C. Short Program

time limit per test

2 seconds

memory limit per test

256 megabytes

input

standard input

output

standard output

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 x_i0 ≤ x_i ≤ 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 & 1 & 3 & 5

Output

1 & 1

Input

3 ^ 1 ^ 2 ^ 3

Output

0

Note

You can read about bitwise operations in .

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.

/* 题意：给出一段程序，只有三种操作，^ & |，然后让你输出一段不超过5行的程序使得运算结果和给出程序的运算结果相同 思路：经过如果操作之后，总共十位二进制数，有：确定为1的，确定为0的，不变的，是原来的相反的，然后分别讨论四种     情况 */#include 
       
        #define MAXN 500005#define MAXK 2using namespace std;int n;char str[MAXN][MAXK];int a[MAXN];int ora,xora,anda;inline int cal(int x){    for(int i=0;i