#include <cmath>
#include <vector>
#include <map>
#include <functional>
#include <queue>
#include <iostream>
#include <string.h>
#include <iomanip>
#include <algorithm>
#include <functional>
#include <cstdint>
#include <climits>
#include <unordered_set>
#include <sstream>

using namespace std;

#define ll long long int

struct UnionFind {
    vector<int> data;
    UnionFind(int size) : data(size, -1)
    {
    }
    bool unionSet(int x, int y) {
        x = root(x); y = root(y);
        if (x != y) {
            if (data[y] < data[x]) swap(x, y);
            data[x] += data[y]; data[y] = x;
        }
        return x != y;
    }
    bool findSet(int x, int y) {
        return root(x) == root(y);
    }
    int root(int x) {
        return data[x] < 0 ? x : data[x] = root(data[x]);
    }
    int size(int x) {
        return -data[root(x)];
    }
};

int main()
{
    int n, M;
    cin >> n >> M;
    map<int,int> v1;
    for(int i = 0;i < n;i++)
    {
        int a;
        cin >> a;
        v1[a]++;
    }
    map<int,int> t;
    map<int,int> v;
    for(auto r : v1)
    {
        v[r.first % M] += r.second;
        t[r.first % M] += r.second / 2;
    }
    int r = 0;
    for (int i = 0; i <= M-i; ++ i) {
        if (i == 0 || i == M-i) {
            r += v[i] / 2;
        } else {
            int p = min(v[i], v[M-i]);
            r += p;
            v[i] -= p;
            v[M-i] -= p;
            r += min(v[i]/2, t[i]);
            r += min(v[M-i]/2, t[M-i]);
        }
    }
    cout << r << endl;
}

### Prompt

Your task is to create a cpp solution to the following problem:

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

### Response

```cpp
#include <cmath>
#include <vector>
#include <map>
#include <functional>
#include <queue>
#include <iostream>
#include <string.h>
#include <iomanip>
#include <algorithm>
#include <functional>
#include <cstdint>
#include <climits>
#include <unordered_set>
#include <sstream>

using namespace std;

#define ll long long int

struct UnionFind {
    vector<int> data;
    UnionFind(int size) : data(size, -1)
    {
    }
    bool unionSet(int x, int y) {
        x = root(x); y = root(y);
        if (x != y) {
            if (data[y] < data[x]) swap(x, y);
            data[x] += data[y]; data[y] = x;
        }
        return x != y;
    }
    bool findSet(int x, int y) {
        return root(x) == root(y);
    }
    int root(int x) {
        return data[x] < 0 ? x : data[x] = root(data[x]);
    }
    int size(int x) {
        return -data[root(x)];
    }
};

int main()
{
    int n, M;
    cin >> n >> M;
    map<int,int> v1;
    for(int i = 0;i < n;i++)
    {
        int a;
        cin >> a;
        v1[a]++;
    }
    map<int,int> t;
    map<int,int> v;
    for(auto r : v1)
    {
        v[r.first % M] += r.second;
        t[r.first % M] += r.second / 2;
    }
    int r = 0;
    for (int i = 0; i <= M-i; ++ i) {
        if (i == 0 || i == M-i) {
            r += v[i] / 2;
        } else {
            int p = min(v[i], v[M-i]);
            r += p;
            v[i] -= p;
            v[M-i] -= p;
            r += min(v[i]/2, t[i]);
            r += min(v[M-i]/2, t[M-i]);
        }
    }
    cout << r << endl;
}

```