2. Spindie

What is the Problem?

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:

DATA21.txt (DATA22.txt for the second try) will contain 10 test cases. The first line of each test case will consist of an integer 𝑁𝑁 representing the number of integers on the spinner, where 1≤𝑁𝑁≤5000. The next line contains the 𝑁𝑁 integers on the spinner, 𝑆𝑆1 through 𝑆𝑆𝑁𝑁, separated by spaces, where 1≤𝑆𝑆𝑖𝑖≤100. The next line will contain five target integers 𝑇𝑇1 through 𝑇𝑇5 separated by spaces, where 1≤𝑇𝑇𝑖𝑖≤1000000. 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