|Codeforces Round #550 (Div. 3)|
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.
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.
5 1 5 7 8 2
6 5 1 2 4 6 3
2 1000000 1000000