Serval and Parenthesis Sequence

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C. Serval and Parenthesis Sequence

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

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||s| as the length of string ss. A strict prefix s[1…l]s[1…l] (1≤l<|s|)(1≤l<|s|) of a string s=s1s2…s|s|s=s1s2…s|s| is string s1s2…sls1s2…sl. 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 ss containing only characters "(", ")" and "?". And what he is going to do, is to replace each of the "?" in ss 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||s| (1≤|s|≤3⋅1051≤|s|≤3⋅105), the length of the string.

The second line contains a string ss, 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

Copy

6
(?????

output

Copy

(()())

input

Copy

10
(???(???(?

output

Copy

:(

Note

It can be proved that there is no solution for the second sample, so print ":(".

解题思路：

#include<iostream>
#include<cstdio>
#include<cstring>
#include<queue>
#include<vector>
#include<string>
#include<cmath>
#include<bitset>
#include<algorithm>
#include<map>
using namespace std;
#define LL long long
#define N 300005
#define maxn 200005
#define inf 0x3f3f3f3f
#define sca(x) scanf("%d",&x)
#define fir first
#define sec second
#define mp(x,y) make_pair(x,y)
#define pb(x) push_back(x)
#define N 105

int n;
int main()
{
    cin>>n;
    string s;
    cin>>s;
    int num1=0,num2=0;
    for(int i=0;i<n;i++){
        if(s[i]=='(')num1++;
        if(s[i]==')')num2++;
    }
    int sum=0;
    for(int i=0;i<n;i++){
        if(s[i]=='(')sum++;
        else if(s[i]==')')sum--;
        else
        {
            if(num1<n/2){
                s[i]='(';
                num1++;
                sum++;
            }else{
                s[i]=')';
                num2++;
                sum--;
            }
        }
        if(i!=n-1&&sum<=0){
            puts(":(");
            return 0;
        }
    }
    if(sum!=0)puts(":(");
    else
    cout<<s<<endl;
}
/*
要满足题意只需要保证两个条件即可，
每时每刻左括号数都大于右括号数，并且最终
左右括号各占一半。
*/