101232: [AtCoder]ABC123 C - Five Transportations

Problem Statement

In 2028 and after a continuous growth, AtCoder Inc. finally built an empire with six cities (City $1, 2, 3, 4, 5, 6$)!

There are five means of transport in this empire:

• Train: travels from City $1$ to $2$ in one minute. A train can occupy at most $A$ people.
• Bus: travels from City $2$ to $3$ in one minute. A bus can occupy at most $B$ people.
• Taxi: travels from City $3$ to $4$ in one minute. A taxi can occupy at most $C$ people.
• Airplane: travels from City $4$ to $5$ in one minute. An airplane can occupy at most $D$ people.
• Ship: travels from City $5$ to $6$ in one minute. A ship can occupy at most $E$ people.

For each of them, one vehicle leaves the city at each integer time (time $0$, $1$, $2$, $...$).

There is a group of $N$ people at City $1$, and they all want to go to City $6$.
At least how long does it take for all of them to reach there? You can ignore the time needed to transfer.

Constraints

• $1 \leq N, A, B, C, D, E \leq 10^{15}$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$
$A$
$B$
$C$
$D$
$E$

Output

Print the minimum time required for all of the people to reach City $6$, in minutes.

Sample Input 1

5
3
2
4
3
5

Sample Output 1

7

One possible way to travel is as follows. First, there are $N = 5$ people at City $1$, as shown in the following image:

In the first minute, three people travels from City $1$ to City $2$ by train. Note that a train can only occupy at most three people.

In the second minute, the remaining two people travels from City $1$ to City $2$ by train, and two of the three people who were already at City $2$ travels to City $3$ by bus. Note that a bus can only occupy at most two people.

In the third minute, two people travels from City $2$ to City $3$ by train, and another two people travels from City $3$ to City $4$ by taxi.

From then on, if they continue traveling without stopping until they reach City $6$, all of them can reach there in seven minutes.
There is no way for them to reach City $6$ in $6$ minutes or less.

Sample Input 2

10
123
123
123
123
123

Sample Output 2

5

All kinds of vehicles can occupy $N = 10$ people at a time. Thus, if they continue traveling without stopping until they reach City $6$, all of them can reach there in five minutes.

Sample Input 3

10000000007
2
3
5
7
11

Sample Output 3

5000000008

Note that the input or output may not fit into a $32$-bit integer type.