#include #include #include #include #include #include #include #include #define rep(i, a, b) for (int i = int(a); i < int(b); i++) using namespace std; using ll = long long int; using P = pair; // clang-format off #ifdef _DEBUG_ #define dump(...) do{ cerr << __LINE__ << ":\t" << #__VA_ARGS__ << " = "; debug_print(__VA_ARGS__); } while(false) template void debug_print(const T &t, const Ts &...ts) { cerr << t; ((cerr << ", " << ts), ...); cerr << endl; } #else #define dump(...) do{ } while(false) #endif template vector make_v(size_t a, T b) { return vector(a, b); } template auto make_v(size_t a, Ts... ts) { return vector(a, make_v(ts...)); } template bool chmin(T &a, const T& b) { if (a > b) {a = b; return true; } return false; } template bool chmax(T &a, const T& b) { if (a < b) {a = b; return true; } return false; } template void print(const T& t, const Ts&... ts) { cout << t; ((cout << ' ' << ts), ...); cout << '\n'; } template void input(Ts&... ts) { (cin >> ... >> ts); } template istream &operator,(istream &in, T &t) { return in >> t; } // clang-format on int main() { cin.tie(nullptr); ios::sync_with_stdio(false); int n; input(n); int len = 1; while (len * len <= n) { len++; } vector isSquare(n + 1, -1); rep(i, 0, len) { isSquare[i * i] = i; } int ans = n + 1; rep(a, 0, len) { if (a * a > n) break; rep(b, a, len) { if (a * a + b * b > n) break; rep(c, b, len) { int rest = n - a * a - b * b - c * c; if (rest < 0 || rest > n || isSquare[rest] == -1) continue; chmin(ans, a + b + c + isSquare[rest]); } } } string out = string(ans, 'A'); rep(a, 0, len) { if (a * a > n) break; rep(b, a, len) { if (a * a + b * b > n) break; rep(c, b, len) { int rest = n - a * a - b * b - c * c; if (rest < 0 || rest > n || isSquare[rest] == -1) continue; if (ans == a + b + c + isSquare[rest]) { string s = ""; vector length; if (a > 0) length.push_back(a); if (b > 0) length.push_back(b); if (c > 0) length.push_back(c); if (rest > 0) length.push_back(rest); sort(length.begin(), length.end()); do { int zero = 0; for (int l : length) { rep(i, 0, l) { s += char('0' + (zero + i) % 2); } zero = (zero + l + 1) % 2; } chmin(out, s); } while (next_permutation(length.begin(), length.end())); } } } } dump(ans); print(out); /* vector length; for (int i = 1; i < len; i += 2) { length.push_back(i); } for (int i = (len - 1) / 2 * 2; i >= 2; i -= 2) { length.push_back(i); } length.push_back(0); reverse(length.begin(), length.end()); const short int inf = 1 << 14; auto dp = make_v(len, n + 1, inf); dp[0][0] = 0; rep(i, 1, len) { int val = length[i]; rep(j, val * val, n + 1) { if (dp[i - 1][j - val * val] < inf) { chmin(dp[i][j], short(dp[i - 1][j - val * val] + val)); } if (dp[i][j - val * val] < inf) { chmin(dp[i][j], short(dp[i][j - val * val] + val)); } } rep(j, 0, n + 1) { chmin(dp[i][j], dp[i - 1][j]); } } dump(dp[len - 1][n]); int sum = n, idx = len - 1; int zero = 0; auto display = [&](int l) { rep(i, 0, l) { cout << char((zero + i) % 2 + '0'); } zero = (zero + l * l + 1) % 2; }; while (sum > 0) { int val = length[idx]; if (sum >= val * val && dp[idx][sum] == dp[idx][sum - val * val] + val) { display(val); sum -= val * val; } else if (sum >= val * val && dp[idx][sum] == dp[idx - 1][sum - val * val] + val) { display(val); sum -= val * val; idx--; } else { idx--; } } cout << endl; */ return 0; }