Unfortunately, Vessel 1 in the previous problem is broken. Now, you cannot use Vessel 1. Although Vessel 2 works perfectly fine.
Is it still possible to equalize the forest? Print "YES" if it is possible, "NO" otherwise.
NOTE: Please use fast i/o for solving this problem.
Input Format: The first line contains number of test cases t (1≤t≤166666). For the next t lines:
The first line contains integer n (1≤n≤100000), the number of trees in the forest. Next line contains n space-separated integers i (0≤i<109), the heights of trees.
It is guaranteed that the sum of n over all test cases doesn’t exceed 106.
Output Format: For each test case print “YES” if it is possible to Equalize the forest, “NO” otherwise.
In the third test case, since Tree[2]=tree[3]=1, we can simply apply Vessel 2 on them and equalise the forest as: [ 2, 2, 2, 2]
In the first and second test case, there is no way to equalize the forest
