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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.StringTokenizer;

public class Main {
    public static void main(String[] args) throws IOException {
        FastScanner scanner = new FastScanner();
        int n = scanner.nextInt();
        Integer[] nums = new Integer[n];
        for (int i = 0; i < nums.length; i++) {
            nums[i] = scanner.nextInt();
        }
        Arrays.sort(nums, (i1, i2)-> Integer.compare(i2, i1));
        long minSum = Math.min(solve(nums, true), solve(nums, false));
        System.out.println(minSum);

    }

    private static long solve(Integer[] numsO, boolean firstEvent) {

        Integer[] nums = new Integer[numsO.length];
        System.arraycopy(numsO, 0, nums, 0, nums.length);
        int firstIndx = searchFirst(nums, firstEvent);
        if(firstIndx == -1){
            firstIndx = 0;
        }

        boolean prevEven = (nums[firstIndx] & 1) == 0;
        nums[firstIndx] = -1;

        for (int i = 0; i < nums.length; i++) {
            if (prevEven){
                for (int j = 0; j < nums.length; j++) {
                    Integer cur = nums[j];
                    if(cur != -1 && (cur & 1) == 1){
                        prevEven = false;
                        nums[j] = -1;
                        break;
                    }
                }
            }else{
                for (int j = 0; j < nums.length; j++) {
                    Integer cur = nums[j];
                    if(cur != -1 && (cur & 1) == 0){
                        prevEven = true;
                        nums[j] = -1;
                        break;
                    }
                }
            }
        }

        return Arrays.stream(nums).filter(i -> i >= 0).mapToLong(i->i).sum();
    }

    private static int searchFirst(Integer[] nums, boolean firstEvent) {
        for (int i = 0; i < nums.length; i++) {
            if (firstEvent){
                if((nums[i] & 1) == 0){
                    return i;
                }
                continue;
            }
            if((nums[i] & 1) == 1){
                return i;
            }

        }
        return -1;
    }

    static class FastScanner {
        StringTokenizer tok = new StringTokenizer("");
        BufferedReader in;

        public FastScanner() {
            in = new BufferedReader(new InputStreamReader(System.in));
        }

        public String next() throws IOException {
            while (!tok.hasMoreElements())
                tok = new StringTokenizer(in.readLine());
            return tok.nextToken();
        }

        public int nextInt() throws IOException {
            return Integer.parseInt(next());
        }

        public long nextLong() throws IOException {
            return Long.parseLong(next());
        }
    }
}
