四维DP

!

#include<bits/stdc++.h>
using namespace std;
const int N = 55;
int w[N][N];
int f[N][N][13][14];
int n, m, k;
const int mod = 1e9 + 7;
int main()
{
    cin >> n >> m >> k;
    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= m; j++) {
            cin >> w[i][j];
            w[i][j]++;
        }
    }
    f[1][1][1][w[1][1]] = 1;
    f[1][1][0][0] = 1;
    for (int i = 1; i <= n; i++) {
        for (int j = 1; j <= m; j++) {
            if (i == 1 && j == 1)
                continue;
            for (int u = 0; u <= k; u++) {
                for (int v = 0; v <= 13; v++) {
                    int& val = f[i][j][u][v];
                    val = (val + f[i - 1][j][u][v]) % mod;
                    val = (val + f[i][j - 1][u][v]) % mod;
                    if (u > 0 && v == w[i][j]) {
                        for (int c = 0; c < v; c++) {
                            val = (val + f[i - 1][j][u - 1][c]) % mod;
                            val = (val + f[i][j - 1][u - 1][c]) % mod;
                        }

                    }
                }
            }
        }
    }
    int res = 0;
    for (int i = 0; i <= 13; i++)
        res = (res + f[n][m][k][i]) % mod;
    cout << res << endl;
    return 0;
}