from typing import NamedTuple, Optional, List
class MaxFlow:
class Edge(NamedTuple):
src: int
dst: int
cap: int
flow: int
class _Edge:
dst: int
cap: int
rev: Optional['MaxFlow._Edge']
def __init__(self, dst: int, cap: int):
self.dst = dst
self.cap = cap
self.rev = None
def __init__(self, n: int):
self._n = n
self._g: List[List[MaxFlow._Edge]] = [[] for _ in range(n)]
self._edges: List[MaxFlow._Edge] = []
def add_edge(self, src: int, dst: int, cap: int) -> int:
assert 0 <= src < self._n
assert 0 <= dst < self._n
assert 0 <= cap
m = len(self._edges)
e = MaxFlow._Edge(dst, cap)
re = MaxFlow._Edge(src, 0)
e.rev = re
re.rev = e
self._g[src].append(e)
self._g[dst].append(re)
self._edges.append(e)
return m
def get_edge(self, i: int) -> Edge:
assert 0 <= i < len(self._edges)
e = self._edges[i]
re = e.rev
return MaxFlow.Edge(
re.dst,
e.dst,
e.cap + re.cap,
re.cap
)
def edges(self) -> List[Edge]:
return [self.get_edge(i) for i in range(len(self._edges))]
def change_edge(self, i: int, new_cap: int, new_flow: int):
assert 0 <= i < len(self._edges)
assert 0 <= new_flow <= new_cap
e = self._edges[i]
e.cap = new_cap - new_flow
e.rev.cap = new_flow
def flow(self, s: int, t: int, flow_limit: Optional[int] = None) -> int:
assert 0 <= s < self._n
assert 0 <= t < self._n
assert s != t
if flow_limit is None:
flow_limit = sum(e.cap for e in self._g[s])
current_edge = [0] * self._n
level = [0] * self._n
def fill(arr: List[int], value: int):
for i in range(len(arr)):
arr[i] = value
def bfs() -> bool:
fill(level, self._n)
queue = []
q_front = 0
queue.append(s)
level[s] = 0
while q_front < len(queue):
v = queue[q_front]
q_front += 1
next_level = level[v] + 1
for e in self._g[v]:
if e.cap == 0 or level[e.dst] <= next_level:
continue
level[e.dst] = next_level
if e.dst == t:
return True
queue.append(e.dst)
return False
def dfs(lim) -> int:
stack = []
edge_stack = []
stack.append(t)
while stack:
v = stack[-1]
if v == s:
flow = min(lim, min(e.cap for e in edge_stack))
for e in edge_stack:
e.cap -= flow
e.rev.cap += flow
return flow
next_level = level[v] - 1
while current_edge[v] < len(self._g[v]):
e = self._g[v][current_edge[v]]
re = e.rev
if level[e.dst] != next_level or re.cap == 0:
current_edge[v] += 1
continue
stack.append(e.dst)
edge_stack.append(re)
break
else:
stack.pop()
if edge_stack:
edge_stack.pop()
level[v] = self._n
return 0
flow = 0
while flow < flow_limit:
if not bfs():
break
fill(current_edge, 0)
while flow < flow_limit:
f = dfs(flow_limit - flow)
flow += f
if f == 0:
break
return flow
# https://atcoder.jp/contests/practice2/tasks/practice2_d
def main() -> None:
import sys
n, m = map(int, sys.stdin.readline().split())
s = n * m
t = s + 1
g = MaxFlow(t + 1)
grid = [list(sys.stdin.readline().strip()) for _ in range(n)]
def enc(i: int, j: int) -> int:
return i * m + j
def dec(v: int) -> (int, int):
return v // m, v % m
for i in range(n):
for j in range(m):
if grid[i][j] == '#':
continue
if (i + j) % 2 == 0:
g.add_edge(s, enc(i, j), 1)
else:
g.add_edge(enc(i, j), t, 1)
dx = [1, 0, -1, 0]
dy = [0, 1, 0, -1]
for i in range(n):
for j in range(m):
if (i + j) % 2 == 1 or grid[i][j] == '#':
continue
for direction in range(4):
ii = i + dx[direction]
jj = j + dy[direction]
if 0 <= ii < n and 0 <= jj < m and grid[ii][jj] == '.':
g.add_edge(enc(i, j), enc(ii, jj), 1)
print(g.flow(s, t))
for e in g.edges():
if e.src == s or e.dst == t or e.flow == 0:
continue
(i, j) = dec(e.src)
(ii, jj) = dec(e.dst)
if i == ii + 1:
grid[ii][jj] = 'v'
grid[i][j] = '^'
elif j == jj + 1:
grid[ii][jj] = '>'
grid[i][j] = '<'
elif i == ii - 1:
grid[i][j] = 'v'
grid[ii][jj] = '^'
else:
grid[i][j] = '>'
grid[ii][jj] = '<'
for s in grid:
print("".join(s))
if __name__ == '__main__':
main()