Description:
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 Format:
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 Format:
Print one integer — the number of good subarrays of the array $$$a$$$.
Note:
None