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 C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp> 
#include <ext/pb_ds/tree_policy.hpp>  
#define ordered_set tree<int, null_type,less<int>, rb_tree_tag,tree_order_statistics_node_update> 
using namespace __gnu_pbds;
using namespace std;
 
const int MAXN = 100000 + 20, MAXM = 20, MOD = 1000 * 1000 * 1000 + 7;
const long long INF = 1e9 + 10;
vector <int> vec[MAXN];

void solve() {
	int n;
	cin >> n;
	
	for (int i = 1, u, v; i < n; i++) {
		cin >> u >> v;
		
		vec[u].push_back(v);
		vec[v].push_back(u);
	}
	
	int cnt = 0;
	for (int i = 1; i <= n; i++) {
		int t = 0;
		for (int j = 0; j < vec[i].size(); j++) {
			if (vec[vec[i][j]].size() == 1)
				t++;
		}
		cnt = max(cnt, t);
	}
	
	if (cnt >= 2)
		cout << "First" << endl;
	else if (n % 2 == 1)
		cout << "First" << endl;
	else
		cout << "Second" << endl;
		
}
 
int main() {
    ios_base::sync_with_stdio(0); cin.tie(0); cout.tie(0);
	solve();
}