Acyclic Graph Edges

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