Buggy python submission (verdict: Runtime Error):
#!/usr/bin/env python3
import sys
sys.setrecursionlimit(10**6)

class UnionFind:
    def __init__(self,size):
        self.size = size
        self.parents = [i for i in range(size)]
        self.ranks = [0 for i in range(size)]

    def ancestor(self,i):
        if self.parents[i] == i:
            return i
        else:
            self.parents[i] = self.ancestor(self.parents[i])
            return self.parents[i]

    def union(self,i,j):
        ip = self.ancestor(i)
        jp = self.ancestor(j)
        if ip == jp:
            return False
        else:
            if self.ranks[ip] > self.ranks[jp]:
                self.parents[jp] = ip
            else:
                self.parents[ip] = jp
                if self.ranks[ip] == self.ranks[jp]:
                    self.ranks[ip]+=1

    def same(self,i,j):
        return self.ancestor(i) == self.ancestor(j)

    def __str__(self):
        parentDict = {}
        for i in range(self.size):
            a = self.ancestor(i)
            if a not in parentDict:
                parentDict[a] = [i]
            else:
                parentDict[a].append(i)
        result = f"===UnionFind description===\nSize:{self.size}\nGroupCount:{len(parentDict)}\n\nGroups:\n"
        for k in parentDict.keys():
            elements = ""
            for elem in parentDict[k]:
                elements+= f" {elem},"
            result += f"Group-{k}(Count:{len(parentDict[k])}):[{elements}]\n"
        return result





def solve(N: int, M: int, p: "List[int]", x: "List[int]", y: "List[int]"):
    U = UnionFind(N)
    for i in range(M):
        U.union(x[i]-1,y[i]-1)
    sum = 0
    for i in range(N):
        if p[i] == i+1 or U.same(p[i]-1,i):
            sum+=1
    print(sum)
    return


# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word
    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    M = int(next(tokens))  # type: int
    p = [int(next(tokens)) for _ in range(N)]  # type: "List[int]"
    x = [int()] * (M)  # type: "List[int]"
    y = [int()] * (M)  # type: "List[int]"
    for i in range(M):
        x[i] = int(next(tokens))
        y[i] = int(next(tokens))
    solve(N, M, p, x, y)

if __name__ == '__main__':
    main()


Fixed submission:
#!/usr/bin/env python3
import sys

sys.setrecursionlimit(10 ** 6)


class UnionFind:
    def __init__(self, size):
        self.size = size
        self.parents = [i for i in range(size)]
        self.ranks = [0 for i in range(size)]

    def ancestor(self, i):
        if self.parents[i] == i:
            return i
        else:
            self.parents[i] = self.ancestor(self.parents[i])
            return self.parents[i]

    def union(self, i, j):
        ip = self.ancestor(i)
        jp = self.ancestor(j)
        if ip == jp:
            return False
        else:
            if self.ranks[ip] > self.ranks[jp]:
                self.parents[jp] = ip
            else:
                self.parents[ip] = jp
                if self.ranks[ip] == self.ranks[jp]:
                    self.ranks[ip] += 1

    def same(self, i, j):
        return self.ancestor(i) == self.ancestor(j)

    def __str__(self):
        parentDict = { }
        for i in range(self.size):
            a = self.ancestor(i)
            if a not in parentDict:
                parentDict[a] = [i]
            else:
                parentDict[a].append(i)
        result = "===UnionFind description===\nSize:" + str(self.size) + "\nGroupCount:" + str(
            len(parentDict)) + "\n\nGroups:\n"
        for k in parentDict.keys():
            elements = ""
            for elem in parentDict[k]:
                elements += " " + str(elem) + ","
            result += "Group-"+str(k)+"(Count:"+str(len(parentDict[k]))+"):["+elements+"]\n"
        return result


def solve(N: int, M: int, p: "List[int]", x: "List[int]", y: "List[int]"):
    U = UnionFind(N)
    for i in range(M):
        U.union(x[i] - 1, y[i] - 1)
    sum = 0
    for i in range(N):
        if p[i] == i + 1 or U.same(p[i] - 1, i):
            sum += 1
    print(sum)
    return


# Generated by 1.1.6 https://github.com/kyuridenamida/atcoder-tools  (tips: You use the default template now. You can remove this line by using your custom template)
def main():
    def iterate_tokens():
        for line in sys.stdin:
            for word in line.split():
                yield word

    tokens = iterate_tokens()
    N = int(next(tokens))  # type: int
    M = int(next(tokens))  # type: int
    p = [int(next(tokens)) for _ in range(N)]  # type: "List[int]"
    x = [int()] * (M)  # type: "List[int]"
    y = [int()] * (M)  # type: "List[int]"
    for i in range(M):
        x[i] = int(next(tokens))
        y[i] = int(next(tokens))
    solve(N, M, p, x, y)


if __name__ == '__main__':
    main()