A permutation of length is an array of integers such that every integer from to appears exactly once. For example, is a permutation of length , while are not permutations.
For a given array of length , the difference array is an array of length such that for each . For example, the difference array of the array is
Alice gives you an array of length . Find a permutation of length such that the difference array of the permutation and the given array are equal. Print if no such permutation exists.
Input format
Output format
For each test case, print if no suitable permutation exists or print space-separated integer denoting the elements of the permutation.
Constraints
In the first test case, the difference array of the permutation is which is equal to the array .
In the second test case, there is no permutation of length for which the difference array is equal to the array .