⣿⢿⣻⡿⣟⣿⢿⣻⡿⣟⣿⢿⣻⡿⣟⣿⢿⣻⡿⣟⣿⢿⣻⡿⣟⣿⢿⣻⡿⣟⣿⢿⣻⡿⣟⣿⢿⣻⡿⣟⣿⢿⣻⡿⣟⣿⢿⣻⡿⣟⣿⢿⣻⡿⣟⣿⢿⣻⡿⣟⣿⢿⣻⢿⣷ ⣿⣻⣽⠛⠛⠚⠛⠛⠛⠛⢺⣟⣯⡟⠛⠚⠛⠛⠛⠛⠚⠛⠛⠛⠛⠚⠛⠛⠛⠛⠚⠛⠛⠛⠛⠚⣻⣯⢿⡛⠚⠛⠛⠛⠛⠚⠛⠛⠛⠛⠚⠛⠛⠛⠛⠚⠛⠛⠛⠛⠚⠛⣿⢯⣿ ⣿⣽⣻⣤⣤⣤⣤⣤⠀⠀⢸⣯⢿⣧⣤⣤⣤⣤⡄⠀⢠⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⣤⣤⣤⠀⠀⣽⢾⣿⠀⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀⠀⣤⣤⣤⣤⣤⡿⣯⣿ ⣿⣞⣯⣿⣽⣯⢿⣽⠀⠀⢸⣯⣿⣽⣯⡿⣽⢯⡇⠀⢸⡿⣽⣯⣿⣽⢯⣟⡿⠀⠀⣿⢯⣿⠀⠀⣾⣻⣿⠂⠀⢸⡿⣽⣯⣿⣽⣯⣿⣽⣯⣿⣽⣯⣇⠀⠠⣿⣯⣿⣽⣯⣟⣷⣿ ⣿⡾⣿⠀⠀⣿⣯⢿⠀⠀⠀⠀ ⠀⠀⢸⣟⡿⡇⠀⢸⣟⣷⡇⠀⠈⣿⣯⣟⠀⠀⡿⣯⣿⠀⠀⠀⠀⠀ ⠀⢸⡿⣽⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⣞⣿ ⠙⠛⠛⠀⠀⣿⡽⣿⣷⣾⡶⣷⢿⡆⠀⢸⣯⢿⡇⠀⢸⣟⣾⡇⠀⢈⣿⢾⡽⠀⠀⣿⣳⣿⠀⠀⢶⡿⣞⣷⣟⣯⢿⣻⡇⠀⢸⣶⣷⣾⣶⣷⡾⣾⣶⢿⣶⣷⣾⣶⣷⡾⣿⣽⣻ ⠀⠀⠀⠀⠀⠻⠿⠷⠿⠾⠿⠯⠿⠇⠀⢸⣽⣻⡇⠀⠘⠿⠾⠇⠀⠠⣿⣻⣽⠀⠀⣟⡷⣿⠀⠀⣻⣽⢿⠷⠯⠿⠿⠿⠇⠀⢸⣟⣾⡷⠿⠾⠽⠷⠿⠿⠾⠷⠿⠾⠷⠿⣷⢯⣿ 🐥⠀⠀⠀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣀⣸⢯⣟⣇⣀⣀⣀⣀⣀⣀⣰⢿⣽⣞⠀⠀⣿⡽⣿⣀⣀⣽⡾⣿⠂⠀⢀⣀⣀⣀⣀⣸⢿⣞⣇⣀⣀⣀⣀⣀⣀⣀⣀⣀⡀⠀⠀⣿⢯⣿ ⠀⠀⠀⠀⠀⣿⣿⣻⣟⣿⣻⣟⣿⣻⣟⡿⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⣼⣻⠀⠀⣟⣿⣻⣟⡿⣧⣿⢿⠃⠀⢸⣿⣻⣟⣿⣻⢿⣼⣟⣿⣻⣟⣿⣻⣟⣿⣻⣟⣿⠀⠀⣿⣟⣿ ⣶⣶⣶⠀⠀⠙⠓⠛⠚⠓⠛⠚⠓⠛⠚⠛⠛⠓⠛⠚⠓⠛⠚⠓⠛⠚⣿⣞⡷⠀⠀⣿⡽⣷⠛⠛⣳⣿⣻⡁⠀⢸⡷⣿⡞⠓⠛⠛⠓⠛⠚⠓⠛⠚⠓⠛⠚⠓⠛⠛⠀⠀⣿⣞⣿ ⣿⣳⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡄⠀⢈⣿⢾⣻⠀⠀⣯⣟⣿⠀⠀⣽⢾⣿⠀⠀⢸⡿⣽⣧⢤⣤⣤⣤⡄⠀⢠⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⢿⣞⣿ ⣿⣽⢾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣟⣾⣳⣯⡇⠀⠠⣿⣻⢷⠀⠀⣿⣞⣿⠀⠀⢾⣻⣽⠂⠀⢸⣿⣽⣾⣻⣷⣻⢾⡇⠀⢸⣟⣾⣳⣟⣾⣳⣟⣾⣳⣯⣿⢯⣿ ⣿⢾⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢸⣟⣷⡇⠀⠐⣿⣽⣯⠀⠀⣷⢯⣿⠀⠀⣻⣽⣿⠁⠀⠀⠀⠀⠀ ⠀⢸⣟⡿⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⣿⢯⣿ ⣿⢯⣿⢶⣶⣾⣶⣾⠀⠀⢰⣾⣶⣾⣶⣾⣶⣶⡆⠀⢸⣟⣾⡇⠀⠠⣿⣳⣯⠀⠀⡿⣯⣿⠀⠀⣽⣞⡿⣿⡶⣷⣶⣾⡆⠀⢸⣯⢿⣟⣶⣶⣷⣶⡷⣾⣶⣶⣶⣷⠀⠀⣿⢯⣿ ⣿⣻⣾⠻⠽⣾⢷⣻⠀⠀⠸⠟⠾⠳⠟⢾⣳⢿⡇⠀⢸⣟⣾⡇⠀⠐⠟⠿⠞⠀⠀⣿⣳⣿⠀⠀⠺⠯⠟⠷⠻⢟⣾⣽⡇⠀⢸⣯⣿⡾⠟⠾⠳⠯⠟⠷⠻⠾⠽⠿⠀⠀⣿⢯⣿ ⣿⣳⣿⠀⠀⣿⣟⣿⠀⠀⢀⣀⣀⡀⠀⢸⣯⢿⡇⠀⢸⣟⣾⣇⣀⣀⣀⣀⣀⣀⣀⣿⣳⣿⠀⠀⣀⣀⣀⣀⣀⣸⣟⣾⡇⠀⢸⡷⣯⡇⠀⢀⣀⣀⣀⣀⣀⣀⣀⣀⠀⠀⣿⢯⣿ ⣿⣽⣻⠀⠀⣿⣻⣾⠀⠀⢸⣟⣿⡇⠀⢸⣯⢿⡇⠀⢸⣿⣷⣿⣯⣿⣽⣿⣽⣯⣿⣾⣯⣿⠀⠀⣿⣿⣿⣯⣿⣿⣾⣿⡇⠀⢸⣿⣽⡇⠀⢸⡿⣽⢯⡿⣽⢯⣟⣿⠀⠀⣿⢯⣿ ⣿⣞⣿⠀⠀⠈⠉⠉⠀⠀⢸⣟⣾⡇⠀⢸⣽⣻⡇⠀⠈⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⣿⣿⣿⠀⠀⠈⠉⠉⠉⠉⢹⣿⣿⡇⠀⠈⠉⠉⠁⠀⢸⣟⣿⡏⠉⠉⣿⢯⣿⠀⠀⣿⢯⣿ ⣿⢾⣻⢶⣖⡶⣶⣲⢶⡶⣾⢯⣟⡇⠀⢸⣯⣟⡇⠀⢰⡶⣖⡶⣶⣲⢶⣖⡶⣶⣲⣯⡷⣿⠀⠀⣴⡶⣶⠀⠀⢸⣷⣻⣧⢶⣶⣲⢶⣲⢶⣞⡿⣾⣏⠀⠀⣿⣻⣿⠀⠀⣿⢯⣿ ⣿⣻⣯⠿⠾⠿⡷⢿⣯⣿⡽⠿⠿⠇⠀⢸⣷⣻⡇⠀⢸⣟⣿⣽⠷⡿⢿⠾⠿⢷⢯⠷⠿⠿⠀⠀⢾⣽⣿⠁⠀⠸⠷⣯⠿⠿⡾⡽⢿⢯⣿⢾⠿⡽⠧⠀⠀⣿⣳⣿⠀⠀⣿⢯⣿ ⣿⣳⣿⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⢸⣷⣻⡇⠀⢸⣟⣾⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⣻⡷⣿⡁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⢀⣿⡽⣿⠀⠀⣿⢯⣿ ⣿⡽⣯⡿⣟⣿⢿⣿⠀⠀⢸⣿⢿⣟⡿⣟⣾⣽⡇⠀⢸⣟⣾⡇⠀⠠⣿⢿⣟⡿⣟⣿⢿⣟⡿⣟⣯⣿⡽⣟⡿⣟⡿⣟⡿⣟⡿⣟⣿⡇⠀⢸⣿⢿⣻⢿⣯⡷⣿⣿⠀⠀⣿⢯⣿ ⣿⡽⣿⠛⠛⠛⠛⠛⠁⠀⢸⣯⣿⡟⠛⠛⠛⠛⠃⠀⢸⡿⣞⡇⠀⠀⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⣟⣿⡟⠛⠛⠛⠛⠃⠀⠈⠛⠛⠛⠛⠛⣽⡷⣿⠀⠀⣿⢯⣿ ⣿⣽⢿⠀⠀⣤⣤⣤⣤⣤⣼⣷⣻⣧⣤⣤⣤⣤⣤⣤⣼⣟⡿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⠀⠀⣤⣤⣤⣤⣤⣼⣻⢾⡇⠀⢠⣤⣤⡄⠀⢠⣤⣤⣤⣤⣤⡿⣽⣿⠀⠀⣿⢯⣿ ⣿⣾⣿⠀⠀⣿⡟⣾⣽⣾⢳⣯⣷⡟⣾⢳⣿⡞⣷⡟⣾⣽⢻⣽⣷⣯⣷⣯⣷⡟⣾⣷⣯⣿⠀⠀⣾⣷⢻⡞⣷⣯⡟⣿⡇⠀⢸⣯⡟⡇⠀⢸⣯⣷⣿⣾⣽⢻⣽⣿⠀⠀⣿⣯⣿ ⣿⢾⣽⠀⠀⣿⡿⣽⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⠉⢉⣿⢾⣻⠉⠉⠉⠉⠉⠀⠀⠈⠉⠉⠉⠉⢹⡿⣽⡇⠀⢸⣯⢿⡇⠀⢸⣯⣷⡏⠉⠉⠉⠉⠉⠀⠀⣿⣞⣿ ⣿⢯⣿⠀⠀⣿⣟⣿⠀⠀⢰⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⡆⠀⠠⣿⣻⣽⠀⠀⣶⣶⣶⣶⣶⣶⣶⣶⣶⣶⣾⣻⢿⡇⠀⢸⣯⡿⣷⣶⡾⣷⣻⣏⠀⠀⣶⣶⣶⣶⣶⢿⣽⣻ ⣿⣻⢿⠀⠀⣿⣻⣾⠀⠀⠸⠿⠾⠷⠿⠾⠷⠿⠾⠷⢿⣞⣷⡇⠀⠠⣿⣻⢾⠀⠀⠿⠾⠷⠿⠾⠷⠿⠾⠷⠿⢾⣽⣿⡇⠀⠸⠷⠿⠷⠯⢿⡷⣿⡧⠀⠀⣿⣳⣿⠾⠽⣿⣞⣿ ⣿⡽⣿⠀⠀⣿⡷⣿⡀⠀⠀⠀⠀⠀⠀⠀⠀⢀⠀⠀ ⢸⣟⣾⡇⠀⠠⣿⢯⡿⠀⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⠀⣸⣷⣻⡇⠀⠀⠀⢀⠀⠀⢸⣿⣳⣏⠀⠀⣿⡽⣿⠀⠀⣿⣾⣿ ⣿⣽⣿⠀⠀⣿⡿⣽⢿⡿⣿⡿⣿⡿⣿⡿⣿⢿⡇⠀⢸⣟⣾⡇⠀⢀⣿⢿⣽⠀⠀⣿⡿⣿⢿⣿⢿⣿⢿⡿⣿⣟⡷⣟⡿⣿⢿⡿⣿⡇⠀⢸⡷⣿⡗⠀⠀⣿⣽⣿⠀⠀⠀⠀⠀ ⣿⢾⣽⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠃⠀⢸⣟⣾⡇⠀⠀⠛⠛⠛⠀⠀⠙⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⠛⢻⡿⣽⡇⠀⠈⠛⠛⠛⠀⠀⠛⠛⠛⠀⠀⠀⠀⠀ ⣿⢯⣿⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡼⣟⣾⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⣤⡼⣟⡿⣧⣤⣤⣤⣤⣤⣤⣤⣤⣤⣄⠀🐔⠀⠀⠀⠀ ⢿⣿⣳⣿⣾⣷⣿⣾⣷⣿⣾⣷⣿⣾⣷⣿⣾⣷⣿⣾⣽⣿⣳⣿⣾⣷⣿⣾⣷⣿⣾⣷⣿⣾⣷⣿⣾⣷⣿⣾⣷⣿⣾⣷⣿⣾⣽⣿⣽⣷⣿⣾⣷⣿⣾⣷⣿⣾⣽⣿⠀⠀⠀⠀⠀