Problem: <image>

William is hosting a party for n of his trader friends. They started a discussion on various currencies they trade, but there's an issue: not all of his trader friends like every currency. They like some currencies, but not others.

For each William's friend i it is known whether he likes currency j. There are m currencies in total. It is also known that a trader may not like more than p currencies.

Because friends need to have some common topic for discussions they need to find the largest by cardinality (possibly empty) subset of currencies, such that there are at least ⌈ n/2 ⌉ friends (rounded up) who like each currency in this subset.

Input

The first line contains three integers n, m and p (1 ≤ n ≤ 2 ⋅ 10^5, 1 ≤ p ≤ m ≤ 60, 1 ≤ p ≤ 15), which is the number of trader friends, the number of currencies, the maximum number of currencies each friend can like.

Each of the next n lines contain m characters. The j-th character of i-th line is 1 if friend i likes the currency j and 0 otherwise. It is guaranteed that the number of ones in each line does not exceed p.

Output

Print a string of length m, which defines the subset of currencies of the maximum size, which are liked by at least half of all friends. Currencies belonging to this subset must be signified by the character 1.

If there are multiple answers, print any.

Examples

Input


3 4 3
1000
0110
1001


Output


1000


Input


5 5 4
11001
10101
10010
01110
11011


Output


10001

Note

In the first sample test case only the first currency is liked by at least ⌈ 3/2 ⌉ = 2 friends, therefore it's easy to demonstrate that a better answer cannot be found.

In the second sample test case the answer includes 2 currencies and will be liked by friends 1, 2, and 5. For this test case there are other currencies that are liked by at least half of the friends, but using them we cannot achieve a larger subset size.

Solution (in JAVA):

Solution:
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.util.Random;
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 << 29);
        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);
            DLoveHate solver = new DLoveHate();
            solver.solve(1, in, out);
            out.close();
        }
    }

    static class DLoveHate {
        public void solve(int testNumber, FastInput in, FastOutput out) {
            int n = in.ri();
            int m = in.ri();
            int p = in.ri();
            long[] bits = new long[n];
            for (int i = 0; i < n; i++) {
                for (int j = 0; j < m; j++) {
                    if (in.rc() == '1') {
                        bits[i] |= 1L << j;
                    }
                }
            }
            int[] sets = new int[1 << p];
            int[] bc = new int[1 << p];
            for (int i = 0; i < 1 << p; i++) {
                bc[i] = Integer.bitCount(i);
            }
            Randomized.shuffle(bits);
            int req = (n + 1) / 2;
            long best = 0;
            int bestSize = 0;
            long end = System.currentTimeMillis() + 2000;
            for (long bit : bits) {
                if (System.currentTimeMillis() > end) {
                    break;
                }
                Arrays.fill(sets, 0);
                IntegerArrayList offsetList = new IntegerArrayList(p);
                for (int i = 0; i < m; i++) {
                    if (Bits.get(bit, i) == 1) {
                        offsetList.add(i);
                    }
                }
                int[] offsets = offsetList.toArray();
                for (int i = 0; i < n; i++) {
                    int v = 0;
                    for (int j = 0; j < offsets.length; j++) {
                        if (Bits.get(bits[i], offsets[j]) == 1) {
                            v |= 1 << j;
                        }
                    }
                    sets[v]++;
                }

                FastWalshHadamardTransform.andFWT(sets, 0, sets.length - 1);
                for (int i = 0; i < sets.length; i++) {
                    if (sets[i] >= req && bc[i] > bestSize) {
                        bestSize = bc[i];
                        best = 0;
                        for (int j = 0; j < offsets.length; j++) {
                            if (Bits.get(i, j) == 1) {
                                best |= 1L << offsets[j];
                            }
                        }
                    }
                }
            }

            for (int i = 0; i < m; i++) {
                out.append(Bits.get(best, i));
            }
            out.println();
        }

    }

    static class Randomized {
        public static void shuffle(long[] data) {
            shuffle(data, 0, data.length);
        }

        public static void shuffle(long[] data, int from, int to) {
            to--;
            for (int i = from; i <= to; i++) {
                int s = nextInt(i, to);
                long tmp = data[i];
                data[i] = data[s];
                data[s] = tmp;
            }
        }

        public static int nextInt(int l, int r) {
            return RandomWrapper.INSTANCE.nextInt(l, r);
        }

    }

    static class SequenceUtils {
        public static boolean equal(int[] a, int al, int ar, int[] b, int bl, int br) {
            if ((ar - al) != (br - bl)) {
                return false;
            }
            for (int i = al, j = bl; i <= ar; i++, j++) {
                if (a[i] != b[j]) {
                    return false;
                }
            }
            return true;
        }

    }

    static class RandomWrapper {
        private Random random;
        public static final RandomWrapper INSTANCE = new RandomWrapper();

        public RandomWrapper() {
            this(new Random());
        }

        public RandomWrapper(Random random) {
            this.random = random;
        }

        public RandomWrapper(long seed) {
            this(new Random(seed));
        }

        public int nextInt(int l, int r) {
            return random.nextInt(r - l + 1) + l;
        }

    }

    static class FastWalshHadamardTransform {
        public static void andFWT(int[] p, int l, int r) {
            if (l == r) {
                return;
            }
            int m = DigitUtils.floorAverage(l, r);
            andFWT(p, l, m);
            andFWT(p, m + 1, r);
            for (int i = 0, until = m - l; i <= until; i++) {
                int a = p[l + i];
                int b = p[m + 1 + i];
                p[l + i] = a + b;
            }
        }

    }

    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 ri() {
            return readInt();
        }

        public int readInt() {
            boolean rev = false;

            skipBlank();
            if (next == '+' || next == '-') {
                rev = next == '-';
                next = read();
            }

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

            return rev ? val : -val;
        }

        public char rc() {
            return readChar();
        }

        public char readChar() {
            skipBlank();
            char c = (char) next;
            next = read();
            return c;
        }

    }

    static class IntegerArrayList implements Cloneable {
        private int size;
        private int cap;
        private int[] data;
        private static final int[] EMPTY = new int[0];

        public IntegerArrayList(int cap) {
            this.cap = cap;
            if (cap == 0) {
                data = EMPTY;
            } else {
                data = new int[cap];
            }
        }

        public IntegerArrayList(int[] data) {
            this(0);
            addAll(data);
        }

        public IntegerArrayList(IntegerArrayList list) {
            this.size = list.size;
            this.cap = list.cap;
            this.data = Arrays.copyOf(list.data, size);
        }

        public IntegerArrayList() {
            this(0);
        }

        public void ensureSpace(int req) {
            if (req > cap) {
                while (cap < req) {
                    cap = Math.max(cap + 10, 2 * cap);
                }
                data = Arrays.copyOf(data, cap);
            }
        }

        public void add(int x) {
            ensureSpace(size + 1);
            data[size++] = x;
        }

        public void addAll(int[] x) {
            addAll(x, 0, x.length);
        }

        public void addAll(int[] x, int offset, int len) {
            ensureSpace(size + len);
            System.arraycopy(x, offset, data, size, len);
            size += len;
        }

        public void addAll(IntegerArrayList list) {
            addAll(list.data, 0, list.size);
        }

        public int[] toArray() {
            return Arrays.copyOf(data, size);
        }

        public String toString() {
            return Arrays.toString(toArray());
        }

        public boolean equals(Object obj) {
            if (!(obj instanceof IntegerArrayList)) {
                return false;
            }
            IntegerArrayList other = (IntegerArrayList) obj;
            return SequenceUtils.equal(data, 0, size - 1, other.data, 0, other.size - 1);
        }

        public int hashCode() {
            int h = 1;
            for (int i = 0; i < size; i++) {
                h = h * 31 + Integer.hashCode(data[i]);
            }
            return h;
        }

        public IntegerArrayList clone() {
            IntegerArrayList ans = new IntegerArrayList();
            ans.addAll(this);
            return ans;
        }

    }

    static class FastOutput implements AutoCloseable, Closeable, Appendable {
        private static final int THRESHOLD = 32 << 10;
        private final Writer os;
        private StringBuilder cache = new StringBuilder(THRESHOLD * 2);

        public FastOutput append(CharSequence csq) {
            cache.append(csq);
            return this;
        }

        public FastOutput append(CharSequence csq, int start, int end) {
            cache.append(csq, start, end);
            return this;
        }

        private void afterWrite() {
            if (cache.length() < THRESHOLD) {
                return;
            }
            flush();
        }

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

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

        public FastOutput append(char c) {
            cache.append(c);
            afterWrite();
            return this;
        }

        public FastOutput append(int c) {
            cache.append(c);
            afterWrite();
            return this;
        }

        public FastOutput println() {
            return append('\n');
        }

        public FastOutput flush() {
            try {
//            boolean success = false;
//            if (stringBuilderValueField != null) {
//                try {
//                    char[] value = (char[]) stringBuilderValueField.get(cache);
//                    os.write(value, 0, cache.length());
//                    success = true;
//                } catch (Exception e) {
//                }
//            }
//            if (!success) {
                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 DigitUtils {
        private DigitUtils() {
        }

        public static int floorAverage(int x, int y) {
            return (x & y) + ((x ^ y) >> 1);
        }

    }

    static class Bits {
        private Bits() {
        }

        public static int get(int x, int i) {
            return (x >>> i) & 1;
        }

        public static int get(long x, int i) {
            return (int) ((x >>> i) & 1);
        }

    }
}