AtCoder Beginner Contest 220
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Problem Statement
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In the $xy$-plane, we have $N$ points, each assigned a weight.
The $i$-th point has the coordinates $(X_i,Y_i)$ and the weight $C_i$.
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We will choose four of the $N$ points to form an isosceles trapezoid whose vertices are the chosen points.
What is the maximum possible total weight of the points chosen here?
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If it is impossible to form an isosceles trapezoid, print -1.
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We remind you that an isosceles trapezoid is a quadrilateral that satisfies all of the following conditions.
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- It is a trapezoid.
- For one of the two parallel sides, the two angles at its ends are equal.
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Constraints
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$4 \leq N \leq 1000$$-10^9 \leq X_i,Y_i \leq 10^9$$1 \leq C_i \leq 10^9$$(X_i,Y_i) \neq (X_j,Y_j)$if$i \neq j$.- All values in input are integers.
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Input
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Input is given from Standard Input in the following format:
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N
X_1 Y_1 C_1
X_2 Y_2 C_2
\vdots
X_N Y_N C_N翻译中…
Output
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Print the answer.
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样例
Input #1
5
0 3 10
3 3 10
-1 0 10
2 0 10000
4 0 10
Output #1
40
We can choose Points $1, 2, 3, 5$ to form an isosceles trapezoid, with the points having a total weight of $40$.
Any other way to choose points would not form an isosceles trapezoid.
Input #2
6
0 1 1
1 4 20
2 7 300
5 6 4000
4 3 50000
3 0 600000
Output #2
650021
Note that a square and a rectangle are also isosceles trapezoids.
Input #3
7
-3 0 1
-2 0 1
-1 0 1
0 0 1
1 0 1
2 0 1
3 0 1
Output #3
-1
We cannot form an isosceles trapezoid.
题目信息
题面与样例版权归 AtCoder 及出题人所有；中文翻译由 AI 生成（CI 管线），如有出入请以原文为准。