A8290 | History

Polycarpus likes studying at school a lot and he is always diligent about his homework. Polycarpus has never had any problems with natural sciences as his great-great-grandfather was the great physicist Seinstein. On the other hand though, Polycarpus has never had an easy time with history.

Everybody knows that the World history encompasses exactly $n$ events: the $i$ -th event had continued from the year $a_{i}$ to the year $b_{i}$ inclusive ( $a_{i}<b_{i}$ ). Polycarpus easily learned the dates when each of $n$ events started and ended (Polycarpus inherited excellent memory from his great-great-granddad). But the teacher gave him a more complicated task: Polycaprus should know when all events began and ended and he should also find out for each event whether it includes another event. Polycarpus' teacher thinks that an event $j$ includes an event $i$ if $a_{j}<a_{i}$ and $b_{i}<b_{j}$ . Your task is simpler: find the number of events that are included in some other event.

The first input line contains integer $n$ ( $1<=n<=10^{5}$ ) which represents the number of events. Next $n$ lines contain descriptions of the historical events, one event per line. The $i+1$ line contains two integers $a_{i}$ and $b_{i}$ ( $1<=a_{i}<b_{i}<=10^{9}$ ) — the beginning and the end of the $i$ -th event. No two events start or finish in the same year, that is, $a_{i}≠a_{j},a_{i}≠b_{j},b_{i}≠a_{j},b_{i}≠b_{j}$ for all $i$ , $j$ (where $i≠j$ ). Events are given in arbitrary order.

Print the only integer — the answer to the problem.