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.*;
import java.math.*;

public class Competitive_1 {
	
	static final int L=1, R=2, U=3, D=4, bias=10000;
	static int dx[]={0,0,-1,1}, dy[]={-1,1,0,0};
	static int n, m, k;
	static char arr[][];
	static int min[][];
	static boolean visited[][][];
	
	public static void main(String[] args) {
		
		new Thread(null, new Runnable(){
					@Override
					public void run(){
						soln();
					}
			}, "1", 1 << 26).start();
		
	}
	
	static void soln(){
		FastReader in = new FastReader();
		int n = in.nextInt();
		String arr[] = new String[n];
		int n0=0x0, n1=0x3FF;
		
		for(int i=0; i<n; i++){
			String op = in.nextLine();
			int num = Integer.parseInt(op.substring(2));
			
			if(op.charAt(0)=='|'){
				n0 |= num;
				n1 |= num;
			}else if(op.charAt(0)=='&'){
				n0 &= num;
				n1 &= num;
			}else{
				n0 ^= num;
				n1 ^= num;
			}
		}
		
		int or=0, and=0x3FF, xor=0;
		for(int i=0; i<10; i++){
			int nn0 = n0 & (1<<i), nn1 = n1 & (1<<i);
			
			if(nn0==0 && nn1==0){
				and ^= 1<<i;
			}else if(nn0>0 && nn1>0){
				or ^= 1<<i;
			}else if(nn0>0 && nn1==0){
				xor ^= 1<<i;
			}
		}
		
		System.out.println(3);
		System.out.println("& " + and);
		System.out.println("| " + or);
		System.out.println("^ " + xor);
	}
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	
	static class FastReader
    {
        BufferedReader br;
        StringTokenizer st;
 
        public FastReader()
        {
            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;
        }
    }
	
}