For 2 arrays $C$ and $D$ both of length $n$, let:
$$f(C, D, n) = C_1 \times D_1 + C_2 \times D_2 + ... + C_n \times D_n$$
Given 2 integer arrays $A, B$ both of length $n$. Find 4 indices $L_A, R_A, L_B, R_B$ and $R_A - L_A + 1= R_B - L_B + 1 = len$ so that the value:
$$f(A[L_A...R_A], B[L_B...R_B], len)$$
is maximum.
### Input
- The first line contains an integer $n$.
- The second line contains $n$ integers $A_i$.
- The third line contains $n$ integers $B_i$.
### Output
- Print the maxmimum value.
### Constraints
- $1 \le n \le 5000$.
- $0 \le |A_i| \le 10^6$.
### Example
Input:
```
5
-1 6 -1 3 0
1 1 1 1 1
```
Output:
```
8
```
