It is a municipality election year. Even though the leader of the country has not changed for two decades, the elections are always transparent and fair. There are (n) political candidates, numbered from (1) to (n), contesting the right to govern. The elections happen using a variation of the Ranked Voting System . In their ballot, each voter will rank all (n) candidates from most preferable to least preferable. That is, each vote is a permutation of (\{1, 2, \ldots, n\}), where the first element of the permutation corresponds to the most preferable candidate. We say that candidate (a) defeats candidate (b) if in more than half of the votes candidate (a) is more preferable than candidate (b). As the election is fair and transparent, the state television has already decreed a list of (m) facts—the (i)-th fact being "candidate (a_i) has defeated candidate (b_i)"—all before the actual election! You are in charge of the election commission and tallying up the votes. You need to present a list of votes that produces the outcome advertised on television, or to determine that it is not possible. However, you are strongly encouraged to find a solution, or you might upset higher-ups. The first line contains integers (n) and (m) ((2 \le n \le 50), (1 \le m \le \frac{n(n-1)}{2})) — the number of parties and the number of pairs with known election outcomes. The (i)-th of the following (m) lines contains two integers (a_i) and (b_i) ((1 \le a_i, b_i \le n), (a_i \ne b_i)) — candidate (a_i) defeats candidate (b_i). Each unordered pair (\{a_i, b_i\}) is given at most once. Print (YES) if there is a list of votes matching the facts advertised on television. Otherwise, print (NO). If there is a valid list of votes, print one such list in the following lines. Print the number (k) of votes cast ((1 \le k \le 50\,000)). It can be shown that