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.*;
import java.util.*;

import static java.lang.Math.*;
import static java.util.Collections.*;
import static java.util.Arrays.*;

public class Main {
    /**
     * Solution
     */
    static class Solution {
        public void solve(Scanner in, PrintWriter out) {
            int n, k, t1 = 0, t2 = 1023;
            char c;
            n = in.nextInt();
            for (int i = 0; i < n; i++) {
                c = in.next().charAt(0);
                k = in.nextInt();
                if(c == '|') {
                    t1 |= k;
                    t2 |= k;
                } else if(c == '^') {
                    t1 ^= k;
                    t2 ^= k;
                } else {
                    t1 &= k;
                    t2 &= k;
                }
            }
            int xor = t1 ^ t2;
            out.print(2 + "\n");
            out.print("& " + xor + "\n");
            out.print("^ " + t1 + "\n");
        }
    }

    public static void main(String[] args) {
        boolean onlineJudge = System.getProperty("ONLINE_JUDGE") != null;
        if (onlineJudge) {
            InputStream inputStream = System.in;
            OutputStream outputStream = System.out;
            Scanner inputReader = new Scanner(inputStream);
            PrintWriter printWriter = new PrintWriter(outputStream);
            Solution solution = new Solution();
            solution.solve(inputReader, printWriter);
            printWriter.close();
        } else {
            InputStream inputStream = null;
            try {
                inputStream = new FileInputStream("./src/com/company/Files/in.txt");
            } catch (FileNotFoundException e) {
                e.printStackTrace();
            }
            OutputStream outputStream = System.out;
            Scanner inputReader = new Scanner(inputStream);
            PrintWriter printWriter = new PrintWriter(outputStream);
            Solution solution = new Solution();
            byte test = 1;
            while (true) {
                try {
                    if (!inputReader.bufferedReader.ready()) break;
                } catch (IOException e) {
                    e.printStackTrace();
                }
                printWriter.print("Test#" + test + ":\n");
                solution.solve(inputReader, printWriter);
                printWriter.print("\n\n");
                test++;
            }
            printWriter.close();
        }
    }
    private static class Scanner {
        private BufferedReader bufferedReader;
        private StringTokenizer stringTokenizer;

        private Scanner(InputStream inputStream) {
            bufferedReader = new BufferedReader(new InputStreamReader(inputStream));
            stringTokenizer = null;
        }

        public String next() {
            while (stringTokenizer == null || !stringTokenizer.hasMoreTokens()) {
                try {
                    stringTokenizer = new StringTokenizer(bufferedReader.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return stringTokenizer.nextToken();
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }


        public long nextLong() {
            return Long.parseLong(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

    }
}