Problem Statement

There are $N$ rectangular cuboid boxes of various sizes.
You want to choose some of these boxes and make nested boxes, like a matryoshka doll, by repeatedly putting a smaller box inside a larger box.
What is the maximum number of levels of nesting you can achieve?

Note the following.
Boxes may be rotated or laid on their side when used.
Box $i$ can be put inside box $j$ only if the width, depth, and height of box $i$ (after being arbitrarily rotated or laid on its side) are each strictly smaller than the width, depth, and height of box $j$, respectively.
Putting two boxes directly inside one box does not count as three levels of nesting.

Input

$N$
$X_1$ $Y_1$ $Z_1$
$X_2$ $Y_2$ $Z_2$
$\vdots$
$X_N$ $Y_N$ $Z_N$

$1 \le N \le 1000$
$1 \le X_i,Y_i,Z_i \lt 10^8$

$N, X_i, Y_i, Z_i$ are all integers.
The number of boxes is $N$.
The size of the $i$-th box is such that its three side lengths are $X_i, Y_i, Z_i$.

Output

Output, as an integer, the maximum number of levels of nesting of the boxes.
If the boxes cannot be nested at all, output $1$.

Sample

4
2 2 2
1 1 1
3 3 3
4 1 4

3

2
1 1 3
2 4 2

2

2
5 5 3
4 3 3

1