Problem Statement :
Polycarp has an array a consisting of n integers.
He wants to play a game with this array. The game consists of several moves. On the first move, he chooses any element and deletes it (after the first move the array contains n−1 elements). For each of the next moves he chooses any element with the only restriction: its parity should differ from the parity of the element deleted on the previous move. In other words, he alternates parities (even-odd-even-odd-… or odd-even-odd-even-…) of the removed elements. Polycarp stops if he can’t make a move.
Formally:
If it is the first move, he chooses any element and deletes it;
If it is the second or any next move:
if the last deleted element was odd, Polycarp chooses any even element and deletes it;
if the last deleted element was even, Polycarp chooses any odd element and deletes it.
If after some move Polycarp cannot make a move, the game ends.
Polycarp’s goal is to minimize the sum of non-deleted elements of the array after the end of the game. If Polycarp can delete the whole array, then the sum of non-deleted elements is zero.
Help Polycarp find this value.
Input Format:
The first line of the input contains one integer n (1≤n≤20001≤n≤2000) — the number of elements of aa.
The second line of the input contains n integers a1,a2,…,ana1,a2,…,an (0≤ai≤1060≤ai≤106), where ai is the i-th element of a.
Output Format:
Print one integer — the minimum possible sum of non-deleted elements of the array after the end of the game.
Given:
5
1 5 7 8 2Output:
0Explanation of given Test Cases :
Here the minimum case occurs when anyone odd number is deleted and then repeating the process all the elements of the array are deleted.