#define PROBLEM "https://yukicoder.me/problems/no/1283"
//#include"../../template/template.hpp"//#include"../../graph/dimension-expanded-graph.hpp"//usingnamespaceNyaan;voidNyaan::solve(){ini(n,m);DimensionExpandedGraph<3>g(n,n,2);vvifee(n,vi(n));rep(i,m){ini(h,w,c);--h,--w;fee[h][w]=c;}autod=g.dijkstra([&](autoa,autof){each(nx,a.near()){if(nx[2]!=a[2])continue;f(nx,1+fee[nx[0]][nx[1]]);if(a[2]==0){autonx2=nx;nx2[2]++;f(nx2,1);}}},{0,0,0});out(min(d[g.id(n-1,n-1,0)],d[g.id(n-1,n-1,1)]));}
#line 1 "verify/verify-yuki/yuki-1283.test.cpp"
#define PROBLEM "https://yukicoder.me/problems/no/1283"
//#line 2 "template/template.hpp"
usingnamespacestd;// intrinstic#include<immintrin.h>#include<algorithm>
#include<array>
#include<bitset>
#include<cassert>
#include<cctype>
#include<cfenv>
#include<cfloat>
#include<chrono>
#include<cinttypes>
#include<climits>
#include<cmath>
#include<complex>
#include<cstdarg>
#include<cstddef>
#include<cstdint>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<deque>
#include<fstream>
#include<functional>
#include<initializer_list>
#include<iomanip>
#include<ios>
#include<iostream>
#include<istream>
#include<iterator>
#include<limits>
#include<list>
#include<map>
#include<memory>
#include<new>
#include<numeric>
#include<ostream>
#include<queue>
#include<random>
#include<set>
#include<sstream>
#include<stack>
#include<streambuf>
#include<string>
#include<tuple>
#include<type_traits>
#include<typeinfo>
#include<unordered_map>
#include<unordered_set>
#include<utility>
#include<vector>// utility#line 1 "template/util.hpp"
namespaceNyaan{usingll=longlong;usingi64=longlong;usingu64=unsignedlonglong;usingi128=__int128_t;usingu128=__uint128_t;template<typenameT>usingV=vector<T>;template<typenameT>usingVV=vector<vector<T>>;usingvi=vector<int>;usingvl=vector<longlong>;usingvd=V<double>;usingvs=V<string>;usingvvi=vector<vector<int>>;usingvvl=vector<vector<longlong>>;template<typenameT>usingminpq=priority_queue<T,vector<T>,greater<T>>;template<typenameT,typenameU>structP:pair<T,U>{template<typename...Args>P(Args...args):pair<T,U>(args...){}usingpair<T,U>::first;usingpair<T,U>::second;P&operator+=(constP&r){first+=r.first;second+=r.second;return*this;}P&operator-=(constP&r){first-=r.first;second-=r.second;return*this;}P&operator*=(constP&r){first*=r.first;second*=r.second;return*this;}template<typenameS>P&operator*=(constS&r){first*=r,second*=r;return*this;}Poperator+(constP&r)const{returnP(*this)+=r;}Poperator-(constP&r)const{returnP(*this)-=r;}Poperator*(constP&r)const{returnP(*this)*=r;}template<typenameS>Poperator*(constS&r)const{returnP(*this)*=r;}Poperator-()const{returnP{-first,-second};}};usingpl=P<ll,ll>;usingpi=P<int,int>;usingvp=V<pl>;constexprintinf=1001001001;constexprlonglonginfLL=4004004004004004004LL;template<typenameT>intsz(constT&t){returnt.size();}template<typenameT,typenameU>inlineboolamin(T&x,Uy){return(y<x)?(x=y,true):false;}template<typenameT,typenameU>inlineboolamax(T&x,Uy){return(x<y)?(x=y,true):false;}template<typenameT>inlineTMax(constvector<T>&v){return*max_element(begin(v),end(v));}template<typenameT>inlineTMin(constvector<T>&v){return*min_element(begin(v),end(v));}template<typenameT>inlinelonglongSum(constvector<T>&v){returnaccumulate(begin(v),end(v),0LL);}template<typenameT>intlb(constvector<T>&v,constT&a){returnlower_bound(begin(v),end(v),a)-begin(v);}template<typenameT>intub(constvector<T>&v,constT&a){returnupper_bound(begin(v),end(v),a)-begin(v);}constexprlonglongTEN(intn){longlongret=1,x=10;for(;n;x*=x,n>>=1)ret*=(n&1?x:1);returnret;}template<typenameT,typenameU>pair<T,U>mkp(constT&t,constU&u){returnmake_pair(t,u);}template<typenameT>vector<T>mkrui(constvector<T>&v,boolrev=false){vector<T>ret(v.size()+1);if(rev){for(inti=int(v.size())-1;i>=0;i--)ret[i]=v[i]+ret[i+1];}else{for(inti=0;i<int(v.size());i++)ret[i+1]=ret[i]+v[i];}returnret;};template<typenameT>vector<T>mkuni(constvector<T>&v){vector<T>ret(v);sort(ret.begin(),ret.end());ret.erase(unique(ret.begin(),ret.end()),ret.end());returnret;}template<typenameF>vector<int>mkord(intN,Ff){vector<int>ord(N);iota(begin(ord),end(ord),0);sort(begin(ord),end(ord),f);returnord;}template<typenameT>vector<int>mkinv(vector<T>&v){intmax_val=*max_element(begin(v),end(v));vector<int>inv(max_val+1,-1);for(inti=0;i<(int)v.size();i++)inv[v[i]]=i;returninv;}vector<int>mkiota(intn){vector<int>ret(n);iota(begin(ret),end(ret),0);returnret;}template<typenameT>Tmkrev(constT&v){Tw{v};reverse(begin(w),end(w));returnw;}template<typenameT>boolnxp(T&v){returnnext_permutation(begin(v),end(v));}// 返り値の型は入力の T に依存// i 要素目 : [0, a[i])template<typenameT>vector<vector<T>>product(constvector<T>&a){vector<vector<T>>ret;vector<T>v;autodfs=[&](autorc,inti)->void{if(i==(int)a.size()){ret.push_back(v);return;}for(intj=0;j<a[i];j++)v.push_back(j),rc(rc,i+1),v.pop_back();};dfs(dfs,0);returnret;}// F : function(void(T&)), mod を取る操作// T : 整数型のときはオーバーフローに注意するtemplate<typenameT>TPower(Ta,longlongn,constT&I,constfunction<void(T&)>&f){Tres=I;for(;n;f(a=a*a),n>>=1){if(n&1)f(res=res*a);}returnres;}// T : 整数型のときはオーバーフローに注意するtemplate<typenameT>TPower(Ta,longlongn,constT&I=T{1}){returnPower(a,n,I,function<void(T&)>{[](T&)->void{}});}template<typenameT>TRev(constT&v){Tres=v;reverse(begin(res),end(res));returnres;}template<typenameT>vector<T>Transpose(constvector<T>&v){usingU=typenameT::value_type;if(v.empty())return{};intH=v.size(),W=v[0].size();vectorres(W,T(H,U{}));for(inti=0;i<H;i++){for(intj=0;j<W;j++){res[j][i]=v[i][j];}}returnres;}template<typenameT>vector<T>Rotate(constvector<T>&v,intclockwise=true){usingU=typenameT::value_type;intH=v.size(),W=v[0].size();vectorres(W,T(H,U{}));for(inti=0;i<H;i++){for(intj=0;j<W;j++){if(clockwise){res[W-1-j][i]=v[i][j];}else{res[j][H-1-i]=v[i][j];}}}returnres;}}// namespace Nyaan#line 58 "template/template.hpp"
// bit operation#line 1 "template/bitop.hpp"
namespaceNyaan{__attribute__((target("popcnt")))inlineintpopcnt(constu64&a){return__builtin_popcountll(a);}inlineintlsb(constu64&a){returna?__builtin_ctzll(a):64;}inlineintctz(constu64&a){returna?__builtin_ctzll(a):64;}inlineintmsb(constu64&a){returna?63-__builtin_clzll(a):-1;}template<typenameT>inlineintgbit(constT&a,inti){return(a>>i)&1;}template<typenameT>inlinevoidsbit(T&a,inti,boolb){if(gbit(a,i)!=b)a^=T(1)<<i;}constexprlonglongPW(intn){return1LL<<n;}constexprlonglongMSK(intn){return(1LL<<n)-1;}}// namespace Nyaan#line 61 "template/template.hpp"
// inout#line 1 "template/inout.hpp"
namespaceNyaan{template<typenameT,typenameU>ostream&operator<<(ostream&os,constpair<T,U>&p){os<<p.first<<" "<<p.second;returnos;}template<typenameT,typenameU>istream&operator>>(istream&is,pair<T,U>&p){is>>p.first>>p.second;returnis;}template<typenameT>ostream&operator<<(ostream&os,constvector<T>&v){ints=(int)v.size();for(inti=0;i<s;i++)os<<(i?" ":"")<<v[i];returnos;}template<typenameT>istream&operator>>(istream&is,vector<T>&v){for(auto&x:v)is>>x;returnis;}istream&operator>>(istream&is,__int128_t&x){stringS;is>>S;x=0;intflag=0;for(auto&c:S){if(c=='-'){flag=true;continue;}x*=10;x+=c-'0';}if(flag)x=-x;returnis;}istream&operator>>(istream&is,__uint128_t&x){stringS;is>>S;x=0;for(auto&c:S){x*=10;x+=c-'0';}returnis;}ostream&operator<<(ostream&os,__int128_tx){if(x==0)returnos<<0;if(x<0)os<<'-',x=-x;stringS;while(x)S.push_back('0'+x%10),x/=10;reverse(begin(S),end(S));returnos<<S;}ostream&operator<<(ostream&os,__uint128_tx){if(x==0)returnos<<0;stringS;while(x)S.push_back('0'+x%10),x/=10;reverse(begin(S),end(S));returnos<<S;}voidin(){}template<typenameT,class...U>voidin(T&t,U&...u){cin>>t;in(u...);}voidout(){cout<<"\n";}template<typenameT,class...U,charsep=' '>voidout(constT&t,constU&...u){cout<<t;if(sizeof...(u))cout<<sep;out(u...);}structIoSetupNya{IoSetupNya(){cin.tie(nullptr);ios::sync_with_stdio(false);cout<<fixed<<setprecision(15);cerr<<fixed<<setprecision(7);}}iosetupnya;}// namespace Nyaan#line 64 "template/template.hpp"
// debug#line 1 "template/debug.hpp"
namespaceDebugImpl{template<typenameU,typename=void>structis_specialize:false_type{};template<typenameU>structis_specialize<U,typenameconditional<false,typenameU::iterator,void>::type>:true_type{};template<typenameU>structis_specialize<U,typenameconditional<false,decltype(U::first),void>::type>:true_type{};template<typenameU>structis_specialize<U,enable_if_t<is_integral<U>::value,void>>:true_type{};voiddump(constchar&t){cerr<<t;}voiddump(conststring&t){cerr<<t;}voiddump(constbool&t){cerr<<(t?"true":"false");}voiddump(__int128_tt){if(t==0)cerr<<0;if(t<0)cerr<<'-',t=-t;stringS;while(t)S.push_back('0'+t%10),t/=10;reverse(begin(S),end(S));cerr<<S;}voiddump(__uint128_tt){if(t==0)cerr<<0;stringS;while(t)S.push_back('0'+t%10),t/=10;reverse(begin(S),end(S));cerr<<S;}template<typenameU,enable_if_t<!is_specialize<U>::value,nullptr_t>=nullptr>voiddump(constU&t){cerr<<t;}template<typenameT>voiddump(constT&t,enable_if_t<is_integral<T>::value>*=nullptr){stringres;if(t==Nyaan::inf)res="inf";ifconstexpr(is_signed<T>::value){if(t==-Nyaan::inf)res="-inf";}ifconstexpr(sizeof(T)==8){if(t==Nyaan::infLL)res="inf";ifconstexpr(is_signed<T>::value){if(t==-Nyaan::infLL)res="-inf";}}if(res.empty())res=to_string(t);cerr<<res;}template<typenameT,typenameU>voiddump(constpair<T,U>&);template<typenameT>voiddump(constpair<T*,int>&);template<typenameT>voiddump(constT&t,enable_if_t<!is_void<typenameT::iterator>::value>*=nullptr){cerr<<"[ ";for(autoit=t.begin();it!=t.end();){dump(*it);cerr<<(++it==t.end()?"":", ");}cerr<<" ]";}template<typenameT,typenameU>voiddump(constpair<T,U>&t){cerr<<"( ";dump(t.first);cerr<<", ";dump(t.second);cerr<<" )";}template<typenameT>voiddump(constpair<T*,int>&t){cerr<<"[ ";for(inti=0;i<t.second;i++){dump(t.first[i]);cerr<<(i==t.second-1?"":", ");}cerr<<" ]";}voidtrace(){cerr<<endl;}template<typenameHead,typename...Tail>voidtrace(Head&&head,Tail&&...tail){cerr<<" ";dump(head);if(sizeof...(tail)!=0)cerr<<",";trace(std::forward<Tail>(tail)...);}}// namespace DebugImpl#ifdef NyaanDebug
#define trc(...) \
do { \
cerr << "## " << #__VA_ARGS__ << " = "; \
DebugImpl::trace(__VA_ARGS__); \
} while (0)
#else
#define trc(...) (void(0))
#endif
#ifdef NyaanLocal
#define trc2(...) \
do { \
cerr << "## " << #__VA_ARGS__ << " = "; \
DebugImpl::trace(__VA_ARGS__); \
} while (0)
#else
#define trc2(...) (void(0))
#endif
#line 67 "template/template.hpp"
// macro#line 1 "template/macro.hpp"
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...) \
int __VA_ARGS__; \
in(__VA_ARGS__)
#define inl(...) \
long long __VA_ARGS__; \
in(__VA_ARGS__)
#define ins(...) \
string __VA_ARGS__; \
in(__VA_ARGS__)
#define in2(s, t) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i]); \
}
#define in3(s, t, u) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i]); \
}
#define in4(s, t, u, v) \
for (int i = 0; i < (int)s.size(); i++) { \
in(s[i], t[i], u[i], v[i]); \
}
#define die(...) \
do { \
Nyaan::out(__VA_ARGS__); \
return; \
} while (0)
#line 70 "template/template.hpp"
namespaceNyaan{voidsolve();}intmain(){Nyaan::solve();}#line 4 "verify/verify-yuki/yuki-1283.test.cpp"
//#line 2 "graph/dimension-expanded-graph.hpp"
template<intDIM,typenameData_t=longlong>structDimensionExpandedGraph{static_assert(is_signed<Data_t>::value,"Data_t must be signed.");usingDG=DimensionExpandedGraph;structA:array<int,DIM>{usingarray<int,DIM>::operator[];#pragma GCC diagnostic ignored "-Wnarrowing"
template<typename...Args>A(Args...args):array<int,DIM>({args...}){}#pragma GCC diagnostic warning "-Wnarrowing"
A&operator+=(constA&r){for(inti=0;i<DIM;i++)(*this)[i]+=r[i];return*this;}A&operator-=(constA&r){for(inti=0;i<DIM;i++)(*this)[i]-=r[i];return*this;}Aoperator+(constA&r){return(*this)+=r;}Aoperator-(constA&r){return(*this)-=r;}intid()const{returnDG::id(*this);}friendintid(constA&a){returnDG::id(a);}boolok()const{returnDG::ok(*this);}friendboolok(constA&a){returnDG::ok(a);}inlineboolis_add()const{return(*this)[0]==ADD;}friendinlineboolis_add(constA&a){returna[0]==ADD;}vector<A>near()const{staticvector<A>res;res.clear();if(is_add()==true)returnres;for(inti=0;i<DIM;i++){Aasc(*this),dec(*this);asc[i]++;dec[i]--;if(asc[i]!=g_size[i])res.push_back(asc);if(dec[i]!=-1)res.push_back(dec);}returnres;}friendvector<A>near(constA&a){returna.near();}};staticintN,add_node;staticAg_size,coeff;staticconstexprintADD=numeric_limits<int>::max();staticintid(constA&a){if(a[0]==ADD)returnN+a[1];intret=0;for(inti=0;i<DIM;i++){ret+=a[i]*coeff[i];}returnret;}template<typename...T>staticintid(constT&...t){returnid(A{t...});}staticboolok(constA&a){if(a[0]==ADD){return0<=a[1]&&a[1]<add_node;}for(inti=0;i<DIM;i++)if(a[i]<0org_size[i]<=a[i])returnfalse;returntrue;}template<typename...T>staticboolok(constT&...t){returnok(A{t...});}template<typename...Args>staticAcast(Args...args){returnA(args...);}staticAad(intn){returnA{DG::ADD,n};};vector<char>grid;explicitDimensionExpandedGraph()=default;template<typename...T>explicitDimensionExpandedGraph(constT&...t){set(t...);}template<typename...T>voidset(constT&...t){N=1;g_size=A{t...};coeff.fill(1);for(inti=0;i<DIM;i++){assert(g_size[i]!=0);for(intj=0;j<i;j++)coeff[j]*=g_size[i];N*=g_size[i];}}voidadd(intn){add_node=n;}voidscan(istream&is=std::cin){grid.reserve(N);intl=g_size[DIM-1];for(inti=0;i<N;i+=l){strings;is>>s;copy(begin(s),end(s),back_inserter(grid));}}friendistream&operator>>(istream&is,DG&g){g.scan(is);returnis;}vector<char>&get_grid(){returngrid;}char&operator()(constA&a){returngrid[id(a)];}template<typename...T>char&operator()(constT&...t){returngrid[id(t...)];}Afind(constchar&c){Aa{};fill(begin(a),end(a),0);a[DIM-1]=-1;while(true){a[DIM-1]++;for(inti=DIM-1;;i--){if(a[i]!=g_size[i])break;if(i==0)returna;a[i]=0;a[i-1]++;}if((*this)(a)==c)returna;}}template<typenameF,typenameDist_t=Data_t>vector<Dist_t>bfs(Ff,As){vector<Dist_t>dist(N+add_node,-1);if(!ok(s))returndist;vector<A>Q;dist[id(s)]=0;Q.push_back(s);while(!Q.empty()){Ac=Q.back();Q.pop_back();intdc=dist[id(c)];f(c,[&](Ad){if(!ok(d))return;if(dist[id(d)]==-1){dist[id(d)]=dc+1;Q.push_back(d);}});}returndist;}template<typenameF,typenameDist_t=Data_t>vector<Dist_t>bfs01(Ff,As){vector<Dist_t>dist(N+add_node,-1);if(!ok(s))returndist;deque<A>Q;dist[id(s)]=0;Q.push_back(s);while(!Q.empty()){Ac=Q.front();Q.pop_front();intdc=dist[id(c)];f(c,[&](Ad,Data_tw){if(!ok(d))return;if(dist[id(d)]==-1){dist[id(d)]=dc+w;if(w==0)Q.push_front(d);elseQ.push_back(d);}});}returndist;}template<typenameF,typenameDist_t=Data_t>staticvector<Dist_t>dijkstra(Ff,As){vector<Dist_t>dist(N,-1);usingP=pair<Dist_t,A>;autocmp=[](P&a,P&b){returna.first>b.first;};priority_queue<P,vector<P>,decltype(cmp)>Q(cmp);assert(id(s)!=-1);dist[id(s)]=0;Q.emplace(0,s);while(!Q.empty()){Dist_tdc;Ac;tie(dc,c)=Q.top();Q.pop();if(dist[id(c)]<dc)continue;f(c,[&](Ad,Dist_tw){if(!ok(d))return;if(dist[id(d)]==-1||dist[id(d)]>dc+w){dist[id(d)]=dc+w;Q.emplace(dc+w,d);}});}returndist;}vector<A>dat;template<typenameF>voiduf(Ff){Adflt;dflt[0]=-1;dat.resize(N+add_node,dflt);Aa{};fill(begin(a),end(a),0);a[DIM-1]=-1;while(true){a[DIM-1]++;for(inti=DIM-1;;i--){if(a[i]!=g_size[i])break;if(i==0)return;a[i]=0;a[i-1]++;}f(a,[&](Au,Av){unite(u,v);});}}// Union FindAfind(Au){returndat[id(u)][0]<0?u:dat[id(u)]=find(dat[id(u)]);}boolsame(Au,Av){returnfind(u)==find(v);}boolunite(Au,Av){if((u=find(u))==(v=find(v)))returnfalse;intiu=id(u),iv=id(v);if(dat[iu]>dat[iv])swap(u,v),swap(iu,iv);dat[iu]+=dat[iv];dat[iv]=u;returntrue;}Data_tsize(Au){return-dat[id(find(u))][0];}};template<intDIM,typenameData_t>intDimensionExpandedGraph<DIM,Data_t>::N=0;template<intDIM,typenameData_t>intDimensionExpandedGraph<DIM,Data_t>::add_node=0;template<intDIM,typenameData_t>typenameDimensionExpandedGraph<DIM,Data_t>::ADimensionExpandedGraph<DIM,Data_t>::g_size;template<intDIM,typenameData_t>typenameDimensionExpandedGraph<DIM,Data_t>::ADimensionExpandedGraph<DIM,Data_t>::coeff;/**
* @brief 次元拡張グラフ
*/#line 6 "verify/verify-yuki/yuki-1283.test.cpp"
//usingnamespaceNyaan;voidNyaan::solve(){ini(n,m);DimensionExpandedGraph<3>g(n,n,2);vvifee(n,vi(n));rep(i,m){ini(h,w,c);--h,--w;fee[h][w]=c;}autod=g.dijkstra([&](autoa,autof){each(nx,a.near()){if(nx[2]!=a[2])continue;f(nx,1+fee[nx[0]][nx[1]]);if(a[2]==0){autonx2=nx;nx2[2]++;f(nx2,1);}}},{0,0,0});out(min(d[g.id(n-1,n-1,0)],d[g.id(n-1,n-1,1)]));}