Minimal Labels

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

inputFormat

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.

outputFormat

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

样例

3 3
1 2
1 3
3 2

1 3 2

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