In math class, Mimi learned about primes! To test her knowledge, her teacher assigned her the following problem for homework:

Given an array of elements, determine the largest prime number which divides every element of the array, or

`DNE`

if no such prime exists.

Mimi was sleeping in class, so she has no idea how to approach this problem! Can you write a program to help her finish her homework?

**Python users are recommended to use PYPY over CPython. There is a significant performance increase.**

#### Constraints

##### Subtask 1 [10%]:

##### Subtask 2 [90%]:

#### Input Specification

The first line of input will contain a single integer, . The next line of input will contain space separated integers, .

#### Output Specification

The output should consist of a single line, either the largest prime which divides all elements in the array, or `DNE`

if no such prime exists.

#### Sample Input

```
5
6 12 18 24 30
```

#### Sample Output

`3`

## Comments

so sad ;( tle'd case 27. Is there any way to make my code any faster? Or is it wrong?

Consider the case where

`res`

is the square of a prime.I'm getting a

`TLE`

on Case #7 with C although I think I am using the optimal algorithm. Does anyone know certain points I might be missing?Consider the following C program:

What do you think will happen?

Thanks. It was the integer overflow error.

It would print squared numbers until the squared number is >= 3_000_000_000. Would it just take too long? Is the int too small?

I don't know why my code is producing a input mismatch exception....

Each can be up to , which does not fit in an int. You'll need long to pass.

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1 is not a prime number