Permuting cows

Niuniu likes cows. He has n cows in his farm. He loves the cows very much, but the cows seem unhappy. Niuniu figures out why this happens. The cows are arranged in a sequence. Two cows may become unhappy when they are adjacent in the sequence. Every cow has a characteristic value, named v_i. The unhappiness between cow i and i+1 is defined as v_i xor v_i+1. (xor is exclusive OR) Niuniu wants the largest unhappiness between each pair of adjacent cows to be as low as possible. You need to tell him a permutation p_i, so that when the i-th position is the p_i-th cow in the new sequence, the largest unhappiness is as low as possible. Among all the permutations, you need to tell him the lexicographically smallest one.

The first line contains one integer n, which is the number of cows. The second line contains n integers, v1 v2 … vn, separated by a space. (2 ≤ n ≤ 300000, 0 ≤ vi ≤ 1000000000)

Print a single line with n numbers, which means the permutation.

8
1 9 2 6 0 8 1 7

1 2 6 5 3 4 7 8

This problem contains a large number of testcases.  Please, check your code carefully before you submit and wait patiently for the result.