Please, try EDU on Codeforces! New educational section with videos, subtitles, texts, and problems.
×

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

B. Parity Alternated Deletions

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputPolycarp 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 $$$n$$$ ($$$1 \le n \le 2000$$$) — 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.

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

Codeforces (c) Copyright 2010-2020 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Jul/07/2020 23:21:17 (i2).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|