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 C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;

public class Hello
{
    public static void Main()
    {
        var n = int.Parse(Console.ReadLine().Trim());
        var a0 = int.Parse(Console.ReadLine().Trim());
        if (a0 != 0) { Console.WriteLine(-1); goto end; }
        var p = 0; var ret = 0; var pre = 0;
        for (int i = 1; i < n; i++)
        {
            var aw = int.Parse(Console.ReadLine().Trim());
            var w = aw - pre;
            if (w >= 2) { Console.WriteLine(-1); goto end; }
            if (w <= 0) { ret += i - 1 - p; p = i - 1; }
            pre = aw;
        }
        ret += n - 1 - p;
        Console.WriteLine(ret);
    end:;
    }
}