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;
void readint(int &x) {
  x = 0;
  char c = getchar();
  while (c < '0' || c > '9') c = getchar();
  while (c >= '0' && c <= '9') x = x * 10 + c - '0', c = getchar();
}
int n;
int a[500500];
unsigned long long p[500500][3];
unsigned long long pre[500500];
int cnt[500500];
map<unsigned long long, int> mp;
int main() {
  srand(19260817);
  readint(n);
  for (int i = 0; i < n; i++) readint(a[i]);
  for (int i = 1; i <= n; i++) {
    for (int j = 0; j < 3; j++) {
      p[i][j] = (unsigned long long)1 * rand() * rand() * rand() * rand();
    }
  }
  memset(cnt, 0, sizeof(cnt));
  unsigned long long pre_hash = 0;
  for (int i = 0; i < n; i++) {
    pre_hash ^= p[a[i]][cnt[a[i]]];
    cnt[a[i]] = (cnt[a[i]] + 1) % 3;
    pre_hash ^= p[a[i]][cnt[a[i]]];
    pre[i] = pre_hash;
  }
  mp[0] = 1;
  memset(cnt, 0, sizeof(cnt));
  int l = 0;
  unsigned long long ans = 0;
  for (int r = 0; r < n; r++) {
    cnt[a[r]]++;
    if (cnt[a[r]] > 3) {
      while (cnt[a[r]] > 3) {
        mp[l ? pre[l - 1] : 0]--;
        cnt[a[l]]--, l++;
      }
    }
    ans += mp[pre[r]];
    mp[pre[r]]++;
  }
  cout << ans << endl;
  return 0;
}
