You are given N (N <= 100 000) d-dimensional (1 <= d <= 5) points, each having integer coordinates (X1, X2, ..., Xd). Then Q (Q <= 100 000) queries follow. For each query you are given a d-dimensional point (not necessarily from the given N) and you are to find the squared Euclidean distance to the closest point from the given N.

The coordinates of all N+Q points are generated randomly between -1 000 000 000 and 1 000 000 000.

The squared Euclidean distance between two points A and B is the sum of (A.Xi-B.Xi)*(A.Xi-B.Xi) for i=1, 2, ..., d.

Input

The first line contains three numbers - N, d and Q.

The next N lines contain d integers each - the coordinates of a point.

The next Q lines contain d integers each - the coordinates of a query point.

Output

Print the answer for each of the Q queries on separate lines.

Example

Input:
2 2 2
1 1
2 2
1 1
3 3

Output:
0
2