#include <cstdlib>
#include <cmath>
#include <climits>
#include <cfloat>
#include <map>
#include <set>
#include <iostream>
#include <string>
#include <vector>
#include <algorithm>
#include <sstream>
#include <complex>
#include <stack>
#include <queue>
#include <cstdio>
#include <cstring>
#include <iterator>
#include <bitset>
#include <unordered_set>
#include <unordered_map>
#include <fstream>
#include <iomanip>
#include <cassert>
//#include <utility>
//#include <memory>
//#include <functional>
//#include <deque>
//#include <cctype>
//#include <ctime>
//#include <numeric>
//#include <list>
//#include <iomanip>

//#if __cplusplus >= 201103L
//#include <array>
//#include <tuple>
//#include <initializer_list>
//#include <forward_list>
//
//#define cauto const auto&
//#else

//#endif

using namespace std;


typedef long long ll;
typedef pair<int, int> pii;
typedef pair<ll, ll> pll;

typedef vector<int> vint;
typedef vector<vector<int> > vvint;
typedef vector<long long> vll, vLL;
typedef vector<vector<long long> > vvll, vvLL;

#define VV(T) vector<vector< T > >

template <class T>
void initvv(vector<vector<T> > &v, int a, int b, const T &t = T()) {
	v.assign(a, vector<T>(b, t));
}

template <class F, class T>
void convert(const F &f, T &t) {
	stringstream ss;
	ss << f;
	ss >> t;
}

#undef _P
#define _P(...) (void)printf(__VA_ARGS__)
#define reep(i,a,b) for(int i=(a);i<(b);++i)
#define rep(i,n) reep((i),0,(n))
#define ALL(v) (v).begin(),(v).end()
#define PB push_back
#define F first
#define S second
#define mkp make_pair
#define RALL(v) (v).rbegin(),(v).rend()
#define DEBUG
#ifdef DEBUG
#define dump(x)  cout << #x << " = " << (x) << endl;
#define debug(x) cout << #x << " = " << (x) << " (L" << __LINE__ << ")" << " " << __FILE__ << endl;
#else
#define dump(x)
#define debug(x)
#endif

#define MOD 1000000007LL
#define EPS 1e-8
#define INF 0x3f3f3f3f
#define INFL 0x3f3f3f3f3f3f3f3fLL
#define maxs(x,y) x=max(x,y)
#define mins(x,y) x=min(x,y)

class UF {
public:
	static const int ufmax = 200052;
	int ufpar[ufmax], ufrank[ufmax], ufcnt[ufmax];
	UF() { init();}
	void init() {int i; rep(i, ufmax) { ufpar[i] = i; ufrank[i] = 0; ufcnt[i] = 1; } }
	int find(int x) {	return (ufpar[x] == x) ? (x) : (ufpar[x] = find(ufpar[x]));}
	int operator[](int x) {return find(x);}
	int count(int x) {return ufcnt[find(x)];}
	void unite(int x, int y) {
		x = find(x); y = find(y);
		if(x == y) return;
		if(ufrank[x] < ufrank[y]) ufpar[x] = y, ufcnt[y] += ufcnt[x];
		else {ufpar[y] = x; ufcnt[x] += ufcnt[y]; if(ufrank[x] == ufrank[y]) ufrank[x]++;}
	}
};


void mainmain() {
	int n;
	cin >> n;
	int Q;
	cin >> Q;
	typedef pair<int, pii> P;
	vector<P> v(Q);
	vll dp(n, INFL);
	rep(i, Q) {
		cin >> v[i].S.F >> v[i].S.S >> v[i].F;
		mins(dp[v[i].S.F], v[i].F + 1LL);
		mins(dp[v[i].S.S], v[i].F + 2LL);
	}
	rep(i, n) {
		int t = (i + 1) % n;
		mins(dp[t], dp[i] + 2);
	}
	rep(i, n) {
		int t = (i + 1) % n;
		mins(dp[t], dp[i] + 2);
	}
	UF uf;
	priority_queue<P> pq;
	rep(i, n) {
		pq.push(mkp(-dp[i], pii(i, (i + 1) % n)));
	}
	rep(i, Q) {
		P t = v[i];
		t.F *= -1;
		pq.push(t);
	}
	ll ans = 0;
	while(pq.size()) {
		P top = pq.top();
		pq.pop();
		if(uf[top.S.F] == uf[top.S.S]) continue;
		ans += -top.F;
		uf.unite(top.S.F, top.S.S);
	}
	cout << ans << endl;
}


signed main() {
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	cout << fixed << setprecision(20);
	mainmain();
}

Measured memory_bytes: 12912