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No.2253 Ignore Subtle Differences

レベル : / 実行時間制限 : 1ケース 2.000秒 / メモリ制限 : 512 MB / スペシャルジャッジ問題 （複数の解が存在する可能性があります）
タグ : （AC するまで非表示） / 解いたユーザー数 100
作問者 : noya2 / テスター : shobonvip 👑 Nachia
お気に入りにしたユーザー ProblemId : 9263 / 自分の提出
問題文最終更新日: 2023-03-24 19:03:05
This statement was translated by AI (claude-opus-5-5, effort medium) and may contain errors or differ in nuance from the original. The original statement takes precedence. Back to the original
yukicoder contest 382 (順位表) の他の問題:

Note

This problem is output only. There is no input.

Problem Statement

It is known that a triangle with positive area formed by $3$ lattice points (points whose $x$ and $y$ coordinates are both integers) on the $xy$-plane can never be equilateral.

Therefore, we call a triangle with positive area formed by $3$ lattice points an almost equilateral triangle if it satisfies the following condition.

  • Letting $a,b,c$ be the lengths of the $3$ sides, $\max(a^2,b^2,c^2)-\min(a^2,b^2,c^2)=1$ holds.

    • Construct $1$ almost equilateral triangle with as large an area as possible.

    Input

    There is no input.

    Output

    Output the coordinates $(x_1,y_1),(x_2,y_2),(x_3,y_3)$ of the $3$ points forming an almost equilateral triangle in the following format. 

    $x_1$ $y_1$
$x_2$ $y_2$
$x_3$ $y_3$
    Here, $x_1,y_1,x_2,y_2,x_3,y_3$ must be integers at least $0$ and less than $10^{9}$. Also, the $3$ points must form a triangle with positive area, and that triangle must be an almost equilateral triangle with area at least $10^{16}$.

    Sample

    Sample 1
    Input
    
            
    Output
    
            
    0 0
1 4
4 1
    
            
    
                This sample output illustrates the output format and is not a correct answer.
            
    
            
    
                
                Indeed, the $3$ points form a triangle with positive area, and that triangle is an almost equilateral triangle.
                However, its area is $\dfrac{15}{2}$, which seems far from a correct answer.

            
    
        
    
    
    


    


    

        
        
        
    
            
            
            
            
            
        
    

        
        
    
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