题目描述

Googlers are crazy about numbers and games, especially number games! Two Googlers, Laurence and Seymour, have invented a new two-player game based on "gNumbers". A number is a gNumber if and only if the sum of the number's digits has no positive divisors other than 1 and itself. (In particular, note that $1$ is a gNumber.)

The game works as follows: First, someone who is not playing the game chooses a starting number $N$. Then, the two players take turns. On a player's turn, the player checks whether the current number C is a gNumber. If it is, the player loses the game immediately. Otherwise, the player chooses a prime factor P of C, and keeps dividing C by P until P is no longer a factor of C. (For example, if the current number were 72, the player could either choose $2$ and repeatedly divide by $2$ until reaching $9$, or choose $3$ and repeatedly divide by $3$ until reaching $8$.) Then the result of the division becomes the new current number, and the other player's turn begins.

Laurence always gets to go first, and he hates to lose. Given a number $N$, he wants you to tell him which player is certain to win, assuming that both players play optimally.

输入格式

The first line of the input gives the number of test cases, $T$. $T$ test cases follow; each consists of a starting number $N$.

输出格式

For each test case, output one line containing "Case #x: y", where $x$ is the test case number (starting from 1) and $y$ is the winner's name: either Laurence or Seymour.

9
2
3
4
6
8
9
30
36300
1000000000000000

Case #1: Seymour
Case #2: Seymour
Case #3: Laurence
Case #4: Laurence
Case #5: Laurence
Case #6: Laurence
Case #7: Seymour
Case #8: Laurence
Case #9: Seymour

提示

In Case #1, $2$ is already a gNumber, since the sum of its digits is $2$, which has no positive divisors other than $1$ and itself. So Laurence immediately loses, which means Seymour wins. The same is true for Case #2.

In Case #3, $4$ is not a gNumber, since the sum of its digits is $4$, which has a positive divisor other than $1$ and itself (namely, $2$). $4$ has one prime factor ($2$), so Laurence must choose this factor and repeatedly divide $4$ by it, which leaves him with $1$. Then, Seymour begins his turn with $1$, which is a gNumber. So he loses and Laurence wins.

Limits

$1 \le T \le 100$.

Small dataset (Test Set 1 - Visible)

$1 < N \le 1000$.

Large dataset (Test Set 2 - Hidden)

$1 < N \le 10^{15}$.