Five Transportations

AtCoder
IDabc123_c
Time2000ms
Memory256MB
Difficulty
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: $N$ $A$ $B$ $C$ $D$ $E$ [samples]
Samples
Input #1
5
3
2
4
3
5
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:
![image](https://img.atcoder.jp/ghi/9c306138eddc8a2e08acfa5da19bdfe8.png)
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.
![image](https://img.atcoder.jp/ghi/bd30b5ab37fc06951c9f5256bb974e4f.png)
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.
![image](https://img.atcoder.jp/ghi/50f2e49a770a30193fc53588ec8475b3.png)
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.
![image](https://img.atcoder.jp/ghi/d6d80dc50abe58190905c8c5ea6ba345.png)
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.
Input #2
10
123
123
123
123
123
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.
Input #3
10000000007
2
3
5
7
11
Output #3
5000000008

Note that the input or output may not fit into a $32$\-bit integer type.
API Response (JSON)
{
  "problem": {
    "name": "Five Transportations",
    "description": {
      "content": "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 $",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc123_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "In 2028 and after a continuous growth, AtCoder Inc. finally built an empire with six cities (City $1, 2, 3, 4, 5, 6$)!\nThere are five means of transport in this empire:\n\n*   Train: travels from City $...",
      "is_translate": false,
      "language": "English"
    }
  ]
}
Full JSON Raw Segments