// High above the clouds there is a rainbow...
#include<bits/stdc++.h>
#define F first
#define S second
#define PB push_back
#define sz(s) int((s).size())
#define bit(n,k) (((n)>>(k))&1)
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
typedef pair<ll,ll> pll;
typedef pair<int,ll> pil;
const int maxn=2e5+10,SQ=50;
const ll inf=1e18;
int a[maxn],b[maxn],_a[maxn],_b[maxn];
ll c[maxn],arr[maxn],arr2[maxn];
int pp[maxn];
vector<pil>v[maxn];
priority_queue<pil> pq;
int main(){
ios_base::sync_with_stdio(false);cin.tie(0);
srand(time(0));
int n,m; cin>>n>>m;
for(int i=0;i<m;i++){
cin>>_a[i]>>_b[i]>>c[i], --_a[i],--_b[i];
}
for(int i=0;i<n;i++){
pp[i]=i;
}
random_shuffle(pp,pp+n);
ll ans=inf;
for(int w=0;w<min(SQ,n);w++){
memset(arr,0,sizeof arr);
memset(arr2,0,sizeof arr2);
for(int i=0;i<n;i++){
v[i].clear();
}
while(sz(pq)){
pq.pop();
}
for(int i=0;i<m;i++){
a[i]=(_a[i]+pp[w])%n, b[i]=(_b[i]+pp[w])%n;
if(a[i]>b[i]) swap(a[i],b[i]);
v[a[i]].PB({b[i],c[i]});
arr[a[i]]+=c[i], arr[b[i]]-=c[i];
}
for(int i=1;i<n;i++){
arr[i]+=arr[i-1];
}
for(int i=0;i<n;i++){
arr[i]=(1+arr[i])/2;
}
ll cnt=0,nw=0;
for(int i=0;i<n;i++){
for(auto x:v[i]){
pq.push(x);
}
nw+=arr2[i];
while(arr[i]-nw>0){
pil x=pq.top();
pq.pop();
ll num= min(arr[i]-nw,x.S);
x.S-=num, nw+=num, arr2[x.F]-=num, cnt+=num;
if(x.S>0) pq.push(x);
}
}
ans=min(ans,cnt);
}
return cout<<ans<<endl,0;
}
// Deathly mistakes:
// * Read the problem curfully.
// * Check maxn.
// * Overflows.
