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.InputStream;
import java.io.PrintStream;
import java.util.*;

public class Main {

    public static void main(String[] args){
        Main obj = new Main();
        obj.solve(System.in, System.out);

    }

    public void solve(InputStream is, PrintStream ps){
        Scanner input = new Scanner(is);
        int n = input.nextInt();
        int zeros = 0;
        int ones = 1023;
        for (int i = 0; i < n; i++) {
            char op = input.next().charAt(0);
            int a = input.nextInt();
            if (op == '&') {
                zeros&=a;
                ones&=a;
            } else if (op == '|') {
                zeros|=a;
                ones|=a;
            } else if (op == '^') {
                zeros^=a;
                ones^=a;
            }
        }

        int andMask = 1023;
        int orMask = 0;
        int xorMask = 0;

        int k = 1;
//        System.out.println(zeros + " " + ones);
        for (int i = 0; i < 10; i++) {
            int temp0 = zeros%(2*k);
            temp0>>=i;
            int temp1 = ones%(2*k);
            temp1>>=i;
//            System.out.println(temp0 + " " + temp1);
            if(temp0==0 && temp1==0) {
                andMask-=k;
            } else if(temp0==1 && temp1==1) {
                orMask+=k;
            } else if(temp0==1 && temp1==0) {
                xorMask+=k;
            }
            k*=2;
        }

//        int z = 0;
//        int o = 1023;
//        z=(((z&andMask)|orMask)^xorMask);
//        o=(((o&andMask)|orMask)^xorMask);
//        System.out.println(zeros + " " + ones);
//        System.out.println(z + " " + o);

        System.out.println("3");
        System.out.println("& " + andMask);
        System.out.println("| " + orMask);
        System.out.println("^ " + xorMask);

//        System.out.println(0&1);
//        System.out.println(1&1);
//        System.out.println(0|0);
//        System.out.println(1|0);
//        System.out.println(0^0);
//        System.out.println(1^0);

//        System.out.println("error");

    }


}
