#include "ancient2.h"
#include <iostream>
#include <vector>
#include <bitset>
using namespace std;
int n, m = 0;
vector <int> ans(1e3, -1);
vector <bitset <1001>> v(1e3);
void get1(int x) {
vector <int> a(x + 3, 0);
vector <int> b(x + 3, 0);
for (int i = 0; i < x; i++) a[i] = b[i] = i + 1;
a[x] = x + 1;
b[x] = x + 2;
a[x + 1] = b[x + 1] = x + 1;
a[x + 2] = b[x + 2] = x + 2;
ans[x] = Query(x + 3, a, b) - x - 1;
}
void solve1() {
for (int i = 0; i < m - 2; i++) get1(i);
}
void get2(int x) {
vector <int> s(1, -1);
s.push_back(1);
for (int i = x + 1; i < n; i++) s.push_back(ans[i]);
s.push_back(-1);
int l = s.size() - 2;
vector <int> pi(l + 1, 0);
pi[0] = -1;
for (int i = 1; i <= l; i++) {
for (int j = pi[i - 1]; j >= 0; j = pi[j]) {
if (s[i] == s[j + 1]) { pi[i] = j + 1; break; }
}
}
vector <int> a(l + 1, 0);
vector <int> b(l + 1, 1);
for (int i = 1; i <= l; i++) {
a[i] = (s[i + 1] == 0 ? i + 1 : a[pi[i]]);
b[i] = (s[i + 1] == 1 ? i + 1 : b[pi[i]]);
}
ans[x] = (Query(l + 1, a, b) == l);
}
void solve2() {
for (int i = n - 1; i > n - m; i--) get2(i);
}
int make_query(int p, int q) {
vector <int> a(2 * p, 0);
vector <int> b(2 * p, 0);
for (int i = 0; i < 2 * p; i++) a[i] = b[i] = (i + 1) % p + i / p * p;
swap(b[q], b[p + q]);
return (Query(2 * p, a, b) >= p);
}
void try_add(int p, int q) {
bitset <1001> b;
for (int i = 0; i < n; i++) b[i] = int(i % p == q);
b[1000] = 0;
for (int i = 0; i < n; i++) if (b[i]) b ^= v[i];
int k = -1;
for (int i = 0; i < n; i++) if (b[i]) k = i;
if (k == -1) return;
b[1000] = int(b[1000]) ^ make_query(p, q);
for (int i = 0; i < n; i++) if (v[i][k]) v[i] ^= b;
v[k] = b;
}
void solve3() {
for (int i = 0; i < n; i++) {
if (ans[i] == -1) continue;
v[i][i] = 1;
v[i][1000] = ans[i];
}
for (int i = 1; i <= 60; i++) {
for (int j = 0; j < i; j++) {
try_add(i, j);
}
}
for (int i = 0; i < n; i++) ans[i] = v[i][1000];
}
string Solve(int N) {
n = N;
solve1();
solve2();
solve3();
string s;
for (int i = 0; i < n; i++) s.push_back('0' + ans[i]);
return s;
}
