Marisa has $n$ colorful potion bottles arranged in a row. Each bottle, labeled $i$, has a color $A_i$ ranging from $0$ to $99$.
Marisa aims to combine all the bottles into a single bottle. She can select two adjacent bottles with colors $a$ and $b$, and mix them to create a new bottle with a color of $(a+b) \mod 100$. The amount of fumes released during this mixing process is given by $a \times b$.
To minimize the amount of fumes released, Marisa needs to determine the minimum amount of fumes when she mixes all $n$ bottles together.
### Input
- A single line contains an integer $n$.
- The second line contains $n$ integers $A_i$.
### Output
- Print the minimum amount of fumes.
### Constraints
- $1 \le n \le 500$.
### Example
Input:
```
3
40 60 20
```
Output:
```
2400
```
