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;
unordered_map<long long, long long> mp, ct;
int n;
long long a[500005], b[500005], cnt[500005], s[500005], ans;
int get_int() { return ((long long)rand() << 16 | rand()) % ((1ll << 31) - 1); }
long long get_ll() { return (long long)get_int() << 30 | get_int(); }
long long xor3(long long a, long long b) {
  long long x, y, pw = 1, res = 0;
  while (a || b) {
    x = a % 3;
    y = b % 3;
    a /= 3;
    b /= 3;
    res += (x + y) % 3 * pw;
    pw *= 3;
  }
  return res;
}
int main() {
  srand(0717);
  ios::sync_with_stdio(false);
  int i, j = 0;
  cin >> n;
  for (i = 1; i <= n; i++) cin >> a[i];
  for (i = 1; i <= n; i++)
    if (mp.count(a[i]))
      b[i] = mp[a[i]];
    else
      b[i] = mp[a[i]] = get_ll();
  ct[0] = 1;
  for (i = 1; i <= n; i++) {
    cnt[a[i]]++;
    s[i] = xor3(s[i - 1], b[i]);
    while (cnt[a[i]] > 3) {
      ct[s[j++]]--;
      cnt[a[j]]--;
    }
    if (ct.count(s[i])) ans += ct[s[i]];
    if (ct.count(s[i]))
      ct[s[i]]++;
    else
      ct[s[i]] = 1;
  }
  cout << ans;
  return 0;
}
