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 Java (OpenJDK 11.0.6) (judge verdict: Wrong Answer)

import java.util.*;

class Main {
  public static void main(String args[]) {
    Scanner scan = new Scanner(System.in);
    ArrayList<Integer> list = new ArrayList<Integer>();
    int P = 200003;
    
    String sN = scan.nextLine();
    int N = Integer.valueOf(sN);
    
    for (int i = 0;i < N;i ++) {
      int val = scan.nextInt();
      list.add(val);
    }
    
    int sum = 0;
    for (int i = 0;i < N-1;i ++) {
      for (int j = i+1;j < N;j ++) {
        int Ai = list.get(i);
        int Aj = list.get(j);
        int mul = Ai * Aj;
        int sur = mul % P;
        sum += sur;
      }
    }
    
    System.out.println(sum);
  }
}