Score : 400 points
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:
Find the maximum possible number of i such that p_i = i after operations.
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
Print the maximum possible number of i such that p_i = i after operations.
5 2 5 3 1 4 2 1 3 5 4
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.
3 2 3 2 1 1 2 2 3
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.
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
8
5 1 1 2 3 4 5 1 5
5
We do not have to perform the operation.