Game of Arrays

Tweek and Craig are good friends and always playing together. And they just invented a new game when doing their math homework.

First of all, they write three arrays $A$, $B$, and $C$, each with $N$ numbers. Then on the black board, they write those arrays as

$$A + B = C$$

If the equation is satisfied, it means for each position $i$ from $1$ to $N$, there are $A_i + B_i = C_i$ holds.

Of course, this equation is not always satisfied at the very beginning.

Fortunately, for arrays $A$, $B$ and $C$, some numbers are $changeable$, while other's are not. Those $changeable$ numbers' positions are determined before the game begins.

During the game, Tweek and Craig will take turns, trying to change a number from an array. Tweek plays first.

In each turn, the player can choose a $changeable$ number from an array, and substract it by one. However, no negative numbers should appear, so the chosen number cannot be $0$ before substraction.

Tweek's goal is to make the equation satisfied during the game, while Craig's goal is to prevent it to happen.

The game ends when the equation is satisfied (a win for Tweek) or there are no possible moves but still $A + B \neq C$ (means there is at least one $i \in \left[1, N\right]$, where $A_i + B_i \neq C_i$, which is a win for Craig).

Given $A$, $B$ and $C$, and the position of $changeable$ numbers for each array, your task is to determine the winner.

First line contains an integer $T$, which indicates the number of test cases.

Every test case begins with an integers $N$, which is the length of array $A$, $B$ and $C$.

The $2^{nd}$ line and $3^{rd}$ line describe the array $A$. The $2^{nd}$ line contains $N$ intergers $A_1$, $A_2$, $\cdots$, $A_N$, indicating the elements in array $A$. The $3^{rd}$ line contains $N$ intergers $u_1$, $u_2$, $\cdots$, $u_N$, and $u_i$ is $1$ if $A_i$ is $changeable$, otherwise $u_i$ is $0$.

The $4^{th}$ line and $5^{th}$ line describe the array $B$. The $4^{th}$ line contains $N$ intergers $B_1$, $B_2$, $\cdots$, $B_N$, indicating the elements in array $B$. The $5^{th}$ line contains $N$ intergers $v_1$, $v_2$, $\cdots$, $v_N$, and $v_i$ is $1$ if $B_i$ is $changeable$,otherwise $v_i$ is $0$.

The $6^{th}$ line and $7^{th}$ line describe the array $C$. The $6^{th}$ line contains $N$ intergers $C_1$, $C_2$, $\cdots$, $C_N$, indicating the elements in array $C$. The $7^{th}$ line contains $N$ intergers $w_1$, $w_2$, $\cdots$, $w_N$, and $w_i$ is $1$ if $C_i$ is $changeable$,otherwise $w_i$ is $0$.

$\cdot$ $1 \leq T \leq 2000$.

$\cdot$ for 75% data, $1 \leq N \leq 10$.

$\cdot$ for 95% data, $1 \leq N \leq 50$.

$\cdot$ for 100% data, $1 \leq N \leq 100$.

$\cdot$ $0 \leq A_i, B_i, C_i \leq 10^9$.

$\cdot$ both $u_i, v_i, w_i$ is either $0$ or $1$.

For every test case, you should output "Case #x: y", where $x$ indicates the case number and counts from $1$, and $y$ is the winner of the game.

3
2
4 3
1 1
4 4
0 1
5 5
0 0
2
4 4
1 1
4 4
0 0
5 5
0 0
2
4 4
1 1
4 4
0 0
4 4
0 0

Case #1: Tweek
Case #2: Craig
Case #3: Tweek

2015ACM/ICPC亚洲区上海站-重现赛（感谢华东理工）