#line 1 "verify/verify-yosupo-string/yosupo-zalgo-suffixarray.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/zalgorithm"
#line 2 "template/template.hpp"
using namespace std;
// 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"
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;
template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;
template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;
template <typename T, typename U>
struct P : pair<T, U> {
template <typename... Args>
P(Args... args) : pair<T, U>(args...) {}
using pair<T, U>::first;
using pair<T, U>::second;
P &operator+=(const P &r) {
first += r.first;
second += r.second;
return *this;
}
P &operator-=(const P &r) {
first -= r.first;
second -= r.second;
return *this;
}
P &operator*=(const P &r) {
first *= r.first;
second *= r.second;
return *this;
}
template <typename S>
P &operator*=(const S &r) {
first *= r, second *= r;
return *this;
}
P operator+(const P &r) const { return P(*this) += r; }
P operator-(const P &r) const { return P(*this) -= r; }
P operator*(const P &r) const { return P(*this) *= r; }
template <typename S>
P operator*(const S &r) const {
return P(*this) *= r;
}
P operator-() const { return P{-first, -second}; }
};
using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;
constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;
template <typename T>
int sz(const T &t) {
return t.size();
}
template <typename T, typename U>
inline bool amin(T &x, U y) {
return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
return (x < y) ? (x = y, true) : false;
}
template <typename T>
inline T Max(const vector<T> &v) {
return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
return accumulate(begin(v), end(v), 0LL);
}
template <typename T>
int lb(const vector<T> &v, const T &a) {
return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
return upper_bound(begin(v), end(v), a) - begin(v);
}
constexpr long long TEN(int n) {
long long ret = 1, x = 10;
for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
return ret;
}
template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
return make_pair(t, u);
}
template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
vector<T> ret(v.size() + 1);
if (rev) {
for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
} else {
for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
}
return ret;
};
template <typename T>
vector<T> mkuni(const vector<T> &v) {
vector<T> ret(v);
sort(ret.begin(), ret.end());
ret.erase(unique(ret.begin(), ret.end()), ret.end());
return ret;
}
template <typename F>
vector<int> mkord(int N, F f) {
vector<int> ord(N);
iota(begin(ord), end(ord), 0);
sort(begin(ord), end(ord), f);
return ord;
}
template <typename T>
vector<int> mkinv(vector<T> &v) {
int max_val = *max_element(begin(v), end(v));
vector<int> inv(max_val + 1, -1);
for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
return inv;
}
vector<int> mkiota(int n) {
vector<int> ret(n);
iota(begin(ret), end(ret), 0);
return ret;
}
template <typename T>
T mkrev(const T &v) {
T w{v};
reverse(begin(w), end(w));
return w;
}
template <typename T>
bool nxp(T &v) {
return next_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 <typename T>
vector<vector<T>> product(const vector<T> &a) {
vector<vector<T>> ret;
vector<T> v;
auto dfs = [&](auto rc, int i) -> void {
if (i == (int)a.size()) {
ret.push_back(v);
return;
}
for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back();
};
dfs(dfs, 0);
return ret;
}
// 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 <typename T>
T Power(T a, long long n, const T &I, const function<void(T &)> &f) {
T res = I;
for (; n; f(a = a * a), n >>= 1) {
if (n & 1) f(res = res * a);
}
return res;
}
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I = T{1}) {
return Power(a, n, I, function<void(T &)>{[](T &) -> void {}});
}
template <typename T>
T Rev(const T &v) {
T res = v;
reverse(begin(res), end(res));
return res;
}
template <typename T>
vector<T> Transpose(const vector<T> &v) {
using U = typename T::value_type;
if(v.empty()) return {};
int H = v.size(), W = v[0].size();
vector res(W, T(H, U{}));
for (int i = 0; i < H; i++) {
for (int j = 0; j < W; j++) {
res[j][i] = v[i][j];
}
}
return res;
}
template <typename T>
vector<T> Rotate(const vector<T> &v, int clockwise = true) {
using U = typename T::value_type;
int H = v.size(), W = v[0].size();
vector res(W, T(H, U{}));
for (int i = 0; i < H; i++) {
for (int j = 0; j < W; j++) {
if (clockwise) {
res[W - 1 - j][i] = v[i][j];
} else {
res[j][H - 1 - i] = v[i][j];
}
}
}
return res;
}
} // namespace Nyaan
#line 58 "template/template.hpp"
// bit operation
#line 1 "template/bitop.hpp"
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
return __builtin_popcountll(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
} // namespace Nyaan
#line 61 "template/template.hpp"
// inout
#line 1 "template/inout.hpp"
namespace Nyaan {
template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
os << p.first << " " << p.second;
return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
is >> p.first >> p.second;
return is;
}
template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
int s = (int)v.size();
for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
for (auto &x : v) is >> x;
return is;
}
istream &operator>>(istream &is, __int128_t &x) {
string S;
is >> S;
x = 0;
int flag = 0;
for (auto &c : S) {
if (c == '-') {
flag = true;
continue;
}
x *= 10;
x += c - '0';
}
if (flag) x = -x;
return is;
}
istream &operator>>(istream &is, __uint128_t &x) {
string S;
is >> S;
x = 0;
for (auto &c : S) {
x *= 10;
x += c - '0';
}
return is;
}
ostream &operator<<(ostream &os, __int128_t x) {
if (x == 0) return os << 0;
if (x < 0) os << '-', x = -x;
string S;
while (x) S.push_back('0' + x % 10), x /= 10;
reverse(begin(S), end(S));
return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
if (x == 0) return os << 0;
string S;
while (x) S.push_back('0' + x % 10), x /= 10;
reverse(begin(S), end(S));
return os << S;
}
void in() {}
template <typename T, class... U>
void in(T &t, U &...u) {
cin >> t;
in(u...);
}
void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
cout << t;
if (sizeof...(u)) cout << sep;
out(u...);
}
struct IoSetupNya {
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"
namespace DebugImpl {
template <typename U, typename = void>
struct is_specialize : false_type {};
template <typename U>
struct is_specialize<
U, typename conditional<false, typename U::iterator, void>::type>
: true_type {};
template <typename U>
struct is_specialize<
U, typename conditional<false, decltype(U::first), void>::type>
: true_type {};
template <typename U>
struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type {
};
void dump(const char& t) { cerr << t; }
void dump(const string& t) { cerr << t; }
void dump(const bool& t) { cerr << (t ? "true" : "false"); }
void dump(__int128_t t) {
if (t == 0) cerr << 0;
if (t < 0) cerr << '-', t = -t;
string S;
while (t) S.push_back('0' + t % 10), t /= 10;
reverse(begin(S), end(S));
cerr << S;
}
void dump(__uint128_t t) {
if (t == 0) cerr << 0;
string S;
while (t) S.push_back('0' + t % 10), t /= 10;
reverse(begin(S), end(S));
cerr << S;
}
template <typename U,
enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr>
void dump(const U& t) {
cerr << t;
}
template <typename T>
void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) {
string res;
if (t == Nyaan::inf) res = "inf";
if constexpr (is_signed<T>::value) {
if (t == -Nyaan::inf) res = "-inf";
}
if constexpr (sizeof(T) == 8) {
if (t == Nyaan::infLL) res = "inf";
if constexpr (is_signed<T>::value) {
if (t == -Nyaan::infLL) res = "-inf";
}
}
if (res.empty()) res = to_string(t);
cerr << res;
}
template <typename T, typename U>
void dump(const pair<T, U>&);
template <typename T>
void dump(const pair<T*, int>&);
template <typename T>
void dump(const T& t,
enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) {
cerr << "[ ";
for (auto it = t.begin(); it != t.end();) {
dump(*it);
cerr << (++it == t.end() ? "" : ", ");
}
cerr << " ]";
}
template <typename T, typename U>
void dump(const pair<T, U>& t) {
cerr << "( ";
dump(t.first);
cerr << ", ";
dump(t.second);
cerr << " )";
}
template <typename T>
void dump(const pair<T*, int>& t) {
cerr << "[ ";
for (int i = 0; i < t.second; i++) {
dump(t.first[i]);
cerr << (i == t.second - 1 ? "" : ", ");
}
cerr << " ]";
}
void trace() { cerr << endl; }
template <typename Head, typename... Tail>
void trace(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"
namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }
#line 2 "string/suffix-array.hpp"
#line 2 "data-structure/sparse-table.hpp"
#line 6 "data-structure/sparse-table.hpp"
using namespace std;
template <typename T>
struct SparseTable {
inline static constexpr T INF = numeric_limits<T>::max() / 2;
int N;
vector<vector<T> > table;
T f(T a, T b) { return min(a, b); }
SparseTable() {}
SparseTable(const vector<T> &v) : N(v.size()) {
int b = 1;
while ((1 << b) <= N) ++b;
table.push_back(v);
for (int i = 1; i < b; i++) {
table.push_back(vector<T>(N, INF));
for (int j = 0; j + (1 << i) <= N; j++) {
table[i][j] = f(table[i - 1][j], table[i - 1][j + (1 << (i - 1))]);
}
}
}
// [l, r)
T query(int l, int r) {
assert(0 <= l and l <= r and r <= N);
if (l == r) return INF;
int b = 31 - __builtin_clz(r - l);
return f(table[b][l], table[b][r - (1 << b)]);
}
};
/**
* @brief Sparse Table
*/
#line 6 "string/suffix-array.hpp"
// remind: SA including empty string
// verify https://judge.yosupo.jp/submission/240
struct SuffixArray {
int _size;
vector<int> sa;
string &s;
SuffixArray(string &str) : _size(str.size()), s(str) {
s.push_back(0);
sa.resize(s.size());
iota(begin(sa), end(sa), 0);
sort(begin(sa), end(sa),
[&](int a, int b) { return s[a] == s[b] ? a > b : s[a] < s[b]; });
vector<int> classes(s.size()), c(s.begin(), s.end()), cnt(s.size());
for (int len = 1; len < (int)s.size(); len <<= 1) {
for (int i = 0; i < (int)s.size(); i++) {
if (i > 0 && c[sa[i - 1]] == c[sa[i]] &&
sa[i - 1] + len < (int)s.size() &&
c[sa[i - 1] + len / 2] == c[sa[i] + len / 2]) {
classes[sa[i]] = classes[sa[i - 1]];
} else {
classes[sa[i]] = i;
}
}
iota(begin(cnt), end(cnt), 0);
copy(begin(sa), end(sa), begin(c));
for (int i = 0; i < (int)s.size(); i++) {
int s1 = c[i] - len;
if (s1 >= 0) sa[cnt[classes[s1]]++] = s1;
}
classes.swap(c);
}
s.pop_back();
}
void output() {
cout << "SA\tidx\tstr" << endl;
for (int i = 0; i < size(); i++) {
cout << i << ": \t" << sa[i] << " \t";
if (sa[i] != _size)
cout << s.substr(sa[i], _size - sa[i]) << endl;
else
cout << "$" << endl;
}
cout << endl;
}
int size() const { return _size + 1; }
int operator[](int k) const { return sa[k]; }
};
struct LCPArray {
const SuffixArray &SA;
vector<int> LCP, rank;
LCPArray(const SuffixArray &sa) : SA(sa) {
LCP.resize(SA.size());
rank.resize(SA.size());
for (int i = 0; i < SA.size(); i++) {
rank[SA[i]] = i;
}
LCP[0] = 0;
for (int i = 0, h = 0; i < SA.size() - 1; i++) {
int j = SA[rank[i] - 1];
h ? h-- : h;
while ((i > j ? i : j) + h < SA.size() - 1 &&
SA.s[i + h] == SA.s[j + h] && ++h)
;
LCP[rank[i] - 1] = h;
}
}
void output() {
cout << "SA\tidx\tLCP\tstr" << endl;
for (int i = 0; i < SA.size(); i++) {
cout << i << "\t" << SA[i] << " \t" << LCP[i] << "\t";
if (SA[i] == SA.size() - 1)
cout << "$";
else
cout << SA.s.substr(SA[i], SA.size() - 1 - SA[i]);
cout << endl;
}
}
};
// verify
// https://onlinejudge.u-aizu.ac.jp/status/users/NyaanNyaan/submissions/1/ALDS1_14_D/judge/3874273/C++14
// https://atcoder.jp/contests/abc135/submissions/7574225
// https://judge.yosupo.jp/submission/241
// https://atcoder.jp/contests/abc141/submissions/7577295
struct StringSearch {
string &s;
const SuffixArray &sa;
const LCPArray &lcp;
SparseTable<int> sparse;
StringSearch(LCPArray &lcp)
: s(lcp.SA.s), sa(lcp.SA), lcp(lcp), sparse(lcp.LCP) {}
pair<int, int> comp(const string &t, int len, int si, int ti = 0) {
int sn = (int)s.size(), tn = (int)t.size();
si += len, ti += len;
while (si < sn && ti < tn) {
if (s[si] != t[ti]) return make_pair(s[si] < t[ti], ti);
si++, ti++;
}
return make_pair((si >= sn && ti < tn), ti);
}
pair<int, int> find_range(int left, int med, int right, int len) {
{
int ng = left - 1, ok = med;
while (ng + 1 < ok) {
int cur = (ng + ok) / 2;
if (sparse.query(cur, med) >= len)
ok = cur;
else
ng = cur;
}
left = ok;
}
{
int ok = med, ng = right + 1;
while (ok + 1 < ng) {
int cur = (ng + ok) / 2;
if (sparse.query(med, cur) >= len)
ok = cur;
else
ng = cur;
}
right = ok;
}
return make_pair(left, right);
}
public:
// Longest Common Prefix between S[i , N) and S[j , N)
int ArbitaryLCP(int i, int j) {
if (i == j) return (int)(s.size()) - i;
return sparse.query(min(lcp.rank[i], lcp.rank[j]),
max(lcp.rank[i], lcp.rank[j]));
}
// String Search O(|T| + log |S|)
// return : [l, r], l and r are indices of Suffix Array
// if T doesn't exist, return (-1, -1)
pair<int, int> find(string &t) {
int left = 1, right = sa.size() - 1, med = left;
int leftlen = 0, rightlen = 0, tlen = t.size();
pair<int, int> ret;
while (left + 1 < right) {
med = (left + right) / 2;
int corres_len = max(min(leftlen, sparse.query(left, med)),
min(rightlen, sparse.query(med, right)));
if (corres_len < max(leftlen, rightlen)) {
if (leftlen < rightlen)
left = med, leftlen = corres_len;
else
right = med, rightlen = corres_len;
continue;
}
ret = comp(t, corres_len, sa[med]);
if (ret.second == tlen) return find_range(left, med, right, tlen);
if (ret.first == 0)
right = med, rightlen = ret.second;
else
left = med, leftlen = ret.second;
}
if (sa.size() <= 3) {
if (comp(t, 0, sa[left]).second == tlen)
return find_range(left, left, right, tlen);
if (comp(t, 0, sa[right]).second == tlen)
return find_range(left, right, right, tlen);
return make_pair(-1, -1);
}
med = left + right - med;
ret = comp(t, min(leftlen, rightlen), sa[med]);
if (ret.second == tlen) return find_range(left, med, right, tlen);
return make_pair(-1, -1);
}
};
// Usage:
// SuffixArray sa(S);
// LCPArray lcp(sa);
// StringSearch search(lcp);
#line 5 "verify/verify-yosupo-string/yosupo-zalgo-suffixarray.test.cpp"
using namespace Nyaan; void Nyaan::solve(){
ins(S);
SuffixArray sa(S);
LCPArray lcp(sa);
StringSearch search(lcp);
rep(i,sz(S)){
cout << (i?" ":"") << search.ArbitaryLCP(0 , i);
}
out();
}
verify/verify-yosupo-string/yosupo-zalgo-suffixarray.test.cpp