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.
//package com.company;
import java.io.*;
import java.math.BigInteger;
import java.util.*;

public class Main
{
    static int[] binaryToArr(int number){
        int[] ret = new int[10];
        int mask = 1;
        for (int i = ret.length - 1; i >= 0; i--) {
            ret[i] = (mask & number) != 0 ? 1: 0;
            mask <<= 1;
        }
        return ret;
    }
    static int[] ret = new int[10];
    static int[] xor = new int[10];
    static void parse(char type, int num){
        int[] b = binaryToArr(num);
        switch (type) {
            case '&': //&
                for (int i = 0; i < 10; i++) {
                    if (b[i] == 0) {
                        ret[i] = 0;
                    }
                }
                break;
            case '|':
                for (int i = 0; i < 10; i++) {
                    if (b[i] == 1) {
                        ret[i] = 1;
                    }
                }
                break;
            case '^':
                for (int i = 0; i < 10; i++) {
                    if (ret[i] == 0 || ret[i] == 1) {
                        ret[i] = b[i] ^ ret[i];
                    } else {
                        if (xor[i] == -1) xor[i] = b[i];
                        else xor[i] = xor[i] ^ b[i];
                    }
                }
        }
    }


    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        for (int i = 0; i < 10; i++) {
            ret[i] = -1; xor[i] = -1;
        }
        for (int i = 0; i < n; i++) {
            char c = sc.next().charAt(0);
            int n1 = sc.nextInt();
            parse(c, n1);

        }
        int mask = 1 << 9;
        int and = 0, or = 0, xor1 = 0;
        for (int i = 0; i < 10; i++) {
            if (ret[i] == 0){
            } else if (ret[i] == 1){
                and += mask;
                or += mask;
            } else if (xor[i] != -1){
                xor1 += xor[i] * mask;
                and += mask;
            } else {
                and += mask;
            }
            mask >>= 1;
        }
        if (xor1 == 0) {
            System.out.println(2);
            System.out.println("& " + and);
            System.out.println("| " + or);
        } else {
            System.out.println(3);
            System.out.println("^ " + xor1);
            System.out.println("& " + and);
            System.out.println("| " + or);
        }

    }
}