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: Wrong Answer)

#[test]
fn test_solve() {
    assert_eq!(solve("4\n0\n1\n1\n2\n"), "3\n");
    assert_eq!(solve("3\n1\n2\n1\n"), "-1\n");
    assert_eq!(solve("9\n0\n1\n1\n0\n1\n2\n2\n1\n2\n"), "8\n");
}
fn solve(src: &str) -> String {
    let mut sc = Scanner::from_str(src);

    let fault = "-1\n".to_string();

    let n: usize = sc.read();
    let a: Vec<usize> = (0..n).map(|_| sc.read()).collect();

    if a[0] != 0 {
        return fault;
    }

    let mut ans = 0;
    for i in 1..n {
        if a[i] == a[i - 1] + 1 {
            ans += 1;
        } else if a[i] <= i {
            ans += a[i];
        } else {
            return fault;
        }
    }

    format!("{}\n", ans)
}
fn main() {
    let mut buf = String::new();
    use std::io::{Read, Write};
    std::io::stdin().read_to_string(&mut buf).unwrap();
    std::io::stdout().write_all(solve(&buf).as_bytes()).unwrap();
}
struct Scanner<'a>(std::str::SplitWhitespace<'a>);
impl<'a> Scanner<'a> {
    fn from_str(src: &str) -> Scanner {
        Scanner(src.split_whitespace())
    }
    fn get(&mut self) -> &str {
        self.0.next().unwrap()
    }
    fn read<T: std::str::FromStr>(&mut self) -> T {
        self.get().parse().ok().unwrap()
    }
}