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.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.HashSet;
import java.util.StringTokenizer;
/* Name of the class has to be "Main" only if the class is public. */
//public 
public  class Codechef
{
    static BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
	static ArrayList<ArrayList<Integer>> list;
    static HashSet<Integer> hs;
    static ArrayList<Integer> tmp;
    public static void or(int arr[],int b[]){
        for(int i=0;i<10;i++){
            if(b[i]==1)
                arr[i]=1;
        }
    }
    public static void xor(int arr[],int b[]){
        for(int i=0;i<10;i++){
            if(b[i]==1){
                if(arr[i]==-1)
                    arr[i]=-2;
                else if(arr[i]==-2)
                    arr[i]=-1;
                else if(arr[i]==0 || arr[i]==1){
                    arr[i]^=1;
                }
            }
        }
    }
    public static void and(int arr[],int b[]){
        for(int i=0;i<10;i++){
            if(b[i]==0)
                arr[i]=0;
        }
    }
	public static void main (String[] args) throws java.lang.Exception
	{
	    //StringTokenizer st=new StringTokenizer(br.readLine());
	    //int n=Integer.parseInt(st.nextToken());
	    int n=Integer.parseInt(br.readLine());
	    int arr[]=new int[10];
	    Arrays.fill(arr,-2);
	    for(;n!=0;n--){
	        StringTokenizer st=new StringTokenizer(br.readLine());
	        String ch=st.nextToken();
	        int tmp=Integer.parseInt(st.nextToken());
	        String s=Integer.toBinaryString(tmp);
	        while(s.length()!=10)
	            s="0"+s;
            int b[]=new int[10];
            for(int i=0;i<10;i++){
                b[i]=s.charAt(i)-'0';
            }
	        if(ch.equals("|")){
	            or(arr,b);
	        }
	        if(ch.equals("&")){
	            and(arr,b);
	        }
	        if(ch.equals("^")){
	            //System.out.println(Arrays.toString(arr));
	            xor(arr,b);
	        }
	    }
	    String o="";
	    for(int i=0;i<10;i++){
	        if(arr[i]==1)
	            o=o+"1";
            else
                o=o+"0";
	    }
	    String x="";
	    for(int i=0;i<10;i++){
	        if(arr[i]==-1)
	            x=x+"1";
            else
                x=x+"0";
	    }
	    String a="";
	    for(int i=0;i<10;i++){
	        if(arr[i]==0)
	            a=a+"0";
            else
                a=a+"1";
	    }
	    int or=Integer.parseInt(o,2);
	    int xor=Integer.parseInt(x,2);
	    int and=Integer.parseInt(a,2);
	    //System.out.println(Arrays.toString(arr));
	    System.out.println("3\n| "+or+"\n^ "+xor+"\n& "+and);
	}
}