Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

E. Alternative Reality

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputIn the year of 3000 travelling around parallel realities became a routine thing. However one has to take into consideration that travelling like that is highly dangerous as you never know beforehand where you're gonna get...

Little Vasya, for instance, found himself in a gaming reality and now he has to successfully complete all levels of a very weird game to get back. The gaming reality is a three-dimensional space where *n* points are given. The game has *m* levels and at the beginning of the *i*-th level the player is positioned at some plane *Q*_{i} that passes through the origin. On each level Vasya has to use special robots to construct and activate *n* powerful energy spheres of the equal radius with centers at the given points. The player chooses the radius of the spheres himself. The player has to spend *R* units of money to construct spheres whose radius equals *R* (consequently, one can construct spheres whose radius equals zero for free). Besides, once for each level a player can choose any point in space and release a laser ray from there, perpendicular to plane *Q*_{i} (this action costs nothing). The ray can either be directed towards the plane or from the plane. The spheres that share at least one point with the ray will be immediately activated. The level is considered completed if the player has managed to activate all spheres. Note that the centers of the spheres are the same for all *m* levels but the spheres do not remain: the player should construct them anew on each new level.

Help Vasya find out what minimum sum of money will be enough to complete each level.

Input

The first line contains two integers *n* and *m* (1 ≤ *n* ≤ 900, 1 ≤ *m* ≤ 100) — the number of energetic spheres and the number of levels in the game correspondingly.

Each of the following *n* lines contains three integers *x*_{i}, *y*_{i}, *z*_{i} (0 ≤ *x*_{i}, *y*_{i}, *z*_{i} ≤ 10^{4}) — the coordinates of the center of the *i*-th sphere. Assume that these points do not change their positions throughout the game.

Then follow *m* lines, each containing three integers *a*_{i}, *b*_{i}, *c*_{i} (0 ≤ *a*_{i}, *b*_{i}, *c*_{i} ≤ 100, *a*_{i}^{2} + *b*_{i}^{2} + *c*_{i}^{2} > 0). These numbers are the coefficients in the equation of plane *Q*_{i} (*a*_{i}*x* + *b*_{i}*y* + *c*_{i}*z* = 0), where the player is positioned at the beginning of the *i*-th level.

Output

Print *m* numbers, one per line: the *i*-th line should contain the minimum sum of money needed to complete the *i*-th level. The absolute or relative error should not exceed 10^{ - 6}.

Examples

Input

4 1

0 0 0

0 1 0

1 0 0

1 1 0

0 0 1

Output

0.7071067812

Input

5 3

0 1 0

1 0 1

1 2 1

2 0 1

1 3 0

1 1 1

1 2 3

3 0 3

Output

1.6329931619

1.6366341768

1.5411035007

Input

2 1

0 20 0

0 0 0

0 10 0

Output

0.0000000000

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Dec/06/2019 17:10:11 (f3).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|