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 c{
	public static void main(String[] args) throws IOException{
		BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
		String[] line;
		
		line = br.readLine().split(" ");
		int N = Integer.parseInt(line[0]);
		
		// 0 is 0, 1 is 1, 2 is ?, 3 is upsidedown?
		int[] type = new int[10];
		Arrays.fill(type, 2);
		
		for(int n=0;n<N;n++){
			line = br.readLine().split(" ");
			char ch = line[0].charAt(0);
			int a = Integer.parseInt(line[1]);
			if(ch == '&'){
				for(int i = 0; i < 10; i++){
					if((1 << i | a) == a){
						
						
						
					}
				}
			}
			for(int i = 0; i < 10; i++){
				// not in the set
				if((1 << i | a) != a){
					if(ch == '&'){
						type[i] = 0;
					}
				}
				// in the set
				if((1 << i | a) == a){
					if(ch == '|'){
						type[i] = 1;
					}
					if(ch == '^'){
						// 0s become 1s, and vice versa
						// still undecided things flip their outputs
						if(type[i] % 2 == 0) type[i]++;
						else type[i]--;
					}
				}
			}
			
		}

		// find:
		// an integer that covers all bits except the 0s
		// an integer that covers all the 1s
		// an integer that covers all the flip-outputs
		int allButZero = 0, allOne = 0, allFlip = 0;
		for(int i = 0; i < 10; i++){
			if(type[i] != 0) allButZero += (1<<i);
			if(type[i] == 1) allOne += (1<<i);
			if(type[i] == 3) allFlip += (1<<i);
		}
		
		System.out.println(3);
		System.out.println("& "+allButZero);
		System.out.println("| "+allOne);
		System.out.println("^ "+allFlip);
	}
}