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\}~.