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:
def sumOfPrimes(x):
    resultArr = []
    result = 0
    i = 2
    while(x > 0):
        if(x - i > 1 or x - i == 0):
            x -= i
            result += 1
            resultArr.append(i)
        else:
            i += 1
    return result, resultArr
x = int(input())
result, resultArr = sumOfPrimes(x)
print(result)
for i in resultArr:
    print(i,end=' ')