#include <map>#include <queue>#include <cstdio>#include <string>#include <vector>#include <algorithm>using namespace std;void dump(const vector<int>& v) { for (int i = 0; i < (int)v.size(); ++i) { printf("%d ", v[i]); } puts("");}vector<int> P[16], Q[16];map<int, int> minv(int n, const vector<int>& p) { map<int, int> ret; for (int i = 0; i < n; ++i) { ret[p[i]] = i; } return ret;}vector<int> inv(int n, const vector<int>& p) { vector<int> ret(n); for (int i = 0; i < n; ++i) { ret[p[i]] = i; } return ret;}vector<int> per(int n, const vector<int>& s, const vector<int>& t) { map<int, int> rt = minv(n, t); vector<int> ret(n); for (int i = 0; i < n; ++i) { ret[i] = rt[s[i]]; } return inv(ret.size(), ret);}vector<string> gao(int n, vector<int> p) { if (n == 1) { if (p[0] == 0) { return vector<string>(1, "0"); } else { return vector<string>(1, "1"); } } else { int s = 1 << n; int m = 1 << (n - 1); vector<int> rp = inv(s, p); vector<int> d(s, 0); for (int i = 0; i < s; ++i) { if (d[i] != 0) { continue; } queue<int> q; d[i] = -1; q.push(i); while (!q.empty()) { int k = q.front(); q.pop(); if (d[k ^ 1] == 0) { d[k ^ 1] = -d[k]; q.push(k ^ 1); } if (d[p[rp[k] ^ 1]] == 0) { d[p[rp[k] ^ 1]] = -d[k]; q.push(p[rp[k] ^ 1]); } } } vector<int> xs, xt, ys, yt; string x, y; for (int i = 0; i < s; i += 2) { if (d[i] == -1) { x += '0'; xs.push_back(i); ys.push_back(i ^ 1); } else { x += '1'; ys.push_back(i); xs.push_back(i ^ 1); } } for (int i = 0; i < s; i += 2) { if (d[p[i]] == -1) { y += '0'; xt.push_back(p[i]); yt.push_back(p[i ^ 1]); } else { y += '1'; yt.push_back(p[i]); xt.push_back(p[i ^ 1]); } } vector<string> ret, left, right; ret.push_back(x); left = gao(n - 1, per(m, xs, xt)); right = gao(n - 1, per(m, ys, yt)); for (int i = 0; i < (int)left.size(); ++i) { ret.push_back(left[i] + right[i]); } ret.push_back(y); return ret; }}void init() { for (int n = 1; n <= 13; ++n) { P[n].resize(1 << n); for (int j = 0; j < (int)P[n].size(); ++j) { P[n][j] = (j >> 1) ^ ((j & 1) << (n - 1)); } Q[n] = inv(P[n].size(), P[n]); }}int main() { bool blank = false; int n; vector<int> p; vector<string> s; init(); while (scanf("%d", &n) != EOF && n > 0) { if (blank) { puts(""); } else { blank = true; } p.resize(1 << n); for (int i = 0; i < (int)p.size(); ++i) { scanf("%d", &p[i]); } s = gao(n, p); for (int i = 0; i < (int)s.size(); ++i) { puts(s[i].c_str()); } } return 0;}
