One day student Vasya was sitting on a lecture and mentioned a string s 1 s 2 ... s n , consisting of letters " a ", " b " and " c " that was written on his desk. As the lecture was boring, Vasya decided to complete the picture by composing a graph G with the following properties: G has exactly n vertices, numbered from 1 to n . For all pairs of vertices i and j , where i ≠ j , there is an edge connecting them if and only if characters s i and s j are either equal or neighbouring in the alphabet. That is, letters in pairs " a "-" b " and " b "-" c " are neighbouring, while letters " a "-" c " are not. Vasya painted the resulting graph near the string and then erased the string. Next day Vasya's friend Petya came to a lecture and found some graph at his desk. He had heard of Vasya's adventure and now he wants to find out whether it could be the original graph G , painted by Vasya. In order to verify this, Petya needs to know whether there exists a string s , such that if Vasya used this s he would produce the given graph G . The first line of the input contains two integers n and m — the number of vertices and edges in the graph found by Petya, respectively. Each of the next m lines contains two integers u i and v i (1 ≤ u i , v i ≤ n , u i ≠ v i ) — the edges of the graph G . It is guaranteed, that there are no multiple edges, that is any pair of vertexes appear in this list no more than once. In the first line print " Yes " (without the quotes), if the string s Petya is interested in really exists and " No " (without the quotes) otherwise. If the string s exists, then print it on the second line of the output. The length of s must be exactly n , it must consist of only letters " a ", " b " and " c " only, and the graph built using this string must coincide with G . If there are multiple possible answers, you may print any of them. In the first sample you are given a graph made of two vertices with an edge between them. So, these vertices can correspond to