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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

public class Main {

	public static void main(String[] args) throws NumberFormatException, IOException {
		// TODO 自動生成されたメソッド・スタブ
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));


		int n = Integer.parseInt(br.readLine());

		int[] input = new int[n];


		for(int i = 0; i < n; i++){
			input[i] = Integer.parseInt(br.readLine());
		}


		//まずは可能かどうかの判定
		//長さが1ならA1も0でなければならない
		if(n == 1){
			if(input[0] == 0){
				System.out.println(0);
				return;
			}
			else {
				System.out.println(-1);
				return;
			}
		}
		//先頭が0で次が2以上は論外
		if(input[0] == 0 && input[1] >= 2){
			System.out.println(-1);
			return;
		}
		for(int i = 0; i < n - 1; i++){
			if(input[i] + 1 < input[i + 1]){
				System.out.println(-1);
				return;
			}
		}
	}
}