Go: package main

import (
	"bufio"
	"fmt"
	"os"
	"strconv"
)

func main() {
	var n int
	fmt.Scan(&n)

	var sc = bufio.NewScanner(os.Stdin)
	sc.Split(bufio.ScanWords)

	ps := make([]int, n)
	for i := range ps {
		sc.Scan()
		p, _ := strconv.Atoi(sc.Text())
		ps[i] = p
	}

	mp := make([]int, n+1)
	ans := make([]byte, 0)
	var pp, max int
	for _, p := range ps {
		mp[p] = 1
		if p < pp {
			if mp[p+1] != 1 {
				fmt.Println(":(")
				return
			}
			ans = append(ans, ')')
		} else {
			for i := max; i < p-1; i++ {
				ans = append(ans, '(')
			}
			ans = append(ans, '(')
			ans = append(ans, ')')
		}
		if p > max {
			max = p
		}
		pp = p
	}
	fmt.Println(string(ans))
}

C++: #include <bits/stdc++.h>
#define trace1(x)                cout<<#x<<": "<<x<<endl
#define trace2(x, y)             cout<<#x<<": "<<x<<" | "<<#y<<": "<<y<<endl
#define trace3(x, y, z)          cout<<#x<<":" <<x<<" | "<<#y<<": "<<y<<" | "<<#z<<": "<<z<<endl
#define trace4(a, b, c, d)       cout<<#a<<": "<<a<<" | "<<#b<<": "<<b<<" | "<<#c<<": "<<c<<" | "<<#d<<": "<<d<<endl
#define trace5(a, b, c, d, e)    cout<<#a<<": "<<a<<" | "<<#b<<": "<<b<<" | "<<#c<<": "<<c<<" | "<<#d<<": "<<d<<" | "<<#e<< ": "<<e<<endl
#define trace6(a, b, c, d, e, f) cout<<#a<<": "<<a<<" | "<<#b<<": "<<b<<" | "<<#c<<": "<<c<<" | "<<#d<<": "<<d<<" | "<<#e<< ": "<<e<<" | "<<#f<<": "<<f<<endl
#define trace7(a, b, c, d, e, f , g) cout<<#a<<": "<<a<<" | "<<#b<<": "<<b<<" | "<<#c<<": "<<c<<" | "<<#d<<": "<<d<<" | "<<#e<< ": "<<e<<" | "<<#f<<": "<< f << " | "<< #g <<": "<<g<<endl
#define trace8(a, b, c, d, e, f , g , h) cout<<#a<<": "<<a<<" | "<<#b<<": "<<b<<" | "<<#c<<": "<<c<<" | "<<#d<<": "<<d<<" | "<<#e<< ": "<<e<<" | "<<#f<<": "<< f << " | " << #g <<": "<< g <<" | "<<#h<< ": " << h << endl
#define rep(i,a,b) for(int i=(int)(a);i<(int)(b);++i)
#define rrep(i,a,b) for(int i=(int)(a);i>=(int)(b);--i)
#define fore(x,a) for(auto &x:a)
#define all(a) (a).begin(),(a).end()
#define rall(a) (a).rbegin(),(a).rend()
#define isin(i,a,b) ((a) <= (i) && (i) <= (b))
#define uni(a) (a).erase(unique(all(a)),(a).end())
#define dup(x,y) (((x)+(y)-1)/(y))
#define fi first
#define se second
#define pb push_back
#define eb emplace_back
#define sz(a) ((long long)(a).size())
#define v(T) vector<T>
#define vv(T) v(v(T))
using namespace std;
using ll  = long long;          using vi  = vector<int>;
using unit= unsigned;           using vl  = vector<ll>;
using ull = unsigned long long; using vvi = vector<vi>;
using P   = pair<int,int>;      using vvl = vector<vl>;
                                using vp  = vector<P>;
void _main(); int main(){ cin.tie(0); ios::sync_with_stdio(false); _main(); }
template<class T>string join(const v(T)&v){ stringstream s; rep(i,0,sz(v))s<<' '<<v[i]; return s.str().substr(1); }
template<class T>istream &operator>>(istream&i, v(T)&v){ fore(x,v){ i >> v; } return i; }
template<class T>ostream &operator<<(ostream&o, const v(T)&v){ o<<"["; fore(x,v)o<<x<<","; o<<"]"; return o; }
template<class T>ostream &operator<<(ostream&o, const deque<T>&v){ o<<"deq["; fore(x,v)o<<x<<","; o<<"]"; return o; }
template<class T>ostream &operator<<(ostream&o, const set<T>&v){ o<<"{"; fore(x,v)o<<x<<","; o<<"}"; return o; }
template<class T>ostream &operator<<(ostream&o, const unordered_set<T>&v){ o<<"{"; fore(x,v)o<<x<<","; o<<"}"; return o; }
template<class T>ostream &operator<<(ostream&o, const multiset<T>&v){ o<<"{"; fore(x,v)o<<x<<","; o<<"}"; return o; }
template<class T>ostream &operator<<(ostream&o, const unordered_multiset<T>&v){ o<<"{"; fore(x,v)o<<x<<","; o<<"}"; return o; }
template<class T1,class T2>ostream &operator<<(ostream &o, const pair<T1,T2>&p){ o<<"("<<p.fi<<","<<p.se<<")"; return o; }
template<class TK,class TV>ostream &operator<<(ostream &o, const map<TK,TV>&m){ o<<"{"; fore(x,m)o<<x.fi<<"=>"<<x.se<<","; o<<"}"; return o; }
template<class TK,class TV>ostream &operator<<(ostream &o, const unordered_map<TK,TV>&m){ o<<"{"; fore(x,m)o<<x.fi<<"=>"<<x.se<<","; o<<"}"; return o; }
template<class T>void YES(T c){ if(c) cout<<"YES"<<endl; else cout<<"NO"<<endl; }
template<class T>void Yes(T c){ if(c) cout<<"Yes"<< endl; else cout<<"No"<<endl; }
template<class T>void POSS(T c){ if(c) cout<<"POSSIBLE"<<endl; else cout<<"IMPOSSIBLE"<<endl; }
template<class T>void Poss(T c){ if(c) cout<<"Possible"<<endl; else cout<<"Impossible"<<endl; }
template<class T>void chmax(T &a, const T &b){ if(a<b) a=b; }
template<class T>void chmin(T &a, const T &b){ if(b<a) a=b; }
template<class T>T gcd(T a, T b){ return (b==0) ? a : gcd(b,a%b); }
template<class T>T lcm(T a, T b){ return a * (b / gcd(a,b)); }
const double  EPS = 1e-10;
const double  PI  = acos(-1.0);
const int     INF = 1001002003;
const ll      LINF= 1001002003004005006LL;
const int dx[] = { -1, 0, 1, 0 , -1,-1, 1, 1 };
const int dy[] = {  0, 1, 0,-1 , -1, 1,-1, 1 };

void ng() {
  puts(":(");
  exit(0);
}

void _main() {
  int N;
  cin >> N;
  vi p(N);
  fore(x, p) cin >> x;

  deque<char> que;
  stack<int> s;
  int nxt = 1;
  rep(i, 0, N) {
    if (p[i] > nxt) {
      que.push_back('(');
      rep(j, nxt, p[i]) {
        que.push_back('(');
        s.push(j);
      }
      que.push_back(')');
      nxt = p[i] + 1;
    } else if (p[i] < nxt) {
      if (p[i] != s.top()) {
        puts(":(");
        return;
      }
      s.pop();
      que.push_back(')');
    } else {
      que.push_back('(');
      que.push_back(')');
      ++nxt;
    }
    // trace3(i, p[i], que);
  }
  fore(x, que) cout << x;
  puts("");
}

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

int n;
vector<int> p;

string solve();

int main() {
  cin >> n;
  p.assign(n, 0);
  for(int i = 0; i < n; ++i) {
    int a;
    cin >> a;
    p[--a] = i;
  }
  cout << solve() << endl;
  return 0;
}

string solve() {
  int now = 0, nows = 0;
  string ans;
  stack<int> st;
  while(st.size() > 0 || nows < n) {
    if(nows < n) st.push(p[nows++]);
    ans += '(';
    while(st.size() > 0 && now == st.top()) {
      ans += ')';
      ++now;
      st.pop();
    }
    if(st.size() > 0 && nows >= n) return ":(";
  }
  return ans;
}