Problem Description

YH has $n$ swords. The $i$-th sword has attack power $a_i$ and defense ability $b_i$.

For a sword $i$, if there exists a $j(j \not = i)$ such that $a_i \le a_j$ and $b_i \le b_j$, then YH considers this sword useless. Otherwise, he considers it useful.

In this problem, it is guaranteed that it is impossible to find two swords $i, j$ such that $a_i = a_j$ and $b_i = b_j$.

Please help YH find the number of useful swords among these $n$ swords.

Input Format

The first line contains an integer $n$.

The next $n$ lines each contain two integers $a_i, b_i$, representing the attack power and defense ability of the $i$-th sword.

Output Format

Print one integer, the number of useful swords.

3
2 3
1 3
5 3

1

4
5 6
2 5
6 9
1 3

1

Hint

For all testdata, $1 \le n \le 100000$, $1 \le a_i, b_i \le 10^9$.

Translated by ChatGPT 5