Find the Derangement of An Array
<p>In combinatorial mathematics, a <strong>derangement</strong> is a permutation of the elements of a set, such that no element appears in its original position.</p>

<p>You are given an integer <code>n</code>. There is originally an array consisting of <code>n</code> integers from <code>1</code> to <code>n</code> in ascending order, return <em>the number of <strong>derangements</strong> it can generate</em>. Since the answer may be huge, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> n = 3
<strong>Output:</strong> 2
<strong>Explanation:</strong> The original array is [1,2,3]. The two derangements are [2,3,1] and [3,1,2].
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> n = 2
<strong>Output:</strong> 1
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= n &lt;= 10<sup>6</sup></code></li>
</ul>
Math; Dynamic Programming; Combinatorics
class Solution:
    def findDerangement(self, n: int) -> int:
        mod = 10**9 + 7
        f = [1] + [0] * n
        for i in range(2, n + 1):
            f[i] = (i - 1) * (f[i - 1] + f[i - 2]) % mod
        return f[n]
