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.
//package round_div2;

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

/**
 * Department : inoipractice
 * Given Birth by V0!D on 26/10/17
 * Always Be Grateful to V0!D Kid !!
 */
public class ShortProgram {

    public static void main(String[] args) throws IOException {
        BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
        int n = Integer.parseInt(in.readLine());
        int a = 0,b = 1023;
        for (int i = 0; i <n ; i++) {
            String[] inp = in.readLine().split(" ");
            char op = inp[0].charAt(0);
            int x = Integer.parseInt(inp[1]);
            switch (op) {
                case '&':
                    a&=x;
                    b&=x;
                    break;
                case '|':
                    a|=x;
                    b|=x;
                    break;
                case '^':
                    a^=x;
                    b^=x;
                    break;
                default:
                    throw new RuntimeException();
            }
        }
        String and="",or="",xor="";
        String outa,outb;
        outa = Integer.toString(a,2);
        outb = Integer.toString(b,2);
        for (int i = 1;i<=10 ;i++ ) {
            int v1=0,v2=0;
            int p1 = outa.length()-i;
            int p2 = outb.length()-i;
            if(p1>=0)
                v1 = Integer.parseInt(Character.toString(outa.charAt(p1)));
            if(p2>=0)
                v2 = Integer.parseInt(Character.toString(outb.charAt(p2)));
            boolean changea,changeb;
            changea = v1!=0;
            changeb = v2!=1;
            if(changea&&changeb){
                //XOR
                xor = "1"+xor;
                and = "1"+and;
                or = "0"+or;
            }
            else if (changea&&!changeb) {
                //OR
                xor = "0"+xor;
                and = "1"+and;
                or = "1"+or;
            }
            else if (!changea&&changeb) {
                //AND
                xor = "0"+xor;
                and = "0"+and;
                or = "0"+or;
            }
            else{
                //NOTHING
                xor = "0"+xor;
                and = "1"+and;
                or = "0"+or;
            }
        }
        int xx,aa,oo;
        xx = Integer.parseInt(xor,2);
        aa = Integer.parseInt(and,2);
        oo = Integer.parseInt(or,2);
        List<String> coms = new ArrayList<>();
        if(xx!=0){
            coms.add("^ "+xx);
        }
        if(aa!=1023){
            coms.add("& "+aa);
        }
        if(oo!=0){
            coms.add("| "+oo);
        }
        System.out.println(coms.size());
        for (String str : coms) {
            System.out.println(str);
        }
    }
}
