Make A Square

All submissions for this problem are available.
Statement
You are give a set of 2d vectors (x,y) [ 10^8 ≤ x,y ≤ 10^8, x ≠ y ] of size n (1 ≤ n ≤ 50000 ). Lets denote the ith vector as vi.
You are to determine if the following system of equations has a solution :
a1*v1 + a2*v2 + a3*v3 + ... ai*v1 + ... an*vn = (k,k) for some arbitrary k.
All ai's are nonnegative integers [ 0 ≤ ai ≤ 10^16 ] and
ALL ai's CANNOT BE ZERO ;).
In other words, you need to find some linear combination of these vectors with positive coefficient such that you end up with a vector(a,b) with a=b.
Input
First line of the input contains an integer t ( 1 ≤ t ≤ 100 ) which denotes the number of test cases to follow.
For each test case, the first line contains n ( number of vectors in the set) . n lines follow, each containing a pair of space separated integers a and b which denote the vector(a,b).
Output
Output should contain exactly t lines, with "YES" or "NO" ( without the quotes  see the sample test case for more details ).
Sample Input
2 3 0 1 1 0 1 0 4 1 2 10 6 5 1 1 1
Sample Output
YES YES
Explanation
Test case 1 : a1 = 0 , a2 = 1, a3 = 1.
Test case 2 : a1 = 2 , a2 = 0 , a3 = 1, a4 = 3.
Author:  anshuman_singh 
Tags  anshuman_singh 
Date Added:  10092010 
Time Limit:  0.115385 sec 
Source Limit:  50000 Bytes 
Languages:  C, CPP14, JAVA, PYTH, PYTH 3.6, PYPY, CS2, PAS fpc, PAS gpc, RUBY, PHP, GO, NODEJS, HASK, rust, SCALA, swift, 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, kotlin, PERL6, TEXT, SCM chicken, PYP3, CLOJ, COB, FS 
Comments
 Please login at the top to post a comment.
SUCCESSFUL SUBMISSIONS
Fetching successful submissions
HELP
If you are still having problems, see a sample solution here. 