Problem: K: Relief (Angel Relief)

Tenma, an angel, decides to save a city.

The city has a rectangular shape divided into north-south $ H $ parcels x east-west $ W $ parcels, with houses in each parcel.

The $ X $ th section from the north and the $ Y $ th section from the west are represented by $ (X, Y) $.

The house in parcel $ (i, j) $ is inhabited by $ A_ {i, j} $ people.

Tenshin chooses a rectangular area whose sides are parallel or vertical to north-south or east-west, and rescues all the people living in it one by one.

Tenshin does this for every possible rectangle.

Find the total number of times Tenma-san rescues people.

input

The integers $ H, W $ are given on the first line, separated by blanks.

Of the following $ H $ lines, the integers $ A_ {i, 1}, A_ {i, 2}, A_ {i, 3}, \ dots, A_ {i, W} $ are blank on the $ i $ line. Given as a delimiter.

output

Output the total number of times Tenma-san rescues people.

Constraint

* $ H, W $ are integers between $ 1 $ and $ 500 $
* $ A_ {i, j} $ are all integers greater than or equal to $ 1 $ and less than or equal to $ 9 $.



Input example 1


twenty two
1 2
4 8


Output example 1


60


For example, if you choose a rectangular area with $ (1, 1) $ in the upper left and $ (2, 2) $ in the lower right, you will rescue $ 15 $ people there one by one, so a total of $ 15 $ times. Relief.

$ 1, 2, 3, 4, 5, 8, 10, 12, 15 $ relief for each of the $ 9 $ rectangular areas, for a total of $ 60 $.

Input example 2


twenty three
one two Three
4 5 6


Output example 2


140






Example

Input

2 2
1 2
4 8


Output

60

Solution (in CPP):

Solution:
//include
//------------------------------------------
#include <vector>
#include <list>
#include <map>
#include <climits>
#include <set>
#include <deque>
#include <stack>
#include <bitset>
#include <algorithm>
#include <functional>
#include <numeric>
#include <utility>
#include <sstream>
#include <iostream>
#include <iomanip>
#include <cstdio>
#include <cmath>
#include <cstdlib>
#include <cctype>
#include <string>
#include <cstring>
#include <ctime>
#include <queue>
#include <random>
#include <complex>
#include <regex>

using namespace std;

#define SHOW_VECTOR(v) {std::cerr << #v << "\t:";for(const auto& xxx : v){std::cerr << xxx << " ";}std::cerr << "\n";}
#define SHOW_MAP(v){std::cerr << #v << endl; for(const auto& xxx: v){std::cerr << xxx.first << " " << xxx.second << "\n";}}


int main() {

    long long H, W;
    cin >> H >> W;

    vector<vector<long long>> A(H, vector<long long>(W));
    for (int i = 0; i < H; i++) for (int j = 0; j < W; j++)cin >> A[i][j];

    vector<long long> x(W);
    for (int i = 0; i < W; i++) x[i] = (i + 1) * (W - i);
    vector<long long> y(H);
    for (int i = 0; i < H; i++) y[i] = (i + 1) * (H - i);

    vector<vector<long long>> B(H, vector<long long>(W, 1));
    for (int i = 0; i < H; i++) for (int j = 0; j < W; j++) B[i][j] *= x[j];
    for (int i = 0; i < W; i++) for (int j = 0; j < H; j++) B[j][i] *= y[j];

    long long ans = 0;
    for (int i = 0; i < H; i++) for (int j = 0; j < W; j++) ans += A[i][j] * B[i][j];

    cout << ans <<endl;

}