Language: C++

#pragma region preprocessor
#ifdef LOCAL
//*
    #define _GLIBCXX_DEBUG  // gcc
/*/
    #define _LIBCPP_DEBUG 0 // clang
//*/
    #define __clock__
    // #define __buffer_check__
#else
    #pragma GCC optimize("Ofast")
    // #define __buffer_check__
    // #define NDEBUG
#endif
#define __precision__ 15
#define iostream_untie true
#include <bits/stdc++.h>
#include <ext/rope>
#define __all(v) std::begin(v), std::end(v)
#define __rall(v) std::rbegin(v), std::rend(v)
#define __popcount(n) __builtin_popcountll(n)
#define __clz32(n) __builtin_clz(n)
#define __clz64(n) __builtin_clzll(n)
#define __ctz32(n) __builtin_ctz(n)
#define __ctz64(n) __builtin_ctzll(n)

#ifdef __clock__
    #include "clock.hpp"
#else
    #define build_clock() ((void)0)
    #define set_clock() ((void)0)
    #define get_clock() ((void)0)
#endif

#ifdef LOCAL
    #include "dump.hpp"
    #define mesg(str) std::cerr << "[ " << __LINE__ << " : " << __FUNCTION__ << " ]  " << str << "\n"
#else
    #define dump(...) ((void)0)
    #define mesg(str) ((void)0)
#endif
#pragma endregion // preprocessor

#pragma region std-overload
namespace std
{
    // hash
    template <class T> size_t hash_combine(size_t seed, T const &key) { return seed ^ (hash<T>()(key) + 0x9e3779b9 + (seed << 6) + (seed >> 2)); }
    template <class T, class U> struct hash<pair<T, U>> { size_t operator()(pair<T, U> const &pr) const { return hash_combine(hash_combine(0, pr.first), pr.second); } };
    template <class tuple_t, size_t index = tuple_size<tuple_t>::value - 1> struct tuple_hash_calc { static size_t apply(size_t seed, tuple_t const &t) { return hash_combine(tuple_hash_calc<tuple_t, index - 1>::apply(seed, t), get<index>(t)); } };
    template <class tuple_t> struct tuple_hash_calc<tuple_t, 0> { static size_t apply(size_t seed, tuple_t const &t) { return hash_combine(seed, get<0>(t)); } };
    template <class... T> struct hash<tuple<T...>> { size_t operator()(tuple<T...> const &t) const { return tuple_hash_calc<tuple<T...>>::apply(0, t); } };
    // iostream
    template <class T, class U> istream &operator>>(istream &is, pair<T, U> &p) { return is >> p.first >> p.second; }
    template <class T, class U> ostream &operator<<(ostream &os, const pair<T, U> &p) { return os << p.first << ' ' << p.second; }
    template <class tuple_t, size_t index> struct tupleis { static istream &apply(istream &is, tuple_t &t) { tupleis<tuple_t, index - 1>::apply(is, t); return is >> get<index>(t); } };
    template <class tuple_t> struct tupleis<tuple_t, SIZE_MAX> { static istream &apply(istream &is, tuple_t &t) { return is; } };
    template <class... T> istream &operator>>(istream &is, tuple<T...> &t) { return tupleis<tuple<T...>, tuple_size<tuple<T...>>::value - 1>::apply(is, t); }
    template <> istream &operator>>(istream &is, tuple<> &t) { return is; }
    template <class tuple_t, size_t index> struct tupleos { static ostream &apply(ostream &os, const tuple_t &t) { tupleos<tuple_t, index - 1>::apply(os, t); return os << ' ' << get<index>(t); } };
    template <class tuple_t> struct tupleos<tuple_t, 0> { static ostream &apply(ostream &os, const tuple_t &t) { return os << get<0>(t); } };
    template <class... T> ostream &operator<<(ostream &os, const tuple<T...> &t) { return tupleos<tuple<T...>, tuple_size<tuple<T...>>::value - 1>::apply(os, t); }
    template <> ostream &operator<<(ostream &os, const tuple<> &t) { return os; }
    template <class Container, typename Value = typename Container::value_type, enable_if_t<!is_same<decay_t<Container>, string>::value, nullptr_t> = nullptr>
    istream& operator>>(istream& is, Container &cont) { for(auto&& e : cont) is >> e; return is; }
    template <class Container, typename Value = typename Container::value_type, enable_if_t<!is_same<decay_t<Container>, string>::value, nullptr_t> = nullptr>
    ostream& operator<<(ostream& os, const Container &cont) { bool flag = 1; for(auto&& e : cont) flag ? flag = 0 : (os << ' ', 0), os << e; return os; }
} // namespace std
#pragma endregion // std-overload

#pragma region executive-setting
namespace setting
{
    using namespace std;
    using namespace chrono;
    system_clock::time_point start_time, end_time;
    long long get_elapsed_time() { end_time = system_clock::now(); return duration_cast<milliseconds>(end_time - start_time).count(); }
    void print_elapsed_time() { cerr << "\n----- Exec time : " << get_elapsed_time() << " ms -----\n\n"; }
    void buffer_check() { char bufc; if(cin >> bufc) cerr << "\n\033[1;35mwarning\033[0m: buffer not empty.\n"; }
    struct setupper
    {
        setupper()
        {
            if(iostream_untie) ios::sync_with_stdio(false), cin.tie(nullptr);
            cout << fixed << setprecision(__precision__);
    #ifdef stderr_path
            freopen(stderr_path, "a", stderr);
    #endif
    #ifdef LOCAL
            cerr << fixed << setprecision(__precision__) << boolalpha << "\n----- stderr at LOCAL -----\n\n";
    #endif
    #ifdef __clock__
            start_time = system_clock::now();
            atexit(print_elapsed_time);
    #endif
    #ifdef __buffer_check__
            atexit(buffer_check);
    #endif
        }
    } __setupper; // struct setupper
} // namespace setting
#pragma endregion // executive-setting

#pragma region fucntion-utility
// lambda wrapper for recursive method.
template <class lambda_type>
class make_recursive
{
    lambda_type func;
public:
    make_recursive(lambda_type &&f) : func(std::move(f)) {}
    template <class... Args> auto operator()(Args &&... args) const { return func(*this, std::forward<Args>(args)...); }
};
template <class T, class... types> T read(types... args) noexcept { typename std::remove_const<T>::type obj(args...); std::cin >> obj; return obj; }
// #define input(type, var, ...) type var{read<type>(__VA_ARGS__)}
// substitute y for x if x > y.
template <class T> inline bool chmin(T &x, const T &y) { return x > y ? x = y, true : false; }
// substitute y for x if x < y.
template <class T> inline bool chmax(T &x, const T &y) { return x < y ? x = y, true : false; }
// binary search on discrete range.
template <class iter_type, class pred_type>
iter_type binary(iter_type __ok, iter_type __ng, pred_type pred)
{
    assert(__ok != __ng);
    std::ptrdiff_t dist(__ng - __ok);
    while(std::abs(dist) > 1)
    {
        iter_type mid(__ok + dist / 2);
        if(pred(mid)) __ok = mid, dist -= dist / 2;
        else __ng = mid, dist /= 2;
    }
    return __ok;
}
// binary search on real numbers.
template <class pred_type>
long double binary(long double __ok, long double __ng, const long double eps, pred_type pred)
{
    assert(__ok != __ng);
    while(std::abs(__ok - __ng) > eps)
    {
        long double mid{(__ok + __ng) / 2};
        (pred(mid) ? __ok : __ng) = mid;
    }
    return __ok;
}
// trinary search on discrete range.
template <class iter_type, class comp_type>
iter_type trinary(iter_type __first, iter_type __last, comp_type comp)
{
    assert(__first < __last);
    std::ptrdiff_t dist(__last - __first);
    while(dist > 2)
    {
        iter_type __left(__first + dist / 3), __right = (__first + dist * 2 / 3);
        if(comp(__left, __right)) __last = __right, dist = dist * 2 / 3;
        else __first = __left, dist -= dist / 3;
    }
    if(dist > 1 && comp(next(__first), __first)) ++__first;
    return __first;
}
// trinary search on real numbers.
template <class comp_type>
long double trinary(long double __first, long double __last, const long double eps, comp_type comp)
{
    assert(__first < __last);
    while(__last - __first > eps)
    {
        long double __left{(__first * 2 + __last) / 3}, __right{(__first + __last * 2) / 3};
        if(comp(__left, __right)) __last = __right;
        else __first = __left;
    }
    return __first;
}
// size of array.
template <class A, size_t N> size_t size(A (&array)[N]) { return N; }
// be careful that val is type-sensitive.
template <class T, class A, size_t N> void init(A (&array)[N], const T &val) { std::fill((T*)array, (T*)(array + N), val); }
#pragma endregion // function-utility

#pragma region using-alias
using namespace std;
using i32 = int_least32_t; using i64 = int_least64_t; using u32 = uint_least32_t; using u64 = uint_least64_t;
using p32 = pair<i32, i32>; using p64 = pair<i64, i64>;
template <class T, class Comp = less<T>> using heap = priority_queue<T, vector<T>, Comp>;
template <class T> using hashset = unordered_set<T>;
template <class Key, class Value> using hashmap = unordered_map<Key, Value>;
using namespace __gnu_cxx;
#pragma endregion // using-alias

#pragma region library

#ifndef Matrix_hpp
#define Matrix_hpp
#include <iostream>
#include <valarray>
#include <vector>

template <class Field>
class matrix
{
    size_t h, w;
    using row_type = std::valarray<Field>;
    using data_type = std::valarray<std::valarray<Field>>;
    data_type data;

    friend std::istream &operator>>(std::istream &is, matrix &x)
    {
        for(size_t i = 0; i != x.h; ++i)
        {
            for(size_t j = 0; j != x.w; ++j) is >> x.data[i][j];
        }
        return is;
    }
    friend std::ostream &operator<<(std::ostream &os, const matrix &x)
    {
        for(size_t i = 0; i != x.h; ++i)
        {
            if(i) os << "\n";
            for(size_t j = 0; j != x.w; ++j) os << (j ? " " : "") << x.data[i][j];
        }
        return os;
    }

    friend matrix transpose(const matrix &x)
    {
        matrix res(x.w, x.h);
        for(size_t i = 0; i != x.w; ++i)
            for(size_t j = 0; j != x.h; ++j)
                res[i][j] = x.data[j][i];
        return res;
    }

public:
    explicit matrix(size_t _n = 0) : h(_n), w(_n) { resize(_n, _n);}
    matrix(size_t _h, size_t _w) : h(_h), w(_w) { resize(_h, _w); }
    matrix(const data_type &_data) : h(_data.size()), w(_data.size() ? _data[0].size() : 0), data(_data) {}
    operator data_type() const { return data; }

    size_t rows() const noexcept { return h; }
    size_t columns() const noexcept { return w; }
    bool square() const noexcept { return h == w; }
    row_type &operator[](const size_t i) noexcept { assert(i < data.size()); return data[i]; }
    void resize(size_t h, size_t w, const Field val = Field(0)) { data.resize(h, std::valarray<Field>(val, w)); }

    static matrix identity(const size_t n) noexcept
    {
        data_type data(row_type(n), n);
        for(size_t i = 0; i != n; ++i) data[i][i] = 1;
        return data;
    }

    matrix operator-() const noexcept { return {-data}; }
    matrix &operator+=(const matrix &other) noexcept { data += other.data; return *this; }
    matrix &operator-=(const matrix &other) { data -= other.data; return *this; }
    matrix &operator*=(matrix other) noexcept
    {
        other = transpose(other);
        for(size_t i = 0; i != h; ++i)
        {
            const row_type copied{data[i]};
            for(size_t j = 0; j != other.h; ++j) data[i][j] = (copied * other.data[j]).sum();
        }
        return *this;
    }
    matrix operator+(const matrix &x) const noexcept { return matrix(*this) += x; }
    matrix operator-(const matrix &x) const noexcept { return matrix(*this) -= x; }
    matrix operator*(const matrix &x) const noexcept { return matrix(*this) *= x; }

    friend matrix pow(matrix mat, long long exp)
    {
        if(exp < 0) exp = -exp, mat = inverse(mat);
        matrix res{identity(mat.rows())};
        for(assert(mat.rows() == mat.columns()); exp; mat *= mat, exp >>= 1) if(exp & 1) res *= mat;
        return res;
    }

    friend matrix inverse(const matrix &mat)
    {
        matrix extended(mat.rows(), mat.rows() * 2), res(mat.rows());
        for(size_t i{mat.rows()}; i--;) extended[i][std::slice(0, mat.rows(), 1)] = mat[i], extended[i][i + mat.rows()] = identity();
        if(Gauss_Jordan(extended).size() != mat.rows()) return matrix{0};
        for(size_t i{mat.rows()}; i--;) res[i] = extended[i][std::slice(mat.rows(), mat.rows(), 1)];
        return res;
    }

    friend std::vector<size_t> Gauss_Jordan(matrix &mat)
    {
        std::vector<size_t> pivots;
        for(size_t j{}, rank{}; j != mat.columns(); ++j)
        {
            row_type *row_ptr = nullptr;
            for(size_t i{rank}; i != mat.rows(); ++i)
            {
                if(mat[i][j] != Field{})
                {
                    const Field fct{mat[i][j]};
                    if(row_ptr) mat[i][std::slice(j, mat.columns() - j, 1)] -= *row_ptr * fct;
                    else
                    {
                        swap(mat[rank], mat[i]);
                        std::slice_array<Field> tmp{mat[rank][std::slice(j, mat.columns() - j, 1)]};
                        tmp = *(row_ptr = new row_type{tmp}) /= fct;
                    }
                }
            }
            if(row_ptr)
            {
                for(size_t k{rank}; k--;)
                {
                    const Field fct{mat[k][j]};
                    mat[k][std::slice(j, mat.columns() - j, 1)] -= *row_ptr * fct;
                }
                ++rank;
                pivots.emplace_back(j);
                delete row_ptr;
            }
        }
        return pivots;
    }

    Field determinant() const
    {
        assert(square());
        data_type copied{data};
        Field res{1};
        for(size_t j = 0; j != w; ++j)
        {
            row_type *row_ptr = nullptr;
            for(size_t i = j; i != h; ++i)
            {
                if(copied[i][j] != Field{0})
                {
                    const Field f = copied[i][j];
                    if(row_ptr) copied[i][std::slice(j, w - j, 1)] -= *row_ptr * f;
                    else
                    {
                        swap(copied[i], copied[j]);
                        if(i != j) res = -res;
                        res *= f;
                        std::slice_array<Field> tmp{copied[j][std::slice(j, w - j, 1)]};
                        tmp = *(row_ptr = new row_type{tmp}) /= f;
                    }
                }
            }
            if(!row_ptr) return 0;
        }
        return res;
    }
}; // class matrix

#endif // Matrix_hpp

#ifndef modint_hpp
#define modint_hpp
#include <cassert>
#include <iostream>

template <int mod>
class modint
{
    int val;
public:
    static constexpr modint identity() noexcept { return 1; }
    constexpr modint() noexcept : val{0} {}
    constexpr modint(long long x) noexcept : val((x %= mod) < 0 ? mod + x : x) {}
    constexpr long long value() const noexcept { return val; }
    constexpr modint operator++(int) noexcept { modint t = *this; return ++val, t; }
    constexpr modint operator--(int) noexcept { modint t = *this; return --val, t; }
    constexpr modint &operator++() noexcept { return ++val, *this; }
    constexpr modint &operator--() noexcept { return --val, *this; }
    constexpr modint operator-() const noexcept { return modint(-val); }
    constexpr modint &operator+=(const modint &other) noexcept { return (val += other.val) < mod ? 0 : val -= mod, *this; }
    constexpr modint &operator-=(const modint &other) noexcept { return (val += mod - other.val) < mod ? 0 : val -= mod, *this; }
    constexpr modint &operator*=(const modint &other) noexcept { return val = (long long)val * other.val % mod, *this; }
    constexpr modint &operator/=(const modint &other) noexcept { return *this *= inverse(other); }
    constexpr modint operator+(const modint &other) const noexcept { return modint(*this) += other; }
    constexpr modint operator-(const modint &other) const noexcept { return modint(*this) -= other; }
    constexpr modint operator*(const modint &other) const noexcept { return modint(*this) *= other; }
    constexpr modint operator/(const modint &other) const noexcept { return modint(*this) /= other; }
    constexpr bool operator==(const modint &other) const noexcept { return val == other.val; }
    constexpr bool operator!=(const modint &other) const noexcept { return val != other.val; }
    constexpr bool operator!() const noexcept { return !val; }
    friend constexpr modint operator+(long long x, modint y) noexcept { return modint(x) + y; }
    friend constexpr modint operator-(long long x, modint y) noexcept { return modint(x) - y; }
    friend constexpr modint operator*(long long x, modint y) noexcept { return modint(x) * y; }
    friend constexpr modint operator/(long long x, modint y) noexcept { return modint(x) / y; }
    static constexpr modint inverse(const modint &other) noexcept
    {
        assert(other != 0);
        int a{mod}, b{other.val}, u{}, v{1}, t{};
        while(b) t = a / b, a ^= b ^= (a -= t * b) ^= b, u ^= v ^= (u -= t * v) ^= v;
        return {u};
    }
    static constexpr modint pow(modint other, long long e) noexcept
    {
        if(e < 0) e = e % (mod - 1) + mod - 1;
        modint res{1};
        while(e) { if(e & 1) res *= other; other *= other, e >>= 1; }
        return res;
    }
    friend std::ostream &operator<<(std::ostream &os, const modint &other) noexcept { return os << other.val; }
    friend std::istream &operator>>(std::istream &is, modint &other) noexcept { long long val; other = {(is >> val, val)}; return is; }
}; // class modint

template <>
class modint<2>
{
    bool val;
public:
    static constexpr modint identity() noexcept { return 1; }
    constexpr modint(bool x = false) noexcept : val{x} {}
    constexpr modint(int x) noexcept : val(x & 1) {}
    constexpr modint(long long x) noexcept : val(x & 1) {}
    constexpr operator bool() const noexcept { return val; }
    constexpr bool value() const noexcept { return val; }
    constexpr modint &operator+=(const modint &other) noexcept { return val ^= other.val, *this; }
    constexpr modint &operator-=(const modint &other) noexcept { return val ^= other.val, *this; }
    constexpr modint &operator*=(const modint &other) noexcept { return val &= other.val, *this; }
    constexpr modint &operator/=(const modint &other) noexcept { assert(other.val); return *this; }
    constexpr modint operator!() const noexcept { return !val; }
    constexpr modint operator-() const noexcept { return *this; }
    constexpr modint operator+(const modint &other) const noexcept { return val != other.val; }
    constexpr modint operator-(const modint &other) const noexcept { return val != other.val; }
    constexpr modint operator*(const modint &other) const noexcept { return val && other.val; }
    constexpr modint operator/(const modint &other) const noexcept { assert(other.val); return *this; }
    constexpr bool operator==(const modint &other) const noexcept { return val == other.val; }
    constexpr bool operator!=(const modint &other) const noexcept { return val != other.val; }
    friend constexpr modint operator+(long long x, modint y) noexcept { return x & 1 ? !y : y; }
    friend constexpr modint operator-(long long x, modint y) noexcept { return x & 1 ? !y : y; }
    friend constexpr modint operator*(long long x, modint y) noexcept { return x & 1 ? y : modint<2>{0}; }
    friend constexpr modint operator/(long long x, modint y) noexcept { assert(y.val); return x & 1 ? y : modint<2>{0}; }
    friend std::ostream &operator<<(std::ostream &os, const modint &other) noexcept { return os << other.val; }
    friend std::istream &operator>>(std::istream &is, modint &other) noexcept { long long val; other.val = (is >> val, val & 1); return is; }
}; // class modint specialization

#endif // modint_hpp

#pragma endregion // library

#pragma region main-code
struct solver; template <class> void main_(); int main() { main_<solver>(); }
template <class solver> void main_()
{
    unsigned t = 1;
#ifdef LOCAL
    t = 1;
#endif
    // t = -1; // infinite loop
    cin >> t; // case number given

    while(t--) solver();
}

struct solver
{

    solver()
    {
        using F2=modint<2>;
        int n; cin>>n;
        vector<i64> a(n); cin>>a;
        string s; cin>>s;
        reverse(__all(a));
        reverse(__all(s));

        if(s.front()=='1')
        {
            cout << 1 << "\n";
            return;
        }

        matrix<F2> A(64,n);
        int col=0;

        auto ext=[&](i64 val)->bool
        {
            auto exA(A);
            for(int i=0; i<64; ++i)
            {
                exA[i][col]=val&1;
                val>>=1;
            }
            auto piv=Gauss_Jordan(exA);
            assert(!piv.empty());
            if(piv.back()==col)
            {
                return true;
            }
            return false;
        };

        for(int i=0,j=0,t=0; i<n; i=j,t^=1)
        {
            while(j<n and s[i]==s[j])
            {
                if(ext(a[j]))
                {
                    if(t)
                    {
                        cout << 1 << "\n";
                        return;
                    }
                    for(i64 cop=a[j],r=0; cop; cop>>=1,r++)
                    {
                        A[r][col]=cop&1;
                    }
                    col++;
                }
                j++;
            }
        }
        cout << 0 << "\n";
    }
};
#pragma endregion // main-code


Compiler output:
a.cc: In lambda function:
a.cc:480:32: error: conversion from 'i64' {aka 'long int'} to 'modint<2>' is ambiguous
  480 |                 exA[i][col]=val&1;
      |                             ~~~^~
a.cc:413:15: note: candidate: 'constexpr modint<2>::modint(long long int)'
  413 |     constexpr modint(long long x) noexcept : val(x & 1) {}
      |               ^~~~~~
a.cc:412:15: note: candidate: 'constexpr modint<2>::modint(int)'
  412 |     constexpr modint(int x) noexcept : val(x & 1) {}
      |               ^~~~~~
a.cc:411:15: note: candidate: 'constexpr modint<2>::modint(bool)'
  411 |     constexpr modint(bool x = false) noexcept : val{x} {}
      |               ^~~~~~
a.cc:406:7: note:   initializing argument 1 of 'constexpr modint<2>& modint<2>::operator=(modint<2>&&)'
  406 | class modint<2>
      |       ^~~~~~~~~
a.cc: In constructor 'solver::solver()':
a.cc:505:38: error: conversion from 'i64' {aka 'long int'} to 'modint<2>' is ambiguous
  505 |                         A[r][col]=cop&1;
      |                                   ~~~^~
a.cc:413:15: note: candidate: 'constexpr modint<2>::modint(long long int)'
  413 |     constexpr modint(long long x) noexcept : val(x & 1) {}
      |               ^~~~~~
a.cc:412:15: note: candidate: 'constexpr modint<2>::modint(int)'
  412 |     constexpr modint(int x) noexcept : val(x & 1) {}
      |               ^~~~~~
a.cc:411:15: note: candidate: 'constexpr modint<2>::modint(bool)'
  411 |     constexpr modint(bool x = false) noexcept : val{x} {}
      |               ^~~~~~
a.cc:406:7: note:   initializing argument 1 of 'constexpr modint<2>& modint<2>::operator=(modint<2>&&)'
  406 | class modint<2>
      |       ^~~~~~~~~