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.*;

public class C {
    FScanner in = new FScanner();
    PrintWriter out = new PrintWriter(new BufferedOutputStream(System.out), true);

    void run() {
        int n = Integer.parseInt(in.nextLine());
        String[] as = new String[n];
        char[] ops = new char[n];
        int[] num = new int[n];
        for (int i = 0; i < n; i++) {
            as[i] = in.nextLine();
            ops[i] = as[i].charAt(0);
            num[i] = Integer.parseInt(as[i].substring(2));
        }
        int start1 = 0;
        int start2 = 1023;
        for (int i = 0; i < n; i++) {
            if (ops[i] == '^') {
                start1 ^= num[i];
            } else if (ops[i] == '|') {
                start1 |= num[i];
            } else if (ops[i] == '&') {
                start1 &= num[i];
            }
        }
        for (int i = 0; i < n; i++) {
            if (ops[i] == '^') {
                start2 ^= num[i];
            } else if (ops[i] == '|') {
                start2 |= num[i];
            } else if (ops[i] == '&') {
                start2 &= num[i];
            }
        }
        int xor = 0, and = 0, or = 1023;
        for (int i = 0; i < 10; i++) {
            if (((start1 >> i) & 1) != 0 && ((start2 >> i) & 1) == 0) {
                xor += 1 << i;
            } else if (((start1 >> i) & 1) == 0 && ((start2 >> i) & 1) == 0) {
                or -= 1 << i;
            } else if (((start1 >> i) & 1) != 0 && ((start2 >> i) & 1) != 0) {
                and += 1 << i;
            }
        }
        out.printf("%d \n", 3);
        out.printf("^ %d \n", xor);
        out.printf("& %d \n", or);
        out.printf("| %d \n", and);
        out.close();
    }

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

    static class FScanner {
        BufferedReader br;
        StringTokenizer st;

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

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

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


        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }

        char[][] nextCharArray(int n, int m) {
            char[][] g = new char[n][m];
            for (int i = 0; i < n; i++)
                g[i] = next().toCharArray();
            return g;
        }

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

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

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