#include "bits/stdc++.h" using namespace std; #ifdef _DEBUG #include "dump.hpp" #else #define dump(...) #endif #define int long long #define rep(i,a,b) for(int i=(a);i<(b);i++) #define rrep(i,a,b) for(int i=(b)-1;i>=(a);i--) #define all(c) begin(c),end(c) const int INF = sizeof(int) == sizeof(long long) ? 0x3f3f3f3f3f3f3f3fLL : 0x3f3f3f3f; const int MOD = 1'000'000'007; template bool chmax(T &a, const T &b) { if (a < b) { a = b; return true; } return false; } template bool chmin(T &a, const T &b) { if (b < a) { a = b; return true; } return false; } template struct ModInt { static const int kMod = MOD; unsigned x; ModInt() :x(0) {} ModInt(signed x_) { x_ %= MOD; if (x_ < 0)x_ += MOD; x = x_; } ModInt(signed long long x_) { x_ %= MOD; if (x_ < 0)x_ += MOD; x = x_; } int get()const { return (int)x; } ModInt &operator+=(ModInt m) { if ((x += m.x) >= MOD)x -= MOD; return *this; } ModInt &operator-=(ModInt m) { if ((x += MOD - m.x) >= MOD)x -= MOD; return *this; } ModInt &operator*=(ModInt m) { x = (unsigned long long)x*m.x%MOD; return *this; } ModInt &operator/=(ModInt m) { return *this *= m.inverse(); } ModInt operator+(ModInt m)const { return ModInt(*this) += m; } ModInt operator-(ModInt m)const { return ModInt(*this) -= m; } ModInt operator*(ModInt m)const { return ModInt(*this) *= m; } ModInt operator/(ModInt m)const { return ModInt(*this) /= m; } ModInt operator-()const { return ModInt(kMod - x); } bool operator==(ModInt m)const { return x == m.x; } bool operator!=(ModInt m)const { return x != m.x; } ModInt inverse()const { signed a = x, b = MOD, u = 1, v = 0; while (b) { signed t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } if (u < 0)u += MOD; return ModInt(u); } }; template ostream &operator<<(ostream &os, const ModInt &m) { return os << m.x; } template istream &operator>>(istream &is, ModInt &m) { signed long long s; is >> s; m = ModInt(s); return is; }; using mint = ModInt<2>; template ModInt pow(ModInt a, unsigned long long k) { ModInt r = 1; while (k) { if (k & 1)r *= a; a *= a; k >>= 1; } return r; } // ガウスの消去法(Gauss elimination) // O(n^3) // // 戻り値: (解が存在するか, rank, 解) // 解が複数ある場合は適当な解を出力する // // Verified: // http://judge.u-aizu.ac.jp/onlinejudge/review.jsp?rid=3437138 // http://judge.u-aizu.ac.jp/onlinejudge/review.jsp?rid=3437187 // https://yukicoder.me/submissions/326809 (mod 2) // https://yukicoder.me/submissions/329080 (mod 2) using Num = mint; using Vec = vector; using Mat = vector; tuple gaussianEliminationMod(Mat A, Vec b) { const int n = A.size(), m = A[0].size(); assert(m <= b.size()); if (n > b.size())b.resize(n); int rank = 0, cj = 0; while (rank < n && cj < m) { // A[rank][cj] が最大になるように for (int i = rank + 1; i < n; i++) { if (A[i][cj].get() > A[rank][cj].get()) { A[i].swap(A[rank]); swap(b[i], b[rank]); } } if (A[rank][cj].get()) { // 係数を 1 に Num d = A[rank][cj]; for (int j = 0; j < m; j++) A[rank][j] /= d; b[rank] /= d; // 前進消去(forward elimination) for (int i = rank + 1; i < n; i++) { Num k = A[i][cj]; for (int j = 0; j < m; j++) A[i][j] -= k * A[rank][j]; b[i] -= k * b[rank]; } rank++; } cj++; } // 0 != b[i] だったら不能 for (int i = rank; i < n; i++) if (b[i].get()) return make_tuple(false, rank, Vec()); // 不定 // rank != m // cj < m => n < m // n == m なら適当な解を構築する // n != m でも解を構築できるようにする if (rank < m || cj < m) { if (n != m) return make_tuple(true, rank, Vec()); int ci = rank; for (int i = 0; i < n; i++) { if (A[i][i].get() == 0) { if (i != ci) { A[i].swap(A[ci]); swap(b[i], b[ci]); } ci++; for (int j = 0; j < m; j++) A[i][j] = 0; A[i][i] = 1; b[i] = 0; // 任意の値で良い } } } // 後退代入(back substitution) // 1 * * | * 1 * 0 | * // 0 1 * | * -> 0 1 0 | * // 0 0 1 | * 0 0 1 | * for (int j = m - 1; j >= 0; j--) for (int i = 0; i < j; i++) b[i] -= b[j] * A[i][j]; return make_tuple(true, rank, b); } signed main() { cin.tie(0); ios::sync_with_stdio(false); int N; cin >> N; vector A(N); rep(i, 0, N) { cin >> A[i]; } Mat a(N, Vec(61)); rep(i, 0, N) { rep(j, 0, 61) { a[i][j] = A[i] >> j & 1; } } Vec b(61); auto res = gaussianEliminationMod(a, b); dump(res); cout << (1LL << get<1>(res)) << endl; return 0; }