Minimal Labels
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 labelv should be smaller than labelu.
- Permutation should be lexicographically smallest among all suitable.
Find such sequence of labels to satisfy all the conditions.
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.
Print n numbers — lexicographically smallest correct permutation of labels of vertices.
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.
Samples
3 3
1 2
1 3
3 2
1 3 2
4 5
3 1
4 1
2 3
3 4
2 4
4 1 2 3
5 4
3 1
2 1
2 3
4 5
3 1 2 4 5