#line 1 "playspace/main.cpp"
#include <bits/stdc++.h>
#line 6 "library/gandalfr/graph/graph.hpp"

#line 3 "library/gandalfr/data_structure/union_find.hpp"

#line 6 "library/gandalfr/data_structure/union_find.hpp"

class union_find {
  private:
    int N;
    mutable std::vector<int> par;
    std::vector<int> nxt;
    int group_num; // 集合の数

  public:
    union_find() : N(0), group_num(0) {}
    union_find(int n) : N(n), par(n, -1), nxt(n), group_num(n) {
        std::iota(nxt.begin(), nxt.end(), 0);
    }

    /**
     * @brief 頂点を n 個に増やす
     * @attention 小さくはできない
     */
    void expand(int n) {
        if (n <= N)
            return;
        par.resize(n, -1);
        nxt.resize(n);
        for (int i = N; i < n; ++i)
            nxt[i] = i;
        group_num += n - N;
        N = n;
    }

    int leader(int x) const {
        return (par[x] < 0 ? x : par[x] = leader(par[x]));
    }

    bool same(int x, int y) const { return leader(x) == leader(y); }

    bool merge(int x, int y) {
        if ((x = leader(x)) == (y = leader(y)))
            return false;
        if (-par[x] > -par[y])
            std::swap(x, y);

        par[x] += par[y];
        par[y] = x;
        std::swap(nxt[x], nxt[y]);
        group_num--;
        return true;
    }

    /**
     * @brief x の属するグループのサイズを返す
     */
    int size(int x) const { return -par[leader(x)]; }

    /**
     * @brief すべてのノードの数
     */
    int size() const { return N; }

    std::vector<int> group_containing_node(int x) const {
        std::vector<int> ret{x};
        for (int cu = nxt[x]; cu != ret[0]; cu = nxt[cu])
            ret.push_back(cu);
        return ret;
    }

    int count_groups() const { return group_num; }

    std::vector<std::vector<int>> all_groups() const {
        std::vector<std::vector<int>> result;
        result.reserve(group_num);
        std::vector<bool> used(N, false);
        for (int i = 0; i < N; ++i) {
            if (!used[i]) {
                result.emplace_back(group_containing_node(i));
                for (int x : result.back()) {
                    used[x] = true;
                }
            }
        }
        return result;
    }
};
#line 3 "library/gandalfr/math/matrix.hpp"

#line 8 "library/gandalfr/math/matrix.hpp"

template <class T> class matrix {
  private:
    int H, W;
    std::valarray<std::valarray<T>> table;

    enum rowtrans_operation_name { SCALE, SWAP, ADD };
    struct rowtrans_operation {
        int op, tar, res;
        T scl;
    };
    using operations_history = std::vector<rowtrans_operation>;

  public:
    matrix() = default;
    matrix(int _H, int _W, T val = 0)
        : H(_H), W(_W), table(std::valarray<T>(val, _W), _H) {}
    matrix(const std::vector<std::vector<T>> &vv)
        : H(vv.size()), W(vv[0].size()), table(std::valarray<T>(W), H) {
        for (int i = 0; i < H; i++)
            for (int j = 0; j < W; j++)
                table[i][j] = vv[i][j];
    }
    matrix(const std::valarray<std::valarray<T>> &vv)
        : H(vv.size()), W(vv[0].size()), table(vv) {}

    /**
     * @brief 行列をリサイズする。
     * @param val 拡張部分の値
     */
    void resize(int _H, int _W, T val = 0) {
        H = _H, W = _W;
        table.resize(_H, std::valarray<T>(val, _H));
    }
    int size_H() const { return H; }
    int size_W() const { return W; }
    void transpose() {
        matrix<T> ret(W, H);
        for (int i = 0; i < H; i++)
            for (int j = 0; j < W; j++)
                ret.table[j][i] = table[i][j];
        *this = ret;
    }

    /**
     * @brief 第 i 行に対して行単位で代入を行う
     * @example A.row_assign(3, {1,2,3});
     */
    void row_assign(int i, const std::valarray<T> &row) {
        assert(0 <= i && i < H);
        assert(W == (int)row.size());
        table[i] = row;
    }

    /**
     * @brief 第 i 行, 第 j 行を入れ替える
     */
    void row_swap(int i, int j) {
        assert(0 <= i && i < H);
        assert(0 <= j && j < H);
        table[i].swap(table[j]);
    }

    /**
     * @attention O(n^3)
     * @attention 整数型では正しく計算できない。double や fraction を使うこと。
     * @attention 枢軸選びをしていないので double では誤差が出るかも。
     */
    operations_history sweep_method() {
        operations_history hist;
        for (int h = 0, w = 0; h < H && w < W; w++) {
            if (table[h][w] == 0) {
                for (int piv = h + 1; piv < H; piv++) {
                    if (table[piv][w] != 0) {
                        hist.push_back({SWAP, h, piv, 0});
                        row_swap(h, piv);
                        break;
                    }
                }
                if (table[h][w] == 0) {
                    continue;
                }
            }
            T inv = 1 / table[h][w];
            hist.push_back({SCALE, -1, w, inv});
            table[h] *= inv;
            for (int j = h + 1; j < H; j++) {
                hist.push_back({ADD, h, j, -table[j][w]});
                table[j] -= table[h] * table[j][w];
            }
            h++;
        }
        return hist;
    }

    int rank() const {
        auto U(*this);
        U.sweep_method();
        int r = 0;
        for (int i = 0; i < H; ++i) {
            for (int j = i; j < W; ++j) {
                if (U.table[i][j] != 0) {
                    r++;
                    break;
                }
            }
        }
        return r;
    }

    T determinant() const {
        assert(H == W);
        matrix<T> U(*this);
        T det = 1;
        auto hist = U.sweep_method();
        if (U.table[H - 1][H - 1] == 0)
            return 0;
        for (auto &[op, tar, res, scl] : hist) {
            switch (op) {
            case SCALE:
                det /= scl;
                break;
            case SWAP:
                det *= -1;
                break;
            }
        }
        return det;
    }

    std::vector<T> solve_system_of_equations(const std::vector<T> &y) {
        assert(H == W);
        std::vector<T> x(y);
        matrix<T> U(*this);
        auto hist = U.sweep_method();
        if (U.table[H - 1][H - 1] == 0)
            return {};

        for (auto &[op, tar, res, scl] : hist) {
            switch (op) {
            case SCALE:
                x[res] *= scl;
                break;
            case SWAP:
                std::swap(x[tar], x[res]);
                break;
            case ADD:
                x[res] += x[tar] * scl;
                break;
            }
        }

        for (int i = H - 1; i >= 0; --i) {
            for (int j = 0; j < i; ++j) {
                x[j] -= U.table[j][i] * x[i];
            }
        }
        return x;
    }

    matrix<T> inverse() const {
        assert(H == W);
        matrix<T> INV(matrix<T>::E(H)), U(*this);
        auto hist = U.sweep_method();
        if (U.table[H - 1][H - 1] == 0)
            return matrix<T>(0, 0);

        for (auto &[op, tar, res, scl] : hist) {
            switch (op) {
            case SCALE:
                INV.table[res] *= scl;
                break;
            case SWAP:
                std::swap(INV.table[tar], INV.table[res]);
                break;
            case ADD:
                INV.table[res] += INV.table[tar] * scl;
                break;
            }
        }

        for (int i = H - 1; i >= 0; --i) {
            for (int j = 0; j < i; ++j) {
                INV.table[j] -= INV.table[i] * U.table[j][i];
            }
        }
        return INV;
    }

    void print() const {
        for (int i = 0; i < H; i++) {
            for (int j = 0; j < W; j++) {
                std::cout << table[i][j] << (j == W - 1 ? "" : " ");
            }
            std::cout << std::endl;
        }
    }

    matrix<T> &operator+=(const matrix<T> &a) {
        this->table += a.table;
        return *this;
    }
    matrix<T> &operator-=(const matrix<T> &a) {
        this->table -= a.table;
        return *this;
    }
    matrix<T> &operator*=(const T &a) {
        this->table *= a;
        return *this;
    }
    matrix<T> &operator*=(const matrix<T> &a) {
        assert(W == a.H);
        matrix<T> a_t(a), ret(H, a.W);
        a_t.transpose();
        for (int i = 0; i < H; i++) {
            for (int j = 0; j < a_t.H; j++) {
                ret.table[i][j] = (table[i] * a_t.table[j]).sum();
            }
        }
        return *this = ret;
    }
    matrix<T> &operator/=(const T &a) {
        this->table /= a;
        return *this;
    }
    /**
     * @brief 行列の冪乗。
     * @param n 指数
     * @attention n が 0 なら単位行列。
     * @attention 演算子の優先度に注意。
     */
    matrix<T> operator^=(long long n) {
        assert(H == W);
        if (n == 0)
            return *this = E(H);
        n--;
        matrix<T> x(*this);
        while (n) {
            if (n & 1)
                *this *= x;
            x *= x;
            n >>= 1;
        }
        return *this;
    }

    matrix<T> operator+() const { return *this; }
    matrix<T> operator-() const { return matrix<T>(*this) *= -1; }
    matrix<T> operator+(const matrix<T> &a) const {
        return matrix<T>(*this) += a;
    }
    matrix<T> operator-(const matrix<T> &a) const {
        return matrix<T>(*this) -= a;
    }
    matrix<T> operator*(const T &a) { return matrix<T>(*this) *= a; }
    matrix<T> operator*(const matrix<T> &a) const {
        return matrix<T>(*this) *= a;
    }
    matrix<T> operator/(const T &a) const { return matrix<T>(*this) /= a; }
    matrix<T> operator^(long long n) const { return matrix<T>(*this) ^= n; }
    friend std::istream &operator>>(std::istream &is, matrix<T> &mt) {
        for (auto &arr : mt.table)
            for (auto &x : arr)
                is >> x;
        return is;
    }
    const T &operator()(int h, int w) const {
        assert(0 <= h && h < H && 0 <= w && w <= W);
        return table[h][w];
    }
    T &operator()(int h, int w) {
        assert(0 <= h && h < H && 0 <= w && w <= W);
        return table[h][w];
    }

    template <typename S> bool operator==(const matrix<S> &other) {
        if (size_H() != other.size_H() || size_W() != other.size_W())
            return false;
        for (int h = 0; h < H; ++h) {
            for (int w = 0; w < W; ++w) {
                if (table[h][w] != other.table[h][w])
                    return false;
            }
        }
        return true;
    }
    template <typename S> bool operator!=(const matrix<S> &other) {
        return !operator==(other);
    }

    /**
     * @brief サイズ n の単位行列。
     */
    static matrix<T> E(int N) {
        matrix<T> ret(N, N);
        for (int i = 0; i < N; i++)
            ret.table[i][i] = 1;
        return ret;
    }
};
#line 7 "library/gandalfr/graph/base_graph.hpp"

namespace internal {
template <class Weight> struct _base_edge {
    int v[2];
    Weight cost;
    int id;
    _base_edge() {}
    _base_edge(int from, int to, Weight cost, int id)
        : v{from, to}, cost(cost), id(id) {}

    // x から見た反対側の端点を返す
    int opp(int x) {
        if (x == v[0]) {
            return v[1];
        } else if (x == v[1]) {
            return v[0];
        } else {
            std::abort();
        }
    }

    friend std::ostream &operator<<(std::ostream &os,
                                    const _base_edge<Weight> &e) {
        e.print(os);
        return os;
    }

  protected:
    virtual void print(std::ostream &os) const = 0;
};
} // namespace internal

template <class Weight> struct edge : public internal::_base_edge<Weight> {
    using internal::_base_edge<Weight>::_base_edge;

    edge reverse() const {
        return {this->v[1], this->v[0], this->cost, this->id};
    }

  protected:
    void print(std::ostream &os) const override {
        os << this->v[0] << " " << this->v[1] << " " << this->cost;
    }
};

template <> struct edge<int> : public internal::_base_edge<int> {
    static inline const int cost = 1;
    using internal::_base_edge<int>::_base_edge;
    edge(int _from, int _to, int _id) : _base_edge<int>(_from, _to, 1, _id) {}

    edge reverse() const { return {v[1], v[0], 1, id}; }

  protected:
    void print(std::ostream &os) const override {
        os << this->v[0] << " " << this->v[1];
    }
};

template <class Flow, class Cost>
struct flow_edge : public internal::_base_edge<Cost> {
  private:
    Flow res, cap;
    using internal::_base_edge<Cost>::cost;

  public:
    flow_edge() {}
    flow_edge(int from, int to, Flow res, Flow cap, int id)
        : internal::_base_edge<Cost>(from, to, 1, id), res(res), cap(cap) {}
    flow_edge(int from, int to, Flow res, Flow cap, Cost cost, int id)
        : internal::_base_edge<Cost>(from, to, cost, id), res(res), cap(cap) {
    }

    // x から見たコスト
    Cost get_cost(int x) {
        if (x == this->v[0]) {
            return this->cost;
        } else if (x == this->v[1]) {
            return -this->cost;
        } else {
            std::abort();
        }
    }

    flow_edge reverse() const {
        return {this->v[1], this->v[0], cap - res, cap, this->cost, this->id};
    }

    // x から見た残余
    Flow residual(int x) const {
        if (x == this->v[0]) {
            return res;
        } else if (x == this->v[1]) {
            return cap - res;
        } else {
            std::abort();
        }
    }

    // x から見て残余がゼロか？
    Flow is_full(int x) const {
        if (x == this->v[0]) {
            return res == 0;
        } else if (x == this->v[1]) {
            return cap - res == 0;
        } else {
            std::abort();
        }
    }

    // x から流量を d だけ追加
    void add_flow(int x, Flow d) {
        if (x == this->v[0]) {
            res -= d;
        } else if (x == this->v[1]) {
            res += d;
        } else {
            std::abort();
        }
    }

  protected:
    void print(std::ostream &os) const override {
        os << this->v[0] << " " << this->v[1] << " " << cap - res << "/" << cap;
    }
};

namespace internal {

template <typename Edge> class _base_graph {
  protected:
    int N;
    std::vector<std::vector<Edge *>> G;
    std::vector<std::unique_ptr<Edge>> E;

  public:
    _base_graph(){};
    _base_graph(int n) : N(n), G(n){};
    _base_graph(int n, int m) : N(n), G(n) { E.reserve(m); };

    /**
     * @return ノードの数
     */
    int count_nodes() const { return N; }

    /**
     * @return 辺の数
     */
    int count_edges() const { return E.size(); }

    /**
     * @param n ノード番号
     * @return ノード n からの隣接頂点のリストの const 参照
     */
    const std::vector<Edge *> &operator[](int n) const { return G[n]; }

    /**
     * @return グラフ全体の辺のポインタのリストの const 参照
     */
    const std::vector<std::unique_ptr<Edge>> &edges() const { return E; }

    void print() const {
        std::cout << this->N << " " << this->E.size() << std::endl;
        for (auto &e : this->E)
            std::cout << *e << std::endl;
    }
};
} // namespace internal
#line 10 "library/gandalfr/graph/graph.hpp"

/**
 * @brief グラフを管理するクラス。
 * @tparam Weight int なら重みなし、そうでないなら重みつきグラフ
 * @tparam is_directed 有向グラフかとうか
 */
template <typename Weight, bool is_directed>
class graph : public internal::_base_graph<edge<Weight>> {
  private:
    union_find uf;
    mutable std::vector<bool> visited; // dfs / bfs のための領域
    Weight W = 0;
    bool forest_flag = true;
    static inline const Weight WEIGHT_MAX = std::numeric_limits<Weight>::max();

    void reset_visited_flag(int node) const {
        for (int x : uf.group_containing_node(node))
            visited[x] = false;
    }

    void reset_visited_flag() const { visited.assign(this->N, false); }

  public:
    graph() {}
    graph(int n) : internal::_base_graph<edge<Weight>>(n), uf(n), visited(n) {}
    graph(int n, int m)
        : internal::_base_graph<edge<Weight>>(n, m), uf(n), visited(n) {}
    graph(const graph &other) : graph(other.N) {
        for (auto &e : other.E) {
            add_edge(*e);
        }
    }

    /**
     * @brief ノードの数をn個まで増やす
     * @param n サイズ
     * @attention 今のノード数より小さい数を渡したとき、変化なし
     */
    void expand(int n) {
        if (n <= this->N)
            return;
        this->N = n;
        this->G.resize(n);
        visited.resize(n);
        uf.expand(n);
    }

    /**
     * @return 木か
     */
    bool is_tree() const { return forest_flag && uf.count_groups() == 1; }

    /**
     * @return 森か
     */
    bool is_forest() const { return forest_flag; }

    /**
     * @return グラフの重み
     */
    Weight weight() const { return W; }

    /**
     * @param e 辺
     * @attention 渡した辺の id は保持される
     */
    void add_edge(const edge<Weight> &e) {
        forest_flag &= uf.merge(e.v[0], e.v[1]);

        this->E.emplace_back(std::make_unique<edge<Weight>>(e));

        this->G[e.v[0]].push_back(this->E.back().get());
        if (!is_directed && e.v[0] != e.v[1])
            this->G[e.v[1]].push_back(this->E.back().get());

        W += e.cost;
    }

    /**
     * @attention 辺の id は、(現在の辺の本数)番目 が振られる
     * @attention WEIGHT が int だとエラー
     */
    void add_edge(int from, int to, Weight cost) {
        static_assert(!std::is_same<Weight, int>::value);
        add_edge({from, to, cost, (int)this->E.size()});
    }

    /**
     * @attention 辺の id は、(現在の辺の本数)番目 が振られる
     * @attention WEIGHT が int 以外だとエラー
     */
    void add_edge(int from, int to) {
        static_assert(std::is_same<Weight, int>::value);
        add_edge({from, to, (int)this->E.size()});
    }

    /**
     * @param x ノード番号
     * @param y ノード番号
     * @return x, y が連結かどうか
     */
    bool are_connected(int x, int y) const { return uf.same(x, y); }

    /**
     * @return 弱連結成分の数
     */
    int count_connected_components() const { return uf.count_groups(); }

    /**
     * @return 弱連結成分のリストのリスト
     */
    std::vector<std::vector<int>> weakly_connected_components() const {
        return uf.all_groups();
    }

    /**
     * @brief ノード x が含まれている弱連結成分のリストを返す
     */
    std::vector<int> component_containing_node(int x) {
        return uf.group_containing_node(x);
    }

    /**
     * @brief グラフを連結なグラフに分けてリストにして返す
     * @example auto[Gs, gr, nd] = G.decompose();
     * @returns
     * 1.グラフのリスト
     * 2.各ノードがグラフのリストの何番目に属するか
     * 3.各ノードがグラフのどのノードになっているか
     */
    std::tuple<std::vector<graph>, std::vector<int>, std::vector<int>>
    decompose() const {
        std::vector<graph> Gs(uf.count_groups());
        std::vector<std::vector<int>> groups(uf.all_groups());
        std::vector<int> group_id(this->N), node_id(this->N);
        for (int i = 0; i < (int)groups.size(); i++) {
            Gs[i].expand(groups[i].size());
            for (int j = 0; j < (int)groups[i].size(); j++) {
                group_id[groups[i][j]] = i;
                node_id[groups[i][j]] = j;
            }
        }
        for (auto &e : this->E) {
            int id = group_id[e->v[0]];
            e->v[0] = node_id[e->v[0]];
            e->v[1] = node_id[e->v[1]];
            Gs[id].add_edge(e);
        }
        return std::make_tuple(std::move(Gs), std::move(group_id),
                               std::move(node_id));
    }

    /**
     * @brief グラフを隣接行列に変換
     * @param invalid 辺のないときの値
     * @attention 自己ループが含まれていない限り、対角成分は 0
     * @attention 多重辺を持たないと仮定
     */
    matrix<Weight> to_adjajency(Weight invalid = 0) const {
        matrix<Weight> ret(this->N, this->N, invalid);
        for (int i = 0; i < this->N; i++)
            ret(i, i) = 0;
        for (auto &e : this->E) {
            ret(e->v[0], e->v[1]) = e->cost;
            if constexpr (!is_directed) {
                ret(e->v[1], e->v[0]) = e->cost;
            }
        }
        return ret;
    }

  private:
    using PAIR = std::pair<Weight, int>;
    using Dijkstra_queue =
        std::priority_queue<PAIR, std::vector<PAIR>, std::greater<PAIR>>;

    void run_bfs(std::vector<int> &dist, std::queue<int> &q) const {
        while (!q.empty()) {
            int cu = q.front();
            q.pop();
            for (auto &e : this->G[cu]) {
                int to = e->opp(cu);
                if (dist[to] != WEIGHT_MAX)
                    continue;
                dist[to] = dist[cu] + 1;
                q.push(to);
            }
        }
    }

    void run_Dijkstra(std::vector<Weight> &dist, Dijkstra_queue &q) const {
        while (!q.empty()) {
            Weight cur_dist = q.top().first;
            int cu = q.top().second;
            q.pop();

            if (visited[cu])
                continue;
            visited[cu] = true;

            for (auto &e : this->G[cu]) {
                int to = e->opp(cu);
                Weight alt = cur_dist + e->cost;
                if (dist[to] <= alt)
                    continue;
                dist[to] = alt;
                q.push({alt, to});
            }
        }
    }

  public:
    /**
     * @brief 最短距離を計算する
     * @param start_node 始点
     * @param invalid 到達不能な頂点に格納される値
     * @return 各ノードまでの最短距離のリスト
     */
    std::vector<Weight> distances(int start_node, Weight invalid) const {
        std::vector<Weight> dist(this->N, WEIGHT_MAX);
        dist[start_node] = 0;

        if constexpr (std::is_same<Weight, int>::value) {
            // BFS algorithm
            std::queue<int> q;
            q.push(start_node);
            run_bfs(dist, q);
        } else {
            // Dijkstra's algorithm
            Dijkstra_queue q;
            q.push({0, start_node});
            reset_visited_flag(start_node);
            run_Dijkstra(dist, q);
        }

        for (auto &x : dist)
            if (x == WEIGHT_MAX)
                x = invalid;
        return dist;
    }

    matrix<Weight> distances_from_all_nodes(Weight invalid = -1) {
        auto mt(to_adjajency(WEIGHT_MAX));

        for (int k = 0; k < this->N; k++)         // 経由する頂点
            for (int i = 0; i < this->N; i++)     // 始点
                for (int j = 0; j < this->N; j++) // 終点
                    if (mt(i, k) != WEIGHT_MAX && mt(k, j) != WEIGHT_MAX)
                        mt(i, j) = std::min(mt(i, j), mt(i, k) + mt(k, j));

        for (int i = 0; i < this->N; ++i)
            for (int j = 0; j < this->N; ++j)
                if (mt(i, j) == WEIGHT_MAX)
                    mt(i, j) = invalid;
        return mt;
    }

    /**
     * @brief 復元付き最短経路
     * @attention 到達可能でないとき、空の配列で返る
     */
    std::vector<edge<Weight>> shortest_path(int start_node, int end_node) {
        if (start_node == end_node)
            return {};

        auto dist = distances(start_node, WEIGHT_MAX);
        if (dist[end_node] == WEIGHT_MAX)
            return {};

        auto R(this->reverse());
        reset_visited_flag(end_node);
        visited[end_node] = true;

        int cu = end_node;
        std::vector<edge<Weight>> route;
        while (cu != start_node) {
            for (auto &e : R[cu]) {
                int to = e->opp(cu);
                if (visited[to])
                    continue;
                if (dist[cu] - e->cost == dist[to]) {
                    visited[cu = to] = true;
                    route.push_back(e->reverse());
                    break;
                }
            }
        }
        std::reverse(route.begin(), route.end());
        return route;
    }

    Weight diameter() const {
        static_assert(!is_directed);
        assert(is_tree());
        std::vector<Weight> dist(distances(0, -1));
        dist = distances(
            std::max_element(dist.begin(), dist.end()) - dist.begin(), -1);
        return *std::max_element(dist.begin(), dist.end());
    }

    graph reverse() const {
        if constexpr (!is_directed) {
            return *this;
        } else {
            graph ret(this->N);
            for (auto &e : this->E) {
                ret.add_edge(e->reverse());
            }
            return ret;
        }
    }

    /**
     * @brief 行きがけ順に dfs
     */
    std::vector<int> preorder(int start) const {
        std::vector<int> result;
        reset_visited_flag(start);
        visited[start] = true;
        auto dfs = [&](auto self, int cu) -> void {
            result.push_back(cu);
            for (auto &e : this->G[cu]) {
                int to = e->opp(cu);
                if (visited[to])
                    continue;
                visited[to] = true;
                self(self, to);
            }
        };
        dfs(dfs, start);
        return result;
    }

    /**
     * @brief 通りがけ順に dfs
     */
    std::vector<int> inorder(int start) const {
        std::vector<int> result;
        reset_visited_flag(start);
        visited[start] = true;
        auto dfs = [&](auto self, int cu) -> void {
            for (auto &e : this->G[cu]) {
                int to = e->opp(cu);
                if (visited[to])
                    continue;
                visited[to] = true;
                result.push_back(cu);
                self(self, to);
            }
            result.push_back(cu);
        };
        dfs(dfs, start);
        return result;
    }

    /**
     * @brief 帰りがけ順に dfs
     */
    std::vector<int> postorder(int start) const {
        std::vector<int> result;
        reset_visited_flag(start);
        visited[start] = true;
        auto dfs = [&](auto self, int cu) -> void {
            for (auto &e : this->G[cu]) {
                int to = e->opp(cu);
                if (visited[to])
                    continue;
                visited[to] = true;
                self(self, to);
            }
            result.push_back(cu);
        };
        dfs(dfs, start);
        return result;
    }

    std::vector<int> topological_sort() {
        static_assert(is_directed);
        std::vector<int> indeg(this->N, 0), sorted;
        for (auto &e : this->E) {
            indeg[e->v[1]]++;
        }

        std::queue<int> q;
        for (int i = 0; i < this->N; i++)
            if (!indeg[i])
                q.push(i);
        while (!q.empty()) {
            int cu = q.front();
            q.pop();
            for (auto e : this->G[cu]) {
                int to = e->opp(cu);
                if (!--indeg[to])
                    q.push(to);
            }
            sorted.push_back(cu);
        }
        return sorted;
    }

    /**
     * @return 最小全域森
     */
    graph minimum_spanning_forest() const {
        static_assert(!is_directed);
        graph ret(this->N);
        std::vector<edge<Weight>> tmp;
        for (auto &e : this->E) {
            tmp.emplace_back(*e);
        }

        std::sort(tmp.begin(), tmp.end(),
                  [](const edge<Weight> &a, const edge<Weight> &b) {
                      if (a.cost == b.cost) {
                          if (a.v[0] == b.v[0]) {
                              return a.v[1] < b.v[1];
                          }
                          return a.v[0] < b.v[0];
                      }
                      return a.cost < b.cost;
                  });

        for (auto &e : tmp)
            if (!ret.are_connected(e.v[0], e.v[1]))
                ret.add_edge(e);
        return ret;
    }

  private:
    /**
     * @see https://ei1333.github.io/luzhiled/snippets/graph/lowlink.html
     * @attention 非連結でも動作
     */
    int run_lowlink(int idx, int k, int par, std::vector<int> &ord,
                    std::vector<int> &low, std::vector<edge<Weight>> &brds,
                    std::vector<int> &apts) {
        visited[idx] = true;
        ord[idx] = k++;
        low[idx] = ord[idx];
        bool is_apt = false;
        int cnt = 0;
        for (auto &e : this->G[idx]) {
            int to = e->opp(idx);
            if (!visited[to]) {
                ++cnt;
                k = run_lowlink(to, k, idx, ord, low, brds, apts);
                low[idx] = std::min(low[idx], low[to]);
                is_apt |= ~par && low[to] >= ord[idx];
                if (ord[idx] < low[to]) {
                    brds.emplace_back(*e);
                }
            } else if (to != par) {
                low[idx] = std::min(low[idx], ord[to]);
            }
        }
        is_apt |= par == -1 && cnt > 1;
        if (is_apt)
            apts.push_back(idx);
        return k;
    }

  public:
    /**
     * @return pair<vector<橋>, vector<関節点>>
     */
    std::pair<std::vector<edge<Weight>>, std::vector<int>> lowlink() {
        static_assert(!is_directed);
        std::vector<edge<Weight>> brds;
        std::vector<int> apts, ord(this->N, 0), low(this->N, 0);
        reset_visited_flag();
        int k = 0;
        for (int i = 0; i < this->N; i++) {
            if (!visited[i])
                k = run_lowlink(i, k, -1, ord, low, brds, apts);
        }
        return {brds, apts};
    }

    // verify: https://atcoder.jp/contests/abc232/submissions/45715440
    // 同型判定
    bool operator==(const graph &other) const {
        if (this->N != other.count_nodes())
            return false;
        if (this->count_edges() != other.count_edges())
            return false;
        if (this->count_connected_components() !=
            other.count_connected_components())
            return false;

        matrix<Weight> adj1(to_adjajency()), adj2(other.to_adjajency());

        std::vector<int> nodes_id(this->N);
        std::iota(nodes_id.begin(), nodes_id.end(), 0);
        do {
            bool ok = true;
            for (int i = 0; i < this->N; i++)
                for (int j = 0; j < this->N; j++) {
                    if (adj1(i, j) != adj2(nodes_id[i], nodes_id[j])) {
                        ok = false;
                        break;
                    }
                }
            if (ok)
                return true;
        } while (std::next_permutation(nodes_id.begin(), nodes_id.end()));
        return false;
    }

    bool operator!=(const graph &other) const { return !operator==(other); }
};
#line 8 "library/gandalfr/other/io_supporter.hpp"

#line 1 "library/atcoder/modint.hpp"



#line 6 "library/atcoder/modint.hpp"
#include <type_traits>

#ifdef _MSC_VER
#include <intrin.h>
#endif

#line 1 "library/atcoder/internal_math.hpp"



#line 5 "library/atcoder/internal_math.hpp"

#ifdef _MSC_VER
#include <intrin.h>
#endif

namespace atcoder {

namespace internal {

// @param m `1 <= m`
// @return x mod m
constexpr long long safe_mod(long long x, long long m) {
    x %= m;
    if (x < 0) x += m;
    return x;
}

// Fast modular multiplication by barrett reduction
// Reference: https://en.wikipedia.org/wiki/Barrett_reduction
// NOTE: reconsider after Ice Lake
struct barrett {
    unsigned int _m;
    unsigned long long im;

    // @param m `1 <= m < 2^31`
    explicit barrett(unsigned int m) : _m(m), im((unsigned long long)(-1) / m + 1) {}

    // @return m
    unsigned int umod() const { return _m; }

    // @param a `0 <= a < m`
    // @param b `0 <= b < m`
    // @return `a * b % m`
    unsigned int mul(unsigned int a, unsigned int b) const {
        // [1] m = 1
        // a = b = im = 0, so okay

        // [2] m >= 2
        // im = ceil(2^64 / m)
        // -> im * m = 2^64 + r (0 <= r < m)
        // let z = a*b = c*m + d (0 <= c, d < m)
        // a*b * im = (c*m + d) * im = c*(im*m) + d*im = c*2^64 + c*r + d*im
        // c*r + d*im < m * m + m * im < m * m + 2^64 + m <= 2^64 + m * (m + 1) < 2^64 * 2
        // ((ab * im) >> 64) == c or c + 1
        unsigned long long z = a;
        z *= b;
#ifdef _MSC_VER
        unsigned long long x;
        _umul128(z, im, &x);
#else
        unsigned long long x =
            (unsigned long long)(((unsigned __int128)(z)*im) >> 64);
#endif
        unsigned int v = (unsigned int)(z - x * _m);
        if (_m <= v) v += _m;
        return v;
    }
};

// @param n `0 <= n`
// @param m `1 <= m`
// @return `(x ** n) % m`
constexpr long long pow_mod_constexpr(long long x, long long n, int m) {
    if (m == 1) return 0;
    unsigned int _m = (unsigned int)(m);
    unsigned long long r = 1;
    unsigned long long y = safe_mod(x, m);
    while (n) {
        if (n & 1) r = (r * y) % _m;
        y = (y * y) % _m;
        n >>= 1;
    }
    return r;
}

// Reference:
// M. Forisek and J. Jancina,
// Fast Primality Testing for Integers That Fit into a Machine Word
// @param n `0 <= n`
constexpr bool is_prime_constexpr(int n) {
    if (n <= 1) return false;
    if (n == 2 || n == 7 || n == 61) return true;
    if (n % 2 == 0) return false;
    long long d = n - 1;
    while (d % 2 == 0) d /= 2;
    constexpr long long bases[3] = {2, 7, 61};
    for (long long a : bases) {
        long long t = d;
        long long y = pow_mod_constexpr(a, t, n);
        while (t != n - 1 && y != 1 && y != n - 1) {
            y = y * y % n;
            t <<= 1;
        }
        if (y != n - 1 && t % 2 == 0) {
            return false;
        }
    }
    return true;
}
template <int n> constexpr bool is_prime = is_prime_constexpr(n);

// @param b `1 <= b`
// @return pair(g, x) s.t. g = gcd(a, b), xa = g (mod b), 0 <= x < b/g
constexpr std::pair<long long, long long> inv_gcd(long long a, long long b) {
    a = safe_mod(a, b);
    if (a == 0) return {b, 0};

    // Contracts:
    // [1] s - m0 * a = 0 (mod b)
    // [2] t - m1 * a = 0 (mod b)
    // [3] s * |m1| + t * |m0| <= b
    long long s = b, t = a;
    long long m0 = 0, m1 = 1;

    while (t) {
        long long u = s / t;
        s -= t * u;
        m0 -= m1 * u;  // |m1 * u| <= |m1| * s <= b

        // [3]:
        // (s - t * u) * |m1| + t * |m0 - m1 * u|
        // <= s * |m1| - t * u * |m1| + t * (|m0| + |m1| * u)
        // = s * |m1| + t * |m0| <= b

        auto tmp = s;
        s = t;
        t = tmp;
        tmp = m0;
        m0 = m1;
        m1 = tmp;
    }
    // by [3]: |m0| <= b/g
    // by g != b: |m0| < b/g
    if (m0 < 0) m0 += b / s;
    return {s, m0};
}

// Compile time primitive root
// @param m must be prime
// @return primitive root (and minimum in now)
constexpr int primitive_root_constexpr(int m) {
    if (m == 2) return 1;
    if (m == 167772161) return 3;
    if (m == 469762049) return 3;
    if (m == 754974721) return 11;
    if (m == 998244353) return 3;
    int divs[20] = {};
    divs[0] = 2;
    int cnt = 1;
    int x = (m - 1) / 2;
    while (x % 2 == 0) x /= 2;
    for (int i = 3; (long long)(i)*i <= x; i += 2) {
        if (x % i == 0) {
            divs[cnt++] = i;
            while (x % i == 0) {
                x /= i;
            }
        }
    }
    if (x > 1) {
        divs[cnt++] = x;
    }
    for (int g = 2;; g++) {
        bool ok = true;
        for (int i = 0; i < cnt; i++) {
            if (pow_mod_constexpr(g, (m - 1) / divs[i], m) == 1) {
                ok = false;
                break;
            }
        }
        if (ok) return g;
    }
}
template <int m> constexpr int primitive_root = primitive_root_constexpr(m);

// @param n `n < 2^32`
// @param m `1 <= m < 2^32`
// @return sum_{i=0}^{n-1} floor((ai + b) / m) (mod 2^64)
unsigned long long floor_sum_unsigned(unsigned long long n,
                                      unsigned long long m,
                                      unsigned long long a,
                                      unsigned long long b) {
    unsigned long long ans = 0;
    while (true) {
        if (a >= m) {
            ans += n * (n - 1) / 2 * (a / m);
            a %= m;
        }
        if (b >= m) {
            ans += n * (b / m);
            b %= m;
        }

        unsigned long long y_max = a * n + b;
        if (y_max < m) break;
        // y_max < m * (n + 1)
        // floor(y_max / m) <= n
        n = (unsigned long long)(y_max / m);
        b = (unsigned long long)(y_max % m);
        std::swap(m, a);
    }
    return ans;
}

}  // namespace internal

}  // namespace atcoder


#line 1 "library/atcoder/internal_type_traits.hpp"



#line 7 "library/atcoder/internal_type_traits.hpp"

namespace atcoder {

namespace internal {

#ifndef _MSC_VER
template <class T>
using is_signed_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value ||
                                  std::is_same<T, __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int128 =
    typename std::conditional<std::is_same<T, __uint128_t>::value ||
                                  std::is_same<T, unsigned __int128>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using make_unsigned_int128 =
    typename std::conditional<std::is_same<T, __int128_t>::value,
                              __uint128_t,
                              unsigned __int128>;

template <class T>
using is_integral = typename std::conditional<std::is_integral<T>::value ||
                                                  is_signed_int128<T>::value ||
                                                  is_unsigned_int128<T>::value,
                                              std::true_type,
                                              std::false_type>::type;

template <class T>
using is_signed_int = typename std::conditional<(is_integral<T>::value &&
                                                 std::is_signed<T>::value) ||
                                                    is_signed_int128<T>::value,
                                                std::true_type,
                                                std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<(is_integral<T>::value &&
                               std::is_unsigned<T>::value) ||
                                  is_unsigned_int128<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<
    is_signed_int128<T>::value,
    make_unsigned_int128<T>,
    typename std::conditional<std::is_signed<T>::value,
                              std::make_unsigned<T>,
                              std::common_type<T>>::type>::type;

#else

template <class T> using is_integral = typename std::is_integral<T>;

template <class T>
using is_signed_int =
    typename std::conditional<is_integral<T>::value && std::is_signed<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using is_unsigned_int =
    typename std::conditional<is_integral<T>::value &&
                                  std::is_unsigned<T>::value,
                              std::true_type,
                              std::false_type>::type;

template <class T>
using to_unsigned = typename std::conditional<is_signed_int<T>::value,
                                              std::make_unsigned<T>,
                                              std::common_type<T>>::type;

#endif

template <class T>
using is_signed_int_t = std::enable_if_t<is_signed_int<T>::value>;

template <class T>
using is_unsigned_int_t = std::enable_if_t<is_unsigned_int<T>::value>;

template <class T> using to_unsigned_t = typename to_unsigned<T>::type;

}  // namespace internal

}  // namespace atcoder


#line 14 "library/atcoder/modint.hpp"

namespace atcoder {

namespace internal {

struct modint_base {};
struct static_modint_base : modint_base {};

template <class T> using is_modint = std::is_base_of<modint_base, T>;
template <class T> using is_modint_t = std::enable_if_t<is_modint<T>::value>;

}  // namespace internal

template <int m, std::enable_if_t<(1 <= m)>* = nullptr>
struct static_modint : internal::static_modint_base {
    using mint = static_modint;

  public:
    static constexpr int mod() { return m; }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    static_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    static_modint(T v) {
        long long x = (long long)(v % (long long)(umod()));
        if (x < 0) x += umod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    static_modint(T v) {
        _v = (unsigned int)(v % umod());
    }

    unsigned int val() const { return _v; }

    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v -= rhs._v;
        if (_v >= umod()) _v += umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        unsigned long long z = _v;
        z *= rhs._v;
        _v = (unsigned int)(z % umod());
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }

    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        if (prime) {
            assert(_v);
            return pow(umod() - 2);
        } else {
            auto eg = internal::inv_gcd(_v, m);
            assert(eg.first == 1);
            return eg.second;
        }
    }

    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }

  private:
    unsigned int _v;
    static constexpr unsigned int umod() { return m; }
    static constexpr bool prime = internal::is_prime<m>;
};

template <int id> struct dynamic_modint : internal::modint_base {
    using mint = dynamic_modint;

  public:
    static int mod() { return (int)(bt.umod()); }
    static void set_mod(int m) {
        assert(1 <= m);
        bt = internal::barrett(m);
    }
    static mint raw(int v) {
        mint x;
        x._v = v;
        return x;
    }

    dynamic_modint() : _v(0) {}
    template <class T, internal::is_signed_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        long long x = (long long)(v % (long long)(mod()));
        if (x < 0) x += mod();
        _v = (unsigned int)(x);
    }
    template <class T, internal::is_unsigned_int_t<T>* = nullptr>
    dynamic_modint(T v) {
        _v = (unsigned int)(v % mod());
    }

    unsigned int val() const { return _v; }

    mint& operator++() {
        _v++;
        if (_v == umod()) _v = 0;
        return *this;
    }
    mint& operator--() {
        if (_v == 0) _v = umod();
        _v--;
        return *this;
    }
    mint operator++(int) {
        mint result = *this;
        ++*this;
        return result;
    }
    mint operator--(int) {
        mint result = *this;
        --*this;
        return result;
    }

    mint& operator+=(const mint& rhs) {
        _v += rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator-=(const mint& rhs) {
        _v += mod() - rhs._v;
        if (_v >= umod()) _v -= umod();
        return *this;
    }
    mint& operator*=(const mint& rhs) {
        _v = bt.mul(_v, rhs._v);
        return *this;
    }
    mint& operator/=(const mint& rhs) { return *this = *this * rhs.inv(); }

    mint operator+() const { return *this; }
    mint operator-() const { return mint() - *this; }

    mint pow(long long n) const {
        assert(0 <= n);
        mint x = *this, r = 1;
        while (n) {
            if (n & 1) r *= x;
            x *= x;
            n >>= 1;
        }
        return r;
    }
    mint inv() const {
        auto eg = internal::inv_gcd(_v, mod());
        assert(eg.first == 1);
        return eg.second;
    }

    friend mint operator+(const mint& lhs, const mint& rhs) {
        return mint(lhs) += rhs;
    }
    friend mint operator-(const mint& lhs, const mint& rhs) {
        return mint(lhs) -= rhs;
    }
    friend mint operator*(const mint& lhs, const mint& rhs) {
        return mint(lhs) *= rhs;
    }
    friend mint operator/(const mint& lhs, const mint& rhs) {
        return mint(lhs) /= rhs;
    }
    friend bool operator==(const mint& lhs, const mint& rhs) {
        return lhs._v == rhs._v;
    }
    friend bool operator!=(const mint& lhs, const mint& rhs) {
        return lhs._v != rhs._v;
    }

  private:
    unsigned int _v;
    static internal::barrett bt;
    static unsigned int umod() { return bt.umod(); }
};
template <int id> internal::barrett dynamic_modint<id>::bt(998244353);

using modint998244353 = static_modint<998244353>;
using modint1000000007 = static_modint<1000000007>;
using modint = dynamic_modint<-1>;

namespace internal {

template <class T>
using is_static_modint = std::is_base_of<internal::static_modint_base, T>;

template <class T>
using is_static_modint_t = std::enable_if_t<is_static_modint<T>::value>;

template <class> struct is_dynamic_modint : public std::false_type {};
template <int id>
struct is_dynamic_modint<dynamic_modint<id>> : public std::true_type {};

template <class T>
using is_dynamic_modint_t = std::enable_if_t<is_dynamic_modint<T>::value>;

}  // namespace internal

}  // namespace atcoder


#line 10 "library/gandalfr/other/io_supporter.hpp"

template <typename T>
std::ostream &operator<<(std::ostream &os, const std::vector<T> &v) {
    for (int i = 0; i < (int)v.size(); i++)
        os << v[i] << (i + 1 != (int)v.size() ? " " : "");
    return os;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::set<T> &st) {
    for (const T &x : st) {
        std::cout << x << " ";
    }
    return os;
}

template <typename T>
std::ostream &operator<<(std::ostream &os, const std::multiset<T> &st) {
    for (const T &x : st) {
        std::cout << x << " ";
    }
    return os;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, const std::deque<T> &dq) {
    for (const T &x : dq) {
        std::cout << x << " ";
    }
    return os;
}
template <typename T1, typename T2>
std::ostream &operator<<(std::ostream &os, const std::pair<T1, T2> &p) {
    os << p.first << ' ' << p.second;
    return os;
}
template <typename T>
std::ostream &operator<<(std::ostream &os, std::queue<T> &q) {
    int sz = q.size();
    while (--sz) {
        os << q.front() << ' ';
        q.push(q.front());
        q.pop();
    }
    os << q.front();
    q.push(q.front());
    q.pop();
    return os;
}

namespace atcoder {
template <int m>
std::ostream &operator<<(std::ostream &os, const static_modint<m> &mi) {
    os << mi.val();
    return os;
}
template <int m>
std::ostream &operator<<(std::ostream &os, const dynamic_modint<m> &mi) {
    os << mi.val();
    return os;
}

}

template <typename T>
std::istream &operator>>(std::istream &is, std::vector<T> &v) {
    for (T &in : v)
        is >> in;
    return is;
}
template <typename T1, typename T2>
std::istream &operator>>(std::istream &is, std::pair<T1, T2> &p) {
    is >> p.first >> p.second;
    return is;
}
namespace atcoder {
template <int m>
std::istream &operator>>(std::istream &is, static_modint<m> &mi) {
    long long n;
    is >> n;
    mi = n;
    return is;
}
template <int m>
std::istream &operator>>(std::istream &is, dynamic_modint<m> &mi) {
    long long n;
    is >> n;
    mi = n;
    return is;
}

}
#line 4 "playspace/main.cpp"
using namespace std;
using ll = long long;
const int INF = 1001001001;
const ll INFLL = 1001001001001001001;
const ll MOD  = 1000000007;
const ll _MOD = 998244353;
#define rep(i, j, n) for(ll i = (ll)(j); i < (ll)(n); i++)
#define rrep(i, j, n) for(ll i = (ll)(n-1); i >= (ll)(j); i--)
#define all(a) (a).begin(),(a).end()
#define debug(a) std::cerr << #a << ": " << a << std::endl
#define LF cout << endl
template<typename T1, typename T2> inline bool chmax(T1 &a, T2 b) { return a < b && (a = b, true); }
template<typename T1, typename T2> inline bool chmin(T1 &a, T2 b) { return a > b && (a = b, true); }
void Yes(bool ok){ std::cout << (ok ? "Yes" : "No") << std::endl; }

int main(void){

    string S, T;
    cin >> S >> T;
    int a = S.back() - '0';
    int b = T.back() - '0';
    cout << ((a - b) % 2 == 0 ? "Possible" : "Impossible") << endl;


}