Problem: A sequence of brackets is called balanced if one can turn it into a valid math expression by adding characters '+' and '1'. For example, sequences '(())()', '()', and '(()(()))' are balanced, while ')(', '(()', and '(()))(' are not.

You are given a binary string s of length n. Construct two balanced bracket sequences a and b of length n such that for all 1≤ i≤ n: 

  * if s_i=1, then a_i=b_i 
  * if s_i=0, then a_i≠ b_i 



If it is impossible, you should report about it.

Input

The first line contains a single integer t (1≤ t≤ 10^4) — the number of test cases.

The first line of each test case contains a single integer n (2≤ n≤ 2⋅ 10^5, n is even).

The next line contains a string s of length n, consisting of characters 0 and 1.

The sum of n across all test cases does not exceed 2⋅ 10^5.

Output

If such two balanced bracked sequences exist, output "YES" on the first line, otherwise output "NO". You can print each letter in any case (upper or lower).

If the answer is "YES", output the balanced bracket sequences a and b satisfying the conditions on the next two lines.

If there are multiple solutions, you may print any.

Example

Input


3
6
101101
10
1001101101
4
1100


Output


YES
()()()
((()))
YES
()()((()))
(())()()()
NO

Note

In the first test case, a="()()()" and b="((()))". The characters are equal in positions 1, 3, 4, and 6, which are the exact same positions where s_i=1.

In the second test case, a="()()((()))" and b="(())()()()". The characters are equal in positions 1, 4, 5, 7, 8, 10, which are the exact same positions where s_i=1.

In the third test case, there is no solution.

Solution (in CPP):

Solution:
#include "bits/stdc++.h"

using namespace std;
 
typedef long long ll;
typedef long double ld;
typedef double db;
typedef string str; 

typedef pair<int,int> pi;
typedef pair<pi, int> pii;
typedef pair<ll,ll> pl; 
typedef pair<db,db> pd; 

typedef vector<int> vi; 
typedef vector<bool> vb; 
typedef vector<ll> vl; 
typedef vector<db> vd; 
typedef vector<str> vs; 
typedef vector<pi> vpi;
typedef vector<pl> vpl; 
typedef vector<pd> vpd; 
template<class T> using V = vector<T>; 
template<class T, size_t SZ> using AR = array<T,SZ>; 

#define mp make_pair
#define f first
#define s second
#define sz(x) (int)(x).size()
#define all(x) begin(x), end(x)
#define rall(x) (x).rbegin(), (x).rend() 
#define sor(x) sort(all(x)) 
#define revs(x) reverse(all(x)) 
#define rsz resize
#define ins insert 
#define ft front() 
#define bk back()
#define pf push_front 
#define pb push_back
#define eb emplace_back 
#define lb lower_bound 
#define ub upper_bound 

#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define For(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define Rof(i,a) ROF(i,0,a)
#define trav(a,x) for (auto& a: x)

template<class T> bool ckmin(T& a, const T& b) { 
        return b < a ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) { 
        return a < b ? a = b, 1 : 0; } 
constexpr int pct(int x) { return __builtin_popcount(x); } 
constexpr int bits(int x) { return 31-__builtin_clz(x); } // floor(log2(x)) 
ll cdiv(ll a, ll b) { return a/b+((a^b)>0&&a%b); } // divide a by b rounded up
ll fdiv(ll a, ll b) { return a/b-((a^b)<0&&a%b); } // divide a by b rounded down
ll half(ll x) { return fdiv(x,2); }

template<class T, class U> T fstTrue(T lo, T hi, U f) { 
        // note: if (lo+hi)/2 is used instead of half(lo+hi) then this will loop infinitely when lo=hi
        hi ++; assert(lo <= hi); // assuming f is increasing
        while (lo < hi) { // find first index such that f is true 
                T mid = half(lo+hi);
                f(mid) ? hi = mid : lo = mid+1; 
        } 
        return lo;
}
template<class T, class U> T lstTrue(T lo, T hi, U f) {
        lo --; assert(lo <= hi); // assuming f is decreasing
        while (lo < hi) { // find first index such that f is true 
                T mid = half(lo+hi+1);
                f(mid) ? lo = mid : hi = mid-1;
        } 
        return lo;
}
template<class T> void remDup(vector<T>& v) { 
        sort(all(v)); v.erase(unique(all(v)),end(v)); }

// INPUT
template<class A> void re(complex<A>& c);
template<class A, class B> void re(pair<A,B>& p);
template<class A> void re(vector<A>& v);
template<class A, size_t SZ> void re(array<A,SZ>& a);

template<class T> void re(T& x) { cin >> x; }
void re(db& d) { str t; re(t); d = stod(t); }
void re(ld& d) { str t; re(t); d = stold(t); }
template<class H, class... T> void re(H& h, T&... t) { re(h); re(t...); }

template<class A> void re(complex<A>& c) { A a,b; re(a,b); c = {a,b}; }
template<class A, class B> void re(pair<A,B>& p) { re(p.f,p.s); }
template<class A> void re(vector<A>& x) { trav(a,x) re(a); }
template<class A, size_t SZ> void re(array<A,SZ>& x) { trav(a,x) re(a); }

// TO_STRING
#define ts to_string
str ts(char c) { return str(1,c); }
str ts(const char* s) { return (str)s; }
str ts(str s) { return s; }
str ts(bool b) { 
        #ifdef LOCAL
                return b ? "true" : "false"; 
        #else 
                return ts((int)b);
        #endif
}
template<class A> str ts(complex<A> c) { 
        stringstream ss; ss << c; return ss.str(); }
str ts(vector<bool> v) {
        str res = "{"; F0R(i,sz(v)) res += char('0'+v[i]);
        res += "}"; return res; }
template<size_t SZ> str ts(bitset<SZ> b) {
        str res = ""; F0R(i,SZ) res += char('0'+b[i]);
        return res; }
template<class A, class B> str ts(pair<A,B> p);
template<class T> str ts(T v) { // containers with begin(), end()
        #ifdef LOCAL
                bool fst = 1; str res = "{";
                for (const auto& x: v) {
                        if (!fst) res += ", ";
                        fst = 0; res += ts(x);
                }
                res += "}"; return res;
        #else
                bool fst = 1; str res = "";
                for (const auto& x: v) {
                        if (!fst) res += " ";
                        fst = 0; res += ts(x);
                }
                return res;

        #endif
}
template<class A, class B> str ts(pair<A,B> p) {
        #ifdef LOCAL
                return "("+ts(p.f)+", "+ts(p.s)+")"; 
        #else
                return ts(p.f)+" "+ts(p.s);
        #endif
}

// OUTPUT
template<class A> void pr(A x) { cout << ts(x); }
template<class H, class... T> void pr(const H& h, const T&... t) { 
        pr(h); pr(t...); }
void ps() { pr("\n"); } // print w/ spaces
template<class H, class... T> void ps(const H& h, const T&... t) { 
        pr(h); if (sizeof...(t)) pr(" "); ps(t...); }

// DEBUG
void DBG() { cerr << "]" << endl; }
template<class H, class... T> void DBG(H h, T... t) {
        cerr << ts(h); if (sizeof...(t)) cerr << ", ";
        DBG(t...); }
#ifdef LOCAL // compile with -DLOCAL, chk -> fake assert
        #define dbg(...) cerr << "Line(" << __LINE__ << ") -> [" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__)
        #define chk(...) if (!(__VA_ARGS__)) cerr << "Line(" << __LINE__ << ") -> function(" \
                 << __FUNCTION__  << ") -> CHK FAILED: (" << #__VA_ARGS__ << ")" << "\n", exit(0);
#else
        #define dbg(...) 0
        #define chk(...) 0
#endif

int gcd(int a, int b) {if (b == 0)return a;return gcd(b, a % b);}
int max(int a,int b, int c){return max(a,max(b,c));}
int min(int a,int b, int c){return min(a,min(b,c));}
ll max(ll a,ll b, ll c){return max(a,max(b,c));}
ll min(ll a,ll b, ll c){return min(a,min(b,c));}
void dbga(int arr[], int n){vi v;For(i,n)v.pb(arr[i]);dbg(v);}
void dbga(ll arr[], int n){vi v;For(i,n)v.pb(arr[i]);dbg(v);}

// FILE I/O
void setIn(str s) { freopen(s.c_str(),"r",stdin); }
void setOut(str s) { freopen(s.c_str(),"w",stdout); }
void unsyncIO() { cin.tie(0)->sync_with_stdio(0); }
void setIO(str s = "") {
        unsyncIO();
        // cin.exceptions(cin.failbit); 
        // throws exception when do smth illegal
        // ex. try to read letter into int
        if (sz(s)) { setIn(s+".in"), setOut(s+".out"); } // for USACO
}
// 576743 29995400689069LL
const int MOD = 1e9+7; // 998244353;
const int MX = 3e5+5;
const ll INF = 1e18;
const ld PI = acos((ld)-1);
const int xd[4] = {1,0,-1,0}, yd[4] = {0,1,0,-1};
mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count());


void solve(){
    int n;re(n);
    str S;re(S);
    int p1=0,p2=0;
    int c1=0,c2=0;
    vector<char> r1(n,'Z');
    vector<char> r2(n,'Z');
    bool w=true;
    bool flag=true;
    For(i,n){
        if(S[i]=='0'){
            r1[i]=flag?'(':')';
            r2[i]=flag?')':'(';
            c1+=(r1[i]=='(');
            c2+=(r2[i]=='(');
            flag=!flag;
        }
    }
    For(i,n){
        if(S[i]=='1'){
            if(c1<n/2 && c2<n/2){
                c1++,c2++;
                r1[i]='(';
                r2[i]='(';
            } else {
                r1[i]=')';
                r2[i]=')';
            }
        }
    }
    For(i,n){
        p1+=(r1[i]=='(')?1:-1;
        p2+=(r2[i]=='(')?1:-1;
        if(min(p1,p2)<0)w=false;
    }
    if(p1!=0 || p2!=0)w=false;
    if(w && flag){
        ps("YES");
        trav(x,r1)pr(x);
        ps();
        trav(x,r2)pr(x);
        ps();
    } else ps("NO");
}

int main() {
        setIO();
        int t=1;
        re(t);
        while(t--)solve();
        // you should actually read the stuff at the bottom
}

/* stuff you should look for
        * int overflow, array bounds
        * special cases (n=1?)
        * do smth instead of nothing and stay organized
        * WRITE STUFF DOWN
        * DON'T GET STUCK ON ONE APPROACH
*/