# Bicoloring

In 1976 the "Four Color Map Theorem" was proven with the assistance of a computer. This theorem states that every map can be colored using only four colors, in such a way that no region is colored using the same color as a neighbor region.

Here you are asked to solve a simpler similar problem. You have to decide whether a given arbitrary connected graph can be bicolored. That is, if one can assign colors (from a palette of two) to the nodes in such a way that no two adjacent nodes have the same color. To simplify the problem you can assume:

no node will have an edge to itself.

the graph is nondirected. That is, if a node $a$ is said to be connected to a node $b$, then you must assume that $b$ is connected to $a$.

the graph will be connected. That is, there will be at least one path from any node to any other node.

## Input

Consists of several test cases. Each test case starts with a line containing the number $n(0≤n≤1000)$ of different nodes. The second line contains the number of edges $l(1≤l≤250000)$. After this $l$ lines will follow, each containing two numbers that specify an edge between the two nodes that they represent. A node in the graph will be labeled using a number $a(1≤a≤n)$. The last test contains $n=0$ and is not to be processed.

## Output

You have to decide whether the input graph can be bicolored or not, and print it as shown below.