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 i64 = int64_t;

const i64 MOD = 1e9+7;

const i64 INF = 1e18+7;


signed main(){
    int n, m;
    cin >> n >> m;
    vector<int> a(n);
    vector<vector<int>> t(m, vector<int>(2, 0));
    map<int,int> ma;
    for(auto& x : a){
        cin >> x;
        ++ma[x];
    }
    for(auto& elm : ma){
        t[elm.first % m][0] += elm.second;
        t[elm.first % m][1] += elm.second & ~1;
    }
    int ans = 0;
    for(int i = 0; i < (m + 2) / 2; ++i){
        int j = m - i;
        if(!i || i == j){
            ans += t[i][0] / 2;
        }else{
            int mi = min(t[i][0], t[j][0]);
            ans += mi;
            t[i][1] = min(t[i][1], t[i][0] - mi);
            t[j][1] = min(t[j][1], t[j][0] - mi);
            ans += t[i][1] / 2;
            ans += t[j][1] / 2;
        }
    }
    cout << ans << endl;
}
