### Background

We remind that the permutation of some final set is a one-to-one mapping of the set onto itself. Less formally, that is a way to reorder elements of the set. For example, one can define a permutation of the set {1,2,3,4,5} as follows:

This record defines a permutation P as follows: P(1) = 4, P(2) = 1, P(3) = 5, etc.

What is the value of the expression P(P(1))? It’s clear, that P(P(1)) = P(4) = 2. And P(P(3)) = P(5) = 3. One can easily see that if P(*n*) is a permutation then P(P(*n*)) is a permutation as well. In our example (check it by yourself)

It is natural to denote this permutation by P^{2}(*n*) = P(P(*n*)). In a general form the definition is as follows: P(*n*) = P^{1}(*n*), P^{k}(*n*) = P(P^{k-1}(*n*)).

Among the permutations there is a very important one — that moves nothing:

It is clear that for every *k* the following relation is satisfied: (E_{N})^{k} = E_{N}. The following less trivial statement is correct (we won’t prove it here, you may prove it yourself incidentally):

*Let P(**n*) be some permutation of an N elements set. Then there exists a positive integer *k*, that P^{k} = E_{N}.

The least positive integer *k* such that P^{k} = E_{N} is called an order of the permutation P.

### Problem

The problem that your program should solve is formulated now in a very simple manner: *“Given a permutation find its order.”*

### Input

The first line contains the only integer *N* (1 ≤ *N* ≤ 1000), that is a number of elements in the set that is rearranged by this permutation. In the second line there are *N* integers of the range from 1 up to *N*, separated by a space, that define a permutation — the numbers P(1), P(2),…, P(*N*).

### Output

You should write the order of the permutation. You may consider that an answer shouldn’t exceed 10^{9}.

### Sample

**Problem Author: **Nikita Shamgunov

**Problem Source: **Ural State University Internal Contest October'2000 Junior Session