A10686. Pavel and barbecue

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 $n$ .

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.

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.

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 $1$ .