#include <cstdio>
#include <iostream>
#include <algorithm>
#include <string>
#include <cstring>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <cmath>
#include <iomanip>
using namespace std;

typedef pair<int, int> P;
#define rep(i, n) for (int i=0; i<(n); i++)
#define all(c) (c).begin(), (c).end()
#define uniq(c) c.erase(unique(all(c)), (c).end())
#define _1 first
#define _2 second
#define pb push_back
#define INF 1145141919
#define MOD 1000000007

int N, M;
int C[100001];
int T[100000];
int G[100000];

signed main() {
  ios::sync_with_stdio(false); cin.tie(0);
  cin >> N >> M;
  rep(i, N) {
    int x;
    cin >> x;
    C[x]++;
    T[x%M]++;
  }
  rep(x, 100001) {
    G[x%M] += C[x]/2;
  }
  int sum = 0;

  // 0, M/2
  rep(x, M) {
    if ((x+x)%M != 0) continue;
    sum += T[x]/2;
    T[x] %= 2;
  }

  // x, y
  rep(x, M) {
    int y = (M-x)%M;
    if (x == y) continue;
    int s = min(T[x], T[y]);
    T[x] -= s;
    T[y] -= s;
    sum += s;
  }
  rep(x, M) {
    sum += min(T[x]/2, G[x]);
  }
  cout << sum << "\n";
  return 0;
}

### Prompt

Construct a Cpp code solution to the problem outlined:

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 <cstdio>
#include <iostream>
#include <algorithm>
#include <string>
#include <cstring>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <cmath>
#include <iomanip>
using namespace std;

typedef pair<int, int> P;
#define rep(i, n) for (int i=0; i<(n); i++)
#define all(c) (c).begin(), (c).end()
#define uniq(c) c.erase(unique(all(c)), (c).end())
#define _1 first
#define _2 second
#define pb push_back
#define INF 1145141919
#define MOD 1000000007

int N, M;
int C[100001];
int T[100000];
int G[100000];

signed main() {
  ios::sync_with_stdio(false); cin.tie(0);
  cin >> N >> M;
  rep(i, N) {
    int x;
    cin >> x;
    C[x]++;
    T[x%M]++;
  }
  rep(x, 100001) {
    G[x%M] += C[x]/2;
  }
  int sum = 0;

  // 0, M/2
  rep(x, M) {
    if ((x+x)%M != 0) continue;
    sum += T[x]/2;
    T[x] %= 2;
  }

  // x, y
  rep(x, M) {
    int y = (M-x)%M;
    if (x == y) continue;
    int s = min(T[x], T[y]);
    T[x] -= s;
    T[y] -= s;
    sum += s;
  }
  rep(x, M) {
    sum += min(T[x]/2, G[x]);
  }
  cout << sum << "\n";
  return 0;
}

```