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.Collections.Generic;
using System.Linq;

namespace c
{
    internal class Program
    {
        public static void Main(string[] args)
        {
            long n = long.Parse(Console.ReadLine());

            long[] a = new long[n];
            for (long i = 0; i < n; i++)
            {
                a[i] = long.Parse(Console.ReadLine());
            }

            //可能判定
            for (long i = 0; i < n; i++)
            {
                if (i == 0)
                {
                    if (a[0] != 0)
                    {
                        Console.WriteLine(-1);
                        return;
                    }

                    continue;
                }
                if (a[i] - a[i - 1] > 1)
                {
                    Console.WriteLine(-1);
                    return;
                }
            }

            long count = 0;
            for (long i = 1; i < n; i++)
            {
                if (a[i] - a[i - 1] == 1)
                {
                    ++count;
                }
                else
                {
                    count += a[i];
                }
            }
            Console.WriteLine(count);
        }
    }
}