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)

#include<stdio.h>
#include<iostream>
#include<algorithm>
#include<stdlib.h>
#include<string.h>
#include<queue>
#define LL long long
using namespace std;
inline int read( )
{
  int sum=0;char c=getchar( );bool f=0;
  while(c<'0'||c>'9') {if(c=='-') f=1;c=getchar( );}
  while(c>='0'&&c<='9') {sum=sum*10+c-'0';c=getchar( );}
  if(f) return -sum;
  return sum;
}
const int N=200005;
int n,cnt;
struct ex{int num,next;}map[N*2];
int head[N],d[N],len;bool del[N];
inline void link(int x,int y)
{
  len++;map[len].num=y;map[len].next=head[x];head[x]=len;d[x]++;
  len++;map[len].num=x;map[len].next=head[y];head[y]=len;d[y]++;
}
queue<int>q;
int main( )
{
  int i,x,y,k;
  n=read( );
  if(n&1) {puts("First");return 0;}
  for(i=1;i<n;i++) x=read( ),y=read( ),link(x,y);
  for(i=1;i<=n;i++) if(d[i]==1) q.push(i);
  while(!q.empty( ))
    {
      x=q.front( );q.pop( );y=0;
      for(i=head[x];i;i=map[i].next)
	if(!del[k=map[i].num]) {y=k;break;}
      if(!y) {puts("First");return 0;}
      del[x]=1;del[y]=1;
      for(i=head[y];i;i=map[i].next)
	if(!del[k=map[i].num]&&(--d[k])==1) q.push(k);
    }
  for(i=1;i<=n;i++) if(!del[i]) {puts("First");return 0;}
  puts("Second");
  return 0;
}