You are given an array a consisting of n integers. We denote the subarray a[l..r] as the array [a_l, a_{l + 1}, ..., a_r] (1 ≤ l ≤ r ≤ n).

A subarray is considered good if every integer that occurs in this subarray occurs there exactly thrice. For example, the array [1, 2, 2, 2, 1, 1, 2, 2, 2] has three good subarrays:

  * a[1..6] = [1, 2, 2, 2, 1, 1]; 
  * a[2..4] = [2, 2, 2]; 
  * a[7..9] = [2, 2, 2]. 



Calculate the number of good subarrays of the given array a.

Input

The first line contains one integer n (1 ≤ n ≤ 5 ⋅ 10^5).

The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ n).

Output

Print one integer — the number of good subarrays of the array a.

Examples

Input


9
1 2 2 2 1 1 2 2 2


Output


3


Input


10
1 2 3 4 1 2 3 1 2 3


Output


0


Input


12
1 2 3 4 3 4 2 1 3 4 2 1


Output


1
#include <bits/stdc++.h>
using namespace std;
const int N = 5e5 + 1;
auto random_address = [] {
  char *p = new char;
  delete p;
  return uint64_t(p);
};
const uint64_t SEED = chrono::steady_clock::now().time_since_epoch().count() *
                      (random_address() | 1);
mt19937_64 rng(SEED);
int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  int n;
  cin >> n;
  vector<unsigned long long> random(n + 1);
  for (int i = 1; i <= n; i++) {
    random[i] = rng();
  }
  unordered_map<unsigned long long, int> prf;
  prf[0]++;
  vector<queue<int>> indices(N + 1);
  vector<int> frq(n + 1, 0);
  vector<unsigned long long> hashval(n + 1, 0);
  unsigned long long ans = 0;
  int start = 0;
  for (int i = 0; i < n; i++) {
    int a;
    cin >> a;
    if (indices[a].size() >= 3) {
      int remove = indices[a].front();
      indices[a].pop();
      while (start <= remove) {
        prf[hashval[start]]--;
        start++;
      }
    }
    int before = frq[a];
    frq[a] = (frq[a] + 1) % 3;
    hashval[i + 1] = hashval[i] + (frq[a] - before) * random[a];
    ans += prf[hashval[i + 1]];
    prf[hashval[i + 1]]++;
    indices[a].push(i);
  }
  cout << ans << "\n";
  return 0;
}
