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;

long long n, m;
vector<long long> cnt, cntd, x;

long long solve();

int main() {
  cin >> n >> m;
  x.resize(n);
  cnt.assign(m, 0);
  cntd.assign(m, 0);
  for(int i = 0; i < n; ++i) cin >> x[i];
  cout << solve() << endl;
  return 0;
}

long long solve() {
  long long ans = 0;
  sort(x.begin(), x.end());
  for(int i = 0; i < n; ++i) ++cnt[x[i] % m];
  for(int i = 0; i < n; ++i)
    if(i + 1 < n && x[i] == x[i + 1]) ++cntd[x[++i] % m];
  for(int i = 0; i <= m / 2; ++i) {
    if(i == 0 || i * 2 == m)
      ans += cnt[i] / 2;
    else {
      int mi = i, ma = m - i;
      if(cnt[mi] > cnt[ma]) swap(mi, ma);
      ans += cnt[mi];
      cnt[ma] -= cnt[mi];
      cnt[mi] = 0;
      while(cnt[ma] > 1 && cntd[ma] > 0) {
        ++ans;
        --cntd[ma];
        cnt[ma] -= 2;
      }
    }
  }
  return ans;
}