Rebel rescue

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Government is surveilling the entire planet in search of black money, and now there are N satellites orbiting Earth. Each satellite has sensors to detect black money transaction on the visible half of the planet. For example, when a satellite is passing over north pole, it's sensors can detect any transaction in the northern hemisphere. This surveillance has become a real pain point for some businessmen, as the satellite sensors are really good. A powerful businessman wants to conduct a big black money transaction somewhere on the planet surface. To do this, he must first sabotage all satellites which would be able to detect the transaction. The businessman can choose any place and time for the transaction, as long as it is on the planet surface. Please help him by finding the minimum number of satellites that must be sabotaged so that the transaction goes undetected. He has promised you a small fraction of the money (in old currency) as a reward for your services.
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The i^{th} satellite orbits along longitude l_{i}, and at time t=0, is in phase p_{i}. Phase of an orbiting body is the angle between north pole, planet center and the orbiting body. If phase p_{i} is less than 180 degree, the body lies on longitude l_{i} somewhere between north pole and south pole. If phase is more than 180 degree, the body lies on longitude l_{i}180 somewhere between south pole and north pole.
Extra Explanation: Note that the formulation of longitude and phase is slightly different from the system of longitudes and latitudes we use to denote points on earth's surface. It is closer to Spherical coordinate system, but we have constrained the azimuth angle (l_{i} in the figure above) to be between 0 and 180, so the azimuth angle of an orbiting satellite does not change, and polar angle can be anywhere between 0 and 360. At time t, the i^{th} satellite is located at x = sin(p_{i} + t) * cos(l_{i}), y = sin(p_{i} + t) * sin(l_{i}), z = cos(p_{i} + t).
Assumptions to be made:
 The transaction takes place on a place which has arbitrarily small(but non zero) area.
 The transaction lasts for arbitrarily short(but non zero) duration.
 All satellites have circular orbit which is very far away from the planet’s surface.
 All satellites orbit at the same distance and the same speed.
 All angles are in degrees.
 The geometric center of the Planet is same as its center of mass.
 No special or general relativistic effects.
Input
The first line of the input contains an integer T denoting the number of test cases. The description of T test cases follows.
The first line of each test case contains a single integer N denoting the number of satellites. The next N lines contain two space separated integers each, p_{i} and l_{i}.
Output
For each test case, output a single line containing the minimum number of satellites that must be sabotaged to conduct a successful transaction.
Constraints:
 1 ≤ T ≤ 10
 3 ≤ N ≤ 50
 0 ≤ l_{i} ≤ 179
 0 ≤ p_{i} ≤ 359
 All l_{i} are distinct.
 All p_{i} are distinct modulo 180.
Example
Input: 2 3 10 90 310 30 305 150 3 10 90 230 30 125 35 Output: 0 0
Sub tasks
 Sub task #1: N = 3 (10 points)
 Sub task #2: N ≤ 20 (30 points)
 Sub task #3: N ≤ 50 (60 points)
Explanation
Example case 1: The businessman can do transaction at time t=0, at longitude 90, and phi 230 (90W, 40S), where no orbiting satellite can see them, so he does not need to sabotage any of them.
Example case 2: The businessman can do transaction at time t=160 (after all satellites have complete 160 degrees of rotation), at longitude 125, and phi 267 (55W, 3S). No satellite has to be sabotaged in this case either.
Author:  utkarsh_lath 
Tags  utkarsh_lath 
Date Added:  18122016 
Time Limit:  1.5 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, SCALA, D, PERL, FORT, WSPC, ADA, CAML, ICK, BF, ASM, CLPS, PRLG, ICON, SCM qobi, PIKE, ST, NICE, LUA, BASH, NEM, LISP sbcl, LISP clisp, SCM guile, JS, ERL, TCL, PERL6, TEXT, SCM chicken, PYP3, CLOJ, FS 
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