Problem Statement

Find the maximum possible length of the longest increasing subsequence of a sequence $A$ satisfying the following condition. Note that sequence indices are 1-indexed.

Condition: The length of the sequence $A$ is $N$, and for every $i$ satisfying $1\le i\le N$, $A_i$ is an integer and $L_i\le A_i\le R_i$ holds.

* The longest increasing subsequence of $A$ means the longest subsequence among the strictly increasing subsequences of $A$.

Input

$N$
$L_1$ $R_1$
$L_2$ $R_2$
$\vdots$
$L_N$ $R_N$

$1\le N\le 10^5$
$1\le L_i\le R_i\le 10^5$ $(1\le i\le N)$

Output

Output the maximum possible length of the longest increasing subsequence. Print a newline at the end.

Sample

5
3 5
1 3
2 7
1 2
2 3

3

1
1 100000

1

5
1 1
2 2
3 3
4 4
5 5

5