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 Main {
    public static void main(String[] args) {
        MyScanner sc = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));
        int n = sc.nextInt();
        int[] op = new int[n];
        int[] x = new int[n];
        for (int i = 0; i < n; ++i) {
            String operation = sc.next();
            x[i] = sc.nextInt();
            op[i] = operation.equals("&") ? 0 : operation.equals("|") ? 1 : 2;
        }
        // bitto gotoni miru
        int value1 = 0;
        int value2 = 0;
        int result0 = 0, result1 = 1023;
        for (int i = 0; i < n; ++i) {
            if (op[i] == 0) {
                result0 &= x[i];
                result1 &= x[i];
            } else if (op[i] == 1) {
                result0 |= x[i];
                result1 |= x[i];
            } else {
                result0 ^= x[i];
                result1 ^= x[i];
            }
        }
        for (int k = 0; k < 10; ++k) {
            int bit0 = result0 & 1 << k;
            int bit1 = result1 & 1 << k;
            if (bit0 == bit1) {
                value1 |= 1 << k;
                value2 |= bit0 == 0 ? 1 << k : 0;
            } else {
                // bit0, bit1 ga 2^k, 0 nara value2 ha 2^k, 0, 2^k nara 0
                value1 |= 0;
                value2 |= bit0;
            }
        }
        out.println(2);
        out.println("| " + value1);
        out.println("^ " + value2);
        out.close();
    }
    // http://codeforces.com/blog/entry/7018
    //-----------PrintWriter for faster output---------------------------------
    public static PrintWriter out;
    //-----------MyScanner class for faster input----------
    public static class MyScanner {
        BufferedReader br;
        StringTokenizer st;
        public MyScanner() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }
        int nextInt() {
            return Integer.parseInt(next());
        }
        long nextLong() {
            return Long.parseLong(next());
        }
        double nextDouble() {
            return Double.parseDouble(next());
        }
        String nextLine(){
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }
}

  	 						    			    				 				