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
#include<bits/stdc++.h>
using namespace std;
using ll = long long;

const int N = 1e5 + 1;
int c[N];
int t0[N], t1[N];

int main() {
  ios::sync_with_stdio(false), cin.tie(0);
  int n, m;
  cin >> n >> m;
  for(int i = 0; i < n; i++) {
    int x; cin >> x; c[x]++;
  }
  for(int i = 1; i < N; i++) {
    t1[i % m] += c[i] / 2 * 2;
    t0[i % m] += c[i] % 2;
  }
  int ans = 0;
  for(int i = 0; i < m; i++) {
    int ii = (m - i) % m;
    if(i == ii) {
      ans += (t0[i] + t1[i]) / 2;
      continue;
    }
    int p = min(t0[i] + t1[i], t0[ii] + t1[ii]);
    ans += p;
    t1[i] -= max(0, p - t0[i]);
    t0[i] = 0;
    t1[ii] -= max(0, p - t0[ii]);
    t0[ii] = 0;
    ans += t1[i]/2;
    t1[i] = 0;
    ans += t1[ii]/2;
    t1[ii] = 0;
  }
  cout << ans << endl;
}
