404193: GYM101446 G Parabolas

There are n parabolas in the plane determined by equations y = (x - a_i)² + b_i. Parabolas cut the plane into several parts (either finite or infinite) of positive area. Your task is to count the number of those parts.

The first line of the input contains one integer n (1 ≤ n ≤ 1000) — number of parabolas. Each of the next n lines contains two integers — coefficients a_i and b_i (|a_i| ≤ 10⁹, |b_i| ≤ 10⁹).

Print one integer — the number of positive area parts that the plane is cut into.

4
0 0
1 1
0 1
2 1

10

3
2 4
3 4
2 4

4