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 <vector>
#include <cstdio>
#include <functional>
#include <iterator>
#include <array>
#include <utility>
#include <map>
namespace XX
{   
    template<template<typename> class Compare, typename T>
    inline T& UP(T& x, const T& y){if(Compare<T>()(y, x)) x = y; return x;}
    template<typename Compare, typename T>
    inline T& UP(T& x, const T& y, Compare comp){if(comp(y, x)) x = y; return x;}

    template<typename T> inline T& GT(T& x, const T& y){return UP<std::greater>(x, y);}
    template<typename T> inline T& LS(T& x, const T& y){return UP<std::less>(x, y);}

    template<typename T>
    struct Mapper
    {
        int operator[](const T& v) { int& ret = table[v]; if(!ret) rtable[ret = table.size()] = v; return ret - 1; }
        template<typename... Args> int operator()(Args... args) { return (*this)[T(args...)]; }
        T rev(int idx){return rtable[idx + 1];}
        std::map<T, int> table;
        std::map<int, T> rtable;
    };

    template<typename T, int S>
    struct ReferenceArray
    {
        struct It {typename std::array<T*, S>::iterator it; T& operator*(){return **it;} void operator++(){it++;} bool operator!=(const It& other){return it != other.it;} };
        int size()const{return _ptr.size();}
        It begin()const{return {_ptr.begin()};}
        It end()const{return {_ptr.end()};}
        T& operator[](int idx)const{return *_ptr[idx];}
        mutable std::array<T*, S> _ptr;
    };
    template<typename T, typename... Args> 
    ReferenceArray<T, sizeof...(Args) + 1> MAKEV(T& arg1, Args&... args) {return {&arg1, &args...};}

    struct Range
    {   
        struct It {   int num, step; int operator*(){return num;} void operator++(){num += step;} bool operator!=(const It& other){return num != other.num;} };
        Range(int ee):b(0),e(ee){}
        Range(int bb, int ee):b(bb), e(ee){}
        It begin(){return {b, (b < e? 1: -1)};}
        It end(){return {e, 0};}
        int b, e;
    };

}



template<typename T> struct ScanfSpecifier{};
#define DEF(T,V) template<> struct ScanfSpecifier<T>{static constexpr const char* value = V;};
DEF(char*,"%s")DEF(int,"%d")DEF(double,"%lf")DEF(float,"%f")DEF(char,"%c")DEF(const char*,"%s")DEF(unsigned long,"%lu")DEF(unsigned int, "%u")
#ifdef _MSC_VER
DEF(long long int,"%I64d")
#else
DEF(long long int,"%lld")
#endif
#undef DEF
template<typename T> int RD(T& arg){return std::scanf(ScanfSpecifier<T>::value, &arg);}
template<int S> int RD(char (&arg)[S]){return std::scanf("%s", arg);}
int RD(char* arg){return std::scanf("%s", arg);}
template<> int RD<char>(char& arg){return std::scanf(" %c", &arg);}
template<typename T, typename... Args> int RD(T& arg1, Args&... args) {return RD(arg1) + RD(args...);}
template<typename T> T RD(){T ret; RD(ret); return ret;}
template<typename It> void RDV(It begin, It end) { while(begin != end) RD(*begin++); }
template<typename C> void RDV(C& c) {RDV(std::begin(c), std::end(c));}
template<typename T> void WT(T arg) {std::printf(ScanfSpecifier<T>::value, arg); }
template<typename T, typename U> void WT(std::pair<T, U> arg) {std::printf("("); WT(arg.first); std::printf(", "); WT(arg.second); std::printf(")");}
template<typename... Args> void WT(Args... args) { int alc = 0; int dummy[] = {((alc++? std::printf(" "): 0), WT(args), 0)...}; }

template<typename... Args> void WTL(Args... args) { WT(args...); std::printf("\n"); }
template<typename It> void WTV(It begin, It end) { int alc = 0; while(begin != end) (alc++? std::printf(" "): 0), WT(*begin++); }
template<typename C> void WTV(const C& c) {WTV(std::begin(c), std::end(c));}
template<typename It> void WTVL(It begin, It end) { WTV(begin, end); std::printf("\n"); }
template<typename C> void WTVL(const C& c) {WTVL(std::begin(c), std::end(c));}





//alias
template<typename T> T& UMAX(T& x, T y){return XX::UP<std::greater>(x, y);}
template<typename T> T& UMIN(T& x, T y){return XX::UP<std::less>(x, y);}
using XX::UP; //(x,y) comp
using RG = XX::Range;
using XX::MAKEV;
using XX::Mapper;
//RD[L],RDV[L],WT[L],WTV[L] for i/o
//template
#include <vector>
#include <string>
#include <cstring>
#include <set>
#include <map>
#include <cstdlib>
#include <algorithm>
#include <functional>
#include <stack>
using namespace std;

const int SIZE = 100009;
vector<int> all[SIZE];
vector<int> stk;
int table[SIZE];
int take[SIZE];
int q[SIZE];

int main()
{
    int N, M;
    RD(N, M);

    int ans = 0;
    map<int, int> q;
    while(N--)
    {
        int v;
        RD(v);
        q[v]++;
    }


    {
        for(int i = 0; i < SIZE; i++)
        {
            if(q[i] & 1)
            {
                q[i]--;
                int v = i % M;
                stk.push_back(v);
                table[v]++;
            }
                if(q[i])
                    all[i % M].push_back(i);
        }

        while(stk.size())
        {
            int v = stk.back();
            stk.pop_back();

            if(take[v])
            {
                take[v]--;
                continue;
            }
            table[v]--;

            int v2 = (M - v);
            if(v2 == M)
                v2 = 0;


            if(table[v2])
            {
                table[v2]--;
                take[v2]++;

                ans++;
            }
            else if(all[v2].size())
            {
                int w = all[v2].back();
                ans++;
                table[v2]++;
                stk.push_back(v2);
                if((q[w] -= 2) == 0)
                    all[v2].pop_back();
            }
        }


    }
    for(int i: RG(SIZE))
        ans += q[i] / 2;
    WTL(ans);

}




