Super Primes

Problem Description

A prime number is a super prime if, after repeatedly removing digits from the right (one digit, then two digits, then three digits, …) until only one digit remains, every remaining number is also prime.

For example, 2333 is a super prime, because 2333, 233, 23, and 2 are all prime.

Write a program that, given an integer $x$, finds all super primes not exceeding $x$.

Input Format

One line: an integer $x$ ($1 \le x \le 10^9$).

Output Format

The first line is an integer $k$, the number of super primes not exceeding $x$. The next line contains $k$ integers: all super primes not exceeding $x$, in increasing order.

Sample Input

100

Sample Output

13
2 3 5 7 23 29 31 37 53 59 71 73 79

Limitation

1 s, 1024 KiB for each test case.