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 Rust (1.15.1) (judge verdict: Accepted)

use std::io::Read;

fn run() {
    let mut s = String::new();
    std::io::stdin().read_to_string(&mut s).unwrap();
    let mut it = s.trim().split_whitespace();
    let n: usize = it.next().unwrap().parse().unwrap();
    let mut left = vec![0; n + 2];
    let mut right = vec![0; n + 2];
    let mut ip = vec![0; n + 1];
    left[n + 1] = n;
    right[0] = 1;
    for i in 1..(n + 1) {
        let p: usize = it.next().unwrap().parse().unwrap();
        ip[p] = i;
        left[i] = i - 1;
        right[i] = i + 1;
    }
    let mut ans = 0;
    for i in 1..n {
        let x = ip[i];
        let l = left[x];
        let r = right[x];
        if l > 0 {
            ans += i * (l - left[l]) * (r - x);
        }
        if r <= n {
            ans += i * (x - l) * (right[r] - r);
        }
        right[l] = r;
        left[r] = l;
    }
    println!("{}", ans);
}

fn main() {
    run();
}