#include <bits/stdc++.h>
using namespace std;

//#pragma GCC optimize("O3,unroll-loops")
//#pragma GCC target("avx2,bmi,bmi2,lzcnt")

using ll = long long int;
using ull = unsigned long long int;
using vi = vector<ll>;
using ii = pair<ll,ll>;
using vii = vector<ii>;
using ld = long double;

#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>
using namespace __gnu_pbds;
template<class T>
using ordered_set = tree < T, null_type, less<T>,
rb_tree_tag,
tree_order_statistics_node_update >;

#ifdef SA_DEBUG
template <class T>
void print(T a) {cerr << a << endl;}
template <class T, class... V> 
void print(T a, V... b) {cerr << a << ", "; print(b...);}
#define dbg(...) cerr << "[" << __LINE__ << "] " << #__VA_ARGS__ << " :: ", print(__VA_ARGS__)
#else
#define dbg(...) 7
#endif

#define eb emplace_back
#define fi first
#define se second

const ll INFL = 2e18;
const int INF = 1e9;
const double PI = acos(-1);
const ll mod = 1e9+7;

mt19937_64 rng(chrono::steady_clock::now().time_since_epoch().count());

template<class T, class V> 
ostream& operator << (ostream &s, pair<T, V> a){
	s << a.fi << ' ' << a.se; return s;
}

template<class T, class V> 
istream& operator >> (istream &s, pair<T, V> &a){
	s >> a.fi >> a.se; return s;
}

template<class T> 
ostream& operator << (ostream &s, vector<T> a){
	for(int i = 0; i < (int)a.size(); i++){
		if(i > 0)s << ' ' ; 
		s << a[i];
	} return s;
}

template<class T> 
istream& operator >> (istream &s, vector<T> &a){
	for(T &x : a)s >> x; 
	return s;
}

template<class T> 
void input(T a[], int l, int r, istream &s = cin){
	while(l <= r)s >> a[l++];
}

template<class T> 
void output(T a[], int l, int r, bool en = true, ostream &s = cout){
	while(l <= r){ s << a[l++];
		if(l <= r) s << ' ';
	} if(en)s << "\n";
}



const int N = 1e6+3, K = 26;
//====================================================================//

using tup = array<int, 3>;
void testcase(){
	int n;
	cin >> n;
	vector<tup> v(n);
	for(int i = 0; i < n; i++){
		v[i][2] = i + 1;
		string s;
		cin >> s;
		int mn = 0, cur = 0;
		for(auto x : s){
			if(x == '(')cur++;
			else cur--;
			mn = min(mn, cur);
		}
		//cur -= mn;
		v[i][0] = cur;
		v[i][1] = -mn;
		//dbg(cur, -mn);
	}
	
	sort(v.begin(), v.end(), [&](tup &a, tup &b){
		int s1 = (a[0] == a[1] ? 0 : (a[0] > a[1] ? 1 : -1));
		int s2 = (b[0] == b[1] ? 0 : (b[0] > b[1] ? 1 : -1));
		if(s1 != s2)return s1 > s2;
		if(s1 == 1)return max(a[0] - b[1], a[1]) > max(b[0] - a[1], b[1]);
		else return max(a[0] - b[1], a[1]) < max(b[0] - a[1], b[1]);
	});
	
	int mn = 0, cur = 0;
	for(auto x : v){
		mn = min(mn, cur - x[1]);
		cur += x[0];
	}
	
	if(mn < 0 || cur != 0)cout << "impossible\n";
	else {
		for(auto x : v){
			cout << x[2] << "\n";
		}
	}
	return;
}





int main(){
	ios::sync_with_stdio(false);
	cin.tie(NULL);
	
	int T = 1;
	//cin >> T;
	
	for(int qq = 1; qq <= T; ++qq){
		//cout << "Case #" << qq << ": ";
		testcase();
	}
	return 0;
}