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.util.*;

public class Main{
    
    static int f(int x,int i){
        return (x>>i)&1;
    }
    public static void main(String[] args){

        Scanner in=new Scanner(System.in);
        int a=0,b=1023,n,t;
        int x=1023,y=0,z=0;
        String s;

        n=in.nextInt();
        while(n--!=0){
            s=in.next();
            t=in.nextInt();
            if(Objects.equals(s,"&")){
                a&=t;
                b&=t;
            }
            if(Objects.equals(s,"|")){
                a|=t;
                b|=t;
            }
            if(Objects.equals(s,"^")){
                a^=t;
                b^=t;
            }
        }
        for(int i=0;i<10;i++){
            if(f(a,i)==0&&f(b,i)==0) x&=~(1<<i);
            if(f(a,i)==1&&f(b,i)==1) y|=(1<<i);
            if(f(a,i)==1&&f(b,i)==0) z|=(1<<i);
        }
        System.out.println(3+"\n& "+x+"\n| "+y+"\n^ "+z);
    }
}