my brute force program... works for all cases ...
still getting WA 1..

#include<stdio.h>
long min = 1000000000;

void recur(int arr[] , int n , int finished[] , int finishedCount , int total , long damage)
{
    int i , k , l , sum , tempfinishedCount , flag , a, b , c;
    if( finishedCount == n )
    {
        if( damage < min ) min = damage;    return ;
    }

    if( damage > min ) return ;

    for( i = 0 ; i < n ; i++ )
    {
        k=(i+1)%n;    l=(k+1)%n;    sum=0;    tempfinishedCount=finishedCount;    flag = 0;
        if( !(a=finished[i]) ){    finished[i] = 1;    finishedCount++;    sum+=arr[i];    flag=1;    }
        if( !(b=finished[k]) ){    finished[k] = 1;      finishedCount++;    sum+=arr[k];    flag=1;    }
        if( !(c=finished[l]) ){    finished[l] = 1;      finishedCount++;    sum+=arr[l];    flag=1;    }

        if(!flag) continue;
        total -= sum;     damage+= total;

        recur( arr , n , finished , finishedCount ,total , damage );

        damage-=total;    total += sum;

        finished[i]=a;    finished[k]=b;    finished[l]=c;    finishedCount=tempfinishedCount;

    }
}

int main()
{
    int n , i ,arr[21] , finished[21]={0} , finishedCount = 0 , total;

    scanf("%d",&n);
    for( i = 0  ; i < n ; i++ )
    {    scanf("%d",&arr[i]);    total+=arr[i];    }

    if( n <=3 ) printf("0\n");
    else
    {
    recur( arr , n , finished , finishedCount , total , 0 );

    printf("%ld\n",min);
}

    return 0;

}