Problem H. Perfect Squares
时间限制 1000 ms
内存限制 32 MB
A number x is called a perfect square if there exists an integer b
satisfying x=b^2. There are many beautiful theorems about perfect squares in mathematics. Among which, Pythagoras Theorem is the most famous. It says that if the length of three sides of a right triangle is a, b and c respectively(a < b <c), then a^2 + b^2=c^2.
In this problem, we also propose an interesting question about perfect squares. For a given n, we want you to calculate the number of different perfect squares mod 2^n. We call such number f(n) for brevity. For example, when n=2, the sequence of {i^2 mod 2^n} is 0, 1, 0, 1, 0……, so f(2)=2. Since f(n) may be quite large, you only need to output f(n) mod 10007.
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输出数据
For each test case, output one line containing "Case #x: y", where x is the case number (starting from 1) and y is f(x).
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样例输出
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