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Suppose you have **N** integers from 1 to N. We define a beautiful arrangement as an array that is constructed by these **N** numbers successfully if one of the following is true for the i_{th} position (1 <= i <= N) in this array:

- The number at the i
_{th}position is divisible by**i**. **i**is divisible by the number at the i_{th}position.

Now given N, how many beautiful arrangements can you construct?

**Example 1:**

Input:2Output:2Explanation:

The first beautiful arrangement is [1, 2]:

Number at the 1st position (i=1) is 1, and 1 is divisible by i (i=1).

Number at the 2nd position (i=2) is 2, and 2 is divisible by i (i=2).

The second beautiful arrangement is [2, 1]:

Number at the 1st position (i=1) is 2, and 2 is divisible by i (i=1).

Number at the 2nd position (i=2) is 1, and i (i=2) is divisible by 1.

**Note:**

**N**is a positive integer and will not exceed 15.

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