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;
using static System.Console;

class Program
{
    public static void Main()
    {
	int n = int.Parse(ReadLine());

	long n1 = 0;
	long n2 = 0;
	long nTail = 0;

	// skip the first zero
	if (int.Parse(ReadLine()) != 0)
	{
	    WriteLine(-1);
	    return;
	}
	
	int curr = 0;
	int last = 0;
	for (int i = 1; i < n; i++)
	{
	    int a = int.Parse(ReadLine());
	    if (a == curr || a == curr + 1)
	    {
		if (a == 1)
		    n1++;
		else
		    n2++;
	    }
	    else if (a <= 1)
	    {
		if (a == 1)
		    n1++;
		if (last > 1)
		    nTail++;
	    }
	    else
	    {
		WriteLine(-1);
		return;
	    }
	    last = curr;
	    curr = a;
	}

	if (curr > 1)
	    nTail++;

	long ans = n1 + 2L * n2 - nTail;
	WriteLine(ans);
    }
}