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 <bits/stdc++.h>
using namespace std;

long long up[510][510];
long long down[510][510];
long long a[510][510];
int h, w;

int main(){
  cin >> h >> w;

  for(int i = 0;i < h;i++){
    for(int j = 0;j < w;j++){
      cin >> a[i][j];
    }
  }

  up[0][0] = 1;
  for(int i = 0;i < w;i++){
    if(i != 0){
      up[0][i] = up[0][i-1]+1;
    }

    for(int j = 1;j < h;j++){
      up[j][i] = up[0][i] * (j+1);
    }
  }

  for(int i = 0;i < h;i++){
    for(int j = 0;j < w;j++){
      down[i][j] = up[h-i-1][w-j-1];
    }
  }

  long long ans = 0;
  for(int i = 0;i < h;i++){
    for(int j = 0;j < w;j++){
      ans += up[i][j] * down[i][j] * a[i][j];
    }
  }

  cout << ans << endl;

  return 0;
}