Score : $100$ points

问题描述

让我们定义一个函数 $f$，其表达式为 $f(x) = x^2 + 2x + 3$。

给定一个整数 $t$，求解 $f(f(f(t)+t)+f(f(t)))$ 的值。

这里保证答案是一个不超过 $2 \times 10^9$ 的整数。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

Let us define a function $f$ as $f(x) = x^2 + 2x + 3$.
Given an integer $t$, find $f(f(f(t)+t)+f(f(t)))$.
Here, it is guaranteed that the answer is an integer not greater than $2 \times 10^9$.

Constraints

• $t$ is an integer between $0$ and $10$ (inclusive).

Input

Input is given from Standard Input in the following format:

$t$

Output

Print the answer as an integer.

Sample Input 1

0

Sample Output 1

1371

The answer is computed as follows.

• $f(t) = t^2 + 2t + 3 = 0 \times 0 + 2 \times 0 + 3 = 3$
• $f(t)+t = 3 + 0 = 3$
• $f(f(t)+t) = f(3) = 3 \times 3 + 2 \times 3 + 3 = 18$
• $f(f(t)) = f(3) = 18$
• $f(f(f(t)+t)+f(f(t))) = f(18+18) = f(36) = 36 \times 36 + 2 \times 36 + 3 = 1371$

Sample Input 2

3

Sample Output 2

722502

Sample Input 3

10

Sample Output 3

1111355571

update @ 2024/3/10 10:09:46