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)

import random
import fractions
from functools import reduce

def main():
    N = int(input().strip())

    S3not2 = []
    S2not3 = []
    S2and3 = []
    for i in range(2, 30000+1):
        if i % 3 == 0 and i % 2 != 0:
            S3not2.append(i)
        elif i % 2 == 0 and i %3 != 0:
            S2not3.append(i)
        elif i % 6 == 0:
            S2and3.append(i)

    if N == 3:
        return '2 5 63'


    S = S2not3[:2] + S3not2[:2]
    S2not3 = S2not3[2:]
    S3not2 = S3not2[2:]
    N -= 4

    if N < len(S2not3):
        if N % 2 == 0:
            S += S2not3[:N]
        else:
            S += S2not3[:N-1]
            S.append(S2and3[0])
    elif N < len(S2not3) + len(S3not2):
        if N % 2 == 0:
            S += S2not3 + S3not2[:N-len(S2not3)]
        else:
            S += S2not3 + S3not2[:N-len(S2not3)-1]
            S.append(S2and3[0])
    else:
        S = S2not3 + S3not2
        S += S2and3[:N-len(S)]

    return ' '.join(map(str, S))


if __name__ == '__main__':
    print(main())