G. Three Occurrences
time limit per test
5 seconds
memory limit per test
512 megabytes
input
standard input
output
standard output

You are given an array $$$a$$$ consisting of $$$n$$$ integers. We denote the subarray $$$a[l..r]$$$ as the array $$$[a_l, a_{l + 1}, \dots, a_r]$$$ ($$$1 \le l \le r \le n$$$).

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 $$$n$$$ ($$$1 \le n \le 5 \cdot 10^5$$$).

The second line contains $$$n$$$ integers $$$a_1$$$, $$$a_2$$$, ..., $$$a_n$$$ ($$$1 \le a_i \le n$$$).

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