Parity Alternated Deletions

$Polycarp$有一个有$n$个数的数组，他会轮流从中删去数，比如：奇数-偶数-奇数-偶数-奇数-偶数-奇数-偶数···$\ \ \ $或：偶数-奇数-偶数-奇数-偶数-奇数-偶数-奇数···直到无法删除。 ### 输入格式： 第一行:一个数字$n( 1 \le n \le 2000 1≤n≤2000 )$表示数组大小。 第二行：$n$个数，表示$a_{1},a_{2},a_{3}...a_{n} (0\le a_{i} \le 10^{6})$中的数。 ### 输出格式： 一个数，表示数组中剩余数的**最小和**。 若整个数组可以删除，**输出$0$**

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.

5
1 5 7 8 2

0

6
5 1 2 4 6 3

0

2
1000000 1000000

1000000