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)

#pragma region

#include <bits/stdc++.h>
using namespace std;
#define ALL(x) (x).begin(), (x).end()
#define POW2(n) (1LL << (n))
#define FOR(i, begin, end) for (register int i = (begin); i < (end); i++)
#define IFOR(i, begin, end) for (register int i = (end)-1; i >= (begin); i--)
#define REP(i, n) FOR(i, 0, n)
#define IREP(i, n) IFOR(i, 0, n)
#define MOD 1000000007
#define debug(x) cerr << #x << " = " << (x) << " (line: " << __LINE__ << ") " << endl;
typedef long long ll;
template <typename T>
istream &operator>>(istream &is, vector<T> &vec) {
  for (auto &v : vec) is >> v;
  return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &vec) {
  os << "vec[ ";
  REP(i, vec.size())
  i == 0
      ? os << vec[i]
      : os << ", " << vec[i];
  os << " ]";
  return os;
}
template <typename T>
ostream &operator<<(ostream &os, const deque<T> &deq) {
  os << "deq[ ";
  REP(i, deq.size())
  i == 0
      ? os << deq[i]
      : os << ", " << deq[i];
  os << " ]";
  return os;
}
template <typename T>
ostream &operator<<(ostream &os, const set<T> &set) {
  os << "{ ";
  for (auto &&s : set) &s == &(*set.begin()) ? os << s : os << ", " << s;
  os << " }";
  return os;
}
template <typename T>
ostream &operator<<(ostream &os, const unordered_set<T> &set) {
  os << "{ ";
  for (auto &&s : set) &s == &(*set.begin()) ? os << s : os << ", " << s;
  os << " }";
  return os;
}
template <typename T>
ostream &operator<<(ostream &os, const multiset<T> &set) {
  os << "{ ";
  for (auto &&s : set) &s == &(*set.begin()) ? os << s : os << ", " << s;
  os << " }";
  return os;
}
template <typename T>
ostream &operator<<(ostream &os, const unordered_multiset<T> &set) {
  os << "{ ";
  for (auto &&s : set) &s == &(*set.begin()) ? os << s : os << ", " << s;
  os << " }";
  return os;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &p) {
  os << "(" << p.first << ", " << p.second << ")";
  return os;
}
template <typename TK, typename TV>
ostream &operator<<(ostream &os, const map<TK, TV> &m) {
  os << "{ ";
  for (auto &&k : m) &k == &(*m.begin()) ? os << k.first << " => " << k.second : os << ", " << k.first << " => " << k.second;
  os << " }";
  return os;
}
template <typename TK, typename TV>
ostream &operator<<(ostream &os, const unordered_map<TK, TV> &m) {
  os << "{ ";
  for (auto &&k : m) &k == &(*m.begin()) ? os << k.first << " => " << k.second : os << ", " << k.first << " => " << k.second;
  os << " }";
  return os;
}

#pragma endregion

int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  cout << fixed << setprecision(16);

  int N;
  cin >> N;
  vector<int> L(N);
  cin >> L;

  vector<int> sticks(1001, 0);
  REP(i, L.size())
  sticks[L[i]]++;

  vector<int> sum(1001, 0);
  FOR(i, 1, sum.size())
  sum[i] = sum[i - 1] + sticks[i];

  int a = 0;
  FOR(i, 1, 1001)
  FOR(j, i + 1, 1001) {
    if (sticks[i] == 0) break;
    if (sticks[j] == 0) continue;
    a += (sum[min(i + j - 1, 1000)] - sum[j]);
  }

  cout << a << "\n";
}