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: Time Limit Exceeded)

#include <stdio.h>
#include <stdint.h>
#include <inttypes.h>
#include <stdlib.h>

typedef unsigned long long int uint64;
typedef long long int          int64;
 
#define MAX(a,b) ((a)>(b)?(a):(b))
#define MIN(a,b) ((a)<(b)?(a):(b))
#define ABS(a) ((a)>(0)?(a):-(a))

void get_N (int64 *n)
{
  int cnt;
  
  cnt = scanf("%lld", n);

  return;
}

void get_NK (int64 *n, int64 *k)
{
  int cnt;
  
  cnt = scanf("%lld %lld", n, k);

  return;
}

typedef struct _tmp_t {
  int64    a;
  int64    b;
} tmp_t;


int compare_a(const void *a, const void *b)
{
  tmp_t *x;
  tmp_t *y;

  x = (tmp_t *)a;
  y = (tmp_t *)b;

  if (x->a > y->a) return 1;
  if (x->a < y->a) return -1;

  return 0;
}

int compare_b(const void *a, const void *b)
{
  tmp_t *x;
  tmp_t *y;

  x = (tmp_t *)a;
  y = (tmp_t *)b;

  if (x->b > y->b) return 1;
  if (x->b < y->b) return -1;

  return 0;
}

void qsort_a (tmp_t *array, int size)
{
  qsort(array, size, sizeof(tmp_t), compare_a);
}

void qsort_b (tmp_t *array, int size)
{
  qsort(array, size, sizeof(tmp_t), compare_b);
}

#define SIZE (2*10*10*10)
int L[SIZE];
unsigned char f[SIZE]; //bit0:i, bit1:j, bit2:k
// x[i][j][k]

int main()
{
  int cnt;
  int N;
  int i,j,k;
  int result = 0;

  cnt = scanf("%d", &N);

  for (i=0; i<N; i++) {
    cnt = scanf("%d", &L[i]);
  }

  for (i=0; i<N; i++) {
    for (j=i; j<N; j++) {
      for (k=j; k<N; k++) {
        if (i==j) continue;
        if (j==k) continue;
        if (k==i) continue;

        if ((L[i] < (L[j] + L[k])) &&
            (L[j] < (L[k] + L[i])) &&
            (L[k] < (L[i] + L[j]))) {
          result++;
//          printf("i=%d j=%d k=%d L[i]=%d L[j]=%d L[k]=%d (OK)\n",
//                 i,j,k,L[i],L[j],L[k]);
          
        }
      }
    }
  }

  printf("%d", result);

  return 0;
}