Problem:


Score : 400 points

Problem Statement

We have a permutation of the integers from 1 through N, p_1, p_2, .., p_N.
We also have M pairs of two integers between 1 and N (inclusive), represented as (x_1,y_1), (x_2,y_2), .., (x_M,y_M).
AtCoDeer the deer is going to perform the following operation on p as many times as desired so that the number of i (1 ≤ i ≤ N) such that p_i = i is maximized:

Choose j such that 1 ≤ j ≤ M, and swap p_{x_j} and p_{y_j}.

Find the maximum possible number of i such that p_i = i after operations.

Constraints

2 ≤ N ≤ 10^5

1 ≤ M ≤ 10^5

p is a permutation of integers from 1 through N.

1 ≤ x_j,y_j ≤ N

x_j ≠ y_j

If i ≠ j, \{x_i,y_i\} ≠ \{x_j,y_j\}.

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N M
p_1 p_2 .. p_N
x_1 y_1
x_2 y_2
:
x_M y_M

Output

Print the maximum possible number of i such that p_i = i after operations.

Sample Input 1

5 2
5 3 1 4 2
1 3
5 4

Sample Output 1

2

If we perform the operation by choosing j=1, p becomes 1 3 5 4 2, which is optimal, so the answer is 2.

Sample Input 2

3 2
3 2 1
1 2
2 3

Sample Output 2

3

If we perform the operation by, for example, choosing j=1, j=2, j=1 in this order, p becomes 1 2 3, which is obviously optimal.
Note that we may choose the same j any number of times.

Sample Input 3

10 8
5 3 6 8 7 10 9 1 2 4
3 1
4 1
5 9
2 5
6 5
3 5
8 9
7 9

Sample Output 3

8

Sample Input 4

5 1
1 2 3 4 5
1 5

Sample Output 4

5

We do not have to perform the operation. 



Sample input:
5 2
5 3 1 4 2
1 3
5 4


Sample output:
2

Submission status: Runtime Error

Solution code:
n,m = map(int,input().split())
p = list(map(int, input().split()))
g = [[] for _ in range(0,n+1)]
visit = [None] * (n+1)
ans = 0
for _ in range(0,m):
    x,y = map(int, input().split())
    g[x].append(y)
    g[y].append(x)
for i in range(1,n+1):
    if visit[i] is not None:
        continue
    stack = [i]
    part = [i]
    visit[i] = 0
    while len(stack) > 0:
        q = stack.pop()
        for qq in g[q]:
            if visit[qq] is None:
                visit[qq] = 0
                part.append(qq)
                stack.append(qq)
    if len(part) >= 2:
        part2 = []
        for i in part:
            part2.append(p[i-1])
        for i in part:
            if i in part2:
                ans += 1
    else:
        if(i == p[i] - 1):
            ans += 1
print(ans)

Submission status: Runtime Error

Solution code:
n,m = map(int,input().split())
ps = list(map(int,input().split()))
lis = [[] for i in range(n)]
for i in range(m):
    tmp = list(map(int,input().split()))
    lis[tmp[0]-1].append(tmp[1])
    lis[tmp[1]-1].append(tmp[0])

def bfs(graph, start):
    queue = [start]
    visited = []
    while queue:
        label = queue.pop(0)
        if label not in visited:
            visited.append(label)
            queue += [x for x in graph[label - 1] if x not in visited]
    all_visited += visited
    return visited

all_visited = []
an = [bfs(lis,1)]
all_visited = [bfs(lis,1)]

for i in range(2,n+1):
    flag = True
    for j in an:
        if i in j:
            flag = False
            break
    if flag:
        an += [bfs(lis,i)]


ans = 0
for i in range(n):
    for j in range(len(an)):
        if (i+1) in an[j] and ps[(i)] in an[j]:
            ans += 1
            break
print(ans)

Submission status: Runtime Error

Solution code:
# n = int(input())
# a, b = map(int, input().split())
# c = list(map(int, input().split()))
# d = [list(map(int, input().split())) for _ in range(n)]



N, M = map(int, input().split())
p = list(map(int, input().split()))
swap = [list(map(int, input().split())) for _ in range(M)]
group = []
find = False

for swap_i in swap:
    find = False
    for group_i in group:
        if swap_i[0] in group_i:
            group_i.add(swap_i[1])
            find = True
        elif swap_i[1] in group_i:
            group_i.add(swap_i[0])
            find = True
        if find:
            break
    if find:
        continue
    else:
        tmp = set()
        tmp.add(swap_i[0])
        tmp.add(swap_i[1])
        group.append(tmp)


for i in range(1, N+1):
    findednot = True
    for group_i in group:
        if i in group_i:
            findednot = False
            break
    if findednot:
        tmp = set()
        tmp.add(i)
        group.append(tmp)
        
tmp_set = 0
for i in range(1, N + 1):
    sttt = False
    for j in range(len(group)):
        if sttt and i in group[j]:
             group[tmp_set] += group[j]
        if i in group[j]:
            tmp_set = j
            sttt = True
    
    
        

ans = 0

for i in range(1, N+1):
    for group_i in group:
        if i in group_i:
            if p[i-1] in group_i:
                ans += 1



for group_i in group:
    print(group_i)
print(ans)

Submission status: Runtime Error

Solution code:
string = input()
k = int(input())
if len(string) >= k:
    substrs = set()
    ls = sorted(list(string))
    for i in range(k):
        for s, c in enumerate(string):
            if c == ls[i]:
                for l in range(1, k+1):
                    substrs.add(string[s:s+l])
    substrs = list(substrs)
    substrs.sort()
    print(substrs[k-1])

else:
    substrs = set()
    for leng in range(1, len(string)+1):
        for s in range(0, len(string) - leng+1):
            substrs.add(string[s:s+leng])
    substrs = list(substrs)
    substrs.sort()
    print(substrs[k-1])

Submission status: Runtime Error

Solution code:
import sys
sys.setrecursionlimit(1000)

n, m = map(int, input().split())
p = [int(x) - 1 for x in input().split()]
g = [list() for _ in range(n)]
for _ in range(m):
    u, v = map(int, input().split())
    u -= 1
    v -= 1
    g[u].append(v)
    g[v].append(u)
v = [False] * n
s = set()
def dfs(i):
    if v[i]: return
    s.add(i)
    v[i] = True
    for k in g[i]: dfs(k)

c = 0
for i in range(n):
    if v[i]: continue
    s = set()
    dfs(i)
    t = {p[k] for k in s}
    c += len(s.intersection(t))
print(c)