Problem:
Score: 500 points

Problem Statement

Given is a permutation P of \{1, 2, \ldots, N\}.

For a pair (L, R) (1 \le L \lt R \le N), let X_{L, R} be the second largest value among P_L, P_{L+1}, \ldots, P_R.

Find \displaystyle \sum_{L=1}^{N-1} \sum_{R=L+1}^{N} X_{L,R}.

Constraints

2 \le N \le 10^5

1 \le P_i \le N

P_i \neq P_j (i \neq j)

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
P_1 P_2 \ldots P_N

Output

Print \displaystyle \sum_{L=1}^{N-1} \sum_{R=L+1}^{N} X_{L,R}.

Sample Input 1

3
2 3 1

Sample Output 1

5

X_{1, 2} = 2, X_{1, 3} = 2, and X_{2, 3} = 1, so the sum is 2 + 2 + 1 = 5.

Sample Input 2

5
1 2 3 4 5

Sample Output 2

30

Sample Input 3

8
8 2 7 3 4 5 6 1

Sample Output 3

136

Solution in PHP7 (7.0.15) (judge verdict: Wrong Answer)

<?php 
$n = fgets(STDIN);
$p = explode(' ', fgets(STDIN));

$w = array();
for($i = 0; $i < $n+1; $i++){
    array_push($w, 0);
}
$first = array();
$second = array();
for($i = 0; $i < $n; $i++){
    array_push($first, $w);
    array_push($second, $w);
}
for($l = 1; $l<$n; $l++){
    $first[$l][$l+1] = max($p[$l-1], $p[$l]);
    $second[$l][$l+1] = min($p[$l-1], $p[$l]);
    for($r = $l + 1; $r < $n; $r++){
        $first[$l][$r+1] = max(
            $first[$l][$r], $p[$r]
        );
        if($second[$l][$r] <= $p[$r] && $p[$r] <= $first[$l][$r]){
            $second[$l][$r+1] = $p[$r];
        }elseif($first[$l][$r] < $p[$r]){
            $second[$l][$r+1] = $first[$l][$r];
        }else{
            $second[$l][$r+1] = $second[$l][$r];
        }
    }
}
$ans = 0;
for($i = 1; $i < $n; $i++){
    $ans += array_sum($second[$i]);
}
echo $ans."\n";