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>

void swap (int *x, int *y) {
  int temp;    // 値を一時保存する変数

  temp = *x;
  *x = *y;
  *y = temp;
}

/* pushdouwn操作 */
void pushdown (int array[], int first, int last) {
  int parent = first;   // 親
  int child = 2*parent;   // 左の子
  while (child <= last) {
    if ((child < last) && (array[child] < array[child+1])) {
       child++;   // 右の子の方が大きいとき、右の子を比較対象に設定
    }
    if (array[child] <= array[parent]) { break; }   // ヒープ済み
    swap(&array[child], &array[parent]);
    parent = child;
    child = 2* parent;
  }
}

/* ヒープソート */
void heap_sort (int array[], int array_size) {
  int i;

  for (i = array_size/2; i >= 1; i--) {
    pushdown(array, i, array_size);   // 全体をヒープ化
  }
  for (i = array_size; i >= 2; i--) {
    swap(&array[1], &array[i]);   // 最大のものを最後に
    pushdown(array, 1, i-1);   // ヒープ再構築
  }
}


int tri(int i, int k, int m){
  if((i<k+m) && (k<m+i) && (m<k+i)){
    return 1;
  }else{
    return 0;
  }
}

int main(void){
  int N,i,m,k;
  scanf("%d", &N);
  int num[N+1];
  for(i=1; i<=N; i++){
    scanf("%d", &num[i]);
  }
 
  heap_sort(num,N);
  
  int count=0;
  for(i=N; i>0;i--){
    for(m=i-1; m>0; m--){
      for(k=m-1; k>0; k--){
        
        if(tri(num[i], num[m], num[k])==1){
      count += 1;
        }else{
          break;
        }
        
      }
    }
  }
  
  printf("%d\n", count);
  return 0;
}