There is a square grid with N rows and M columns. Each square contains an integer: 0 or 1. The square at the i-th row from the top and the j-th column from the left contains a_{ij}.

Among the 2^{N+M} possible pairs of a subset A of the rows and a subset B of the columns, find the number of the pairs that satisfy the following condition, modulo 998244353:

* The sum of the |A||B| numbers contained in the intersection of the rows belonging to A and the columns belonging to B, is odd.

Constraints

* 1 \leq N,M \leq 300
* 0 \leq a_{i,j} \leq 1(1\leq i\leq N,1\leq j\leq M)
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N M
a_{11} ... a_{1M}
:
a_{N1} ... a_{NM}


Output

Print the number of the pairs of a subset of the rows and a subset of the columns that satisfy the condition, modulo 998244353.

Examples

Input

2 2
0 1
1 0


Output

6


Input

2 3
0 0 0
0 1 0


Output

8
import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
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
 */
public class Main {
    public static void main(String[] args) throws Exception {
        Thread thread = new Thread(null, new TaskAdapter(), "", 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);
            TaskE solver = new TaskE();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class TaskE {
        public void solve(int testNumber, FastInput in, FastOutput out) {
            int n = in.readInt();
            int m = in.readInt();
            boolean[][] mat = new boolean[n][m];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    mat[i][j] = in.readChar() == '1';
                }
            }
            GeneralizedLinearBasis glb = new GeneralizedLinearBasis(m);
            for (int i = 0; i < n; i++) {
                glb.add(mat[i]);
            }

            NumberTheory.Modular mod = new NumberTheory.Modular(998244353);
            NumberTheory.Power pow = new NumberTheory.Power(mod);
            int rowSet = mod.subtract(pow.pow(2, n), pow.pow(2, n - glb.size()));
            int ans = mod.mul(rowSet, pow.pow(2, m - 1));

            out.println(ans);
        }

    }

    static class NumberTheory {
        public static class Modular {
            int m;

            public Modular(int m) {
                this.m = m;
            }

            public Modular(long m) {
                this.m = (int) m;
                if (this.m != m) {
                    throw new IllegalArgumentException();
                }
            }

            public Modular(double m) {
                this.m = (int) m;
                if (this.m != m) {
                    throw new IllegalArgumentException();
                }
            }

            public int valueOf(int x) {
                x %= m;
                if (x < 0) {
                    x += m;
                }
                return x;
            }

            public int valueOf(long x) {
                x %= m;
                if (x < 0) {
                    x += m;
                }
                return (int) x;
            }

            public int mul(int x, int y) {
                return valueOf((long) x * y);
            }

            public int subtract(int x, int y) {
                return valueOf(x - y);
            }

            public String toString() {
                return "mod " + m;
            }

        }

        public static class Power {
            final NumberTheory.Modular modular;

            public Power(NumberTheory.Modular modular) {
                this.modular = modular;
            }

            public int pow(int x, long n) {
                if (n == 0) {
                    return modular.valueOf(1);
                }
                long r = pow(x, n >> 1);
                r = modular.valueOf(r * r);
                if ((n & 1) == 1) {
                    r = modular.valueOf(r * x);
                }
                return (int) r;
            }

        }

    }

    static class FastOutput implements AutoCloseable, Closeable {
        private StringBuilder cache = new StringBuilder(10 << 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);
                os.flush();
                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);
            }
        }

        public String toString() {
            return cache.toString();
        }

    }

    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) {
                    bufLen = -1;
                }
                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 char readChar() {
            skipBlank();
            char c = (char) next;
            next = read();
            return c;
        }

    }

    static class GeneralizedLinearBasis {
        private boolean[][] basis;
        private int size;
        private int dimension;
        private boolean[] or;
        private boolean[] buf;

        public GeneralizedLinearBasis(int dimension) {
            this.dimension = dimension;
            basis = new boolean[dimension][dimension];
            or = new boolean[dimension];
            buf = new boolean[dimension];
        }

        public void add(boolean[] bits) {
            System.arraycopy(bits, 0, buf, 0, dimension);
            bits = buf;
            for (int i = dimension - 1; i >= 0; i--) {
                if (!bits[i]) {
                    continue;
                }
                if (or[i]) {
                    for (int j = 0; j < dimension; j++) {
                        bits[j] = bits[j] != basis[i][j];
                    }
                    continue;
                }
                or[i] = true;
                size++;
                System.arraycopy(bits, 0, basis[i], 0, dimension);
                for (int j = i + 1; j < dimension; j++) {
                    if (!or[j] || !basis[j][i]) {
                        continue;
                    }
                    for (int k = 0; k < dimension; k++) {
                        basis[j][k] = basis[j][k] != basis[i][k];
                    }
                }
                return;
            }
        }

        public int size() {
            return size;
        }

    }
}

