2015
09-18

# Easy Problem Once More

Define matrix , if for every m(1 ≤ m ≤ n),

then matrix A can be called as partially negative matrix. Here matrix
, and {i1,..,im} is a sub set of {1,..,n}.If you are not familiar with determinant of a matrix, please read the Note part of this problem.
For example, matrix is a partially negative matrix because |-2|, |-6| andare negative.
A symmetric matrix is a square matrix that equals to its transpose. Formally, matrix A is symmetric if A = AT. For example, is a symmetric matrix.
Given two N-dimensional vector x and b, and we guarantee that there will be at least
one 0 value in vector b. You task is to judge if there exists a symmetric partially
negative matrix A, which fulfills Ax = b.

There are several test cases. Proceed to the end of file.
Each test case is described in three lines.
The first line contains one integer N (2 ≤ N ≤ 100000) .
The second line contains N integers xi (-1000000 < xi < 1000000, 1 ≤ i ≤ N), which is vector x.
The third line contains N integers bi (-1000000 < bi < 1000000, 1 ≤ i ≤ N), which is vector b. There will be at least one bi which equals to zero.

There are several test cases. Proceed to the end of file.
Each test case is described in three lines.
The first line contains one integer N (2 ≤ N ≤ 100000) .
The second line contains N integers xi (-1000000 < xi < 1000000, 1 ≤ i ≤ N), which is vector x.
The third line contains N integers bi (-1000000 < bi < 1000000, 1 ≤ i ≤ N), which is vector b. There will be at least one bi which equals to zero.

2
2 1
0 6

Yes
HintThere exists a symmetric partially negative matrix

Note

Determinant of an n ×  n matrix A is  defined as below:

Here the sum is computed over all permutations σ of the set {1, 2, ..., n}.
A permutation is a function that reorders this set of integers.
The value in the  ith position after the reordering σ is denoted σi.
For example, for n = 3, the original sequence 1, 2, 3 might be reordered to σ = [2, 3, 1],with σ[sub]1[/sub] = 2, σ[sub]2[/sub] = 3, and σ[sub]3[/sub] = 1.
The set of all such permutations (also known as the symmetric group on n elements) is denoted Sn.
For each permutation σ, sgn(σ) denotes the signature of σ, a value that is +1
whenever the reordering given by σ can be achieved by successively interchanging two entries an even number of times,
and −1 whenever it can be achieved by an odd number of such interchanges.