You are given a set $S$ consisting of $N$ disjoint segments of integers. That is, $S$ can be represented as the union of $N$ disjoint intervals of integers $[L_i,R_i]$. Let's call a set independent if it has the property that no element of the set is exactly $2$ times another. Please find the size of the largest independent subset of $S$.

Input Specification

The first line will contain a single integer $N$.

The next $N$ lines will each contain $2$ integers $L_i$ and $R_i$, representing that $S$ contains all integers in the range $[L_i,R_i]$.

Output Specification

Output one integer, the size of the largest independent subset of $S$.

Constraints

$1\le N\le {10}^5$

$1\le L_i\le R_i\le {10}^{18}$

For all pairs $(i,j)$ such that $i\ne j$, either $L_i>R_j$ or $L_j>R_i$.

Subtask 1 [10%]

$1\le L_i\le R_i\le 20$

Subtask 2 [20%]

$L_i=R_i$

Subtask 3 [30%]

$1\le N\le 2000$

$1\le L_i\le R_i\le {10}^{12}$

Subtask 4 [40%]

No additional constraints.

Sample Input

3
5 7
9 11
1 3

Sample Output

6

Explanation

In this case, $S=\{1,2,3,5,6,7,9,10,11\}$.

One of the largest independent subsets of $S$ is $\{2,5,6,7,9,11\}$.