Decrementing

AtCoder

IDagc010_d

Time2000ms

Memory256MB

Difficulty—

There are $N$ integers written on a blackboard. The $i$\-th integer is $A_i$, and the greatest common divisor of these integers is $1$. Takahashi and Aoki will play a game using these integers. In this game, starting from Takahashi the two player alternately perform the following operation: * Select one integer on the blackboard that is not less than $2$, and subtract $1$ from the integer. * Then, divide all the integers on the black board by $g$, where $g$ is the greatest common divisor of the integers written on the blackboard. The player who is left with only $1$s on the blackboard and thus cannot perform the operation, loses the game. Assuming that both players play optimally, determine the winner of the game. ## Constraints * $1 ≦ N ≦ 10^5$ * $1 ≦ A_i ≦ 10^9$ * The greatest common divisor of the integers from $A_1$ through $A_N$ is $1$. ## Input The input is given from Standard Input in the following format: $N$ $A_1$ $A_2$ … $A_N$ [samples]

Samples

Input #1

3
3 6 7

Output #1

First

Takahashi, the first player, can win as follows:

*   Takahashi subtracts $1$ from $7$. Then, the integers become: $(1,2,2)$.
*   Aoki subtracts $1$ from $2$. Then, the integers become: $(1,1,2)$.
*   Takahashi subtracts $1$ from $2$. Then, the integers become: $(1,1,1)$.

Input #2

4
1 2 4 8

Output #2

First

Input #3

5
7 8 8 8 8

Output #3

Second

API Response (JSON)

{
  "problem": {
    "name": "Decrementing",
    "description": {
      "content": "There are $N$ integers written on a blackboard. The $i$\\-th integer is $A_i$, and the greatest common divisor of these integers is $1$. Takahashi and Aoki will play a game using these integers. In thi",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "agc010_d"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "There are $N$ integers written on a blackboard. The $i$\\-th integer is $A_i$, and the greatest common divisor of these integers is $1$.\nTakahashi and Aoki will play a game using these integers. In thi...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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