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.*;
import java.io.*;
import java.math.*;
public class Main {
	static Scanner cin = new Scanner(System.in);
	static PrintWriter cout = new PrintWriter(System.out);
	static int solve(int t, int n, String[] str, int[] a) {
		for (int i = 1; i <= n; ++ i) {
			char c = str[i].charAt(0);
			if (c == '&') t &= a[i];
			if (c == '|') t |= a[i];
			if (c == '^') t ^= a[i];
		}
		return t;
	}
	static void show(int n, int[] a) {
		for (int i = 1; i <= n; ++ i) {
			cout.print(a[i] + " ");
		}
		cout.println();
		cout.flush();
	}
	public static void main(String[] args) {
		int n = cin.nextInt();
		int[][] a = new int[10][n + 1];
		String[] str = new String[n + 1];
		for (int i = 1; i <= n; ++ i) {
			str[i] = cin.next();
			int x = cin.nextInt();
			for (int j = 0; j < 10; ++ j) {
				a[j][i] = (x & 1);
				x >>= 1;
			}
		}
//		for (int i = 1; i <= n; ++ i) {
//			for (int j = 0; j < 10; ++ j) cout.print(a[j][i] + " "); 
//			cout.println();
//			cout.flush();
//		}

		int c1 = 0, c2 = 0, c3 = 0;
		for (int i = 0; i < 10; ++ i) {
			int t0 = solve(0, n, str, a[i]);
			int t1 = solve(1, n, str, a[i]);
			if (t0 == 0 && t1 == 0) continue;
			if (t0 == 0 && t1 == 1) {
				c1 += (1 << i);
			}
			if (t0 == 1 && t1 == 0) {
				c1 += (1 << i);
				c3 += (1 << i);
			}
			if (t0 == 1 && t1 == 1) {
				c3 += (1 << i);
			}
		}
		cout.println(3);
		cout.println("& " + c1);
		cout.println("| " + c2);
		cout.println("^ " + c3);
		cout.flush();
	}
}