## JPM - Just Primes

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

• 1 ≤ T ≤ 50,000
• 1 ≤ N ≤ 50,000
• ### 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