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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;
class Program
{
    static int n;
    static int[] a;
    static int ans = 0;
    static void Main()
    {
        n = int.Parse(Console.ReadLine());
        a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = int.Parse(Console.ReadLine());
        if (a[0] != 0)
        {
            Console.WriteLine(-1);
            Environment.Exit(0);
        }
        for (int i = 1; i < n; i++)
        {
            if (a[i] > a[i - 1] + 1)
            {
                Console.WriteLine(-1);
                Environment.Exit(0);
            }
        }
        List<int> l = new List<int>();
        for (int i = 0; i < n; i++)
        {
            if (a[i] == 0)
                continue;
            l.Add(a[i]);
            try
            {
                if (a[i] <= a[i + 1])
                    continue;
            }
            catch { }
            Check(l);
            l = new List<int>();
        }
        Console.WriteLine(ans);
    }
    static void Check(List<int> l)
    {
        bool f = true;
        for (int i = 0; i < l.Count - 1; i++)
            f = f && l[i] + 1 == l[i + 1];
        if (f)
            ans += l[l.Count - 1];
        else
        {
            for (int i = 0; i < l.Count - 1; i++)
            {
                if (l[i] == l[i + 1] && l[i] != 0)
                {
                    ans++;
                    l[i]--;
                    break;
                }
            }
            Check(l);
        }
    }
}