Problem:
Score : 800 points

Problem Statement

Let’s take a prime P = 200\,003.
You are given N integers A_1, A_2, \ldots, A_N.
Find the sum of ((A_i \cdot A_j) \bmod P) over all N \cdot (N-1) / 2 unordered pairs of elements (i < j).

Please note that the sum isn't computed modulo P.

Constraints

2 \leq N \leq 200\,000

0 \leq A_i < P = 200\,003

All values in input are integers.

Input

Input is given from Standard Input in the following format.

N
A_1 A_2 \cdots A_N

Output

Print one integer — the sum over ((A_i \cdot A_j) \bmod P).

Sample Input 1

4
2019 0 2020 200002

Sample Output 1

474287

The non-zero products are:

2019 \cdot 2020 \bmod P = 78320

2019 \cdot 200002 \bmod P = 197984

2020 \cdot 200002 \bmod P = 197983

So the answer is 0 + 78320 + 197984 + 0 + 0 + 197983 = 474287.

Sample Input 2

5
1 1 2 2 100000

Sample Output 2

600013

Solution in C++ (GCC 9.2.1) (judge verdict: Wrong Answer)

#line 2 "/Users/kaage/Desktop/ProgrammingWorkspace/library/other/template.hpp"
#define _CRT_SECURE_NO_WARNINGS
#pragma target("avx2")
#pragma optimize("O3")
#pragma optimize("unroll-loops")
#include <algorithm>
#include <bitset>
#include <cassert>
#include <cfloat>
#include <climits>
#include <cmath>
#include <complex>
#include <ctime>
#include <deque>
#include <fstream>
#include <functional>
#include <iomanip>
#include <iostream>
#include <iterator>
#include <list>
#include <map>
#include <memory>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <string.h>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>
#define rep(i,n) for(int i=0;i<(n);i++)
#define REP(i,n) for(int i=1;i<=(n);i++)
#define all(V) V.begin(),V.end()
typedef long long lint;
typedef unsigned long long ulint;
typedef std::pair<int, int> P;
typedef std::pair<lint, lint> LP;
constexpr int INF = INT_MAX/2;
constexpr lint LINF = LLONG_MAX/2;
constexpr double eps = DBL_EPSILON;
constexpr double PI=3.141592653589793238462643383279;
template<class T>
class prique :public std::priority_queue<T, std::vector<T>, std::greater<T>> {};
template <class T, class U>
inline bool chmax(T& lhs, const U& rhs) {
	if (lhs < rhs) {
		lhs = rhs;
		return 1;
	}
	return 0;
}
template <class T, class U>
inline bool chmin(T& lhs, const U& rhs) {
	if (lhs > rhs) {
		lhs = rhs;
		return 1;
	}
	return 0;
}
inline lint gcd(lint a, lint b) {
	while (b) {
		lint c = a;
		a = b; b = c % b;
	}
	return a;
}
inline lint lcm(lint a, lint b) {
	return a / gcd(a, b) * b;
}
bool isprime(lint n) {
	if (n == 1)return false;
	for (int i = 2; i * i <= n; i++) {
		if (n % i == 0)return false;
	}
	return true;
}
template<typename T>
T mypow(T a, lint b) {
	T res(1);
	while(b){
		if(b&1)res*=a;
		a*=a;
		b>>=1;
	}
	return res;
}
lint modpow(lint a, lint b, lint m) {
	lint res(1);
	while(b){
		if(b&1){
			res*=a;res%=m;
		}
		a*=a;a%=m;
		b>>=1;
	}
	return res;
}
template<typename T>
void printArray(std::vector<T>& vec) {
	rep(i, vec.size()){
		std::cout << vec[i];
		std::cout<<(i==(int)vec.size()-1?"\n":" ");
	}
}
template<typename T>
void printArray(T l, T r) {
	T rprev = std::prev(r);
	for (T i = l; i != rprev; i++) {
		std::cout << *i << " ";
	}
	std::cout << *rprev << std::endl;
}
#line 2 "main.cpp"
#define double long double
#line 3 "/Users/kaage/Desktop/ProgrammingWorkspace/library/algebraic/ModInt.hpp"
class ModInt {
	lint value;
public:
	static const unsigned int modulo;
	ModInt() : value(0) {}
	template<typename T>
	ModInt(T value = 0) : value(value) {
		if (value < 0)value = -(lint)(-value % modulo) + modulo;
		this->value = value % modulo;
	}
	inline ModInt inv()const{return mypow(*this,modulo-2);}
	inline operator int()const { return value; }
	inline ModInt& operator+=(const ModInt& x) {
		value += x.value;
		if (value >= modulo)value -= modulo;
		return *this;
	}
	inline ModInt& operator++() {
		if (value == modulo - 1)value = 0;
		else value++;
		return *this;
	}
	inline ModInt operator-()const {
		return ModInt(0) -= *this;
	}
	inline ModInt& operator-=(const ModInt& x) {
		value -= x.value;
		if (value < 0)value += modulo;
		return *this;
	}
	inline ModInt& operator--() {
		if (value == 0)value = modulo - 1;
		else value--;
		return *this;
	}
	inline ModInt& operator*=(const ModInt& x) {
		value = value * x.value % modulo;
		return *this;
	}
	inline ModInt& operator/=(const ModInt& rhs) {
		return *this*=rhs.inv();
	}
	template<typename T> ModInt operator+(const T& rhs)const { return ModInt(*this) += rhs; }
	template<typename T> ModInt& operator+=(const T& rhs) { return operator+=(ModInt(rhs)); }
	template<typename T> ModInt operator-(const T& rhs)const { return ModInt(*this) -= rhs; }
	template<typename T> ModInt& operator-=(const T& rhs) { return operator-=(ModInt(rhs)); }
	template<typename T> ModInt operator*(const T& rhs)const { return ModInt(*this) *= rhs; }
	template<typename T> ModInt& operator*=(const T& rhs) { return operator*=(ModInt(rhs)); }
	template<typename T> ModInt operator/(const T& rhs)const { return ModInt(*this) /= rhs; }
	template<typename T> ModInt& operator/=(const T& rhs) { return operator/=(ModInt(rhs)); }
};
std::istream& operator>>(std::istream& ist, ModInt& x) {
	lint a;
	ist >> a;
	x = a;
	return ist;
}
#line 3 "/Users/kaage/Desktop/ProgrammingWorkspace/library/algebraic/MyComplex.hpp"
class MyComplex{
	double realvalue, imagvalue;
public:
	MyComplex() :realvalue(0), imagvalue(0) {}
	template<typename T,typename U>MyComplex(const T& realvalue, const U& imagvalue) : realvalue(realvalue), imagvalue(imagvalue) {}
	template<typename T>MyComplex(const T& realvalue) : realvalue(realvalue), imagvalue(0) {}
	template<typename T>MyComplex(const std::complex<T>& c) :realvalue(c.real()), imagvalue(c.imag()) {}
	double& real(){ return this->realvalue; }
	double& imag(){ return this->imagvalue; }
	double abs()const{ return hypot(realvalue, imagvalue); }
	MyComplex& operator+=(const MyComplex& rhs) {
		this->realvalue += rhs.realvalue;
		this->imagvalue += rhs.imagvalue;
		return *this;
	}
	MyComplex& operator-=(const MyComplex& rhs) {
		this->realvalue -= rhs.realvalue;
		this->imagvalue -= rhs.imagvalue;
		return *this;
	}
	MyComplex& operator*=(const MyComplex& rhs) {
		double pastreal = this->realvalue;
		this->realvalue = this->realvalue * rhs.realvalue - this->imagvalue * rhs.imagvalue;
		this->imagvalue = pastreal * rhs.imagvalue + rhs.realvalue * this->imagvalue;
		return *this;
	}
	MyComplex& operator/=(const MyComplex& rhs) {
		*this *= MyComplex(rhs.realvalue, -rhs.imagvalue);
		double dnm = rhs.realvalue * rhs.realvalue - rhs.imagvalue * rhs.imagvalue;
		this->realvalue /= dnm;
		this->imagvalue /= dnm;
		return *this;
	}

	template<typename T>MyComplex operator+(const T& rhs)const {return MyComplex(*this)+=rhs;}
	template<typename T>MyComplex& operator+=(const T& rhs)const {return operator+=(MyComplex(rhs));}
	template<typename T>MyComplex operator-(const T& rhs)const {return MyComplex(*this)-=rhs;}
	template<typename T>MyComplex& operator-=(const T& rhs)const {return operator-=(MyComplex(rhs));}
	template<typename T>MyComplex operator*(const T& rhs)const {return MyComplex(*this)*=rhs;}
	template<typename T>MyComplex& operator*=(const T& rhs)const {return operator*=(MyComplex(rhs));}
	template<typename T>MyComplex operator/(const T& rhs)const {return MyComplex(*this)/=rhs;}
	template<typename T>MyComplex& operator/=(const T& rhs)const {return operator/=(MyComplex(rhs));}
};
#line 4 "/Users/kaage/Desktop/ProgrammingWorkspace/library/algebraic/FastFourierTransform.hpp"
class FastFourierTransform {
private:
	static void dft(std::vector<MyComplex>& a){
		int sz=a.size();
		if(sz==1)return;
		MyComplex root=std::polar(1.0,(inverse?-1:1)*2.0*acos(-1)/sz);
		std::vector<MyComplex> b(sz),roots((sz>>1)+1,1);
		rep(i,sz>>1)roots[i+1]=roots[i]*root;
		for(int i=sz>>1,w=1;w<sz;i>>=1,w<<=1){
			for(int j=0;j<i;j++){
				for(int k=0;k<w;k++){
					b[k+((w*j)<<1)]=a[k+w*j]+a[k+w*j+(sz>>1)];
					b[k+((w*j)<<1)+w]=roots[w*j]*(a[k+w*j]-a[k+w*j+(sz>>1)]);
				}
			}
			std::swap(a,b);
		}
	}
public:
	static bool inverse;
	template<typename T>
	static std::vector<double> multiply(std::vector<T> f, std::vector<T> g) {
		if(f.size()<g.size())std::swap(f,g);
		std::vector<MyComplex> nf, ng;
		int sz = 1;
		while (sz < f.size() + g.size())sz *= 2;
		nf.resize(sz); ng.resize(sz);
		rep(i, f.size()) {
			nf[i] = f[i];
			if(i<g.size())ng[i] = g[i];
		}
		inverse=false;
		dft(nf);dft(ng);
		rep(i, sz)nf[i] *= ng[i];
		inverse=true;
		dft(nf);
		std::vector<double> res(sz);
		rep(i, sz)res[i]=nf[i].real() / sz;
		return res;
	}
};
bool FastFourierTransform::inverse=false;
#line 5 "main.cpp"
const unsigned int ModInt::modulo=200003;
int n,a[200010],c[200010],l[200010];
int main(){
	std::cin>>n;
	rep(i,n){
		std::cin>>a[i];
		c[a[i]]++;
	}
	ModInt pow=1;
	rep(i,200002){
		l[pow]=i;
		pow*=2;
	}
	std::vector<lint> f(200003),g;
	REP(i,200002)f[l[i]]=c[i];
	g=f;
	std::vector<double> mul=FastFourierTransform::multiply(f,g);
	g.assign(200003,0);
	rep(i,mul.size())g[i%200002]+=mul[i]+0.5;
	lint ans=0;
	rep(i,200003)ans+=modpow(2,i,200003)*g[i];
	rep(i,200003)ans-=(lint)i*i%200003*c[i];
	std::cout<<ans/2<<std::endl;
	return 0;
}