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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

/**
 * code generated by JHelper
 * More info: https://github.com/AlexeyDmitriev/JHelper
 * @author yassin
 */

#include <fstream>

#include <iostream>
#include <vector>
#include <string>
#include <utility>
#include <algorithm>
#include <map>
#include <set>
#include <cmath>
#include <cstdlib>
#include <tuple>
#include <queue>
#include <functional>
#include <stack>
#include <numeric>
#include <cassert>

using namespace std;

class agcD {
public:
    void solve(istream& in, ostream& out) {
        int N;
        in >> N;
        vector<vector<int>> g(N);
        for (int i = 0; i + 1 < N; ++i) {
            int a, b;
            in >> a >> b;
            g[a-1].push_back(b-1);
            g[b-1].push_back(a-1);
        }
        
        queue<int> q;
        for (int u = 0; u < N; ++u) {
            if (g[u].size() == 1U) { //leaf
                q.push(u);
            }
        }
        
        vector<int> fin(N, 0);
        while (!q.empty()) {
            int u = q.front();
            q.pop();
            if (fin[u]) {
                continue;
            }
            int i;
            for (i = 0; i < (int)g[u].size() && fin[g[u][i]]; ++i);
            if (i == (int)g[u].size()) {
                out << "First\n";
                return;
            }
            
            fin[u] = fin[g[u][i]] = 1;
            for (int v : g[u]) {
                if (!fin[v] && g[v].size() == 1U) {
                    q.push(v);
                }
            }
        }
        
        out << "Second\n";
    }
};


int main() {
	std::ios::sync_with_stdio(false); cin.tie(nullptr);

	agcD solver;
	std::istream& in(std::cin);
	std::ostream& out(std::cout);
	solver.solve(in, out);
	return 0;
}