There are a set of points $*S*$ on the plane. This set doesn't contain the origin $*O*(0, 0)$, and for each two distinct points in the set $*A*$ and $*B*$, the triangle $*OAB*$ has strictly positive area.

Consider a set of pairs of points $(*P*_{1}, *P*_{2}), (*P*_{3}, *P*_{4}), ..., (*P*_{2*k* - 1}, *P*_{2*k*})$. We'll call the set good if and only if:

• $*k* ≥ 2$.
• All $*P*_{*i*}$ are distinct, and each $*P*_{*i*}$ is an element of $*S*$.
• For any two pairs $(*P*_{2*i* - 1}, *P*_{2*i*})$ and $(*P*_{2*j* - 1}, *P*_{2*j*})$, the circumcircles of triangles $*OP*_{2*i* - 1}*P*_{2*j* - 1}$ and $*OP*_{2*i*}*P*_{2*j*}$ have a single common point, and the circumcircle of triangles $*OP*_{2*i* - 1}*P*_{2*j*}$ and $*OP*_{2*i*}*P*_{2*j* - 1}$ have a single common point.

Calculate the number of good sets of pairs modulo $1000000007$ $(10^{9} + 7)$.

Input

The first line contains a single integer $*n*$ $(1 ≤ *n* ≤ 1000)$ — the number of points in $*S*$. Each of the next $*n*$ lines contains four integers $*a*_{*i*}, *b*_{*i*}, *c*_{*i*}, *d*_{*i*}$ $(0 ≤ |*a*_{*i*}|, |*c*_{*i*}| ≤ 50; 1 ≤ *b*_{*i*}, *d*_{*i*} ≤ 50; (*a*_{*i*}, *c*_{*i*}) ≠ (0, 0))$. These integers represent a point .

No two points coincide.

Output

Print a single integer — the answer to the problem modulo $1000000007$ $(10^{9} + 7)$.