The encyclopedia consists of N different web pages, numbered from 1 to N. There are M links present across the pages, the ith of which is present on page A[i] and links to a different page B[i].

A page may include multiple links, including multiple leading to the same other page.

A session spent on this website involves beginning on one of the N pages, and then navigating around using the links until you decide to stop. That is, while on page i, you may either move to any of the pages linked to from it, or stop your browsing session.

Assuming you can choose which page you begin the session on, what's the maximum number of different pages you can visit in a single session? Note that a page only counts once even if visited multiple times during the session.

Constraints:
2 <= N <= 500000
1 <= M <= 500000
1 <= A[i], B[i] <= N
A[i] != B[i]

Sample Test Case #1
N = 5
M = 6
A = [3, 5, 3, 1, 3, 2]
B = [2, 1, 2, 4, 5, 4]
Expected Return Value = 4

Sample Test Case #2
N = 10
M = 9
A = [3, 2, 5, 9, 10, 3, 3, 9, 4]
B = [9, 5, 7, 8, 6, 4, 5, 3, 9]
Expected Return Value = 5

Sample Explanation
In the first case, you can only visit at most 4 different page. For example, the sequence of pages 3 --> 5 --> 1 --> 4.
In the third case, you can only visit at most 5 different pages -− for example, the sequence of pages 3 --> 4 --> 9 --> 3 --> 5 --> 7 (note that page 3 only counts once).

The main difficulty in this problem is that the graph can be cyclic so I am not sure if DP can be applied.