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J - LCM from 1 to n
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Time Limit: 4 second(s) Memory Limit: 64 MB

Given an integer n, you have to find

lcm(1, 2, 3, ..., n)

lcm means least common multiple. For example lcm(2, 5, 4) = 20, lcm(3, 9) = 9, lcm(6, 8, 12) = 24.

Input

Input starts with an integer T (≤ 10000), denoting the number of test cases.

Each case starts with a line containing an integer n (2 ≤ n ≤ 108).

Output

For each case, print the case number and lcm(1, 2, 3, ..., n). As the result can be very big, print the result modulo 232.

Sample Input

Output for Sample Input

5

10

5

200

15

20

Case 1: 2520

Case 2: 60

Case 3: 2300527488

Case 4: 360360

Case 5: 232792560

 


Problem Setter: Jane Alam Jan
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