You are given two arrays of integers a and b, which are both sorted in an ascending order and contain unique elements (i.e. no duplicates).

You can take several (possibly zero) numbers from the array b and add them to a at any positions in any order.

You want the array a to be an arithmetic progression after this.

Your task is to find the maximal length of the resulting arithmetic progression represented by array a that can be achieved.

If it is impossible to obtain an array forming an arithmetic progression, return -1.

Example

For a = [0, 4, 8, 16] and b = [0, 2, 6, 12, 14, 20], the output should be maxArithmeticLength(a, b) = 6.

You can add b[3] = 12 and b[5] = 20 to a and obtain array [0, 4, 8, 12, 16, 20], which is an arithmetic progression of length 6 (the sequence increases by 4 from each element to the next).

It is impossible to obtain a longer arithmetic progression, so the answer is 6.

For a = [5, 7, 13, 14] and b = [9, 11, 15], the output should be maxArithmeticLength(a, b) = -1.

It is impossible to obtain an arithmetic progression with these elements, so the answer is -1.

An array a of unique integers sorted in ascending order.

Guaranteed constraints:
2 ≤ a.length ≤ 1000,
0 ≤ a[i] ≤ 105.

An array b of unique integers sorted in ascending order.

Guaranteed constraints:
2 ≤ b.length ≤ 1000,
0 ≤ b[i] ≤ 105.