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:
import sys

def input(): return sys.stdin.readline().strip()
def list2d(a, b, c): return [[c] * b for i in range(a)]
def list3d(a, b, c, d): return [[[d] * c for j in range(b)] for i in range(a)]
def list4d(a, b, c, d, e): return [[[[e] * d for j in range(c)] for j in range(b)] for i in range(a)]
def ceil(x, y=1): return int(-(-x // y))
def INT(): return int(input())
def MAP(): return map(int, input().split())
def LIST(N=None): return list(MAP()) if N is None else [INT() for i in range(N)]
def Yes(): print('Yes')
def No(): print('No')
def YES(): print('YES')
def NO(): print('NO')
sys.setrecursionlimit(10**9)
INF = 10**18
MOD = 10**9 + 7
EPS = 10**-10

class MinCostFlow:
    """ 最小費用流(ダイクストラ版)：O(F*E*logV) """

    INF = 10**18

    def __init__(self, N):
        self.N = N
        self.G = [[] for i in range(N)]
        self.pos = []

    def copy(self):
        res = MinCostFlow(self.N)
        res.G = [[a[:] for a in b] for b in self.G]
        res.pos = [a[:] for a in self.pos]
        return res

    def add_edge(self, fr, to, cap, cost):
        self.pos.append((fr, len(self.G[fr])))
        self.G[fr].append([to, cap, cost, len(self.G[to])])
        self.G[to].append([fr, 0, -cost, len(self.G[fr])-1])

    def flow(self, s, t, f):
        from heapq import heappush, heappop

        N = self.N; G = self.G
        INF = MinCostFlow.INF

        res = 0
        H = [0] * N
        prv_v = [0] * N
        prv_e = [0] * N

        while f:
            dist = [INF] * N
            dist[s] = 0
            que = [(0, s)]

            while que:
                c, v = heappop(que)
                if dist[v] < c:
                    continue
                for i, (to, cap, cost, _) in enumerate(G[v]):
                    if cap > 0 and dist[to] > dist[v] + cost + H[v] - H[to]:
                        dist[to] = r = dist[v] + cost + H[v] - H[to]
                        prv_v[to] = v; prv_e[to] = i
                        heappush(que, (r, to))
            if dist[t] == INF:
                return INF

            for i in range(N):
                H[i] += dist[i]

            d = f; v = t
            while v != s:
                d = min(d, G[prv_v[v]][prv_e[v]][1])
                v = prv_v[v]
            f -= d
            res += d * H[t]
            v = t
            while v != s:
                e = G[prv_v[v]][prv_e[v]]
                e[1] -= d
                G[v][e[3]][1] += d
                v = prv_v[v]
        return res

    def get_edge(self, i):
        e = self.G[self.pos[i][0]][self.pos[i][1]]
        re = self.G[e[0]][e[3]]
        # from, to, cap, flow, cost
        return (self.pos[i][0], e[0], e[1]+re[1], re[1], e[2])

    def get_edges(self):
        M = len(self.pos)
        res = []
        for i in range(M):
            res.append(self.get_edge(i))
        return res

N, K = MAP()
grid = [[] for i in range(N)]
for i in range(N):
    grid[i] = LIST()

offset = 10**12
mcf = MinCostFlow(N*2+2)
s = N*2
t = N*2 + 1
# 利益なしだけどいくらでも通れる辺を追加して、到達不可にならないようにする
mcf.add_edge(s, t, N*N, offset)
for i in range(N):
    mcf.add_edge(s, i, K, 0)
    mcf.add_edge(N+i, t, K, 0)
    for j in range(N):
        mcf.add_edge(i, N+j, 1, offset-grid[i][j])

mn = mcf.flow(s, t, N*N)
mn -= offset*N*N
ans = [['.' for j in range(N)] for i in range(N)]
edges = mcf.get_edges()
for fr, to, cap, f, c in edges:
    if fr != s and to != t and f:
        h = fr
        w = to - N
        ans[h][w] = 'X'
print(-mn)
for i in range(N):
    print(''.join(ans[i]))