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 PYTHON):

Solution:
#!/usr/bin/python

def ir(): return int(raw_input())

n = ir()

a = []
while True:
    if   n == 0: break
    elif n == 2: a.append(2); break
    elif n == 3: a.append(3); break
    else       : n -= 2; a.append(2)

print len(a)    
print ' '.join(map(str, a))