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.*;

/*
TASK: CFC
LANG: JAVA
 */
public class CFC {
    static int n;
    static String cho;
    static int cnst;
    static int[] kek;
    public static void main(String[] args) throws IOException {
        FastScanner in = new FastScanner(System.in);
        n = in.nextInt();
        kek = new int[10];
        Arrays.fill(kek , 2);
        for(int i = 0;i < n; i++){
            cho = in.next();
            cnst = in.nextInt();
            if(cho.equals("|")){
                for(int j = 0; j < 10; j++){
                    if(cnst % 2 == 1) kek[j] = 1;
                    cnst /= 2;
                }
            }
            else if(cho.equals("^")){
                for(int j = 0;j < 10; j++){
                    if(cnst % 2 == 1){
                        if(kek[j] == 0){
                            kek[j] = 1;
                        }
                        else if(kek[j] == 1){
                            kek[j] = 0;
                        }
                        else if(kek[j] == 2){
                            kek[j] = 3;
                        }
                        else if(kek[j] == 3){
                            kek[j] = 2;
                        }
                    }
                    cnst /= 2;
                }
            }
            else{
                for(int j = 0;j < 10; j++){
                    if(cnst % 2 == 0)kek[j] = 0;
                    cnst /= 2;
                }
            }
        }
        int and = 0;
        int or = 0;
        int xor = 0;
        for(int i = 9;i >= 0; i--){
            and *= 2;
            or *= 2;
            xor *= 2;
            if(kek[i] == 3)xor++;
            if(kek[i] == 1)or++;
            if(kek[i] == 0)and++;
        }
        and = 1023 - and;
        System.out.println(3);
        System.out.println("& " + and);
        System.out.println("| " + or);
        System.out.println("^ " + xor);
    }

    private static class FastScanner {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public FastScanner(InputStream stream) {
            this.stream = stream;
        }

        int read() {
            if (numChars == -1)
                throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) return -1;
            }
            return buf[curChar++];
        }

        boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }

        boolean isEndline(int c) {
            return c == '\n' || c == '\r' || c == -1;
        }

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

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

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

        public String next() {
            int c = read();
            while (isSpaceChar(c)) c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isSpaceChar(c));
            return res.toString();
        }

        public String nextLine() {
            int c = read();
            while (isEndline(c))
                c = read();
            StringBuilder res = new StringBuilder();
            do {
                res.appendCodePoint(c);
                c = read();
            } while (!isEndline(c));
            return res.toString();
        }
    }
}
