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)

fn read<T: std::str::FromStr>() -> T
{
    std::io::Read::bytes(std::io::stdin())
                    .map(|c| c.unwrap() as char)
                    .skip_while(|c| c.is_whitespace())
                    .take_while(|c| !c.is_whitespace())
                    .collect::<String>()
                    .parse().ok().unwrap()
}

fn main() {
    let n: usize = read();

    let mut prev: i64 = read();
    if prev != 0 {
        println!("-1");
        return;
    }

    let mut ans: i64 = 0;
    for _ in 1..n {
        let num: i64 = read();
        let d = num - prev;
        if d > 1 {
            println!("-1");
            return;
        } else if d == 1 {
            ans += 1;
        } else {
            ans += num;
        }

        prev = num;
    }

    println!("{}", ans);
}