Description

Every day, Farmer John walks through his pasture to check on the well-being of each of his cows. Onh

is farm he has two breeds of cows, Holsteins and Guernseys. His HH Holsteins are conveniently number

ed 1…H, and his GG Guernseys are conveniently numbered 1…G (1≤H≤1000,1≤G≤1000). Each cowis loc

ated at a point in the 2D plane (not necessarily distinct).Farmer John starts his tour at Holstein 1

, and ends at Holstein HH. He wants to visit each cow along the way, and for convenience in maintain

ing his checklist of cows visited so far, he wants to visit the Holsteins and Guernseys in theorder

in which they are numbered. In the sequence of all H+GH+G cows he visits, the Holsteins numbered 1…

H should appear as a (not necessarily contiguous) subsequence, and likewise for the Guernseys. Other

wise stated, the sequence of all H+GH+G cows should be formed by interleaving the list of Holsteins

numbered 1…H with the list of Guernseys numbered 1…GWhen FJ moves from one cow to another cow trav

eling a distance of D, he expends D2 energy. Please help him determine the minimum amount ofenergy r

equired to visit all his cows according to a tour as described above.

Format

Input

The first line of input contains H and G, separated by a space.

The next H lines contain the xx and yy coordinates of the HH Holsteins, and the next G lines after

that contain coordinates of the Guernseys. Each coordinate is an integer in the range 0…1000

Output

Write a single line of output, giving the minimum energy required for FJ's tour of all the cows.

Samples

3 2
0 0
1 0
2 0
0 3
1 3

20