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: Accepted)

#include <bits/stdc++.h>
using namespace std;

using ll = long long;
using pii = pair<int, int>;

template <typename T> constexpr T inf;
template <> constexpr int inf<int> = 1e9;
template <> constexpr ll inf<ll> = 1e18;
template <> constexpr double inf<double> = 1e18;

template<typename T>
std::vector<T> table(int n, T v) { return std::vector<T>(n, v); }
 
template <class... Args>
auto table(int n, Args... args) {
    auto val = table(args...);
    return std::vector<decltype(val)>(n, std::move(val));
}


int main() {
    int N;
    cin >> N;
    if(N == 3) {
        cout << 2 << ' ' << 5 << ' ' << 63 << endl;
        return 0;
    }

    vector<int> two, three, six;
    for(int i = 2; i <= 30000; ++i) {
        if(i % 6 == 0) {
            six.push_back(i);
        } else if(i % 2 == 0) {
            two.push_back(i);
        } else if(i % 3 == 0) {
            three.push_back(i);
        }
    }
    reverse(begin(six), end(six));
    reverse(begin(two), end(two));
    reverse(begin(three), end(three));

    vector<int> ans;
    int m = N;
    ans.push_back(two.back()); two.pop_back();
    ans.push_back(two.back()); two.pop_back();
    ans.push_back(three.back()); three.pop_back();
    ans.push_back(three.back()); three.pop_back();
    m -= 4;
    while(m >= 2 && two.size() >= 2) {
        ans.push_back(two.back()); two.pop_back();
        ans.push_back(two.back()); two.pop_back();
        m -= 2;
    }
    while(m >= 2 && three.size() >= 2) {
        ans.push_back(three.back()); three.pop_back();
        ans.push_back(three.back()); three.pop_back();
        m -= 2;
    }
    while(m > 0) {
        ans.push_back(six.back());
        six.pop_back();
        m--;
    }
    sort(begin(ans), end(ans));

    for(int i = 0; i < N; ++i) {
        cout << ans[i] << " \n"[i + 1 == N];
    }

    // debug
    bool check = true;
    int sum = accumulate(begin(ans), end(ans), 0);
    int g = 0;
    for(int i = 0; i < N; ++i) {
        g = __gcd(ans[i], g);
        check &= __gcd(sum - ans[i], ans[i]) != 1;
    }
    check &= g == 1;
    assert(check);
}