#include <iostream>
#include <string>
#include <vector>
using namespace std;
void bracket() {
string s;
cin >> s;
if (s == "()") {
cout << "NO\n";
return;
}
int n = s.length();
string p1 = "";
string p2 = "";
for (int i = 0; i < n; ++i) {
p1 += "()";
}
for (int i = 0; i < n; ++i) {
p2 += "(";
}
for (int i = 0; i < n; ++i) {
p2 += ")";
}
cout << "YES\n";
if (p1.find(s) == string::npos) {
cout << p1 << "\n";
} else {
cout << p2 << "\n";
}
}
int main() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
int t;
cin >> t;
while (t--) {
bracket();
}
return 0;
}
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