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 double PI = acos(-1);
typedef long long ll;
typedef pair<int64_t,int64_t> pll;
int dx[]={1,-1,0,0,1,-1,1,-1};
int dy[]={0,0,1,-1,1,-1,-1,1};
#define INF (2147483647)
#define mod (1000000007)
#define limit (7368791)
#define rep(i,a,b) for (int64_t i = (a); i < (b); i++)
#define REP(i,n) rep(i,0,n)
#define ALL(a) begin(a),end(a)
#define sz(s) (s).size()
#define pb push_back
#define mp make_pair
#define fi first
#define se second


void solve()
{
    int n;cin>>n;
    vector<int>l(n);
    REP(i,n)cin>>l[i];
    sort(ALL(l));
    int ans=0;
    REP(i,n)rep(j,i+1,n)rep(k,j+1,n)
        if(l[k]<l[i]+l[j])ans++;
    cout<<ans<<endl;
}

int main()
{
    cin.tie(0);
	ios::sync_with_stdio(false);
    solve();
    return 0;
}