#line 1 "/home/maspy/compro/library/my_template.hpp"
#if defined(LOCAL)
#include <my_template_compiled.hpp>
#else

// https://codeforces.com/blog/entry/96344
#pragma GCC optimize("Ofast,unroll-loops")
// いまの CF だとこれ入れると動かない？
// #pragma GCC target("avx2,popcnt")

#include <bits/stdc++.h>

using namespace std;

using ll = long long;
using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using i128 = __int128;
using u128 = unsigned __int128;
using f128 = __float128;

template <class T>
constexpr T infty = 0;
template <>
constexpr int infty<int> = 1'010'000'000;
template <>
constexpr ll infty<ll> = 2'020'000'000'000'000'000;
template <>
constexpr u32 infty<u32> = infty<int>;
template <>
constexpr u64 infty<u64> = infty<ll>;
template <>
constexpr i128 infty<i128> = i128(infty<ll>) * 2'000'000'000'000'000'000;
template <>
constexpr double infty<double> = infty<ll>;
template <>
constexpr long double infty<long double> = infty<ll>;

using pi = pair<ll, ll>;
using vi = vector<ll>;
template <class T>
using vc = vector<T>;
template <class T>
using vvc = vector<vc<T>>;
template <class T>
using vvvc = vector<vvc<T>>;
template <class T>
using vvvvc = vector<vvvc<T>>;
template <class T>
using vvvvvc = vector<vvvvc<T>>;
template <class T>
using pq = priority_queue<T>;
template <class T>
using pqg = priority_queue<T, vector<T>, greater<T>>;

#define vv(type, name, h, ...) vector<vector<type>> name(h, vector<type>(__VA_ARGS__))
#define vvv(type, name, h, w, ...) vector<vector<vector<type>>> name(h, vector<vector<type>>(w, vector<type>(__VA_ARGS__)))
#define vvvv(type, name, a, b, c, ...) \
  vector<vector<vector<vector<type>>>> name(a, vector<vector<vector<type>>>(b, vector<vector<type>>(c, vector<type>(__VA_ARGS__))))

// https://trap.jp/post/1224/
#define FOR1(a) for (ll _ = 0; _ < ll(a); ++_)
#define FOR2(i, a) for (ll i = 0; i < ll(a); ++i)
#define FOR3(i, a, b) for (ll i = a; i < ll(b); ++i)
#define FOR4(i, a, b, c) for (ll i = a; i < ll(b); i += (c))
#define FOR1_R(a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR2_R(i, a) for (ll i = (a)-1; i >= ll(0); --i)
#define FOR3_R(i, a, b) for (ll i = (b)-1; i >= ll(a); --i)
#define overload4(a, b, c, d, e, ...) e
#define overload3(a, b, c, d, ...) d
#define FOR(...) overload4(__VA_ARGS__, FOR4, FOR3, FOR2, FOR1)(__VA_ARGS__)
#define FOR_R(...) overload3(__VA_ARGS__, FOR3_R, FOR2_R, FOR1_R)(__VA_ARGS__)

#define FOR_subset(t, s) for (ll t = (s); t >= 0; t = (t == 0 ? -1 : (t - 1) & (s)))
#define all(x) x.begin(), x.end()
#define len(x) ll(x.size())
#define elif else if

#define eb emplace_back
#define mp make_pair
#define mt make_tuple
#define fi first
#define se second

#define stoi stoll

int popcnt(int x) { return __builtin_popcount(x); }
int popcnt(u32 x) { return __builtin_popcount(x); }
int popcnt(ll x) { return __builtin_popcountll(x); }
int popcnt(u64 x) { return __builtin_popcountll(x); }
int popcnt_sgn(int x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(u32 x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(ll x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
int popcnt_sgn(u64 x) { return (__builtin_parity(x) & 1 ? -1 : 1); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 1, 2)
int topbit(int x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(u32 x) { return (x == 0 ? -1 : 31 - __builtin_clz(x)); }
int topbit(ll x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
int topbit(u64 x) { return (x == 0 ? -1 : 63 - __builtin_clzll(x)); }
// (0, 1, 2, 3, 4) -> (-1, 0, 1, 0, 2)
int lowbit(int x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(u32 x) { return (x == 0 ? -1 : __builtin_ctz(x)); }
int lowbit(ll x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }
int lowbit(u64 x) { return (x == 0 ? -1 : __builtin_ctzll(x)); }

template <typename T>
T kth_bit(int k) {
  return T(1) << k;
}
template <typename T>
bool has_kth_bit(T x, int k) {
  return x >> k & 1;
}

template <typename T>
T floor(T a, T b) {
  return a / b - (a % b && (a ^ b) < 0);
}
template <typename T>
T ceil(T x, T y) {
  return floor(x + y - 1, y);
}
template <typename T>
T bmod(T x, T y) {
  return x - y * floor(x, y);
}
template <typename T>
pair<T, T> divmod(T x, T y) {
  T q = floor(x, y);
  return {q, x - q * y};
}

template <typename T, typename U>
T SUM(const vector<U> &A) {
  T sm = 0;
  for (auto &&a: A) sm += a;
  return sm;
}

#define MIN(v) *min_element(all(v))
#define MAX(v) *max_element(all(v))
#define LB(c, x) distance((c).begin(), lower_bound(all(c), (x)))
#define UB(c, x) distance((c).begin(), upper_bound(all(c), (x)))
#define UNIQUE(x) sort(all(x)), x.erase(unique(all(x)), x.end()), x.shrink_to_fit()

template <typename T>
T POP(deque<T> &que) {
  T a = que.front();
  que.pop_front();
  return a;
}
template <typename T>
T POP(pq<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(pqg<T> &que) {
  T a = que.top();
  que.pop();
  return a;
}
template <typename T>
T POP(vc<T> &que) {
  T a = que.back();
  que.pop_back();
  return a;
}

template <typename F>
ll binary_search(F check, ll ok, ll ng, bool check_ok = true) {
  if (check_ok) assert(check(ok));
  while (abs(ok - ng) > 1) {
    auto x = (ng + ok) / 2;
    (check(x) ? ok : ng) = x;
  }
  return ok;
}
template <typename F>
double binary_search_real(F check, double ok, double ng, int iter = 100) {
  FOR(iter) {
    double x = (ok + ng) / 2;
    (check(x) ? ok : ng) = x;
  }
  return (ok + ng) / 2;
}

template <class T, class S>
inline bool chmax(T &a, const S &b) {
  return (a < b ? a = b, 1 : 0);
}
template <class T, class S>
inline bool chmin(T &a, const S &b) {
  return (a > b ? a = b, 1 : 0);
}

// ? は -1
vc<int> s_to_vi(const string &S, char first_char) {
  vc<int> A(S.size());
  FOR(i, S.size()) { A[i] = (S[i] != '?' ? S[i] - first_char : -1); }
  return A;
}

template <typename T, typename U>
vector<T> cumsum(vector<U> &A, int off = 1) {
  int N = A.size();
  vector<T> B(N + 1);
  FOR(i, N) { B[i + 1] = B[i] + A[i]; }
  if (off == 0) B.erase(B.begin());
  return B;
}

// stable sort
template <typename T>
vector<int> argsort(const vector<T> &A) {
  vector<int> ids(len(A));
  iota(all(ids), 0);
  sort(all(ids), [&](int i, int j) { return (A[i] == A[j] ? i < j : A[i] < A[j]); });
  return ids;
}

// A[I[0]], A[I[1]], ...
template <typename T>
vc<T> rearrange(const vc<T> &A, const vc<int> &I) {
  vc<T> B(len(I));
  FOR(i, len(I)) B[i] = A[I[i]];
  return B;
}

template <typename T, typename... Vectors>
void concat(vc<T> &first, const Vectors &... others) {
  vc<T> &res = first;
  (res.insert(res.end(), others.begin(), others.end()), ...);
}
#endif
#line 1 "/home/maspy/compro/library/other/io.hpp"
#define FASTIO
#include <unistd.h>

// https://judge.yosupo.jp/submission/21623
namespace fastio {
static constexpr uint32_t SZ = 1 << 17;
char ibuf[SZ];
char obuf[SZ];
char out[100];
// pointer of ibuf, obuf
uint32_t pil = 0, pir = 0, por = 0;

struct Pre {
  char num[10000][4];
  constexpr Pre() : num() {
    for (int i = 0; i < 10000; i++) {
      int n = i;
      for (int j = 3; j >= 0; j--) {
        num[i][j] = n % 10 | '0';
        n /= 10;
      }
    }
  }
} constexpr pre;

inline void load() {
  memcpy(ibuf, ibuf + pil, pir - pil);
  pir = pir - pil + fread(ibuf + pir - pil, 1, SZ - pir + pil, stdin);
  pil = 0;
  if (pir < SZ) ibuf[pir++] = '\n';
}

inline void flush() {
  fwrite(obuf, 1, por, stdout);
  por = 0;
}

void rd(char &c) {
  do {
    if (pil + 1 > pir) load();
    c = ibuf[pil++];
  } while (isspace(c));
}

void rd(string &x) {
  x.clear();
  char c;
  do {
    if (pil + 1 > pir) load();
    c = ibuf[pil++];
  } while (isspace(c));
  do {
    x += c;
    if (pil == pir) load();
    c = ibuf[pil++];
  } while (!isspace(c));
}

template <typename T>
void rd_real(T &x) {
  string s;
  rd(s);
  x = stod(s);
}

template <typename T>
void rd_integer(T &x) {
  if (pil + 100 > pir) load();
  char c;
  do
    c = ibuf[pil++];
  while (c < '-');
  bool minus = 0;
  if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
    if (c == '-') { minus = 1, c = ibuf[pil++]; }
  }
  x = 0;
  while ('0' <= c) { x = x * 10 + (c & 15), c = ibuf[pil++]; }
  if constexpr (is_signed<T>::value || is_same_v<T, i128>) {
    if (minus) x = -x;
  }
}

void rd(int &x) { rd_integer(x); }
void rd(ll &x) { rd_integer(x); }
void rd(i128 &x) { rd_integer(x); }
void rd(u32 &x) { rd_integer(x); }
void rd(u64 &x) { rd_integer(x); }
void rd(u128 &x) { rd_integer(x); }
void rd(double &x) { rd_real(x); }
void rd(long double &x) { rd_real(x); }
void rd(f128 &x) { rd_real(x); }

template <class T, class U>
void rd(pair<T, U> &p) {
  return rd(p.first), rd(p.second);
}
template <size_t N = 0, typename T>
void rd_tuple(T &t) {
  if constexpr (N < std::tuple_size<T>::value) {
    auto &x = std::get<N>(t);
    rd(x);
    rd_tuple<N + 1>(t);
  }
}
template <class... T>
void rd(tuple<T...> &tpl) {
  rd_tuple(tpl);
}

template <size_t N = 0, typename T>
void rd(array<T, N> &x) {
  for (auto &d: x) rd(d);
}
template <class T>
void rd(vc<T> &x) {
  for (auto &d: x) rd(d);
}

void read() {}
template <class H, class... T>
void read(H &h, T &... t) {
  rd(h), read(t...);
}

void wt(const char c) {
  if (por == SZ) flush();
  obuf[por++] = c;
}
void wt(const string s) {
  for (char c: s) wt(c);
}
void wt(const char *s) {
  size_t len = strlen(s);
  for (size_t i = 0; i < len; i++) wt(s[i]);
}

template <typename T>
void wt_integer(T x) {
  if (por > SZ - 100) flush();
  if (x < 0) { obuf[por++] = '-', x = -x; }
  int outi;
  for (outi = 96; x >= 10000; outi -= 4) {
    memcpy(out + outi, pre.num[x % 10000], 4);
    x /= 10000;
  }
  if (x >= 1000) {
    memcpy(obuf + por, pre.num[x], 4);
    por += 4;
  } else if (x >= 100) {
    memcpy(obuf + por, pre.num[x] + 1, 3);
    por += 3;
  } else if (x >= 10) {
    int q = (x * 103) >> 10;
    obuf[por] = q | '0';
    obuf[por + 1] = (x - q * 10) | '0';
    por += 2;
  } else
    obuf[por++] = x | '0';
  memcpy(obuf + por, out + outi + 4, 96 - outi);
  por += 96 - outi;
}

template <typename T>
void wt_real(T x) {
  ostringstream oss;
  oss << fixed << setprecision(15) << double(x);
  string s = oss.str();
  wt(s);
}

void wt(int x) { wt_integer(x); }
void wt(ll x) { wt_integer(x); }
void wt(i128 x) { wt_integer(x); }
void wt(u32 x) { wt_integer(x); }
void wt(u64 x) { wt_integer(x); }
void wt(u128 x) { wt_integer(x); }
void wt(double x) { wt_real(x); }
void wt(long double x) { wt_real(x); }
void wt(f128 x) { wt_real(x); }

template <class T, class U>
void wt(const pair<T, U> val) {
  wt(val.first);
  wt(' ');
  wt(val.second);
}
template <size_t N = 0, typename T>
void wt_tuple(const T t) {
  if constexpr (N < std::tuple_size<T>::value) {
    if constexpr (N > 0) { wt(' '); }
    const auto x = std::get<N>(t);
    wt(x);
    wt_tuple<N + 1>(t);
  }
}
template <class... T>
void wt(tuple<T...> tpl) {
  wt_tuple(tpl);
}
template <class T, size_t S>
void wt(const array<T, S> val) {
  auto n = val.size();
  for (size_t i = 0; i < n; i++) {
    if (i) wt(' ');
    wt(val[i]);
  }
}
template <class T>
void wt(const vector<T> val) {
  auto n = val.size();
  for (size_t i = 0; i < n; i++) {
    if (i) wt(' ');
    wt(val[i]);
  }
}

void print() { wt('\n'); }
template <class Head, class... Tail>
void print(Head &&head, Tail &&... tail) {
  wt(head);
  if (sizeof...(Tail)) wt(' ');
  print(forward<Tail>(tail)...);
}

// gcc expansion. called automaticall after main.
void __attribute__((destructor)) _d() { flush(); }
} // namespace fastio
using fastio::read;
using fastio::print;
using fastio::flush;

#if defined(LOCAL)
#define SHOW(...) SHOW_IMPL(__VA_ARGS__, SHOW6, SHOW5, SHOW4, SHOW3, SHOW2, SHOW1)(__VA_ARGS__)
#define SHOW_IMPL(_1, _2, _3, _4, _5, _6, NAME, ...) NAME
#define SHOW1(x) print(#x, "=", (x)), flush()
#define SHOW2(x, y) print(#x, "=", (x), #y, "=", (y)), flush()
#define SHOW3(x, y, z) print(#x, "=", (x), #y, "=", (y), #z, "=", (z)), flush()
#define SHOW4(x, y, z, w) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w)), flush()
#define SHOW5(x, y, z, w, v) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", (v)), flush()
#define SHOW6(x, y, z, w, v, u) print(#x, "=", (x), #y, "=", (y), #z, "=", (z), #w, "=", (w), #v, "=", (v), #u, "=", (u)), flush()
#else
#define SHOW(...)
#endif

#define INT(...)   \
  int __VA_ARGS__; \
  read(__VA_ARGS__)
#define LL(...)   \
  ll __VA_ARGS__; \
  read(__VA_ARGS__)
#define U32(...)   \
  u32 __VA_ARGS__; \
  read(__VA_ARGS__)
#define U64(...)   \
  u64 __VA_ARGS__; \
  read(__VA_ARGS__)
#define STR(...)      \
  string __VA_ARGS__; \
  read(__VA_ARGS__)
#define CHAR(...)   \
  char __VA_ARGS__; \
  read(__VA_ARGS__)
#define DBL(...)      \
  double __VA_ARGS__; \
  read(__VA_ARGS__)

#define VEC(type, name, size) \
  vector<type> name(size);    \
  read(name)
#define VV(type, name, h, w)                     \
  vector<vector<type>> name(h, vector<type>(w)); \
  read(name)

void YES(bool t = 1) { print(t ? "YES" : "NO"); }
void NO(bool t = 1) { YES(!t); }
void Yes(bool t = 1) { print(t ? "Yes" : "No"); }
void No(bool t = 1) { Yes(!t); }
void yes(bool t = 1) { print(t ? "yes" : "no"); }
void no(bool t = 1) { yes(!t); }
#line 1 "/home/maspy/compro/library/game/graph_game.hpp"

#line 2 "/home/maspy/compro/library/graph/base.hpp"

template <typename T>
struct Edge {
  int frm, to;
  T cost;
  int id;
};

template <typename T = int, bool directed = false>
struct Graph {
  static constexpr bool is_directed = directed;
  int N, M;
  using cost_type = T;
  using edge_type = Edge<T>;
  vector<edge_type> edges;
  vector<int> indptr;
  vector<edge_type> csr_edges;
  vc<int> vc_deg, vc_indeg, vc_outdeg;
  bool prepared;

  class OutgoingEdges {
  public:
    OutgoingEdges(const Graph* G, int l, int r) : G(G), l(l), r(r) {}

    const edge_type* begin() const {
      if (l == r) { return 0; }
      return &G->csr_edges[l];
    }

    const edge_type* end() const {
      if (l == r) { return 0; }
      return &G->csr_edges[r];
    }

  private:
    const Graph* G;
    int l, r;
  };

  bool is_prepared() { return prepared; }

  Graph() : N(0), M(0), prepared(0) {}
  Graph(int N) : N(N), M(0), prepared(0) {}

  void build(int n) {
    N = n, M = 0;
    prepared = 0;
    edges.clear();
    indptr.clear();
    csr_edges.clear();
    vc_deg.clear();
    vc_indeg.clear();
    vc_outdeg.clear();
  }

  void add(int frm, int to, T cost = 1, int i = -1) {
    assert(!prepared);
    assert(0 <= frm && 0 <= to && to < N);
    if (i == -1) i = M;
    auto e = edge_type({frm, to, cost, i});
    edges.eb(e);
    ++M;
  }

#ifdef FASTIO
  // wt, off
  void read_tree(bool wt = false, int off = 1) { read_graph(N - 1, wt, off); }

  void read_graph(int M, bool wt = false, int off = 1) {
    for (int m = 0; m < M; ++m) {
      INT(a, b);
      a -= off, b -= off;
      if (!wt) {
        add(a, b);
      } else {
        T c;
        read(c);
        add(a, b, c);
      }
    }
    build();
  }
#endif

  void build() {
    assert(!prepared);
    prepared = true;
    indptr.assign(N + 1, 0);
    for (auto&& e: edges) {
      indptr[e.frm + 1]++;
      if (!directed) indptr[e.to + 1]++;
    }
    for (int v = 0; v < N; ++v) { indptr[v + 1] += indptr[v]; }
    auto counter = indptr;
    csr_edges.resize(indptr.back() + 1);
    for (auto&& e: edges) {
      csr_edges[counter[e.frm]++] = e;
      if (!directed)
        csr_edges[counter[e.to]++] = edge_type({e.to, e.frm, e.cost, e.id});
    }
  }

  OutgoingEdges operator[](int v) const {
    assert(prepared);
    return {this, indptr[v], indptr[v + 1]};
  }

  vc<int> deg_array() {
    if (vc_deg.empty()) calc_deg();
    return vc_deg;
  }

  pair<vc<int>, vc<int>> deg_array_inout() {
    if (vc_indeg.empty()) calc_deg_inout();
    return {vc_indeg, vc_outdeg};
  }

  int deg(int v) {
    if (vc_deg.empty()) calc_deg();
    return vc_deg[v];
  }

  int in_deg(int v) {
    if (vc_indeg.empty()) calc_deg_inout();
    return vc_indeg[v];
  }

  int out_deg(int v) {
    if (vc_outdeg.empty()) calc_deg_inout();
    return vc_outdeg[v];
  }

#ifdef FASTIO
  void debug() {
    print("Graph");
    if (!prepared) {
      print("frm to cost id");
      for (auto&& e: edges) print(e.frm, e.to, e.cost, e.id);
    } else {
      print("indptr", indptr);
      print("frm to cost id");
      FOR(v, N) for (auto&& e: (*this)[v]) print(e.frm, e.to, e.cost, e.id);
    }
  }
#endif

  vc<int> new_idx;
  vc<bool> used_e;

  // G における頂点 V[i] が、新しいグラフで i になるようにする
  // {G, es}
  // sum(deg(v)) の計算量になっていて、
  // 新しいグラフの n+m より大きい可能性があるので注意
  Graph<T, directed> rearrange(vc<int> V, bool keep_eid = 0) {
    if (len(new_idx) != N) new_idx.assign(N, -1);
    int n = len(V);
    FOR(i, n) new_idx[V[i]] = i;
    Graph<T, directed> G(n);
    vc<int> history;
    FOR(i, n) {
      for (auto&& e: (*this)[V[i]]) {
        if (len(used_e) <= e.id) used_e.resize(e.id + 1);
        if (used_e[e.id]) continue;
        int a = e.frm, b = e.to;
        if (new_idx[a] != -1 && new_idx[b] != -1) {
          history.eb(e.id);
          used_e[e.id] = 1;
          int eid = (keep_eid ? e.id : -1);
          G.add(new_idx[a], new_idx[b], e.cost, eid);
        }
      }
    }
    FOR(i, n) new_idx[V[i]] = -1;
    for (auto&& eid: history) used_e[eid] = 0;
    G.build();
    return G;
  }

  Graph<T, true> to_directed_tree(int root = -1) {
    if (root == -1) root = 0;
    assert(!is_directed && prepared && M == N - 1);
    Graph<T, true> G1(N);
    vc<int> par(N, -1);
    auto dfs = [&](auto& dfs, int v) -> void {
      for (auto& e: (*this)[v]) {
        if (e.to == par[v]) continue;
        par[e.to] = v, dfs(dfs, e.to);
      }
    };
    dfs(dfs, root);
    for (auto& e: edges) {
      int a = e.frm, b = e.to;
      if (par[a] == b) swap(a, b);
      assert(par[b] == a);
      G1.add(a, b, e.cost);
    }
    G1.build();
    return G1;
  }

private:
  void calc_deg() {
    assert(vc_deg.empty());
    vc_deg.resize(N);
    for (auto&& e: edges) vc_deg[e.frm]++, vc_deg[e.to]++;
  }

  void calc_deg_inout() {
    assert(vc_indeg.empty());
    vc_indeg.resize(N);
    vc_outdeg.resize(N);
    for (auto&& e: edges) { vc_indeg[e.to]++, vc_outdeg[e.frm]++; }
  }
};
#line 2 "/home/maspy/compro/library/graph/reverse_graph.hpp"

template <typename GT>
GT reverse_graph(GT& G) {
  static_assert(GT::is_directed);
  GT G1(G.N);
  for (auto&& e: G.edges) { G1.add(e.to, e.frm, e.cost, e.id); }
  G1.build();
  return G1;
}
#line 3 "/home/maspy/compro/library/game/graph_game.hpp"

// 有向グラフ、動けない人が負け
// 各ノードに対して手番のプレイヤが決まっていて、交互
// 勝者は最短、敗者は最長手数を目指す
struct Graph_Game {
  vc<bool> win;
  vc<bool> lose;
  vc<int> end_turn;
  vc<int> best_strategy;

  template <typename GT>
  Graph_Game(GT& G) {
    auto RG = reverse_graph(G);
    auto [indeg, outdeg] = G.deg_array_inout();
    int N = G.N;
    win.assign(N, 0);
    lose.assign(N, 0);
    end_turn.assign(N, infty<int>);
    best_strategy.assign(N, -1);
    deque<int> que;
    FOR(v, N) {
      if (outdeg[v] == 0) que.eb(v);
    }

    while (!que.empty()) {
      auto v = POP(que);
      if (win[v] || lose[v]) continue;
      lose[v] = 1;
      for (auto&& e: G[v]) {
        if (lose[e.to]) win[v] = 1;
        if (!win[e.to]) lose[v] = 0;
      }
      assert(win[v] ^ lose[v]);
      if (win[v]) {
        for (auto&& e: G[v]) {
          if (chmin(end_turn[v], end_turn[e.to] + 1)) {
            best_strategy[v] = e.to;
          }
        }
      }
      if (lose[v]) {
        end_turn[v] = 0;
        for (auto&& e: G[v]) {
          if (chmax(end_turn[v], end_turn[e.to] + 1)) {
            best_strategy[v] = e.to;
          }
        }
      }
      for (auto&& e: RG[v]) {
        outdeg[e.to]--;
        if (lose[v] || outdeg[e.to] == 0) que.eb(e.to);
      }
    }
  }
};
#line 4 "main.cpp"

/*
pawn,queen,rook,bsp,knight

2*5*64*64*64
手番 / x / black king / white king / white x

移動ルール
飛び越えに注意
移動先が valid かどうかを判定

king+bsp,king+knightで勝つパターンはないはず（1*2を同時に抑える必要があるので）
よってpromotionは queen or rook としてよい

king+rookは必ず勝てるらしい
なのでpromotionした瞬間にstaleでもなく取り返されもしないならば勝ち

2*64*64*64
これでよい

座標は abc,123 とする
player==0:white
*/

/*
0 king
1 pawn
2 rook
3 queen
A,B,other
*/
bool ATK[4][64][64][64];

// すているメイト
bool SMATE[4][64][64][64];

void init_ATK() {
  FOR(a, 64) FOR(b, 64) FOR(c, 64) {
    auto [x1, y1] = divmod<int>(a, 8);
    auto [x2, y2] = divmod<int>(b, 8);
    auto [x3, y3] = divmod<int>(c, 8);
    ATK[0][a][b][c] = (abs(x1 - x2) <= 1 && abs(y1 - y2) <= 1);
    if (x1 == x2) {
      if (y2 == y1 + 1) { ATK[1][a][b][c] = 1; }
      if (y1 == 1 && y2 == y1 + 2) {
        if (!(x3 == x1 && y3 == 2)) ATK[1][a][b][c] = 1;
      }
    }
    // rook
    if (x1 == x2) {
      if (x1 != x3) {
        ATK[2][a][b][c] = 1;
      } else {
        ATK[2][a][b][c] = (y1 - y3) * (y2 - y3) > 0;
      }
    }
    if (y1 == y2) {
      if (y1 != y3) {
        ATK[2][a][b][c] = 1;
      } else {
        if ((x1 - x3) * (x2 - x3) > 0) ATK[2][a][b][c] = 1;
      }
    }
    // queen
    if (ATK[2][a][b][c]) ATK[3][a][b][c] = 1;
    int s1 = x1 - y1, s2 = x2 - y2, s3 = x3 - y3;
    int t1 = x1 + y1, t2 = x2 + y2, t3 = x3 + y3;
    FOR(2) {
      swap(s1, t1);
      swap(s2, t2);
      swap(s3, t3);
      if (s1 == s2) {
        if (s1 != s3) {
          ATK[3][a][b][c] = 1;
        } else {
          if ((t1 - t3) * (t2 - t3) > 0) ATK[3][a][b][c] = 1;
        }
      }
    }
  }
}

bool can_get(int player, int BK, int WK, int v, int k) {
  if (player == 1) {
    if (ATK[0][BK][WK][v]) return 1;
    if (ATK[0][BK][v][WK]) { return !ATK[0][WK][v][0]; }
    return 0;
  }
  return ATK[0][WK][BK][v] || ATK[k][v][BK][WK];
}

void init_SMATE() {
  FOR(a, 64) FOR(b, 64) FOR(c, 64) {
    FOR(k, 4) {
      SMATE[k][a][b][c] = 1;
      if (can_get(1, a, b, c, k)) SMATE[k][a][b][c] = 0;
      if (can_get(0, a, b, c, k)) SMATE[k][a][b][c] = 0;
      auto [x1, y1] = divmod<int>(a, 8);
      FOR(dx, -1, 2) {
        FOR(dy, -1, 2) {
          if (dx == 0 && dy == 0) continue;
          int x2 = x1 + dx, y2 = y1 + dy;
          if (!(0 <= x2 && x2 < 8)) continue;
          if (!(0 <= y2 && y2 < 8)) continue;
          int aa = x2 * 8 + y2;
          if (aa == b) continue;
          if (aa == c) continue;
          if (ATK[0][b][aa][c]) continue;
          if (ATK[k][c][aa][b]) continue;
          SMATE[k][a][b][c] = 0;
        }
      }
    }
  }
}

bool valid(int player, int BK, int WK, int v, int k) {
  assert(1 <= k && k <= 3);
  if (BK == WK) return 0;
  if (BK == v) return 0;
  if (WK == v) return 0;
  auto [x3, y3] = divmod<int>(v, 8);
  if (k == 1) {
    if (y3 == 0 || y3 == 7) return 0;
  }
  if (player == 1) {
    if (ATK[0][BK][WK][v]) return 0;
    return 1;
  }
  assert(k == 1);
  if (ATK[0][WK][BK][v]) return 0;
  if (ATK[k][v][BK][WK]) return 0;
  return 1;
}

const int N = 1 << 19;
const int WIN = N, DRAW = N + 1, LOSE = N + 2;

bool isin(int x, int y) { return (0 <= x && x < 8 && 0 <= y && y < 8); };
int idx2(int x, int y) { return 8 * x + y; };
int idx4(int p, int a, int b, int c) {
  int ans = 0;
  ans += p << 18;
  ans += a << 12;
  ans += b << 6;
  ans += c;
  assert(ans < (1 << 19));
  return ans;
}

vc<int> get_move(int player, int a, int b, int c) {
  if (player == 0) {
    vc<int> out;
    if (can_get(0, a, b, c, 1)) {
      out.eb(WIN);
      return out;
    } else {
      // king
      auto [x, y] = divmod<int>(b, 8);
      FOR(dx, -1, 2) FOR(dy, -1, 2) {
        if (dx == 0 && dy == 0) continue;
        int x1 = x + dx, y1 = y + dy;
        if (!isin(x1, y1)) continue;
        int b1 = 8 * x1 + y1;
        if (valid(1, a, b1, c, 1)) out.eb(idx4(1, a, b1, c));
      }
      // move pawn
      auto [px, py] = divmod<int>(c, 8);
      vc<int> cand;
      cand.eb(py + 1);
      if (py == 1) {
        if (b != c + 1 && a != c + 1) cand.eb(py + 2);
      }
      for (auto& ny: cand) {
        int c1 = idx2(px, ny);
        if (ny < 7) {
          if (valid(1, a, b, c1, 1)) out.eb(idx4(1, a, b, c1));
        }
        FOR(k, 2, 4) {
          // promotion
          if (ny == 7 && valid(1, a, b, c1, k)) {
            bool win = 1;
            // とりかえされない
            if (can_get(1, a, b, c1, k)) win = 0;
            // ステイルメイトではない
            if (SMATE[k][a][b][c1]) win = 0;
            if (win) return {WIN};
          }
        }
      }
    }
    UNIQUE(out);
    if (out.empty()) { return {DRAW}; }
    return out;
  }
  // player 1
  vc<int> out;
  if (can_get(1, a, b, c, 1)) {
    out.eb(DRAW);
    return out;
  }
  auto [x, y] = divmod<int>(a, 8);
  FOR(dx, -1, 2) FOR(dy, -1, 2) {
    if (dx == 0 && dy == 0) continue;
    int x1 = x + dx, y1 = y + dy;
    if (!isin(x1, y1)) continue;
    int a1 = 8 * x1 + y1;
    if (valid(0, a1, b, c, 1)) out.eb(idx4(0, a1, b, c));
  }
  if (out.empty()) out.eb(DRAW);
  return out;
}

tuple<int, int, int, int> TO_4(int x) {
  int c = x & 63;
  x /= 64;
  int b = x & 63;
  x /= 64;
  int a = x & 63;
  x /= 64;
  return {x, a, b, c};
}

void solve() {
  Graph<int, 1> G(N + 3);
  G.add(DRAW, DRAW);
  FOR(player, 2) {
    FOR(a, 64) FOR(b, 64) FOR(c, 64) {
      if (!valid(player, a, b, c, 1)) continue;
      vc<int> out = get_move(player, a, b, c);
      int v = idx4(player, a, b, c);
      for (auto& w: out) { G.add(v, w); }
    }
  }
  G.build();

  Graph_Game X(G);

  auto get = [&]() -> int {
    STR(S);
    int x = (S[0] - 'a');
    int y = (S[1] - '1');
    return idx2(x, y);
  };

  INT(T);
  FOR(T) {
    int b = get(), c = get(), a = get();
    STR(S);
    int p = (S == "w" ? 0 : 1);
    int v = idx4(p, a, b, c);
    // for (auto& w: get_move(p, a, b, c)) { print(w, X.win[w], X.lose[w], TO_4(w)); }

    bool draw = 1;
    if (X.win[v]) {
      assert(p == 0);
      draw = 0;
    }
    if (X.lose[v]) {
      assert(p == 1);
      draw = 0;
    }
    print(draw ? "Draw" : "Win");
  }
}

signed main() {
  init_ATK();
  init_SMATE();
  solve();
}