Alan is planning to adopt a cat!

In front of him is a line of ~N~ cats. Alan is selecting a cat based on 3 categories: cuteness ~a_i~, cleanliness ~b_i~, and coolness ~c_i~. A cat ~x~ is considered an alpha cat if there exists no cat ~y~ with ~a_y > a_x~, ~b_y > b_x~, and ~c_y > c_x~. In other words, cat ~x~ is alpha if no other cat outperforms cat ~x~ in every category.

For example, consider a cat with values ~[5, 2, 8]~ and a different cat with values ~[3, 2, 5]~. The first cat does not outperform the second cat in every category, since their ~b_i~ is equal. Next, consider a cat with values ~[5, 4, 8]~ and a different cat with values ~[3, 2, 5]~. The first cat outperforms the second cat in every category.

Help Alan find the number of alpha cats!

Input Specification

The first line will contain one integer ~N (1 \leq N \leq 10^3)~, the number of cats.

Each of the next ~N~ lines will contain 3 space-separated integers, ~a_i (0 \leq a_i \leq 10^9)~ , ~b_i (0 \leq b_i \leq 10^9)~, and ~c_i (0 \leq c_i \leq 10^9)~.

Output Specification

Output the number of alpha cats.

Sample Input

4
3 3 4
2 2 4
9 1 3
2 2 3

Sample Output

3

Explanation

All cats are alpha cats except for the last cat. The first cat outperforms the last cat in every category.