Dima liked the present he got from Inna very much. He liked the present he got from Seryozha even more. 

Dima felt so grateful to Inna about the present that he decided to buy her n hares. Inna was very happy. She lined up the hares in a row, numbered them from 1 to n from left to right and started feeding them with carrots. Inna was determined to feed each hare exactly once. But in what order should she feed them?

Inna noticed that each hare radiates joy when she feeds it. And the joy of the specific hare depends on whether Inna fed its adjacent hares before feeding it. Inna knows how much joy a hare radiates if it eats when either both of his adjacent hares are hungry, or one of the adjacent hares is full (that is, has been fed), or both of the adjacent hares are full. Please note that hares number 1 and n don't have a left and a right-adjacent hare correspondingly, so they can never have two full adjacent hares.

Help Inna maximize the total joy the hares radiate. :)

Input

The first line of the input contains integer n (1 ≤ n ≤ 3000) — the number of hares. Then three lines follow, each line has n integers. The first line contains integers a1 a2 ... an. The second line contains b1, b2, ..., bn. The third line contains c1, c2, ..., cn. The following limits are fulfilled: 0 ≤ ai, bi, ci ≤ 105.

Number ai in the first line shows the joy that hare number i gets if his adjacent hares are both hungry. Number bi in the second line shows the joy that hare number i radiates if he has exactly one full adjacent hare. Number сi in the third line shows the joy that hare number i radiates if both his adjacent hares are full.

Output

In a single line, print the maximum possible total joy of the hares Inna can get by feeding them.

Examples

Input

4
1 2 3 4
4 3 2 1
0 1 1 0


Output

13


Input

7
8 5 7 6 1 8 9
2 7 9 5 4 3 1
2 3 3 4 1 1 3


Output

44


Input

3
1 1 1
1 2 1
1 1 1


Output

4
import java.util.*;
import java.io.*;
public class Main {
	public static Scanner in = new Scanner(System.in);
	static void swap(int []a,int i,int j) {
		int t = a[i];
		a[i]=a[j];
		a[j]=t;
	}
	static void select(int []a,int k) {
		int x = a[0];
		for(int i=1;i<a.length;i++) {
			if(a[i]<=x) {
				swap(a,i,x);
				x=i;
			}
		}
		
	}
	static int solve(int n,int v,int k,boolean vis[][],int dp[][]) {
		
		//System.out.println(n+" "+v+" "+k);
		if(n<0) return 0;
		if(k==0 && n>0) return 0;
		if(n==0 && k==0) {
			vis[0][0]=true;
			return dp[n][k]=1;
		}
		if(vis[n][k]) return dp[n][k];
		vis[n][k]=true;
		for(int i=v;i>=1;i--)
			dp[n][k]+=(solve(n-i,i,k-1,vis,dp))%1988;
		return dp[n][k];
	}
    public static void main(String[] args) {
    	int n = in.nextInt();
    	int a[]=new int[n],b[]=new int[n],c[]=new int[n];
    	for(int i=0;i<n;i++) a[i]=in.nextInt();
    	for(int i=0;i<n;i++) b[i]=in.nextInt();
    	for(int i=0;i<n;i++) c[i]=in.nextInt();
    	if(n==1) {
    		System.out.println(a[0]);
    		return;
    	}
    	int dp[][]=new int[n][2];
    	dp[1][1]=b[1]+a[0];
    	dp[1][0]=a[1]+b[0];
    	for(int i=2;i<n;i++) {
    		dp[i][0]=a[i]+(i>0?(Math.max(dp[i-1][1]+c[i-1]-b[i-1],dp[i-1][0]-a[i-1]+b[i-1])):0);
    		dp[i][1]=b[i]+(i>0?(Math.max(dp[i-1][1],dp[i-1][0])):0);
    	}
    	System.out.println(Math.max(dp[n-1][0],dp[n-1][1]));
    	//System.out.println(solve(7,7,3,new boolean[5001][5001],new int[5001][5001]));
    	/*int n = in.nextInt(),m=in.nextInt();
    	int dp[][]=new int[n+1][n+1];
    	dp[0][0]=1;
    	//for(int i=1;i<=n;i++) {
				for(int j=1;j<=n;j++) {
					for(int k=0;k<=n;k++) {
					if(j-k>=0)
						dp[j][k]+=dp[j-k][k];
					dp[j][k]+=dp[j-1][k];
					dp[j][k]%=1988;
				}
			}
    	//}
    	//dp[m]=sum of all such dp[i]
    	System.out.println(dp[n][m]);
    	/*long a[]=new long[n];
    	long dp[][][]=new long[n][n][2];
    	long max[][][]=new long[n][n][2];
    	long sum[][]=new long[n][n];

    	for(int i=0;i<n;i++) a[i]=in.nextInt();
    	for(int i=0;i<n;i++) {
    		sum[i][i]=a[i];
    		for(int j=i-1;j>=0;j--) {
    			sum[i][j]=sum[i][j+1]+a[j];
    		}
    	}
    	dp[0][1][0]=a[0];
    	//dp[1][2][0]=a[0]+a[1];
    	for(int j=n-2;j>=0;j--) {
			max[0][j][0]=Math.max(max[0][j+1][0],dp[0][j][0]);
			max[0][j][1]=Math.max(max[0][j+1][1],dp[0][j][1]);
			max[1][j][0]=Math.max(max[1][j+1][0],dp[1][j][0]);
			max[1][j][1]=Math.max(max[1][j+1][1],dp[1][j][1]);
		}

    	for(int i=1;i<n;i++) {
    		for(int j=1;j<=i;j++) {
    			if(i-j>=0) {
    				dp[i][j][0]=Math.max(dp[i][j][0],max[i-j][(j+1)/2][1]+sum[i][i-j+1]);
    				dp[i][j][1]=Math.max(dp[i][j][1],max[i-j][(j+1)/2][0]);
    			}
    		}
    		max[i][n-1][0]=dp[i][n-1][0];
    		max[i][n-1][1]=dp[i][n-1][1];
    		for(int j=n-2;j>=0;j--) {
    			max[i][j][0]=Math.max(max[i][j+1][0],dp[i][j][0]);
    			max[i][j][1]=Math.max(max[i][j+1][1],dp[i][j][1]);
    		}
    	}
    	long ans=0;
    	for(int i=0;i<n;i++) {
    		ans=Math.max(dp[n-1][i][0],ans);
    	}
    	System.out.println(ans);*/
    }
    static public long read(long []t,int i) {
    	long sum=0;
    	while(i>0) {
    		sum+=t[i];
    		i-=(i&-i);
    	}
    	return sum;
    }
    static public void upd(long []t,int i) {
    	while(i<1000002) {
    		t[i]++;
    		i+=(i&-i);
    	}
    }
   /* public static Scanner in = new Scanner(System.in);
    public static void main(String[] args) {
    	int n = in.nextInt(),m=in.nextInt();
    	HashSet<String> h = new HashSet<String>();
    	for(int i=0;i<n;i++) {
    		h.add(in.next());
    	}
    	int cn=0;
    	for(int j=0;j<m;j++) {
    		if(h.contains(in.next())) cn++;
    	}
    	n-=cn;
    	m-=cn;
    	if(m-n<(cn%2)) System.out.println("YES");
    	else System.out.println("NO");
     }
    /*
    public static void main(String[] args) {
       int n = in.nextInt();
       Segments s[] = new Segments[n];
       ArrayList<Long> xcord = new ArrayList<Long>();
       for(int i=0;i<n;i++) {
    	   long x,y;
    	   s[i]=new Segments(x=in.nextLong(),y=in.nextLong());
    	   in.nextInt();
    	   xcord.add(2*x);
    	   xcord.add(2*y);
       }
       Collections.sort(xcord);
       ArrayList<Long> nxcord = new ArrayList<Long>();
       for(int i=0;i<xcord.size()-1;i++) {
    	   nxcord.add((xcord.get(i)+xcord.get(i+1))/2);
       }
       xcord.addAll(nxcord);
       Collections.sort(xcord);
       
       for(int i=0;i<xcord.size();i++) {
    	   int j=i+1;
    	   long p = xcord.get(i);
    	   while(j<n && xcord.get(j)==xcord.get(i)) j++;
    	   int cn=0;
    	   for(int k=0;k<n;k++) {
    		   if(s[i].s<p && s[i].f>p) cn++;
    	   }
    	   for(int k=i-1;k>=0;k--) {
    		   
    	   }
       }
    }*/
    
}
class Segments{
	long s,f;
	Segments(long s,long f){
		this.s = s;
		this.f = f;
	}
}
/*
class dir{
	boolean l,r,u,d;
}
class Node extends ArrayList<Node>{

	private static final long serialVersionUID = 1L;
	double x,y;
	int i;
	boolean visited=false;
	Node(int x,int y,int i){
		this.x = x;
		this.y = y;
		this.i=i;
	}
	void reset(){
		visited = false;
	}
	boolean dfs(dir d,double mid,double w,double h,double [][]dists,double cmpr){
		visited = true;
		if(x+mid>=w)
			d.r=true;
		if(x-mid<=0.0)
			d.l=true;
		if(y+mid>=h)
			d.u=true;
		if(y-mid<=0.0)
			d.d=true;
		if((d.l && d.d) || (d.u && d.r) 
				|| (d.l && d.r) || (d.u && d.d)) {
			return true;
		}
		for(Node n : this) {
			if(!n.visited) {
				boolean fl=false;
				if(dists[i][n.i]<=cmpr)
					fl|=n.dfs(d,mid,w,h,dists,cmpr);
				if(fl) return fl;
			}
		}
		return false;
	}
	double dist(Node n1,Node n2) {
		return sq(n1.x-n2.x)+sq(n1.y-n2.y);
	}
	double sq(double a) {
		return a*a;
	}
}
class ChristmasBinaryTree{
    public int count(long d, int[] left, int[] right) {
    	int n = left.length;
    	int dp[][][]=new int[120][120][64];
    	for(int i=0;i<n;i++) {
    		dp[i][left[i]][0]=1;
    		dp[i][right[i]][0]=1;
    	}
    	while(d>0) {
    		long k=0;
    		for(;1<<k<=d;k++) {
    			for(int i=0;i<n;i++) {
    				for(int j=0;j<n;j++) {
    					for(int l=0;l<n;l++) {
    						dp[i][l][(int)k+1]+=
    								dp[i][j][(int)k]*dp[j][l][(int)k];
    						
    					}
    				}
    			}
    		}
        	int ndp[][][]=new int[120][120][64];
    		for(int i=0;i<n;i++) {
    			for(int j=0;j<n;j++) {
    				ndp[i][j][0]=dp[i][j][(int)k];
    			}
    		}
    		dp=ndp;
    		d-=1<<(k-1);
    	}
    	int cn=0;
    	for(int i=0;i<n;i++) {
    		for(int j=0;j<n;j++) {
    			cn+=dp[i][j][0]*dp[i][j][0];
    		}
    	}
    	return cn;
    }
}
/*
public class Main {
	private static InputReader in = new InputReader(System.in);
	public static void main(String args[]) {
		StringBuilder s = new StringBuilder();
		int t = in.readInt();
		while(t>0) {
			
			t--;
		}
		System.out.println(s);
	}

	/*public static int solve(String s, int i,int j,
    		int dp[][],boolean visited[][]) {
    	if(i>j) return 0;
    	if(i==j) return dp[i][j]=1;
    	if(visited[i][j]) return dp[i][j];
    	visited[i][j]=true;
    	solve(s,i+1,j,dp,visited);
    	solve(s,i,j-1,dp,visited);
    	if(s.charAt(i)==s.charAt(j)) {
    		if(i+1==j)
    			return dp[i][j]=2;
    		else {
    			return dp[i][j]=dp[i+1][j]+dp[i][j-1]-dp[i+1][j-1]+1;
    		}
    	}else {
    		if(i+1==j) return dp[i][j]=1;
    		return dp[i][j]=dp[i+1][j]+dp[i][j-1]-dp[i+1][j-1];
    	}
    }*/
	/*
    public static void main(String args[]) {
    	int t = in.nextInt();
    	while(t>0) {
    		int m = in.nextInt(), n = in.nextInt();
    		long p = in.nextLong();
    		long dp[][][]=new long[11][300][300];

    		for(int i=1;i<=m;i++)
    			dp[1][i][i]=1;
    		for(int i=1;i<n;i++) {
    			for(int j=1;j<m;j++) {
    				for(int k=1;k<=j;k++) {
    					for(int l=k;l>=1;l--) {
    						if(j+l<=m)
    							dp[i+1][j+l][l]+=dp[i][j][k];
    					}
    				}
    			}
    		}
    		System.out.println(dp[n][m-1][2]);
    		for(int i=n;i>0;i--) {
    			for(int j=1;j<=m;j++) {
    				if(dp[i][m-j][j]>=p) {
    					//System.out.print(j+" ");
    					m-=j;
    					break;
    				}else {
    					p-=dp[i][m-j][j];
    					System.out.print(p+" ");
    				}
    			}
    		}
    		System.out.println();
    		t--;
    	}

    }*/

class sh implements Comparable<sh>{
	int h,w,i;
	sh(int a,int b,int c){
		w=a;
		h=b;
		i=c;
	}
	@Override
	public int compareTo(sh o) {
		if(w==o.w) return h-o.h;
		return w-o.w;
	}

}

class InputReader {

	private InputStream stream;
	private byte[] buf = new byte[1024];
	private int curChar;
	private int numChars;
	private SpaceCharFilter filter;

	public InputReader(InputStream stream) {
		this.stream = stream;
	}

	public byte 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 int readInt() {
		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 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);
	}
}

class IOUtils {

	public static int[] readIntArray(InputReader in, int size) {
		int[] array = new int[size];
		for (int i = 0; i < size; i++)
			array[i] = in.readInt();
		return array;
	}
} 
