Intersection of Cuboids

AtCoder

IDabc361_b

Time2000ms

Memory256MB

Difficulty—

> You are trying to implement collision detection in a 3D game. In a $3$\-dimensional space, let $C(a,b,c,d,e,f)$ denote the cuboid with a diagonal connecting $(a,b,c)$ and $(d,e,f)$, and with all faces parallel to the $xy$\-plane, $yz$\-plane, or $zx$\-plane. (This definition uniquely determines $C(a,b,c,d,e,f)$.) Given two cuboids $C(a,b,c,d,e,f)$ and $C(g,h,i,j,k,l)$, determine whether their intersection has a positive volume. ## Constraints * $0 \leq a < d \leq 1000$ * $0 \leq b < e \leq 1000$ * $0 \leq c < f \leq 1000$ * $0 \leq g < j \leq 1000$ * $0 \leq h < k \leq 1000$ * $0 \leq i < l \leq 1000$ * All input values are integers. ## Input The input is given from Standard Input in the following format: $a$ $b$ $c$ $d$ $e$ $f$ $g$ $h$ $i$ $j$ $k$ $l$ [samples]

Samples

Input #1

0 0 0 4 5 6
2 3 4 5 6 7

Output #1

Yes

The positional relationship of the two cuboids is shown in the figure below, and their intersection has a volume of $8$.
![image](https://img.atcoder.jp/abc361/12ad1f07f2801946704198807bbb3395.png)

Input #2

0 0 0 2 2 2
0 0 2 2 2 4

Output #2

No

The two cuboids touch at a face, where the volume of the intersection is $0$.

Input #3

0 0 0 1000 1000 1000
10 10 10 100 100 100

Output #3

Yes

API Response (JSON)

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    "name": "Intersection of Cuboids",
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      "content": "> You are trying to implement collision detection in a 3D game. In a $3$\\-dimensional space, let $C(a,b,c,d,e,f)$ denote the cuboid with a diagonal connecting $(a,b,c)$ and $(d,e,f)$, and with all fa",
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      "memory_limit": 262144
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    "difficulty": "None",
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      "statement_type": "Markdown",
      "content": "> You are trying to implement collision detection in a 3D game.\n\nIn a $3$\\-dimensional space, let $C(a,b,c,d,e,f)$ denote the cuboid with a diagonal connecting $(a,b,c)$ and $(d,e,f)$, and with all fa...",
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