Plane Division

Problem statement

The curve given by one implicit function $Ax ^ 2 + Bxy + Cy ^ 2 + Dx + Ey + F = 0$ and the straight line given by $N$ implicit functions $A_ix + B_iy + C_i = 0$ is there. Find out how many regions the plane is divided by these curves and straight lines.

The following is a diagram of the Sample Input dataset.

Constraint

• $1 \ leq N \ leq 20$
• $-100 \ leq A, B, C, D, E, F \ leq 100$
• $-100 \ leq A_i, B_i, C_i \ leq 100$
• $A_i \ neq 0$ or $B_i \ neq 0$
• The curve can be an ellipse (including a perfect circle), a parabola, or a hyperbola.
• The same straight line may exist.

input

Input follows the following format. All given numbers are integers.

$N$ $A$ $B$ $C$ $D$ $E$ $F$ $A_1$ $B_1$ $C_1$ $...$ $A_N$ $B_N$ $C_N$

output

Output the number of areas on one line.

Examples

Input

1 1 0 1 0 0 -1 1 -1 0

Output

4

Input

2 1 0 0 0 -1 0 2 -1 -1 6 9 1

Output

7

Input

2 1 0 -1 0 0 -1 3 0 6 -5 0 -10

Output

6

inputFormat

Input dataset.

Constraint

• $1 \ leq N \ leq 20$
• $-100 \ leq A, B, C, D, E, F \ leq 100$
• $-100 \ leq A_i, B_i, C_i \ leq 100$
• $A_i \ neq 0$ or $B_i \ neq 0$
• The curve can be an ellipse (including a perfect circle), a parabola, or a hyperbola.
• The same straight line may exist.

input

Input follows the following format. All given numbers are integers.

$N$ $A$ $B$ $C$ $D$ $E$ $F$ $A_1$ $B_1$ $C_1$ $...$ $A_N$ $B_N$ $C_N$

outputFormat

output

Output the number of areas on one line.

Examples

Input

1 1 0 1 0 0 -1 1 -1 0

Output

4

Input

2 1 0 0 0 -1 0 2 -1 -1 6 9 1

Output

7

Input

2 1 0 -1 0 0 -1 3 0 6 -5 0 -10

Output

6

样例

2
1 0 -1 0 0 -1
3 0 6
-5 0 -10

6