#include using namespace std; using pii=pair; using tii=tuple; using qii=tuple; using ll=long long; using ull=unsigned long long; using ld=long double; constexpr int INF=1e9; constexpr ll INF_ll=1e18; #define rep(i,n) for (int i=0;i<(int)(n);i++) #define replr(i,l,r) for (int i=(int)(l);i<(int)(r);i++) #define all(v) v.begin(),v.end() #define len(v) ((int)v.size()) template inline bool chmin(T &a,T b){ if(a>b){ a=b; return true; } return false; } template inline bool chmax(T &a,T b){ if(a(now-start).count(); return ms; } int get_ms_all_program(){ auto now=chrono::system_clock::now(); int ms=chrono::duration_cast(now-program_start).count(); return ms; } } mt19937 mt; uint32_t rand_int(uint32_t r){ //[0,r) assert(r!=0); return ((uint64_t)mt()*r)>>32; } int rand_int(int l,int r){ //[l,r) assert(l> A; #include using mint=atcoder::static_modint; vector>> C; namespace Solver{ double calc_score(vector ans){ double ret=0; rep(i,N){ rep(j,i+1){ mint now=0; rep(k,N){ now+=ans[k]*C[i][j][k]; } int v=now.val(); ret+=pow(min(abs(A[i][j]-v),mod-abs(A[i][j]-v)),2); } } return ret; } void solve(){ vector ans(N,0); double pre_score=calc_score(ans); while(Timer::get_ms()<1900){ int x=rand_int(N); vector new_ans=ans; new_ans[x]=rand_int(mod); double new_score=calc_score(new_ans); if(chmin(pre_score,new_score)) ans=new_ans; } rep(i,N) cout << ans[i].val() << ' '; cout << '\n'; int score=0; rep(i,N){ rep(j,i+1){ mint now=0; rep(k,N){ now+=ans[k]*C[i][j][k]; } int v=now.val(); chmax(score,min(abs(A[i][j]-v),mod-abs(A[i][j]-v))); } } score=mod/2-score; cerr << score << '\n'; } } int main(){ ios::sync_with_stdio(false); cin.tie(nullptr); Timer::snap(); int _; cin >> _; A.resize(N); rep(i,N){ A[i].resize(i+1); rep(j,i+1){ cin >> A[i][j]; } } C.assign(N,vector>(N,vector(N,0))); rep(i,N) C[N-1][i][i]=1; for(int i=N-2;0<=i;i--){ rep(j,i+1){ rep(k,N){ C[i][j][k]+=C[i+1][j][k]; C[i][j][k]+=C[i+1][j+1][k]; } } } Solver::solve(); exit(0); }