#include<bits/stdc++.h>
using namespace std;

typedef pair<int, int> pii;

int N, M;
vector<vector<int> > R;
vector<int> P;

int main() {
    scanf("%d %d", &N, &M);
    R.resize(M);
    for(int i = 0; i < N; i++) {
        int t; scanf("%d", &t);
        R[t % M].push_back(t);
    }
    P = vector<int>(M, 0);
    for(int i = 0; i < M; i++) {
        sort(R[i].begin(), R[i].end());
        for(int j = 0; j < R[i].size(); j++) {
            if(j != R[i].size() - 1 && R[i][j] == R[i][j + 1]) {
                P[i]++;
                j++;
            }
        }
    }
    int ans = (int)R[0].size() / 2 + (M % 2 == 0? (int)R[M / 2].size() / 2 : 0);
    for(int i = 1; i < (M + 1) / 2; i++) {
        int cnt1 = R[i].size();
        int cnt2 = R[M - i].size();
        while(cnt1 != cnt2) {
            if(cnt1 < cnt2) {
                if(P[M - i] == 0) break;
                else cnt2 -= 2, P[M - i]--;
            }
            else {
                if(P[i] == 0) break;
                else cnt1 -= 2, P[i]--;
            }
        }
        ans += ((int)R[i].size() + (int)R[M - i].size() - (max(cnt1, cnt2) - min(cnt1, cnt2))) / 2;
    }

    cout << ans;
}

### Prompt

Please provide a cpp coded solution to the problem described below:

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<bits/stdc++.h>
using namespace std;

typedef pair<int, int> pii;

int N, M;
vector<vector<int> > R;
vector<int> P;

int main() {
    scanf("%d %d", &N, &M);
    R.resize(M);
    for(int i = 0; i < N; i++) {
        int t; scanf("%d", &t);
        R[t % M].push_back(t);
    }
    P = vector<int>(M, 0);
    for(int i = 0; i < M; i++) {
        sort(R[i].begin(), R[i].end());
        for(int j = 0; j < R[i].size(); j++) {
            if(j != R[i].size() - 1 && R[i][j] == R[i][j + 1]) {
                P[i]++;
                j++;
            }
        }
    }
    int ans = (int)R[0].size() / 2 + (M % 2 == 0? (int)R[M / 2].size() / 2 : 0);
    for(int i = 1; i < (M + 1) / 2; i++) {
        int cnt1 = R[i].size();
        int cnt2 = R[M - i].size();
        while(cnt1 != cnt2) {
            if(cnt1 < cnt2) {
                if(P[M - i] == 0) break;
                else cnt2 -= 2, P[M - i]--;
            }
            else {
                if(P[i] == 0) break;
                else cnt1 -= 2, P[i]--;
            }
        }
        ans += ((int)R[i].size() + (int)R[M - i].size() - (max(cnt1, cnt2) - min(cnt1, cnt2))) / 2;
    }

    cout << ans;
}

```