Serval soon said goodbye to Japari kindergarten, and began his life in Japari Primary School.

In his favorite math class, the teacher taught him the following interesting definitions.

A parenthesis sequence is a string, containing only characters "(" and ")".

A correct parenthesis sequence is a parenthesis sequence that can be transformed into a correct arithmetic expression by inserting characters "1" and "+" between the original characters of the sequence. For example, parenthesis sequences "()()", "(())" are correct (the resulting expressions are: "(1+1)+(1+1)", "((1+1)+1)"), while ")(" and ")" are not. Note that the empty string is a correct parenthesis sequence by definition.

We define that |s| as the length of string s. A strict prefix s[1... l] (1≤ l< |s|) of a string s = s_1s_2... s_{|s|} is string s_1s_2... s_l. Note that the empty string and the whole string are not strict prefixes of any string by the definition.

Having learned these definitions, he comes up with a new problem. He writes down a string s containing only characters "(", ")" and "?". And what he is going to do, is to replace each of the "?" in s independently by one of "(" and ")" to make all strict prefixes of the new sequence not a correct parenthesis sequence, while the new sequence should be a correct parenthesis sequence.

After all, he is just a primary school student so this problem is too hard for him to solve. As his best friend, can you help him to replace the question marks? If there are many solutions, any of them is acceptable.

Input

The first line contains a single integer |s| (1≤ |s|≤ 3 ⋅ 10^5), the length of the string.

The second line contains a string s, containing only "(", ")" and "?".

Output

A single line contains a string representing the answer.

If there are many solutions, any of them is acceptable.

If there is no answer, print a single line containing ":(" (without the quotes).

Examples

Input


6
(?????


Output


(()())

Input


10
(???(???(?


Output


:(

Note

It can be proved that there is no solution for the second sample, so print ":(".
#include <bits/stdc++.h>
namespace myland {
using namespace std;
namespace _abbr {
const double EPS(1e-8);
const double PI(acos(-1.0));
const int INF(0x3f3f3f3f);
const long long INFL(0x3f3f3f3f3f3f3f3fll);
const int MOD(1e9 + 7);
}  // namespace _abbr
using namespace _abbr;
namespace _solve {}
using namespace _solve;
namespace _calculate {
bool odd(long long x) { return x & 1; }
bool even(long long x) { return (x & 1) ^ 1; }
bool posi(long long x) { return x > 0; }
bool nega(long long x) { return x < 0; }
bool zero(long long x) { return x == 0; }
bool prime(long long x) {
  if (x < 2) return 0;
  for (int i = 2; i * i <= x; i++)
    if (x % i == 0) return 0;
  return 1;
}
long long droot(long long x) { return 1 + (x - 1) % 9; }
long long upd(long long a, long long b) { return a % b ? a / b + 1 : a / b; };
long long random(long long a, long long b) {
  return a + rand() * rand() % (b - a + 1);
};
long long bitn(long long x) {
  long long c = 0;
  while (x) c++, x >>= 1;
  return c;
}
template <class T>
T sqr(T x) {
  return x * x;
}
long long qpow(long long a, long long n, long long mod = MOD) {
  long long res(1);
  while (n) {
    if (n & 1) (res *= a) %= mod;
    (a *= a) %= mod;
    n >>= 1;
  }
  return res % mod;
}
long long inv(long long a, long long mod = MOD) { return qpow(a, mod - 2); }
template <class T>
void tomin(T& a, T b) {
  if (b < a) a = b;
}
template <class T>
void tomax(T& a, T b) {
  if (b > a) a = b;
}
}  // namespace _calculate
using namespace _calculate;
namespace _simple_algo {
long long stol(const string& s) {
  long long x = 0;
  for (char c : s) x = x * 10 + c - 48;
  return x;
}
string ltos(long long x) {
  string s = "";
  if (x == 0) return "0";
  while (x) s = char(x % 10 + 48) + s, x /= 10;
  return s;
}
bool pal(const string& s) {
  int l = s.size();
  for (int i = 0, j = l - 1; i < j; i++, j--)
    if (s[i] != s[j]) return 0;
  return 1;
}
}  // namespace _simple_algo
using namespace _simple_algo;
namespace _io {
template <class T>
void rd(T& x) {
  cin >> x;
}
long long rd() {
  long long x = 0, f = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return x * f;
}
void rd(int& x) { x = rd(); }
void rd(long long& x) { x = rd(); }
template <class A, class B>
void rd(A& a, B& b) {
  rd(a), rd(b);
}
template <class A, class B>
void rd(pair<A, B>& p) {
  cin >> p.first >> p.second;
}
template <class T>
void wt(const T& x) {
  cout << x << endl;
}
template <class T>
void wt(const T& x, char c) {
  cout << x << c;
}
template <class T>
void wt(const T& x, const string& s) {
  cout << x << s;
}
template <class T>
void wt(const T& x, int rnd) {
  cout << fixed << setprecision(rnd) << x << endl;
}
template <class T>
void wt(const vector<T>& v) {
  for (T x : v) wt(x, ' ');
  wt("");
}
template <class A, class B>
void wt(const pair<A, B>& make_pair) {
  cout << make_pair.first << ' ' << make_pair.second << endl;
}
}  // namespace _io
using namespace _io;
}  // namespace myland
using namespace myland;
const int N(3e5 + 5);
int n;
char s[N];
bool ok() {
  int c1(0), c2(0), n1(0), n2(0);
  for (int i = 0; i <= n - 1; i++) c1 += s[i] == '(', c2 += s[i] == ')';
  if (c1 > n / 2 || c2 > n / 2) return 0;
  for (int i = 0; i <= n - 1; i++) {
    if (s[i] == '?') {
      if (c1 >= n / 2)
        s[i] = ')', n1++;
      else
        s[i] = '(', n2++, c1++;
    } else {
      if (s[i] == '(')
        n2++;
      else
        n1++;
    }
    if (n1 >= n2 && i != n - 1) return 0;
  }
  return 1;
}
int main() {
  rd(n);
  scanf("%s", s);
  if (n & 1) wt(":("), exit(0);
  if (ok())
    wt(s);
  else
    wt(":("), exit(0);
}
