github.com/captn3m0/codechef.git

---
{"languages_supported":{"0":"NA"},"title":"MKSQR","category":"NA","old_version":true,"problem_code":"MKSQR","tags":{"0":"NA"},"layout":"problem"}
---

<h3> All submissions for this problem are available. </h3><h3>Statement</h3>
<p>
You are give a set of 2-d vectors (x,y) [ -10^8 ≤ x,y ≤ 10^8, x ≠ y ] of size n (1 ≤ n ≤ 50000 ). Lets denote the ith vector as vi. <br />
You are to determine if the following system of equations has a solution : <br />
        <quote>a1*v1 + a2*v2 + a3*v3 + ... ai*v1 + ... an*vn = (k,k) for some arbitrary k. </quote> <br />
All ai's are non-negative integers [ 0 ≤ ai ≤ 10^16 ] and <br />
ALL ai's CANNOT BE ZERO ;). <br />
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. <br />
</p>

<h3>Input</h3>
<p>
First line of the input contains an integer t ( 1 ≤ t ≤ 100 ) which denotes the number of test cases to follow. <br />
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). <br />
</p>

<h3>Output</h3>
<p>
Output should contain exactly t lines, with "YES" or "NO" ( without the quotes - see the sample test case for more details ).
</p>

<h3>Sample Input</h3>
<pre>
2
3
0 1
-1 0
1 0

4
1 2
10 -6
-5 -1
1 -1
</pre>

<h3>Sample Output</h3>
<pre>
YES
YES
</pre>

<h3>Explanation</h3>
<p>
Test case 1 : a1 = 0 , a2 = 1, a3 = 1. <br />
Test case 2 : a1 = 2 , a2 = 0 , a3 = 1, a4 = 3.  <br />
</p>