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 <sstream>
#include <fstream>
#include <cassert>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <iostream>
#include <iomanip>
#include <algorithm>
#include <vector>
#include <set>
#include <stack>
#include <map>
#include <string>
#include <queue>
#include <bitset>
using namespace std;

#define int long long
#define FOR(i, a, b) for (int i = (a), _##i = (b); i <= _##i; ++i)
#define FORD(i, a, b) for (int i = (a), _##i = (b); i >= _##i; --i)
#define REP(i, a) for (int i = 0, _##i = (a); i < _##i; ++i)
#define REPD(i,n) for(int i = (n)-1; i >= 0; --i)

#define DEBUG(X) { cerr << #X << " = " << (X) << endl; }
#define PR(A, n) { cerr << #A << " = "; FOR(_, 1, n) cerr << A[_] << ' '; cerr << endl; }
#define PR0(A, n) { cerr << #A << " = "; REP(_, n) cerr << A[_] << ' '; cerr << endl; }

#define sqr(x) ((x) * (x))
#define ll long long
#define double long double
typedef pair<int, int> II;
#define __builtin_popcount __builtin_popcountll
#define SZ(x) ((int)(x).size())
#define ALL(a) (a).begin(), (a).end()
#define MS(a,x) memset(a, x, sizeof(a))
#define next ackjalscjaowjico
#define prev ajcsoua0wucckjsl
#define y1 alkscj9u20cjeijc
#define left lajcljascjljl
#define right aucouasocjolkjl
#define y0 u9cqu3jioajc

#define TWO(X) (1LL<<(X))
#define CONTAIN(S,X) ((S) & TWO(X))

int rand16() {
    return rand() & (TWO(16) - 1);
}
int my_rand() {
    return rand16() << 15 | rand16();
}

double safe_sqrt(double x) { return sqrt(max((double)0.0, x)); }
int GI(int& x) { return scanf("%lld", &x); }

const int BLACK = 1;
const int WHITE = 0;

const int MN = 100111;
vector<int> ke[MN];
int n;
int color[MN];

void dfs(int u, int fu) {
    int cnt = 0;
    color[u] = BLACK;
    for(int v : ke[u]) if (v != fu) {
        ++cnt;
        dfs(v, u);

        if (color[v] == BLACK) color[u] = WHITE;
    }
}

int32_t main() {
    ios::sync_with_stdio(0);
    cin.tie(0);
    cout << (fixed) << setprecision(9) << boolalpha;
    while (cin >> n) {
        FOR(i,1,n) ke[i].clear();
        FOR(i,2,n) {
            int u, v; cin >> u >> v;
            ke[u].push_back(v);
            ke[v].push_back(u);
        }
        memset(color, -1, sizeof color);
        dfs(1, -1);

        int nWhite = 0, nBlack = 0;
        FOR(i,1,n) if (color[i] == WHITE) ++nWhite; else ++nBlack;

        if (nBlack > n / 2) cout << "First"; else cout << "Second";
        cout << endl;
    }
    return 0;
}