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: Accepted)

#include <bits/stdc++.h>
using namespace std;
const long long INF = 1e18;
const long long MOD = 1e9+7;
#define int long long
#define REP(i,n) for(int (i)=0;(i)<(n);(i)++)
#define REPR(i,n) for(int (i)=(n-1);(i)>=0;(i)--)
#define FOR(i,a,b) for(int (i)=(a);(i)<(b);(i)++)
#define FORR(i,a,b) for(int (i)=(a-1);(i)>=(b);(i)--)
#define ALL(x) (x).begin(), (x).end()
#define pb push_back
#define fst first
void print() {cout<<endl;}template <class Head,class... Tail>void print(Head&&head,Tail&&...tail){cout<<head;if(sizeof...(tail)!=0)cout<<" ";print(forward<Tail>(tail)...);}template <class T>void print(vector<T>&vec){for(auto&a:vec){cout<<a;if(&a!=&vec.back())cout<<" ";}cout<<endl;}template <class T>void print(vector<vector<T>>&df){for(auto&vec:df){print(vec);}}

signed main(){
    int n;
    cin >> n;
    vector<int> L;
    REP(i, n){
        int a;
        cin >> a;
        L.push_back(a);
    }
    sort(ALL(L));
    int ans = 0;
    REP(i, n-2){
        FOR(j, i+1, n-1){
            FOR(k, j+1, n){
                int a = L[i], b = L[j], c = L[k];
                if (a < b + c and b < a + c and c < a + b)
                    ans++;
            }
        }
    }
    print(ans);
}