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;
#define ll long long
#define REP(i,n) for(long long i=0;i<n;++i)
#define REPP(i,m,n) for(long long i=m;i<n;++i)
#define rep(i,n) for(long long i = n-1;i>=0;--i)
#define repp(i,n,m) for(long long i = n-1; i >= m; --i)
#define ALL(N) (N.begin(),N.end())
#define de cout << "line : " << __LINE__ << " debug" << endl;
#define pb push_back
#define pq priority_queue
#define Dcout(N) cout << setprecision(20) << N << endl
constexpr int MOD = 1000000007;
constexpr int INF = 2147483647;
constexpr long long INFF = 9223372036854775807;

signed main() {
    cin.tie(0);
	ios::sync_with_stdio(false);
    int N;cin >> N;
    vector<int> A(N);
    REP(i,N) cin >> A[i];
    sort ALL(A);A.pb(INF);
    ll ans = 0;
    REP(i,N){
        repp(j,i,0){
            auto Iter = upper_bound(A.begin(),A.begin()+j,A[i]-A[j]);
            auto cnt = A.begin()+j - Iter;
            ans += cnt;
        }
    }
    cout << ans << endl;
}