Little Dima has two sequences of points with integer coordinates: sequence (a1, 1), (a2, 2), ..., (an, n) and sequence (b1, 1), (b2, 2), ..., (bn, n).

Now Dima wants to count the number of distinct sequences of points of length 2·n that can be assembled from these sequences, such that the x-coordinates of points in the assembled sequence will not decrease. Help him with that. Note that each element of the initial sequences should be used exactly once in the assembled sequence.

Dima considers two assembled sequences (p1, q1), (p2, q2), ..., (p2·n, q2·n) and (x1, y1), (x2, y2), ..., (x2·n, y2·n) distinct, if there is such i (1 ≤ i ≤ 2·n), that (pi, qi) ≠ (xi, yi).

As the answer can be rather large, print the remainder from dividing the answer by number m.

Input

The first line contains integer n (1 ≤ n ≤ 105). The second line contains n integers a1, a2, ..., an (1 ≤ ai ≤ 109). The third line contains n integers b1, b2, ..., bn (1 ≤ bi ≤ 109). The numbers in the lines are separated by spaces.

The last line contains integer m (2 ≤ m ≤ 109 + 7).

Output

In the single line print the remainder after dividing the answer to the problem by number m. 

Examples

Input

1
1
2
7


Output

1


Input

2
1 2
2 3
11


Output

2

Note

In the first sample you can get only one sequence: (1, 1), (2, 1). 

In the second sample you can get such sequences : (1, 1), (2, 2), (2, 1), (3, 2); (1, 1), (2, 1), (2, 2), (3, 2). Thus, the answer is 2.
import java.io.*;
import java.math.BigInteger;
import java.util.*;

public class Main {
    public static void main(String[] args) {
        new Solution().run();
    }
}



final class Solution implements Runnable {

    static long MOD;

    int badCount = 0;

    long f(long n) {
        long res = 1;
        for (int i = 2; i <= n; i++) {
            int k = i;
            while (k % 2 == 0 && badCount > 0) {
                badCount--;
                k /= 2;
            }
            res = (res * k) % MOD;

        }
        return res;
    }

    int solve() throws Throwable {
        int n = in.nextInt();
        int[] a = new int[n];
        int[] b = 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();
            if (b[i] == a[i])
                badCount++;
        }

        HashMap<Integer, Integer> map = new HashMap<>();
        for (int i = 0; i < n; i++) {
            int k = a[i];
            Integer cur = map.get(k);
            if (cur == null)
                map.put(k, 1);
            else
                map.put(k, cur + 1);
        }

        for (int i = 0; i < n; i++) {
            int k = b[i];
            Integer cur = map.get(k);
            if (cur == null)
                map.put(k, 1);
            else
                map.put(k, cur + 1);
        }

        MOD = in.nextInt();

        long ans = 1;
        for (Map.Entry<Integer, Integer> entry : map.entrySet()) {
            ans = (ans * f(entry.getValue())) % MOD;
        }
        if (badCount > 0)
            ans = 0;
        out.print(ans);
        return 0;
    }


    FastScanner in;
    PrintWriter out;

    @Override
    public void run() {
        try {
            boolean ONLINE_JUDGE = false;
            try {
                Locale.setDefault(Locale.US);
                ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;
            } catch (SecurityException e) {
                System.err.println("Operation forbidden");
            }


            long time = System.currentTimeMillis();
            if (ONLINE_JUDGE) {
                in = new FastScanner(new InputStreamReader(System.in));
                out = new PrintWriter(System.out);
            } else {
                in = new FastScanner(new FileReader("input.txt"));
                out = new PrintWriter("output.txt");
            }

            int ret = solve();
            out.close();
            in.close();

            long delta = System.currentTimeMillis() - time;

            long freeMem = Runtime.getRuntime().freeMemory();
            long totalMem = Runtime.getRuntime().totalMemory();

            System.err.printf("Time: %.3f s\n", delta / 1000.0f);
            System.err.printf("Memory: %.3f MB\n", (float)(totalMem - freeMem) / (1 << 20));

            if (ret != 0)
                System.exit(ret);

        } catch (Throwable t) {
            t.printStackTrace(System.err);
            System.exit(-1);
        }
    }
}

@SuppressWarnings("unused")
final class FastScanner {
    BufferedReader bufferedReader;
    StringTokenizer stringTokenizer;

    public FastScanner(Reader r) {
        bufferedReader = new BufferedReader(r);
    }

    public String nextToken() throws IOException, NullPointerException {
        while (stringTokenizer == null || !stringTokenizer.hasMoreTokens())
            stringTokenizer = new StringTokenizer(bufferedReader.readLine());
        return stringTokenizer.nextToken();
    }

    public String nextLine() throws IOException {
        return bufferedReader.readLine();
    }

    public int nextInt() throws IOException, NullPointerException {
        return Integer.parseInt(nextToken());
    }

    public long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    public BigInteger nextBigInteger() throws IOException {
        return new BigInteger(nextToken());
    }

    public float nextFloat() throws IOException {
        return Float.parseFloat(nextToken());
    }

    public double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    public int read() throws IOException {
        return bufferedReader.read();
    }

    public void close() throws IOException {
        bufferedReader.close();
    }

    @Override
    protected void finalize() throws Throwable {
        super.finalize();
        close();
    }
}

final class DisjointSetUnion {
    int[] parent;
    int[] rank;

    public DisjointSetUnion(int size) {
        parent = new int[size];
        rank = new int[size];
        for (int i = 0; i < size; i++)
            parent[i] = i;
    }

    public int getLeader(int element) {
        if (parent[element] == element)
            return element;
        else
            return parent[element] = getLeader(parent[element]);
    }

    public boolean union(int x, int y) {
        x = getLeader(x);
        y = getLeader(y);
        if (x == y)
            return true;
        if (rank[x] < rank[y]) {
            int temp = x;
            x = y;
            y = temp;
        }
        parent[y] = x;
        if (rank[x] == rank[y])
            ++rank[x];
        return false;
    }
}

@SuppressWarnings("unused")
final class Utils {
    private Utils() {}

    public static long sqr(long x) {
        return x * x;
    }

    public static int gcd(int x, int y) {
        while (y > 0) {
            x %= y;
            int temp = x;
            x = y;
            y = temp;
        }
        return x;
    }

    public static int lcm(int x, int y) {
        return x / gcd(x, y) * y;
    }

    public static long gcd(long x, long y) {
        while (y > 0) {
            x %= y;
            long temp = x;
            x = y;
            y = temp;
        }
        return x;
    }

    public static long lcm(long x, long y) {
        return x / gcd(x, y) * y;
    }

    public static long modInverse(long x, long mod) {
        return BigInteger.valueOf(x).modInverse(BigInteger.valueOf(mod)).longValue();
    }
}