#include <bits/stdc++.h>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/pb_ds/tree_policy.hpp>

using namespace std;
using namespace __gnu_pbds;

#define fi first
#define se second
#define mp make_pair
#define pb push_back
#define fbo find_by_order
#define ook order_of_key

typedef long long ll;
typedef pair<ll,ll> ii;
typedef vector<int> vi;
typedef long double ld; 
typedef tree<int, null_type, less<int>, rb_tree_tag, tree_order_statistics_node_update> pbds;
typedef set<int>::iterator sit;
typedef map<int,int>::iterator mit;
typedef vector<int>::iterator vit;

struct DSU
{
	int S;
	
	struct node
	{
		int p; ll sum;
	};
	vector<node> dsu;
	
	DSU(int n)
	{
		S = n;
		for(int i = 0; i < n; i++)
		{
			node tmp;
			tmp.p = i; tmp.sum = 0;
			dsu.pb(tmp);
		}
	}
	
	void reset(int n)
	{
		dsu.clear();
		S = n;
		for(int i = 0; i < n; i++)
		{
			node tmp;
			tmp.p = i; tmp.sum = 0;
			dsu.pb(tmp);
		}
	}
	
	int rt(int u)
	{
		if(dsu[u].p == u) return u;
		dsu[u].p = rt(dsu[u].p);
		return dsu[u].p;
	}
	
	void merge(int u, int v)
	{
		u = rt(u); v = rt(v);
		if(u == v) return ;
		if(rand()&1) swap(u, v);
		dsu[v].p = u;
		dsu[u].sum += dsu[v].sum;
	}
	
	bool sameset(int u, int v)
	{
		if(rt(u) == rt(v)) return true;
		return false;
	}
	
	ll getstat(int u)
	{
		return dsu[rt(u)].sum;
	}
};

struct Graph
{
	struct edge
	{
		int v; ll weight;
	};
	vector<vector<edge> > adj;
	int n;
	
	Graph(int _n)
	{
		adj.resize(_n);
		n = _n;
	}
	
	void addedge(int u, int v, ll c)
	{
		edge tmp;
		tmp.v = v; tmp.weight = c;
		adj[u].pb(tmp);
		tmp.v = u;
		adj[v].pb(tmp);
	}
	
	void reset()
	{
		adj.clear();
	}
	
	vi dist;
	vi par;
	
	void bfs(int s)
	{
		ll INFI = ll(1e18);
		dist.assign(n, INFI);
		par.assign(n, -1);
		dist[s] = 0; par[s] = -1;
		queue<int> q; q.push(s);
		while(!q.empty())
		{
			int u = q.front(); q.pop();
			for(int i = 0; i < adj[u].size(); i++)
			{
				int v = adj[u][i].v;
				if(dist[v] >= INFI)
				{
					dist[v] = dist[u] + 1;
					par[v] = u;
					q.push(v);
				}
			}
		}
	}
	
	void bfs01(int s)
	{
		ll INFI = ll(1e18);
		dist.assign(n, INFI);
		par.assign(n, -1);
		dist[s] = 0; par[s] = -1;
		deque<int> q; q.pb(s);
		while(!q.empty())
		{
			int u = q.front(); q.pop_front();
			for(int i = 0; i < adj[u].size(); i++)
			{
				int v = adj[u][i].v; ll w = adj[u][i].weight;
				if(dist[v] >= INFI)
				{
					if(w == 1)
					{
						dist[v] = dist[u] + 1;
						par[v] = u;
						q.push_back(v);
					}
					else
					{
						dist[v] = dist[u];
						par[v] = u;
						q.push_front(v);
					}
				}
			}
		}
	}
	
	void dijkstra(int s)
	{
		ll INFI = ll(1e18);
		dist.assign(n, INFI);
		par.assign(n, -1);
		dist[s] = 0; par[s] = -1;
		priority_queue<ii, vector<ii>, greater<ii> > pq;
		pq.push(ii(0, s));
		while(!pq.empty())
		{
			int u = pq.top().se; ll d = pq.top().fi; pq.pop();
			for(int i = 0; i < adj[u].size(); i++)
			{
				int v = adj[u][i].v; ll w = adj[u][i].weight;
				if(d + w < dist[v])
				{
					dist[v] = d + w;
					par[v] = u;
					pq.push(ii(dist[v], v));
				}
			}
		}
	}
	
	vector<vector<ll> > d;
	
	void Floyd()
	{
		ll INFIN = ll(1e18);
		d.resize(n);
		for(int i = 0; i < n; i++)
		{
			d[i].assign(n, INFIN);
		}
		for(int i = 0; i < n; i++)
		{
			for(int j = 0; j < adj[i].size(); j++)
			{
				d[i][adj[i][j].v] = adj[i][j].weight;
			}
			d[i][i] = 0;
		}
		for(int k = 0; k < n; k++)
		{
			for(int i = 0; i < n; i++)
			{
				for(int j = 0; j < n; j++)
				{
					d[i][j] = min(d[i][j], d[i][k] + d[k][j]);
				}
			}
		}
	}
	
	bool BellmanFord(int s) //returns true if negative weight cycle exists
	{
		ll INFI = ll(1e18);
		dist.assign(n, INFI);
		par.assign(n, -1);
		dist[s] = 0;
		for(int step = 1; step <= n; step++)
		{
			for(int i = 0; i < n; i++)
			{
				for(int j = 0; j < adj[i].size(); j++)
				{
					int u = i; int v = adj[i][j].v; ll w = adj[i][j].weight;
					if(dist[v] > dist[u] + w)
					{
						if(step == n)
						{
							return true;
						}
						dist[v] = dist[u] + w;
					}
				}
			}
		}
		return false;
	}
	
	ll shortest(int s, int e) //returns the distance by Dijkstra
	{
		return dist[e];
	}
	
	vector<pair<ll, ii> > edges;
	
	ll Kruskal()
	{
		DSU dsu(n);
		for(int i = 0; i < n; i++)
		{
			for(int j = 0; j < adj[i].size(); j++)
			{
				int u = i; int v = adj[i][j].v; ll w = adj[i][j].weight;
				edges.pb(mp(w, mp(u, v)));
			}
		}
		sort(edges.begin(), edges.end());
		ll ans = 0; int cnt = 0;
		for(int i = 0; i < edges.size(); i++)
		{
			int u = edges[i].se.fi; int v = edges[i].se.se;
			if(dsu.sameset(u, v)) continue;
			dsu.merge(u, v);
			cnt++; ans += edges[i].fi;
			if(cnt >= n - 1) break;
		}
		return ans;
	}
};

Graph G(200001);
ll cost[200001];

int main()
{
	ios_base::sync_with_stdio(0); cin.tie(0);
	int n,q;
	cin>>n>>q;
	G = Graph(n);
	for(int i = 0; i < n; i++)
	{
		cost[i] = ll(1e18);
	}
	for(int i = 0; i < q; i++)
	{
		ll s,e,c;
		cin>>s>>e>>c;
		G.addedge(s,e,c);
		cost[s]=min(cost[s],c+1);
		cost[e]=min(cost[e],c+2);
	}
	for(int i = 1; i < n; i++)
	{
		cost[i] = min(cost[i], cost[i-1]+2);
	}
	cost[0] = min(cost[0], cost[n-1]+2);
	for(int i = 1; i < n; i++)
	{
		cost[i] = min(cost[i], cost[i-1]+2);
		G.addedge(i-1,i,cost[i-1]);
	}
	G.addedge(n-1,0,cost[n-1]);
	cout<<G.Kruskal()<<'\n';
}


Measured memory_bytes: 61612