# Codeforces #879C

Written by    21:58 November 6, 2017

879C

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 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

output

input

output

input

output

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.

### 思路

\begin{aligned}f(x) = \ & xAND({xa_1})AND({xa_2})AND({xa_3})…\\&\ OR({xo_1})OR({xo_2})OR({xo_3})…\\&\ XOR({xx_1})XOR({xx_2})XOR({xx_3})…\\ =\ &xAND({xa_i}) OR({xo_j})XOR({xx_k}), \ (0\leq x \leq 1023)\end{aligned}

$$f(0)=1, f(1023) = 1 \Rightarrow {xa_i}=1, {xo_j}=1, {xx_k}=0$$

$$f(0)=1, f(1023) = 0 \Rightarrow {xa_i}=1, {xo_j}=0, {xx_k}=1$$

$$f(0)=0, f(1023) = 1 \Rightarrow {xa_i}=1, {xo_j}=0, {xx_k}=0$$

$$f(0)=0, f(1023) = 0 \Rightarrow {xa_i}=0, {xo_j}=0, {xx_k}=0$$

Category : acmstudy

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