Problem:
Score : 1500 points

Problem Statement

#nck {
width: 30px;
height: auto;
}

Shik's job is very boring. At day 0, his boss gives him a string S_0 of length N which consists of only lowercase English letters. In the i-th day after day 0, Shik's job is to copy the string S_{i-1} to a string S_i. We denote the j-th letter of S_i as S_i[j].

Shik is inexperienced in this job. In each day, when he is copying letters one by one from the first letter to the last letter, he would make mistakes. That is, he sometimes accidentally writes down the same letter that he wrote previously instead of the correct one. More specifically, S_i[j] is equal to either S_{i-1}[j] or S_{i}[j-1]. (Note that S_i[1] always equals to S_{i-1}[1].)

You are given the string S_0 and another string T.
Please determine the smallest integer i such that S_i could be equal to T. If no such i exists, please print -1.

Constraints

1 \leq N \leq 1,000,000

The lengths of S_0 and T are both N.

Both S_0 and T consist of lowercase English letters.

Input

The input is given from Standard Input in the following format:

N
S_0
T

Output

Print the smallest integer i such that S_i could be equal to T. If no such i exists, print -1 instead.

Sample Input 1

5
abcde
aaacc

Sample Output 1

2

S_0 = abcde, S_1 = aaccc and S_2 = aaacc is a possible sequence such that S_2 = T.

Sample Input 2

5
abcde
abcde

Sample Output 2

0

Sample Input 3

4
acaa
aaca

Sample Output 3

2

Sample Input 4

5
abcde
bbbbb

Sample Output 4

-1

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.util.Arrays;
import java.io.IOException;
import java.io.UncheckedIOException;
import java.io.Closeable;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.InputStream;

/**
 * Built using CHelper plug-in Actual solution is at the top
 * 
 * @author daltao
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "daltao", 1 << 27);
        thread.start();
        thread.join();
    }

    static class TaskAdapter implements Runnable {
        @Override
        public void run() {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            FastInput in = new FastInput(inputStream);
            FastOutput out = new FastOutput(outputStream);
            TaskF solver = new TaskF();
            solver.solve(1, in, out);
            out.close();
        }
    }
    static class TaskF {
        public void solve(int testNumber, FastInput in, FastOutput out) {
            int n = in.readInt();
            char[] s = new char[n];
            char[] t = new char[n];
            in.readString(s, 0);
            in.readString(t, 0);

            if (Arrays.equals(s, t)) {
                out.println(0);
                return;
            }
            int ans = 0;
            int scan = n;
            int[] delay = new int[n + 1];
            for (int i = n - 1; i >= 0; i--) {
                if (scan > i) {
                    // scan = i + 1
                    scan = i;
                    delay[scan] = Math.max(0, delay[scan + 1] - 1);
                }
                while (scan > 0 && s[scan] != t[i]) {
                    scan--;
                    delay[scan] = Math.max(0, delay[scan + 1] - 1);
                }
                if (s[scan] != t[i]) {
                    out.println(-1);
                    return;
                }
                delay[scan] = delay[scan + 1] + 1;
                ans = Math.max(ans, i - scan + delay[scan + 1]);
            }

            out.println(ans);
        }

    }
    static class FastInput {
        private final InputStream is;
        private byte[] buf = new byte[1 << 13];
        private int bufLen;
        private int bufOffset;
        private int next;

        public FastInput(InputStream is) {
            this.is = is;
        }

        private int read() {
            while (bufLen == bufOffset) {
                bufOffset = 0;
                try {
                    bufLen = is.read(buf);
                } catch (IOException e) {
                    throw new RuntimeException(e);
                }
                if (bufLen == -1) {
                    return -1;
                }
            }
            return buf[bufOffset++];
        }

        public void skipBlank() {
            while (next >= 0 && next <= 32) {
                next = read();
            }
        }

        public int readInt() {
            int sign = 1;

            skipBlank();
            if (next == '+' || next == '-') {
                sign = next == '+' ? 1 : -1;
                next = read();
            }

            int val = 0;
            if (sign == 1) {
                while (next >= '0' && next <= '9') {
                    val = val * 10 + next - '0';
                    next = read();
                }
            } else {
                while (next >= '0' && next <= '9') {
                    val = val * 10 - next + '0';
                    next = read();
                }
            }

            return val;
        }

        public int readString(char[] data, int offset) {
            skipBlank();

            int originalOffset = offset;
            while (next > 32) {
                data[offset++] = (char) next;
                next = read();
            }

            return offset - originalOffset;
        }

    }
    static class FastOutput implements AutoCloseable, Closeable {
        private StringBuilder cache = new StringBuilder(1 << 20);
        private final Writer os;

        public FastOutput(Writer os) {
            this.os = os;
        }

        public FastOutput(OutputStream os) {
            this(new OutputStreamWriter(os));
        }

        public FastOutput println(int c) {
            cache.append(c).append('\n');
            return this;
        }

        public FastOutput flush() {
            try {
                os.append(cache);
                cache.setLength(0);
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
            return this;
        }

        public void close() {
            flush();
            try {
                os.close();
            } catch (IOException e) {
                throw new UncheckedIOException(e);
            }
        }

    }
}