The SUM problem can be formulated as follows: given four lists A, B, C, D of integer values, compute how many quadruplet (a, b, c, d ) ∈ A x B x C x D are such that a + b + c + d = 0 . In the following, we assume that all lists have the same size n .

The first line of the input file contains the size of the lists n (this value can be as large as 4000). We then have n lines containing four integer values (with absolute value as large as 2²⁸ ) that belong respectively to A, B, C and D .

For each input file, your program has to write the number quadruplets whose sum is zero.

6

-45 22 42 -16

-41 -27 56 30

-36 53 -37 77

-36 30 -75 -46

26 -38 -10 62

-32 -54 -6 45

5

Sample Explanation: Indeed, the sum of the five following quadruplets is zero: (-45, -27, 42, 30), (26, 30, -10, -46), (-32, 22, 56, -46),(-32, 30, -75, 77), (-32, -54, 56, 30).

#include<iostream>

#include<stdio.h>

#include<algorithm>

#include<string.h>

using namespace std;

const int N=+;

int n;

int a[N],b[N],c[N],d[N];

int ab[N*N],cd[N*N];

int main()

{

    scanf("%d",&n);

    for(int i=;i<=n;i++)

    {

        scanf("%d%d%d%d",&a[i],&b[i],&c[i],&d[i]);

    }

    int k=;

    for(int i=;i<=n;i++)

    {

        for(int j=;j<=n;j++)

        {

            ab[k]=a[i]+b[j];

            cd[k]=c[i]+d[j];

            k++;

        }

    }

    sort(cd,cd+k);

    long long ans=;

    for(int i=;i<k;i++)

    {

        int tmp=-ab[i];

        ans+=(long long )(upper_bound(cd,cd+k,tmp)-lower_bound(cd,cd+k,tmp));

    }

    printf("%I64d\n",ans);

    return ;

}