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;
long long hs[505050], cnt[505050], a[505050], pr[505050], ans;
vector<long long> v[505050];
map<long long, long long> mp;
int n;
int main() {
  srand(9904);
  cin >> n;
  for (int i = 1; i <= n; i++) {
    hs[i] = ((long long)rand() << 30) + (rand() << 16) + rand();
  }
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
  }
  mp[0] = 1;
  int l = 0;
  for (int i = 1; i <= n; i++) {
    v[a[i]].push_back(i);
    if (v[a[i]].size() > 3) {
      while (l < v[a[i]][v[a[i]].size() - 4]) {
        mp[pr[l]]--;
        l++;
      }
    }
    pr[i] = pr[i - 1] - cnt[a[i]] * hs[a[i]];
    cnt[a[i]]++;
    cnt[a[i]] %= 3;
    pr[i] += cnt[a[i]] * hs[a[i]];
    ans += mp[pr[i]];
    mp[pr[i]]++;
  }
  cout << ans << endl;
  return 0;
}
