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 test {
    static boolean DEBUG_FLAG = false;
    int INF = (int)1e9;
    long MOD = 1000000007;
    long M = (long)1e18;
    
    static void debug(String s) {
        if(DEBUG_FLAG) {
            System.out.print(s);
        }
    }
    
    
    
    void solve(InputReader in, PrintWriter out) throws IOException {
        int n = in.nextInt();
        int a = 0, b = 1023, c = 0;
        for(int i=0; i<n; i++) {
            char x = in.next().charAt(0);
            int y = in.nextInt();
            if(x=='&') {
                a = a & y;
                b = b & y;
            } else if(x=='|') {
                a = a | y;
                b = b | y;
            } else {
                a = a ^ y;
                b = b ^ y;
            }
        }
        int x = 0, y = 0;
        for(int i=0; i<10; i++) {
            int k = 1<<i;
            if(((a&k)!=0)&&((b&k)!=0)) {
                x += k;
            } else if(((a&k)==0)&&((b&k)==0)) {
                x += k;
                y += k;
            } else if(((a&k)!=0)&&((b&k)==0)) {
                y += k;
            }
        }
        out.println(2);
        out.println("| "+x+" \n^ "+y);
    }
    
    
    public static void main(String[] args) throws IOException {
        if(args.length>0 && args[0].equalsIgnoreCase("d")) {
            DEBUG_FLAG = true;
        }
        InputReader in = new InputReader();
        PrintWriter out = new PrintWriter(System.out);
        int t = 1;//in.nextInt();
        long start = System.nanoTime();
        while(t-- >0) {
            new test().solve(in, out);
        }
        long end = System.nanoTime();
        debug("\nTime: " + (end-start)/1e6 + " \n\n");
        out.close();
    }
    
    static class InputReader {
        static BufferedReader br;
        static StringTokenizer st;
    
        public InputReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        
        String next() {
            while (st == null || !st.hasMoreTokens()) {
                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());
        }
    }
}