TopCoder Statistics - Problem Statement

Problem Statement

Cat Noku has a list of N paintbrushes to use for his next masterpiece. The paintbrushes are labeled from 0 to N-1, and are described by the int[]s x1,y1,x2,y2. Each paintbrush is a nondegenerate triangle. The vertices of paintbrush i have coordinates (0,0), (x1[i],y1[i]), (x2[i],y2[i]).

Noku will go through his paintbrushes from 0 to N-1 and he will use the int[] prob to help him paint his masterpiece. Initially his masterpiece is a single point. He repeats the following procedure for each paintbrush.

He chooses to use paintbrush i with probability prob[i] / 100.
If he chooses to use the paintbrush i, he will place the brush (without rotating it) so that the point (0,0) of the paintbrush will lie somewhere on the boundary of his current masterpiece.
He will then make a stroke with the paintbrush. During the stroke, the brush will move (again, without any rotation) around the entire boundary of the current masterpiece in such a way that the point (0,0) of the paintbrush always lies on the boundary of the current masterpiece. The region painted by the stroke is added to the masterpiece.

Compute and return the expected area of Noku's final masterpiece.

Definition

Class:: TrianglePainting
Method:: expectedArea
Parameters:: int[], int[], int[], int[], int[]
Returns:: double
Method signature:: double expectedArea(int[] x1, int[] y1, int[] x2, int[] y2, int[] prob)
(be sure your method is public)

Notes

Your return value must have an absolute or relative error smaller than or equal to 1e-6.

Constraints

N will be between 1 and 2,500, inclusive.
x1,y1,x2,y2,prob will each have exactly N elements.
Each element of x1,y1,x2,y2 will be between -100 and 100, inclusive.
Each triangle will have a positive area.
Each element of prob will be between 1 and 100, inclusive.

Examples

{1,-2,-4}

{2,3,-1}

{2,2,-2}

{-1,-1,1}

{100,100,100}

Returns: 52.5

Cat Noku has the following paintbrushes: All the paintbrushes will be used. The final masterpiece will look as follows: Note that in the drawing of the final masterpiece each color represents just the area added to the masterpiece after using the brush of the corresponding color, and not the area actually painted by that brush.
{1,-2,-4}

{2,3,-1}

{2,2,-2}

{-1,-1,1}

{50,50,50}

Returns: 15.0
{1}

{1}

{1}

{-1}

{1}

Returns: 0.01
{1,1,1,1,1,1,1,1,1,1}

{-1,1,-1,1,-1,1,-1,1,-1,1}

{1,1,1,1,1,1,1,1,1,1}

{1,-1,1,-1,1,-1,1,-1,1,-1}

{10,20,30,40,50,60,70,80,90,100}

Returns: 31.899999999999995
{-6,-2,-10,9,8,-1,10,5,7,3}

{-5,2,-5,6,6,-10,8,7,-4,-5}

{5,-1,-1,-8,6,7,10,-6,6,3}

{0,-5,-7,4,10,0,10,-3,-3,-4}

{71,100,43,59,51,41,11,53,3,27}

Returns: 940.1964999999999
{34,-71,19,78,69,-73,27,64,-100,70,-87,50,8,-97,46,-46,-30,-40,-30,-23,77,81,48,93,-40,70, 37,-66,53,-87,-85,38,-90,63,-16,24,-2,-60,-88,67,-56,-8,-80,-19,-84,35,95,-24,-26,-15}

{58,-24,-80,33,-98,61,99,79,-34,29,-1,-70,70,90,43,25,-50,-54,73,18,36,8,41,3,26,-6,-80, -22,65,33,-100,-1,80,-19,-6,-8,-4,-86,-43,-34,0,-93,-61,92,74,-77,32,-78,-56,-21}

{-78,-100,-1,27,67,-31,-82,-24,44,-26,12,36,-36,-71,-84,3,59,28,-26,-79,-47,56,-75,-44, -85,-72,56,53,-27,53,-19,-65,14,62,96,-44,12,-20,-57,83,59,71,85,-62,21,24,-38,20,52,-64}

{90,-41,79,18,7,-85,-88,-16,12,38,-7,12,-27,-43,-30,-93,48,-19,58,54,70,73,81,89,-35,-75, 63,-73,66,-90,-25,44,-53,59,-14,83,18,-35,-81,49,-11,-63,-87,-92,-83,-43,60,-42,5,-96}

{9,61,1,16,78,4,12,1,17,4,30,28,13,6,4,14,11,6,55,9,66,5,14,8, 70,3,2,6,3,15,8,1,2,12,1,20,37,1,3,66,3,11,2,1,21,2,1,1,27,11}

Returns: 306025.109
{91,82,-48,89,-100,-60,-79,54,-52,65,-5,15,-76,34,1,-60,-64,-83,91,-5,89,77, -76,-19,-90,-35,-35,19,-53,19,-11,65,-44,-72,62,27,100,-90,-70,24,56,-76,-81, -11,-71,17,100,-70,-17,-18,-82,-80,-15,-79,-97,-81,-60,-11,-84,12,-85,98,79, -46,100,2,-54,-44,-32,-44,-21,31,67,-80,16,-32,83,-44}

{-54,-49,-80,-38,65,42,63,72,46,31,-43,47,26,85,-30,-80,-66,3,83,15,-51,-54, -67,-67,57,-32,86,97,25,82,-8,-26,11,-53,41,56,-24,-13,87,89,-1,6,-37,-79,-52, 20,-78,96,-98,-13,72,33,79,66,88,-5,-7,-65,83,13,-50,-50,81,8,-86,-65,-16,92, 35,-43,-83,-82,53,-34,22,99,29,64}

{77,43,37,-21,40,52,64,-57,-48,-15,-27,98,5,-64,27,45,61,14,58,70,-27,-65,47, -94,91,-94,79,-49,10,-14,98,-82,-65,12,-46,46,27,21,68,-32,91,64,-97,0,-48,80, -56,-92,62,4,100,-29,92,-58,-28,-25,61,52,-78,54,4,-27,-78,-15,-55,-46,-62,3, 46,-76,45,-52,-31,-6,26,-70,-8,90}

{-80,24,1,-50,86,96,17,56,-90,-35,88,-87,42,4,-70,-52,-98,57,-98,46,92,9,35, -96,-50,12,72,73,-10,-77,30,-14,23,-71,13,-79,26,-36,3,-37,-61,71,-30,-27,0,10, 53,63,15,59,-2,52,-61,12,70,41,2,-34,64,-83,-41,30,-73,-46,-61,-13,-79,87,-74, 32,-90,92,-8,61,41,41,8,42}

{12,22,57,72,11,26,92,78,58,38,44,100,51,98,43,61,87,41,50,50,35,28,80,57,94, 83,51,4,48,6,5,33,35,29,88,66,55,55,2,59,69,45,62,69,48,53,59,29,50,21,77,90,42, 87,1,78,1,53,86,83,45,87,65,16,23,14,98,3,71,96,7,61,26,15,33,72,12,59}

Returns: 8622114.009799998
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Returns: 1.6785411992222028E9
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Returns: 4.942664953601302E9
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Returns: 4.275237849905995E8
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Returns: 3.5805049096776924E9
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Returns: 1.0244525307599005E9
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Returns: 1.1062442519524016E9
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Returns: 1.4451174177353966E9
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Returns: 2.9625622521960945E9
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Returns: 6.782126103467998E9
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Returns: 9.74174480472703E8
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Returns: 4.820537126679594E9
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Returns: 6.985396807981489E9
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Returns: 5.6603954459E10
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Returns: 5.71059143065E10
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Returns: 5.8369086946E10
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Returns: 5.6575016289E10
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Returns: 5.80749892605E10
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}

Returns: 4.92291914555E10
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Returns: 4.95922667165E10
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Returns: 4.9949547877E10
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Returns: 4.98145307765E10
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}

Returns: 5.06122967755E10
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Returns: 2.0541013182695918E9
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Returns: 2.164009317301395E9
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Returns: 2.177259015747303E9
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Returns: 2.1762868976833005E9
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5,1,4,83,7,52,2,6,30,7,1,1,50,2,1,82,68,5,17,78,52,1,80,25,10,21,1,7,1,5,10,21,2,53,8,81,7,23,32,50,48,13,1,3,5,87,7,96,6,55,6,52,4,1,93,1,8,21,7,1,1,51,8,1,4,18,9,19,22,80,21,9,2,74,23,92,85,3,1,42,44,4,96,32,31,92,1,85,43,21,5,18,56,2,77,33,1,9,51,79,1,2,1,22,32,77,26,22,6,6,2,5,16,1,4,2,1,23,3,13,66,1,46,66,10,14,5,8,2,95,7,1,84,8,1,82,4,1,1,7,29,2,60,3,1,10,16,1,37,1,13,19,23,3,7,81,25,89,3,6,5,1,1,45,1,32,10,4,66,11,41,1,6,26,4,2,9,1,18,48,20,1,3,7,10,2,16,4,63,4,15,1,83,24,28,92,7,6,3,12,1,10,3,74,14,2,28,69,3,1,5,1,1,19,11,39,2,2,67,41,1,1,40,47,47,84,3,32,15,40,25,1,5,12,40,56,17,55,21,96,7,1,21,40,3,2,31,8,5,15,26,16,89,16,20,7,5,8,5,6,1,14,2,66,34,7,83,3,94,13,58,4,4,5,9,61,1,2,72,22,41,28,1,5,12,28,13,1,65,2,31,35,10,23,1,34,4,22,2,2,3,1,1,12,23,36,1,59,29,3,7,1,9,36,18,56,17,3,1,2,3,22,8,1,94,1,1,18,33,3,9,5,13,92,2,59,24,1,3,14,80,1,93,19,6,2,7,14,56,84,40,7,24,1,47,32,99,2,3,7,2,6,3,60,73,89,15,1,14,6,1,26,7,49,29,3,90,1,1,42,1,54,1,64,51,17,95,4,5,5,1,1,1,70,67,6,4,57,45,45,4,1,44,46,7,77,56,1,12,2,36,61,2,9,20,1,3,50,9,3,7,47,5,8,90,9,49,2,11,6,15,1,19,3,74,13,17,38,3,10,2,66,13,23,42,81,71,4,41,1,4,6,34,3,42,2,19,5,16,7,21,57,35,1,1,99,7,1,3,99,6,3,16,4,7,4,3,5,51,16,25,20,76,11,21,10,1,3,1,4}

Returns: 2.191414616376697E9
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{2,5,4,34,4,93,2,16,11,29,47,22,19,22,23,27,2,58,3,2,61,51,2,79,16,22,61,64,53,2,1,18,51,4,18,10,1,69,42,79,1,2,3,2,2,52,4,29,19,10,5,4,1,28,1,52,91,8,37,31,17,10,3,6,45,52,4,87,18,69,82,1,72,3,85,32,4,6,1,2,5,4,12,6,2,1,1,53,41,1,73,43,1,28,5,5,6,54,95,2,3,19,26,5,7,48,2,8,1,32,37,16,16,54,1,10,18,27,18,23,10,17,2,1,36,22,60,11,2,4,43,5,81,37,18,4,2,12,16,91,94,87,32,6,66,63,4,65,81,3,36,67,1,1,37,23,15,34,24,17,12,15,1,48,1,2,3,88,66,14,20,4,9,10,32,5,7,8,24,61,4,31,2,2,11,28,19,3,4,19,6,1,11,64,7,12,9,8,28,15,18,2,9,96,27,17,59,1,6,75,71,20,44,33,6,7,30,10,27,91,5,84,64,1,50,1,71,9,10,2,24,30,1,3,1,6,10,21,47,45,14,6,3,11,16,26,11,19,4,11,31,45,4,11,4,3,2,28,36,22,10,9,11,9,1,1,7,10,28,89,5,12,9,5,3,6,23,4,51,15,1,6,2,71,78,22,79,1,68,1,37,1,50,10,31,57,31,1,3,28,28,30,1,2,6,8,18,11,17,12,86,1,1,1,8,97,2,33,47,26,14,1,35,3,5,3,18,26,10,69,30,1,2,3,1,3,53,34,2,5,23,5,1,1,1,3,3,1,21,2,2,22,3,12,5,5,1,3,2,10,4,6,20,4,1,8,1,16,3,1,22,47,2,5,11,24,26,15,12,42,5,2,4,34,51,15,1,17,3,1,3,28,6,8,19,3,2,10,12,9,91,18,56,39,1,1,14,26,9,1,1,2,8,24,41,1,5,28,6,1,9,2,1,4,2,4,50,87,1,55,35,63,4,41,62,30,40,25,10,54,41,4,97,25,10,5,22,7,1,4,8,34,2,18,25,6,2,26,24,2,20,12,79,1,1,7,1,28,3,7,38,2,48,4,1,13,50,36,2,7,3,11,44,50,13,1,3,3,52,11,85,36,5,10,34,2,5,1,25,18,5,9,39,10,14,49,7,1,2,9,18,91,52,1,4,56,1,10,35,16,13,14,2,4,2,5,51,42,2,43,1,14,7,27,8,12,1,11,14,53,29,3,5,7,30,12,8,2,1,63,48,1,89,19,1,65,18,11,8,19,72,40,54,18,2,6,5,47,25,53,9,1,85,39,4,8,17,2,62,1,1,1,1,1,83,51,7,10,74,2,10,10,27,30,2,42,32,4,1,1,7,1,2,44,6,9,8,2,2,2,2,9,31,4,8,3,1,2,6,2,36,71,31,72,1,1,70,3,92,65,15,1,3,1,3,3,1,14,20,11,2,2,57,60,5,1,34,17,45,7,7,27,28,9,3,3,27,20,2,18,1,1,3,73,43,3,1,45,4,9,67,1,4,1,14,2,7,66,28,3,3,1,2,26,23,17,3,1,1,19,12,95,13,7,24,77,22,2,16,1,6,5,16,1,30,17,22,3,1,1,4,6,5,9,1,10,27,6,75,7,15,19,69,14,1,2,2,7,2,1,5,15,3,1,1,78,5,15,1,4,42,12,25,9,42,1,16,23,1,20,48,1,1,1,1,1,80,13,2,14,9,16,29,7,21,1,30,21,67,3,59,54,2,53,11,1,8,10,11,30,7,25,3,81,1,14,1,3,35,60,1,2,26,34,76,43,63,1,26,38,31,64,4,54,5,21,2,60,4,90,9,59,8,4,94,3,49,9,15,2,1,2,1,86,8,1,7,86,83,4,15,16,9,3,23,66,8,52,26,43,16,15,44,3,17,1,3,4,81,4,13,57,46,1,2,16,16,1,2,42,86,10,78,3,1,7,2,57,3,5,4,12,1,55,16,6,1,5,2,21,29,7,52,56,1,9,46,21,3,51,16,1,42,1,1,2,5,10,2,36,1,81,1,9,34,13,1,18,2,78,37,1,5,31,47,1,3,28,1,4,1,8,1,2,1,11,2,60,2,3,5,42,4,10,29,5,30,28,1,3,37,1,3,54,1,6,3,5,15,10,65,9,23,5,12,14,1,19,40,20,14,6,1,25,6,5,1,54,4,1,82,12,1,4,19,8,3,1,5,7,5,76,1,2,4,12,62,14,11,50,3,65,22,4,3,3,63,99,1,29,5,8,27,2,53,13,1,1,76,3,5,3,2,46,72,1,1,31,10,89,60,96,20,15,1,3,11,5,7,62,72,72,83,40,2,32,4,2,3,1,27,77,93,2,19,2,1,24,1,43,3,1,8,37,57,42,2,9,3,31,29,38,16,2,3,1,22,97,1,24,7,71,20,6,6,1,1,1,28,54,44,6,72,6,8,7,1,40,10,17,2,17,3,1,1,19,16,18,41,13,18,1,1,39,7,10,5,66,25,7,4,33,1,1,3,2,9,5,1,1,2,24,2,1,67,1,2,97,71,47,13,19,10,8,1,15,1,53,16,1,94,37,46,1,26,1,1,27,1,13,5,52,11,87,2,1,44,1,10,14,4,36,20,12,13,5,14,50,81,22,6,1,2,4,1,4,4,3,29,3,38,16,6,36,26,2,16,6,35,35,1,87,69,7,1,12,8,1,10,1,48,8,16,33,2,65,55,3,2,26,1,80,1,11,9,35,4,3,25,73,14,4,82,17,1,73,36,2,6,50,6,1,8,3,15,36,15,2,9,99,15,3,64,2,68,10,33,3,17,30,6,7,38,80,1,84,39,1,1,6,4,1,69,3,1,1,48,9,2,20,84,1,3,2,21,1,7,1,82,21,24,1,4,3,24,5,25,12,1,7,38,9,1,10,1,2,24,1,7,8,4,7,1,33,1,4,23,2,31,5,7,58,2,9,1,9,9,28,3,15,94,58,18,32,19,18,3,2,23,7,99,3,71,43,1,22,1,83,20,19,1,34,19,6,57,2,10,1,40,1,28,28,74,7,4,34,22,5,44,23,43,3,52,7,9,11,28,14,87,19,1,4,5,39,17,7,1,9,92,65,5,1,75,72,29,13,17,31,36,4,25,2,16,69,6,10,7,51,33,38,3,7,77,5,18,1,85,3,11,59,60,64,88,26,2,40,6,1,8,2,2,21,23,4,5,1,21,19,37,3,14,1,1,6,18,2,1,1,48,1,5,15,2,36,32,52,4,1,85,1,30,26,1,49,2,72,5,1,5,4,57,1,59,40,10,1,2,62,1,50,6,18,15,54,35,1,13,3,29,3,21,10,1,5,9,1,2,52,2,17,58,2,11,33,1,2,2,72,35,8,1,82,4,33,5,34,5,17,37,7,96,51,2,10,22,51,6,25,17,22,14,3,28,9,5,53,27,2,18,36,3,4,2,42,44,12,2,2,10,31,2,10,1,3,13,4,1,3,64,55,18,23,3,3,2,2,7,44,8,70,1,67,3,72,7,4,10,1,13,1,19,1,3,5,1,11,15,4,10,61,19,16,9,3,1,4,1,1,94,19,92,2,6,9,6,1,52,5,87,9,17,2,59,19,13,1,9,1,5,6,8,11,39,88,8,9,17,13,3,3,16,79,4,28,11,8,17,26,6,51,3,55,7,2,17,2,13,32,1,5,11,8,2,27,92,13,1,28,22,2,8,49,13,3,5,17,13,68,78,2,6,10,39,82,1,12,14,5,8,83,16,33,36,3,35,8,13,2,28,65,4,41,5,1,5,11,31,8,1,4,8,1,21,10,8,23,7,1,1,77,12,6,20,5,53,12,49,1,2,1,1,28,1,24,4,4,23,89,48,3,15,8,8,5,5,60,70,1,37,22,10,3,14,1,16,1,22,2,3,6,10,10,10,2,6,12,10,15,3,1,1,59,2,1,87,6,25,10,4,26,88,3,2,53,10,85,9,39,17,1,4,2,4,1,48,8,1,1,4,1,12,26,2,26,26,4,4,10,5,1,1,13,26,18,3,1,8,89,1,1,2,4,1,14,41,51,3,57,10,16,1,45,69,1,36,6,49,1,3,1,10,15,38,3,1,11,1,5,97,1,18,1,96,3,11,4,70,12,28,2,44,52,18,30,52,2,7,1,29,37,1,2,94,37,2,42,14,8,14,10,8,30,67,2,16,61,3,23,5,23,2,5,2,2,88,2,51,35,14,14,19,1,52,1,15,1,1,16,27,3,1,2,38,12,36,1,2,57,28,41,11,2,29,1,8,1,2,1,39,94,71,5,1,3,19,8,46,41,6,1,34,2,12,80,9,2,1,36,1,3,91,11,30,62,66,25,6,3,6,1,13,15,2,95,22,23,86,37,38,2,27,4,1,2,5,1,38,9,38,3,7,21,1,2,56,40,27,2,12,5,5,5,50,66,2,10,4,7,2,15,3,6,95,62,2,2,3,1,1,92,5,2,26,4,2,23,1,1,7,1,43,6,60,92,3,38,1,26,6,2,1,5,3,91,12,2,3,2,72,7,65,8,1,57,29,71,2,1,24,11,60,6,2,7,1,11,35,73,1,32,45,17,1,13,7,3,47,35,2,1,1,42,6,64,1,13,9,4,6,2,49,11,74,28,7,1,82,74,1,6,69,1,12,8,97,60,4,17,12,76,7,34,9,64,91,21,32,55,64,11,1,3,18,39,2,22,27,31,7,1,8,8,2,5,45,18,9,39,1,71,91,49,6,1,85,3,20,57,1,12,1,2,81,3,1,22,94,3,15,1,5,14,4,11,16,2,1,62,54,3,5,15,15,13,2,76,17,2,23,1,19,9,6,1,54,7,2,18,21,22,86,1,1,7,61,9,5,6,49,2,32,43,14,14,73,12,73,1,2,3,16,2,1,62,20,64,11,27,94,83,1,11,60,1,23,1,3,4,1,77,1,62,98,39,67,34,24,3,6,10,2,18,7,19,1,60,4,3,6,27,8,32,84,89,43,5,7,1,88,26,1,2,7,44,53,59,16,11,1,3,47,39,6,4,1,26,7,1,1,2,9,55,78,1,21,4,1,9,8,17,4,3,32,1,8,55,11,55,2,15,10,1,86,2,29,32,3,4,11,57,2,13,3,46,5,30,18,57,3,2,6,71,10,25,9,1,1,4,30,22,4,2,2,64,4,1,2,21,2,55,2,2,26,1,3,1,7,6,3,65,40,77,60,4,5,5,5,12,4,6,41,16,8,3,20,3,53,57,1,1,47,6,1,9,62,57,5,79,3,2,16,1,6,19,11,30,1,1,22,2,4,28,32,65,2,2,23,33,18,41,8,40,25,96,34,2,96,20,40,10,87,13,2,22,74,85,1,18,6,2,1,8,7,7,39,10,10,34,2,6,91,11,3,36,2,9,77,26,25,8,2,3,73,61,14,1,1,14,10,3,80,22,2,63,1,5,1,1,21,57,1,80,38,2,76,1,20,5,3,46,40,55,92,14,61,2,5,62,1,60,3,1,25,1,6,3,3,7,8,1,51,3,1,22,1,18,28,2,29,52,5,1,1,1,20,23,13,73,6,2,1,47,13,12,89,19,54,13,7,3,1,50,8,77,5,2,23,77,6,20}

Returns: 7.13289358695503E8
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{89,48,16,18,4,17,1,24,1,14,70,44,19,2,82,1,18,30,2,3,2,3,15,33,86,22,1,94,57,60,10,10,3,7,2,11,4,25,10,1,45,15,16,62,1,7,14,3,1,3,64,21,98,59,4,1,15,15,5,80,1,2,6,5,34,2,1,8,5,13,46,58,34,38,7,2,44,10,46,3,32,4,5,1,67,48,33,2,7,49,32,9,19,90,15,11,76,2,6,11,7,45,5,44,73,2,10,7,78,95,1,53,10,21,79,30,8,9,41,3,1,1,7,49,7,17,45,40,26,64,4,1,3,5,6,87,8,77,1,15,1,19,3,1,5,43,45,28,6,7,26,6,5,5,57,46,4,1,10,12,5,4,18,1,31,1,7,3,34,3,33,1,1,1,4,23,2,5,21,2,1,75,1,6,32,2,52,5,99,4,91,34,56,1,68,1,53,1,36,9,2,4,38,2,3,4,5,30,10,38,24,24,10,20,2,25,81,12,35,12,20,3,1,7,2,58,5,84,47,22,5,3,19,3,10,3,1,8,10,32,26,18,1,31,79,13,3,52,2,33,3,21,2,3,13,1,89,1,16,29,8,14,64,22,27,1,36,62,13,20,11,36,2,18,1,2,1,2,1,30,25,59,1,30,4,6,39,22,53,26,75,18,31,1,1,24,80,61,11,35,1,41,5,58,1,4,19,1,13,59,6,29,75,53,3,2,6,5,5,14,3,10,25,3,37,5,1,2,4,4,5,1,77,10,88,57,1,34,13,1,23,55,13,3,7,2,4,32,1,14,66,1,2,7,90,9,51,72,18,1,1,9,24,25,16,2,13,3,15,30,4,7,61,40,5,12,5,20,75,16,2,1,35,13,12,3,9,2,46,1,1,36,28,9,34,34,6,8,80,9,33,47,8,32,53,2,14,24,1,19,59,52,9,2,1,1,15,18,33,23,36,8,7,13,4,2,4,74,5,22,1,3,10,1,6,94,31,23,83,53,4,3,1,2,38,28,1,21,45,82,15,3,44,38,2,42,1,2,3,1,22,91,4,6,1,42,6,5,25,95,6,55,45,2,48,61,1,3,3,1,11,1,19,42,3,9,87,1,35,1,17,46,35,3,47,49,3,9,1,64,13,13,6,70,3,2,28,37,2,31,40,7,10,38,7,35,1,14,51,1,9,14,37,2,3,24,40,17,17,2,11,55,65,95,51,19,15,7,2,70,31,2,62,18,1,42,8,9,3,10,8,2,2,1,1,64,55,2,12,10,2,1,33,35,3,3,40,4,1,76,19,1,1,84,7,72,1,64,17,22,69,1,21,5,25,9,2,4,5,7,14,28,3,1,1,7,23,29,44,11,5,80,1,61,5,4,5,88,61,4,69,1,7,1,4,1,1,10,31,7,4,86,28,35,10,2,66,4,4,23,6,28,86,58,12,25,22,1,8,9,4,7,4,12,17,2,7,2,2,8,49,3,15,9,10,33,3,10,50,2,17,47,16,6,53,7,36,3,1,62,6,1,4,25,1,3,11,25,7,54,6,2,1,2,3,15,40,44,2,36,60,1,8,21,1,5,6,56,18,7,20,1,93,3,26,31,33,2,3,36,35,4,12,1,31,1,1,17,21,40,1,5,3,97,18,1,5,2,11,31,4,38,20,3,15,95,90,45,10,42,1,3,24,2,8,3,14,1,4,29,12,3,62,1,22,59,23,8,82,63,1,18,69,2,1,15,1,98,35,9,8,2,19,1,5,16,2,1,2,68,2,5,19,16,2,29,1,38,44,24,8,3,6,3,7,71,58,1,18,34,86,8,2,1,1,94,3,1,1,17,1,16,2,42,11,21,40,3,2,60,2,30,4,63,13,46,25,12,4,1,2,14,49,53,54,27,3,41,13,7,3,2,1,3,21,1,1,3,4,89,33,14,6,4,90,19,1,32,53,28,1,3,34,56,14,10,4,1,5,17,1,18,1,1,11,67,1,2,9,5,17,2,29,49,3,30,8,16,18,4,74,7,53,7,9,35,76,23,12,1,1,5,12,12,50,77,4,1,6,4,57,94,64,59,46,59,22,3,96,1,11,57,20,6,6,6,3,92,3,1,2,2,2,20,6,6,12,2,14,1,60,8,29,84,7,55,5,82,1,8,77,11,35,2,18,29,4,55,7,43,25,15,28,4,11,57,73,23,5,2,2,2,4,11,57,9,4,53,3,9,33,44,1,41,1,1,19,75,5,55,49,14,15,8,4,1,1,8,35,4,47,1,1,1,1,3,15,1,17,5,4,9,31,45,84,2,4,1,3,1,3,24,1,1,3,2,20,2,10,8,1,1,54,23,64,36,4,26,1,57,24,1,53,1,25,1,23,29,3,30,47,52,3,38,61,21,1,61,1,4,3,5,62,4,88,45,3,66,12,42,38,97,34,2,6,7,2,38,38,16,3,1,4,1,3,1,3,66,3,3,1,3,1,3,14,10,42,63,36,12,2,4,59,3,39,13,40,51,3,5,10,7,36,16,46,36,2,5,1,5,90,1,38,23,19,1,41,46,86,2,9,1,4,52,46,3,12,4,7,2,1,12,2,2,4,1,4,38,16,3,10,53,12,28,4,2,5,43,11,4,87,9,50,59,7,6,1,6,82,9,59,3,40,4,94,1,6,19,2,1,2,1,23,12,16,7,9,8,20,2,4,13,15,10,5,9,1,55,8,7,22,4,16,1,5,19,43,1,7,85,23,13,4,63,1,41,4,1,5,61,56,74,1,18,4,2,2,34,5,71,8,3,87,2,1,12,4,82,14,3,38,4,80,26,38,12,93,20,39,32,1,2,15,5,10,2,3,48,2,11,1,2,1,20,33,15,60,2,91,2,16,4,2,25,57,1,1,63,4,4,53,5,10,9,44,1,21,40,1,4,4,4,37,25,92,35,1,7,22,13,3,82,4,2,11,39,49,11,2,1,22,1,98,25,32,7,28,12,67,46,1,2,18,11,3,3,54,5,3,11,10,1,82,86,2,48,9,6,51,90,63,49,6,8,12,5,3,42,7,5,22,1,4,9,14,14,1,29,17,13,10,8,1,3,4,32,1,72,78,95,59,3,1,25,4,3,2,6,17,2,2,12,2,98,16,44,18,13,59,27,46,62,4,14,3,1,29,15,4,17,3,14,9,8,14,1,4,5,21,34,11,1,24,69,16,2,2,1,19,1,1,3,1,6,1,3,1,9,20,25,79,13,1,42,23,1,4,1,17,20,29,6,51,82,41,2,5,81,23,98,3,85,19,7,12,2,33,11,82,4,86,24,2,2,36,4,96,1,1,24,25,59,6,4,1,32,4,35,17,2,24,3,39,3,23,1,1,1,10,22,35,10,7,3,1,1,5,3,54,2,7,30,1,1,5,75,2,46,1,4,3,12,15,12,96,1,9,71,60,9,85,10,58,3,7,1,1,2,2,5,3,85,5,1,53,4,26,77,1,35,16,2,47,59,12,2,7,38,5,3,18,49,8,10,45,35,1,1,2,1,1,26,10,8,56,30,1,1,85,1,6,21,2,3,85,43,37,51,86,70,12,4,6,47,28,4,1,2,1,32,10,2,21,5,5,2,87,11,8,1,2,1,4,17,5,61,52,22,1,4,6,11,8,1,67,3,15,28,2,11,23,1,1,5,6,43,8,2,3,1,10,15,17,13,17,9,17,10,2,18,46,91,15,31,1,15,19,56,2,8,78,2,6,5,14,4,2,69,57,58,3,1,36,1,1,7,10,40,61,73,1,1,8,2,10,11,8,4,1,27,4,21,67,9,22,1,4,6,5,70,69,32,4,7,2,5,6,24,31,1,3,4,17,5,4,58,48,39,1,23,23,8,47,4,5,12,4,1,30,41,10,49,4,79,15,35,2,74,1,27,1,9,27,1,2,12,79,45,29,18,37,1,2,2,34,1,2,7,99,5,10,3,35,1,18,2,12,53,2,2,5,25,62,1,4,17,9,16,41,13,24,66,81,21,7,4,2,5,5,9,1,48,57,22,1,3,18,68,2,55,8,1,4,3,2,3,20,2,8,61,7,1,54,1,21,5,2,46,31,7,2,83,5,1,5,2,30,3,7,47,4,3,1,68,5,4,40,51,3,3,34,23,18,2,11,2,5,65,1,25,1,2,7,51,25,14,52,9,27,28,6,8,1,1,4,15,1,8,11,17,21,13,3,2,1,2,34,3,1,83,8,19,12,54,1,1,1,2,17,2,5,9,16,1,40,11,47,20,1,82,2,72,8,1,33,7,62,3,11,23,91,3,9,1,59,70,65,29,55,3,63,71,97,10,7,1,91,6,33,1,1,49,3,44,27,1,4,1,1,21,40,3,37,61,8,1,62,12,25,48,2,4,12,56,16,87,4,1,25,9,15,1,24,14,2,2,9,5,6,50,5,59,1,88,98,1,15,13,5,1,4,1,20,2,92,8,22,16,1,56,1,18,7,1,88,4,38,6,36,36,7,1,92,94,3,13,68,81,42,92,56,24,28,1,32,1,6,29,5,4,1,2,4,3,11,1,2,2,43,38,22,6,24,20,5,22,4,64,1,19,60,1,43,35,1,13,10,87,3,1,53,1,30,60,4,1,1,16,10,1,1,59,19,1,7,12,2,43,36,43,2,35,54,24,41,44,4,1,11,10,49,2,2,22,45,16,6,4,1,48,62,28,2,12,2,3,1,1,19,2,2,2,13,1,23,7,3,2,4,51,2,45,6,23,45,34,1,1,29,16,87,3,5,4,41,7,58,1,99,10,1,3,24,3,30,89,1,2,2,48,7,93,5,13,3,1,3,43,61,7,1,32,12,56,9,7,3,42,1,17,1,5,5,37,2,1,33,5,19,5,4,4,1,20,28,26,2,2,82,2,22,95,56,7,3,12,1,11,4,9,29,14,39,18,20,74,10,15,56,4,5,27,10,2,2,49,3,40,3,7,5,6,69,79,19,2,1,1,1,43,48,1,34,96,1,14,77,2,31,2,7,1,1,1,2,6,96,2,1,6,22,32,17,1,2,1,7,26,8,7,36,8,9,8,1,4,1,13,95,2,3,9,2,71,19,1,4,2,2,89,3,35,1,36,32,1,9,4,22,3,6,11,19,86,2,14,5,56,10,2,89,2,5,22,9,1,16,48,6,64,1,32,5,36,28,24,1,34,70,11,3,9,32,4,8,53,5,4,1,2,34,31,13,3,65,4,3,4,1,14,81,28,3,27,10,1,28,3,94,16,9,5,32,8,5,11,22,16,18,92,5,71,59,31,1,2,5,8,39,12,1,25,66,34,2,21,14,48,7,1,11,2,2,3,1,58,7,11,10,29,17,6,9,1,6,84,7,4,47,51,50,20,15,29,16,1,7,1,40,46,84,77,64,1,10,2,8,13,78,68,7,3,8,1,16,1,1,8,1,95,86,13,3,16,11,2,42,14,95,18,8,88,10,1,24,6,33,1,72,3,6,72,48,9,42,46,4,11,1,1,1,37,1,36,8,63,3,29,1,8,21,9,50,2,1,30,11,1,3,29,3,16,66,5,1,13,54,4,2,46,74,92,11,5,93,43,13,1,2,44,6,21,87,11,13,1,16,8,1,4,1,4,2,6,6,20,25,1,69,5}

Returns: 7.556891535961992E8
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,6,30,21,51,25,2,78,2,2,26,2,2,1,15,35,38,24,8,47,17,4,1,3,1,2,4,6,33,1,1,11,7,11,8,5,45,12,2,11,1,58,5,1,36,6,7,58,32,29,1,1,36,7,42,11,1,8,9,4,7,1,5,54,1,7,8,42,11,24,9,37,1,18,3,10,2,4,1,8,1,19,72,19,59,1,3,39,52,13,28,8,1,35,74,2,9,4,1,39,4,40,1,16,7,11,34,35,16,31,6,6,8,5,1,1,1,6,52,5,5,57,59,7,33,5,2,30,25,1,1,4,1,1,4,4,12,18,18,38,19,5,22,1,3,3,5,3,3,68,2,5,25,3,1,22,54,2,42,17,4,33,10,60,16,2,5,21,2,3,2,44,73,1,1,2,29,12,11,3,9,2,1,4,60,71,22,25,2,1,10,30,39,6,30,2,32,46,41,2,6,15,2,5,21,18,70,1,14,1,6,16,3,32,63,1,3,11,19,35,84,7,2,1,11,68,6,36,2,1,13,33,12,1,1,4,9,5,16,1,25,11,5,17,3,12,87,2,2,11,51,15,33,15,6,59,2,78,36,13,27,12,1,2,4,60,74,8,16,9,5,18,3,14,18,5,4,1,6,46,25,48,13,7,56,78,18,84,14,42,79,44,2,49,20,4,5,20,15,2,2,8,10,24,1,7,68,15,8,3,1,66,28,19,38,7,10,23,6,1,3,18,78,97,62,12,2,15,1,3,4,2,1,13,95,7,52,31,2,64,18,4,2,36,8,10,80,1,83,2,3,4,70,33,4,10,71,8,49,1,5,19,25,1,9,49,1,75,5,10,1,4,1,1,1,6,60,29,48,3,2,5,1,48,39,8,33,85,4,7,13,33,90,6,9,4,2,2,1,6,1,7,18,1,17,4,33,36,27,86,36,62,12,31,27,2,2,41,3,6,32,16,1,1,1,5,3,4,1,47,87,4,1,11,24,11,7,9,16,13,5,1,1,27,28,1,23,13,9,52,3,1,3,10,66,10,23,90,5,2,19,43,14,4,9,37,2,5,60,18,14,1,8,2,11,10,1,1,8,41,3,1,1,88,4,39,59}

Returns: 6.94600561875901E8
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{1,74,1,3,32,13,1,3,1,3,1,1,1,6,4,3,33,10,67,10,40,72,8,5,12,16,11,1,2,72,4,95,76,1,3,1,56,22,2,16,1,44,3,56,2,1,5,1,18,1,8,2,19,1,11,44,1,10,8,37,10,13,1,45,3,1,71,8,2,10,26,3,1,1,42,13,2,3,11,23,11,6,6,1,2,92,9,29,1,2,4,1,3,5,5,20,48,3,62,99,76,58,3,8,1,24,2,7,36,6,3,12,6,47,1,59,3,63,5,10,1,81,49,73,13,80,38,93,38,9,28,57,82,30,53,1,17,37,4,26,7,3,2,6,9,1,11,7,2,7,19,17,13,10,59,3,1,47,1,29,23,4,3,3,17,34,7,1,2,23,8,6,2,3,73,3,1,37,1,1,2,1,4,16,52,2,77,6,14,27,7,1,2,5,7,8,1,3,17,4,6,15,1,6,3,1,10,3,1,7,6,26,7,8,19,8,6,3,38,85,10,24,7,11,52,2,1,15,9,4,51,25,18,21,1,82,92,94,14,1,11,47,58,1,28,6,26,2,29,59,5,19,82,43,1,12,1,2,5,4,1,1,71,71,25,2,31,1,9,4,3,1,5,4,66,1,1,20,14,37,4,12,1,15,10,92,1,67,4,36,2,57,19,15,9,3,4,7,2,20,2,22,1,50,14,2,37,6,6,4,9,85,40,15,47,51,1,68,15,47,75,73,35,7,1,5,92,2,1,64,4,4,2,1,2,3,13,2,1,10,48,4,5,57,11,11,4,1,38,12,31,90,13,97,81,16,19,46,38,4,1,64,9,1,1,2,16,12,12,9,4,55,4,1,20,9,2,22,8,19,62,14,1,61,6,4,1,3,19,8,16,29,1,11,37,11,55,8,2,3,3,14,22,4,20,17,2,8,36,1,19,21,47,2,6,23,7,1,45,19,7,16,1,2,2,3,54,3,2,7,11,12,34,46,3,26,1,29,21,2,56,14,3,25,6,5,98,54,61,67,11,9,12,2,20,1,10,60,1,15,1,21,96,15,26,1,5,73,56,14,60,4,1,9,6,5,35,62,65,12,1,15,12,37,2,1,46,3,18,2,10,77,3,7,5,9,19,1,1,99,1,6,37,89,16,86,13,7,80,1,2,36,11,2,3,8,46,1,7,3,3,30,99,15,11,1,5,2,23,5,4,10,1,8,3,88,13,1,1,68,4,37,6,3,89,36,18,10,3,65,3,69,31,65,8,9,55,13,51,44,9,61,11,5,5,7,12,21,46,56,4,22,10,87,40,2,2,27,88,2,24,1,1,28,78,1,2,5,65,24,26,2,4,84,9,15,33,31,20,5,25,72,9,1,16,10,14,5,11,11,45,14,2,39,20,1,3,3,98,1,26,16,12,13,9,1,23,19,47,10,2,62,13,53,12,3,7,12,22,30,2,12,3,14,4,8,1,15,1,1,87,2,36,23,3,17,1,24,1,30,23,5,2,8,48,4,4,32,2,3,2,67,3,16,7,25,3,3,18,1,2,2,1,98,3,1,1,47,13,3,23,13,3,61,51,20,3,2,53,23,6,2,1,1,9,1,1,11,58,3,8,17,41,6,2,9,12,2,18,72,8,2,1,2,5,67,6,65,4,46,4,1,65,1,9,1,30,48,36,2,99,1,38,18,16,13,15,25,43,1,14,19,3,59,1,4,8,8,5,83,67,76,24,63,5,89,20,2,4,2,87,3,5,44,5,33,1,12,4,7,3,1,2,35,6,88,5,17,2,18,4,33,5,4,1,9,31,26,8,1,2,2,13,21,6,3,87,8,44,9,1,1,3,49,3,7,48,10,59,6,54,73,3,11,20,2,42,39,5,1,8,3,3,48,17,1,9,59,7,41,1,17,1,23,26,7,7,15,13,19,3,15,3,29,1,1,54,6,37,4,43,1,8,1,14,1,4,14,4,2,23,3,1,6,26,4,1,21,14,43,40,7,25,81,24,1,7,6,66,2,24,82,10,27,33,3,1,18,3,2,25,22,2,1,23,24,26,55,1,2,8,4,23,1,99,6,4,10,10,11,8,3,10,4,2,6,6,1,25,4,42,1,3,69,11,13,3,4,1,14,2,1,38,2,2,38,6,34,28,19,8,18,2,14,71,3,65,7,33,23,9,5,1,67,84,1,6,1,1,85,7,7,1,80,4,80,3,2,2,21,22,6,1,2,4,1,60,8,79,1,4,2,34,6,5,5,2,5,17,7,10,87,14,8,1,44,4,5,3,14,80,27,2,66,1,74,1,3,19,16,7,2,69,1,10,1,4,68,27,85,16,66,14,54,45,2,12,11,5,4,12,1,67,79,1,5,11,2,1,1,42,8,46,1,36,10,9,22,8,38,8,2,79,1,4,36,4,49,1,12,2,4,8,85,18,9,61,8,2,4,1,65,59,9,41,13,5,26,52,2,6,7,37,94,5,12,30,3,3,1,68,12,44,26,7,29,12,8,11,31,16,1,30,8,47,10,6,2,1,47,71,6,47,1,46,3,41,6,59,3,2,11,6,5,3,31,6,4,12,2,24,10,1,46,5,84,1,29,5,64,5,6,1,15,15,1,3,1,43,46,2,13,6,11,9,4,1,6,6,16,47,25,8,20,66,48,21,2,12,77,43,53,79,81,7,1,2,1,3,13,2,88,74,1,59,39,27,6,1,38,16,11,1,2,43,1,2,1,1,35,3,1,1,8,14,85,25,1,30,21,10,9,82,7,6,71,4,15,27,2,1,11,4,47,7,1,6,1,17,8,4,7,89,49,34,19,25,88,13,2,12,14,48,15,3,5,15,2,5,1,1,29,21,20,12,64,63,6,15,1,6,50,76,39,55,52,4,12,18,90,8,93,23,6,49,56,1,10,53,5,2,2,1,17,21,12,8,38,5,30,60,49,54,8,5,2,1,32,5,2,43,1,66,2,5,1,33,3,26,60,4,74,4,59,2,17,7,3,10,16,1,5,5,10,1,1,1,28,19,28,68,24,7,6,86,1,16,1,26,12,7,3,38,92,19,72,17,3,5,1,5,1,2,56,12,2,1,17,4,1,43,3,1,8,3,2,1,12,4,79,1,4,1,5,44,5,18,57,45,27,4,87,10,19,91,13,6,21,64,3,5,21,6,2,97,53,17,3,1,51,8,3,6,15,1,35,1,1,1,39,16,2,3,2,28,99,54,29,40,9,6,24,43,71,2,40,30,69,56,19,17,64,11,13,62,3,2,21,64,3,13,1,5,1,4,1,1,1,17,5,51,2,17,94,30,3,5,6,49,10,58,4,3,11,5,10,1,1,20,5,2,1,90,28,22,1,38,32,4,1,15,1,69,19,2,92,1,16,1,1,1,14,55,25,42,16,94,27,49,14,49,6,7,6,5,6,50,25,42,34,15,1,6,5,12,2,3,55,13,73,7,19,62,36,9,21,81,14,98,5,9,72,1,13,1,2,27,4,1,12,66,4,60,1,21,79,49,2,4,1,3,3,28,68,1,3,2,7,25,1,73,4,5,1,41,13,3,9,20,1,41,94,1,5,8,3,3,6,1,18,14,1,5,60,32,2,14,25,17,5,60,2,1,9,2,23,2,13,3,3,11,7,35,24,21,2,1,2,19,2,1,7,11,3,1,14,9,55,20,26,35,2,73,1,4,2,10,19,7,3,1,18,28,5,3,13,6,4,23,36,4,51,4,3,12,82,26,7,1,28,2,4,34,3,57,4,15,2,2,1,53,90,4,55,1,86,41,79,10,2,9,2,51,3,53,16,1,18,16,26,60,48,14,36,3,5,22,23,2,8,29,71,1,3,3,2,1,22,13,1,1,34,8,5,82,13,93,61,21,38,2,1,1,3,1,34,2,8,25,60,9,61,91,3,1,7,2,11,1,4,27,59,36,63,1,25,35,40,10,1,42,5,20,23,2,33,6,12,2,88,12,5,1,7,72,1,6,24,94,3,17,12,4,18,1,1,1,20,11,5,77,7,6,4,5,8,67,20,85,15,3,1,1,87,37,2,3,8,5,3,88,77,2,3,2,7,1,23,40,1,6,2,52,8,69,10,2,6,18,3,6,8,8,5,8,10,6,2,3,58,63,33,66,9,7,29,4,10,91,39,1,2,17,32,5,2,17,16,8,1,9,2,10,34,78,53,3,52,2,1,1,8,2,1,19,1,79,8,1,98,6,2,43,40,33,11,89,35,1,16,11,51,2,3,5,13,15,72,17,2,76,3,2,5,2,4,2,6,37,26,7,34,4,47,44,18,7,16,17,1,73,5,8,36,76,4,35,64,1,60,15,3,4,72,35,2,12,28,2,9,52,1,4,27,2,1,58,13,2,55,1,13,74,6,1,3,14,25,25,16,6,13,5,10,2,1,1,12,12,11,7,18,38,5,8,2,33,15,9,1,4,33,2,2,2,83,1,6,1,7,4,6,1,2,35,13,4,74,9,46,93,7,14,1,77,19,13,11,2,7,1,16,27,2,2,2,14,7,4,3,69,2,1,2,3,10,1,42,20,1,20,15,2,17,8,67,27,21,1,4,19,5,2,46,1,25,7,1,30,50,2,18,12,3,1,18,40,4,1,30,2,60,11,31,7,73,3,17,1,9,7,4,70,81,12,4,31,71,25,29,55,35,37,76,1,27,19,77,8,98,1,22,12,76,2,2,25,6,4,5,6,3,58,1,6,1,17,1,2,2,44,25,1,4,15,5,23,47,3,1,12,4,1,32,80,38,1,66,5,52,15,57,8,11,4,2,3,98,52,2,1,19,11,10,55,16,41,2,44,1,16,22,26,35,23,2,60,4,1,24,12,1,2,12,25,3,82,2,96,31,1,11,56,1,7,9,87,2,1,25,10,36,1,3,1,63,50,15,10,11,49,67,3,10,3,15,63,57,2,12,55,16,6,1,25,25,8,55,3,66,11,34,51,26,5,11,10,60,38,93,1,21,2,84,5,12,2,25,46,31,1,1,2,18,13,80,16,18,2,77,1,2,45,3,4,3,1,11,2,11,17,8,25,9,18,2,1,8,20,31,5,11,24,1,3,1,19,5,33,60,73,15,28,1,39,4,12,8,5,1,9,3,1,16,3,38,6,65,7,30,7,55,45,8,25,16,1,4,2,1,2,11,13,1,3,1,1,2,1,21,26,8,1,46,29,65,40,3,13,1,9,2,4,27,5,93,30,4,28,17,43,1,5,1,92,77,5,47,1,39,25,1,96,39,88,10,66,8,36,10,32,7,1,14,58,1,67,13,5,3,10,22,7,1,37,4,14,7,75,1,1,5,34,71,2,11,16,5,14,99,92,4,5,97,6,83,2,6,2,63,31,6,2,77,1,1,44,1,1,44,2,4,2,6,59,21,6,15,2,3,76,1,7,3,88,20,41,99,1,4,77,2,2,9,5,10,2,3,20,2,24,4,23,2,4,18,52,11,13,95,1,3,10,9,21,12,1,45,8,1,7,7,12,37,5,7,1,1,67,92,98,22,2,89,3,4,22,43,44,71,18,14,64,2,5,2,1,67,1,1,5,9,10,1,36,1,6,17,1,1,4,11,3,12,24,84,6,8,38,61,24,94,29,2,3,34,26,78,75,1}

Returns: 7.254901098920991E8
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{4,1,49,3,7,15,12,16,23,32,82,1,4,10,2,1,5,16,99,73,1,6,5,3,1,35,18,27,27,10,10,30,3,47,11,42,6,1,85,64,10,6,1,2,2,1,2,42,43,2,1,15,2,2,3,11,5,9,35,9,1,17,11,13,16,13,53,5,8,2,7,8,44,27,1,5,4,83,1,10,2,2,1,1,60,44,34,1,31,4,37,1,1,24,1,90,1,33,21,24,1,41,6,13,8,1,17,3,2,10,2,4,16,2,81,64,49,12,54,13,95,1,40,9,18,12,3,9,5,1,11,10,80,44,1,2,24,1,28,1,25,32,34,3,7,1,1,3,5,10,10,95,19,1,12,4,25,18,3,55,20,66,2,19,1,94,2,29,2,2,5,13,1,71,1,79,3,8,39,38,5,31,26,18,16,14,15,25,50,33,3,3,18,10,1,12,3,18,12,34,5,70,19,3,19,22,72,56,16,2,10,21,5,4,1,21,1,48,1,12,16,1,12,8,19,5,8,94,11,7,1,3,21,15,38,3,47,26,70,20,29,49,6,80,2,40,8,60,8,3,2,16,4,4,2,5,1,2,5,89,15,8,7,47,8,2,33,18,44,15,3,1,24,13,12,2,29,37,31,27,1,12,32,54,1,2,19,87,3,2,78,1,9,5,2,10,1,23,51,19,1,70,92,7,16,51,80,2,12,75,2,6,24,31,2,2,2,2,49,2,1,48,3,11,1,1,32,6,76,5,26,1,2,15,96,10,3,1,24,2,9,1,21,13,1,1,1,4,9,14,2,8,4,16,1,15,84,9,12,1,1,13,8,6,2,8,7,1,61,14,11,1,79,22,14,54,4,16,2,37,2,10,10,64,2,2,1,59,10,7,1,9,1,22,3,2,76,1,3,12,3,1,13,1,16,5,12,1,12,4,8,11,1,13,1,9,52,1,2,57,2,2,18,2,34,3,49,9,9,2,1,55,1,84,5,14,7,1,20,2,1,4,3,7,5,11,9,55,10,9,1,4,4,30,97,34,13,10,20,9,5,3,9,22,1,1,2,1,52,52,74,1,4,55,1,3,46,3,74,36,6,4,4,68,15,34,12,80,1,68,65,40,12,1,85,83,28,60,6,42,4,27,72,1,3,10,4,44,1,1,10,11,6,4,8,4,9,15,10,2,66,3,1,7,46,21,62,4,4,9,8,62,48,72,23,2,11,40,2,3,31,53,4,53,17,1,3,4,8,9,11,2,4,62,24,22,15,3,3,5,62,6,18,13,2,1,61,1,1,1,4,39,58,4,88,78,5,1,6,4,9,2,8,36,63,53,1,6,15,65,34,8,16,82,10,1,42,5,4,15,62,7,2,19,4,14,5,29,4,4,7,91,1,36,5,53,23,80,35,21,2,11,2,9,12,37,6,1,21,21,7,21,21,3,1,1,11,7,12,8,96,47,70,3,1,11,72,1,2,7,51,4,39,13,83,3,38,10,2,1,16,10,6,2,11,14,26,45,19,1,1,10,5,4,24,15,8,6,43,1,2,5,21,2,4,1,1,28,27,43,1,9,12,55,2,4,1,1,2,46,28,3,9,6,51,41,16,4,6,6,18,64,3,73,37,2,4,5,3,39,15,21,2,15,13,4,1,43,62,31,3,1,3,2,47,1,10,4,6,8,8,12,65,6,52,2,2,1,87,1,1,2,5,48,1,50,8,10,2,99,2,82,1,8,1,31,91,19,7,3,57,12,16,29,5,1,6,92,39,74,19,6,39,18,20,19,1,10,6,23,5,13,22,3,2,56,3,23,14,47,7,16,1,1,8,1,8,44,2,2,96,6,6,2,2,4,2,84,31,7,77,33,24,60,7,20,8,1,3,97,24,5,97,26,7,10,1,17,3,2,12,2,32,64,72,2,9,10,5,9,68,3,2,6,11,12,25,7,63,3,35,90,8,2,9,1,50,19,5,28,9,93,8,5,34,1,38,15,81,13,39,2,3,15,3,6,4,93,1,22,56,11,4,9,1,28,10,2,17,80,69,11,13,18,2,3,58,16,27,79,5,1,34,2,2,25,1,8,15,13,51,22,1,45,3,5,1,2,27,40,6,1,14,86,9,11,5,23,47,4,4,4,50,1,3,17,11,4,4,88,90,36,13,45,2,6,2,2,38,4,15,7,77,7,10,7,9,1,3,1,2,4,81,14,1,3,14,87,1,20,9,2,27,30,82,24,18,20,5,3,1,18,32,92,87,9,40,11,1,50,2,11,8,18,74,90,11,4,2,12,1,64,16,42,5,71,1,3,4,4,7,32,1,1,4,21,4,1,28,1,1,27,2,2,34,47,55,1,2,7,72,3,68,17,34,5,13,2,25,21,3,80,15,3,1,1,23,5,6,12,89,4,81,29,4,37,4,2,5,17,5,20,59,20,1,25,1,5,6,56,36,30,67,5,44,16,6,56,3,3,19,1,3,47,13,47,14,2,6,86,56,4,33,13,6,1,5,6,2,5,27,13,11,5,32,26,6,10,1,34,81,36,18,14,2,36,87,1,14,75,32,28,74,95,48,2,23,2,65,21,3,4,32,12,6,14,2,14,23,2,4,78,3,16,1,9,6,4,6,22,3,98,38,4,9,24,10,2,53,42,2,32,96,4,1,80,14,3,29,4,1,9,11,15,4,2,1,1,25,30,73,2,54,3,7,64,13,24,51,2,5,84,13,1,15,14,1,87,6,91,77,50,13,86,15,57,8,3,6,34,66,1,2,1,2,83,1,98,2,55,5,40,6,64,4,1,73,6,9,4,11,56,6,4,35,11,49,3,27,56,4,1,13,59,4,3,1,1,11,2,15,4,3,1,46,45,3,1,92,28,3,87,32,2,6,8,2,49,89,1,1,3,23,12,1,1,13,34,4,20,99,1,8,1,91,59,2,12,8,1,13,34,16,2,14,19,60,62,1,35,3,3,2,14,49,11,40,29,12,1,3,25,2,17,29,13,2,12,1,10,3,8,4,66,7,38,40,9,1,34,6,1,94,7,5,2,7,2,2,51,2,37,9,40,38,4,8,6,52,2,12,1,8,5,90,56,56,9,4,4,12,23,1,5,4,4,32,22,2,1,2,50,12,3,1,31,1,1,87,10,11,58,1,77,1,6,18,1,31,34,3,15,33,45,99,9,2,1,21,1,1,14,5,2,10,5,6,8,1,1,2,18,1,20,13,1,25,1,22,14,20,55,14,1,9,5,12,25,9,3,5,3,40,1,3,96,91,28,1,3,18,1,8,18,2,1,19,4,82,61,22,6,1,91,2,15,9,1,23,25,17,68,1,3,5,13,3,1,36,72,7,2,20,9,2,25,2,53,3,5,7,56,13,3,21,27,8,6,71,4,9,6,2,17,44,10,58,24,1,3,32,5,16,64,4,48,6,1,26,35,7,7,5,9,1,39,3,65,29,2,4,1,97,3,2,4,5,29,50,35,68,1,95,39,20,3,12,19,21,30,10,51,6,15,5,74,40,1,6,13,1,45,14,4,1,20,24,1,13,9,7,54,1,3,6,36,5,1,9,6,1,25,8,42,40,12,3,1,7,35,37,1,1,94,2,59,1,27,1,50,3,30,2,3,2,1,10,25,17,25,31,45,1,2,13,27,5,69,42,3,29,1,12,49,42,8,1,1,75,3,86,3,27,21,56,4,4,4,10,38,29,43,5,8,12,5,3,69,22,38,18,2,13,2,80,38,2,4,2,1,99,63,1,46,47,61,17,2,66,1,9,11,5,8,7,5,4,1,1,2,2,6,5,1,36,2,5,12,15,11,11,1,5,33,11,28,77,45,4,2,1,7,1,2,6,19,20,2,28,98,10,5,10,3,19,3,1,11,4,17,7,30,33,3,68,90,2,1,26,3,4,4,11,13,1,71,3,25,6,4,13,99,1,14,2,2,2,2,5,18,1,51,7,6,12,2,64,35,23,92,4,5,1,23,58,32,73,10,5,95,60,15,2,28,69,16,2,1,6,30,1,1,2,2,8,1,7,11,26,21,62,6,67,15,45,40,3,7,3,1,65,45,13,84,1,7,40,64,2,9,3,6,35,1,8,38,1,34,1,1,67,75,63,17,3,4,2,15,3,7,2,4,50,25,53,9,3,1,19,86,52,23,1,61,21,45,98,78,38,4,1,7,11,5,13,11,35,4,9,60,44,8,24,86,1,23,2,19,4,46,3,1,4,69,1,5,1,6,53,64,18,40,6,1,12,2,3,42,10,26,4,2,58,89,24,3,2,2,1,54,17,4,50,3,1,63,16,14,20,2,13,7,12,4,4,7,30,4,50,11,44,87,37,7,11,2,9,32,38,27,7,3,14,34,8,4,37,13,86,21,3,9,1,64,2,3,1,1,19,57,60,82,58,9,41,15,4,3,2,17,41,6,44,37,6,1,1,7,2,1,17,43,32,14,31,6,4,8,53,21,60,41,1,13,25,1,45,25,88,1,12,29,26,1,33,2,1,1,5,36,79,2,3,7,18,33,2,4,78,50,27,20,22,78,3,5,3,43,22,40,1,68,97,29,72,4,3,56,2,2,10,5,81,7,4,7,37,47,22,1,1,1,1,10,14,2,81,10,1,6,24,54,1,2,75,4,17,84,3,10,28,2,6,3,1,3,88,63,1,28,45,2,18,96,71,1,14,1,48,78,17,2,2,90,1,1,3,86,24,30,2,1,13,4,29,3,66,50,32,38,13,5,2,2,4,7,2,4,4,3,4,18,11,2,56,40,1,3,4,23,1,7,1,1,4,59,79,1,17,4,2,1,2,93,12,16,2,5,5,98,28,37,1,32,18,24,1,4,8,1,13,2,91,23,22,2,10,7,30,11,7,6,1,4,34,4,5,3,5,1,1,1,16,1,2,3,8,5,20,23,94,1,3,4,1,64,59,61,1,68,14,1,6,94,3,22,9,7,1,13,22,48,3,41,46,29,4,36,62,60,4,16,5,2,74,10,3,8,11,20,72,24,14,6,27,3,74,4,55,14,26,11,1,34,72,45,14,22,1,8,1,5,11,18,2,68,66,40,30,1,2,1,47,53,18,1,3,1,9,2,1,5,1,7,4,32,93,16,42,27,28,10,18,3,1,91,33,30,21,52,26,36,19,2,22,57,25,10,14,1,3,8,1,2,24,7,54,58,15,45,1,9,24,14,1,18,16,6,75,21,94,5,2,5,70,92,31,6,10,1,19,73,4,1,49,30,2,23,4,86,1,26,27,70,1,19,23,3,11,9,41,26,10,24,33,1,6,8,9,5,4,14,7,63,3,18,1,2,2,7,17,5,3,24,27,1,12,1,94,19,1,1,1,5,12,18,1,16,10,14,4,6,1,59,5,6,47,4,2,2,65,16,25,1,1,4,20,1,75,24,6,8,59,37,1,9,1,20,4,4,1,10,51,5,65,1,2,6,1,6,1,2,34,10,27,1,3,4,4,1,4,50,8,1,6,7,6,2,3,2,21,21,17,9,3,2,4,2,44,1,2,36,1,3,3,50,4,16,16,2,22,7,1,23,10,19,1,38,1,2,8,2,16,24,3,32,84,1,10,1,1,2,31,36,1,1,3,71,6,13,2,9,3,10,37,8,25,71,1,2}

Returns: 6.943798484075007E8
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Returns: 1.1448728730054939E9
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2,45,5,9,13,13,25,19,1,9,78,75,28,57,41,20,2,23,6,1,5,2,3,1,20,2,34,85,7,1,1,3,58,18,5,3,3,1,1,57,15,3,10,9,19,21,47,53,10,23,80,83,1,1,74,3,57,1,27,1,29,8,6,1,2,55,4,3,1,48,3,91,16,1,22,5,4,3,3,3,69,10,3,1,97,49,42,7,2,12,26,5,5,12,1,22,2,22,13,5,30,41,19,90,7,6,26,3,2,24,9,1,12,5,36,43,33,3,20,2,65,1,13,10,3,9,84,9,93,37,10,99,20,34,36,3,1,5,77,70,1,92,25,84,64,10,67,1,30,21,1,30,18,64,54,3,18,9,1,46,1,16,5,1,2,8,4,1,54,5,27,90,12,3,49,1,1,12,83,5,6,41,11,8,1,39,1,3,18,91,7,15,4,6,25,1,1,51,43,96,12,1,16,4,24,1,4,3,11,14,27,40,12,8,1,11,49,64,20,32,1,1,9,1,2,53,3,15,2,22,98,1,6,1,85,10,2,2,29,10,7,1,13,81,63,1,25,2,10,31,2,40,80,9,4,79,3,46,6,41,14,2,2,1,25,53,13,8,20,1,43,29,2,7,34,7,70,7,10,40,7,1,61,5,2,2,1,83,4,4,2,9,1,4,80,12,11,20,23,6,40,8,42,21,4,16,1,84,51,4,34,26,1,4,14,3,36,61,12,2,1,36,6,2,45,34,2,50,20,49,3,1,13,2,68,5,3,95,3,21,1,8,7,37,31,10,5,24,13,10,3,3,16,14,1,6,10,33,4,76,41,13,7,8,54,2,1,5,1,4,24,13,9,6,5,16,8,8,1,9,2,30,1,2,5,38,3,18,4,24,11,15,1,9,3,58,1,3,94,33,3,10,1,5,23,6,72,31,1,10,4,3,23,2,13,20,3,2,15,58,3,2,27,45,52,67,22,17,1,1,5,39,9,36,4,10,23,17,31,4,1,31,2,5,56,7,2,1,1,12,41,1,2,11,4,12,6,1,31,31,19,24,10,15,28,1,3,6,5,6,62,32,3,8,1,3,8,33,4,3,4,1,2,1,8,68,19,10,6,32,2,28,1,58,86}

Returns: 1.0969983204778953E9
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Returns: 1.1866517983107023E9

Statistics

Problem Statement for "TrianglePainting"

Problem Statement

Definition

Notes

Constraints

Examples