#include <algorithm>
#include <cstring>
#include <deque>
#include <functional>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <vector>
using namespace std;
using ll = long long;

int main() {
  int N, M;
  while (cin >> N >> M) {
    map<int, int> mp;
    for (int i = 0; i < N; i++) {
      int x;
      cin >> x;
      ++mp[x];
    }
    vector<int> g(M, 0), m(M, 0);
    for (auto e : mp) {
      int x = e.first % M, cnt = e.second;
      m[x] += cnt;
      g[x] += cnt / 2;
    }
    int res = 0;
    for (int i = 0; i <= M - i; i++) {
      int j = (M - i) % M;
      if (i == j) {
        res += m[i] / 2;
      } else {
        int best = 0;
        for (int lower = 0, upper = min(m[i], m[j]); lower <= upper; lower++) {
          int ai = min(g[i], (m[i] - lower) / 2);
          int aj = min(g[j], (m[j] - lower) / 2);
          best = max(best, ai + aj + min(m[i] - 2 * ai, m[j] - 2 * aj));
        }
        res += best;
      }
    }
    cout << res << endl;
  }
  return 0;
}

### Prompt

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

Takahashi is playing with N cards.

The i-th card has an integer X_i on it.

Takahashi is trying to create as many pairs of cards as possible satisfying one of the following conditions:

* The integers on the two cards are the same.
* The sum of the integers on the two cards is a multiple of M.



Find the maximum number of pairs that can be created.

Note that a card cannot be used in more than one pair.

Constraints

* 2≦N≦10^5
* 1≦M≦10^5
* 1≦X_i≦10^5

Input

The input is given from Standard Input in the following format:


N M
X_1 X_2 ... X_N


Output

Print the maximum number of pairs that can be created.

Examples

Input

7 5
3 1 4 1 5 9 2


Output

3


Input

15 10
1 5 6 10 11 11 11 20 21 25 25 26 99 99 99


Output

6

### Response

```cpp
#include <algorithm>
#include <cstring>
#include <deque>
#include <functional>
#include <iostream>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <vector>
using namespace std;
using ll = long long;

int main() {
  int N, M;
  while (cin >> N >> M) {
    map<int, int> mp;
    for (int i = 0; i < N; i++) {
      int x;
      cin >> x;
      ++mp[x];
    }
    vector<int> g(M, 0), m(M, 0);
    for (auto e : mp) {
      int x = e.first % M, cnt = e.second;
      m[x] += cnt;
      g[x] += cnt / 2;
    }
    int res = 0;
    for (int i = 0; i <= M - i; i++) {
      int j = (M - i) % M;
      if (i == j) {
        res += m[i] / 2;
      } else {
        int best = 0;
        for (int lower = 0, upper = min(m[i], m[j]); lower <= upper; lower++) {
          int ai = min(g[i], (m[i] - lower) / 2);
          int aj = min(g[j], (m[j] - lower) / 2);
          best = max(best, ai + aj + min(m[i] - 2 * ai, m[j] - 2 * aj));
        }
        res += best;
      }
    }
    cout << res << endl;
  }
  return 0;
}

```