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Number of users: 275

Number of users with 100 points: 119

Average result: 58.4436

# Divine Divisor

### Memory limit: 64 MB

An integer is given. We say that an integer is a divisor of with multiplicity ( is integer) if and does not divide . For example, the number has the following divisors: 2 with multiplicity 4, 3 with multiplicity 1, 4 with multiplicity 2, 6 with multiplicity 1, and so on.

We say that a number is a *divine divisor* of the number
if is a divisor of with multiplicity and has no divisors
with multiplicities greater than .
For example, the sole divine divisor of 48 is 2 (with multiplicity 4),
and the divine divisors of 6 are: 2, 3 and 6 (each with multiplicity 1).

Your task is to determine the multiplicity of divine divisors of and the number of its divine divisors.

## Input

The number is given on the standard input, though in a somewhat unusual way. The first line holds a single integer (). The second line holds integers () separated by single spaces. These denote that .

## Output

The first line of the standard output should hold the maximum integer such that there exists a divisor of such that . The second line should hold a single integer that is the number of (divine) divisors of with multiplicity .

## Example

For the input data:

3 4 3 4

the correct result is:

4 1

whereas for the input:

1 6

the correct result is:

1 3

## Grading

Should your program print out the correct multiplicity of a divine divisor of , but fail to print in the second line the correct number of divine divisors of (or fail to print that number at all), it will be awarded 50% of the score for that particular test, scaled accordingly if it exceeds half the time limit.

*Task author: Jakub Radoszewski.*