You are given a sequence of positive integers $*x*_{1}, *x*_{2}, ..., *x*_{*n*}$ 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 $*n*$ ($1 ≤  *n* ≤ 10^{5}$). The second line contains $*n*$ space-separated integers $*x*_{1}, *x*_{2}, ..., *x*_{*n*}$ ($2 ≤  *x*_{*i*} ≤ 10^{9}$). The third line contains two integers $*a*$ and $*b*$ ($0  ≤ *b* ≤  *a* ≤ 10^{9}$, $*a* - *b* ≤ 10^{6}$).

Output

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