Notice that the memory limit is non-standard.

Recently Arthur and Sasha have studied correct bracket sequences. Arthur understood this topic perfectly and become so amazed about correct bracket sequences, so he even got himself a favorite correct bracket sequence of length 2n. Unlike Arthur, Sasha understood the topic very badly, and broke Arthur's favorite correct bracket sequence just to spite him.

All Arthur remembers about his favorite sequence is for each opening parenthesis ('(') the approximate distance to the corresponding closing one (')'). For the i-th opening bracket he remembers the segment [li, ri], containing the distance to the corresponding closing bracket.

Formally speaking, for the i-th opening bracket (in order from left to right) we know that the difference of its position and the position of the corresponding closing bracket belongs to the segment [li, ri].

Help Arthur restore his favorite correct bracket sequence!

Input

The first line contains integer n (1 ≤ n ≤ 600), the number of opening brackets in Arthur's favorite correct bracket sequence. 

Next n lines contain numbers li and ri (1 ≤ li ≤ ri < 2n), representing the segment where lies the distance from the i-th opening bracket and the corresponding closing one. 

The descriptions of the segments are given in the order in which the opening brackets occur in Arthur's favorite sequence if we list them from left to right.

Output

If it is possible to restore the correct bracket sequence by the given data, print any possible choice.

If Arthur got something wrong, and there are no sequences corresponding to the given information, print a single line "IMPOSSIBLE" (without the quotes).

Examples

Input

4
1 1
1 1
1 1
1 1


Output

()()()()


Input

3
5 5
3 3
1 1


Output

((()))


Input

3
5 5
3 3
2 2


Output

IMPOSSIBLE


Input

3
2 3
1 4
1 4


Output

(())()
import java.util.*;

public class EMain {
    static class Pair{
        int size;
        ArrayList<Pair> children = new ArrayList<Pair>();
        void out(StringBuilder builder){
            builder.append('(');
            for(Pair child : children){
                child.out(builder);
            }
            builder.append(')');
        }
    }
    final String IMPOSSIBLE = "IMPOSSIBLE";


    public void solve() {
        Parser parser = new Parser();
        int n = parser.nextInteger();
        int [][] ranges = parser.nextIntegers(2, n);
        int [] fromBound = ranges[0];
        int [] toBound = ranges[1];

        Stack<Pair> topLevel = new Stack<Pair>();
        for(int i = n-1; i >= 0; --i){
            Pair now = new Pair();
            int size = 1;
            while(size < fromBound[i]){
                if(topLevel.size() == 0){
                    System.out.print(IMPOSSIBLE);
                    return;
                }
                Pair pop = topLevel.pop();
                size += pop.size;
                now.children.add(pop);
            }
            if(size > toBound[i]){
                System.out.print(IMPOSSIBLE);
                return;
            }
            now.size = size + 1;
            topLevel.push(now);
        }

        StringBuilder builder = new StringBuilder();
        while(!topLevel.empty()){
            Pair pair = topLevel.pop();
            pair.out(builder);
        }

        System.out.print(builder.toString());
    }

    public static void main(String[] args) {
        new EMain().solve();
    }

    static public class Parser{
        Scanner scanner;

        public Parser() {
            scanner = new Scanner(System.in);
        }

        public Parser(String str) {
            scanner = new Scanner(str);
        }

        long nextLong(){
            return scanner.nextLong();
        }

        int nextInteger(){
            return scanner.nextInt();

        }

        double nextDouble(){
            return scanner.nextDouble();
        }

        String nextLine(){
            return scanner.nextLine();
        }

        int[] nextIntegers(int count){
            int[] result = new int[count];
            for(int i = 0; i < count; ++i){
                result[i] = nextInteger();
            }
            return result;
        }

        long[] nextLongs(int count){
            long[] result = new long[count];
            for(int i = 0; i < count; ++i){
                result[i] = nextLong();
            }
            return result;
        }

        int[][] nextIntegers(int fields, int count){
            int[][] result = new int[fields][];
            for(int i = 0; i < fields; ++i){
                result[i] = new int[count];
            }
            for(int c = 0; c < count; ++c){
                for(int i = 0; i < fields; ++i){
                    result[i][c] = nextInteger();
                }
            }
            return result;
        }
    }

    static public class Matrix{
        static public final int size = 101;
        static public final long base = 1000000007;

        static public class Vector{
            long[] data = new long[size];
        }
        private long[] data;

        public Matrix() {
            data = new long[size * size];
        }

        long get(int row, int column){
            return data[row * size + column];
        }

        long set(int row, int column, long value){
            int index = row * size + column;
            long result = data[index];
            data[index] = value;
            return result;
        }

        public Matrix mul(Matrix other){
            Matrix result = new Matrix();
            for(int r = 0; r < size; ++r){
                for(int c = 0; c < size; ++c){
                    long value = 0;
                    for(int i = 0; i < size; ++i){
                        value += get(r, i) * other.get(i, c);
                        value %= base;
                    }
                    result.set(r, c, value);
                }
            }
            return result;
        }




    }
}
