Problem:
Score : 600 points

Problem Statement

Nagase is a top student in high school. One day, she's analyzing some properties of special sets of positive integers.

She thinks that a set S = \{a_{1}, a_{2}, ..., a_{N}\} of distinct positive integers is called special if for all 1 \leq i \leq N, the gcd (greatest common divisor) of a_{i} and the sum of the remaining elements of S is not 1.

Nagase wants to find a special set of size N. However, this task is too easy, so she decided to ramp up the difficulty. Nagase challenges you to find a special set of size N such that the gcd of all elements are 1 and the elements of the set does not exceed 30000.

Constraints

3 \leq N \leq 20000

Input

Input is given from Standard Input in the following format:

N

Output

Output N space-separated integers, denoting the elements of the set S. S must satisfy the following conditions :

The elements must be distinct positive integers not exceeding 30000.

The gcd of all elements of S is 1, i.e. there does not exist an integer d > 1 that divides all elements of S.

S is a special set.

If there are multiple solutions, you may output any of them. The elements of S may be printed in any order. It is guaranteed that at least one solution exist under the given contraints.

Sample Input 1

3

Sample Output 1

2 5 63

\{2, 5, 63\} is special because gcd(2, 5 + 63) = 2, gcd(5, 2 + 63) = 5, gcd(63, 2 + 5) = 7. Also, gcd(2, 5, 63) = 1. Thus, this set satisfies all the criteria.

Note that \{2, 4, 6\} is not a valid solution because gcd(2, 4, 6) = 2 > 1.

Sample Input 2

4

Sample Output 2

2 5 20 63

\{2, 5, 20, 63\} is special because gcd(2, 5 + 20 + 63) = 2, gcd(5, 2 + 20 + 63) = 5, gcd(20, 2 + 5 + 63) = 10, gcd(63, 2 + 5 + 20) = 9. Also, gcd(2, 5, 20, 63) = 1. Thus, this set satisfies all the criteria.

Solution in C++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#define _CRT_SECURE_NO_WARNINGS
#define _USE_MATH_DEFINES
#define _SILENCE_CXX17_RESULT_OF_DEPRECATION_WARNING
#include "bits/stdc++.h"
#define rep(i, n) for(int i=0; i<(n); ++i)
#define FOR(i, m, n) for(int i=(m); i<(n); ++i)
#define rrep(i, n) for(int i=(n)-1; i>=0; --i)
#define rfor(i, m, n) for(int i=(m); i>=(n); --i)
#define sz(x) ((int)(x).size())
#define all(x) (x).begin(),(x).end()
#define rall(x) (x).rbegin(),(x).rend()
#define range_it(a, l, r) (a).begin() + (l), (a).begin() + (r)

using namespace std;
using LL = long long;		using ld = long double;
using VB = vector<bool>;	using VVB = vector<VB>;
using VI = vector<int>;		using VVI = vector<VI>;
using VL = vector<LL>;		using VVL = vector<VL>;
using VS = vector<string>;	using VD = vector<double>;
using PII = pair<int, int>;	using VP = vector<PII>;
using PLL = pair<LL, LL>;	using VPL = vector<PLL>;
template<class T>using Grid = vector<vector<T>>;
template<class T>using PQ = priority_queue<T>;
template<class T>using PQS = priority_queue<T, vector<T>, greater<T>>;
constexpr int inf = (int)1e9;
constexpr LL inf_ll = (LL)1e18, MOD = 1000000007;
constexpr ld PI = M_PI, EPS = 1e-12;

template<class T>inline void Sort(T& a)noexcept { sort(all(a)); }
template<class T>inline void RSort(T& a)noexcept { sort(rall(a)); }
template<class T>inline void Reverse(T& a)noexcept { reverse(all(a)); }
template<class T>inline void Unique(T& a)noexcept { a.erase(unique(all(a)), a.end()); }
template<class T>inline T Sorted(T a)noexcept { Sort(a); return a; }
template<class T>inline T RSorted(T a)noexcept { RSort(a); return a; }
template<class T>inline T Reversed(T a)noexcept { Reverse(a); return a; }
template<class T>inline T Uniqued(T a)noexcept { Unique(a); return a; }
template<class T>inline auto Max(const T& a)noexcept { return *max_element(all(a)); }
template<class T>inline auto Min(const T& a)noexcept { return *min_element(all(a)); }
template<class T>inline int MaxPos(const T& a)noexcept { return max_element(all(a)) - a.begin(); }
template<class T>inline int MinPos(const T& a)noexcept { return min_element(all(a)) - a.begin(); }
template<class T, class U>inline int Count(const T& a, const  U& v)noexcept { return count(all(a), v); }
template<class T, class U>inline int Find(const T& a, const U& v)noexcept { auto pos = find(all(a), v); return pos == a.end() ? -1 : pos - a.begin(); }
template<class T, class U>inline U Sum(const T& a, const U& v)noexcept { return accumulate(all(a), v); }
template<class T, class U>inline int Lower(const T& a, const U& v)noexcept { return lower_bound(all(a), v) - a.begin(); }
template<class T, class U>inline int Upper(const T& a, const U& v)noexcept { return upper_bound(all(a), v) - a.begin(); }
template<class T, class P>inline void RemoveIf(T& a, P f)noexcept { a.erase(remove_if(all(a), f), a.end()); }
template<class T>inline T Age(T n, T m)noexcept { return (n + m - 1) / m; }
template<class T>inline T Age2(T n, T m)noexcept { return Age(n, m) * m; }
template<class T>inline T Tri(T n)noexcept { return (n & 1) ? (n + 1) / 2 * n : n / 2 * (n + 1); }
template<class T = long long>inline T BIT(int b)noexcept { return T{ 1 } << b; }
template<class T>inline T Gcd(T n, T m)noexcept { return m ? Gcd(m, n % m) : n; }
template<class T>inline T Lcm(T n, T m)noexcept { return n / Gcd(n, m) * m; }
template<class T>inline T Pow(T a, T n)noexcept { T r = 1; while (n > 0) { if (n & 1)r *= a; a *= a; n /= 2; }return r; }
template<class T>inline T Powmod(T a, T n, T m = MOD)noexcept { T r = 1; while (n > 0) { if (n & 1)r = r * a % m, n--; else a = a * a % m, n /= 2; }return r; }
template<class T>inline bool chmax(T& a, const T& b)noexcept { if (a < b) { a = b; return true; } return false; }
template<class T>inline bool chmin(T& a, const T& b)noexcept { if (a > b) { a = b; return true; } return false; }
template<class T>inline bool inRange(const T& v, const T& min, const T& max)noexcept { return min <= v && v <= max; }
inline string operator*(string s, int n)noexcept { string ret; rep(i, n)ret += s; return ret; }

// --- input --- //
#if defined(_WIN32) || defined(ONLINE_JUDGE)
#define getchar_unlocked _getchar_nolock
#define putchar_unlocked _putchar_nolock
#endif
inline int gc()noexcept { return getchar_unlocked(); }
template<class T>inline void InputF(T& v)noexcept { cin >> v; }
inline void InputF(char& v)noexcept { while (isspace(v = gc())); }
inline void InputF(string& v)noexcept {
	char c; for (InputF(c); !isspace(c); c = gc())v += c;
}
inline void InputF(int& v)noexcept {
	bool neg = false; v = 0; char c; InputF(c);
	if (c == '-') { neg = true; c = gc(); }
	for (; isdigit(c); c = gc())v = v * 10 + (c - '0');
	if (neg)v = -v;
}
inline void InputF(long long& v)noexcept {
	bool neg = false; v = 0; char c; InputF(c);
	if (c == '-') { neg = true; c = gc(); }
	for (; isdigit(c); c = gc())v = v * 10 + (LL)(c - '0');
	if (neg)v = -v;
}
inline void InputF(double& v)noexcept {
	double dp = 1; bool neg = false, adp = false; v = 0; char c; InputF(c);
	if (c == '-') { neg = true; c = gc(); }
	for (; isdigit(c) || c == '.'; c = gc()) {
		if (c == '.')adp = true;
		else if (adp)v += (c - '0') * (dp *= 0.1);
		else v = v * 10 + (c - '0');
	}
	if (neg)v = -v;
}
template<class T, class U>inline void InputF(pair<T, U>& v)noexcept {
	InputF(v.first); InputF(v.second);
}
template<class T>inline void InputF(vector<T>& v)noexcept {
	for (auto& e : v)InputF(e);
}
template<class T>inline T InputF() { T v; InputF(v); return v; }
struct InputV {
	int n, m;
	InputV(int N) :n(N), m(0) {}
	InputV(pair<int, int> N) :n(N.first), m(N.second) {}
	template<class T>operator vector<T>()noexcept {
		vector<T> v(n); InputF(v); return v;
	}
	template<class T>operator vector<vector<T>>()noexcept {
		vector<vector<T>> v(n, vector<T>(m)); InputF(v); return v;
	}
};
struct Input {
	template<class T>operator T()noexcept { return InputF<T>(); }
	int operator--(int) { int v; InputF(v); v--; return v; }
	InputV operator[](int n)noexcept { return InputV(n); }
	InputV operator[](pair<int, int> n)noexcept { return InputV(n); }
	void operator()() {}
	template<class H, class...T>void operator()(H&& h, T&& ...t) {
		InputF(h); operator()(forward<T>(t)...);
	}
	template<class T, size_t W>array<vector<T>, W> get(int H) {
		array<vector<T>, W> ret;
		rep(i, H)rep(j, W) { T x = *this; ret[j].push_back(x); }
		return ret;
	}
}in;
#define input(type) InputF<type>()

// --- output --- //
struct BoolStr {
	const char* t, * f; BoolStr(const char* _t, const char* _f) :t(_t), f(_f) {}
}Yes("Yes", "No"), yes("yes", "no"), YES("YES", "NO"), Int("1", "0");
struct DivStr {
	const char* d, * l; DivStr(const char* _d, const char* _l) :d(_d), l(_l) {}
}spc(" ", "\n"), no_spc("", "\n"), end_line("\n", "\n"), comma(",", "\n"), no_endl(" ", "");
class Output {
	BoolStr B{ Yes }; DivStr D{ spc }; bool isPrint = true;
	void p(double v) { printf("%.20f", v); } void p(long double v) { printf("%.20Lf", v); }
	void p(int v) { printf("%d", v); }	void p(LL v) { printf("%lld", v); }
	void p(char v) { putchar(v); }		void p(bool v) { printf("%s", v ? B.t : B.f); }
	template<class T>void p(const T& v) { cout << v; }
	template<class T, class U>void p(const pair<T, U>& v) { p(v.first); printf("%s", D.d); p(v.second); }
	template<class T>void p(const vector<T>& v) { rep(i, sz(v)) { if (i)printf("%s", D.d); p(v[i]); } }
	template<class T>void p(const vector<vector<T>>& v) { rep(i, sz(v)) { if (i)printf("%s", D.l); p(v[i]); } }
	void p(const BoolStr& v) { B = v; isPrint = false; } void p(const DivStr& v) { D = v; isPrint = false; }
public:
	void operator()() { printf("%s", D.l); }
	template<class H>void operator()(H&& h) {
		p(h); if (isPrint)printf("%s", D.l); isPrint = true;
	}
	template<class H, class...T>void operator()(H&& h, T&& ...t) {
		p(h); if (isPrint)printf("%s", D.d); isPrint = true; operator()(forward<T>(t)...);
	}
	template<class...T>void exit(T&& ...t) {
		operator()(forward<T>(t)...); std::exit(EXIT_SUCCESS);
	}
}out;

// --- dump --- //
#if __has_include("dump.hpp")
#include "dump.hpp"
#else
#define dump(...) (void(0))
#endif

template<class F>auto MakeVector(size_t size, F f) {
	vector<decay_t<result_of_t<F(size_t)>>> res(size);
	for (size_t i = 0; i < size; ++i)res[i] = f(i);
	return res;
}
template<class T>vector<T> Slice(const vector<T>& v, size_t i, size_t len) {
	return i < v.size() ? vector<T>(v.begin() + i, v.begin() + min(i + len, v.size())) : vector<T>();
}
template<class T, class F>void Each(T& v, F f) {
	for (auto& e : v)f(e);
}
template<class T, class F>auto Map(const vector<T>& v, F f) {
	vector<decay_t<result_of_t<F(T)>>> res(v.size());
	size_t i = 0; for (const auto& e : v)res[i++] = f(e);
	return res;
}
template<class T, class F>auto MapIndex(const vector<T>& v, F f) {
	vector<decay_t<result_of_t<F(size_t, T)>>> res(v.size());
	for (size_t i = 0; i < v.size(); ++i)res[i] = f(i, v[i]);
	return res;
}
template<class T, class F>vector<T> Select(const vector<T>& v, F f) {
	vector<T> res;
	for (const auto& e : v)if (f(e))res.push_back(e);
	return res;
}
template<class T, class F>vector<size_t>TrueIndex(const vector<T>& v, F f) {
	vector<size_t> res;
	size_t i = 0; for (const auto& e : v) {
		if (f(e))res.push_back(i); i++;
	}
	return res;
}

// ---------------------------------------------------------------- //

vector<bool> Eratosthenes(int n) {
	vector<bool> p(n + 1, true);
	p[0] = p[1] = false;
	for (int i = 0; i <= n; ++i)if (p[i])
		for (int j = i * 2; j <= n; j += i)p[j] = false;
	return p;
}

vector<int> Prime(int n) {
	vector<int> ret;
	auto p = Eratosthenes(n);
	for (int i = 0; i <= n; ++i)
		if (p[i])ret.push_back(i);
	return ret;
}

int main() {
	int N = in;

	const int MAX_A = 30000;
	auto eratos = Eratosthenes(MAX_A);

	auto solve = [&](int n, const VI& primes) {

		vector<bool> ans(MAX_A + 1);
		ans[primes[0]] = true;
		ans[primes[1]] = true;
		n -= 2;

		for (auto p : primes) {
			for (int i = p; n >= 2 && i <= MAX_A; i += p) {
				if (!ans[i]) {
					ans[i] = true;
					n--;
				}
			}
		}
		int multi = 1, sum = 0;
		rep(i, MAX_A + 1) {
			if (ans[i]) {
				sum += i;
				if (eratos[i])
					multi *= i;
			}
		}
		for (int i = (sum / multi + 1) * multi; i - sum <= MAX_A; i += multi) {
			int num = i - sum;
			if (!ans[num] && Gcd(i, num) != 1) {
				ans[num] = true;
				break;
			}
		}

		auto a = TrueIndex(ans, [](bool b) {return b; });
		if (sz(a) == N)
			out.exit(a);
	};

	auto primes = Prime(MAX_A);
	solve(N, primes);
	while (!primes.empty()) {
		primes.erase(primes.begin());
		solve(N, primes);
	}
}