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 main(args: Array<String>) = IO().exec {
    val n = int()
    val p = IntArray(n){int()-1}
    val indices = IntArray(n)
    for (i in n) indices[p[i]] = i
    val s = TreeSet<Int>()
    var ret = 0L
    for (x in (0 until n).reversed()) {
        val i = indices[x]
        s.add(i)
        val l = IntArray(2){-1}
        val r = IntArray(2){n}
        do {
            l[1] = s.lower(i) ?: break
            l[0] = s.lower(l[1]) ?: break
        } while (false)
        do {
            r[0] = s.higher(i) ?: break
            r[1] = s.higher(r[0]) ?: break
        } while (false)
        val ls = IntArray(2)
        val rs = IntArray(2)
        ls[0] = l[1] - l[0]
        ls[1] = i - l[1]
        rs[0] = r[0] - i
        rs[1] = r[1] - r[0]
        ret += (x + 1) * (ls[0].toLong() * rs[0] + ls[1].toLong() * rs[1])
    }
    println(ret)
}

// region template
operator fun Int.iterator() = 0.until(this).iterator()

class IO {
    val printable = 33..126
    val buffer = ByteArray(1024)
    var ptr = 0
    var buflen = 0
    val out = java.io.PrintWriter(System.out)
    fun hasNextByte(): Boolean = if (ptr < buflen) true else {
        ptr = 0
        buflen = System.`in`.read(buffer)
        buflen > 0
    }

    fun readByte(): Byte = if (hasNextByte()) buffer[ptr++] else -1
    fun hasNext(): Boolean {
        while (hasNextByte() && buffer[ptr] !in printable) ptr++
        return hasNextByte()
    }

    fun string(): String {
        if (!hasNext()) throw java.util.NoSuchElementException()
        val sb = StringBuilder()
        var b = readByte()
        while (b in printable) {
            sb.appendCodePoint(b.toInt())
            b = readByte()
        }
        return sb.toString()
    }

    fun long(): Long {
        if (!hasNext()) throw java.util.NoSuchElementException()
        var n = 0L
        var minus = false
        var b = readByte()
        if (b == '-'.toByte()) {
            minus = true
            b = readByte()
        }
        if (b !in '0'.toByte()..'9'.toByte()) {
            throw NumberFormatException()
        }
        while (true) {
            if (b in '0'.toByte()..'9'.toByte()) {
                n *= 10
                n += b - '0'.toByte()
            } else if (b == (-1).toByte() || b !in printable) {
                return if (minus) -n else n
            } else {
                throw NumberFormatException()
            }
            b = readByte()
        }
    }

    fun int(): Int {
        val nl = long()
        if (nl !in Integer.MIN_VALUE..Integer.MAX_VALUE) throw NumberFormatException()
        return nl.toInt()
    }

    fun double(): Double = string().toDouble()
    fun print(obj: Any) = out.print(obj)
    fun print(i: Int) = out.print(i)
    fun print(l: Long) = out.print(l)
    fun println(obj: Any) = out.println(obj)
    fun println(i: Int) = out.println(i)
    fun println(l: Long) = out.println(l)
    inline fun exec(block: IO.() -> Unit) {
        block()
        out.flush()
    }

    inline fun println(block: IO.() -> Any) {
        println(block())
        out.flush()
    }
}
// endregion