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# Strengthen It

Problem Description

You are given an undirected graph having A nodes and |B| edges, ith edge connecting nodes B[i][1] and B[i][2].

Strength of a connected component is defined as the number of edges existing in that component.

Given an integer C, you have to tell the maximum strength that a connected component in the given graph can have, if we are allowed to add exactly C edges to the graph.

Problem Constraints

1 <= A <= 105

1 <= |B| <= 2 * 105

1 <= B[i][0], B[i][1] <= A

0 <= C <= 109

Input Format

First argument is an integer A

Second argument is a 2D matrix B having size |B| X 2

Third argument is an integer C

Output Format

Return an integer denoting the maximum strength achievable in the graph.

Example Input

Input 1:

``` A = 7
B = [
[1, 2]
[2, 3]
[3, 1]
[4, 5]
[5, 6]
[6, 1]
]
C = 1```

Input 2:

``` A = 3
B = [
[1, 2]
[2, 2]
[2, 3]
[3, 1]
]
C = 2```

Example Output

Output 1:

` 7`

Output 2:

` 6`

Example Explanation

Explanation 1:

``` Initially there are 3 components in the graph.
We can add an edge between node 1 and node 4.
Now the resultant graph will have 2 components with strengths 7 and 0.
Maximum achievable strength after adding one edge = 7.```

Explanation 2:

``` The graph contains only a single component.
If we add 2 edges in the component, the strength becomes 6.```

NOTE: You only need to implement the given function. Do not read input, instead use the arguments to the function. Do not print the output, instead return values as specified. Still have a question? Checkout Sample Codes for more details.
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