Prefixes and Suffixes

Description:

Input:

The first line of the input contains one integer number $$$n$$$ ($$$2 \le n \le 100$$$) — the length of the guessed string $$$s$$$.

The next $$$2n-2$$$ lines are contain prefixes and suffixes, one per line. Each of them is the string of length from $$$1$$$ to $$$n-1$$$ consisting only of lowercase Latin letters. They can be given in arbitrary order.

It is guaranteed that there are exactly $$$2$$$ strings of each length from $$$1$$$ to $$$n-1$$$. It is also guaranteed that these strings are prefixes and suffixes of some existing string of length $$$n$$$.

Output:

Print one string of length $$$2n-2$$$ — the string consisting only of characters 'P' and 'S'. The number of characters 'P' should be equal to the number of characters 'S'. The $$$i$$$-th character of this string should be 'P' if the $$$i$$$-th of the input strings is the prefix and 'S' otherwise.

If there are several possible answers, you can print any.

Sample Input:

5
ba
a
abab
a
aba
baba
ab
aba

Sample Output:

SPPSPSPS

Sample Input:

3
a
aa
aa
a

Sample Output:

PPSS

Sample Input:

2
a
c

Sample Output:

PS

Note:

The only string which Ivan can guess in the first example is "ababa".

The only string which Ivan can guess in the second example is "aaa". Answers "SPSP", "SSPP" and "PSPS" are also acceptable.

In the third example Ivan can guess the string "ac" or the string "ca". The answer "SP" is also acceptable.