## ECOO '16 R1 P2 - Spindie

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Points: 7 (partial)
Time limit: 1.0s
Memory limit: 64M

Problem types

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 to . The first spinner number is the base score. Then if a die roll is through , the player adds the next spinner number to their score. If they roll a , 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

The input will contain test cases.

The first line of each test case will consist of an integer representing the number of integers on the spinner, where .

The next line contains the integers on the spinner, through , separated by spaces, where .

The next line will contain five target integers through separated by spaces, where .

For each test case, your program should output a single line consisting of 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 test cases, but the test data will contain .

#### 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

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