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 Inf = 0x3f3f3f3f;
const long long INF = 0x3f3f3f3f3f3f3f3fll;
int n;
int a[1 << 19];
int cnt[1 << 19];
unsigned long long ha[1 << 19], hs[1 << 19];
mt19937_64 Rand;
int main() {
  scanf("%d", &n);
  for (int i = 1; i <= (n); i++) scanf("%d", a + i);
  for (int i = 0; i < (1 << 19); i++) ha[i] = Rand();
  for (int i = 1; i <= (n); i++) {
    hs[i] = hs[i - 1];
    hs[i] -= ha[a[i]] * cnt[a[i]];
    cnt[a[i]] = (cnt[a[i]] + 1) % 3;
    hs[i] += ha[a[i]] * cnt[a[i]];
  }
  memset(cnt, 0, sizeof(cnt));
  cnt[0] = 1;
  map<unsigned long long, int> cs;
  int r = 0;
  long long ans = 0;
  cs[0]++;
  for (int i = 0; i < (n); i++) {
    cnt[a[i]]--, cs[hs[i]]--;
    while (r < n && cnt[a[r + 1]] < 3) {
      r++;
      cnt[a[r]]++;
      cs[hs[r]]++;
    }
    ans += cs[hs[i]];
  }
  printf("%lld\n", ans);
  return 0;
}
