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.HashMap;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner s = new Scanner(System.in);

        int[] bitStatus = new int[11]; // 0 = original, 1 = up, 2 = down, 3 = toggle
        int n = s.nextInt();

        HashMap<Integer, Integer> xorMap = new HashMap<Integer, Integer>() {{
            put(0, 3);
            put(1, 2);
            put(2, 1);
            put(3, 0);
        }};


        for (int i = 0; i < n; i++) {
            String cmd = s.next();
            int num = s.nextInt();

            for (int bit = 0; bit <= 9; bit++, num >>= 1) {
                boolean bitVal = (num & 1) != 0;
                if (cmd.equals("|") && bitVal) {
                    bitStatus[bit] = 1;
                }
                if (cmd.equals("&") && !bitVal) {
                    bitStatus[bit] = 2;
                }
                if (cmd.equals("^") && bitVal) {
                    bitStatus[bit] = xorMap.get(bitStatus[bit]);
                }
            }
        }

        int orMask = 0, xorMask = 0;
        for (int bit = 0; bit <= 9; bit++) {
            if (bitStatus[bit] == 0) {
            } else if (bitStatus[bit] == 1) {
                orMask ^= 1 << bit;
            } else if (bitStatus[bit] == 2) {
                orMask ^= 1 << bit;
                xorMask ^= 1 << bit;
            } else if (bitStatus[bit] == 3) {
                xorMask ^= 1 << bit;
            }
        }

        System.out.println((orMask != 0 ? 1 : 0) + (xorMask != 0 ? 1 : 0));

        if (orMask != 0) {
            System.out.println("| " + orMask);
        }
        if (xorMask != 0) {
            System.out.println("^ " + xorMask);
        }
    }
}