Problem:
Score : 700 points

Problem Statement

There is a sequence X of length N, where every element is initially 0. Let X_i denote the i-th element of X.

You are given a sequence A of length N. The i-th element of A is A_i. Determine if we can make X equal to A by repeating the operation below. If we can, find the minimum number of operations required.

Choose an integer i such that 1\leq i\leq N-1. Replace the value of X_{i+1} with the value of X_i plus 1.

Constraints

1 \leq N \leq 2 \times 10^5

0 \leq A_i \leq 10^9(1\leq i\leq N)

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N
A_1
:
A_N

Output

If we can make X equal to A by repeating the operation, print the minimum number of operations required. If we cannot, print -1.

Sample Input 1

4
0
1
1
2

Sample Output 1

3

We can make X equal to A as follows:

Choose i=2. X becomes (0,0,1,0).

Choose i=1. X becomes (0,1,1,0).

Choose i=3. X becomes (0,1,1,2).

Sample Input 2

3
1
2
1

Sample Output 2

-1

Sample Input 3

9
0
1
1
0
1
2
2
1
2

Sample Output 3

8

Solution in Rust (1.15.1) (judge verdict: Accepted)

use std::io::{stdin,BufRead,BufReader};

fn main() {
    let mut buf = String::new();
    stdin().read_line(&mut buf).unwrap();
    let n = buf.trim().parse::<usize>().unwrap();
    let mut a: Vec<usize> = BufReader::new(stdin()).lines()
        .map(|l| l.unwrap().trim().parse::<usize>().unwrap())
        .collect();
    for (i, &n) in a.iter().enumerate() {
        if n > i {
            println!("-1");
            return;
        }
    }
    a.reverse();
    let mut tmp = n + 1;
    let mut total = 0;
    for i in a {
        if tmp < n + 1 && i + 1 < tmp {
            println!("-1");
            return;
        }
        if i + 1 != tmp {
            total += i;
        }
        tmp = i;
    }
    println!("{}", total);
}