Strongly Connected Edges

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

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 integers a and b: there is an edge between nodes a and b. You may assume that the graph is simple, i.e., there are at most one edge between two nodes and every edge connects two distinct nodes.

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. If there are no solutions, only print IMPOSSIBLE.

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
1 3
2 3

Output

1 2
2 3
3 1