Neatness

题意翻译

Simon 的房子的俯视图呈一个 $n \times n$ 的正方形。我们用 $\left(x,y\right)$，表示第 $x$ 行，第 $y$ 列的房间。现在用 $1$ 表示这些房间里的灯是开着的，$0$ 表示关着。已知 Simon 的卧室在 $\left(x_0,y_0\right)$，他现在想要从卧室出发关掉所有的灯。现有一下几种操作： 1. 输出 $1$，表示将所在房间的灯打开，**在此之前它的灯必须是关着的**。 1. 输出 $2$，表示将所在房间的灯关闭，**在此之前它的灯必须是开着的**。 1. 输出 $U,D,L,R$，分别表示朝上，下，左，右面走一格，**此时你需要保证 Simon 面向的方向上至少有一盏亮着的灯，否则不能走**。 你需要构造一种方案使得 Simon 从卧室出发，关掉所有的灯并返回卧室。注意你的操作次数应小于等于 $3 \times 10^6$。

题目描述

Simon loves neatness. So before he goes to bed, Simon wants to complete all chores in the house. Simon's house looks like a rectangular table consisting of $ n $ rows and $ n $ columns from above. All rows of the table are numbered from $ 1 $ to $ n $ from top to bottom. All columns of the table are numbered from $ 1 $ to $ n $ from left to right. Each cell of the table is a room. Pair $ (x,y) $ denotes the room, located at the intersection of the $ x $ -th row and the $ y $ -th column. For each room we know if the light is on or not there. Initially Simon is in room $ (x_{0},y_{0}) $ . He wants to turn off the lights in all the rooms in the house, and then return to room $ (x_{0},y_{0}) $ . Suppose that at the current moment Simon is in the room $ (x,y) $ . To reach the desired result, he can perform the following steps: 1. The format of the action is "1". The action is to turn on the light in room $ (x,y) $ . Simon cannot do it if the room already has light on. 2. The format of the action is "2". The action is to turn off the light in room $ (x,y) $ . Simon cannot do it if the room already has light off. 3. The format of the action is "dir" ( $ dir $ is a character). The action is to move to a side-adjacent room in direction $ dir $ . The direction can be left, right, up or down (the corresponding dir is L, R, U or D). Additionally, Simon can move only if he see a light in the direction $ dir $ . More formally, if we represent the room, Simon wants to go, as $ (nx,ny) $ , there shold be an integer $ k $ $ (k>0) $ , that room $ (x+(nx-x)k,y+(ny-y)k) $ has a light. Of course, Simon cannot move out of his house. Help Simon, find the sequence of actions that lets him achieve the desired result.

输入输出格式

输入格式

The first line contains three positive integers $ n,x_{0},y_{0} $ $ (2<=n<=500,1<=x_{0},y_{0}<=n) $ . Next $ n $ lines contain the description of rooms in the house. The $ i $ -th line contains $ n $ space-separated integers $ a_{i1},a_{i2},...,a_{in} $ . If number $ a_{ij} $ equals zero, then room $ (i,j) $ has light off, and if number $ a_{ij} $ equals one, then room $ (i,j) $ has light on. It is guaranteed that at least one room has light on.

输出格式

If there is no desired sequence of actions, print "NO" (without the quotes). Otherwise, print "YES" (without the quotes) and the description of the required sequence of actions as a string. Note that you do not have to minimize the length of the sequence of actions but you shouldn't use more than $ 3·10^{6} $ actions.

输入输出样例

输入样例 #1

3 1 1
1 0 0
0 1 0
1 0 0

输出样例 #1

YES
D1R2L2D2UU2

输入样例 #2

3 1 1
1 0 0
0 1 0
0 0 1

输出样例 #2

NO