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There is a total of \(N\) young programmers which are preparing for the second part of competitive season
during a winter camp in Krapina Zagreb. Mr. Malnar, a big promoter of order, discipline and hard work,
told the programmers to form a line and gave each of them a certain number (possibly zero) tasks. He
gave away a total of N different tasks and he knows that the \(i-th\) programmer in line will be happy if
they got exactly \(i\) tasks.
In how many different ways could Mr. Malnar give out the tasks in such a way that at least one
programmer was happy? Two ways of giving out the tasks are considered different if there exists a
programmer and a task such that in one way that programmer received that task while in the other one
they didn’t.
Subtask
Score
Constraints
1
22
\(1 \le N \le 7\)
2
33
\(1 \le N \le 20\)
3
55
No additional constraints.
The first line contains an integer \(N\) (\(1 \le N \le 350\)) from task description.
Output the sought number of ways modulo \(10^{9} + 7\).
1123314192940893Clarification of the second example:
Ways of giving out the tasks in which at least one programmer is happy are:
1. First task to first programmer, second task to the second one.
2. Second task to the first programmer, first task to the second one.
3. Both tasks to the second programmer.
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