Bug Races

Time Limit: 10 Seconds
Memory Limit: 65536 KB

Two species of bugs, *Red iNT* and *Green fLOAT*, are living in *Blue Matrix*. They have a race at *Code Cube* every four years. *Code Cube* is a cuboid with integer dimensions. Bugs will run from the corner of *Code Cube* to the opposite corner in the race, choosing the shortest route. However, *Red iNT* can only run on the surfaces of the cuboid, and the shortest distance it runs is always an integer. *Green fLOAT* can run inside the cuboid, and the shortest distance it runs may be any real number. The race seems to be unfair, but *iNT* runs much more faster than *fLOAT*, so both have chance to win.

The scale of a *Code Cube* is defined as the maximum dimension of it. There are two different minimum cuboids satisfying the requirements above, 2×2×3 and 1×3×3, where the distances of *Red iNT*'s routes are both 5 and the distances of *Green fLOAT*'s routes are sqrt(17) and sqrt(19). Of course, the distances vary from one cuboid to another cuboid. Now the problem comes that bugs want to know the mean squared distances for all cuboids with the same scale.

#### Input

The input contains thousands of lines of integers *n*, which indicates the scale of *Code Cube*. *n* will be between 1 and 1000000, inclusive.

#### Output

Output the mean squared distance *Red iNT* runs and the one *Green fLOAT* runs as irreducible fraction, or "NaN" if both the numerator and the denominator are zero. See sample for more details.

#### Sample Input

1
2
3
4
1000

#### Sample Output

NaN NaN
NaN NaN
25/1 18/1
25/1 21/1
220986875/114 538411225/342

Author:

**WU, Zejun**
Contest:

**ZOJ Monthly, November 2010**
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