There are great quantity of planets in the Magic Galaxy, and each planet has a unique number from 1,2,3,4,... and so on. Each planet is connected to other planets through some transmission channels. Each transmission channel connects two different planets, and we suppose that each transmission channel is undirected (with no direction).
Little Gyro is also a fan of science fiction. In the Magic Galaxy, Little Gyro wants to reconnect these planets and build his own galaxy by doing the following steps:
1. At first, Little Gyro disconnect all the transmission channels which already connected.
2. Then, given a integer set A which size is n, which contains n integers. In the galaxy, Little Gyro will connect planet i and planet j with a transmission channel, if and only if i and j satisfied | i - j | ∈ A, so that Little Gyro may construct his galaxy into a Bipartite Network Structure.
3. However, Little Gyro considers the figure of his galaxy is not magic, After that, Little Gyro will delete the minimum number of connected planets to break the Bipartite Network Structure.
Now given the set A with n integers, Little Gyro wants to know the minimum number of all the deleted planets.
Note: Bipartite Network Structure is an undirected network, If the Magic Galaxy can be divided into two disjoint planet areas (A, B), and for every two planets i and j associated with the transmission channel (i, j) belonging to the two different planet areas (i ∈ A, j ∈ B) respectively, then call the network as a Bipartite Network Structure. And the Bipartite Network Structure should not exists a circle consisting of odd number of planets.

Each input file only contains one test case.
The first line contains an integer n (1 ≤ n ≤ 2×), indicating the size of the set A.
The second line contains n integers  (1 ≤  ≤ ), indicating the given set.

For each test case output an integer indicating the number of all the deleted planets at least.

5
1 2 3 4 5

2

2
1 3

0