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

public class ShortProgram879C {
    public static void main(String[] args) throws IOException {
        FastScanner in = new FastScanner();
        int n = in.nextInt();
        int zeroes = 0;
        int ones = 1023;
        for (int i = 0; i < n; i++) {
            char c = in.nextToken().charAt(0);
            int j = in.nextInt();
            if (c == '|') {
                zeroes = zeroes | j;
                ones = ones | j;
            } else if (c == '&') {
                zeroes = zeroes & j;
                ones = ones & j;
            } else {
                zeroes = zeroes ^ j;
                ones = ones ^ j;
            }
        }
        
        int and = 0;
        int or = 0;
        int xor = 0;
        for (int i = 1; i < 1024; i = i * 2) {
            boolean zero = zeroes % (2 * i) == i;
            if (zero) zeroes -= i;
            boolean one = ones % (2 * i) == i;
            if (one) ones -= i;
            if (zero && one) {
                and += i;
                or += i;
            } else if (zero) {
                and += i;
                xor += i;
            } else if (one) {
                and += i;
            }
        }
        
        System.out.println(3);
        System.out.println("& " + and);
        System.out.println("| " + or);
        System.out.println("^ " + xor);
                
    }

    public static class FastScanner {
        BufferedReader br;
        StringTokenizer st;

        public FastScanner(String s) {
            try {
                br = new BufferedReader(new FileReader(s));
            } catch (FileNotFoundException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
        }

        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() {
            st = null;
            try {
                return br.readLine();
            } catch (IOException e) {
                // TODO Auto-generated catch block
                e.printStackTrace();
            }
            return null;
        }

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

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

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