In the game of "Spindie", players take turns spinning a spinner and rolling a die.

On each turn, they spin the spinner three times and roll the die between each pair of spins (i.e. the sequence on a single turn is: Spin, Roll, Spin, Roll, Spin). Each spin of the spinner lands on some integer and each roll of the die results in an integer from $1$ to $6$. The first spinner number is the base score. Then if a die roll is $1$ through $5$, the player adds the next spinner number to their score. If they roll a $6$, the next number is used to multiply their score. The winner is the player with the highest score after a set number of rounds.

Here are some example turns of Spindie:

Spin	Roll	Spin	Roll	Spin	Score
$10$	$4$	$7$	$1$	$8$	$(10+7)+8=25$
$1$	$3$	$2$	$6$	$5$	$(1+2)\times 5=15$
$6$	$6$	$6$	$6$	$6$	$(6\times 6)\times 6=216$

The input will contain $10$ test cases.

The first line of each test case will consist of an integer $N$ representing the number of integers on the spinner, where $1\le N\le 5000$.

The next line contains the $N$ integers on the spinner, $S_1$ through $S_N$, separated by spaces, where $1\le S_i\le 100$.

The next line will contain five target integers $T_1$ through $T_5$ separated by spaces, where $1\le T_i\le {10}^6$.

For each test case, your program should output a single line consisting of $5$ letters. Each letter should represent one of the five targets (in order). If the target represents a possible score in a single round of Spindie, then output a T. If it is not possible, output an F.

Note that the sample data below contains only $5$ test cases, but the test data will contain $10$.

Sample Input

5
23 74 7 64 47
128605 205 2162 2709 71346
3
26 5 11
407 962 455 21 902
4
23 75 89 24
933 484 13248 102 44640
9
23 61 77 83 12 92 1 7 65
72900 144 5704 145 6370
7
87 20 94 99 14 26 87
241956 177 749331 221 4066

Sample Output

FFTFF
TTFTF
FFTFF
FTTTF
TFTFF

Educational Computing Organization of Ontario - statements, test data and other materials can be found at ecoocs.org