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.

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.

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.

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

见题面 Input 部分

见题面 Output 部分