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