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A. Pavel and barbecue

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputPavel 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 2*n* 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* ≥ 2*n*), so that after *k* seconds each skewer visits each of the 2*n* 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 2*n* 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.

Codeforces (c) Copyright 2010-2021 Mike Mirzayanov

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