| A simple game consists of a grid of **R**x**C** buttons. Each button will be | |
| either lighted, or unlighted. Whenever you push a button, the state of that | |
| button, and its (up to) four neighbors will toggle -- lighted buttons will | |
| become unlighted and unlighted buttons will become lighted. Note that the | |
| neighbors do not 'wrap' and thus a corner button has only two neighbors, while | |
| an edge buttons has three. | |
| In this problem you will be given an initial configuration of the buttons. | |
| Your task is to push the right buttons so that, when you are done, all of the | |
| lights are turned on. If there are multiple ways to do this, you should | |
| determine the minimum number of buttons pushes that it can be done in. | |
| ### Input | |
| You will first read an integer **N** the number of test cases. For each test | |
| case, you will read two integers **R** and **C**. This will be followed by | |
| **R** whitespace-separated tokens, each containing **C** characters. A 'X' | |
| indicates a lighted button, while a '.' indicates an unlighted button. | |
| ### Constraints | |
| * **N** = 20 | |
| * 1 ≤ **R**,**C** ≤ 18 | |
| ### Output | |
| For each test case you should output the minimum number of button presses | |
| required to turn on all the lights. If there is no way to do this, you should | |
| output -1. | |