{"raw_statement":[{"iden":"problem statement","content":"A robot is at the origin of a coordinate plane where the positive $x$\\-axis points to the right and the positive $y$\\-axis points upwards. Initially, the robot is facing the positive $x$\\-direction.\nYou will perform the following operation for $i=1,\\ldots,N$ in this order.\n\n*   Rotate the robot $90$ degrees clockwise or counterclockwise. Then, the robot moves forward $A_i$ units in the direction it is facing.\n\nCan the direction of rotation be chosen so that the robot will be at the coordinates $(X,Y)$ after the $N$ operations?\nIf it is possible, determine which direction, clockwise or counterclockwise, should be chosen for each operation."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 80$\n*   $1 \\leq A_i \\leq 10^7$\n*   $-10^9\\leq X,Y \\leq 10^9$\n*   All input values are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$ $X$ $Y$\n$A_1$ $\\ldots$ $A_N$"},{"iden":"sample input 1","content":"3 -2 4\n3 2 1"},{"iden":"sample output 1","content":"Yes\nLLR\n\nInitially, the robot is at $(0,0)$ and facing the positive $x$\\-direction. The following choices can put the robot at the coordinates $(X,Y)$ after the $N$ operations.\n\n*   First operation: Rotate the robot $90$ degrees counterclockwise to face the positive $y$\\-direction. The robot moves forward $A_1=3$ units in the direction it is facing, and moves to $(0,3)$.\n*   Second operation: Rotate the robot $90$ degrees counterclockwise to face the negative $x$\\-direction. The robot moves forward $A_2=2$ units in the direction it is facing, and moves to $(-2,3)$.\n*   Third operation: Rotate the robot $90$ degrees clockwise to face the positive $y$\\-direction. The robot moves forward $A_3=1$ unit in the direction it is facing, and moves to $(-2,4)$.\n\n![image](https://img.atcoder.jp/abc326/79baf4537d56c0df5c5d254e6e7f9616.png)"},{"iden":"sample input 2","content":"1 0 0\n1"},{"iden":"sample output 2","content":"No"},{"iden":"sample input 3","content":"4 0 0\n1 1 1 1"},{"iden":"sample output 3","content":"Yes\nLRRR\n\nOutputs such as `LLLL` and `RRRR` are also accepted."},{"iden":"sample input 4","content":"14 2543269 -1705099\n3 14 159 2653 58979 323846 2643383 2795028 841971 69399 37510 58 20 9"},{"iden":"sample output 4","content":"Yes\nLLLLLLLLLRLRRR"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}