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.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Collections;
import java.util.Scanner;

public class Kek {
	static int op_xor(int a, int b) {
		return a ^ b;
	}

	static int op_and(int a, int b) {
		return a & b;
	}

	static int op_or(int a, int b) {
		return a | b;
	}

	static int[] to_bin(int x) {
		int i = 9;
		int ans[] = new int[10];
		while (x != 0) {
			ans[i--] = x % 2;
			x /= 2;
		}
		return ans;
	}

	static int from_bin(int a, int b, int c, int mas[]) {
		int x = 0;
		int k = 1;
		for (int i = mas.length - 1; i >= 0; i--) {
			if (mas[i] == a)
				x += k * b;
			else
				x += k * c;
			k *= 2;
		}
		return x;
	}

	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		PrintWriter out = new PrintWriter(System.out);
		int n = in.nextInt();
		int mas[][] = new int[n][10];
		char op[] = new char[n];
		int ans[] = new int[10];
		for (int i = 0; i < n; i++) {
			op[i] = in.next().charAt(0);
			mas[i] = to_bin(in.nextInt());
		}
		for (int i = 9; i >= 0; i--) {
			int a = 0;
			int b = 1;
			for (int j = 0; j < n; j++) {
				if (op[j] == '^') {
					a = op_xor(a, mas[j][i]);
					b = op_xor(b, mas[j][i]);
				} else if (op[j] == '|') {
					a = op_or(a, mas[j][i]);
					b = op_or(b, mas[j][i]);
				} else {
					a = op_and(a, mas[j][i]);
					b = op_and(b, mas[j][i]);
				}
			}
			if (a == 0 && b == 0)
				ans[i] = 2;
			else if (a == 0 && b == 1)
				ans[i] = 0;
			else if (a == 1 && b == 1)
				ans[i] = 1;
			else
				ans[i] = -1;
		}
		out.println(3);
		out.println("& " + from_bin(2, 0, 1, ans));
		out.println("| " + from_bin(1, 1, 0, ans));
		out.print("^ " + from_bin(-1, 1, 0, ans));
		in.close();
		out.close();
	}
}