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.util.*;
import java.io.*;
import java.lang.*;
import java.math.*;
public class A {
    public static void main(String[] args) throws Exception {
        BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
        // Scanner scan = new Scanner(System.in);
        // PrintWriter out = new PrintWriter(new OutputStreamWriter(System.out));
        int n = Integer.parseInt(bf.readLine());

        int[] a = new int[n];
        char[] c = new char[n];
        for(int i=0; i<n; i++) {
          StringTokenizer st = new StringTokenizer(bf.readLine());
          String s = st.nextToken();
          c[i] = s.charAt(0);
          a[i] = Integer.parseInt(st.nextToken());

        }
        int ans1 = 0;
        int ans2 = 0;
        int ans3 = 0;
        for(int i=0; i<10; i++) {

          boolean x = true;
          boolean y = false;
          for(int j=0; j<n; j++) {
            if(c[j] == '|') x = x || (a[j] % 2 == 1);
            else if(c[j] == '^') x = x ^ (a[j] % 2 == 1);
            else if(c[j] == '&') x = x && (a[j] % 2 == 1);
            if(c[j] == '|') y = y || (a[j] % 2 == 1);
            else if(c[j] == '^') y = y ^ (a[j] % 2 == 1);
            else if(c[j] == '&') y = y && (a[j] % 2 == 1);
            a[j] /= 2;
          }
          if(x && y) {
            ans1 += 1 << (i);
            ans2 += 1 << (i);
            ans3 += 0 << (i);
          }
          if(!x && y) {
            ans1 += 1 << (i);
            ans2 += 0 << (i);
            ans3 += 1 << (i);
          }
          if(x && !y) {
            ans1 += 1 << (i);
            ans2 += 0 << (i);
            ans3 += 0 << (i);
          }
          if(!x && !y) {
            ans1 += 0 << (i);
            ans2 += 0 << (i);
            ans3 += 0 << (i);
          }


        }
        System.out.println("3");
        System.out.println("& " + ans1);
        System.out.println("| " + ans2);
        System.out.println("^ " + ans3);

        // StringTokenizer st = new StringTokenizer(bf.readLine());
        // int[] a = new int[n];
        // for(int i=0; i<n; i++) a[i] =  Integer.parseInt(st.nextToken());

        // out.close(); System.exit(0);
    }


}
