Building a Fence

Leopold just won a large estate in a lottery. Besides the main mansion, where he now intends to live, the estate holds several other grand buildings. The grounds have no fence, which worries Leopold, so he wants to build one to keep out trespassers. To save money he decides it is enough for the fence to enclose the main mansion, subject to one important restriction: the fence must not run too close to any building. Seen from above, each building is contained in a surrounding forbidden rectangle, and no part of the fence may lie in the interior of any forbidden rectangle. The sides of every rectangle are parallel to the x- and y-axes, and every part of the fence must also be parallel to the x-axis or the y-axis.

Compute the minimum possible length of a valid fence that encloses the main mansion.

Figure 1: The main mansion (black) together with three other buildings and their forbidden rectangles. The thick line shows one shortest valid fence enclosing the main mansion.

The first line contains a positive integer m (1 ≤ m ≤ 100), the number of buildings. Each of the next m lines describes one forbidden rectangle with four space-separated integers tx, ty, bx, and by, where (tx, ty) is the upper-left corner and (bx, by) is the lower-right corner of the rectangle. All coordinates satisfy 0 ≤ tx < bx ≤ 10000 and 0 ≤ ty < by ≤ 10000. The first rectangle is the forbidden rectangle enclosing the main mansion.

Print one line containing a single positive integer: the minimum length of a valid fence enclosing the main mansion.