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:
# n = int(input())
# #s = sum( int(i) for i in str(n) )
#
# if (n > 2 and n%2 == 0) or (n > 3 and n%3 == 0) or (n > 5 and n%5 == 0) or n == 1 or n == 0:
#     print(n,"is NOT prime")
# else:
#     print(n, "is prime")

n = int(input())
k = n // 2
n = n%2
op = []
for _ in range(k):
    op.append(2)
if n == 1:
    op.pop(-1)
    op.append(3)
print(k)
print(*op)