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:
import java.util.*;
import java.io.*;

public class Main {
    /*
     * HashMap<> map=new HashMap<>(); TreeMap<> map=new TreeMap<>();
     * map.put(p,map.getOrDefault(p,0)+1); for(Map.Entry<> mx:map.entrySet()){ int
     * v=mx.getValue(),k=mx.getKey(); }for (int i = 1; i <= 1000; i++) fac[i] =
     * fac[i - 1] * i % mod; ArrayList<Pair<Character,Integer>> l=new ArrayList<>();
     * ArrayList<> l=new ArrayList<>(); HashSet<> has=new HashSet<>();
     * PriorityQueue<Integer> pq=new PriorityQueue<>(new Comparator<Integer>(){
     * public int compare(Integer a,Integer b){ return Integer.compare(b,a); } });
     * Arrays.sort(ar,new Comparator<int[]>() { public int compare(int[] a, int[] b)
     * { return Double.compare(a[0], b[0]); } });
     */
    PrintWriter out;
    FastReader sc;
    long mod = (long) (1e9 + 7);
    long maxlong = Long.MAX_VALUE;
    long minlong = Long.MIN_VALUE;

    /******************************************************************************************
     *****************************************************************************************/
    public void sol() {
        int n = ni();
        char[] s = rl();
        int a = 0, b = 0;
        for (int i = 0; i < n; i++) {
            if (s[i] == ')')
                b++;
            else
                a++;
        }
        if (a != b) {
            no();
            return;
        }
        int p = 0;
        for (int i = 0; i < n; i++) {
            if (s[i] == '(')
                p++;
            else
                p--;
            if (p < -1) {
                no();
                return;
            }
        }
        yes();
    }

    public static void main(String[] args) {
        Main g = new Main();
        g.out = new PrintWriter(System.out);
        g.sc = new FastReader();
        int t = 1;
        // t=g.ni();
        while (t-- > 0)
            g.sol();
        g.out.flush();
    }

    /****************************************************************************************
     *****************************************************************************************/
    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

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

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

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

        String nextLine() {
            String str = "";
            try {
                str = br.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return str;
        }
    }

    public int ni() {
        return sc.nextInt();
    }

    public long nl() {
        return sc.nextLong();
    }

    public double nd() {
        return sc.nextDouble();
    }

    public char[] rl() {
        return sc.nextLine().toCharArray();
    }

    public String rl1() {
        return sc.nextLine();
    }

    public void pl(Object s) {
        out.println(s);
    }

    public void ex() {
        out.println();
    }

    public void pr(Object s) {
        out.print(s);
    }

    public String next() {
        return sc.next();
    }

    public long abs(long x) {
        return Math.abs(x);
    }

    public int abs(int x) {
        return Math.abs(x);
    }

    public double abs(double x) {
        return Math.abs(x);
    }

    public long min(long x, long y) {
        return Math.min(x, y);
    }

    public int min(int x, int y) {
        return Math.min(x, y);
    }

    public double min(double x, double y) {
        return Math.min(x, y);
    }

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

    public long lcm(long a, long b) {
        return (a / gcd(a, b)) * b;
    }

    void sort1(int[] a) {
        ArrayList<Integer> l = new ArrayList<>();
        for (int i : a) {
            l.add(i);
        }
        Collections.sort(l, Collections.reverseOrder());
        for (int i = 0; i < a.length; i++) {
            a[i] = l.get(i);
        }
    }

    void sort(int[] a) {
        ArrayList<Integer> l = new ArrayList<>();
        for (int i : a) {
            l.add(i);
        }
        Collections.sort(l);
        for (int i = 0; i < a.length; i++) {
            a[i] = l.get(i);
        }
    }

    void sort(long[] a) {
        ArrayList<Long> l = new ArrayList<>();
        for (long i : a) {
            l.add(i);
        }
        Collections.sort(l);
        for (int i = 0; i < a.length; i++) {
            a[i] = l.get(i);
        }
    }

    void sort1(long[] a) {
        ArrayList<Long> l = new ArrayList<>();
        for (long i : a) {
            l.add(i);
        }
        Collections.sort(l, Collections.reverseOrder());
        for (int i = 0; i < a.length; i++) {
            a[i] = l.get(i);
        }
    }

    void sort(double[] a) {
        ArrayList<Double> l = new ArrayList<>();
        for (double i : a) {
            l.add(i);
        }
        Collections.sort(l);
        for (int i = 0; i < a.length; i++) {
            a[i] = l.get(i);
        }
    }

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

    int swap(int a, int b) {
        return a;
    }

    long swap(long a, long b) {
        return a;
    }

    double swap(double a, double b) {
        return a;
    }

    boolean isPowerOfTwo(int x) {
        return x != 0 && ((x & (x - 1)) == 0);
    }

    boolean isPowerOfTwo(long x) {
        return x != 0 && ((x & (x - 1)) == 0);
    }

    public long max(long x, long y) {
        return Math.max(x, y);
    }

    public int max(int x, int y) {
        return Math.max(x, y);
    }

    public double max(double x, double y) {
        return Math.max(x, y);
    }

    long sqrt(long x) {
        return (long) Math.sqrt(x);
    }

    int sqrt(int x) {
        return (int) Math.sqrt(x);
    }

    void input(int[] ar, int n) {
        for (int i = 0; i < n; i++)
            ar[i] = ni();
    }

    void input(long[] ar, int n) {
        for (int i = 0; i < n; i++)
            ar[i] = nl();
    }

    void fill(int[] ar, int k) {
        Arrays.fill(ar, k);
    }

    void yes() {
        pl("YES");
    }

    void no() {
        pl("NO");
    }

    long[] sieve(int n) {
        long[] k = new long[n + 1];
        boolean[] pr = new boolean[n + 1];
        for (int i = 1; i <= n; i++) {
            k[i] = i;
            pr[i] = true;
        }
        for (int i = 2; i <= n; i++) {
            if (pr[i]) {
                for (int j = i + i; j <= n; j += i) {
                    pr[j] = false;
                    if (k[j] == j) {
                        k[j] = i;
                    }
                }
            }
        }
        return k;
    }

    int strSmall(int[] arr, int target) {
        int start = 0, end = arr.length - 1;
        int ans = -1;
        while (start <= end) {
            int mid = (start + end) / 2;
            if (arr[mid] >= target) {
                end = mid - 1;
            } else {
                ans = mid;
                start = mid + 1;
            }
        }
        return ans;
    }

    int strSmall(ArrayList<Integer> arr, int target) {
        int start = 0, end = arr.size() - 1;
        int ans = -1;
        while (start <= end) {
            int mid = (start + end) / 2;
            if (arr.get(mid) > target) {
                start = mid + 1;
                ans = start;
            } else {
                end = mid - 1;
            }
        }
        return ans;
    }

    long mMultiplication(long a, long b) {
        long res = 0;
        a %= mod;

        while (b > 0) {
            if ((b & 1) > 0) {
                res = (res + a) % mod;
            }
            a = (2 * a) % mod;

            b >>= 1;
        }
        return res;
    }

    long nCr(int n, int r, long p) {

        if (n < r)
            return 0;
        if (r == 0)
            return 1;
        long[] fac = new long[n + 1];
        fac[0] = 1;

        for (int i = 1; i <= n; i++)
            fac[i] = fac[i - 1] * i % p;
        return (fac[n] * modInverse(fac[r], p) % p * modInverse(fac[n - r], p) % p) % p;
    }

    long power(long x, long y, long p) {
        long res = 1;
        x = x % p;

        while (y > 0) {
            if (y % 2 == 1)
                res = (res * x) % p;
            y = y >> 1;
            x = (x * x) % p;
        }

        return res;
    }

    long modInverse(long n, long p) {
        return power(n, p - 2, p);
    }

    public static class Pair implements Comparable<Pair> {
        long first;
        long second;

        public Pair(long x, long y) {
            this.first = x;
            this.second = y;
        }

        public int hashCode() {
            return this.hashCode();
        }

        public int compareTo(Pair other) {
            if (this.first == other.first) {
                return Long.compare(this.second, other.second);
            }
            return Long.compare(this.first, other.first);
        }

        public boolean equals(Object o) {

            // If the object is compared with itself then return true
            if (o == this) {
                return true;
            }
            /*
             * Check if o is an instance of Complex or not "null instanceof [type]" also
             * returns false
             */
            if (!(o instanceof Pair)) {
                return false;
            }

            // typecast o to Complex so that we can compare data members
            Pair c = (Pair) o;

            // Compare the data members and return accordingly
            return Long.compare(first, c.first) == 0 && Long.compare(second, c.second) == 0;
        }

    }
}