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B - KEYENCE building

Score : $200$ points

Problem Statement

There are $N$ people numbered $1$ to $N$.

Person $i$ guessed the building area of KEYENCE headquarters building to be $S_i$ square meters.

The shape of KEYENCE headquarters building is shown below, where $a$ and $b$ are some positive integers.
That is, the building area of the building can be represented as $4ab+3a+3b$.

Based on just this information, how many of the $N$ people are guaranteed to be wrong in their guesses?

Constraints

• $1 \leq N \leq 20$
• $1 \leq S_i \leq 1000$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$

$S_1$ $\ldots$ $S_N$

Output

Print the answer.

3
10 20 39

1

The area would be $10$ square meters if $a=1,b=1$, and $39$ square meters if $a=2,b=3$.

However, no pair of positive integers $a$ and $b$ would make the area $20$ square meters.

Thus, we can only be sure that Person $2$ guessed wrong.

5
666 777 888 777 666

3