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;
struct fast_ios { fast_ios(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_;
#define FOR(i, begin, end) for(int i=(begin);i<(end);i++)
#define REP(i, n) FOR(i,0,n)
#define IFOR(i, begin, end) for(int i=(end)-1;i>=(begin);i--)
#define IREP(i, n) IFOR(i,0,n)
#define Sort(v) sort(v.begin(), v.end())
#define Reverse(v) reverse(v.begin(), v.end())
#define all(v) v.begin(),v.end()
#define SZ(v) ((int)v.size())
#define Lower_bound(v, x) distance(v.begin(), lower_bound(v.begin(), v.end(), x))
#define Upper_bound(v, x) distance(v.begin(), upper_bound(v.begin(), v.end(), x))
#define Max(a, b) a = max(a, b)
#define Min(a, b) a = min(a, b)
#define bit(n) (1LL<<(n))
#define Ans(f, y, n) if(f) cout << y << endl; else cout << n << endl;
#define debug(x) cout << #x << "=" << x << endl;
#define vdebug(v) cout << #v << "=" << endl; REP(i, v.size()){ cout << v[i] << ","; } cout << endl;
#define mdebug(m) cout << #m << "=" << endl; REP(i, m.size()){ REP(j, m[i].size()){ cout << m[i][j] << ","; } cout << endl;}
#define pb push_back
#define f first
#define s second
#define int long long
#define INF 1000000000000000000

using vec = vector<int>;
using mat = vector<vec>;
using Pii = pair<int, int>;
using PiP = pair<int, Pii>;
using PPi = pair<Pii, int>;
using bools = vector<bool>;
using pairs = vector<Pii>;

template<typename T> void readv(vector<T> &a){ REP(i, a.size()) cin >> a[i]; }
void readv_m1(vector<int> &a){ REP(i, a.size()){cin >> a[i]; a[i]--;} }

//int dx[4] = {1,0,-1,0};
//int dy[4] = {0,1,0,-1};

int mod = 1000000007;
//int mod = 998244353;
#define Add(x, y) x = (x + (y)) % mod
#define Mult(x, y) x = (x * (y)) % mod
#define AddMult(x, y, z) x = (x + (y) * (z)) % mod

class UnionFind
{
public:
    vector<int> par;
    vector<int> sz;

    UnionFind(int N){
        par = vector<int>(N);
        REP(i, N) par[i] = i;
        sz = vector<int>(N, 1);
    }

    int find(int x){
        if(par[x] == x) return x;
        else return par[x] = find(par[x]);
    }

    void unite(int x, int y){
        x = find(x);
        y = find(y);
        if(x == y) return;

        if(sz[x] < sz[y]) swap(x, y);

        par[y] = x;
        sz[x] += sz[y];
    }

    bool is_union(int x, int y){
        x = find(x);
        y = find(y);
        return x == y;
    }

    int union_size(int x){
        return sz[find(x)];
    }

};


signed main(){

    int N, M; cin >> N >> M;
    UnionFind UF(N);
    int a, b;
    REP(i, M){
        cin >> a >> b;
        UF.unite(a - 1, b - 1);
    }
    int sz1 = UF.union_size(0), sz2 = UF.union_size(1);
    int r = N - sz1 - sz2;
    if(sz1 < sz2) swap(sz1, sz2);
    sz1 += r;
    int ans = sz1 * (sz1 - 1) / 2 + sz2 * (sz2 - 1) / 2 - M;
    cout << ans << endl;

    return 0;
}