Sequence Growing Easy

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

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

N A_1 : A_N

outputFormat

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

样例

3
1
2
1

-1