This problem is really simple, or is it? Given a positive integer N, calculate the minimum number of distinct primes needed such that their sum equals to N. A prime number is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers. The first few prime numbers are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, ... and so on.

Input

The first line contains an integer T, denoting the number of test cases. Each of the next subsequent T lines contain a positive integer N.

Constraints

<li>1 ≤ T ≤ 50,000</li> <li>1 ≤ N ≤ 50,000</li>

Output

For each test case, first print the case number followed by the minimum number of distinct primes such that their sum equals to N. If N cannot be represented by a summation of distinct primes, then print the case number followed by -1. Refer to the sample input/output for more clarity of the format.

Sample Input

10
1
2
3
10
27
100
1000
4572
4991
49999

Sample Output

Case 1: -1
Case 2: 1
Case 3: 1
Case 4: 2
Case 5: 3
Case 6: 2
Case 7: 2
Case 8: 2
Case 9: 3
Case 10: 1

Challenge

Too easy? Try the harder version here - Just Primes II