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)

/*2019/10/19 */
/*template*/
#include<stdio.h>
#include<stdlib.h>
#include<math.h>
#include<string.h>
#define MOD 1000000007
#define MIN 999999999
#define MAX -999999999
typedef long long int ll;
typedef unsigned long long int ull;
void llswap(ll *x,ll *y){ll tmp;tmp=*x;*x=*y;*y=tmp;}
void swap(int *x,int *y){int tmp;tmp=*x;*x=*y;*y=tmp;}
int rmax(int x,int y){return x>y?x:y;}
int rmin(int x,int y){return x>y?y:x;}
ll llrmax(ll x,ll y){return x>y?x:y;}
ll llrmin(ll x,ll y){return x>y?y:x;}
int asc(const void *a,const void *b){if(*(int*)a < *(int*)b)return -1;else if(*(int*)a == *(int*)b)return 0;else return 1;}
int desc(const void *a,const void *b){if(*(int*)a < *(int*)b)return 1;else if(*(int*)a == *(int*)b)return 0;else return -1;}
int llasc(const void *a,const void *b){if(*(ll*)a < *(ll*)b)return -1;else if(*(ll*)a == *(ll*)b)return 0;else return 1;}
int lldesc(const void *a,const void *b){if(*(ll*)a < *(ll*)b)return 1;else if(*(ll*)a == *(ll*)b)return 0;else return -1;}
int gcd(int x,int y){if(y==0)return x;return gcd(y,x%y);}
 
//int asc_t(const void *a,const void *b){if(((pair_t*)a)->d < ((pair_t*)b)->d)return -1;else if(((pair_t*)a)->d == ((pair_t*)b)->d)return 0;else return 1;}
//int asc_t(const void *a,const void *b){if(((pair_t*)a)->d < ((pair_t*)b)->d)return 1;else if(((pair_t*)a)->d == ((pair_t*)b)->d)return 0;else return -1;}
int main(){
    int n,l[2000];
    scanf("%d",&n);
    for(int i=0;i<n;i++){
        scanf("%d",&l[i]);
    }
    int ans=0;
    qsort(l,n,sizeof(int),asc);
    for(int i=0;i<n;i++){
        for(int j=i+1;j<n;j++){
            for(int k=j+1;k<n;k++){
                if(l[i]<l[j]+l[k]&&l[j]<l[i]+l[k]&&l[k]<l[i]+l[j]){
                    ans++;
                }else{
                    break;
                }
            }
        }
    }
    printf("%d\n",ans);
    return 0;
}