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: Accepted)

#include<iostream>
#include<algorithm>
#include<vector>
#include<queue>
using namespace std;
typedef long long ll;
vector<ll> node[100005];
bool matched[100005],used[100005];
void dfs(ll pos){
  for(int i=0;i<node[pos].size();i++){
    ll son=node[pos][i];
    if(!used[son]){
      used[son]=true;
      dfs(son);
      if(!matched[pos]&&!matched[son]){
        matched[pos]=true;
        matched[son]=true;
      }
    }
  }
}
int main(){
  ll n;
  cin>>n;
  for(int i=1;i<n;i++){
    ll s,t;
    cin>>s>>t;
    node[s].push_back(t);
    node[t].push_back(s);
  }
  for(int i=1;i<=n;i++) {
    used[i]=false;
    matched[i]=false;
  }
  used[1]=true;
  dfs(1);
  for(int i=1;i<=n;i++){
    if(!matched[i]){
      cout<<"First"<<endl;
      return 0;
    }
  }
  cout<<"Second"<<endl;
  return 0;
}