In a land far, far away from here there are no roads. How are people supposed to visit their family? Please help them by building a nice new road.

Build one big looping road that goes through the squares of the map. Every country (marked by thicker lines) has to be visited exactly once, not more. All of the borders between countries have to have roads on at least one side: two squares with a piece of border between them cannot both stay empty. In case there is a number written in a country, this indicates through how many squares in this country the road goes.

## Example

The region in the bottom right has only two exits, so the road must enter and leave through those exits. The region in the bottom left has only two neighbouring regions, so it has to connect to both of them. There is only one piece of border between it and its right neighbour, so it has to connect there. Now, the road enters and leaves the bottom centre region already, so the other square in this regions stays empty. This then means that the road has to visit the squares to the left, top, and right of this empty square.

Since two of the squares in the L-shaped middle right region are marked, the road has to connect them. Now, the top right square cannot be used anymore since it has only one remaining neighbour. Therfore the top right region has only one remaining square, with only two exists, so the road must go through it. Then, the remaining square of the L-shaped region stays empty and its three neighbours have to be marked as well. Now it is straightforward to complete the tour.

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