There are $N$ mountains in a circle, called Mountain $1$, Mountain $2$, $...$, Mountain $N$ in clockwise order. $N$ is an odd number.

Between these mountains, there are $N$ dams, called Dam $1$, Dam $2$, $...$, Dam $N$. Dam $i$ ($1 \leq i \leq N$) is located between Mountain $i$ and $i+1$ (Mountain $N+1$ is Mountain $1$).

When Mountain $i$ ($1 \leq i \leq N$) receives $2x$ liters of rain, Dam $i-1$ and Dam $i$ each accumulates $x$ liters of water (Dam $0$ is Dam $N$).

One day, each of the mountains received a non-negative even number of liters of rain.

As a result, Dam $i$ ($1 \leq i \leq N$) accumulated a total of $A_i$ liters of water.

Find the amount of rain each of the mountains received. We can prove that the solution is unique under the constraints of this problem.

Input is given from Standard Input in the following format:

```
$N$
$A_1$ $A_2$ $...$ $A_N$
```

Print $N$ integers representing the number of liters of rain Mountain $1$, Mountain $2$, $...$, Mountain $N$ received, in this order.

-   All values in input are integers.
-   $3 \leq N \leq 10^5-1$
-   $N$ is an odd number.
-   $0 \leq A_i \leq 10^9$
-   The situation represented by input can occur when each of the mountains receives a non-negative even number of liters of rain.

4 0 4

If we assume Mountain $1$, $2$, and $3$ received $4$, $0$, and $4$ liters of rain, respectively, it is consistent with this input, as follows:

• Dam $1$ should have accumulated $\frac{4}{2} + \frac{0}{2} = 2$ liters of water.
• Dam $2$ should have accumulated $\frac{0}{2} + \frac{4}{2} = 2$ liters of water.
• Dam $3$ should have accumulated $\frac{4}{2} + \frac{4}{2} = 4$ liters of water.