ ⠀⠠⣾⠃⠀⡀⠀⠀⠀⢸⡇⣿⠀⠀⠀⠀⠀⠀⣠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢢⠀⠀⠀⠀⠀⠀⠹⣿⡇⠀⢄⢈⠢⣀⣿⡷⠦ ⠀⣼⡷⠀⢀⠔⠂⡰⠁⢈⡇⡇⠀⠀⠀⠀⢀⡴⠁⠀⠀⣠⣶⣶⣿⣿⣿⣶⣦⡀⠀⠀⠳⡀⠀⠀⠀⠀⠀⣿⣧⡀⠀⡙⠱⣌⢻⣿⡂ ⠰⢿⣧⠞⢁⡤⠊⠀⠀⣼⣇⡇⠀⡠⠔⠊⠁⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠑⠢⢄⠀⢠⣿⡟⡇⠠⡘⢦⠈⢺⣯⠁ ⠀⠸⣿⠶⠋⣠⠎⢀⡞⠙⣿⡇⠀⡇⣸⡀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⣀⠈⡆⣸⣿⡻⠀⠀⠻⣄⡳⣼⣿⡀ ⠀⠀⢿⣶⠏⢁⣶⠟⠀⠀⣿⣧⠀⠀⣿⣿⡄⠀⠀⠀⠀⠀⠈⠉⢻⣿⣛⠉⠀⠀⠀⠀⠀⢠⣾⣿⡆⠁⣿⡟⡇⠀⣦⡑⠂⣱⣿⣿⠇ ⠀⠀⠈⢻⣷⡊⠀⢀⣀⢤⢿⡟⢴⠄⠘⣻⣿⣄⡀⠀⠀⠀⣀⣠⢿⡿⣄⣀⡀⠀⠀⠠⣴⢿⣿⡿⠁⢰⣿⡇⢣⠀⢌⣣⣷⠟⠁⠀⠀ ⠀⠀⠀⠀⠙⣿⣿⣋⡿⢫⣿⣧⣰⠀⠀⢇⢻⣏⠉⡛⡟⠋⠉⠀⢸⡇⠀⠉⠉⣻⣿⠟⠁⢰⡟⠀⠀⣼⣿⣇⢠⡇⣸⠟⠏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠿⠿⠶⣿⢿⣿⡏⡄⠀⠈⣶⢿⡀⢸⣷⠀⠀⠀⠸⠀⠀⠀⢀⣿⡟⠀⢠⡿⠀⠀⣄⠹⠻⣿⣄⣹⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣰⢸⡏⠀⢼⡟⢡⡀⠀⠸⣈⢷⡈⢻⡄⠀⠀⠀⠀⠀⠀⢸⡟⠁⢠⣿⠃⢸⣾⣿⠀⠀⢻⡙⠏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢉⢸⠁⠀⠘⢇⣾⠁⠀⠀⠙⡆⠳⡌⢷⡀⠀⠀⠀⠀⣠⡟⣠⣶⡿⠃⠈⡈⠛⣇⠀⠀⢸⠧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢸⣸⡆⠀⠀⢸⣡⣶⣇⠀⠀⠈⢦⡙⢦⡛⠶⠦⠤⠖⣫⣾⣿⡿⠀⣤⢠⣇⠀⠁⠀⢠⢿⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣏⢿⡄⠀⠘⢻⣿⠿⡇⠀⠀⠀⠉⠪⣿⣿⣶⣶⣾⣟⡩⠀⠀⠀⣿⣼⡟⠀⠀⠀⡞⣤⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠘⡌⣷⡀⠀⠈⢻⣴⣷⣶⠀⠀⠀⡀⠀⠉⠚⠓⠚⠁⠀⠀⠀⠐⣿⠿⠀⠀⠀⡸⢁⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣎⠃⠀⠀⠀⠋⢃⣸⡺⠂⠀⣧⡼⢷⡄⢠⣄⡄⢀⣼⡟⣰⠻⠀⠀⠀⡰⢡⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠣⡀⠀⠀⠀⠛⠙⠁⠀⠘⠛⠁⢻⣿⠋⣿⡧⠈⢈⡴⠁⠀⠀⠀⠀⢁⠜⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠉⠀⠙⠁⠰⠋⠀⠀⠀⠀⠀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠒⠲⠀⠀⡀⠰⠐⠁⠐⡀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡾⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠉⣿⣠⣤⠴⠶⣶⠆⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⢶⡄⠀ ⠀⠀⢠⡟⠁⠀⠀⠙⢷⣄⠀⠀⠀⠀⠀⣀⣠⣼⠇⠀⠉⠁⠀⢠⣾⣋⡀⠀⠀⠀⠀⠀⣠⡶⠛⠉⠀⠘⣷⠀ ⠀⠀⣼⠁⠀⠀⠀⠀⠀⢹⣦⣤⠶⠞⠛⠉⢩⡟⠀⠀⠀⠀⢀⣈⣹⣿⠛⠛⠶⢦⣤⡾⠋⠀⠀⠀⠀⠀⢻⡄ ⠀⠀⡏⠀⠀⢀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠉⠉⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⢸⡇ ⠀⢸⡇⠀⠀⣼⡇⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠘⣿ ⠀⢸⠇⠀⠀⣿⠀⠀⠀⠀⠀⣴⠟⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡶⣶⣄⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿ ⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣾⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣏⣴⣿⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿ ⠀⣿⠀⠀⠀⣿⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿ ⢰⡏⠀⠀⠀⣷⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⣿⠀⠀⠀⠀⠀⣿⠀⠀⠀⣿ ⢸⡇⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠿⠿⠟⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠿⠿⠟⠁⠀⠀⠀⠀⠀⣿⠀⠀⢰⡿ ⠘⢷⣄⣀⣀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⣸⠇ ⠀⠀⠉⠉⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣄⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠴⠾⠋⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣯⣽⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⣿⣿⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠹⣧⠀⠀⠀⠀⠀⠀⠀⠿⠿⠿⠿⠛⠉⠀⠙⠻⠿⠶⠶⠀⠀⠀⠀⠀⠀⠀⠀⣾⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⢷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣼⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⢶⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡴⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠳⠶⢦⣤⣤⣄⣀⣀⣀⣀⣀⣀⣤⣴⠶⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠀⣀⣀⣀⣀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣰⣿⣿⡻⠟⠋⠉⠉⣻⠟⠉⠉⠉⠛⢯⡛⢿⣿⣷⣤⣀⠀⠀⠀⠀⠀ ⠀⣠⣴⠾⠛⢋⣿⠟⠋⠀⠀⠀⠀⢀⡟⠀⠀⠀⠀⠀⠀⠈⠂⣹⣿⡈⠙⠻⢶⣄⡀⠀ ⣸⠏⠀⠀⠀⣾⣋⣀⣀⡀⠀⠀⠀⢸⠁⠀⠀⢀⣀⣀⣀⡀⠀⠈⠻⣧⠀⠀⠀⠉⠻⣦ ⢿⡀⠀⣿⣿⠟⣫⣽⣿⣿⣿⣿⣶⣶⣶⡶⠛⣻⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⢀⣿ ⠸⣧⠀⠈⣿⢸⣿⣿⣿⣿⣿⣿⣿⠁⢹⡇⣼⣿⣿⣿⣿⣿⣿⣿⠁⣼⡇⠀⠀⠀⣼⠇ ⠀⠹⣷⡀⢹⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⠏⠀⣿⡇⠀⣠⡾⠋⠀ ⠀⠀⠈⢿⣿⢿⡿⠿⠿⣿⠟⠉⠀⠀⠀⠀⠙⠛⢿⡿⠿⠛⠉⠀⠀⡿⣷⣾⠏⠀⠀⠀ ⠀⠀⠀⠈⠋⠘⣷⠀⢀⡿⢰⣾⣟⣛⣿⣿⣷⡄⠀⢻⣆⠀⠀⠀⢰⡇⠘⠋⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠹⣧⣼⠃⠈⣧⣼⣿⣇⣈⣿⠃⠀⠀⣿⣀⣀⣴⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢿⣆⠀⠈⠙⢿⡛⠉⠁⠀⠀⣠⡿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡿⢶⣶⣾⣿⣶⣤⣤⣶⢿⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⣧⡼⠁⠉⠏⠁⠈⢹⣠⣾⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣧⠀⠀⠀⠀⠀⣸⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣤⣤⣤⡾⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⢶⣾⣶⠾⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢀⠀⢀⠀⠀⡀⠀ ⠀⠈⠘⠛⠚⠛⠻⠛⠓⠃⠟⠻⠓⠐⠒⠒⠛⠁⠀⠀⠠⠇⠗⠟⠛⠚⠛⠒⠁⠐⠟⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡟⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡿⠀⢻⡆⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠉⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⠜⠀⠈⣷⠀⠀⠀⠀⠀⠀⢀⣴⠟⠁⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠾⠛⠁⠀⠀⠀⣿⠀⠀⠀⠀⣠⡶⢟⠁⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⣿⠀⣀⣴⠞⠋⡰⠋⠀⠀⠀⠀⣠⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠀⠀⠀⠀⠀⠀⠀⢀⣴⣷⠾⠋⠁⢀⡞⠁⠀⠀⠀⠀⢠⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠞⠋⠁⠀⠀⠀⠀⠀⠀⣠⣴⡶⠛⠉⠀⠀⠀⠀⣼⠁⠀⠀⠀⠀⠀⢸⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⡤⠴⠖⠒⠚⠛⠉⠉⠙⠛⠒⠲⢤⣄⣤⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀⢸⢸⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣴⠤⠶⠶⠶⠦⠤⣤⣄⣀⣀⣀⣀⣾⠉⣡⠴⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠃⠀⠀⠀⠀⠀⠀⡎⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⢉⣡⡤⠟⠛⠳⢤⡀⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣄⠀⠀⠀⠀⠀⠀⣰⠇⣠⡴⠀⠀⠀⠀⡸⠃⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣠⣿⣄⣠⣖⣲⣦⡤⠇⠀⠀⠀⠀⠀⠀⢀⣤⠤⠭⣵⣒⢶⣺⣷⢊⣟⣦⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠶⠶⠶⠾⠛⠻⠿⣮⣁⠀⠀⠰⢁⣼⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢻⣤⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠤⠤⠤⠀⠀⠈⠉⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⣢⣾⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⣿⡙⢶⣄⡀⠀⠀⠀⠀⠀⠀⠈⠉⠁⠀⠀⠀⠈⠓⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⡴⣶⣵⠾⠋⢳⣶⣄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡞⢿⡉⢿⣾⠟⢯⣙⣲⣶⢤⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣶⣾⣿⠾⣟⡉⠀⠀⠀⠀⠈⠿⢿⣶⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⡇⡞⠉⢻⣿⢀⠞⣇⢿⣩⣟⢻⡛⣿⢿⢿⣿⣷⣦⣄⠀⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣦⡀⠙⢦⠀⠀⠀⠀⠀⠈⠻⣿⣆⠀⠀⠀⠀⣴⡗⠀⠀ ⢻⡇⠀⠀⢿⣸⠀⠈⠀⠁⠈⠛⠿⠻⣏⢦⠶⢧⣙⢙⣧⡀⢀⠀⢿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢳⣜⣿⣆⠀⠀⣸⠀⠀⠀⠀⠀⠀⠀⠙⢿⣦⣤⣠⠞⣽⢀⣰⠀ ⠀⠁⠀⠀⠘⢿⠀⠀⠀⠀⠀⠀⠀⠀⠘⢷⡀⠀⢉⣿⠾⡇⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⡀⠀⠹⡍⠁⠀⣠⠏⠀⠀⠀⠀⠀⠀⠀⠀⣰⡟⠈⢻⣦⡷⠋⡟⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡾⠋⢀⣠⡇⠀⠈⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⢀⣀⣙⣷⡦⡷⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⢀⣴⠟⠀⢀⡾⠋⠀⣾⠁⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡟⠁⢀⣰⣟⡾⠁⠀⣠⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠇⣠⡤⠶⠾⠟⠉⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⣰⡿⠋⠀⠀⣻⡄⠀⣼⣧⡀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠟⠀⣤⣼⣹⠟⠀⣀⠼⠃⠀⠀⠀⠀⠀⠀⠀⠀⣠⡾⠋⣰⠋⠀⠀⠀⠀⠀⠀⠀⢸⠏⠀⠀⠀⠀⠀⣠⡾⠏⠀⢀⡤⠛⢹⠋⠋⢁⣿⠋⠉ ⠀⠀⠀⢀⣄⠀⠀⠀⠀⠀⠀⢀⡾⠋⠀⣤⣯⡽⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠴⠚⠁⣠⡜⠁⠀⠀⠀⠀⠀⠀⠀⢠⡏⠀⠀⠀⠀⣠⡾⠋⠁⠀⠐⣏⠀⢠⡏⠀⢀⡾⠋⠀⠀ ⠀⠀⠀⠀⣿⡇⢸⣆⠀⠀⣰⣿⣄⢸⢦⡷⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⣠⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⠏⠀⠀⢀⣠⡾⠋⠀⠀⢰⠋⠉⣿⠛⠋⢀⣴⢟⣁⢤⡤⠀ ⠀⠀⠀⠀⢹⣽⣾⡜⢶⣾⠳⣿⣨⠿⠋⠀⠀⢀⣀⡤⠤⢶⣄⠀⠀⠀⠀⠀⠀⣸⠀⣰⠃⠀⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⣀⡴⣟⠿⠀⠀⠀⠀⠸⠦⠼⠁⢀⣴⠟⠻⠽⠾⠭⠤⠤ ⠀⠀⠀⠀⠀⢿⡿⣧⣈⠽⠞⠋⠀⠀⢀⣠⠶⠛⠁⠀⠀⠀⠈⢹⡟⠛⠻⠆⣴⠃⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⣸⣥⣴⠟⠫⠛⠁⢠⠴⠲⡄⠀⠀⠀⣠⣴⠟⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠘⠷⣄⣀⣀⣀⣠⡴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠹⣧⣀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⢠⣾⣯⠾⠛⠉⠀⣀⣀⠀⠀⢺⣀⣀⡏⢀⣤⡾⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣦⣄⣻⣄⠀⠀⠀⢀⣠⠾⢿⣿⣶⣦⣀⠀⡞⠉⢹⠃⠀⠀⢈⣡⡶⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡉⠉⠉⠉⠛⠛⠋⢁⣀⣀⠀⠉⠻⢻⡄⠻⠤⠏⣀⣤⡶⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⢾⡿⣟⣆⠀⢰⢦⠀⠀⠈⠧⣸⠆⠀⢀⣼⣁⣠⣴⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡴⠋⣀⣽⣿⡀⠈⠛⠀⠀⠀⠀⣀⣤⣾⡿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢴⠿⠒⠋⠉⠀⠘⡻⢦⡤⠴⠶⠶⡛⡛⢉⣡⣞⡵⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣾⣿⣿⣿⣦⣴⣶⣶⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⣀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣶⠿⠟⠛⠛⠋⠉⠉⠉⠉⠉⠉⠛⠛⠛⠿⢷⣦⣤⣀⡹⠿⠿⠛⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣴⣶⣶⣾⠟⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣿⣿⣶⣶⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⠟⠉⠀⠀⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠟⠀⠀⠀⠉⠙⢿⣦⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢦⣽⣿⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⣰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣷⠀⠀⠀⠀⠀ ⠀⠀⢰⣿⡏⣤⠀⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣻⡀⠀⠀⢤⢠⣼⣿⡆⠀⠀⠀⠀ ⠀⠀⠀⢿⣿⠁⠀⠀⠀⠀⣴⡾⠁⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣀⠀⠀⠀⠀⠀⠈⢻⣇⠀⠀⠈⣇⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣿⠀⡀⣀⠀⢠⣿⠃⠀⠀⢀⣾⣿⣿⡿⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⡷⠀⠀⠀⠀⠀⢸⣿⠀⢠⣠⣿⣿⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⢿⣷⣇⣽⠀⢈⡏⠀⠀⠀⠸⣿⣿⣿⣦⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⣤⠥⠀⠀⠀⠀⣿⣿⣧⣾⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠛⠿⣿⣧⣾⣿⡄⠀⠀⠀⠙⠿⠿⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠛⠛⠋⠀⠀⠀⠀⠀⢸⣿⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⣿⡇⣴⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢶⣼⣿⣀⣠⣤⣤⣤⣀⠀⠀⠀⠀⠀ ⠀⠀⣠⣶⣾⠿⠛⠛⠻⢷⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣿⡿⠋⠉⠉⠉⠛⢿⣦⡀⠀⠀ ⢀⣾⡿⠋⠀⠀⠀⠀⠀⠀⠙⣿⡆⢀⠀⠀⠀⠀⠀⠀⠀⠘⢿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣤⣿⡟⠀⠀⠀⠀⠀⠀⠀⠹⣿⡆⠀ ⣼⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⣸⣷⣿⣷⣧⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⢠⡾⣠⣇⣠⣿⣿⣿⡇⠀⢀⠀⠀⠀⢀⠀⠀⢹⣷⠀ ⣿⣷⡀⠀⣷⠀⠀⠀⣼⣦⣴⣿⠏⠙⠻⠿⣷⡿⠷⣶⣶⡾⠿⠿⠷⢶⣶⣦⣤⣾⣿⣷⣿⣿⠿⠿⠛⠛⠙⠻⣿⣤⣾⣇⠀⢀⣸⣇⣀⣼⣿⠃ ⠘⢿⣿⣾⣿⣷⣴⣾⡿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠻⠿⠿⠿⠟⠛⠛⠁⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣤⣤⣄⣀⣤⣤⣤⣤⣤⣀⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣠⣼⣿⡿⣛⡿⠛⠉⠉⠉⠉⣻⡿⠉⠁⠈⠉⠙⠛⢯⣝⠻⣿⣿⣷⣦⣄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣀⣴⣶⠿⠟⢻⣿⠟⠽⠋⠀⠀⠀⠀⠀⢀⡿⠁⠀⠀⠀⠀⠀⠀⠀⠈⠳⠈⢿⣷⠈⠙⠻⢿⣶⣄⡀⠀⠀⠀ ⠀⣰⡿⠛⠁⠀⠀⢰⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣿⣧⠀⠀⠀⠈⠛⢿⣶⣄⠀ ⢀⣿⠁⠀⢀⣀⣀⣿⣯⣤⣤⣤⣤⣤⣤⣀⡀⠀⠸⠀⠀⢀⣠⣤⣤⣤⣤⣤⣤⣤⣄⣀⣘⣿⣧⠀⠀⠀⠀⠀⠙⣿⡇ ⠀⣿⡄⠀⠘⣿⣿⠟⢉⣴⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⢉⣽⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⢀⣿⠇ ⠀⢹⣷⠀⠀⠘⣿⢀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⢹⣿⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠀⢸⣿⡇⠀⠀⠀⢀⣾⡟⠀ ⠀⠀⢻⣷⡀⠀⢿⡾⣿⣿⣿⣿⣿⣿⣿⣿⣿⠇⠀⠀⢿⣄⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⣿⣿⡇⠀⠀⣠⣾⠟⠀⠀ ⠀⠀⠀⠙⢿⣦⣬⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠈⠿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⣿⣿⡇⢠⣾⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠈⢿⣿⠿⣿⠛⠛⠛⢻⡟⠋⠀⣀⣀⣀⣀⣀⡀⠈⠙⠛⣿⡛⠛⠋⠁⠀⠀⠀⣿⠹⣷⣿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠈⠛⠀⢻⣧⠀⠀⣸⡇⢰⣿⣋⣛⣛⣹⣽⣿⣷⡀⠀⠘⢿⣄⠀⠀⠀⠀⢰⣿⠀⠹⠋⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⡆⢠⣿⠀⠘⣿⠈⣿⣿⡏⠉⢿⣿⠇⠀⠀⠸⣿⠀⠀⠀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣇⠀⠀⠙⢿⣿⣸⣿⣿⠟⠃⠀⠀⠀⢠⣿⣶⣶⣿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⡀⠀⠀⠈⣻⣅⠀⠀⠀⠀⠀⢠⣾⢋⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⡟⢿⣿⣿⣿⣿⣿⣷⣶⣶⢾⡿⣯⣾⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣇⣸⠋⠉⠉⡏⠉⠉⠉⢻⠈⣤⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣟⠀⠀⠀⠁⠀⠀⠀⢸⣿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣆⠀⠀⠀⠀⠀⢠⣾⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⢿⣶⣶⣶⣾⢿⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣦⣤⣴⣶⠿⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⡀⣄⣀⣀⣀⡀⣀⢀⣀⢀⣀⣀⣀⣀⠀⠀⡀⣀⢀⣀⡀⠀⠀⢤⠀⡄⡤⢀⡀⣀⢠⣄⣀⠠⡄⠀⢠⢄⠀⠀ ⠀⠀⠀⠂⠋⡛⠛⡓⢃⠓⠚⠘⡛⠛⢛⠛⠛⠓⠘⠒⠓⠛⠃⠃⠀⠀⠒⠒⠃⠚⠛⠚⠓⠛⠚⠓⠛⠀⠐⠘⠋⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⣤⣤⣤⣤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣾⣿⡿⠿⠟⠛⠉⠉⠙⠛⠻⠿⣿⣷⣶⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⣿⠿⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡿⠛⠁⠀⠀⠀⣀⣤⣤⣿⡆⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⣷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⣿⠋⠀⠀⠀⠀⠠⣾⠟⠋⠁⠋⠀⣼⣷⣀⠀⠀⠀⠀⠀⠀⠀⢶⡄⢨⡙⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⢶⣿⢿⣿⣿⣇⣀⠀⠀⠀⠀⠀⠀⠹⢿⣷⣾⣧⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⡿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠾⠿⠿⠿⠟⠋⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠙⠛⢿⣶⣤⣀⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⣿⡿⠟⠁⡀⠀⠀⠀⠀⢀⣀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⠖⠛⠉⠁⠈⢉⣻⣆⠀ ⠀⠀⠀⠀⠀⠀⢸⣿⠏⠀⠀⠀⢻⡆⠀⢀⣴⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⢠⡟⠀⣶⣿⣿⣿⣿⣿⣿⣿⠀ ⠀⠀⠀⠀⠀⠀⣿⡏⠀⠀⠀⠀⢸⣿⣀⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⡖⠀⢀⣴⠋⠀⠀⠀⠘⣧⣄⣙⢛⣻⣿⣿⣿⣿⣷⠀ ⠀⠀⠀⠀⠀⢠⣿⠀⠀⠀⠀⠀⢸⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣴⣾⣿⣶⣶⠟⠁⠀⠀⠀⠀⠀⠈⠙⠛⢿⣿⣿⣿⣿⣿⣿⠃ ⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠀⣿⣿⣿⠁⢠⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠞⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣿⣿⣿⡏⠀ ⠀⠀⠀⠀⣸⣿⠁⠀⠀⠀⠀⠀⠇⢻⣿⢀⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣿⣿⣿⡟⠀⠀ ⠀⠀⠀⣰⣿⠃⣠⠀⠀⠀⠀⠀⠀⢸⣿⡿⠀⢠⠀⠀⠀⠀⠀⠀⢸⡧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣶⣿⣿⣿⣿⡿⠋⠀⠀⠀ ⠀⠀⣰⣿⠃⣼⠁⠀⠀⠀⠀⠀⠀⠘⣿⣷⣤⣿⣀⣴⠆⠀⠀⠀⣿⣤⣤⣄⣄⣀⣀⣀⣀⠀⣠⣴⡶⢛⠛⠛⠛⠛⠋⠉⠻⣷⡄⠀⠀⠀ ⠀⣰⣿⠃⣸⡇⡼⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⡇⠀⣆⠀⠀⢻⣿⣿⣿⣿⣯⣉⠙⠛⠙⠿⣁⣠⡾⢷⣤⡀⠀⠀⠀⠀⢸⣿⠀⠀⠀ ⢰⣿⣏⣴⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣷⣾⣿⡆⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣦⠽⢿⣦⣤⣀⣀⣾⠏⠀⠀⠀ ⠘⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠈⠙⠻⠿⠿⠿⠿⠿⣿⣿⣯⠴⠚⠿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀ ⠀⠈⠻⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⣿⣿⣿⡿⣁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠉⠀⠀⠀⠈⠉⢉⣿⠏⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠙⢿⣿⡄⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⣿⣿⣿⡟⠉⠀⠀⢠⣾⣿⣿⣿⣿⣷⣶⣦⣤⣤⣤⣤⣴⣷⣴⡾⠟⠉⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠻⣿⣶⣤⣀⣀⣀⣀⣠⣾⣿⣿⣿⣿⡿⠀⠀⠀⠀⠉⢸⣿⢿⣿⣿⣿⣿⡿⣿⣿⣿⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠛⠿⢿⣿⣿⣿⠿⠟⠻⣿⣿⣿⠇⠀⠀⡀⠀⠀⡿⠁⢸⣿⡟⢿⡏⠀⠘⣿⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⡄⠀⣼⠁⡄⢀⡇⠀⢸⣿⡇⢸⣇⠀⠀⢸⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣾⠏⣰⡇⠈⠀⠀⢸⣿⣧⡀⢿⠀⠀⣼⣿⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⣾⠇⣠⣿⡇⠀⠀⠀⣼⡏⣿⠃⠀⠀⣰⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣿⣿⣿⣷⣄⡀⠀⣿⡇⠸⡇⠀⢠⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠃⣠⣿⠿⠙⣿⣇⢰⣿⣇⠀⠀⢀⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠛⠉⠀⠀⣿⣿⣿⣿⣿⡀⠀⣾⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣿⣿⠋⠛⢹⣧⣼⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠟⠁⠀⠀⠀⢻⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣤⠶⠶⠛⠛⠛⠛⠓⠲⠶⢦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⡴⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠶⣤⡀⠀⠀⠀⢀⣀⣀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⣴⠟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⢷⣤⡾⠛⠉⠉⠛⢷⣄⠀ ⠀⠀⠀⠀⣰⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣷⡀⢠⠶⢦⠀⢹⡆ ⠀⠀⢀⣾⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⡾⠋⠁⠀⠉⠛⢶⣄⠀⠀⠀⠀⠀⠀⠀⠈⢻⣎⠀⣸⠇⢸⡇ ⠀⢀⣾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⢻⡿⠋⢀⣾⠃ ⠀⣸⠿⠖⠀⠀⠀⠀⠀⠰⠿⠿⠷⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⡀⠀⠀⠀⠀⠀⠀⠀⣿⡶⠟⠁⠀ ⠀⣿⢦⡀⠀⠀⠀⠀⢀⡴⠶⣒⣲⢶⣄⠀⢻⣆⠀⠀⠀⠀⠀⠀⠀⠀⢸⣇⠀⠀⠀⠀⠀⠀⠀⢸⡇⠀⠀⠀ ⢸⣿⡏⣇⠀⠀⠀⢰⣏⣴⣿⣿⣿⣷⣜⣷⠀⢻⣦⡀⠀⠀⠀⠀⠀⠀⢸⡟⠀⠀⠀⠀⠀⠀⠀⠀⣧⠀⠀⠀ ⢸⣿⡇⣿⠀⠀⠀⣸⢸⣿⣿⣿⣿⣿⣿⢸⠆⠀⠙⠿⣦⣄⣀⣀⣀⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀ ⢸⣿⣷⣿⢿⣿⡿⠿⣦⡻⣿⣿⣿⡿⢏⡾⠀⠀⠀⠀⠀⠉⠙⠛⠋⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡇⠀⠀⠀ ⠀⣯⡿⣹⣦⡏⠀⠀⠈⠻⣶⡶⠶⠶⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠇⠀⠀⠀ ⠀⣿⠃⢀⣿⣿⡀⠀⠀⠀⠘⢷⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡿⠀⠀⠀⠀ ⠀⢿⣤⣼⣧⣼⣧⡀⠀⠀⣴⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⠿⠋⠀⠀⠀⠀⣸⠃⠀⠀⠀⠀ ⠀⠈⢿⡙⢿⣄⣘⣿⡶⠶⠾⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡟⠁⠀⠀⠀⠀⠀⣴⠏⠀⠀⠀⠀⠀ ⠀⠀⠈⠻⣦⣀⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣷⣀⠀⠀⠀⢀⣼⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠙⢻⣶⣤⣄⣀⡀⠀⠀⣶⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣈⣽⢿⡄⠀⠈⣿⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠻⣦⡿⠉⠛⠛⠻⠿⣧⠀⢠⣿⠤⠤⠴⠶⠶⠿⣿⣿⠃⠘⣷⠀⢸⡇⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣧⡼⠁⠀⠀⠀⠀⠀⠠⠖⠂⠀⠀⠘⠷⠟⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠈⠀⠈⠿⠂⠀⠀⠈⠀⠀⠀⠀⠈⠀⠢⢄⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢲⠈⠑⢄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⣀⠀⠀⠑⡠⢰⠀⠀⠉⠭⢁⡠⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠹⣯⣯⣿⣷⠀⣠⠃⠏⡄⠀⢢⡀⠉⠀⡀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠈⠙⠛⠛⠁⠀⢄⠀⢡⠀⢀⠁⠸⡋⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠁⢄⠻⢿⠇⠀⠑⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠢⠀⠀⣴⣨⣵⣮⣷⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠄⣀⣿⣿⣿⣿⡿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣾⣿⣿⣿⣡⣾⣦⣽⣛⡿⣿⡿⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⠀⣸⣿⡿⣿⣿⢿⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⣿⡿⠃⡄⣼⠊⣽⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⡇⠬⣼⠃⣰⣿⡟⠁⠀⠀⡠⠂⠀⠀⠀⠀⠀ ⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣿⢓⢘⠉⢳⣿⠏⠀⣀⠔⠊⠀⠀⠀⠀⠀⠀⠀ ⠈⠙⠦⡀⠀⠀⠀⠀⠀⢀⠘⢿⣿⣮⡤⡜⠋⣠⣾⢄⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠘⡄⠀⠀⠁⠀⠀⠐⢌⠻⡿⣿⣽⣿⣿⡿⠁⠈⠑⠄⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⡔⠉⠈⠿⠷⡙⡖⠄⠀ ⠀⠀⠀⢠⢾⡷⠀⠀⠀⠖⢧⠓⡇⠀ ⠀⠀⠀⢸⢣⣣⡾⠃⢠⣶⠀⢱⠧⠀ ⠀⠀⠀⠘⠢⢬⣁⡇⠀⡝⠽⣇⠀⠀ ⢀⡀⠀⠀⣠⠙⠋⠀⠀⠀⠀⠺⡄⠀ ⠛⡔⢁⠞⢹⡄⠀⠀⠀⠀⠀⠠⡄⠀ ⠀⡇⡎⠀⠀⣿⡄⠀⠙⠀⣀⡞⠀⠀ ⠀⢿⣇⣠⣴⣿⡇⠀⣸⡾⢛⠃⠸⡄ ⠀⠀⠹⠀⠀⠼⣀⠉⡉⡀⠈⠂⠤⠾ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣠⡶⠛⠉⢉⠀⠈⠉⠙⠳⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢠⡞⠁⠀⠰⠚⢙⣰⣄⠀⠀⠀⢌⡗⡄⠀⠀⠀ ⠀⠀⠀⢀⣴⠟⠀⠀⠀⠀⠘⠛⠛⠉⠁⠀⠀⠀⠉⡙⠶⠤⡀ ⠀⠀⠀⡾⠁⠀⣆⣴⠋⠀⠀⠀⠀⠀⡄⢀⠄⠀⣎⠲⣿⣿⣿ ⠀⠀⢠⠇⠀⢀⣿⠃⠀⠀⠀⠀⠒⠻⠟⠁⠀⠀⠀⠉⢿⣿⡟ ⠀⢀⡞⠀⠀⠀⢸⡎⡀⠀⠀⢠⠀⠀⠀⠀⠀⢀⣤⣶⣿⡟⠁ ⢀⡞⣜⠄⠀⠀⠸⣿⣿⣃⡄⠸⣿⣷⣔⣒⣯⡕⢄⡀⠀⣳⠀ ⠘⢿⣿⡄⠀⠀⠀⢻⣿⣿⡇⠀⠈⠛⠛⠛⠿⠝⠛⠿⣿⠁⠀ ⠀⠀⠙⢧⣀⠀⢀⣼⣿⣿⠋⠀⢺⣿⣷⣶⣶⣶⠗⠚⠁⠀⠀ ⠀⠀⠀⠀⠉⠛⠛⠉⠻⡇⢠⡀⡎⢸⡿⡁⢹⣇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣣⡇⠀⣸⠇⠁⣼⠇⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢏⡽⠛⣆⣿⠈⣼⠏⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠟⠉⣶⡏⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠃⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠠⢌⡉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠄⠒⠒⠒⠂⠄⡀⠀ ⠀⠀⠀⢡⠆⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠁⠀⠀⠀⠀⠀⠀⠈⢂ ⠀⠀⡐⢁⠀⠀⠀⠈⠂⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠈ ⣀⡀⠀⠉⠀⠀⠀⠀⢀⣿⠐⠤⠤⡀⢀⡀⠠⠤⠀⠒⠒⠃⠠⢀⡎⠉⢻⠀⠀⠀ ⠘⠠⠖⠦⠀⠠⠀⣠⡾⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠒⢀⠀⠦⠠⠞⠀⠀⢠ ⠀⠀⠀⠀⠀⠀⢿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠀⠀⠀⠑⢄⣀⣀⣀⠴⠃ ⠀⠀⠀⠀⠀⠀⠈⠄⠀⠆⠀⠀⠀⠀⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠸⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠈⠢⡘⡀⠀⢀⠀⠀⣀⠄⠊⠁⠈⠢⡀⠀⠀⠀⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠈⠉⠉⠀⠀⠀⠳⣄⠀⢨⠢⣄⠀⢂⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠸⠀⠄⡀⡄⠀⠀⠀⠀⠀⠀⠀⢡⠀⡆⠀⠂⢀⠇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣀⠆⠐⠀⡇⡇⠀⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⢠⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠈⠉⠀⠁⣔⠁⡀⠀⠀⠀⠀⠀⠈⠁⠊⠀⢀⡄⠀⠌⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣏⠢⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣘⠭⡉⠉⠉⠇⠀⠈⠐⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⢜⡀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢡⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⡍⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣧⠟⣶⣲⠒⠐⢤⡤⡤⢸⡇⠀⠀⠀⠢⣀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠏⣹⠀⠻⢇⣀⡀⢸⡷⠀⢘⣷⠀⠀⠀⠀⠈⢄⠀⠀⠀⠀⠀⠀⠀ ⠸⡀⠙⢧⣀⠀⠛⠄⠀⠀⡠⠂⠹⡀⠀⠀⠀⠀⠘⠀⠀⢠⡀⠀⠀⠀ ⠀⠑⠒⠉⣹⣶⣦⣤⣴⣦⣶⣶⣾⣉⠢⢄⣀⣀⠜⠀⠀⠀⡃⠱⡀⠀ ⠀⠀⠀⢰⡟⠉⠉⠉⠉⠉⠉⠉⠉⠀⠣⡄⠀⠀⠀⠀⠀⢀⠃⠀⣱⡆ ⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⢄⠀⠀⠀⠀⠎⠀⢀⣾⠇ ⠀⠀⠀⣞⡇⠀⢐⠀⡄⠀⠀⠀⢰⡯⠈⠀⠀⠑⣦⡉⠠⠤⠴⣿⠷⠀ ⠀⠀⠨⠿⠇⠀⢸⠀⡇⠀⠀⢺⢿⣄⡀⠀⠀⠀⢰⠈⠉⠉⠉⠁⠀⠀ ⠀⠀⣧⣷⢠⠀⣸⢠⠗⡀⠀⣼⣼⣿⣅⢀⣀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⠉⠁⠀⠁⠉⠉⠁⠈⠁⠈⠀⠁⠈⠉⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣤⡴⠋⠳⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣀⠤⠖⠒⠒⠛⣉⡙⢦⠀⠘⢦⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢠⡤⠆⠀⣾⠟⢁⠀⠀⠀⠀⢠⠀⠉⠳⡷⡀⠈⠳⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠏⠀⢠⢸⡏⣴⠃⠐⠲⣄⠀⢸⡤⢦⡀⢻⠙⣦⣀⠘⢦⠀⠀ ⠀⠀⠀⠀⠀⠀⡞⠀⠀⢸⠸⠁⣏⠀⠴⣤⠈⢳⠀⢻⡾⣣⠾⢿⣿⣿⡟⠳⣥⠀ ⠀⠀⠀⠀⠀⡼⠁⠀⠀⢸⡀⠀⢹⡀⠶⣿⠃⢸⢁⠴⣟⠁⣠⣾⣿⡿⠁⠀⣹⢲ ⠀⠀⠀⠀⡤⠁⠀⠀⠀⠀⣧⠀⠠⠿⠒⠒⠀⡜⠁⠀⠛⠛⠛⣿⡟⠁⠀⣰⠋⢸ ⠀⠀⠀⢠⡇⠀⠀⠀⠀⠀⢸⠀⠀⣀⣀⡀⠈⠀⢀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⡾ ⠀⠀⠀⠘⣇⠀⠀⠀⠀⠀⢸⡐⠋⠹⣦⣀⠀⠀⠀⠀⠉⠁⣀⠤⣪⠃⠀⠀⢰⠇ ⠀⠀⠀⠀⢻⡄⠀⠀⠀⠀⣸⠷⣤⣀⠀⠉⠉⠓⠒⠒⠊⠉⣁⠶⢳⠀⠀⢠⡏⠀ ⢰⡆⠀⠀⠀⢻⣆⠀⠀⠀⣿⠀⠀⠈⠉⣿⡓⠒⠒⠒⠚⣏⡇⠀⠈⠷⠶⠋⠀⠀ ⡇⢱⣠⡀⠀⠀⠹⣷⣄⣸⠏⠀⠀⣠⠖⠣⣟⣷⢲⡖⣿⣻⣅⠀⠀⠀⠀⠀⠀⠀ ⢧⠀⠏⢳⠀⠀⠀⠀⠉⠉⠀⢀⡞⠁⠀⠀⠀⠉⠉⠉⡟⠉⠺⢇⠀⠀⠀⠀⠀⠀ ⠸⣆⠀⠀⢇⣦⡀⠀⠀⣀⣤⠏⠀⠀⡄⠀⠀⠀⡀⠀⠣⢄⡴⢸⡆⠀⠀⠀⠀⠀ ⠀⠙⣆⠀⠀⠁⢳⣠⠞⠁⠈⡀⠀⢸⠁⠀⠀⢸⠁⠀⠀⡶⠇⡼⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⠳⣄⡀⣸⠃⠀⠀⠀⠈⠳⣼⡀⠀⠀⢸⡀⠀⠜⢁⠞⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⠹⡇⠀⠀⠀⣀⣀⣀⣿⡇⠀⡀⠤⠿⠶⢶⡃⠀⠙⠛⠛⢗⠦⡀⠀ ⠀⠀⠀⠀⠀⠀⢷⡀⢠⠊⠀⢄⠀⢍⢳⡆⠀⠠⡀⠘⢆⣿⠀⠀⠈⢱⢀⣧⠇⠀ ⠀⠀⠀⠀⠀⠀⠀⠙⢻⣄⣀⣸⣀⣸⡼⠷⣄⣀⣵⣤⠾⠛⠛⠒⠒⠛⡋⠁⠀⠀

⠀⡤⠊⠱⣦⠴⠒⠠⠔⠍⠢⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢇⢠⣃⢻⠄⣀⠀⠀⠄⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢘⢹⣦⠀⠠⣶⠈⠀⢸⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢼⡙⠀⡾⡥⠂⡤⠎⡱⣼⠂⠀⠀⠀⠀⠀⠀⠀⢶⠖⠖⢤⢄⠀⠀ ⠀⠓⠚⠻⡨⠎⠉⠒⠗⠙⠤⠄⡀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠸⡄⠀ ⠀⠀⠀⠀⢡⠀⠀⠀⠀⠀⠀⠀⠈⠒⠂⠀⠤⠄⡀⡠⠃⠀⢈⡇⠀ ⠀⠀⠀⠀⢸⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣠⡟⠀⠀ ⠀⠀⠀⠀⠘⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⡀⠀⠀⠀ ⠀⠀⢀⡀⠠⠊⠳⢤⡀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⠀⠀ ⠀⠠⠃⠀⣀⣀⣀⣠⠉⢢⠀⠀⢸⢹⠒⠂⠢⠴⢄⠀⠀⠈⠒⡄⠀ ⢠⠁⢀⠎⠀⠀⠀⠀⠀⠀⠆⠀⠀⠃⠂⢄⠀⠈⢢⠁⠄⡀⠀⢡⠀ ⠈⠓⠈⠀⠀⠀⠀⠀⠀⠀⠘⠀⠀⠀⠀⢠⠃⠀⡎⠀⠀⠈⠄⠀⢆ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡖⠀⡆⢴⠃⢀⠜⠀⠀⠀⠀⡔⡖⢸ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠁⠉⠀⠀⠀⠀⠀⠀⠀⠀⢠⣭⣭⠅

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣠⣤⢤⣄⣀⣀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⡤⢶⣾⣿⣿⣿⣿⣭⢻⣻⣿⣿⣿⣇⣤⡷⣄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣠⣾⣿⣾⣿⣿⣿⣿⣿⣿⣿⠋⠁⠑⡄⠀⠉⠙⠻⣿⣵⡀⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠐⠀⠀⠀⠀⠈⢿⣿⡀ ⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣧ ⠀⣠⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⢀⣤⣤⣄⡀⠀⠀⠀⠀⠀⣠⣤⡘⣿ ⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡅⠽⠿⣿⠿⢷⡄⠀⠀⠀⠾⢿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠊⢁⣶⣿⣿⣦⠀⢠⣿⡇ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠸⣿⣿⣿⣿⠂⠸⡟⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⡀⢀⣸⣿⣿⣿⣗⡧⡘⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣬⣈⠉⠉⠉⠉⢁⠌⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡟⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⡼⠁⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠿⡿⡿⠃⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢗⣂⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⣠⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⣀⣀⡀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⠒⡩⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⡲⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⠼⢇⣶⠁⠀⠀⠀⠠⠀⠀⠀⠀⢀⣄⠀⠀⠳⣌⠑⢄⠀⠀⠀⠀ ⠀⣀⡠⠔⢃⢴⣇⠃⢀⣾⣿⣿⠔⠀⠀⠀⠀⢾⣿⣿⡦⠀⣟⣧⡌⠹⣄⡀⠀ ⢠⠏⢀⠀⠁⢸⡼⠀⠀⠉⢉⠋⠀⠀⠀⠀⠀⠈⢂⠉⠀⠀⠹⣿⠠⡐⢌⢻⠤ ⣺⡀⠐⠡⠃⢸⡇⠀⡀⠄⠁⠀⣴⣿⣿⣿⣷⡄⠀⠃⢀⡀⠀⣿⡆⡨⡑⢽⠃ ⠸⣗⡀⠈⡔⢹⡇⠈⣤⠀⠀⠀⠸⢿⣿⣿⠿⠁⠀⠀⣀⡘⢸⣿⠁⢐⢔⢼⡇ ⠀⠻⣤⠚⢁⣸⡗⡄⠻⣧⡀⠀⠀⣀⣾⣕⡀⠀⠀⣴⣿⠃⣼⡿⡠⣓⡴⠛⠁ ⠀⠀⠙⣭⣝⣿⣧⠆⠘⣹⡌⢽⠉⠁⠘⠀⠉⣿⠋⢰⠃⠀⣿⡇⢅⠏⠃⠀⠀ ⠀⠀⠀⠀⣷⡇⢹⢢⠀⠸⡳⡘⡆⠀⠀⠀⢰⠏⣠⠏⢰⡷⠀⢛⠎⠀⠀⠀⠀ ⠀⠀⠀⠀⣾⡀⠈⣞⣄⠀⠑⡑⣝⢤⣀⠠⣪⣾⠋⣀⡌⠃⢀⣮⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢸⣧⠀⠹⡟⡇⡀⠈⠊⢷⣶⡾⠏⠈⢈⣿⠇⠀⡘⡞⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢫⡃⠀⠘⠋⡧⠄⣄⢦⡀⣄⢀⡴⠰⠏⠀⠰⣱⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠑⠄⠀⠈⠁⠀⠉⢸⠏⠻⢂⠔⠁⠀⠀⠕⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠄⠤⠄⠀⠄⠤⠄⠀⠀⠀⠀⠀⠀⠀⠀⠀

⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⢿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿⣿⣿⡿⢛⡉⠉⠧⠍⢻⣿⣟⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣻⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠿⠓⠛⠛⠛⠒⠻⠿⠛⠟⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠛⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠛⠿⣿⣿⣿⣿⣟⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⢿⣿⣿⣿⣿⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠟⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⢿⣟⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⣠⣴⣶⣤⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣴⣦⣤⣄⠀⠈⢻⣿⣿⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⢰⣿⣿⣶⣶⣾⣶⣤⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣼⣿⣿⣮⣽⣿⠷⣄⠈⢿⣽⣿⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠆⠉⠉⠉⠉⠉⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠈⠈⠙⣿⢹⣿ ⠐⠂⠠⠴⠀⢤⣭⣭⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿ ⣄⣽⣿⠿⢿⣿⡿⣧⣼⠃⠀⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣿ ⡿⠟⣁⣰⡿⠋⢉⣿⣿⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣶⣿⣿⣶⠶⢴⣿⣶⣦⣤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣶⣿⣿⣿⣧⣾⣿⣿⠟⠀⠀⠀⠈⣷⠀⠀⠀⠀⠀⢠⣶⣿⣿⠆⠤⠀⠆⣛⠛⣧⣤⡈⡉⠻⣿⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣧⡀⢀⡤⠊⠁⠀⠀⠀⠀⣰⣿⣿⣿⣶⣷⣤⣦⣴⣶⣦⣤⣤⣴⣶⣶⣾⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣗⣶⡾⠁⠀⠀⠀⢠⠆⢽⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡔⠤⠀⠀⠀⠀⠀⢦⣀⣀⣼⣿ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡀⠀⠀⠀⠀⠀⠀⢹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠁⠀⠀⠀⠀⠀⠘⣷⣿⣿⣿ ⠛⢻⣿⣿⣿⣿⣿⣿⣿⣿⣷⠃⠀⠀⠀⠀⠀⠘⠻⣶⣬⡙⠛⢛⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠛⢛⣿⡿⠃⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⣿ ⢠⣾⠃⣻⣿⣿⣿⣿⣿⣿⣿⣆⡀⠀⠀⠀⠀⠀⠀⠻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣾⣿⣿⠋⠀⠀⠀⠀⢀⣤⣀⣴⣿⣽⣜⣿⣿ ⣿⢃⠅⣹⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣤⣀⠀⠀⠀⠸⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠁⠀⠀⠀⣀⣴⠛⢻⣿⣿⣿⣷⣿⣿⣿ ⡿⠀⠀⠛⣾⣿⣿⣿⠿⠟⣿⣿⢿⡿⠃⡟⠻⣷⣦⢀⣴⡆⠹⡏⣹⣿⣿⣿⣿⣿⣿⡛⡿⠁⠀⠀⠀⠀⣿⢟⡄⠀⠀⠻⣿⣿⣿⣿⣿⣿ ⡇⠈⠀⣰⣿⠛⠁⠀⠀⠀⠀⠁⣾⠃⠀⠇⠀⣹⣿⣼⣿⡗⢠⣿⣿⠿⢛⣿⠛⡉⣦⣴⠀⠲⣦⣀⣰⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣿⣿⣿ ⠶⢀⣼⠿⠁⠀⠀⠀⠀⠀⠀⡜⠁⠀⠀⠀⠀⠈⢹⣿⣿⣷⣿⣿⣿⣦⡾⣿⠗⣶⣉⣷⣤⣴⣿⣿⡄⠀⠀⠀⠀⠀⠀⠀⠀⢹⣿⢿⠿⢿ ⠿⠛⠁⠀⠀⠀⠀⠀⠀⣠⠞⠀⠀⠀⠀⠀⠀⠘⠘⢿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠸⠿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⡴⠃⠀⠀⢠⠃⠀⠀⠀⠀⠀⠀⠙⠻⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢠⠞⠀⠀⠀⢠⣿⡄⠀⠀⠀⠀⠀⠀⠀⠳⢤⣛⣹⠋⠛⠛⠿⠛⠛⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡟⠀⠀⠀⣤⡏⣴⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣴⠃⠀⠀⣾⡟⣽⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⠜⠁⢀⣰⣿⣷⣿⣿⣿⠛⠛⢦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⡴⠋⠀⠀⢬⣿⣿⠟⠃⠀⠀⠀⠀⠀⠃⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⠎⠀⠀⠀⠀⠀⠀⠀⠀ ⡤⠊⠀⠀⣠⣽⡿⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣴⣾⣿⣳⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣀⣰⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣰⣶⣾⣿⣿⣿⣿⣿⣿⡒⠀⠀⠀⣀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠀⠀⢻⣿⣿⠀⠀⠀⠀⠰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠒⠒⠤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠓⢦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡈⠀⠀⠙⣆⠀⠈⠳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⡄⠀⠹⢀⠀⠂⠈⠙⢶⠢⠴⠤⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠠⠄⠀⣀⣀⡀⡀⠀⠀⠀⠈⣆⢢⢸⠀⠀⠀⠀⠀⠘⠂⢀⣠⠔⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢿⡟⣻⣟⣿⣿⣿⣄⠀⠀⢀⡎⠈⡟⣆⠀⠀⠐⣄⠀⠀⠛⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣿⣿⣿⣿⣿⣷⠀⠠⠜⠀⠀⠑⢹⡀⠀⠀⠘⢧⠀⢠⣤⣤⠸⠃ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⠛⠛⠛⠋⠀⠀⠀⢠⡀⠀⠀⢡⠀⠀⠀⠈⠁⠈⣿⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠓⠦⠤⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣙⢆⠀⠈⣦⣴⣾⣦⠀⠀⠘⠆⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠒⢄⠈⠛⢿⡟⠁⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⣄⠀⠀⠀⠀⣴⠖⣘⣻⣦⣬⣱⠆⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠄⠀⢰⠻⣿⣿⣿⣿⣿⣿⣿⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⣄⣀⣹⣿⣿⣿⣿⣿⣿⣿⠿⠁⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⣴⣶⣶⣶⣦⡆⢀⣤⣐⠺⣿⣿⣿⣿⣿⣿⣿⣿⡿⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣤⣾⣿⣿⣿⣷⣶⣭⣟⡿⣿⣿⡿⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⢀⣿⣿⣿⣿⠿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢀⠀⠀⠀⢀⣾⣿⣿⣿⠋⠻⠛⢻⡏⣽⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⣿⠟⠀⣦⠀⣼⠗⠋⢹⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣨⣾⣿⣿⠏⠀⣰⠻⢼⡏⠀⣀⣿⣿⣿⠿⠀⠀⠀⠀⠀⠀⣀⠄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⣿⣿⡇⠞⢰⣶⡟⠀⢀⣿⣿⣿⠏⠀⠀⠀⠀⠀⣀⠾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢹⣿⣿⠷⠄⠸⠛⠛⢦⣿⣿⣿⠃⠀⠀⠀⢀⡴⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣇⣠⡀⢦⠀⠀⢸⣿⡿⠃⠀⢀⡤⠶⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠙⠶⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠻⣏⣿⣿⣷⣦⣀⠤⡼⠟⠃⢀⣴⣾⢳⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠈⢲⡄⠀⠀⠀⠀⠀⠄⠀⠀⠀⠁⠀⠈⢿⣿⣿⣾⣷⡶⢿⣤⣶⣿⣿⣿⣷⠈⠑⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠙⠶⣄⡙⢻⠿⢿⣛⣛⣿⣿⣿⡿⡟⠇⠀⠀⠀⠈⠑⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠶⣶⣶⣶⡒⠶⣄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡞⠁⠀⠀⠘⡿⠛⠻⣆⠹⡏⢱⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⢀⣠⣿⣷⣤⠀⠀⠀⠀⢠⡶⣮⠀⡇⢸⠃⠀⠀ ⠀⠀⠀⠀⠀⠀⡏⣄⢻⡏⠁⣀⣄⠀⠀⠘⠉⠙⢧⡇⣿⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⣧⢻⣄⠱⡈⣿⠟⠀⢠⣶⣶⠀⠀⢹⣾⡧⠀⠀ ⠀⠀⠀⠀⠀⠀⢻⡄⠉⠙⠻⡇⡆⠀⠀⠙⢿⠴⣲⡏⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠉⢙⣶⣤⡗⠒⠀⠚⠓⠊⠹⣷⠀⠀⠀⠀ ⠀⢀⣀⠀⠀⠀⠀⣠⡞⠉⠟⠀⠀⠀⠀⠀⠀⠀⠀⢿⡇⠀⠀⠀ ⣴⡷⢋⣴⠆⢀⣾⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢹⠀⠀⠀ ⠈⢀⣾⠁⢠⠟⠁⠈⢿⣆⠀⠀⠀⢀⣀⠀⠀⠀⠀⢈⢻⠀⠀⠀ ⠀⢸⣿⢀⡟⠀⠀⠀⢸⣿⣦⠀⠀⠈⡟⠀⠀⠀⣠⡿⠀⢇⠀⠀ ⠀⠘⣿⣼⡇⠀⠀⠀⣼⣿⣿⠀⠀⠀⣧⣀⣤⣾⣿⠀⠀⢸⡀⠀ ⠀⠀⠹⣿⣧⣠⣶⣶⣿⣿⣿⠆⠀⢀⣼⡿⠟⠉⡼⠀⠠⠾⢧⡀ ⠀⠀⠀⠈⠻⡉⢀⠀⣄⢈⡇⠀⠛⠋⢁⢣⠀⠀⠱⣤⡀⣳⢱⣹ ⠀⠀⠀⠀⠀⠉⠉⠁⠉⠁⠙⠲⠤⠼⠼⠟⠀⠀⠀⠀⠉⠉⠉⠀

⠀⠀⠀⠀⢠⡀⠘⡏⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠤⠄⠒⠒⠠⠤⢄⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠸⡌⠲⡇⠀⠈⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠈⠑⢦⡀⠀ ⠀⠀⠀⠀⠀⢳⡤⠇⠀⠀⠀⢹⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡄ ⠀⠀⠀⠀⡰⠊⠀⠀⠀⠀⠀⠀⠙⢤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸ ⠀⠀⠀⡼⠁⣠⣤⠀⠀⠀⠀⠀⠀⠀⠈⢰⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⢀⣠⣤⣀⡀⠀⠀⠀⠀⠀ ⠀⠀⠊⠀⠀⠈⠁⠀⠀⠀⠀⠀⠀⠀⢠⣿⡏⠙⢦⣤⣤⣀⠀⡀⠀⠀⢀⣀⣀⠤⠤⠐⠒⠒⠒⠚⠢⠄⡀⠀⡟⠉⠀⠉⢿⡆⠀⠀⠀⠀ ⢻⡟⠀⠀⢀⣀⠴⠀⠀⠀⠀⠀⠀⣠⣿⡟⠀⠀⠀⠀⠀⠀⠁⠈⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠈⠱⣅⠀⠀⠀⣼⠃⠀⠀⠀⢀ ⠀⠈⠙⠛⠐⠒⠈⠉⠉⠑⠄⣠⣶⡿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠱⡀⠐⠚⠓⠒⠊⠁⠀⠀⠀⠀⡼ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⡟⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡀⠀⠀⠀⠀⠘⢦⡀⠀⠀⠀⠀⠀⢀⣠⠞⠁ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡟⠁⠀⠀⠀⠀⠀⠀⠙⠛⢶⠶⠖⠛⠋⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣆⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢦⡀⠘⡄⠀⠀⠀⠠⡀⠀⠀⠀⠀⠀⢀⡴⠚⠉⠀⠈⠣⡀⠀⠀⠀⠀⠀⠀⡼⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢉⠂⠹⡄⠀⠀⠀⣧⣀⣀⣠⠴⠞⠁⠀⠸⡀⠀⠀⠀⠙⢦⡀⠀⠀⠀⠀⠇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⣷⠀⠀⠀⡇⠁⠀⠀⠀⠀⠀⠀⠀⠙⢦⣀⠀⠀⠀⡎⠲⣄⡀⠀⠘⢆⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⠀⠿⡄⠀⢸⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⣄⠀⠰⡄⠀⠙⡄⠀⠈⣷⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⡸⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡸⠀⢠⠏⠀⠀⠀⠀⢰⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⢰⠁⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⠇⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢾⠁⠀⠟⠀⠀⡇⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠀⠀⣰⠃⠀⠀⠀⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣎⡄⠀⣸⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⣤⠄⠀⠴⠃⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⡤⠚⠁⢀⠛⣦⡴⠿⠛⠓⢦⡤⠛⡄⠈⠑⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡀⠀⠀⡼⠐⣿⢆⡄⠀⠀⠀⠀⢸⡀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠈⠣⣀⣼⣥⡤⠘⠋⠀⢤⣤⣀⠀⠀⢣⣄⠀⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⡧⣴⣶⡄⠀⠀⢠⣶⣦⠀⠀⠀⢸⡇⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⡤⢴⠃⠙⢻⣷⡆⡀⠀⠙⠋⣠⠤⡀⠈⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀ ⠸⣇⡀⠙⢙⡏⠻⡖⠉⢃⡖⠚⠃⢀⣷⣶⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠐⠿⣛⠋⠛⠊⠓⡾⢆⠀⠀⠀⠀ ⠀⠘⠧⠴⠻⢿⣯⣉⣲⡋⠉⠲⢤⣿⡾⠛⢇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⢆⠀⠀⠁⣸⣇⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠙⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠉⠢⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⢠⣿⡄⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢱⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠑⠒⠒⠢⠤⠤⣀⡀⠀⣠⠏⠀⠀⠀⠈⣸⠁⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠛⠀⠀⠀⠀⢀⣺⠏⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢻⡀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⣶⣾⡿⠇⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⣧⡀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢈⡿⣆⡀⠀⡇⠀⠀⠀⠀⠀⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣀⡀⠤⠔⠊⠀⠈⠛⠦⣧⡀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⡞⠁⠀⠀⠀⠀⠀⠀⠀⠀⡎⠙⠢⡀⠀⠀⠀⠠⡟⢻⠳⠶⠤⣠⣄⣀⣳⡄⠀⠀⠀⠀⠀⠳⠤⣄⠀⠀⠀ ⠀⢀⡜⠀⠀⢀⡔⠒⠒⠒⠒⠒⠚⠁⠀⠀⢳⠀⠀⠀⠀⢷⠈⣆⠀⠀⠀⠈⠈⣏⠉⠢⡀⠀⠀⠀⠀⠀⢹⡇⠀⠀ ⠀⡞⠀⠀⢀⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡆⠀⠀⠀⢸⠀⠈⠒⠤⡀⠀⠀⠈⢲⡄⠑⠢⢄⡀⠀⠀⠀⢇⠀⠀ ⠀⠻⣆⠤⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡀⠀⠀⢸⠀⠀⠀⠀⢸⠆⠀⠀⢸⠏⠀⠀⠀⠈⢢⠀⠀⠘⡄⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⢸⠀⠀⠀⣠⠎⠀⠀⢀⠇⠀⠀⠀⠀⠀⠈⣇⠀⠀⠹⡄ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣷⡦⠄⠸⠀⢀⣾⠃⠀⠀⢀⡎⠀⠀⠀⠀⠀⠀⢠⡾⢲⠖⠀⣷ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⢿⣿⣀⠤⠞⠀⠀⠙⠒⠒⠒⠉⠀⠀⠀⠀⠀⠀⠀⠸⠷⠼⠤⠔⠋ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣖⣒⣒⣒⠒⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣤⣤⣤⣶⣶⣶⣶⣶⣿⣿⣿⣿⣿⣥⣼⣿⣿⡖⠒⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⠶⢿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣾⠈⣿⣙⣻⣿⣿⣿⣿⣿⡇⣤⣴⣿⢷⣄⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣠⣾⣯⣐⣲⣿⣿⣿⣿⣿⣿⣿⣷⣿⣿⣿⣷⠾⠛⠉⠣⡄⠈⠉⠙⠛⠿⠿⣿⣶⣼⡷⣄⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⠋⠀⠀⠀⠀⠘⡄⠀⠀⠀⠀⠀⠀⠙⢿⣷⣿⣦⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⢀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⣿⣧⠀⠀ ⠀⠀⠀⠀⠀⠀⣴⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢏⠀⠀⠀⠀⠀⠀⠀⠀⠐⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣿⣿⡆⠀ ⠀⠀⠀⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣿⣷⠀ ⠀⠀⢀⣼⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠁⠀⠀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⠈⢻⣿⡆ ⠀⣠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠀⣠⣾⣿⣿⣿⣿⣷⣆⠀⠀⠀⠀⠀⠀⠀⣠⣴⣿⣿⣿⣷⣼⣿⡇ ⣰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⡐⠲⠿⠿⣿⣿⠿⠿⢿⣷⠀⠀⠀⠀⠀⠀⠻⠿⣿⣿⣿⣿⣿⣿⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡄⠀⠀⠀⠀⠀⢠⡼⠋⠀⣠⣴⣾⣿⣶⣀⠀⠀⠉⠈⣿⣿⡟⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣆⠀⠀⠀⠀⠀⠀⠀⣰⣿⣿⣿⣹⣿⣿⣧⠀⠀⣼⣿⣿⠃⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡆⠀⠀⠀⠀⠀⠀⢻⣿⣿⣿⣿⣿⣿⡿⠄⠀⢿⣿⠏⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⡀⠀⠀⠀⠀⠀⣤⣿⣿⣿⣿⣿⣟⣡⣄⠀⣸⠃⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣧⠀⣄⠀⠀⣤⣼⣿⣿⣿⣿⣿⣿⣿⠟⡶⠃⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣷⣄⡉⠈⠉⠉⠉⠉⠉⠋⠉⠉⢀⡜⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣶⣶⣤⣤⣤⣤⣤⣤⣶⡟⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⢀⣿⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢀⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⣠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡛⠛⠻⠛⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⡓⠂⢠⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡏⢹⣸⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡿⡿⠛⢁⣼⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣤⣶⣄⢀⣀⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣤⣤⣤⣤⣀⣀⠀⠀⠹⣿⣿⣿⣿⠟⠁⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⣠⣴⠾⠛⠉⠉⠉⠀⠀⠀⠀⠀⠉⠉⠉⠛⠷⣶⣼⣿⣉⣁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣠⡾⠛⠉⠛⠟⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⡏⠉⠙⠛⢶⣄⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⣾⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⣿⣧⠀⠀⠀⠀ ⠀⠀⢠⣿⠃⠀⠀⠀⠀⠀⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠈⢿⡇⠀⠀⠀ ⠀⠀⠹⣿⡎⠀⠀⠀⣠⡾⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⢻⡆⠀⠀⣆⣿⡇⠀⠀⠀ ⠀⠀⠀⣿⡀⠀⡀⠀⣿⠁⠀⢠⣾⣿⡿⠆⠀⠀⠀⠀⠀⠀⢀⣾⣿⡿⠆⠀⠀⠀⢈⣿⠀⣄⣾⡿⠁⠀⠀⠀ ⠀⠀⠀⠘⣿⣧⣇⢀⣇⠀⠀⠘⣿⣿⣷⡆⠀⠀⠀⠀⠀⠀⠈⢿⣿⣷⠖⠀⠀⠀⢸⣿⣷⠿⠋⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠉⠙⠻⣿⣆⡀⠀⠀⠉⠉⠀⠀⠀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⣸⣿⠁⣀⣀⣀⠀⠀⠀⠀ ⠀⢀⣠⡶⠾⠛⠓⠶⣿⡟⠀⠀⠀⠀⠀⠀⠠⣾⣿⣿⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⣿⠟⠋⠉⠛⠻⣦⡀⠀ ⢀⣾⠋⠀⠀⠀⠀⠀⠘⣿⣠⣄⡀⠀⠀⠀⠀⠛⠿⠟⠁⠀⠀⠀⠀⠀⡀⡀⠀⣴⣾⡏⠀⠀⠀⠀⠀⠈⣿⡄ ⢸⣯⠀⢠⠀⠀⢀⣄⣠⣿⠿⢿⣷⣤⣦⣀⣤⣤⣤⣤⣀⣀⣀⣼⣆⣼⣷⣿⡾⠿⢿⣧⣀⣦⠀⠀⣤⠀⣸⡧ ⠘⠿⣷⣾⣷⣤⠾⠿⠛⠁⠀⠀⠀⠁⠀⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠁⠀⠀⠀⠀⠉⠛⠻⠷⠾⠿⠟⠛⠁

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⡿⣆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣧⡈⠓⠦⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠰⣶⠦⠤⠤⠤⠤⠤⠤⣿⣿⡄⠀⠈⠙⠓⠦⢄⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠘⢲⣄⡀⡀⠀⠀⠀⠀⠨⠷⠀⠀⠀⠀⠀⠀⠉⠳⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⢀⡴⠋⢉⡁⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣴⠋⠂⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢱⣀⣦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣀⣠⠞⠁⣴⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⠥⠾⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠉⠉⠙⢻⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠻⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡞⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣶⡄⠀⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢠⡇⠀⡶⢦⣴⣤⣀⣀⣀⣄⠀⠀⣀⠀⠀⠀⢀⢀⠀⠀⢸⡿⣿⠀⠀⠀⠀⠀⠀⠈⢧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣼⣿⣿⡷⠀⢸⣿⡆⢸⠀⠉⠁⠈⠛⢻⣿⡟⠛⡿⠛⠂⢸⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠙⠦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣠⣾⠟⠛⣿⠇⠀⢸⣿⣿⡿⠀⠀⠀⠀⠀⢸⣿⣿⣦⡇⠀⠀⢸⣿⣇⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣍⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢰⠏⠀⣠⡟⠀⠀⠈⠻⡿⠃⣀⡀⠀⠀⠀⠈⣿⣿⣿⠁⠀⠀⠈⡉⣿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢦⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣯⠀⠘⣿⣿⣠⠀⠀⠀⠀⠀⠹⣿⡽⠃⠀⠀⠈⠉⠀⠀⠀⠀⠰⠁⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡗⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣇⠀⠀⠈⠻⣿⡢⣀⡀⢀⡴⠞⠙⠦⣄⠀⠀⠀⠀⠀⠀⢀⡴⠃⠀⢹⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⣦⠀⠀⠀⣈⣿⢿⣋⠷⠀⠀⠀⠀⠀⠙⠀⠀⠀⠐⠚⠉⠀⠀⠀⢀⣸⣿⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣺⡄⠀⠀⠀⠀⠘⢿⠲⢄⠀⠀⠀⠀⠀ ⠀⠀⠙⠷⠶⠛⠋⠀⠀⣿⣿⣶⣶⣬⣥⣀⣤⣤⣤⣤⣤⣤⣤⣴⣾⣷⣿⣿⠁⠙⠦⣄⡀⠀⠀⠀⠀⠀⢠⣴⠟⠀⠀⠀⠀⠀⠀⠘⡇⠈⠳⡄⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢰⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡶⢤⣄⡈⠙⠲⠤⠤⢤⡴⠟⠁⠀⠀⠀⠀⠀⠀⠀⢠⡇⠀⠀⢹⡀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⣴⡫⡖⠉⠉⠉⠉⠛⠻⠛⠛⠋⠙⠛⠉⠉⠉⠉⠉⠉⠁⠀⠀⢯⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⣧⡾⣦ ⠀⠀⠀⠀⠀⠀⠈⣹⣸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣏⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠇⠀⠀⠀⢠⡟⣿⢸ ⠀⠀⠀⠀⠀⠀⠀⢿⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡏⠀⠀⠀⠀⢈⣼⣿⣿ ⠀⠀⠀⠀⠀⠀⠀⠾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⣄⠀⠀⠀⠀⠀⠀⠀⢀⡰⠟⠀⠀⠀⠀⢀⣼⢿⣿⠁ ⠀⠀⠀⠀⠀⢀⣤⣴⣯⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢤⡴⢖⠒⠒⠀⠀⠀⠈⠳⢤⣤⣤⠤⠔⠒⠉⠀⠀⠀⠀⣀⣴⣻⣵⠟⠁⠀ ⠀⠀⠀⠀⠀⠀⣼⢋⣿⡆⡤⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⡶⠀⢰⣿⣿⡷⠀⠀⠀⠀⠀⠀⠀⠀⢙⣦⣠⡀⠀⠐⠲⣦⣴⣶⣿⡿⣟⣽⡿⠃⠀ ⠀⠀⠀⠀⠀⣸⣧⣿⣿⡇⡇⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⣄⣿⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢻⡛⠶⠤⢤⣀⣀⣀⣀⡡⠼⠟⠁⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣿⠿⣿⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⣿⡏⣽⣧⡂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⡴⠋⣠⠀⡇⠀⠀⠀⠀⠀⣿⠀⠀⢸⠀⠀⠀⠀⠀⠀⢺⡃⠻⣿⣽⣶⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⣷⣀⣿⣼⠁⣴⡀⠀⠀⠀⣿⠀⣤⡿⢓⠀⠀⠀⠀⠀⣿⡆⣸⣿⣿⣷⡀⢠⠇⠀⠀⠀⠀⠀⠀⠘⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠈⠻⠿⠿⣿⡀⣿⠄⢉⣶⣴⡟⠛⠿⣇⢸⡦⣄⠈⣇⠀⡿⠶⣿⠟⡟⠻⠷⢾⠁⠲⢶⢦⠀⣀⣀⢰⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠉⠉⠀⠀⠀⠀⠀⠻⠾⠛⠛⠛⠛⠚⠃⠀⠘⠛⠓⠒⠒⠛⠛⠛⠛⠛⠛⠛⠛⠋⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⠀⠀⠀⢀⣤⠖⠒⢦⣄⠀⠀⣠⣄⣠⣄⠀⠀⠀⡴⠒⠲⢤⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢠⡖⠋⠁⠀⠀⡎⢹⣷⠟⠛⠛⠉⠉⠙⣦⠞⢁⡗⠀⠀⠙⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⡇⠀⠀⠀⣸⠃⢺⣿⠆⣠⠀⠀⠀⠀⠀⠀⢸⡀⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢧⡀⠀⣴⢃⣀⠈⢿⡞⠁⠀⣀⣀⠀⠀⠀⠈⢷⡀⠀⠀⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠈⢱⠛⢛⡉⠉⠁⠀⠀⠀⢨⣉⡉⠓⠂⠀⠀⠀⡟⠒⠶⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢸⠀⣿⣿⡿⠀⠀⠀⠀⢻⣿⣶⠀⠀⠀⠀⠈⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢠⡴⢶⡟⠀⠙⢛⣷⣿⢭⡀⠀⠈⠙⠃⣀⡶⢦⡀⠀⣽⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡀⠀⠀⢠⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢹⡅⠀⠙⠒⠲⡟⠳⣷⡶⠋⠒⢠⠦⠼⠏⠀⢈⣧⣤⣾⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⣿⠻⠍⠛⢯⠉⠲⣴⢶⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢹⡳⠀⣰⣾⣷⣴⠚⠳⣤⡴⠛⠦⣄⠀⢰⣞⣹⣿⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠉⠲⣄⠀⠀⠀⠸⠀⢹⡆⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠉⠉⠁⠈⠉⢿⡓⠶⠾⠖⠀⠀⠈⠛⠻⠖⠛⠀⠈⢲⣦⢤⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⠞⡵⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠳⣤⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠄⠀⠀⠀⣴⣿⡷⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠉⠓⠒⠶⠶⠦⠤⢄⣀⡀⠀⠀⢀⡾⠃⠀⠀⠀⠀⠁⣸⠃⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠓⢶⠋⠀⠀⠀⠀⠀⡠⠾⡷⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢀⣾⠀⠀⠀⠀⠀⠀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⡴⣶⡋⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⠆⠀⠀⠀⠀⠀⢳⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢿⣻⡿⠿⠙⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⣷⣀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣧⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣼⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⡠⠇⠙⠳⣷⡄⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣠⠤⠔⠚⠋⠁⠀⠀⠀⠀⠀⠉⢻⡷⣄⠀⠀⠀⠀⠀⠀⠀⢸⣄⣀⣀⠀⠀⠀⠀⠀⠀⠀⣄⠀⠀⠀⠀⠀⠀⠀⠀⢻⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⠁⠈⠳⣄⠀⠀⠀⠀⠀⠸⡏⠋⡟⠛⠓⠾⠦⠶⣤⣀⣈⣧⡀⠀⠀⠀⠀⠀⠀⠘⠓⠶⣆⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣰⠃⠀⠀⠀⣠⠖⠒⠒⠒⠒⠒⠢⠾⠏⠀⠀⠀⠸⡄⠀⠀⠀⠀⢠⢷⡀⢻⡀⠀⠀⠀⠀⠉⠀⢿⠀⠙⢦⠀⠀⠀⠀⠀⠀⠀⠀⢻⣟⠀⠀⠀⠀⠀⠀⠀ ⠀⡼⠃⠀⠀⠀⡰⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢷⠀⠀⠀⠀⠀⣾⠃⠈⠳⢤⣀⠀⠀⠀⠀⠈⠣⣄⡀⠳⣄⣀⠀⠀⠀⠀⠀⠈⢟⠀⠀⠀⠀⠀⠀⠀ ⠰⣧⡄⠀⠀⡼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣇⠀⠀⠀⠀⣾⠀⠀⠀⠀⠈⠳⣆⠀⠀⠀⠀⣼⣧⠀⠀⠈⠙⠦⣄⠀⠀⠀⠸⡄⠀⠀⠀⠀⠀⠀ ⠀⠹⠷⠴⠚⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡄⠀⠀⠀⣿⠀⠀⠀⠀⠀⠀⡿⠀⠀⠀⠀⡿⠋⠀⠀⠀⠀⠀⠘⣆⠀⠀⠀⢳⡄⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣷⠀⠀⠀⣿⠀⠀⠀⠀⢀⡼⠃⠀⠀⠀⣸⠁⠀⠀⠀⠀⠀⠀⠀⢸⡆⠀⠀⠀⢳⡀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣿⣠⣀⡀⢹⡀⠀⢠⣞⠟⠀⠀⠀⠀⣰⠇⠀⠀⠀⠀⠀⠀⠀⠀⣀⣧⢤⡤⡤⠀⢧⡀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⣿⢷⠋⠈⠁⣤⠇⠀⠸⣿⣀⣀⣀⣠⠖⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⣟⣇⢸⡇⠀⣔⡟⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠚⠓⠒⠚⠉⠀⠀⠀⠀⠉⠉⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠛⠚⠓⠊⠉⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣉⣙⣋⣉⡉⠓⠂⠀⠀⠀⠒

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⣀⣀⣀⣀⣀⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣤⡾⠛⠉⠉⠉⠉⠀⠀⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠛⠶⣄⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⡿⡋⠁⠀⣰⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣄⠈⠻⣦⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⢿⠞⠀⣀⣼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠳⡷⣄⠈⠻⣦⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⡽⣣⢖⣋⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠰⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠤⡀⠀⠀⠀⠀⠀⠙⣞⣦⡀⠀⠙⢷⣄⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⣠⣾⠏⠀⠀⣰⡟⢞⡟⠀⠀⠀⢀⣤⣶⡶⣶⣤⠀⠀⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⢿⣿⣶⡦⣀⠀⠀⠀⠘⣞⣾⣆⠀⠈⠻⢷⣤⣀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⣀⣠⡼⠟⠁⢀⡴⢣⣿⠇⡼⠁⠀⠀⣰⣿⣿⣯⣿⣿⣻⣧⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⢸⡿⣿⣿⣽⣷⣯⢦⡀⠀⠀⢻⠘⣿⣷⣄⠀⠀⢽⣿⠀⠀⠀⠀⠀⠀ ⠀⠀⢙⣶⠋⠉⠀⠀⣀⠴⠋⠀⣿⡏⣼⠇⠀⠀⠈⢻⡿⣿⣿⣿⣿⣿⠇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢷⡿⠿⣿⣿⣛⠉⠁⠀⠈⢿⢷⣾⣿⠈⠳⢄⠀⠙⠾⣿⣿⣀⠀⠀ ⠀⢀⣼⡟⠀⠀⢀⠀⠀⠀⠀⢸⣿⢠⣿⠀⠀⠀⠀⠀⠈⠀⠀⢠⡾⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠳⡄⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⣿⠀⢠⡀⠈⠢⣀⠈⢿⣷⣦⣀ ⠀⣠⣟⠀⢀⠴⠋⡠⠀⢠⠆⠀⣿⢸⡏⠀⠀⠀⠀⠀⠀⠀⣠⠏⠀⠀⠀⠀⢀⣀⣤⣤⣤⣤⣄⡀⠀⠀⠀⠀⠙⣆⠀⠀⠀⠀⠀⠀⠀⠘⣿⣿⠀⠀⠙⢢⡳⡌⠳⣼⣿⣬⡉ ⡰⣿⡟⠀⢀⠔⠋⢀⡴⠋⠀⠀⣿⢸⡇⠀⠀⠀⠀⢀⣀⠴⠃⠀⠀⠀⢠⣾⣿⣿⣿⣿⣿⣿⣿⣿⣷⡄⠀⠀⠀⠘⠧⣀⠀⠀⠀⠀⠀⢀⣿⣿⢸⠀⠀⢢⠀⠙⢦⡈⣿⢷⡀ ⠾⢿⣷⡔⠁⢀⡴⠋⠁⠀⢀⣤⣿⣸⡇⠀⢠⠴⠒⠋⠁⠀⠀⠀⠀⠀⠸⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⡇⠀⠀⠀⠀⠀⠈⠓⠲⢤⡀⠀⢸⣿⣿⢸⠀⠐⣆⠳⣄⠀⠓⣿⡄⠀ ⠀⢹⣿⣧⠖⠁⢀⡴⠃⢀⡾⠙⣷⣿⡇⠀⣏⠀⢷⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⠃⠀⠀⠀⠀⠀⠀⠀⢀⡀⢣⠀⣾⣿⠏⡏⠀⠀⠮⣆⠘⢧⢀⣿⣷⠀ ⠀⠈⣿⣇⣤⠶⢋⡴⡠⣾⠁⠀⣿⣿⡇⠀⠘⠀⣾⣦⠀⠀⠀⠀⠀⠀⠀⠈⠛⠻⢿⣿⣿⣿⡿⠛⠁⠀⠀⠀⠀⠀⠀⢀⣴⣿⢆⢸⠀⣿⣿⣼⠀⠠⣄⠢⣌⠟⣎⣹⣿⣿⠀ ⠀⠀⢻⣿⡟⠀⣫⢞⠝⠁⠀⠀⣼⣹⣧⢀⡀⠀⣿⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⣾⣿⠦⠄⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⡟⡟⠀⢰⣿⡏⣿⠀⠀⢿⡳⣄⢠⣾⠿⡿⠟⠀ ⠀⠀⠈⠙⣿⣟⣁⡀⠀⣀⣠⢤⡟⣿⡏⠜⡤⠀⢃⢻⣿⣷⣄⡀⠀⠀⠀⠠⣀⣠⡼⢿⡿⣦⣐⣄⡀⠀⠀⠠⠤⣴⡟⣿⡿⡸⠀⠀⣾⣿⡇⡙⣆⠈⢦⣘⣮⣿⠻⠀⠀⠀⠀ ⠀⠀⠀⠀⠉⢻⣿⢿⠞⣙⣿⢟⣾⣿⣇⢠⡇⠀⠸⡇⢻⣷⡉⠛⠛⣿⠛⠛⠉⠉⠀⢸⡇⠀⠉⠉⠛⢻⣿⣿⠟⠉⠀⣾⡇⠀⠀⢠⣿⣿⣧⢠⡝⡇⢸⡟⢿⠃⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⢹⣞⢿⣿⣠⣾⣿⣿⣿⣿⢁⠀⠀⠹⣌⣻⡟⠀⢹⣿⡄⠀⠀⠀⠀⢸⠀⠀⠀⠀⢀⣿⢻⡏⠀⠀⣻⡿⠀⠀⡐⠸⣿⣿⣿⡀⠹⣧⡿⠁⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠉⠙⢛⣩⣿⠹⠻⢿⢇⡼⠀⠀⠀⠹⡏⢿⡄⠈⣿⡇⠀⠀⠀⠀⠘⠀⠀⠀⠀⢸⣯⡿⠀⠀⣰⣿⠁⣄⡀⣿⡄⠙⠈⢿⣿⣦⡿⠁⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⢠⡏⢸⡇⠀⠰⡾⡞⢁⣦⠀⠀⠀⢧⣈⢷⡄⠙⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⣼⡟⠁⠀⣴⣿⠃⠀⣱⣷⡿⡇⠀⡇⢸⣆⠹⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⢸⡇⠀⠀⠇⡇⣸⡯⠀⠀⠀⠈⢻⡀⠻⣄⠸⣷⡀⠀⠀⠀⠀⠀⠀⣴⡟⢀⣤⣾⡿⠃⠀⠁⠹⠋⣧⠀⠀⠁⢀⡟⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⣧⢼⡇⠀⠀⠀⢣⡟⣠⣰⡃⠀⠀⠀⠱⡄⠙⣦⡘⢿⣦⣄⣀⣀⣠⡾⢋⣴⣿⣿⠟⠀⣀⠀⢸⠀⠀⠛⠁⠀⢀⣾⡇⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣼⡷⡀⠀⠀⢸⣷⢛⣿⣇⡆⠀⠀⠀⠘⠦⣌⠻⣶⣬⣉⠉⠉⣀⣴⣿⠿⠟⠕⠁⢠⢻⡟⣿⡖⠀⠀⠀⠀⡼⠉⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢧⢱⣷⠀⠀⠀⠁⣿⢹⠋⣿⠃⠀⠀⠀⠀⠈⠓⢼⡻⣯⣭⣭⣿⢟⡡⠔⠂⠀⠀⠀⣾⣿⣿⡇⠀⠀⠀⢠⡇⡈⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠸⡏⢿⣇⠀⠀⠀⠛⢿⣰⣿⣾⡆⠀⠀⠀⢀⠀⠀⠈⠁⠒⠒⠒⠉⠀⠀⠀⠠⠀⠚⣿⠻⣦⠀⠀⠀⢀⡟⢠⣷⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠻⣬⠻⡆⠀⠀⠀⠸⠟⠾⠀⣷⢼⣆⠀⠈⡇⣰⢿⣤⠀⠀⣀⢀⠀⠀⣰⣿⠅⢠⢿⡆⠁⠀⠀⢀⡞⢀⢯⡟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣧⡐⠀⠀⠀⠀⠀⣼⣴⢿⠃⠀⠀⣦⣷⠏⢪⣿⣄⡾⣿⣿⠀⡼⠫⠏⣰⠏⠀⠀⠀⠀⠀⡞⠀⣯⠎⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠙⣄⠀⠀⠀⠀⠀⠀⠈⠀⠀⠈⠈⠁⠀⠁⣿⣏⠀⣿⣞⠇⠀⢀⠾⠁⠀⠀⠂⠀⠀⠈⣠⠞⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠓⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣴⠋⠘⠀⠘⠉⠀⠴⠋⠀⠀⠀⠀⠀⠀⠀⠴⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠈⠈⢀⠀⠀⡀⡇⠉⠐⢈⠀⡐⡉⣙⠚⠛⠇⠐⠀⡁⠸⠆⠋⠀⠘⡃⡔⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

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⣿⡇⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⡅⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⠼⣤⠀⣤⢤⣀⣤⠤⣄⡀⡄⠀⡄⠀⠀⢼⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣄⣼⠰⣎⣹⡇⣿⣀⣽⠉⣧⡠⡇⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢰⠉⠁⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠔⠁⠈⢠⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⡄⠀⠀⠀⠑⠢⠤⠀⠤⠤⠤⠀⠀⠒⠁⠀⠀⠀⡞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢁⠀⢀⠶⠰⢀⠀⠀⠀⠀⠀⠀⠀⠆⠀⠀⠰⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣎⠇⣬⣇⢢⠀⠀⠀⠀⢀⠀⠀⡄⣠⣄⠡⠀⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⡜⢻⣿⣿⡷⠀⠀⠀⢂⠀⠀⡂⢼⣿⣿⠆⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣞⠫⠌⠉⡹⣁⢢⡑⢌⠂⠋⡜⢀⠀⠃⠈⢀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢨⡏⣳⢈⠐⣱⠣⠒⠈⣀⠴⣰⠀⠀⢈⠀⠀⠀⠄⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡇⠡⠦⣾⠃⠁⢨⣴⣿⣿⣿⣶⡤⠀⢈⠠⠄⢊⠣⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢩⠐⣭⢱⠐⢢⠛⣿⣿⣿⣿⣿⣯⠀⠀⢡⠈⠀⠀⠑⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠌⢳⡀⠬⢺⡽⣿⣿⡿⣟⠭⠀⢄⠂⡀⠀⠀⠀⢡⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⠂⠀⠀⠡⢁⠋⡜⢩⠉⠍⢛⠅⡻⠑⡈⠦⡐⣁⠂⢀⠀⠈⠂⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿ ⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢠⢓⣀⡒⢁⠂⡀⢀⠀⠁⢈⠰⠁⢈⠀⠐⡀⠱⢀⠢⡘⠀⡠⡀⢶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿🐶

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⠀⠀⠀⠀⠀⢻⣿⣿⣿⣷⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣿⣿⣿⡿⡽⣞⡽⣻⢟⣿⣿⣿⣿⣿⣿⠟⠁⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣿⣿⠞⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⢀⣾⣿⣇⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣼⢳⣝⣮⣿⣿⣿⣿⠿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠴⠀⣾⣿⠋⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⠀⣼⣿⠇⠈⠛⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢿⣿⣿⣿⣿⣿⣿⠿⠛⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⣀⠀⣛⠀⣿⣟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⢀⣿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢶⣀⣿⣯⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢀⣿⡏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠈⠿⣿⣇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⣿⣧⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣿⣯⠀⠀⠀⠀⣴⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣇⡀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠘⢿⣿⣦⣴⣾⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠹⣿⣷⡀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣠⣿⣿⣏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠡⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣧⠀⠀⠀⠀⠀⠀⠀ ⠀⣰⣿⣿⡿⠏⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠠⠧⠀⢿⣿⣧⠀⠀⠀⠀⠀⠀ ⢰⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⣿⣿⠀⠀⠀⠀⠀⠀ ⢸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢻⣿⡂⠀⠀⠀⠀⠀ ⠸⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣸⣿⡇⠀⠀⠀⠀⠀ ⢀⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠿⣿⣷⠀⠀⠀⠀⠀ ⠈⠿⣿⣶⣦⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢾⣿⠀⠀⠀⠀⠀ ⠀⠀⣸⣿⣯⡉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣻⣿⠀⠀⠀⠀⠀ ⣶⣾⣿⣿⠟⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣽⣿⠀⠀⠀⠀⠀ ⢽⣿⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣤⣀⣾⣿⣤⡄⠀⠀⠀ ⠈⣿⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠙⠛⠿⣿⣿⣿⠀⠀⠀ ⢰⣿⣿⣿⣶⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣄⡀⣴⣿⣿⡇⠀⠀⠀ ⠈⣿⣿⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⠛⠁⣿⣿⠀⠀⠀⠀⠀ ⠀⠙⣿⣷⣄⠀⢀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⢿⣿⠀⠀⠀⠀⠀ ⠀⠀⢻⣿⣿⠙⠉⠁⣠⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⠀⣿⣿⠀⠀⠀⠀⠀ ⠀⠀⠈⢻⣿⡆⠀⠀⠿⠃⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢐⠀⣽⣿⠀⠀⠀⠀⠀ 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