#include <bits/stdc++.h>
using namespace std;
//#pragma GCC optimize(3)
#define DB double
#define LL long long
#define ULL unsigned long long
#define in128 __int128
#define cint const int
#define cLL const LL
#define For(z,e1,e2) for(int z=(e1);z<=(e2);z++)
#define Rof(z,e1,e2) for(int z=(e2);z>=(e1);z--)
#define For_(z,e1,e2) for(int z=(e1);z<(e2);z++)
#define Rof_(z,e1,e2) for(int z=(e2);z>(e1);z--)
#define inint(e) scanf("%d",&e)
#define inll(e) scanf("%lld",&e)
#define inpr(e1,e2) scanf("%d%d",&e1,&e2)
#define in3(e1,e2,e3) scanf("%d%d%d",&e1,&e2,&e3)
#define outint(e) printf("%d\n",e)
#define outint_(e) printf("%d%c",e," \n"[i==n])
#define outint2_(e,e1,e2) printf("%d%c",e," \n"[(e1)==(e2)])
#define outll(e) printf("%lld\n",e)
#define outll_(e) printf("%lld%c",e," \n"[i==n])
#define outll2_(e,e1,e2) printf("%lld%c",e," \n"[(e1)==(e2)])
#define exc(e) if(e) continue
#define stop(e) if(e) break
#define ret(e) if(e) return
#define ll(e) ((LL)(e))
#define pb push_back
#define ft first
#define sc second
#define clean(e) while(!e.empty()) e.pop()
#define all(ev) ev.begin(),ev.end()
#define debug(x) cerr<<#x<<'='<<x<<'\n'
cLL mod=998244353;
template <typename Type> void get_min(Type &w1,const Type w2) { if(w2<w1) w1=w2; }
template <typename Type> void get_max(Type &w1,const Type w2) { if(w2>w1) w1=w2; }
template <typename Type> Type up_div(Type w1,Type w2) { return (w1/w2+(w1%w2?1:0)); }
template <typename Type> Type gcd(Type X_,Type Y_) { Type R_=X_%Y_; while(R_) { X_=Y_; Y_=R_; R_=X_%Y_; } return Y_; }
template <typename Type> Type md(Type w1,const Type w2=mod) { w1%=w2; if(w1<0) w1+=w2; return w1; }
template <typename Type> Type md_(Type w1,const Type w2=mod) { w1%=w2; if(w1<=0) w1+=w2; return w1; }
void ex_gcd(LL &X_,LL &Y_,LL A_,LL B_)
{ if(!B_) { X_=1ll; Y_=0ll; return ; } ex_gcd(Y_,X_,B_,A_%B_); X_=md(X_,B_); Y_=(1ll-X_*A_)/B_; }
LL inv(LL A_,LL B_=mod) { LL X_=0ll,Y_=0ll; ex_gcd(X_,Y_,A_,B_); return X_; }
template <typename Type> void add(Type &w1,const Type w2,const Type M_=mod) { w1=md(w1+w2,M_); }
void mul(LL &w1,cLL w2,cLL M_=mod) { w1=md(w1*md(w2,M_),M_); }
LL pw(LL X_,LL Y_,LL M_=mod) { LL S_=1ll; while(Y_) { if(Y_&1) mul(S_,X_,M_); Y_>>=1; mul(X_,X_,M_); } return S_; }
mt19937 gen(time(NULL)); int rd() { return abs((int)gen()); }
cint N=35,M=500,W=1.6e5;
int n,m;
bool vis[M],b[W+1];
vector <int> prim;
struct Ed
{
    int x,y,w;
};
vector <Ed> v;
LL f[W+1];
struct Node
{
    LL x,y;
    bool operator == (const Node &A) const
    {
        return (x==A.x&&y==A.y);
    }
    Node operator + (const Node &A) const
    {
        return {md(x+A.x),md(y+A.y)};
    }
    Node operator - (const Node &A) const
    {
        return {md(x-A.x),md(y-A.y)};
    }
    Node operator - () const
    {
        return {md(-x),md(-y)};
    }
    Node operator * (const Node &A) const
    {
        return {md(x*A.y+y*A.x),md(y*A.y)};
    }
    Node operator / (const Node &A) const
    {
        LL t=inv(A.y);
        return {md((x*A.y-y*A.x)%mod*(t*t%mod)),md(y*t)};
    }
    bool operator ! () const
    {
        return (x==0ll&&y==0ll);
    }
}a[N][N];
LL dfs(int k)
{
    if(!k) return 1ll;
    bool sp=false;
    if(!a[k][k])
    {
        For_(i,1,k)
        {
            exc(!a[i][k]);
            For(j,1,k) swap(a[i][j],a[k][j]);
            sp=true;
            break;
        }
    }
    Node iv=-Node{0ll,1ll}/a[k][k];
    // if((iv*a[k][k])==Node{0ll,mod-1ll}||a[k][k].y==0ll) printf("Yes\n");
    // else printf("No\n");
    For_(i,1,k)
    {
        auto t=iv*a[i][k];
        For(j,1,k)
            a[i][j]=a[i][j]+(a[k][j]*t);
        if(a[i][k].x|a[i][k].y)
        {
            // assert(false);
            return 0ll;
        }
    }
    return dfs(k-1)*(sp?-1ll:1ll);
}
LL mat_tree()
{
    Node s={0ll,dfs(n-1)};
    For_(i,1,n)
    {
        s=s*a[i][i];
        // printf("> %lld,%lld\n",a[i][i].x,a[i][i].y);
    }
    // printf("%lld,%lld\n",s.x,s.y);
    return md(s.x);
}
ULL xor_shift(ULL x)
{
    x^=x<<25;
    x^=x<<(19+(int)(x%11));
    x^=x>>17;
    x^=x<<14;
    return x;
}
int uf[N];
int fin(int w)
{
    return (w==uf[w]?w:(uf[w]=fin(uf[w])));
}
map <ULL,LL> mp;
vector <int> h;
void add_ed(int x,int y,int w)
{
    Node f={1ll*w,1ll};
    a[x][x]=a[x][x]+f,a[y][y]=a[y][y]+f;
    a[x][y]=a[x][y]-f,a[y][x]=a[y][x]-f;
}
LL work(int g)
{
    ULL hs=1686688681;
    For(i,1,n) uf[i]=i;
    int cnt=0;
    h.clear();
    For(i,1,m)
    {
        auto [x,y,w]=v[i];
        exc(w%g);
        h.pb(i);
        hs=xor_shift(hs^i);
        int fx=fin(x),fy=fin(y);
        exc(fx==fy);
        cnt++;
        if(fx>fy) swap(fx,fy);  uf[fy]=fx;
    }
    if(cnt!=n-1) return 0ll;
    if(mp.count(hs)) return mp[hs];
    For(i,1,n) For(j,1,n) a[i][j]={0ll,0ll};
    for(auto i:h)
        add_ed(v[i].x,v[i].y,v[i].w);
    // printf("%d->%lld\n",g,mat_tree());
    return (mp[hs]=mat_tree());
}
void main_solve()
{
    For(i,2,W)
    {
        if(!b[i]) prim.pb(i);
        for(auto j:prim)
        {
            stop(i*j>W);
            b[i*j]=true;
            stop(i%j==0);
        }
    }
    inpr(n,m);
    v.pb({0,0,0});
    For(i,1,m)
    {
        int x,y,w; in3(x,y,w);
        v.pb({x,y,w});
    }
    // work(1);
    For(i,1,W)
    {
        f[i]=work(i);
        // if(f[i]) printf("%d:%lld\n",i,f[i]);
    }
    for(auto i:prim)
    {
        for(int j=1;j*i<=W;j++)
            add(f[j],-f[j*i]);
    }
    // printf("again\n");
    // For(i,1,W)
    //     if(f[i]) printf("%d:%lld\n",i,f[i]);   
    LL ans=0ll;
    For(i,1,W) add(ans,f[i]*i);
    outll(ans);
}
int main()
{
    // ios::sync_with_stdio(0); cin.tie(0);
    // freopen("in.txt","r",stdin);
    // freopen("out.txt","w",stdout);
    // srand(time(NULL));
    // main_init();
    // int _; inint(_); For(__,1,_) // T>1 ?
        // printf("\n------------\n\n"),
        main_solve();
    return 0;
}
/*

*/