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)

#include <bits/stdc++.h>
using namespace std;

using ll = long long int;

const int MAX = (int)(1e5 + 5);
const ll INF = (ll)(1e10 + 5);

const int MAX_N = (int)(2e3 + 5);

ll n;
int l[MAX_N];

ll count_exclude(int i, int j) {
  int summation = l[i] + l[j];

  int index = lower_bound(l, l + n, summation) - l;

  ll part = (ll)(n - index);

  return part;
}

int main(void) {
  // Here your code !
  scanf("%lld", &n);

  for (int i = 0; i < n; ++i) {
    scanf("%d", &(l[i]));
  }

  sort(l, l + n);

  ll whole = n * (n - 1) * (n - 2) / 6;

  for (int i = 0; i < n; ++i) {
    for (int j = i + 1; j < n; ++j) {
      whole -= count_exclude(i, j);
    }
  }

  ll ans = whole;

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

  return 0;
}