#include #include #define rep(i,n) for(int i=0;i vi; typedef vector vl; typedef vector> vvi; typedef vector> vvl; typedef long double ld; typedef pair P; template ostream& operator<<(ostream& os, const static_modint& a) {os << a.val(); return os;} template ostream& operator<<(ostream& os, const dynamic_modint& a) {os << a.val(); return os;} template istream& operator>>(istream& is, static_modint& a) {long long x; is >> x; a = x; return is;} template istream& operator>>(istream& is, dynamic_modint& a) {long long x; is >> x; a = x; return is;} template istream& operator>>(istream& is, vector& v){int n = v.size(); assert(n > 0); rep(i, n) is >> v[i]; return is;} template ostream& operator<<(ostream& os, const pair& p){os << p.first << ' ' << p.second; return os;} template ostream& operator<<(ostream& os, const vector& v){int n = v.size(); rep(i, n) os << v[i] << (i == n - 1 ? "\n" : " "); return os;} template ostream& operator<<(ostream& os, const vector>& v){int n = v.size(); rep(i, n) os << v[i] << (i == n - 1 ? "\n" : ""); return os;} template ostream& operator<<(ostream& os, const set& se){for(T x : se) os << x << " "; os << "\n"; return os;} template ostream& operator<<(ostream& os, const unordered_set& se){for(T x : se) os << x << " "; os << "\n"; return os;} template ostream& operator<<(ostream& os, const atcoder::segtree& seg){int n = seg.max_right(0, [](S){return true;}); rep(i, n) os << seg.get(i) << (i == n - 1 ? "\n" : " "); return os;} template ostream& operator<<(ostream& os, const atcoder::lazy_segtree& seg){int n = seg.max_right(0, [](S){return true;}); rep(i, n) os << seg.get(i) << (i == n - 1 ? "\n" : " "); return os;} template void chmin(T& a, T b){a = min(a, b);} template void chmax(T& a, T b){a = max(a, b);} const int MOD = 100000000; const int K = 700; random_device seed; mt19937 mt(seed()); int main(){ int n; cin >> n; vector> a(n); rep(i, n){ a[i].resize(i + 1); cin >> a[i]; } auto diff = [&](int x, int y){ return min(abs(x - y), MOD - abs(x - y)); }; auto calc = [&](vector c) -> int{ int x = 0; for(int i = n - 1; i >= 0; i--){ rep(j, (i + 1)){ chmax(x, diff(c[j], a[i][j])); } vector c_new(i); rep(j, i){ c_new[j] = (c[j] + c[j + 1]) % MOD; } swap(c, c_new); } return MOD / 2 - x; }; uniform_int_distribution<> distN(0, n - 1); uniform_int_distribution<> distA(0, MOD - 1); vector> val(n, vector(K)); vector> score(n, vector(K, MOD)); vector>> cond(n, vector>(K)); vector> retro(n, vector(K, -1)); rep(i, n) rep(k, K) val[i][k] = distA(mt); rep(i, n){ if(i == 0){ rep(k, K){ score[0][k] = diff(a[n - 1][0], val[i][k]); cond[0][k] = {val[i][k]}; } }else { rep(k1, K){ rep(k2, K){ int score_new = score[i - 1][k1]; vector cond_new = cond[i - 1][k1]; int need = score[i][k2]; if(score_new >= need) continue; { cond_new.push_back(val[i][k2]); chmax(score_new, diff(cond_new[i], a[n - 1][i])); if(score_new >= need) continue; } for(int j = i; j >= 0; j--){ cond_new[j] += cond_new[j + 1]; if(cond_new[j] > MOD) cond_new[j] -= MOD; chmax(score_new, diff(cond_new[j], a[(n - 1) - i + j][j])); if(score_new >= need) break; } if(score_new < score[i][k2]){ score[i][k2] = score_new; cond[i][k2] = cond_new; retro[i][k2] = k1; } } } } } vector ans(n); int score_ans = MOD / 2; rep(k, K){ if(score[n - 1][k] < score_ans){ score_ans = score[n - 1][k]; int idx = k; for(int i = n - 1; i >= 0; i--){ ans[i] = val[i][idx]; idx = retro[i][idx]; } } } cout << ans; return 0; }