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 Scala (2.11.7) (judge verdict: Wrong Answer)



import scala.collection.SortedSet

object Main {

  def main(args: Array[String]): Unit = {

    val N = readLine().toInt
    val array = readLine().split(" ").map(_.toInt)

    val ordered = array.zipWithIndex.sortBy(-_._1)


    var answer = 0
    ordered.foldLeft(SortedSet[Int]()){
      case (indexList, (v,i)) => {
        val low = (List(-1,-1) ++ indexList.until(i).takeRight(2)).takeRight(2)
        val high = (indexList.from(i).take(2).toList ++ List(array.length,array.length)).take(2)

        //println(s"${v} : ${i} = " + ((low(1) - low(0)) * (high(0) - i) + (i - low(1)) * (high(1) - high(0))))

        answer += ((low(1) - low(0)) * (high(0) - i) + (i - low(1)) * (high(1) - high(0))) * v
        indexList + i
      }
    } 


    println(answer)
    

  }
}