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.Scanner;

public class ShortProgram {
	
	public static void main(String[] args) {
		
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		char[] ops = new char[n];
		int[] params = new int[n];
		for(int i = 0; i < n; i++) {
			ops[i] = sc.next().charAt(0);
			params[i] = sc.nextInt();
		}
		
		char[] result = {'x', 'x', 'x', 'x', 'x', 'x', 'x', 'x', 'x', 'x'};
		for(int i = 0; i < n; i++) {
			for(int j = 0; j < 10; j++) {
				boolean param = ((params[i] >> j) & 1) == 1;
				if(ops[i] == '&' && !param) {
					result[j] = '0';
				} else if(ops[i] == '|' && param) {
					result[j] = '1';
				} else if(ops[i] == '^' && param) {
					if(result[j] == '0')
						result[j] = '1';
					else if(result[j] == '1')
						result[j] = '0';
					else if(result[j] == 'x')
						result[j] = 'X';
					else
						result[j] = 'x';
				}
			}
		}
		
		int cand = 0;
		int cxor = 0;
		for(int i = 0; i < 10; i++) {
			if(result[i] == '1') {
				cxor |= 1 << i;
			} else if(result[i] == 'x') {
				cand |= 1 << i;
			} else if(result[i] == 'X') {
				cand |= 1 << i;
				cxor |= 1 << i;
			}
		}
		
		System.out.println(2);
		System.out.println("& " + cand);
		System.out.println("^ " + cxor);
		
	}
	
}