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.*;
import java.util.*;

public class Codeforces878A {

	public static void main(String[] args) throws IOException {
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		StringTokenizer st = new StringTokenizer(br.readLine());
		int n = Integer.parseInt(st.nextToken());
		int k1 = 0;
		int k2 = 1023;
		
		for (int i = 0; i < n; i++) {
			st = new StringTokenizer(br.readLine());
			char andOrXor = st.nextToken().charAt(0);
			int todo = Integer.parseInt(st.nextToken());
			
			if (andOrXor == '&') {
				k1 = k1&todo;
				k2 = k2&todo;
			}
			else if (andOrXor == '|') {
				k1 = k1|todo;
				k2 = k2|todo;
			}
			else {
				k1 = k1^todo;
				k2 = k2^todo;
			}
		}
		
		int[] and = new int[10];
		int[] or = new int[10];
		int[] xor = new int[10];
		for (int i = 0; i < 10; i++) {
			and[i] = 1;
		}
		
		for (int i = 0; i < 10; i++) {
			if (((k1>>i)%2 == 0) && ((k2>>i)%2 == 0)) {
				and[i] = 0;
			}
			else if (((k1>>i)%2 == 1) && ((k2>>i)%2 == 1)) {
				or[i] = 1;
			}
			else if (((k1>>i)%2 == 1) && ((k2>>i)%2 == 0)) {
				xor[i] = 1;
			}
		}
		
		int andint = 0;
		int orint = 0;
		int xorint = 0;
		for (int i = 0; i < 10; i++) {
			andint += (and[i] * 1<<i);
			orint += (or[i] * 1<<i);
			xorint += (xor[i] * 1<<i);
		}
		
		System.out.println(3);
		System.out.println("& " + andint);
		System.out.println("| " + orint);
		System.out.println("^ " + xorint);
		
	}

}
