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.IOException;
import java.io.PrintWriter;
import java.util.*;
import java.io.*;

public class Main {

    public void solve() throws IOException {
        int n = nextInt();
        Character[] a = new Character[n];
        int[] c = new int[n];
        int[] b0 = new int[10];
        int[] b1 = new int[10];
        for (int i = 0; i < n; i++) {
            a[i] = nextToken().charAt(0);
            c[i] = nextInt();
        }
        int z = 0;
        for (int i = 0; i < n; i++) {
            if (a[i] == '|') {
                z = z | c[i];
            }
            if (a[i] == '&') {
                z = z & c[i];
            }
            if (a[i] == '^') {
                z = z ^ c[i];
            }
        }
        int t = 0;
        while (z > 0) {
            if (z % 2 == 1) {
                b0[t] = 1;
            }
            t++;
            z /= 2;
        }
        z = 1023;
        for (int i = 0; i < n; i++) {
            if (a[i] == '|') {
                z = z | c[i];
            }
            if (a[i] == '&') {
                z = z & c[i];
            }
            if (a[i] == '^') {
                z = z ^ c[i];
            }
        }
        t = 0;
        while (z > 0) {
            if (z % 2 == 1) {
                b1[t] = 1;
            }
            t++;
            z /= 2;
        }
        int ai = 0;
        int al = 0;
        int ax = 0;

        for (int i = 9; i >= 0; i--) {
            ai *= 2;
            al *= 2;
            ax *= 2;
            if (b0[i] == 1 || b1[i] == 1) {
                ai++;
            }
            if(b0[i] == 1 && b1[i] == 1){
                al++;
            }
            if(b0[i] == 1 && b1[i] == 0){
                ax++;
            }
        }
        out.println(3);
        out.println("& " + ai);
        out.println("| " + al);
        out.println("^ " + ax);


    }

    BufferedReader br;
    StringTokenizer sc;
    PrintWriter out;

    public String nextToken() throws IOException {
        while (sc == null || !sc.hasMoreTokens()) {
            try {
                sc = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                return null;
            }
        }
        return sc.nextToken();
    }

    public boolean hasNext() throws IOException {
        while (sc == null || !sc.hasMoreTokens()) {
            try {
                sc = new StringTokenizer(br.readLine());
            } catch (Exception e) {
                return false;
            }
        }
        return true;
    }

    public Integer nextInt() throws IOException {
        return Integer.parseInt(nextToken());
    }

    public Long nextLong() throws IOException {
        return Long.parseLong(nextToken());
    }

    public Double nextDouble() throws IOException {
        return Double.parseDouble(nextToken());
    }

    public static void main(String[] args) throws IOException {
        try {
            Locale.setDefault(Locale.US);
        } catch (Exception e) {
        }
        new Main().run();
    }

    public void run() {
        try {
            br = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
//            br = new BufferedReader(new FileReader("match.in"));
//            out = new PrintWriter(new File("match.out"));
            solve();
            out.close();
        } catch (Exception e) {
            e.printStackTrace();
            System.exit(1);
        }
    }
}