Given $n$ numbers $q_i$, the definition of $F_j$ is given as follows:

$$F_j = \sum_{i < j} \frac{q_i q_j}{(i - j)^2} - \sum_{i > j} \frac{q_i q_j}{(i - j)^2}$$

Let $E_i = F_i / q_i$. Calculate $E_i$.

Input

The input contains an integer $n$, followed by $n$ lines, each containing a number, where the $i$-th line represents $q_i$.

Output

The output contains $n$ lines, where the $i$-th line outputs $E_i$. The error compared to the standard answer should not exceed $1e-2$.

Examples

Input 1

5 
4006373.885184 
15375036.435759 
1717456.469144 
8514941.004912 
1410681.345880

Output 1

-16838672.693 
3439.793 
7509018.566 
4595686.886 
10903040.872

Constraints

For 30% of the data, $n \le 1000$. For 50% of the data, $n \le 60000$. For 100% of the data, $n \le 100000$, $0 < q_i < 1000000000$.

Definition of Fj