Buggy python submission (verdict: Time Limit Exceeded):
class UnionFind:
    def __init__(self, n, p):
        '木の初期化をする'
        # zero-index
        self.p  = [-1] * n
        self.rank = [1]*n
        # one -index
        self.g  = [set([i]) for i in range(n+1)]
        self.gp = [set([i]) for i in p]

    def find(self, x):
        'x の親を返す'
        if self.p[x] == -1:
            return x
        else:
            self.p[x] = self.find(self.p[x])
            return self.p[x]

    def unite(self, x, y):
        'rankの低い親を高い方のの親にする'
        if not self.same(x,y):
            x = self.find(x)
            y = self.find(y)
            if self.rank[x] > self.rank[y]:
                x,y = y,x
            elif self.rank[x] == self.rank[y]:
                self.rank[x] += 1
            self.g[y+1] = self.g[y+1] | self.g[x+1]
            self.gp[y+1]= self.gp[y+1]| self.gp[x+1]
            self.p[x] = y # x の親を y にする
            return True
        else:
            return False

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

def main():
    n,m = map(int,input().split())
    p = [0] + list(map(int,input().split()))

    uf = UnionFind(n,p)
    for i in range(m):
        x,y = map(int,input().split())
        uf.unite(x-1,y-1)

    parent = [False]*n
    ans = 0
    for i in range(n):
        j = uf.find(i)
        if not parent[j]:
            parent[j] = True
            ans += len(uf.g[j+1]) + len(uf.gp[j+1]) - len(uf.g[j+1] | uf.gp[j+1])
    # ans = 0
    # for j in parent:
    #     ans += len(uf.g[j+1]) + len(uf.gp[j+1]) - len(uf.g[j+1] | uf.gp[j+1])
    print(ans)
main()


Fixed submission:
class UnionFind:
    def __init__(self, n, p):
        '木の初期化をする'
        # zero-index
        self.p  = [-1] * n
        self.rank = [1]*n

    def find(self, x):
        'x の親を返す'
        if self.p[x] == -1:
            return x
        else:
            self.p[x] = self.find(self.p[x])
            return self.p[x]

    def unite(self, x, y):
        'rankの低い親を高い方のの親にする'
        if not self.same(x,y):
            x = self.find(x)
            y = self.find(y)
            if self.rank[x] > self.rank[y]:
                x,y = y,x
            elif self.rank[x] == self.rank[y]:
                self.rank[x] += 1
            self.p[x] = y # x の親を y にする
            return True
        else:
            return False

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

def main():
    n,m = map(int,input().split())
    p = list(map(int,input().split()))

    uf = UnionFind(n,p)
    for i in range(m):
        x,y = map(int,input().split())
        uf.unite(x-1,y-1)

    ans = 0
    for i,j in enumerate(p):
        ans += uf.same(i, j-1)
    print(ans)
main()

Buggy python submission (verdict: Time Limit Exceeded):
class UnionFind:
    def __init__(self, n, p):
        '木の初期化をする'
        # zero-index
        self.p  = [-1] * n
        self.rank = [1]*n
        # one -index
        self.g  = [set([i]) for i in range(n+1)]
        self.gp = [set([i]) for i in p]

    def find(self, x):
        'x の親を返す'
        if self.p[x] == -1:
            return x
        else:
            self.p[x] = self.find(self.p[x])
            return self.p[x]

    def unite(self, x, y):
        'rankの低い親を高い方のの親にする'
        if not self.same(x,y):
            x = self.find(x)
            y = self.find(y)
            if self.rank[x] > self.rank[y]:
                x,y = y,x
            elif self.rank[x] == self.rank[y]:
                self.rank[x] += 1
            self.g[y+1] = self.g[y+1] | self.g[x+1]
            self.gp[y+1]= self.gp[y+1]| self.gp[x+1]
            self.p[x] = y # x の親を y にする
            return True
        else:
            return False

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

def main():
    n,m = map(int,input().split())
    p = [0] + list(map(int,input().split()))

    uf = UnionFind(n,p)
    for i in range(m):
        x,y = map(int,input().split())
        uf.unite(x-1,y-1)

    parent = set()
    for i in range(n):
        parent.add(uf.find(i))
    ans = 0
    for i in parent:
        ans += len(uf.g[i+1]) + len(uf.gp[i+1]) - len(uf.g[i+1] | uf.gp[i+1])
    print(ans)
main()


Fixed submission:
class UnionFind:
    def __init__(self, n, p):
        '木の初期化をする'
        # zero-index
        self.p  = [-1] * n
        self.rank = [1]*n

    def find(self, x):
        'x の親を返す'
        if self.p[x] == -1:
            return x
        else:
            self.p[x] = self.find(self.p[x])
            return self.p[x]

    def unite(self, x, y):
        'rankの低い親を高い方のの親にする'
        if not self.same(x,y):
            x = self.find(x)
            y = self.find(y)
            if self.rank[x] > self.rank[y]:
                x,y = y,x
            elif self.rank[x] == self.rank[y]:
                self.rank[x] += 1
            self.p[x] = y # x の親を y にする
            return True
        else:
            return False

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

def main():
    n,m = map(int,input().split())
    p = list(map(int,input().split()))

    uf = UnionFind(n,p)
    for i in range(m):
        x,y = map(int,input().split())
        uf.unite(x-1,y-1)

    ans = 0
    for i,j in enumerate(p):
        ans += uf.same(i, j-1)
    print(ans)
main()

Buggy python submission (verdict: Time Limit Exceeded):
class UnionFind:
    def __init__(self, n):
        '木の初期化をする'
        # zero-index
        self.p  = [-1] * n
        self.rank = [1]*n
        # one -index
        # self.g  = [set([i]) for i in range(n+1)]
        # self.gp = [set([i]) for i in p]

    def find(self, x):
        'x の親を返す'
        if self.p[x] == -1:
            return x
        else:
            self.p[x] = self.find(self.p[x])
            return self.p[x]

    def unite(self, x, y):
        'rankの低い親を高い方のの親にする'
        if not self.same(x,y):
            x = self.find(x)
            y = self.find(y)
            if self.rank[x] > self.rank[y]:
                x,y = y,x
            elif self.rank[x] == self.rank[y]:
                self.rank[x] += 1
            # self.g[y+1] = self.g[y+1] | self.g[x+1]
            # self.gp[y+1]= self.gp[y+1]| self.gp[x+1]
            self.p[x] = y # x の親を y にする
            return True
        else:
            return False

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

def main():
    n,m = map(int,input().split())
    p = [set([int(i)]) for i in input().split()]
    r = [set([int(i)]) for i in range(1,n+1)]
    uf = UnionFind(n)
    for i in range(m):
        x,y = map(int,input().split())
        uf.unite(x-1,y-1)
    parent = set()
    for i in range(n):
        parent.add(uf.find(i))
        p[uf.find(i)] = p[uf.find(i)] | p[i]
        r[uf.find(i)] = r[uf.find(i)] | r[i]

    ans = 0
    for i in parent:
        ans += len(p[i]) + len(r[i]) - len(p[i] | r[i])
    print(ans)
main()


Fixed submission:
class UnionFind:
    def __init__(self, n, p):
        '木の初期化をする'
        # zero-index
        self.p  = [-1] * n
        self.rank = [1]*n

    def find(self, x):
        'x の親を返す'
        if self.p[x] == -1:
            return x
        else:
            self.p[x] = self.find(self.p[x])
            return self.p[x]

    def unite(self, x, y):
        'rankの低い親を高い方のの親にする'
        if not self.same(x,y):
            x = self.find(x)
            y = self.find(y)
            if self.rank[x] > self.rank[y]:
                x,y = y,x
            elif self.rank[x] == self.rank[y]:
                self.rank[x] += 1
            self.p[x] = y # x の親を y にする
            return True
        else:
            return False

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

def main():
    n,m = map(int,input().split())
    p = list(map(int,input().split()))

    uf = UnionFind(n,p)
    for i in range(m):
        x,y = map(int,input().split())
        uf.unite(x-1,y-1)

    ans = 0
    for i,j in enumerate(p):
        ans += uf.same(i, j-1)
    print(ans)
main()

Buggy python submission (verdict: Time Limit Exceeded):
class UnionFind:
    def __init__(self, n):
        '木の初期化をする'
        # zero-index
        self.p  = [-1] * n
        self.rank = [1]*n
        # one -index
        # self.g  = [set([i]) for i in range(n+1)]
        # self.gp = [set([i]) for i in p]

    def find(self, x):
        'x の親を返す'
        if self.p[x] == -1:
            return x
        else:
            self.p[x] = self.find(self.p[x])
            return self.p[x]

    def unite(self, x, y):
        'rankの低い親を高い方のの親にする'
        if not self.same(x,y):
            x = self.find(x)
            y = self.find(y)
            if self.rank[x] > self.rank[y]:
                x,y = y,x
            elif self.rank[x] == self.rank[y]:
                self.rank[x] += 1
            # self.g[y+1] = self.g[y+1] | self.g[x+1]
            # self.gp[y+1]= self.gp[y+1]| self.gp[x+1]
            self.p[x] = y # x の親を y にする
            return True
        else:
            return False

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


n,m = map(int,input().split())
p = [set([int(i)]) for i in input().split()]
r = [set([int(i)]) for i in range(1,n+1)]
uf = UnionFind(n)
for i in range(m):
    x,y = map(int,input().split())
    uf.unite(x-1,y-1)
parent = set()
for i in range(n):
    parent.add(uf.find(i))
    p[uf.find(i)] = p[uf.find(i)] | p[i]
    r[uf.find(i)] = r[uf.find(i)] | r[i]

ans = 0
for i in parent:
    ans += len(p[i]) + len(r[i]) - len(p[i] | r[i])
print(ans)


Fixed submission:
class UnionFind:
    def __init__(self, n, p):
        '木の初期化をする'
        # zero-index
        self.p  = [-1] * n
        self.rank = [1]*n

    def find(self, x):
        'x の親を返す'
        if self.p[x] == -1:
            return x
        else:
            self.p[x] = self.find(self.p[x])
            return self.p[x]

    def unite(self, x, y):
        'rankの低い親を高い方のの親にする'
        if not self.same(x,y):
            x = self.find(x)
            y = self.find(y)
            if self.rank[x] > self.rank[y]:
                x,y = y,x
            elif self.rank[x] == self.rank[y]:
                self.rank[x] += 1
            self.p[x] = y # x の親を y にする
            return True
        else:
            return False

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

def main():
    n,m = map(int,input().split())
    p = list(map(int,input().split()))

    uf = UnionFind(n,p)
    for i in range(m):
        x,y = map(int,input().split())
        uf.unite(x-1,y-1)

    ans = 0
    for i,j in enumerate(p):
        ans += uf.same(i, j-1)
    print(ans)
main()

Buggy python submission (verdict: Time Limit Exceeded):
class UnionFind:
    def __init__(self, n, p):
        '木の初期化をする'
        # zero-index
        self.p  = [-1] * n
        self.rank = [1]*n
        # one -index
        self.g  = [set([i]) for i in range(n+1)]
        self.gp = [set([i]) for i in p]

    def find(self, x):
        'x の親を返す'
        if self.p[x] == -1:
            return x
        else:
            self.p[x] = self.find(self.p[x])
            return self.p[x]

    def unite(self, x, y):
        'rankの低い親を高い方のの親にする'
        if not self.same(x,y):
            x = self.find(x)
            y = self.find(y)
            if self.rank[x] > self.rank[y]:
                x,y = y,x
            elif self.rank[x] == self.rank[y]:
                self.rank[x] += 1
            self.g[y+1] = self.g[y+1] | self.g[x+1]
            self.gp[y+1]= self.gp[y+1]| self.gp[x+1]
            self.p[x] = y # x の親を y にする
            return True
        else:
            return False

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


n,m = map(int,input().split())
p = [0] + list(map(int,input().split()))

uf = UnionFind(n,p)
for i in range(m):
    x,y = map(int,input().split())
    uf.unite(x-1,y-1)

parent = set()
for i in range(n):
    parent.add(uf.find(i))
ans = 0
for i in parent:
    ans += len(uf.g[i+1]) + len(uf.gp[i+1]) - len(uf.g[i+1] | uf.gp[i+1])
print(ans)


Fixed submission:
class UnionFind:
    def __init__(self, n, p):
        '木の初期化をする'
        # zero-index
        self.p  = [-1] * n
        self.rank = [1]*n

    def find(self, x):
        'x の親を返す'
        if self.p[x] == -1:
            return x
        else:
            self.p[x] = self.find(self.p[x])
            return self.p[x]

    def unite(self, x, y):
        'rankの低い親を高い方のの親にする'
        if not self.same(x,y):
            x = self.find(x)
            y = self.find(y)
            if self.rank[x] > self.rank[y]:
                x,y = y,x
            elif self.rank[x] == self.rank[y]:
                self.rank[x] += 1
            self.p[x] = y # x の親を y にする
            return True
        else:
            return False

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

def main():
    n,m = map(int,input().split())
    p = list(map(int,input().split()))

    uf = UnionFind(n,p)
    for i in range(m):
        x,y = map(int,input().split())
        uf.unite(x-1,y-1)

    ans = 0
    for i,j in enumerate(p):
        ans += uf.same(i, j-1)
    print(ans)
main()

Buggy python submission (verdict: Time Limit Exceeded):
class UnionFind:
    def __init__(self, n, p):
        '木の初期化をする'
        # zero-index
        self.p  = [-1] * n
        self.rank = [1]*n
        # one -index
        self.g  = [set([i]) for i in range(n+1)]
        self.gp = [set([i]) for i in p]

    def find(self, x):
        'x の親を返す'
        if self.p[x] == -1:
            return x
        else:
            self.p[x] = self.find(self.p[x])
            return self.p[x]

    def unite(self, x, y):
        'rankの低い親を高い方のの親にする'
        if not self.same(x,y):
            x = self.find(x)
            y = self.find(y)
            if self.rank[x] > self.rank[y]:
                x,y = y,x
            elif self.rank[x] == self.rank[y]:
                self.rank[x] += 1
            self.g[y+1] = self.g[y+1] | self.g[x+1]
            self.gp[y+1]= self.gp[y+1]| self.gp[x+1]
            self.p[x] = y # x の親を y にする
            return True
        else:
            return False

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


n,m = map(int,input().split())
p = [0] + list(map(int,input().split()))

uf = UnionFind(n,p)
for i in range(m):
    x,y = map(int,input().split())
    uf.unite(x-1,y-1)

parent = set()
for i in range(n):
    parent.add(uf.find(i))
ans = 0
for i in parent:
    ans += len(uf.g[i+1]) + len(uf.gp[i+1]) - len(uf.g[i+1] | uf.gp[i+1])
print(ans)


Fixed submission:
class UnionFind:
    def __init__(self, n, p):
        '木の初期化をする'
        # zero-index
        self.p  = [-1] * n
        self.rank = [1]*n

    def find(self, x):
        'x の親を返す'
        if self.p[x] == -1:
            return x
        else:
            self.p[x] = self.find(self.p[x])
            return self.p[x]

    def unite(self, x, y):
        'rankの低い親を高い方のの親にする'
        if not self.same(x,y):
            x = self.find(x)
            y = self.find(y)
            if self.rank[x] > self.rank[y]:
                x,y = y,x
            elif self.rank[x] == self.rank[y]:
                self.rank[x] += 1
            self.p[x] = y # x の親を y にする
            return True
        else:
            return False

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

def main():
    n,m = map(int,input().split())
    p = list(map(int,input().split()))

    uf = UnionFind(n,p)
    for i in range(m):
        x,y = map(int,input().split())
        uf.unite(x-1,y-1)

    ans = 0
    for i,j in enumerate(p):
        ans += uf.same(i, j-1)
    print(ans)
main()