You are given a sequence of positive integers x₁, x₂, ..., x_n and two non-negative integers a and b. Your task is to transform a into b. To do that, you can perform the following moves:

subtract 1 from the current a;
subtract a mod x_i (1 ≤ i ≤ n) from the current a.

Operation a mod x_i means taking the remainder after division of number a by number x_i.

Now you want to know the minimum number of moves needed to transform a into b.

Input

The first line contains a single integer n (1 ≤ n ≤ 10⁵). The second line contains n space-separated integers x₁, x₂, ..., x_n (2 ≤ x_i ≤ 10⁹). The third line contains two integers a and b (0 ≤ b ≤ a ≤ 10⁹, a - b ≤ 10⁶).

Output

Print a single integer — the required minimum number of moves needed to transform number a into number b.

Number Transformation II

Examples