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.util.*;
import java.io.*;
import java.math.*;

public class Main {

    static Scanner input = new Scanner(new BufferedReader(new InputStreamReader(System.in)));

    public static void main(String[] args) {
        int n = input.nextInt();
        int argZERO = 0, argONE = 1023, arg;
        for (int i = 0; i < n; i++) {
            switch (input.next()) {
                case "|":
                    arg = input.nextInt();
                    argZERO |= arg;
                    argONE |= arg;
                    break;
                case "&":
                    arg = input.nextInt();
                    argZERO &= arg;
                    argONE &= arg;
                    break;
                case "^":
                    arg = input.nextInt();
                    argZERO ^= arg;
                    argONE ^= arg;
                    break;
            }
        }
        System.out.println(3);
        System.out.println("| " + (argONE & argZERO));
        System.out.println("& " + (argONE | argZERO));
        System.out.println("^ " + ((argONE ^ 1023) & (argZERO ^ 0)));
    }
}