Problem Statement

You are going to participate in a speedrun contest held on yukicoder.

In the speedrun contest, problems divided into $4$ difficulty levels, $1, 1.5, 2, 2.5$, are given.

There are $A$ problems of difficulty $1$, and it takes $P$ minutes to solve $1$ of them.

There are $B$ problems of difficulty $1.5$, and it takes $Q$ minutes to solve $1$ of them.

There are $C$ problems of difficulty $2$, and it takes $R$ minutes to solve $1$ of them.

There are $D$ problems of difficulty $2.5$, and it takes $S$ minutes to solve $1$ of them.

The duration of the speedrun contest is $T$ minutes. Find the maximum number of problems you can solve within the time limit.

Note that if the total time spent solving problems is exactly $T$ minutes, all of those problems are considered to have been solved within the time limit.

Constraints

• All inputs are integers.
• $1 \leq A, B, C, D \leq 10^9$
• $1 \leq P, Q, R, S \leq 10^9$
• $1 \leq T \leq 4 \times 10^{18}$

Input

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

$A$ $B$ $C$ $D$
$P$ $Q$ $R$ $S$ $T$

Output

Output the maximum number of problems that can be solved within the contest time.

Sample

1 3 3 3
5 10 15 20 120

9

1 3 3 3
5 10 10 15 120

10

2 7 1 8
2 8 1 8 28

5