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.*;
import java.math.*;

public class utkarsh {

    InputStream is;
    PrintWriter out;
    
    long maxl = (long) 4e18, mod = (long)1e9 + 7L;
    
    void solve(){
        //Enter code here utkarsh
        int n = ni();
        int x, a[] = new int[10];
        Arrays.fill(a, 2);
        char c;
        while(n-- > 0){
            c = nc();
            x = ni();
            if(c == '&'){
                for(int i = 0; i < 10; i++){
                    if((x & (1 << i)) == 0) a[i] = 0;
                }
            }else if(c == '|'){
                for(int i = 0; i < 10; i++){
                    if((x & (1 << i)) != 0) a[i] = 1;
                }
            }else{
                for(int i = 0; i < 10; i++){
                    if((x & (1 << i)) != 0){
                        if(a[i] == 0 || a[i] == 1)  a[i] = 1 - a[i];
                        else    a[i] = -a[i];
                    }
                }
            }
        }
        //out.println(a[0] +" "+ a[1]);
            int p, q, r, z;
            p = 1023;
            q = 0;
            r = 0;
            for(int i = 0; i < 10; i++){
                if(a[i] == 0){
                    p ^= (1 << i);
                }else if(a[i] == 1){
                    q |= (1 << i);
                }else if(a[i] == -2){
                    r ^= (1 << i);
                }
            }
            z = 0;
            if(p != 1023)   z++;
            if(q != 0)  z++;
            if(r != 0)  z++;
            out.println(z);
            if(p != 1023)   out.println("& "+ p);
            if(q != 0)  out.println("| "+ q);
            if(r != 0)  out.println("^ "+ r);
    }
    
    long modpow(long base, long exp, long modulus) { base %= modulus; long result = 1L; while (exp > 0) { if ((exp & 1)==1) result = (result * base) % modulus; base = (base * base) % modulus; exp >>= 1; } return result;
    }
    
    public static void main(String[] args) { new utkarsh().run();
    }
    void run(){ is = System.in; out = new PrintWriter(System.out); solve(); out.flush();
    }
    
    byte input[] = new byte[1024];
    int len = 0, ptr = 0;
    
    int readByte(){ if(ptr >= len){ ptr = 0; try{ len = is.read(input); }catch(IOException e){ throw new InputMismatchException(); } if(len <= 0){ return -1; } } return input[ptr++];
    }
    boolean isSpaceChar(int c){ return !( c >= 33 && c <= 126 ); 
    }
    int skip(){ int b = readByte(); while(b != -1 && isSpaceChar(b)){ b = readByte(); } return b;
    }
    
    char nc(){ return (char)skip();
    }
    String ns(){ int b = skip(); StringBuilder sb = new StringBuilder(); while(!isSpaceChar(b)){ sb.appendCodePoint(b); b=readByte(); } return sb.toString();
    }
    int ni(){ int n = 0,b = readByte(); boolean minus = false; while(b != -1 && !( (b >= '0' && b <= '9') || b == '-')){ b = readByte(); } if(b == '-'){ minus = true; b = readByte(); } if(b == -1){ return -1; } while(b >= '0' && b <= '9'){ n = n * 10 + (b - '0'); b = readByte(); } return minus ? -n : n;
    }
    long nl(){ long n = 0L; int b = readByte(); boolean minus = false; while(b != -1 && !( (b >= '0' && b <= '9') || b == '-')){ b = readByte(); } if(b == '-'){ minus = true; b = readByte(); } while(b >= '0' && b <= '9'){ n = n * 10 + (b - '0'); b = readByte(); } return minus ? -n : n;
    }
    double nd(){ return Double.parseDouble(ns());
    }
    float nf(){ return Float.parseFloat(ns());
    }
    int[] na(int n){ int a[] = new int[n]; for(int i = 0; i < n; i++){ a[i] = ni(); } return a;
    }
    char[] ns(int n){ char c[] = new char[n]; int i,b = skip(); for(i = 0; i < n; i++){ if(isSpaceChar(b)){ break; } c[i] = (char)b; b = readByte(); } return i == n ? c : Arrays.copyOf(c,i);
    }
}
