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.*;
import java.io.*;
public class Main {

	public static void main(String[] args) throws Exception{
		long num = 1000000007;

		// TODO Auto-generated method stub
 		BufferedReader bf = new BufferedReader(new InputStreamReader(System.in));
 		PrintWriter out = new PrintWriter(System.out);
 		int n = Integer.parseInt(bf.readLine());
 		long sum =0;
 		long sumsq = 0;
 		StringTokenizer st = new StringTokenizer(bf.readLine());
 		for(int j =0;j<n;j++){
 			int k = Integer.parseInt(st.nextToken());
 			sum+=(long)(k);
 			sumsq+=(long)((long)(k)*(long)(k));
 			sumsq%=num;
 			sum%=num;
 		}
 		
 		long ans = sum*sum;
 		ans%=num;
 		ans-=sumsq;
 		ans = (ans%num+num)%num;
 		if (ans%2 == 1)
 			ans+=num;
 		ans/=2;
 		
 		out.println(ans);
	 		
 		out.close();
 		
 		
 		
 	}
}
 	
 
//StringJoiner sj = new StringJoiner(" "); 
//sj.add(strings)
//sj.toString() gives string of those stuff w spaces or whatever that sequence is

 		
 		
 		
 		
	


