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: Runtime Error)

using System;
using static System.Console;

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

	// skip the first zero
	if (int.Parse(ReadLine()) != 0)
	{
	    WriteLine(-1);
	    return;
	}

	b = new int[n+2];
	long ans = 0;
	
	int curr = 0;
	int left = -1;
	for (int i = 2; i <= n; i++)
	{
	    int a = b[i] = int.Parse(ReadLine());
	    if (curr == 0 && a == 0) continue;
	    
	    if (a == curr || a == curr + 1)
	    {
		if (left < 0) left = i;
	    }
	    else if (a == 0 || a == 1)
	    {
		ans += CountSub(left, i);
		if (a == 1) left = i;
		else left = -1;
	    }
	    else
	    {
		WriteLine(-1);
		return;
	    }
	    curr = a;
	}
	ans += CountSub(left, n+1);
	    
	WriteLine(ans);
    }

    static long CountSub(int l, int r)
    {
	long ret = 0;

	bool tail = true;
	for (int i = r-1; i >= l; i--)
	{
	    int a = b[i];
	    if (tail && a != b[i+1])
	    {
		ret++;
	    }
	    else
	    {
		tail = false;
		if (a == 1) ret++;
		else ret += 2;
	    }	    
	}

	//WriteLine($"constsub {l} {r} : {ret}");

	return ret;
    }
}