Score : $200$ points

问题陈述

有 $N$ 名编号为 $1$ 到 $N$ 的人。

第 $i$ 个人猜测 KEYENCE 总部大楼的建筑面积为 $S_i$ 平方米。

KEYENCE 总部大楼的形状如下所示，其中 $a$ 和 $b$ 是某些 正整数。
即，该大楼的建筑面积可以表示为 $4ab+3a+3b$。

仅根据这一信息，可以确保有多少名 $N$ 人的猜测是错误的？

以上为通义千问 qwen-max 翻译，仅供参考。

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.

Sample Input 1

3
10 20 39

Sample Output 1

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.

Sample Input 2

5
666 777 888 777 666

Sample Output 2

3

update @ 2024/3/10 09:56:58