#include <algorithm>
#include <iostream>
#include <cstring>
#include <cstdio>
#include <string>
#include <vector>
#include <cmath>
#include <queue>
#include <set>
#include <map>
using namespace std;

typedef long long ll;
typedef pair<int, int> pii;
#define fst first
#define snd second

void Max(int &x, int y) {
    if (x < y) x = y;
}

void Min(int &x, int y) {
    if (x > y) x = y;
}


int a[100010], c[100010];
int main(void) {

    int n, m;
    cin >> n >> m;
    for (int i = 1; i <= n; ++ i) {
        int x;
        cin >> x;
        ++ a[x % m];
        c[i] = x;
    }

    int ans = 0;
    for (int i = 0; i < m; ++ i) {
        if (i == (m - i) % m) {
            ans += a[i] / 2;
            a[i] %= 2;
            continue;
        }
        int x = min(a[i], a[m - i]);
        ans += x;
        a[i] -= x; a[m - i] -= x;
    }

    sort(c + 1, c + n + 1);
    for (int i = 2; i <= n; ++ i) {
        int x = c[i] % m;
        if (a[x] >= 2 && c[i - 1] == c[i]) {
            ++ ans;
            a[x] -= 2;
            ++ i;
        }
    }

    cout << ans << endl;

    return 0;
}
### Prompt

Please formulate 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 <algorithm>
#include <iostream>
#include <cstring>
#include <cstdio>
#include <string>
#include <vector>
#include <cmath>
#include <queue>
#include <set>
#include <map>
using namespace std;

typedef long long ll;
typedef pair<int, int> pii;
#define fst first
#define snd second

void Max(int &x, int y) {
    if (x < y) x = y;
}

void Min(int &x, int y) {
    if (x > y) x = y;
}


int a[100010], c[100010];
int main(void) {

    int n, m;
    cin >> n >> m;
    for (int i = 1; i <= n; ++ i) {
        int x;
        cin >> x;
        ++ a[x % m];
        c[i] = x;
    }

    int ans = 0;
    for (int i = 0; i < m; ++ i) {
        if (i == (m - i) % m) {
            ans += a[i] / 2;
            a[i] %= 2;
            continue;
        }
        int x = min(a[i], a[m - i]);
        ans += x;
        a[i] -= x; a[m - i] -= x;
    }

    sort(c + 1, c + n + 1);
    for (int i = 2; i <= n; ++ i) {
        int x = c[i] % m;
        if (a[x] >= 2 && c[i - 1] == c[i]) {
            ++ ans;
            a[x] -= 2;
            ++ i;
        }
    }

    cout << ans << endl;

    return 0;
}
```