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.util.ArrayList;
import java.util.List;
import java.util.Scanner;

public class Main {
	
	// 0 init
	// 1 set 0
	// 2 set 1
	// 3 xor
	private static int[] state = new int[20];
	
	public static void main(String[] args) {
		
		Scanner scan = new Scanner(System.in);
		int i , j , n = scan.nextInt();
		for (i = 0;i < n;i ++) {
			String operation = scan.next();
			int v = scan.nextInt(); 
			if (operation.equals("|")) {
				for (j = 0;j < 10;j ++) {
					if ((v & (1 << j)) != 0) {					
						state[j] = 2;
					}
				}
			} else if (operation.equals("^")) {
				for (j = 0;j < 10;j ++) {
					if ((v & (1 << j)) != 0) {
						if (state[j] == 0) {
							state[j] = 3;
						} else if (state[j] == 3) {
							state[j] = 0;
						} else if (state[j] == 1) {
							state[j] = 2;
						} else {
							state[j] = 1;
						}					
					}
				}
			} else {
				for (j = 0;j < 10;j ++) {
					if ((v & (1 << j)) == 0) {
						state[j] = 1;
					}
				}
			}
		}
		List<String> ans = new ArrayList<>();
		// check set 0
		int value = 0;
		for (i = 0;i < 10;i ++) {
			if (state[i] == 1) {
				value = value | (1 << i);
			}
		}
		if (value > 0) {
			ans.add(String.format("| %d" , value));
			ans.add(String.format("^ %d" , value));
		}
		
		// check set 1
		value = 0;
		for (i = 0;i < 10;i ++) {
			if (state[i] == 2) {
				value = value | (1 << i);
			}
		}
		if (value > 0) {
			ans.add(String.format("| %d" , value));
		}
		
		// check state 3
		value = 0;
		for (i = 0;i < 10;i ++) {
			if (state[i] == 3) {
				value = value | (1 << i);
			}
		}
		if (value > 0) {
			ans.add(String.format("^ %d" , value));
		}
		
		System.out.println(ans.size());
		for (String string : ans) {
			System.out.println(string);
		}
		
	}
	
    
}









	