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.InputStreamReader;
import java.util.*;

public class C {
    public static void main(String[] args) throws IOException {
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        Integer n = Integer.parseInt(br.readLine());

        int[] temp = new int[10];
        for(int i = 0; i < 10; i++) {
            // 0 -> unset
            // 1 -> set
            // 2 -> flip
            // 3 -> pass through
            temp[i] = 3;
        }

        for(int i = 0; i < n; i++) {

            String s[] = br.readLine().split(" ");
            Integer val = Integer.parseInt(s[1]);


            if(s[0].equals("&")) {
                for(int j = 9; j >= 0; j--) {
                    int bit = val & 1;
                    if(bit == 0) {
                        temp[j] = 0;
                    }
                    val >>= 1;
                }
            } else if(s[0].equals("|")) {
                for(int j = 9; j >= 0; j--) {
                    int bit = val & 1;
                    if(bit == 1) {
                        temp[j] = 1;
                    }
                    val >>= 1;
                }
            } else if(s[0].equals("^")) {
                for(int j = 9; j >= 0; j--) {
                    int bit = val & 1;
                    if(bit == 1) {
                        if(temp[j] == 3) {
                            temp[j] = 2;
                        } else if(temp[j] == 2) {
                            temp[j] = 3;
                        } else if(temp[j] == 1) {
                            temp[j] = 0;
                        } else if(temp[j] == 0) {
                            temp[j] = 1;
                        }
                    }
                    val >>= 1;
                }
            }
        }

        System.out.println(2);
        int res = 0;
        for (int i = 0; i < 10; i++) {
            res <<= 1;
            res += (temp[i] == 0 || temp[i] == 1) ? 0 : 1;
        }
        System.out.println("& " + res);

        res = 0;
        for (int i = 0; i < 10; i++) {
            res <<= 1;
            if(temp[i] == 2) {
                res += 1;
            } else if(temp[i] == 1) {
                res += 1;
            } else {
                res += 0;
            }
        }

        System.out.println("^ " + res);
    }
}