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

public class Main {

    public static void main(String[] args) {
        MyScanner in = new MyScanner();

        int n = in.nextInt();

        int bits0 = 0;
        int bits1 = (1 << 10) - 1;

        for (int i = 0; i < n; i++) {
            char op = in.next().charAt(0);
            int num = in.nextInt();

            switch (op) {
                case '|':
                    bits0 |= num;
                    bits1 |= num;
                    break;
                case '&':
                    bits0 &= num;
                    bits1 &= num;
                    break;
                case '^':
                    bits0 ^= num;
                    bits1 ^= num;
                    break;
            }
        }

        int or = 0, and = (1 << 10) - 1, xor = 0;

        for (int i = 0; i < 10; i++) {
            int bit = 1 << i;

            if ((bits0 & bit) > 0 && (bits1 & bit) > 0)
                or |= bit;
            else if ((bits0 & bit) == 0 && (bits1 & bit) == 0)
                and &= ~bit;
            else if ((bits0 & bit) > 0 && (bits1 & bit) == 0)
                xor |= bit;
        }

        System.out.println(3);
        System.out.println("| " + or);
        System.out.println("& " + and);
        System.out.println("^ " + xor);
    }

    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;

        MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt() {
            return Integer.parseInt(next());
        }
    }
}
