Time limit:

$1$

$5$

$$seconds

Gabriella has just made an incredible breakthrough in the

world of encryption! Her new encryption algorithm allows

communication between two people. Most of the details of

this new encryption scheme are incomprehensible, but the

crucial part of the encryption algorithm involves two

intervals of positive integers.

The strength of the encryption algorithm is equal to the number of pairs of positive integers

$($

one from each interval

$)$

$$that are relatively prime

$($

that is

$,$

$$no positive integer other than

$1$

$$divides both numbers

$)$

$.$