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#F0702. Minimal Labels

    ID: 708 传统题 2000ms 256MiB 尝试: 0 已通过: 0 难度: 8 上传者: 标签>数据结构搜索图论贪心算法思想挑战难度共享题库Codeforces英文题面题目来源题面语言

Minimal Labels

题目描述

E. Minimal Labels
time limit per test
1 second
memory limit per test
256 megabytes
input
standard input
output
standard output

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

题目来源：fps-www.educg.net-codeforce-1-2833.xml.zip；FPS 共享题包，题包内第 116 题。保留原作者与原赛事署名。