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: \begin{itemize} \item no node will have an edge to itself. \item 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 $a$. \item the graph will be connected. That is, there will be at least one path from any node to any other node. \end{itemize} \InputFile Consists of several test cases. Each test case starts with a line containing the number $n~(0 \le n \le 1000)$ of different nodes. The second line contains the number of edges $l~(1 \le l \le 250000)$. 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 $a~(1 \le a \le n)$. The last test contains $n = 0$ and is not to be processed. \OutputFile You have to decide whether the input graph can be bicolored or not, and print it as shown below. \includegraphics{https://static.e-olymp.com/content/24/249b876dd10ab00c90c099f5775f9c2fcc84593b.gif}