Competitions

# Minimum Sum

Two arrays of positive integers are given: a1..n and b1..n. Find the permutation i1, i2, ..., in of numbers 1, 2, ..., n, for which the sum

a1 * bi1 + ... + an * bin

is minimal. Each number must be included in permutation only once.

#### Input

The first line contains the number of elements n (n100) in arrays. The second line contains the elements of the first array, and the third line contains the elements of the second array. The array elements do not exceed 106.

#### Output

Print the minimal value of required sum.

Time limit 1 second
Memory limit 128 MiB
Input example #1
5
7 2 4 3 10
5 11 6 9 6

Output example #1
165