// Slower C++ solution:
#include <cmath>

#include <cstdio>

#include <cstring>

#include <algorithm>

using std::min; using std::max;

using std::swap; using std::sort;

typedef long long ll;



template<typename T>

void read(T &x) {

	int flag = 1; x = 0; char ch = getchar();

	while(ch < '0' || ch > '9') { if(ch == '-') flag = -flag; ch = getchar(); }

	while(ch >= '0' && ch <= '9') x = x * 10 + ch - '0', ch = getchar(); x *= flag;

}



const int _ = 4e5 + 10;

int n, q, d[_], cnt, fa[_];

struct Edge { int u, v, w; } e[_];

inline bool operator < (const Edge &a, const Edge &b) { return a.w < b.w; }

inline void ChkMin(int &a, int b) { if(a > b) a = b; }

inline void addEdge(int u, int v, int w) { e[++cnt] = (Edge){u, v, w}; }

int find(int x) { return fa[x] == x ? x : fa[x] = find(fa[x]); }

bool unionn(int x, int y) {

	int fx = find(x), fy = find(y);

	if(fx == fy) return 0;

	fa[fx] = fy; return 1;

}



int main () {

#ifdef OFFLINE_JUDGE

	freopen("233.in", "r", stdin);

	freopen("233.out", "w", stdout);

#endif

	read(n), read(q);

	memset(d, 127, sizeof d);

	for(int i = 1, a, b, c; i <= q; ++i) {

		read(a), read(b), read(c), addEdge(a, b, c);

		ChkMin(d[a], c + 1), ChkMin(d[b], c + 2);

	}

	for(int i = 0; i < n; ++i) ChkMin(d[i], d[(i - 1 + n) % n] + 2);

	for(int i = 0; i < n; ++i) ChkMin(d[i], d[(i - 1 + n) % n] + 2);

	for(int i = 0; i <= n; ++i) addEdge(i, (i + 1) % n, d[i]);

	sort(e + 1, e + cnt + 1);

	for(int i = 1; i < n; ++i) fa[i] = i;

	int blo = n; ll ans = 0;

	for(int i = 1; i <= cnt && blo > 1; ++i)

		if(unionn(e[i].u, e[i].v)) ans += e[i].w, --blo;

	printf("%lld\n", ans);

	return 0;

} 


// Faster C++ solution for the same problem (measured speedup: 9.44446378822179x):
#include <map>

#include <cmath>

#include <string>

#include <cstdio>

#include <cstring>

#include <algorithm>

using std::map; using std::string;

using std::min; using std::max;

using std::swap; using std::sort;

typedef long long ll;



template<typename T>

void read(T &x) {

	int flag = 1; x = 0; char ch = getchar();

	while(ch < '0' || ch > '9') { if(ch == '-') flag = -flag; ch = getchar(); }

	while(ch >= '0' && ch <= '9') x = x * 10 + ch - '0', ch = getchar(); x *= flag;

}

#if __cplusplus >= 201103l

template<typename T, typename... V>

void read(T &x, V&... v) { read(x), read(v...); }

#endif



const int _ = 4e5 + 10;

int n, q, ff[_], d[_];

struct Edge { int u, v, w; } e[_]; int cnt;

inline bool operator < (const Edge &a, const Edge &b) { return a.w < b.w; }

inline void addEdge(int u, int v, int w) { e[++cnt] = {u, v, w}; }

void ChkMin(int &a, int b) { if(b < a) a = b; }

int find(int x) { return ff[x] == x ? x : ff[x] = find(ff[x]); }



int main () {

	read(n, q), memset(d, 127, sizeof(d[0]) * n);

	for(int i = 1, x, y, z; i <= q; ++i)

		read(x, y, z), addEdge(x, y, z), ChkMin(d[x], z + 1), ChkMin(d[y], z + 2);

	for(int i = 0; i < n; ++i) ChkMin(d[i], d[(i + n - 1) % n] + 2);

	for(int i = 0; i < n; ++i) ChkMin(d[i], d[(i + n - 1) % n] + 2);

	for(int i = 0; i < n; ++i) addEdge(i, (i + 1) % n, d[i]), ff[i] = i;

	sort(e + 1, e + cnt + 1); int blo = n; ll MST = 0;

	for(int i = 1; i <= cnt && blo > 1; ++i) {

		int u = find(e[i].u), v = find(e[i].v);

		if(u == v) continue; ff[u] = v, MST += e[i].w, --blo;

	}

	printf("%lld\n", MST);

	return 0;

}