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
#include<bits/stdc++.h>
using namespace std;
typedef long long int ll;
int main()
{
	ll i,j,t=1;
	//cin>>t;
	for(i=0;i<t;i++)
	{
		ll n,s=0,ans=0;
		cin>>n;
		ll a[n+5];
		for(j=0;j<n;j++)
		{
			cin>>a[j];
			s+=a[j];
		}
		
		ll m=1000000007;
		for(j=0;j<n;j++)
		{
			s-=a[j];
			ans=(ans+((a[j]%m)*(s%m))%m)%m;
		}
		cout<<ans;
	}
}