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≤n≤2000) — the number of elements of a.
The second line of the input contains n integers a1, a2, ..., an (0≤ai≤10^6), where ai 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