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 target("avx2")
#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include<bits/stdc++.h>

template <typename Tp>
constexpr auto countr_zero(Tp n)
-> typename std::enable_if<std::is_unsigned<Tp>::value, int>::type
{
    using value_type = typename std::make_unsigned<Tp>::type;
    int bits = (sizeof(value_type) * CHAR_BIT);
    if (n == 0) return bits;
    int res = 0;
    for (int i = bits / 2; i > 0; i /= 2) {
        value_type mask = ((static_cast<value_type>(1) << i) - 1);
        if (!(n & mask)) res += i, n >>= i;
    }
    return res;
}

namespace fast {
    static constexpr size_t buf_size = 1 << 17;
    static constexpr size_t margin = 1;
    static char inbuf[buf_size + margin] = {};
    static __attribute__((aligned(8))) char outbuf[buf_size + margin] = {};
    static __attribute__((aligned(8))) char minibuf[32];
    static constexpr size_t int_digits = 20;  // 18446744073709551615
    static constexpr uintmax_t digit_mask = 0x3030303030303030;
    static constexpr uintmax_t first_mask = 0x00FF00FF00FF00FF;
    static constexpr uintmax_t second_mask = 0x0000FFFF0000FFFF;
    static constexpr uintmax_t third_mask = 0x00000000FFFFFFFF;
    static constexpr uintmax_t tenpow[] = {
            1, 10, 100, 1000, 10000, 100000, 1000000, 10000000, 100000000,
            1000000000, 10000000000, 100000000000, 1000000000000, 10000000000000,
            100000000000000, 1000000000000000, 10000000000000000, 100000000000000000,
            1000000000000000000, 10000000000000000000u,
    };
    static __attribute__((aligned(8))) char inttab[40000] = {};  // 4-digit integers (10000 many)
    static char S_sep = ' ', S_end = '\n';
    template <typename Tp>
    using enable_if_integral = std::enable_if<std::is_integral<Tp>::value, Tp>;

    class scanner {
        char* pos = inbuf;
        char* endpos = inbuf + buf_size;

        void M_read_from_stdin() {
            endpos = inbuf + fread(pos, 1, buf_size, stdin);
        }
        void M_reread_from_stdin() {
            ptrdiff_t len = endpos - pos;
            if (!(inbuf + len <= pos)) return;
            memcpy(inbuf, pos, len);
            char* tmp = inbuf + len;
            endpos = tmp + fread(tmp, 1, buf_size-len, stdin);
            *endpos = 0;
            pos = inbuf;
        }

    public:
        scanner() { M_read_from_stdin(); }

        template <typename Integral,
                typename enable_if_integral<Integral>::type* = nullptr>
        void scan_parallel(Integral& x) {
            if (__builtin_expect(endpos <= pos + int_digits, 0))
                M_reread_from_stdin();
            bool ends = false;
            typename std::make_unsigned<Integral>::type y = 0;
            bool neg = false;
            if (std::is_signed<Integral>::value && *pos == '-') {
                neg = true;
                ++pos;
            }
            do {
                memcpy(minibuf, pos, 8);
                intmax_t c = *(intmax_t*)minibuf;
                intmax_t d = (c & digit_mask) ^ digit_mask;
                int skip = 8;
                int shift = 8;
                if (d) {
                    int ctz = countr_zero<uintmax_t>(d);
                    if (ctz == 4) break;
                    c &= (1L << (ctz-5)) - 1;
                    int discarded = (68-ctz) / 8;
                    shift -= discarded;
                    c <<= discarded * 8;
                    skip -= discarded;
                    ends = true;
                }
                c |= digit_mask;
                c ^= digit_mask;
                c = ((c >> 8) + c*10) & first_mask;
                c = ((c >> 16) + c*100) & second_mask;
                c = ((c >> 32) + c*10000) & third_mask;
                y = y*tenpow[shift] + c;
                pos += skip;
            } while (!ends);
            x = (neg? -y: y);
            ++pos;
        }

        template <typename Integral,
                typename enable_if_integral<Integral>::type* = nullptr>
        void scan_serial(Integral& x) {
            if (__builtin_expect(endpos <= pos + int_digits, 0))
                M_reread_from_stdin();
            bool neg = false;
            if (std::is_signed<Integral>::value && *pos == '-') {
                neg = true;
                ++pos;
            }
            typename std::make_unsigned<Integral>::type y = *pos-'0';
            while (*++pos >= '0') y = 10*y + *pos-'0';
            x = (neg? -y: y);
            ++pos;
        }

        template <typename Integral,
                typename enable_if_integral<Integral>::type* = nullptr>
        // Use scan_parallel(x) only when x may be too large (about 10^12).
        // Otherwise, even when x <= 10^9, scan_serial(x) may be faster.
        void scan(Integral& x) { scan_serial(x); }

        void scan_serial(std::string& s) {
            // until first whitespace
            s = "";
            do {
                char* startpos = pos;
                while (*pos > ' ') ++pos;
                s += std::string(startpos, pos);
                if (*pos != 0) {
                    ++pos;  // skip the space
                    break;
                }
                M_reread_from_stdin();
            } while (true);
        }

        void scan(std::string& s) { scan_serial(s); }

        template <typename Tp, typename... Args>
        void scan(Tp& x, Args&&... xs) {
            scan(x);
            scan(std::forward<Args>(xs)...);
        }
    };

    class printer {
        char* pos = outbuf;

        void M_flush_stdout() {
            fwrite(outbuf, 1, pos-outbuf, stdout);
            pos = outbuf;
        }

        static int S_int_digits(uintmax_t n) {
            if (n < tenpow[16]) {  // 1
                if (n < tenpow[8]) {  // 2
                    if (n < tenpow[4]) {  // 3
                        if (n < tenpow[2]) {  // 4
                            if (n < tenpow[1]) return 1;  // 5
                            return 2;  // 5
                        }
                        if (n < tenpow[3]) return 3;  // 4
                        return 4;  // 4
                    }
                    if (n < tenpow[6]) {  // 4
                        if (n < tenpow[5]) return 5;  // 5
                        return 6;  // 5
                    }
                    if (n < tenpow[7]) return 7;  // 5
                    return 8;  // 5
                }
                if (n < tenpow[12]) {  // 3
                    if (n < tenpow[10]) {  // 4
                        if (n < tenpow[9]) return 9;  // 5
                        return 10;  // 5
                    }
                    if (n < tenpow[11]) return 11;  // 5
                    return 12;  // 5
                }
                if (n < tenpow[14]) {  // 4
                    if (n < tenpow[13]) return 13;  // 5
                    return 14;  // 5
                }
                if (n < tenpow[15]) return 15;  // 5
                return 16;  // 5
            }
            if (n < tenpow[18]) {  // 2
                if (n < tenpow[17]) return 17;  // 3
                return 18;  // 3
            }
            return 19;  // 2
            if (n < tenpow[19]) return 19;  // 3
            return 20;  // 3
        }

        void M_precompute() {
            uintmax_t const digit1 = 0x0200000002000000;
            uintmax_t const digit2 = 0xf600fffff6010000;
            uintmax_t const digit3 = 0xfff600fffff60100;
            uintmax_t const digit4 = 0xfffff600fffff601;
            uintmax_t counter = 0x3130303030303030;
            for (int i = 0, i4 = 0; i4 < 10; ++i4, counter += digit4)
                for (int i3 = 0; i3 < 10; ++i3, counter += digit3)
                    for (int i2 = 0; i2 < 10; ++i2, counter += digit2)
                        for (int i1 = 0; i1 < 5; ++i1, ++i, counter += digit1)
                            *((uintmax_t*)inttab + i) = counter;
        }

    public:
        printer() { M_precompute(); }
        ~printer() { M_flush_stdout(); }

        void print(char c) {
            if (__builtin_expect(pos + 1 >= outbuf + buf_size, 0)) M_flush_stdout();
            *pos++ = c;
        }

        template <size_t N>
        void print(char const(&s)[N]) {
            if (__builtin_expect(pos + N >= outbuf + buf_size, 0)) M_flush_stdout();
            memcpy(pos, s, N-1);
            pos += N-1;
        }

        void print(char const* s) {
            // FIXME: strlen や memcpy などで定数倍高速化したい
            while (*s != 0) {
                *pos++ = *s++;
                if (pos == outbuf + buf_size) M_flush_stdout();
            }
        }

        void print(std::string const& s) { print(s.data()); }

        template <typename Integral,
                typename enable_if_integral<Integral>::type* = nullptr>
        void print(Integral x) {
            if (__builtin_expect(pos + int_digits >= outbuf + buf_size, 0))
                M_flush_stdout();
            if (x == 0) {
                *pos++ = '0';
                return;
            }
            if (x < 0) {
                *pos++ = '-';
                if (__builtin_expect(x == std::numeric_limits<Integral>::min(), 0)) {
                    switch (sizeof x) {
                        case 2: print("32768"); return;
                        case 4: print("2147483648"); return;
                        case 8: print("9223372036854775808"); return;
                    }
                }
                x = -x;
            }

            typename std::make_unsigned<Integral>::type y = x;
            int len = S_int_digits(y);
            pos += len;
            char* tmp = pos;
            int w = (pos - outbuf) & 3;
            if (w > len) w = len;
            for (int i = w; i > 0; --i) {
                *--tmp = y % 10 + '0';
                y /= 10;
            }
            len -= w;
            while (len >= 4) {
                tmp -= 4;
                *(unsigned*)tmp = *((unsigned*)inttab + (y % 10000));
                len -= 4;
                if (len) y /= 10000;
            }
            while (len-- > 0) {
                *--tmp = y % 10 + '0';
                y /= 10;
            }
        }

        template <typename Tp, typename... Args>
        void print(Tp const& x, Args&&... xs) {
            if (sizeof...(Args) > 0) {
                print(x);
                print(S_sep);
                print(std::forward<Args>(xs)...);
            }
        }

        template <typename Tp>
        void println(Tp const& x) { print(x), print(S_end); }

        template <typename Tp, typename... Args>
        void println(Tp const& x, Args&&... xs) {
            print(x, std::forward<Args>(xs)...);
            print(S_end);
        }

        static void set_sep(char c) { S_sep = c; }
        static void set_end(char c) { S_end = c; }
    };
}  // fast::

fast::scanner ebin;
fast::printer ebout;

// thank you ebi-chan!

int main(){
    using namespace std;
    constexpr unsigned long P{200003};
    unsigned long N;
    ebin.scan(N);
    vector<unsigned long> A(N);
    for(auto&& i : A)ebin.scan(i);
    A.erase(remove(begin(A), end(A), 0), end(A));
    N = size(A);
    unsigned long ans{0};
    for(unsigned long i{1}; i < N; ++i)for(unsigned long j{0}; j < i; ++j)ans += A[i] * A[j] % P;
    ebout.println(ans);
    return 0;
}