Problem: Everybody in Russia uses Gregorian calendar. In this calendar there are 31 days in January, 28 or 29 days in February (depending on whether the year is leap or not), 31 days in March, 30 days in April, 31 days in May, 30 in June, 31 in July, 31 in August, 30 in September, 31 in October, 30 in November, 31 in December.

A year is leap in one of two cases: either its number is divisible by 4, but not divisible by 100, or is divisible by 400. For example, the following years are leap: 2000, 2004, but years 1900 and 2018 are not leap.

In this problem you are given n (1 ≤ n ≤ 24) integers a1, a2, ..., an, and you have to check if these integers could be durations in days of n consecutive months, according to Gregorian calendar. Note that these months could belong to several consecutive years. In other words, check if there is a month in some year, such that its duration is a1 days, duration of the next month is a2 days, and so on.

Input

The first line contains single integer n (1 ≤ n ≤ 24) — the number of integers.

The second line contains n integers a1, a2, ..., an (28 ≤ ai ≤ 31) — the numbers you are to check.

Output

If there are several consecutive months that fit the sequence, print "YES" (without quotes). Otherwise, print "NO" (without quotes).

You can print each letter in arbitrary case (small or large).

Examples

Input

4
31 31 30 31


Output

Yes



Input

2
30 30


Output

No



Input

5
29 31 30 31 30


Output

Yes



Input

3
31 28 30


Output

No



Input

3
31 31 28


Output

Yes

Note

In the first example the integers can denote months July, August, September and October.

In the second example the answer is no, because there are no two consecutive months each having 30 days.

In the third example the months are: February (leap year) — March — April – May — June.

In the fourth example the number of days in the second month is 28, so this is February. March follows February and has 31 days, but not 30, so the answer is NO.

In the fifth example the months are: December — January — February (non-leap year).

Solution (in JAVA):

Solution:
//package codes;

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.stream.Collectors;

//import codes.Reference.i;

public class MonthsAndYears {
	public static void main(String[] args) {
		// TODO Auto-generated method stub
		
		long n = i.l();
		String s=i.s();
		
		String chk1 = "31 28 31 30 31 30 31 31 30 31 30 31 31 29 31 30 31 30 31 31 30 31 30 31 31 28 31 30 31 30 31 31 30 31 30 31";
		String chk2 = "31 28 31 30 31 30 31 31 30 31 30 31 31 28 31 30 31 30 31 31 30 31 30 31 31 28 31 30 31 30 31 31 30 31 30 31";
		String chk3 = "31 29 31 30 31 30 31 31 30 31 30 31 31 28 31 30 31 30 31 31 30 31 30 31 31 28 31 30 31 30 31 31 30 31 30 31";
		String chk4 = "31 28 31 30 31 30 31 31 30 31 30 31 31 28 31 30 31 30 31 31 30 31 30 31 31 29 31 30 31 30 31 31 30 31 30 31";
		System.out.println(ans(s,chk1,chk2,chk3,chk4));
	}
	private static String ans(String s, String chk1, String chk2, String chk3, String chk4) {
		// TODO Auto-generated method stub
		if(chk1.contains(s))
			return "Yes";
		if(chk2.contains(s))
			return "Yes";
		if(chk3.contains(s))
			return "Yes";
		if(chk4.contains(s))
			return "Yes";
		return "No";
	}
	static private class i
	{
		//input taking methods
		static BufferedReader b = new BufferedReader(new InputStreamReader(System.in));
		
		public static String[] sa()
	    {
	    	try {
				return b.readLine().split(" ");
			} catch (IOException e) {
				
				e.printStackTrace();
			}
	    	return null;
	    }
		
		public static long l()
		{
			try {
				return Long.parseLong(b.readLine());
			} catch (IOException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
	    	return 0;
		}
		
		public static String s()
		{
			try {
				return b.readLine();
			} catch (IOException e) {
				// TODO Auto-generated catch block
				e.printStackTrace();
			}
	    	return null;
		}
		
		public static long[] la()
		{
			return Arrays.stream(sa()).parallel().mapToLong(Long::parseLong).toArray();
		}
		
		public static ArrayList<Long> lal()
		{
			return (ArrayList<Long>)Arrays.stream(la()).parallel().boxed().collect(Collectors.toList());
		}
		public static StringBuilder so(String a)
		{
			return new StringBuilder(a);
		}

	}
	/*
	 HashMap<String,Integer> map = new HashMap<String,Integer>();
	 if(!map.containsKey(key))
	 {
	 	map.put(key,value);
	 }
	 else
	 {
	 	map.replace(key,map.get(key));
	 } 
	 */
	static private class algo{
		
		public static boolean isPrime(int a)
		{
			for(int i=2;i<a;i++)
			{
				if(a%i==0)
				{
					return false;
				}
			}
			return true;
		}
		static String reverse(String s)
		{
			return i.so(s).reverse().toString();
		}
		static String replace(String s,int st,int e,String repl)
		{
			return i.so(s).replace(st, e, repl).toString();
		}
		static String insert(String s,int pos,String ins)
		{
			return i.so(s).insert(pos, ins).toString();
		}
		static long sod(long n) 
	    { 
	        long sum; 
	        for (sum = 0; n > 0; sum += n % 10, 
	                                  n /= 10); 
	  
	        return sum; 
	    } 

		static int gcd(int a, int b) 
	    { 
			if (a == 0) 
				return b;  
			return gcd(b % a, a);  
	    } 
		
	    static int lcm(int a, int b) 
	    { 
	        return (a*b)/gcd(a, b); 
	    }
	    static long sumOfSquares(long[] a)
	    {
	    	
	    	return (long) Arrays.stream(a).mapToDouble(i->i*i).sum();
	    }
	    //use of filter
	    //Arrays.stream(a).filter(k->k==1).count();
	    //            array       variable->condition returning boolean  . lot fof functionsa re available
	    
	    static String[] generateBinSeq(int cnt)
	    {
	    	int loopvar=(int) Math.pow(2, cnt);
			String a[][] = new String[cnt+1][loopvar];
			
			for(int i=1;i<=cnt;i++)
			{
				int temp = (int) Math.pow(2, i);
				for(int j=0;j<temp;j++)
				{
					if(i==1 || i==2)
					{
						if(i==1)
						{
							a[i][0]="0";
							a[i][1]="1";
							continue;
						}
						else
						{
							a[2][0]="00";a[2][1]="01";a[2][2]="10";a[2][3]="11";
							continue;
						}
					}
					else
					{
						if(j<(temp/2))
						{
							a[i][j] = a[i-1][j]+"0"; 
						}
						else
						{
							a[i][j] = a[i-1][j%((temp+1)/2)]+"1";
						}
				
					}
						
				}
			}
	    
			return a[cnt];
	    }
	    
	 // USe this snippet for calling
//	    int ndx = algo.bs(a,key,0,a.length-1);
//		if(ndx<0)
//			ndx=0;
//		if(ndx==a.length)
//			ndx=a.length-1;

	    static public int bs(long a[],long key,int s,int e)
		{
			int m = (s+e)/2;
			if(s>e)
				return s;
				
			if(a[m]==key)
				return m;
			else if(a[m]>key)
				return bs(a,key,s,m-1);
			else
				return bs(a,key,m+1,e);
			
		}
	 // USe this snippet for calling
//	    int ndx = bsa(al,key,0,al.size()-1);
//		if(ndx<0)
//			ndx=0;
//		if(ndx==al.size())
//			ndx=al.size()-1;
	    static public int bsa(ArrayList<Long> a,long key,int s,int e)
		{
			int m = (s+e)/2;
			if(s>e)
				return s;
				
			if(a.get(m)==key)
				return m;
			else if(a.get(m)>key)
				return bsa(a,key,s,m-1);
			else
				return bsa(a,key,m+1,e);
			
		}
	    static public long fact(long a)
	    {
	    	long i,fact=1;  
	    	 long number=a;   
	    	  for(i=1;i<=number;i++){    
	    	      fact=fact*i;    
	    	  } 
	    	  return fact;
	    }
	    
	}
}