So you heard that the theater folks could use a good hack now and again. You took the class, and by now you've managed some pretty spectacular set hacks, but your fingers are itching for a keyboard. The next production is \textit{Into the Woods}, and one of the big effects scenes occurs when the prince comes to Cinderella's house with the slipper. As everyone knows, the evil step-sisters are going to have their toes chopped off. The teacher has decided that they should pretend to cut the correct toes, but they really can't figure out which ones must go. Eh, why not? Write a program to calculate which toes must be removed for the shoe to fit. Each toe is modeled as an ellipse. The toes' bottoms are aligned on a baseline which is also an axis of the ellipse modelling the shoe's toe. The images of the toes along this line do not overlap but do form a continuous line. In other words, the toes are side-by-side but not necessarily flush against each other. The toes are also centered in the shoe. See figure~\ref{fig:foot} for an illustration. \begin{figure}[h!b] \centering %\begin{minipage}{.4\linewidth} \unitlength = 2.5pt \begin{picture}(90,40)(-10,-6) \put(5,7.5){\ellipse{10}{15}} \put(16,9){\ellipse{12}{18}} \put(29.5,10){\ellipse{15}{20}} \put(46,11){\ellipse{18}{22}} \put(65,12.5){\ellipse{20}{25}} \put(65,12.5){\vector(0,1){12.5}} \put(65,12.5){\vector(0,-1){12.5}} \put(65,25){\makebox(0,0)[b]{toe height}} \put(65,12.5){\vector(1,0){10}} \put(65,12.5){\vector(-1,0){10}} \put(77,12.5){\makebox(0,0)[bl]{toe width}} \qbezier(-5,0)(-5,24)(37.5,24) \qbezier(37.5,24)(80,24)(80,0) \put(-7,12){\vector(0,1){12}} \put(-7,12){\vector(0,-1){12}} \put(-10,12){\makebox(0,0)[r]{shoe extent}} \put(37.5,-2){\vector(1,0){42.5}} \put(37.5,-2){\vector(-1,0){42.5}} \put(37.5,-4){\makebox(0,0){shoe width}} \end{picture} %\end{minipage} \caption{A generalized foot and shoe, with toe 5 marked for chopping} \label{fig:foot} \end{figure} The input will be six pairs of real numbers. The first five pairs give the length and width of the five toes. The last pair will give the extent and width of the shoe's toe. See figure~\ref{fig:foot} for the generalized foot layout. The output should state which toes, if any, must be removed. Height and width of toe #1: 15 \,10 Height and width of toe #2: 18 \,12 Height and width of toe #3: 20 \,15 Height and width of toe #4: 22 \,18 Height and width of toe #5: 25 \,20 Extent and width of the shoe's toe: 24 \,85 This sister loses toe 5. Height and width of toe #1: 3 \,1 Height and width of toe #2: 4 \,1.5 Height and width of toe #3: 4 \,2.1 Height and width of toe #4: 5 \,2.3 Height and width of toe #5: 6.2 \,3 Extent and width of the shoe's toe: 7 \,7 This sister loses toes 1, 2, and 5. Height and width of toe #1: 2 \,1 Height and width of toe #2: 3 \,1 Height and width of toe #3: 4 \,1 Height and width of toe #4: 5 \,1 Height and width of toe #5: 4 \,1 Extent and width of the shoe's toe: 6 \,4 This sister loses toes 1 and 5. Height and width of toe #1: 2 \,1.5 Height and width of toe #2: 3.1 \,1.8 Height and width of toe #3: 3.4 \,2.2 Height and width of toe #4: 4 \,2.2 Height and width of toe #5: 4.5 \,3 Extent and width of the shoe's toe: 4 \,9 This sister loses toes 1, 2, 4, and 5. Height and width of toe #1: 2 \,1 Height and width of toe #2: 2.3 \,1.1 Height and width of toe #3: 2.3 \,1.2 Height and width of toe #4: 2.5 \,1.7 Height and width of toe #5: 2.7 \,2 Extent and width of the shoe's toe: 4 \,8 This sister loses no toes. So much for Cinderella.