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.

Examples

Input

4
0
1
1
2

Output

3

Input

3
1
2
1

Output

-1

Input

9
0
1
1
0
1
2
2
1
2

Output

8

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