Greedy

#include <bits/stdc++.h>

using namespace std;

#define ll     long long
#define _test   int _TEST; cin>>_TEST; while(_TEST--)
#define ff     first
#define ss     second
#define pb     push_back

int main()
{
    _test
    {
        int n;
        string s;
        cin>>n>>s;

        vector<int> v;

        for(int i=0; i<n;)
        {
            int j = i+1;
            while(j<n && s[i]==s[j])
                j++;

            v.pb(j-i);
            i = j;
        }

        int tot = accumulate(v.begin(), v.end(), 0);

        if(n%2 || tot%2)
        {
            cout<<"NO\n";
            continue;
        }

        vector<vector<int>> dp(n+10, vector<int> (n+10, -1));

        dp[v.size()][0] = 1;

        function<int(int, int)> check = [&](int ind, int value)
        {
            if(ind == v.size())
                return (int)(value == 0);

            if(dp[ind][value] != -1)        return dp[ind][value];

            int x = 0;
            int y = 0;

            x = check(ind+1, value+v[ind]);

            if(value-v[ind] >= 0)     y = check(ind+1, value-v[ind]);

            return dp[ind][value] = (x|y);
        };

        if(check(1, v[0]))
        {
            cout<<"YES\n";

            n = v.size();
            string ans = "";

            for(int i=0; i<v[0]; i++)       ans += '(';

            int value = v[0];

            for(int i=1; i<n; i++)
            {
                if(dp[i+1][value+v[i]] == 1)
                {
                    for(int j=0; j<v[i]; j++)       ans += '(';
                    value += v[i];
                }
                else
                {
                    for(int j=0; j<v[i]; j++)       ans += ')';
                    value -= v[i];
                }
            }
            cout<<ans<<"\n";
        }
        else
            cout<<"NO\n";
    }
}