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.
//package com.company;
import java.util.Scanner;
public class Main
{
    static Scanner userInput = new Scanner(System.in);
    public static void main(String[] args)
    {
        int n;
        n = userInput.nextInt();
        int one=(1<<10)-1,zero = 0,i,op;
        char c;
        for(i=0;i<n;i++)
        {
            c=userInput.next().charAt(0);
            op=userInput.nextInt();
            switch (c)
            {
                case '|':zero|=op;
                    one|=op;
                    break;
                case '&':zero&=op;
                    one&=op;
                    break;
                case '^':zero^=op;
                    one^=op;
                    break;
            }
        }
        int orr=0,andd=((1<<10)-1),xorr=0;
        for(i=0;i<10;i++)
        {
            int z=(1<<i);
            z=z&zero;
            int o=(1<<i);
            o=o&one;
            if(z!=0&&o!=0)
            {
                orr|=(1<<i);
            }
            else if(z==0&&o==0)
            {
                andd&=(~(1<<i));
            }
            else if(z!=0&&o==0)
            {
                xorr|=(1<<i);
            }
        }
        System.out.println(3);
        System.out.println('|'+" "+orr);
        System.out.println('&'+" "+andd);
        System.out.println('^'+" "+xorr);

    }

}
