#include "ancient2.h"
#include<bits/stdc++.h>
#define pb push_back
#define all(v) v.begin(),v.end()
#define forf(i,s,e) for(int i = s; i<=e; i++)
#define forb(i,s,e) for(int i = s; i>=e; i--)
#define idx(i,v) lower_bound(all(v),i)-v.begin()
#define comp(v) v.erase(unique(all(v)),v.end())
#define sz(v) (int)v.size()
#define fs first
#define se second
#define SP << " " <<
#define LN << "\n"
#define IO cin.tie(0);cout.tie(0);ios_base::sync_with_stdio(false);
using namespace std;
typedef long long ll;
ll inf = 1e18;
const int N = 1000;
string ans;
void go(int n){
vector<int> A(n+2), B(n+2);
forf(i,0,n-1) A[i] = i+1,B[i] = i+1;
A[n-1] = n, B[n-1] =n+1;
A[n] = n, B[n] = n, A[n+1] = n+1, B[n+1] = n+1;
if(Query(sz(A),A,B) == n) ans[n-1] = '0';
else ans[n-1] = '1';
}
void go2(int s){
ans[s] = '0';
string t; forf(i,s,N-1) t.pb(ans[i]);
int n = sz(t); t.pb('-');
vector<int> A(n+1), B(n+1);
forf(i,0,n){
int l = min(n,i+1);
while(l){
string tmp = t.substr(i+1-l,l-1) + '0';
if(t.substr(0,l) == tmp) break;
l--;
}
A[i] = l;
l = min(n,i+1);
while(l){
string tmp = t.substr(i+1-l,l-1) + '1';
if(t.substr(0,l) == tmp) break;
l--;
}
B[i] = l;
}
if(Query(sz(A),A,B) != n) ans[s] = '1';
}
bool cyc(int p, int q){
vector<int> A(2*p), B(2*p);
forf(i,0,p-1) A[i] = (i+1)%p, B[i] = (i+1)%p,
A[i+p] = p+(i+1)%p, B[i+p] = p+(i+1)%p;
B[q] = p+(q+1)%p; B[p+q] = (q+1)%p;
return (Query(sz(A),A,B) >= p);
}
const int s = 100, e = 900;
void solve(){
const int n = e-s+1;
vector<bitset<n+1> > mat(n,bitset<n+1>(0));
int cnt = 0;
forf(i,1,100) forf(j,0,i-1){
if(cnt == n) break;
bitset<n+1> tmp(0);
forf(k,s,e) if(k%i == j) tmp[k-s]=true;
forf(k,0,s-1) if(k%i == j && ans[k] == '1') tmp[n] = !tmp[n];
forf(k,e+1,N-1) if(k%i == j && ans[k] == '1') tmp[n] = !tmp[n];
int c = 0;
while(c<n){
if(tmp[c]) {
if (mat[c][c]) tmp ^= mat[c];
else {
mat[c] = tmp, cnt++;
mat[c][n] = mat[c][n] ^ cyc(i, j);
break;
}
}
else c++;
}
}
forf(r,0,n-1) forf(i,0,r-1) if(mat[i][r]) mat[i] ^= mat[r];
forf(i,s,e) ans[i] = '0'+mat[i-s][n];
}
std::string Solve(int N) {
ans.resize(N,'-');
forf(i,1,s) go(i);
forb(i,N-1,e+1) go2(i);
solve();
return ans;
}
