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