Sums of Symmetric Pairs (Tổng từng cặp đối xứng)

Source: Phước Hưng OJ

Version: Phuoc Hung OJ Extended

Problem

Given $a_0,a_1,\ldots,a_{n-1}$, let

For every $0\le i<k$, define

If $n$ is odd, keep the unpaired middle element unchanged:

Thus the result length is $m=\lceil n/2\rceil$. Print $b_0,\ldots,b_{m-1}$.

Input

The first line contains $n$. The second line contains $n$ integers $a_i$.

Output

Print the $m=\lceil n/2\rceil$ integers of $b$ on one line.

Subtask

Subtask 1 (20 points): $1\le n\le10$, $|a_i|\le10^3$.

Subtask 2 (30 points): $1\le n\le5000$, $|a_i|\le10^6$.

Subtask 3 (50 points): $1\le n\le2\cdot10^5$, $|a_i|\le10^9$.

Example

Input

7
2 5 -1 8 4 9 3

Output

5 14 3 8

Explanation

The sample follows the mathematical definition above.