Two best friends Serozha and Gena play a game.

Initially there is one pile consisting of n stones on the table. During one move one pile should be taken and divided into an arbitrary number of piles consisting of a1 > a2 > ... > ak > 0 stones. The piles should meet the condition a1 - a2 = a2 - a3 = ... = ak - 1 - ak = 1. Naturally, the number of piles k should be no less than two.

The friends play in turns. The player who cannot make a move loses. Serozha makes the first move. Who will win if both players play in the optimal way?

Input

The single line contains a single integer n (1 ≤ n ≤ 105).

Output

If Serozha wins, print k, which represents the minimal number of piles into which he can split the initial one during the first move in order to win the game.

If Gena wins, print "-1" (without the quotes).

Examples

Input

3


Output

2


Input

6


Output

-1


Input

100


Output

8
import java.util.*;
import java.io.*;
import java.text.*;
public class Main{
    //SOLUTION BEGIN
    //Into the Hardware Mode
    void pre() throws Exception{}
    void solve(int TC)throws Exception{
        int n = ni();
        int[] grundy = new int[1+n], pre = new int[1+n];
        for(int i = 1; i<= n; i++){
            int sum = 0;
            TreeSet<Integer> set = new TreeSet<>();
            for(int k = 2; k <= i; k++){
                sum += k-1;
                if(sum >= i)break;
                if((i-sum)%k != 0)continue;
                int x = (i-sum)/k;
                set.add(pre[x+k-1]^pre[x-1]);
            }
            for(int x = 0; set.contains(x); x++)grundy[i]++;
            pre[i] = pre[i-1]^grundy[i];
        }
        if(grundy[n] == 0)pn(-1);
        else{
            int sum = 0;
            for(int k = 2; k <= n; k++){
                sum += k-1;
                if(sum >= n)break;
                if((n-sum)%k != 0)continue;
                int x = (n-sum)/k;
                if((pre[x+k-1]^pre[x-1]) == 0){
                    pn(k);
                    return;
                }
            }
        }
    }
    class Point{
        int ind;
        double x, y;
        public Point(int I, double X, double Y){ind = I;x = X;y = Y;}
        public Point(double X, double Y){ind = -1;x = X;y = Y;}
        double dist(Point p){return Math.sqrt((x-p.x)*(x-p.x) + (y-p.y)*(y-p.y));}
    }
    class Segment{
        int ind;
        Point a, b;
        public Segment(int I, Point A, Point B){ind = I;a = A;b = B;}
    }
    //SOLUTION END
    void hold(boolean b)throws Exception{if(!b)throw new Exception("Hold right there, Sparky!");}
    void exit(boolean b){if(!b)System.exit(0);}
    long IINF = (long)1e18, mod = (long)1e9+7;
    final int INF = (int)1e9, MX = (int)2e6+5;
    DecimalFormat df = new DecimalFormat("0.0000000");
    double PI = 3.141592653589793238462643383279502884197169399, eps = 1e-7;
    static boolean multipleTC = false, memory = false, fileIO = false;
    FastReader in;PrintWriter out;
    void run() throws Exception{
        if(fileIO){
            in = new FastReader("C:/users/user/desktop/inp.in");
            out = new PrintWriter("C:/users/user/desktop/out.out");
        }else {
            in = new FastReader();
            out = new PrintWriter(System.out);
        }
        //Solution Credits: Taranpreet Singh
        int T = (multipleTC)?ni():1;
        pre();
        for(int t = 1; t<= T; t++)solve(t);
        out.flush();
        out.close();
    }
    public static void main(String[] args) throws Exception{
        if(memory)new Thread(null, new Runnable() {public void run(){try{new Main().run();}catch(Exception e){e.printStackTrace();}}}, "1", 1 << 28).start();
        else new Main().run();
    }
    
    int digit(long s){int ans = 0;while(s>0){s/=10;ans++;}return ans;}
    long gcd(long a, long b){return (b==0)?a:gcd(b,a%b);}
    int gcd(int a, int b){return (b==0)?a:gcd(b,a%b);}
    int bit(long n){return (n==0)?0:(1+bit(n&(n-1)));}
    void p(Object o){out.print(o);}
    void pn(Object o){out.println(o);}
    void pni(Object o){out.println(o);out.flush();}
    String n()throws Exception{return in.next();}
    String nln()throws Exception{return in.nextLine();}
    int ni()throws Exception{return Integer.parseInt(in.next());}
    long nl()throws Exception{return Long.parseLong(in.next());}
    double nd()throws Exception{return Double.parseDouble(in.next());}
 
    class FastReader{
        BufferedReader br;
        StringTokenizer st;
        public FastReader(){
            br = new BufferedReader(new InputStreamReader(System.in));
        }
 
        public FastReader(String s) throws Exception{
            br = new BufferedReader(new FileReader(s));
        }
 
        String next() throws Exception{
            while (st == null || !st.hasMoreElements()){
                try{
                    st = new StringTokenizer(br.readLine());
                }catch (IOException  e){
                    throw new Exception(e.toString());
                }
            }
            return st.nextToken();
        }
 
        String nextLine() throws Exception{
            String str = "";
            try{   
                str = br.readLine();
            }catch (IOException e){
                throw new Exception(e.toString());
            }  
            return str;
        }
    }   
}