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<cstdio>
#include<functional>
#include<algorithm>
using namespace std;
int main(void)
{
	int h,w,a[501][501],i,j,k,hs[501],ws[501],x,flg;
	long long sum;
	scanf("%d %d",&h,&w);
	for(i=1;i<=h;i++)	{
		for(j=1;j<=w;j++)	{
			scanf("%d",&a[i][j]);
		}
	}
	if(h%2==1)	flg=1;
	else flg=0;
	for(i=1;i<=(h+1)/2;i++)	{
		hs[i]=0;	
		for(j=1;j<=(h+1)/2;j++)	{
			x=min(i,j);
			hs[i]+=x;
			if(!(flg==1 && j==h/2+1))	hs[i]+=x;
		}
		hs[h-i+1]=hs[i];
	}
	if(w%2==1)	flg=1;
	else flg=0;
	for(i=1;i<=(w+1)/2;i++)	{
		ws[i]=0;	
		for(j=1;j<=(w+1)/2;j++)	{
			x=min(i,j);
			ws[i]+=x;
			if(!(flg==1 && j==w/2+1))	ws[i]+=x;
		}
		ws[w-i+1]=ws[i];
	}	
//	for(i=1;i<=h;i++)	printf("hs=%d\n",hs[i]);
//	for(i=1;i<=w;i++)	printf("ws=%d\n",ws[i]);
	
	
	sum=0;
	for(i=1;i<=h;i++)	{
		for(j=1;j<=w;j++)	{
			sum+=(long long)a[i][j]*hs[i]*ws[j];
		}
	}
	printf("%lld\n",sum);
	return 0;
}