Bouquet

After visiting Keukenhof, one of the world's largest flower gardens, Lieke became very fond of flowers. She decided to pick some tulips growing next to the road to build a beautiful bouquet. However, the strict tulip protection laws in the Netherlands limit which flowers she can collect.

There are $N$ tulips numbered from $0$ to $N-1$ growing in a line along the road, from left to right. The protection law assigns two integers, $l_i$ and $r_i$, to tulip $i$. If Lieke picks tulip $i$, then the $l_i$ tulips immediately to its left and the $r_i$ tulips immediately to its right cannot be in the bouquet. If fewer than $l_i$ tulips lie to the left (or fewer than $r_i$ to the right), all tulips on that side are excluded.

Find the maximum number of tulips Lieke can pick while following the law.

The first line contains a single integer $N$, the number of tulips.

The next $N$ lines describe the protection law. The $i$th line contains two integers $l_i$ and $r_i$.

Print a single integer, the maximum number of tulips Lieke can pick.

• $1 \leq N \leq 2 \cdot 10^5$.
• $0 \leq l_i, r_i \leq N$ for $i = 0,1,\ldots, N-1$.

In the first sample, if Lieke picks tulip $0$, she cannot pick the two tulips on the right. Picking tulip $1$ does not prohibit her from picking tulip $2$, but tulip $2$ prohibits her from picking tulip $1$, so she cannot pick both. The maximum is $1$.

In the second sample, the maximum is $3$. The way to get it is shown in the picture below. Other choices give a smaller answer.