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 Python (3.4.3) (judge verdict: Wrong Answer)

n=int(input())
if n==3:
    print("2 5 63")
elif n==6:
    print("3 4 6 8 9 10")
elif n==7:
    print("2 3 4 6 8 10 15")
else:
    res=[]
    count = 0
    for i in range(1,50000):
        if i % 2 == 0 or i % 3 == 0:
            res.append(i)
            count += 1
        if count == n-1:
            break

    s=sum(res)
    t=res[-1]
    f1 = s%2
    f2 = s%3
    if f1==0 and f2 == 0:
        flag = 0
    elif f1==0 and f2==1:
        flag = 2
    elif f1==0 and f2==2:
        flag = 4
    if f1==1 and f2 == 0:
        flag = 3
    elif f1==1 and f2==1:
        flag = 5
    elif f1==1 and f2==2:
        flag = 1

    if flag == 5 or flag ==1:
        res.pop(1)
        f=0
        for i in range(t+1,t+10):
            if i % 2==0:
                res.append(i)
                f+=1
            if f==2:
                break

    else:
        for i in range(t+1,t+10):
            if i % 6 == flag:
                res.append(i)
                break

    print(" ".join(map(str, res)))