You are given two strings A and B representing essays of two students who are suspected cheaters. For any two strings C, D we define their similarity score S(C,D) as 4⋅ LCS(C,D) - |C| - |D|, where LCS(C,D) denotes the length of the Longest Common Subsequence of strings C and D. 

You believe that only some part of the essays could have been copied, therefore you're interested in their substrings.

Calculate the maximal similarity score over all pairs of substrings. More formally, output maximal S(C, D) over all pairs (C, D), where C is some substring of A, and D is some substring of B. 

If X is a string, |X| denotes its length.

A string a is a substring of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters from the beginning and several (possibly, zero or all) characters from the end.

A string a is a subsequence of a string b if a can be obtained from b by deletion of several (possibly, zero or all) characters. 

Pay attention to the difference between the substring and subsequence, as they both appear in the problem statement. 

You may wish to read the [Wikipedia page about the Longest Common Subsequence problem](https://en.wikipedia.org/wiki/Longest_common_subsequence_problem).

Input

The first line contains two positive integers n and m (1 ≤ n, m ≤ 5000) — lengths of the two strings A and B. 

The second line contains a string consisting of n lowercase Latin letters — string A.

The third line contains a string consisting of m lowercase Latin letters — string B. 

Output

Output maximal S(C, D) over all pairs (C, D), where C is some substring of A, and D is some substring of B. 

Examples

Input


4 5
abba
babab


Output


5

Input


8 10
bbbbabab
bbbabaaaaa


Output


12

Input


7 7
uiibwws
qhtkxcn


Output


0

Note

For the first case:

abb from the first string and abab from the second string have LCS equal to abb.

The result is S(abb, abab) = (4 ⋅ |abb|) - |abb| - |abab| = 4 ⋅ 3 - 3 - 4 = 5.
import java.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Calendar;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.SortedSet;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

/**
 * #
 *
 * @author pttrung
 */
public class B_Round_683_Div1 {
    public static long MOD = 1000000007;
    static int[][] dp;
    static boolean[][] check;

    public static void main(String[] args) throws FileNotFoundException {
        // PrintWriter out = new PrintWriter(new FileOutputStream(new File(
        // "output.txt")));
        PrintWriter out = new PrintWriter(System.out);
        Scanner in = new Scanner();
        int n = in.nextInt();
        int m = in.nextInt();
        check = new boolean[n][m];
        dp = new int[n][m];
        String a = in.next();
        String b = in.next();
        int result = 0;
        for (int i = 0; i < n; i++) {
            for (int j = 0; j < m; j++) {
                result = Integer.max(result, cal(i, j, a, b));
            }
        }
        out.println(result);
        out.close();
    }

    static int cal(int x, int y, String a, String b) {
        if (x == a.length() || y == b.length()) {
            return 0;
        }
        if (check[x][y]) {
            return dp[x][y];
        }
        int result = 0;
        if (a.charAt(x) == b.charAt(y)) {
            result = 2 + cal(x + 1, y + 1, a, b);
        } else {
            result = Integer.max(result, cal(x + 1, y, a, b) - 1);
            result = Integer.max(result, cal(x, y + 1, a, b) - 1);
        }
        check[x][y] = true;
        return dp[x][y] = result;
    }


    public static int[] KMP(String val) {
        int i = 0;
        int j = -1;
        int[] result = new int[val.length() + 1];
        result[0] = -1;
        while (i < val.length()) {
            while (j >= 0 && val.charAt(j) != val.charAt(i)) {
                j = result[j];
            }
            j++;
            i++;
            result[i] = j;
        }
        return result;

    }

    public static boolean nextPer(int[] data) {
        int i = data.length - 1;
        while (i > 0 && data[i] < data[i - 1]) {
            i--;
        }
        if (i == 0) {
            return false;
        }
        int j = data.length - 1;
        while (data[j] < data[i - 1]) {
            j--;
        }
        int temp = data[i - 1];
        data[i - 1] = data[j];
        data[j] = temp;
        Arrays.sort(data, i, data.length);
        return true;
    }

    public static int digit(long n) {
        int result = 0;
        while (n > 0) {
            n /= 10;
            result++;
        }
        return result;
    }

    public static double dist(long a, long b, long x, long y) {
        double val = (b - a) * (b - a) + (x - y) * (x - y);
        val = Math.sqrt(val);
        double other = x * x + a * a;
        other = Math.sqrt(other);
        return val + other;

    }

    public static class Point implements Comparable<Point> {

        int x, y;

        public Point(int start, int end) {
            this.x = start;
            this.y = end;
        }

        @Override
        public int hashCode() {
            int hash = 5;
            hash = 47 * hash + this.x;
            hash = 47 * hash + this.y;
            return hash;
        }

        @Override
        public boolean equals(Object obj) {
            if (obj == null) {
                return false;
            }
            if (getClass() != obj.getClass()) {
                return false;
            }
            final Point other = (Point) obj;
            if (this.x != other.x) {
                return false;
            }
            if (this.y != other.y) {
                return false;
            }
            return true;
        }

        @Override
        public int compareTo(Point o) {
            return Integer.compare(x, o.x);
        }
    }

    public static class FT {

        long[] data;

        FT(int n) {
            data = new long[n];
        }

        public void update(int index, long value) {
            while (index < data.length) {
                data[index] += value;
                index += (index & (-index));
            }
        }

        public long get(int index) {
            long result = 0;
            while (index > 0) {
                result += data[index];
                index -= (index & (-index));
            }
            return result;

        }
    }

    public static long gcd(long a, long b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }

    public static long pow(long a, int b) {
        if (b == 0) {
            return 1;
        }
        if (b == 1) {
            return a;
        }

        long val = pow(a, b / 2);
        if (b % 2 == 0) {
            return val * val;
        } else {
            return val * (val * a);

        }
    }

    static class Scanner {

        BufferedReader br;
        StringTokenizer st;

        public Scanner() throws FileNotFoundException {
            // System.setOut(new PrintStream(new BufferedOutputStream(System.out), true));
            br = new BufferedReader(new InputStreamReader(System.in));
            //  br = new BufferedReader(new InputStreamReader(new FileInputStream(new File("input.txt"))));
        }

        public String next() {

            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    throw new RuntimeException();
                }
            }
            return st.nextToken();
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }

        public boolean endLine() {
            try {
                String next = br.readLine();
                while (next != null && next.trim().isEmpty()) {
                    next = br.readLine();
                }
                if (next == null) {
                    return true;
                }
                st = new StringTokenizer(next);
                return st.hasMoreTokens();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }
    }
}