B'Piet Mondrian is an artist most famous for his minimalist works, consisting only of the four colors red, yellow, blue, and white. Most people attribute this to his style, but the truth is that his paint behaves in a very strange way where mixing two primary colors only produces another primary color! A sequence of primary colors (red, yellow, blue) is mixed as follows. While there are at least two colors, look at the first two. If they are distinct, replace them with the missing color. If they are the same, remove them from the sequence. In the end, if there is one color, that is the resulting color. Otherwise, if the sequence is empty, we say the resulting color is white. Here are two example mixings: Piet has a color palette with cells numbered from 1 to n . Each cell contains a primary color or is empty. Piet is very secretive, and will not share his palette with you, so you do not know what colors belong to each cell. However, he did perform k operations. There are four kinds of operations: Piet only tells you the list of operations he performs in chronological order, the indexes involved, and the resulting color of each mix operation. For each mix operation, you also know the order in which the cells are mixed. Given this information, determine the color of each cell in the initial palette. That is, you should find one possible state of the palette (before any operations were performed), or say that the described situation is impossible. The first line contains two integers n and k ( 1 <= n,k <= 1000 ) -- the number of cells in the palette and the number of operations, respectively. The next k lines describe the operations. The i -th line begins with the name of the i -th operation and an integer m ( 1 <= m <= n ) -- the number of indexes involved. Then follow m integers j_1, ldots,j_m ( 1 <= j_i <= n ) -- the indexes of the operation. It is guaranteed that all j_i '...