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++14 (GCC 5.4.1) (judge verdict: Accepted)

#pragma GCC optimize ("O3")
#include <bits/stdc++.h>
#define ll long long
#define oo (int)1e9
#define IO ios_base::sync_with_stdio(0),cin.tie(0),cout.tie(0);
using namespace std;
const int N = 2e3 + 5, M = 2 * N + 5;

int a[N];
int main(){
    int n;
    scanf("%d", &n);
    for(int i = 0 ; i < n ; ++i)
        scanf("%d", a + i);
    sort(a, a + n);
    int ans = 0;
    for(int i = 0 ; i < n ; ++i){
        for(int j = i + 1 ; j < n ; ++j){
            int tani = lower_bound(a, a + n, a[i] + a[j]) - a - 1;
            ans += (tani - j);
        }
    }
    printf("%d\n", ans);
}