Problem C

Number Theory

Input: Standard Input

Output: Standard Output

Time Limit: 1 Second

 

Given a positive integer n, you are to find am integer f, such that:

f3 = a13 + a23 + … + an3

 

where all a1, a2, ..., an are distinct positive integers.

For example,

if n = 3, one valid f is 71, since 713=143+233+703=357911.

if n = 4, one valid f is 100, since 1003=563+583+673+693=1000000.

 

Your number f may be big, but it has at most 250 digits.

 

Input

The first line contains the number of tests t(1<=t<=20). Each case contains a single line with a positive integer n(1<=n<=100).

 

Output

For each test case, print the case number and n+1 numbers: f, a1, a2, ...an. If no f exists, print a -1 and n zeros.

 

Sample Input                             Output for Sample Input

3

3

2

4

Case 1: 71 14 23 70

Case 2: -1 0 0

Case 3: 100 56 58 67 69


Problem idea, statement, solution provider: Rujia Liu, Member of Elite Problemsetters' Panel

Problem Solution and Special Judge: Monirul Hasan, Member of Elite Problemsetters' Panel