A directed acyclic graph consists of $n$ nodes and $m$ edges. The nodes are numbered $1,2,\dots,n$.

Calculate for each node the number of nodes you can reach from that node (including the node itself).

Input

The first input line has two integers $n$ and $m$: the number of nodes and edges.

Then there are $m$ lines describing the edges. Each line has two distinct integers $a$ and $b$: there is an edge from node $a$ to node $b$.

Output

Print $n$ integers: for each node the number of reachable nodes.

Constraints

• $1 \le n \le 5 \cdot 10^4$
• $1 \le m \le 10^5$

Example

Input:

5 6
1 2
1 3
1 4
2 3
3 5
4 5

Output:

5 3 2 2 1