#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_mod_2(int x) { return __builtin_parity(x); }
int popcnt_mod_2(u32 x) { return __builtin_parity(x); }
int popcnt_mod_2(ll x) { return __builtin_parityll(x); }
int popcnt_mod_2(u64 x) { return __builtin_parityll(x); }
// (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 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 3 "main.cpp"

#line 2 "/home/maspy/compro/library/flow/mincostflow.hpp"

// atcoder library のものを改変
namespace internal {
template <class E>
struct csr {
  vector<int> start;
  vector<E> elist;
  explicit csr(int n, const vector<pair<int, E>>& edges) : start(n + 1), elist(edges.size()) {
    for (auto e: edges) { start[e.first + 1]++; }
    for (int i = 1; i <= n; i++) { start[i] += start[i - 1]; }
    auto counter = start;
    for (auto e: edges) { elist[counter[e.first]++] = e.second; }
  }
};

template <class T>
struct simple_queue {
  vector<T> payload;
  int pos = 0;
  void reserve(int n) { payload.reserve(n); }
  int size() const { return int(payload.size()) - pos; }
  bool empty() const { return pos == int(payload.size()); }
  void push(const T& t) { payload.push_back(t); }
  T& front() { return payload[pos]; }
  void clear() {
    payload.clear();
    pos = 0;
  }
  void pop() { pos++; }
};

} // namespace internal

/*
・atcoder library をすこし改変したもの
・DAG = true であれば、負辺 OK （1 回目の最短路を dp で行う）
ただし、頂点番号は toposort されていることを仮定している。
*/
template <class Cap = int, class Cost = ll, bool DAG = false>
struct Min_Cost_Flow {
public:
  Min_Cost_Flow() {}
  explicit Min_Cost_Flow(int n, int source, int sink) : n(n), source(source), sink(sink) {
    assert(0 <= source && source < n);
    assert(0 <= sink && sink < n);
    assert(source != sink);
  }

  // frm, to, cap, cost
  int add(int frm, int to, Cap cap, Cost cost) {
    assert(0 <= frm && frm < n);
    assert(0 <= to && to < n);
    assert(0 <= cap);
    assert(DAG || 0 <= cost);
    if (DAG) assert(frm < to);
    int m = int(_edges.size());
    _edges.push_back({frm, to, cap, 0, cost});
    return m;
  }

  void debug() {
    print("flow graph");
    print("frm, to, cap, cost");
    for (auto&& [frm, to, cap, flow, cost]: _edges) { print(frm, to, cap, cost); }
  }

  struct edge {
    int frm, to;
    Cap cap, flow;
    Cost cost;
  };

  edge get_edge(int i) {
    int m = int(_edges.size());
    assert(0 <= i && i < m);
    return _edges[i];
  }
  vector<edge> edges() { return _edges; }

  // (流量, 費用)
  pair<Cap, Cost> flow() { return flow(infty<Cap>); }
  // (流量, 費用)
  pair<Cap, Cost> flow(Cap flow_limit) { return slope(flow_limit).back(); }
  vector<pair<Cap, Cost>> slope() { return slope(infty<Cap>); }
  vector<pair<Cap, Cost>> slope(Cap flow_limit) {
    int m = int(_edges.size());
    vector<int> edge_idx(m);

    auto g = [&]() {
      vector<int> degree(n), redge_idx(m);
      vector<pair<int, _edge>> elist;
      elist.reserve(2 * m);
      for (int i = 0; i < m; i++) {
        auto e = _edges[i];
        edge_idx[i] = degree[e.frm]++;
        redge_idx[i] = degree[e.to]++;
        elist.push_back({e.frm, {e.to, -1, e.cap - e.flow, e.cost}});
        elist.push_back({e.to, {e.frm, -1, e.flow, -e.cost}});
      }
      auto _g = internal::csr<_edge>(n, elist);
      for (int i = 0; i < m; i++) {
        auto e = _edges[i];
        edge_idx[i] += _g.start[e.frm];
        redge_idx[i] += _g.start[e.to];
        _g.elist[edge_idx[i]].rev = redge_idx[i];
        _g.elist[redge_idx[i]].rev = edge_idx[i];
      }
      return _g;
    }();

    auto result = slope(g, flow_limit);

    for (int i = 0; i < m; i++) {
      auto e = g.elist[edge_idx[i]];
      _edges[i].flow = _edges[i].cap - e.cap;
    }

    return result;
  }

  // O(F(N+M)) くらい使って経路復元
  vvc<int> path_decomposition() {
    vvc<int> TO(n);
    for (auto&& e: edges()) { FOR(e.flow) TO[e.frm].eb(e.to); }
    vvc<int> res;
    vc<int> vis(n);

    while (!TO[source].empty()) {
      vc<int> path = {source};
      vis[source] = 1;
      while (path.back() != sink) {
        int to = POP(TO[path.back()]);
        while (vis[to]) { vis[POP(path)] = 0; }
        path.eb(to), vis[to] = 1;
      }
      for (auto&& v: path) vis[v] = 0;
      res.eb(path);
    }
    return res;
  }

  vc<Cost> get_potentials() { return potential; }

private:
  int n, source, sink;
  vector<edge> _edges;

  // inside edge
  struct _edge {
    int to, rev;
    Cap cap;
    Cost cost;
  };

  vc<Cost> potential;

  vector<pair<Cap, Cost>> slope(internal::csr<_edge>& g, Cap flow_limit) {
    if (DAG) assert(source == 0 && sink == n - 1);
    vector<pair<Cost, Cost>> dual_dist(n);
    vector<int> prev_e(n);
    vector<bool> vis(n);
    struct Q {
      Cost key;
      int to;
      bool operator<(Q r) const { return key > r.key; }
    };
    vector<int> que_min;
    vector<Q> que;
    auto dual_ref = [&]() {
      for (int i = 0; i < n; i++) { dual_dist[i].second = infty<Cost>; }
      fill(vis.begin(), vis.end(), false);
      que_min.clear();
      que.clear();

      // que[0..heap_r) was heapified
      size_t heap_r = 0;

      dual_dist[source].second = 0;
      que_min.push_back(source);
      while (!que_min.empty() || !que.empty()) {
        int v;
        if (!que_min.empty()) {
          v = que_min.back();
          que_min.pop_back();
        } else {
          while (heap_r < que.size()) {
            heap_r++;
            push_heap(que.begin(), que.begin() + heap_r);
          }
          v = que.front().to;
          pop_heap(que.begin(), que.end());
          que.pop_back();
          heap_r--;
        }
        if (vis[v]) continue;
        vis[v] = true;
        if (v == sink) break;
        Cost dual_v = dual_dist[v].first, dist_v = dual_dist[v].second;
        for (int i = g.start[v]; i < g.start[v + 1]; i++) {
          auto e = g.elist[i];
          if (!e.cap) continue;
          Cost cost = e.cost - dual_dist[e.to].first + dual_v;
          if (dual_dist[e.to].second > dist_v + cost) {
            Cost dist_to = dist_v + cost;
            dual_dist[e.to].second = dist_to;
            prev_e[e.to] = e.rev;
            if (dist_to == dist_v) {
              que_min.push_back(e.to);
            } else {
              que.push_back(Q{dist_to, e.to});
            }
          }
        }
      }
      if (!vis[sink]) { return false; }

      for (int v = 0; v < n; v++) {
        if (!vis[v]) continue;
        dual_dist[v].first -= dual_dist[sink].second - dual_dist[v].second;
      }
      return true;
    };

    auto dual_ref_dag = [&]() {
      FOR(i, n) dual_dist[i].se = infty<Cost>;
      dual_dist[source].se = 0;
      fill(vis.begin(), vis.end(), false);
      vis[0] = true;

      FOR(v, n) {
        if (!vis[v]) continue;
        Cost dual_v = dual_dist[v].fi, dist_v = dual_dist[v].se;
        for (int i = g.start[v]; i < g.start[v + 1]; i++) {
          auto e = g.elist[i];
          if (!e.cap) continue;
          Cost cost = e.cost - dual_dist[e.to].fi + dual_v;
          if (dual_dist[e.to].se > dist_v + cost) {
            vis[e.to] = true;
            Cost dist_to = dist_v + cost;
            dual_dist[e.to].second = dist_to;
            prev_e[e.to] = e.rev;
          }
        }
      }
      if (!vis[sink]) { return false; }

      for (int v = 0; v < n; v++) {
        if (!vis[v]) continue;
        dual_dist[v].fi -= dual_dist[sink].se - dual_dist[v].se;
      }
      return true;
    };

    Cap flow = 0;
    Cost cost = 0, prev_cost_per_flow = -1;
    vector<pair<Cap, Cost>> result = {{Cap(0), Cost(0)}};
    while (flow < flow_limit) {
      if (DAG && flow == 0) {
        if (!dual_ref_dag()) break;
      } else {
        if (!dual_ref()) break;
      }
      Cap c = flow_limit - flow;
      for (int v = sink; v != source; v = g.elist[prev_e[v]].to) { c = min(c, g.elist[g.elist[prev_e[v]].rev].cap); }
      for (int v = sink; v != source; v = g.elist[prev_e[v]].to) {
        auto& e = g.elist[prev_e[v]];
        e.cap += c;
        g.elist[e.rev].cap -= c;
      }
      Cost d = -dual_dist[source].first;
      flow += c;
      cost += c * d;
      if (prev_cost_per_flow == d) { result.pop_back(); }
      result.push_back({flow, cost});
      prev_cost_per_flow = d;
    }
    dual_ref();
    potential.resize(n);
    FOR(v, n) potential[v] = dual_dist[v].fi;
    return result;
  }
};
#line 2 "/home/maspy/compro/library/flow/bflow.hpp"
template <class Flow = ll, class Cost = ll>
struct MinCostFlow {
private:
  static constexpr int SCALING_FACTOR = 2;
  using V_id = uint32_t;
  using E_id = uint32_t;

  struct Edge {
    friend struct MinCostFlow;

  private:
    V_id frm, to;
    Flow flow, cap;
    Cost cost;
    E_id rev;

  public:
    Edge() = default;

    Edge(const V_id frm, const V_id to, const Flow cap, const Cost cost,
         const E_id rev)
        : frm(frm), to(to), flow(0), cap(cap), cost(cost), rev(rev) {}

    [[nodiscard]] Flow residual_cap() const { return cap - flow; }
  };

public:
  struct EdgePtr {
    friend struct MinCostFlow;

  private:
    const MinCostFlow *instance;
    const V_id v;
    const E_id e;

    EdgePtr(const MinCostFlow *instance, const V_id v, const E_id e)
        : instance(instance), v(v), e(e) {}

    [[nodiscard]] const Edge &edge() const { return instance->g[v][e]; }
    [[nodiscard]] const Edge &rev() const {
      const Edge &e = edge();
      return instance->g[e.to][e.rev];
    }

  public:
    [[nodiscard]] V_id frm() const { return rev().to; }
    [[nodiscard]] V_id to() const { return edge().to; }
    [[nodiscard]] Flow flow() const { return edge().flow; }
    [[nodiscard]] Flow lower() const { return -rev().cap; }
    [[nodiscard]] Flow upper() const { return edge().cap; }
    [[nodiscard]] Cost cost() const { return edge().cost; }
    [[nodiscard]] Cost gain() const { return -edge().cost; }
  };

private:
  V_id n;
  std::vector<std::vector<Edge>> g;
  std::vector<Flow> b;

public:
  MinCostFlow(int n) : n(n) {
    g.resize(n);
    b.resize(n);
  }

  V_id add_vertex() {
    ++n;
    g.resize(n);
    b.resize(n);
    return n - 1;
  }

  std::vector<V_id> add_vertices(const size_t size) {
    std::vector<V_id> ret;
    for (V_id i = 0; i < size; ++i) ret.emplace_back(n + i);
    n += size;
    g.resize(n);
    b.resize(n);
    return ret;
  }

  void add(const V_id frm, const V_id to, const Flow lo, const Flow hi,
           const Cost cost) {
    const E_id e = g[frm].size(), re = frm == to ? e + 1 : g[to].size();
    assert(lo <= hi);
    g[frm].emplace_back(Edge{frm, to, hi, cost, re});
    g[to].emplace_back(Edge{to, frm, -lo, -cost, e});
    edges.eb(EdgePtr{this, frm, e});
  }

  void add_source(const V_id v, const Flow amount) { b[v] += amount; }
  void add_sink(const V_id v, const Flow amount) { b[v] -= amount; }

private:
  static Cost constexpr unreachable = std::numeric_limits<Cost>::max();
  Cost farthest;
  vc<Cost> potential, dist;
  vc<Edge *> parent;
  pqg<pair<Cost, int>> pq;
  vc<V_id> excess_vs, deficit_vs;
  vc<EdgePtr> edges;
  Edge &rev(const Edge &e) { return g[e.to][e.rev]; }

  void push(Edge &e, const Flow amount) {
    e.flow += amount;
    g[e.to][e.rev].flow -= amount;
  }

  Cost residual_cost(const V_id frm, const V_id to, const Edge &e) {
    return e.cost + potential[frm] - potential[to];
  }

  bool dual(const Flow delta) {
    dist.assign(n, unreachable);
    parent.assign(n, nullptr);
    excess_vs.erase(
        remove_if(all(excess_vs), [&](const V_id v) { return b[v] < delta; }),
        end(excess_vs));
    deficit_vs.erase(
        remove_if(all(deficit_vs), [&](const V_id v) { return b[v] > -delta; }),
        end(deficit_vs));
    for (const auto v: excess_vs) pq.emplace(dist[v] = 0, v);
    farthest = 0;
    size_t deficit_count = 0;
    while (!pq.empty()) {
      const auto [d, u] = pq.top();
      pq.pop();
      if (dist[u] < d) continue;
      farthest = d;
      if (b[u] <= -delta) ++deficit_count;
      if (deficit_count >= deficit_vs.size()) break;
      for (auto &e: g[u]) {
        if (e.residual_cap() < delta) continue;
        const auto v = e.to;
        const auto new_dist = d + residual_cost(u, v, e);
        if (new_dist >= dist[v]) continue;
        pq.emplace(dist[v] = new_dist, v);
        parent[v] = &e;
      }
    }
    pq = decltype(pq)();
    for (V_id v = 0; v < n; ++v) {
      potential[v] += std::min(dist[v], farthest);
    }
    return deficit_count > 0;
  }

  void primal(const Flow delta) {
    for (const auto t: deficit_vs) {
      if (dist[t] > farthest) continue;
      Flow f = -b[t];
      V_id v;
      for (v = t; parent[v] != nullptr && f >= delta; v = parent[v]->frm) {
        f = std::min(f, parent[v]->residual_cap());
      }
      f = std::min(f, b[v]);
      if (f < delta) continue;
      for (v = t; parent[v] != nullptr;) {
        auto &e = *parent[v];
        push(e, f);
        const size_t u = parent[v]->frm;
        parent[v] = nullptr;
        v = u;
      }
      b[t] += f;
      b[v] -= f;
    }
  }

  void saturate_negative(const Flow delta) {
    excess_vs.clear();
    deficit_vs.clear();
    for (auto &es: g)
      for (auto &e: es) {
        const Flow rcap = e.residual_cap();
        const Cost rcost = residual_cost(e.frm, e.to, e);
        if (rcost < 0 && rcap >= delta) {
          push(e, rcap);
          b[e.frm] -= rcap;
          b[e.to] += rcap;
        }
      }
    for (V_id v = 0; v < n; ++v)
      if (b[v] != 0) { (b[v] > 0 ? excess_vs : deficit_vs).emplace_back(v); }
  }

public:
  std::pair<bool, i128> solve() {
    potential.resize(n);
    for (auto &es: g)
      for (auto &e: es) {
        const Flow rcap = e.residual_cap();
        if (rcap < 0) {
          push(e, rcap);
          b[e.frm] -= rcap;
          b[e.to] += rcap;
        }
      }
    Flow inf_flow = 1;
    for (const auto &es: g)
      for (const auto &e: es) inf_flow = std::max(inf_flow, e.residual_cap());
    Flow delta = 1;
    while (delta <= inf_flow) delta *= SCALING_FACTOR;

    for (delta /= SCALING_FACTOR; delta; delta /= SCALING_FACTOR) {
      saturate_negative(delta);
      while (dual(delta)) primal(delta);
    }

    i128 value = 0;
    for (const auto &es: g)
      for (const auto &e: es) { value += i128(e.flow) * e.cost; }
    value /= 2;

    if (excess_vs.empty() && deficit_vs.empty()) {
      return {true, value};
    } else {
      return {false, value};
    }
  }

  template <class T>
  T get_result_value() {
    T value = 0;
    for (const auto &es: g)
      for (const auto &e: es) { value += (T)(e.flow) * (T)(e.cost); }
    value /= (T)2;
    return value;
  }

  std::vector<Cost> get_potential() {
    std::fill(potential.begin(), potential.end(), 0);
    for (int i = 0; i < (int)n; i++)
      for (const auto &es: g)
        for (const auto &e: es)
          if (e.residual_cap() > 0)
            potential[e.to]
                = std::min(potential[e.to], potential[e.frm] + e.cost);
    return potential;
  }

  std::vector<EdgePtr> get_edges() { return edges; }
};
#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 3 "/home/maspy/compro/library/graph/shortest_path/dijkstra.hpp"

template <typename T, typename GT>
pair<vc<T>, vc<int>> dijkstra_dense(GT& G, int s) {
  const int N = G.N;
  vc<T> dist(N, infty<T>);
  vc<int> par(N, -1);
  vc<bool> done(N);
  dist[s] = 0;
  while (1) {
    int v = -1;
    T mi = infty<T>;
    FOR(i, N) {
      if (!done[i] && chmin(mi, dist[i])) v = i;
    }
    if (v == -1) break;
    done[v] = 1;
    for (auto&& e: G[v]) {
      if (chmin(dist[e.to], dist[v] + e.cost)) par[e.to] = v;
    }
  }
  return {dist, par};
}

template <typename T, typename GT, bool DENSE = false>
pair<vc<T>, vc<int>> dijkstra(GT& G, int v) {
  if (DENSE) return dijkstra_dense<T>(G, v);
  auto N = G.N;
  vector<T> dist(N, infty<T>);
  vector<int> par(N, -1);
  using P = pair<T, int>;

  priority_queue<P, vector<P>, greater<P>> que;

  dist[v] = 0;
  que.emplace(0, v);
  while (!que.empty()) {
    auto [dv, v] = que.top();
    que.pop();
    if (dv > dist[v]) continue;
    for (auto&& e: G[v]) {
      if (chmin(dist[e.to], dist[e.frm] + e.cost)) {
        par[e.to] = e.frm;
        que.emplace(dist[e.to], e.to);
      }
    }
  }
  return {dist, par};
}

// 多点スタート。[dist, par, root]
template <typename T, typename GT>
tuple<vc<T>, vc<int>, vc<int>> dijkstra(GT& G, vc<int> vs) {
  assert(G.is_prepared());
  int N = G.N;
  vc<T> dist(N, infty<T>);
  vc<int> par(N, -1);
  vc<int> root(N, -1);

  using P = pair<T, int>;

  priority_queue<P, vector<P>, greater<P>> que;

  for (auto&& v: vs) {
    dist[v] = 0;
    root[v] = v;
    que.emplace(T(0), v);
  }

  while (!que.empty()) {
    auto [dv, v] = que.top();
    que.pop();
    if (dv > dist[v]) continue;
    for (auto&& e: G[v]) {
      if (chmin(dist[e.to], dist[e.frm] + e.cost)) {
        root[e.to] = root[e.frm];
        par[e.to] = e.frm;
        que.push(mp(dist[e.to], e.to));
      }
    }
  }
  return {dist, par, root};
}
#line 7 "main.cpp"

/*
potential p[v]
距離を L 以上にしたい : L<=p[t]-p[s]
辺 (u,v,w)
伸ばす量 max(0,p[v]-p[u]-w)
- t から s に費用-L, 容量INF
- u から v に費用 w, 容量 1
これの循環流
*/

template <typename T = ll, bool DAG = false>
struct Longest_Shortest_Path {
  int N, s, t;
  T F, L, K;
  bool solved;
  vc<tuple<int, int, T, T>> dat;
  vc<T> pot;
  Longest_Shortest_Path(int N, int s, int t) : N(N), s(s), t(t), F(0), solved(0) {}

  // 現在の長さ, 長さを+1するコスト
  void add(int frm, int to, T length, T cost) {
    assert(0 <= frm && frm < N && 0 <= to && to < N && !solved);
    if (DAG) assert(frm < to);
    dat.eb(frm, to, length, cost);
  }

  T init_dist() {
    Graph<T, 1> G(N);
    for (auto& [a, b, c, d]: dat) G.add(a, b, c);
    G.build();
    auto [dist, par] = dijkstra<T>(G, s);
    return dist[t];
  }

  // 距離が L 以上になるようにせよ. return: min cost.
  T solve_by_target_length(T target_length) {
    L = target_length;
    assert(!solved && L >= init_dist());
    solved = 1;
    Min_Cost_Flow<T, T, DAG> G(N, s, t);
    for (auto& [a, b, length, cost]: dat) { G.add(a, b, cost, length); }
    T ans = -infty<T>;
    for (auto& [x, y]: G.slope()) {
      if (chmax(ans, x * L - y)) F = x;
    }
    return K = ans;
  }

  // コストが K で最大距離にせよ. return: max dist.
  T solve_by_cost(T K) {}

  // frm, to, cost. add_edge 順.
  vc<T> get_potentials() {
    assert(solved);
    if (len(pot)) return pot;
    Min_Cost_Flow<T, T, DAG> G(N, s, t);
    for (auto& [a, b, length, cost]: dat) { G.add(a, b, cost, length); }
    G.flow(F);
    pot = G.get_potentials();
    Graph<T, 1> resG(N);
    auto add = [&](int a, int b, T x) -> void {
      x = x + pot[a] - pot[b];
      resG.add(a, b, x);
    };
    for (auto& e: G.edges()) {
      if (e.cap > e.flow) add(e.frm, e.to, e.cost);
      if (e.flow > 0) add(e.to, e.frm, -e.cost);
    }
    add(s, t, L), add(t, s, -L);
    resG.build();
    vc<T> dist = dijkstra<ll>(resG, s).fi;
    FOR(x, N) pot[x] += dist[x];
    return pot;
  }

  // 変更後の長さ
  vc<T> get_edges() {
    get_potentials();
    vc<T> res;
    for (auto [frm, to, length, cost]: dat) { res.eb(max<T>(length, pot[to] - pot[frm])); }
    return res;
  }
};

void solve() {
  LL(H, W, K);
  ll N = H * W;
  ll s = N, t = N + 1;
  auto idx = [&](int x, int y) -> int {
    if (y == 0) return s;
    if (y == W - 1) return t;
    return W * x + y;
  };

  Longest_Shortest_Path<ll, false> X(N + 2, s, t);

  auto isin = [&](int x, int y) -> bool { return (0 <= x && x < H && 0 <= y && y < W); };
  int dx[] = {1, 0, -1, 0, 1, 1, -1, -1};
  int dy[] = {0, 1, 0, -1, 1, -1, 1, -1};

  VV(ll, A, H, W - 1);
  VV(ll, B, H - 1, W);

  vc<tuple<int, int, int>> pos;

  FOR(x, H) {
    FOR(y, W) {
      FOR(d, 2) {
        int x1 = x + dx[d], y1 = y + dy[d];
        if (!isin(x, y)) continue;
        if (!isin(x1, y1)) continue;
        ll c = (d == 0 ? B[x][y] : A[x][y]);
        X.add(idx(x, y), idx(x1, y1), c, 1);
        X.add(idx(x1, y1), idx(x, y), c, 1);
        pos.eb(d, x, y);
        pos.eb(d, x, y);
      }
    }
  }
  ll init = X.init_dist();

  ll cost = X.solve_by_target_length(init + K);
  vi L = X.get_edges();
  FOR(n, len(pos)) {
    auto [t, x, y] = pos[n];
    if (t == 0) chmax(B[x][y], L[n]);
    if (t == 1) chmax(A[x][y], L[n]);
  }

  print(cost);
  FOR(x, len(A)) print(A[x]);
  FOR(x, len(B)) print(B[x]);
}

signed main() {
  INT(T);
  FOR(T) solve();
}