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 <iostream>
#include <vector>
#include <algorithm>

int main() {
    int N, M;
    std::cin >> N >> M;
    std::vector<std::vector<int> > xs(M);
    for (int i = 0; i < N; ++i) {
        int x;
        std::cin >> x;
        xs[x % M].push_back(x);
    }
    std::vector<int> ntaken(M);
    int ret = 0;
    for (int i = 1; i < (M+1)/2; ++i) {
        int take = std::min(int(xs[i].size()),
                            int(xs[M-i].size()));
        ntaken[i] += take;
        ntaken[M-i] += take;
        ret += take;
    }

    if ((M % 2) == 0) {
        int npair = int(xs[M/2].size()) / 2;
        ntaken[M/2] += 2*npair;
        ret += npair;
    }
    int np = int(xs[0].size()) / 2;
    ntaken[0] += 2*np;
    ret += np;
    for (int i = 0; i < M; ++i) {
        int npairs = 0;
        std::sort(xs[i].begin(), xs[i].end());
        for (int y = 1; y < xs[i].size(); ++y) {
            if (xs[i][y] == xs[i][y-1]) {
                ++npairs;
                ++y;
            }
        }
        npairs = std::min(npairs, (int(xs[i].size()) - ntaken[i]) / 2);
        ret += npairs;
    }

    std::cout << ret << std::endl;

    return 0;
}
