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C. Cyclic Coloring

time limit per test

4 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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*).

Input

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.

Output

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*.

Examples

Input

4 4

1 2

2 1

3 4

4 3

Output

2

Input

5 2

1 4

2 5

Output

5

Input

4 5

1 2

2 3

3 1

2 4

4 1

Output

3

Input

4 4

1 1

1 2

2 1

1 2

Output

1

Note

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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