Fence Planning#10321
Farmer John's cows, conveniently numbered , have a complex social structure revolving around "moo networks" — smaller groups of cows that communicate within their group but not with other groups.
Each cow is situated at a distinct location on the 2D map of the farm, and we know that pairs of cows moo at each-other. Two cows that moo at each-other belong to the same moo network.
In an effort to update his farm, Farmer John wants to build a rectangular fence, with its edges parallel to the and axes. Farmer John wants to make sure that at least one moo network is completely enclosed by the fence (cows on the boundary of the rectangle count as being enclosed). Please help Farmer John determine the smallest possible perimeter of a fence that satisfies this requirement. It is possible for this fence to have zero width or zero height.
The first line contains n~(2 \le n \le 10^5) and m~(1 \le m < 10^5). The next lines each contain the and coordinates of a cow (nonnegative integers of size at most 10^8). The next lines each contain two integers and describing a moo connection between cows and . Every cow has at least one moo connection, and no connection is repeated in the input.
Print the smallest perimeter of a fence satisfying Farmer John's requirements.
Example 1