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4136: Minimal Labels

内存限制：256 MB 时间限制：2 S
题面：传统 评测方式：文本比较 上传者：
提交：9 通过：4
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题目描述

原题：https://codeforces.com/problemset/problem/825/E
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.
Examples
Input 
3 3
1 2
1 3
3 2
Output 
1 3 2
Input 
4 5
3 1
4 1
2 3
3 4
2 4
Output 
4 1 2 3
Input 
5 4
3 1
2 1
2 3
4 5
Output 
3 1 2 4 5

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