Background

The kindergarten attached to the University of Aizu is a kindergarten where children who love programming gather. Yu, one of the kindergarten children, loves rectangles as much as programming. Yu-kun decided to write a program to calculate the maximum score that can be obtained, thinking of a new play to get points using three rectangles.

Problem

Given the rectangles A and B of the H × W cells and the rectangle C of the h × w cells. (H and W represent the number of vertical and horizontal squares of rectangles A and B, respectively, and h and w represent the number of vertical and horizontal squares of rectangle C, respectively.)

As shown in Fig. 1, an integer is written in each cell of A, and each cell of B is colored white or black. Each cell in C is also colored white or black.


Figure 1
Figure 1


If there is a rectangle in B that has exactly the same pattern as C, you can get the sum of the integers written in the corresponding squares in A as a score.

For example, when the rectangles A, B, and C as shown in Fig. 1 are used, the same pattern as C is included in B as shown by the red line in Fig. 2, so 193 points can be obtained from that location.


Figure 2
Figure 2


If there is one or more rectangles in B that have exactly the same pattern as C, how many points can be obtained in such rectangles?

However, if there is no rectangle in B that has the same pattern as C, output "NA" (excluding "). Also, the rectangle cannot be rotated or inverted.

Constraints

The input satisfies the following conditions.

* All inputs are integers
* 1 ≤ H, W ≤ 50
* 1 ≤ h ≤ H
* 1 ≤ w ≤ W
* -100 ≤ a (i, j) ≤ 100
* b (i, j), c (i, j) is 0 or 1

Input

The input format is as follows.


H W
a (1,1) a (1,2) ... a (1, W)
a (2,1) a (2,2) ... a (2, W)
::
a (H, 1) a (H, 2) ... a (H, W)
b (1,1) b (1,2) ... b (1, W)
b (2,1) b (2,2) ... b (2, W)
::
b (H, 1) b (H, 2) ... b (H, W)
h w
c (1,1) c (1,2) ... c (1, w)
c (2,1) c (2,2) ... c (2, w)
::
c (h, 1) c (h, 2) ... c (h, w)


a (i, j) is the integer written in the square (i, j) of the rectangle A, b (i, j) is the color of the square (i, j) of the rectangle B, and c (i, j) Represents the color of the square (i, j) of the rectangle C. As for the color of the square, 0 is white and 1 is black.

Output

If there is a place in rectangle B that has exactly the same pattern as rectangle C, output the one with the highest score among such places.

If no such location exists, print “NA” (excluding “).

Examples

Input

4 4
10 2 -1 6
8 1 -100 41
22 47 32 11
-41 99 12 -8
1 0 0 1
0 0 1 0
0 1 0 1
0 0 1 0
2 3
1 0 1
0 1 0


Output

193


Input

3 3
5 1 3
2 5 9
0 1 5
1 0 0
0 1 1
0 1 1
1 1
1


Output

9


Input

3 4
4 1 9 1
9 1 -1 3
2 -4 1 10
1 1 0 1
0 1 1 1
1 1 0 0
1 4
1 1 1 1


Output

NA
#ifndef _WIN32
#include<iostream>
#endif
#include<cmath>
#include<iomanip>
#include<algorithm>
#include<vector>
#include<string>
using namespace std;
typedef long long LL;
#define FOR(i,bg,ed) for(int (i)=(bg);(i)<(ed);(i)++)
#define REP(i,n) FOR(i,0,n)
struct cww {
	cww() {
		ios::sync_with_stdio(false);
		cin.tie(0);
	}
};
template<typename T>
inline bool chmax(T& l, T r) {
	bool res = l < r;
	if (res)l = r;
	return res;
}

typedef vector<LL> V;
typedef vector<V> VV;
const LL INF = 1e15;
int main() {
	int R, C, RR, CC;
	cin >> R >> C;
	VV X(R,V(C)), Y(R, V(C));
	REP(i, R)REP(j, C)cin >> X[i][j];
	REP(i, R)REP(j, C)cin >> Y[i][j];

	cin >> RR >> CC;
	VV Z(RR, V(CC));
	REP(i, RR)REP(j, CC)cin >> Z[i][j];
	LL res = -INF;
	REP(i, R)REP(j, C)if (i + RR <= R&&j + CC <= C) {
		bool f = true;

		REP(a, RR)
			REP(b, CC)
			f &= (Y[i + a][j + b] == Z[a][b]);
		if (f) {
			LL ans = 0;
			REP(a,RR)
				REP(b, CC)
					ans += X[i + a][j + b];
			

			chmax(res, ans);
		}


	}

	if (res == -INF)cout << "NA" << endl;
	else cout << res << endl;
}
