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.Scanner;

public class Problem879C {
    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);
        int N = in.nextInt();
        char[] op = new char[N];
        int[] x = new int[N];
        int a = 1023;
        int b = 0;
        for (int i = 0; i < N; i++) {
            op[i] = in.next().charAt(0);
            x[i] = in.nextInt();
            a = eval(op[i], a, x[i]);
            b = eval(op[i], b, x[i]);
        }

        int or = 0, xor = 0, and = 0;
        for (int i = 0; i < 10; i++) {
            int n = 1 << i;

            if ((a & n) != 0 && (b & n) != 0) {
                or |= n;
                and |= n;
            } else if ((b & n) != 0) {
                xor |= n;
                and |= n;
            } else if ((a & n) != 0) {
                and |= n;
            }
        }

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

    static int eval(char c, int x, int y) {
        int res = x;
        if (c == '|') {
            res |= y;
        } else if (c == '&') {
            res &= y;
        } else {
            res ^= y;
        }
        return res;
    }
}