H.cpp

#include <algorithm>
#include <iostream>
#include <string>
#include <vector>
using namespace std;
int main() {
int N;
while (cin >> N) {
vector<vector<int>> fv, bv;
int tot = 0;
for (int i = 0; i < N; i++) {
string S;
cin >> S;
int b = 0, mn = 0;
for (int j = 0; j < S.size(); j++) {
b += (S[j] == '(') - (S[j] == ')');
mn = min(mn, b);
}
if (b >= 0) fv.push_back({-mn, b, i}); else bv.push_back({b-mn, -b, i});
tot += b;
}
if (tot) goto fail;
for (int i = 0; i < 2; i++) {
auto& v = i ? fv : bv;
sort(v.begin(), v.end());
for (int j = 0, cur = 0; j < v.size(); j++) {
if (cur < v[j][0]) goto fail;
cur += v[j][1];
}
}
reverse(bv.begin(), bv.end());
for (auto const& v : fv) cout << v[2]+1 << endl;
for (auto const& v : bv) cout << v[2]+1 << endl;
continue;
fail:
cout << "impossible" << endl;
}
}