Problem:
Score : 100 points

Problem Statement

You are given a grid of N rows and M columns. The square at the i-th row and j-th column will be denoted as (i,j).
A nonnegative integer A_{i,j} is written for each square (i,j).

You choose some of the squares so that each row and column contains at most K chosen squares.
Under this constraint, calculate the maximum value of the sum of the integers written on the chosen squares.
Additionally, calculate a way to choose squares that acheives the maximum.

Constraints

1 \leq N \leq 50

1 \leq K \leq N

0 \leq A_{i,j} \leq 10^9

All values in Input are integer.

Input

Input is given from Standard Input in the following format:

N K
A_{1,1} A_{1,2} \cdots A_{1,N}
A_{2,1} A_{2,2} \cdots A_{2,N}
\vdots
A_{N,1} A_{N,2} \cdots A_{N,N}

Output

On the first line, print the maximum value of the sum of the integers written on the chosen squares.

On the next N lines, print a way that achieves the maximum.

Precisely, output the strings t_1,t_2,\cdots,t_N, that satisfies t_{i,j}=X if you choose (i,j) and t_{i,j}=. otherwise.

You may print any way to choose squares that maximizes the sum.

Sample Input 1

3 1
5 3 2
1 4 8
7 6 9

Sample Output 1

19
X..
..X
.X.

Sample Input 2

3 2
10 10 1
10 10 1
1 1 10

Sample Output 2

50
XX.
XX.
..X

Solution in C++ (GCC 9.2.1 with AC Library v1.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#include <atcoder/all>
using namespace std;
using namespace atcoder;

//////////////////////////////   Begin Macros

#define all(x) (x).begin(), (x).end()
#define rall(x) (x).rbegin(), (x).rend()
#define in(x, a, b) (a <= x and x < b)
#define rep(i, N) for (int i = 0; i < (int)(N); i++)
#define reprev(i, N) for (int i = (int)(N)-1; i >= 0; i--)
#define rep1(i, N) for (int i = 1; i <= (int)(N); i++)
#define rep1rev(i, N) for (int i = (int)(N); i >= 0; i--)
#define forbe(i, b, e) for (int i = (b); i < (e); i++)
#define forberev(i, b, e) for (int i = (e)-1; i >= (b); i--)
#define forfl(i, f, l) for (int i = (f); i <= (l); i++)
#define forflrev(i, f, l) for (int i = (l); i >= (f); i--)
using ll = long long;
using pii = pair<int, int>;
using pil = pair<int, ll>;
using pli = pair<ll, int>;
using pll = pair<ll, ll>;

template <typename T>
bool chmax(T &m, const T q)
{
  if (m < q)
  {
    m = q;
    return true;
  }
  else
    return false;
}
template <typename T>
bool chmin(T &m, const T q)
{
  if (m > q)
  {
    m = q;
    return true;
  }
  else
    return false;
}
template <typename T1, typename T2>
pair<T1, T2> operator+(const pair<T1, T2> &l, const pair<T1, T2> &r) { return {l.first + r.first, l.second + r.second}; }
template <typename T1, typename T2>
pair<T1, T2> operator-(const pair<T1, T2> &l, const pair<T1, T2> &r) { return {l.first - r.first, l.second - r.second}; }
template <typename T>
pair<T, T> operator*(const pair<T, T> &l, const T &r) { return {l.first * r, l.second * r}; }
template <typename T>
pair<T, T> operator/(const pair<T, T> &l, const T &r) { return {l.first / r, l.second / r}; }
template <typename T>
istream &operator>>(istream &is, vector<T> &vec)
{
  for (auto &v : vec)
    is >> v;
  return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &vec)
{
  os << "[";
  for (auto v : vec)
    os << v << ",";
  os << "]";
  return os;
}
template <typename T>
ostream &operator<<(ostream &os, const deque<T> &vec)
{
  os << "deq[";
  for (auto v : vec)
    os << v << ",";
  os << "]";
  return os;
}
template <typename T>
ostream &operator<<(ostream &os, const set<T> &vec)
{
  os << "{";
  for (auto v : vec)
    os << v << ",";
  os << "}";
  return os;
}
template <typename T>
ostream &operator<<(ostream &os, const unordered_set<T> &vec)
{
  os << "{";
  for (auto v : vec)
    os << v << ",";
  os << "}";
  return os;
}
template <typename T>
ostream &operator<<(ostream &os, const multiset<T> &vec)
{
  os << "{";
  for (auto v : vec)
    os << v << ",";
  os << "}";
  return os;
}
template <typename T>
ostream &operator<<(ostream &os, const unordered_multiset<T> &vec)
{
  os << "{";
  for (auto v : vec)
    os << v << ",";
  os << "}";
  return os;
}
template <typename T1, typename T2>
istream &operator>>(istream &is, pair<T1, T2> &pa)
{
  is >> pa.first >> pa.second;
  return is;
}
template <typename T1, typename T2>
ostream &operator<<(ostream &os, const pair<T1, T2> &pa)
{
  os << "(" << pa.first << "," << pa.second << ")";
  return os;
}
template <typename... Ts>
istream &operator>>(istream &is, tuple<Ts...> &theTuple)
{
  apply([&is](Ts &... tupleArgs) { ((is >> tupleArgs), ...); }, theTuple);
  return is;
}
template <typename... Ts>
ostream &operator<<(ostream &os, const tuple<Ts...> &theTuple)
{
  apply([&os](const Ts &... tupleArgs) {
    os << '(';
    size_t n(0);
    ((os << tupleArgs << (++n < sizeof...(Ts) ? "," : "")), ...);
    os << ')';
  },
        theTuple);
  return os;
}
template <typename TK, typename TV>
ostream &operator<<(ostream &os, const map<TK, TV> &mp)
{
  os << "{";
  for (auto v : mp)
    os << v.first << "=>" << v.second << ",";
  os << "}";
  return os;
}
template <typename TK, typename TV>
ostream &operator<<(ostream &os, const unordered_map<TK, TV> &mp)
{
  os << "{";
  for (auto v : mp)
    os << v.first << "=>" << v.second << ",";
  os << "}";
  return os;
}

template <typename T>
void reset(vector<T> &v, const T reset_to)
{
  for (auto &x : v)
    x = reset_to;
}
inline int popcount(const unsigned int x) { return __builtin_popcount(x); }
#define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl;

ll nC2(ll n)
{
  return n * (n - 1) / 2;
}

const int intinf = numeric_limits<int>::max();
const ll llinf = numeric_limits<ll>::max();
const pii udlr[4] = {{1, 0}, {0, 1}, {-1, 0}, {0, -1}};

//////////////////////////////   End Macros

void solve()
{
  const ll BIG = 1e9;
  int N, K;
  cin >> N >> K;
  mcf_graph<int, ll> g(2 * N + 2);
  int s = 2 * N, t = s + 1;
  g.add_edge(s, t, N * K, BIG);
  rep(i, N) g.add_edge(s, i, K, 0);
  rep(j, N) g.add_edge(N + j, t, K, 0);

  rep(i, N) rep(j, N)
  {
    int a;
    cin >> a;
    g.add_edge(i, N + j, 1, BIG - a);
  }

  ll min_cost = g.flow(s, t, N * K).second;
  cout << (1LL * N * K * BIG - min_cost) << endl;

  vector<string> grid(N, string(N, '.'));
  auto edges = g.edges();
  for (auto e : edges)
  {
    if (e.from == s or e.to == t or e.flow == 0)
      continue;

    int i = e.from, j = e.to - N;
    grid[i][j] = 'X';
  }
  rep(i, N) cout << grid[i] << endl;
}

int main()
{
  cerr << "start" << endl;
  // srand(time(0));
  cout << fixed << setprecision(15);

  solve();
  return 0;
}