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: Time Limit Exceeded)


//#pragma GCC optimize ("-O3")
#include <iostream>
#include <cmath>
#include <vector>
#include <stack>
#include <cstdio>
#include <string>
#include <bitset>
#include <list>
#include <set>
#include <algorithm>
#include <numeric>
#include <unordered_map>
#include <functional>
#include <queue>
#include <regex>
#include <cassert>
#include <map>
#include <type_traits>
#include <array>
#include <cassert>
#include <typeinfo>
#include <time.h>
#include <iomanip>
#include <random>
#include <sstream>
#include <complex>
#ifdef _MSC_VER
#include <intrin.h>
#define popcnt __popcnt64
//#  define __builtin_popcount __popcnt
#else
#define popcnt __builtin_popcountll
#endif
//#include "boost/variant.hpp"



using namespace std;

typedef long long ll;
constexpr ll MOD = 1000000007ll;
constexpr ll INF = 1LL << 60;

#define rep(i, N, M) for(ll i=N, i##_len=(M); i<i##_len; ++i)
#define rep_skip(i, N, M, ...) for(ll i=N, i##_len=(M); i<i##_len; i+=(skip))
#define rrep(i, N, M)  for(ll i=(M)-1, i##_len=(N-1); i>i##_len; --i)
#define repbit(bit, N, DIG) rep(bit, (N), (1LL<< (DIG)))
#define pb push_back
#define fir first
#define sec second
#define all(a)  (a).begin(),(a).end()
#define rall(a) (a).rbegin(), (a).rend()
#define perm(c) sort(all(c));for(bool c##perm=1;c##perm;c##perm=next_permutation(all(c))) //perm(c){write(c)} writes all permutation of c 
constexpr ll dceil(ll x, ll y) { if (y < 0) { x *= -1; y *= -1; }; return x > 0 ? (x + y - 1) / y : x / y; } // ceil for x/y
constexpr ll dfloor(ll x, ll y) { if (y < 0) { x *= -1; y *= -1; };  return x > 0 ? x / y : -dceil((-x), y); } // floor for x/y

typedef pair<double, double> pd;
typedef pair<ll, ll> pll;
typedef vector<ll> vll;
typedef vector<vll> vvll;
typedef vector<pll> vpll;
typedef vector<bool> vb;
typedef vector<vb> vvb;
typedef vector<string> vs;
template<typename T> using pq_greater = priority_queue<T, vector<T>, greater<T>>;
template<typename T> using vpt = vector<complex<T>>;

template<int n>
struct tll_impl {
	using type = decltype(tuple_cat(tuple<ll>(), declval<typename tll_impl<n - 1>::type>()));
};
template<>
struct tll_impl<1> {
	using type = tuple<ll>;
};
template<int n>
using tll = typename tll_impl<n>::type;

template<class T>
constexpr ll SZ(T& v) { return static_cast<ll>(v.size()); };

template<int n, typename T>
struct vec_t_impl {
	using type = vector<typename vec_t_impl<n-1,T>::type>;
};
template<typename T>
struct vec_t_impl<1,T> {
	using type = vector<T>;
};
template<int n, typename T>
using vec_t = typename vec_t_impl<n, T>::type;
// check 
static_assert(is_same<vec_t<3,ll>, vector<vector<vector<ll>>>>::value, "");

// decompose vector into basetype and dimension.
template<typename T> 
struct vec_dec {
	static constexpr int dim = 0;
	using type  = T;
};
template<typename T>
struct vec_dec<vector<T>> {
	static constexpr int dim = vec_dec<T>::dim+1;
	using type  = typename vec_dec<T>::type;
};
static_assert(is_same<typename vec_dec<vec_t<3, ll>>::type, ll>::value, "");
static_assert(vec_dec<vec_t<3, ll>>::dim == 3, "");

template<typename T = ll>
vector<T> makev(size_t a) { return vector<T>(a); }

template<typename T = ll, typename... Ts>
auto makev(size_t a, Ts... ts) {
	return vector<decltype(makev<T>(ts...))>(a, makev<T>(ts...));
} // ex:  auto dp =  makev<ll>(4,5) => vector<vector<ll>> dp(4,vector<ll>(5));

template < typename T >
struct is_vector : std::false_type {}; // check if T is vector

template < typename T >
struct is_vector<vector<T>> : std::true_type {};
static_assert(is_vector<vector<ll>>::value == true && is_vector<ll>::value == false, "");

// check if T is vector
template < typename T>
struct is_pair : std::false_type {};

template < typename T, typename S >
struct is_pair<pair<T, S>> : std::true_type {};
static_assert(is_pair<pll>::value == true && is_pair<ll>::value == false, "");

template<typename T, typename V, typename enable_if<!is_vector<T>::value, nullptr_t>::type = nullptr>
void fill_v(T& t, const V& v) { t = v; }

template<typename T, typename V, typename enable_if<is_vector<T>::value, nullptr_t>::type = nullptr>
void fill_v(T& t, const V& v) {
	for (auto &&x : t)
		fill_v(x, v);
} // ex:  fill_v(dp, INF);

namespace std {
	template<class T> bool operator<(const complex<T>& a, const complex<T>& b) {
		return a.real() == b.real() ? a.imag() < b.imag() : a.real() < b.real();
	}
};

template<typename T, typename S> istream& operator>>(istream& istr, pair<T, S>& x) { return istr>> x.first >> x.second; }
template<typename T> istream& operator>>(istream& istr, vector<T>& x) {	rep(i, 0, x.size()) istr >> x[i]; return istr; }
template<typename T> istream& operator>>(istream& istr, complex<T>& x) { T r, i; istr >> r >> i; x.real(r); x.imag(i); return istr; }

template<typename T, typename Delim_t = string, typename enable_if<!is_vector<T>::value, nullptr_t>::type = nullptr>
void write(T& x, Delim_t delim = " ") { cout << x << delim; }
template<typename T, typename Delim_t = string, typename enable_if<is_vector<T>::value, nullptr_t>::type = nullptr>
void write(T& x, Delim_t delim = " ") { rep(i, 0, x.size()) write(x[i], (i == (x.size() - 1) ? "" : delim)); cout << '\n'; }

template<typename T> void chmin(T &a, T b) {
	if (a > b) a = b;
}
template<typename T> void chmax(T &a, T b) {
	if (a < b) a = b;
}

vll seq(ll i, ll j) {
	vll res(j - i);
	rep(k, i, j) res[k] = i + k;
	return res;
}

constexpr ll POW_0(ll x, ll y) {
	if (y == 0)return 1;
	if (y == 1)return x ;
	if (y == 2)return x * x ;
	if (y % 2 == 0)return POW_0(POW_0(x, y / 2), 2LL);
	return ((POW_0(POW_0(x, y / 2), 2LL)) * (x)) ;
}

constexpr ll POW(ll x, ll y, ll mod = 0) {
	if (mod == 0)return POW_0(x, y);
	if (y == 0)return 1;
	if (y == 1)return x % mod;
	if (y == 2)return x * x % mod;
	if (y % 2 == 0)return POW(POW(x, y / 2, mod), 2LL, mod) % mod;
	return ((POW(POW(x, y / 2, mod), 2LL, mod)) * (x % mod)) % mod;
}

template<
	typename Inputs,
	typename Functor,
	typename T = typename Inputs::value_type>
	void sort_by(Inputs& inputs, Functor f) {
	std::sort(std::begin(inputs), std::end(inputs),
		[&f](const T& lhs, const T& rhs) { return f(lhs) < f(rhs); });
}

template<
	int pos,
	typename Inputs,
	typename T = typename Inputs::value_type>
	void sort_by(Inputs& inputs) {
	std::sort(std::begin(inputs), std::end(inputs),
		[](const T& lhs, const T& rhs) { return get<pos>(lhs) < get<pos>(rhs); });
}

template<
	typename Inputs,
	typename Functor,
	typename T = typename Inputs::value_type>
	void stable_sort_by(Inputs& inputs, Functor f) {
	std::stable_sort(std::begin(inputs), std::end(inputs),
		[&f](const T& lhs, const T& rhs) { return f(lhs) < f(rhs); });
}

template<typename Inputs>
void sort_uniq(Inputs& inputs) {
	sort(all(inputs));
	inputs.erase(unique(all(inputs)), inputs.end());
}

vector<string> split(const string& s, char delim) {
	vector<string> elems;
	stringstream ss(s);
	string item;
	if (s.size() > 0 && s.front() == delim) {
		elems.push_back("");
	}
	while (getline(ss, item, delim)) {
		if (!item.empty()) {
			elems.push_back(item);
		}
	}
	if (s.size() > 0 && s.back() == delim) {
		elems.push_back("");
	}
	return elems;
}

template<class T>
map<T,ll> inv_map(vector<T>& x) {
	map<T, ll> res;
	rep(i, 0, x.size()) {
		res[x[i]] = i;
	}
	return res;
}
template<class K, class V>
map<V, K> inv_map(map<K, V>& m) {
	map<V, K> res;
	for(const auto& x: m) {
		res[x.second] = x.first;
	}
	return res;
}
template<class T, class val_t = typename T::value_type, enable_if_t<!is_same<T, set<val_t>>::value >* = nullptr >
constexpr bool exist(const T& container, val_t val) { return find(all(container), val) != container.end(); }
template<class T, class val_t = typename T::value_type,  enable_if_t<is_same<T, set<val_t>>::value >* = nullptr >
constexpr bool exist(const T& container, val_t val) { return container.find(val) != container.end(); }

// inner prod: |a||b|cos(theta)
template<class T> T dot(complex<T> a, complex<T> b) {	return a.real() * b.real() + a.imag() * b.imag(); }
// outer prod |a||b|sin(theta)
template<class T> T cross(complex<T> a, complex<T> b) { return a.real() * b.imag() - a.imag() * b.real(); }




//ビット bit に i 番目のフラグが立っているかどうか	if (bit & (1 << i))
//ビット bit に i 番目のフラグが消えているかどうか	if (!(bit & (1 << i)))
//ビット bit に i 番目のフラグを立てる	bit｜ = (1 << i)
//ビット bit に i 番目のフラグを消す	bit &= ~(1 << i)
//ビット bit に何個のフラグが立っているか	__builtin_popcount(bit)
//ビット bit に i 番目のフラグを立てたもの	bit｜(1 << i)
//ビット bit に i 番目のフラグを消したもの	bit & ~(1 << i)

template<ll bit = 2LL>
ll at_bit(ll n, ll i) {
	return n / POW(bit, i) % bit;
}

template<>
ll at_bit<2>(ll n, ll i) {
	return (n >> i) % 2LL;
}

template<ll bit>
ll get_bit(ll i) {
	return POW(bit, i);
}

template<>
ll get_bit<2>(ll i) {
	return 1LL << i;
}

template<ll bit = 2>
ll get_max_bit(ll n) {
	ll tmp = bit;
	ll at = 0;
	while (tmp <= n) {
		at++;
		tmp *= bit;
	}
	return at;
}

template<>
ll get_max_bit<2>(ll n) {
	ll tmp = 2;
	ll at = 0;
	while (tmp <= n) {
		at++;
		tmp <<= 1;
	}
	return at;
}

ll check_bit(ll N, int POS) { return (N & (1LL << POS)); }
// Function to return maximum XOR subset in set by gaussian elimination
ll max_subset_xor(vector<ll>& v)
{
	int n = v.size();
	int ind = 0;  // Array index
	for (int bit = 61; bit >= 0; bit--)
	{
		int x = ind;
		while (x < n && check_bit(v[x], bit) == 0)
			x++;
		if (x == n)
			continue; // skip if there is no number below ind where current bit is 1
		swap(v[ind], v[x]);
		for (int j = 0; j < n; j++){
			if (j != ind && check_bit(v[j], bit))
				v[j] ^= v[ind];
		}
		ind++;
	}
	return accumulate(all(v), 0LL, [](ll x, ll y) {return x ^ y; });
}




















int main() {

	cin.tie(0);
	cout.tie(0);
	ios::sync_with_stdio(false);
	cout << fixed << setprecision(12);

	ll n; cin >> n;
	constexpr ll P = 200003;
	vll a(n); cin >> a;
	a.erase(remove(all(a), 0), a.end());
	sort(all(a));
	n = a.size();

	ll res = 0;
	ll tot = 0;
	vll a_acc(n + 1);
	rrep(i, 0, n) {
		a_acc[i] = a[i] + a_acc[i + 1];
	}
	rep(i, 0, n) {
		tot += a[i] * a_acc[i + 1];
	}

	ll head = 0;
	rep(i, 0, n) {
		auto x = a[i];
		auto y_pre = i+1;
		rep(k, 1, P + 1) {
			auto y = (k * P + x -1) / x ;
			ll yind = lower_bound(all(a), y) - a.begin();
			chmin(yind, n);

			// calc w
			ll cnt = max(yind - y_pre, 0ll);
			if (cnt == 0)
				continue;
			ll w = cnt * (k-1);
			head += w;
			y_pre = max(yind, y_pre);
			if (yind == n)
				break;
		}

		cerr << head << endl;
	}

	
	cout << tot - head *P << endl;


	return 0;
}