Logic is not taught in Canadian math classes anymore, and Leo sets out to fix that by adding this logic question to Project Feng.

Leo will give you , () statements, like so:

Exactly of these statements are true.

Exactly of these statements are true.

Exactly of these statements are true.

...

Exactly of these statements are true.

for all . Leo tells you that some of these statements are true, and others are false. He then asks you, how many of these statements are true?

#### Input Specification

The first line will contain the positive integer . The next lines each contain a single positive integer, the sequence to .

#### Output Specification

Output a single nonnegative integer, the number of statements that are true. If there are multiple correct answers, output the greatest. If there are no possible answers, output `Paradox!`

.

#### Sample Input 1

```
4
0
1
2
3
```

#### Sample Output 1

`1`

#### Sample Input 2

```
4
4
4
4
4
```

#### Sample Output 2

`4`

#### Sample Input 3

```
1
0
```

#### Sample Output 3

`Paradox!`

#### Explanation for Sample 3

This is an Epimenides paradox. If the statement is true, then it must be false. It the statement is false, then it must be true.

## Comments

I've completed every test case except for 4, 6, 12. Can someone explain how 0 can be an answer?

Hello World! What the heck is going on?!! I tried my code with A TON OF TEST CASES MYSELF, but it doesn't work. Maybe I'm stupid but I am genuinely confused! my code: n = int(raw_input()) a = [] for i in range(0, n): a.append(int(raw_input())) m = 0 for i in range(0, n + 1): if i == a.count(i): m = i if m != 0: print m else: print "Paradox!" python2

See https://dmoj.ca/problem/vmss7wc16c1p2#comment-2503

helpI'm always getting 4, 6, and 12 wrong and I don't know why. I think my code is right... Also should 4 1 2 2 4 print 2 or 4?Same question

That test case should print 2. I think your program needs to differentiate between a paradox and 0.

It does, I don't know why it doesn't work!!!

call me dumb but i seriously dont know how its defining either a number is true of false.

Are you talking about the paradox case?

no in general. i dont understand the problem as a whole. how do i know if a number is true?

I’m pretty sure that there is probably some error with my program, but by any chance are there any A values which are greater than N (in the test cases)?

No, you're right. Sorry for not picking up this earlier, most solutions don't depend on the limit of .

Problem statement fixed.

You can print out zero.

Fixed.

Not according to my screen

Can confirm - if you print 0, you get some test cases correct.