You are given a boolean function of three variables which is defined by its truth table. You need to find an expression of minimum length that equals to this function. The expression may consist of: 

  * Operation AND ('&', ASCII code 38) 
  * Operation OR ('|', ASCII code 124) 
  * Operation NOT ('!', ASCII code 33) 
  * Variables x, y and z (ASCII codes 120-122) 
  * Parentheses ('(', ASCII code 40, and ')', ASCII code 41) 



If more than one expression of minimum length exists, you should find the lexicographically smallest one.

Operations have standard priority. NOT has the highest priority, then AND goes, and OR has the lowest priority. The expression should satisfy the following grammar:

E ::= E '|' T | T

T ::= T '&' F | F

F ::= '!' F | '(' E ')' | 'x' | 'y' | 'z'

Input

The first line contains one integer n — the number of functions in the input (1 ≤ n ≤ 10 000).

The following n lines contain descriptions of functions, the i-th of them contains a string of length 8 that consists of digits 0 and 1 — the truth table of the i-th function. The digit on position j (0 ≤ j < 8) equals to the value of the function in case of <image>, <image> and <image>.

Output

You should output n lines, the i-th line should contain the expression of minimum length which equals to the i-th function. If there is more than one such expression, output the lexicographically smallest of them. Expressions should satisfy the given grammar and shouldn't contain white spaces.

Example

Input

4
00110011
00000111
11110000
00011111


Output

y
(y|z)&amp;x
!x
x|y&amp;z

Note

The truth table for the second function:

<image>
//package contests.c913;

import java.io.*;
import java.util.*;

public class C913E implements Runnable {

    private void solve() throws Exception {
        String[][] m = new String[256][3];
        m[0b00001111][0] = "x";
        m[0b00110011][0] = "y";
        m[0b01010101][0] = "z";

        boolean changed;
        String s;
        int r;
        int tt = 0;
        do {
            tt++;
            changed = false;

            for (int i = 0; i < 256; i++) {
                for (int j = 0; j < 3; j++) {
                    if (m[i][j] == null) continue;

                    if (j > 0) {
                        s = "(" + m[i][j] + ")";
                        if (shouldReplace(m[i][0], s)) {
                            m[i][0] = s;
                            changed = true;
                        }
                    }

                    if (j == 0) {
                        r = (~i) & 0b11111111;
                        s = "!" + m[i][j];
                        if (shouldReplace(m[r][0], s)) {
                            m[r][0] = s;
                            changed = true;
                        }
                    }

                    for (int x = 0; x < 256; x++) {
                        for (int y = 0; y < 3; y++) {
                            if (m[x][y] == null) continue;

                            if (j < 2 && y < 2) {
                                r = i & x;
                                s = m[i][j] + "&" + m[x][y];
                                if (shouldReplace(m[r][1], s)) {
                                    m[r][1] = s;
                                    changed = true;
                                }
                            }

                            r = i | x;
                            s = m[i][j] + "|" + m[x][y];
                            if (shouldReplace(m[r][2], s)) {
                                m[r][2] = s;
                                changed = true;
                            }
                        }
                    }
                }
            }

        } while (changed);

        int n = i();
        for (int i = 0; i < n; i++) {
            int a = Integer.parseInt(s(), 2);
            System.out.println(get(m, a));
        }
    }

    boolean shouldReplace(String current, String candidate) {
        return current == null ||
                current.length() > candidate.length() ||
                current.length() == candidate.length() && current.compareTo(candidate) > 0;
    }

    String get(String[][] m, int n) {
        String s = m[n][0];
        if (shouldReplace(s, m[n][1])) s = m[n][1];
        if (shouldReplace(s, m[n][2])) s = m[n][2];
        return s;
    }

    public void run() {
        long start = System.currentTimeMillis();

        try {
            solve();
        } catch (Exception e) {
            throw new RuntimeException(e);
        } finally {
            out.close();
        }

        if (!isOj)
            System.out.println(System.currentTimeMillis() - start + "ms");
    }

    public static void main(String[] args) throws Exception {
        new C913E().run();
    }

    InputStream inputStream;
    FastWriter out;

    private C913E() {
        this(System.in, System.out);
    }

    public C913E(InputStream inputStream, OutputStream outputStream) {
        this.inputStream = inputStream;
        this.out = new FastWriter(outputStream);
    }

    //@formatter:off
    private final byte[] inbuf = new byte[1024];
    private int lenbuf = 0, ptrbuf = 0;

    private int readByte() {
        if (lenbuf == -1) throw new InputMismatchException();
        if (ptrbuf >= lenbuf) {
            ptrbuf = 0;
            try {
                lenbuf = inputStream.read(inbuf);
            } catch (IOException e) {
                throw new InputMismatchException();
            }
            if (lenbuf <= 0) return -1;
        }
        return inbuf[ptrbuf++];
    }

    private boolean isSpaceChar(int c) {
        return !(c >= 33 && c <= 126);
    }

    private int skip() {
        int b;
        while ((b = readByte()) != -1 && isSpaceChar(b)) ;
        return b;
    }

    private char c() { return (char) skip(); }
    private char[] ca(int n) {
        char[] buf = new char[n];
        int b = skip(), p = 0;
        while (p < n && !(isSpaceChar(b))) {
            buf[p++] = (char) b;
            b = readByte();
        }
        return n == p ? buf : Arrays.copyOf(buf, p);
    }
    private char[][] caa(int n, int m) {
        char[][] map = new char[n][];
        for (int i = 0; i < n; i++) map[i] = ca(m);
        return map;
    }

    private int i() { return (int) l(); }
    private int[] ia(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++) a[i] = i();
        return a;
    }
    private int[][] iaa(int n, int m) {
        int[][] map = new int[n][];
        for (int i = 0; i < n; i++) map[i] = ia(m);
        return map;
    }
    private int[][] iaaT(int n, int m) {
        int[][] map = new int[m][];
        for (int i = 0; i < m; i++) map[i] = new int[n];
        for (int i = 0; i < n; i++) {
            int[] t = ia(m);
            for (int j = 0; j < m; j++) map[j][i] = t[j];
        }
        return map;
    }

    private long l() {
        long num = 0;
        int b;
        boolean minus = false;
        while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
        if (b == '-') {
            minus = true;
            b = readByte();
        }

        while (true) {
            if (b >= '0' && b <= '9') {
                num = num * 10 + (b - '0');
            } else {
                return minus ? -num : num;
            }
            b = readByte();
        }
    }
    private long[] la(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++) a[i] = l();
        return a;
    }

    private double d() { return Double.parseDouble(s()); }

    private String s() {
        int b = skip();
        StringBuilder sb = new StringBuilder();
        while (!(isSpaceChar(b))) { // when nextLine, (isSpaceChar(b) && b != ' ')
            sb.appendCodePoint(b);
            b = readByte();
        }
        return sb.toString();
    }

    //@formatter:on

    public static class FastWriter {
        private static final int BUF_SIZE = 1 << 13;
        private final byte[] buf = new byte[BUF_SIZE];
        private final OutputStream out;
        private int ptr = 0;
        private boolean isFirst = true;

        public FastWriter(OutputStream os) {
            this.out = os;
        }

        private FastWriter write(byte b) {
            buf[ptr++] = b;
            if (ptr == BUF_SIZE)
                innerflush();
            return this;
        }

        private FastWriter write(char c) {
            return write((byte) c);
        }

        private FastWriter write(char[] s) {
            for (char c : s) {
                buf[ptr++] = (byte) c;
                if (ptr == BUF_SIZE) innerflush();
            }
            return this;
        }

        private FastWriter write(String s) {
            s.chars().forEach(c -> {
                buf[ptr++] = (byte) c;
                if (ptr == BUF_SIZE) innerflush();
            });
            return this;
        }

        public static int countDigits(int l) {
            if (l >= 1000000000) return 10;
            if (l >= 100000000) return 9;
            if (l >= 10000000) return 8;
            if (l >= 1000000) return 7;
            if (l >= 100000) return 6;
            if (l >= 10000) return 5;
            if (l >= 1000) return 4;
            if (l >= 100) return 3;
            if (l >= 10) return 2;
            return 1;
        }

        private FastWriter write(int x) {
            if (x == Integer.MIN_VALUE) {
                return write((long) x);
            }
            if (ptr + 12 >= BUF_SIZE) innerflush();
            if (x < 0) {
                write((byte) '-');
                x = -x;
            }
            int d = countDigits(x);
            for (int i = ptr + d - 1; i >= ptr; i--) {
                buf[i] = (byte) ('0' + x % 10);
                x /= 10;
            }
            ptr += d;
            return this;
        }

        public static int countDigits(long l) {
            if (l >= 1000000000000000000L) return 19;
            if (l >= 100000000000000000L) return 18;
            if (l >= 10000000000000000L) return 17;
            if (l >= 1000000000000000L) return 16;
            if (l >= 100000000000000L) return 15;
            if (l >= 10000000000000L) return 14;
            if (l >= 1000000000000L) return 13;
            if (l >= 100000000000L) return 12;
            if (l >= 10000000000L) return 11;
            if (l >= 1000000000L) return 10;
            if (l >= 100000000L) return 9;
            if (l >= 10000000L) return 8;
            if (l >= 1000000L) return 7;
            if (l >= 100000L) return 6;
            if (l >= 10000L) return 5;
            if (l >= 1000L) return 4;
            if (l >= 100L) return 3;
            if (l >= 10L) return 2;
            return 1;
        }

        private FastWriter write(long x) {
            if (x == Long.MIN_VALUE) {
                return write("" + x);
            }
            if (ptr + 21 >= BUF_SIZE) innerflush();
            if (x < 0) {
                write((byte) '-');
                x = -x;
            }
            int d = countDigits(x);
            for (int i = ptr + d - 1; i >= ptr; i--) {
                buf[i] = (byte) ('0' + x % 10);
                x /= 10;
            }
            ptr += d;
            return this;
        }

        private FastWriter write(double x, int precision) {
            if (x < 0) {
                write('-');
                x = -x;
            }
            x += Math.pow(10, -precision) / 2;
            //		if(x < 0){ x = 0; }
            write((long) x).write(".");
            x -= (long) x;
            for (int i = 0; i < precision; i++) {
                x *= 10;
                write((char) ('0' + (int) x));
                x -= (int) x;
            }
            return this;
        }

        public FastWriter writeDelimeter() {
            if (isFirst) {
                isFirst = false;
            } else {
                write(' ');
            }
            return this;
        }

        public FastWriter writeNewline() {
            write('\n');
            isFirst = true;
            return this;
        }

        private void innerflush() {
            try {
                out.write(buf, 0, ptr);
                ptr = 0;
            } catch (IOException e) {
                throw new RuntimeException("innerflush");
            }
        }

        public void flush() {
            innerflush();
            try {
                out.flush();
            } catch (IOException e) {
                throw new RuntimeException("flush");
            }
        }

        public void close() {
            writeNewline();
            flush();
        }
    }

    //@formatter:off
    private void w(int x) { out.writeDelimeter().write(x); }
    private void w(long x) { out.writeDelimeter().write(x); }
    private void w(double x) { out.writeDelimeter().write(x, 16); }
    private void lnw(int x) { out.writeNewline().write(x); }
    private void lnw(long x) { out.writeNewline().write(x); }

    private static int log(int a) {
        if (a <= 0) throw new RuntimeException("log(a): a <= 0");
        return Integer.SIZE - 1 - Integer.numberOfLeadingZeros(a);
    }
    private static int log(long a) {
        if(a <= 0) throw new RuntimeException("log(a): a <= 0");
        return Long.SIZE - 1 - Long.numberOfLeadingZeros(a);
    }
    private static int max(int a, int b) {return Math.max(a, b);}
    private static long max(long a, long b) {return Math.max(a, b);}
    private static int min(int a, int b) {return Math.min(a, b);}
    private static int min(int a, int b, int c) {return min(a, min(b, c));}
    private static int min(int... x) {if (x.length == 1) return x[0]; if (x.length == 2) return min(x[0], x[1]); if (x.length == 3) return min(x[0], min(x[1], x[2])); int min = x[0]; for (int i = 1; i < x.length; ++i) if (x[i] < min) min = x[i]; return min;}
    private static long min(long a, long b) {return Math.min(a, b);}
    private static long min(long a, long b, long c) {return min(a, min(b, c));}
    private static long min(long... x) {if (x.length == 1) return x[0]; if (x.length == 2) return min(x[0], x[1]); if (x.length == 3) return min(x[0], min(x[1], x[2])); long min = x[0]; for (int i = 1; i < x.length; ++i) if (x[i] < min) min = x[i]; return min;}
    private static int pow(int a, int b) {if (a == 0) return 0; int r = 1; while (b > 0) {if ((b & 1) > 0) r *= a; a *= a; b >>= 1;} return r;}
    private static long pow(long a, int b) {if (a == 0) return 0; long r = 1; while (b > 0) {if ((b & 1) > 0) r *= a; a *= a; b >>= 1;} return r;}
    //@formatter:on

    private final boolean isOj = System.getProperty("ONLINE_JUDGE") != null;
}
