DCC intensive Care Contest (Replay)

Boss Baby is the boss of all babies. He has been exploring prime numbers lately, and new recently made a conjecture resembling one of Goldbach's conjectures. Boss baby’s conjecture is that any number greater than or equal 10 can be expressed as the sum of a prime, square of two prime. It’s very easy work for him but he is busy to stop the dastardly plot of the CEO of Puppy Co.  He wants your help verify his conjecture for small numbers.

Note: 1 is not a prime number.

Input

The first line of the input contains an integer T (T ≤ 10⁶) denoting the number of test cases. Each test case will consist of a number greater than 10 and less than 10⁶, one per line.

Output

For each case, print the case number and the 3 primes P₁, P₂, P₃ on a line, where P₁ + P₂² + P₃² is equal to the number from the input. (P₁, P₂, P₃ must be printed in sort order.) If no such primes exist, print "0 0 0" instead (quotes for clarity). If there are multiple triplets of primes that satisfy the equation, print the least one in sorted order.

Sample

Input:
3
18
20
23

Output:
Case 1: 2 3 5
Case 2: 2 3 3
Case 3: 3 3 5

Note

For second Case 20

• 2, 3, 3 (2 + 3² + 3²) = 20
• 2, 3, 7 (2² + 3² + 7) = 20

are possible, but 2, 3, 3 is the least one