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#1467. 三角和

统计

第 $n$ 个三角数 $T(n) = 1 + \dots + n$ 是前 $n$ 个整数的和。它代表边长为 $n$ 的三角形阵列中的点数。例如 $T(4)$:

x x x x x x x x x x

编写一个程序来计算三角数的加权和:

$$W(n) = \sum_{k=1}^{n} k \cdot T(k+1)$$

输入格式

输入的第一行包含一个整数 $N$ ($1 \le N \le 1000$),表示随后数据集的数量。

每个数据集由单行组成,包含一个整数 $n$ ($1 \le n \le 300$),表示三角形一侧的点数。

输出格式

对于每个数据集,输出一行,包含数据集编号(从 $1$ 到 $N$)、一个空格、该数据集的 $n$ 值、一个空格,以及该 $n$ 对应的三角数加权和 $W(n)$。

样例

输入 1

4
3
4
5
10

输出 1

1 3 45
2 4 105
3 5 210
4 10 2145

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