Score : $525$ points

问题描述

有 $N$ 个箱子。第 $i$ 个箱子的形状为长方体，其高度、宽度和深度分别为 $h_i, w_i$ 和 $d_i$。

确定是否存在两个箱子，在必要时经过旋转后，其中一个箱子的高度、宽度和深度严格大于另一个箱子的对应尺寸。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

There are $N$ boxes. The $i$-th box has a shape of a rectangular cuboid whose height, width, and depth are $h_i,w_i$, and $d_i$, respectively.

Determine if there are two boxes such that one's height, width, and depth are strictly greater than those of the other after rotating them if necessary.

Constraints

• $2 \leq N \leq 2 \times 10^5$
• $1 \leq h_i,w_i,d_i \leq 10^9$
• All input values are integers.

Input

The input is given from Standard Input in the following format:

$N$

$h_1$ $w_1$ $d_1$

$\vdots$

$h_N$ $w_N$ $d_N$

Output

Print Yes if there are two boxes such that one's height, width, and depth are strictly greater than those of the other after rotating them if necessary; print No otherwise.

Sample Input 1

3
19 8 22
10 24 12
15 25 11

Sample Output 1

Yes

If you rotate the $2$-nd box to swap its height and depth, the $3$-rd box will have greater height, depth, and width.

Sample Input 2

3
19 8 22
10 25 12
15 24 11

Sample Output 2

No

Sample Input 3

2
1 1 2
1 2 2

Sample Output 3

No

update @ 2024/3/10 08:46:48