This is yet another problem on regular bracket sequences.

A bracket sequence is called regular, if by inserting "+" and "1" into it we get a correct mathematical expression. For example, sequences "(())()", "()" and "(()(()))" are regular, while ")(", "(()" and "(()))(" are not. You have a pattern of a bracket sequence that consists of characters "(", ")" and "?". You have to replace each character "?" with a bracket so, that you get a regular bracket sequence.

For each character "?" the cost of its replacement with "(" and ")" is given. Among all the possible variants your should choose the cheapest.

Input

The first line contains a non-empty pattern of even length, consisting of characters "(", ")" and "?". Its length doesn't exceed 5·104. Then there follow m lines, where m is the number of characters "?" in the pattern. Each line contains two integer numbers ai and bi (1 ≤ ai, bi ≤ 106), where ai is the cost of replacing the i-th character "?" with an opening bracket, and bi — with a closing one.

Output

Print the cost of the optimal regular bracket sequence in the first line, and the required sequence in the second.

Print -1, if there is no answer. If the answer is not unique, print any of them. 

Examples

Input

(??)
1 2
2 8


Output

4
()()
import java.io.BufferedReader;
import java.io.File;
import java.io.FileInputStream;
import java.io.FileNotFoundException;
import java.io.FileOutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintStream;
import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Comparator;
import java.util.PriorityQueue;
import java.util.StringTokenizer;

public class Main {
    
	public static void main( String[] args ) throws FileNotFoundException {
    	new CodeForces_3D().doit();
    }
}
class CodeForces_3D {
	InputReader ir;
	PrintStream ps;
	public void doit() throws FileNotFoundException {
		ir = new InputReader( System.in );
		//Scan sn = new Scan( System.in );
		//Scan sn = new Scan( new FileInputStream("1006.in") );
		ps = System.out;
		//ps = new PrintStream(new FileOutputStream(new File("test")));
		PriorityQueue<Change> q = new PriorityQueue<Change>();
		char[] str = ir.next().toCharArray();
		int blance = 0;
		long ans = 0;
		for ( int i = 0; i < str.length; i++ ) {
			if ( str[i] == '?' ) {
				int l = ir.nextInt();
				int r = ir.nextInt();
				blance--;
				str[ i ] = ')';
				ans += r;
				q.add( new Change(l-r, i) );
			} else if ( str[i] == '(' ) blance++;
			else if ( str[i] == ')' ) blance--;
			if ( blance < 0 ) {
				if ( q.isEmpty() ) {
					ps.println("-1");
					return ;
				}
				Change temp = q.poll();
				blance += 2;
				str[ temp.pos ] = '(';
				ans += temp.cost;
			}
		}
		if ( blance == 0 ) {
			ps.println( ans );
			ps.println( String.valueOf(str) );
		} else {
			ps.println("-1");
		}
	}
}
class Change implements Comparable<Change> {
	int cost, pos;
	public Change( int c, int p ) {
		cost = c;
		pos = p;
	}
	@Override
	public int compareTo(Change o) {
		return cost - o.cost;
	}
}
class InputReader {
	private BufferedReader reader;
	private StringTokenizer tokenizer;
	
	public InputReader(InputStream stream) {
		reader = new BufferedReader(new InputStreamReader(stream));
		tokenizer = null;
	}
	public String next() {
		while (tokenizer == null || !tokenizer.hasMoreTokens()) {
			try {
				tokenizer = new StringTokenizer(reader.readLine());
			} catch (IOException e) {
				throw new RuntimeException(e);
			}
		}
		return tokenizer.nextToken();
	}
	public int nextInt() {
		return Integer.parseInt(next());
	}
	public long nextLong() {
		return Long.parseLong( next() );
	}
	public double nextDouble() {
		return Double.parseDouble( next() );
	}
}
class Scan {
	InputStream inp;
	public Scan(InputStream in) {
		inp = in;
	}
	public int nextInt() {
		boolean isN = false;
		int res = 0;
		int t;
		try {
			t = inp.read();
			if (t == -1) return -1;
			while (t != -1 && t != '-' && (t > '9' || t < '0')) t = inp.read();
			if ( t == '-' ) {
				isN = true;
				t = inp.read();
			}
			while (t != -1 && t >= '0' && t <= '9') {
				res = res * 10 + (t - '0');
				t = inp.read();
			}
		} catch (IOException e) {
			e.printStackTrace();
		}
		if ( isN ) res = -res;
		return res;
	}
	public double nextDouble() {
		double res = 0, Dec = 0.1;
		boolean isN = false, isD = false;
    	int t;
    	try {
    		t = inp.read();
			if ( t == -1 ) return -1;
			while ( t != '-' && t != '.' && (t < '0' || t > '9') ) t = inp.read();
			if ( t == '-' ) {
				isN = true;
				res = 0;
			} else if ( t == '.' ) {
				isD = true;
				res = 0;
			} else res = (double) t - '0';
			if ( !isD ) {
				t = inp.read();
				while ( t >= '0' && t <= '9' ) {
					res = res * 10 + (t - '0');
					t = inp.read();
				}
			}
			if ( t != '.' ) {
				if ( isN ) res = -res;
				return res;
			} else {
				t = inp.read();
				while ( t >= '0' && t <= '9' ) {
					res += Dec * (t - '0');
					Dec *= 0.1;
					t= inp.read();
				}
			}
			if ( isN ) res = -res;
		} catch (IOException e) {
			e.printStackTrace();
		}
    	return res;
    }
}