Problem: 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.

Examples

Input

4 1
1 3


Output

2


Input

2 0


Output

0


Input

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


Output

12

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
#define int long long
#define rep(i,n) for(int i=0;i<n;i++)
#define MOD 1000000007
#define INF 1000000000000000
#define fi first
#define se second
#define all(v) v.begin(),v.end()
int dx[]={0,1,0,-1},dy[]={1,0,-1,0};
struct edge{int to,cost;};
typedef pair<int,int> P;
int gcd(int a,int b){
	if(b==0)return a;
	return gcd(b,a%b);
}
int lcm(int a,int b){
	return a/gcd(a,b)*b;
}
bool prime(int a){
	if(a==1)return false;
	for(int i=2;i*i<=a;i++){
		if(a%i==0)return false;
	}
	return true;
}
bool kosa(double ax,double ay,double bx,double by,double cx,double cy,double dx,double dy){//線分の交差判定
	double ta=(cx-dx)*(ay-cy)+(cy-dy)*(cx-ax);
	double tb=(cx-dx)*(by-cy)+(cy-dy)*(cx-bx);
	double tc=(ax-bx)*(cy-ay)+(ay-by)*(ax-cx);
	double td=(ax-bx)*(dy-ay)+(ay-by)*(ax-dx);
	return tc*td<0&&ta*tb<0;
}
int kaijo(int n){
	int ans=1;
	for(int i=2;i<=n;i++){
		ans*=i;
		ans%=MOD;
	}
	return ans;
}
int modpow(int a,int b){
	if(b==0)return 1;
	if(b%2)return modpow(a,b-1)*a%MOD;
	return modpow(a,b/2)*modpow(a,b/2)%MOD;
}
int comb(int a,int b){
	return kaijo(a)*modpow(kaijo(a-b),MOD-2)%MOD*modpow(kaijo(b),MOD-2)%MOD;
}
int par[111111],siz[111111],n,m,a[111111],b[111111],cnt[111111];
void init(int x){
	rep(i,x){
		par[i]=i;
		siz[i]=1;
	}
}
int find(int x){
	if (par[x]==x)return x;
	return par[x]=find(par[x]);
}
void unite(int x,int y){
	x=find(x);
	y=find(y);
	if(x==y)return;
	if(siz[x]<siz[y]){
		par[x]=y;
		siz[y]+=siz[x];
	}
	else{
		par[y]=x;
		siz[x]+=siz[y];
	}
}
bool same(int x,int y) {
	return find(x)==find(y);
}
int Size(int f){
	return siz[find(f)];
}
signed main(){
	cin>>n>>m;
	init(n);
	rep(i,m){
		cin>>a[i]>>b[i];
		a[i]--,b[i]--;
		unite(a[i],b[i]);
	}
	int i=Size(0),j=Size(1),k=n-min(i,j),l=min(i,j);
	int p=k*(k-1)/2,q=l*(l-1)/2,r=p+q-m;
	cout<<r<<endl;
	return 0;
}