Twin Primes

Problem Description

Given two integers $m, n$ ($0 \le m \le n \le 10^7$), output all pairs of twin primes in the interval $[m, n]$. Twin primes are pairs of primes that differ by $2$, such as $3$ and $5$, $5$ and $7$, $11$ and $13$, and so on.

Input Format

Two integers $m, n$ ($0 \le m \le n \le 10^7$).

Output Format

Output all twin-prime pairs in the interval [m, n] in ascending order, each enclosed in parentheses as (a,b) with no space in between.

If there is no twin-prime pair in this interval, output none.

Sample Input 1

0 1

Sample Output 1

none

Sample Input 2

1 10

Sample Output 2

(3,5)(5,7)