Buggy python submission (verdict: Runtime Error):
# Dinic's algorithm
#https://tjkendev.github.io/procon-library/python/max_flow/dinic.htmlより
from collections import deque
class Dinic:
    def __init__(self, N):
        self.N = N
        self.G = [[] for i in range(N)]

    def add_edge(self, fr, to, cap):
        forward = [to, cap, None]
        forward[2] = backward = [fr, 0, forward]
        self.G[fr].append(forward)
        self.G[to].append(backward)

    def add_multi_edge(self, v1, v2, cap1, cap2):
        edge1 = [v2, cap1, None]
        edge1[2] = edge2 = [v1, cap2, edge1]
        self.G[v1].append(edge1)
        self.G[v2].append(edge2)

    def bfs(self, s, t):
        self.level = level = [None]*self.N
        deq = deque([s])
        level[s] = 0
        G = self.G
        while deq:
            v = deq.popleft()
            lv = level[v] + 1
            for w, cap, _ in G[v]:
                if cap and level[w] is None:
                    level[w] = lv
                    deq.append(w)
        return level[t] is not None

    def dfs(self, v, t, f):
        if v == t:
            return f
        level = self.level
        for e in self.it[v]:
            w, cap, rev = e
            if cap and level[v] < level[w]:
                d = self.dfs(w, t, min(f, cap))
                if d:
                    e[1] -= d
                    rev[1] += d
                    return d
        return 0

    def flow(self, s, t):
        flow = 0
        INF = 10**9 + 7
        G = self.G
        while self.bfs(s, t):
            *self.it, = map(iter, self.G)
            f = INF
            while f:
                f = self.dfs(s, t, INF)
                flow += f
        return flow

N,M = map(int, input().split())
S = [list(input()) for i in range(N)]
dc = Dinic(N*M+2)
 
s =N*M
t = N*M+1
for i in range(N):
    for j in range(M):
        if (i+j) % 2 == 0:
            dc.add_edge(s,M*i+j,1)
        else:
            dc.add_edge(M*i+j,t,1)
 
for i in range(N):
    for j in range(M):
        if j+1 < M and S[i][j] == "." and S[i][j+1] == ".":
            u,v = M*i+j,M*i+j+1
            if (i+j) % 2 == 1:
                u,v = v,u
            dc.add_edge(u, v, 1)
        if i+1 < N and S[i][j] == "." and S[i + 1][j] == ".":
            u,v = M*i+j, M*(i+1)+j
            if (i+j) % 2 == 1:
                u,v = v,u
            dc.add_edge(u,v,1)
 
print(dc.flow(s, t))
for u in range(N*M+2):
    for v, cap, _ in dc.graph[u]:
        ui, uj = divmod(u, M)
        vi, vj = divmod(v, M)
        if (ui+uj) % 2 == 0 and cap == 0 and u != s and u != t and v != s and v!= t:
            if ui+1 == vi:
                S[ui][uj] = "v"
                S[vi][vj] = "^"
            elif ui == vi+1:
                S[ui][uj] = "^"
                S[vi][vj] = "v"
            elif uj+1 == vj:
                S[ui][uj] = ">"
                S[vi][vj] = "<"
            elif uj == vj+1:
                S[ui][uj] = "<"
                S[vi][vj] = ">"
 
for res in S:
    print("".join(res))

Fixed submission:
from collections import deque
import sys
sys.setrecursionlimit(1<<30)
class Dinic:
    def __init__(self,N):
        self.N = N
        self.graph = [[] for _ in range(N)]
    
    def add_edge(self,v,w,cap):
        edge = [w,cap,None]
        edge[2] = rev_edge = [v,0,edge]
        self.graph[v].append(edge)
        self.graph[w].append(rev_edge)
    
    def bfs(self,s,t):
        self.level = [None]*self.N
        d = deque([s])
        self.level[s] = 0
        while d:
            v = d.popleft()
            nlevel = self.level[v]+1
            for w,cap,_ in self.graph[v]:
                if cap and self.level[w] is None:
                    self.level[w] = nlevel
                    d.append(w)
        return self.level[t] is not None
    
    def dfs(self,s,v,f):
        if v == s:
            return f
        for rev in self.it[v]:
            w,_,e = rev
            cap = e[1]
            if cap and self.level[w] is not None:
                if self.level[v] > self.level[w]:
                    d = self.dfs(s,w,min(f,cap))
                    if d:
                        e[1] -= d
                        rev[1] += d
                        return d
        return 0
    
    def max_flow(self,s,t):
        flow = 0
        INF = 10**9
        while self.bfs(s,t):
            *self.it, = map(iter,self.graph)
            f = INF
            while f:
                f = self.dfs(s,t,INF)
                flow += f
        return flow


N,M = map(int, input().split())
S = [list(input()) for i in range(N)]
dc = Dinic(N*M+2)

s =N*M
t = N*M+1
for i in range(N):
    for j in range(M):
        if (i + j) % 2 == 0:
            dc.add_edge(s,M*i+j,1)
        else:
            dc.add_edge(M*i+j,t,1)

for i in range(N):
    for j in range(M):
        if j+1 < M and S[i][j] == "." and S[i][j+1] == ".":
            u,v = M*i+j,M*i+j+1
            if (i+j) % 2 == 1:
                u,v = v,u
            dc.add_edge(u, v, 1)
        if i+1 < N and S[i][j] == "." and S[i + 1][j] == ".":
            u,v = M*i+j, M*(i+1)+j
            if (i+j) % 2 == 1:
                u,v = v,u
            dc.add_edge(u, v, 1)

print(dc.max_flow(s, t))
for u in range(N*M+2):
    for v, cap, _ in dc.graph[u]:
        ui, uj = divmod(u, M)
        vi, vj = divmod(v, M)
        if (ui+uj) % 2 == 0 and cap == 0 and u != s and u != t and v != s and v!= t:
            if ui+1 == vi:
                S[ui][uj] = "v"
                S[vi][vj] = "^"
            elif ui == vi+1:
                S[ui][uj] = "^"
                S[vi][vj] = "v"
            elif uj+1 == vj:
                S[ui][uj] = ">"
                S[vi][vj] = "<"
            elif uj == vj+1:
                S[ui][uj] = "<"
                S[vi][vj] = ">"

for res in S:
    print("".join(res))

Buggy python submission (verdict: Runtime Error):
# Dinic's algorithm
#https://tjkendev.github.io/procon-library/python/max_flow/dinic.htmlより
from collections import deque
class Dinic:
    def __init__(self, N):
        self.N = N
        self.G = [[] for i in range(N)]

    def add_edge(self, fr, to, cap):
        forward = [to, cap, None]
        forward[2] = backward = [fr, 0, forward]
        self.G[fr].append(forward)
        self.G[to].append(backward)

    def add_multi_edge(self, v1, v2, cap1, cap2):
        edge1 = [v2, cap1, None]
        edge1[2] = edge2 = [v1, cap2, edge1]
        self.G[v1].append(edge1)
        self.G[v2].append(edge2)

    def bfs(self, s, t):
        self.level = level = [None]*self.N
        deq = deque([s])
        level[s] = 0
        G = self.G
        while deq:
            v = deq.popleft()
            lv = level[v] + 1
            for w, cap, _ in G[v]:
                if cap and level[w] is None:
                    level[w] = lv
                    deq.append(w)
        return level[t] is not None

    def dfs(self, v, t, f):
        if v == t:
            return f
        level = self.level
        for e in self.it[v]:
            w, cap, rev = e
            if cap and level[v] < level[w]:
                d = self.dfs(w, t, min(f, cap))
                if d:
                    e[1] -= d
                    rev[1] += d
                    return d
        return 0

    def flow(self, s, t):
        flow = 0
        INF = 10**9 + 7
        G = self.G
        while self.bfs(s, t):
            *self.it, = map(iter, self.G)
            f = INF
            while f:
                f = self.dfs(s, t, INF)
                flow += f
        return flow

N,M = map(int, input().split())
S = [list(input()) for i in range(N)]
dc = mf_graph(N*M+2)
 
s =N*M
t = N*M+1
for i in range(N):
    for j in range(M):
        if (i+j) % 2 == 0:
            dc.add_edge(s,M*i+j,1)
        else:
            dc.add_edge(M*i+j,t,1)
 
for i in range(N):
    for j in range(M):
        if j+1 < M and S[i][j] == "." and S[i][j+1] == ".":
            u,v = M*i+j,M*i+j+1
            if (i+j) % 2 == 1:
                u,v = v,u
            dc.add_edge(u, v, 1)
        if i+1 < N and S[i][j] == "." and S[i + 1][j] == ".":
            u,v = M*i+j, M*(i+1)+j
            if (i+j) % 2 == 1:
                u,v = v,u
            dc.add_edge(u,v,1)
 
print(dc.flow(s, t))
for u in range(N*M+2):
    for v, cap, _ in dc.graph[u]:
        ui, uj = divmod(u, M)
        vi, vj = divmod(v, M)
        if (ui+uj) % 2 == 0 and cap == 0 and u != s and u != t and v != s and v!= t:
            if ui+1 == vi:
                S[ui][uj] = "v"
                S[vi][vj] = "^"
            elif ui == vi+1:
                S[ui][uj] = "^"
                S[vi][vj] = "v"
            elif uj+1 == vj:
                S[ui][uj] = ">"
                S[vi][vj] = "<"
            elif uj == vj+1:
                S[ui][uj] = "<"
                S[vi][vj] = ">"
 
for res in S:
    print("".join(res))

Fixed submission:
from collections import deque
import sys
sys.setrecursionlimit(1<<30)
class Dinic:
    def __init__(self,N):
        self.N = N
        self.graph = [[] for _ in range(N)]
    
    def add_edge(self,v,w,cap):
        edge = [w,cap,None]
        edge[2] = rev_edge = [v,0,edge]
        self.graph[v].append(edge)
        self.graph[w].append(rev_edge)
    
    def bfs(self,s,t):
        self.level = [None]*self.N
        d = deque([s])
        self.level[s] = 0
        while d:
            v = d.popleft()
            nlevel = self.level[v]+1
            for w,cap,_ in self.graph[v]:
                if cap and self.level[w] is None:
                    self.level[w] = nlevel
                    d.append(w)
        return self.level[t] is not None
    
    def dfs(self,s,v,f):
        if v == s:
            return f
        for rev in self.it[v]:
            w,_,e = rev
            cap = e[1]
            if cap and self.level[w] is not None:
                if self.level[v] > self.level[w]:
                    d = self.dfs(s,w,min(f,cap))
                    if d:
                        e[1] -= d
                        rev[1] += d
                        return d
        return 0
    
    def max_flow(self,s,t):
        flow = 0
        INF = 10**9
        while self.bfs(s,t):
            *self.it, = map(iter,self.graph)
            f = INF
            while f:
                f = self.dfs(s,t,INF)
                flow += f
        return flow


N,M = map(int, input().split())
S = [list(input()) for i in range(N)]
dc = Dinic(N*M+2)

s =N*M
t = N*M+1
for i in range(N):
    for j in range(M):
        if (i + j) % 2 == 0:
            dc.add_edge(s,M*i+j,1)
        else:
            dc.add_edge(M*i+j,t,1)

for i in range(N):
    for j in range(M):
        if j+1 < M and S[i][j] == "." and S[i][j+1] == ".":
            u,v = M*i+j,M*i+j+1
            if (i+j) % 2 == 1:
                u,v = v,u
            dc.add_edge(u, v, 1)
        if i+1 < N and S[i][j] == "." and S[i + 1][j] == ".":
            u,v = M*i+j, M*(i+1)+j
            if (i+j) % 2 == 1:
                u,v = v,u
            dc.add_edge(u, v, 1)

print(dc.max_flow(s, t))
for u in range(N*M+2):
    for v, cap, _ in dc.graph[u]:
        ui, uj = divmod(u, M)
        vi, vj = divmod(v, M)
        if (ui+uj) % 2 == 0 and cap == 0 and u != s and u != t and v != s and v!= t:
            if ui+1 == vi:
                S[ui][uj] = "v"
                S[vi][vj] = "^"
            elif ui == vi+1:
                S[ui][uj] = "^"
                S[vi][vj] = "v"
            elif uj+1 == vj:
                S[ui][uj] = ">"
                S[vi][vj] = "<"
            elif uj == vj+1:
                S[ui][uj] = "<"
                S[vi][vj] = ">"

for res in S:
    print("".join(res))

Buggy python submission (verdict: Runtime Error):
from collections import deque

class mf_graph:
    def __init__(self,N):
        self.N = N
        self.graph = [[] for _ in range(N)]
    
    def add_edge(self,v,w,cap):
        edge = [w,cap,None]
        edge[2] = rev_edge = [v,0,edge]
        self.graph[v].append(edge)
        self.graph[w].append(rev_edge)
    
    def bfs(self,s,t):
        self.level = [None]*self.N
        dq = deque([s])
        self.level[s] = 0
        while dq:
            v = dq.popleft()
            nlevel = self.level[v]+1
            for w,cap,_ in self.graph[v]:
                if cap and self.level[w] is None:
                    self.level[w] = nlevel
                    dq.append(w)
        return self.level[t] is not None
    
    def dfs(self,s,v,f):
        if v == s:
            return f
        for rev in self.it[v]:
            w,_,e = rev
            cap = e[1]
            if cap and self.level[w] is not None:
                if self.level[v] > self.level[w]:
                    d = self.dfs(s,w,min(f,cap))
                    if d:
                        e[1] -= d
                        rev[1] += d
                        return d
        return 0
    
    def flow(self,s,t,flow_limit=float('inf')):
        flow = 0
        while self.bfs(s,t):
            *self.it, = map(iter,self.graph)
            f = flow_limit
            while f:
                f = self.dfs(s,t,flow_limit-flow)
                flow += f
        return flow

    def min_cut(self,s):
        visited = [False]*self.N
        dq = deque([s])
        while dq:
            v = dq.pop()
            visited[v] = True
            for w,cap,_ in self.graph[v]:
                if cap and not visited[w]:
                    dq.append(w)
import sys
input = sys.stdin.buffer.readline().rstrip

N,M = map(int, input().split())
S = [list(input()) for i in range(N)]
dc = mf_graph(N*M+2)

s =N*M
t = N*M+1
for i in range(N):
    for j in range(M):
        if (i + j) % 2 == 0:
            dc.add_edge(s,M*i+j,1)
        else:
            dc.add_edge(M*i+j,t,1)

for i in range(N):
    for j in range(M):
        if j+1 < M and S[i][j] == "." and S[i][j+1] == ".":
            u,v = M*i+j,M*i+j+1
            if (i+j) % 2 == 1:
                u,v = v,u
            dc.add_edge(u, v, 1)
        if i+1 < N and S[i][j] == "." and S[i + 1][j] == ".":
            u,v = M*i+j, M*(i+1)+j
            if (i+j) % 2 == 1:
                u,v = v,u
            dc.add_edge(u, v, 1)

print(dc.flow(s, t))
for u in range(N*M+2):
    for v, cap, _ in dc.graph[u]:
        ui, uj = divmod(u, M)
        vi, vj = divmod(v, M)
        if (ui+uj) % 2 == 0 and cap == 0 and u != s and u != t and v != s and v!= t:
            if ui+1 == vi:
                S[ui][uj] = "v"
                S[vi][vj] = "^"
            elif ui == vi+1:
                S[ui][uj] = "^"
                S[vi][vj] = "v"
            elif uj+1 == vj:
                S[ui][uj] = ">"
                S[vi][vj] = "<"
            elif uj == vj+1:
                S[ui][uj] = "<"
                S[vi][vj] = ">"

for res in S:
    print("".join(res))


Fixed submission:
from collections import deque
import sys
sys.setrecursionlimit(1<<30)
class Dinic:
    def __init__(self,N):
        self.N = N
        self.graph = [[] for _ in range(N)]
    
    def add_edge(self,v,w,cap):
        edge = [w,cap,None]
        edge[2] = rev_edge = [v,0,edge]
        self.graph[v].append(edge)
        self.graph[w].append(rev_edge)
    
    def bfs(self,s,t):
        self.level = [None]*self.N
        d = deque([s])
        self.level[s] = 0
        while d:
            v = d.popleft()
            nlevel = self.level[v]+1
            for w,cap,_ in self.graph[v]:
                if cap and self.level[w] is None:
                    self.level[w] = nlevel
                    d.append(w)
        return self.level[t] is not None
    
    def dfs(self,s,v,f):
        if v == s:
            return f
        for rev in self.it[v]:
            w,_,e = rev
            cap = e[1]
            if cap and self.level[w] is not None:
                if self.level[v] > self.level[w]:
                    d = self.dfs(s,w,min(f,cap))
                    if d:
                        e[1] -= d
                        rev[1] += d
                        return d
        return 0
    
    def max_flow(self,s,t):
        flow = 0
        INF = 10**9
        while self.bfs(s,t):
            *self.it, = map(iter,self.graph)
            f = INF
            while f:
                f = self.dfs(s,t,INF)
                flow += f
        return flow


N,M = map(int, input().split())
S = [list(input()) for i in range(N)]
dc = Dinic(N*M+2)

s =N*M
t = N*M+1
for i in range(N):
    for j in range(M):
        if (i + j) % 2 == 0:
            dc.add_edge(s,M*i+j,1)
        else:
            dc.add_edge(M*i+j,t,1)

for i in range(N):
    for j in range(M):
        if j+1 < M and S[i][j] == "." and S[i][j+1] == ".":
            u,v = M*i+j,M*i+j+1
            if (i+j) % 2 == 1:
                u,v = v,u
            dc.add_edge(u, v, 1)
        if i+1 < N and S[i][j] == "." and S[i + 1][j] == ".":
            u,v = M*i+j, M*(i+1)+j
            if (i+j) % 2 == 1:
                u,v = v,u
            dc.add_edge(u, v, 1)

print(dc.max_flow(s, t))
for u in range(N*M+2):
    for v, cap, _ in dc.graph[u]:
        ui, uj = divmod(u, M)
        vi, vj = divmod(v, M)
        if (ui+uj) % 2 == 0 and cap == 0 and u != s and u != t and v != s and v!= t:
            if ui+1 == vi:
                S[ui][uj] = "v"
                S[vi][vj] = "^"
            elif ui == vi+1:
                S[ui][uj] = "^"
                S[vi][vj] = "v"
            elif uj+1 == vj:
                S[ui][uj] = ">"
                S[vi][vj] = "<"
            elif uj == vj+1:
                S[ui][uj] = "<"
                S[vi][vj] = ">"

for res in S:
    print("".join(res))

Buggy python submission (verdict: Runtime Error):
from collections import deque

class mf_graph:
    def __init__(self,N):
        self.N = N
        self.graph = [[] for _ in range(N)]
    
    def add_edge(self,v,w,cap):
        edge = [w,cap,None]
        edge[2] = rev_edge = [v,0,edge]
        self.graph[v].append(edge)
        self.graph[w].append(rev_edge)
    
    def bfs(self,s,t):
        self.level = [None]*self.N
        dq = deque([s])
        self.level[s] = 0
        while dq:
            v = dq.popleft()
            nlevel = self.level[v]+1
            for w,cap,_ in self.graph[v]:
                if cap and self.level[w] is None:
                    self.level[w] = nlevel
                    dq.append(w)
        return self.level[t] is not None
    
    def dfs(self,s,v,f):
        if v == s:
            return f
        for rev in self.it[v]:
            w,_,e = rev
            cap = e[1]
            if cap and self.level[w] is not None:
                if self.level[v] > self.level[w]:
                    d = self.dfs(s,w,min(f,cap))
                    if d:
                        e[1] -= d
                        rev[1] += d
                        return d
        return 0
    
    def flow(self,s,t,flow_limit=float('inf')):
        flow = 0
        while self.bfs(s,t):
            *self.it, = map(iter,self.graph)
            f = flow_limit
            while f:
                f = self.dfs(s,t,flow_limit-flow)
                flow += f
        return flow

    def min_cut(self,s):
        visited = [False]*self.N
        dq = deque([s])
        while dq:
            v = dq.pop()
            visited[v] = True
            for w,cap,_ in self.graph[v]:
                if cap and not visited[w]:
                    dq.append(w)


N,M = map(int, input().split())
S = [list(input()) for i in range(N)]
dc = mf_graph(N*M+2)

s =N*M
t = N*M+1
for i in range(N):
    for j in range(M):
        if (i+j) % 2 == 0:
            dc.add_edge(s,M*i+j,1)
        else:
            dc.add_edge(M*i+j,t,1)

for i in range(N):
    for j in range(M):
        if j+1 < M and S[i][j] == "." and S[i][j+1] == ".":
            u,v = M*i+j,M*i+j+1
            if (i+j) % 2 == 1:
                u,v = v,u
            dc.add_edge(u,v,1)
        if i+1 < N and S[i][j] == "." and S[i + 1][j] == ".":
            u,v = M*i+j, M*(i+1)+j
            if (i+j) % 2 == 1:
                u,v = v,u
            dc.add_edge(u, v, 1)

print(dc.flow(s, t,10**9))
for u in range(N*M+2):
    for v,cap,_in dc.graph[u]:
        ui,uj = divmod(u,M)
        vi,vj = divmod(v,M)
        if (ui+uj) % 2 == 0 and cap == 0 and u != s and u != t and v != s and v!= t:
            if ui+1 == vi:
                S[ui][uj] = "v"
                S[vi][vj] = "^"
            elif ui == vi+1:
                S[ui][uj] = "^"
                S[vi][vj] = "v"
            elif uj+1 == vj:
                S[ui][uj] = ">"
                S[vi][vj] = "<"
            elif uj == vj+1:
                S[ui][uj] = "<"
                S[vi][vj] = ">"

for res in S:
    print("".join(res))


Fixed submission:
from collections import deque
import sys
sys.setrecursionlimit(1<<30)
class Dinic:
    def __init__(self,N):
        self.N = N
        self.graph = [[] for _ in range(N)]
    
    def add_edge(self,v,w,cap):
        edge = [w,cap,None]
        edge[2] = rev_edge = [v,0,edge]
        self.graph[v].append(edge)
        self.graph[w].append(rev_edge)
    
    def bfs(self,s,t):
        self.level = [None]*self.N
        d = deque([s])
        self.level[s] = 0
        while d:
            v = d.popleft()
            nlevel = self.level[v]+1
            for w,cap,_ in self.graph[v]:
                if cap and self.level[w] is None:
                    self.level[w] = nlevel
                    d.append(w)
        return self.level[t] is not None
    
    def dfs(self,s,v,f):
        if v == s:
            return f
        for rev in self.it[v]:
            w,_,e = rev
            cap = e[1]
            if cap and self.level[w] is not None:
                if self.level[v] > self.level[w]:
                    d = self.dfs(s,w,min(f,cap))
                    if d:
                        e[1] -= d
                        rev[1] += d
                        return d
        return 0
    
    def max_flow(self,s,t):
        flow = 0
        INF = 10**9
        while self.bfs(s,t):
            *self.it, = map(iter,self.graph)
            f = INF
            while f:
                f = self.dfs(s,t,INF)
                flow += f
        return flow


N,M = map(int, input().split())
S = [list(input()) for i in range(N)]
dc = Dinic(N*M+2)

s =N*M
t = N*M+1
for i in range(N):
    for j in range(M):
        if (i + j) % 2 == 0:
            dc.add_edge(s,M*i+j,1)
        else:
            dc.add_edge(M*i+j,t,1)

for i in range(N):
    for j in range(M):
        if j+1 < M and S[i][j] == "." and S[i][j+1] == ".":
            u,v = M*i+j,M*i+j+1
            if (i+j) % 2 == 1:
                u,v = v,u
            dc.add_edge(u, v, 1)
        if i+1 < N and S[i][j] == "." and S[i + 1][j] == ".":
            u,v = M*i+j, M*(i+1)+j
            if (i+j) % 2 == 1:
                u,v = v,u
            dc.add_edge(u, v, 1)

print(dc.max_flow(s, t))
for u in range(N*M+2):
    for v, cap, _ in dc.graph[u]:
        ui, uj = divmod(u, M)
        vi, vj = divmod(v, M)
        if (ui+uj) % 2 == 0 and cap == 0 and u != s and u != t and v != s and v!= t:
            if ui+1 == vi:
                S[ui][uj] = "v"
                S[vi][vj] = "^"
            elif ui == vi+1:
                S[ui][uj] = "^"
                S[vi][vj] = "v"
            elif uj+1 == vj:
                S[ui][uj] = ">"
                S[vi][vj] = "<"
            elif uj == vj+1:
                S[ui][uj] = "<"
                S[vi][vj] = ">"

for res in S:
    print("".join(res))

Buggy python submission (verdict: Runtime Error):
from collections import deque

class mf_graph:
    def __init__(self,N):
        self.N = N
        self.graph = [[] for _ in range(N)]
    
    def add_edge(self,v,w,cap):
        edge = [w,cap,None]
        edge[2] = rev_edge = [v,0,edge]
        self.graph[v].append(edge)
        self.graph[w].append(rev_edge)
    
    def bfs(self,s,t):
        self.level = [None]*self.N
        dq = deque([s])
        self.level[s] = 0
        while dq:
            v = dq.popleft()
            nlevel = self.level[v]+1
            for w,cap,_ in self.graph[v]:
                if cap and self.level[w] is None:
                    self.level[w] = nlevel
                    dq.append(w)
        return self.level[t] is not None
    
    def dfs(self,s,v,f):
        if v == s:
            return f
        for rev in self.it[v]:
            w,_,e = rev
            cap = e[1]
            if cap and self.level[w] is not None:
                if self.level[v] > self.level[w]:
                    d = self.dfs(s,w,min(f,cap))
                    if d:
                        e[1] -= d
                        rev[1] += d
                        return d
        return 0
    
    def flow(self,s,t,flow_limit=float('inf')):
        flow = 0
        while self.bfs(s,t):
            *self.it, = map(iter,self.graph)
            f = flow_limit
            while f:
                f = self.dfs(s,t,flow_limit-flow)
                flow += f
        return flow

    def min_cut(self,s):
        visited = [False]*self.N
        dq = deque([s])
        while dq:
            v = dq.pop()
            visited[v] = True
            for w,cap,_ in self.graph[v]:
                if cap and not visited[w]:
                    dq.append(w)


N,M = map(int, input().split())
S = [list(input()) for i in range(N)]
dc = mf_graph(N*M+2)

s =N*M
t = N*M+1
for i in range(N):
    for j in range(M):
        if (i + j) % 2 == 0:
            dc.add_edge(s,M*i+j,1)
        else:
            dc.add_edge(M*i+j,t,1)

for i in range(N):
    for j in range(M):
        if j+1 < M and S[i][j] == "." and S[i][j+1] == ".":
            u,v = M*i+j,M*i+j+1
            if (i+j) % 2 == 1:
                u,v = v,u
            dc.add_edge(u, v, 1)
        if i+1 < N and S[i][j] == "." and S[i + 1][j] == ".":
            u,v = M*i+j, M*(i+1)+j
            if (i+j) % 2 == 1:
                u,v = v,u
            dc.add_edge(u, v, 1)

print(dc.max_flow(s, t))
for u in range(N*M+2):
    for v, cap, _ in dc.graph[u]:
        ui, uj = divmod(u, M)
        vi, vj = divmod(v, M)
        if (ui+uj) % 2 == 0 and cap == 0 and u != s and u != t and v != s and v!= t:
            if ui+1 == vi:
                S[ui][uj] = "v"
                S[vi][vj] = "^"
            elif ui == vi+1:
                S[ui][uj] = "^"
                S[vi][vj] = "v"
            elif uj+1 == vj:
                S[ui][uj] = ">"
                S[vi][vj] = "<"
            elif uj == vj+1:
                S[ui][uj] = "<"
                S[vi][vj] = ">"

for res in S:
    print("".join(res))


Fixed submission:
from collections import deque
import sys
sys.setrecursionlimit(1<<30)
class Dinic:
    def __init__(self,N):
        self.N = N
        self.graph = [[] for _ in range(N)]
    
    def add_edge(self,v,w,cap):
        edge = [w,cap,None]
        edge[2] = rev_edge = [v,0,edge]
        self.graph[v].append(edge)
        self.graph[w].append(rev_edge)
    
    def bfs(self,s,t):
        self.level = [None]*self.N
        d = deque([s])
        self.level[s] = 0
        while d:
            v = d.popleft()
            nlevel = self.level[v]+1
            for w,cap,_ in self.graph[v]:
                if cap and self.level[w] is None:
                    self.level[w] = nlevel
                    d.append(w)
        return self.level[t] is not None
    
    def dfs(self,s,v,f):
        if v == s:
            return f
        for rev in self.it[v]:
            w,_,e = rev
            cap = e[1]
            if cap and self.level[w] is not None:
                if self.level[v] > self.level[w]:
                    d = self.dfs(s,w,min(f,cap))
                    if d:
                        e[1] -= d
                        rev[1] += d
                        return d
        return 0
    
    def max_flow(self,s,t):
        flow = 0
        INF = 10**9
        while self.bfs(s,t):
            *self.it, = map(iter,self.graph)
            f = INF
            while f:
                f = self.dfs(s,t,INF)
                flow += f
        return flow


N,M = map(int, input().split())
S = [list(input()) for i in range(N)]
dc = Dinic(N*M+2)

s =N*M
t = N*M+1
for i in range(N):
    for j in range(M):
        if (i + j) % 2 == 0:
            dc.add_edge(s,M*i+j,1)
        else:
            dc.add_edge(M*i+j,t,1)

for i in range(N):
    for j in range(M):
        if j+1 < M and S[i][j] == "." and S[i][j+1] == ".":
            u,v = M*i+j,M*i+j+1
            if (i+j) % 2 == 1:
                u,v = v,u
            dc.add_edge(u, v, 1)
        if i+1 < N and S[i][j] == "." and S[i + 1][j] == ".":
            u,v = M*i+j, M*(i+1)+j
            if (i+j) % 2 == 1:
                u,v = v,u
            dc.add_edge(u, v, 1)

print(dc.max_flow(s, t))
for u in range(N*M+2):
    for v, cap, _ in dc.graph[u]:
        ui, uj = divmod(u, M)
        vi, vj = divmod(v, M)
        if (ui+uj) % 2 == 0 and cap == 0 and u != s and u != t and v != s and v!= t:
            if ui+1 == vi:
                S[ui][uj] = "v"
                S[vi][vj] = "^"
            elif ui == vi+1:
                S[ui][uj] = "^"
                S[vi][vj] = "v"
            elif uj+1 == vj:
                S[ui][uj] = ">"
                S[vi][vj] = "<"
            elif uj == vj+1:
                S[ui][uj] = "<"
                S[vi][vj] = ">"

for res in S:
    print("".join(res))