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;
inline long long read() {
  char c = getchar();
  long long f = 1, x = 0;
  while (c < '0' || c > '9') {
    if (c == '-') f = -1;
    c = getchar();
  }
  while (c >= '0' && c <= '9') x = x * 10 + (c - '0'), c = getchar();
  return x * f;
}
void MOD(int &x) {
  if (x >= 1000000007) x -= 1000000007;
}
long long c[500010][3], a[500010];
int cnt[500010], pre[500010], pos[500010];
int Rand() { return rand() << 15 | rand(); }
long long RAND() { return 1ll * Rand() * Rand(); }
map<long long, int> mp;
int main() {
  srand(124);
  int n;
  n = read();
  for (int i = 1; i <= n; i++)
    c[i][0] = RAND(), c[i][1] = RAND(), c[i][2] = c[i][0] ^ c[i][1];
  int l = 0;
  long long ans = 0;
  mp[0]++;
  for (int i = 1; i <= n; i++) {
    int x;
    x = read();
    cnt[x]++;
    a[i] = a[i - 1] ^ c[x][cnt[x] % 3];
    pre[i] = pos[x];
    pos[x] = i;
    while (pre[pre[pre[i]]] > l) {
      mp[a[l]]--;
      l++;
    }
    if (mp.count(a[i])) ans += mp[a[i]];
    mp[a[i]]++;
  }
  printf("%lld\n", ans);
}
