C.cpp

#include <bits/stdc++.h>
using namespace std;

//----------------------------------- DEBUG -----------------------------------
#define sim template < class c
#define ris return * this
#define dor > debug & operator <<
#define eni(x) sim > typename \
enable_if<sizeof dud<c>(0) x 1, debug&>::type operator<<(c i) {
sim > struct rge { c b, e; };
sim > rge<c> range(c i, c j) { return rge<c>{i, j}; }
sim > auto dud(c* x) -> decltype(cerr << *x, 0);
sim > char dud(...);
struct debug {
#ifdef LOCAL
~debug() { cerr << endl; }
eni(!=) cerr << boolalpha << i; ris; }
eni(==) ris << range(begin(i), end(i)); }
sim, class b dor(pair < b, c > d) {
  ris << "(" << d.first << ", " << d.second << ")";
}
sim dor(rge<c> d) {
  *this << "[";
  for (auto it = d.b; it != d.e; ++it)
    *this << ", " + 2 * (it == d.b) << *it;
  ris << "]";
}
#else
sim dor(const c&) { ris; }
#endif
};
#define imie(...) " [" << #__VA_ARGS__ ": " << (__VA_ARGS__) << "] "
// debug & operator << (debug & dd, P p) { dd << "(" << p.x << ", " << p.y << ")"; return dd; }

//----------------------------------- END DEBUG --------------------------------

// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2016/p0200r0.html
template<class Fun> class y_combinator_result {
    Fun fun_;
public:
    template<class T> explicit y_combinator_result(T &&fun): fun_(std::forward<T>(fun)) {}
    template<class ...Args> decltype(auto) operator()(Args &&...args) { return fun_(std::ref(*this), std::forward<Args>(args)...); }
};
template<class Fun> decltype(auto) y_combinator(Fun &&fun) { return y_combinator_result<std::decay_t<Fun>>(std::forward<Fun>(fun)); }
 

mt19937 rng(chrono::steady_clock::now().time_since_epoch().count());

#define trav(a,x) for (auto& a : x)
#define uid(a, b) uniform_int_distribution<int>(a, b)(rng)

//----------------------------------- DEFINES ----------------------------------- 

#define sz(x) (int)(x).size()
#define mp make_pair
#define eb emplace_back
#define pb push_back
#define lb lower_bound
#define ub upper_bound
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
#define ins insert
#define nl '\n'
#define Stringize( L )     #L 
#define MakeString( M, L ) M(L)
#define $Line MakeString( Stringize, __LINE__ )
#define Reminder __FILE__ "(" $Line ") : Warning: "

//----------------------------------- END DEFINES -------------------------------- 

//-------------------------- CUSTOM UNORDERED MAP HASH ---------------------------

struct custom_hash{
    static uint64_t splitmix64(uint64_t x){
        x += 0x9e3779b97f4a7c15;
        x = (x ^ (x >> 30)) * 0xbf58476d1ce4e5b9;
        x = (x ^ (x >> 27)) * 0x94d049bb133111eb;
        return x ^ (x >> 31);
    }
    size_t operator()(uint64_t a) const {
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        return splitmix64(a + FIXED_RANDOM);
    }
    template<class T> size_t operator()(T a) const {
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        hash<T> x;
        return splitmix64(x(a) + FIXED_RANDOM);
    }
    template<class T, class H> size_t operator()(pair<T, H> a) const {
        static const uint64_t FIXED_RANDOM = chrono::steady_clock::now().time_since_epoch().count();
        hash<T> x;
        hash<H> y;
        return splitmix64(x(a.first) * 37 + y(a.second) + FIXED_RANDOM);
    }
};
template<class T, class H>using umap=unordered_map<T,H,custom_hash>;

//----------------------- CUSTOM UNORDERED MAP HASH END--------------------------

void run_cases() {
    int n;
    cin >> n;
    string s;
    cin >> s;
    string a = "", b = "";
    if(s.back() != s.front()) {
        cout << "NO" << nl;
        return;
    } 
    if(s.back() == '0') {
        cout << "NO" << nl;
        return;
    }

    int score_a = 0, score_b = 0;

    int cnt1 = 0;
    for(auto u: s) {
        cnt1 += (u - '0');
    }
    if(cnt1 & 1) {
        cout << "NO" << nl;
        return;
    }

    int p1 = 0;
    for(auto u: s) {
        if(u == '1') {
            if(p1 < cnt1 / 2) {
                a += '(';
                b += '(';
                score_a++;
                score_b++;
            } else {
                a += ')';
                b += ')';
                score_a--;
                score_b--;
                if(score_a < 0 || score_b < 0) {
                    cout << "NO" << nl;
                    return;
                }
            }
            p1++;
        } else {
            if(score_a > score_b) {
                swap(score_a, score_b);
                swap(a, b);
            }
            a += '(';
            b += ')';
            score_a++;
            score_b--;
            if(score_a < 0 || score_b < 0) {
                cout << "NO" << nl;
                return;
            }
        }
    }

    cout << "YES" << nl;
    cout << a << nl;
    cout << b << nl;


}

int main() {
    ios_base::sync_with_stdio(0); cin.tie(nullptr);

    int tests = 1;
    cin >> tests;

    for(int test = 1;test <= tests;test++) {
        run_cases();
    }
}