A10986 | 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 $label_{v}$ should be smaller than $label_{u}$ .
- Permutation should be lexicographically smallest among all suitable.

Find such sequence of labels to satisfy all the conditions.

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.

Print $n$ numbers — lexicographically smallest correct permutation of labels of vertices.