- Prepare
- Algorithms
- Game Theory
- Game of Stones

# Game of Stones

# Game of Stones

Two players called and are playing a game with a starting number of stones. Player always plays first, and the two players move in alternating turns. The game's rules are as follows:

- In a single move, a player can remove either , , or stones from the game board.
- If a player is unable to make a move, that player loses the game.

Given the starting number of stones, find and print the name of the winner. is named `First`

and is named `Second`

. Each player plays optimally, meaning they will not make a move that causes them to lose the game if a winning move exists.

For example, if , can make the following moves:

- removes stones leaving . will then remove stones and win.
- removes stones leaving . cannot move and loses.

would make the second play and win the game.

**Function Description**

Complete the *gameOfStones* function in the editor below. It should return a string, either `First`

or `Second`

.

gameOfStones has the following parameter(s):

*n*: an integer that represents the starting number of stones

**Input Format**

The first line contains an integer , the number of test cases.

Each of the next lines contains an integer , the number of stones in a test case.

**Constraints**

**Output Format**

On a new line for each test case, print `First`

if the first player is the winner. Otherwise print `Second`

.

**Sample Input**

```
8
1
2
3
4
5
6
7
10
```

**Sample Output**

```
Second
First
First
First
First
First
Second
First
```

**Explanation**

In the sample, we have testcases.

If , can't make any moves and loses the game.

If , removes stones and wins the game.

If , removes stones in their first move, leaving stone on the board and winning the game.

If , removes stones in their first move, leaving stone on the board and winning the game.

If , removes all stones from the game board, winning the game.

If , removes stones in their first move, leaving stone on the board and winning the game.

If , can make any of the following three moves:

- Remove stones, leaving stones on the board. then removes stones, winning the game.
- Remove stones, leaving stones on the board. then removes stones, leaving stone left on the board and winning the game.
- Remove stones, leaving stones on the board. then removes the remaining stones and wins the game.

All possible moves result in winning.

If , can remove either or stones to win the game.