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>
#include <type_traits>
using namespace std;

using ll = int64_t;

#define rep(i, n) for (int i = 0; i < (n); ++i)
#define rrep(i, n) for (int i = 1; i <= (n); ++i)
#define drep(i, n) for (int i = (n)-1; i >= 0; --i)
#define ddrep(i, n) for (int i = n; i > 0; --i)
#define srep(i, s, t) for (int i = s; i < t; ++i)

#define rng(a) a.begin(), a.end()
#define pb push_back
#define eb emplace_back
#define fi first
#define se second

#define chmax(x, y) (x = max(x, y))
#define chmin(x, y) (x = min(x, y))

using pi = pair<int, int>;
using vi = vector<int>;
using vvi = vector<vi>;
using ld = long double;

template <class T, class U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
	os << "(" << p.first << "," << p.second << ")";
	return os;
}

template <class T> ostream &operator<<(ostream &os, const vector<T> &v) {
	os << "{";
	rep(i, (int)v.size()) {
		if (i)
			os << ",";
		os << v[i];
	}
	os << "}";
	return os;
}

template <typename T, size_t S> void printArray(const T (&array)[S]) {
	for (auto val : array)
		std::cout << val << ", ";
	std::cout << "\n";
}

const int mod = 1e9 + 7;
const int inf = 1e9 + 5;

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

	int n; std::cin >> n;
	vi l(n); rep(i, n) std::cin >> l[i];
	sort(rng(l));
	int ans = 0;
	rep(i, n) srep(j, i+1, n) {
		auto mi = upper_bound(l.begin() + j + 1, l.end(), l[j] - l[i]);
		auto ma = lower_bound(l.begin() + j + 1, l.end(), l[i] + l[j]);
		ans += max((int)(ma - mi), 0);
	}
	std::cout << ans << "\n";
}