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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Globalization;
using System.Diagnostics;
using static System.Console;
using Pair = System.Collections.Generic.KeyValuePair<int, int>;

class Program
{
    static void Main()
    {
        //SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
        new Program().Solve();
        Out.Flush();
    }
    Scanner cin = new Scanner();
    Random rnd = new Random();
    Stopwatch sw = new Stopwatch();
    readonly int[] dd = { 0, 1, 0, -1, 0 };
    readonly int mod = 1000000007;
    readonly string alfa = "abcdefghijklmnopqrstuvwxyz";


    void Solve()
    {
        int N = cin.Nextint;
        var G = Enumerable.Range(0, N).Select(i => new List<int>()).ToArray();
        for (int i = 0; i < N - 1; i++)
        {
            int a = cin.Nextint - 1;
            int b = cin.Nextint - 1;
            G[a].Add(b);
            G[b].Add(a);
        }

        if (N == 2)
        {
            WriteLine("Second");
            return;
        }
        int max = 0;
        bool flag = false;
        for (int i = 0; i < N; i++)
        {
            int cnt = 0;
            max = Math.Max(max, G[i].Count);
            foreach (var v in G[i])
            {
                if (G[v].Count == 1) cnt++;
            }
            if (cnt >= 2)
            {
                flag = true;
            }
        }
        if (flag && N - 1 <= max)
        {
            WriteLine("First");
        }
        else
        {
            WriteLine("Second");
        }
        /*if (N - 1 <= max)
        {
            WriteLine("First");
        }
        else
        {
            WriteLine("Second");
        }*/
    }

}

class Scanner
{
    string[] s; int i;
    char[] cs = new char[] { ' ' };
    public Scanner() { s = new string[0]; i = 0; }
    public string[] Scan { get { return ReadLine().Split(); } }
    public int[] Scanint { get { return Array.ConvertAll(Scan, int.Parse); } }
    public long[] Scanlong { get { return Array.ConvertAll(Scan, long.Parse); } }
    public double[] Scandouble { get { return Array.ConvertAll(Scan, double.Parse); } }
    public string Next
    {
        get
        {
            if (i < s.Length) return s[i++];
            string st = ReadLine();
            while (st == "") st = ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            i = 0;
            return Next;
        }
    }
    public int Nextint { get { return int.Parse(Next); } }
    public long Nextlong { get { return long.Parse(Next); } }
    public double Nextdouble { get { return double.Parse(Next); } }
}