A bracket sequence is a string that is one of the following:

1. An empty string;
2. The concatenation of `(`, A, and `)` in this order, for some bracket sequence A ;
3. The concatenation of A and B in this order, for some non-empty bracket sequences A and B /



Given are N strings S_i. Can a bracket sequence be formed by concatenating all the N strings in some order?

Constraints

* 1 \leq N \leq 10^6
* The total length of the strings S_i is at most 10^6.
* S_i is a non-empty string consisting of `(` and `)`.

Input

Input is given from Standard Input in the following format:


N
S_1
:
S_N


Output

If a bracket sequence can be formed by concatenating all the N strings in some order, print `Yes`; otherwise, print `No`.

Examples

Input

2
)
(()


Output

Yes


Input

2
)(
()


Output

No


Input

4
((()))
((((((
))))))
()()()


Output

Yes


Input

3
(((
)
)


Output

No
import java.util.*;
import java.io.*;
import static java.lang.Math.*;

public class Main {
    public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		
		// 入力
		int n = sc.nextInt();
		String[] s = new String[n];
		for(int i = 0; i < n; i++){
		    s[i] = sc.next();
		}
		
		// 計算
		String result = "Yes";
		ArrayList<int[]> up = new ArrayList<int[]>();
		ArrayList<int[]> down = new ArrayList<int[]>();
		int total = 0;
		for(int i = 0; i < n; i++){
		    int cnt = 0;
		    int minus = 0;
		    for(int j = 0; j < s[i].length(); j++){
		        if(s[i].charAt(j) == '(') cnt++;
		        if(s[i].charAt(j) == ')') cnt--;
		        minus = min(minus, cnt);
		    }
		    if(cnt >= 0){
		        up.add(new int[]{i, minus, cnt});
		    }else{
		        down.add(new int[]{i, minus-cnt, -cnt});
		    }
		    total += cnt;
		}
		if(total != 0) result = "No";
		Collections.sort(up, (x, y) -> Integer.compare(y[1], x[1]));
		Collections.sort(down, (x, y) -> Integer.compare(y[1], x[1]));
		int cnt = 0;
		for(int[] u : up){
		    if(cnt + u[1] < 0){
		        result = "No";
		        break;
		    }else{
		        cnt += u[2];
		    }
		}
		cnt = 0;
		for(int[] d : down){
		    if(cnt + d[1] < 0){
		        result = "No";
		        break;
		    }else{
		        cnt += d[2];
		    }
		}
		
		// 出力
		System.out.println(result);
	}
	
	public static class Scanner {
		private BufferedReader br; private StringTokenizer tok;
		public Scanner(InputStream is) throws IOException { br = new BufferedReader(new InputStreamReader(is));}
		private void getLine() throws IOException { while(!hasNext()) tok = new StringTokenizer(br.readLine());}
		private boolean hasNext() { return tok != null && tok.hasMoreTokens();}
		public String next() throws IOException { getLine(); return tok.nextToken();}
		public int nextInt() throws IOException { return Integer.parseInt(next());}
		public long nextLong() throws IOException { return Long.parseLong(next());}
		public double nextDouble() throws IOException { return Double.parseDouble(next());}
	}
}

