#include <bits/stdc++.h>
#include <unistd.h>

using namespace std;

#define DEBUG(x) cerr<<#x<<": "<<x<<endl;
#define DEBUG_VEC(v) cerr<<#v<<":";for(int i=0;i<v.size();i++) cerr<<" "<<v[i]; cerr<<endl
#define DEBUG_MAT(v) cerr<<#v<<endl;for(int i=0;i<v.size();i++){for(int j=0;j<v[i].size();j++) {cerr<<v[i][j]<<" ";}cerr<<endl;}


typedef long long ll;
#define vi vector<int>
#define vl vector<ll>
#define vii vector< vector<int> >
#define vll vector< vector<ll> >
#define vs vector<string>
#define pii pair<int,int>
#define pis pair<int,string>
#define psi pair<string,int>
#define pll pair<ll,ll>
template<class S, class T> pair<S, T> operator+(const pair<S, T> &s, const pair<S, T> &t) { return pair<S, T>(s.first + t.first, s.second + t.second); }
template<class S, class T> pair<S, T> operator-(const pair<S, T> &s, const pair<S, T> &t) { return pair<S, T>(s.first - t.first, s.second - t.second); }
template<class S, class T> ostream& operator<<(ostream& os, pair<S, T> p) { os << "(" << p.first << ", " << p.second << ")"; return os; }
#define X first
#define Y second
#define rep(i,n) for(int i=0;i<(n);i++)
#define rep1(i,n) for(int i=1;i<=(n);i++)
#define rrep(i,n) for(int i=(n)-1;i>=0;i--)
#define rrep1(i,n) for(int i=(n);i>0;i--)
#define REP(i,a,b) for(int i=a;i<b;i++)
#define in(x, a, b) (a <= x && x < b)
#define all(c) c.begin(),c.end()
template<class T> bool chmax(T &a, const T &b) { if (a<b) { a = b; return 1; } return 0; }
template<class T> bool chmin(T &a, const T &b) { if (a>b) { a = b; return 1; } return 0; }
#define UNIQUE(v) v.erase(std::unique(v.begin(), v.end()), v.end());
const ll inf = 1000000001;
const ll INF = (ll)1e18 + 1;
//const ll MOD = 1000000007;
const ll MOD = 998244353;
const double pi = 3.14159265358979323846;
#define Sp(p) cout<<setprecision(15)<< fixed<<p<<endl;
int dx[4] = { -1,0, 1,0 }, dy[4] = { 0,1,0,-1 };
int dx2[8] = { 1,1,0,-1,-1,-1,0,1 }, dy2[8] = { 0,1,1,1,0,-1,-1,-1 };
#define fio() cin.tie(0); ios::sync_with_stdio(false);
// #define mp make_pair
//#define endl '\n'


class UnionFind {
public:
  int n;
  vi par; //親
  vi ran; //木の深さ
  vi num; //要素数
  int g; // group数
 
  UnionFind(int _n) {
    n = _n;
    g = n;
    par.resize(n); ran.resize(n); num.resize(n);
    for (int i = 0; i < n; i++) {
      par[i] = i; ran[i] = 0; num[i] = 1;
    }
  }
 
  //木の根を求める
  int find(int x) {
    if (par[x] == x) {
      return x;
    }
    else {
      return par[x] = find(par[x]);
    }
  }
 
  //xとyの属する集合を併合
  void unite(int x, int y) {
    x = find(x); y = find(y);
    int numsum = num[x] + num[y];
    if (x == y) {
      return;
    }
    if (ran[x]<ran[y]) {
      par[x] = y;
    }
    else {
      par[y] = x;
      if (ran[x] == ran[y]) {
        ran[x]++;
      }
    }
    num[x] = num[y] = numsum;
    g--;
  }
 
  //xとyが同じ集合に属するか否か
  bool same(int x, int y) {
    return find(x) == find(y);
  }
 
};


int main() {
  using P = pair<ll, pii>;
  priority_queue<P, vector<P>, greater<P>> pq;
  
  int n, q;
  cin >> n >> q;
  rep (i, q) {
    int u, v, c;
    cin >> u >> v >> c;
    if (u != v) {
      pq.push(P(c, pii(u, v)));
    }
    u++; u %= n; c++;
    if (u != v) {
      pq.push(P(c, pii(u, v)));
    }
  }

  UnionFind uf(n);
  ll ans = 0;
  while (uf.g != 1) {
    P now = pq.top();
    pq.pop();
    ll cost = now.first;
    int u = now.second.first;
    int v = now.second.second;
    if (uf.same(u, v)) continue;
    uf.unite(u, v);
    ans += cost;
    pq.push(P(cost + 2, pii((u + 1) % n, (v + 1) % n)));
  }
  cout << ans << endl;
}


Measured memory_bytes: 10728