Welcome to ZOJ
128 - The 2013 ACM-ICPC Asia Changsha Regional Contest - E
Easy Problem Once More

Time Limit: 2 Seconds      Memory Limit: 65536 KB

Define matrix A ∈ Rn × n, if for every m(1 ≤ mn), , then matrix A can be called as partially negative matrix. Here matrix , and {i1, ... , im } is a subset 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| and are 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. Your 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 ≤ iN), which is vector x.
The third line contains N integers bi (-1000000 < bi < 1000000, 1 ≤ iN), which is vector b. There will be at least one bi which equals to zero.


For each test case, output “Yes” if there exists such a matrix A, or “No” if there is no such matrix.

Sample Input

2 1
0 6

Samlpe Output



There exists a symmetric partially negative matrix .


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 σ1 = 2, σ2 = 3, and σ3 = 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.

Author: WU, Hao
Submit    Status