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: Wrong Answer)

#include "bits/stdc++.h"
using namespace std;
#define REP(i, n) for(ll i = 0;i < n;i++)
#define ll long long
#define MOD 1000000007
using vi = vector<ll>; // intの1次元の型に vi という別名をつける
using vvi = vector<vi>; // intの2次元の型に vvi という別名をつける

ll n,k,x,y;

int main(){
  ll ans=0;
  cin >> n;
  vi l(n);
  //vi lend(1000000);
  vi lowb(1000);
  vi upb(1000);

  vi dp(1001);
  
  REP(i,n){
    cin>>l[i];
    dp[l[i]]++;
  }
  sort(l.begin(), l.end());



  
  for(int i=0;i<1001;i++){
    if (dp[i]==0)continue;
    dp[i]-=1;
    for(int j=i;j<1001;j++){
      if (dp[j]==0){
        continue;
      }else{
        
        dp[j]-=1;


        //int k=max(j-i,i);

        int k=i;
        if (k<=j-i){
          k=j-i+1;
        }
        
        for(;k<=j;k++){
          if (dp[k]>0){
            ans++;
            //cout<<i<<" "<<k<<" "<<j<<endl;
          }
        }

        
        dp[j]+=1;
      }


    }

    dp[i]+=1;
  }
    




cout<<ans<<endl;

  return 0;
}