Problem: 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.

Solution (in JAVA):

Solution:
import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;


public class A443 {
	static String OPS = "&|^";
	public static void main(String[] args) {
		FS scan = new FS(System.in);
		int N = scan.nextInt();
		int[] op = new int[2*N];
		for(int i=0;i<N;i++){
			op[2*i] = OPS.indexOf(scan.next());
			op[2*i+1] = scan.nextInt();
//			op[2*i] = (int)(Math.random()*3);
//			op[2*i+1] = (int)(Math.random()*1024);
		}
		int A = op[1];
		for(int i=2;i<2*N;i+=2){
			if(op[i]==0)A&=op[i+1];
			if(op[i]==1)A|=op[i+1];
			if(op[i]==2)A^=op[i+1];
		}
		
		
		int[] sol = new int[1024];
		for(int i=0;i<1024;i++){
			if(i>0&&i<1023)continue;
			sol[i] = i;
			for(int j=0;j<2*N;j+=2){
				int type = op[j], x = op[j+1];
				if(type==0)sol[i]&=x;
				else if(type==1)sol[i]|=x;
				else sol[i]^=x;
			}
		}
		for(int i=0;i<1024;i++){
			for(int j=0;j<3;j++){
				for(int k=0;k<1024;k++){
					for(int l=0;l<3;l++){
						boolean valid = true;
						for(int m = 0;m <1024;m++){
							if(m>0&&m<1023)continue;
							int val = m;
							if(j==0)val&=i;
							if(j==1)val|=i;
							if(j==2)val^=i;
							if(l==0)val&=k;
							if(l==1)val|=k;
							if(l==2)val^=k;
							if(val!=sol[m]){
								valid=false;
								break;
							}
						}
						if(valid){
							System.out.println(2);
							System.out.println(OPS.charAt(j)+" "+i);
							System.out.println(OPS.charAt(l)+" "+k);
							return;
						}
					}
				}
			}
		}
	}
	private static class FS {
		BufferedReader br;
		StringTokenizer st;
		public FS(InputStream in) {
			br = new BufferedReader(new InputStreamReader(in));
		}
		String next(){
			while(st==null||!st.hasMoreElements()){
				try{st = new StringTokenizer(br.readLine());}
				catch(IOException e){e.printStackTrace();}
			}
			return st.nextToken();
		}
		int nextInt() {return Integer.parseInt(next());}
		long nextLong() {return Long.parseLong(next());}
		double nextDouble() { return Double.parseDouble(next());}
	}
}