Problem: Bachgold problem is very easy to formulate. Given a positive integer n represent it as a sum of maximum possible number of prime numbers. One can prove that such representation exists for any integer greater than 1.

Recall that integer k is called prime if it is greater than 1 and has exactly two positive integer divisors — 1 and k. 

Input

The only line of the input contains a single integer n (2 ≤ n ≤ 100 000).

Output

The first line of the output contains a single integer k — maximum possible number of primes in representation.

The second line should contain k primes with their sum equal to n. You can print them in any order. If there are several optimal solution, print any of them.

Examples

Input

5


Output

2
2 3


Input

6


Output

3
2 2 2

Solution (in PYTHON3):

Solution:
# num = int(input())
# biggest_prime = 1
# prime_sum_list = []
# for i in range(1, num):
#     factors = 1
#     for j in range(2, i // 2 + 1):
#         if i % j == 0:
#             break
#     else:
#         biggest_prime = i
#
# print(biggest_prime)

num = int(input())
print(num // 2)
if num % 2 == 0:
    # print(num // 2)
    print('2 ' * (num // 2))
else:
    print('2 ' * (num // 2 - 1), '3', sep='')