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Three at the Top - Repovive Premier Round 7 | Repovive

20G. Three at the Top

3500 pts2s256 MB

You are given a permutation $p_1,p_2,\ldots,p_n$ .

You must color every position with one of three colors: red, green, or blue.

A coloring is called valid if the following condition holds for every subarray of length at least $2$ :

the positions containing the largest and the second-largest values in the subarray have different colors.

The score of a valid coloring is the number of subarrays of length at least $3$ in which the positions containing the three largest values have pairwise different colors.

Find the maximum possible score of a valid coloring.

Constraints

$1 \le n \le 2 \times 10^5$
$p$ is a permutation of $1,2,\ldots,n$

Input

\begin{array}{l} n \\ p_1 \quad p_2 \quad \cdots \quad p_n \end{array}

Output

ans

Samples

Input

1
1

Explanation

There is no subarray of length at least $3$ , so every valid coloring has score $0$ .

Output

Input

4
2 1 3 4

Explanation

Coloring positions $1,2,3,4$ red, green, blue, red is valid. The subarrays $[1,3]$ and $[2,4]$ contribute to its score.

In every valid coloring, positions $1,2,3$ have pairwise different colors. Position $4$ must differ from position $3$ , so at least one of $[2,4]$ and $[1,4]$ cannot contribute. Therefore, a score greater than $2$ is impossible.

Output

Input

5
1 2 3 4 5

Explanation

Color the positions red, green, blue, red, green, in this order. This coloring is valid, and every subarray of length at least $3$ contributes to its score. There are $6$ such subarrays, so no larger score is possible.

Output

You are given a permutation $p_1,p_2,\ldots,p_n$ .

You must color every position with one of three colors: red, green, or blue.

A coloring is called valid if the following condition holds for every subarray of length at least $2$ :

the positions containing the largest and the second-largest values in the subarray have different colors.

The score of a valid coloring is the number of subarrays of length at least $3$ in which the positions containing the three largest values have pairwise different colors.

Find the maximum possible score of a valid coloring.

$1 \le n \le 2 \times 10^5$
$p$ is a permutation of $1,2,\ldots,n$

\begin{array}{l} n \\ p_1 \quad p_2 \quad \cdots \quad p_n \end{array}

ans

There is no subarray of length at least $3$ , so every valid coloring has score $0$ .

Coloring positions $1,2,3,4$ red, green, blue, red is valid. The subarrays $[1,3]$ and $[2,4]$ contribute to its score.

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20G. Three at the Top

Constraints

Input

Output

Samples

20G. Three at the Top

Constraints

Input

Output

Samples