Minimal Labels

1000ms

262144K

Description:

You are given a directed acyclic graph with n vertices and m edges. There are no self-loops or multiple edges between any pair of vertices. Graph can be disconnected.

You should assign labels to all vertices in such a way that:

Labels form a valid permutation of length n — an integer sequence such that each integer from 1 to n appears exactly once in it.
If there exists an edge from vertex v to vertex u then label_v should be smaller than label_u.
Permutation should be lexicographically smallest among all suitable.

Find such sequence of labels to satisfy all the conditions.

Input:

The first line contains two integer numbers n, m (2 ≤ n ≤ 10⁵, 1 ≤ m ≤ 10⁵).

Next m lines contain two integer numbers v and u (1 ≤ v, u ≤ n, v ≠ u) — edges of the graph. Edges are directed, graph doesn't contain loops or multiple edges.

Output:

Print n numbers — lexicographically smallest correct permutation of labels of vertices.

Sample Input:

Sample Output:

1 3 2

Sample Input:

Sample Output:

4 1 2 3

Sample Input:

Sample Output:

3 1 2 4 5

Informação

Provedor Codeforces

Código CF825E