A matrix keypad consists of an $rc$ grid of buttons.

Additionally, there is one wire for each row and one wire

for each column. These wires are exposed through pins

so the keypad can be connected to a larger circuit.

When a button at row i and column $j$ is pressed, the wire

for row i and the wire for column $j$ will carry an electrical

current. If just a single button is pressed, it can be

identified by sequentially checking if a current can be

detected at each row wire and at each column wire.

Unfortunately, when multiple buttons are pressed at the

same time, it may not be possible to uniquely identify which buttons are pressed.

The only information you can have is this: for each wire, whether there is at least

one button along that wire being pressed.

The software you are using to detect which buttons are pressed was poorly

implemented. After probing the keypad, it stores the information in an $rc$ grid

of $\frac{0}{1}$ values. The value stored in row i and column $j$ of this grid is $1$ if there is at

least one button in row i and at least one $($possibly different$)$ button in column $j$

that is pressed. Otherwise, the value that is stored at this position is $0.$

Your job is to interpret as much information from such a grid as possible.

Determine which buttons are definitely pressed and which buttons are definitely

not pressed.

Input

The first line of input contains a single positive integer $T200$ indicating the

number of test cases. The first line of each test case contains two integers $r$ and $c$

where $1r10$ and $1c10.$ This indicates that the keypad is an $rc$ grid

of buttons.

The remaining $r$ lines of a test case describe the grid. The $i$ th row contains a

string of consecutive $0$ and $1$ characters. These will not be separated by spaces.