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.

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.

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.

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

见题面 Input 部分

见题面 Output 部分