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

public class Main implements Runnable {

    int maxn = (int)2e5+111;
    int mod = (int)1e9+7;
    int inf = (int)1e9;
    int n,m,k;
    int a[] = new int[maxn];

    void solve() throws Exception {

        int n = in.nextInt();
        int normalYear[] = {31,28,31,30,31,30,31,31,30,31,30,31};
        int nightYear[] = {31,29,31,30,31,30,31,31,30,31,30,31};
        int fullYear [] = {31,28,31,30,31,30,31,31,30,31,30,31,31,28,31,30,31,30,31,31,30,31,30,31,31,28,31,30,31,30,31,31,30,31,30,31,31,29,31,30,31,30,31,31,30,31,30,31,
                31,28,31,30,31,30,31,31,30,31,30,31,31,28,31,30,31,30,31,31,30,31,30,31,31,28,31,30,31,30,31,31,30,31,30,31,31,29,31,30,31,30,31,31,30,31,30,31};

        for (int i=0; i<n; i++) {
            a[i] = in.nextInt();
        }

        for (int i=0; i<fullYear.length-n; i++) {
            boolean ok = true;
            for (int j=0; j<n; j++) {
                if (fullYear[i+j]!=a[j]) {
                    ok = false;
                    break;
                }
            }
            if (ok) {
                out.println("YES");
                return;
            }
        }

        out.println("NO");
    }

    class Pair implements Comparable<Pair> {
        int x;
        int y;
        public Pair (int x, int y) {
            this.x = x;
            this.y = y;

        }

        @Override
        public boolean equals(Object o) {
            if (this == o) return true;
            if (o == null || getClass() != o.getClass()) return false;

            Pair pair = (Pair) o;

            if (x != pair.x) return false;
            return y == pair.y;
        }

        @Override
        public int hashCode() {
            int result = x;
            result = 31 * result + y;
            return result;
        }

        @Override
        public int compareTo(Pair p) {
            if (this.y>p.y) {
                return 1;
            } else if(this.y == p.y) {
                if (this.x>p.x) return 1;
                else if (this.x==p.x) return 0;
                else return -1;
            } else {
                return -1;
            }
        }
    }


    String fileInName = "input.txt";
    boolean file = false;
    boolean isAcmp = true;

    static Throwable throwable;
    public static void main (String [] args) throws Throwable {
        Thread thread = new Thread(null, new Main(), "", (1 << 26));
        thread.start();
        thread.join();
        thread.run();
        if (throwable != null)
            throw throwable;
    }

    FastReader in;
    PrintWriter out;

    public void run() {
        String fileIn = "input.txt";
        String fileOut = "output.txt";

        try {
            if (isAcmp) {
                if (file) {
                    in = new FastReader(new BufferedReader(new FileReader(fileIn)));
                    out = new PrintWriter (fileOut);
                } else {
                    in = new FastReader(new BufferedReader(new InputStreamReader(System.in)));
                    out = new PrintWriter(System.out);
                }
            } else if (file) {
                in = new FastReader(new BufferedReader(new FileReader(fileInName+".in")));
                out = new PrintWriter (fileInName + ".out");
            } else {
                in = new FastReader(new BufferedReader(new InputStreamReader(System.in)));
                out = new PrintWriter(System.out);
            }

            solve();
        } catch(Exception e) {
            throwable = e;
        } finally {
            out.close();
        }

    }
}

class FastReader {
    BufferedReader bf;
    StringTokenizer tk = null;

    public FastReader(BufferedReader bf) {
        this.bf = bf;
    }

    public String nextToken () throws Exception {
        if (tk==null || !tk.hasMoreTokens()) {
            tk = new StringTokenizer(bf.readLine());
        }
        if (!tk.hasMoreTokens()) return nextToken();
        else
            return tk.nextToken();
    }

    public int nextInt() throws Exception {
        return Integer.parseInt(nextToken());
    }

    public long nextLong() throws Exception {
        return Long.parseLong(nextToken());
    }

    public double nextDouble() throws Exception {
        return Double.parseDouble(nextToken());
    }
}