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.StringTokenizer;

/**
 * Created by omar on 25/10/17.
 */
public class A {
    public static void main(String[] args) throws Exception {
        Scanner sc = new Scanner(System.in);
        PrintWriter out = new PrintWriter(System.out);

        int n = sc.nextInt();
        char[] op = new char[n];
        int[] num = new int[n];
        for (int i = 0; i < n; i++) {
            StringTokenizer st = new StringTokenizer(sc.nextLine());
            op[i] = st.nextToken().charAt(0);
            num[i] = Integer.parseInt(st.nextToken());
        }

        int[][] bits = new int[11][2];
        for (int i = 0; i < 11; i++) {
            for (int j = 0; j < 2; j++) {
                int curNum = j == 0 ? 0 : (1 << i);
                for (int k = 0; k < n; k++)
                    if (op[k] == '|') curNum |= num[k];
                    else if (op[k] == '^') curNum  ^= num[k];
                    else curNum &= num[k];
                bits[i][j] = (curNum & (1 << i)) == 0 ? 0 : 1;
            }
        }

        System.err.println(bits[0][0] + " " +bits[0][1]);
        int and = 0, or1 = 0, xor = 0, or2 = 0;
        for (int i = 0; i < 10; i++) {
//            if (!(bits[i][0] == 0 && bits[i][1] == 0)) and |= (1 << i);
//            if (!(bits[i][0] == 0 && bits[i][1] == 1)) or1 |= (1 << i);
            if (bits[i][0] == 0 && bits[i][1] == 0) or1 |= (1 << i);
            else if (bits[i][0] == 0 && bits[i][1] == 1) and |= (1 << i);
            else if (bits[i][0] == 1 && bits[i][1] == 0) {
                xor |= (1 << i);
                and |= (1 << i);
            }
            else if (bits[i][0] == 1 && bits[i][1] == 1) {
                or2 |= (1 << i);
                or1 |= (1 << i);
                and |= (1 << i);
            }
        }

        System.err.println(Integer.toBinaryString(and));
        System.err.println(Integer.toBinaryString(or1));
        System.err.println(Integer.toBinaryString(xor));
        System.err.println(Integer.toBinaryString(or2));

        out.println(4);
        out.println("| " + or1);
        out.println("| " + or2);
        out.println("& " + and);
        out.println("^ " + xor);


        out.flush();
        out.close();
    }
    static class Scanner {
        StringTokenizer st;
        BufferedReader br;

        public Scanner(InputStream s) {
            br = new BufferedReader(new InputStreamReader(s));
        }

        public String next() throws IOException {
            while (st == null || !st.hasMoreTokens())
                st = new StringTokenizer(br.readLine());
            return st.nextToken();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }

        public String nextLine() throws IOException {
            return br.readLine();
        }

        public double nextDouble() throws IOException {
            String x = next();
            StringBuilder sb = new StringBuilder("0");
            double res = 0, f = 1;
            boolean dec = false, neg = false;
            int start = 0;
            if (x.charAt(0) == '-') {
                neg = true;
                start++;
            }
            for (int i = start; i < x.length(); i++)
                if (x.charAt(i) == '.') {
                    res = Long.parseLong(sb.toString());
                    sb = new StringBuilder("0");
                    dec = true;
                } else {
                    sb.append(x.charAt(i));
                    if (dec)
                        f *= 10;
                }
            res += Long.parseLong(sb.toString()) / f;
            return res * (neg ? -1 : 1);
        }

        public boolean ready() throws IOException {
            return br.ready();
        }

        public boolean nextEmpty() throws IOException
        {
            String s = nextLine();
            st = new StringTokenizer(s);
            return s.isEmpty();
        }
    }
}
