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 Kotlin (1.0.0) (judge verdict: Accepted)

import java.util.*

fun simple(P: List<Long>): Long {
    var res = 0L
    for (i in P.indices) {
        for (k in 2..P.size - i) {
            val l = P.subList(i, i + k).sorted()
            res += l[l.size - 2]
        }
    }
    return res
}

fun main(args: Array<String>) {
    val N = readLine()!!.toInt()
    val P = readLine()!!.split(" ").map{it.toLong()}
    val Q = Array(N + 1) {0}

    for (i in P.indices) {
        Q[P[i].toInt()] = i
    }

    val st = TreeSet<Long>()
    var res = 0L

    for (k in N downTo 1) {
        val idx = Q[k].toLong()

        val l = st.lower(idx)
        val ll = idx - (l ?: -1L)
        val l2 = if (l == null) null else st.lower(l)
        val l2l = idx - (l2 ?: -1L)
        val r = st.higher(idx)
        val rl = (r ?: N.toLong()) - idx
        val r2 = if (r == null) null else st.higher(r)
        val r2l = (r2 ?: N.toLong()) - idx

        res += (l2l - ll) * rl * k
        res += ll * (r2l - rl) * k

        st.add(idx)
    }

    println(res)
//    println(simple(P))
}