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:
n=input()
two=0
three=0
d={0:[0,0],2:[1,0],3:[0,1],4:[2,0],5:[1,1],6:[3,0],7:[2,1],8:[4,0],9:[3,1],10:[5,0]}
if n%10==1:
    two=n/10*5-1
    three=1 
else:
    two=n/10*5 + d[n%10][0]
    three=d[n%10][1]
print two+three
for i in range(two):
    print 2,
for i in range(three):
    print 3,