Let's play a puzzle using eight cubes placed on a 3 × 3 board leaving one empty square.

Faces of cubes are painted with three colors. As a puzzle step, you can roll one of the cubes to the adjacent empty square. Your goal is to make the specified color pattern visible from above by a number of such steps.

The rules of this puzzle are as follows.

1. Coloring of Cubes: All the cubes are colored in the same way as shown in Figure 3. The opposite faces have the same color.

<image>

Figure 3: Coloring of a cube



2. Initial Board State: Eight cubes are placed on the 3 × 3 board leaving one empty square. All the cubes have the same orientation as shown in Figure 4. As shown in the figure, squares on the board are given x and y coordinates, (1, 1), (1, 2), .. ., and (3, 3). The position of the initially empty square may vary.

<image>

Figure 4: Initial board state



3. Rolling Cubes: At each step, we can choose one of the cubes adjacent to the empty square and roll it into the empty square, leaving the original position empty. Figure 5 shows an example.

<image>

Figure 5: Rolling a cube



4. Goal: The goal of this puzzle is to arrange the cubes so that their top faces form the specified color pattern by a number of cube rolling steps described above.



Your task is to write a program that finds the minimum number of steps required to make the specified color pattern from the given initial state.



Input

The input is a sequence of datasets. The end of the input is indicated by a line containing two zeros separated by a space. The number of datasets is less than 16. Each dataset is formatted as follows.


x y
F11 F21 F31
F12 F22 F32
F13 F23 F33


The first line contains two integers x and y separated by a space, indicating the position (x, y) of the initially empty square. The values of x and y are 1, 2, or 3.

The following three lines specify the color pattern to make. Each line contains three characters F1j, F2j, and F3j, separated by a space. Character Fij indicates the top color of the cube, if any, at position (i, j) as follows:


B: Blue
W: White
R: Red
E: the square is Empty.


There is exactly one 'E' character in each dataset.

Output

For each dataset, output the minimum number of steps to achieve the goal, when the goal can be reached within 30 steps. Otherwise, output "-1" for the dataset.

Example

Input

1 2
W W W
E W W
W W W
2 1
R B W
R W W
E W W
3 3
W B W
B R E
R B R
3 3
B W R
B W R
B E R
2 1
B B B
B R B
B R E
1 1
R R R
W W W
R R E
2 1
R R R
B W B
R R E
3 2
R R R
W E W
R R R
0 0


Output

0
3
13
23
29
30
-1
-1
import java.util.*;
import static java.lang.Math.*;

public class Main {
	final Scanner sc=new Scanner(System.in);
	public static void main(String[] args) {
		new Main().init();
	}
	void init(){
		//long start=System.currentTimeMillis();
		new AOJ1268();
		//System.out.println(" ["+ (System.currentTimeMillis()-start) +"msec]");
	}
	
	class AOJ1268{
		HashMap<String,Integer> visited;
		String fin;
		//TODO debug
		int C=0;
		final int[] vx={0,1,0,-1}, vy={-1,0,1,0};
		AOJ1268(){
			while(true){
				int X=sc.nextInt(),Y=sc.nextInt();
				if((X|Y)==0)	break;
				solve(X-1,Y-1);
			}
		}
		void solve(int X,int Y){
			// TODO debug
			C=0;
			StringBuilder tmp=new StringBuilder();
			for(int i=0; i<9; i++){
				String in=sc.next();
				int c=0;
				if(in.equals("W"))	c=1;
				if(in.equals("B"))	c=2;
				if(in.equals("R"))	c=3;
				tmp.append(c);
			}
			fin=tmp.toString();
			int l=-1,r=31,mid=0;
			while(l+1<r){
				mid=(l+r)/2;
				StringBuilder init=new StringBuilder("131313131313131313");
				init.setCharAt((Y*3+X)*2,'0');
				init.setCharAt((Y*3+X)*2+1,'0');
				visited=new HashMap<String, Integer>();
				if(IDDFS(0,mid,init,X,Y,-1))	r=mid;
				else						l=mid;
			}
			System.out.println(r>30?-1:r);
			//System.out.println((r>30?-1:r)+" "+C+"step");
//			int ans=-1;
//			for(int i=0; i<=30; i++){
//				StringBuilder init=new StringBuilder("131313131313131313");
//				init.setCharAt((Y*3+X)*2,'0');
//				init.setCharAt((Y*3+X)*2+1,'0');
//				visited=new HashMap<String, Integer>();
//				if(IDDFS(0,i,init,X,Y)){
//					ans=i;
//					break;
//				}
//			}
//			//System.out.println(ans);
//			System.out.println(ans+" "+C+"step");
		}
		boolean IDDFS(int depth,int lim,StringBuilder dice,int ex,int ey,int loffset){
			//TODO debug
			++C;
			int hs=0;
			for(int i=0; i<9; i++)	if(dice.charAt(i*2)!=fin.charAt(i) && dice.charAt(i*2)!='0')	hs++;
			if(hs==0)	return true;
			if(depth+hs>lim)	return false;
			for(int v=0; v<4; v++){
				int xx=ex+vx[v], yy=ey+vy[v],offset=(3*yy+xx)*2,eoffset=(3*ey+ex)*2;
				if(!(0<=xx && xx<3 && 0<=yy && yy<3))	continue;
				if(offset==loffset)	continue;
				char nt='a',ns='a',ot=dice.charAt(offset),os=dice.charAt(offset+1);
				if(abs(vx[v])==1){
					nt=turnR((dice.charAt(offset)-'0'),(dice.charAt(offset+1)-'0'));
					ns=dice.charAt(offset+1);
				}else{
					nt=dice.charAt(offset+1);
					ns=dice.charAt(offset);
				}
				dice.setCharAt(offset, dice.charAt(eoffset));
				dice.setCharAt(offset+1, dice.charAt(eoffset+1));
				dice.setCharAt(eoffset, nt);
				dice.setCharAt(eoffset+1, ns);
				//if(!visited.containsKey(dice.toString()) || visited.get(dice.toString())>depth){
					//visited.put(dice.toString(), depth);
					if(IDDFS(depth+1,lim,dice,xx,yy,eoffset))	return true;
				//}
				dice.setCharAt(eoffset, dice.charAt(offset));
				dice.setCharAt(eoffset+1, dice.charAt(offset+1));
				dice.setCharAt(offset, ot);
				dice.setCharAt(offset+1, os);
			}
			return false;
		}
		char turnR(int t,int s){
			for(int i=1; i<=3; i++)if(t!=i && s!=i)return (char)(i+'0');
			return 'b';
		}
	}
	
	class AOJ1268old{
		HashMap<String,Integer> visited;
		String fin;
		//TODO debug
		int C=0;
		final int[] vx={0,1,0,-1}, vy={-1,0,1,0};
		AOJ1268old(){
			while(true){
				int X=sc.nextInt(),Y=sc.nextInt();
				if((X|Y)==0)	break;
				solve(X,Y);
			}
		}
		void solve(int X,int Y){
			// TODO debug
			C=0;
			StringBuilder tmp=new StringBuilder();
			for(int i=0; i<9; i++){
				String in=sc.next();
				int c=0;
				if(in.equals("W"))	c=1;
				if(in.equals("B"))	c=2;
				if(in.equals("R"))	c=3;
				tmp.append(c);
			}
			fin=tmp.toString();
			int ans=-1;
			for(int i=0; i<=30; i++){
				ColoredDice[][] init=new ColoredDice[3][3];
				for(int j=0; j<9; j++)	init[j%3][j/3]=new ColoredDice(((X-1)+3*(Y-1))==j?0:1);
				visited=new HashMap<String, Integer>();
				if(IDDFS(0,i,init)){
					ans=i;
					break;
				}
			}
			//System.out.println(ans);
			System.out.println(ans+" "+C+"step");
		}
		boolean IDDFS(int depth,int max,ColoredDice[][] d){
			//TODO debug
			++C;
			int hs=0,ex=-1,ey=-1;
			for(int i=0; i<9; i++){
				if(d[i%3][i/3].top==0){
					ex=i%3;	ey=i/3;
				}
				else if(d[i%3][i/3].top!=fin.charAt(i)-'0')hs++;
			}
			if(hs==0)	return true;
			if(depth+hs>max)	return false;
			for(int v=0; v<4; v++){
				int xx=ex+vx[v], yy=ey+vy[v];
				if(!(0<=xx && xx<3 && 0<=yy && yy<3))	continue;
				ColoredDice tmp=d[xx][yy];
				d[xx][yy]=d[ex][ey];
				d[ex][ey]=tmp.turn(vx[v], vy[v]);
				StringBuilder sb=new StringBuilder();
				for(int j=0; j<9; j++)sb.append(d[j%3][j/3].toString());
				if(!visited.containsKey(sb.toString()) || visited.get(sb.toString())>depth){
					visited.put(sb.toString(), depth);
					if(IDDFS(depth+1,max,d))	return true;
				}
				d[ex][ey]=d[xx][yy];
				d[xx][yy]=tmp.turn(vx[v], vy[v]);
			}
			return false;
		}
		class ColoredDice{
			private int top=1,	bottom=1,
						east=2,	west=2,
						north=3,south=3;
			ColoredDice(int t){
				if(t==2)	turnEast();
				if(t==3)	turnNorth();
				if(t==0){
					top=0;	bottom=0;	east=0;
					west=0;	north=0;	south=0;
				}
			}
			ColoredDice turn(int x,int y){
				if(abs(x)==1)	return turnEast();
				if(abs(y)==1)	return turnNorth();
				return null;
			}
			ColoredDice turnEast(){
				int tmp=east;
				east=top;
				top=west;
				west=bottom;
				bottom=tmp;
				return this;
			}
			ColoredDice turnWest(){
				int tmp=west;
				west=top;
				top=east;
				east=bottom;
				bottom=tmp;
				return this;
			}
			ColoredDice turnSouth(){
				int tmp=south;
				south=top;
				top=north;
				north=bottom;
				bottom=tmp;
				return this;
			}
			ColoredDice turnNorth(){
				int tmp=north;
				north=top;
				top=south;
				south=bottom;
				bottom=tmp;
				return this;
			}
			int getTop(){
				return top;
			}
			@Override public String toString(){
				return ""+top+south;
			}
		}
	}

	
	// Asia 2003JP#D Weather forecast(DFS)
	class AOJ1243DFS{
		final int[] v={0,-8,-4,1,2,4,8,-1,-2};
		ArrayList<HashSet<String>> visited;
		AOJ1243DFS(){
			while(true){
				int N=sc.nextInt();
				if(N==0)	break;
				System.out.println(solve(N)?1:0);
			}
		}
		boolean solve(int N){
			boolean[][] s=new boolean[17][N+1];
			visited=new ArrayList<HashSet<String>>();
			visited.add(new HashSet<String>());
			for(int y=1; y<=N; y++){
				visited.add(new HashSet<String>());
				for(int x=1; x<=16; x++)s[x][y]=(sc.nextInt()==1);
			}
			if(s[6][1] || s[7][1] || s[10][1] || s[11][1])	return false;
			return DFS(6,2,N,"11116",s);
		}
		boolean DFS(int cx,int depth,int N,String r,boolean[][] s){
			if(depth>N)	return true;
			for(int i=0; i<9; i++){
				if(!(cx==1||cx==5||cx==9) && v[i]==2)continue;
				if(!(cx==3||cx==7||cx==11) && v[i]==-2)continue;
				int c=cx+v[i];
				if(!((1<=c && c<=3)||(5<=c && c<=7)||(9<=c && c<=11)))	continue;
				if(s[c][depth] || s[c+1][depth] || s[c+4][depth] || s[c+5][depth])	continue;
				int[] r2=decode(r);
				switch(c){
				case 1:r2[0]=-1;	break;
				case 3:r2[1]=-1;	break;
				case 11:r2[2]=-1;	break;
				case 9:r2[3]=-1;	break;
				}
				boolean f=true;
				for(int j=0; j<4; j++)if(++r2[j]>6)f=false;
				if(!f)continue;
				String r3=encode(r2,c);
				if(visited.get(depth).contains(r3))continue;
				visited.get(depth).add(r3);
				if(DFS(c,depth+1,N,r3,s))	return true;
			}
			return false;
		}
		int[] decode(String r){
			int[] ret=new int[4];
			for(int i=0; i<4; i++)ret[i]=r.charAt(i)-'0';
			return ret;
		}
		String encode(int[] r,int c){
			StringBuilder ret=new StringBuilder();
			for(int i=0; i<4; i++)ret.append(r[i]);
			ret.append(c);
			return ret.toString();
		}
	}
	
	
	// Asia 2003JP#D Weather forecast(BFS)
	class AOJ1243BFS{
		final int[] v={0,-8,-4,1,2,4,8,-1,-2};
		AOJ1243BFS(){
			while(true){
				int N=sc.nextInt();
				if(N==0)	break;
				System.out.println(solve(N)?1:0);
			}
		}
		boolean solve(int N){
			boolean[][] s=new boolean[17][N+1];
			ArrayList<HashSet<String>> closed=new ArrayList<HashSet<String>>();
			for(int y=1; y<=N; y++){
				closed.add(new HashSet<String>());
				for(int x=1; x<=16; x++)s[x][y]=(sc.nextInt()==1);
			}
			if(s[6][1] || s[7][1] || s[10][1] || s[11][1])	return false;
			LinkedList<State> open=new LinkedList<Main.AOJ1243BFS.State>();
			open.add(new State(2, 6, "11116"));
			while(!open.isEmpty()){
				State now=open.poll();
				if(now.day>N)	return true;
				for(int i=0; i<9; i++){
					if(!(now.c==1||now.c==5||now.c==9) && v[i]==2)continue;
					if(!(now.c==3||now.c==7||now.c==11) && v[i]==-2)continue;
					int cc=now.c+v[i];
					if(!((1<=cc && cc<=3)||(5<=cc && cc<=7)||(9<=cc && cc<=11)))	continue;
					if(s[cc][now.day] || s[cc+1][now.day] || s[cc+4][now.day] || s[cc+5][now.day])	continue;
					int[] r=now.decode();
					switch(cc){
					case 1:r[0]=-1;		break;
					case 3:r[1]=-1;		break;
					case 11:r[2]=-1;	break;
					case 9:r[3]=-1;		break;
					}
					boolean f=true;
					for(int j=0; j<4; j++)if(++r[j]>6)f=false;
					if(!f)continue;
					State next=new State(now.day+1, cc, r);
					if(next.day>N)	return true;
					if(closed.get(now.day).contains(next.r))continue;
					open.add(next);
					closed.get(now.day).add(next.r);
				}
			}
			return false;
		}
		class State{
			int c,day;
			String r;
			State(int day,int c,String r){
				this.day=day;
				this.c=c;
				this.r=r;
			}
			State(int day,int c,int[] r){
				this.day=day;
				this.c=c;
				StringBuilder tmp=new StringBuilder();
				for(int i=0; i<4; i++)tmp.append(r[i]);
				tmp.append(c);
				this.r=tmp.toString();
			}
			int[] decode(){
				int[] ret=new int[4];
				for(int i=0; i<4; i++)ret[i]=r.charAt(i)-'0';
				return ret;
			}
		}
	}
	
	
	// Confusing Login Names
	class AOJ1252{
		AOJ1252(){
			while(true){
				int N=sc.nextInt();
				if(N==0)	break;
				solve(N);
			}
		}
		void solve(int N){
			int D=sc.nextInt();
			String[] names=new String[N];
			for(int i=0; i<N; i++)	names[i]=sc.next();
			Arrays.sort(names);
			ArrayList<TreeSet<String>> state1=new ArrayList<TreeSet<String>>(),state2=new ArrayList<TreeSet<String>>();
			//ArrayList<HashSet<String>> state1=new ArrayList<HashSet<String>>(),state2=new ArrayList<HashSet<String>>();
			for(int i=0; i<N; i++){
				TreeSet<String> tmp=new TreeSet<String>();
				//HashSet<String> tmp=new HashSet<String>();
				for(int j=0; j<names[i].length(); j++){
					tmp.add(new StringBuilder(names[i]).deleteCharAt(j).toString());
					for(int k=0; k<26; k++){
						char c=(char)('a'+k);
						tmp.add(new StringBuilder(names[i]).insert(j, c).toString());
						StringBuilder sb=new StringBuilder(names[i]);
						sb.setCharAt(j, c);
						tmp.add(sb.toString());
					}
					tmp.add(swap(j,min(j+1,names[i].length()-1),names[i]));
				}
				for(int k=0; k<26; k++)	tmp.add(names[i]+(char)('a'+k));
				state1.add(tmp);
			}
			if(D>1)	state2=state1;
			else{
				for(int i=0; i<N; i++){
					TreeSet<String> tmp=new TreeSet<String>();
					//HashSet<String> tmp=new HashSet<String>();
					tmp.add(names[i]);
					state2.add(tmp);
				}
			}
			
			TreeSet<Pair> ans=new TreeSet<Main.AOJ1252.Pair>();
			for(int i=0; i<N; i++){
				for(int j=i+1; j<N; j++){
					if(names[i].length()-names[j].length()>4)	continue;
					for(String s:state1.get(i)){
						if(state2.get(j).contains(s))	ans.add(new Pair(names[i],names[j]));
					}
				}
			}
			for(Pair p:ans)	System.out.println(p);
			System.out.println(ans.size());
		}
		String swap(int a,int b,String str){
			StringBuilder sb=new StringBuilder(str);
			char tmp=sb.charAt(a);
			sb.setCharAt(a, sb.charAt(b));
			sb.setCharAt(b, tmp);
			return sb.toString();
		}
		class Pair implements Comparable<Pair>{
			String s1,s2;
			Pair(String s1,String s2){
				this.s1=s1;
				this.s2=s2;
			}
			@Override public int compareTo(Pair p){
				if(s1==p.s2 && s2==p.s1)	return 0;
				return s1.compareTo(p.s1)!=0?s1.compareTo(p.s1) :s2.compareTo(p.s2);
			}
			@Override public String toString(){
				return s1+","+s2;
			}
		}
	}
	
	
	// Gap
	class AOJ1245{
		AOJ1245(){
			int N=sc.nextInt();
			while(--N>=0)	solve();
		}
		void solve(){
			StringBuilder init=new StringBuilder(),fin=new StringBuilder();
			for(int i=1; i<=4; i++){
				init.append("##");
				for(int j=1; j<=7; j++){
					init.append(sc.nextInt());
					fin.append(i);	fin.append(j);
				}
				fin.append("##");
			}
			for(int i=0; i<32; i++){
				if(init.charAt(i*2+1)=='1')	nSwap(i*2,(init.charAt(i*2)-'0'-1)*16,init);
			}
			int ans=-1;
			PriorityQueue<State1> open=new PriorityQueue<State1>();
			open.add(new State1(init,0));
			HashMap<String,Integer> closed=new HashMap<String, Integer>();
			closed.put(init.toString(),0);
			while(!open.isEmpty()){
				State1 now=open.poll();
				if(now.sb.toString().equals(fin.toString())){
					ans=now.step;
					break;
				}
				for(int i=0; i<32; i++){
					if(now.sb.charAt(i*2)=='#' && now.sb.charAt((i-1)*2)!='#'){
						int s=now.sb.charAt((i-1)*2)-'0',v=now.sb.charAt((i-1)*2+1)-'0';
						if(v>=7)	continue;
						boolean bf=false;
						for(int j=0; j<32; j++){
							if(now.sb.charAt(j*2)-'0'==s && now.sb.charAt(j*2+1)-'0'==v+1){
								StringBuilder tmp=new StringBuilder(now.sb);
								nSwap(i*2,j*2,tmp);
								if(tmp.toString().equals(fin.toString())){
									ans=now.step+1;
									open.clear();
									bf=true;
									break;
								}
								if(closed.containsKey(tmp.toString()) && closed.get(tmp.toString())<=now.step+1)	break;
								open.add(new State1(tmp,now.step+1));
								closed.put(tmp.toString(),now.step+1);
								break;
							}
						}
						if(bf)	break;
					}
				}
			}
			System.out.println(ans);
		}
		void nSwap(int a,int b,StringBuilder sb){
			if(a==b)	return;
			swap(a,b,sb);
			swap(++a,++b,sb);
		}
		void swap(int a,int b,StringBuilder sb){
			char tmp=sb.charAt(a);
			sb.setCharAt(a, sb.charAt(b));
			sb.setCharAt(b, tmp);
		}
		class State1 implements Comparable<State1>{
			StringBuilder sb;
			int step;
			State1(StringBuilder sb,int step){
				this.sb=sb;	this.step=step;
			}
			@Override public int compareTo(State1 o) {
				return this.step-o.step;
			}
		}
	}
	
	class AOJ1258{
		final int INF=Integer.MAX_VALUE/4;
		AOJ1258(){
			while(true){
				int M=sc.nextInt(),C=sc.nextInt(),N=sc.nextInt();
				if(((M|C)|N)==0)	break;
				System.out.println(solve(M,C,N));
			}
		}
		int solve(int M,int C,int N){
			LinkedList<LinkedList<Integer>> q=new LinkedList<LinkedList<Integer>>();
			for(int i=0; i<N; i++){
				q.add(new LinkedList<Integer>());
				int K=sc.nextInt();
				for(int j=0; j<K; j++)	q.getLast().add(sc.nextInt());
			}
			Store store=new Store(M,C);
			int ans=0;
			while(!q.isEmpty()){
				int r=q.getFirst().poll();
				ans+=store.take(r);
				ans+=store.put(r);
				//debug
				//System.out.println(store);
				if(q.getFirst().isEmpty())	q.removeFirst();
				else	q.addLast(q.poll());
			}
			return ans;
		}
		class Store{
			int M,C,time;
			ArrayList<ArrayList<Book>> desks;
			Store(int m,int c){
				this.M=m;	this.C=c;	this.time=0;
				desks=new ArrayList<ArrayList<Book>>();
				for(int i=0; i<M; i++)	desks.add(new ArrayList<Book>());
			}
			int take(int r){
				int ret=M+1;
				for(int i=0; i<M; i++){
					for(int j=0; j<desks.get(i).size(); j++){
						if(desks.get(i).get(j).id==r){
							desks.get(i).remove(j);
							ret=i+1;
							break;
						}
					}
					if(ret<M+1)	break;
				}
				return ret;
			}
			int put(int r){
				int ret=M+1;
				if(desks.get(0).size()<C){
					desks.get(0).add(new Book(r,time++));
					ret=1;
				}else{
					ret=0;
					Pair tmpIdx=new Pair(M,0);
					for(int i=1; i<M; i++){
						if(desks.get(i).size()<C){
							tmpIdx.first=i;
							desks.get(i).add(new Book(INF,INF));
							tmpIdx.second=desks.get(i).size()-1;
							break;
						}
					}
					ret+=tmpIdx.first+1;
					int oldestTime=desks.get(0).get(0).t,oldestIdx=0;
					for(int i=1; i<desks.get(0).size(); i++){
						if(oldestTime>desks.get(0).get(i).t){
							oldestTime=desks.get(0).get(i).t;
							oldestIdx=i;
						}
					}
					Book oldest=desks.get(0).remove(oldestIdx);
					ret+=1;
					int empIdx=M;
					for(int i=1; i<M; i++){
						if(desks.get(i).size()<C){
							desks.get(i).add(oldest);
							empIdx=i;
							break;
						}
					}
					ret+=empIdx+1;
					if(tmpIdx.first<M)	desks.get(tmpIdx.first).remove(tmpIdx.second);
					ret+=tmpIdx.first+1;
					desks.get(0).add(new Book(r,time++));
					ret+=1;
				}
				return ret;
			}
			@Override public String toString(){return desks.toString();}
		}
		class Book{
			int id,t;
			Book(int id,int t){this.id=id;this.t=t;}
			@Override public String toString(){return "ID"+id+" T"+t;}
		}
		class Pair implements Comparable<Pair>{
			int first,second;
			Pair(int first,int second){this.first=first; this.second=second;}
			@Override public String toString(){return "("+first+","+second+")";}
			@Override public int compareTo(Pair p){
				if(this.first<p.first)	return -1;
				if(this.first>p.first)	return 1;
				if(this.second<p.second)	return -1;
				if(this.second>p.second)	return 1;
				return 0;
			}
			@Override public int hashCode(){
				return 17+31*first+second;
			}
			@Override public boolean equals(Object obj){
				if(this==obj)	return true;
				if(obj==null)	return false;
				if(this.getClass() != obj.getClass())	return false;
				Pair p=(Pair)obj;
				if(this.first==p.first&&this.second==p.second)	return true;
				return false;
			}
		}
	}
	
	class AOJ1262{
		final double INF=Double.MAX_VALUE/4.0;
		AOJ1262(){
			while(true){
				int N=sc.nextInt();
				if(N==0)	break;
				System.out.printf("%.4f\n",solve(N));
			}
		}
		double solve(int N){
			int[] a=new int[N+1];
			for(int i=1; i<=N; i++)	a[i]=sc.nextInt();
			double b=sc.nextDouble();
			int r=sc.nextInt();
			double v=sc.nextDouble(),e=sc.nextDouble(),f=sc.nextDouble();
			double[][] dp=new double[N+1][N+1];
			for(int i=1; i<=N; i++)for(int j=0; j<=N; j++)dp[i][j]=INF;
			//flash(dp,N);
			double tmp=0.0;
			for(int i=0; i<a[1]; i++)	tmp+=exp(i,r,v,e,f);
			dp[1][0]=tmp;
			for(int w=1; w<N; w++){
				for(int h=0; h<w; h++){
					int d=a[w+1]-a[w],x=a[w]-a[h];
					double exp=0.0;
					for(int i=0; i<d; i++)	exp+=exp(x++,r,v,e,f);
					//debug
					//System.out.println(exp);
					dp[w+1][h]=dp[w][h]+exp;
					double exp2=0.0;
					for(int i=0; i<d; i++)	exp2+=exp(i,r,v,e,f);
					dp[w+1][w]=min(dp[w+1][w], dp[w][h]+exp2+b);
				}
				//debug
				//System.out.println("new "+dp[w+1][w]);
			}
			//flash(dp,N);
			double ans=INF;
			for(int i=0; i<=N; i++)	ans=min(ans,dp[N][i]);
			return ans;
		}
		double exp(int x,double r,double v,double e,double f){
			return x>=r?(1/(v-e*(x-r))):(1/(v-f*(r-x)));
		}
		void flash(double[][] dp,int N){
			for(int y=0; y<=N; y++){
				for(int x=0; x<=N; x++)	System.out.printf("%3.3f ",dp[x][y]>=INF?-1:dp[x][y]);
				System.out.println();
			}
		}
	}
}