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

typedef long long ll;
typedef unsigned long long ull;
typedef pair<int,int> pii;
typedef pair<ll, ll> pll;
typedef pair<ull, ull> pullull;
typedef pair<ll, int> plli;
typedef pair<int, pii> pipii;
typedef vector<vector<int> > mati;
typedef vector<vector<double> > matd;
typedef vector<ll> vll;
typedef vector<vector<ll>> vvll;
typedef vector<vector<vector<ll>>> vvvll;
typedef vector<bool> vb;
typedef vector<vector<bool>> vvb;
typedef vector<vector<vector<bool>>> vvvb;
typedef vector<pll> vpll;
typedef vector<vpll> vvpll;

#define FOR(i,x,y) for(ll i=(ll)x; i<(ll)y; ++i)
#define REP(i,y) FOR(i, 0, y)
#define RFOR(i,x,y) for(ll i=(ll)x; i>=(ll)y; --i)
#define RREP(i,x) RFOR(i, x, 0)
#define ALL(a) a.begin(), a.end()
#define pb push_back
#define debug_printf(x...) cerr << "line " << __LINE__ << " : "; debug_printf_in(x);

template <typename First>
void debug_printf_in(First first){
  cerr << first << endl;
  return;
}

template <typename First, typename... Rest>
void debug_printf_in(First first, Rest... rest){
  cerr << first << " ";
  debug_printf_in(rest...);
  return;
}

void IN(void){
  return;
}

template <typename First, typename... Rest>
void IN(First& first, Rest&... rest){
  cin >> first;
  IN(rest...);
  return;
}

template <typename First>
void OUT(First first){
  cout << first << endl;
  return;
}

template <typename First, typename... Rest>
void OUT(First first, Rest... rest){
  cout << first << " ";
  OUT(rest...);
  return;
}

template<class t, class u> void chmax(t&a,u b){if(a<b)a=b;};
template<class t, class u> void chmin(t&a,u b){if(a>b)a=b;};
int popcount(int t){return __builtin_popcount(t);} //GCC
int popcount(ll t){return __builtin_popcountll(t);} //GCC

template <typename T>
void vec_print(vector<T> VEC){
  REP(i, VEC.size()){
    cout << VEC[i] << " ";
  }
  cout << "\n";
};

template <typename T>
void mat_print(vector<vector<T> > MAT){
  REP(i, MAT.size()){
    REP(j, MAT[i].size()){
      cout << MAT[i][j] << " ";
    }
    cout << "\n";
  }
};

template <typename CLASS1, typename CLASS2>
class HOGE{
  public:
    CLASS1 key;
    CLASS2 value;
    HOGE(void){
      return;
    };
    HOGE(CLASS1 key, CLASS2 value){
      this->key = key;
      this->value = value;
    };
    ~HOGE(void){
      return;
    };

    void print(void){
      cout << "key : " << key << ", value : " << value << "\n";
      return;
    };
    
    bool operator==(const HOGE &obj){
      return (this->value == obj.value);
    };
    bool operator<(const HOGE &obj){
      return (this->value < obj.value);
    };
    bool operator>(const HOGE &obj){
      return (this->value > obj.value);
    };
};

template <typename CLASS1, typename CLASS2>
bool operator==(const HOGE<CLASS1, CLASS2> &hoge1, const HOGE<CLASS1, CLASS2> &hoge2){
  return hoge1.value == hoge2.value;
};

template <typename CLASS1, typename CLASS2>
bool operator<(const HOGE<CLASS1, CLASS2> &hoge1, const HOGE<CLASS1, CLASS2> &hoge2){
  return hoge1.value < hoge2.value;
};

template <typename CLASS1, typename CLASS2>
bool operator>(const HOGE<CLASS1, CLASS2> &hoge1, const HOGE<CLASS1, CLASS2> &hoge2){
  return hoge1.value > hoge2.value;
};

constexpr int INF = (1<<30);
constexpr ll INFLL = 1LL<<62;
constexpr long double EPS = 1e-12;
constexpr ll MOD = (ll)((1E+9)+7);

ll N, M;
vll X;
vll dp;
vll dp2;

int main(){
  cin.tie(0); // cut the cin and cout (default, std::flush is performed after std::cin)
  ios::sync_with_stdio(false); // cut the iostream and stdio (DON'T endl; BUT "\n";)

  IN(N,M);
  X.resize(N);
  ll X_max = M;
  REP(i,N){
    IN(X[i]);
    chmax(X_max, X[i]);
  }
  dp.resize(X_max+1, 0);
  REP(i,N){
    dp[X[i]]++;
  }
  dp2.resize(M, 0);
  REP(i,X_max+1){
    if(dp[i]>0){
      dp2[i%M] += dp[i]%2;
    }
  }
  FOR(i,M,X_max+1){
    dp[i%M] += dp[i];
  }

  /*
  printf("\n");
  REP(i,M){
    printf("%lld ", dp[i]);
  }
  printf("\n");
  REP(i,M){
    printf("%lld ", dp2[i]);
  }
  printf("\n");
  */

  ll ans = 0;

  REP(i,M){
    ll j = M-i;
    if(i==0){
      ans += dp[0]/2;
    }else if(i==j){
      ans += dp[i]/2;
      break;
    }else if(i>j){
      break;
    }else{
      ll tmp1 = i;
      ll tmp2 = j;
      if(dp[tmp1]<dp[tmp2]) swap(tmp1, tmp2);
      ans += dp[tmp2];
      ll tmp3 = min(dp[tmp2], dp2[tmp1]);
      //debug_printf(i, j, dp[tmp1], dp[tmp2], dp2[tmp1], tmp3, ans);
      dp[tmp1] -= tmp3;
      dp[tmp2] -= tmp3;
      dp2[tmp1] -= tmp3;
      //debug_printf(i, j, dp[tmp1], dp[tmp2], dp2[tmp1], tmp3, ans);
      if(dp[tmp2]==0){
        //debug_printf(dp[tmp1], dp2[tmp1]);
        ans += (dp[tmp1]-dp2[tmp1])/2;
      }else{
        //debug_printf(dp[tmp1], dp[tmp2]);
        ans += (dp[tmp1] - dp[tmp2])/2;
      }
      //debug_printf(i, j, ans);
    }
    //debug_printf(i, ans);
  }

  OUT(ans);

  return 0;
}