Problem:
Score : 100 points

Problem Statement

You are given an undirected graph G. G has N vertices and M edges. The vertices are numbered from 1 through N, and the i-th edge (1 ≤ i ≤ M) connects Vertex a_i and b_i. G does not have self-loops and multiple edges.

You can repeatedly perform the operation of adding an edge between two vertices. However, G must not have self-loops or multiple edges as the result. Also, if Vertex 1 and 2 are connected directly or indirectly by edges, your body will be exposed to a voltage of 1000000007 volts. This must also be avoided.

Under these conditions, at most how many edges can you add? Note that Vertex 1 and 2 are never connected directly or indirectly in the beginning.

Constraints

2 ≤ N ≤ 10^5

0 ≤ M ≤ 10^5

1 ≤ a_i < b_i ≤ N

All pairs (a_i, b_i) are distinct.

Vertex 1 and 2 in G are not connected directly or indirectly by edges.

Input

Input is given from Standard Input in the following format:

N M
a_1 b_1
:
a_M b_M

Output

Print the maximum number of edges that can be added.

Sample Input 1

4 1
1 3

Sample Output 1

2

As shown above, two edges can be added. It is not possible to add three or more edges.

Sample Input 2

2 0

Sample Output 2

0

No edge can be added.

Sample Input 3

9 6
1 4
1 8
2 5
3 6
4 8
5 7

Sample Output 3

12

Solution in PyPy3 (2.4.0) (judge verdict: Runtime Error)

n, m = [ int(v) for v in input().split() ]
connect_list = [ [] for i in range(n) ]
for i in range(m):
    a, b = [ int(v)-1 for v in input().split() ]
    connect_list[a].append(b)
    connect_list[b].append(a)


def dfs(a):
    color = [ 0 for i in range(n) ]
    color[a] = 1
    stack = collections.deque([a])
    r = 0

    while stack:
        s = stack.pop()
        color[s] = 2
        r += 1
        for i in connect_list[s]:
            if color[i] == 0:
                color[i] = 1
                stack.append(i)
    return r

x, y = dfs(0), dfs(1)
x, y = max(x, y), min(x, y)

def part_edge(a):
    return a*(a-1)//2

x = n - y
total_edge = part_edge(x) + part_edge(y)
print(total_edge-m)