Problem:
Score: 400 points

Problem Statement

Print a sequence a_1, a_2, ..., a_N whose length is N that satisfies the following conditions:

a_i (1 \leq i \leq N) is a prime number at most 55 555.

The values of a_1, a_2, ..., a_N are all different.

In every choice of five different integers from a_1, a_2, ..., a_N, the sum of those integers is a composite number.

If there are multiple such sequences, printing any of them is accepted.

Notes

An integer N not less than 2 is called a prime number if it cannot be divided evenly by any integers except 1 and N, and called a composite number otherwise.

Constraints

N is an integer between 5 and 55 (inclusive).

Input

Input is given from Standard Input in the following format:

N

Output

Print N numbers a_1, a_2, a_3, ..., a_N in a line, with spaces in between.

Sample Input 1

5

Sample Output 1

3 5 7 11 31

Let us see if this output actually satisfies the conditions.

First, 3, 5, 7, 11 and 31 are all different, and all of them are prime numbers.

The only way to choose five among them is to choose all of them, whose sum is a_1+a_2+a_3+a_4+a_5=57, which is a composite number.

There are also other possible outputs, such as 2 3 5 7 13, 11 13 17 19 31 and 7 11 5 31 3.

Sample Input 2

6

Sample Output 2

2 3 5 7 11 13

2, 3, 5, 7, 11, 13 are all different prime numbers.

2+3+5+7+11=28 is a composite number.

2+3+5+7+13=30 is a composite number.

2+3+5+11+13=34 is a composite number.

2+3+7+11+13=36 is a composite number.

2+5+7+11+13=38 is a composite number.

3+5+7+11+13=39 is a composite number.

Thus, the sequence 2 3 5 7 11 13 satisfies the conditions.

Sample Input 3

8

Sample Output 3

2 5 7 13 19 37 67 79

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.Arrays;
import java.util.Random;
import java.util.StringTokenizer;

public class Main {
    int n;

    public static void main(String args[]) {
        new Main().run();
    }

    void run() {
        FastReader sc = new FastReader();
        n = sc.nextInt();
        solve();
    }

    void solve() {
        boolean[] isPrime = new boolean[55555+1];
        for (int i = 2; i <= 55555; i++) {
            isPrime[i] = true;
        }

        // mark non-primes <= n using Sieve of Eratosthenes
        for (int factor = 2; factor*factor <= 55555; factor++) {

            // if factor is prime, then mark multiples of factor as nonprime
            // suffices to consider mutiples factor, factor+1, ...,  n/factor
            if (isPrime[factor]) {
                for (int j = factor; factor*j <= 55555; j++) {
                    isPrime[factor*j] = false;
                }
            }
        }
        int count = 0;
        int[] ans = new int[n];
        for (int j = 2; j <= 55555; j++) {
            if (isPrime[j] && j % 5 == 1) {
                ans[count++] = j;
            }
            if (count == n) break;
        }
        int[] primes = {2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541};
        //int[] ans = randomArray(n, primes);
        /*
        while(!check(ans)) {
            ans = randomArray(n, primes);
        }
        */
        for (int i = 0; i < n; i++) {
            System.out.print(ans[i]);
            if (i < n - 1) {
                System.out.print(" ");
            }
            System.out.println();
        }
        /*
        while(true) {
            outer:
            for (int i = 0; i < n - 4; i++) {
                for (int j = i + 1; i < n - 3; i++) {
                    for (int k = j + 1; k < n - 2; k++) {
                        for (int l = k + 1; l < n - 1; l++) {
                            for (int m = l + 1; m < n; m++) {
                                int sum = ans[i] + ans[j] + ans[k] + ans[l] + ans[m];
                                if (Arrays.binarySearch(primes, sum) >= 0) {
                                    for (int c = 0; c < ans.length; c++) {
                                        System.out.print(ans[c]);
                                        if (c < ans.length - 1) {
                                            System.out.print(" ");
                                        }
                                    }
                                    System.out.println();
                                    return;
                                } else {
                                    ans[m] = primes[m + count++];
                                    break outer;
                                }
                            }
                        }
                    }
                }
            }
        }
        */
    }

    int[] randomArray(int n, int[] primes) {
        int[] ret = new int[n];
        Random rn = new Random();
        boolean[] used = new boolean[primes.length];
        for (int i = 0; i < n; i++) {
            int newRand = rn.nextInt(primes.length);
            while (used[newRand]) {
                newRand = rn.nextInt(primes.length);
            }
            used[newRand] = true;
            ret[i] = primes[newRand];
        }
        return ret;
    }

    boolean check(int[] ans) {
        for (int i = 0; i < n - 4; i++) {
            for (int j = i + 1; i < n - 3; i++) {
                for (int k = j + 1; k < n - 2; k++) {
                    for (int l = k + 1; l < n - 1; l++) {
                        for (int m = l + 1; m < n; m++) {
                            int sum = ans[i] + ans[j] + ans[k] + ans[l] + ans[m];
                            if (isPrime(sum)) {
                                return false;
                            }
                        }
                    }
                }
            }
        }
        return true;
    }

    private static boolean isPrime(int num) {
        if (num < 2) return false;
        if (num == 2) return true;
        if (num % 2 == 0) return false;
        for (int i = 3; i * i <= num; i += 2)
            if (num % i == 0) return false;
        return true;
    }

    static class FastReader {
        BufferedReader br;
        StringTokenizer st;

        public FastReader() {
            br = new BufferedReader(new
                    InputStreamReader(System.in));
        }

        String next() {
            while (st == null || !st.hasMoreElements())
            {
                try
                {
                    st = new StringTokenizer(br.readLine());
                }
                catch (IOException e)
                {
                    e.printStackTrace();
                }
            }
            return st.nextToken();
        }

        int nextInt()
        {
            return Integer.parseInt(next());
        }

        long nextLong()
        {
            return Long.parseLong(next());
        }

        double nextDouble()
        {
            return Double.parseDouble(next());
        }

        String nextLine() {
            String str = "";
            try
            {
                str = br.readLine();
            }
            catch (IOException e)
            {
                e.printStackTrace();
            }
            return str;
        }
    }
}