E. Cars time limit per test2 secondsmemory limit per test512 megabytesinputstandard inputoutputstandard outputThere are n cars on a coordinate axis OX. Each car is located at an integer point initially and no two cars are located at the same point. Also, each car is oriented either left or right, and they can move at any constant positive speed in that direction at any moment.More formally, we can describe the i-th car with a letter and an integer: its orientation ori_i and its location x_i. If ori_i = L, then x_i is decreasing at a constant rate with respect to time. Similarly, if ori_i = R, then x_i is increasing at a constant rate with respect to time. We call two cars irrelevant if they never end up in the same point regardless of their speed. In other words, they won't share the same coordinate at any moment.We call two cars destined if they always end up in the same point regardless of their speed. In other words, they must share the same coordinate at some moment.Unfortunately, we lost all information about our cars, but we do remember m relationships. There are two types of relationships:1 i j —i-th car and j-th car are irrelevant.2 i j —i-th car and j-th car are destined.Restore the orientations and the locations of the cars satisfying the relationships, or report that it is impossible. If there are multiple solutions, you can output any.Note that if two cars share the same coordinate, they will intersect, but at the same moment they will continue their movement in their directions.InputThe first line contains two integers, n and m (2 \leq n \leq 2 \cdot 10^5; 1 \leq m \leq min(2 \cdot 10^5, \frac{n(n-1)}{2}) — the number of cars and the number of restrictions respectively.Each of the next m lines contains three integers, type, i, and j (1 \leq type \leq 2; 1 \leq i,j \leq n; i≠j).If type = 1, i-th car and j-th car are irrelevant. Otherwise, i-th car and j-th car are destined.It is guaranteed that for each pair of cars, there are at most 1 relationship between.OutputIn the first line, print either "YES" or "NO" (in any case), whether it is possible to restore the orientations and the locations of the cars satisfying the relationships.If the answer is "YES", print n lines each containing a symbol and an integer: ori_i and x_i (ori_i \in \{L, R\}; -10^9 \leq x_i \leq 10^9) — representing the information of the i-th car.If the orientation is left, then ori_i = L. Otherwise ori_i = R.x_i is the where the i-th car is located. Note that all x_i should be distinct. We can prove that if there exists a solution, then there must be a solution satisfying the constraints on x_i.ExamplesInput
4 4
1 1 2
1 2 3
2 3 4
2 4 1
Output
YES
R 0
L -3
R 5
L 6
Input
3 3
1 1 2
1 2 3
1 1 3
Output
NO

4 4
1 1 2
1 2 3
2 3 4
2 4 1

YES R 0 L -3 R 5 L 6 
['2-sat', 'constructive algorithms', 'dfs and similar', 'dsu', 'graphs', 'greedy', 'sortings', '*2200']