Description

Given $n$ numbers $q_1,q_2, \dots q_n$, define

$$F_j~=~\sum_{i = 1}^{j - 1} \frac{q_i \times q_j}{(i - j)^2}~-~\sum_{i = j + 1}^{n} \frac{q_i \times q_j}{(i - j)^2}$$$$E_i~=~\frac{F_i}{q_i}$$

For $1 \leq i \leq n$, find the value of $E_i$.

Input Format

The first line contains an integer $n$.

Each of the following $n$ lines contains a real number. The number on the $(i+1)$-th line represents $q_i$.

Output Format

Output $n$ lines, each containing a real number. The number on the $i$-th line represents $E_i$.

Your output is considered correct if it differs from the standard answer by at most $10^{-2}$.

5
4006373.885184
15375036.435759
1717456.469144
8514941.004912
1410681.345880

-16838672.693
3439.793
7509018.566
4595686.886
10903040.872

Hint

Constraints
For $30\%$ of the testdata, $n \leq 1000$.
For $50\%$ of the testdata, $n \leq 6 \times 10^4$.
For $100\%$ of the testdata, $1 \leq n \leq 10^5$, $0 < q_i < 10^9$.

Translated by ChatGPT 5