Description

我方现在有N个据点，司令部建立这些点围成的区域中。现在敌人准备爆掉其中一些点。使得无论我方将司令部建在哪里，最终都不会在剩下的点围成的区域中。

Format

Input

The first line of the input file contains a single integer n (3 <= n <= 50 000) — the number of watchtowers. The next n lines of the input file contain the Cartesian coordinates of watchtowers, one pair of coordinates per line. Coordinates are integer and do not exceed 10^6^ by absolute value. Towers are listed in the order of traversal of their convex hull in clockwise direction.

Output

Write to the output file the number of watchtowers the enemy has to blow up to compromise headquarters protection if the headquarters are placed optimally.

Samples

5
0 0
0 10
10 20
20 10
25 0

2