SPOJ in Gyumri

   For a number t denote as h(t) maximal k such that t is divisible by 2^k. For example, h(24) = 3, h(5) = 0. Let l(t) = 2^h(t), for example, l(24) = 8, l(5) = 1.

   Consider array a[1], a[2], …, a[n] of integer numbers. Fenwick tree for this array is the array b[1], b[2], …, b[n] such that

b[i] = ∑ⁱ_{j = i − l(i) + 1} a[j].

So

b[1] = a[1],

b[2] = a[1] + a[2],

b[3] = a[3],

b[4] = a[1] + a[2] + a[3] + a[4],

b[5] = a[5],

b[6] = a[5] + a[6],

...

   For example, the Fenwick tree for the array

a = (3, −1, 4, 1, −5, 9)

is the array

b = (3, 2, 4, 7, −5, 4).

   Let us call an array self-fenwick if it coincides with its Fenwick tree. For example, the array above is not self-fenwick, but the array a = (0, −1, 1, 1, 0, 9) is self-fenwick.

   You are given an array a. You are allowed to change values of some elements without changing their order to get a new array a' which must be self-fenwick. Find the way to do it by changing as few elements as possible.

   The first line of the input file contains n (1 ≤ n ≤ 100000.) — the number of elements in the array. The second line contains n integer numbers — the elements of the array. The elements of the input array do not exceed 10⁹ by their absolute values.

   Output n numbers — the elements of the array a'. If there are several solutions, output any one.