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.*;
import java.util.*;

public class C implements Runnable{
	public static void main (String[] args) {new Thread(null, new C(), "_cf", 1 << 28).start();}

	public void run() {
		FastScanner fs = new FastScanner();
		PrintWriter out = new PrintWriter(System.out);

		int n = fs.nextInt();
		int a = 1023, b = 0; //all bits on and no bits on
		for(int i = 0; i < n; i++) {
			char op = fs.next().charAt(0);
			int x = fs.nextInt();
			if(op == '^') {
				a ^= x;
				b ^= x;
			} else if(op == '|') {
				a |= x;
				b |= x;
			} else {
				a &= x;
				b &= x;
			}
		}

		int[] res = new int[2];
		for(int j = 0; j < 10; j++) {
			int msk = (((a & (1 << j)) > 0) ? 2 : 0) + (((b & (1 << j)) > 0) ? 1 : 0);
			if(msk == 0) {
				res[0] |= (1 << j);
				res[1] |= (1 << j);
			}
			else if(msk == 1) {
				res[1] |= (1 << j);
			}
			else if(msk == 2) {
			}
			else {
				res[0] |= (1 << j);
			}
		}
		
		out.println(2);
		out.println("| " + res[0]);
		out.println("^ " + res[1]);

		out.close();
	}

	void sort (int[] a) {
		int n = a.length;
		for(int i = 0; i < 1000; i++) {
			Random r = new Random();
			int x = r.nextInt(n), y = r.nextInt(n);
			int temp = a[x];
			a[x] = a[y];
			a[y] = temp;
		}
		Arrays.sort(a);
	}

	class FastScanner {
		BufferedReader br;
		StringTokenizer st;
		public FastScanner() {
			try	{
				br = new BufferedReader(new InputStreamReader(System.in));
				//				br = new BufferedReader(new FileReader("testdata.out"));
				st = new StringTokenizer("");
			} catch (Exception e){e.printStackTrace();}
		}
		public String next() {
			if (st.hasMoreTokens())	return st.nextToken();
			try {st = new StringTokenizer(br.readLine());}
			catch (Exception e) {e.printStackTrace();}
			return st.nextToken();
		}
		public int nextInt() {return Integer.parseInt(next());}
		public long nextLong() {return Long.parseLong(next());}
		public double nextDouble() {return Double.parseDouble(next());}

		public String nextLine() {
			String line = "";
			try {line = br.readLine();}
			catch (Exception e) {e.printStackTrace();}
			return line;
		}
		public Integer[] nextIntegerArray(int n) {
			Integer[] a = new Integer[n];
			for(int i = 0; i < n; i++) a[i] = nextInt();
			return a;
		}
		public int[] nextIntArray(int n) {
			int[] a = new int[n];
			for(int i = 0; i < n; i++) a[i] = nextInt();
			return a;
		}
		public char[] nextCharArray() {return nextLine().toCharArray();}
	}

}