Deep In The Ocean#6697

Deep In The Ocean

1 second
128 megabytes
Very hard

After eating brain zombie starts to play a new game. In this game she has vertices. Some pairs of vertices are connected by edges. Every vertex has the same even number of adjacent edges. Zombie needs to keep some edges so that every vertex has two adjacent edges. If zombie does it she will eat brain of creature sleeping deep in the ocean. Help her!

Input

In the first line there are two integers and representing the number of vertices and the number of edges (1 \leq n \leq 1000, 0 \leq m \leq 50000). Following lines contain and (1 \leq u, v \leq n) - numbers of distinct vertices which are connected. Every pair is connected by at most one edge.

Output

If it is possible to eat the brain of the creature, print - the number of edges kept, following lines must contain and - numbers of vertices. If there is no way to keep edges, print "Impossible".

Examples

Example 1

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Example 2

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