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

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

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

1. X is accessible to Y
2. Y is accessible to X

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

Input

- The first line contain N and M, the number of nodes and edges (1 ≤ N ≤ 150000; 1 ≤ M ≤ 300000)

- M next lines, each line contains x and y, there is an edge from x to y.

Output

- First line print number of popular nodes.

- Second line print popular nodes in increasing order.

Example

Input:
5 4
1 2
3 2
2 4
4 5
Output:
3
2 4 5