Aryo has got a lot of intervals for his 2418 th birthday. He is really excited and decided to color all these intervals with some colors. He has a simple rule for himself. He calls a coloring nice if there exists no three intervals a , b and c such that the following conditions are satisfied simultaneously: a , b and c are colored with the same color, , , . Moreover he found out that for every intervals i and j , there is at least one point in i which isn't in j . Given some set of intervals. You have to find the minimum number k , such that Aryo can find a nice coloring with k colors. The first line contains a single integer n ( 1 ≤ n ≤ 10 3 ), number of intervals. The following n lines contain a interval description each. Each interval is described by two numbers s i , e i which are the start and end points of it ( - 10 5 < s i , e i < 10 5 , s i ≤ e i ). See samples for clarity. A square bracket stands for including of the corresponding endpoint, while a round bracket stands for excluding. Write a single integer k — the minimum number of colors needed for a nice coloring.