Holstein's Tour

Farmer John has two breeds of cows on his farm: Holsteins and Guernseys. The Holsteins are numbered from $1$ to $H$, and the Guernseys are numbered from $1$ to $G$. Each cow is located at a point in the 2D plane. Farmer John begins his tour at Holstein $1$ and must finish at Holstein $H$. He needs to visit every cow, but for convenience he wishes to visit the cows in the order of their numbering within each breed. In other words, in the overall tour of $H+G$ cows, the sequence of Holsteins $1,2,\ldots,H$ and the sequence of Guernseys $1,2,\ldots,G$ must each appear as a (not necessarily contiguous) subsequence.

When moving from one cow at point $(x_1, y_1)$ to the next cow at point $(x_2, y_2)$, Farmer John expends energy equal to the square of the Euclidean distance, i.e.,

Your task is to determine the minimum total energy required for Farmer John to complete his tour under these conditions.

inputFormat

The first line of input contains two integers $H$ and $G$ ($1 \leq H \leq 1000$, $1 \leq G \leq 1000$), representing the number of Holsteins and Guernseys respectively. The next $H$ lines each contain two integers, representing the $x$ and $y$ coordinates of the Holstein cows in order. The following $G$ lines each contain two integers, representing the $x$ and $y$ coordinates of the Guernsey cows in order.

outputFormat

Output a single integer which is the minimum total energy that Farmer John expends in his tour.

sample

2 1
0 0
1 0
0 1

3