发布时间: 2017年6月19日 00:24 时间限制: 1000ms 内存限制: 128M

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*4n+1*

This problem is based on an exercise of David Hilbert, who pedagogically suggested that one study the theory of

numbers. Here, we do only a bit of that.

An **H**-number is a positive number which is one more than a multiple of four: 1, 5, 9, 13, 17, 21,... are the **H**-numbers. For this problem we pretend that these are the *only* numbers. The **H**-numbers are closed under multiplication.

As with regular integers, we partition the **H**-numbers into units, **H**-primes, and **H**-composites. 1 is the only unit. An **H**-number **h** is **H**-prime if it is not the unit, and is the product of two **H**-numbers in only one way: 1 × **h**. The rest of the numbers are **H**-composite.

For examples, the first few **H**-composites are: 5 × 5 = 25, 5 × 9 = 45, 5 × 13 = 65, 9 × 9 = 81, 5 × 17 = 85.

Your task is to count the number of **H**-semi-primes. An **H**-semi-prime is an **H**-number which is the product of exactly two **H**-primes. The two **H**-primes may be equal or different. In the example above, all five numbers are **H**-semi-primes. 125 = 5 × 5 × 5 is not an **H**-semi-prime, because it's the product of three **H**-primes.

Each line of input contains an **H**-number ≤ 1,000,001. The last line of input contains 0 and this line should not be processed.

For each inputted **H**-number **h**, print a line stating **h** and the number of **H**-semi-primes between 1 and **h** inclusive, separated by one space in the format shown in the sample.

Please Input Input Here

Please Input Output Here

复制

21 85 789 0

21 0 85 5 789 62