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.ArrayList;
import java.util.Scanner;

/**
 * @author Jaseem
 */
public class ShortProgram {
    char [] operations;
    int [] constants;
    ArrayList<Character> resultOperations;
    ArrayList<Integer>  resultConstants;
    int n;
    int operate(int input){
        for(int i=0; i<n;i++){
            switch (operations[i]){
                case '|': input=input|constants[i]; break;
                case '^':input=input^constants[i]; break;
                case '&':input=input&constants[i];break;
            }
        }
        return input;
    }
    void solve(){
        int outputForZero=operate(0);
        int outputForOnes=operate(1023);
        resultConstants=new ArrayList<>();
        resultOperations=new ArrayList<>();
        int or=0;
        int xor=0;
        int and=1023;
        for(int i=0;i<10;i++){
            if((outputForZero&(1<<i))==0 && (outputForOnes&(1<<i))==0){
                and=and^(1<<i);
            }
            else if((outputForZero&(1<<i))!=0 && (outputForOnes&(1<<i))==0){
                //xor 1
                xor=xor^(1<<i);
            }
            else if((outputForZero&(1<<i))!=0 && (outputForOnes&(1<<i))!=0){
                //or 1
                or=or^(1<<i);
            }
        }
        if(and!=1023){
            resultOperations.add('&');
            resultConstants.add(and);
        }
        if(or!=0){
            resultOperations.add('|');
            resultConstants.add(or);
        }
         if(xor!=0){
            resultOperations.add('^');
            resultConstants.add(xor);
        }
    }
    void print(){
        System.out.println(resultConstants.size());
        for(int i=0;i<resultConstants.size();i++){
            System.out.println(resultOperations.get(i)+" "+resultConstants.get(i));
        }
    }
    public static void main(String[] args) {
        ShortProgram shortProgram=new ShortProgram();
        Scanner reader=new Scanner(System.in);
        int n=reader.nextInt();
        shortProgram.n=n;
        shortProgram.operations=new char[n];
        shortProgram.constants=new int[n];
        for(int i=0;i<n;i++){
            shortProgram.operations[i]=reader.next().charAt(0);
            shortProgram.constants[i]=reader.nextInt();
        }
        shortProgram.solve();
        shortProgram.print();
    }
}