Can a modified $19\times19$ checkerboard be tiled with decominoes ($10\times1$ rectangles)

Question

Consider a $19\times19$ checkerboard with the center square removed, the four corner squares removed, and with four extra squares-one above the center square of the top row, one below the bottom square of the bottom row, one to the right of the center square of the right-most column, and one to the left of the center square of the left-most column. Can this modified checkerboard be tiled with decominoes ($10\times1$ rectangles)? If so, explain how? If not, explain why.

So I did $19$ \times $19$ which is $361$ squares. So we are removing the center, the four corners but replacing the four corners with extra squares. So that means we will have $360$ squares. Since $10$ is a factor of $360$ then this might be possible but Im having a hard time proceeding from here.

I tried creating an array but $19\times19$ checkerboard is such a big number so I am assuming there is a different approach to this question.

Answer 1

HINT: There’s only one way to cover the extra square at the top. Once it’s been covered, there’s only one way to cover the squares in what’s left of the top row of the original $19\times 19$ square. How are you going to cover the extra squares at the sides?

Answer 2

The only way to fill the squares with the $X$ is the one in the picture. Once you have this there is only one way to fill the square with the $Y$. But then, what happens with the WOOPSIES squares?