Professor Vasechkin had a notebook with an outstanding set of non-negative integers A₁, A₂,..., A_n. Somehow the most remarkable fact that made this set so outstanding appeared to be the impossibility to find such a subset of two or more elements, that XOR of elements in the subset would equal to zero. One day the professor managed to create a new set of integers B₁, B₂,..., B_n(n-1)/2 through applying the XOR operations to all pairs of elements of A set. The set B was not written in any particular order. Unfortunately due to his natural absent-mindedness professor lost the A set and now he is very confused but still obliged to ask you of a considerable favor. Please restore the set in accordance with the remaining B set.
The first line describes M — the amount of numbers in B set (1 ≤ M ≤ 100, M = N x (N - 1) / 2 for some number N). The second line describes M numbers — B₁, B₂,..., B_M (0 ≤ B_i ≤ 2³¹ - 1).

Print the A set in one line through a blank. All elements of A should be from 0 to 2³¹ - 1 inclusively. If there are several solutions of the problem, you can choose any of them. It is guaranteed that there exists at least one A set that satisfies the condition.

sample input	sample output
6 30 19 66 13 92 81	94 64 77 28