Idempotent functions

Description:

Input:

In the first line of the input there is a single integer n (1 ≤ n ≤ 200) — the size of function f domain.

In the second line follow f(1), f(2), ..., f(n) (1 ≤ f(i) ≤ n for each 1 ≤ i ≤ n), the values of a function.

Output:

Output minimum k such that function f^(k)(x) is idempotent.

Sample Input:

4
1 2 2 4

Sample Output:

1

Sample Input:

3
2 3 3

Sample Output:

2

Sample Input:

3
2 3 1

Sample Output:

3

Note:

In the first sample test function f(x) = f⁽¹⁾(x) is already idempotent since f(f(1)) = f(1) = 1, f(f(2)) = f(2) = 2, f(f(3)) = f(3) = 2, f(f(4)) = f(4) = 4.

In the second sample test:

• function f(x) = f⁽¹⁾(x) isn't idempotent because f(f(1)) = 3 but f(1) = 2;
• function f(x) = f⁽²⁾(x) is idempotent since for any x it is true that f⁽²⁾(x) = 3, so it is also true that f⁽²⁾(f⁽²⁾(x)) = 3.

In the third sample test:

• function f(x) = f⁽¹⁾(x) isn't idempotent because f(f(1)) = 3 but f(1) = 2;
• function f(f(x)) = f⁽²⁾(x) isn't idempotent because f⁽²⁾(f⁽²⁾(1)) = 2 but f⁽²⁾(1) = 3;
• function f(f(f(x))) = f⁽³⁾(x) is idempotent since it is identity function: f⁽³⁾(x) = x for any meaning that the formula f⁽³⁾(f⁽³⁾(x)) = f⁽³⁾(x) also holds.