#include <bits/stdc++.h>
using namespace std;
template <typename T, size_t N>
int SIZE(const T (&t)[N]) {
  return N;
}
template <typename T>
int SIZE(const T &t) {
  return t.size();
}
string to_string(const string s, int x1 = 0, int x2 = 1e9) {
  return '"' + ((x1 < s.size()) ? s.substr(x1, x2 - x1 + 1) : "") + '"';
}
string to_string(const char *s) { return to_string((string)s); }
string to_string(const bool b) { return (b ? "true" : "false"); }
string to_string(const char c) { return string({c}); }
template <size_t N>
string to_string(const bitset<N> &b, int x1 = 0, int x2 = 1e9) {
  string t = "";
  for (int __iii__ = min(x1, SIZE(b)), __jjj__ = min(x2, SIZE(b) - 1);
       __iii__ <= __jjj__; ++__iii__) {
    t += b[__iii__] + '0';
  }
  return '"' + t + '"';
}
template <typename A, typename... C>
string to_string(const A(&v), int x1 = 0, int x2 = 1e9, C... coords);
int l_v_l_v_l = 0, t_a_b_s = 0;
template <typename A, typename B>
string to_string(const pair<A, B> &p) {
  l_v_l_v_l++;
  string res = "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
  l_v_l_v_l--;
  return res;
}
template <typename A, typename... C>
string to_string(const A(&v), int x1, int x2, C... coords) {
  int rnk = rank<A>::value;
  string tab(t_a_b_s, ' ');
  string res = "";
  bool first = true;
  if (l_v_l_v_l == 0) res += '\n';
  res += tab + "[";
  x1 = min(x1, SIZE(v)), x2 = min(x2, SIZE(v));
  auto l = begin(v);
  advance(l, x1);
  auto r = l;
  advance(r, (x2 - x1) + (x2 < SIZE(v)));
  for (auto e = l; e != r; e = next(e)) {
    if (!first) {
      res += ", ";
    }
    first = false;
    l_v_l_v_l++;
    if (e != l) {
      if (rnk > 1) {
        res += '\n';
        t_a_b_s = l_v_l_v_l;
      };
    } else {
      t_a_b_s = 0;
    }
    res += to_string(*e, coords...);
    l_v_l_v_l--;
  }
  res += "]";
  if (l_v_l_v_l == 0) res += '\n';
  return res;
}
void dbgm() { ; }
template <typename Heads, typename... Tails>
void dbgm(Heads H, Tails... T) {
  cerr << to_string(H) << " | ";
  dbgm(T...);
}
bool custom_compare(pair<string, int> &a, pair<string, int> &b) {
  string x = a.first;
  string y = b.first;
  int size = x.size();
  for (int i = 1; i <= size; i++) {
    if (x[i - 1] == y[i - 1]) continue;
    if (i & 1) {
      return x[i - 1] < y[i - 1];
    } else {
      return x[i - 1] > y[i - 1];
    }
  }
  return false;
}
long long calc_power(long long n, long long b, long long modd = -1) {
  long long res = 1;
  while (b > 0) {
    if (b & 1) {
      if (modd == -1)
        res = (res * n);
      else
        res = (res * n) % modd;
    }
    if (modd == -1)
      n = n * n;
    else
      n = n * n % (modd);
    b >>= 1;
  }
  return modd == -1 ? res : res % modd;
}
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long lcm(long long a, long long b) { return a / gcd(a, b) * b; }
long long modinv(long long a, long long m) { return calc_power(a, m - 2, m); }
int n, m;
vector<pair<string, int>> p;
void testcase() {
  cin >> n >> m;
  for (int i = 0; i < n; i++) {
    string s;
    cin >> s;
    p.push_back({s, i + 1});
  }
  sort(p.begin(), p.end(), custom_compare);
  for (int i = 0; i < n; i++) cout << p[i].second << " ";
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  ;
  testcase();
}

### Prompt

In Cpp, your task is to solve the following problem:

Andi and Budi were given an assignment to tidy up their bookshelf of n books. Each book is represented by the book title — a string s_i numbered from 1 to n, each with length m. Andi really wants to sort the book lexicographically ascending, while Budi wants to sort it lexicographically descending.

Settling their fight, they decided to combine their idea and sort it asc-desc-endingly, where the odd-indexed characters will be compared ascendingly, and the even-indexed characters will be compared descendingly.

A string a occurs before a string b in asc-desc-ending order if and only if in the first position where a and b differ, the following holds:

  * if it is an odd position, the string a has a letter that appears earlier in the alphabet than the corresponding letter in b; 
  * if it is an even position, the string a has a letter that appears later in the alphabet than the corresponding letter in b. 

Input

The first line contains two integers n and m (1 ≤ n ⋅ m ≤ 10^6).

The i-th of the next n lines contains a string s_i consisting of m uppercase Latin letters — the book title. The strings are pairwise distinct.

Output

Output n integers — the indices of the strings after they are sorted asc-desc-endingly.

Example

Input


5 2
AA
AB
BB
BA
AZ


Output


5 2 1 3 4

Note

The following illustrates the first example.

<image>

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
template <typename T, size_t N>
int SIZE(const T (&t)[N]) {
  return N;
}
template <typename T>
int SIZE(const T &t) {
  return t.size();
}
string to_string(const string s, int x1 = 0, int x2 = 1e9) {
  return '"' + ((x1 < s.size()) ? s.substr(x1, x2 - x1 + 1) : "") + '"';
}
string to_string(const char *s) { return to_string((string)s); }
string to_string(const bool b) { return (b ? "true" : "false"); }
string to_string(const char c) { return string({c}); }
template <size_t N>
string to_string(const bitset<N> &b, int x1 = 0, int x2 = 1e9) {
  string t = "";
  for (int __iii__ = min(x1, SIZE(b)), __jjj__ = min(x2, SIZE(b) - 1);
       __iii__ <= __jjj__; ++__iii__) {
    t += b[__iii__] + '0';
  }
  return '"' + t + '"';
}
template <typename A, typename... C>
string to_string(const A(&v), int x1 = 0, int x2 = 1e9, C... coords);
int l_v_l_v_l = 0, t_a_b_s = 0;
template <typename A, typename B>
string to_string(const pair<A, B> &p) {
  l_v_l_v_l++;
  string res = "(" + to_string(p.first) + ", " + to_string(p.second) + ")";
  l_v_l_v_l--;
  return res;
}
template <typename A, typename... C>
string to_string(const A(&v), int x1, int x2, C... coords) {
  int rnk = rank<A>::value;
  string tab(t_a_b_s, ' ');
  string res = "";
  bool first = true;
  if (l_v_l_v_l == 0) res += '\n';
  res += tab + "[";
  x1 = min(x1, SIZE(v)), x2 = min(x2, SIZE(v));
  auto l = begin(v);
  advance(l, x1);
  auto r = l;
  advance(r, (x2 - x1) + (x2 < SIZE(v)));
  for (auto e = l; e != r; e = next(e)) {
    if (!first) {
      res += ", ";
    }
    first = false;
    l_v_l_v_l++;
    if (e != l) {
      if (rnk > 1) {
        res += '\n';
        t_a_b_s = l_v_l_v_l;
      };
    } else {
      t_a_b_s = 0;
    }
    res += to_string(*e, coords...);
    l_v_l_v_l--;
  }
  res += "]";
  if (l_v_l_v_l == 0) res += '\n';
  return res;
}
void dbgm() { ; }
template <typename Heads, typename... Tails>
void dbgm(Heads H, Tails... T) {
  cerr << to_string(H) << " | ";
  dbgm(T...);
}
bool custom_compare(pair<string, int> &a, pair<string, int> &b) {
  string x = a.first;
  string y = b.first;
  int size = x.size();
  for (int i = 1; i <= size; i++) {
    if (x[i - 1] == y[i - 1]) continue;
    if (i & 1) {
      return x[i - 1] < y[i - 1];
    } else {
      return x[i - 1] > y[i - 1];
    }
  }
  return false;
}
long long calc_power(long long n, long long b, long long modd = -1) {
  long long res = 1;
  while (b > 0) {
    if (b & 1) {
      if (modd == -1)
        res = (res * n);
      else
        res = (res * n) % modd;
    }
    if (modd == -1)
      n = n * n;
    else
      n = n * n % (modd);
    b >>= 1;
  }
  return modd == -1 ? res : res % modd;
}
long long gcd(long long a, long long b) {
  if (b == 0) return a;
  return gcd(b, a % b);
}
long long lcm(long long a, long long b) { return a / gcd(a, b) * b; }
long long modinv(long long a, long long m) { return calc_power(a, m - 2, m); }
int n, m;
vector<pair<string, int>> p;
void testcase() {
  cin >> n >> m;
  for (int i = 0; i < n; i++) {
    string s;
    cin >> s;
    p.push_back({s, i + 1});
  }
  sort(p.begin(), p.end(), custom_compare);
  for (int i = 0; i < n; i++) cout << p[i].second << " ";
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  ;
  testcase();
}

```