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Problem 896

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Divisible Ranges

A contiguous range of positive integers is called a divisible range if all the integers in the range can be arranged in a row such that the $n$-th term is a multiple of $n$.

For example, the range $[6..9]$ is a divisible range because we can arrange the numbers as $7,6,9,8$.

In fact, it is the $4$th divisible range of length $4$, the first three being $[1..4], [2..5], [3..6]$.

Find the $36$th divisible range of length $36$.

Give as answer the smallest number in the range.

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可整除区间

如果某个区间内的正整数可以经过重排使得第$n$项是$n$的倍数，则称之为可整除区间。
例如，区间$[6..9]$可以重排成$7,6,9,8$，因此它是一个可整除区间。

实际上，它是第$4$个长度为$4$的可整除区间，前三个分别是$[1..4]$，$[2..5]$，$[3..6]$。

求第$36$个长度为$36$的可整除区间。

给出该区间内的最小整数作为答案。

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