The ~~unfortunate~~ very, very, very, lucky members of Trudeau's Computer Science Club are given another chance to become an exec. To actually be able to become an exec, one must solve an annoying problem that has been approved by ZQFMGB12. No one has bothered to try it in the past, but today that will change!

ZQFMGB12 has put out a simple true/false test for everyone to try. Each question is labelled from to . The test is extremely boring because all of the questions follow this rather strict format:

Question | Description |
---|---|

`p==q` | If the answers for question and question are equal, answer `true` to this question. Otherwise, answer `false` . |

`!p` | Put the opposite of question 's answer. |

There is actually a reason for this unusual test format. Tests are fairly compact and easy to grade, yet it is difficult to answer all the questions perfectly.

This test might be impossible because ZQFMGB12 is too lazy to check for a solution. Does a perfect solution exist, and can you provide an example?

#### Constraints

**Subtask 1 [20%]**

**Subtask 2 [20%]**

Questions will only be in the form `!p`

.

**Subtask 3 [60%]**

No further constraints.

#### Input Specification

The first line contains integer .

The questions are on separate lines. Question is on line number .

#### Output Specification

If no perfect solution exists, output `No perfect solution found`

.

Otherwise, provide lines of output. The line of output should contain your answer to the question, which could either be `true`

or `false`

.

#### Sample Input 1

```
5
1==1
!3
!2
3==2
!1
```

#### Sample Output 1

```
true
false
true
false
false
```

#### Sample Input 2

```
1
!1
```

#### Sample Output 2

`No perfect solution found`

#### Explanation for Sample 2

If the answer is `false`

, then the grader would look for the opposite of `false`

. The opposite of `false`

is not provided, so the answer is labelled incorrect.

If the answer is `true`

, then the grader would look for the opposite of `true`

. The answer would also be labelled incorrect.

There is no way to answer the question correctly, so no perfect solution exists.

#### Sample Input 3

```
4
!2
1==4
1==2
!3
```

#### Sample Output 3

`No perfect solution found`

## Comments

Isn't sample output 3 just : True False False True

Since 1==4, 3 should be True, not False.

Umm... Can someone explain Sample Input 1?? How is !3 outputting false?

`!3`

means to put the opposite of question 3's answer.The sample output is a perfect solution, and question 2's answer is indeed the opposite of question 3's answer.

What about sample input 3? !2 is the opposite of 2==4, !3 is the opposite of 1==2... So..?

No matter how you choose your combination of true/false, you cannot satisfy all of the questions.

It is not possible to provide a perfect solution for Sample Input 3.

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do you want coke or chocolate milk with your salt?

I'll have water. Have fun solving the problem.