Minimum Sum

There are two arrays of positive integers $a[\mathrm{1..}n]$ and $b[\mathrm{1..}n]$. Find a permutation $i_1,i_2,...,i_n$ of numbers $1,2,...,n$, for which the sum

is minimal. Each number should appear only once in the permutation.

Input

The first line contains the number of elements $n(n\le 100)$ in the 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 $10^6$.

Output

Print the minimal value of required sum.

Examples