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;
int main()
{
    int n, m;
    cin >> n >> m;
    vector<int> x(n);
    for(int i = 0; i < n; i++)
    {
        cin >> x[i];
    }
    vector<int> per(m);
    set<int> s;
    vector<int> same(m);
    for(int i = 0; i < n; i++)
    {
        int cand = x[i] % m;
        if(s.insert(x[i]).second == false)
        {
            same[cand]++;
            s.erase(s.find(x[i]));
        }
        per[cand]++;
    }
    int ans = 0;
    for(int i = 0; i <= m/2; i++)
    {
        if(i == 0 || (m%2==0 && i == m/2))
        {
            int l = per[i];
            ans += l/2;
            continue;
        }
        int l = per[i];
        int r = per[m-i];
        if(l > r)
        {
            ans += r;
            l -= r;
            ans += min(same[i], l / 2);
        }
        else
        {
            ans += l;
            r -= l;
            ans += min(same[m-i], r/2);
        }
    }
    cout << ans << endl;
}
