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 D2 {
    public static long time = 0;

    public static void main(String[] args) throws Exception {
        time = System.currentTimeMillis();
        solve();
        out.flush();
    }

    public static void solve() throws Exception {
        int n1 = ni();
        int[] l1 = nil(n1);
        int[] l2 = nil(n1);
        int[] l3 = nil(n1);
        if (n1 == 1){
            pn(l1[0]);
            return;
        }
        int before = l1[0];
        int after = l2[0];
        for (int i =1; i < n1 - 1; i++){
            int kbefore = Integer.MIN_VALUE;
            int kafter = Integer.MIN_VALUE;
            kbefore = Math.max(before + l2[i], kbefore);
            kbefore = Math.max(after + l1[i], kbefore);
            kafter = Math.max(before + l3[i], kafter);
            kafter = Math.max(after + l2[i], kafter);
            before = kbefore;
            after = kafter;
//          px(before,after);
        }
        if (n1 >= 2){
            before += l2[n1 -1];
            after += l1[n1 -1];
        }
//      px(before, after);
        pn(Math.max(before, after) );
    }

    public static BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
    public static StringTokenizer st = null;

    public static String nx() throws Exception {
        for (; st == null || !st.hasMoreTokens();) {
            String k1 = in.readLine();
            if (k1 == null) return null;
            st = new StringTokenizer(k1);
        }
        return st.nextToken();
    }

    public static int ni() throws Exception {
        return Integer.parseInt(nx());
    }

    public static long nl() throws Exception {
        return Long.parseLong(nx());
    }

    public static double nd() throws Exception {
        return Double.parseDouble(nx());
    }

    private static int[] nil(int n1) throws Exception {
        int[] l1 = new int[n1];
        for (int i = 0; i < n1; i++) {
            l1[i] = ni();
        }
        return l1;
    }

    public static void px(Object... l1) {
        System.out.println(Arrays.deepToString(l1));
    }

    public static boolean FLUSH = false;
    public static PrintWriter out = new PrintWriter(System.out, FLUSH);

    public static void p(Object... l1) {
        for (int i = 0; i < l1.length; i++) {
            if (i != 0) out.print(' ');
            out.print(l1[i].toString());
        }
    }

    public static void pn(Object... l1) {
        for (int i = 0; i < l1.length; i++) {
            if (i != 0) out.print(' ');
            out.print(l1[i].toString());
        }
        out.println();
    }

    public static void pn(Collection l1) {
        boolean first = true;
        for (Object e : l1) {
            if (first) first = false;
            else out.print(' ');
            out.print(e.toString());
        }
        out.println();
    }

}
