| In the game of Hold'em Numbers, 4 players play with a deck of **N** cards, | |
| where each card has a distinct number from the range [1..**N**] on it. Each | |
| player is dealt two cards and the player who has the highest sum of the two | |
| numbers wins. If multiple players have the highest sum, the one of them who | |
| holds the highest card wins. All 8 cards are dealt simultaneously so it's | |
| impossible for two players to have the same card. | |
| After seeing your two cards you can bet $1. If you win the hand you get $4 | |
| back but if another player wins you lose your dollar. You can also fold, in | |
| which case you don't win nor lose any money. Your opponents play very | |
| aggressively and they will always bet. After the winner is determined all | |
| cards are reshuffled to play another hand for the total of **H** games. It's | |
| possible you get dealt the same hand more than once. | |
| You want to maximize your winnings and only bet if your expected winnings are | |
| strictly greater than zero. To help yourself you decided to write a program | |
| that for the given deck size and hands you were dealt returns whether you | |
| should bet or fold. | |
| ### Input | |
| The first line of the input consists of a single integer **T**, the number of | |
| test cases. | |
| Each test case starts with a line containing two integers **N** and **H** | |
| The subsequent **H** lines each contain two integers, **C1** and **C2**, the | |
| cards you were dealt. | |
| ### Output | |
| For each test case **i** numbered from 1 to **T**, output "Case #**i**: ", | |
| followed by a string of **H** characters. Each character being either "B" if | |
| you should bet, or "F" if should fold. The order of characters corresponds to | |
| the order of hands given in the input. | |
| ### Constraints | |
| 1 ≤ **T** ≤ 20 | |
| 8 ≤ **N** ≤ 100 | |
| 1 ≤ **H** ≤ 10000 | |
| 1 ≤ **C1**, **C2** ≤ **N** | |
| **C1** ≠ **C2** | |
| ### Examples | |
| In the first three examples we are playing a single hand with a deck of eight | |
| cards. The first case is a clear winner so you should bet. The second case | |
| gives no chance to win and you should fold. Finally the third case gives you | |
| 40% chance of winning. This is good enough to make the bet profitable. | |