Contest Duration: - (local time) (110 minutes) Back to Home
D - Decrementing /

Time Limit: 2 sec / Memory Limit: 256 MB

### 問題文

• 黒板の中から 2 以上の数を 1 つ選び、その数から 1 を引く。
• その後、黒板に書かれた数の最大公約数を g として、すべての数を g で割る。

### 制約

• 1 ≦ N ≦ 10^5
• 1 ≦ A_i ≦ 10^9
• A_1 から A_N の最大公約数は 1

### 入力

N
A_1 A_2 … A_N


### 入力例 1

3
3 6 7


### 出力例 1

First


• 高橋君が 7 から 1 を引く。このとき、操作後は (1,2,2) となる。
• 青木君が 2 から 1 を引く。このとき、操作後は (1,1,2) となる。
• 高橋君が 2 から 1 を引く。このとき、操作後は (1,1,1) となる。

### 入力例 2

4
1 2 4 8


### 出力例 2

First


### 入力例 3

5
7 8 8 8 8


### 出力例 3

Second


Score : 1000 points

### Problem Statement

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 1s 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


### Output

If Takahashi will win, print First. If Aoki will win, print Second.

### Sample Input 1

3
3 6 7


### Sample 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).

### Sample Input 2

4
1 2 4 8


### Sample Output 2

First


### Sample Input 3

5
7 8 8 8 8


### Sample Output 3

Second