Problem: Implication is a function of two logical arguments, its value is false if and only if the value of the first argument is true and the value of the second argument is false. 

Implication is written by using character '<image>', and the arguments and the result of the implication are written as '0' (false) and '1' (true). According to the definition of the implication: 

<image>

<image>

<image>

<image>

When a logical expression contains multiple implications, then when there are no brackets, it will be calculated from left to fight. For example,

<image>. 

When there are brackets, we first calculate the expression in brackets. For example,

<image>.

For the given logical expression <image> determine if it is possible to place there brackets so that the value of a logical expression is false. If it is possible, your task is to find such an arrangement of brackets.

Input

The first line contains integer n (1 ≤ n ≤ 100 000) — the number of arguments in a logical expression.

The second line contains n numbers a1, a2, ..., an (<image>), which means the values of arguments in the expression in the order they occur.

Output

Print "NO" (without the quotes), if it is impossible to place brackets in the expression so that its value was equal to 0.

Otherwise, print "YES" in the first line and the logical expression with the required arrangement of brackets in the second line.

The expression should only contain characters '0', '1', '-' (character with ASCII code 45), '>' (character with ASCII code 62), '(' and ')'. Characters '-' and '>' can occur in an expression only paired like that: ("->") and represent implication. The total number of logical arguments (i.e. digits '0' and '1') in the expression must be equal to n. The order in which the digits follow in the expression from left to right must coincide with a1, a2, ..., an.

The expression should be correct. More formally, a correct expression is determined as follows:

  * Expressions "0", "1" (without the quotes) are correct. 
  * If v1, v2 are correct, then v1->v2 is a correct expression. 
  * If v is a correct expression, then (v) is a correct expression. 



The total number of characters in the resulting expression mustn't exceed 106.

If there are multiple possible answers, you are allowed to print any of them.

Examples

Input

4
0 1 1 0


Output

YES
(((0)-&gt;1)-&gt;(1-&gt;0))


Input

2
1 1


Output

NO


Input

1
0


Output

YES
0

Solution (in JAVA):

Solution:
//package practice;
/**
 * Created by Rajan Waliya on 02-Sep-15.
 */

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

//public
class E550 {

    Reader sc;
    PrintWriter out;

    void solve() throws IOException {
        int n = sc.nextInt();
        //String[] sa = sc.readLine().split(" ");
        String[] sa = new String[n];
        for(int i=0;i<n;i++){
            sa[i]=sc.next();
        }

        if(n==1){
            if(sa[0].equals("0")){
                out.println("YES");
                out.println("0");
            }else{
                out.println("NO");
            }
            return;
        }
        if(sa[n-1].equals("1")){
            out.println("NO");
            return;
        }
        StringBuilder sb = new StringBuilder();


        if(sa[n-2].equals("1")){
            //no need of paranthesis
            for(int i=0;i<n-1;i++){
                sb.append(sa[i]).append("->");
            }sb.append(sa[n - 1]);
            out.println("YES");
            out.println(sb);
            return;
        }

        //otherwise
        int f=-1;
        for(int i=n-3;i>=0;i--){
            if(sa[i].equals("0")){f=i;break;}
        }
        if(f==-1){
            out.println("NO");
            return;
        }

        sb = new StringBuilder();
        for(int i=0;i<f;i++){
            sb.append(sa[i]).append("->");
        }
        sb.append("(").append(sa[f]).append("->").append("(");
        for(int i=f+1;i<n-2;i++){
            sb.append(sa[i]).append("->");
        }sb.append(sa[n - 1]);
        sb.append(")").append(")").append("->");
        sb.append(0);
        out.println("YES");
        out.println(sb);

    }


    //_______congratulation!!! main logic has ended, no need to understand what is after this line.________
    void runIO() throws Exception {
        sc = new Reader();
        out = new PrintWriter(System.out);
        solve();
        out.close();
    }

    public static void main(String[] args) throws Exception {
        new E550().runIO();
    }

    static class Reader {
        final private int BUFFER_SIZE = 1 << 16;
        private DataInputStream din;
        private byte[] buffer;
        private int bufferPointer, bytesRead;

        public Reader() {
            din = new DataInputStream(System.in);
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public Reader(String file_name) throws IOException {
            din = new DataInputStream(new FileInputStream(file_name));
            buffer = new byte[BUFFER_SIZE];
            bufferPointer = bytesRead = 0;
        }

        public String readLine() throws IOException {
            byte[] buf = new byte[64];
            int cnt = 0, c;
            while ((c = read()) != -1) {
                if (c == '\n')
                    break;
                buf[cnt++] = (byte) c;
            }
            return new String(buf, 0, cnt);
        }

        public int nextInt() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public long nextLong() throws IOException {
            long ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10L + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public double nextDouble() throws IOException {
            double ret = 0, div = 1;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (c == '.')
                while ((c = read()) >= '0' && c <= '9')
                    ret += (c - '0') / (div *= 10);
            if (neg)
                return -ret;
            return ret;
        }

        private void fillBuffer() throws IOException {
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
            if (bytesRead == -1)
                buffer[0] = -1;
        }

        private byte read() throws IOException {
            if (bufferPointer == bytesRead)
                fillBuffer();
            return buffer[bufferPointer++];
        }

        public String next() throws IOException {
            StringBuilder sb = new StringBuilder();
            byte c;
            while ((c = read()) <= ' ') ;
            do {
                sb.append((char) c);
            } while ((c = read()) > ' ');
            return sb.toString();
        }

        public int nextInt2() throws IOException {
            int ret = 0;
            byte c = read();
            while (c <= ' ')
                c = read();
            boolean neg = (c == '-');
            if (neg)
                c = read();
            do {
                ret = ret * 10 + c - '0';
            } while ((c = read()) >= '0' && c <= '9');
            if (neg)
                return -ret;
            return ret;
        }

        public void close() throws IOException {
            if (din == null)
                return;
            din.close();
        }
    }

}