Codeforces Round 443 (Div. 1) |
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Finished |

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bitmasks

constructive algorithms

*1600

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A. Short Program

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputPetya 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* ≤ 5·10^{5}) — 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*_{i} 0 ≤ *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 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.

Codeforces (c) Copyright 2010-2024 Mike Mirzayanov

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