Training Site # BiColouring

Input: Standard Input (stdin)
Output: Standard Output (stdout)
Memory limit: 64 megabytes
Time limit: 2.0 seconds

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

### Input

The input consists of several test cases. Each test case starts with a line containing the number n ( 1 < n < 200) of different nodes. The second line contains the number of edges l. 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 ( ). An input with n = 0 will mark the end of the input 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.

Miguel Revilla 2000-08-21

• ### Sample Input 1

3
3
0 1
1 2
2 0
9
8
0 1
0 2
0 3
0 4
0 5
0 6
0 7
0 8
0


### Sample Output 1

NOT BICOLORABLE.
BICOLORABLE.