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 Go (1.14.1) (judge verdict: Time Limit Exceeded)

package main

import (
	"bufio"
	"flag"
	"fmt"
	"os"
	"sort"
	"strconv"
	"testing"
)

/*-----------Main-----------*/

func main() {
	const P = 200003
	n := readI()
	a := readIs(n)
	ans := 0
	for i := 0; i < n; i++ {
		if a[i] == 0 {
			continue
		}
		for j := i + 1; j < n; j++ {
			if a[j] == 0 {
				continue
			}
			ans += a[i] * a[j] % P
		}
	}
	fmt.Println(ans)
}

/*-----------Utilities-----------*/

var sc = bufio.NewScanner(os.Stdin)

func init() {
	testing.Init()
	if flag.Parse(); flag.Arg(0) == "debug" {
		debug()
	}
	const maxBuf = 200100
	var buf []byte = make([]byte, maxBuf)
	sc.Split(bufio.ScanWords)
	sc.Buffer(buf, maxBuf)
}

func debug() {
	testFile, err := os.Open("./test/sample-2.in")
	if err != nil {
		fmt.Println("Error : There is no testfile.")
		os.Exit(1)
	}
	sc = bufio.NewScanner(testFile)
}

func readS() string {
	sc.Scan()
	return sc.Text()
}

func readSs(a int) []string {
	b := make([]string, a)
	for i := 0; i < a; i++ {
		b[i] = readS()
	}
	return b
}

func readI() int {
	sc.Scan()
	r, _ := strconv.Atoi(sc.Text())
	return r
}

func readIs(a int) []int {
	b := make([]int, a)
	for i := 0; i < a; i++ {
		b[i] = readI()
	}
	return b
}

func readF() float64 {
	sc.Scan()
	r, _ := strconv.ParseFloat(sc.Text(), 64)
	return r
}

func readFs(a int) []float64 {
	b := make([]float64, a)
	for i := 0; i < a; i++ {
		b[i] = readF()
	}
	return b
}

func max(a []int) int {
	l := len(a)
	m := a[0]
	for i := 1; i < l; i++ {
		if a[i] > m {
			m = a[i]
		}
	}
	return m
}

func min(a []int) int {
	l := len(a)
	m := a[0]
	for i := 1; i < l; i++ {
		if a[i] < m {
			m = a[i]
		}
	}
	return m
}

func sortI(a []int) []int {
	sort.Ints(a)
	return a
}

func reverse(a []int) []int {
	l := len(a)
	r := make([]int, l)
	for i := 0; i < l; i++ {
		r[i] = a[l-i-1]
	}
	return r
}

func countI(a []int, b int) int {
	l := len(a)
	var c int
	for i := 0; i < l; i++ {
		if a[i] == b {
			c++
		}
	}
	return c
}