Sprague Grundy Dividing Piles

/* Sprague Grundy Dividing Piles */

/*********************** let the play begin() *********************************/

int gr[MAX];int ans,f[MAX],root,pre[MAX];

void grundy(int n){
    int y = 0;
    for(int i = 2;;i++){// Number of ways of dividing
        if(i*(i-1)>=2*n)break;
        int x = n - (i*(i-1))/2;
        if(x%i)continue;
        x/=i;
        y = pre[x-1]^pre[x+i-1];
        if(!y&&ans==-1&&n==root)ans = i;//if xor of second step is zero that means 1st player will win because
       // cout<<y<<endl;// second player starts from 2nd step. that's why !y comes .
        f[y] = n;//keep tracking the grundy values
    }
    int cc = 0;
    while(f[cc]==n)cc++;//mex of all grundies is grundy for n
    gr[n] = cc;
    pre[n] = cc;
    pre[n]^=pre[n-1];


}


int main()
{
    booster()
    ///read("input.txt");

    int n;
    cin>>n;
    root = n;
    ans = -1;
    for(int i = 3;i<=n;i++){
        grundy(i);
    }
    if(gr[n])cout<<ans;
    else cout<<-1;


    return 0;
}