Problem Statement

Cherry-chan has recently developed a time machine. Using this time machine, her goal is to travel to the world exactly $T$ days from now.

Here, if $T \lt 0$, "$T$ days from now" means $|T|$ days ago.

Cherry-chan can perform the following any number of times, $0$ or more: choose $1$ of the $3$ types of actions below and execute it.

• Without using the time machine, wait until the next day (taking $1$ day).
• Using the time machine, spend $X$ days to travel to the world $A$ days after the moment before the move.
• Using the time machine, spend $Y$ days to travel to the world $B$ days before the moment before the move.

Find the minimum number of days experienced by Cherry-chan $(= 3$ types of actions' total days spent $)$ required to travel to the world $T$ days from now.

In this problem, assume the following.

• The time between actions is negligible.
• Cherry-chan can travel to any world, no matter how far in the past or in the future.
• The length of $1$ day is the same, no matter how far in the past or in the future.
• Once she boards the time machine, she can get off only in the world $A$ days later or $B$ days earlier. Therefore, a move that crosses over the day $T$ days from now does not count as having traveled to the world $T$ days from now.

It can be proven that, under the constraints of this problem, Cherry-chan can travel to the world $T$ days from now.

Constraints

• $-10^7 \leq T \leq 10^7,~T \neq 0$
• $1 \leq X \lt A \leq 10^7$
• $1 \leq Y \leq 10^7$
• $1 \leq B \leq 10^7$
• All inputs are integers.

Input

The input is given from standard input in the following format.

$T$
$X$ $A$
$Y$ $B$

Output

Output, as an integer on $1$ line, the minimum number of days experienced by Cherry-chan that is required.

Sample

8
2 9
3 2

6

1
50 100
100 100

1

-2611
21 46
26 11

6195