A12539 | Parity Alternated Deletions

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 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.

The first line of the input contains one integer $n$ ( $1 \le n \le 2000$ ) — the number of elements of $a$ .

The second line of the input contains $n$ integers $a_1, a_2, \dots, a_n$ ( $0 \le a_i \le 10^6$ ), where $a_i$ is the $i$ -th element of $a$ .

Print one integer — the minimum possible sum of non-deleted elements of the array after end of the game.