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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;

public class Main {
    public void solve(BufferedReader stdin, PrintWriter stdout) throws NumberFormatException, IOException {
        int n = Integer.parseInt(stdin.readLine());
        long[] a = new long[n];
        for (int i = 0; i < n; i++) {
            a[i] = Long.parseLong(stdin.readLine());
        }

        if (a[0] != 0) {
            stdout.println(-1);
            return ;
        }

        long ans = 0;
        for (int i = 1; i < n; i++) {
            if (a[i] == 0) {
                ans += 0;
            } else if (a[i] == 1) {
                ans += 1;
            } else {
                long d = a[i] - a[i - 1];
                if (d == 0) {
                    ans += a[i];
                } else if (d == 1) {
                    ans += 1;
                } else {
                    stdout.println(-1);
                    return;
                }
            }
        }

        stdout.println(ans);
    }

    public static void main(String[] args) throws NumberFormatException, IOException {
        BufferedReader stdin = new BufferedReader(new InputStreamReader(System.in));
        PrintWriter stdout = new PrintWriter(System.out, false);
        new Main().solve(stdin, stdout);
        stdout.flush();
    }
}