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.math.BigInteger;
import java.util.*;

public class Main {

    void solve() throws IOException {
        int n = readInt();
        int[] a = readIntArray(n);
        int[] arr = {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, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31};
        n = arr.length;
        boolean flag;
        for (int i = 0; i < n - a.length; i++) {
            flag = true;
            for (int j = 0; j < a.length; j++) {
                if (arr[i + j] != a[j]) flag = false;
            }
            if (flag) {
                out.println("Yes");
                return;
            }
        }
        out.println("No");

    }

    int checkBit(int mask, int bit) {
        return (mask >> bit) & 1;
    }

    public static void main(String[] args) throws IOException {

        new Main().run();
    }

    boolean isLower(char a) {
        return ((int) a) >= 97 ? true : false;
    }

    int INF = Integer.MAX_VALUE / 10;

    int[][] STEPS = {{0, 1}, {1, 0}, {-1, 0}, {0, -1}};

    BufferedReader in;
    PrintWriter out;
    StringTokenizer tok;
    Random rnd = new Random();
    static final boolean ONLINE_JUDGE = System.getProperty("ONLINE_JUDGE") != null;

    Main() throws FileNotFoundException {

        try {
            in = new BufferedReader(new FileReader("input.txt"));
            out = new PrintWriter("output.txt");
        } catch (Exception e) {
            in = new BufferedReader(new InputStreamReader(System.in));
            out = new PrintWriter(System.out);
        }

        tok = new StringTokenizer("");
    }

    long checkBit(long mask, int bit) {
        return (mask >> bit) & 1;
    }

    void run() throws IOException {
        solve();
        out.close();
    }

    char varChar;
    int varInt, varInt1, varInt2;
    long varLong;

    long sqrt(long m) {
        long l = 0;
        long r = m;
        long answer = 0;
        long mid = 0;
        while (l <= r) {
            mid = (l + r) / 2;
            if (mid * mid <= m) {
                answer = mid;
                l = mid + 1;
            } else r = mid - 1;
        }
        return answer;
    }

    int countPow(int m, int n) {
        varInt = 0;
        while (m % n == 0 && m > 0) {
            varInt++;
            m /= n;
        }
        return varInt;
    }

    long binPow(long a, long b) {
        if (b == 0) {
            return 1;
        }
        if (b % 2 == 1) {
            return a * binPow(a, b - 1);
        } else {
            varLong = binPow(a, b / 2);
            return varLong * varLong;
        }

    }

    int gcd(int a, int b) {
        return b == 0 ? a : gcd(b, a % b);
    }

    long pow(long x, long k) {
        varLong = 1;
        for (int i = 0; i < k; ++i) {
            varLong *= x;
        }
        return varLong;
    }

    class Fenwik {
        private long[] t;
        private int length;

        Fenwik(int[] a) {
            this.length = a.length + 100;
            this.t = new long[length];
            for (int i = 0; i < a.length; ++i) {
                this.inc(i, a[i]);
            }
        }

        void inc(int i, int delta) {
            for (; i < this.length; i = i | (i + 1)) {
                this.t[i] += delta;
            }
        }

        long getSum(int r) {
            long sum = 0;

            for (; r >= 0; r = (r & (r + 1)) - 1) {
                sum += this.t[r];
            }

            return sum;
        }

    }

    // ////////////////////////////////////////////////////////////////////

    String delimiter = " ";

    String readLine() throws IOException {
        return in.readLine();
    }

    String readString() throws IOException {
        while (!tok.hasMoreTokens()) {
            String nextLine = readLine();
            if (null == nextLine)
                return null;

            tok = new StringTokenizer(nextLine);
        }

        return tok.nextToken(delimiter);
    }

    int readInt() throws IOException {
        return Integer.parseInt(readString());
    }

    long readLong() throws IOException {
        return Long.parseLong(readString());
    }

    double readDouble() throws IOException {
        return Double.parseDouble(readString());
    }

    int[] readIntArray(int b) {
        int a[] = new int[b];
        for (int i = 0; i < b; i++) {
            try {
                a[i] = readInt();
            } catch (IOException e) {
                e.printStackTrace();
            }
        }
        return a;
    }

    int[] readSortedIntArray(int size) throws IOException {
        Integer[] array = new Integer[size];

        for (int index = 0; index < size; ++index) {
            array[index] = readInt();
        }
        Arrays.sort(array);

        int[] sortedArray = new int[size];
        for (int index = 0; index < size; ++index) {
            sortedArray[index] = array[index];
        }

        return sortedArray;
    }

    int[] sortedIntArray(int size, int[] array) throws IOException {
        for (int index = 0; index < size; ++index) {
            array[index] = readInt();
        }
        Arrays.sort(array);

        int[] sortedArray = new int[size];
        for (int index = 0; index < size; ++index) {
            sortedArray[index] = array[index];
        }

        return sortedArray;
    }

    int minInt(int... values) {
        int min = Integer.MAX_VALUE;
        for (int value : values) {
            min = Math.min(min, value);
        }
        return min;
    }

    int maxInt(int... values) {
        int max = Integer.MIN_VALUE;
        for (int value : values) {
            max = Math.max(max, value);
        }
        return max;
    }

    long minLong(long... values) {
        long min = Long.MAX_VALUE;
        for (long value : values) {
            min = Math.min(min, value);
        }
        return min;
    }

    long maxLong(long... values) {
        long max = Long.MIN_VALUE;
        for (long value : values) {
            max = Math.max(max, value);
        }
        return max;
    }

    boolean checkIndex(int index, int size) {
        return (0 <= index && index < size);
    }

    int abs(int a) {
        return Math.abs(a);
    }
}