시간 제한 메모리 제한 제출 정답 맞은 사람 정답 비율
1 초 256 MB 1 1 1 100.000%

문제

There are $N$ cups numbered 0 through $N-1$. For each $i (1 \leq i \leq N-1)$, the cup $i$ contains $A_i$ beans, and this cup is labeled with an integer $C_i$.

Two people will play the following game:

  • In each turn, the player chooses a bean from one of the cups except for the cup $0$.
  • If he chooses a bean from the cup $i$, he must move it to one of the cups $i-C_i, \ldots, i-1$.
  • The players take turns alternately. If a player can't choose a bean, he loses.

Who will win if both players play optimally?

입력

$N$
$C_1$ $A_1$
$C_2$ $A_2$
$\vdots$
$C_{N-1}$ $A_{N-1}$

출력

Print the name of the winner: "First" or "Second".

제한

  • $2 \leq N \leq 10^5$
  • $1 \leq C_i \leq i$
  • $0 \leq A_i \leq 10^9$
  • At least one of $A_i$ is nonzero.
  • All values in the input are integers.

예제 입력 1

3
1 0
1 1

예제 출력 1

Second

예제 입력 2

7
1 1
2 0
1 0
2 0
4 1
3 0

예제 출력 2

First

예제 입력 3

7
1 1
2 0
1 9
2 10
4 3
3 5

예제 출력 3

Second

노트

Notes to the Sample 1:

  • In the first turn, the first player must move a bean from $2$ to $1$.
  • In the second turn, the second player must move a bean from $1$ to $0$.
  • In the third turn, the first player can't choose a bean and loses.