Three Occurrences

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

inputFormat

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).

outputFormat

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

样例

10
1 2 3 4 1 2 3 1 2 3

0