gNumbers

Googlers love numbers, and they love games built on numbers even more. Two Googlers, Laurence and Seymour, invented a two player game around gNumbers. A number is a gNumber when the sum of its digits has no positive divisor other than 1 and itself. By that definition 1 is a gNumber.

The game runs like this. Someone who is not playing picks a starting number $N$. The two players then alternate turns. On a turn the player checks whether the current number $C$ is a gNumber. If it is, that player loses at once. Otherwise the player picks a prime factor $P$ of $C$ and divides $C$ by $P$ repeatedly until $P$ no longer divides it. For example, with a current number of 72 the player can pick 2 and divide down to 9, or pick 3 and divide down to 8. The result of the division becomes the new current number, and the other player takes a turn.

Laurence always moves first, and he hates to lose. Given $N$, determine which player wins when both play optimally.

The first line contains the number of test cases $T$. Each of the next $T$ lines contains one starting number $N$.

For each test case, print one line in the form "Case #x: y", where x is the test case number starting from 1 and y is the winner's name, either Laurence or Seymour.

• $1 \le T \le 100$
• $1 < N \le 10^{15}$

For $N = 2$ the digit sum is 2, and 2 has no positive divisor other than 1 and itself, so 2 is already a gNumber. Laurence loses immediately and Seymour wins. The same holds for $N = 3$.

For $N = 4$ the digit sum is 4, and 4 has the positive divisor 2 besides 1 and itself, so 4 is not a gNumber. The only prime factor of 4 is 2, so Laurence must pick 2 and divide until 1 is left. Seymour then starts his turn on 1, which is a gNumber, so Seymour loses and Laurence wins.