/**
 * date   : 2025-01-04 16:54:13
 * author : Nyaan
 */

#define NDEBUG

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 <tr2/dynamic_bitset>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

// utility

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>
  constexpr 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


// bit operation

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


// inout

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


// debug


#ifdef NyaanDebug
#define trc(...) (void(0))
#else
#define trc(...) (void(0))
#endif

#ifdef NyaanLocal
#define trc2(...) (void(0))
#else
#define trc2(...) (void(0))
#endif


// macro

#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)


namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }


//


template <typename T, typename F>
struct SegmentTree {
  int N;
  int size;
  vector<T> seg;
  const F f;
  const T I;

  SegmentTree(F _f, const T &I_) : N(0), size(0), f(_f), I(I_) {}

  SegmentTree(int _N, F _f, const T &I_) : f(_f), I(I_) { init(_N); }

  SegmentTree(const vector<T> &v, F _f, T I_) : f(_f), I(I_) {
    init(v.size());
    for (int i = 0; i < (int)v.size(); i++) {
      seg[i + size] = v[i];
    }
    build();
  }

  void init(int _N) {
    N = _N;
    size = 1;
    while (size < N) size <<= 1;
    seg.assign(2 * size, I);
  }

  void set(int k, T x) { seg[k + size] = x; }

  void build() {
    for (int k = size - 1; k > 0; k--) {
      seg[k] = f(seg[2 * k], seg[2 * k + 1]);
    }
  }

  void update(int k, T x) {
    k += size;
    seg[k] = x;
    while (k >>= 1) {
      seg[k] = f(seg[2 * k], seg[2 * k + 1]);
    }
  }

  void add(int k, T x) {
    k += size;
    seg[k] += x;
    while (k >>= 1) {
      seg[k] = f(seg[2 * k], seg[2 * k + 1]);
    }
  }

  // query to [a, b)
  T query(int a, int b) {
    T L = I, R = I;
    for (a += size, b += size; a < b; a >>= 1, b >>= 1) {
      if (a & 1) L = f(L, seg[a++]);
      if (b & 1) R = f(seg[--b], R);
    }
    return f(L, R);
  }

  T &operator[](const int &k) { return seg[k + size]; }

  // check(a[l] * ...  * a[r-1]) が true となる最大の r
  // (右端まですべて true なら N を返す)
  template <class C>
  int max_right(int l, C check) {
    assert(0 <= l && l <= N);
    assert(check(I) == true);
    if (l == N) return N;
    l += size;
    T sm = I;
    do {
      while (l % 2 == 0) l >>= 1;
      if (!check(f(sm, seg[l]))) {
        while (l < size) {
          l = (2 * l);
          if (check(f(sm, seg[l]))) {
            sm = f(sm, seg[l]);
            l++;
          }
        }
        return l - size;
      }
      sm = f(sm, seg[l]);
      l++;
    } while ((l & -l) != l);
    return N;
  }

  // check(a[l] * ... * a[r-1]) が true となる最小の l
  // (左端まで true なら 0 を返す)
  template <typename C>
  int min_left(int r, C check) {
    assert(0 <= r && r <= N);
    assert(check(I) == true);
    if (r == 0) return 0;
    r += size;
    T sm = I;
    do {
      r--;
      while (r > 1 && (r % 2)) r >>= 1;
      if (!check(f(seg[r], sm))) {
        while (r < size) {
          r = (2 * r + 1);
          if (check(f(seg[r], sm))) {
            sm = f(seg[r], sm);
            r--;
          }
        }
        return r + 1 - size;
      }
      sm = f(seg[r], sm);
    } while ((r & -r) != r);
    return 0;
  }
};

//
// #include "string/string-search.hpp"



using namespace std;



namespace internal {
using i64 = long long;
using u64 = unsigned long long;
using u128 = __uint128_t;

template <int BASE_NUM = 2>
struct Hash : array<u64, BASE_NUM> {
  using array<u64, BASE_NUM>::operator[];
  static constexpr int n = BASE_NUM;

  Hash() : array<u64, BASE_NUM>() {}

  static constexpr u64 md = (1ull << 61) - 1;

  constexpr static Hash set(const i64 &a) {
    Hash res;
    fill(begin(res), end(res), cast(a));
    return res;
  }
  Hash &operator+=(const Hash &r) {
    for (int i = 0; i < n; i++)
      if (((*this)[i] += r[i]) >= md) (*this)[i] -= md;
    return *this;
  }
  Hash &operator+=(const i64 &r) {
    u64 s = cast(r);
    for (int i = 0; i < n; i++)
      if (((*this)[i] += s) >= md) (*this)[i] -= md;
    return *this;
  }
  Hash &operator-=(const Hash &r) {
    for (int i = 0; i < n; i++)
      if (((*this)[i] += md - r[i]) >= md) (*this)[i] -= md;
    return *this;
  }
  Hash &operator-=(const i64 &r) {
    u64 s = cast(r);
    for (int i = 0; i < n; i++)
      if (((*this)[i] += md - s) >= md) (*this)[i] -= md;
    return *this;
  }
  Hash &operator*=(const Hash &r) {
    for (int i = 0; i < n; i++) (*this)[i] = modmul((*this)[i], r[i]);
    return *this;
  }
  Hash &operator*=(const i64 &r) {
    u64 s = cast(r);
    for (int i = 0; i < n; i++) (*this)[i] = modmul((*this)[i], s);
    return *this;
  }

  Hash operator+(const Hash &r) { return Hash(*this) += r; }
  Hash operator+(const i64 &r) { return Hash(*this) += r; }
  Hash operator-(const Hash &r) { return Hash(*this) -= r; }
  Hash operator-(const i64 &r) { return Hash(*this) -= r; }
  Hash operator*(const Hash &r) { return Hash(*this) *= r; }
  Hash operator*(const i64 &r) { return Hash(*this) *= r; }
  Hash operator-() const {
    Hash res;
    for (int i = 0; i < n; i++) res[i] = (*this)[i] == 0 ? 0 : md - (*this)[i];
    return res;
  }
  friend Hash pfma(const Hash &a, const Hash &b, const Hash &c) {
    Hash res;
    for (int i = 0; i < n; i++) res[i] = modfma(a[i], b[i], c[i]);
    return res;
  }
  friend Hash pfma(const Hash &a, const Hash &b, const i64 &c) {
    Hash res;
    u64 s = cast(c);
    for (int i = 0; i < n; i++) res[i] = modfma(a[i], b[i], s);
    return res;
  }

  Hash pow(long long e) {
    Hash a{*this}, res{Hash::set(1)};
    for (; e; a *= a, e >>= 1) {
      if (e & 1) res *= a;
    }
    return res;
  }

  static Hash get_basis() {
    static auto rand_time =
        chrono::duration_cast<chrono::nanoseconds>(
            chrono::high_resolution_clock::now().time_since_epoch())
            .count();
    static mt19937_64 rng(rand_time);
    Hash h;
    for (int i = 0; i < n; i++) {
      while (isPrimitive(h[i] = rng() % (md - 1) + 1) == false)
        ;
    }
    return h;
  }

 private:
  static u64 modpow(u64 a, u64 b) {
    u64 r = 1;
    for (a %= md; b; a = modmul(a, a), b >>= 1) r = modmul(r, a);
    return r;
  }
  static bool isPrimitive(u64 x) {
    for (auto &d : vector<u64>{2, 3, 5, 7, 11, 13, 31, 41, 61, 151, 331, 1321})
      if (modpow(x, (md - 1) / d) <= 1) return false;
    return true;
  }
  static inline constexpr u64 cast(const long long &a) {
    return a < 0 ? a + md : a;
  }
  static inline constexpr u64 modmul(const u64 &a, const u64 &b) { 
    u128 d = u128(a) * b;
    u64 ret = (u64(d) & md) + u64(d >> 61);
    return ret >= md ? ret - md : ret;
  }
  static inline constexpr u64 modfma(const u64 &a, const u64 &b, const u64 &c) {
    u128 d = u128(a) * b + c;
    u64 ret = (d >> 61) + (u64(d) & md);
    return ret >= md ? ret - md : ret;
  }
};

}  // namespace internal

/**
 * @brief ハッシュ構造体
 * @docs docs/internal/internal-hash.md
 */


template <typename Str, int BASE_NUM = 2>
struct RollingHash {
  using Hash = internal::Hash<BASE_NUM>;
  Str data;
  vector<Hash> hs, pw;
  int s;
  static Hash basis;

  RollingHash(const Str &S = Str()) { build(S); }

  void build(const Str &S) {
    data = S;
    s = S.size();
    hs.resize(s + 1);
    pw.resize(s + 1);
    pw[0] = Hash::set(1);
    hs[0] = Hash::set(0);
    for (int i = 1; i <= s; i++) {
      pw[i] = pw[i - 1] * basis;
      hs[i] = pfma(hs[i - 1], basis, S[i - 1]);
    }
  }

  Hash get(int l, int r = -1) const {
    if (r == -1) r = s;
    return pfma(hs[l], -pw[r - l], hs[r]);
  }

  // T の hash を返す
  static Hash get_hash(const Str &T) {
    Hash ret = Hash::set(0);
    for (int i = 0; i < (int)T.size(); i++) ret = pfma(ret, basis, T[i]);
    return ret;
  }

  // a + b の hash を返す
  // 引数 : a, b, b の長さ
  static Hash unite(Hash a, Hash b, long long bsize) {
    return pfma(a, basis.pow(bsize), b);
  }

  int find(Str &T, int lower = 0) const {
    auto ths = get_hash(T);
    for (int i = lower; i <= s - (int)T.size(); i++)
      if (ths == get(i, i + (int)T.size())) return i;
    return -1;
  }

  static int lcp(const RollingHash &a, const RollingHash &b, int al, int bl) {
    int ok = 0, ng = min(a.size() - al, b.size() - bl) + 1;
    while (ok + 1 < ng) {
      int med = (ok + ng) / 2;
      (a.get(al, med + al) == b.get(bl, med + bl) ? ok : ng) = med;
    }
    return ok;
  }

  static int strcmp(const RollingHash &a, const RollingHash &b, int al, int bl,
                    int ar = -1, int br = -1) {
    if (ar == -1) ar = a.size();
    if (br == -1) br = b.size();
    int n = min<int>({lcp(a, b, al, bl), ar - al, br - bl});
    return al + n == ar                      ? bl + n == br ? 0 : -1
           : bl + n == br                    ? 1
           : a.data[al + n] < b.data[bl + n] ? -1
                                             : 1;
  }

  int size() const { return s; }
};

template <typename Str, int BASE_NUM>
typename RollingHash<Str, BASE_NUM>::Hash RollingHash<Str, BASE_NUM>::basis =
    internal::Hash<BASE_NUM>::get_basis();
using roriha = RollingHash<string, 2>;

/**
 * @brief Rolling Hash
 * @docs docs/string/rolling-hash.md
 */


using namespace Nyaan;

void q() {
  auto kth = [&](const string& S, int i) { return S[i % sz(S)]; };
  auto calc_lcp = [&](const string& S, const string& T) {
    for (int i = 0; i <= 2 * max(sz(S), sz(T)); i++) {
      char c1 = kth(S, i);
      char c2 = kth(T, i);
      if (c1 != c2) return i;
    }
    return inf;
  };

  ini(N);
  V<string> S(N);
  in(S);

  string T;
  vi pos(N, -1);
  rep(i, N) {
    pos[i] = sz(T);
    T += S[i];
    T += "$";
  }
  {
    RollingHash ss = T;
    vi v = mkiota(N);
    auto comp = [&](int i, int j) {
      int szi = sz(S[i]), szj = sz(S[j]);
      if (szi <= szj) {
        trc("hoge");
        int lcp1 = ss.lcp(ss, ss, pos[i], pos[j]);
        trc(lcp1);
        if (lcp1 < szi) return S[i][lcp1] < S[j][lcp1];
        int lcp2 = ss.lcp(ss, ss, pos[j], pos[j] + szi);
        trc(lcp2);
        if (lcp2 < szj - szi) return S[j][lcp2] < S[j][szi + lcp2];
        int lcp3 = ss.lcp(ss, ss, pos[j] + szj - szi, pos[i]);
        trc(lcp3);
        if (lcp3 < szi) return S[j][szj - szi + lcp3] < S[i][lcp3];
        return false;
      }
      trc("huga");
      int lcp1 = ss.lcp(ss, ss, pos[i], pos[j]);
      trc(lcp1);
      if (lcp1 < szj) return S[i][lcp1] < S[j][lcp1];
      int lcp2 = ss.lcp(ss, ss, pos[i] + szj, pos[i]);
      trc(lcp2, T.substr(pos[i] + szj), T.substr(pos[i]));
      if (lcp2 < szi - szj) return S[i][szj + lcp2] < S[i][lcp2];
      int lcp3 = ss.lcp(ss, ss, pos[j], pos[i] + szi - szj);
      trc(lcp3);
      if (lcp3 < szj) return S[j][lcp3] < S[i][szi - szj + lcp3];
      return false;
    };
    /*
    auto comp2 = [&](int i, int j) {
      int res = comp(i, j);
      string X = S[i] + S[j];
      string Y = S[j] + S[i];
      int nai = X < Y;
      if (res != nai) {
        trc(i, j, S[i], S[j], res, nai);
        exit(1);
      }
      return res;
    };
    */
    sort(all(v), comp);
    trc(v);
    V<string> newS;
    rep(i, N) newS.push_back(S[v[i]]);
    S = newS;
    trc(S);
  }
  V<int> lcp(N - 1);
  rep(i, N - 1) lcp[i] = calc_lcp(S[i], S[i + 1]);
  SegmentTree seg(lcp, [](int a, int b) { return min(a, b); }, inf);
  ll ans = 0;

  auto dfs = [&](auto rc, int l, int r) -> void {
    trc(l, r);
    if (r - l < 3) return;
    int len = seg.query(l, r - 1);
    if (len == inf) return;
    int u = -1, v = -1;
    {
      int ng = l - 1, ok = r;
      // l 文字目が初めて N 以上になる i は？
      while (ng + 1 < ok) {
        int m = (ok + ng) / 2;
        (kth(S[m], len) >= 'N' ? ok : ng) = m;
      }
      u = ok;
    }
    {
      int ng = l - 1, ok = r;
      // l 文字目が初めて P 以上になる i は？
      while (ng + 1 < ok) {
        int m = (ok + ng) / 2;
        (kth(S[m], len) >= 'P' ? ok : ng) = m;
      }
      v = ok;
    }
    ans += 1LL * (u - l) * (v - u) * (r - v);
    rc(rc, l, u);
    rc(rc, u, v);
    rc(rc, v, r);
  };
  dfs(dfs, 0, N);
  out(ans);
}

void Nyaan::solve() {
  int t = 1;
  // in(t);
  while (t--) q();
}