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.*;
import java.util.Arrays;
import java.util.StringTokenizer;


public class Main {
    static final int clear = 0, set = 1, toggle = 2, keep = 3;

    public static void main(String[] args) throws IOException {
        Scanner sc = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);
        int m = 10;
        int[] state = new int[m];
        Arrays.fill(state, keep);
        int n = sc.nextInt();
        while (n-- > 0) {
            char op = sc.nextChar();
            int x = sc.nextInt();
            if (op == '|') {
                for (int i = 0; i < m; i++)
                    if ((x & 1 << i) != 0) state[i] = getNewState(state[i], set);
            }
            if (op == '^') {
                for (int i = 0; i < m; i++)
                    if ((x & 1 << i) != 0) state[i] = getNewState(state[i], toggle);
            }
            if (op == '&') {
                for (int i = 0; i < m; i++)
                    if ((x & 1 << i) == 0) state[i] = getNewState(state[i], clear);
            }
        }
        int and = (1 << 10) - 1, or = 0, xor = 0;
        for (int i = 0; i < m; i++)
            if (state[i] == set) or |= 1 << i;
            else if (state[i] == toggle) xor |= 1 << i;
            else if (state[i] == clear) and &= ~(1 << i);
        out.println(3);
        out.println("& " + and);
        out.println("| " + or);
        out.println("^ " + xor);
        out.flush();
        out.close();
    }

    static int getNewState(int oldState, int newState) {
        if (newState == clear || newState == set) return newState;
        if (oldState == set || oldState == clear) return 1 - oldState;
        if (oldState == toggle) return keep;
        return toggle;
    }


    static class Scanner {

        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream system) {
            br = new BufferedReader(new InputStreamReader(system));
        }

        boolean ready() throws IOException {
            return br.ready();
        }


        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens()) st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public double nextDouble() throws IOException {
            return Double.parseDouble(next());
        }

        public char nextChar() throws IOException {
            return next().charAt(0);
        }

        public Long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public int[] nextIntArray(int n) throws IOException {
            int[] a = new int[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

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


        public Integer[] nextIntegerArray(int n) throws IOException {
            Integer[] a = new Integer[n];
            for (int i = 0; i < n; i++)
                a[i] = nextInt();
            return a;
        }

        public double[] nextDoubleArray(int n) throws IOException {
            double[] ans = new double[n];
            for (int i = 0; i < n; i++)
                ans[i] = nextDouble();
            return ans;
        }

        public short nextShort() throws IOException {
            return Short.parseShort(next());
        }

    }

}