URI Online Judge | 1027

Critical Wave

By Monirul Hasan Tomal, Southeast University Bangladesh

Timelimit: 2

The task is simple. Through some critical points in 2D, you have to draw a wave like curve. Your goal is to include as many points as possible.


Two consecutive points on the curve should have a difference of 2 in their y coordinate.

Input

There will be no more than 222 test cases. Each test case starts with an integer N, the number of points in the test case. In the next N lines, there will be N pair of integers giving the x and y coordinate of the points. There will be no more than 1000 points in each test case. All coordinates are integers -- they'd fit in a signed 2 byte integer data type. The data must be read of default input.

Output

For each test case print a number -- the maximum number of critical points that can be included in a curve drawn from the given points.

Input Sample Output Sample

10
0 1
1 0
1 -1
2 -2
3 1
3 -1
3 -2
4 1
4 -1
5 -1
10
0 2
2 0
1 -1
2 -2
3 1
3 -1
3 -2
4 1
4 -1
5 –1

4
3