#include <bits/stdc++.h>
using namespace std;
using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using ll = long long int;
using vll = vector<ll>;
using vvll = vector<vll>;
using vvvll = vector<vvll>;
using vd = vector<double>;
using vvd = vector<vd>;
using vvvd = vector<vvd>;
using P = pair<int, int>;
using Pll = pair<ll, ll>;
using cdouble = complex<double>;
const double eps = 1e-7;
bool feq(double x, double y) { return abs(x - y) <= eps; }
bool inrange(ll x, ll t) { return x >= 0 && x < t; }
bool inrange(vll xs, ll t) {
  for (const auto &x : xs)
    if (!(x >= 0 && x < t)) return false;
  return true;
}
int ceillog2(ll x) { return int(ceil(log2(x))); }
int floorlog2(ll x) { return int(floor(log2(x))); }
template <class T>
T reversed(T container) {
  reverse(container.begin(), container.end());
  return container;
}
template <class T>
void printv(const vector<T> &v) {
  for (const T &x : v) cout << x << " ";
  cout << "\n";
}
template <class T>
void printmx(const vector<vector<T>> &mx) {
  for (const vector<T> &v : mx) printv(v);
}
ll rndf(double x) { return (ll)(x + (x >= 0 ? 0.5 : -0.5)); }
ll floorsqrt(ll x) {
  ll m = (ll)sqrt((double)x);
  return m + (m * m <= x ? 0 : -1);
}
ll ceilsqrt(ll x) {
  ll m = (ll)sqrt((double)x);
  return m + (x <= m * m ? 0 : 1);
}
ll rnddiv(ll a, ll b) { return (a / b + (a % b * 2 >= b ? 1 : 0)); }
ll ceildiv(ll a, ll b) { return (a / b + (a % b == 0 ? 0 : 1)); }
ll gcd(ll m, ll n) {
  if (n == 0)
    return m;
  else
    return gcd(n, m % n);
}
ll lcm(ll m, ll n) { return m * n / gcd(m, n); }
class Random_Int {
 private:
  mt19937 *mt;
  uniform_int_distribution<> *distr_int;

 public:
  Random_Int(int m) {
    mt = new std::mt19937(
        (unsigned)(std::chrono::duration_cast<chrono::nanoseconds>(
                       chrono::high_resolution_clock::now().time_since_epoch())
                       .count()));
    distr_int = new uniform_int_distribution<>(0, m - 1);
  }
  int get() { return (*distr_int)(*mt); }
};
class String_Comparator {
 private:
  const vll MOD_cands = {1000000007, 1000000403, 1000000787, 1000001447,
                         1000001819, 1000002359, 1000002803, 1000003919,
                         1000004207, 1000004519};
  ll MOD;
  int max_length;
  vll bases;
  vvll pows;
  Random_Int *ri;

 public:
  String_Comparator(int max_length, int n_base = 3) {
    Random_Int *rm = new Random_Int(int(MOD_cands.size()));
    this->MOD = this->MOD_cands[rm->get()];
    this->max_length = max(1, max_length);
    this->ri = new Random_Int(int(this->MOD) - 256);
    this->bases.resize(n_base);
    this->pows.resize(n_base, vll(this->max_length + 1));
    for (int k = 0; k < int(n_base); k++) {
      this->bases[k] = this->ri->get() + 256;
      this->pows[k][0] = 1;
      for (int i = 1; i <= int(this->max_length); i++) {
        pows[k][i] = pows[k][i - 1] * this->bases[k] % this->MOD;
      }
    }
  }
  vvll make_hashs(const string &s) {
    int n = int(s.length());
    vvll ret(this->bases.size(), vll(n + 1));
    for (int k = 0; k < int(this->bases.size()); k++) {
      for (int i = 1; i <= int(n); i++) {
        ret[k][i] = (ret[k][i - 1] * this->bases[k] + s[i - 1]) % this->MOD;
      }
    }
    return ret;
  }
  bool is_equal(const vvll &hashs0, const vvll &hashs1, const int s0,
                const int s1, const int l) {
    for (int k = 0; k < int(this->bases.size()); k++) {
      ll val0 = (hashs0[k][s0 + l] - hashs0[k][s0] * pows[k][l]) % this->MOD;
      ll val1 = (hashs1[k][s1 + l] - hashs1[k][s1] * pows[k][l]) % this->MOD;
      if (val0 < 0) val0 += this->MOD;
      if (val1 < 0) val1 += this->MOD;
      if (val0 != val1) return false;
    }
    return true;
  }
  vll get_hashs(const vvll &hashs, const int s, const int l) {
    vll ret(bases.size());
    for (int k = 0; k < int(this->bases.size()); k++) {
      ret[k] = (hashs[k][s + l] - hashs[k][s] * pows[k][l]) % this->MOD;
      if (ret[k] < 0) ret[k] += this->MOD;
    }
    return ret;
  }
};
template <class val_t, class bsargv_t>
val_t lower_bsearch(val_t l, val_t r, const bsargv_t &v,
                    bool (*evalfunc)(val_t, const bsargv_t &)) {
  if (r - l == 1) {
    if (evalfunc(l, v))
      return l;
    else
      return l - 1;
  }
  val_t m = (l + r) / 2;
  if (evalfunc(m, v))
    return lower_bsearch<val_t, bsargv_t>(m, r, v, evalfunc);
  else
    return lower_bsearch<val_t, bsargv_t>(l, m, v, evalfunc);
}
struct bsargv_t {
  int n;
  String_Comparator *sc;
  vvll hashs0, hashs1;
  int i0, i1;
};
bool evalfunc(int val, const bsargv_t &v) {
  if (v.i0 + val <= v.n && v.i1 + val <= v.n &&
      v.sc->is_equal(v.hashs0, v.hashs1, v.i0, v.i1, val)) {
    return true;
  } else {
    return false;
  }
}
struct ans_t {
  int l, r;
  bool operator<(const ans_t &another) const {
    return (l + r < another.l + another.r);
  }
};
string core(int n, const string &s, const vi &os, const vi &es) {
  ans_t ans = {1, 0};
  vi oseq(n / 2 + 2, -1);
  vi eseq(n / 2 + 2, -1);
  for (int i = 0; i < int(ceildiv(n, 2)); i++) {
    if (os[i] > 0) {
      oseq[i - os[i] + 1] = max(oseq[i - os[i] + 1], i);
    }
  }
  for (int i = 0; i < int(n / 2); i++) {
    if (es[i] > 0) {
      eseq[i - es[i] + 1] = max(eseq[i - es[i] + 1], i);
    }
  }
  bool is_par = true;
  int omax = -1, emax = -1;
  for (int i = 0; i < int(n / 2 + 1); i++) {
    omax = max(omax, oseq[i]);
    emax = max(emax, eseq[i]);
    ans_t buf = {i, i};
    ans = max(ans, buf);
    if (omax >= 0) {
      int ro = omax;
      if (ro >= i) {
        ans_t bufo = buf;
        bufo.l += (ro - i + 1) * 2 - 1;
        ans = max(ans, bufo);
      }
    }
    if (emax >= 0) {
      int re = emax;
      if (re >= i) {
        ans_t bufe = buf;
        bufe.l += (re - i + 1) * 2;
        ans = max(ans, bufe);
      }
    }
    if (i >= n - 1 - i || s[i] != s[n - 1 - i]) {
      is_par = false;
      break;
    }
  }
  return s.substr(0, ans.l) + s.substr(n - ans.r, ans.r);
}
string solve(bsargv_t &v) {
  string s;
  cin >> s;
  string t = s;
  reverse(t.begin(), t.end());
  v.n = s.length();
  v.hashs0 = v.sc->make_hashs(s);
  v.hashs1 = v.sc->make_hashs(t);
  vi os(v.n), es(v.n);
  for (int i = 0; i < int(v.n); i++) {
    v.i0 = i;
    v.i1 = v.n - 1 - i;
    os[i] = lower_bsearch(0, v.n, v, evalfunc);
  }
  for (int i = 0; i < int(v.n - 1); i++) {
    v.i0 = i + 1;
    v.i1 = v.n - 1 - i;
    es[i] = lower_bsearch(0, v.n, v, evalfunc);
  }
  string ans0 = core(v.n, s, os, es);
  reverse(os.begin(), os.end());
  reverse(es.begin(), es.end());
  for (int i = 0; i < int(v.n - 1); i++) {
    es[i] = es[i + 1];
  }
  es[v.n - 1] = 0;
  string ans1 = core(v.n, t, os, es);
  reverse(ans1.begin(), ans1.end());
  string ans = (ans0.length() >= ans1.length() ? ans0 : ans1);
  return ans;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  ;
  int n;
  cin >> n;
  bsargv_t v;
  v.sc = new String_Comparator(1000003);
  for (int _ = 0; _ < int(n); _++) {
    cout << solve(v) << "\n";
  }
}

### Prompt

Construct a cpp code solution to the problem outlined:

This is the easy version of the problem. The difference is the constraint on the sum of lengths of strings and the number of test cases. You can make hacks only if you solve all versions of this task.

You are given a string s, consisting of lowercase English letters. Find the longest string, t, which satisfies the following conditions: 

  * The length of t does not exceed the length of s. 
  * t is a palindrome. 
  * There exists two strings a and b (possibly empty), such that t = a + b ( "+" represents concatenation), and a is prefix of s while b is suffix of s. 

Input

The input consists of multiple test cases. The first line contains a single integer t (1 ≤ t ≤ 1000), the number of test cases. The next t lines each describe a test case.

Each test case is a non-empty string s, consisting of lowercase English letters.

It is guaranteed that the sum of lengths of strings over all test cases does not exceed 5000.

Output

For each test case, print the longest string which satisfies the conditions described above. If there exists multiple possible solutions, print any of them.

Example

Input


5
a
abcdfdcecba
abbaxyzyx
codeforces
acbba


Output


a
abcdfdcba
xyzyx
c
abba

Note

In the first test, the string s = "a" satisfies all conditions.

In the second test, the string "abcdfdcba" satisfies all conditions, because:

  * Its length is 9, which does not exceed the length of the string s, which equals 11. 
  * It is a palindrome. 
  * "abcdfdcba" = "abcdfdc" + "ba", and "abcdfdc" is a prefix of s while "ba" is a suffix of s. 



It can be proven that there does not exist a longer string which satisfies the conditions.

In the fourth test, the string "c" is correct, because "c" = "c" + "" and a or b can be empty. The other possible solution for this test is "s".

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
using vi = vector<int>;
using vvi = vector<vi>;
using vvvi = vector<vvi>;
using ll = long long int;
using vll = vector<ll>;
using vvll = vector<vll>;
using vvvll = vector<vvll>;
using vd = vector<double>;
using vvd = vector<vd>;
using vvvd = vector<vvd>;
using P = pair<int, int>;
using Pll = pair<ll, ll>;
using cdouble = complex<double>;
const double eps = 1e-7;
bool feq(double x, double y) { return abs(x - y) <= eps; }
bool inrange(ll x, ll t) { return x >= 0 && x < t; }
bool inrange(vll xs, ll t) {
  for (const auto &x : xs)
    if (!(x >= 0 && x < t)) return false;
  return true;
}
int ceillog2(ll x) { return int(ceil(log2(x))); }
int floorlog2(ll x) { return int(floor(log2(x))); }
template <class T>
T reversed(T container) {
  reverse(container.begin(), container.end());
  return container;
}
template <class T>
void printv(const vector<T> &v) {
  for (const T &x : v) cout << x << " ";
  cout << "\n";
}
template <class T>
void printmx(const vector<vector<T>> &mx) {
  for (const vector<T> &v : mx) printv(v);
}
ll rndf(double x) { return (ll)(x + (x >= 0 ? 0.5 : -0.5)); }
ll floorsqrt(ll x) {
  ll m = (ll)sqrt((double)x);
  return m + (m * m <= x ? 0 : -1);
}
ll ceilsqrt(ll x) {
  ll m = (ll)sqrt((double)x);
  return m + (x <= m * m ? 0 : 1);
}
ll rnddiv(ll a, ll b) { return (a / b + (a % b * 2 >= b ? 1 : 0)); }
ll ceildiv(ll a, ll b) { return (a / b + (a % b == 0 ? 0 : 1)); }
ll gcd(ll m, ll n) {
  if (n == 0)
    return m;
  else
    return gcd(n, m % n);
}
ll lcm(ll m, ll n) { return m * n / gcd(m, n); }
class Random_Int {
 private:
  mt19937 *mt;
  uniform_int_distribution<> *distr_int;

 public:
  Random_Int(int m) {
    mt = new std::mt19937(
        (unsigned)(std::chrono::duration_cast<chrono::nanoseconds>(
                       chrono::high_resolution_clock::now().time_since_epoch())
                       .count()));
    distr_int = new uniform_int_distribution<>(0, m - 1);
  }
  int get() { return (*distr_int)(*mt); }
};
class String_Comparator {
 private:
  const vll MOD_cands = {1000000007, 1000000403, 1000000787, 1000001447,
                         1000001819, 1000002359, 1000002803, 1000003919,
                         1000004207, 1000004519};
  ll MOD;
  int max_length;
  vll bases;
  vvll pows;
  Random_Int *ri;

 public:
  String_Comparator(int max_length, int n_base = 3) {
    Random_Int *rm = new Random_Int(int(MOD_cands.size()));
    this->MOD = this->MOD_cands[rm->get()];
    this->max_length = max(1, max_length);
    this->ri = new Random_Int(int(this->MOD) - 256);
    this->bases.resize(n_base);
    this->pows.resize(n_base, vll(this->max_length + 1));
    for (int k = 0; k < int(n_base); k++) {
      this->bases[k] = this->ri->get() + 256;
      this->pows[k][0] = 1;
      for (int i = 1; i <= int(this->max_length); i++) {
        pows[k][i] = pows[k][i - 1] * this->bases[k] % this->MOD;
      }
    }
  }
  vvll make_hashs(const string &s) {
    int n = int(s.length());
    vvll ret(this->bases.size(), vll(n + 1));
    for (int k = 0; k < int(this->bases.size()); k++) {
      for (int i = 1; i <= int(n); i++) {
        ret[k][i] = (ret[k][i - 1] * this->bases[k] + s[i - 1]) % this->MOD;
      }
    }
    return ret;
  }
  bool is_equal(const vvll &hashs0, const vvll &hashs1, const int s0,
                const int s1, const int l) {
    for (int k = 0; k < int(this->bases.size()); k++) {
      ll val0 = (hashs0[k][s0 + l] - hashs0[k][s0] * pows[k][l]) % this->MOD;
      ll val1 = (hashs1[k][s1 + l] - hashs1[k][s1] * pows[k][l]) % this->MOD;
      if (val0 < 0) val0 += this->MOD;
      if (val1 < 0) val1 += this->MOD;
      if (val0 != val1) return false;
    }
    return true;
  }
  vll get_hashs(const vvll &hashs, const int s, const int l) {
    vll ret(bases.size());
    for (int k = 0; k < int(this->bases.size()); k++) {
      ret[k] = (hashs[k][s + l] - hashs[k][s] * pows[k][l]) % this->MOD;
      if (ret[k] < 0) ret[k] += this->MOD;
    }
    return ret;
  }
};
template <class val_t, class bsargv_t>
val_t lower_bsearch(val_t l, val_t r, const bsargv_t &v,
                    bool (*evalfunc)(val_t, const bsargv_t &)) {
  if (r - l == 1) {
    if (evalfunc(l, v))
      return l;
    else
      return l - 1;
  }
  val_t m = (l + r) / 2;
  if (evalfunc(m, v))
    return lower_bsearch<val_t, bsargv_t>(m, r, v, evalfunc);
  else
    return lower_bsearch<val_t, bsargv_t>(l, m, v, evalfunc);
}
struct bsargv_t {
  int n;
  String_Comparator *sc;
  vvll hashs0, hashs1;
  int i0, i1;
};
bool evalfunc(int val, const bsargv_t &v) {
  if (v.i0 + val <= v.n && v.i1 + val <= v.n &&
      v.sc->is_equal(v.hashs0, v.hashs1, v.i0, v.i1, val)) {
    return true;
  } else {
    return false;
  }
}
struct ans_t {
  int l, r;
  bool operator<(const ans_t &another) const {
    return (l + r < another.l + another.r);
  }
};
string core(int n, const string &s, const vi &os, const vi &es) {
  ans_t ans = {1, 0};
  vi oseq(n / 2 + 2, -1);
  vi eseq(n / 2 + 2, -1);
  for (int i = 0; i < int(ceildiv(n, 2)); i++) {
    if (os[i] > 0) {
      oseq[i - os[i] + 1] = max(oseq[i - os[i] + 1], i);
    }
  }
  for (int i = 0; i < int(n / 2); i++) {
    if (es[i] > 0) {
      eseq[i - es[i] + 1] = max(eseq[i - es[i] + 1], i);
    }
  }
  bool is_par = true;
  int omax = -1, emax = -1;
  for (int i = 0; i < int(n / 2 + 1); i++) {
    omax = max(omax, oseq[i]);
    emax = max(emax, eseq[i]);
    ans_t buf = {i, i};
    ans = max(ans, buf);
    if (omax >= 0) {
      int ro = omax;
      if (ro >= i) {
        ans_t bufo = buf;
        bufo.l += (ro - i + 1) * 2 - 1;
        ans = max(ans, bufo);
      }
    }
    if (emax >= 0) {
      int re = emax;
      if (re >= i) {
        ans_t bufe = buf;
        bufe.l += (re - i + 1) * 2;
        ans = max(ans, bufe);
      }
    }
    if (i >= n - 1 - i || s[i] != s[n - 1 - i]) {
      is_par = false;
      break;
    }
  }
  return s.substr(0, ans.l) + s.substr(n - ans.r, ans.r);
}
string solve(bsargv_t &v) {
  string s;
  cin >> s;
  string t = s;
  reverse(t.begin(), t.end());
  v.n = s.length();
  v.hashs0 = v.sc->make_hashs(s);
  v.hashs1 = v.sc->make_hashs(t);
  vi os(v.n), es(v.n);
  for (int i = 0; i < int(v.n); i++) {
    v.i0 = i;
    v.i1 = v.n - 1 - i;
    os[i] = lower_bsearch(0, v.n, v, evalfunc);
  }
  for (int i = 0; i < int(v.n - 1); i++) {
    v.i0 = i + 1;
    v.i1 = v.n - 1 - i;
    es[i] = lower_bsearch(0, v.n, v, evalfunc);
  }
  string ans0 = core(v.n, s, os, es);
  reverse(os.begin(), os.end());
  reverse(es.begin(), es.end());
  for (int i = 0; i < int(v.n - 1); i++) {
    es[i] = es[i + 1];
  }
  es[v.n - 1] = 0;
  string ans1 = core(v.n, t, os, es);
  reverse(ans1.begin(), ans1.end());
  string ans = (ans0.length() >= ans1.length() ? ans0 : ans1);
  return ans;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  ;
  int n;
  cin >> n;
  bsargv_t v;
  v.sc = new String_Comparator(1000003);
  for (int _ = 0; _ < int(n); _++) {
    cout << solve(v) << "\n";
  }
}

```