You are given $n$ boxes and each box contains two small boxes of Red and Blue color. The size of the Red and Blue colored boxes are $b_i$ and $r_i$ respectively.

Consider a sequence of distinct integers $x_1, x_2, \ldots, x_k\ (1 \le x_i \le n)$.

Consider  $x$ to be a suitable sequence if, for every $1 \le i < k\ holds\ b_{x_i} < r_{x_{i+1}}\ and\ r_{x_i} < b_{x_{i+1}}$.

Determine the maximum possible size of the suitable sequence.

Input format

• First line: $n$ representing the number of available boxes $(1 \leq n \leq 5 \cdot 10^5)$
• Next $n$ lines: Two positive integers $r_i$ and $b_i$ $(1\leq r_i,\ b_i \leq 10^9)$

Output format

Print only one integer representing the size of the maximum suitable sequence.