CF878A · Short Program

• 难度：1600
• 标签：bitmasks、constructive algorithms
• 链接：https://codeforces.com/problemset/problem/878/A
• 时间限制：2 seconds　内存限制：256 megabytes
• 出现位置：Day18-bitmask建模-异或-贪心DP

英文原题面

Statement

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.

样例

样例 1

输入：

3
| 3
^ 2
| 1

输出：

2
| 3
^ 2

样例 2

输入：

3
& 1
& 3
& 5

输出：

1
& 1

样例 3

输入：

3
^ 1
^ 2
^ 3

输出：

0

样例解释（英文原文）

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.