Three Occurrences
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 $a$.
The first line contains one integer $n$ ($1 \le n \le 5 \cdot 10^5$).
The second line contains $n$ integers $a_1$, $a_2$, ..., $a_n$ ($1 \le a_i \le n$).
Print one integer — the number of good subarrays of the 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 $a$.
Samples
9
1 2 2 2 1 1 2 2 2
3
10
1 2 3 4 1 2 3 1 2 3
0
12
1 2 3 4 3 4 2 1 3 4 2 1
1