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.
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.