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.

Input

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

The second line of the input contains n integers a_1, a_2, ..., a_n (0 ≤ a_i ≤ 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.

Examples

Input


5
1 5 7 8 2


Output


0


Input


6
5 1 2 4 6 3


Output


0


Input


2
1000000 1000000


Output


1000000

import java.util.*;

public class B {

    static int MAX_N = 2000;
    static int oddCount = 0, evenCount = 0, sum = 0;
    static Integer[] odd = new Integer[MAX_N], even = new Integer[MAX_N];

    public static void main(String[] args) {
        Scanner in = new Scanner(System.in);

        int N = in.nextInt();

        while (N-- > 0) {
            int num = in.nextInt();
            if (num%2 == 0) even[evenCount++] = num;
            else odd[oddCount++] = num;

            sum += num;
        }

        Arrays.sort(odd, 0, oddCount, Collections.reverseOrder());
        Arrays.sort(even, 0, evenCount, Collections.reverseOrder());

        int ans = Math.min(getRemainingAfterRemove(true), getRemainingAfterRemove(false));
        System.out.println(ans);
    }

    static int getRemainingAfterRemove(boolean startWithOdd) {
        boolean nextParityOdd = startWithOdd;
        int oddPos = 0, evenPos = 0, sumRemoved = 0;
        while ((nextParityOdd && oddPos < oddCount) || (!nextParityOdd && evenPos < evenCount)) {
            if (nextParityOdd) sumRemoved += odd[oddPos++];
            else sumRemoved += even[evenPos++];
            nextParityOdd = !nextParityOdd;
        }

        return sum - sumRemoved;
    }
}
