Description:

CRB has a farm. His farm has a shape of convex polygon. There are K barns in the farm. All of them are strictly inside the polygon. CRB wants to build a fence enclosing all the barns. He prepared 2K posts and steel strips of exactly the same length with the perimeter of his farm. A post can only be placed on the vertex of the polygon(farm), and steel strips must enclose all posts. Now, CRB wonders whether he can build a fence with currently available resources or not. Can you help him?

Input:

There are multiple test cases. The first line of input contains an integer T, indicating the number of test cases. For each test case:

The first line contains an integer N – the number of vertices of the convex polygon(the shape of CRB‘s farm).

Then N lines follow, i-th line containing two integers x and y, the coordinates of i-th vertex. The vertices are given in counter-clockwise order.

The first line contains an integer K – the number of barns.

Each of the next K lines contains two integers x and y, the coordinates of the barn.

1 ≤ T ≤ 9

3 ≤ N, K ≤ 2 * 105

−109 ≤ x, y ≤ 109

All points(including farm vertices and barns) are pairwise different.

It is guaranteed that the barns never all lie on a line.

Output:

For each test case, output “Yes” if it is possible to build a fence, otherwise output “No”.

If possible, output a solution in the following format:

On the first line, output an integer M - the number of posts used to build a fence.

On the next line, you should output the indices of the vertices(1-based) where you place posts in increasing order.

Your solution will be accepted if M ≤ 2K and the length of the fence is not longer than the perimeter of the farm. Also, the barns must be strictly inside the fence.

Sample Input:

1 5 0 1 3 0 4 2 2 3 0 3 3 2 1 3 1 3 2

Sample Output:

Yes 4 1 2 3 4

Source:

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