time limit per test: 0.25 sec. memory limit per test: 4096 KB

input: standard output: standard

Find all pairs of prime numbers (A, B) such that A<=B and their sum is also a prime number and does not exceed N.

Input

The input of the problem consists of the only integer N (1<=N<=10^6).

Output

On the first line of the output file write the number of pairs meeting the requirements. Then output all pairs one per line (two primes separated by a space).