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
//package com.company;

import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;

public class B {


    public static void main(String[] args) throws Exception {

        FastReader in = new FastReader(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        int n = in.nextInt();
        Integer even[] = new Integer[n];
        Integer odd[] = new Integer[n];

        Arrays.fill(even, 0);
        Arrays.fill(odd, 0);

        int evs = 0;
        int ods = 0;

        int ev = 0;
        int od = 0;
        for (int i = 0; i < n; i++) {
            int a = in.nextInt();
            if (a % 2 == 0) {
                even[i] = a;
                evs += a;
                ev++;
            } else {
                odd[i] = a;
                ods += a;
                od++;
            }


        }


        Arrays.sort(even, Collections.reverseOrder());
        Arrays.sort(odd, Collections.reverseOrder());

        int tempE = evs;
        int tempO = ods;

        int o = 0;
        int e = 0;

        for (int i = 0; i < n; i++) {
            if (i % 2 == 0) {
                if (e == ev) {
                    break;
                }
                tempE -= even[e];
                e++;
            } else {
                if (o == od) {
                    break;
                }
                tempO -= odd[o];
                o++;
            }
        }

        int min = tempE > tempO ? tempE : tempO;

        tempE = evs;
        tempO = ods;

        o = 0;
        e = 0;
        for (int i = 0; i < n; i++) {
            if (i % 2 == 1) {
                if (e == ev) {
                    break;
                }
                tempE -= even[e];
                e++;
            } else {
                if (o == od) {
                    break;
                }
                tempO -= odd[o];
                o++;
            }
        }
        int tempM = tempE > tempO ? tempE : tempO;
        min = min < tempM ? min : tempM;

        pw.println(min);

        pw.close();
    }


    static class FastReader {
        InputStream is;
        private byte[] inbuf = new byte[1024];
        private int lenbuf = 0, ptrbuf = 0;

        public FastReader(InputStream is) {
            this.is = is;
        }

        public int readByte() {
            if (lenbuf == -1) throw new InputMismatchException();
            if (ptrbuf >= lenbuf) {
                ptrbuf = 0;
                try {
                    lenbuf = is.read(inbuf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (lenbuf <= 0) return -1;
            }
            return inbuf[ptrbuf++];
        }

        public boolean isSpaceChar(int c) {
            return !(c >= 33 && c <= 126);
        }

        public int skip() {
            int b;
            while ((b = readByte()) != -1 && isSpaceChar(b)) ;
            return b;
        }

        public String next() {
            int b = skip();
            StringBuilder sb = new StringBuilder();
            while (!(isSpaceChar(b))) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }

        public String nextLine() {
            int b = readByte();
            StringBuilder sb = new StringBuilder();
            while (b != '\n' || b != '\r') {
                sb.appendCodePoint(b);
            }
            return sb.toString();
        }

        public int nextInt() {
            int num = 0, b;
            boolean minus = false;
            while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
            if (b == '-') {
                minus = true;
                b = readByte();
            }
            while (true) {
                if (b >= '0' && b <= '9') {
                    num = (num << 3) + (num << 1) + (b - '0');
                } else {
                    return minus ? -num : num;
                }
                b = readByte();
            }
        }

        public long nextLong() {
            long num = 0;
            int b;
            boolean minus = false;
            while ((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-')) ;
            if (b == '-') {
                minus = true;
                b = readByte();
            }

            while (true) {
                if (b >= '0' && b <= '9') {
                    num = (num << 3) + (num << 1) + (b - '0');
                } else {
                    return minus ? -num : num;
                }
                b = readByte();
            }
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public char[] next(int n) {
            char[] buf = new char[n];
            int b = skip(), p = 0;
            while (p < n && !(isSpaceChar(b))) {
                buf[p++] = (char) b;
                b = readByte();
            }
            return n == p ? buf : Arrays.copyOf(buf, p);
        }

        public char nextChar() {
            return (char) skip();
        }
    }


}

