Problem:
Score : 400 points

Problem Statement

Fennec and Snuke are playing a board game.

On the board, there are N cells numbered 1 through N, and N-1 roads, each connecting two cells. Cell a_i is adjacent to Cell b_i through the i-th road. Every cell can be reached from every other cell by repeatedly traveling to an adjacent cell. In terms of graph theory, the graph formed by the cells and the roads is a tree.

Initially, Cell 1 is painted black, and Cell N is painted white. The other cells are not yet colored.
Fennec (who goes first) and Snuke (who goes second) alternately paint an uncolored cell.
More specifically, each player performs the following action in her/his turn:

Fennec: selects an uncolored cell that is adjacent to a black cell, and paints it black.

Snuke: selects an uncolored cell that is adjacent to a white cell, and paints it white.

A player loses when she/he cannot paint a cell. Determine the winner of the game when Fennec and Snuke play optimally.

Constraints

2 \leq N \leq 10^5

1 \leq a_i, b_i \leq N

The given 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

If Fennec wins, print Fennec; if Snuke wins, print Snuke.

Sample Input 1

7
3 6
1 2
3 1
7 4
5 7
1 4

Sample Output 1

Fennec

For example, if Fennec first paints Cell 2 black, she will win regardless of Snuke's moves.

Sample Input 2

4
1 4
4 2
2 3

Sample Output 2

Snuke

Solution in C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>

#define REP(i, n) for(decltype(n) i = 0; i < n; i++)

#define ALL(c)   c.begin(), c.end()
#define SORT(c)  std::sort(ALL(c))
#define RSORT(c) std::sort(ALL(c), std::greater<decltype(c)::value_type>())

using namespace std;
using ll = long long;

const int MOD  = (int)1e9 + 7;
const int INF  = (int)1e9 + 1;
const ll  LINF = (ll)1e18 + 1;

class UnionFind {
    using ll = long long;
public:
    struct Node {
        ll parent, weight, size, rank;
        Node(const ll& _parent = 0,
             const ll& _weight = 0,
             const ll& _size   = 1,
             const ll& _rank   = 0) :
            parent(_parent),
            weight(_weight),
            size(_size),
            rank(_rank) { }
    };

    explicit UnionFind(const ll& num_node) {
        node_.reserve(num_node);
        for(ll i = 0; i < num_node; i++) {
            node_.emplace_back(i);
        }
    }

    const std::vector<Node>& getNode() const {
        return node_;
    }

    ll searchAndZipRoot(const ll& x) {
        if(node_[x].parent == x) {
            return x;
        }
        else {
            node_[x].weight += node_[node_[x].parent].weight;
            return node_[x].parent = searchAndZipRoot(node_[x].parent);
        }
    }

    void unite(const ll& x,
               const ll& y,
               const ll& weight = 0) {
        auto rx = searchAndZipRoot(x);
        auto ry = searchAndZipRoot(y);
        if(rx != ry) {
            auto yw = weight + calcWeight(x) - calcWeight(y);
            if(node_[rx].rank < node_[ry].rank) {
                std::swap(rx, ry);
                yw *= -1;
            }
            node_[ry].parent  = rx;
            node_[ry].weight  = yw;
            node_[rx].size   += node_[ry].size;
            if(node_[rx].rank == node_[ry].rank) {
                node_[rx].rank++;
            }
        }
    }

    ll calcWeight(const ll& x) {
        searchAndZipRoot(x);
        return node_[x].weight;
    }

    ll calcDiff(const ll& x,
                const ll& y) {
        return std::abs(calcWeight(x) - calcWeight(y));
    }

    ll calcSize(const ll& x) {
        return node_[searchAndZipRoot(x)].size;
    }

    template<class... A>
    bool checkWhetherRootIsSame(const A&... nodes) {
        auto node_list = std::initializer_list<ll>{nodes...};
        if(node_list.size() < 2) return false;
        auto v = searchAndZipRoot(*node_list.begin());
        for(size_t i = 1; i < node_list.size(); i++) {
            if(v != searchAndZipRoot(*(node_list.begin() + i))) return false;
        }
        return true;
    }

private:
    std::vector<Node> node_;
};

class CommonGraph {
    using ll = long long;
public:
    struct Edge {
        enum class Type { Directed, Undirected };
        int    src, dst;
        ll     cost, capacity, flow;
        size_t rev;
        Edge() = default;
        Edge(const int&    _src,
             const int&    _dst,
             const ll&     _cost     = 0,
             const ll&     _capacity = 0,
             const ll&     _frow     = 0,
             const size_t& _rev      = 0) :
            src(_src),
            dst(_dst),
            cost(_cost),
            capacity(_capacity),
            flow(_frow),
            rev(_rev) { }
    };
    friend std::ostream& operator <<(std::ostream& os, const Edge& obj) {
        os << "src : "  << obj.src      << ", "
           << "dst : "  << obj.dst      << ", "
           << "cost : " << obj.cost     << ", "
           << "cap : "  << obj.capacity << ", "
           << "flow : " << obj.flow     << ", "
           << "rev : "  << obj.rev;
        return os;
    }

    struct Vertex {
        ll cost;
        Vertex(const ll& _cost) : cost(_cost) { }
    };

    enum class Type { Normal, Flow };

    CommonGraph(const int&        num_vertex,
                const Type&       type,
                const Edge::Type& edge_type) :
        vertex_(num_vertex, 0),
        edge_(num_vertex),
        num_edge_(0),
        total_cost_(0),
        type_(type),
        edge_type_(edge_type) { }

    ll getTotalCost() const {
        return total_cost_;
    }

    const std::vector<Vertex>& getVertex() const {
        return vertex_;
    }

    const std::vector<std::vector<Edge>>& getEdge() const {
        return edge_;
    }

    /**
     *  辺を追加する
     */
    void addEdge(const int& src,
                 const int& dst,
                 const ll&  cost,
                 const ll&  capacity = 0) {
        switch(type_) {
            case Type::Normal: {
                switch(edge_type_) {
                    case Edge::Type::Directed: {
                        edge_[src].emplace_back(src, dst, cost);
                        break;
                    }
                    case Edge::Type::Undirected: {
                        edge_[src].emplace_back(src, dst, cost);
                        edge_[dst].emplace_back(dst, src, cost);
                        break;
                    }
                }
                break;
            }
            case Type::Flow: {
                switch(edge_type_) {
                    case Edge::Type::Directed: {
                        edge_[src].emplace_back(src, dst, cost,  capacity, 0, edge_[dst].size());
                        edge_[dst].emplace_back(dst, src, -cost,        0, 0, edge_[src].size() - 1);
                        break;
                    }
                    case Edge::Type::Undirected: {
                        edge_[src].emplace_back(src, dst, cost, capacity, 0, edge_[dst].size());
                        edge_[dst].emplace_back(dst, src, cost, capacity, 0, edge_[src].size() - 1);
                        break;
                    }
                }
                break;
            }
        }
        num_edge_++;
        total_cost_ += cost;
    }

    /**
     *  辺の情報を標準出力する
     */
    void dumpEdgeInfo() {
        for(const auto& v : edge_) {
            for(const auto& e : v) {
                std::cout << "[" << e << "]" << std::endl;
            }
            std::cout << std::endl;
        }
    }

    /**
     *  最大流問題を解く(Dinic法)
     *  @src_index:  始点
     *  @sink_index: 終点
     *  @Return:     最大流
     */
    ll calcMaxFlow(const int& src_index,
                   const int& sink_index) {
        if(type_ != Type::Flow) {
            throw std::logic_error("Graph type is invalid");
        }
        std::vector<int> level(vertex_.size()), iter(vertex_.size());
        std::function<int(void)> levelize
            = [&]() {
                  level.assign(vertex_.size(), -1);
                  level[src_index] = 0;
                  queue<int> Q; Q.push(src_index);
                  while(!Q.empty()) {
                      int u = Q.front(); Q.pop();
                      if(u == sink_index) break;
                      for(const auto& e : edge_[u]) {
                          if(e.flow < e.capacity && level[e.dst] < 0) {
                              Q.push(e.dst);
                              level[e.dst] = level[u] + 1;
                          }
                      }
                  }
                  return level[sink_index];
              };
        function<ll(int, ll)> augment
            = [&](int u, ll cur) {
                  if(u == sink_index) return cur;
                  for(size_t i = iter[u]; i < edge_[u].size(); ++i) {
                      auto& e = edge_[u][i];
                      auto& r = edge_[e.dst][e.rev];
                      if(e.flow < e.capacity && level[u] < level[e.dst]) {
                          auto f = augment(e.dst, min(cur, e.capacity - e.flow));
                          if(0 < f) { e.flow += f; r.flow -= f; return f; }
                      }
                  }
                  return 0LL;
              };
        for(auto& v : edge_) for(auto& e : v) e.flow = 0;
        auto flow = 0LL;
        while(0 <= levelize()) {
            std::fill(iter.begin(), iter.end(), 0);
            for(ll f; 0 < (f = augment(src_index, INF)); flow += f);
        }
        return flow;
    }

    /**
     *  頂点間の最小コストを求める(BFS)
     *  @min_cost:    最小コスト
     *  @start_index: 始点
     *  @goal_index:  終点
     *  @Return:      始点-終点が非連結の場合falseを返す
     */
    bool calcMinCostByBFS(ll&        min_cost,
                          const int& start_index,
                          const int& goal_index) {
        if(type_ != Type::Normal) {
            throw std::logic_error("Graph type is invalid");
        }
        std::fill(vertex_.begin(), vertex_.end(), std::numeric_limits<ll>::max());
        vertex_[start_index] = 0;
        queue<int> Q; Q.push(start_index);
        while(!Q.empty()) {
            const auto src = Q.front(); Q.pop();
            for(const auto& v : edge_[src]) {
                const auto& dst  = v.dst;
                const auto  cost = vertex_[src].cost + v.cost;
                if(cost < vertex_[dst].cost) {
                    vertex_[dst] = cost; Q.push(dst);
                }
            }
        }
        min_cost = vertex_[goal_index].cost;
        return (min_cost == std::numeric_limits<ll>::max()) ? false : true;
    }

    /**
     *  最小全域木を求める(Kruskal法)
     *  @Return: 最小全域木を返す
     *           グラフが非連結の場合、連結成分ごとに最小全域木を構成する
     */
    CommonGraph generateMinimumSpanningTree() {
        if(type_ != Type::Normal || edge_type_ != Edge::Type::Undirected) {
            throw std::logic_error("Graph type is invalid");
        }
        auto num_v = vertex_.size();
        CommonGraph mst(num_v, Type::Normal, Edge::Type::Undirected);
        std::vector<Edge> mst_e;
        mst_e.reserve(num_edge_ * 2);
        for(const auto& v : edge_) for(const auto& e : v) mst_e.push_back(e);
        auto sort_rule = [](const Edge& l, const Edge& r) { return l.cost < r.cost; };
        sort(mst_e.begin(), mst_e.end(), sort_rule);
        UnionFind uf(num_v);
        for(const auto& e : mst_e) {
            if(!uf.checkWhetherRootIsSame(e.src, e.dst)) {
                mst.addEdge(e.src, e.dst, e.cost);
                uf.unite(e.src, e.dst);
            }
        }
        return mst;
    }

    /**
     *  全頂点間の最短距離を求める(Warshall-Floyd法)
     *  @Return: array[i][j] :: 頂点iから頂点jまでの最短距離
     */
    std::vector<std::vector<ll>> calcMinCostBetweenAllVertices() {
        if(type_ != Type::Normal) {
            throw std::logic_error("Graph type is invalid");
        }
        std::vector<std::vector<ll>> dp(vertex_.size(),
                                        std::vector<ll>(vertex_.size(),
                                                        std::numeric_limits<uint>::max()));
        for(const auto& v : edge_) for(const auto& e : v) dp[e.src][e.dst] = e.cost;
        for(size_t i = 0; i < vertex_.size(); i++)
            for(size_t j = 0; j < vertex_.size(); j++)
                for(size_t k = 0; k < vertex_.size(); k++)
                    dp[j][k] = std::min(dp[j][k], dp[j][i] + dp[i][k]);
        return dp;
    }

private:
    std::vector<Vertex>            vertex_;
    std::vector<std::vector<Edge>> edge_;
    ll                             num_edge_;
    ll                             total_cost_;
    const Type                     type_;
    const Edge::Type               edge_type_;
};

void dfs(const CommonGraph& g,
         vector<int>& table,
         int index) {
    for(const auto& edge : g.getEdge()[index]) {
        table[edge.src] = 1;
        if(table[edge.dst] == 0) {
            dfs(g, table, edge.dst);
        }
    }
}

int main() {
    cin.tie(0);
    ios::sync_with_stdio(false);

    int N;
    std::cin >> N;

    CommonGraph g(N,
                  CommonGraph::Type::Normal,
                  CommonGraph::Edge::Type::Undirected);
    REP(i, N - 1) {
        int a, b;
        std::cin >> a >> b;
        g.addEdge(a - 1, b - 1, 1);
    }

    vector<int> table(N, 0);
    table[N - 1] = -1;
    dfs(g, table, 0);
    int b_drawble = accumulate(ALL(table), 0);

    fill(ALL(table), 0);
    table[0] = -1;
    dfs(g, table, N - 1);
    int w_drawble = accumulate(ALL(table), 0);

    std::cout << ((b_drawble < w_drawble) ? "Snuke" : "Fennec") << std::endl;

    return 0;
}