⣿⣟⡿⣟⣿⣻⢿⣻⣟⡿⣟⣿⣻⢿⣻⣟⡿⣟⣿⣻⢿⣻⣟⡿⣟⣿⣻⢿⣻⣟⡿⣟⣿⣻⢿⣻⣟⡿⣟⣿⣻⢿⣻⣟⡿⣟⣿⣻⢿⣻⡇
⣿⣞⡿⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡇
⣿⣞⣿⣽⢾⣟⣯⡷⣿⣻⣽⢾⣟⣯⡷⣿⣻⣽⢾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⢿⣻⣽⡾⣟⣯⣷⡇
⣿⣞⡿⣞⣯⡿⣞⣿⣳⡿⣽⣻⡾⣯⣟⣷⢿⣽⡾⣷⡀⠀⠀⠀⠀⠀⠀⠀⠈⣿⣳⢿⣯⡷⣟⣯⡿⣾⣽⣟⡷⣯⣿⣻⢾⣽⣟⡷⣯⣿⣽⡇
⣿⣞⣿⣻⣽⣻⢯⣷⢿⣽⣟⡷⣿⣽⣻⢾⣯⣟⣿⡽⣧⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⢿⣾⡽⣿⣽⣻⢷⣻⡾⣿⣽⣞⡿⣯⣷⣻⢿⣽⡾⣽⡇
⣿⢾⡽⣷⣻⣽⢿⣽⡍⠈⠉⠉⠁⠉⠉⠙⣽⣯⣷⣟⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡽⣟⣾⣟⡷⣯⣟⡿⣽⣟⣷⣟⣾⢿⣽⣾⣻⣟⣾⣽⢿⡇
⣿⢯⣿⢯⣟⣾⣯⡷⣿⡄⠀⠀⠀⠀⠀⠀⠀⣿⣟⣷⣻⣾⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣯⣷⢿⣽⣻⣽⣻⣟⣾⣽⢾⣯⢿⣞⡷⣟⣾⣻⢾⣿⡇
⣿⢯⣟⣯⣿⣳⣯⢿⣽⡇⠀⠀⠀⠀⠀⠀⠀⣿⡾⣯⣷⣟⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⢷⣻⣯⣟⣷⣯⡷⣿⡽⣾⣻⣽⣯⣟⡿⣯⢿⡽⣟⣾⡇
⣿⢯⣟⣷⢯⣷⣟⣯⣷⡇⠀⠀⠀⠀⠀⠀⠀⣿⣟⣷⣻⣾⠀⠀⠀⠀⠀⠀⠀⠀⣿⡯⢿⣻⢾⣽⣾⣳⡿⣽⣻⣽⣟⣾⣳⡿⣽⣻⣯⢿⣻⣽⡇
⣿⢯⣿⢾⣻⡷⣯⣟⣾⡅⠀⠀⠀⠀⠀⠀⠀⣿⣯⣟⡷⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠈⠛⣽⣯⣷⢿⣻⣽⡾⣽⡾⣯⣟⣿⣳⢿⣻⣽⣽⡇
⣿⣻⡾⣟⣯⣿⣽⢾⣯⡇⠀⠀⠀⠀⠀⠀⠀⣿⣷⣻⢿⣽⠀⠀⠀⠀⠀⠀⠀⠀⣿⡇⠀⠀⠀⠀⠈⠛⣽⣟⣷⢿⣯⣟⣷⣟⡷⣿⣻⣽⢷⣽⣽
⣿⣳⣿⣻⢷⣻⡾⣯⣷⡇⠀⠀⠀⠀⠀⠀⠀⣿⡷⣟⣯⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣧⡀⠀⠀⠀⠀⠀⠀⠈⠙⠻⣾⣽⢾⣯⢿⣳⡿⣽⣻⢿⣽⡇
⣿⣳⣯⣟⡿⣽⣻⡷⣯⡇⠀⠀⠀⠀⠀⠀⠀⣿⡿⣽⣻⢾⠀⠀⠀⠀⠀⠀⠀⠀⣿⣷⣻⣶⡄⠀⠀⠀⠀⠀⠀⠀⢸⣯⢿⡾⣟⣯⢿⣻⣽⢿⣽⡇
⣿⣳⢿⡾⣟⣿⣳⡿⣯⡇⠀⠀⠀⠀⠀⠀⠀⣿⡿⣽⣯⢿⠀⠀⠀⠀⠀⠀⠀⠀⣿⡷⣯⣷⢿⠀⠀⠀⠀⠀⠀⠀⢸⣟⣯⣿⣻⡽⣟⡿⣾⣻⣽⡇
⣿⣽⣻⣽⣟⡷⣿⡽⣷⡇⠀⠀⠀⠀⠀⠀⠀⣿⣟⣷⣻⢿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣷⣯⣿⠀⠀⠀⠀⠀⠀⠀⢸⣯⡷⣟⣷⢿⣻⣽⡷⣿⣽⡇
⣿⣞⣯⡷⣿⡽⣷⣟⣯⡇⠀⠀⠀⠀⠀⠀⠀⣿⣟⣾⣻⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣾⣳⢿⠀⠀⠀⠀⠀⠀⠀⢸⡷⣟⣯⡿⣯⣟⡷⣿⣽⣽⡇
⣿⣞⣯⢿⣳⣿⣻⢾⣽⡇⠀⠀⠀⠀⠀⠀⠀⣿⣟⡾⣷⣻⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣾⣻⢿⠀⠀⠀⠀⠀⠀⠀⢸⣟⣯⡿⣽⣷⣻⣟⣷⣻⣽⡇
⣿⣞⣿⣻⣽⣾⣻⢯⣷⡇⠀⠀⠀⠀⠀⠀⠀⣿⣯⢿⣽⣻⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⣾⢯⣿⠀⠀⠀⠀⠀⠀⠀⢸⣯⡷⣿⣻⣞⣷⣯⢿⣽⣽⡇
⣿⢾⣳⣿⣳⣯⣟⣿⣳⡇⠀⠀⠀⠀⠀⠀⠀⣿⣽⣯⢿⣽⠀⠀⠀⠀⠀⠀⠀⠀⣿⣟⡾⣿⣽⠀⠀⠀⠀⠀⠀⠀⢸⣷⣻⣽⢷⣻⡷⣯⣿⣻⣽⡇
⣿⣻⣽⡾⣷⣻⢾⣯⣟⡇⠀⠀⠀⠀⠀⠀⠀⠈⠓⠛⢫⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⢿⣳⣿⠀⠀⠀⠀⠀⠀⠀⢸⣷⣻⡽⣟⣯⢿⣳⣯⢿⣽⡇
⣿⣽⢾⣻⢷⣟⡿⣾⡽⡇⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀⠀⠀⣿⣯⣟⡿⣾⠀⠀⠀⠀⠀⠀⠀⢸⣷⣻⣽⢿⣽⣻⢯⣟⣿⣽⡇
⣿⢾⣻⣯⢿⡾⣿⣽⣻⢿⣀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀⢸⣿⠀⠀⠀⠀⠀⠀ ⠀ ⣿⣷⣻⣽⢿⠀⠀⠀⠀⠀⠀⠀⠸⣷⣻⡽⣿⣞⡿⣯⢿⣾⣽⡇
⣿⣻⣽⡾⣿⡽⣷⢯⣟⣿⣻⢶⣄⡀⠀⠀⠀⣀⣠⣴⣿⣻⣄⠀⠀⠀⠀⠀⣠⣿⣳⣯⣟⣿⣄⠀⠀⠀⠀⠀⠀⠀⢻⣽⣻⢷⣻⣽⣟⡿⣾⣽⡇
⣿⣽⢾⣻⢷⣟⣯⣿⣻⣞⣯⣿⣞⡿⣿⣻⣟⡿⣽⣻⣞⣯⡿⣟⣿⣻⣟⡿⣿⣻⢷⣻⣷⣻⣾⣽⣻⣽⣻⢿⣽⣻⣟⡾⣷⣻⣟⣯⣷⣽⡇
⣿⢾⣟⣯⣿⢾⣻⣞⣷⢿⣽⡾⣽⣻⢷⡿⣽⣻⢯⣷⢿⣽⣻⢯⣟⣷⣻⣽⡷⣿⣻⣟⡾⣷⣻⣾⣽⣳⡿⣯⣷⢿⣞⣿⡽⣷⣻⣽⢾⣽⡇
⣿⣻⡾⣯⣟⣿⣻⣽⡾⣟⡷⣿⣻⡽⣿⣽⣻⣽⢿⣽⣻⣾⣻⢯⣿⣞⣯⣷⢿⣳⡿⣞⣿⡽⣷⣻⣾⣽⣻⢷⣯⡿⣾⢯⣿⣽⣻⢾⣟⣽⡇