#include <bits/stdc++.h>
using namespace std;
typedef signed long long ll;

#undef _P
#define _P(...) (void)printf(__VA_ARGS__)
#define FOR(x,to) for(x=0;x<(to);x++)
#define FORR(x,arr) for(auto& x:arr)
#define FORR2(x,y,arr) for(auto& [x,y]:arr)
#define ITR(x,c) for(__typeof(c.begin()) x=c.begin();x!=c.end();x++)
#define ALL(a) (a.begin()),(a.end())
#define ZERO(a) memset(a,0,sizeof(a))
#define MINUS(a) memset(a,0xff,sizeof(a))
//-------------------------------------------------------

int T;
ll N;

ll modpow(ll a, ll n,ll mo) {
	ll r=1;a%=mo;
	while(n) r=r*((n%2)?a:1)%mo,a=a*a%mo,n>>=1;
	return r;
}

void solve() {
	int i,j,k,l,r,x,y; string s;
	
	cin>>T;
	while(T--) {
		cin>>N;
		if(N==1) {
			cout<<1<<endl;
			continue;
		}
		N=2*N-1;
		y=N;
		int v=1;
		for(x=2;x*x<=y;x++) {
			j=1;
			while(y%x==0) y/=x,j*=x;
			if(j>1) v*=j/x*(x-1);
		}
		if(y>1) v*=(y-1);
		ll mi=3LL<<30;
		for(x=1;x*x<=v;x++) if(v%x==0) {
			if(x<mi && modpow(2,x,N)==1) mi=x;
			if(v/x<mi && modpow(2,v/x,N)==1) mi=v/x;
		}
		cout<<mi<<endl;
		
	}
}


int main(int argc,char** argv){
	string s;int i;
	if(argc==1) ios::sync_with_stdio(false), cin.tie(0);
	FOR(i,argc-1) s+=argv[i+1],s+='\n'; FOR(i,s.size()) ungetc(s[s.size()-1-i],stdin);
	cout.tie(0); solve(); return 0;
}