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.io.PrintWriter;
import java.util.*;

public class C {


    public static void main(String[] args) {

        MyScanner in = new MyScanner();
        PrintWriter out = new PrintWriter(System.out);

        int n = in.nextInt();

        int allSet = 1023;
        int zero = 0;

        for(int i=0;i<n;++i){
            String command = in.next();
            int x = in.nextInt();

            if("&".equals(command)){
                allSet &= x;
//                out.println(allSet);
                zero &= x;
            }

            if("^".equals(command)){
                allSet ^= x;
                zero ^= x;
            }

            if("|".equals(command)){
                allSet |= x;
                zero |= x;
            }
        }

        int orBits = 0;
        int xorBits = 0;
        int andBits = 1023;

        int commandCount = 1;
        boolean useAnd = false;
        boolean useXor = false;

        for(int i=0;i<10;++i){
            if((allSet&(1<<i))!=0 && (zero&(1<<i))!=0){
                orBits|=1<<i;
            }

            if((allSet&(1<<i))==0 && (zero&(1<<i))!=0){
                useXor = true;
                xorBits|=1<<i;
            }

            if((allSet&(1<<i))==0 && (zero&(1<<i))==0){
//                out.println(allSet+" "+i);
                useAnd = true;
                andBits^=1<<i;
            }
        }

        if(useAnd){
            commandCount++;
        }
        if(useXor){
            commandCount++;
        }


        out.println(commandCount);
        if(useXor) {
            out.println("^ " + xorBits);
        }
        if(useAnd) {
            out.println("& " + andBits);
        }
        out.println("| "+orBits);

        out.close();
    }

    // -----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        public MyScanner() {
            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();
        }

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

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

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

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

    }
    // --------------------------------------------------------

}