Problem:
Score : 400 points

Problem Statement

Takahashi has N sticks that are distinguishable from each other. The length of the i-th stick is L_i.

He is going to form a triangle using three of these sticks. Let a, b, and c be the lengths of the three sticks used. Here, all of the following conditions must be satisfied:

a < b + c

b < c + a

c < a + b

How many different triangles can be formed? Two triangles are considered different when there is a stick used in only one of them.

Constraints

All values in input are integers.

3 \leq N \leq 2 \times 10^3

1 \leq L_i \leq 10^3

Input

Input is given from Standard Input in the following format:

N
L_1 L_2 ... L_N

Constraints

Print the number of different triangles that can be formed.

Sample Input 1

4
3 4 2 1

Sample Output 1

1

Only one triangle can be formed: the triangle formed by the first, second, and third sticks.

Sample Input 2

3
1 1000 1

Sample Output 2

0

No triangles can be formed.

Sample Input 3

7
218 786 704 233 645 728 389

Sample Output 3

23

Solution in C (GCC 5.4.1) (judge verdict: Runtime Error)

#include <stdio.h>
#define mod 1000000007
#define max 10000000
long long int catalan[max];

void Gcatalan(int n)
{
    int i,j;
    catalan[0]=catalan[1]=1;
    for(i=2;i<=n;i++)
    {
        for(j=0; j<i; j++)
        {
            catalan[i] += (catalan[j] * catalan[i-j-1]) % mod;
            catalan[i] = catalan[i]%mod;
        }
    }
}
int main()
{
    long long int n, i, cnt=0;
    scanf("%d",&n);
    long long int a[n];
    for(i=0; i<n; i++)
    {
        scanf("%lld", &a[i]);
    }
    for(i=0; i<n-2; i++)
    {
        if(a[i]<(a[i+1]+a[i+2]) && a[i+1]<(a[i]+a[i+2]) && a[i+2]<(a[i]+a[i+1]))
            cnt++;
    }
    if(cnt < 2)
    {
        printf("%lld\n", cnt);
        return 0;
    }
    Gcatalan(cnt);
    int ans = catalan[cnt]+1-(cnt*(cnt-1));
    printf("%lld\n", ans);
    return 0;
}