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 JavaScript (node.js v5.12) (judge verdict: Wrong Answer)

function Main(input) {
	input = input.split("\n");
	var n = input[0];
	var arry = input.slice(1,n+1);
	var ret = 0;
	
	for(var i = 0; i < n; i++){
		if(i == 0 && arry[i] != 0 || arry[i] - arry[i-1] > 1){
			console.log(-1);
			return;
		}
		
		if(arry[i] == arry[i-1]){
			ret += Number(arry[i]);
		} else if (arry[i] != 0){
			ret++;
		}
	}
	console.log(ret);
	
	return ;
}
Main(require("fs").readFileSync("/dev/stdin", "utf8"));