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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

// Algo falla
public class C {

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		
		int ones = 1023;
		int zeros = 0;
		
		int n = Integer.parseInt(br.readLine());
				
		for(int i=0; i<n; i++) {
			String[] l = br.readLine().split(" ");
			char c = l[0].charAt(0);
			int x = Integer.parseInt(l[1]);
			
			if(c == '^') {
				ones ^= x;
				zeros ^= x;
			}else if(c == '&') {
				ones &= x;
				zeros &= x;
			}else {
				ones |= x;
				zeros |= x;
			}			
		}
		
		int or = 0;
		int and = 1023;
		int xor = 0;
		for(int i=0; i<10; i++) {
			if((zeros&(1<<i)) != 0 && (ones&(1<<i)) != 0) {
				or |= (1<<i);
			}else if((zeros&(1<<i)) == 0 && (ones&(1<<i)) == 0) {
				and ^= (1<<i);
			}else if((zeros&(1<<i)) != 0) {
				xor |= (1<<i);
			}
		}
		
		System.out.println("3");
		System.out.println("| " + or);
		System.out.println("& " + and);
		System.out.println("^ " + xor);
	}

}
