#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <climits>
#include <cfloat>
#include <map>
#include <utility>
#include <ctime>
#include <set>
#include <iostream>
#include <memory>
#include <string>
#include <cstring>
#include <vector>
#include <algorithm>
#include <functional>
#include <fstream>
#include <sstream>
#include <complex>
#include <stack>
#include <queue>
#include <cstring>
#include <numeric>
#include <cassert>
using namespace std;
const int MAXN = 505;
const int MOD = 5201314;
char graph[MAXN][MAXN];
int f[2][MAXN][MAXN];
int N, M;

// ensure 0 <= a, b < MOD
inline int add(int a, int b)
{
    a += b;
    if (a >= MOD) {
        a -= MOD;
    }
    return a;
}

int main()
{
    int T;
    cin >> T;
    while(T--){
        memset(graph,0,sizeof(graph));
        memset(f,0,sizeof(f));
        
        
        scanf("%d", &N);
        M = N;
        for (int i = 1; i <= N; ++i) {
            scanf("%s", graph[i]+1);
        }

        if (graph[1][1] != graph[N][M]) {
            puts("0");
            return 0;
        }
        f[1][1][N] = 1;
        int half = (N+M)/2;
        for (int l = 2; l <= half; ++l) {
            int tl = N+M-l;
            int n = l&1;
            int nn = 1-n;
            for (int r = 1; r <= N; ++r) {
                for (int tr = r; tr <= N; ++tr) {
                    f[n][r][tr] = 0;
                    int c = l+1-r;
                    int tc = tl+1-tr;
                    if (c < 1 || c > M || tc < 1 || tc > M || c > tc) {
                        continue;
                    }
                    if (graph[r][c] != graph[tr][tc]) {
                        continue;
                    }
                    int &tmp = f[n][r][tr];
                    tmp = add(tmp, f[nn][r-1][tr]);
                    tmp = add(tmp, f[nn][r-1][tr+1]);
                    tmp = add(tmp, f[nn][r][tr]);
                    tmp = add(tmp, f[nn][r][tr+1]);
                }
            }
        }
        int ans = 0;
        for (int i = 1; i <= N; ++i) {
            for (int j = 1; j <= N; ++j) {
                ans = add(ans, f[half&1][i][j]);
            }
        }
        printf("%d\n", ans);
    }
}