Problem
In this problem, you have to find the last three digits before the decimal point for the number (3 + √5)n.
For example, when n = 5, (3 + √5)5 = 3935.73982... The answer is 935.
For n = 2, (3 + √5)2 = 27.4164079... The answer is 027.
Input
The first line of input gives the number of cases, T. T test cases follow, each on a separate line. Each test case contains one positive integer n.
Output
For each input case, you should output:
Case #X: Y
where X is the number of the test case and Y is the last three integer digits of the number (3 + √5)n. In case that number has fewer than three integer digits, add leading zeros so that your output contains exactly three digits.
Limits
Time limit: 30 2 seconds per test set.
Memory limit: 1GB.
1 < T < 100
Small dataset (Test set 1 - Visible; 15 Points)
2 < n < 30
Large dataset (Test set 2 - Hidden; 35 Points)
2 < n < 2000000000
Sample
2 5 2
Case #1: 935 Case #2: 027