B"One particularly well-known fact about zombies is that they move and think terribly slowly. While we still don't know why their movements are so sluggish, the problem of laggy thinking has been recently resolved. It turns out that the reason is not (as previously suspected) any kind of brain defect xe2 x80 x93 it's the opposite! Independent researchers confirmed that the nervous system of a zombie is highly complicated xe2 x80 x93 it consists of n brains (much like a cow has several stomachs). They are interconnected by brain connectors, which are veins capable of transmitting thoughts between brains. There are two important properties such a brain network should have to function properly: If both properties are satisfied, we say that the nervous system is valid. Unfortunately (?), if the system is not valid, the zombie stops thinking and becomes (even more) dead. Your task is to analyze a given nervous system of a zombie and find out whether it is valid. The first line of the input contains two space-separated integers n and m (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89n, xe2 x80 x89m xe2 x80 x89 xe2 x89 xa4 xe2 x80 x891000) denoting the number of brains (which are conveniently numbered from 1 to n) and the number of brain connectors in the nervous system, respectively. In the next m lines, descriptions of brain connectors follow. Every connector is given as a pair of brains a xe2 x80 x82b it connects (1 xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89a, xe2 x80 x89b xe2 x80 x89 xe2 x89 xa4 xe2 x80 x89n, a xe2 x80 x89 xe2 x89 xa0 xe2 x80 x89b). The output consists of one line, containing either yes or no depending on whether the nervous system is valid. "...