\def\T{\ytableausetup{boxsize=0.6cm}
\begin{ytableau}
    1 & 2 & 6 & 7 & 14 & 19 \\
    3 & 8 & 9 & 15 & 18 & 21 \\
    4 & 10 & 11 & 16 & 20 & 23 \\
    5 & 12 & 13 & 17 & 22 & 24
\end{ytableau}}

\def\PT{
\ytableausetup{boxsize=0.6cm}
\begin{ytableau}
    1 & 5 & 6 & 13 & 17 & 18 \\
    2 & 7 & 8 & 14 & 19 & 20 \\
    3 & 9 & 10 & 15 & 21 & 22 \\
    4 & 11 & 12 & 16 & 23 & 24
\end{ytableau}
}

\def\MT{
\begin{tikzpicture}[scale=0.45]
\draw[style = dashed, <->] (0,0)--(25,0);
\node at (1,-0.5) {\tiny 1};
\node at (2,-0.5) {{\tiny 2}};
\node at (3,-0.5) {{\tiny3}};
\node at (4,-0.5) {{\tiny4}};
\node at (5,-0.5) {{\tiny5}};
\node at (6,-0.5) {\tiny6};
\node at (7,-0.5) {\tiny7};
\node at (8,-0.5) {{\tiny8}};
\node at (9,-0.5) {{\tiny9}};
\node at (10,-0.5) {{\tiny10}};
\node at (11,-0.5) {{\tiny11}};
\node at (12,-0.5) {\tiny12};
\node at (13,-0.5) {\tiny13};
\node at (14,-0.5) {{\tiny14}};
\node at (15,-0.5) {{\tiny15}};
\node at (16,-0.5) {{\tiny16}};
\node at (17,-0.5) {{\tiny17}};
\node at (18,-0.5) {\tiny18};
\node at (19,-0.5) {\tiny19};
\node at (20,-0.5) {{\tiny20}};
\node at (21,-0.5) {{\tiny21}};
\node at (22,-0.5) {{\tiny22}};
\node at (23,-0.5) {{\tiny23}};
\node at (24,-0.5) {{\tiny24}};

\draw[radius=.08, fill=black](1,0)circle;
\draw[radius=.08, fill=black](2,0)circle;
\draw[radius=.08, fill=black](3,0)circle;
\draw[radius=.08, fill=black](4,0)circle;
\draw[radius=.08, fill=black](5,0)circle;
\draw[radius=.08, fill=black](6,0)circle;
\draw[radius=.08, fill=black](7,0)circle;
\draw[radius=.08, fill=black](8,0)circle;
\draw[radius=.08, fill=black](9,0)circle;
\draw[radius=.08, fill=black](10,0)circle;
\draw[radius=.08, fill=black](11,0)circle;
\draw[radius=.08, fill=black](12,0)circle;
\draw[radius=.08, fill=black](13,0)circle;
\draw[radius=.08, fill=black](14,0)circle;
\draw[radius=.08, fill=black](15,0)circle;
\draw[radius=.08, fill=black](16,0)circle;
\draw[radius=.08, fill=black](17,0)circle;
\draw[radius=.08, fill=black](18,0)circle;
\draw[radius=.08, fill=black](19,0)circle;
\draw[radius=.08, fill=black](20,0)circle;
\draw[radius=.08, fill=black](21,0)circle;
\draw[radius=.08, fill=black](22,0)circle;
\draw[radius=.08, fill=black](23,0)circle;
\draw[radius=.08, fill=black](24,0)circle;

\draw[style=thick, color=black] (3,0) arc (0:180: .5cm);
\draw[style=thick, color=black] (4,0) arc (0:180: .5cm);
\draw[style=thick, color=black] (5,0) arc (0:180: .5cm);

\draw[style=thick, color=black] (15,0) arc (0:180: .5cm);
\draw[style=thick, color=black] (16,0) arc (0:180: .5cm);
\draw[style=thick, color=black] (17,0) arc (0:180: .5cm);

\draw[style=thick, color=black] (24,0) arc (0:180: .5cm);

\draw[style=thick] (18,0) arc [start angle=0,end angle=180,x radius=8.5cm, y radius=2cm];

\draw[style=thick, color=black] (8,0) arc (0:180: .5cm);
\draw[style=thick, color=black] (10,0) arc (0:180: .5cm);
\draw[style=thick, color=black] (12,0) arc (0:180: .5cm);

\draw[style=thick] (9,0) arc [start angle=0,end angle=180,x radius=1.5cm, y radius=1cm];
\draw[style=thick] (11,0) arc [start angle=0,end angle=180,x radius=1.5cm, y radius=1cm];
\draw[style=thick] (13,0) arc [start angle=0,end angle=180,x radius=1.5cm, y radius=1cm];

\draw[style=thick] (20,0) arc [start angle=0,end angle=180,x radius=1cm, y radius=1cm];
\draw[style=thick] (21,0) arc [start angle=0,end angle=180,x radius=1cm, y radius=1cm];
\draw[style=thick] (22,0) arc [start angle=0,end angle=180,x radius=1cm, y radius=1cm];
\draw[style=thick] (23,0) arc [start angle=0,end angle=180,x radius=1cm, y radius=1cm];

\end{tikzpicture}
}

\def\MTcolor{
\begin{tikzpicture}[scale=0.5]
\draw[style = dashed, <->] (0,0)--(25,0);
\node at (1,-0.5) {\color{Cerulean}\tiny 1};
\node at (2,-0.5) {\color{Cerulean}{\tiny 2}};
\node at (3,-0.5) {{\tiny3}};
\node at (4,-0.5) {{\tiny4}};
\node at (5,-0.5) {{\tiny5}};
\node at (6,-0.5) {\tiny6};
\node at (7,-0.5) {\color{Cerulean}\tiny7};
\node at (8,-0.5) {\color{Cerulean}{\tiny8}};
\node at (9,-0.5) {{\tiny9}};
\node at (10,-0.5) {{\tiny10}};
\node at (11,-0.5) {{\tiny11}};
\node at (12,-0.5) {\tiny12};
\node at (13,-0.5) {\color{Cerulean}\tiny13};
\node at (14,-0.5) {\color{Cerulean}{\tiny14}};
\node at (15,-0.5) {{\tiny15}};
\node at (16,-0.5) {{\tiny16}};
\node at (17,-0.5) {{\tiny17}};
\node at (18,-0.5) {\tiny18};
\node at (19,-0.5) {\color{Cerulean}\tiny19};
\node at (20,-0.5) {\color{Cerulean}{\tiny20}};
\node at (21,-0.5) {{\tiny21}};
\node at (22,-0.5) {{\tiny22}};
\node at (23,-0.5) {{\tiny23}};
\node at (24,-0.5) {{\tiny24}};

\draw[radius=.08, fill=Cerulean](1,0)circle;
\draw[radius=.08, fill=Cerulean](2,0)circle;
\draw[radius=.08, fill=black](3,0)circle;
\draw[radius=.08, fill=black](4,0)circle;
\draw[radius=.08, fill=black](5,0)circle;
\draw[radius=.08, fill=black](6,0)circle;
\draw[radius=.08, fill=Cerulean](7,0)circle;
\draw[radius=.08, fill=Cerulean](8,0)circle;
\draw[radius=.08, fill=black](9,0)circle;
\draw[radius=.08, fill=black](10,0)circle;
\draw[radius=.08, fill=black](11,0)circle;
\draw[radius=.08, fill=black](12,0)circle;
\draw[radius=.08, fill=Cerulean](13,0)circle;
\draw[radius=.08, fill=Cerulean](14,0)circle;
\draw[radius=.08, fill=black](15,0)circle;
\draw[radius=.08, fill=black](16,0)circle;
\draw[radius=.08, fill=black](17,0)circle;
\draw[radius=.08, fill=black](18,0)circle;
\draw[radius=.08, fill=Cerulean](19,0)circle;
\draw[radius=.08, fill=Cerulean](20,0)circle;
\draw[radius=.08, fill=black](21,0)circle;
\draw[radius=.08, fill=black](22,0)circle;
\draw[radius=.08, fill=black](23,0)circle;
\draw[radius=.08, fill=black](24,0)circle;

\draw[style=thick, color=black] (4,0) arc (0:180: .5cm);
\draw[style=thick, color=black] (5,0) arc (0:180: .5cm);
\draw[style=thick, color=black] (6,0) arc (0:180: .5cm);

\draw[style=thick, color=black] (10,0) arc (0:180: .5cm);
\draw[style=thick, color=black] (11,0) arc (0:180: .5cm);
\draw[style=thick, color=black] (12,0) arc (0:180: .5cm);

\draw[style=thick, color=black] (16,0) arc (0:180: .5cm);
\draw[style=thick, color=black] (17,0) arc (0:180: .5cm);
\draw[style=thick, color=black] (18,0) arc (0:180: .5cm);

\draw[style=thick, color=black] (22,0) arc (0:180: .5cm);
\draw[style=thick, color=black] (23,0) arc (0:180: .5cm);
\draw[style=thick, color=black] (24,0) arc (0:180: .5cm);

\draw[style=thick, color=Cerulean] (14,0) arc (0:180: .5cm);
\draw[style=thick, color=Cerulean] (20,0) arc (0:180: .5cm);

\draw[style=thick, color=Cerulean] (7,0) arc [start angle=0,end angle=180,x radius=2.5cm, y radius=1.5cm];
\draw[style=thick, color=Cerulean] (13,0) arc [start angle=0,end angle=180,x radius=2.5cm, y radius=1.5cm];

\draw[style=thick, color=Cerulean] (8,0) arc [start angle=0,end angle=180,x radius=3.5cm, y radius=2.5cm];
\draw[style=thick, color=Cerulean] (19,0) arc [start angle=0,end angle=180,x radius=6cm, y radius=2.5cm];

\end{tikzpicture}
}


\def\MTpreprocess{
\begin{tikzpicture}[scale=0.45]
\draw[style = dashed, <->] (0,0)--(25,0);
\node at (1,-0.5) {\tiny 1};
\node at (2,-0.5) {{\tiny 2}};
\node at (3,-0.5) {{\tiny3}};
\node at (4,-0.5) {{\tiny4}};
\node at (5,-0.5) {{\tiny5}};
\node at (6,-0.5) {\tiny6};
\node at (7,-0.5) {\tiny7};
\node at (8,-0.5) {{\tiny8}};
\node at (9,-0.5) {{\tiny9}};
\node at (10,-0.5) {{\tiny10}};
\node at (11,-0.5) {{\tiny11}};
\node at (12,-0.5) {\tiny12};
\node at (13,-0.5) {\tiny13};
\node at (14,-0.5) {{\tiny14}};
\node at (15,-0.5) {{\tiny15}};
\node at (16,-0.5) {{\tiny16}};
\node at (17,-0.5) {{\tiny17}};
\node at (18,-0.5) {\tiny18};
\node at (19,-0.5) {\tiny19};
\node at (20,-0.5) {{\tiny20}};
\node at (21,-0.5) {{\tiny21}};
\node at (22,-0.5) {{\tiny22}};
\node at (23,-0.5) {{\tiny23}};
\node at (24,-0.5) {{\tiny24}};

\draw[style=thick, color=black] (3,0) arc (0:180: .5cm);
\draw[style=thick, color=black] (4,0) arc (0:180: .5cm);
\draw[style=thick, color=black] (5,0) arc (0:180: .5cm);

\draw[style=thick, color=black] (15,0) arc (0:180: .5cm);
\draw[style=thick, color=black] (16,0) arc (0:180: .5cm);
\draw[style=thick, color=black] (17,0) arc (0:180: .5cm);

\draw[style=thick, color=Cerulean] (24,0) arc (0:180: .5cm);

\draw[style=thick, color=Cerulean] (18,0) arc [start angle=0,end angle=180,x radius=8.5cm, y radius=2cm];

\draw[style=thick, color=black] (8,0) arc (0:180: .5cm);
\draw[style=thick, color=black] (10,0) arc (0:180: .5cm);
\draw[style=thick, color=black] (12,0) arc (0:180: .5cm);

\draw[style=thick] (9,0) arc [start angle=0,end angle=180,x radius=1.5cm, y radius=1cm];
\draw[style=thick] (11,0) arc [start angle=0,end angle=180,x radius=1.5cm, y radius=1cm];
\draw[style=thick] (13,0) arc [start angle=0,end angle=180,x radius=1.5cm, y radius=1cm];

\draw[style=thick, color=Cerulean] (20,0) arc [start angle=0,end angle=180,x radius=1cm, y radius=1cm];
\draw[style=thick, color=Cerulean] (21,0) arc [start angle=0,end angle=180,x radius=1cm, y radius=1cm];
\draw[style=thick, color=Cerulean] (22,0) arc [start angle=0,end angle=180,x radius=1cm, y radius=1cm];
\draw[style=thick, color=Cerulean] (23,0) arc [start angle=0,end angle=180,x radius=1cm, y radius=1cm];

\draw[radius=.08, fill=black](1,0)circle;
\draw[radius=.08, fill=black](2,0)circle;
\draw[radius=.08, fill=black](3,0)circle;
\draw[radius=.08, fill=black](4,0)circle;
\draw[radius=.08, fill=black](5,0)circle;
\draw[radius=.08, fill=black](6,0)circle;
\draw[radius=.08, fill=black](7,0)circle;
\draw[radius=.08, fill=black](8,0)circle;
\draw[radius=.08, fill=black](9,0)circle;
\draw[radius=.08, fill=black](10,0)circle;
\draw[radius=.08, fill=black](11,0)circle;
\draw[radius=.08, fill=black](12,0)circle;
\draw[radius=.08, fill=black](13,0)circle;
\draw[radius=.08, fill=black](14,0)circle;
\draw[radius=.08, fill=black](15,0)circle;
\draw[radius=.08, fill=black](16,0)circle;
\draw[radius=.08, fill=black](17,0)circle;
\draw[radius=.08, fill=black](18,0)circle;
\draw[radius=.08, fill=black](19,0)circle;
\draw[radius=.08, fill=black](20,0)circle;
\draw[radius=.08, fill=black](21,0)circle;
\draw[radius=.08, fill=black](22,0)circle;
\draw[radius=.08, fill=black](23,0)circle;
\draw[radius=.08, fill=black](24,0)circle;

\end{tikzpicture}
}

\def\MTpostprocess{
\begin{tikzpicture}[scale=0.45]
\draw[style = dashed, <->] (0,0)--(25,0);
\node at (1,-0.5) {\tiny 1};
\node at (2,-0.5) {{\tiny 2}};
\node at (3,-0.5) {{\tiny3}};
\node at (4,-0.5) {{\tiny4}};
\node at (5,-0.5) {{\tiny5}};
\node at (6,-0.5) {\tiny6};
\node at (7,-0.5) {\tiny7};
\node at (8,-0.5) {{\tiny8}};
\node at (9,-0.5) {{\tiny9}};
\node at (10,-0.5) {{\tiny10}};
\node at (11,-0.5) {{\tiny11}};
\node at (12,-0.5) {\tiny12};
\node at (13,-0.5) {\tiny13};
\node at (14,-0.5) {{\tiny14}};
\node at (15,-0.5) {{\tiny15}};
\node at (16,-0.5) {{\tiny16}};
\node at (17,-0.5) {{\tiny17}};
\node at (18,-0.5) {\tiny18};
\node at (19,-0.5) {\tiny19};
\node at (20,-0.5) {{\tiny20}};
\node at (21,-0.5) {{\tiny21}};
\node at (22,-0.5) {{\tiny22}};
\node at (23,-0.5) {{\tiny23}};
\node at (24,-0.5) {{\tiny24}};

\draw[style=thick, color=black] (2,0) arc (0:180: .5cm);
\draw[style=thick, color=black] (3,0) arc (0:180: .5cm);
\draw[style=thick, color=black] (4,0) arc (0:180: .5cm);

\draw[style=thick, color=black] (14,0) arc (0:180: .5cm);
\draw[style=thick, color=black] (15,0) arc (0:180: .5cm);
\draw[style=thick, color=black] (16,0) arc (0:180: .5cm);

\draw[style=thick, color=Cerulean] (7,0) arc (0:180: .5cm);
\draw[style=thick, color=Cerulean] (9,0) arc (0:180: .5cm);
\draw[style=thick, color=Cerulean] (11,0) arc (0:180: .5cm);

\draw[style=thick, color=Cerulean] (8,0) arc [start angle=0,end angle=180,x radius=1.5cm, y radius=1cm];
\draw[style=thick, color=Cerulean] (10,0) arc [start angle=0,end angle=180,x radius=1.5cm, y radius=1cm];
\draw[style=thick, color=Cerulean] (12,0) arc [start angle=0,end angle=180,x radius=1.5cm, y radius=1cm];

\draw[style=thick, color=Cerulean] (19,0) arc (0:180: .5cm);
\draw[style=thick, color=Cerulean] (21,0) arc (0:180: .5cm);
\draw[style=thick, color=Cerulean] (23,0) arc (0:180: .5cm);

\draw[style=thick, color=Cerulean] (20,0) arc [start angle=0,end angle=180,x radius=1.5cm, y radius=1cm];
\draw[style=thick, color=Cerulean] (22,0) arc [start angle=0,end angle=180,x radius=1.5cm, y radius=1cm];
\draw[style=thick, color=Cerulean] (24,0) arc [start angle=0,end angle=180,x radius=1.5cm, y radius=1cm];

\draw[radius=.08, fill=black](1,0)circle;
\draw[radius=.08, fill=black](2,0)circle;
\draw[radius=.08, fill=black](3,0)circle;
\draw[radius=.08, fill=black](4,0)circle;
\draw[radius=.08, fill=black](5,0)circle;
\draw[radius=.08, fill=black](6,0)circle;
\draw[radius=.08, fill=black](7,0)circle;
\draw[radius=.08, fill=black](8,0)circle;
\draw[radius=.08, fill=black](9,0)circle;
\draw[radius=.08, fill=black](10,0)circle;
\draw[radius=.08, fill=black](11,0)circle;
\draw[radius=.08, fill=black](12,0)circle;
\draw[radius=.08, fill=black](13,0)circle;
\draw[radius=.08, fill=black](14,0)circle;
\draw[radius=.08, fill=black](15,0)circle;
\draw[radius=.08, fill=black](16,0)circle;
\draw[radius=.08, fill=black](17,0)circle;
\draw[radius=.08, fill=black](18,0)circle;
\draw[radius=.08, fill=black](19,0)circle;
\draw[radius=.08, fill=black](20,0)circle;
\draw[radius=.08, fill=black](21,0)circle;
\draw[radius=.08, fill=black](22,0)circle;
\draw[radius=.08, fill=black](23,0)circle;
\draw[radius=.08, fill=black](24,0)circle;

\end{tikzpicture}
}

\def\MTcomponents{
\begin{tikzpicture}[scale=0.45]
\draw[style = dashed, <->] (0,0)--(25,0);
\node at (1,-0.5) {\tiny 1};
\node at (2,-0.5) {{\tiny 2}};
\node at (3,-0.5) {{\tiny3}};
\node at (4,-0.5) {{\tiny4}};
\node at (5,-0.5) {{\tiny5}};
\node at (6,-0.5) {\tiny6};
\node at (7,-0.5) {\tiny7};
\node at (8,-0.5) {{\tiny8}};
\node at (9,-0.5) {{\tiny9}};
\node at (10,-0.5) {{\tiny10}};
\node at (11,-0.5) {{\tiny11}};
\node at (12,-0.5) {\tiny12};
\node at (13,-0.5) {\tiny13};
\node at (14,-0.5) {{\tiny14}};
\node at (15,-0.5) {{\tiny15}};
\node at (16,-0.5) {{\tiny16}};
\node at (17,-0.5) {{\tiny17}};
\node at (18,-0.5) {\tiny18};
\node at (19,-0.5) {\tiny19};
\node at (20,-0.5) {{\tiny20}};
\node at (21,-0.5) {{\tiny21}};
\node at (22,-0.5) {{\tiny22}};
\node at (23,-0.5) {{\tiny23}};
\node at (24,-0.5) {{\tiny24}};

\node at (3.5,-1.25) {{\color{Cerulean}\small$C_1$}};
\node at (9.5,-1.25) {{\color{OrangeRed}\small$C_2$}};
\node at (15.5,-1.25) {{\color{ForestGreen}\small$C_3$}};
\node at (20.5,-1.25) {{\color{BurntOrange}\small$C_4$}};

\draw[style=thick, color=Cerulean] (3,0) arc (0:180: .5cm);
\draw[style=thick, color=Cerulean] (4,0) arc (0:180: .5cm);
\draw[style=thick, color=Cerulean] (5,0) arc (0:180: .5cm);

\draw[style=thick, color=ForestGreen] (15,0) arc (0:180: .5cm);
\draw[style=thick, color=ForestGreen] (16,0) arc (0:180: .5cm);
\draw[style=thick, color=ForestGreen] (17,0) arc (0:180: .5cm);

\draw[style=thick, color=BurntOrange] (24,0) arc (0:180: .5cm);

\draw[style=thick, color=BurntOrange] (18,0) arc [start angle=0,end angle=180,x radius=8.5cm, y radius=2cm];

\draw[style=thick, color=OrangeRed] (8,0) arc (0:180: .5cm);
\draw[style=thick, color=OrangeRed] (10,0) arc (0:180: .5cm);
\draw[style=thick, color=OrangeRed] (12,0) arc (0:180: .5cm);

\draw[style=thick, color=OrangeRed] (9,0) arc [start angle=0,end angle=180,x radius=1.5cm, y radius=1cm];
\draw[style=thick, color=OrangeRed] (11,0) arc [start angle=0,end angle=180,x radius=1.5cm, y radius=1cm];
\draw[style=thick, color=OrangeRed] (13,0) arc [start angle=0,end angle=180,x radius=1.5cm, y radius=1cm];

\draw[style=thick, color=BurntOrange] (20,0) arc [start angle=0,end angle=180,x radius=1cm, y radius=1cm];
\draw[style=thick, color=BurntOrange] (21,0) arc [start angle=0,end angle=180,x radius=1cm, y radius=1cm];
\draw[style=thick, color=BurntOrange] (22,0) arc [start angle=0,end angle=180,x radius=1cm, y radius=1cm];
\draw[style=thick, color=BurntOrange] (23,0) arc [start angle=0,end angle=180,x radius=1cm, y radius=1cm];

\draw[radius=.08, fill=black](1,0)circle;
\draw[radius=.08, fill=black](2,0)circle;
\draw[radius=.08, fill=black](3,0)circle;
\draw[radius=.08, fill=black](4,0)circle;
\draw[radius=.08, fill=black](5,0)circle;
\draw[radius=.08, fill=black](6,0)circle;
\draw[radius=.08, fill=black](7,0)circle;
\draw[radius=.08, fill=black](8,0)circle;
\draw[radius=.08, fill=black](9,0)circle;
\draw[radius=.08, fill=black](10,0)circle;
\draw[radius=.08, fill=black](11,0)circle;
\draw[radius=.08, fill=black](12,0)circle;
\draw[radius=.08, fill=black](13,0)circle;
\draw[radius=.08, fill=black](14,0)circle;
\draw[radius=.08, fill=black](15,0)circle;
\draw[radius=.08, fill=black](16,0)circle;
\draw[radius=.08, fill=black](17,0)circle;
\draw[radius=.08, fill=black](18,0)circle;
\draw[radius=.08, fill=black](19,0)circle;
\draw[radius=.08, fill=black](20,0)circle;
\draw[radius=.08, fill=black](21,0)circle;
\draw[radius=.08, fill=black](22,0)circle;
\draw[radius=.08, fill=black](23,0)circle;
\draw[radius=.08, fill=black](24,0)circle;


\end{tikzpicture}
}
