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

/**
 */
public class Main879C {
	public static void main(String[] args) {
		run(System.in, System.out);
	}

	public static void run(InputStream in, PrintStream out) {

		try (Scanner sc = new Scanner(in)) {
			int n = sc.nextInt();
			sc.nextLine();
			//System.err.println("####");
			int a = 1023;
			int b = 0;
		
			for (int i = 0; i < n; i++) {
				String s = sc.nextLine();
				char op  = s.charAt(0);
				int val = Integer.parseInt(s.substring(2));
				//System.err.println(s);
				switch(op) {
				case '|' : a |= val;b|=val;break;
				case '&' : a &= val;b&=val;break;
				case '^' : a ^= val;b^=val;break;
				}
			}
			
			//System.err.println(a+ " " + Integer.toBinaryString(a));
			//System.err.println(b + " " + Integer.toBinaryString(b));

			out.println("3");
			out.println("| " + (a&b));
			out.println("& " + (a|b));
			out.print("^ " + (~a&b));
		}
	}

}