Problem: We have a grid with A horizontal rows and B vertical columns, with the squares painted white. On this grid, we will repeatedly apply the following operation:

* Assume that the grid currently has a horizontal rows and b vertical columns. Choose "vertical" or "horizontal".
* If we choose "vertical", insert one row at the top of the grid, resulting in an (a+1) \times b grid.
* If we choose "horizontal", insert one column at the right end of the grid, resulting in an a \times (b+1) grid.
* Then, paint one of the added squares black, and the other squares white.



Assume the grid eventually has C horizontal rows and D vertical columns. Find the number of ways in which the squares can be painted in the end, modulo 998244353.

Constraints

* 1 \leq A \leq C \leq 3000
* 1 \leq B \leq D \leq 3000
* A, B, C, and D are integers.

Input

Input is given from Standard Input in the following format:


A B C D


Output

Print the number of ways in which the squares can be painted in the end, modulo 998244353.

Examples

Input

1 1 2 2


Output

3


Input

2 1 3 4


Output

65


Input

31 41 59 265


Output

387222020

Solution (in JAVA):

Solution:
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.BufferedOutputStream;
import java.io.UncheckedIOException;
import java.util.Objects;
import java.nio.charset.Charset;
import java.util.StringTokenizer;
import java.io.Writer;
import java.io.OutputStreamWriter;
import java.io.BufferedReader;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author mikit
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        LightScanner in = new LightScanner(inputStream);
        LightWriter out = new LightWriter(outputStream);
        BExtension solver = new BExtension();
        solver.solve(1, in, out);
        out.close();
    }

    static class BExtension {
        private static final int MOD = 998244353;

        public void solve(int testNumber, LightScanner in, LightWriter out) {
            int a1 = in.ints(), b1 = in.ints(), a2 = in.ints(), b2 = in.ints();
            int ad = a2 - a1, bd = b2 - b1;
            ModMath mod = new ModMath(MOD);
            if (ad == 0 || bd == 0) {
                out.ans(mod.pow(a1, bd) * mod.pow(b1, ad) % MOD).ln();
                return;
            }
            long[][][] dp = new long[2][a2 + 1][b2 + 1];
            dp[0][a1][b1] = 1;
            for (int i = a1 + 1; i <= a2; i++) dp[0][i][b1] = dp[0][i - 1][b1] * b1 % MOD;
            for (int i = b1 + 1; i <= b2; i++) {
                dp[0][a1][i] = dp[0][a1][i - 1] * (a1 - 1) % MOD;
                dp[1][a1][i] += dp[0][a1][i - 1];
                dp[1][a1][i] += dp[1][a1][i - 1] * a1;
                dp[1][a1][i] %= MOD;
            }

            for (int i = a1 + 1; i <= a2; i++) {
                for (int j = b1 + 1; j <= b2; j++) {
                    dp[1][i][j] += dp[0][i][j - 1];
                    dp[1][i][j] += dp[1][i][j - 1] * i % MOD;
                    dp[1][i][j] %= MOD;


                    //dp[0][i][j] += dp[0][i][j - 1] * (i - 1) % MOD;
                    dp[0][i][j] += dp[0][i - 1][j] * j % MOD;
                    dp[0][i][j] += dp[1][i - 1][j] * j % MOD;
                    dp[0][i][j] %= MOD;
                }
            }
            long ans = (dp[0][a2][b2] + dp[1][a2][b2]) % MOD;
            out.ans(ans).ln();
            //Arrays.stream(dp[0]).map(Arrays::toString).forEach(System.out::println);
            //Arrays.stream(dp[1]).map(Arrays::toString).forEach(System.out::println);

        /*
        long inv2 = new ModMath(MOD).inv(2);

        dp[0][a1][b1] = 1;
        for (int i = a1 + 1; i <= a2; i++) {
            dp[0][i][b1] = dp[0][i - 1][b1] * (b1 - 1) % MOD;
            dp[1][i][b1] = (dp[1][i - 1][b1] + dp[0][i - 1][b1]) % MOD;
        }
        for (int i = b1 + 1; i <= b2; i++) {
            dp[0][a1][i] = dp[0][a1][i - 1] * (a1 - 1) % MOD;
            dp[2][a1][i] = (dp[2][a1][i - 1] + dp[0][a1][i - 1]) % MOD;
        }


        for (int i = a1 + 1; i <= a2; i++) {
            for (int j = b1 + 1; j <= b2; j++) {
                dp[0][i][j] += dp[0][i - 1][j] * (j - 1) % MOD;
                dp[0][i][j] += dp[0][i][j - 1] * (i - 1) % MOD;
                dp[0][i][j] += dp[1][i][j - 1] * (i - 1) % MOD;
                dp[0][i][j] += dp[2][i - 1][j] * (j - 1) % MOD;
                //dp[0][i][j] += dp[0][i - 1][j - 1] * (i - 1) % MOD * (j - 1) % MOD;
                //dp[0][i][j] += dp[1][i - 1][j - 1] * (i - 1) % MOD * (j - 1) % MOD;
                //dp[0][i][j] += dp[2][i - 1][j - 1] * (i - 1) % MOD * (j - 1) % MOD;
                dp[0][i][j] %= MOD;

                dp[1][i][j] += dp[0][i - 1][j];
                dp[1][i][j] += dp[1][i - 1][j];
                dp[1][i][j] += dp[2][i - 1][j];
                dp[1][i][j] += dp[1][i - 1][j] * (j - 1) % MOD;
                dp[1][i][j] %= MOD;

                dp[2][i][j] += dp[0][i][j - 1];
                dp[2][i][j] += dp[1][i][j - 1];
                dp[2][i][j] += dp[2][i][j - 1];
                dp[2][i][j] += dp[2][i][j - 1] * (i - 1) % MOD;
                dp[2][i][j] %= MOD;
            }
        }

        long ans = (dp[0][a2][b2] + dp[1][a2][b2] + dp[2][a2][b2]) % MOD;
        out.ans(ans).ln();*/
        }

    }

    static class LightScanner implements AutoCloseable {
        private BufferedReader reader = null;
        private StringTokenizer tokenizer = null;

        public LightScanner(InputStream in) {
            reader = new BufferedReader(new InputStreamReader(in));
        }

        public String string() {
            while (tokenizer == null || !tokenizer.hasMoreTokens()) {
                try {
                    tokenizer = new StringTokenizer(reader.readLine());
                } catch (IOException e) {
                    throw new UncheckedIOException(e);
                }
            }
            return tokenizer.nextToken();
        }

        public int ints() {
            return Integer.parseInt(string());
        }

        public void close() {
            try {
                this.reader.close();
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
        }

    }

    static class ModMath {
        private static final int DEFAULT_MOD = 1_000_000_007;
        private final long mod;

        public ModMath(long mod, boolean unsafe) {
        /*if (!unsafe && !IntMath.isPrime(mod)) {
            throw new RuntimeException("This class is designed for primes!");
        }*/
            this.mod = mod;
        }

        public ModMath(long mod) {
            this(mod, false);
        }

        public ModMath() {
            this(DEFAULT_MOD, true);
        }

        public long mod(long x) {
            x %= mod;
            return x < 0 ? x + mod : x;
        }

        public long inv(long x) {
            //return pow(x, mod - 2);
            return mod(LongEuclidSolver.solve(x, mod).x);
        }

        public long pow(long x, long y) {
            y %= (mod - 1);
            if (y < 0) {
                return pow(inv(x), -y);
            } else if (y == 0) {
                return 1;
            } else if (y % 2 == 0) {
                long z = pow(x, y / 2);
                return (z * z) % mod;
            } else {
                return (x % mod) * pow(x, y - 1) % mod;
            }
        }

    }

    static interface Verified {
    }

    static class LongEuclidSolver {
        private LongEuclidSolver() {
        }

        public static Vec3l solve(long a, long b) {
            LongEuclidSolver.ReferenceLong p = new LongEuclidSolver.ReferenceLong(), q = new LongEuclidSolver.ReferenceLong();
            long d = solve(a, b, p, q);
            return new Vec3l(p.val, q.val, d);
        }

        private static long solve(long a, long b, LongEuclidSolver.ReferenceLong p, LongEuclidSolver.ReferenceLong q) {
            if (b == 0) {
                p.val = 1;
                q.val = 0;
                return a;
            } else {
                long d = solve(b, a % b, q, p);
                q.val -= (a / b) * p.val;
                return d;
            }
        }

        private static class ReferenceLong {
            private long val;

        }

    }

    static class Vec3i implements Comparable<Vec3i> {
        public int x;
        public int y;
        public int z;

        public Vec3i(int x, int y, int z) {
            this.x = x;
            this.y = y;
            this.z = z;
        }

        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Vec3i vec3i = (Vec3i) o;
            return x == vec3i.x &&
                    y == vec3i.y &&
                    z == vec3i.z;
        }

        public int hashCode() {
            return Objects.hash(x, y, z);
        }

        public String toString() {
            return "(" + x + ", " + y + ", " + z + ")";
        }

        public int compareTo(Vec3i o) {
            if (x == o.x) {
                if (y == o.y) {
                    return Integer.compare(z, o.z);
                }
                return Integer.compare(y, o.z);
            }
            return Integer.compare(x, o.x);
        }

    }

    static class LightWriter implements AutoCloseable {
        private final Writer out;
        private boolean autoflush = false;
        private boolean breaked = true;

        public LightWriter(Writer out) {
            this.out = out;
        }

        public LightWriter(OutputStream out) {
            this(new OutputStreamWriter(new BufferedOutputStream(out), Charset.defaultCharset()));
        }

        public LightWriter print(char c) {
            try {
                out.write(c);
                breaked = false;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public LightWriter print(String s) {
            try {
                out.write(s, 0, s.length());
                breaked = false;
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
            return this;
        }

        public LightWriter ans(String s) {
            if (!breaked) {
                print(' ');
            }
            return print(s);
        }

        public LightWriter ans(long l) {
            return ans(Long.toString(l));
        }

        public LightWriter ln() {
            print(System.lineSeparator());
            breaked = true;
            if (autoflush) {
                try {
                    out.flush();
                } catch (IOException ex) {
                    throw new UncheckedIOException(ex);
                }
            }
            return this;
        }

        public void close() {
            try {
                out.close();
            } catch (IOException ex) {
                throw new UncheckedIOException(ex);
            }
        }

    }

    static class Vec3l implements Comparable<Vec3l> {
        public long x;
        public long y;
        public long z;

        public Vec3l(long x, long y, long z) {
            this.x = x;
            this.y = y;
            this.z = z;
        }

        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;
            Vec3i vec3i = (Vec3i) o;
            return x == vec3i.x &&
                    y == vec3i.y &&
                    z == vec3i.z;
        }

        public int hashCode() {
            return Objects.hash(x, y, z);
        }

        public String toString() {
            return "(" + x + ", " + y + ", " + z + ")";
        }

        public int compareTo(Vec3l o) {
            if (x == o.x) {
                if (y == o.y) {
                    return Long.compare(z, o.z);
                }
                return Long.compare(y, o.z);
            }
            return Long.compare(x, o.x);
        }

    }
}