Problem: There are two persons, numbered 0 and 1, and a variable x whose initial value is 0. The two persons now play a game. The game is played in N rounds. The following should be done in the i-th round (1 \leq i \leq N):

* Person S_i does one of the following:
* Replace x with x \oplus A_i, where \oplus represents bitwise XOR.
* Do nothing.



Person 0 aims to have x=0 at the end of the game, while Person 1 aims to have x \neq 0 at the end of the game.

Determine whether x becomes 0 at the end of the game when the two persons play optimally.

Solve T test cases for each input file.

Constraints

* 1 \leq T \leq 100
* 1 \leq N \leq 200
* 1 \leq A_i \leq 10^{18}
* S is a string of length N consisting of `0` and `1`.
* All numbers in input are integers.

Input

Input is given from Standard Input in the following format. The first line is as follows:


T


Then, T test cases follow. Each test case is given in the following format:


N
A_1 A_2 \cdots A_N
S


Output

For each test case, print a line containing `0` if x becomes 0 at the end of the game, and `1` otherwise.

Example

Input

3
2
1 2
10
2
1 1
10
6
2 3 4 5 6 7
111000


Output

1
0
0

Solution (in JAVA):

Solution:
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.NoSuchElementException;
import java.util.PrimitiveIterator;
import java.util.function.IntFunction;
import java.util.function.IntUnaryOperator;
import java.util.function.LongBinaryOperator;
import java.util.function.LongPredicate;
import java.util.function.LongUnaryOperator;



public class Main {
    public static void main(String[] args) {
        StringBuilder out = new StringBuilder();
        solve(out);
        PrintWriter pw = new PrintWriter(System.out);
        pw.println(out);
        pw.flush();
        pw.close();
    }

    public static void solve(StringBuilder out) {
        int t = In.ni();
        T:while (t --> 0) {
            int n = In.ni();
            long[] a = In.nl(n);
            char[] s = In.nc();
            LongXorBases b = new LongXorBases();
            for (int i = n - 1; i >= 0; i--) {
                if (s[i] == '0') {
                    b.appendBase(a[i]);
                } else {
                    if (!b.isExpressible(a[i])) {
                        out.append(1).append('\n');
                        continue T;
                    }
                }
            }
            out.append(0).append('\n');
        }
    }
}


/**
 * @author https://atcoder.jp/users/suisen
 */
final class In {
    public static final FastScanner fsc = new FastScanner();
    public static int ni() {return fsc.nextInt();}
    public static int[] ni(final int n) {
        final int[] a = new int[n];
        for (int i = 0; i < n; i++) a[i] = fsc.nextInt();
        return a;
    }
    public static int[] ni(final int n, final IntUnaryOperator f) {
        final int[] a = new int[n];
        for (int i = 0; i < n; i++) a[i] = f.applyAsInt(fsc.nextInt());
        return a;
    }
    public static int[][] ni(final int n, final int m) {
        final int[][] a = new int[n][m];
        for (int i = 0; i < n; i++) a[i] = ni(m);
        return a;
    }
    public static int[][] ni(final int n, final int m, final IntUnaryOperator f) {
        final int[][] a = new int[n][m];
        for (int i = 0; i < n; i++) a[i] = ni(m, f);
        return a;
    }
    public static long nl() {return fsc.nextLong();}
    public static long[] nl(final int n) {
        final long[] a = new long[n];
        for (int i = 0; i < n; i++) a[i] = fsc.nextLong();
        return a;
    }
    public static long[] nl(final int n, final LongUnaryOperator f) {
        final long[] a = new long[n];
        for (int i = 0; i < n; i++) a[i] = f.applyAsLong(fsc.nextLong());
        return a;
    }
    public static long[][] nl(final int n, final int m) {
        final long[][] a = new long[n][m];
        for (int i = 0; i < n; i++) a[i] = nl(m);
        return a;
    }
    public static long[][] nl(final int n, final int m, final LongUnaryOperator f) {
        final long[][] a = new long[n][m];
        for (int i = 0; i < n; i++) a[i] = nl(m, f);
        return a;
    }
    public static char[] nc() {return fsc.next().toCharArray();}
    public static char[][] nc(final int n) {
        final char[][] c = new char[n][];
        for (int i = 0; i < n; i++) c[i] = nc();
        return c;
    }
    public static double nd() {return fsc.nextDouble();}
    public static double[] nd(final int n) {
        final double[] a = new double[n];
        for (int i = 0; i < n; i++) a[i] = fsc.nextDouble();
        return a;
    }
    public static double[][] nd(final int n, final int m) {
        final double[][] a = new double[n][m];
        for (int i = 0; i < n; i++) a[i] = nd(m);
        return a;
    }
    public static String ns() {return fsc.next();}
    public static String[] ns(final int n) {
        final String[] s = new String[n];
        for (int i = 0; i < n; i++) s[i] = fsc.next();
        return s;
    }
    public static boolean[][] grid(final int h, final int w, final char trueCharacter) {
        final boolean[][] grid = new boolean[h][w];
        for (int i = 0; i < h; i++) {
            final char[] s = fsc.next().toCharArray();
            for (int j = 0; j < w; j++) grid[i][j] = s[j] == trueCharacter;
        }
        return grid;
    }
}


final class FastScanner {
    private final InputStream in = System.in;
    private final byte[] buffer = new byte[1024];
    private int ptr = 0;
    private int buflen = 0;
    private boolean hasNextByte() {
        if (ptr < buflen) return true;
        ptr = 0;
        try {buflen = in.read(buffer);}
        catch (final IOException e) {e.printStackTrace();}
        return buflen > 0;
    }
    private int readByte() {return hasNextByte() ? buffer[ptr++] : -1;}
    public boolean hasNext() {
        while (hasNextByte() && !(33 <= buffer[ptr] && buffer[ptr] <= 126)) ptr++;
        return hasNextByte();
    }
    public String next() {
        if (!hasNext()) throw new NoSuchElementException();
        final StringBuilder sb = new StringBuilder();
        int b = readByte();
        while (33 <= b && b <= 126) {sb.appendCodePoint(b); b = readByte();}
        return sb.toString();
    }
    public long nextLong() {
        if (!hasNext()) throw new NoSuchElementException();
        long n = 0;
        boolean minus = false;
        int b = readByte();
        if (b == '-') {minus = true; b = readByte();}
        if (b < '0' || '9' < b) throw new NumberFormatException();
        for (; ; b = readByte()) {
            if ('0' <= b && b <= '9') n = n * 10 + b - '0';
            else if (b == -1 || !(33 <= b && b <= 126)) return minus ? -n : n;
            else throw new NumberFormatException();
        }
    }
    public int nextInt() {return Math.toIntExact(nextLong());}
    public double nextDouble() {return Double.parseDouble(next());}
}


class LongXorBases {
    private final LongArrayList v;
    public LongXorBases() {v = new LongArrayList();}
    public LongXorBases(int[] a) {this(); for (int e : a) appendBase(e);}
    private long solve(long e) {
        PrimitiveIterator.OfLong iter = v.iterator();
        while (iter.hasNext()) {long vi = iter.nextLong(); e = Math.min(e, e ^ vi);}
        return e;
    }
    public boolean isExpressible(long e) {return solve(e) == 0;}
    public void appendBase(long e) {v.addIf(solve(e), w -> w != 0);}
}


/**
 * @author https://atcoder.jp/users/suisen
 * 
 * 1. DESTRUCTIVE methods for long arrays.
 * 2. methods that receives arrays and return some results (except for long arrays).
 */
final class LongArrays {
    private LongArrays(){}
    public static void swap(final long[] a, final int u, final int v) {
        final long tmp = a[u]; a[u] = a[v]; a[v] = tmp;
    }
    public static void reverse(final long[] a, final int begin, final int end) {
        for (int i = begin; i < begin + (end - begin) / 2; i++) swap(a, i, begin + end - i - 1);
    }
    public static void reverse(final long[] a) {reverse(a, 0, a.length);}
    public static void sortDescending(final long[] a) {Arrays.sort(a); reverse(a);}
    public static long reduce(final long[] a, final LongBinaryOperator op) {
        long ret = a[0]; for (int i = 1; i < a.length; i++) ret = op.applyAsLong(ret, a[i]);
        return ret;
    }
    public static void map(final long[] a, final LongUnaryOperator op) {Arrays.setAll(a, i -> op.applyAsLong(a[i]));}
    public static int filter(final long[] src, final long[] dst, final LongPredicate p) {
        int idx = 0;
        for (final long e : src) if (p.test(e)) dst[idx++] = e;
        return idx;
    }
    public static int filterIndex(final long[] dst, final int beginIndex, final int endIndex, final LongPredicate p) {
        int idx = 0;
        for (int i = beginIndex; i < endIndex; i++) if (p.test(i)) dst[idx++] = i;
        return idx;
    }
    public static int filterIndex(final long dst[], final int endIndex, final LongPredicate p) {
        return filterIndex(dst, 0, endIndex, p);
    }
    public static void accumulate(final long[] a, final LongBinaryOperator op) {
        for (int i = 1; i < a.length; i++) a[i] = op.applyAsLong(a[i - 1], a[i]);
    }
    public static void accumulate(final long[] a) {
        for (int i = 1; i < a.length; i++) a[i] += a[i - 1];
    }
    public static void permute(long[] a, int[] p) {
        int n = p.length;
        boolean[] settled = new boolean[n];
        for (int i = 0; i < n; i++) {
            for (int j = i; !settled[j]; j = p[j]) {
                if (p[j] == i) {
                    settled[j] = true;
                    break;
                }
                swap(a, j, p[j]);
                settled[j] = true;
            }
        }
    }
    public static int compare(final long[] a, final long[] b) {
        for (int i = 0; i < a.length; i++) {
            if (i >= b.length) return -1;
            if (a[i] > b[i]) return 1;
            if (a[i] < b[i]) return -1;
        }
        return a.length < b.length ? 1 : 0;
    }
    public static boolean equals(final long[] a, final long[] b) {return compare(a, b) == 0;}
    public static String join(final long[] a, final String sep) {
        final StringBuilder sb = new StringBuilder();
        for (int i = 0; i < a.length; i++) {
            sb.append(a[i]);
            if (i < a.length - 1) sb.append(sep);
        }
        return sb.toString();
    }
    public static String joinWithPrefixAndSuffix(final long[] a, final IntFunction<String> idxToPre, final IntFunction<String> idxToSuf, final String sep) {
        final StringBuilder sb = new StringBuilder();
        for (int i = 0; i < a.length; i++) {
            sb.append(idxToPre.apply(i)).append(a[i]).append(idxToSuf.apply(i));
            if (i < a.length - 1) sb.append(sep);
        }
        return sb.toString();
    }
}



/**
 * @author https://atcoder.jp/users/suisen
 */
final class LongArrayList implements Iterable<Long> {
    private long[] a;
    private int tail = 0;
    private static final int DEFAULT_SIZE = 64;
    public LongArrayList(final int capacity) {this.a = new long[Math.max(1, capacity)];}
    public LongArrayList() {this(DEFAULT_SIZE);}
    public void add(final long v) {
        if (tail == a.length) grow();
        a[tail++] = v;
    }
    public long removeLast() {return a[tail--];}
    public long get(final int i) {
        if (i >= a.length) throw new IndexOutOfBoundsException("Index " + i + " out of bounds for length " + size());
        return a[i];
    }
    public void set(final int i, final long v) {
        if (i >= a.length) throw new IndexOutOfBoundsException("Index " + i + " out of bounds for length " + size());
        a[i] = v;
    }
    private void grow() {
        final long[] b = new long[a.length << 1];
        System.arraycopy(a, 0, b, 0, a.length);
        a = b;
    }
    public int size() {return tail;}
    public void reverse(final int begin, final int end) {LongArrays.reverse(a, begin, end);}
    public void reverse() {LongArrays.reverse(a, 0, tail);}
    public long[] toArray() {
        final long[] ret = new long[tail];
        System.arraycopy(a, 0, ret, 0, tail);
        return ret;
    }
    public boolean addIf(final long v, final LongPredicate p) {
        if (p.test(v)) {add(v); return true;}
        return false;
    }
    public PrimitiveIterator.OfLong iterator() {return new LongArrayListIterator();}
    private class LongArrayListIterator implements PrimitiveIterator.OfLong {
        private int i = 0;
        public boolean hasNext() {return i < tail;}
        public long nextLong() {return a[i++];}
    }
}