There is a given list of strings where each string contains only lowercase letters from $a-j$, inclusive. The set of strings is said to be a GOOD SET if no string is a prefix of another string. In this case, print GOOD SET. Otherwise, print BAD SET on the first line followed by the string being checked.

Note If two strings are identical, they are prefixes of each other.

Example

$words=[\text{'abcd'},\text{'bcd'},\text{'abcd'},\text{'bcde'}]$

Here 'abcd' is a prefix of 'abcde' and 'bcd' is a prefix of 'bcde'. Since 'abcde' is tested first, print

BAD SET
abcde

$words=[\text{'ab'},\text{'bc'},\text{'cd'}]$.

No string is a prefix of another so print

GOOD SET

Function Description

Complete the noPrefix function in the editor below.

noPrefix has the following parameter(s):

• string words[n]: an array of strings

Prints

• string(s): either GOOD SET or BAD SET on one line followed by the word on the next line. No return value is expected.

Input Format

First line contains $n$, the size of $words[]$.

Then next $n$ lines each contain a string, $words[i]$.

Constraints

$1\leq n\leq10^5$

$1\leq$ the length of words[i] $\leq60$

All letters in $words[i]$ are in the range 'a' through 'j', inclusive.

Sample Input00

STDIN Function
----- --------
7 words[] size n = 7
aab words = ['aab', 'defgab', 'abcde', 'aabcde', 'bbbbbbbbbb', 'jabjjjad']
defgab
abcde
aabcde
cedaaa
bbbbbbbbbb
jabjjjad

Sample Output00

BAD SET
aabcde

Explanation

'aab' is prefix of 'aabcde' so it is a BAD SET and fails at string 'aabcde'.

Sample Input01

4
aab
aac
aacghgh
aabghgh

Sample Output01

BAD SET
aacghgh

Explanation

'aab' is a prefix of 'aabghgh', and aac' is prefix of 'aacghgh'. The set is a BAD SET. 'aacghgh' is tested before 'aabghgh', so and it fails at 'aacghgh'.

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