A. Condorcet Electionstime limit per test2 secondsmemory limit per test1024 megabytesinputstandard inputoutputstandard outputIt 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.InputThe 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.OutputPrint $$$\texttt{YES}$$$ if there is a list of votes matching the facts advertised on television. Otherwise, print $$$\texttt{NO}$$$.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 if there is a valid list of votes, there is one with at most $$$50\,000$$$ votes.Then print $$$k$$$ lines. The $$$i$$$-th of these lines consists of a permutation of $$$\{1, 2, \ldots, n\}$$$ describing the $$$i$$$-th vote. The first number in the permutation is the most preferable candidate and the last one is the least preferable candidate.For $$$1\le i\le m$$$, $$$a_i$$$ shall appear earlier than $$$b_i$$$ in more than $$$k{/}2$$$ of the $$$k$$$ permutations. For pairs of candidates $$$\{a, b\}$$$ not appearing in the election requirements list, the outcome can be arbitrary, including neither of $$$a$$$ and $$$b$$$ defeating the other.ExamplesInput2 11 2OutputYES
1
1 2Input3 31 22 33 1OutputYES
3
1 2 3
2 3 1
3 1 2
NoteIn the second sample, Observe that candidate $$$1$$$ defeats candidate $$$2$$$ because it goes earlier in two out of three voters' permutations, which is more than half of all votes. Similarly, candidate $$$2$$$ defeats candidate $$$3$$$, and candidate $$$3$$$ defeats candidate $$$1$$$.