CF183C.Cyclic Coloring

普及/提高-

通过率：0%

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题目描述

You are given a directed graph $G$ with $n$ vertices and $m$ arcs (multiple arcs and self-loops are allowed). You have to paint each vertex of the graph into one of the $k$ $(k<=n)$ colors in such way that for all arcs of the graph leading from a vertex $u$ to vertex $v$ , vertex $v$ is painted with the next color of the color used to paint vertex $u$ .

The colors are numbered cyclically $1$ through $k$ . This means that for each color $i$ (i<k) its next color is color $i+1$ . In addition, the next color of color $k$ is color $1$ . Note, that if $k=1$ , then the next color for color $1$ is again color $1$ .

Your task is to find and print the largest possible value of $k$ $(k<=n)$ such that it's possible to color $G$ as described above with $k$ colors. Note that you don't necessarily use all the $k$ colors (that is, for each color $i$ there does not necessarily exist a vertex that is colored with color $i$ ).

输入格式

The first line contains two space-separated integers $n$ and $m$ ( $1<=n,m<=10^{5}$ ), denoting the number of vertices and the number of arcs of the given digraph, respectively.

Then $m$ lines follow, each line will contain two space-separated integers $a_{i}$ and $b_{i}$ ( $1<=a_{i},b_{i}<=n$ ), which means that the $i$ -th arc goes from vertex $a_{i}$ to vertex $b_{i}$ .

Multiple arcs and self-loops are allowed.

输出格式

Print a single integer — the maximum possible number of the colors that can be used to paint the digraph (i.e. $k$ , as described in the problem statement). Note that the desired value of $k$ must satisfy the inequality $1<=k<=n$ .

输入输出样例

输入#1
```
4 4
1 2
2 1
3 4
4 3
```
输出#1
```
2
```
输入#2
```
5 2
1 4
2 5
```
输出#2
```
5
```
输入#3
```
4 5
1 2
2 3
3 1
2 4
4 1
```
输出#3
```
3
```
输入#4
```
4 4
1 1
1 2
2 1
1 2
```
输出#4
```
1
```

说明/提示

For the first example, with $k=2$ , this picture depicts the two colors (arrows denote the next color of that color).

With $k=2$ a possible way to paint the graph is as follows.

It can be proven that no larger value for $k$ exists for this test case.

For the second example, here's the picture of the $k=5$ colors.

A possible coloring of the graph is:

For the third example, here's the picture of the $k=3$ colors.

A possible coloring of the graph is:

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