Given an undirected graph, your task is to choose a direction for each edge so that the resulting directed graph is acyclic.

Input

The first input line has two integers $n$ and $m$: the number of nodes and edges. The nodes are numbered $1,2,\dots,n$.

After this, there are $m$ lines describing the edges. Each line has two distinct integers $a$ and $b$: there is an edge between nodes $a$ and $b$.

Output

Print $m$ lines describing the directions of the edges. Each line has two integers $a$ and $b$: there is an edge from node $a$ to node $b$. You can print any valid solution.

Constraints

• $1 \le n \le 10^5$
• $1 \le m \le 2 \cdot 10^5$
• $1 \le a,b \le n$

Example

Input:

3 3
1 2
2 3
3 1

Output:

1 2
3 2
3 1