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.util.Arrays;
import java.util.Scanner;
import java.util.stream.IntStream;

/**
 * Created by shhuan on 2017/11/5.
 */
public class Main_878A {

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

		int N = scanner.nextInt();
		scanner.nextLine();

		int M = 2;
		int[] T = new int[] {0, 1023};
		int[] S = new int[] {0, 1023};
		for (int i = 0; i < N; i++) {
			String[] ops = scanner.nextLine().split(" ");
			String op = ops[0];
			int val = Integer.parseInt(ops[1]);
			switch (op) {
				case "&":
					for (int j = 0; j < M; j++) {
						T[j] &= val;
					}
					break;
				case "|":
					for (int j = 0; j < M; j++) {
						T[j] |= val;
					}
					break;
				case "^":
					for (int j = 0; j < M; j++) {
						T[j] ^= val;
					}
					break;
				default:
			}
		}


		int a = 0;
		int b = 0;
		int c = 0;
		for (int i = 10; i >= 0; i--) {
			a <<= 1;
			b <<= 1;
			c <<= 1;
			c |= 1;

			final int k = i;
			int[] TI = Arrays.stream(T).map(v -> (v>>k)&1).toArray();
			if (Arrays.stream(TI).allMatch(v -> v==1)) {
				b |= 1;
			} else if (Arrays.stream(TI).allMatch(v -> v==0)) {
				c >>= 1;
				c <<= 1;
			} else {
				int[] SI = Arrays.stream(S).map(v -> (v>>k)&1).toArray();
				if (IntStream.range(0, M).allMatch(j -> SI[j] != TI[j])) {
					a |= 1;
				}
			}
		}

		System.out.println(3);
		System.out.println("^ " + a);
		System.out.println("| " + b);
		System.out.println("& " + c);


	}
}
