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 ":(".
import java.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.BitSet;
import java.util.Calendar;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.SortedSet;
import java.util.Stack;
import java.util.StringTokenizer;
import java.util.TreeMap;
import java.util.TreeSet;

/**
 * #
 *
 * @author pttrung
 */
public class C_Round_551_Div2 {

    public static long MOD = 998244353;
    static int[][][][] dp;

    public static void main(String[] args) throws FileNotFoundException {
        // PrintWriter out = new PrintWriter(new FileOutputStream(new File(
        // "output.txt")));
        PrintWriter out = new PrintWriter(System.out);
        Scanner in = new Scanner();
        int n = in.nextInt();
        String data = in.next();

        if (n % 2 != 0) {
            out.println(":(");
        } else if ((data.charAt(0) != '(' && data.charAt(0) != '?') || (data.charAt(n - 1) != ')' && data.charAt(n - 1) != '?')) {
            out.println(":(");
        } else {
            //System.out.println("HE HE");
            int count = 0;
            for (int i = n - 2; i > 0; i--) {
                if (data.charAt(i) == '?' || data.charAt(i) == ')') {
                    count++;
                } else {
                    count--;
                }
            }
            boolean ok = true;
            int cur = 0;
            char[] re = new char[n];
            for (int i = 1; i < n - 1 && ok; i++) {
                //System.out.println(cur + " " + count + " " + data.charAt(i));
                if (data.charAt(i) == '(') {
                    cur++;
                    re[i] = data.charAt(i);
                    count++;
                } else if (data.charAt(i) == ')') {
                    cur--;
                    count--;
                    re[i] = data.charAt(i);
                } else {
                    count--;
                    if (count - cur > 0) {
                        re[i] = '(';
                        cur++;
                    } else {
                        re[i] = ')';
                        cur--;
                    }
                }
                ok &= cur >= 0;
            }
            if (ok && cur == 0) {
                out.print("(");
                for (int i = 1; i < n - 1; i++) {
                    out.print(re[i]);
                }
                out.println(")");
            } else {
                out.println(":(");
            }
        }
        out.close();
    }

    static int add(int index, String a, int l, Node node) {

        int v = a.charAt(a.length() - index - 1) - 'A';
        int re = -1;

        if (index + 1 < l) {
            int nxt = a.charAt(a.length() - index - 2) - 'A';
            if (node.nxt[nxt] == null) {
                node.nxt[nxt] = new Node();
            }
            re = add(index + 1, a, l, node.nxt[nxt]);
        }

        if (re == -1 && !node.mark) {
            node.mark = true;
            re = index + 1;
        }
        return re;

    }

    static class Node {
        Node[] nxt = new Node[26];
        boolean mark = false;
    }

    static class P {
        int x, y, v;

        public P(int x, int y, int v) {
            this.x = x;
            this.y = y;
            this.v = v;
        }
    }

    static int cal(String a, String b) {
        int result = 0;
        for (int i = 0; i < Integer.min(a.length(), b.length()); i++) {
            if (a.charAt(a.length() - i - 1) == b.charAt(b.length() - i - 1)) {
                result = i + 1;
            } else {
                return result;
            }

        }
        return result;
    }


    public static int[] KMP(String val) {
        int i = 0;
        int j = -1;
        int[] result = new int[val.length() + 1];
        result[0] = -1;
        while (i < val.length()) {
            while (j >= 0 && val.charAt(j) != val.charAt(i)) {
                j = result[j];
            }
            j++;
            i++;
            result[i] = j;
        }
        return result;

    }

    public static boolean nextPer(int[] data) {
        int i = data.length - 1;
        while (i > 0 && data[i] < data[i - 1]) {
            i--;
        }
        if (i == 0) {
            return false;
        }
        int j = data.length - 1;
        while (data[j] < data[i - 1]) {
            j--;
        }
        int temp = data[i - 1];
        data[i - 1] = data[j];
        data[j] = temp;
        Arrays.sort(data, i, data.length);
        return true;
    }

    public static int digit(long n) {
        int result = 0;
        while (n > 0) {
            n /= 10;
            result++;
        }
        return result;
    }

    public static double dist(long a, long b, long x, long y) {
        double val = (b - a) * (b - a) + (x - y) * (x - y);
        val = Math.sqrt(val);
        double other = x * x + a * a;
        other = Math.sqrt(other);
        return val + other;

    }

    public static class Point implements Comparable<Point> {

        int x, y;

        public Point(int start, int end) {
            this.x = start;
            this.y = end;
        }

        @Override
        public int hashCode() {
            int hash = 5;
            hash = 47 * hash + this.x;
            hash = 47 * hash + this.y;
            return hash;
        }

        @Override
        public boolean equals(Object obj) {
            if (obj == null) {
                return false;
            }
            if (getClass() != obj.getClass()) {
                return false;
            }
            final Point other = (Point) obj;
            if (this.x != other.x) {
                return false;
            }
            if (this.y != other.y) {
                return false;
            }
            return true;
        }

        @Override
        public int compareTo(Point o) {
            return Integer.compare(x, o.x);
        }
    }

    public static class FT {

        long[] data;

        FT(int n) {
            data = new long[n];
        }

        public void update(int index, long value) {
            while (index < data.length) {
                data[index] += value;
                index += (index & (-index));
            }
        }

        public long get(int index) {
            long result = 0;
            while (index > 0) {
                result += data[index];
                index -= (index & (-index));
            }
            return result;

        }
    }

    public static long gcd(long a, long b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }

    public static long pow(long a, long b, long MOD) {
        if (b == 0) {
            return 1;
        }
        if (b == 1) {
            return a;
        }
        long val = pow(a, b / 2, MOD);
        if (b % 2 == 0) {
            return val * val % MOD;
        } else {
            return val * (val * a % MOD) % MOD;

        }
    }

    static class Scanner {

        BufferedReader br;
        StringTokenizer st;

        public Scanner() throws FileNotFoundException {
            // System.setOut(new PrintStream(new BufferedOutputStream(System.out), true));
            br = new BufferedReader(new InputStreamReader(System.in));
            //  br = new BufferedReader(new InputStreamReader(new FileInputStream(new File("input.txt"))));
        }

        public String next() {

            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    throw new RuntimeException();
                }
            }
            return st.nextToken();
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }

        public boolean endLine() {
            try {
                String next = br.readLine();
                while (next != null && next.trim().isEmpty()) {
                    next = br.readLine();
                }
                if (next == null) {
                    return true;
                }
                st = new StringTokenizer(next);
                return st.hasMoreTokens();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }
    }
}