1322: Singer House
Time Limit: 2 Sec Memory Limit: 256 MBSubmit: 0 Solved: 0
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Description
time limit per test
2 secondsmemory limit per test
512 megabytesinput
standard inputoutput
standard outputIt is known that passages in Singer house are complex and intertwined. Let's define a Singer k-house as a graph built by the following process: take complete binary tree of height k and add edges from each vertex to all its successors, if they are not yet present.
Singer 4-house Count the number of non-empty paths in Singer k-house which do not pass the same vertex twice. Two paths are distinct if the sets or the orders of visited vertices are different. Since the answer can be large, output it modulo 109+7.
Input
The only line contains single integer k (1≤k≤400).
Output
Print single integer− the answer for the task modulo 109+7.
Examples
Input
2
Output
9
Input
3
Output
245
Input
20
Output
550384565
Note
There are 9 paths in the first example (the vertices are numbered on the picture below): 1, 2, 3, 1-2, 2-1, 1-3, 3-1, 2-1-3, 3-1-2.
Singer 2-house