Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

D. Pawn

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputOn some square in the lowest row of a chessboard a stands a pawn. It has only two variants of moving: upwards and leftwards or upwards and rightwards. The pawn can choose from which square of the lowest row it can start its journey. On each square lay from 0 to 9 peas. The pawn wants to reach the uppermost row having collected as many peas as possible. As there it will have to divide the peas between itself and its *k* brothers, the number of peas must be divisible by *k* + 1. Find the maximal number of peas it will be able to collect and which moves it should make to do it.

The pawn cannot throw peas away or leave the board. When a pawn appears in some square of the board (including the first and last square of the way), it necessarily takes all the peas.

Input

The first line contains three integers *n*, *m*, *k* (2 ≤ *n*, *m* ≤ 100, 0 ≤ *k* ≤ 10) — the number of rows and columns on the chessboard, the number of the pawn's brothers. Then follow *n* lines containing each *m* numbers from 0 to 9 without spaces — the chessboard's description. Each square is described by one number — the number of peas in it. The first line corresponds to the uppermost row and the last line — to the lowest row.

Output

If it is impossible to reach the highest row having collected the number of peas divisible by *k* + 1, print -1.

Otherwise, the first line must contain a single number — the maximal number of peas the pawn can collect given that the number must be divisible by *k* + 1. The second line must contain a single number — the number of the square's column in the lowest row, from which the pawn must start its journey. The columns are numbered from the left to the right with integral numbers starting from 1. The third line must contain a line consisting of *n* - 1 symbols — the description of the pawn's moves. If the pawn must move upwards and leftwards, print L, if it must move upwards and rightwards, print R. If there are several solutions to that problem, print any of them.

Examples

Input

3 3 1

123

456

789

Output

16

2

RL

Input

3 3 0

123

456

789

Output

17

3

LR

Input

2 2 10

98

75

Output

-1

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Nov/13/2019 16:27:15 (h1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|