Two numbers are called friends if they are different and the sum of the divisors of each number (including 1, but excluding the own number) is equal to the other number.

For instance, 2620 and 2924 are friends: 2620 is divisible by 1, 2, 4, 5, 10, 20, 131, 262, 524, 655 and 1310; that sum 2924. 2924 is divisible by 1, 2, 4, 17, 34, 43, 68, 86, 172, 731 and 1462; that sum 2620.

Write a program that prints if pairs of numbers are friends.

**Input**

Input is a sequence of pairs of natural numbers *a*, *b*
with 2≤ *a* <*b*.

**Output**

For each pair *a*, *b* of the input, print if they are friends
or are not according to the format of the example.

**Observation**

This problem is from “The British Informatics Olympiad for schools and colleges”.

Public test cases

**Input**

2620 2924 333 666 365 366

**Output**

2620 and 2924 are friends 333 and 666 are not friends 365 and 366 are not friends

Information

- Author
- Jordi Petit
- Language
- English
- Translator
- Carlos Molina
- Original language
- Catalan
- Other languages
- Catalan
- Official solutions
- C++
- User solutions
- C++