Alice likes building toy walls. She has a lot of $1 \times 2$ bricks and a limited supply of $1 \times 3$ bricks. Both types of bricks have a height of 1 and can not be rotated.

Alice is going to build a one unit thick wall of length $l$ and height $h$ out of these bricks. A wall is \textit{solid} if there are no seams directly above another seam.


\newcommand\anotherImage[2]{ % {caption}{image}
    \begin{minipage}[b]{5cm}\begin{center}
         \begin{tikzpicture}[scale=0.5]#2\end{tikzpicture}

         #1
    \end{center}\end{minipage}

}

\newcommand\anotherBrick{}
\def\anotherBrick(#1, #2, #3){\draw (#2, #1) rectangle ({#2 + #3}, {#1 + 1});}

\begin{center}\begin{tabular}{c c c}
    \anotherImage{Good seam placement}{
        \foreach \y in {1,...,2} {
            \foreach \x in {1,3,...,6} {
                \draw ({mod(\y + 1, 2) + \x - 1}, \y) rectangle ({mod(\y + 1, 2) + \x + 1}, \y - 1);
            }
        }
    } &
    \anotherImage{Bad seam placement}{
        \anotherBrick(2, 0, 3) \anotherBrick(2, 3, 2) \anotherBrick(2, 5, 2)
        \anotherBrick(1, 0, 2) \anotherBrick(1, 2, 3) \anotherBrick(1, 5, 2)
        \anotherBrick(0, 0, 2) \anotherBrick(0, 2, 2) \anotherBrick(0, 4, 3)

        \draw[ultra thick] (2, 1) ellipse (0.4 and 0.8);
        \draw[ultra thick] (5, 2) ellipse (0.4 and 0.8);
    } &
    \anotherImage{Solid $7 \times 4$ wall}{
        \pgfmathsetmacro{\l}{7}
        \pgfmathsetmacro{\h}{4}
        \pgfmathsetmacro{\c}{\l - 3}
        \foreach \y in {1,...,\h} {
            \foreach \x in {1,3,...,\c} {
                 \draw ({mod(\y + 1, 2) * 3 + \x - 1}, \y) rectangle ({mod(\y + 1, 2) * 3 + \x + 1}, \y - 1);
            }
        }
        \draw[ultra thick] (0, 0) rectangle (\l, \h);
    } \\
\end{tabular}\end{center}


Help Alice determine the minimum number of $1 \times 3$ bricks required to build a solid wall of length $l$ and height $h$.