Problem: Petya's friends made him a birthday present — a bracket sequence. Petya was quite disappointed with his gift, because he dreamed of correct bracket sequence, yet he told his friends nothing about his dreams and decided to fix present himself. 

To make everything right, Petya is going to move at most one bracket from its original place in the sequence to any other position. Reversing the bracket (e.g. turning "(" into ")" or vice versa) isn't allowed. 

We remind that bracket sequence s is called correct if: 

  * s is empty; 
  * s is equal to "(t)", where t is correct bracket sequence; 
  * s is equal to t_1 t_2, i.e. concatenation of t_1 and t_2, where t_1 and t_2 are correct bracket sequences. 



For example, "(()())", "()" are correct, while ")(" and "())" are not. Help Petya to fix his birthday present and understand whether he can move one bracket so that the sequence becomes correct.

Input

First of line of input contains a single number n (1 ≤ n ≤ 200 000) — length of the sequence which Petya received for his birthday.

Second line of the input contains bracket sequence of length n, containing symbols "(" and ")".

Output

Print "Yes" if Petya can make his sequence correct moving at most one bracket. Otherwise print "No".

Examples

Input


2
)(


Output


Yes


Input


3
(()


Output


No


Input


2
()


Output


Yes


Input


10
)))))(((((


Output


No

Note

In the first example, Petya can move first bracket to the end, thus turning the sequence into "()", which is correct bracket sequence.

In the second example, there is no way to move at most one bracket so that the sequence becomes correct.

In the third example, the sequence is already correct and there's no need to move brackets.

Solution (in JAVA):

Solution:

/**
 * Date: 4 Sep, 2019
 * Link: 
 * 
 * @author Prasad-Chaudhari
 * @linkedIn: https://www.linkedin.com/in/prasad-chaudhari-841655a6/
 * @git: https://github.com/Prasad-Chaudhari
 */
import java.io.BufferedReader;
import java.io.BufferedWriter;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.OutputStreamWriter;
import java.util.Arrays;

public class newProgram12 {

    public static void main(String[] args) throws IOException {
        // TODO code application logic here
        FastIO in = new FastIO();
        int n = in.ni();
        String s = in.next();
        char c[] = new char[n + 1];
        for (int i = 0; i < n; i++) {
            c[i] = s.charAt(i);
        }
        int count = 0;
        for (int i = 0; i < n; i++) {
            if (c[i] == '(') {
                count++;
            } else {
                if (c[i] == ')') {
                    if (count < 0) {
                        System.out.println("No");
                        return;
                    }
                    count--;
                }
            }
        }
        if (count == 0) {
            System.out.println("Yes");
            return;
        }
        for (int i = 0; i < n; i++) {
            if (s.charAt(i) == ')') {
                if (c[n] != ')') {
                    c[n] = ')';
                    c[i] = 'a';
                } else {
                    c[i] = s.charAt(i);
                }
            } else {
                c[i] = s.charAt(i);
            }
        }
        count = 0;
        for (int i = 0; i <= n; i++) {
            if (c[i] == '(') {
                count++;
            } else {
                if (c[i] == ')') {
                    if (count < 0) {
                        System.out.println("No");
                        return;
                    }
                    count--;
                }
            }
        }
        if (count == 0)
            System.out.println("Yes");
        else {
            System.out.println("No");
        }
        in.bw.flush();
    }

    static class FastIO {

        private final BufferedReader br;
        private final BufferedWriter bw;
        private String s[];
        private int index;
        private final StringBuilder sb;

        public FastIO() throws IOException {
            br = new BufferedReader(new InputStreamReader(System.in));
            bw = new BufferedWriter(new OutputStreamWriter(System.out, "UTF-8"));
            s = br.readLine().split(" ");
            sb = new StringBuilder();
            index = 0;
        }

        public int ni() throws IOException {
            return Integer.parseInt(nextToken());
        }

        public double nd() throws IOException {
            return Double.parseDouble(nextToken());
        }

        public long nl() throws IOException {
            return Long.parseLong(nextToken());
        }

        public String next() throws IOException {
            return nextToken();
        }

        public String nli() throws IOException {
            try {
                return br.readLine();
            } catch (IOException ex) {

            }
            return null;
        }

        public int[] gia(int n) throws IOException {
            int a[] = new int[n];
            for (int i = 0; i < n; i++) {
                a[i] = ni();
            }
            return a;
        }

        public int[] gia(int n, int start, int end) throws IOException {
            validate(n, start, end);
            int a[] = new int[n];
            for (int i = start; i < end; i++) {
                a[i] = ni();
            }
            return a;
        }

        public double[] gda(int n) throws IOException {
            double a[] = new double[n];
            for (int i = 0; i < n; i++) {
                a[i] = nd();
            }
            return a;
        }

        public double[] gda(int n, int start, int end) throws IOException {
            validate(n, start, end);
            double a[] = new double[n];
            for (int i = start; i < end; i++) {
                a[i] = nd();
            }
            return a;
        }

        public long[] gla(int n) throws IOException {
            long a[] = new long[n];
            for (int i = 0; i < n; i++) {
                a[i] = nl();
            }
            return a;
        }

        public long[] gla(int n, int start, int end) throws IOException {
            validate(n, start, end);
            long a[] = new long[n];
            for (int i = start; i < end; i++) {
                a[i] = nl();
            }
            return a;
        }

        public int[][][] gwtree(int n) throws IOException {
            int m = n - 1;
            int adja[][] = new int[n + 1][];
            int weight[][] = new int[n + 1][];
            int from[] = new int[m];
            int to[] = new int[m];
            int count[] = new int[n + 1];
            int cost[] = new int[n + 1];
            for (int i = 0; i < m; i++) {
                from[i] = i + 1;
                to[i] = ni();
                cost[i] = ni();
                count[from[i]]++;
                count[to[i]]++;
            }
            for (int i = 0; i <= n; i++) {
                adja[i] = new int[count[i]];
                weight[i] = new int[count[i]];
            }
            for (int i = 0; i < m; i++) {
                adja[from[i]][count[from[i]] - 1] = to[i];
                adja[to[i]][count[to[i]] - 1] = from[i];
                weight[from[i]][count[from[i]] - 1] = cost[i];
                weight[to[i]][count[to[i]] - 1] = cost[i];
                count[from[i]]--;
                count[to[i]]--;
            }
            return new int[][][] { adja, weight };
        }

        public int[][][] gwg(int n, int m) throws IOException {
            int adja[][] = new int[n + 1][];
            int weight[][] = new int[n + 1][];
            int from[] = new int[m];
            int to[] = new int[m];
            int count[] = new int[n + 1];
            int cost[] = new int[n + 1];
            for (int i = 0; i < m; i++) {
                from[i] = ni();
                to[i] = ni();
                cost[i] = ni();
                count[from[i]]++;
                count[to[i]]++;
            }
            for (int i = 0; i <= n; i++) {
                adja[i] = new int[count[i]];
                weight[i] = new int[count[i]];
            }
            for (int i = 0; i < m; i++) {
                adja[from[i]][count[from[i]] - 1] = to[i];
                adja[to[i]][count[to[i]] - 1] = from[i];
                weight[from[i]][count[from[i]] - 1] = cost[i];
                weight[to[i]][count[to[i]] - 1] = cost[i];
                count[from[i]]--;
                count[to[i]]--;
            }
            return new int[][][] { adja, weight };
        }

        public int[][] gtree(int n) throws IOException {
            int adja[][] = new int[n + 1][];
            int from[] = new int[n - 1];
            int to[] = new int[n - 1];
            int count[] = new int[n + 1];
            for (int i = 0; i < n - 1; i++) {
                from[i] = i + 1;
                to[i] = ni();
                count[from[i]]++;
                count[to[i]]++;
            }
            for (int i = 0; i <= n; i++) {
                adja[i] = new int[count[i]];
            }
            for (int i = 0; i < n - 1; i++) {
                adja[from[i]][--count[from[i]]] = to[i];
                adja[to[i]][--count[to[i]]] = from[i];
            }
            return adja;
        }

        public int[][] gg(int n, int m) throws IOException {
            int adja[][] = new int[n + 1][];
            int from[] = new int[m];
            int to[] = new int[m];
            int count[] = new int[n + 1];
            for (int i = 0; i < m; i++) {
                from[i] = ni();
                to[i] = ni();
                count[from[i]]++;
                count[to[i]]++;
            }
            for (int i = 0; i <= n; i++) {
                adja[i] = new int[count[i]];
            }
            for (int i = 0; i < m; i++) {
                adja[from[i]][--count[from[i]]] = to[i];
                adja[to[i]][--count[to[i]]] = from[i];
            }
            return adja;
        }

        public void print(String s) throws IOException {
            bw.write(s);
        }

        public void println(String s) throws IOException {
            bw.write(s);
            bw.newLine();
        }

        public void print(int s) throws IOException {
            bw.write(s + "");
        }

        public void println(int s) throws IOException {
            bw.write(s + "");
            bw.newLine();
        }

        public void print(long s) throws IOException {
            bw.write(s + "");
        }

        public void println(long s) throws IOException {
            bw.write(s + "");
            bw.newLine();
        }

        public void print(double s) throws IOException {
            bw.write(s + "");
        }

        public void println(double s) throws IOException {
            bw.write(s + "");
            bw.newLine();
        }

        private String nextToken() throws IndexOutOfBoundsException, IOException {
            if (index == s.length) {
                s = br.readLine().split(" ");
                index = 0;
            }
            return s[index++];
        }

        private void validate(int n, int start, int end) {
            if (start < 0 || end >= n) {
                throw new IllegalArgumentException();
            }
        }
    }

    static class Data implements Comparable<Data> {

        int a, b;

        public Data(int a, int b) {
            this.a = a;
            this.b = b;
        }

        @Override
        public int compareTo(Data o) {
            if (a == o.a) {
                return Integer.compare(b, o.b);
            }
            return Integer.compare(a, o.a);
        }

        public static void sort(int a[]) {
            Data d[] = new Data[a.length];
            for (int i = 0; i < a.length; i++) {
                d[i] = new Data(a[i], 0);
            }
            Arrays.sort(d);
            for (int i = 0; i < a.length; i++) {
                a[i] = d[i].a;
            }
        }
    }
}