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:
//package round689;

import java.io.*;
import java.util.ArrayDeque;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.Queue;

public class F4 {
	InputStream is;
	FastWriter out;
	String INPUT = "";

	void solve()
	{
		int n = ni();
		int[] a = na(n);
		char[] s = ns().toCharArray();
		Arrays.sort(s);
		int asm = 0;
		for(char c : s){
			asm |= 1<<"+-*".indexOf(c);
		}
		if(asm == 3){
			asm = 1;
		}
		if(asm == 7){
			asm = 5;
		}
		if(Integer.bitCount(asm) == 1){
			int rem = n-1;
			for(int v : a){
				out.print(v);
				if(--rem >= 0){
					out.print(s[0]);
				}
			}
			out.println();
			return;
		}
		// asm=5 or 6
		if(asm == 6){
			int z = n;
			for(int i = 0;i < n;i++){
				if(a[i] == 0){
					z = i;
					break;
				}
			}
			for(int i = 0;i < n;i++){
				out.print(a[i]);
				if(i < n-1){
					out.print(i+1 == z ? "-" : "*");
				}
			}
			out.println();
			return;
		}

		// asm=5
		int[][] items = new int[n][];
		int p = 0;
		int I = 1000000;
		// 5 (26) 5 (26) 5

		// A b C d E
		// ACE
		// A+b+CE
		// AC+d+E
		// A+b+C+d+E

		// 3 3 3 3 3
		// 27
		// 15

		for(int i = 0;i < n;){
			if(a[i] < 2){
				int j = i;
				while(j < n && a[j] == a[i])j++;
				items[p++] = new int[]{a[i], j-i, '+'};
				i = j;
			}else{
				int j = i;
				while(j < n && a[j] >= 2)j++;
				int pr = 1;
				for(int k = i;k < j;k++){
					pr = pr * a[k];
					if(pr > I)pr = I;
				}
				items[p++] = new int[]{pr, j-i};
				i = j;
			}
		}
		items = Arrays.copyOf(items, p);

		for(int i = 0;i < p;){
			int j = i;
			while(j < p && items[j][0] != 0)j++;
			// [i,j)
			long II = Long.MAX_VALUE / I;
			long prod = 1;
			for(int k = i;k < j;k++){
				if(k == i || k == j-1 && items[k][0] == 1)continue;
				prod = Math.min(II, prod * items[k][0]);
			}
			if(prod >= II){
				for(int k = i;k < j;k++) {
					if (items[k][0] == 1) {
						if (k == i || k == j - 1) {
							items[k][2] = '+';
						} else {
							items[k][2] = '*';
						}
					}
				}
			}else{
				long[] dp = new long[j-i+1];
				String[] arg = new String[j-i+1];
				arg[0] = "";
				for(int k = 1;k < j-i+1;k++){
					long lmax = items[k-1+i][0] == 1 ? dp[k-1] + items[k-1+i][1] : -1;
					long pro = 1;
					int larg = k-1;
					for(int l = k-1;l >= 0;l--){
						pro = pro * items[l+i][0];
						long v = dp[l] + pro;
						if(v > lmax){
							lmax = v;
							larg = l;
						}
					}
					StringBuilder sb = new StringBuilder(arg[larg]);
					sb.append("+");
					for(int u = larg+1;u < k;u++){
						sb.append("*");
					}
					arg[k] = sb.toString();
					dp[k] = lmax;
				}
				arg[j-i] += "+";

				for(int k = 1;k <= j-i;k++){
					if(items[i+k-1][0] == 1) {
						items[i + k - 1][2] = arg[j-i].charAt(k - 1) == '+' && arg[j-i].charAt(k) == '+' ? '+' : '*';
					}
				}
			}

			i = j+1;
		}

		char[] os = new char[n];
		int q = 0;
		for(int i = 0;i < p;i++){
			if(items[i][0] == 0){
				for(int j = 0;j < items[i][1]-1;j++){
					os[q++] = '*';
				}
				os[q++] = '+';
			}else if(items[i][0] >= 2){
				for(int j = 0;j < items[i][1]-1;j++){
					os[q++] = '*';
				}
				if(i+1 < p && items[i+1][0] == 1 && items[i+1][2] == '*') {
					os[q++] = '*';
				}else{
					os[q++] = '+';
				}
			}else{
				for(int j = 0;j < items[i][1]-1;j++){
					os[q++] = (char)items[i][2];
				}
				if(i+1 < p && items[i+1][0] >= 2 && items[i][2] == '*') {
					os[q++] = '*';
				}else{
					os[q++] = '+';
				}
			}
		}

		char[] h = new char[2*n-1];
		for(int i = 0;i < n;i++){
			h[2*i] = (char)('0'+a[i]);
//			out.print(a[i]);
			if(i < n-1){
//				out.print(os[i]);
				h[2*i+1] = os[i];
			}
		}
		out.println(new String(h));
	}

	void run() throws Exception
	{
		is = oj ? System.in : new ByteArrayInputStream(INPUT.getBytes());
		out = new FastWriter(System.out);
		
		long s = System.currentTimeMillis();
		solve();
		out.flush();
		tr(System.currentTimeMillis()-s+"ms");
	}
	
	public static void main(String[] args) throws Exception { new F4().run(); }
	
	private byte[] inbuf = new byte[1024];
	public int lenbuf = 0, ptrbuf = 0;
	
	private int readByte()
	{
		if(lenbuf == -1)throw new InputMismatchException();
		if(ptrbuf >= lenbuf){
			ptrbuf = 0;
			try { lenbuf = is.read(inbuf); } catch (IOException e) { throw new InputMismatchException(); }
			if(lenbuf <= 0)return -1;
		}
		return inbuf[ptrbuf++];
	}
	
	private boolean isSpaceChar(int c) { return !(c >= 33 && c <= 126); }
	private int skip() { int b; while((b = readByte()) != -1 && isSpaceChar(b)); return b; }
	
	private double nd() { return Double.parseDouble(ns()); }
	private char nc() { return (char)skip(); }
	
	private String ns()
	{
		int b = skip();
		StringBuilder sb = new StringBuilder();
		while(!(isSpaceChar(b))){ // when nextLine, (isSpaceChar(b) && b != ' ')
			sb.appendCodePoint(b);
			b = readByte();
		}
		return sb.toString();
	}
	
	private char[] ns(int n)
	{
		char[] buf = new char[n];
		int b = skip(), p = 0;
		while(p < n && !(isSpaceChar(b))){
			buf[p++] = (char)b;
			b = readByte();
		}
		return n == p ? buf : Arrays.copyOf(buf, p);
	}

	private int[] na(int n)
	{
		int[] a = new int[n];
		for(int i = 0;i < n;i++)a[i] = ni();
		return a;
	}

	private long[] nal(int n)
	{
		long[] a = new long[n];
		for(int i = 0;i < n;i++)a[i] = nl();
		return a;
	}

	private char[][] nm(int n, int m) {
		char[][] map = new char[n][];
		for(int i = 0;i < n;i++)map[i] = ns(m);
		return map;
	}

	private int[][] nmi(int n, int m) {
		int[][] map = new int[n][];
		for(int i = 0;i < n;i++)map[i] = na(m);
		return map;
	}

	private int ni() { return (int)nl(); }

	private long nl()
	{
		long num = 0;
		int b;
		boolean minus = false;
		while((b = readByte()) != -1 && !((b >= '0' && b <= '9') || b == '-'));
		if(b == '-'){
			minus = true;
			b = readByte();
		}

		while(true){
			if(b >= '0' && b <= '9'){
				num = num * 10 + (b - '0');
			}else{
				return minus ? -num : num;
			}
			b = readByte();
		}
	}

	public static class FastWriter
	{
		private static final int BUF_SIZE = 1<<13;
		private final byte[] buf = new byte[BUF_SIZE];
		private final OutputStream out;
		private int ptr = 0;

		private FastWriter(){out = null;}

		public FastWriter(OutputStream os)
		{
			this.out = os;
		}

		public FastWriter(String path)
		{
			try {
				this.out = new FileOutputStream(path);
			} catch (FileNotFoundException e) {
				throw new RuntimeException("FastWriter");
			}
		}

		public FastWriter write(byte b)
		{
			buf[ptr++] = b;
			if(ptr == BUF_SIZE)innerflush();
			return this;
		}

		public FastWriter write(char c)
		{
			return write((byte)c);
		}

		public FastWriter write(char[] s)
		{
			for(char c : s){
				buf[ptr++] = (byte)c;
				if(ptr == BUF_SIZE)innerflush();
			}
			return this;
		}

		public FastWriter write(String s)
		{
			s.chars().forEach(c -> {
				buf[ptr++] = (byte)c;
				if(ptr == BUF_SIZE)innerflush();
			});
			return this;
		}

		private static int countDigits(int l) {
			if (l >= 1000000000) return 10;
			if (l >= 100000000) return 9;
			if (l >= 10000000) return 8;
			if (l >= 1000000) return 7;
			if (l >= 100000) return 6;
			if (l >= 10000) return 5;
			if (l >= 1000) return 4;
			if (l >= 100) return 3;
			if (l >= 10) return 2;
			return 1;
		}

		public FastWriter write(int x)
		{
			if(x == Integer.MIN_VALUE){
				return write((long)x);
			}
			if(ptr + 12 >= BUF_SIZE)innerflush();
			if(x < 0){
				write((byte)'-');
				x = -x;
			}
			int d = countDigits(x);
			for(int i = ptr + d - 1;i >= ptr;i--){
				buf[i] = (byte)('0'+x%10);
				x /= 10;
			}
			ptr += d;
			return this;
		}

		private static int countDigits(long l) {
			if (l >= 1000000000000000000L) return 19;
			if (l >= 100000000000000000L) return 18;
			if (l >= 10000000000000000L) return 17;
			if (l >= 1000000000000000L) return 16;
			if (l >= 100000000000000L) return 15;
			if (l >= 10000000000000L) return 14;
			if (l >= 1000000000000L) return 13;
			if (l >= 100000000000L) return 12;
			if (l >= 10000000000L) return 11;
			if (l >= 1000000000L) return 10;
			if (l >= 100000000L) return 9;
			if (l >= 10000000L) return 8;
			if (l >= 1000000L) return 7;
			if (l >= 100000L) return 6;
			if (l >= 10000L) return 5;
			if (l >= 1000L) return 4;
			if (l >= 100L) return 3;
			if (l >= 10L) return 2;
			return 1;
		}

		public FastWriter write(long x)
		{
			if(x == Long.MIN_VALUE){
				return write("" + x);
			}
			if(ptr + 21 >= BUF_SIZE)innerflush();
			if(x < 0){
				write((byte)'-');
				x = -x;
			}
			int d = countDigits(x);
			for(int i = ptr + d - 1;i >= ptr;i--){
				buf[i] = (byte)('0'+x%10);
				x /= 10;
			}
			ptr += d;
			return this;
		}

		public FastWriter write(double x, int precision)
		{
			if(x < 0){
				write('-');
				x = -x;
			}
			x += Math.pow(10, -precision)/2;
			//		if(x < 0){ x = 0; }
			write((long)x).write(".");
			x -= (long)x;
			for(int i = 0;i < precision;i++){
				x *= 10;
				write((char)('0'+(int)x));
				x -= (int)x;
			}
			return this;
		}

		public FastWriter writeln(char c){
			return write(c).writeln();
		}

		public FastWriter writeln(int x){
			return write(x).writeln();
		}

		public FastWriter writeln(long x){
			return write(x).writeln();
		}

		public FastWriter writeln(double x, int precision){
			return write(x, precision).writeln();
		}

		public FastWriter write(int... xs)
		{
			boolean first = true;
			for(int x : xs) {
				if (!first) write(' ');
				first = false;
				write(x);
			}
			return this;
		}

		public FastWriter write(long... xs)
		{
			boolean first = true;
			for(long x : xs) {
				if (!first) write(' ');
				first = false;
				write(x);
			}
			return this;
		}

		public FastWriter writeln()
		{
			return write((byte)'\n');
		}

		public FastWriter writeln(int... xs)
		{
			return write(xs).writeln();
		}

		public FastWriter writeln(long... xs)
		{
			return write(xs).writeln();
		}

		public FastWriter writeln(char[] line)
		{
			return write(line).writeln();
		}

		public FastWriter writeln(char[]... map)
		{
			for(char[] line : map)write(line).writeln();
			return this;
		}

		public FastWriter writeln(String s)
		{
			return write(s).writeln();
		}

		private void innerflush()
		{
			try {
				out.write(buf, 0, ptr);
				ptr = 0;
			} catch (IOException e) {
				throw new RuntimeException("innerflush");
			}
		}

		public void flush()
		{
			innerflush();
			try {
				out.flush();
			} catch (IOException e) {
				throw new RuntimeException("flush");
			}
		}

		public FastWriter print(byte b) { return write(b); }
		public FastWriter print(char c) { return write(c); }
		public FastWriter print(char[] s) { return write(s); }
		public FastWriter print(String s) { return write(s); }
		public FastWriter print(int x) { return write(x); }
		public FastWriter print(long x) { return write(x); }
		public FastWriter print(double x, int precision) { return write(x, precision); }
		public FastWriter println(char c){ return writeln(c); }
		public FastWriter println(int x){ return writeln(x); }
		public FastWriter println(long x){ return writeln(x); }
		public FastWriter println(double x, int precision){ return writeln(x, precision); }
		public FastWriter print(int... xs) { return write(xs); }
		public FastWriter print(long... xs) { return write(xs); }
		public FastWriter println(int... xs) { return writeln(xs); }
		public FastWriter println(long... xs) { return writeln(xs); }
		public FastWriter println(char[] line) { return writeln(line); }
		public FastWriter println(char[]... map) { return writeln(map); }
		public FastWriter println(String s) { return writeln(s); }
		public FastWriter println() { return writeln(); }
	}

	public void trnz(int... o)
	{
		for(int i = 0;i < o.length;i++)if(o[i] != 0)System.out.print(i+":"+o[i]+" ");
		System.out.println();
	}

	// print ids which are 1
	public void trt(long... o)
	{
		Queue<Integer> stands = new ArrayDeque<>();
		for(int i = 0;i < o.length;i++){
			for(long x = o[i];x != 0;x &= x-1)stands.add(i<<6|Long.numberOfTrailingZeros(x));
		}
		System.out.println(stands);
	}

	public void tf(boolean... r)
	{
		for(boolean x : r)System.out.print(x?'#':'.');
		System.out.println();
	}

	public void tf(boolean[]... b)
	{
		for(boolean[] r : b) {
			for(boolean x : r)System.out.print(x?'#':'.');
			System.out.println();
		}
		System.out.println();
	}

	public void tf(long[]... b)
	{
		if(INPUT.length() != 0) {
			for (long[] r : b) {
				for (long x : r) {
					for (int i = 0; i < 64; i++) {
						System.out.print(x << ~i < 0 ? '#' : '.');
					}
				}
				System.out.println();
			}
			System.out.println();
		}
	}

	public void tf(long... b)
	{
		if(INPUT.length() != 0) {
			for (long x : b) {
				for (int i = 0; i < 64; i++) {
					System.out.print(x << ~i < 0 ? '#' : '.');
				}
			}
			System.out.println();
		}
	}

	private boolean oj = System.getProperty("ONLINE_JUDGE") != null;
	private void tr(Object... o) { if(!oj)System.out.println(Arrays.deepToString(o)); }
}