Pocky Game

AtCoder

IDagc048_d

Time2000ms

Memory256MB

Difficulty—

There are $N$ piles of stones lying in a row. The $i$\-th pile from the left contains $A_i$ stones. Two players, FirstLeft and SecondRight, play a game. They alternately play a turn, with FirstLeft going first. In each turn, the player does the following operation: * In FirstLeft's turn: he removes one or more stones from the **leftmost** pile with one or more stones. * In SecondRight's turn: he removes one or more stones from the **rightmost** pile with one or more stones. The player who becomes unable to play his turn loses. Determine the winner of the game when the players act optimally. Solve $T$ test cases in an input file. ## Constraints * $1 \leq T \leq 100$ * $1 \leq N \leq 100$ * $1 \leq A_i \leq 10^9$ ## Input Input is given from Standard Input in the following format. The first line of input is as follows: $T$ Then, $T$ test cases follow, each of which is in the following format: $N$ $A_1$ $A_2$ $\cdots$ $A_N$ [samples]

Samples

Input #1

Output #1

First
First
Second

For example, in the third game, one possible scenario is as follows:

*   FirstLeft takes $2$ stones from the leftmost pile. The piles now contain $0,1,2$ stone(s).
*   SecondRight takes $1$ stone from the rightmost pile. The piles now contain $0,1,1$ stone(s).
*   FirstLeft takes $1$ stone from the middle pile. The piles now contain $0,0,1$ stone(s).
*   SecondRight takes $1$ stone from the rightmost pile. The piles now contain $0,0,0$ stones.
*   FirstLeft is unable to do his operation and loses.

API Response (JSON)

{
  "problem": {
    "name": "Pocky Game",
    "description": {
      "content": "There are $N$ piles of stones lying in a row. The $i$\\-th pile from the left contains $A_i$ stones. Two players, FirstLeft and SecondRight, play a game. They alternately play a turn, with FirstLeft go",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc048_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ piles of stones lying in a row. The $i$\\-th pile from the left contains $A_i$ stones.\nTwo players, FirstLeft and SecondRight, play a game. They alternately play a turn, with FirstLeft go...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments