Problem Statement

You are given an integer sequence $A=(A_1,\ldots,A_N)$ and positive integers $a$, $b$, and $c$.

You can perform the following operation on this sequence any number of times, possibly zero.

• Choose an integer $i$ such that $1\leq i\leq N$. Replace $A_i$ with $A_i+1$.

Your objective is to make the sequence $A$ contain at least one multiple of $a$, at least one multiple of $b$, and at least one multiple of $c$. Find the minimum number of operations required to achieve this objective.

Constraints

• $1\leq N\leq 2\times 10^5$
• $1\leq a, b, c \leq 10^6$
• $1\leq A_i\leq 10^{18}$

Input

The input is given from Standard Input in the following format:

N a b c
A_1 \cdots A_N

Output

Print the minimum number of operations required to achieve the objective.