Lucky Country

题意翻译

如果一个数中不包含除 $4$ 和 $7$ 之外的数字则是幸运数。有 $n$ 个岛屿，通过双向道路连接。这些岛屿被分为几个地区。每个岛属于恰好一个区域，同一区域中的任何两个岛之间存在道路，不同区域的任何两个岛之间没有路径。如果一个地区的岛屿数量是一个幸运数字，则这个地区是幸运的。问最少增加几条道路能创建一个幸运地区。 Translated by marshal 王子祥

题目描述

Petya loves lucky numbers. Everybody knows that positive integers are lucky if their decimal representation doesn't contain digits other than $ 4 $ and $ 7 $ . For example, numbers $ 47 $ , $ 744 $ , $ 4 $ are lucky and $ 5 $ , $ 17 $ , $ 467 $ are not. One night Petya was sleeping. He was dreaming of being the president of some island country. The country is represented by islands connected by two-way roads. Between some islands there is no road way, even through other islands, that's why the country is divided into several regions. More formally, each island belongs to exactly one region, there is a path between any two islands located in the same region; there is no path between any two islands from different regions. A region is lucky if the amount of islands in it is a lucky number. As a real president, Petya first decided to build a presidential palace. Being a lucky numbers' fan, Petya wants to position his palace in one of the lucky regions. However, it is possible that initially the country has no such regions. In this case Petya can build additional roads between different regions, thus joining them. Find the minimum number of roads needed to build to create a lucky region.

输入输出格式

输入格式

The first line contains two integers $ n $ and $ m $ ( $ 1<=n,m<=10^{5} $ ). They are the number of islands and the number of roads correspondingly. Next $ m $ lines contain road descriptions. Each road is defined by the numbers of islands that it connects: that is, by two integers $ u $ and $ v $ ( $ 1<=u,v<=n $ ). Some roads can connect an island with itself; there can be more than one road between a pair of islands. Numbers in each line are separated by exactly one space character.

输出格式

If there's no solution, output the only number "-1" (without the quotes). Otherwise, output the minimum number of roads $ r $ that need to be built to get a lucky region.

输入输出样例

输入样例 #1

4 3
1 2
2 3
1 3

输出样例 #1

1

输入样例 #2

5 4
1 2
3 4
4 5
3 5

输出样例 #2

-1

题意翻译

如果一个数中不包含除 $4$ 和 $7$ 之外的数字则是幸运数。有 $n$ 个岛屿，通过双向道路连接。这些岛屿被分为几个地区。每个岛属于恰好一个区域，同一区域中的任何两个岛之间存在道路，不同区域的任何两个岛之间没有路径。如果一个地区的岛屿数量是一个幸运数字，则这个地区是幸运的。问最少增加几条道路能创建一个幸运地区。 Translated by marshal 王子祥