Problem: Petya learned a new programming language CALPAS. A program in this language always takes one non-negative integer and returns one non-negative integer as well.

In the language, there are only three commands: apply a bitwise operation AND, OR or XOR with a given constant to the current integer. A program can contain an arbitrary sequence of these operations with arbitrary constants from 0 to 1023. When the program is run, all operations are applied (in the given order) to the argument and in the end the result integer is returned.

Petya wrote a program in this language, but it turned out to be too long. Write a program in CALPAS that does the same thing as the Petya's program, and consists of no more than 5 lines. Your program should return the same integer as Petya's program for all arguments from 0 to 1023.

Input

The first line contains an integer n (1 ≤ n ≤ 5·105) — the number of lines.

Next n lines contain commands. A command consists of a character that represents the operation ("&", "|" or "^" for AND, OR or XOR respectively), and the constant xi 0 ≤ xi ≤ 1023.

Output

Output an integer k (0 ≤ k ≤ 5) — the length of your program.

Next k lines must contain commands in the same format as in the input.

Examples

Input

3
| 3
^ 2
| 1


Output

2
| 3
^ 2


Input

3
&amp; 1
&amp; 3
&amp; 5


Output

1
&amp; 1


Input

3
^ 1
^ 2
^ 3


Output

0

Note

You can read about bitwise operations in <https://en.wikipedia.org/wiki/Bitwise_operation>.

Second sample:

Let x be an input of the Petya's program. It's output is ((x&1)&3)&5 = x&(1&3&5) = x&1. So these two programs always give the same outputs.

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.math.BigInteger;
import java.util.*;
import java.util.concurrent.ThreadLocalRandom;
import java.util.concurrent.atomic.AtomicLong;
import java.util.stream.Collectors;
import java.util.stream.IntStream;
import java.util.stream.Stream;

public class Main2 {

    static long mod = 1000000007L;
    static FastScanner scanner;

    static char[] types;
    static int[] consts;

    public static void main(String[] args) {
        scanner = new FastScanner();
        int n = scanner.nextInt();
        types = new char[n];
        consts = new int[n];

        for (int i = 0; i < n; i++) {
            types[i] = scanner.nextToken().charAt(0);
            consts[i] = scanner.nextInt();
        }

        int xor = 0;
        int[] result = new int[10];
        int mask = 1;
        for (int i = 0; i < n; i++) {
            if (types[i] == '^') xor ^= consts[i];
        }
        for (int i = 0; i < 10; i++) {
            int withZero = applyAll(0) & mask;
            int withOne = applyAll(mask) & mask;
            if (withZero != withOne) {
                result[i] = 2;
            } else if (withZero == 0) {
                result[i] = 0;
            } else {
                result[i] = 1;
            }
            mask <<= 1;
        }

        int and1 = toValue(IntStream.of(result).map(ii -> ii == 2 ? 1 : 0).toArray());
        int or = toValue(IntStream.of(result).map(ii -> ii == 1 ? 1 : 0).toArray());
        int and2 = toValue(IntStream.of(result).map(ii -> ii != 0 ? 1 : 0).toArray());
        System.out.println(4);
        System.out.println("^ " + xor);
        System.out.println("& " + and1);
        System.out.println("| " + or);
        System.out.println("& " + and2);
    }

    static int toValue(int[] bits) {
        int mask = 1;
        int val = 0;
        for (int i = 0; i < 10; i++) {
            if (bits[i] == 1) val |= mask;
            mask <<= 1;
        }
        return val;
    }

    static int applyAll(int val) {
        int cur = val;
        for (int i = 0; i < types.length; i++) {
            cur = apply(cur, types[i], consts[i]);
        }
        return cur;
    }


    static int apply(int val, char type, int cst) {
        switch (type) {
            case '&': return val & cst;
            case '|': return val | cst;
            case '^': return val ^ cst;
        }
        throw new IllegalArgumentException("e");
    }

    static class Pos implements Comparable<Pos> {
        int val, ind;

        public Pos(int val, int ind) {
            this.val = val;
            this.ind = ind;
        }

        @Override
        public int compareTo(Pos o) {
            return Integer.compare(val, o.val);
        }
    }

    static class Pt{
        long x, y;

        public Pt(long x, long y) {
            this.x = x;
            this.y = y;
        }
    }
    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String nextToken() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    // TODO Auto-generated catch block
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        String nextLine() {
            try {
                return br.readLine();
            } catch (Exception e) {
                e.printStackTrace();
                throw new RuntimeException();
            }
        }

        int nextInt() {
            return Integer.parseInt(nextToken());
        }

        long nextLong() {
            return Long.parseLong(nextToken());
        }

        double nextDouble() {
            return Double.parseDouble(nextToken());
        }

        int[] nextIntArray(int n) {
            int[] res = new int[n];
            for (int i = 0; i < n; i++) res[i] = nextInt();
            return res;
        }

        long[] nextLongArray(int n) {
            long[] res = new long[n];
            for (int i = 0; i < n; i++) res[i] = nextLong();
            return res;
        }

        String[] nextStringArray(int n) {
            String[] res = new String[n];
            for (int i = 0; i < n; i++) res[i] = nextToken();
            return res;
        }
    }

    static class PrefixSums {
        long[] sums;

        public PrefixSums(long[] sums) {
            this.sums = sums;
        }

        public long sum(int fromInclusive, int toExclusive) {
            if (fromInclusive > toExclusive) throw new IllegalArgumentException("Wrong value");
            return sums[toExclusive] - sums[fromInclusive];
        }

        public static PrefixSums of(int[] ar) {
            long[] sums = new long[ar.length + 1];
            for (int i = 1; i <= ar.length; i++) {
                sums[i] = sums[i - 1] + ar[i - 1];
            }
            return new PrefixSums(sums);
        }

        public static PrefixSums of(long[] ar) {
            long[] sums = new long[ar.length + 1];
            for (int i = 1; i <= ar.length; i++) {
                sums[i] = sums[i - 1] + ar[i - 1];
            }
            return new PrefixSums(sums);
        }
    }

    static class ADUtils {
        static void sort(int[] ar) {
            Random rnd = ThreadLocalRandom.current();
            for (int i = ar.length - 1; i > 0; i--)
            {
                int index = rnd.nextInt(i + 1);
                // Simple swap
                int a = ar[index];
                ar[index] = ar[i];
                ar[i] = a;
            }
            Arrays.sort(ar);
        }

        static void sort(long[] ar) {
            Random rnd = ThreadLocalRandom.current();
            for (int i = ar.length - 1; i > 0; i--)
            {
                int index = rnd.nextInt(i + 1);
                // Simple swap
                long a = ar[index];
                ar[index] = ar[i];
                ar[i] = a;
            }
            Arrays.sort(ar);
        }
    }

    static class MathUtils {
        static long[] FIRST_PRIMES = {
                2,     3,      5,      7,     11,     13,     17,     19,     23,     29,
                31,     37,     41,     43,     47,     53,     59,     61,     67,     71,
                73,     79,     83,     89  ,   97 ,    101,    103,    107,    109,    113,
                127,    131,    137,    139,    149,    151,    157,    163,    167,    173,
                179,    181,    191,    193,    197,    199,    211,    223,    227,    229,
                233,    239,    241,    251,    257,    263,    269,    271,    277,    281,
                283,    293,    307,    311,    313,    317,    331,    337,    347,    349,
                353,    359,    367,    373,    379,    383,    389,    397,    401,    409,
                419,    421,    431,    433,    439,    443,    449,    457,    461,    463,
                467,    479,    487,    491,    499,    503,    509,    521,    523,    541,
                547,    557,    563,    569,    571,    577,    587,    593,    599,    601,
                607,    613,    617,    619,    631,    641,    643,    647,    653,    659,
                661,    673,    677,    683,    691,    701,    709,    719,    727,    733,
                739,    743,    751,    757,    761,    769,    773,    787,    797,    809,
                811,    821,    823,    827,    829,    839,    853,    857,    859,    863,
                877,    881,    883,    887,    907,    911,    919,    929,    937,    941,
                947,    953,    967,    971,    977,    983,    991,    997,   1009,   1013,
                1019,   1021,   1031,   1033,   1039,   1049,   1051};

        static long[] primes(long to) {
            long[] result = Arrays.copyOf(FIRST_PRIMES, 10000);
            int size = FIRST_PRIMES.length;
            a:
            for (long t = 1061; t <= to; t++) {
                for (int i = 0; i < size; i++) {
                    if (t % result[i] == 0) {
                        continue a;
                    }
                }
                result[size++] = t;
            }
            return Arrays.copyOf(result, size);
        }

        static long modpow(long b, long e, long m) {
            long result = 1;

            while (e > 0) {
                if ((e & 1) == 1) {
            /* multiply in this bit's contribution while using modulus to keep
             * result small */
                    result = (result * b) % m;
                }
                b = (b * b) % m;
                e >>= 1;
            }

            return result;
        }

        static long submod(long x, long y, long m) {
            return (x - y + m) % m;
        }
    }
}