_If you can't remember which character corresponds to which rule, remember that "輪" contains a loop, and "切" doesn't!_
_--- Lavaloid_
Grammy is a puzzle master. Today, she is playing a variant of "Wagiri" puzzle.
The puzzle consists of a simple connected graph with $n$ vertices with some Chinese characters on it. Each edge has a "Lun" or "Qie" symbol on it.
The goal is to delete some of the edges to form a **connected** subgraph (including all of the vertices) such that:
- Each remaining edge with the character \`\`Lun'' on it must be on at least one cycle formed by the remaining edges.
- Each remaining edge with the character \`\`Qie'' on it must not be on any cycle formed by the remaining edges.
For example, the picture on the left illustrates an unsolved puzzle, and the picture on the right shows a solution to the puzzle, in which the highlighted edges are chosen in the final subgraph.
Grammy wants to find a solution to the puzzle. Please help Grammy find a solution, or report that no solution exists.
输入格式
The first line contains $2$ integers $n,m$ ($1 \leq n \leq 10^5, n-1 \leq m \leq 2\times 10^5$), denoting the number of vertices and the number of edges.
Each of the next $m$ lines contains $2$ integers $u_i,v_i$ ($1 \leq u_i,v_i \leq n$) and a string $t_i$ ( $t_i \in {"\texttt{Lun}","\texttt{Qie}"}$ ), denoting that there is an edge between $u_i$ and $v_i$, and the type of this edge is $t_i$.
It is guaranteed that the given graph is a simple connected graph, that is, there are no self-loops or multiple edges, and all vertices are directly or indirectly connected by edges.
输出格式
If the solution does not exist, output "$\texttt{NO}$" on a single line.
Otherwise, output "$\texttt{YES}$" on the first line, then output a single integer $m'$ ($0 \leq m' \leq m$) on the second line, followed by $m'$ lines, each of which contains two integers $u_i,v_i$, denoting a remaining edge in your solution. If there are multiple solutions, output any.