Problem: In mathematics, a subsequence is a sequence that can be derived from another sequence by deleting some elements without changing the order of the remaining elements. For example, the sequence BDF is a subsequence of ABCDEF. A substring of a string is a continuous subsequence of the string. For example, BCD is a substring of ABCDEF.

You are given two strings s1, s2 and another string called virus. Your task is to find the longest common subsequence of s1 and s2, such that it doesn't contain virus as a substring.

Input

The input contains three strings in three separate lines: s1, s2 and virus (1 ≤ |s1|, |s2|, |virus| ≤ 100). Each string consists only of uppercase English letters.

Output

Output the longest common subsequence of s1 and s2 without virus as a substring. If there are multiple answers, any of them will be accepted. 

If there is no valid common subsequence, output 0.

Examples

Input

AJKEQSLOBSROFGZ
OVGURWZLWVLUXTH
OZ


Output

ORZ


Input

AA
A
A


Output

0

Solution (in JAVA):

Solution:

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.lang.reflect.Array;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.List;

public class B {

    static int[][][] dp;
    static Pointer[][][] pointers;
    static String virus;
    static List<Integer>[][] prevs;

    public static void main(String[] args) throws Exception {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);

        String s1 = in.nextToken();
        String s2 = in.nextToken();
        virus = in.nextToken();

        int[] F = buildPartialMatch(virus);
        //prevs[char][i] = previous state that when take char, will lead to state i
        List<Integer>[][] prevs = (List<Integer>[][]) Array.newInstance(List[].class, 26);
        for(int c = 0; c < 26; c++){
            prevs[c] = (List<Integer>[]) Array.newInstance(List.class, F.length);
            for(int i = 0; i < F.length; i++){
                prevs[c][i] = new ArrayList<Integer>();
            }
        }

        int[][] auto = buildAutomaton(virus, F);
        for(int i = 0; i <= virus.length(); i++){
            for(int c = 0; c < 26; c++){
                prevs[c][auto[i][c]].add(i);
            }
        }
        
        int s1l = s1.length();
        int s2l = s2.length();

        //LCS considering s1[..i], s2[..j], such that suffix matches k-length prefix of virus
        dp = new int[s1l][s2l][virus.length()];
        pointers = new Pointer[s1l][s2l][virus.length()];

        for(int i = 0; i < s1l; i++){
            for(int j = 0; j < s2l; j++){
                for(int k = 0; k < virus.length(); k++){
                    dp[i][j][k] = -1;
                    char c1 = s1.charAt(i);
                    char c2 = s2.charAt(j);
                    if(c1 == c2){
                        for(int prev : prevs[c1-'A'][k]){
                            if(prev == virus.length()) continue;
                            update(i,j,k,i-1,j-1,prev,1);
                        }
                    }
                    update(i,j,k,i-1,j,k,0);
                    update(i,j,k,i,j-1,k,0);
                }   
            }   
        }

        int bestK = -1;
        for(int k = 0; k < virus.length(); k++){
            if(bestK == -1 || dp[s1l-1][s2l-1][bestK] < dp[s1l-1][s2l-1][k]){
                bestK = k;
            }
        }

        StringBuilder sb = new StringBuilder();
        int i = s1l-1;
        int j = s2l-1;
        int k = bestK;
        while(true){
            if(i < 0 || j < 0 ) break;
            Pointer p = pointers[i][j][k];
            if(p == null) break;
            if(p.i == i-1 && p.j == j-1){
                sb.append(s1.charAt(i));
            }

            i = p.i;
            j = p.j;
            k = p.k;
        }

        StringBuilder revsb = new StringBuilder();
        for(int ii = sb.length()-1; ii >= 0; ii--){
            revsb.append(sb.charAt(ii));
        }

        if(revsb.length() == 0) out.println(0);
        else out.println(revsb);
        out.close();
    }

    //which state will I be if at state i, and encounter char c, assume UPPERCASE
    static int[][] buildAutomaton(String s, int[] F) {
        int[][] auto = new int[F.length][26];
        auto[0][s.charAt(0)-'A'] = 1;
        for(int i = 1; i < F.length; i++){
            System.arraycopy(auto[F[i]], 0, auto[i], 0, 26);
            if(i != s.length())
                auto[i][s.charAt(i)-'A'] = i+1;
        }
        return auto;
    }

    static void update(int i, int j, int k, int ii, int jj, int kk, int offset){
        int newval = -1;
        if(ii < 0 || jj < 0){
            if(kk != 0) return;
            newval = offset;
        }else{
            if(dp[ii][jj][kk] == -1) return;
            newval = dp[ii][jj][kk] + offset;
        }

        if(dp[i][j][k] < newval){
            dp[i][j][k] = newval;
            pointers[i][j][k] = new Pointer(ii,jj,kk);
        }
    }

    // O(n), F[m] = i, consider first m chars of s, the length of longest PROPER suffix-prefix is i 
    static int[] buildPartialMatch(String s){
        int[] F = new int[s.length()+1];
        F[0] = F[1] = 0;
        for(int i = 2; i <= s.length(); i++){
            int j = F[i-1];
            char extension = s.charAt(i-1);
            while(true) {
                if(s.charAt(j) == extension) {
                    F[i] = j+1;
                    break;
                }

                if(j == 0) {
                    F[i] = 0;
                    break;
                }
                j = F[j];
            }
        }
        return F;
    }

    static class Pointer{
        public int i;
        public int j;
        public int k;
        public Pointer(int i, int j, int k) {
            this.i = i;
            this.j = j;
            this.k = k;
        }
    }

    static 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 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 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 String nextToken() {
            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 isWhitespace(c);
        }

        public static boolean isWhitespace(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        public interface SpaceCharFilter {
            public boolean isSpaceChar(int ch);
        }
    }
}