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;
mt19937 rando(chrono::steady_clock::now().time_since_epoch().count());
int N;
int arr[500005];
int fre[500005];
int coel[500005];
int coer[500005];
long long sd[500005];
map<long long, int> mp;
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  cin >> N;
  for (int i = 1; i <= N; i++) {
    sd[i] = uniform_int_distribution<long long>(LLONG_MIN, LLONG_MAX)(rando);
    cin >> arr[i];
  }
  long long hshr = 0, hshl = 0;
  mp[0] = 1;
  long long ans = 0;
  for (int l = 1, r = 1; r <= N; r++) {
    hshr -= coer[arr[r]] * sd[arr[r]];
    fre[arr[r]]++;
    coer[arr[r]]++;
    coer[arr[r]] %= 3;
    hshr += coer[arr[r]] * sd[arr[r]];
    while (fre[arr[r]] > 3) {
      mp[hshl]--;
      fre[arr[l]]--;
      hshl -= coel[arr[l]] * sd[arr[l]];
      coel[arr[l]]++;
      coel[arr[l]] %= 3;
      hshl += coel[arr[l]] * sd[arr[l]];
      l++;
    }
    ans += mp[hshr];
    mp[hshr]++;
  }
  cout << ans;
}
