Sum of product of pairs

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

inputFormat

input are integers.

Input

Input is given from Standard Input in the following format:

N A_1 \ldots A_N

outputFormat

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

样例

3
1 2 3

11