Migrated from Lutece 271 Sequence

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Description

Giving a collection S of points on two dimension plane. ($S =$ {$(x_0,y_0), (x_1,y_1), \cdots$}) We define a point is greater than another point when all its coordinate on two axis are both greater than or equel to another one. Namely, $p$ is greater than $q$ when $x_p \geq x_q$ and $y_p \geq y_q$. A sequence is a list points < $p_1, p_2, \cdots$> satisfy that $i < j => p_i$ is greater than $p_j$. You can use the elements in $S$ to construct sequences, how many sequences needed to cover a $S$ at least?

Input

The input consists of several test cases. Each test case start with a line containing a number $n(0 < n \leq 1000000)$, the number of points in $S$. Then $n$ lines follows, each line containing two number, $x_i, y_i(0 \leq x_i, y_i < 100000)$, the position of point $i$. The input end with EOF.

Output

You have to print minium number of sequences needed to cover $S$ in a single line for each case.

Samples

4
1 1
2 2
3 3
4 4

4
1 5
2 6
2 3
3 4

1
2

Resources

厦门大学第四届程序设计竞赛 现场决赛