Given a directed graph G , N vertices and M arcs. 

A node X called "acessible" to Y if there is a path from X to Y

A node X called "popular" if every node Y in V fulfill one of two conditions :

1. X is acessible to Y

2. Y is acessible to X

The Problem :  Given graph G, count the number of popular node.

Input

- The first line contain N and M, the number of nodes and arcs (1 <= N <= 150000; 1 <= M <= 300000)

- M next lines, each line contains x and y, there is a arcs connect from x to y.  

Output

- First line print number of popular nodes.

- Second line print populars node in increasing order. 

Example

Input:

5 4

1 2

3 2

2 4

4 5

Output:

3

2 4 5