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E. Minimal Labels

time limit per test

1 secondmemory limit per test

256 megabytesinput

standard inputoutput

standard outputYou 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* ≤ 10^{5}, 1 ≤ *m* ≤ 10^{5}).

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

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

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