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)

//
//  atc1019.cpp
//  National Olympiad in Informatics in Provinces
//
//  Created by 黄子齐 on 2019/10/19.
//  Copyright © 2019 黄子齐. All rights reserved.
//

#include <stdio.h>
#include <algorithm>
const int N = 5e3+10;
int n;
int a[N];
int main() {
//    freopen("mytestdata.in", "r", stdin);
    scanf("%d", &n);
    for (int i=1; i<=n; i++) {
        scanf("%d", &a[i]);
    }
    std::sort(a+1, a+n+1);
    int ans = 0;
    for (int i=1; i<n-1; i++) {
        int r = i+2;
        for (int j=i+1; j<n; j++) {
            if (r == j) ++r;
            ans += r-j-1;
            while (r<=n && a[i]+a[j]>a[r]) {
                ++ans; ++r;
            }
        }
    }
    printf("%d\n", ans);
    return 0;
}