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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
greedyimplementationmathnumber theory
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