B"Bashar was practicing for the national programming contest. Because of sitting too much in front of the computer without doing physical movements and eating a lot Bashar became much fatter. Bashar is going to quit programming after the national contest and he is going to become an actor (just like his father), so he should lose weight. In order to lose weight, Bashar is going to run for k kilometers. Bashar is going to run in a place that looks like a grid of n rows and m columns. In this grid there are two one-way roads of one-kilometer length between each pair of adjacent by side cells, one road is going from the first cell to the second one, and the other road is going from the second cell to the first one. So, there are exactly (4 n m - 2n - 2m) roads. Let's take, for example, n = 3 and m = 4 . In this case, there are 34 roads. It is the picture of this case (arrows describe roads): Bashar wants to run by these rules: Bashar asks you if it is possible to run by such rules. If it is possible, you should tell him how should he run. You should give him a steps to do and since Bashar can't remember too many steps, a should not exceed 3000 . In every step, you should give him an integer f and a string of moves s of length at most 4 which means that he should repeat the moves in the string s for f times. He will perform the steps in the order you print them. For example, if the steps are 2 RUD, 3 UUL then the moves he is going to move are RUD + RUD + UUL + UUL + UUL = RUDRUDUULUULUUL. Can you help him and give him a correct sequence of moves such that the total distance he will run is equal to k kilometers or say, that it is impossible? The only line contains three integers n , m and k ( 1 <= q n, m <= q 500 , 1 <= q k <= q 10 ^{9} ), which are the number of rows and the number of columns in the gr"...