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)

//header
#ifdef LOCAL
    #include "cxx-prettyprint-master/prettyprint.hpp"
    #define debug(x) cout << x << endl
#else
    #define debug(...) 42
#endif
    #pragma GCC optimize("Ofast")
    #include <bits/stdc++.h>
    //types
    using namespace std;
    using ll = long long;
    using ld = long double;
    typedef pair < ll , ll > Pl;
    typedef pair < int, int > Pi;
    typedef vector<ll> vl;
    typedef vector<int> vi;
    template< typename T >
    using mat = vector< vector< T > >;
    template< int mod >
    struct modint {
        int x;

        modint() : x(0) {}

        modint(int64_t y) : x(y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {}

        modint &operator+=(const modint &p) {
            if((x += p.x) >= mod) x -= mod;
            return *this;
        }

        modint &operator-=(const modint &p) {
            if((x += mod - p.x) >= mod) x -= mod;
            return *this;
        }

        modint &operator*=(const modint &p) {
            x = (int) (1LL * x * p.x % mod);
            return *this;
        }

        modint &operator/=(const modint &p) {
            *this *= p.inverse();
            return *this;
        }

        modint operator-() const { return modint(-x); }

        modint operator+(const modint &p) const { return modint(*this) += p; }

        modint operator-(const modint &p) const { return modint(*this) -= p; }

        modint operator*(const modint &p) const { return modint(*this) *= p; }

        modint operator/(const modint &p) const { return modint(*this) /= p; }

        bool operator==(const modint &p) const { return x == p.x; }

        bool operator!=(const modint &p) const { return x != p.x; }

        modint inverse() const {
            int a = x, b = mod, u = 1, v = 0, t;
            while(b > 0) {
            t = a / b;
            swap(a -= t * b, b);
            swap(u -= t * v, v);
            }
            return modint(u);
        }

        modint pow(int64_t n) const {
            modint ret(1), mul(x);
            while(n > 0) {
            if(n & 1) ret *= mul;
            mul *= mul;
            n >>= 1;
            }
            return ret;
        }

        friend ostream &operator<<(ostream &os, const modint &p) {
            return os << p.x;
        }

        friend istream &operator>>(istream &is, modint &a) {
            int64_t t;
            is >> t;
            a = modint< mod >(t);
            return (is);
        }

        static int get_mod() { return mod; }
    };
    //abreviations
    #define all(x) (x).begin(), (x).end()
    #define rall(x) (x).rbegin(), (x).rend()
    #define rep_(i, a_, b_, a, b, ...) for (int i = (a), max_i = (b); i < max_i; i++)
    #define rep(i, ...) rep_(i, __VA_ARGS__, __VA_ARGS__, 0, __VA_ARGS__)
    #define rev(i,n) for(int i=n-1;i>=0;i--)
    #define SZ(x) ((int)(x).size())
    #define pb(x) push_back(x)
    #define eb(x) emplace_back(x)
    #define ff first
    #define ss second
    #define mp make_pair
    #define print(x) cout << x << endl
    //functions
    ll gcd(ll a, ll b) { return b ? gcd(b, a%b) : a; }
    template<class T>bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; }
    template<class T>bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; }
    template< typename T >
    T mypow(T x, ll n) {
        T ret = 1;
        while(n > 0) {
            if(n & 1) (ret *= x);
            (x *= x);
            n >>= 1;
        }
        return ret;
    }
    ll modpow(ll x, ll n, const ll mod) {
        ll ret = 1;
        while(n > 0) {
            if(n & 1) (ret *= x);
            (x *= x);
            n >>= 1;
            x%=mod;
            ret%=mod;
        }
        return ret;
    }
    uint64_t my_rand(void) {
        static uint64_t x = 88172645463325252ULL;
        x = x ^ (x << 13); x = x ^ (x >> 7);
        return x = x ^ (x << 17);
    }
    //graph template
    template< typename T >
    struct edge {
        int src, to;
        T cost;

        edge(int to, T cost) : src(-1), to(to), cost(cost) {}

        edge(int src, int to, T cost) : src(src), to(to), cost(cost) {}

        edge &operator=(const int &x) {
            to = x;
            return *this;
        }
        operator int() const { return to; }
    };

    template< typename T >
    using Edges = vector< edge< T > >;
    template< typename T >
    using WeightedGraph = vector< Edges< T > >;
    using UnWeightedGraph = vector< vector< int > >;

//constant
#define INF 1000000000LL
#define mod 998244353LL
typedef modint<mod> mint;
#define eps 0.0000000000008
//library

//main
int main(){
    cin.tie(0);
    ios::sync_with_stdio(0);
    cout << fixed << setprecision(20);
    int n; cin>>n;
    mat<int> g(n);
    rep(i, n-1){
        int a, b; cin >>a>>b;
        a--;b--;
        g[a].pb(b);
        g[b].pb(a);
    }  
    rep(v, n){
        int cnt = 0;
        for(auto &nv:g[v]){
            if(g[nv].size() == 1)cnt++;
        }
        if(cnt>=2){
            cout << "First" << endl;
            return 0;
        }
    } 
    cout << "Second" << endl;
    return 0;
}