Nice partition P22494

In this problem, we say that a partition of the numbers {1, …, 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 · 10⁴.

Output

For every n, print the number of nice partitions of {1, …, n} modulo 10⁸ + 7.