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.lang.annotation.Retention;
import java.util.*;
import java.math.BigInteger;
import java.util.Map.Entry;

import static java.lang.Math.*;

public class C extends PrintWriter {

    void run() {
        int xor = 0, or = 0;

        int n = nextInt(), m = 10;

        int[][] t = new int[m][n];

        for (int i = 0; i < n; i++) {
            char op = next().charAt(0);
            int x = nextInt();
            int index = n - i - 1;

            for (int j = 0; j < m; j++) {
                boolean bit = (x & (1 << j)) != 0;

                if (op == '|' && bit) {
                    t[j][index] = 1;
                }

                if (op == '&' && !bit) {
                    t[j][index] = 2;
                }

                if (op == '^' && bit) {
                    t[j][index] = 3;
                }
            }
        }

        int[][] a = { { 0, 1, 2, 3 }, { 1, 1, 1, 1 }, { 2, 2, 2, 2 }, { 3, 2, 1, 0 } };

        for (int j = 0; j < m; j++) {
            int s = 0;
            for (int v : t[j]) {
                s = a[s][v];
            }

            int bit = 1 << j;

            if (s == 1) {
                or |= bit;
            }

            if (s == 2) {
                or |= bit;
                xor |= bit;
            }

            if (s == 3) {
                xor |= bit;
            }

            // println(j + " " + s);

        }

        println("2");
        println("| " + or);
        println("^ " + xor);
    }

    boolean skip() {
        while (hasNext()) {
            next();
        }
        return true;
    }

    int[][] nextMatrix(int n, int m) {
        int[][] matrix = new int[n][m];
        for (int i = 0; i < n; i++)
            for (int j = 0; j < m; j++)
                matrix[i][j] = nextInt();
        return matrix;
    }

    String next() {
        while (!tokenizer.hasMoreTokens())
            tokenizer = new StringTokenizer(nextLine());
        return tokenizer.nextToken();
    }

    boolean hasNext() {
        while (!tokenizer.hasMoreTokens()) {
            String line = nextLine();
            if (line == null) {
                return false;
            }
            tokenizer = new StringTokenizer(line);
        }
        return true;
    }

    int[] nextArray(int n) {
        int[] array = new int[n];
        for (int i = 0; i < n; i++) {
            array[i] = nextInt();
        }
        return array;
    }

    long[] nextLongArray(int n) {
        long[] array = new long[n];
        for (int i = 0; i < n; i++) {
            array[i] = nextLong();
        }
        return array;
    }

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

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

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

    String nextLine() {
        try {
            return reader.readLine();
        } catch (IOException err) {
            return null;
        }
    }

    public C(OutputStream outputStream) {
        super(outputStream);
    }

    static BufferedReader reader;
    static StringTokenizer tokenizer = new StringTokenizer("");
    static Random rnd = new Random();
    static boolean OJ;

    public static void main(String[] args) throws IOException {
        OJ = System.getProperty("ONLINE_JUDGE") != null;
        C solution = new C(System.out);
        if (OJ) {
            reader = new BufferedReader(new InputStreamReader(System.in));
            solution.run();
        } else {
            reader = new BufferedReader(new FileReader(new File(C.class.getName() + ".txt")));
            long timeout = System.currentTimeMillis();
            while (solution.hasNext()) {
                solution.run();
                solution.println();
                solution.println("----------------------------------");
            }
            solution.println("time: " + (System.currentTimeMillis() - timeout));
        }
        solution.close();
        reader.close();
    }
}