Given an array A of integers, choose 2 non-empty disjoint subsets X and Y such that ratio of sum of elements of X and Y is as close to 1 as possible.

Given,

Α : {a₁, a₂, .... a_N}

Find,

X : {x₁, x₂....x_K}

Y : {y₁, y₂.....y_M}

where, X ⊂ A, Y ⊂ A, K > 0 and M > 0 and there does not exist an i, such that a_i ∈ X and a_i ∈ Y, and Q = abs (1.0 - Σx_i / Σy_i) is minimum possible. Note that there can exist i and j such that a_i ∈ X and a_j ∈ Y, i ≠ j but a_i = a_j.

Output this minimum possible value of Q with precision up to exactly 6 decimal places.

CONSTRAINTS

2 ≤ N ≤ 16
1 ≤ a_i ≤ 10⁶, ∀ i ∈ [1, N]

INPUT

The first line of test file contains a single integer N. Next line contains N space separated integers representing the array A.

OUTPUT

Print in a single line, the value of Q with exactly 6 decimal places.