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;
using System.Diagnostics;
using System.Collections.Generic;
using static System.Math;

class P
{
    static void Main()
    {
        int n = int.Parse(Console.ReadLine());
        int[] a = Enumerable.Repeat(0, n).Select(_ => int.Parse(Console.ReadLine())).ToArray();
        //始めは0
        //狭義単調増加列に分解

        //後ろから見ていって、Ni-1がそうあるべきだと考える

        //1 1みたいになったときは再構築しないとダメ
        //a[i-1]+1==a[i]のときはラッキーで+1
        
        //到達不能の検出漏れはない
        //到達可能なのに不能と判定されているかも。-> ない (13WA->13WA)
        //個数のミスだよなあ もうちょっと少なく出来る又は多い必要がある
        long res = 0;
        for (int i = a.Length - 1; i >= 1; i--)
        {
            if (a[i] - a[i - 1] > 1)
            {
                res = -1;
                goto end;
            }

            if (a[i - 1] + 1 == a[i]) res++;
            else res += a[i];
        }
        end:;
        if (a[0] != 0) res = -1;
        Console.WriteLine(res);
    }
}