G. Parabolas
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output

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

Input

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 ai and bi (|ai| ≤ 109, |bi| ≤ 109).

Output

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

Examples
Input
4
0 0
1 1
0 1
2 1
Output
10
Input
3
2 4
3 4
2 4
Output
4