Problem: 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.

Examples

Input

3 1
5 3 2
1 4 8
7 6 9


Output

19
X..
..X
.X.


Input

3 2
10 10 1
10 10 1
1 1 10


Output

50
XX.
XX.
..X

Solution (in PYTHON3):

Solution:
from heapq import heappop, heappush

# use 64 bit signed integer max
NUMERIC_LIMITS = (1 << 63) - 1


class McfGraph:
  def __init__(self, n):
    self._n = n
    self.g = [[] for _ in range(n)]
    self.pos = []

  def add_edge(self, frm, to, cap, cost):
    m = len(self.pos)
    self.pos.append([frm, len(self.g[frm])])
    self.g[frm].append(self._edge(to, len(self.g[to]), cap, cost))
    self.g[to].append(self._edge(frm, len(self.g[frm]) - 1, 0, -cost))
    return m

  class edge:
    __slots__ = "frm", "to", "cap", "flow", "cost"

    def __init__(self, frm, to, cap, flow, cost):
      self.frm, self.to = frm, to
      self.cap, self.flow, self.cost = cap, flow, cost

  def get_edge(self, i):
    _e = self.g[self.pos[i][0]][self.pos[i][1]]
    _re = self.g[_e.to][_e.rev]
    return self.edge(self.pos[i][0], _e.to, _e.cap + _re.cap, _re.cap, _e.cost)

  def edges(self):
    for i in range(len(self.pos)):
      yield self.get_edge(i)

  def flow(self, s, t, flow_limit=NUMERIC_LIMITS):
    return self.slope(s, t, flow_limit)[-1]

  def dual_ref(self, s, t):
    dist = [NUMERIC_LIMITS] * self._n
    self.pv = [-1] * self._n
    self.pe = [-1] * self._n
    vis = [False] * self._n
    que = []
    dist[s] = 0
    heappush(que, (0, s))
    while que:
      _, v = heappop(que)
      if vis[v]:
        continue
      vis[v] = True
      if v == t:
        break
      for i in range(len(self.g[v])):
        e = self.g[v][i]
        if vis[e.to] or not e.cap:
          continue
        cost = e.cost - self.dual[e.to] + self.dual[v]
        if dist[e.to] - dist[v] > cost:
          dist[e.to] = dist[v] + cost
          self.pv[e.to] = v
          self.pe[e.to] = i
          heappush(que, (dist[e.to], e.to))
    if not vis[t]:
      return False
    for v in range(self._n):
      if not vis[v]:
        continue
      self.dual[v] -= dist[t] - dist[v]
    return True

  def slope(self, s, t, flow_limit=NUMERIC_LIMITS):
    self.dual = [0] * self._n

    flow = 0
    cost, prev_cost = 0, -1
    result = [(flow, cost)]
    while flow < flow_limit:
      if not self.dual_ref(s, t):
        break
      c = flow_limit - flow
      v = t
      while v != s:
        c = min(c, self.g[self.pv[v]][self.pe[v]].cap)
        v = self.pv[v]
      v = t
      while v != s:
        e = self.g[self.pv[v]][self.pe[v]]
        e.cap -= c
        self.g[v][e.rev].cap += c
        v = self.pv[v]
      d = -self.dual[s]
      flow += c
      cost += c * d
      if prev_cost == d:
        result.pop()
      result.append((flow, cost))
      prev_cost = cost
    return result

  class _edge:
    __slots__ = "to", "rev", "cap", "cost"

    def __init__(self, to, rev, cap, cost):
      self.to, self.rev, self.cap, self.cost = to, rev, cap, cost


def atcoder_practice2_e():
    import sys
    input = sys.stdin.buffer.readline

    N, K = list(map(int, input().split()))
    A = [tuple(map(int, input().split())) for _ in range(N)]
    BIG = 10 ** 9

    g = McfGraph(2 * N + 2)
    s = 2 * N
    t = 2 * N + 1

    g.add_edge(s, t, N * K, BIG)

    for i in range(N):
        g.add_edge(s, i, K, 0)
        g.add_edge(N + i, t, K, 0)
    for i in range(N):
        for j in range(N):
            g.add_edge(i, N + j, 1, BIG - A[i][j])

    result = g.flow(s, t, N * K)
    print(N * K * BIG - result[1])

    grid = [["."] * N for _ in range(N)]
    edges = g.edges()
    for e in edges:
        if e.frm == s or e.to == t or e.flow == 0:
            continue
        grid[e.frm][e.to - N] = "X"

    for g in grid:
        print("".join(g))


if __name__ == "__main__":
    atcoder_practice2_e()