Problem:
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

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.ArrayDeque;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		new Main().run();
	}

	void run() {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int[] a = new int[N - 1];
		int[] b = new int[N - 1];
		int[] deg = new int[N];
		ArrayList<Integer>[] g = new ArrayList[N];
		for (int i = 0; i < N; ++i) {
			g[i] = new ArrayList<>();
		}
		for (int i = 0; i < N - 1; ++i) {
			a[i] = sc.nextInt();
			b[i] = sc.nextInt();
			--a[i];
			--b[i];
			g[a[i]].add(b[i]);
			g[b[i]].add(a[i]);
			++deg[a[i]];
			++deg[b[i]];
		}

		ArrayDeque<Integer> que = new ArrayDeque<>();
		for (int i = 0; i < N; ++i) {
			if (deg[i] == 1) {
				que.add(i);
			}
		}
		boolean[] used = new boolean[N];
		while (!que.isEmpty()) {
			int v = que.poll();
			if (used[v])
				continue;
			boolean update = false;
			for (int dst : g[v]) {
				if (used[dst])
					continue;
				for (int u : g[dst]) {
					if (!used[u]) {
						--deg[u];
						if (deg[u] == 1) {
							que.add(u);
						}
					}
				}
				used[dst] = true;
				update = true;
				--deg[dst];
			}
			if (!update) {
				System.out.println("First");
				return;
			}
		}
		System.out.println("Second");
	}

	private static void tr(Object... o) {
		System.out.println(Arrays.deepToString(o));
	}
}