You're given a row with n chairs. We call a seating of people "maximal" if the two following conditions hold:

  1. There are no neighbors adjacent to anyone seated. 
  2. It's impossible to seat one more person without violating the first rule. 



The seating is given as a string consisting of zeros and ones (0 means that the corresponding seat is empty, 1 — occupied). The goal is to determine whether this seating is "maximal".

Note that the first and last seats are not adjacent (if n ≠ 2).

Input

The first line contains a single integer n (1 ≤ n ≤ 1000) — the number of chairs.

The next line contains a string of n characters, each of them is either zero or one, describing the seating.

Output

Output "Yes" (without quotation marks) if the seating is "maximal". Otherwise print "No".

You are allowed to print letters in whatever case you'd like (uppercase or lowercase).

Examples

Input

3
101


Output

Yes


Input

4
1011


Output

No


Input

5
10001


Output

No

Note

In sample case one the given seating is maximal.

In sample case two the person at chair three has a neighbour to the right.

In sample case three it is possible to seat yet another person into chair three.
								import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.InputMismatchException;
import java.util.TreeMap;
import java.util.TreeSet;
	
												public class Solution1 implements Runnable
												{
													static final long MAX = 1000000007L;
													static class InputReader
													{
														private InputStream stream;
														private byte[] buf = new byte[1024];
														private int curChar;
														private int numChars;
														private SpaceCharFilter filter;
														private BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
												 
														public InputReader(InputStream stream)
														{
															this.stream = stream;
														}
														
														public int read()
														{
															if (numChars==-1) 
																throw new InputMismatchException();
															
															if (curChar >= numChars)
															{
																curChar = 0;
																try 
																{
																	numChars = stream.read(buf);
																}
																catch (IOException e)
																{
																	throw new InputMismatchException();
																}
																
																if(numChars <= 0)				
																	return -1;
															}
															return buf[curChar++];
														}
													 
														public String nextLine()
														{
															String str = "";
												            try
												            {
												                str = br.readLine();
												            }
												            catch (IOException e)
												            {
												                e.printStackTrace();
												            }
												            return str;
														}
														public int nextInt()
														{
															int c = read();
															
															while(isSpaceChar(c)) 
																c = read();
															
															int sgn = 1;
															
															if (c == '-') 
															{
																sgn = -1;
																c = read();
															}
															
															int res = 0;
															do 
															{
																if(c<'0'||c>'9') 
																	throw new InputMismatchException();
																res *= 10;
																res += c - '0';
																c = read();
															}
															while (!isSpaceChar(c)); 
															
															return res * sgn;
														}
														
														public long nextLong() 
														{
															int c = read();
															while (isSpaceChar(c))
																c = read();
															int sgn = 1;
															if (c == '-') 
															{
																sgn = -1;
																c = read();
															}
															long res = 0;
															
															do 
															{
																if (c < '0' || c > '9')
																	throw new InputMismatchException();
																res *= 10;
																res += c - '0';
																c = read();
															}
															while (!isSpaceChar(c));
																return res * sgn;
														}
														
														public double nextDouble() 
														{
															int c = read();
															while (isSpaceChar(c))
																c = read();
															int sgn = 1;
															if (c == '-') 
															{
																sgn = -1;
																c = read();
															}
															double res = 0;
															while (!isSpaceChar(c) && c != '.') 
															{
																if (c == 'e' || c == 'E')
																	return res * Math.pow(10, nextInt());
																if (c < '0' || c > '9')
																	throw new InputMismatchException();
																res *= 10;
																res += c - '0';
																c = read();
															}
															if (c == '.') 
															{
																c = read();
																double m = 1;
																while (!isSpaceChar(c)) 
																{
																	if (c == 'e' || c == 'E')
																		return res * Math.pow(10, nextInt());
																	if (c < '0' || c > '9')
																		throw new InputMismatchException();
																	m /= 10;
																	res += (c - '0') * m;
																	c = read();
																}
															}
															return res * sgn;
														}
														
														public String readString() 
														{
															int c = read();
															while (isSpaceChar(c))
																c = read();
															StringBuilder res = new StringBuilder();
															do 
															{
																res.appendCodePoint(c);
																c = read();
															} 
															while (!isSpaceChar(c));
															
															return res.toString();
														}
													 
														public boolean isSpaceChar(int c) 
														{
															if (filter != null)
																return filter.isSpaceChar(c);
															return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
														}
													 
														public String next() 
														{
															return readString();
														}
														
														public interface SpaceCharFilter 
														{
															public boolean isSpaceChar(int ch);
														}
													}
												 	
													public static void main(String args[]) throws Exception
													{
														new Thread(null, new Solution1(),"Solution",1<<26).start();
													}
														
													public static int gcd(int a, int b)
												    {
												        if (a == 0)
												            return b;
												         
												        return gcd(b%a, a);
												    }
													int lcm(int a, int b)
													{
													    return (a*b)/gcd(a, b);
													}
													
													int level = 20;
													int root = 1;
													TreeSet<Integer> arr[];
													public void run() 
													{
														InputReader sc= new InputReader(System.in);
														PrintWriter w= new PrintWriter(System.out);
														int n = sc.nextInt();
														String s=  sc.next();
														if(n == 1) {
															if(s.charAt(0) == '1') {
																w.println("Yes");
															}else {
																w.println("NO");
															}
															w.close();
															System.exit(0);
														}
														for(int i = 1;i < s.length();i++) {
															if(s.charAt(i) == '1' && s.charAt(i-1) == '1') {
																w.println("NO");
																w.close();
																System.exit(0);
															}
														}
														boolean flag = true;
														for(int i = 0;i < s.length();i++) {
															if(s.charAt(i) == '0' && i != 0 && i != s.length()-1) {
																if(s.charAt(i+1) == '0' && s.charAt(i-1) == '0') {
																	flag = false;
																}
															}
															if(i == 0 && s.charAt(i) == '0') {
																if(s.charAt(1) == '0') {
																	flag = false;
																}
															}if(i == s.length()-1 && s.charAt(i) == '0') {
																if(s.charAt(i-1) == '0') {
																	flag = false;
																}
															}
														}
														if(flag) {
															w.println("Yes");
														}else {
															w.println("No");
														}
														w.close(); 
													}
													
													static class Pair implements Comparable<Pair>{
														long x;
														long y;
														
														Pair(){}	
														Pair(long x,long y){
															this.x = x;
															this.y = y;
															
														}
														public int compareTo(Pair p){
															if(p.x == this.x) {
																return Long.compare(this.y,p.y);
															}
															return Long.compare(this.x,p.x);
														}
													}
													
									}