9906: ABC309 —— F - Box in Box
[Creator : ]
Description
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.
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.
Input
The input is given from Standard Input in the following format:
```
$N$
$h_1$ $w_1$ $d_1$
$\vdots$
$h_N$ $w_N$ $d_N$
```
```
$N$
$h_1$ $w_1$ $d_1$
$\vdots$
$h_N$ $w_N$ $d_N$
```
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.
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.
- $1 \leq h_i,w_i,d_i \leq 10^9$
- All input values are integers.
Sample 1 Input
3
19 8 22
10 24 12
15 25 11
Sample 1 Output
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 2 Input
3
19 8 22
10 25 12
15 24 11
Sample 2 Output
No
Sample 3 Input
2
1 1 2
1 2 2
Sample 3 Output
No