Problem: Barbara was late for her math class so as a punishment the teacher made her solve the task on a sheet of paper. Barbara looked at the sheet of paper and only saw n numbers a_1, a_2, …, a_n without any mathematical symbols. The teacher explained to Barbara that she has to place the available symbols between the numbers in a way that would make the resulting expression's value as large as possible. To find out which symbols were available the teacher has given Barbara a string s which contained that information.

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It's easy to notice that Barbara has to place n - 1 symbols between numbers in total. The expression must start with a number and all symbols must be allowed (i.e. included in s). Note that multiplication takes precedence over addition or subtraction, addition and subtraction have the same priority and performed from left to right. Help Barbara and create the required expression!

Input

The first line of the input contains a single integer n (1 ≤ n ≤ 10^5) — the amount of numbers on the paper.

The second line of the input contains n integers a_1, a_2, …, a_n (0 ≤ a_i ≤ 9), where a_i is the i-th element of a.

The third line of the input contains the string s (1 ≤ |s| ≤ 3) — symbols allowed in the expression. It is guaranteed that the string may only consist of symbols "-", "+" and "*". It is also guaranteed that all symbols in the string are distinct.

Output

Print n numbers separated by n - 1 symbols — a mathematical expression with the greatest result. If there are multiple equally valid results — output any one of them.

Examples

Input


3
2 2 0
+-*


Output


2*2-0


Input


4
2 1 1 2
+*


Output


2+1+1+2

Note

The following answers also fit the first example: "2+2+0", "2+2-0", "2*2+0".

Solution (in JAVA):

Solution:
import java.io.BufferedOutputStream;
import java.io.Closeable;
import java.io.DataInputStream;
import java.io.Flushable;
import java.io.IOException;
import java.io.InputStream;
import java.io.OutputStream;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.InputMismatchException;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
	static class TaskAdapter implements Runnable {
		@Override
		public void run() {
			long startTime = System.currentTimeMillis();
			InputStream inputStream = System.in;
			OutputStream outputStream = System.out;
			FastReader in = new FastReader(inputStream);
			Output out = new Output(outputStream);
			FMathematicalExpression solver = new FMathematicalExpression();
			solver.solve(1, in, out);
			out.close();
			System.err.println(System.currentTimeMillis()-startTime+"ms");
		}
	}

	public static void main(String[] args) throws Exception {
		Thread thread = new Thread(null, new TaskAdapter(), "", 1<<28);
		thread.start();
		thread.join();
	}

	static class FMathematicalExpression {
		public FMathematicalExpression() {
		}

		public String solve(int[] arr) {
			int n = arr.length;
			StringBuilder ans = new StringBuilder();
			int l, r;
			for(l = 0; l<n&&arr[l]==1; l++) {
				ans.append("1+");
			}
			if(l==n) {
				return ans.substring(0, ans.length()-1);
			}
			for(r = n-1; r>=0&&arr[r]==1; r--) ;
			solve(ans, Arrays.copyOfRange(arr, l, r+1));
			ans.append("+1".repeat(Math.max(0, n-(r+1))));
			return ans.toString();
		}

		public void solve(StringBuilder ans, int[] arr) {
			int n = arr.length;
			{
				long cur = 1;
				for(int i = 0; i<n; i++) {
					if(cur>2*n/arr[i]) {
						for(int j = 0; j<n; j++) {
							if(j>0) {
								ans.append("*");
							}
							ans.append(arr[j]);
						}
						return;
					}
					cur *= arr[i];
				}
			}
			ArrayList<Integer> al = new ArrayList<>(n);
			int prev = -1;
			for(int i = 0; i<n; i++) {
				if(prev!=1||arr[i]!=1) {
					al.add(i);
				}
				prev = arr[i];
			}
			long[] pmul = new long[n+1], psum = new long[n+1];
			pmul[0] = 1;
			for(int i = 0; i<n; i++) {
				pmul[i+1] = pmul[i]*arr[i];
				psum[i+1] = psum[i]+arr[i];
			}
			long[] dp = new long[n+1];
			int[] next = new int[n+1];
			Collections.reverse(al);
			for(int i: al) {
				next[i] = n;
				dp[i] = pmul[n]/pmul[i];
				for(int j: al) {
					if(j<=i) {
						break;
					}
					long cur = dp[j];
					if(arr[i]==1) {
						cur += psum[j]-psum[i];
					}else {
						cur += pmul[j]/pmul[i];
					}
					if(cur>dp[i]) {
						dp[i] = cur;
						next[i] = j;
					}
				}
			}
			for(int i = 0; i<n; ) {
				String s = i>0 ? "+" : "", o = arr[i]==1 ? "+" : "*";
				int end = next[i];
				for(; i<end; i++) {
					if(s!=null) {
						ans.append(s);
						s = null;
					}else {
						ans.append(o);
					}
					ans.append(arr[i]);
				}
			}
		}

		public void solve(int kase, InputReader in, Output pw) {
			int n = in.nextInt();
			int[] arr = in.nextInt(n);
			boolean add, sub, mul;
			{
				String s = in.next(3);
				add = s.contains("+");
				sub = s.contains("-");
				mul = s.contains("*");
			}
			if(!mul) {
				for(int i = 0; i<n; i++) {
					if(i>0) {
						if(add) {
							pw.print("+");
						}else {
							pw.print("-");
						}
					}
					pw.print(arr[i]);
				}
			}else {
				if(!add) {
					for(int i = 0; i<n; i++) {
						if(i>0) {
							if(sub&&arr[i]==0) {
								pw.print("-");
							}else {
								pw.print("*");
							}
						}
						pw.print(arr[i]);
					}
				}else {
					for(int i = 0; i<n; ) {
						if(i>0) {
							pw.print("+");
						}
						if(arr[i]==0) {
							pw.print(arr[i++]);
						}else {
							int start = i;
							for(; i<n&&arr[i]!=0; i++) ;
							pw.print(solve(Arrays.copyOfRange(arr, start, i)));
						}
					}
				}
			}
			pw.println();
		}

	}

	static class Output implements Closeable, Flushable {
		public StringBuilder sb;
		public OutputStream os;
		public int BUFFER_SIZE;
		public String lineSeparator;

		public Output(OutputStream os) {
			this(os, 1<<16);
		}

		public Output(OutputStream os, int bs) {
			BUFFER_SIZE = bs;
			sb = new StringBuilder(BUFFER_SIZE);
			this.os = new BufferedOutputStream(os, 1<<17);
			lineSeparator = System.lineSeparator();
		}

		public void print(int i) {
			print(String.valueOf(i));
		}

		public void print(String s) {
			sb.append(s);
			if(sb.length()>BUFFER_SIZE >> 1) {
				flushToBuffer();
			}
		}

		public void println() {
			sb.append(lineSeparator);
		}

		private void flushToBuffer() {
			try {
				os.write(sb.toString().getBytes());
			}catch(IOException e) {
				e.printStackTrace();
			}
			sb = new StringBuilder(BUFFER_SIZE);
		}

		public void flush() {
			try {
				flushToBuffer();
				os.flush();
			}catch(IOException e) {
				e.printStackTrace();
			}
		}

		public void close() {
			flush();
			try {
				os.close();
			}catch(IOException e) {
				e.printStackTrace();
			}
		}

	}

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

		public FastReader(InputStream is) {
			din = new DataInputStream(is);
			buffer = new byte[BUFFER_SIZE];
			bufferPointer = bytesRead = 0;
		}

		public String next() {
			StringBuilder ret = new StringBuilder(64);
			byte c = skip();
			while(c!=-1&&!isSpaceChar(c)) {
				ret.appendCodePoint(c);
				c = read();
			}
			return ret.toString();
		}

		public String next(int maxLength) {
			byte[] ret = new byte[maxLength];
			byte c = skip();
			int ind = 0;
			while(c!=-1&&!isSpaceChar(c)) {
				ret[ind++] = c;
				c = read();
			}
			return new String(ret, 0, ind);
		}

		public int nextInt() {
			int ret = 0;
			byte c = skipToDigit();
			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;
		}

		private boolean isSpaceChar(byte b) {
			return b==' '||b=='\r'||b=='\n'||b=='\t'||b=='\f';
		}

		private byte skip() {
			byte ret;
			while(isSpaceChar((ret = read()))) ;
			return ret;
		}

		private boolean isDigit(byte b) {
			return b>='0'&&b<='9';
		}

		private byte skipToDigit() {
			byte ret;
			while(!isDigit(ret = read())&&ret!='-') ;
			return ret;
		}

		private void fillBuffer() {
			try {
				bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE);
			}catch(IOException e) {
				e.printStackTrace();
				throw new InputMismatchException();
			}
			if(bytesRead==-1) {
				buffer[0] = -1;
			}
		}

		private byte read() {
			if(bytesRead==-1) {
				throw new InputMismatchException();
			}else if(bufferPointer==bytesRead) {
				fillBuffer();
			}
			return buffer[bufferPointer++];
		}

	}

	static interface InputReader {
		String next();

		int nextInt();

		default String next(int maxLength) {
			return next();
		}

		default int[] nextInt(int n) {
			int[] ret = new int[n];
			for(int i = 0; i<n; i++) {
				ret[i] = nextInt();
			}
			return ret;
		}

	}
}