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: Accepted)

using System;
using System.Linq;//リストの使用
using System.Collections.Generic;
class Program
{
	static void Main()
	{
		long n = long.Parse(Console.ReadLine());//int.Parseは文字列を整数に変換。
		long[] nums = new long[n];
    for(long i = 0; i < n; i++)
    {
      nums[i] = long.Parse(Console.ReadLine());
    }
		long answer = 0;
    long numMemo = 0;
    bool isPossible = true;

    if(nums[0] != 0) isPossible = false;
    else
    {
      for(long i = 1; i < n; i++)
      {
      //Console.WriteLine(answer);
        if(nums[i] > numMemo+1)
        {
          isPossible = false;
          break;
        }
        else if(nums[i] == numMemo+1)
        {
          answer++;
          numMemo = nums[i];
        }
        else if(nums[i] < numMemo+1)
        {
          answer += nums[i];
          numMemo = nums[i];
        }
      }
    }
    
		Console.WriteLine((isPossible) ? answer : -1);
	}
}