Rectangle

frog has a piece of paper divided into n rows and m columns. Today, she would like to draw a rectangle whose perimeter is not greater than k .

Find the number of ways of drawing.

Input

The input consists of multiple tests. For each test:

The first line contains 3 integer n , m , k ( 1 ≤ n , m ≤ 5 ⋅ 10 4 , 0 ≤ k ≤ 10 9 ).

Output

For each test, write 1 integer which denotes the number of ways of drawing.

Sample Input

 2 2 6

    1 1 0

    50000 50000 1000000000

Sample Output

 8

    0

    1562562500625000000

#include<queue>

#include<math.h>

#include<stdio.h>

#include<string.h>

#include<iostream>

#include<algorithm>

using namespace std;

#define N 115

long long n,m,k,sum;

int main()

{

    while(~scanf("%lld%lld%lld",&n,&m,&k))

    {

        sum=0;

        for(long long i=1;k-2*i>=2&&i<=n;i++)

        {

            long long mi=min((k-2*i)/2,m);

            long long x=n-i+1,y=m+1;

            sum+=x*(mi*y-(1+mi)*mi/2);

        }

        printf("%lld\n",sum);

    }

    return 0;

}

//freopen("1.txt", "r", stdin);

    //freopen("2.txt", "w", stdout);

//**************************************

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