Pavel cooks barbecue. There are n skewers, they lay on a brazier in a row, each on one of n positions. Pavel wants each skewer to be cooked some time in every of n positions in two directions: in the one it was directed originally and in the reversed direction.

Pavel has a plan: a permutation p and a sequence b_1, b_2, ..., b_{n}, consisting of zeros and ones. Each second Pavel move skewer on position i to position p_{i}, and if b_{i} equals 1 then he reverses it. So he hope that every skewer will visit every position in both directions.

Unfortunately, not every pair of permutation p and sequence b suits Pavel. What is the minimum total number of elements in the given permutation p and the given sequence b he needs to change so that every skewer will visit each of 2n placements? Note that after changing the permutation should remain a permutation as well.

There is no problem for Pavel, if some skewer visits some of the placements several times before he ends to cook. In other words, a permutation p and a sequence b suit him if there is an integer k (k ≥ 2n), so that after k seconds each skewer visits each of the 2n placements.

It can be shown that some suitable pair of permutation p and sequence b exists for any n.

-----Input-----

The first line contain the integer n (1 ≤ n ≤ 2·10^5) — the number of skewers.

The second line contains a sequence of integers p_1, p_2, ..., p_{n} (1 ≤ p_{i} ≤ n) — the permutation, according to which Pavel wants to move the skewers.

The third line contains a sequence b_1, b_2, ..., b_{n} consisting of zeros and ones, according to which Pavel wants to reverse the skewers.

-----Output-----

Print single integer — the minimum total number of elements in the given permutation p and the given sequence b he needs to change so that every skewer will visit each of 2n placements.

-----Examples-----

Input 4 4 3 2 1 0 1 1 1

Output 2

Input 3 2 3 1 0 0 0

Output 1

-----Note-----

In the first example Pavel can change the permutation to 4, 3, 1, 2.

In the second example Pavel can change any element of b to 1.