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:
# r = 0
# ans = []
# for i in range(int(input())):
#     s = input().split('|')
#     if (s[0] == 'OO' or s[1] == 'OO') and r == 0:
#         if s[0] == 'OO':
#             ans.append('++|' + s[1])
#         else:
#             ans.append(s[0] + '|++')
#         r = 1
#     else:
#         ans.append(s[0] + '|' + s[1])
# if r == 1:
#     print('YES')
#     for i in ans:
#         print(i)
# else:
#     print('NO')
n = int(input())
print(n // 2)
for i in range(1, n // 2):
    print(2, end=' ')
if n % 2 == 0:
    print(2)
else:
    print(3)