Problem A
Matrix Multiplication

Given three matrices $A$, $B$, and $C$ of size $n \cdot x$, $y \cdot m$, and $n \cdot m$, respectively, output:

1. “Inner matrix dimensions must agree” (without the quotes) if you cannot perform the matrix multiplication operation because of the quoted reason.

2. “WA” (without the quotes — “WA” stands from the keyword “Wrong Answer”) if the multiplication of matrix $A$ and $B$ does not produce matrix $C$.

3. “AC” (without the quotes — “AC” stands from the keyword “Accepted”) if the multiplication of matrix $A$ and $B$ correctly produces matrix $C$.

Input

The first line of input contains an integer $TC$ ($1 \leq TC \leq 77$), denoting the number of test cases.

Each test case first starts with a blank line (as a visual separator for human reader — this should not cause too much problem for your code), then four groups of data:

• A line that contains four integers: $n$, $x$, $y$, and $m$ ($1 \leq n, x, y, m \leq 1000$; $TC \cdot 3 \cdot n \cdot m \leq 3*10^7$),

• Then, $n$ rows of $x$ columns of integers between [$0$..$7$] that describe matrix $A$,

• Followed by $y$ rows of $m$ columns of integers between [$0$..$7$] that describe matrix $B$, and

• Finally by $n$ rows of $m$ columns of integers between [$0$..$max(x, y) \cdot 7 \cdot 7$] that describe matrix $C$.

Unfortunately for this problem, we need to explicitly provide the (big) input to you. Therefore you need to use Fast/Buffered I/O methods for this task.

Output

For each test case, print the required answer in one line.

Subtasks

1. ($11$ Points): ($1 \leq n, x, y, m \leq 1$).

2. ($29$ Points): ($1 \leq n, x, y, m \leq 77$).

3. ($23$ Points): ($1 \leq n, x, y, m \leq 500$).

4. ($37$ Points): No additional constraints.

2

1 1 1 1
7
7
49

1 1 1 1
7
7
48

AC
WA

3

2 1 2 3
1
7
2 5 1
2 5 1
2 5 1
14 35 7

2 1 1 3
1
7
2 5 1
2 5 1
14 35 6

2 1 1 3
1
7
2 5 1
2 5 1
14 35 7

Inner matrix dimensions must agree
WA
AC