Crazy Professor

#include <iostream>
#include <cstdio>
#include <cstdlib>
#include <cmath>
#include <algorithm>
#include <climits>
#include <cstring>
#include <string>
#include <set>
#include <map>
#include <queue>
#include <stack>
#include <vector>
#include <list>
#define rep(i,m,n) for(i=m;i<=n;i++)
#define rsp(it,s) for(set<int>::iterator it=s.begin();it!=s.end();it++)
#define mod 1000000007
#define inf 0x3f3f3f3f
#define vi vector<int>
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define ll long long
#define pi acos(-1.0)
#define pii pair<int,int>
#define Lson L, mid, rt<<1
#define Rson mid+1, R, rt<<1|1
const int maxn=2e5+10;
using namespace std;
ll gcd(ll p,ll q){return q==0?p:gcd(q,p%q);}
ll qpow(ll p,ll q){ll f=1;while(q){if(q&1)f=f*p;p=p*p;q>>=1;}return f;}
int n,m,k,t,p[maxn],now[maxn];
vi mo[maxn];
int find(int x)
{
    return p[x]==x?x:p[x]=find(p[x]);
}
int main()
{
    int i,j;
    scanf("%d",&k);
    rep(i,1,maxn-10)p[i]=i;
    for(i=1;;i++)
    {
        ll q=((ll)i*i/k+1)*k;
        while((j=q-(ll)i*i)<i)
        {
            int x=find(j),y=find(i);
            if(x==y)return 0*printf("%d\n",i);
            else p[x]=y;
            now[j]=i;
            q+=k;
        }
        q=(ll)(i/k+1)*k;
        for(int x:mo[(q-i)%k])
        {
            if(now[x]==i)continue;
            int y=find(x),r=find(i);
            if(y==r)return 0*printf("%d\n",i);
            else p[y]=r;
        }
        mo[(ll)i*i%k].pb(i);
    }
    //system("Pause");
    return 0;
}