#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 bit_exist(x, n) ((x >> n) & 1)
#define debug(x) cout << #x << "=" << x << endl;
#define vdebug(v) cout << #v << "=" << endl; REP(i_debug, v.size()){ cout << v[i_debug] << ","; } cout << endl;
#define mdebug(m) cout << #m << "=" << endl; REP(i_debug, m.size()){ REP(j_debug, m[i_debug].size()){ cout << m[i_debug][j_debug] << ","; } cout << endl;}
#define pb push_back
#define f first
#define s second
#define int long long
#define INF 1000000000000000000
template<typename T> istream &operator>>(istream &is, vector<T> &v){ for (auto &x : v) is >> x; return is; }
template<typename T> ostream &operator<<(ostream &os, vector<T> &v){ for(int i = 0; i < v.size(); i++) { cout << v[i]; if(i != v.size() - 1) cout << endl; }; return os; }
template<typename T> void Out(T x) { cout << x << endl; }
template<typename T1, typename T2> void Ans(bool f, T1 y, T2 n) { if(f) Out(y); else Out(n); }

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>;

//int dx[4] = {1,0,-1,0};
//int dy[4] = {0,1,0,-1};
//char d[4] = {'D','R','U','L'};

const int mod = 1000000007;
//const int mod = 998244353;
#define Add(x, y) x = (x + (y)) % mod
#define Mult(x, y) x = (x * (y)) % 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, Q; cin >> N >> Q;
    vec A(Q), B(Q), C(Q);
    priority_queue<PiP, vector<PiP>, greater<PiP>> que;
    REP(i, Q){
        cin >> A[i] >> B[i] >> C[i];
        que.push(PiP(C[i], Pii(A[i], B[i])));
        que.push(PiP(C[i] + 1, Pii(B[i], (A[i] + 1) % N)));
    }
    UnionFind UF(N);
    int ans = 0;
    while(UF.union_size(0) < N){
        PiP tmp = que.top(); que.pop();
        int c = tmp.f, a = tmp.s.f, b = tmp.s.s;
        //cout << c << "," << a << "," << b << endl;
        if(!UF.is_union(a, b)){
            ans += c;
            UF.unite(a, b);
            que.push(PiP(c + 2, Pii((a + 1) % N, (b + 1) % N)));
        }
    }
    Out(ans);

    return 0;
}


Measured memory_bytes: 19436