Minimum Retailers

Each merchant corresponds to a closed interval. Delete the fewest merchants so that the remaining merchants include a center merchant whose interval intersects the interval of every other remaining merchant. Sharing an endpoint counts as intersecting. All intervals do not need a common point, and it is not enough for them to be connected as a whole.

输入格式

The first line contains n, followed by n lines of start end. The original bounds are 1≤n≤100000, 1≤start≤end≤10^9, and duplicate intervals are allowed.

输出格式

Output a single integer, the answer.

样例 1

输入：

5
3 8
4 5
6 7
10 11
12 13

输出：

2

样例 2

输入：

2
1 2
2 3

输出：

0

样例 3

输入：

3
1 1
3 3
5 5

输出：

2

样例说明

The answers are 2, 0 and 2. In the first example the center [3,8] touches two disjoint small intervals at once, so the maximum simultaneous coverage cannot be used instead.