#include<iostream>
#include<string>
#include<algorithm>    
#include<cmath>
#include<map>
#include<vector>
#include<math.h>
#include<stdio.h>
#include<stack>
#include<queue>
#include<tuple>
#include<cassert>
#include<set>
#include<functional>
//#include<bits/stdc++.h>
#define int long long
using namespace std;
const int INF = 1000000000000;
const int mod = 1000000007;
int dx[4] = { 1, 0, -1, 0 }, dy[4] = { 0, 1, 0, -1 };
int test[12345678], aa[12345678];
signed main() {
	int n, m, a, ans = 0; cin >> n >> m;
	for (int h = 0; h < n; h++) {
		cin >> a; test[a % m]++; aa[a]++;
	}
	ans += test[0] / 2; test[0] = 0;
	for (int h = 1; h < m; h++) {
		//cout << test[h] << ' ' << test[m - h] << endl;
		if (h != (m - h)) {
			int x = test[h], y = test[m - h];
			ans += min(x, y); test[h] -= min(x, y); test[m - h] -= min(x, y);
		}
		else {
			ans += test[h] / 2; test[h] = 0;
		}
		//cout << ans << endl;
	}
	for (int h = 1; h <= 100000; h++) {
		ans += min(test[h % m], aa[h]) / 2;
		test[h % m] -= aa[h] / 2 * 2; test[h % m] = max(test[h % m], (long long)0);
	}
	cout << ans << endl;
	return 0;
}
### Prompt

Create a solution in Cpp for 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<iostream>
#include<string>
#include<algorithm>    
#include<cmath>
#include<map>
#include<vector>
#include<math.h>
#include<stdio.h>
#include<stack>
#include<queue>
#include<tuple>
#include<cassert>
#include<set>
#include<functional>
//#include<bits/stdc++.h>
#define int long long
using namespace std;
const int INF = 1000000000000;
const int mod = 1000000007;
int dx[4] = { 1, 0, -1, 0 }, dy[4] = { 0, 1, 0, -1 };
int test[12345678], aa[12345678];
signed main() {
	int n, m, a, ans = 0; cin >> n >> m;
	for (int h = 0; h < n; h++) {
		cin >> a; test[a % m]++; aa[a]++;
	}
	ans += test[0] / 2; test[0] = 0;
	for (int h = 1; h < m; h++) {
		//cout << test[h] << ' ' << test[m - h] << endl;
		if (h != (m - h)) {
			int x = test[h], y = test[m - h];
			ans += min(x, y); test[h] -= min(x, y); test[m - h] -= min(x, y);
		}
		else {
			ans += test[h] / 2; test[h] = 0;
		}
		//cout << ans << endl;
	}
	for (int h = 1; h <= 100000; h++) {
		ans += min(test[h % m], aa[h]) / 2;
		test[h % m] -= aa[h] / 2 * 2; test[h % m] = max(test[h % m], (long long)0);
	}
	cout << ans << endl;
	return 0;
}
```