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 main() {
    let mut s = String::new();
    std::io::stdin().read_to_string(&mut s).unwrap();
    let mut s = s.split_whitespace();
    let n: isize = s.next().unwrap().parse().ok().unwrap();
    let mut ip = vec![0; n as usize];
    for i in 0..n {
        let p: usize = s.next().unwrap().parse().ok().unwrap();
        ip[p - 1] = i;
    }
    let mut li: Vec<_> = (-1..n).collect();
    let mut ri: Vec<_> = (1..n + 1).collect();
    let mut a = 0;
    for pi in 0..n {
        let i = g(&ip, pi);
        let l = g(&li, i);
        let r = g(&ri, i);
        let l2 = if l == -1 { -1 } else { g(&li, l) };
        let r2 = if r == n { n } else { g(&ri, r) };
        a += (pi + 1) * ((l - l2) * (r - i) + (r2 - r) * (i - l));
        if l >= 0 {
            ri[l as usize] = r
        }
        if r < n {
            li[r as usize] = l
        }
    }
    println!("{}", a)
}
fn g(v: &[isize], i: isize) -> isize {
    v[i as usize]
}