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.*;
import java.io.*;

public class October28C {
    public static int powersOfTwo[] = {1,2,4,8,16,32,64,128,256,512};
    public static void main(String[] args) {
        /*File f = new File("INPUT.txt");
        InputStream is = null;
        try {
            is = new FileInputStream(f);
        } catch (FileNotFoundException e) {
            e.printStackTrace();
        }
        Scanner sc = new Scanner(is);*/
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int res[] = new int[10];
        for (int i = 0; i < 10; i++){
            res[i] = -10;
        }
        for (int i = 0; i < n; i++){
            String command = sc.next();
            char operation = command.charAt(0);
            int arg = sc.nextInt();
            //System.out.println(operation);
            //System.out.println(arg);
            int argBits[] = getBits(arg);
            //System.out.println(operation + " " + Arrays.toString(argBits));
            if (operation == '|'){
                for (int j = 0; j < 10; j++){
                    if (argBits[j] == 1) {
                        res[j] = 1;
                        //System.out.println("| -> changing to 1 in " + j);
                    }

                }
            }
            else if (operation == '&'){
                for (int j = 0; j < 10; j++){
                    if (argBits[j] == 0) res[j] = 0;
                }
            }
            else {
                for (int j = 0; j < 10; j++){
                    if (argBits[j] == 1)
                    {
                        if (res[j] == -10) res[j] = -1;
                        else if (res[j] == -1) res[j] = -10;
                        else if (res[j] == 0) res[j] = 1;
                        else if (res[j] == 1) res[j] = 0;
                    }
                }
            }
        }
        int OrArg = 0;
        int AndArg = 1023;
        boolean isXorNeeded = false;
        int XorArg = 0;
        for (int i = 0; i < 10; i++){
            if (res[i] == 1) OrArg += powersOfTwo[i];
            else if (res[i] == 0) AndArg -= powersOfTwo[i];
            else if (res[i] == -1){
                isXorNeeded = true;
                XorArg += powersOfTwo[i];
            }
        }
        //System.out.println(Arrays.toString(res));
        if (isXorNeeded){
            System.out.println(3);
            System.out.println("^ " + XorArg);
        }
        else System.out.println(2);
        System.out.println("| " + OrArg);
        System.out.println("& " + AndArg);
    }
    public static int[] getBits(int x){
        int bits[] = new int[10];
        for (int i = 9; i >= 0; i--){
            if (x >= powersOfTwo[i]){
                bits[i] = 1;
                x = x - powersOfTwo[i];
            }
        }
        return bits;
    }
}