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Contest: Task: Related: TaskC TaskE

Score : $900$ points

Problem Statement

There is a tree with $N$ vertices numbered $1$ through $N$. The $i$-th of the $N-1$ edges connects vertices $a_i$ and $b_i$.

Initially, each vertex is uncolored.

Takahashi and Aoki is playing a game by painting the vertices. In this game, they alternately perform the following operation, starting from Takahashi:

  • Select a vertex that is not painted yet.
  • If it is Takahashi who is performing this operation, paint the vertex white; paint it black if it is Aoki.

Then, after all the vertices are colored, the following procedure takes place:

  • Repaint every white vertex that is adjacent to a black vertex, in black.

Note that all such white vertices are repainted simultaneously, not one at a time.

If there are still one or more white vertices remaining, Takahashi wins; if all the vertices are now black, Aoki wins. Determine the winner of the game, assuming that both persons play optimally.

Constraints

  • $2 ≤ N ≤ 10^5$
  • $1 ≤ a_i,b_i ≤ N$
  • $a_i ≠ b_i$
  • The input graph is a tree.

Input

Input is given from Standard Input in the following format:

$N$
$a_1$ $b_1$
:
$a_{N-1}$ $b_{N-1}$

Output

Print First if Takahashi wins; print Second if Aoki wins.

Sample Input 1

3
1 2
2 3

Sample Output 1

First

Below is a possible progress of the game:

  • First, Takahashi paint vertex $2$ white.
  • Then, Aoki paint vertex $1$ black.
  • Lastly, Takahashi paint vertex $3$ white.

In this case, the colors of vertices $1$, $2$ and $3$ after the final procedure are black, black and white, resulting in Takahashi's victory.

Sample Input 2

4
1 2
2 3
2 4

Sample Output 2

First

Sample Input 3

6
1 2
2 3
3 4
2 5
5 6

Sample Output 3

Second