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: Wrong Answer)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Collections;
import java.util.Comparator;
import java.util.HashMap;
import java.util.Iterator;
import java.util.List;
import java.util.Map;
import java.util.Set;

public class Main {
	final int _intMax = Integer.MAX_VALUE; // =2147483647>10^9
	final int _intMin = Integer.MIN_VALUE;
	final long _longMax = Long.MAX_VALUE; // =9223372036854775807L>10^18
	final long _longMin = Long.MIN_VALUE;
	final char[] _azAry = { 'a', 'b', 'c', 'd', 'e', 'f', 'g', 'h', 'i', 'j', 'k', 'l', 'm', 'n', 'o', 'p', 'q', 'r',
			's', 't', 'u', 'v', 'w', 'x', 'y', 'z' };

	int[] p = { 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, };
	List<Integer> pl = new ArrayList<>();

	void init() {
		for (int i = 2; i <= 55555; i++) {
			if (isPrime(i))
				pl.add(i);
		}
	}

	boolean check(List<Integer> l) {
		int sum = 0;
		for (int i = 0; i < 5; i++) {
			sum += l.get(i);
		}
		if (isPrime(sum))
			return false;
		for (int i = 5; i < l.size(); i++) {
			sum -= l.get(i - 5);
			sum += l.get(i);
			if (isPrime(sum))
				return false;
		}
		return true;
	}

	void solve() {
		init();
		int n = readNum();
		while (true) {
			List<Integer> l = new ArrayList<>();
			while (l.size() < n) {
				int idx = (int) (Math.random() * pl.size());
				int pp = pl.get(idx);
				if (l.contains(pp))
					continue;
				l.add(pp);
			}
			if (check(l)) {
				for (int i = 0; i < n - 1; i++) {
					p(l.get(i)).p(" ");
				}
				p(l.get(n - 1));
				return;
			}
		}
	}

	public static boolean isPrime(int num) {
		if (num < 2)
			return false;
		else if (num == 2)
			return true;
		else if (num % 2 == 0)
			return false; // 偶数はあらかじめ除く

		double sqrtNum = Math.sqrt(num);
		for (int i = 3; i <= sqrtNum; i += 2) {
			if (num % i == 0) {
				// 素数ではない
				return false;
			}
		}

		// 素数である
		return true;
	}

	// -----------------------------------------------------
	// 2018/05/05 r26
	// -----------------------------------------------------
	List<Character> getazList() {
		List<Character> list = new ArrayList<>();
		for (char ch : _azAry)
			list.add(ch);
		return list;
	}

	int getDx(int idx) {
		int[] dx = { 0, 1, 1, 1, 0, -1, -1, -1 };
		return dx[idx];
	}

	int getDy(int idx) {
		int[] dy = { -1, -1, 0, 1, 1, 1, 0, -1 };
		return dy[idx];
	}

	class Bitmap {
		int mx;
		int my;
		boolean[][] map;

		public Bitmap(int mx, int my) {
			this.mx = mx;
			this.my = my;
			map = new boolean[my + 2][mx + 2];
		}

		public boolean is(int x, int y) {
			return map[y][x];
		}

		public void set(int x, int y, boolean b) {
			map[y][x] = b;
		}
	}

	class CharList implements Iterable<Character> {
		class CharComparator implements Comparator<Character> {
			int sign;

			public CharComparator(boolean bAsc) {
				sign = bAsc ? 1 : -1;
			}

			public int compare(Character o1, Character o2) {
				return sign * Character.compare(o1, o2);
			}
		}

		List<Character> list = new ArrayList<>();
		CharComparator asc = new CharComparator(true);
		CharComparator desc = new CharComparator(false);

		public void add(char ch) {
			list.add(ch);
		}

		public char get(int idx) {
			return list.get(idx);
		}

		public char getLast() {
			return list.get(list.size() - 1);
		}

		public Iterator<Character> iterator() {
			return list.iterator();
		}

		public void remove(int idx) {
			list.remove(idx);
		}

		public void removeLast() {
			list.remove(list.size() - 1);
		}

		public int size() {
			return list.size();
		}

		public void sort(boolean bAsc) {
			if (bAsc)
				Collections.sort(list, asc);
			else
				Collections.sort(list, desc);
		}

		public String toString() {
			StringBuilder sb = new StringBuilder();
			for (char ch : list)
				sb.append(ch);
			return sb.toString();
		}
	}

	class Counter<K> {
		Map<K, Integer> map = new HashMap<>();

		public Counter() {
		}

		public Counter(Iterable<K> itr) {
			for (K obj : itr) {
				add(obj);
			}
		}

		public void add(K key) {
			Integer cnt = map.get(key);
			if (cnt == null)
				map.put(key, 1);
			else
				map.put(key, cnt + 1);
		}

		public int get(K key) {
			Integer cnt = map.get(key);
			if (cnt == null)
				return 0;
			else
				return cnt;
		}

		public Set<K> keySet() {
			return map.keySet();
		}
	}

	class IntList implements Iterable<Integer> {
		class Info {
			int idx;
			int val;

			public Info(int idx, int val) {
				this.idx = idx;
				this.val = val;
			}

			public String toString() {
				return "(" + idx + ", " + val + ")";
			}
		}

		class InfoComparator implements Comparator<Info> {
			int sign;

			public InfoComparator(boolean bAsc) {
				sign = bAsc ? 1 : -1;
			}

			public int compare(Info o1, Info o2) {
				return sign * Integer.compare(o1.val, o2.val);
			}
		}

		List<Info> list = new ArrayList<>();
		InfoComparator asc = new InfoComparator(true);
		InfoComparator desc = new InfoComparator(false);

		public IntList() {
		}

		public IntList(int[] ia) {
			for (int i = 0; i < ia.length; i++)
				add(ia[i]);
		}

		public void add(int val) {
			list.add(new Info(list.size(), val));
		}

		public void add(int idx, int val) {
			list.add(new Info(idx, val));
		}

		public int getIdx(int idx) {
			return list.get(idx).idx;
		}

		public int getVal(int idx) {
			return list.get(idx).val;
		}

		public int getLastVal() {
			return list.get(list.size() - 1).val;
		}

		public Iterator<Integer> iterator() {
			List<Integer> vallist = new ArrayList<>();
			for (Info info : list)
				vallist.add(info.val);
			return vallist.iterator();
		}

		public void remove(int idx) {
			list.remove(idx);
		}

		public void removeLast() {
			list.remove(list.size() - 1);
		}

		public int size() {
			return list.size();
		}

		public void sort(boolean bAsc) {
			if (bAsc)
				Collections.sort(list, asc);
			else
				Collections.sort(list, desc);
		}
	}

	class Point {
		int x;
		int y;

		public Point(int x, int y) {
			this.x = x;
			this.y = y;
		}

		public Point(Point pt) {
			this.x = pt.x;
			this.y = pt.y;
		}

		public boolean equals(Object o) {
			if (o instanceof Point) {
				Point that = (Point) o;
				return (x == that.x) && (y == that.y);
			}
			return false;
		}

		public long getManhattanDistance(Point pt) {
			return abs((long) pt.x - this.x) + abs((long) pt.y - this.y);
		}

		public int hashCode() {
			return x + (y * 31);
		}

		public String toString() {
			return "(" + x + ", " + y + ")";
		}
	}

	class PointList implements Iterable<Point> {
		class PointComparator implements Comparator<Point> {
			int mode;

			public PointComparator(int prop, boolean bAsc) {
				switch (prop) {
				case 1:
					if (bAsc)
						this.mode = 11;
					else
						this.mode = 12;
					break;
				case 2:
					if (bAsc)
						this.mode = 21;
					else
						this.mode = 22;
					break;
				default:
					throw new RuntimeException();
				}
			}

			public int compare(Point p1, Point p2) {
				switch (mode) {
				case 11:
					return 1 * Integer.compare(p1.x, p2.x);
				case 12:
					return -1 * Integer.compare(p1.x, p2.x);
				case 21:
					return 1 * Integer.compare(p1.y, p2.y);
				case 22:
					return -1 * Integer.compare(p1.y, p2.y);
				}
				throw new IllegalStateException();
			}
		}

		List<Point> list = new ArrayList<>();

		public void add(int x, int y) {
			list.add(new Point(x, y));
		}

		public Point get(int idx) {
			return list.get(idx);
		}

		public Iterator<Point> iterator() {
			return list.iterator();
		}

		public void remove(int idx) {
			list.remove(idx);
		}

		public int size() {
			return list.size();
		}

		public void sort(int prop, boolean bAsc) {
			PointComparator c = new PointComparator(prop, bAsc);
			Collections.sort(list, c);
		}
	}

	class StrList implements Iterable<String> {
		class StrComparator implements Comparator<String> {
			int sign;

			public StrComparator(boolean bAsc) {
				sign = bAsc ? 1 : -1;
			}

			public int compare(String o1, String o2) {
				return sign * o1.compareTo(o2);
			}
		}

		List<String> list = new ArrayList<>();
		StrComparator asc = new StrComparator(true);
		StrComparator desc = new StrComparator(false);

		public StrList() {
		}

		public StrList(String[] sa) {
			for (int i = 0; i < sa.length; i++)
				list.add(sa[i]);
		}

		public void add(String s) {
			list.add(s);
		}

		public String get(int idx) {
			return list.get(idx);
		}

		public Iterator<String> iterator() {
			return list.iterator();
		}

		public int size() {
			return list.size();
		}

		public void sort(boolean bAsc) {
			if (bAsc)
				Collections.sort(list, asc);
			else
				Collections.sort(list, desc);
		}
	}

	int abs(int a) {
		return (a >= 0) ? a : -a;
	}

	long abs(long a) {
		return (a >= 0) ? a : -a;
	}

	long ceil(long a, long b) {
		if (a < 0) {
			return -1 * floor(-a, b);
		}
		return ((a + b - 1) / b) * b;
	}

	long floor(long a, long b) {
		if (a < 0) {
			return -1 * ceil(-a, b);
		}
		return (a / b) * b;
	}

	int max(int a, int b) {
		return (a > b) ? a : b;
	}

	long max(long a, long b) {
		return (a > b) ? a : b;
	}

	int min(int a, int b) {
		return (a < b) ? a : b;
	}

	long min(long a, long b) {
		return (a < b) ? a : b;
	}

	int reed(long a, int n) {
		while (n-- > 0)
			a /= 10;
		return (int) (a % 10);
	}

	int sqrt(long a) {
		return (int) Math.sqrt(a);
	}

	int pint(String s) {
		return Integer.parseInt(s);
	}

	long plong(String s) {
		return Long.parseLong(s);
	}

	String readLine() {
		try {
			return _in.readLine();
		} catch (IOException e) {
			throw new RuntimeException(e);
		}
	}

	int readNum() {
		String line = readLine();
		return pint(line);
	}

	long readLong() {
		String line = readLine();
		return plong(line);
	}

	String[] readFlds() {
		String line = readLine();
		return line.split(" ");
	}

	String[] readLines(int n) {
		String[] lines = new String[n];
		for (int i = 0; i < n; i++)
			lines[i] = readLine();
		return lines;
	}

	CharList readChars() {
		CharList list = new CharList();
		String line = readLine();
		for (int i = 0; i < line.length(); i++)
			list.add(line.charAt(i));
		return list;
	}

	int[] readNums() {
		String[] flds = readFlds();
		int[] nums = new int[flds.length];
		for (int i = 0; i < flds.length; i++)
			nums[i] = pint(flds[i]);
		return nums;
	}

	int[] readNums(int n) {
		int[] nums = new int[n];
		for (int i = 0; i < n; i++)
			nums[i] = readNum();
		return nums;
	}

	long[] readLongs() {
		String[] flds = readFlds();
		long[] nums = new long[flds.length];
		for (int i = 0; i < flds.length; i++)
			nums[i] = plong(flds[i]);
		return nums;
	}

	long[] readLongs(int n) {
		long[] nums = new long[n];
		for (int i = 0; i < n; i++)
			nums[i] = readLong();
		return nums;
	}

	Main pln() {
		_out.println();
		return this;
	}

	Main p(char c) {
		_out.print(c);
		return this;
	}

	Main p(char c, int n) {
		for (int i = 0; i < n; i++)
			p(c);
		return this;
	}

	Main pln(char c) {
		_out.println(c);
		return this;
	}

	Main p(double d) {
		_out.print(d);
		return this;
	}

	Main pln(double d) {
		_out.println(d);
		return this;
	}

	Main p(long l) {
		_out.print(l);
		return this;
	}

	Main pln(long l) {
		_out.println(l);
		return this;
	}

	Main p(String s) {
		_out.print(s);
		return this;
	}

	Main p(String s, int idx) {
		_out.print(s.charAt(idx));
		return this;
	}

	Main pln(String s) {
		_out.println(s);
		return this;
	}

	Main pln(int[] ia) {
		for (int i = 0; i < ia.length; i++)
			_out.println(ia[i]);
		return this;
	}

	Main pln(long[] la) {
		for (int i = 0; i < la.length; i++)
			_out.println(la[i]);
		return this;
	}

	static BufferedReader _in;
	static PrintWriter _out;
	static boolean _bElapsed = false;

	public static void main(String[] args) {
		long start = System.currentTimeMillis();
		_in = new BufferedReader(new InputStreamReader(System.in));
		_out = new PrintWriter(System.out);
		new Main().solve();
		_out.flush();
		long end = System.currentTimeMillis();
		if (_bElapsed)
			System.err.println((end - start) + "ms");
	}
}