On 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
import java.io.*;
import java.util.*;
import java.math.*;
import java.lang.*;
import java.util.LinkedList;
import java.util.Queue;
import static java.lang.Math.*;

public class Cf294 implements Runnable 
{
	static class InputReader 
	{
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
		private SpaceCharFilter filter;
		private BufferedReader br = new BufferedReader(new InputStreamReader(System.in));

		public InputReader(InputStream stream) 
		{
			this.stream = stream;
		}
		
		public int read()
		{
			if (numChars==-1) 
				throw new InputMismatchException();
            
			if (curChar >= numChars) 
			{
				curChar = 0;
				try
				{
					numChars = stream.read(buf);
				}
				catch (IOException e)
				{
					throw new InputMismatchException();
				}
                
				if(numChars <= 0)               
					return -1;
			}
			return buf[curChar++];
		}
     
		public String nextLine()
		{
			String str = "";
			try
			{
				str = br.readLine();
			}
			catch (IOException e)
			{
				e.printStackTrace();
			}	
			return str;
		}
		public int[] nextArray(int n)
		{
			int arr[] = new int[n];
			int i;
			for(i=0;i<n;i++)
			{
				arr[i] = nextInt();
			}
			return arr;
		}
		public int nextInt() 
		{
			int c = read();
            
			while(isSpaceChar(c)) 
				c = read();
		
			int sgn = 1;
        
			if (c == '-') 
			{
				sgn = -1;
				c = read();
			}
            
			int res = 0;
			do
			{
				if(c<'0'||c>'9') 
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			}
			while (!isSpaceChar(c)); 
        
			return res * sgn;
		}
        
		public long nextLong() 
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-')
			{
				sgn = -1;
				c = read();
			}
			long res = 0;
			
			do 
			{
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			}	
			while (!isSpaceChar(c));
				return res * sgn;
		}
		
		public double nextDouble() 
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-')
			{
				sgn = -1;
				c = read();
			}
			double res = 0;
			while (!isSpaceChar(c) && c != '.') 
			{
				if (c == 'e' || c == 'E')
					return res * Math.pow(10, nextInt());
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			}
			if (c == '.') 
			{
				c = read();
				double m = 1;
				while (!isSpaceChar(c))
				{
					if (c == 'e' || c == 'E')
						return res * Math.pow(10, nextInt());
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					m /= 10;
					res += (c - '0') * m;
					c = read();
				}
			}
			return res * sgn;
		}
    
		public String readString() 
		{
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuilder res = new StringBuilder();
			do 
			{
				res.appendCodePoint(c);
				c = read();
			} 
			while (!isSpaceChar(c));
            
			return res.toString();
		}
     
		public boolean isSpaceChar(int c) 
		{
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
     
		public String next()
		{
			return readString();
		}
        
		public interface SpaceCharFilter
		{
			public boolean isSpaceChar(int ch);
		}
		
		public int[] nextIntArray(int n)
		{
			int i;
			int arr[] = new int[n];
			for(i=0;i<n;i++)
			{
				arr[i] = nextInt();
			}
			return arr;
		}
		
		public long[] nextLongArray(int n)
		{
			int i;
			long arr[] = new long[n];
			for(i=0;i<n;i++)
			{
				arr[i] = nextLong();
			}
			return arr;
		}
		
		public double[] nextDoubleArray(int n)
		{
			int i;
			double arr[] = new double[n];
			for(i=0;i<n;i++)
			{
				arr[i] = nextDouble();
			}
			return arr;
		}
		
		public Integer[] IntegerArray(int n)
		{
			int i;
			Integer arr[] = new Integer[n];
			for(i=0;i<n;i++)
			{
				arr[i] = nextInt();
			}
			return arr;
		}
		
		public Long[] LongArray(int n)
		{
			int i;
			Long arr[] = new Long[n];
			for(i=0;i<n;i++)
			{
				arr[i] = nextLong();
			}
			return arr;
		}
		
		public Double[] DoubleArray(int n)
		{
			int i;
			Double arr[] = new Double[n];
			for(i=0;i<n;i++)
			{
				arr[i] = nextDouble();
			}
			return arr;
		}
		
		public ArrayList<ArrayList<Integer>> getGraph(int n,int m)
		{
			ArrayList<ArrayList<Integer>> g =new ArrayList<>();
			int i;
			for(i=0;i<=n;i++)
			{
				g.add(new ArrayList<>());
			}
			for(i=0;i<m;i++)
			{
				int x = nextInt();
				int y = nextInt();
				g.get(x).add(y);
				g.get(y).add(x);
			}
			return g;
		}
		
		public ArrayList<ArrayList<Integer>> getTree(int n)
		{
			ArrayList<ArrayList<Integer>> g =new ArrayList<>();
			int i;
			for(i=0;i<=n;i++)
			{
				g.add(new ArrayList<>());
			}
			for(i=0;i<n-1;i++)
			{
				int x = nextInt();
				int y = nextInt();
				g.get(x).add(y);
				g.get(y).add(x);
			}
			return g;
		}
	}
	
	public static int maxInt(int arr[])
	{
		int max = Integer.MIN_VALUE;
		for(int i : arr)
		{
			max = Math.max(i,max);
		}
		return max;
	}
	
	public static int minInt(int arr[])
	{
		int min = Integer.MAX_VALUE;
		for(int i : arr)
		{
			min = Math.min(i,min);
		}
		return min;
	}
	
	public static long maxLong(long arr[])
	{
		long max = Long.MIN_VALUE;
		for(long i : arr)
		{
			max = Math.max(i,max);
		}
		return max;
	}
	
	public static long minLong(long arr[])
	{
		long min = Long.MAX_VALUE;
		for(long i : arr)
		{
			min = Math.min(i,min);
		}
		return min;
	}
	
	public static double maxDouble(double arr[])
	{
		double max = Double.MIN_VALUE;
		for(double i : arr)
		{
			max = Math.max(i,max);
		}
		return max;
	}
	
	public static double minDouble(double arr[])
	{
		double min = Double.MAX_VALUE;
		for(double i : arr)
		{
			min = Math.min(i,min);
		}
		return min;
	}
	
	void merge(int arr[], int l, int m, int r) 
	{ 
		int n1 = m - l + 1; 
		int n2 = r - m; 
	  

		int L[] = new int [n1]; 
		int R[] = new int [n2]; 
	  

		for (int i=0; i<n1; ++i) 
		    L[i] = arr[l + i]; 
		for (int j=0; j<n2; ++j) 
		    R[j] = arr[m + 1+ j]; 
  
  
  

		int i = 0, j = 0; 
	  

		int k = l; 
		while (i < n1 && j < n2) 
		{ 
		    if (L[i] <= R[j]) 
		    { 
			arr[k] = L[i]; 
			i++; 
		    } 
		    else
		    { 
			arr[k] = R[j]; 
			j++; 
		    } 
		    k++; 
		} 

		while (i < n1) 
		{ 
		    arr[k] = L[i]; 
		    i++; 
		    k++; 
		} 
	  
   
		while (j < n2) 
		{ 
		    arr[k] = R[j]; 
		    j++; 
		    k++; 
		} 
	} 
  
    
	void sort(int arr[], int l, int r) 
	{ 
		if (l < r) 
		{ 
			int m = (l+r)/2; 
			sort(arr, l, m); 
			sort(arr , m+1, r); 
			merge(arr, l, m, r); 
		} 
	}
	
	static class Pair
	{
		int x,y;
		public Pair(int x,int y)
		{
			this.x = x;
			this.y = y;
		}
		public static Comparator<Pair> sortX = new Comparator<Pair>(){
			public int compare(Pair p1,Pair p2)
			{
				if(p1.x==p2.x)
				{
					return (int)(p1.y-p2.y);
				}
				return (int)(p1.x-p2.x);
			}
		};
		
		public static Comparator<Pair> sortY = new Comparator<Pair>(){
			public int compare(Pair p1,Pair p2)
			{
				if(p1.y==p2.y)
				{
					return (int)(p1.x-p2.x);
				}
				return (int)(p1.y-p2.y);
			}
		};
		
		public static Comparator<Pair> custom = new Comparator<Pair>(){
			public int compare(Pair p1,Pair p2)
			{
				if((p1.y-p1.x==p2.y-p2.x))
					return (int)(p1.x-p2.x);
				return (int)((p2.y-p2.x)-(p1.y-p2.x));
			}
		};
		
		public boolean equals(Object obj) 
		{
			if (obj == null) return false;
			if (!(obj instanceof Pair))
				return false;
			return (this.x == ((Pair) obj).x && this.y == ((Pair)obj).y);
		}

		public int hashCode()
		{
			if(x<0 || y<0)
			{
				return (int)(-5*x+-32*y);
			}
			return (int)(5*(x+y));
		}
	}
	
	static class DPair
	{
		Pair s,d;
		public DPair(Pair s,Pair d)
		{
			this.s = s;
			this.d = d;
		}
		
		public boolean equals(Object obj) 
		{
			if (obj == null) return false;
			if (!(obj instanceof DPair))
				return false;
			return (this.s.x == ((DPair) obj).s.x && this.s.y == ((DPair) obj).s.y && this.d.x == ((DPair)obj).d.x && this.d.y == ((DPair) obj).d.y);
		}
		public int hashCode()
		{
			return 5*(s.x+s.y+d.x+d.y);
		}
	}
	
	static class DSU
	{
		public static int rank[],parent[];
		int n;
		HashMap<Integer,Integer> map = new HashMap<>();
		
		public DSU(int n)
		{
			rank = new int[n+1];
			parent = new int[n+1];
			this.n = n;
			makeSet(n);
		}
		
		public void makeSet(int n)
		{
			for(int i=1;i<=n;i++)
			{
				parent[i] = i;
				map.put(i,1);
			}
		}
		
		public static int find(int x)
		{
			if(parent[x]!=x)
			{
				parent[x] = find(parent[x]);
			}
			return parent[x];
		}
		
		public void union(int x,int y)
		{
			int xRoot = find(x);
			int yRoot = find(y);
			
			if(xRoot==yRoot)
			{
				return;
			}
			
			if(rank[xRoot] < rank[yRoot])
			{
				parent[xRoot] = yRoot;
				rank[yRoot] = rank[xRoot] + 1;
				map.put(yRoot,map.getOrDefault(yRoot,1)+map.getOrDefault(xRoot,1));
				if(map.getOrDefault(xRoot,0)!=0)
				{
					map.remove(xRoot);
				}
			}
			else if(rank[yRoot] < rank[xRoot])
			{
				parent[yRoot] = xRoot;
				rank[xRoot] = rank[yRoot] + 1;
				map.put(xRoot,map.getOrDefault(xRoot,1) + map.getOrDefault(yRoot,1));
				if(map.getOrDefault(yRoot,0)!=0)
				{
					map.remove(yRoot);
				}
			}
			else
			{
				parent[yRoot] = xRoot;
				rank[xRoot] = rank[yRoot] + 1;
				map.put(xRoot,map.getOrDefault(xRoot,1)+map.getOrDefault(yRoot,1));
				if(map.getOrDefault(yRoot,0)!=0)
				{
					map.remove(yRoot);
				}
			}
		}
	}
	
	static class SegmentTree
	{
		public static int tree[];
		public SegmentTree(int arr[], int n) 
		{
			int x = (int) (Math.ceil(Math.log(n) / Math.log(2))); 
			int size = 2 * (int) Math.pow(2, x) - 1; 
			tree = new int[size];
			constructTree(arr, 0, n - 1, 0);
		}
		
		public int getMid(int s, int e) 
		{ 
			return s + (e - s) / 2; 
		} 
		
		public int minVal(int x, int y) 
		{ 
			return (x < y) ? x : y; 
		} 
		
		public int constructTree(int arr[], int s, int e, int ind) 
		{ 
			if (s == e) 
			{ 
				tree[ind] = arr[s]; 
				return arr[s]; 
			} 
			int mid = getMid(s, e); 
			tree[ind] = constructTree(arr, s, mid, ind * 2 + 1) +  constructTree(arr, mid + 1, e, ind * 2 + 2); 
			return tree[ind]; 
		}
		
		public long getSum(int n, int l, int r) 
		{ 
			if (l < 0 || r > n - 1 || l > r) 
			{				
				return -1; 
			} 
			return getSumR(0, n - 1, l, r, 0); 
		}
		
		public long getSumR(int s, int e, int l, int r, int ind) 
		{ 
			if (l <= s && r >= e)
			{
				return tree[ind]; 
			}
			if (e < l || s > r) 
			{
				return 0; 
			}
			int mid = getMid(s, e); 
			return getSumR(s, mid, l, r, 2 * ind + 1) + getSumR(mid + 1, e, l, r, 2 * ind + 2); 
		} 
		
		public  void updateValue(int arr[], int n, int i, int val) 
		{ 
			if (i < 0 || i > n - 1) 
			{ 
				return; 
			} 
			int diff = val - arr[i]; 
			arr[i] = val; 
			updateValueR(0, n - 1, i, diff, 0); 
		} 
		
		public void updateValueR(int s, int e, int i, int diff, int ind) 
		{ 
			if (i < s || i > e) 
			{
				return; 
			}
			tree[ind] = tree[ind] + diff; 
			if (e != s) 
			{ 
				int mid = getMid(s, e); 
				updateValueR(s, mid, i, diff, 2 * ind + 1); 
				updateValueR(mid + 1, e, i, diff, 2 * ind + 2); 
			} 
		}
		
		////FOR MIN APLLICATION
		public int constructMinTree(int arr[], int s, int e, int ind) 
		{ 
			if (s == e) 
			{ 
				tree[ind] = arr[s]; 
				return arr[s]; 
			} 
			int mid = getMid(s, e); 
			tree[ind] = minVal(constructMinTree(arr, s, mid, ind * 2 + 1), constructMinTree(arr, mid + 1, e, ind * 2 + 2)); 
			return tree[ind]; 
		} 
		
		
		public int getMin(int n,int l,int r)
		{
			if (l < 0 || r > n - 1 || l > r) 
			{				
				return -1; 
			} 
			return getMinR(0, n - 1, l, r, 0); 
		}
	
		public void updateValueMin(int arr[],int s, int e, int index, int value, int node) 
		{ 
			if (index < s || index > e) 
			{ 
				return; 
			} 
			if (s == e) 
			{  
				arr[index] = value; 
				tree[node] = value; 
			}  
			else
			{ 
				int mid = getMid(s, e); 
				if (index >= s && index <= mid)
				{					
					updateValueMin(arr,s, mid, index, value, 2 * node + 1); 
				}
				else
				{
					updateValueMin(arr,mid + 1, e, index, value, 2 * node + 2);   
				}
				tree[node] = Math.min(tree[2 * node + 1], tree[2 * node + 2]); 
			} 
			return; 
		} 
	
		public int getMinR(int s, int e, int l, int r, int index) 
		{ 
			if (l <= s && r >= e) 
			{
				return tree[index]; 
			}
			if (e < l || s > r) 
			{
				return Integer.MAX_VALUE; 
			}
			int mid = getMid(s, e); 
			return minVal(getMinR(s, mid, l, r, 2 * index + 1) , getMinR(mid + 1, e, l, r, 2 * index + 2));
		}
	}
	
	public static int gcd(int a, int b)
	{
		if (a == 0)
			return b; 
		return gcd(b % a, a); 
	}

	public static int lcm(int a, int b)
	{
		return (a / gcd(a, b)) * b;
	}
	
	public static void main(String args[]) throws Exception 
	{
		new Thread(null, new Cf294(),"Main",1<<27).start();
	}	
	
	public static boolean isValid(int n, int m, int x, int y)
	{
		return (x>=0 && x<=n-1 && y>=0 && y<=m-1);
	}
	
	public static boolean visited[][][];
	
	public static void solver(int dp[][][],StringBuilder[][][] res, int x,int y, char arr[][], int k,int n,int m, int start)
	{
		if(x==0)
		{
			dp[x][y][(arr[x][y]-'0')%k] = arr[x][y]-'0';
			solver(dp,res,x+1,y+1,arr,k,n,m,(arr[x][y]-'0')%k);
			solver(dp,res,x+1,y-1,arr,k,n,m,(arr[x][y]-'0')%k);
		}
		else
		{
			if(isValid(n,m,x-1,y-1) && isValid(n,m,x,y) && dp[x-1][y-1][start]!=-1)
			{
				int rem = arr[x][y]-'0' + dp[x-1][y-1][start];
				int curr_rem = rem%k;
				if(dp[x][y][curr_rem]<rem)
				{
					dp[x][y][curr_rem] = rem;
					res[x][y][curr_rem] = new StringBuilder("L");
					res[x][y][curr_rem].append(res[x-1][y-1][start]);
					solver(dp,res,x+1,y+1,arr,k,n,m,curr_rem);
				    solver(dp,res,x+1,y-1,arr,k,n,m,curr_rem);
				}
			}
			if(isValid(n,m,x-1,y+1) && isValid(n,m,x,y) && dp[x-1][y+1][start]!=-1)
			{
				int rem = arr[x][y]-'0' + dp[x-1][y+1][start];
				int curr_rem = rem%k;
				if(dp[x][y][curr_rem]<rem)
				{
					dp[x][y][curr_rem] = rem;
					res[x][y][curr_rem] = new StringBuilder("R");
					res[x][y][curr_rem].append(res[x-1][y+1][start]);
					solver(dp,res,x+1,y+1,arr,k,n,m,curr_rem);
				    solver(dp,res,x+1,y-1,arr,k,n,m,curr_rem);
				}
			}
		}
	}
	
	public void run()	
	{
		InputReader in = new InputReader(System.in);
		PrintWriter w = new PrintWriter(System.out);
	//	int TESTCASES = in.nextInt();
	//	while(TESTCASES-->0)
		{
			int n = in.nextInt();
			int m = in.nextInt();
			int k = in.nextInt();
			k = k+1;
			char arr[][] = new char[n][m];
			int i,j;
			for(i=0;i<n;i++)
			{
				String s = in.next();
				arr[i] = s.toCharArray();
			}
			int dp[][][] = new int[n][m][k];
			StringBuilder[][][] res = new StringBuilder[n][m][k+1];
			visited = new boolean[n][m][k];
			for(i=0;i<n;i++)
			{
				for(j=0;j<m;j++)
				{
				    for(int l = 0;l<k;l++)
				    {
				        dp[i][j][l] = -1;
				        res[i][j][l] = new StringBuilder("");
				    }
				}
			}
			int ind = 0;
			int resu = -1;
			for(i=0;i<m;i++)
			{
				solver(dp,res, 0, i, arr, k, n, m, ind);
			}
			String s = "";
			int col = 0;
			for(i=0;i<m;i++)
			{
			    if(dp[n-1][i][0] > resu)
			    {
                    col = i+1;
                    resu = dp[n-1][i][0];
                    s = res[n-1][i][0].toString();
                }
			}
			if(resu != -1) 
			{
                w.println(resu);
                w.println(col);
                w.println(s);
            }
            else
            {
                w.println("-1");
            }
		}
		w.flush();
		w.close();
	}
}