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
n=int(input())
O=[]
E=[]
OO=[]
EE=[]
p=input().rstrip().split(' ')
for i in range(0,len(p)):
    if int(p[i])%2==0:
        E.append(int(p[i]))
        EE.append(int(p[i]))
    else:
        O.append(int(p[i]))
        OO.append(int(p[i]))
if len(E)+1==len(O) or len(O)+1==len(E) or len(O)==len(E):
    print(0)
else:
    O.sort(key=int,reverse=True)
    OO.sort(key=int,reverse=True)
    E.sort(key=int,reverse=True)
    EE.sort(key=int,reverse=True)
    i=0;
    while(len(O)!=0 or len(E)!=0):
        if i%2==0:
            if len(O)!=0:
                i+=1;
                del(O[0])
            else:
                break;
        else:
            if len(E)!=0:
                i+=1;
                del(E[0])
            else:
                break;
    G=0;
    while(len(OO)!=0 or len(EE)!=0):
        if G%2==0:
            if len(EE)!=0:
                G+=1;
                del(EE[0])
            else:
                break;
        else:
            if len(OO)!=0:
                G+=1;
                del(OO[0])
            else:
                break;
    S=0;
    D=0;
    for i in range(0,len(O)):
        S=S+int(O[i])
    for i in range(0,len(E)):
        S=S+int(E[i])
    for i in range(0,len(OO)):
        D=D+int(OO[i])
    for i in range(0,len(EE)):
        D=D+int(EE[i])
    print(min(S,D))
