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>
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
const long long INF = 0x3f3f3f3f3f3f3f3f;
const long long llinf = (1LL << 60);
const int inf = (1 << 30);
const int nmax = 5e5 + 50;
const long long mod = 1e9 + 7;
using namespace std;
int n, i, j, l, a;
map<long long, int> mp;
long long tot, h[nmax], v[nmax], f[nmax], b;
vector<int> p[nmax];
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cerr.tie(0);
  cout.tie(0);
  srand(9904);
  cin >> n;
  for (i = 1; i <= n; i++)
    v[i] = ((long long)rand() << 30) + (rand() << 16) + rand();
  mp[0] = 1;
  for (i = 1; i <= n; i++) {
    cin >> a;
    b = f[a];
    f[a] = (f[a] + 1) % 3;
    h[i] = h[i - 1] + (f[a] - b) * v[a];
    if ((int)p[a].size() > 2)
      l = p[a][(int)p[a].size() - 3] - 1;
    else
      l = j - 1;
    for (; j <= l; j++) mp[h[j]]--;
    tot += 1LL * mp[h[i]];
    mp[h[i]]++;
    p[a].push_back(i);
  }
  cout << tot << endl;
  return 0;
}
