Country X telecom services decided to upgrade the network connectivity. For this goal every city has to be connected to a single mesh-network. However, the cable is really pricy, so its overall length must be kept as low as possible. Find this length.

You have Country X map. Each city is represented by a black pixel on the map.

The answer is expected to have not less than 5 decimal points.

Simplified example:

Third-world banana republics like Country W, also face this problem. Country W map.

Minimum length: 3*sqrt(5) + 6*2 = 18.70820