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 main {
    public static BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    public static PrintWriter pw = new PrintWriter(System.out);
    public static String line;
    public static StringTokenizer st;
    public static ArrayList<ArrayList<Integer>> adjList;
    public static int[] dx = {-1, 0, 1, 0, -1, 1, 1, -1};
    public static int[] dy = {0, 1, 0, -1, 1, 1, -1, -1};
    public static int INF = 0x3f3f3f3f;
    public static int MOD = 1000000007;

    public static void main(String[] args) throws Exception{
        int N = Integer.parseInt(br.readLine());
        char[] op = new char[N];
        int[] n = new int[N];
        for(int i = 0; i < N; i++){
            st = new StringTokenizer(br.readLine());
            op[i] = st.nextToken().charAt(0);
            n[i] = Integer.parseInt(st.nextToken());
        }
        int[] A = new int[10];
        Arrays.fill(A, -1);
        for(int i = 0; i < N; i++){
            for(int j = 0; j < 10; j++){
                if((n[i] & (1 << j)) != 0){
                    if(op[i] == '|'){
                        A[j] = 1;
                    } else if(op[i] == '^'){
                        if(A[j] == 0){
                            A[j] = 1;
                        } else if(A[j] == 1){
                            A[j] = 0;
                        } else if(A[j] == 2){
                            A[j] = -1;
                        } else{
                            A[j] = 2;
                        }
                    }
                } else if(op[i] == '&'){
                    A[j] = 0;
                }
            }
            // System.out.println(Arrays.toString(A));
        }
        int and = (1 << 10) - 1;
        int xor = 0;
        int or = 0;
        for(int i = 0; i < 10; i++){
            if(A[i] == 0){
                and ^= (1 << i);
            } else if(A[i] == 1){
                or |= (1 << i);
            } else if(A[i] == 2){
                xor |= (1 << i);
            }
        }

        pw.print(3 + "\n");
        pw.print("& " + and + "\n");
        pw.print("| " + or + "\n");
        pw.print("^ " + xor + "\n");

        // pw.print(op[0] + " " + ans + "\n");
        pw.close(); 
        br.close();
    }
}

class Pair{
    public int x, y, k, dir;

    Pair(int _x, int _y, int _k, int dir){
        x = _x;
        y = _y;
        k = _k;
        this.dir = dir;
    }
}
class Point implements Comparable<Point>{
    public double x, y;

    Point(double x, double y){
        this.x = x;
        this.y = y;
    }

    public int compareTo(Point p){
        if(x != p.x) return x < p.x ? -1 : 1;
        else if(y != p.y) return y < p.y ? -1 : 1;
        return 0;
    }
}