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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int[] nums=new int[sc.nextInt()];
        int[] nums2=new int[nums.length];
        int output=0;
        for(int i=0;i<nums.length;i++){
            nums[i]=sc.nextInt();
        }
        for(int i=0;i<nums.length;i++){
            if(i==0){
                if(nums[i]!=0){
                    System.out.println(-1);
                    return;
                }else{
                    nums2[i]=0;
                }
            }else{
                nums2[i]=nums[i]-nums[i-1];
            }
        }
        for(int i=0;i<nums.length;i++){
            if(nums2[i]==1){
                output+=1;
            }else if(nums2[i]<1){
                output+=nums[i];
            }else{
                System.out.println(-1);
                return;
            }
        }
        System.out.println(output);
        
        
        

}

}