C. Prefixes and Suffixes

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

Ivan wants to play a game with you. He picked some string ss of length nn consisting only of lowercase Latin letters.

You don't know this string. Ivan has informed you about all its improper prefixes and suffixes (i.e. prefixes and suffixes of lengths from 11 to n−1n−1), but he didn't tell you which strings are prefixes and which are suffixes.

Ivan wants you to guess which of the given 2n−22n−2 strings are prefixes of the given string and which are suffixes. It may be impossible to guess the string Ivan picked (since multiple strings may give the same set of suffixes and prefixes), but Ivan will accept your answer if there is at least one string that is consistent with it. Let the game begin!

Input

The first line of the input contains one integer number nn (2≤n≤1002≤n≤100) — the length of the guessed string ss.

The next 2n−22n−2 lines are contain prefixes and suffixes, one per line. Each of them is the string of length from 11 to n−1n−1 consisting only of lowercase Latin letters. They can be given in arbitrary order.

It is guaranteed that there are exactly 22 strings of each length from 11 to n−1n−1. It is also guaranteed that these strings are prefixes and suffixes of some existing string of length nn.

Output

Print one string of length 2n−22n−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 ii-th character of this string should be 'P' if the ii-th of the input strings is the prefix and 'S' otherwise.

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

Examples

input

Copy

5
ba
a
abab
a
aba
baba
ab
aba

output

Copy

SPPSPSPS

input

Copy

3
a
aa
aa
a

output

Copy

PPSS

input

Copy

2
a
c

output

Copy

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.

這題看別人寫的題解又臭又長，看不懂，無奈的我發了一個半小時看題+理解把這題寫出來了

找出長度為n-1的兩個字串，例第一個：abab和baba，那麼原始串的可能性只有兩個：abab+baba的最後一個=ababa，或者是baba+abab的最後一個=babab，隨便拿一個出來，然後將題目給的那些串一個個在a上是否是字首或字尾，是continue，若都不是，a就是另一種情況了：：AC程式碼：

#include<bits/stdc++.h>
using namespace std;
string s1,s2,s[200],a;
bool vis[200];
int main()
{
	int n;
	scanf("%d",&n);
	for(int i=1;i<=2*n-2;i++)
	{
		cin>>s[i];
		if(s[i].size()==n-1)
		{
			if(s1.size()==0) s1=s[i];
			else s2=s[i];
		}
	}
	bool flag=0;
	a=s1+s2[s2.size()-1];
	for(int i=1;i<=2*n-2;i++)
	{
		string te=a.substr(0,s[i].size());//a中長度與S[i]相同的字首 
		string tw=a.substr(a.size()-s[i].size(),a.size());//a中長度與S[i]相同的字尾 
		if(te==s[i]||tw==s[i]) continue;
		else {
			flag=1;break;
		}
	}
	if(flag)	a=s2+s1[s1.size()-1];
	
	for(int i=1;i<=2*n-2;i++)
	{
		string te=a.substr(0,s[i].size());
		if(te==s[i]&&!vis[s[i].size()]) printf("P"),vis[s[i].size()]=1;
		else printf("S");
	}
	puts("");
}