template <typename T>
struct basis {
    array<T, sizeof(T) * 8> p;
    int cnt = 0;

    basis(const vector<T>& v) {
        for (auto&& x : v) {
            insert(x);
        }
    }

    bool insert(T x) {
        for (size_t i = sizeof(T) * 8 - 1; ~i; --i) {
            if (not (x >> i)) continue;
            if (not p[i]) {
                p[i] = x;
                cnt += 1;
                return true;
            }
            x ^= p[i];
        }
        return false;
    }

    vector<T> value(void) const {
        vector<T> res;
        for (size_t i = sizeof(T) * 8 - 1; ~i; --i) {
            if (not p[i]) continue;
            res.emplace_back(p[i]);
        }
        return res;
    }
};