Given a number n. Construct an array of n numbers from 0 to n.

Example

if n=3

arr[n]=[1,2,3].

Find the number of arrangements in which no object occurs at its original position.

Answer=2

[3,1,2],[2,3,1]

It is called **Derangement** of n numbers.

you can easily find the formula using inclusion exclusion principal and it’s proof on web.

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somebody edit question title as “Derangement of numbers :D”.