Given a directed graph, print the order of visiting vertex using Deep-First Search algorithm from vertex ~0~ and smallest vertex is prioritized than other vertices.

Input

• The first line consists of two positive integers, the number ~n~ vertices ~(n\leq 10^5)~ and the number of edges m ~(m \leq 2 \times 10^5)~.
• Then there are ~m~ lines, each containing two integers ~u~ and ~v~ representing an edge from ~u~ to ~v~.~(u,v < 10^5)~.

Output

• Print the list of vertex separated by spaces.

Example Input

4 4
0 3
3 2
1 0
0 1

Example Output

0 1 3 2