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: Accepted)

#include <stdio.h>
#include <stdlib.h>
#include <string.h>


// ヒープソート(昇順) *****************

int A[200001], B[200001], tmp; // Bでソート(Aは従属) 必要に応じて要素数と型を変える
int length;                    // 要素数:sort()を呼び出す前に設定する


void swap(int i, int j) {
    int tmp;
    tmp  = A[i];
    A[i] = A[j];
    A[j] = tmp;
    tmp  = B[i];
    B[i] = B[j];
    B[j] = tmp;
}

void downheap(int k, int r) {
    int j, v, w;
    v = B[k];
    w = A[k];
    while (1) {
        j = 2 * k + 1;
        if (j > r) break;
        if (j != r) {
            if (B[j + 1] > B[j]) {
                j = j + 1;
            }
        }
        if (v >= B[j]) break;
        B[k] = B[j];
        A[k] = A[j];
        k = j;
    }
    B[k] = v;
    A[k] = w;
}

void sort() {
    int i;
    for (i = (length - 2) / 2; i >= 0; i--) {
        downheap(i, length - 1);
    }
    for (i = length - 1; i > 0; i--) {
        swap(0, i);
        downheap(0, i - 1);
    }
}

// ***************** ヒープソート(昇順) 


int main() {
  unsigned int N, result;
  int i, j, k;
  scanf ("%d", &N);
  
  for (i=0;i<N;i++) {
      scanf("%d", &B[i]);
  }
  
  length = N;
  sort();
  
  result = 0;
  for (i=0;i<N-2;i++) {
    for (j=i+1;j<N-1;j++) {
      for (k=j+1;k<N;k++) {
        if (B[k]<B[i]+B[j]) result++;
        else break;
      }
    }
  }
  
  
  printf("%d", result);
  return 0;
}