Parity Alternated Deletions
Description
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.
Input
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 $a$.
Output
Print one integer — the minimum possible sum of non-deleted elements of the array after end of the game.
Samples
5
1 5 7 8 2
0
6
5 1 2 4 6 3
0
2
1000000 1000000
1000000