Nice partition

In this problem, we say that a partition of the numbers $\{1, \dots, n\}$ is nice if

it has at least two subsets,
and every subset has at least two elements.

Additionally, we only consider partitions that are qualitatively different.

For instance, for $n = 5$ we only have one nice partition: $\{\{1, 2\}, \{3, 4, 5\}\}$ . Notice that $\{\{1, 2, 3, 4, 5\}\}$ would not fulfil the first property above, $\{\{2\}, \{1, 3, 4, 5\}\}$ would not fulfil the second property above, while $\{\{2, 3\}, \{1, 4, 5\}\}$ would be basically the same partition as the only one given.

Given $n$ , how many nice partitions do we have?

Input

Input consists of several cases, each one with an $n$ between 1 and $3 \cdot 10^4$ .

Output

For every $n$ , print the number of nice partitions of $\{1, \dots, n\}$ modulo $10^8 + 7$ .

Problem information

Author: Xavier Molinero

Generation: 2026-01-25T10:15:23.161Z