#D4392. Covered Points
Covered Points
Covered Points
You are given n segments on a Cartesian plane. Each segment's endpoints have integer coordinates. Segments can intersect with each other. No two segments lie on the same line.
Count the number of distinct points with integer coordinates, which are covered by at least one segment.
Input
The first line contains a single integer n (1 ≤ n ≤ 1000) — the number of segments.
Each of the next n lines contains four integers Ax_i, Ay_i, Bx_i, By_i (-10^6 ≤ Ax_i, Ay_i, Bx_i, By_i ≤ 10^6) — the coordinates of the endpoints A, B (A ≠ B) of the i-th segment.
It is guaranteed that no two segments lie on the same line.
Output
Print a single integer — the number of distinct points with integer coordinates, which are covered by at least one segment.
Examples
Input
9 0 0 4 4 -1 5 4 0 4 0 4 4 5 2 11 2 6 1 6 7 5 6 11 6 10 1 10 7 7 0 9 8 10 -1 11 -1
Output
42
Input
4 -1 2 1 2 -1 0 1 0 -1 0 0 3 0 3 1 0
Output
7
Note
The image for the first example:
Several key points are marked blue, the answer contains some non-marked points as well.
The image for the second example:
inputFormat
Input
The first line contains a single integer n (1 ≤ n ≤ 1000) — the number of segments.
Each of the next n lines contains four integers Ax_i, Ay_i, Bx_i, By_i (-10^6 ≤ Ax_i, Ay_i, Bx_i, By_i ≤ 10^6) — the coordinates of the endpoints A, B (A ≠ B) of the i-th segment.
It is guaranteed that no two segments lie on the same line.
outputFormat
Output
Print a single integer — the number of distinct points with integer coordinates, which are covered by at least one segment.
Examples
Input
9 0 0 4 4 -1 5 4 0 4 0 4 4 5 2 11 2 6 1 6 7 5 6 11 6 10 1 10 7 7 0 9 8 10 -1 11 -1
Output
42
Input
4 -1 2 1 2 -1 0 1 0 -1 0 0 3 0 3 1 0
Output
7
Note
The image for the first example:
Several key points are marked blue, the answer contains some non-marked points as well.
The image for the second example:
样例
4
-1 2 1 2
-1 0 1 0
-1 0 0 3
0 3 1 0
7