1875: Bachgold Problem
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Description
time limit per test
1 secondmemory limit per test
256 megabytesinput
standard inputoutput
standard outputBachgold 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≤100000).
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