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Let a, b, c, d be integers. The complex number a+bj, where j2 = -1, is a factor of c+dj, if there exist integers e and f such that
c + dj = (a + bj)(e + fj).
A complex number a + bj where a and b are integers is a Gaussian prime if the factors are 1, -1, -a - bj and a + bj only.
The following are Gaussian primes: 1 + j, 1 - j, 1 + 2j, 1 - 2j, 3 and 7.
The Gaussian prime factors of 5 are:
1 + 2j and 1 - 2j, or
2 + j and 2 - j, or
-1 - 2j and -1 + 2j, or
-2 - j and -2 + j.
Write a program that finds all the Gaussian prime factors of a positive integer.
One line of input per case. The line represents a positive integer n.
2 5 6 700
Case #1: 1+j, 1-j Case #2: 1+2j, 1-2j Case #3: 1+j, 1-j, 3 Case #4: 1+j, 1-j, 1+2j, 1-2j, 7
Output the Gaussian prime factors in ascending order of a. If there are more than one factors with the same a, output them in ascending order of b by absolute value. If two conjugate factors coexist, the one with a positive imaginary part precedes that with a negative imaginary part.
| 时间上限 | 内存上限 |
| 1000 | 65536 |