Problem C. Comparison of topologies ≡

Statement

Consider a set of rings on the plane. Each of these rings can be described by coordinates of its center (x, y), internal and external radius: q, r. It is known that any two circles bounding different rings do not cross each other.

Let us define a continuous mapping on this set that includes the next operations:

• to move a center of any ring along the continuous curve;
• to resize internal (or external) radius of the ring.

It is assumed that during these operations the bounding circles shouldn't intersect. Also, any ring shouldn't become singular (circle or point) during resizing. In other words, this mapping must keep the basic topological properties of the initial set.

Your program must, given two sets of the rings M₁ and M₂, determine whether there exist a continuous mapping to obtain M₂ from M₁ or not. It is assumed that order of rings in these sets may be different.

Input file format

Input file contains integer n — number of rings in the each set, followed by 4 × n floating point numbers x_i, y_i, q_i, r_i — parameters of the rings of M₁, and then followed by another 4 × n numbers — similar parameters of the rings of M₂,

Output file format

Output file must contain a single integer 1 — if M₂ can be obtained by continuous mapping from M₁ or 0 — otherwise.

Constraints

All input values have no more than 3 digits after the decimal point.

 − 10⁵ < x_i, y_i < 10⁵, 0 < q_i < r_i < 10⁵, 1 ≤ n ≤ 2000

Sample tests

 3
 0.000  0.000  1.000  2.000
 0.000  0.000  0.500  1.500
 5.000 -7.000  1.000  2.000
 0.000  0.000  1.000  6.000
-5.000  9.000  0.500  2.000
 0.000  0.000  0.500  1.500

1

 3
 0.000 -2.500  4.790  6.800
 0.000 -2.180  3.260  4.000
 9.810  2.630  1.000  1.500
 0.000 -8.500  2.000  6.800
-0.940 -4.000  0.500  1.500
-3.970 -8.970  1.000  1.500

0