Given a directed graph, find a valid topological ordering of its vertices. A topological order is a linear ordering of vertices such that for every directed edge u → v, vertex u comes before v in the ordering.

Input

The first line contains two positive integers: n, the number of vertices (0 < n < 10^5), and m, the number of edges (m ≤ 2 x 10^5)

The next m lines each contains two integers u, v (0 ≤ u, v < n), representing an edge from node u to node v.

Output

Print n space-separated integers representing a valid topological order of the vertices.

If there is more than one valid ordering, any of them is acceptable.

If no valid topological ordering exists, print -1.

Example

Input

6 6
5 2
5 0
4 0
4 1
2 3
3 1

Output

4 5 2 3 1 0