#include <bits/stdc++.h>
 
using namespace std;
 
int main() {
  ios::sync_with_stdio(false); cin.tie(0);
  int t;
  cin >> t;
  while (t--) {
	string s;
	cin >> s;
	int n = s.size();
	string a, b;
	for (int i = 0; i < 2 * n; ++i) {
	  a += "()"[i & 1];
	  b += ")("[i < n];
	}
	if (a.find(s) == string::npos) {
	  cout << "YES\n" << a << '\n';
	} else if (b.find(s) == string::npos) {
	  cout << "YES\n" << b << '\n';
	} else {
	  cout << "NO\n";
	}
  }
}

#include<bits/stdc++.h>
 
using namespace std;
 
int main()
{
	int t;
	cin >> t;
	for(int i = 0; i < t; i++)
	{
		int m, k, a1, ak;
		cin >> m >> k >> a1 >> ak;
		int taken_k = m / k;
		int taken_1 = m % k;
		int taken_fancy_1 = max(0, taken_1 - a1);
		int left_regular_1 = max(0, a1 - taken_1);
		int taken_fancy_k = max(0, taken_k - ak);
		int to_replace = min(left_regular_1 / k, taken_fancy_k);
		int ans = taken_fancy_1 + taken_fancy_k - to_replace;
		cout << ans << endl;
	}
}

#include<bits/stdc++.h>
 
using namespace std;
 
int main()
{
	int t;
	cin >> t;
	for(int i = 0; i < t; i++)
	{
		int m, k, a1, ak;
		cin >> m >> k >> a1 >> ak;
		// function which calculates the number of fancy coins taken
		// if we take exactly x coins of value k
		auto f = [m, k, a1, ak](int x)
		{
			int taken_1 = m - k * x;
			return max(0, taken_1 - a1) + max(0, x - ak);
		};
		
		int lf = 0;
		int rg = m / k;
		while(rg - lf > 2)
		{
			int mid = (lf + rg) / 2;
			if(f(mid) < f(mid + 1))
				rg = mid + 1;
			else
				lf = mid;
		}
		int ans = 1e9;
		for(int i = lf; i <= rg; i++) ans = min(ans, f(i));
		cout << ans << endl;
	}
}

#include <bits/stdc++.h>
 
using namespace std;
 
int main() {
  ios::sync_with_stdio(false); cin.tie(0);
  int t;
  cin >> t;
  while (t--) {
    int n;
    cin >> n;
    int ans = 0;
    int mn = n + 1, mnWin = n + 1;
    while (n--) {
      int x;
      cin >> x;
      if (mn < x && x < mnWin) {
      	ans += 1;
      	mnWin = x;
      }
      mn = min(mn, x);
    }
    cout << ans << '\n';
  }
}

#include <bits/stdc++.h>
 
using namespace std;
 
using li = long long;
 
const int N = 111;
 
int n;
string s;
int dp[2][N][N * N];
 
int main() {
  cin >> s;
  n = s.size();
  dp[0][0][0] = 0;
  for (int i = 0; i < n; ++i) {
    for (int j = 0; j <= i + 1; ++j) {
      for (int cnt = 0; cnt <= j * (i + 1 - j); ++cnt) {
        dp[1][j][cnt] = n;   
      }
    }
    for (int j = 0; j <= i; ++j) {
      for (int cnt = 0; cnt <= j * (i - j); ++cnt) {
        dp[1][j + 1][cnt] = min(dp[1][j + 1][cnt], dp[0][j][cnt] + (s[i] != '0'));
        dp[1][j][cnt + j] = min(dp[1][j][cnt + j], dp[0][j][cnt] + (s[i] != '1'));
      }
    } 
    swap(dp[0], dp[1]);
  }
  int cnt0 = count(s.begin(), s.end(), '0');
  cout << dp[0][cnt0][cnt0 * (n - cnt0) / 2] / 2 << '\n';
}

#include <bits/stdc++.h>
 
#define forn(i, n) for (int i = 0; i < int(n); i++)
 
using namespace std;
 
const int INF = 1e9;
const int AL = 26;
 
struct query{
	int f, t, ans;
};
 
struct edge{
	int u, w;
};
 
int main() {
	cin.tie(0);
	iostream::sync_with_stdio(false);
	string s;
	cin >> s;
	int n = s.size();
	
	int m;
	cin >> m;
	vector<query> a(m);
	forn(i, m){
		cin >> a[i].f >> a[i].t;
		--a[i].f, --a[i].t;
		a[i].ans = abs(a[i].f - a[i].t);
	}
	
	int k = n - 1 + AL * AL;
	vector<vector<edge>> g(k);
	forn(i, n - 1){
		int j = n - 1 + (s[i] - 'a') * AL + (s[i + 1] - 'a');
		g[i].push_back({j, 0});
		g[j].push_back({i, 1});
		if (i > 0){
			g[i].push_back({i - 1, 1});
			g[i - 1].push_back({i, 1});
		}
	}
	
	for (int st = n - 1; st < k; ++st){
		vector<int> d(k, INF);
		d[st] = 0;
		deque<int> q;
		q.push_back(st);
		while (!q.empty()){
			int v = q.front();
			q.pop_front();
			for (auto it : g[v]){
				if (d[it.u] <= d[v] + it.w) continue;
				d[it.u] = d[v] + it.w;
				if (it.w == 0) q.push_front(it.u);
				else q.push_back(it.u);
			}
		}
		forn(i, m){
			a[i].ans = min(a[i].ans, d[a[i].f] + d[a[i].t] - 1);
		}
	}
	
	forn(i, m) cout << a[i].ans << '\n';
	return 0;
}

#include <bits/stdc++.h>
 
#define forn(i, n) for (int i = 0; i < int(n); i++)
 
using namespace std;
 
const int INF = 1e9;
 
struct bracket{
	int a, b, c;
};
 
struct point{
	int x, y;
};
 
long long cross(const point &a, const point &b){
	return a.x * 1ll * b.y - a.y * 1ll * b.x;
}
 
long long dot(const point &a, const bracket &b){
	return a.x * 1ll * b.a + a.y * 1ll * b.b;
}
 
bool operator <(const point &a, const point &b){
	return cross(a, b) > 0;
}
 
int main() {
	int t;
	cin >> t;
	while (t--){
		int n;
		cin >> n;
		vector<bracket> val;
		forn(i, 2 * n){
			int a, b;
			string c;
			cin >> a >> b >> c;
			val.push_back({a, b, c[0] == '(' ? 1 : -1});
		}
		map<point, vector<int>> opts;
		forn(i, 2 * n) forn(j, 2 * n){
			int dx = val[i].b - val[j].b;
			int dy = val[j].a - val[i].a;
			if (dx <= 0 || dy <= 0) continue;
			opts[{dx, dy}].push_back(i);
			opts[{dx, dy}].push_back(j);
		}
		opts[{1, INF}];
		vector<int> ord(2 * n), rord(2 * n);
		iota(ord.begin(), ord.end(), 0);
		sort(ord.begin(), ord.end(), [&](int i, int j){
			long long di = dot({INF, 1}, val[i]);
			long long dj = dot({INF, 1}, val[j]);
			if (di != dj) return di < dj;
			return val[i].c > val[j].c;
		});
		forn(i, 2 * n) rord[ord[i]] = i;
		int neg = 0, cur = 0;
		vector<int> bal(1, 0);
		for (int i : ord){
			cur += val[i].c;
			bal.push_back(cur);
			neg += cur < 0;
		}
		bool ans = neg == 0;
		vector<int> prv;
		for (auto it : opts){
			vector<int> tot = prv;
			for (int x : it.second) tot.push_back(x);
			sort(tot.begin(), tot.end(), [&](int i, int j){
				return rord[i] < rord[j];
			});
			tot.resize(unique(tot.begin(), tot.end()) - tot.begin());
			for (int x : tot) neg -= bal[rord[x] + 1] < 0;
			vector<int> tmp = tot;
			sort(tot.begin(), tot.end(), [&](int i, int j){
				long long di = dot(it.first, val[i]);
				long long dj = dot(it.first, val[j]);
				if (di != dj) return di < dj;
				return val[i].c > val[j].c;
			});
			vector<int> nrord(tot.size());
			forn(i, tot.size()) nrord[i] = rord[tmp[i]];
			forn(i, tot.size()) rord[tot[i]] = nrord[i];
			for (int x : tot){
				bal[rord[x] + 1] = bal[rord[x]] + val[x].c;
				neg += bal[rord[x] + 1] < 0;
			}
			if (neg == 0){
				ans = true;
				break;
			}
			prv = it.second;
		}
		puts(ans ? "YES" : "NO");
	}
	return 0;
}