bee 1027 - Critical Wave

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.

There will be an imaginary line y = a, which we call the major axis for the curve.
All the points on the curve should have different x coordinates. Their y coordinates should be of form a-1 or a+1.

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