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:
class UnionFind():
    def __init__(self, n):
        self.n = n
        self.parents = [-1] * n

    def find(self, x):
        if self.parents[x] < 0:
            return x
        else:
            li = []
            while self.parents[x] >= 0:
                li.append(x)
                x = self.parents[x]
            for y in li:
                self.parents[y] = x
            return x

    def union(self, x, y):
        x = self.find(x)
        y = self.find(y)

        if x == y:
            return

        if self.parents[x] > self.parents[y]:
            x, y = y, x

        self.parents[x] += self.parents[y]
        self.parents[y] = x

    def size(self, x):
        return -self.parents[self.find(x)]

    def same(self, x, y):
        return self.find(x) == self.find(y)

    def members(self, x):
        root = self.find(x)
        return [i for i in range(self.n) if self.find(i) == root]

    def roots(self):
        return [i for i, x in enumerate(self.parents) if x < 0]

    def group_count(self):
        return len(self.roots())

    def all_group_members(self):
        return {r: self.members(r) for r in self.roots()}

    def __str__(self):
        return '\n'.join('{}: {}'.format(r, self.members(r)) for r in self.roots())

import sys
input = sys.stdin.buffer.readline
N,Q = map(int,input().split())
uf = UnionFind(N)
for i in range(Q):
    t,u,v = map(int,input().split())
    if t == 0:
        uf.union(u,v)
    else:
        if uf.same(u,v):
            print(1)
        else:
            print(0)