Given is an integer N. Find the minimum possible positive integer k such that (1+2+\cdots+k) is a multiple of N. It can be proved that such a positive integer k always exists.

Constraints

* 1 \leq N \leq 10^{15}
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N


Output

Print the answer in a line.

Examples

Input

11


Output

10


Input

20200920


Output

1100144
import java.util.*;
import java.io.*;
 
public class Main {
    public static void main(String[] args) throws Exception {
        FastScanner sc = new FastScanner(System.in);
        PrintWriter pw = new PrintWriter(System.out);
        long n = sc.nextLong()*2;
        ArrayList<Long> arr = new ArrayList<Long>();
        long max = (long)Math.sqrt(n);
        for(long i = 1; i <= max; i++){
            if(n%i == 0){
                arr.add(i);
                arr.add(n/i);
            }
        }
        Collections.sort(arr);
        //pw.println(arr);
        long[] a = {0,-1};
        long[] b = new long[2];
        long ans = Long.MAX_VALUE;
        for(long v : arr){
            b[0] = v;
            b[1] = n/v;
            long[] ret = MathLib.crt(a,b);
            //pw.println(ret[0] + " " + ret[1]);
            if(ret[0] != 0 && ret[1] != 0){
                ans = Math.min(ret[0],ans);
            }
        }
        pw.println(ans);
        pw.flush();
    }

    static class GeekInteger {
        public static void save_sort(int[] array) {
            shuffle(array);
            Arrays.sort(array);
        }
 
        public static int[] shuffle(int[] array) {
            int n = array.length;
            Random random = new Random();
            for (int i = 0, j; i < n; i++) {
                j = i + random.nextInt(n - i);
                int randomElement = array[j];
                array[j] = array[i];
                array[i] = randomElement;
            }
            return array;
        }
 
    }
}

class MathLib{
    private static long safe_mod(long x, long m){
        x %= m;
        if(x<0) x += m;
        return x;
    }

    private static long[] inv_gcd(long a, long b){
        a = safe_mod(a, b);
        if(a==0) return new long[]{b,0};

        long s=b, t=a;
        long m0=0, m1=1;
        while(t>0){
            long u = s/t;
            s -= t*u;
            m0 -= m1*u;
            long tmp = s; s = t; t = tmp;
            tmp = m0; m0 = m1; m1 = tmp;
        }
        if(m0<0) m0 += b/s;
        return new long[]{s,m0};
    }

    public static long pow_mod(long x, long n, long m){
        assert(n >= 0 && m >= 1);
        long ans = 1;
        while(n > 0){
            if(n%2==1) ans = (ans * x) % m;
            x = (x*x) % m;
            n /= 2;
        }
        return ans;
    }

    public static long[] crt(long[] r, long[] m){
        assert(r.length == m.length);
        int n = r.length;

        long r0=0, m0=1;
        for(int i=0; i<n; i++){
            assert(1 <= m[i]);
            long r1 = safe_mod(r[i], m[i]), m1 = m[i];
            if(m0 < m1){
                long tmp = r0; r0 = r1; r1 = tmp;
                tmp = m0; m0 = m1; m1 = tmp;
            }
            if(m0%m1 == 0){
                if(r0%m1 != r1) return new long[]{0,0};
                continue;
            }

            long[] ig = inv_gcd(m0, m1);
            long g = ig[0], im = ig[1];

            long u1 = m1/g;
            if((r1-r0)%g != 0) return new long[]{0,0};

            long x = (r1-r0) / g % u1 * im % u1;

            r0 += x * m0;
            m0 *= u1;
            if(r0<0) r0 += m0;
            //System.err.printf("%d %d\n", r0, m0);
        } 
        return new long[]{r0, m0};
    }
    public static long floor_sum(long n, long m, long a, long b){
        long ans = 0;
        if(a >= m){
            ans += (n-1) * n * (a/m) / 2;
            a %= m;
        }
        if(b >= m){
            ans += n * (b/m);
            b %= m;
        }

        long y_max = (a*n+b) / m;
        long x_max = y_max * m - b;
        if(y_max == 0) return ans;
        ans += (n - (x_max+a-1)/a) * y_max;
        ans += floor_sum(y_max, a, m, (a-x_max%a)%a);
        return ans;
    }
}
class FastScanner {
    private BufferedReader reader = null;
    private StringTokenizer tokenizer = null;
    public FastScanner(InputStream in) {
        reader = new BufferedReader(new InputStreamReader(in));
        tokenizer = null;
    }

    public String next() {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                tokenizer = new StringTokenizer(reader.readLine());
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken();
    }

    public String nextLine() {
        if (tokenizer == null || !tokenizer.hasMoreTokens()) {
            try {
                return reader.readLine();
            } catch (IOException e) {
                throw new RuntimeException(e);
            }
        }
        return tokenizer.nextToken("\n");
    }

    public long nextLong() {
        return Long.parseLong(next());
    }

    public int nextInt() {
        return Integer.parseInt(next());
    }

    public double nextDouble() {
         return Double.parseDouble(next());
    }
    
    public String[] nextArray(int n) {
        String[] a = new String[n];
        for (int i = 0; i < n; i++)
            a[i] = next();
        return a;
    }

    public int[] nextIntArray(int n) {
        int[] a = new int[n];
        for (int i = 0; i < n; i++)
            a[i] = nextInt();
        return a;
    }

    public long[] nextLongArray(int n) {
        long[] a = new long[n];
        for (int i = 0; i < n; i++)
            a[i] = nextLong();
        return a;
    } 
}
