#include <bits/stdc++.h>
using namespace std;
#define ll long long
#define inf 0x3f3f3f3f
#define ri register int
#define il inline
#define fi first
#define se second
#define mp make_pair
#define pi pair<int,int>
#define mem0(x) memset((x),0,sizeof (x))
#define mem1(x) memset((x),0x3f,sizeof (x))
#define pb push_back
#define gc getchar
template<class T>void in(T &x)
{
x = 0; bool f = 0; char c = gc();
while (c < '0' || c > '9') {if (c == '-') f = 1; c = gc();}
while ('0' <= c && c <= '9') {x = (x << 3) + (x << 1) + (c ^ 48); c = gc();}
if (f) x = -x;
}
#undef gc
#define N 200010
#define M N<<3
#define int ll
struct Edge {
int u, v, w, nx;
Edge() {}
Edge(int uu, int vv, int ww, int nxt) {
u = uu, v = vv, w = ww, nx = nxt;
}
friend bool operator<(const Edge& a, const Edge& b) {
return a.w < b.w;
}
} edge[M];
int cnt, head[M];
il void add(int u, int v, int w) {
edge[++cnt] = Edge(u, v, w, head[u]);
head[u] = cnt;
}
int f[N];
int find(int x) {
return x == f[x] ? x : f[x] = find(f[x]);
}
bool cmpy(int x, int y) {
int fx = find(x), fy = find(y);
if (fx == fy) return 0;
if (fy > fx) f[fy] = fx;
else f[fx] = fy;
return 1;
}
int n, q;
int d[N];
signed main() {
in(n), in(q);
mem1(d);
for (ri i = 1, a, b, c; i <= q; ++i) {
in(a), in(b), in(c);
add(a, b, c);
d[a] = min(d[a], c + 1);
d[b] = min(d[b], c + 2);
}
for (ri i = 0; i < n; ++i) {
d[i] = min(d[i], d[(i - 1 + n) % n] + 2);
}
for (ri i = 0; i < n; ++i) {
d[i] = min(d[i], d[(i - 1 + n) % n] + 2);
}
for (ri i = 0; i <= n; ++i) {
add(i, (i + 1) % n, d[i]);
}
sort(edge + 1, edge + 1 + cnt);
for (ri i = 1; i < n; ++i) f[i] = i;
int lt = n, ans = 0;
for (ri i = 1; i <= cnt && lt > 1; ++i) {
if (cmpy(edge[i].u, edge[i].v)) {
ans += edge[i].w;
--lt;
}
}
printf("%lld", ans);
return 0;
}