{"raw_statement":[{"iden":"problem statement","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 this game, starting from Takahashi the two player alternately perform the following operation:\n\n*   Select one integer on the blackboard that is not less than $2$, and subtract $1$ from the integer.\n*   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.\n\nThe 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."},{"iden":"constraints","content":"*   $1 ≦ N ≦ 10^5$\n*   $1 ≦ A_i ≦ 10^9$\n*   The greatest common divisor of the integers from $A_1$ through $A_N$ is $1$."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$\n$A_1$ $A_2$ … $A_N$"},{"iden":"sample input 1","content":"3\n3 6 7"},{"iden":"sample output 1","content":"First\n\nTakahashi, the first player, can win as follows:\n\n*   Takahashi subtracts $1$ from $7$. Then, the integers become: $(1,2,2)$.\n*   Aoki subtracts $1$ from $2$. Then, the integers become: $(1,1,2)$.\n*   Takahashi subtracts $1$ from $2$. Then, the integers become: $(1,1,1)$."},{"iden":"sample input 2","content":"4\n1 2 4 8"},{"iden":"sample output 2","content":"First"},{"iden":"sample input 3","content":"5\n7 8 8 8 8"},{"iden":"sample output 3","content":"Second"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}