Given are N integers A_1,\ldots,A_N.

Find the sum of A_i \times A_j over all pairs (i,j) such that 1\leq i < j \leq N, modulo (10^9+7).

Constraints

* 2 \leq N \leq 2\times 10^5
* 0 \leq A_i \leq 10^9
* All values in input are integers.

Input

Input is given from Standard Input in the following format:


N
A_1 \ldots A_N


Output

Print \sum_{i=1}^{N-1}\sum_{j=i+1}^{N} A_i A_j, modulo (10^9+7).

Examples

Input

3
1 2 3


Output

11


Input

4
141421356 17320508 22360679 244949


Output

437235829
import java.util.Scanner;

public class Main {
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        // 配列
        int n = sc.nextInt();
        long[] a = new long[n];
        long e = 1000000007L;
        long sum = 0;
        for(int i=0;i<n;i++){
            a[i] = sc.nextInt();
            sum += a[i];
            if(sum >= e) {
                sum -= e;
            }
        }
        long ans =0;
        long mul = 0;
        for(int i=0; i<n;i++) {
            if(sum < a[i]) {
                mul = sum + e - a[i];
            } else {
                mul = sum - a[i];
            }

            ans = (ans + (a[i] * mul)) % e;
        }

        if(ans%2 == 0) {
        System.out.println(ans/ 2);
        } else {
            System.out.println((ans + e)/ 2);
        }
    }
   
}

