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
#include<bits/stdc++.h>
using namespace std;

long long n,ans;
bool p;

void exgcd(long long a,long long b,long long &d,long long &x,long long &y){
	if(!b)d=a,x=1,y=0;
	else exgcd(b,a%b,d,y,x),y-=(a/b)*x;
}

int main(){
	scanf("%lld",&n);
	n*=2LL;
	ans=n-1;
	for(long long i=1;i*i<=n;i++)if(n%i==0){
		long long d,x,y;
		exgcd(i,n/i,d,x,y);
		if(d>1)continue;
		if(x>0&&i*x-1>0)ans=min(ans,i*x-1);
		if(x<0&&i*(-x)>0)ans=min(ans,i*(-x)); 
	}
	printf("%lld\n",ans);
	return 0;
}